Part A: The actual dimensions of the pool are 10 feet long and 5 feet wide.
Part B: the cost of the cover for the pool would be $15.00.
What is dimension?Dimension is a measure of a physical property of an object, such as its length, breadth, height, or mass.
Part A: The actual dimensions of the pool can be determined by using the given scale. To do this, we need to convert the given measurements in inches to feet. We can do this by dividing the given measurements in inches by the scale, which is 2 inches equals 7 feet.
The actual length of the pool is 20 ÷ 2 = 10 feet.
The actual width of the pool is 10 ÷ 2 = 5 feet.
Therefore, the actual dimensions of the pool are 10 feet long and 5 feet wide.
Part B: To calculate how much it would cost to buy a cover for the pool, we need to determine the area of the pool. We can do this by multiplying the length by the width of the pool.
Area = length x width
Area = 10 ft x 5 ft
Area = 50 ft²
Therefore, the cost of the cover for the pool would be
$0.30 x 50 ft² = $15.00.
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Question :
The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below. the length is 20 and the width is 10
Part A What are the actual dimensions of the pool? Blueprint: 10 in. Actual: ft Blueprint: 20 in. Actual: ft
Part B How much would it cost to buy a cover for the pool that costs $0.30 per square foot?
What is m24 if m25 = (2x)° and m24 = (x +9)°?
4
X
5
m24 =
The value of angle m<4 is 66 degrees
What are supplementary angles?The angles on a straight line are supplementary, this means that the angles sum up to 180 degrees.
From the information given, we have that;
m<4 = x + 9 degreesm< 5 = 2x degreesEquate the angles to 180 degrees
We have;
m<4 + m<5 = 180
Substitute the expression for each of the angles , we have;
x + 9 + 2x = 180
collect the like terms
3x = 180 - 9
subtract the values
3x = 171
Divide by the coefficient
x = 57
But m<4 = 57 + 9 = 66 degrees
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PLEASE HELP ME SOLVE THIS PROBLEM!!
Answer:
mm eh its too hard im onwy one!
Step-by-step explanation:
What is 1/2 + p = -3 ?
Answer:
p= -3-1/2
p= -7/2
Step-by-step explanation:
(you transpose the fraction /take the liketerms)
( you transpose your fraction will change the sign and become negative then -3-0.5or -3-1/2=-7/2.)then you substitute to the original equation 1/2+p=-3 check your answer .
I'LL MARK THE BRAINLIEST
In this figure, 14.2% of the area is painted green. How much of the area is painted green?
Answer:
8.449 square centimeters
Step-by-step explanation:
Area of the figure = area of square + area of triangle
[tex] {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5[/tex]
[tex].142 \times 59.5 = 8.449[/tex]
So 8.449 square centimeters of this figure is green.
Yellow Sticker Company’s variable expenses are 40% of sales. The company has monthly fixed expenses of $15,000 and sells each unit for $0.50. The monthly target operating income is $8,250.
a. What is the monthly margin of safety in dollars if Yellow Sticker Company achieves its operating income goal?
If Yellow Sticker Business meets its operating income goal, the quarterly safety margin in dollars will be $4,583.33.
Which financial objectives are sound?Budgeting, debt reduction, and setting up an emergency fund are important short-term objectives. Key insurance policies should be included in medium-term goals, whilst retirement should be the primary emphasis of long-term objectives.
Next, we deduct our break-even sales from actual sales at the goal operating income level to determine the margin of safety:
Real sales are determined by dividing target operating income by total fixed costs and contribution margin ratio.
Real sales equal $8,250 plus $15,000 / 0.60.
Real sales were $29,583.33
Safety margin = Real sales Breakeven sales
Margin of safety is calculated as $29,583.33 - ($0.50 x 50,000 units).
$25,000 - 29,583.33 is the margin of safety.
$4,583.33 is the safety margin.
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Customers at two clothing stores were asked about their color preferences in shirts. The responses of the customers at each store are summarized in the table.
Based on the information in the table, which statement best describes the customers' preferences on shirt colors?
A. At both stores, more customers prefer white shirts than shirts in either of the other two colors.
B. At store 2, the same number of customers prefer blue and black shirts.
C. At both stores, fewer customers prefer blue shirts than shirts in either of the other two colors.
D. At store 1, more customers prefer either blue or black shirts than white shirts.
Answer:
Based on the information in the table, the statement that best describes the customers' preferences on shirt colors is:
A. At both stores, more customers prefer white shirts than shirts in either of the other two colors.
Looking at the table, we can see that at store 1, 30 customers prefer white shirts, while only 20 prefer blue and 10 prefer black. Similarly, at store 2, 25 customers prefer white shirts, while only 15 prefer blue and 10 prefer black. Therefore, we can conclude that at both stores, more customers prefer white shirts than shirts in either of the other two colors.
