Answer:
Step-by-step explanation:
7,300 = 5,500 + 300x
7,300 - 5,500 = 300x
1,800 = 300x
x = 6
Answer:
greater than or equal to 6
Step-by-step explanation:
i just took the plato test
What is the 6th term in the sequence described by the following recursive formula?
a1=9
an=an−1−4
Answer:
[tex] a_{6} = - 11[/tex]
Final answer:
The 6th term in the recursive sequence with the first term 9 and each subsequent term decreasing by 4 from the previous term is -11.
Explanation:
To find the 6th term in the sequence described by the recursive formula given:
a1=9
an=an-1−4
We will apply the formula recursively to determine each term up to the 6th term.
First term (a1): 9
Second term (a2): a1 − 4 = 9 − 4 = 5
Third term (a3): a2 − 4 = 5 − 4 = 1
Fourth term (a4): a3 − 4 = 1 − 4 = -3
Fifth term (a5): a4 − 4 = -3 − 4 = -7
Sixth term (a6): a5 − 4 = -7 − 4 = -11
Therefore, the 6th term in the sequence is -11.
The army bus has 12 seats on one side. Two soldiers can sit in each seat. If five seats are reserved for equipment, how many buses will they need for 1120 soldiers
Answer:
80 buses will be required for 1120 soldiers.
Step-by-step explanation:
Given:
Number of seats on One side = 12 seats.
Now Given:
five seats are reserved for equipment.
So we can say that;
Number of seats used by soldiers = [tex]12-5=7\ seats[/tex]
Number of soldiers on Each seat =2
So we will now find number of soldiers on each bus.
number of soldiers on each bus is equal to Number of seats used by soldiers multiplied by Number of soldiers on Each seat.
framing in equation form we get;
number of soldiers on each bus = [tex]7\times2 = 14\ soldiers[/tex]
Now we know that;
For 14 soldiers = 1 bus
So 1120 soldiers = Number of buses required for 1120 soldiers.
By Using Unitary method we get;
Number of buses required for 1120 soldiers = [tex]\frac{1120}{14} =80[/tex]
Hence 80 buses will be required for 1120 soldiers.
Jordy looked at a package of M&M's.He realized 1/3 of the M&M's is blue 1/4 were red and 1/8 were yellow. What color M&M's did Jordy have the most?
Answer:
Blue M&M's
Step-by-step explanation:
Let the total M&M's bought be 100%.
If 1/3 of the M&M's is blue this means we have 1/3 of 100 of blue M&M's i.e 33.3% are blue.
If 1/4 were red, then we have 1/4 of 100 of red M&M's i.e 25% of reds
If 1/8 of the M&M's were yellow, this means there are 1/8 of 100% M&M's i.e 12.5% of yellow.
According to the results, Jordy have more of blue M&M's
In order to get an. A in science,Jack must get at least 92% on his next test. If tbe test has 30 questions, what is the minimum number he must correctly answer.
Jack needs to correctly answer at least 28 out of the 30 questions to achieve a minimum of 92% on his science test.
To determine the minimum number of questions Jack must correctly answer to get at least 92% on his next 30-question science test, we can use the following calculation:
Minimum number of correct answers = 92% of total questions
= 0.92 × 30
= 27.6
Since Jack cannot answer a fraction of a question, he must round up to ensure the minimum percentage is met. Therefore, Jack must correctly answer at least 28 questions out of 30 to achieve a 92% score or higher.
What is the surface area of a cube that has a side length of 2.2 meters? Use the formula S A = 6 s squared, where SA is the surface area of the cube and s is the length of each side
Answer:
Step-by-step explanation:
surface area=6*2.2²=6×4.84=29.04 m²
Answer:
29.04
Step-by-step explanation:
just took the test
Let f ( x ) = x 2 + 6 x + 6 f ( x ) = x 2 + 6 x + 6 , and g ( x ) = 1 g ( x ) = 1 . Find all values for the variable x x , for which f ( x ) = g ( x ) f ( x ) = g ( x ) .
Answer:
Therefore the value of x are = -1 and -5 for which f(x)=g(x).
