Answer:
Step-by-step explanation:
Total staff is 32
Security guards = 5/8 of 32
= 5/8 × 32
= 5 × 4
= 20 security guards
There were total 20 security guards.
What is fraction?Fractions are used to represent smaller pieces of a whole.
Given that, There are a total of 32 staff members working in the aquarium, 5/8 of the staff are security guards.
Total staff is 32
Security guards = 5/8 of 32
= 5/8 × 32
= 5 × 4
= 20
Hence, there were 20 security guards.
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A random sample of 225 measurements is selected from a population, and the sample mean and standard deviation are x =32.5 and s = 30.0, respectively. It is claimed that the population mean exceeds 30. State the null and an appropriate alternative hypothesis, and perform a test at 5% significance level.
Answer:
[tex]t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25[/tex]
[tex]p_v =P(t_{(224)}>1.25)=0.106[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.
Step-by-step explanation:
Data given and notation
[tex]\bar X=32.5[/tex] represent the sample mean
[tex]s=30[/tex] represent the sample standard deviation
[tex]n=225[/tex] sample size
[tex]\mu_o =30[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean exceeds 30, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 30[/tex]
Alternative hypothesis:[tex]\mu > 30[/tex]
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=225-1=224[/tex]
Since is a one side rigth tailed test the p value would be:
[tex]p_v =P(t_{(224)}>1.25)=0.106[/tex]
Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.
PLZ HELP WORTH 50 PTS, WILL MARK BRANLIEST!!!!!
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.
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.
Sprinklers are being installed to water a lawn. Each sprinkler waters in a circle. Can the lawn be watered completely by 4 installed sprinklers?
(1) The lawn is rectangular and its area is 32 square yards.
(2) Each sprinkler can completely water a circular area of lawn with a maximum radius of 2 yards.
Answer:yes, the lawn can be watered completely by 4 installed sprinklers.
Step-by-step explanation:
The lawn is rectangular and its area is 32 square yards. Sprinklers are to be installed and each sprinkler waters in a circle. The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
If each sprinkler can completely water a circular area of lawn with a maximum radius of 2 yards., the the maximum area that can be watered by each sprinkler would be
Area = 3.14 × 2² = 12.56 yards²
If 4 sprinklers are completely installed, then the total area that they can water would be
12.56 × 4 = 50.24 yards²
Therefore, the lawn can be watered completely by 4 installed sprinklers.
For his phone service, Ivan pays a monthly fee of $14, and he pays an additional $0.05 per minute of use. The least he has been charged in a month is $74.75.What are the possible numbers of minutes he has used his phone in a month?
Answer:
1215 minutes are the possible numbers he has used his phone in a month.
Step-by-step explanation:
He has a monthly fee of 14$ then to the least that he has been charged we need to substract the monthly fee as follows:
Monthly charged = 74,75-14
Monthly charged= 60,75$
Then he pays an additional 0,05 $/minute of use, to know the consume:
Minutes= [tex]\frac{60,75}{0,05}[/tex]
Minutes= 1215 possible numbers of minutes he has used his phone.
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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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.
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7. If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths make sense for possible values of b? Select two options
Final answer:
To find the possible values of b in the equation 2a + b = 15.7 in an isosceles triangle, we can assume different values for a and solve for b. Two lengths that make sense for possible values of b are 5.7 and 3.7.
Explanation:
To determine which lengths make sense for possible values of b in the equation 2a + b = 15.7, we need to consider the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Since the triangle is isosceles, two sides have the same length, which is represented by a. Let's assume that a = 5 (one possible value) and substitute it into the equation: 2(5) + b = 15.7. Solving for b, we get b = 5.7. This means that a possible value for b is 5.7. Another option is when a = 6, which gives us b = 3.7. Therefore, the two lengths that make sense for possible values of b are 5.7 and 3.7.
The amounts below represent the last twelve transactions made to Juan's checking account.Positive numbers represent deposits and negative numbers represent debits from his account. $28 -$20 $67 -$22 -$15 $17 -$38 $41 $53 -$13 $30 $75A) $75B) $113C) $37D) -$113
Answer:
Option B. Range of the given sample data is 113.
Step-by-step explanation:
The given question is incomplete; here is the complete question.
Find the range for the given sample data.
The amounts below represent the last twelve transactions made to Juan's checking account. Positive numbers represent deposits and negative numbers represent debits from his account.
