Answer: The probability of drawing 5 cards in either ascending or descending order out of the deck of 52 standard playing cards is 0.84%.
Step-by-step explanation: We have the following cards in a deck: 1(ace), 2, 3, 4, 5, 6, 7, 8, 9, 10, 12(Jack), 13(Queen), 14(King) (thirteen different in total). There are 4 copies of each of them yielding 52 cards in total. First to draw all of the cards in the ascending order all of the drawn cards need to be different. Imagine you have 13 piles of 4 identical cards. Let us calculate the number of ways you can select 5 different ones (the order matters). First you select 5 different piles (this secures that each card is different) and this is possible to do in [tex]\frac{13!}{(13-5)!}[/tex] (we use the formula for variations since the order matters). Now, each card in the pile can be selected in [tex]4[/tex] different ways so the total number of sequences with [tex]5[/tex] different cards is [tex]4^5\frac{13!}{(13-5)!}[/tex]. Now we select out of these sequences the clases of those that contain exactly the same cards but in different order. Only 4 of the sequences within the same class will be in ascending order out of 4*5! which is the total number of the sequences within the class! This means that we have to multiply our total number of sequences of 5 different cards by [tex]\frac{4}{4\cdot 5!}=\frac{1}{5!}[/tex] and this yields the final answer of total number of ascending sequences to be
[tex]4^5\frac{13!}{(13-5)!5!}.[/tex]
The total number of possible ways to draw 5 out of 52 cards is just
[tex]\frac{52!}{(52-5)!}.[/tex]
This yields for the probability
[tex]\frac{4^5\frac{13!}{(13-5)!5!}}{\frac{52!}{(52-5)!}}=0.42\%[/tex]
Exactly the same calculation applies for the descending order. So the probabilty of the cards being in either ascending or descending order is just the sum of these two (the events are mutually exclusive, you cannot have both the ascending and descending order at the same time) yielding the final probability of [tex]0.84\%[/tex].
If Company M ordered a total of 50 computers and printers and Company N ordered a total of 60 computers and printers, how many computers did Company M order?
(1) Company M and Company N ordered the same number of computers.
(2) Company N ordered 10 more printers than Company M.
Answer:
Available information is not sufficient to solve the questions
Step-by-step explanation:
Let Cm = Computers Ordered by Company M
Let Cn = Computers Ordered by Company N
Let Pm = Printers Ordered by Company M
Let Pn = Printers Ordered by Company N
Cm + Pm = 50 --- Equation 1
Cn + Pn = 60 ----- Equation 2
1. Company M and N ordered the same number of computers
Here,
Cm = Cn
Substitute Cm for Cn in equation 2
Cm + Pm = 50
Cm + Pn = 60
Subtract Equation 2 from 1
Pm - Pn = 50 - 60
Pm - Pn = -10
Pm = Pn - 10
Substitute Pn-10 for Pm in equation 1
Cm + Pn - 10 = 50
Make Pn the subject of formula
Cm = 50+10-Pn
Cm = 60 - Pn
Hence, the number of computers ordered by Company M is 60 minus the number of printers ordered by Company n
2. Company N ordered 10 more printers than Company M.
Here,
Pn = 10 + Pm
Make Pm the subject of formula
Pm = Pn - 10
Substitute Pn-10 for Pm in equation 1
Cm + Pn - 10 = 50
Make Cm the Subject of formula
Cm = 50 + 10 - Pn
Cm = 60 - Pn
Hence, the number of computers ordered by Company M is 60 minus the number of printers ordered by Company n
Condition 1 and 2 points to the same result
Seventy five percent of the students in sixth grade voted to to the planiterium on their field trip if 24 voted to go to the planiterium, how many students are there in the sixth grade?
There are 25 white cars, 15 blue cars, 21 red cars, and 30 black cars on a dealership lot. What is the probability of selecting a red car off the lot? Round to three decimals.
Answer:
The probability of selecting a red car off the lot is 0.231.
Step-by-step explanation:
Given:
Number of white cars = 25
Number of blue cars = 15
Number of red cars = 21
Number of black cars = 30
We need to find the probability of selecting a red car off the lot.
Solution:
First we will find the Total number of cars in the lot.
Now we can say that;
Total number of cars in the lot is equal to sum of Number of white cars and Number of blue cars and Number of red cars and Number of black cars.
framing in equation form we get;
Total number of cars in the lot = [tex]25+15+21+30 = 91[/tex]
Now to find the probability of selecting a red car off the lot we will divide Number of red cars by Total number of cars in the lot.
framing in equation form we get;
P(red) = [tex]\frac{21}{91}=0.2307[/tex]
Rounding to three decimals we get;
P(red) = 0.231
Hence The probability of selecting a red car off the lot is 0.231.
The probability of selecting a red car off the lot, rounded to three decimals, is 0.231.
First, we need to find the total number of cars on the lot by adding up the number of cars of each color:
Total number of cars = Number of white cars + Number of blue cars + Number of red cars + Number of black cars
Total number of cars = 25 + 15 + 21 + 30
Total number of cars = 91
Next, we find the probability of selecting a red car by dividing the number of red cars by the total number of cars:
Probability of selecting a red car = Number of red cars / Total number of cars
Probability of selecting a red car = 21 / 91
To round to three decimals, we perform the division:
Probability of selecting a red car = 0.2308
Rounded to three decimals, the probability is 0.231.