Step-by-step explanation:
Given,
f(x)=x²+6x+6 and g(x)=1
f(x)=g(x)
⇒x²+6x+6=1
⇒x²+6x+6-1=0
⇒x²+6x+5=0
⇒x²+5x+x+5=0
⇒x(x+5)+1(x+5)=0
⇒(x+5)(x+1)=0
⇒x+5=0 or x+1=0
⇒x=-5 x=-1
Therefore the value of x are = -1 and -5.
To find the values of x for which f(x) equals g(x), we set the equations x² + 6x + 6 equal to 1 and solve. The quadratic equation factors to yield x = -1 and x = -5 as solutions.
To find the values of x for which f(x) equals g(x), we need to set the functions equal to each other and solve for x:
Given:
f(x) = x² + 6x + 6
g(x) = 1
We need to solve for x when:
x² + 6x + 6 = 1
Subtract 1 from both sides to set the equation to zero:
x² + 6x + 5 = 0
Next, we factor the quadratic equation:
(x + 1)(x + 5) = 0
Set each factor to zero and solve for x:
x + 1 = 0
x = -1
x + 5 = 0
x = -5
Thus, the values of x for which f(x) = g(x) are x = -1 and x = -5.
A youth club receives a discount on each pizza purchased for a party. The original price of each pizza is x dollars. The club leader purchases 8 pizzas for a total of (8x-32) dollars. Factor the expression
Answer:
The factored form is [tex](8x-32)=8(x-4)[/tex]
Step-by-step explanation:
Given : A youth club receives a discount on each pizza purchased for a party. The original price of each pizza is x dollars. The club leader purchases 8 pizzas for a total of (8x-32) dollars.
To find : Factor the expression ?
Solution :
The original price of each pizza is x dollars.
The club leader purchases 8 pizzas for a total of [tex](8x-32)[/tex] dollars.
To factor the expression we have to take common term out.
So, [tex]8x=8\times x[/tex]
[tex]32=8\times 4[/tex]
8 is common take out,
[tex](8x-32)=8(x-4)[/tex]
Factors are 8 and (x-4).
Therefore, the factored form is [tex](8x-32)=8(x-4)[/tex]
To factor the expression (8x - 32), we take out the common factor of 8, resulting in the factored form of 8(x - 4), indicating a $4 discount per pizza.
Explanation:The question is asking to factor the expression, which represents the total cost for purchasing 8 pizzas after receiving a discount from the original price x dollars per pizza. The expression given is (8x - 32) dollars.
To factor this expression, we look for a common factor in both terms which is 8.
Factoring out the 8, we get 8(x - 4). This means the club receives a discount of $4 per pizza since (8x - 32) factors into 8 times (x - 4).
The addition law is potentially helpful when we are interested in computing the probability of
Answer:
The union of two event
Step-by-step explanation:
Addition law of probability define that probability of two event is total sum of probability of any event subtract the probability of both events
There are two rules in addition law:
Addition law 1 - when both event are mutually exclusive, then probability of either event is the sum of each event probability.
P( A or B) = P(A) +P(B)
Addition law 2 - when both events are non mutually exclusive then there in addition to the individual probability there is some overlap .
P( A or B) = P(A) +P(B) - P(A and B)
It should be noted that addition law is potentially helpful when we are interested in computing the probability of The union of two event.
According to this question, we are to discuss about Addition law of probability.
As a result of this we can see that Addition law of probability explain about probability for either of two mutually exclusive events which is occurring and also the probability of two non-mutually exclusive events that is occurring.
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i require some assistance :(, please help ASAP. Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents. (b^2)^3
Answer:
My guess is 2b^5
Step-by-step explanation:
This question is kinda tricky. LMK if its correct
Consider the following If statement, which is syntactically correct but uses poor style and indentation: if (x >= y) if (y > 0) x = x * y; else if (y < 4) x = x - y; Assume that x and y are int variables containing the values 9 and 3, respectively, before execution of the above statement. After execution of the statement, what value will x contain?
Answer:
27
Step-by-step explanation:
int x = 9;
int y = 3;
if (x >= y)
if (y > 0)
x = x * y;
else if (y < 4)
x = x - y;
First, the first if statement check for the value of x>=y which is true. The another if-statement check if y>0, which is true and it execute the statement x = x * y that is x = 9 * 3 and x = 27.