$28 -$20 $67 -$22 -$15 $17 -$38 $41 $53 -$13 $30 $75
Option A. $75
Option B. $113
Option C. $37
Option D. -$113
Transaction done by Juan can be arrange from lowest to highest
-38 -22 -20 - 15 -13 17 28 30 41 53 67 75
Now we know rage of the sample data = Highest value - Lowest value
= 75 - (-38)
= 113
Therefore, range of the given sample data is 113.
Option B is the answer.
Simplify the expression.
(9x + 1/2)+(4x − 8 1/2)
PLZ RESPOND QUICK THIS IS FOR A MIDTERM AND THEY ARE SO ANNOYING!!!
Answer:
The simplified expression is:
⇒ [tex]13x-8[/tex]
Step-by-step explanation:
Given expression:
[tex](9x + \frac{1}{2})+(4x-8\frac{1}{2})[/tex]
To simplify the given expression.
Solution:
In order to simplify, we will combine the like terms by removing the parenthesis.
We have:
⇒ [tex]9x + \frac{1}{2}+4x-8\frac{1}{2}[/tex]
Combining like terms.
⇒ [tex]9x+4x+\frac{1}{2}-8\frac{1}{2}[/tex]
⇒ [tex]13x+\frac{1}{2}-8\frac{1}{2}[/tex]
In order to combine fractions, we will combine the whole number and the fraction separately.
⇒ [tex]13x-8+(\frac{1}{2}-\frac{1}{2})[/tex]
⇒ [tex]13x-8+0[/tex]
Thus, the simplified expression is:
⇒ [tex]13x-8[/tex]
Consider the two functions. Which statement is true? A) Function 1 has a greater rate of change by 2 B) Function 2 has a greater rate of change by 2 C) Function 1 has a greater rate of change by 3 2 D) Function 2 has a greater rate of change by 3 2
Answer:
D. Function 2 has a greater rate of change by
3
2
Step-by-step explanation:
Function 2 has a greater rate of change by
3
2
m =
y2 − y1
x2 − x1
Function 1 has a slope of
1
2
.
x-int = (−4, 0)
y-int = (0, 2)
m =
2 − 0
0 − (−4)
=
2
4
=
1
2
Function 2 has a slope of 2.
m =
5 − 3
3 − 2
=
2
1
= 2
thus,
2 −
1
2
=
4
2
−
1
2
=
3
2
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
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.
In Missy's sports card collection,3/4 of the cards are baseball cards. In franks collection 8/12 are baseball cards. Frank says they have the same fraction of baseball cards. Is he correct?
Frank is incorrect because both fractions are not same.
Step-by-step explanation:
We have to compare both fractions in their simplest forms to compare them
Given
Baseball cards in Missy's Collection: [tex]\frac{3}{4}[/tex]
Baseball cards in Frank's Collection: [tex]\frac{8}{12}[/tex]
Converting the fraction in simplest form will give us:
[tex]\frac{2}{3}[/tex]
Both the fractions are not same as one is 3/4 and one is 2/3.
Hence,
Frank is incorrect
Keywords: Fractions, decimals
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A trains leaves Cincinnati at 2:00 pm.A second train leaves the same station in the same direction at 4:00 pm.The second train travels 24 mph faster than the first.If the second train overtakes the first at 7:00 pm, what is the speed of each train?
Answer:
Speed of first train = 36 mph
Speed of second train = 60 mph
Step-by-step explanation:
Given:
First train leaves Cincinnati at 2:00 PM
Second train leaves same station at 4:00 PM
Speed of second train is 24 mph faster than first train.
The second train overtakes the first at 7:00 PM
To find the speeds of each train.
Solution:
First train:
Let speed of first train be = [tex]x\ mph[/tex]
Time of travel between 2:00 PM to 7:00 PM = [tex]7-2=5\ h[/tex]
Distance traveled by 1st train in 5 hours in miles = [tex]Speed\times time = x\times 5 = 5x[/tex]
Second train:
Then, speed of second train will be = [tex](x+24)\ mph[/tex]
Time of travel between 4:00 PM to 7:00 PM =[tex]7-4 = 3\ h[/tex]
Distance traveled by second train in 3 hours in miles = [tex]Speed\times time = (x+24)\times 3=3x+72[/tex]
At 7:00 PM both trains meet as the second train overtakes the first. This means the distance traveled by both the trains is same at 7:00 PM as they both leave from same stations.