A college’s data about the incoming freshmen indicates that the mean of their high school GPAs was 3.4, with a standard deviation of 0.35; the distribution was roughly mound-shaped and only slightly skewed. The students are randomly assigned to freshman writing seminars in groups of 25. What might the mean GPA of one of these seminar groups be? Describe the appropriate sampling distribution model—shape, center, and spread— with attention to assumptions and conditions. Make a sketch using the 68–95–99.7 Rule.
Answer:
Step-by-step explanation:
u = 3.4
stdev = 0.35
n = 25
E = u = 3.4
SD = [tex]\frac{stdev}{\sqrt{n} } =\frac{0.35}{\sqrt{25} }[/tex] = 0.07
The calculation of the 68% population covers with 1 standard deviation is as follows:
u - SD = 3.4 - 0.07 = 3.33
u + SD = 3.4 + 0.07 = 3.47
Range = (3.33, 3.47)
The calculation of the 95% population covers within 2 standard deviations is as follows:
u - 2SD = 3.4 - 2(0.07) = 3.26
u + 2SD = 3.4 + 2(0.07) = 3.54
Range = (3.26, 3.54)
The calculation of the 99.7% population covers within 3 standard deviations is as follows:
u - 3SD = 3.4 - 3(0.07) = 3.19
u + 3SD = 3.4 + 3(0.07) = 3.61
Range = (3.19, 3.61)
From the information, observe that the shape of the distribution is symmetrical.
Therefore, the graph is as shows the attached image.
This shows that approximately:
68% of the observations will have mean between 3.33 and 3.47
95% of the observations will have mean between 3.26 and 3.54
99.7% of the observations will have mean between 3.19 and 3.61
Lia is cooking.She needs 2 3/4 cups of flour and 4 3/4 cups of cornmeal.Lia wants to bake sure she has a bowl big enough to hold the flour and cornmeal.Which answer should Lia use to find the total amount of flour and cornmeal she needs??
Answer:
Lia needs [tex]7\frac{2}{4}\ cups[/tex] of flour and corn meal.
Step-by-step explanation:
Given:
Amount of flour needed = [tex]2\frac{3}{4} \ cups[/tex]
[tex]2\frac{3}{4} \ cups[/tex] can be Rewritten as [tex]\frac{11}{4}\ cups[/tex]
Amount of flour needed = [tex]\frac{11}{4}\ cups[/tex]
Amount of Corn meal needed = [tex]4\frac{3}{4}\ cups[/tex]
[tex]4\frac{3}{4}\ cups[/tex] can be Rewritten as [tex]\frac{19}{4}\ cups[/tex]
Amount of Corn meal needed = [tex]\frac{19}{4}\ cups[/tex]
We need to find the total amount of of flour and cornmeal she needs.
Solution:
Now we can say that;
the total amount of of flour and cornmeal she needs is equal to sum of Amount of flour needed and Amount of Corn meal needed.
framing in equation form we get;
the total amount of of flour and cornmeal she needs = [tex]\frac{11}{4}+\frac{19}{4}=\frac{11+19}{4}=\frac{30}{4}\ cups\ \ OR\ \ 7\frac{2}{4}\ cups[/tex]
Since Answers are not given:
Kindly chose the answer which contains below data.
Hence Lia needs [tex]7\frac{2}{4}\ cups[/tex] of flour and corn meal.
The campsite shop sells boxes of funshine cereal. The base of each box is a 180mm x 60 mm rectangle. The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle
the maximum number of boxes that will fit on the shelf is 21.
To find out the maximum number of boxes that will fit on the shelf, we need to calculate the area of the shelf and the area of each box, then divide the total area of the shelf by the area of each box.
Given:
- Shelf dimensions: 65 cm x 35 cm
- Box dimensions: 180 mm x 60 mm
First, let's convert all dimensions to the same unit. Let's choose millimeters for consistency:
Shelf dimensions:
- Length: [tex]\(65 \, \text{cm} \times 10 \, \text{mm/cm} = 650 \, \text{mm}\)[/tex]
- Width: [tex]\(35 \, \text{cm} \times 10 \, \text{mm/cm} = 350 \, \text{mm}\)[/tex]
Now, let's calculate the area of the shelf:
[tex]\[ \text{Shelf area} = \text{Shelf length} \times \text{Shelf width} \][/tex]
[tex]\[ \text{Shelf area} = 650 \, \text{mm} \times 350 \, \text{mm} \][/tex]
[tex]\[ \text{Shelf area} = 227,500 \, \text{mm}^2 \][/tex]
Now, let's calculate the area of each box:
[tex]\[ \text{Box area} = \text{Box length} \times \text{Box width} \][/tex]
[tex]\[ \text{Box area} = 180 \, \text{mm} \times 60 \, \text{mm} \][/tex]
[tex]\[ \text{Box area} = 10,800 \, \text{mm}^2 \][/tex]
Now, to find out the maximum number of boxes that will fit on the shelf, we divide the shelf area by the area of each box:
[tex]\[ \text{Maximum number of boxes} = \frac{\text{Shelf area}}{\text{Box area}} \][/tex]
[tex]\[ \text{Maximum number of boxes} = \frac{227,500 \, \text{mm}^2}{10,800 \, \text{mm}^2} \][/tex]
[tex]\[ \text{Maximum number of boxes} \approx 21.06 \][/tex]
Since we can't have a fraction of a box, the maximum number of boxes that will fit on the shelf is 21.
complete question given below:
The campsite shop sells boxes of Funshine Cereal.
The base of each box is a 180 mm x 60 mm rectangle.
The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle.