The else-if block is not executed because the if-statement attached to it has been executed already.
Angie has some red and blue beads. 40% of her beads were red. When she lost 50 blue beads, the number of blue beads was reduced by 1/3 its original number of beads. How many beads did Angie have in the end?
Answer:
Step-by-step explanation:
Let x represent the total number of red and blue beads
Angie has some red and blue beads. 40% of her beads were red. This means that the total number of red beads is
40/100 × x = 0.4x
The number of blue beads would be
x - 0.4x = 0.6x
When she lost 50 blue beads, the number of blue beads was reduced by 1/3 its original number of beads. This means that
0.6x - 50 = 0.6x - 0.6x/3
0.6x - 50 = 0.6x - 0.2x = 0.4x
0.6x - 0.4x = 50
0.2x = 50
x = 50/0.2 = 250
The number of blue beads that Angie had initially is
0.6 × 250 = 150
The number of blue beads that Angie has left is
150 - 50 = 100 beads
The number of beads that Angie has in the end is
250 - 50 = 200 beads
Describe how to solve any equation in the form ax + b = c for the variable x.
Subtract b from both sides: ax=c-b
Divide both sides by a: x=(c-b)/a
Hope this helped
Explanation:
To solve any equation that is linear in the variable of interest, you first look at what is done to the variable, using the Order of Operations as your guide.
Here, the variable is ...
multiplied by "a"the product has "b" added to it.You find the value of the variable by reversing these steps, starting from the last one on the list and working up the list.
To "undo" the addition of "b", we add its opposite (-b) to the equation. The rules of equality tell you that anything you do to one side of the equation must also be done to the other side, so we add -b to both sides:
ax +b -b = c -b
ax = c -b . . . . . . . . simplify
To "undo" the multiplication by "a", we multiply by its reciprocal. That is, we multiply by 1/a, or, equivalently, divide by "a". Again, we must do this to both sides of the equation:
(1/a)ax = (1/a)(c -b)
x = (c -b)/a . . . . . . . simplify
__
In short, we subtract the added constant (b) and divide by the multiplier (a).
what has a head, a tail, is brown, and has no legs
Answer:
A penny
Step-by-step explanation:
a penny
_______
_______
Find and equation for the line with the given properties. Express the equation in general form. Slope -6/7; containing the point (10,-9) what is the equation for the line?
Answer:
[tex]6x+7y+3=0[/tex]
Step-by-step explanation:
We are asked to find the equation of the line in general form, which has a of -6/7 and containing the point (10,-9).
We know that genera equation of a line is in form [tex]Ax+By+C=0[/tex], where, A, B and C are real numbers.
First of all, we will write our equation in point-slope form as:
[tex]y-y_1=m(x-x_1)[/tex], where,
m = Slope of line,
[tex](x_1,y_1)[/tex] = Given point on line.
[tex]y-(-9)=-\frac{6}{7}(x-10)[/tex]
[tex]y+9=-\frac{6}{7}x+\frac{60}{7}[/tex]
[tex]y*7+9*7=-\frac{6}{7}x*7+\frac{60}{7}*7[/tex]
[tex]7y+63=-6x+60[/tex]
[tex]6x+7y+63-60=-6x+6x+60-60[/tex]
[tex]6x+7y+3=0[/tex]
Therefore, our required equation would be [tex]6x+7y+3=0[/tex].
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A woman is selected by a marketing company to participate in a paid focus group. The company says that the woman was selected because everyone in five randomly selected towns was being selected. Which type of sampling did the marketing company use?
A) Stratified sampling
B) Systematic sampling
C) Random sampling
D) Convenience sampling
E) Cluster sampling
Stratified sampling method - where population were divided into different groups called strata and the sample is then drawn from EACH group.
Systematic sampling method - sampling method using probability where elements are chosen from a target population.
Random sampling - each sample chosen has equal probability to be chosen.
Convenience sampling method - Not a random sampling method where the sample is being chosen as per ease of access.