Thus, we have:
[tex]5x=3x+72[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by [tex]3x[/tex]
[tex]5x-3x=3x-3x+72[/tex]
[tex]2x=72[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}=\frac{72}{2}[/tex]
∴ [tex]x=36[/tex]
Speed of first train = 36 mph
Speed of second train = [tex]36+24=[/tex] 60 mph
Final answer:
The speed of the first train is 36 mph and the speed of the second train, which is 24 mph faster, is 60 mph. This was determined by setting up an equation based on the equal distances covered by both trains when the second overtakes the first.
Explanation:
The question involves solving a rate, time, and distance problem typically found in algebra or kinematics. To find the speeds of the two trains, we can set up an equation based on the fact that the distance covered by both trains is the same at the point where the second train overtakes the first. Let's define the speed of the first train as s (in mph). Therefore, the speed of the second train will be s + 24 mph. Since the first train leaves at 2:00 pm and is overtaken at 7:00 pm, it travels for 5 hours. The second train, leaving two hours later at 4:00 pm, travels for 3 hours.
The distance covered by each train can be expressed as their speed multiplied by the time traveled. For the first train, it's s 5 hours, and for the second train, it's (s + 24) 3 hours. Setting these two distances equal gives us:
s 5 = (s + 24) imes 3
Solving for s gives:
s imes 5 = 3s + 72
5s - 3s = 72
2s = 72
s = 36
So, the speed of the first train is 36 mph, and the speed of the second train is 60 mph (36 + 24).
Mrs. King gets a 15% discount on merchandise bought in the store where she works. Last week she bought several items that totaled $57.25 before the discount. How much did she have to pay using her discount? Round off the amount to the nearest cent.
Answer:
48.6625 before rounding, I'm sure the instruction told you where it preferred you to round.
Step-by-step explanation:
1. Convert percent value to a decimal.
The way to do this is by moving the period at 15.00 two places to the left.
2. Now that you have the decimal .15, multiply it by Mrs. King's subtotal (57.25).
you should get 8.5875.
3. Subtract the discount amnt. (8.5875) from the subtotal (57.25).
You should get 48.6625.
What is the value of x
Help is needed.
Answer:
x = 27.2.
Step-by-step explanation:
As BD || CE the triangles ABD and ACE are similar.
AB = 25 - 8 = 17.
AB / AC = AD / AE ( similar triangles)
17 / 25 = x / 40
x = 17*40 / 25
= 27.2.
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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Matt wants to build a rectangular enclosure for this animal. One wide of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Matt has 1000 feet of fencing. You can find the dimensions that maximize the area of the enclosed.
Answer:
500 feet by 250 feet.
Step-by-step explanation:
Let the length be x and the width y feet.
As we have 1000 feet of wire:
x + 2y = 1000
2y = 1000 - x
y = 500 - 0.5x
So the area = x(500 - 0.5x)
A = 500x - 0.5x^2
For a maximum area the derivative
A' = 500 -x = 0
x = 500 feet.
2y = 1000 - 500
y = 250 feet.
Chris types at an average speed of 35 words per minute. He has already typed 1,500 words of his final paper. The paper has to be more than 3,250 words. Which of the following inequalities could be used to solve for x, the number of minutes it will take Chris to type his paper?
Answer:
1750 + 35x ≥ 3250
Step-by-step explanation:
Average speed = 35 words
He has already typed 1500 words on his final paper
The paper must be more than 3250 words.
To find at least how many more words he has to type, we will subtract 1500 from 3250
3250 - 1500 = 1750 words
The equation will be 35x ≥ 1750
x is the number of minutes
The equation could be
1750 + 35x ≥ 3250
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
I like math because I get it done fast. And I get A's. And I made myself and my parents do it. I make my parents do it and myself. Thats why I love math
Answer:
proud of you keep ya head up
Step-by-step explanation:
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.
Fred’s company is planning a new logo. The diagrams show two similar versions of the planned logo.
A) calculate the lengths of the sides marked a and b.
B) the smaller of the two versions of the logo costs £4.48 to paint with gold paint. Calculate the cost of the logo with the same gold paint.
Answer:
a=7.2*1.5=10.8 cm
b=6.3/1.5=4.2 cm
[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]
Step-by-step explanation:
Proportional Geometric Shapes
A) We are given two similar shapes of a logo. They are to be proportional. We only need to find the proportion ratio of two of them to find the rest of the lengths.