Work out the maximum number of boxes that will fit on the shelf.
the maximum number of boxes that will fit on the shelf is 21.
To find the maximum number of boxes that fit on the shelf, we divide the shelf area by the area of each box.
Given:
- Shelf dimensions: 65 cm x 35 cm
- Box dimensions: 180 mm x 60 mm
First, let's convert the shelf dimensions to millimeters for consistency:
Shelf dimensions:
- Length: [tex]\(65 \, \text{cm} \times 10 \, \text{mm/cm} = 650 \, \text{mm}\)[/tex]
- Width: [tex]\(35 \, \text{cm} \times 10 \, \text{mm/cm} = 350 \, \text{mm}\)[/tex]
Now, calculate the area of the shelf:
[tex]\[ \text{Shelf area} = \text{Shelf length} \times \text{Shelf width} \]\[ \text{Shelf area} = 650 \, \text{mm} \times 350 \, \text{mm} \]\[ \text{Shelf area} = 227,500 \, \text{mm}^2 \][/tex]
Next, calculate the area of each box:
[tex]\[ \text{Box area} = \text{Box length} \times \text{Box width} \]\[ \text{Box area} = 180 \, \text{mm} \times 60 \, \text{mm} \]\[ \text{Box area} = 10,800 \, \text{mm}^2 \][/tex]
Now, find the maximum number of boxes that fit on the shelf:
[tex]\[ \text{Maximum number of boxes} = \frac{\text{Shelf area}}{\text{Box area}} \]\[ \text{Maximum number of boxes} = \frac{227,500 \, \text{mm}^2}{10,800 \, \text{mm}^2} \]\[ \text{Maximum number of boxes} \approx 21.06 \][/tex]
Since we can't have a fraction of a box, the maximum number of boxes that will fit on the shelf is 21.
The probable question maybe:
The campsite shop sells boxes of Funshine Cereal.
The base of each box is a 180 mm x 60 mm rectangle.
The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle.
Work out the maximum number of boxes that will fit on the shelf.
in a group of 40 student students, the probability that at most 15 of them like to hike? A 44% B 64% C 55% D 38%e to hike is 36%. What is the probability that at least 16 of them like to hike
Answer:
64%
Step-by-step explanation:
pain
The answer is B) 64%.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Let X be the number of students out of 40 who like to hike. We know that P(X ≤ 15) = 0.36 and we want to find P(X ≥ 16).
Note that P(X ≥ 16) is the complement of P(X ≤ 15). That is,
P(X ≥ 16) = 1 - P(X ≤ 15) = 1 - 0.36 = 0.64
Therefore, the answer is B) 64%.
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Which of the following integrals cannot be evaluated using a simple substitution? (4 points) Select one:
a. the integral of the square root of the quantity x minus 1, dx
b. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
c. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
d. the integral of x times the square root of the quantity x squared minus 1, dx
Answer:
B. and C.
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationIntegration
IntegralsIndefinite IntegralsIntegration Constant CU-Substitution
Step-by-step explanation:
*Note:
It seems like B and C are both the same answer.
Let's define our answer choices:
a. [tex]\displaystyle \int {\sqrt{x - 1}} \, dx[/tex]
b. [tex]\displaystyle \int {\frac{1}{\sqrt{1 - x^2}}} \, dx[/tex]
c. [tex]\displaystyle \int {\frac{1}{\sqrt{1 - x^2}}} \, dx[/tex]
d. [tex]\displaystyle \int {x\sqrt{x^2 - 1}} \, dx[/tex]
Let's run u-substitution through each of the answer choices:
a. [tex]\displaystyle u = x - 1 \rightarrow du = dx \ \checkmark[/tex]
∴ answer choice A can be evaluated with a simple substitution.
b. [tex]\displaystyle u = 1 - x^2 \rightarrow du = -2x \ dx[/tex]
We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.
∴ answer choice B cannot be evaluated using a simple substitution.
C. [tex]\displaystyle u = 1 - x^2 \rightarrow du = -2x \ dx[/tex]
We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.
∴ answer choice C cannot be evaluated using a simple substitution.
D. [tex]\displaystyle u = x^2 - 1 \rightarrow du = 2x \ dx \ \checkmark[/tex]
Using a little rewriting and integration properties, this integral can be evaluated using a simple substitution.
∴ answer choice D can be evaluated using a simple substitution.
Out of all the choices, we see that B and C cannot be evaluated using a simple substitution.
∴ our answer choices should be B and C.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Keisha bought cups of coffee and bagels for the people in her office. Each bagel cost $2 and each cup of coffee cost $1.50. Keisha spent a total of $40 to buy 23 items. Let x represent the number of bagels and y represent the number of cups of coffee.
Answer:
The number of bagels is 11 and the cups of coffee is 12.
Step-by-step explanation:
Given:
Keisha bought cups of coffee and bagels for the people in her office. Each bagel cost $2 and each cup of coffee cost $1.50.
Keisha spent a total of $40 to buy 23 items.
Now, to find the number of cups of bagels and coffee.
As given in question:
Let [tex]x[/tex] represent the number of bagels.
And [tex]y[/tex] represent the number of cups of coffee.
So, the total number of items:
[tex]x+y=23[/tex]
[tex]x=23-y[/tex] ......(1)
Now, the total money spent on items:
[tex]2x+1.50y=40[/tex]
Substituting the value of [tex]x[/tex] from equation (1):
[tex]2(23-y)+1.50y=40[/tex]
[tex]46-2y+1.50y=40[/tex]
[tex]46-0.50y=40[/tex]
Subtracting both sides by 46 we get:
[tex]-0.50y=-6[/tex]
Dividing both sides by -0.50 we get:
[tex]y=12.[/tex]
The number of cups of coffee = 12.