Cluster sampling method - population were divided into different groups as known as clusters. The clusters were then chosen randomly as the samples. Each individuals in the clusters chosen are used as the samples.
Answer: E. Cluster sampling where selected towns refer to the clusters and were chosen randomly.
The type of sampling used by the researcher is cluster sampling.
What is cluster sampling?Cluster sampling is a technique used when it becomes difficult to study the target population spread across a wide area and simple random sampling cannot be applied.
The researcher divides the entire population into sections or clusters. Then the researcher randomly selects a few clusters from the total clusters for the research.
In this case, the clusters are the five randomly selected towns. Everyone in these selected towns is included in the sample. This makes it a cluster sample.
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use a property to write an equivalent expression 6x7
Answer:
Step-by-step explanation:
6 X 7 = 42
This is simply the sum of 6 in seven places or 7 in six places.
What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?
Answer:
The destination airport identifier code.
Step-by-step explanation:
What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?
A destination identifier code should be entered.
if no stopover for more than 60 minutes is expected, enter ICAO four letter identifier in item 16 of the flight plan. and indicate when to stopover
Item 16 on an IFR flight plan is used to indicate the destination aerodrome, which is the airport where the aircraft is planning to land. For an IFR flight with an intended stopover of 30 minutes, you would enter the ICAO code or the three-let...
Explanation:Item 16 on an IFR flight plan is used to indicate the destination aerodrome, which is the airport where the aircraft is planning to land.
For an IFR flight with an intended stopover of 30 minutes, you would enter the ICAO code or the three-letter identifier for the destination aerodrome in item 16.
In this case, you would enter the ICAO code or three-letter identifier for the airport where you will land after the intended stopover, and not the stopover airport itself.
Sonya, who is paid time and a half for hours worked in excess of 40 hours, had gross weekly wages $725 for 52 hours worked. What is her regular hourly rate?
Answer: her regular hourly rate is $12.5
Step-by-step explanation:
Let x represent the regular payment that Sonya receives per hour for the first 40 hours of work. This means that her total pay for the first 40 hours of work is
40 × x = $40x
Sonya is paid time and a half for hours worked in excess of 40 hours. This means that her hourly pay for working more than 40 hours would be x + 0.5x = $1.5x
She worked for 52 hours. This means that the extra hours that she worked is
52 - 40 = 12 hours
Total pay for 12 extra hours is
12 × 1.5x = 18x
If she had gross weekly wages of $725, then
40x + 18x = 725
58x = 725
x = 725/58 = $12.5
To find Sonya's regular hourly rate, we need to calculate her overtime pay and then subtract it from her total weekly wages.
Explanation:To find Sonya's regular hourly rate, we need to calculate her overtime pay and then subtract it from her total weekly wages. Sonya earned $725 for 52 hours worked. Since she is paid time and a half for hours worked more than 40, she worked 12 overtime hours (52 - 40 = 12).
Her overtime pay is calculated by multiplying her regular hourly rate by 1.5, so her overtime pay is 1.5 * regular hourly rate * 12 hours. Subtracting her overtime pay from her total wages gives us her regular wages, so we have the equation: $725 - (1.5 * regular hourly rate * 12) = regular wages. Solving for regular hourly rate will give us the answer.
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Researchers randomly divide participants into groups. Each group takes a different amount of omega-3 fatty acid supplements daily for a month. One group receives a placebo. The researchers measure the impact on cholesterol levels in the blood. What is the purpose of random assignment in this experiment? Check all that apply. To ensure that all people with high cholesterol have an equal chance of being selected for the study To increase the accuracy of the research results and prevent skewness in the data To produce treatment groups with similar characteristics To control confounding
Answer: To produce treatment groups with similar characteristics
Step-by-step explanation:
The purpose of this experiment is to determine that the treatments groups with similar characteristics are produced. Every groups is taking different amount of the supplement so this study ensures that by randomly assigning the supplements, we can check the cholesterol level in the blood. In this way, similar characteristics in groups are imparted so we can then make treatment groups of same characteristics.