The upper sides have 7.5 cm and 5 cm respectively. This gives us the ratio
[tex]\displaystyle r=\frac{7.5}{5}=1.5[/tex]
Which means all the measures of the smaller logo are 1.5 smaller than those of the larger. This means
b=6.3/1.5=4.2 cm
a=7.2*1.5=10.8 cm
B) To paint the logos, we need to cover its surface, so the ratio of the surface is 1.5*1.5=2.25
This means the cost to paint the larger logo is
[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]
Answer:
A) a = 10.8, b = 4.2
B) £10.08
Step-by-step explanation:
A) 7.5/5 = 1.5
a = 7.2 x 1.5 = 10.8
5/7.5 = 2/3
b = 6.3 x 2/3 = 4.2
B) 1.5 x 1.5 = 2.25
£4.48 x 2.25 = £10.08
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
The number of lacrosse sticks sold at a sporting goods store in November decreases by 35% from the number sold in October. In October, 80 sticks were sold. How many lacrosse sticks were sold in November?
Answer:the number of lacrosse sticks that were sold in November is 52
Step-by-step explanation:
The number of lacrosse sticks sold at a sporting goods store in November decreases by 35% from the number sold in October. If the number of lacrosse sticks sold in October is 80, then the amount by which it decreased would be
35/100 × 80 = 0.35 × 80 = 28
Therefore, the number of lacrosse sticks that were sold in November would be
80 - 28 = 52
(sum of interior angles = 180 (n-2) where n is the number of sides of the polygon)
1. if the sum of the interior angles of a polygon equals 1980, how many sides does the polygon have ?
2. how many degrees are there in the sum of the interior angles of a nine sides polygon ?
3. how many sides does a polygon have if the sum of its interior angles is 1620 ?
4. how many degrees are there in the sum of the interior angles of an eighteen sides polygon ?
5. how many degrees are there in the sum of the interior angles of a seventeen sides polygon ?
6. what is the sum of the interior angles of a quadrilateral ?
(i don't need an explanation, just the answers)
Answer:
Step-by-step explanation:
The sum of the interior angles = 180 (n-2)
where n is the number of sides of the polygon.
1) if the sum of the interior angles of a polygon equals 1980,
180(n - 2) = 1980
180n - 360 = 1980
180n = 1980 + 360 = 2340
n = 2340/180 = 13
2) if n = 9, the number of degrees would be
180(n - 2) = 180(9 - 2)
= 180 × 7 = 1260 degrees
3) 180(n - 2) = 1620
n - 2 = 1620/180 = 9
n = 9 + 2 = 11
4) n = 18
The number of degrees would be
180(n - 2) = 180(18 - 2) = 2880 degrees.
5) n = 17
The number of degrees would be
180(n - 2) = 180(17 - 2) = 2700 degrees.
6) the sum of the interior angles of a quadrilateral is 360 degrees.
Javon, Sam, and Antoine are baking cookies. Javon has 3/2 cup of flour, Sam has 4 1/3 cups of flour, and Antoine has 3 4/6 cups of flour. How many cups of flour do they have altogether?
Answer:
They have [tex]9\frac{3}{6}\ cups[/tex] of flour altogether.
Step-by-step explanation:
Given:
Amount of flour Javon has = [tex]\frac{3}{2}\ cup[/tex]
Amount of flour Sam has = [tex]4\frac{1}{3}\ cups[/tex]
[tex]4\frac{1}{3}\ cups[/tex] can be Rewritten as [tex]\frac{13}{3}\ cups[/tex]
Amount of flour Sam has = [tex]\frac{13}{3}\ cups[/tex]
Amount of flour Antoine has = [tex]3\frac{4}{6}\ cups[/tex]
[tex]3\frac{4}{6}\ cups[/tex] can Rewritten as [tex]\frac{22}{6}\ cups[/tex]
Amount of flour Antoine has = [tex]\frac{22}{6}\ cups[/tex]
We need to find the amount of cups of flour they have altogether.
Solution:
Now we can say that;
the amount of cups of flour they have altogether can be calculated by sum of Amount of flour Javon has and Amount of flour Sam has and Amount of flour Antoine has.
framing in equation form we get;
amount of cups of flour they have altogether = [tex]\frac{3}{2}+\frac{13}{3}+\frac{22}{6}[/tex]
Now to solve we need to make the denominator common by using L.C.M we get;
amount of cups of flour they have altogether = [tex]\frac{3\times3}{2\times3}+\frac{13\times2}{3\times2}+\frac{22\times1}{6\times1}=\frac{9}{6}+\frac{26}{6}+\frac{22}{6}[/tex]
Now Denominators are common so we will add the numerators we get;
amount of cups of flour they have altogether = [tex]\frac{9+26+22}{6}= \frac{57}{6}\ cups\ \ OR \ \ 9\frac{3}{6}\ cups[/tex]
Hence They have [tex]9\frac{3}{6}\ cups[/tex] of flour altogether.