Now, to get the number of bagel we substitute the value of [tex]y[/tex] in equation (1):
[tex]x=23-y[/tex]
[tex]x=23-12[/tex]
[tex]x=11.[/tex]
The number of bagels = 11.
Therefore, the number of bagels is 11 and the cups of coffee is 12.
How do the values of the 4s in 64.723 and 9.048 compare?
Select from the drop-down menu to correctly complete the statement.
The value of the 4 in 64.723 is times the value of the 4 in 9.048.
A) 10 B)100 C)1000
Answer:
C.
is the right answer
Step-by-step explanation:
The value of the 4 in 64.723 is 100 times the value of the 4 in 9.048. The correct option is B
What is a number system?A system of writing numbers is known as a number system. It is the mathematical notation for consistently using digits or other symbols to represent the numbers in a given set.
It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
Given that there are two numbers 64.723 and 9.048. The value of the number 4 in one number is 100 times the other. As it is at one-hundredth place of another number
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Consider the following piece-wise function. Which of the below correctly describes the graph shown?
Answer:
The 3th answer is correct.
for x<2, form graph we know that if x=0 than y=-3.
For x<2 in 3th we have y=1/2x-3, so for x=0, y=(1/2)*0-3=0-3=-3. It fits.
For x=2, from graph we have that y=-2.
For x>=2 in 3th we have y=3x-8, so for x=2, y=3*2-8=-2. It fits.
These answer fit also i for first, but breakpoint for y from graph is point 2 not point -2, so the answer is 3th.
In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below. Purchased Gum Kept the Money Students Given Four Quarters 25 15 14 Students Given a $1 Bill 29 a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill. The probability is (Round to three decimal places as needed.) b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill. The probability is (Round to three decimal places as needed.) c. what do the preceding results suggest? A. A student given a $1 bill is more likely to have kept the money. B. A student given a $1 bill is more likely to have spent the money than a student given four quarters. C. A student given a $1 bill is more likely to have kept the money than a student given four quarters. D. A student given a $1 bill is more likely to have spent the money.
Answer:
a) [tex] P(A|B) = \frac{15/83}{44/83} =\frac{15}{44}=0.341[/tex]
b) [tex] P(B|A) = \frac{29/83}{44/83} =\frac{29}{44}=0.659[/tex]
c) A. A student given a $1 bill is more likely to have kept the money.
Because the probability 0.659 is atmoslt two times greater than 0.341
Step-by-step explanation:
Assuming the following table:
Purchased Gum Kept the Money Total
Students Given 4 Quarters 25 14 39
Students Given $1 Bill 15 29 44
Total 40 43 83
a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given $1 Bill"
A="The student spent the money"
For this case we want this conditional probability:
[tex] P(A|B) =\frac{P(A and B)}{P(B)}[/tex]
We have that [tex] P(A)= \frac{40}{83} , P(B)= \frac{44}{83}, P(A and B)= \frac{15}{83}[/tex]
And if we replace we got:
[tex] P(A|B) = \frac{15/83}{44/83} =\frac{15}{44}=0.341[/tex]
b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given $1 Bill"
A="The student kept the money"
For this case we want this conditional probability:
[tex] P(A|B) =\frac{P(A and B)}{P(B)}[/tex]
We have that [tex] P(A)= \frac{43}{83} , P(B)= \frac{44}{83}, P(A and B)= \frac{29}{83}[/tex]
And if we replace we got:
[tex] P(B|A) = \frac{29/83}{44/83} =\frac{29}{44}=0.659[/tex]
c. what do the preceding results suggest?
For this case the best solution is:
A. A student given a $1 bill is more likely to have kept the money.
Because the probability 0.659 is atmoslt two times greater than 0.341
Using the principles of conditional probability, we find that a student given a $1 bill is more likely to spend the money (probability approximately 0.641) than keep it (probability approximately 0.359). Therefore, option B is the correct interpretation of these results.
Explanation:To answer this question, we should first understand that this problem is fundamentally about conditional probability, the probability of an event given that another event has occurred. Let's take this step by step.
Part a: Here, we want to find the probability of selecting a student who spent the money, given that the student was given a $1 bill. This number would be the number of $1 bill students who bought gum divided by the total number of $1 bill students. This equates to 25/(25+14) = 0.641. So, the probability is approximately 0.641.
Part b: In this situation, we're looking for the probability of selecting a student who kept the money, given that the student was given a $1 bill. This would be the number of $1 bill students who kept the money divided by the total number of $1 bill students, or 14/(25+14) = 0.359. The probability is approximately 0.359.
Part c: These results suggest that the appropriate solution is B: 'A student given a $1 bill is more likely to have spent the money than a student given four quarters.'
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Luis made some trail mix. He mixed 4 2/3 cups popcorn, 1 1/4 cups of peanuts, 1 1/3 cups of raisins, and 3/4 cup of sunflower seeds. He gave 5 of his friends an equal amount of trail mix each. How much did each friend get?
Answer:
1 2/3
Step-by-step explanation:
Luis mixed all the trails thus:
4 2/3 + 1 1/4 + 1 1/3 + 3/4
= 15/3 + 5/4 + 4/3 + 3/4
= 60+15+16+9/12
Total trail mixed by Luis equals 100/12
He then divided 100/12 among his 5 friends thus:
100/12 ÷ 5
= 20/12
= 1 2/3 per friend.