The purpose of random assignment in experiments is to avoid bias, increase the research results' accuracy, help in producing treatment groups with similar characteristics, and control confounding variables. In this case, it ensures that all participants have an equal chance of receiving any level of omega-3 fatty acid or placebo.
Explanation:The purpose of random assignment in this experiment is multifold. Firstly, it ensures all participants, regardless of their cholesterol levels, have an equal chance of being selected. This prevents bias in the sample selection. Secondly, it increases the accuracy of the research results by preventing skewness in the data. The random assignment ensures that every participant has an equal chance of receiving any level of the omega-3 fatty acid supplement or the placebo. This helps produce treatment groups with similar characteristics, which in turn allows for fair comparisons to be made. Finally, it aids in controlling confounding variables. These are factors other than the independent variable (in this case, omega-3 fatty acid supplements) that may affect the dependent variable (cholesterol level), and random assignment helps to equalize these among the groups.
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Brandon eats half the amount of pie that Mollie eats.Yuki eats four times as much pie as Brandon. Mollie eats 1/4 of the pie. How much pie does Anna eat?
Answer: Anna eats 1/8 of pie
Step-by-step explanation: Let total pie =1
Mollie eats 1/4 of pie
Brandon eats half the amount of pie that Mollie eats i.e 1/2 of (1/4)
⇒1/8
Yuki eats 4 times as much as pie as Brandon i.e 4*(1/8)
⇒1/2
Total pie eaten by Mollie +Brandon+Yuki = 1/4+1/8+1/2
⇒7/8
Therefore Anna eats (1-7/8)
⇒ 1/8 of pie
The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the number of months since January 2001. (m = 0 represents January 2001.)
A sine function is written to represent the data.
What is the amplitude, period, and vertical shift of this equation?
Drag a value into each box to correctly complete the statements.
Answer:
Part A) The amplitude = 24
Part B) The period = 24
Part C) Vertical shift = 36
Step-by-step explanation:
The general equation of the sine function:
y = A sin (Bx) + C
Where A is the amplitude and B = 360°/Period and C is the vertical shift
See the attached figure which represents the graph of m and f(m)
So,
Part A:
The function has minimum at 12 and maximum at 60
The difference is = 60 - 12 = 48
So, The amplitude = 48/2 = 24
Part B:
Period: The period of a periodic function is the interval on which the cycle of the graph that's repeated in both directions lies.
We can deduce that the function completes one cycle within 24 months
So, the period = 24
Part C:
Vertical shift is obtained at m = 0
So, f(m) = 36
36 = A sin (0) + C
C = 36 ⇒ Vertical shift
So, The amplitude = 24
The period = 24
Vertical shift = 36
Answer:
Answer:
Part A) The amplitude = 24
Part B) The period = 24
Part C) Vertical shift = 36
Step-by-step explanation:
The general equation of the sine function:
y = A sin (Bx) + C
Where A is the amplitude and B = 360°/Period and C is the vertical shift
See the attached figure which represents the graph of m and f(m)
So,
Part A:
The function has minimum at 12 and maximum at 60
The difference is = 60 - 12 = 48
So, The amplitude = 48/2 = 24
Part B:
Period: The period of a periodic function is the interval on which the cycle of the graph that's repeated in both directions lies.
We can deduce that the function completes one cycle within 24 months
So, the period = 24
Part C:
Vertical shift is obtained at m = 0
So, f(m) = 36
36 = A sin (0) + C
C = 36 ⇒ Vertical shift
So, The amplitude = 24
The period = 24
Vertical shift = 36
Step-by-step explanation:
Mr wells drew a plan for a rectangle dog run three of the vertices are (2 1/3, 7 1/2), (12, 7 1/2), and (12, 1) what are the coordinates of the fourth vertex
Answer:
Step-by-step explanation:
let 4th fourth vertex be D (x,y)
A(2 1/3,7 1/2),B(12, 7 1/2),C(12,1)
or A(7/3,15/2),B(12,15/2),C(12,1)
Mid-point of diagonal AC is P((7/3+12)/2,(15/2+1))
Mid -point of diagonal BD is P((12+x)/2,(15/2+y)/2)
(Because mid -point of diagonal is same.)