Let the universe be the set U = {1, 2, 3,..., 10}. Let A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5}, and C = {2, 4, 6, 8}. List the elements of each set.(a) \overline{A} \cap C =\\
|\overline{A} \cap C| =\\
(b) B - \overline{C} = \\
|B - \overline{C}| \\
(c) B \cup A = \\
|B \cup A| =\\
(d) \overline{B} \cap (A - C) = \\
|\overline{B} \cap (A - C)| =\\
(e) (A - B) \cap (B - C) =\\
|(A - B) \cap (B - C)|
In a universe of numbers 1 to 10, sets A, B, and C hold specific values. We explore intersections, differences, and unions. A's complement intersects C to give {2, 6, 8}, while B minus C's complement reveals {2, 4}. Their union boasts {1, 2, 3, 4, 5, 7, 10}, while B's complement meets A minus C in {7, 10}. Finally, (A minus B) and (B minus C) share no elements, resulting in an empty set.
Explanation:Set Operations in U
Here's the breakdown of each set operation and the resulting sets:
(a) \overline{A} ∩ C:
\overline{A}: The complement of A, which includes all elements in U that are not in A. In this case, U \ A = {2, 3, 5, 6, 8, 9}.
\overline{A} ∩ C: The intersection of U \ A and C. This gives us {2, 6, 8}.
|\overline{A} ∩ C|: The cardinality (number of elements) of the intersection. Therefore, |\overline{A} ∩ C| = 3.
(b) B - \overline{C}:
\overline{C}: The complement of C, which includes all elements in U that are not in C. In this case, U \ C = {1, 3, 5, 7, 9, 10}.
B - \overline{C}: The difference between B and U \ C. This removes elements from B that are also in U \ C. Therefore, B - \overline{C} = {2, 4}.
|B - \overline{C}|: The cardinality of the difference. Hence, |B - \overline{C}| = 2.
(c) B ∪ A:
B ∪ A: The union of B and A, which includes all elements that are in either B or A or both. In this case, B ∪ A = {1, 2, 3, 4, 5, 7, 10}.
|B ∪ A|: The cardinality of the union. Therefore, |B ∪ A| = 7.
(d) \overline{B} ∩ (A - C):
\overline{B}: The complement of B, which includes all elements in U that are not in B. In this case, U \ B = {6, 7, 8, 9, 10}.
A - C: The difference between A and C. This removes elements from A that are also in C. Therefore, A - C = {1, 7, 10}.
\overline{B} ∩ (A - C): The intersection of U \ B and A - C. This gives us {7, 10}.
|\overline{B} ∩ (A - C)|: The cardinality of the intersection. Hence, |\overline{B} ∩ (A - C)| = 2.
(e) (A - B) ∩ (B - C):
A - B: The difference between A and B. This removes elements from A that are also in B. Therefore, A - B = {7, 10}.
B - C: The difference between B and C. As mentioned earlier, B - C = {2, 4}.
(A - B) ∩ (B - C)**: The intersection of A - B and B - C. Since no elements are shared between these sets, the intersection is empty.
|(A - B) ∩ (B - C)|**: The cardinality of the empty set is 0. Therefore, |(A - B) ∩ (B - C)| = 0.
Joaquin can send up to 250 to text messages each month so far this month he has sent 141 text messages let t represent the number of text messages Joaquin can send during the rest of the month
Question is Incomplete,Complete Question is given below;
Joaquin can send 250 text each month so far this month he has sent 141 text message let T represent the number of text messages Joaquin can send during the rest of the month. Write an inequality to model the situation. Solve the inequality for t.
Answer:
The Inequality modelling the situation is [tex]141+t\leq 250[/tex].
Joaquin can send at the most 109 messages for the remaining of the month.
Step-by-step explanation:
Given:
Number of messages already sent = 141
Total number of messages he can send = 250
We need to write the inequality to model the situation and solve for the same.
Solution:
Let remaining number of messages he can send be 't'.
Now we know that;
Number of messages already sent plus remaining number of messages he can send should be less than or equal to Total number of messages he can send.
framing in equation form we get;
[tex]141+t\leq 250[/tex]
Hence The Inequality modelling the situation is [tex]141+t\leq 250[/tex].
On Solving the above equality we will find the value of 't'.
Now we will subtract both side by 141 using subtraction property of inequality we get;
[tex]141+t-141\leq 250-141\\\\t\leq 109[/tex]
Hence Joaquin can send at the most 109 messages for the remaining of the month.