Answer:
1 3/5
Step-by-step explanation:
the answer is 1.6 but you have to convert is to a fraction because there are no decimal numbers theres. if you convert it , it will be 1 3/5
Show your work
What are the roots of the polynomial equation?
You can use any method you would like to solve.
0=x^4-3x^3+10x^2-24+16
Answer:
1, 2, and ±i√8
Step-by-step explanation:
0 = x⁴ − 3x³ + 10x² − 24x + 16
Using grouping:
0 = x⁴ − 3x³ + 2x² + 8x² − 24x + 16
0 = x² (x² − 3x + 2) + 8 (x² − 3x + 2)
0 = (x² + 8) (x² − 3x + 2)
0 = (x² + 8) (x − 1) (x − 2)
The roots are 1, 2, and ±i√8.
Tickets for a minor league baseball game for an adult and two children cost a total of $21 the adult ticket is three dollars more than a child's ticket. Find the cost of the child's ticket and an adult ticket.
Answer:the cost of one child's ticket is $6
the cost of one adult ticket is $9
Step-by-step explanation:
Let x represent the cost of one child's ticket
Let y represent the cost of one adult ticket.
Tickets for a minor league baseball game for an adult and two children cost a total of $21. This means that
2x + y = 21 - - - - - - - - - - 1
The adult ticket is three dollars more than a child's ticket. This means that
y = x + 3
Substituting y = x + 3 into equation 1, it becomes
2x + x + 3 = 21
3x + 3 = 21
3x = 21 - 3 = 18
x = 18/3 = 6
y = x + 3 = 6 + 3
y = 9
Return the bottles: Shawna Return some bottles to the store. She received 1.85 in quarters, dimes, nickels. Use these clues to determine the number of each kind of coin. She received at least one of each coin. There are more dimes and nickels. There is an even number of quarters. There are as many quarters and nickels together as there are dimes.
Answer:
There are 7 dimes, 3 nickels, and 4 quarters.
Mrs.Jackson earned a $500 bonus for signing a 1 year contract to work as a nurse. Her salary is $22 per hour. If her first weeks check including the bonus is $1204 how many hours did mrs. Jackson work?
Answer:
Mrs. Jackson worked 32 hours.
Step-by-step explanation:
Given:
Mrs.Jackson earned a $500 bonus for signing a 1 year contract to work as a nurse.
Her salary is $22 per hour.
If her first weeks check including the bonus is $1204.
Now, to find the hours Mrs. Jackson work.
Amount of bonus = $500.
Total salary = $1204.
So, we deduct the amount of bonus from the total salary:
[tex]1204-500=\$704.[/tex]
The remaining salary = $704.
As, given her salary is $22 per hour.
Now, to get the hours she work we divide the remaining salary $704 by $22:
[tex]704\div 22[/tex]
[tex]=32\ hours.[/tex]
Therefore, Mrs. Jackson worked 32 hours.
A swimming pool is filled with water by using two taps A and B. Alone, it takes tap A 3 hours less than B to fill the same pool. Together, they take 2 hours to fill the pool. How many hours does it take each tap to fill the swimming pools separately?
Answer:
Tap A 3hrs
Tap B 6hrs
Step-by-step explanation:
Let the volume of the swimming pool be Xm^3.
Now, to get the appropriate volume, we know we need to multiply the rate by the time. Let the rate of the taps be R1 and R2 respectively, while the time taken to fill the swimming pool be Ta and Tb respectively.
x/Ta= Ra
x/Tb= Rb
X/(Ra + Rb)= 2
Ta = Tb - 3
From equation 2:
X = 2( Ra + Rb)
Substituting the values of Ra and Rb Using the first set of equations
X = 2( x/Ta + x/Tb)
But Ta = Tb - 3
1/2 = 1/(Tb - 3)+ 1/Tb
0.5 = (Tb + Tb-3)/Tb(Tb - 3)
At this juncture let’s say Tb = y
0.5 = (2y - 3)/y(y - 3)
y(y-3 ) = 4y - 6
y^2 -3y - 4y + 6 = 0
y^2 -7y + 6= 0
Solving the quadratic equation, we get y =
y = Tb = 6hrs or 1hr
We remove one hour as we know that Tap A takes 3hrs left than tap B and there is nothing like negative hours
Now, we get Ta by Tb -3 = 6 - 3 = 3hrs
Which sampling method is MOST appropriate in estimating the average number of votes for each candidate in an election across a county of three towns if town A has one million retirees, town B has two million business owners, and town C has three million office workers?
A. Simple random sampling, because the people in the sample are accessible and available.
B. Stratified sampling, because there are specific subgroups to investigate.
C. Systematic sampling, because it is difficult to identify items using a simple random sampling method.
D. Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement
E. All the above sampling methods
Answer:
B. Stratified sampling, because there are specific subgroups to investigate.
Step-by-step explanation:
Stratified Sampling is a sampling method and is used when the population has subgroups with different characteristics. Random sampling is applied in each of the sub-groups proportional to their size and then these samples combined together to create sample of the study.
Since there are three towns with people from different occupations ( retirees,business owners, office workers), it is better to use stratified sampling method.
The correct answer is option B). Stratified sampling, because there are specific subgroups to investigate.
To determine the most appropriate sampling method, one must consider the composition of the population and the goal of the study. In this scenario, the population consists of three distinct groups: retirees in town A, business owners in town B, and office workers in town C. Each group represents a different stratum within the overall population of the county.