(12+x)/2=(7/3+12)/2
12+x=7/3+12
x=7/3
(15/2+1)/2=(15/2+y)/2
15/2+1=15/2+y
y=1
so fourth vertex is (7/3,1)
To find the coordinates of the fourth vertex of the rectangle, we use the information provided about the positions of the third vertex and the Car X figure. The coordinates of the fourth vertex are (13 2/3, 7 1/2) and (12, 2).
Explanation:To find the coordinates of the fourth vertex of the rectangle, we can use the fact given that the third vertex is one and two-thirds perpendicular hash marks to the right of the center top hash mark. Since the center top hash mark is at (12, 7 1/2), the third vertex is at (12 + 1 2/3, 7 1/2), which simplifies to (13 2/3, 7 1/2).
Now, we need to find the position of the fourth vertex. According to the given information, the fourth vertex is in the same position as the Car X figure, which means it is one perpendicular hash mark above the center right hash mark. Since the center right hash mark is at (12, 1), the fourth vertex is at (12, 1 + 1), which simplifies to (12, 2).
Therefore, the coordinates of the fourth vertex are (13 2/3, 7 1/2) and (12, 2).
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Below is the table of values of a function. Write the output when the input is n input 1,5,6,n output 4,8,9
Answer:
output = n+3.
Step-by-step explanation:
input : 1 5 6 n
output: 4 8 9 -
Here , 4= 1+3 , 8= 5+3 ,9 = 6+3
So,
output = input +3
When input =n
Then output = n+3.
what is 5x -2=38
A 36
B 8
C 7
D 13
What is the slope of this line?
Slope of this line is -2.5
Step-by-step explanation:
Step 1: Slope of the line, m = (y2 - y1)/(x2 - x1)Here, from the graph, x1 = -2, x2 = -4, y1 = 3, y2 = 8
⇒ m = (8 - 3)/(-4 - -2) = 5/-2 = -2.5
Suppose triangle DEF = triangle WXY. Which choice below shows corresponding parts to congruent triangles that are congruent? Explain your answer. (A) angle E = angle X; DF = XY (B) angle D = angle Y; EF = XY ( C) angle E = angle X; DF = XY; (D) angle F = angle X; DE = WX
Answer:
(C ) angle E = angle X; DF = XY
Step-by-step explanation:
a triangle is said to be congruent if SAS(two sides and included angle)
SSS (all the sides are equal), ASA (two angles and an included sides).
therefore, if angle E and angle X are equal
line DF and line XY are also equal.
The following data reflect the number of customers who return merchandise for a refund on Monday. Note these data reflect the population of all 10 Mondays for which data are available. 40 12 17 25 9 46 13 22 16 7Based on these data, what is the standard deviation?
Answer:
The standard deviation of given data is 12.36
Step-by-step explanation:
We are given the following data in the question:
40, 12, 17, 25, 9, 46, 13, 22, 16,7
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{207}{10} = 20.7[/tex]
Sum of squares of differences =
372.49 + 75.69 + 13.69 + 18.49 + 136.89 + 640.09 + 59.29 + 1.69 + 22.09 + 187.69 = 1528.1
[tex]\sigma = \sqrt{\dfrac{1528.1}{10}} = 12.36[/tex]
Thus, the standard deviation of given data is 12.36
Final answer:
The standard deviation of the provided data set (number of merchandise returns on Mondays) is approximately 14.8.
Explanation:
To calculate the standard deviation of the provided data set (40, 12, 17, 25, 9, 46, 13, 22, 16, 7), we will follow these steps:
Find the mean of the data set.Subtract the mean from each data point and square the result.Calculate the sum of the squared differences.Divide this sum by the number of data points (since we have the population standard deviation).Take the square root of the result from step 4.Let's apply these steps:
The mean (average) is (40 + 12 + 17 + 25 + 9 + 46 + 13 + 22 + 16 + 7) / 10 = 20.7Squared differences (rounded to two decimal places) would be: (40 - 20.7)², (12 - 20.7)², (17 - 20.7)², and so on.The sum of these squared differences is approximately 2190.1Divide by the number of points, 2190.1 / 10 = 219.01The square root of 219.01 is approximately 14.8Therefore, the standard deviation is about 14.8.
1) A family consisting of three persons—A, B, and C—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that
(a) All three family members are assigned to the same station? (Round your answer to three decimal places.)
(b) At most two family members are assigned to the same station? (Round your answer to three decimal places.)
(c) Every family member is assigned to a different station? (Round your answer to three decimal places.)
Answer:
Step-by-step explanation:
Let us record the station number 1, 2 or 3 for each family member A, B or C.
I am attaching a table containing total outcomes. Outcomes are presented along rows while the assigned station to each member is written along columns. For ease of understanding, 1 3 2 in the table should be interpreted as family member A being assigned to station 1, member B to station 3 and member C to station number 2, respectively.
From table it is clear that the total outcomes possible are 27.
We know that, probability can be defined as,
[tex]PROBABITILY = \frac{NUMBER\;OF\;DESIRED\;OUTCOMES}{TOTAL\;NUMBER\;OF\;OUTCOMES}[/tex]
a) All Members Assigned to the Same Station.
Cases for all members being assigned to same station are as follows:
[1 1 1], [2 2 2], [3 3 3] (outcome number 1, 14 and 27 in the table).
Therefore,
[tex]PROBABILITY\;(Case\;a) = \frac{3}{27}\\\\PROBABILITY\;(Case\;a) = 0.111[/tex]
b) At Most Two Members Assigned to the Same Station.
It means that maximum of 2 members can have the same station. Cases for this situation are as follows:
[1 1 2], [1 1 3], [1 2 1], [1 2 2], [1 3 1], [1 3 3], [2 1 1], [2 1 2], [2 2 1], [2 2 3], [2 3 2],
[2 3 3], [3 1 1], [3 1 3], [3 2 2], [3 2 3], [3 3 1], [3 3 2]
(outcome number 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 17, 18, 19, 21, 23, 24, 25 and 26 in the table).
Therefore,
[tex]PROBABILITY\;(Case\;b) = \frac{18}{27}\\\\PROBABILITY\;(Case\;b) = 0.666[/tex]
c) All Members Assigned to a Different Station.
For this scenario, we have the following results:
[1 2 3], [1 3 2], [2 1 3], [2 3 1], [3 1 2], [3 2 1] (outcome number 6, 8, 12, 16, 20 and 22 in the table).
Therefore,
[tex]PROBABILITY\;(Case\;c) = \frac{6}{27}\\\\PROBABILITY\;(Case\;c) = 0.222[/tex]
Miles earns a 6% commission on each vehicles he sells. Today he sold a truck for 18500 and a car for 9600. What is the total amount of his commision on these vehicles
Answer:
The total amount of commission on these vehicles is 1686.
Step-by-step explanation:
Given:
Miles earns a 6% commission on each vehicles he sells.
Today he sold a truck for 18500 and a car for 9600.
Now, to get the total amount of his commision on these vehicles.
Percent of commission Miles earns on each vehicles he sells = 6%.
He sold a truck for = 18500.
He sold a car for = 9600.
So, the total amount of vehicles:
[tex]18500+9600=28100.[/tex]
Now, to get the total amount of commission on vehicles:
[tex]6\%\ of\ 28100[/tex]
[tex]=\frac{6}{100} \times 28100[/tex]
[tex]=0.06\times 28100[/tex]
[tex]=1686.[/tex]
Therefore, the total amount of commission on these vehicles is 1686.
Tesha withdrew $22.75 each weak for four weeks from her savings account to pay for her piano lessons. By how much did these lessons change her savings account balance
Final answer:
Tesha's savings account balance was decreased by $91.00 after withdrawing $22.75 each week for four weeks to pay for piano lessons.
Explanation:
To calculate the change in Tesha's savings account balance due to payment for her piano lessons, we need to multiply the weekly withdrawal amount by the number of weeks. Tesha withdrew $22.75 each week for four weeks.
Multiply the weekly withdrawal amount by the number of weeks: $22.75 × 4.This results in a total withdrawal of $91.00 over the four weeks ($22.75 × 4 = $91.00).Therefore, Tesha's lessons decreased her savings account balance by $91.00 after four weeks.