Stratified sampling is a method that divides the population into subgroups, or strata, based on certain characteristics, such as age, occupation, or town of residence in this case. This method ensures that each subgroup is represented in the sample in proportion to its size in the overall population. Here's why stratified sampling is the most appropriate method for this situation:
1. Representation: Stratified sampling ensures that each town's unique demographic is represented in the sample. This is important because each group may have different voting patterns.
2. Precision: By sampling each stratum separately, the estimates of the average number of votes for each candidate can be more precise because the variance within each subgroup is likely to be lower than the variance across the entire population.
3. Comparability: Stratified sampling allows for direct comparison between the different strata, which in this case are the three towns.
4. Efficiency: If the strata are chosen such that the variance within each stratum is minimized, the overall variance of the estimate can be reduced, leading to a more efficient estimate.
Now, let's consider the other options:
A. Simple random sampling: While this method is unbiased, it may not provide representation from each of the three towns in proportion to their population sizes. This could lead to an inaccurate estimate if one group's voting behavior is significantly different from the others.
C. Systematic sampling: This method involves selecting elements from the population at regular intervals. It can be difficult to implement if there is no clear ordering of the population, and it may not ensure representation from each town.
D. Cluster sampling: This method would be appropriate if the population were spread across a wide area and could be divided into clusters that are more convenient to sample. However, since the population is already divided into distinct groups within specific towns, stratified sampling is a better choice.
E. All the above sampling methods: While each method has its own merits, not all are equally suitable for this particular scenario. Stratified sampling is the most appropriate because it specifically addresses the heterogeneity of the population across the three towns.
A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line?
A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
E) (7, 14)
====================================================
m = 1/7 is the slope
(x,y) = (0,0) is the origin the line goes through
y = mx+b
0 = (1/7)*0 + b
0 = 0+b
b = 0 is the y intercept
y = mx+b
y = (1/7)x+0
y = (1/7)x is the equation of the line
----------------------
To plot the equation of this line, mark the point (0,0) first.
Then move up 1 unit and to the right 7 units to arrive at (7,1) as the second point.
Draw a straight line through (0,0) and (7,1) as shown in the diagram below.
Point P is (0,0) and point Q is (7,1)
Points A through E in the same diagram represent the answer choices A through E.
Of the answer choices, only point D is on this line, so point D is the answer.
---------------
A non-visual way to find the answer is to plug each (x,y) coordinate from each answer choice into the equation we found above.
So for choice A we plug in x = 0 and y = 7
y = (1/7)*x
7 = (1/7)*0
7 = 0
we end up with a false equation, so choice A is ruled out. Similar stories happen with B, C, and E as well.
With choice D however, we plug in x = 14 and y = 2, and we get...
y = (1/7)*x
2 = (1/7)*14
2 = 14/7
2 = 2
Since we get a true equation, this confirms that (14,2) is on the graph of y = (1/7)x.
Defining the wrong choice:
For choice "A" when [tex]\bold{x=0, y=7 \ and\ m =\frac{1}{7}}[/tex], and put the value in [tex]\bold{y=mx}[/tex] it will give [tex]\bold{7=0}[/tex], which is wrong.For choice "B" when [tex]\bold{x=1, y=7 \ and\ m =\frac{1}{7}}[/tex], and put the value in [tex]\bold{y=mx}[/tex] it will give [tex]\bold{7=\frac{1}{7}}[/tex], which is wrong.For choice "C" when [tex]\bold{x=7, y=7 \ and\ m =\frac{1}{7}}[/tex], and put the value in [tex]\bold{y=mx}[/tex] it will give [tex]\bold{7=1}[/tex], which is wrong.For choice "E" when [tex]\bold{x=7, y=14 \ and\ m =\frac{1}{7}}[/tex], and put the value in [tex]\bold{y=mx}[/tex] it will give [tex]\bold{14=2}[/tex], which is wrong.Therefore, "Choice D" is the correct choice.
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Answer:
The cubic polynomial is: x³ - x² - 6x.
Step-by-step explanation:
Given the degree and the roots of the polynomial we can find it.
An n - degree polynomial has n roots.
Here, given that the degree of the polynomial is 3 and three roots are given. Also, if (x - a) is a factor of a polynomial then x = a is a root of the polynomial. The converse is also true.
Since, the roots of the polynomial are given to -2, 0, 3 then it should have had the following factors.
(x + 2)(x - 0)(x - 3) = 0
Multiplying them we get:
⇒ [tex]$ (x^2 + 2x)(x - 3) $[/tex]
[tex]$ = x^3 - 3x^2 + 2x^2 - 6x $[/tex]
[tex]$ = x^3 - x^2 - 6x $[/tex] which is the required cubic polynomial.
Hence, the answer.
geometry 7.2 puzzle time where did columbus land when he found america
Christopher Columbus landed on an island in the Bahamas, which he named San Salvador, on October 12, 1492, mistakenly believing he had reached Asia. This event is considered a pivotal moment in history, marking the beginning of European exploration and colonization of the Americas.
Explanation:Christopher Columbus, an Italian explorer sponsored by Spain, embarked on his voyage to find a direct sea route to Asia by sailing west. Contrary to his expectations, he landed in the Americas on October 12, 1492. Columbus made landfall on an island in the Bahamas, which the native Lucayans called Guanahani. He renamed it San Salvador. Following this, Columbus explored other islands in the Caribbean, including an island he named Hispaniola (present-day Dominican Republic and Haiti), still believing he had reached the East Indies.
Columbus’ mistaken belief that he had landed in Asia led to the indigenous peoples he encountered being called “Indios”, which is the origin of the term “Indian” for native peoples of the Americas. Despite his error, Columbus's voyages are considered a pivotal moment in history, marking the beginning of widespread European exploration and colonization of the Americas.
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Answer the following questions about the problem above. Write in complete sentences to get full credit.
1. What is the slope for section "d" of Mrs. Washington's commute.
2. What does it mean that the slope is negative in context of the problem?
3. Why are the slopes different over different intervals?
4. How long does it take Mrs. Washington to get home? How did you know this?
Step-by-step explanation:
[tex]slope \: of \: section \: d \: = gradient = \frac{y2 - y1}{x2 - x1} \\slope = \frac{6 - 0}{32 - 20} = \frac{6}{12} = \frac{1}{2} = 0.5 [/tex]The slope is negative because it moves downward from the left.If it were to move upwards from the left it would be a positive slope.The slope intervals are different because;the factors responsible for slope are not constant during the journey. i.e the time taken and the distance covered for each part of the journey are differentThe speed for each part of the journey is different.For a : Speed = distance / time
Distance covered = y2 - y1 = 20 - 15 = 5
Time taken = x2 - x1 = 8 - 0 = 8
Speed in part a : 5/8 = 0.625
4. It takes her 32 minutes to get home. We can see from the graph that it is the total time taken throughout the whole journey.
A poster is 8 in taller than it is wide. It is mounted on a backing board that provides a 2 in border on each side of the poster. If the area of the backing board is 308 in2 what are the dimensions of the poster
Answer:
The dimensions of poster are 32.5 in wide and 40.5 in tall.
Step-by-step explanation:
Given:
A poster is 8 in taller than it is wide.
It is mounted on a backing board that provides a 2 in border on each side of the poster.
The area of the backing board is 308 in².
Now, to find the dimensions of the poster.
Let [tex]x[/tex] be the length of the poster.
And [tex]y[/tex] be the width of the poster.
As given, poster is 8 in taller than it is wide.
So,
[tex]x=y+8[/tex] ......(1)
Area = 308 in².
So, it is mounted on a backing board that provides a 2 in border on each side of the poster.
According to question:
[tex]2\times (2(y+4))+2\times (2\times x)=308[/tex]
Now. substituting the value from equation (1) in the place of [tex]x[/tex] we get:
[tex]2\times (2y+8)+2(2\times (y+8))=308[/tex]
[tex]2\times (2y+8)+2(2y+16)=308[/tex]
[tex]4y+16+4y+32=308[/tex]
[tex]8y+48=308[/tex]
Subtracting both sides by 48 we get:
[tex]8y=260[/tex]
Dividing both sides by 8 we get:
[tex]y=32.5\ in.[/tex]
The width of the poster = 32.5 in.
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]x=y+8[/tex]
[tex]x=32.5+8[/tex]
[tex]x=40.5\ in.[/tex]
Length of the poster = 40.5 in.
Therefore, the dimensions of poster are 32.5 in wide and 40.5 in tall.
What is the solution of the system? y= 10x - 3 y= 7x + 2
Answer:
(5/3, 41/3)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define Systems
y = 10x - 3
y = 7x + 2
Step 2: Solve for x
Substitution
Substitute in y: 10x - 3 = 7x + 2[Subtraction Property of Equality] Subtract 7x on both sides: 3x - 3 = 2[Addition Property of Equality] Add 3 on both sides: 3x = 5[Division Property of Equality] Divide 3 on both sides: x = 5/3Step 3: Solve for y
Define original equation: y = 7x + 2Substitute in x: y = 7(5/3) + 2Multiply: y = 35/3 + 2Add: y = 41/3Step 4: Check
Verify the solution set to the systems of equations by graphing the systems.
Where the 2 lines intersect is the solution set to the systems of equations.
We see graphically that point (1.666667, 13.66667), equivalent to (5/3, 41/3).
∴ (5/3, 41/3) or x = 5/3 and y = 41/3 is the solution to the systems of equations.
Final answer:
The solution to the system of equations y = 10x - 3 and y = 7x + 2 is x = 5/3 and y = 19/3.
Explanation:
The solution of the system of equations given by y = 10x - 3 and y = 7x + 2 can be found by setting the two expressions for y equal to each other since they both equal y. This yields the equation 10x - 3 = 7x + 2. Solving for x, we first subtract 7x from both sides to get 3x - 3 = 2. Then we add 3 to both sides to get 3x = 5. Finally, dividing both sides by 3 gives us x = 5/3. Substituting x back into either original equation, we get y = 10(5/3) - 3 or y = 7(5/3) + 2, both of which simplify to y = 19/3. Therefore, the solution to the system is x = 5/3 and y = 19/3.
When one-fourth of a number is added to one-fifth of the number, the sum is 18. What is the number?
Step-by-step explanation:
Let the number be n.
When one-fourth of a number is added to one-fifth of the number, the sum is 18
[tex]\frac{n}{4}+\frac{n}{5}=18\\\\\frac{5n+4n}{4\times 5}=18\\\\9n=4\times 5\times 18\\\\n=20\times 2\\\\n=40[/tex]
The number is 40.
Answer:
unknown number is 40
Step-by-step explanation:
Let x be the unknown number
one-fourth of a number is added to one-fifth of the number
[tex]\frac{1}{4}x+\frac{1}{5} x[/tex]
sum is 18
[tex]\frac{1}{4}x+\frac{1}{5} x=18[/tex]
To solve for x take LCD 20
[tex]\frac{5}{20}x+\frac{4}{20} x=18\\ \frac{9}{20} x=18\\[/tex]
multiply both sides by 20
[tex]9x= 360[/tex]
divide both sides by 9
x=40
Need help on geometry
Answer:
[tex]2\sqrt {10}[/tex]
Step-by-step explanation:
Given:
[tex]x=3\sqrt 5[/tex]
[tex]y=\sqrt 5[/tex]
As seen from the triangle, the triangle is a right angled triangle. Two sides of the triangle are given and we are asked to find the third side.
'x' is the hypotenuse as this side is opposite side to the right angled.
'y' and 'z' are the two legs of the triangle.
Now, using pythagoras theorem,
[tex]x^2=y^2+z^2\\\\(3\sqrt 5)^2=(\sqrt 5)^2+z^2\\\\9\times 5=5+z^2\\\\45-5=z^2\\\\40=z^2\\\\z=\sqrt {40}\\\\z=2\sqrt {10}[/tex]
Therefore, the measure of the side 'z' is [tex]2\sqrt {10}[/tex].
Hence, the third option is correct.
Mary plants roseas in 1/4 of her garden. She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. What fraction of Mary's garden has tulips?
Answer:the fraction of Mary's garden that has tulips is 2/3
Step-by-step explanation:
Let x represent the full area if Mary's garden.
Mary plants roses in 1/4 of her garden. This means that the portion of the garden on which she planted roses would be 1/4 × x = x/4
She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. This means that the portion if the garden that she has left to plant more flowers would be 1/12 × x = x/12
The portion of the garden on which she planted tulips would be
x - (x/4 + x/12) = x - (3x + x)/12 = x - 4x/12
x - x/3 = (3x - x)/3 = 2x/3
Therefore, the fraction of Mary's garden that has tulips would be
(2x/3) /x = 2/3
Final answer:
Mary has 2/3 of her garden planted with tulips.
Explanation:
To find the fraction of Mary's garden that has tulips, we need to first determine the fraction of her garden that she has planted with roses. We are given that Mary plants roses in 1/4 of her garden, so the fraction of her garden that she has planted with roses is 1/4. Since she has 1/12 of her garden left to plant more flowers, the fraction of her garden that she has planted with tulips is the remaining fraction, which is 1 - 1/4 - 1/12.
Let's simplify this expression. First, find a common denominator for 1/4 and 1/12, which is 12. Rewrite 1/4 with the denominator 12 as 3/12, and rewrite 1/12 with the denominator 12 as 1/12. Now we can subtract these fractions:
1 - 3/12 - 1/12 = 12/12 - 3/12 - 1/12 = 8/12 = 2/3
Therefore, 2/3 of Mary's garden has tulips.
Write an equation for Greg ordered some books online for $6 each. He paid a total of $3 for shipping. The total cost of the purchase was $75.00. How many books did he buy?
Final answer:
Greg bought 12 books online. To find the number of books, set up the equation 6n + 3 = 75, subtract the shipping fee, and divide by the price per book.
Explanation:
Greg ordered books online for $6 each and paid a total of $75, which includes a $3 shipping fee. To determine the number of books Greg bought, you need to set up an equation that represents the total cost.
The cost of the books alone can be represented by 6 times the number of books (6n), and when you add the shipping cost of $3, it equals the total cost of $75. So the equation would be:
6n + 3 = 75
To solve for n, which is the number of books Greg purchased, follow these steps:
Subtract the shipping fee from the total cost: 75 - 3 = 72.
Divide the result by the cost per book: 72 ÷ 6 = 12.
Therefore, Greg bought 12 books.
Angle 1, angle 2, and angle 3 are adjacent angles, with angle 1 supplementary to angle 2 and angle 2 complementary to angle 3. If angle 1 measures (8x + 3) and angle 2 measures (5x - 18), find the measure of angle 3
Answer:
Step-by-step explanation:
If angle 1 and angle 2 are supplementary, then
∠1 + ∠2 = 180°
If angle 2 and angle 3 are complementary, then
∠2 + ∠3 = 90°
We are given the values for angles 1 and 2, so:
(8x + 3) + ( 5x - 18) = 180 so
13x - 15 = 180 and
13x = 195 so
x = 15
Sub 15 in for x in angle 2 to find the measure of angle 2:
∠2 = 5(15) - 18 so
∠2 = 57°
That means that to find angle 3,
57° + ∠3 = 90 so
∠3 = 33°
The measure of angle 3 is found to be 33 degrees, using the relationships that angle 1 is supplementary to angle 2 and angle 2 is complementary to angle 3, along with their given expressions in terms of x.
Explanation:To find the measure of angle 3, we must use the relationships between the angles given: angle 1 is supplementary to angle 2 and angle 2 is complementary to angle 3.
Since angle 1 and angle 2 are supplementary, their sum is 180 degrees. The equation is therefore:
(8x + 3) + (5x - 18) = 180
Solving for x gives:
13x - 15 = 180
x = 195 / 13
x = 15
Substitute x back into the expression for angle 2:
(5x - 18) = (5(15) - 18) = 57 degrees
Since angle 2 and angle 3 are complementary, they add up to 90 degrees:
angle 2 + angle 3 = 90
57 + angle 3 = 90
Subtract 57 from both sides to find angle 3:
angle 3 = 90 - 57
angle 3 = 33 degrees
Therefore, the measure of angle 3 is 33 degrees.
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