Option B is incorrect because the table shows that at store 2, 20 customers prefer blue shirts while 10 prefer black shirts. Therefore, a different number of customers prefer blue and black shirts.
Option C is also incorrect because at both stores, more customers prefer white shirts than blue shirts, and the same number of customers prefer black and blue shirts.
Option D is incorrect because at store 1, only 10 customers prefer black shirts, while 20 prefer blue and 30 prefer white. Therefore, more customers prefer white or blue shirts than black shirts.
A warehouse contains 55 boxes. Then a truck delivers a number of boxes at 12:00 p.m. and a team of workers immediately begins to unload the boxes at a constant rate. At 3:30 p.m., the warehouse contains 90 boxes. How many boxes are in the warehouse when the truck is finally empty at 8:30 p.m.?
Answer:
Let's call the number of boxes delivered by the truck x. We know that the warehouse initially contains 55 boxes, and the truck delivers x boxes, so the total number of boxes in the warehouse after the delivery is 55 + x.
We also know that the workers unload the boxes at a constant rate, which we can express as a number of boxes per hour. Let's call this rate r. Since the workers unload boxes for 3.5 hours (from 12:00 p.m. to 3:30 p.m.), we can express the number of boxes unloaded as:
Number of boxes unloaded = r * 3.5
Therefore, the total number of boxes in the warehouse at 3:30 p.m. is:
55 + x - r * 3.5
We're told that this number is 90, so we can write the equation:
55 + x - r * 3.5 = 90
Simplifying this equation, we get:
x - r * 3.5 = 35
We're also told that the truck is empty at 8:30 p.m., which means that all the boxes it delivered have been unloaded by then. So the total number of boxes in the warehouse at 8:30 p.m. is:
55 + (x - r * 8)
where 8 is the number of hours between 12:00 p.m. and 8:00 p.m.
We can use the equation x - r * 3.5 = 35 to solve for x in terms of r:
x = 35 + r * 3.5
Substituting this into the equation for the total number of boxes at 8:30 p.m., we get:
55 + (35 + r * 3.5 - r * 8)
Simplifying this expression, we get:
55 - 35 + 28r
= 20 + 28r
Therefore, the warehouse contains 20 + 28r boxes at 8:30 p.m.
In ΔIJK, i = 100 inches, mm∠I=115° and mm∠J=23°. Find the length of j, to the nearest inch.
The measure of the side J of the triangle ΔIJK will be 43 units.
What is the law of sine?The law of sines defines the ratio of triangle sides, and their respective sine angles are equivalent. The law of sines is also known as the sine law, sine rule, and sine formula.
Given that in the triangle i = 100 inches, m∠I=115° and m∠J=23°. The measure of the length J will be calculated as:-
100 / sin115 = J / sin23
J = (100) x sin23 / sin115
J = 100 x 0.43
J = 43 units
The length of side J will be 43 units.
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Suppose that Y1, . . . , Yn is a sample of size n from a Exp(θ), with θ > 0, E[Y1] = θ and V(Y1) = θ^2
.
a) Find the distribution of Y¯Bar and Y(1) = min(Y1, . . . , Yn).
b) Find the constants c1 and c2 such that T1 = c1Y(1) and T2 = c2Y¯Bar are unbiased the estimators of θ. Compare the MSE of T1 and T2
c) Show that Q(Y1, . . . , Yn; θ) = 2nY(1)/θ ∼ Chi-sqaure(2).
d) Construct a two-sided 1 − α confidence interval for θ using the pivot in c).
Answer:
See below.
Step-by-step explanation:
a)
Since Y1, ..., Yn are independent and identically distributed, we have Y¯Bar ~ Exp(θ/n) and Y(1) ~ Exp(nθ).
b)
We want to find c1 and c2 such that E[T1] = θ and E[T2] = θ. We have E[Y(1)] = 1/θ and E[Y¯Bar] = θ/n, so setting T1 = c1Y(1) gives E[T1] = c1/θ = θ, and setting T2 = c2Y¯Bar gives E[T2] = c2θ/n = θ. Thus, c1 = θ^2 and c2 = n. To compare the MSE of T1 and T2, we compute,
MSE(T1) = V(T1) + [E(T1) - θ]^2
= V(θY(1)) + [θ - θ]^2
= θ^2V(Y(1))
= θ^2/θ^2
= 1
MSE(T2) = V(T2) + [E(T2) - θ]^2
= V(nY¯Bar) + [θ - θ]^2
= n^2V(Y¯Bar)/n^2
= V(Y¯Bar)/n
= (θ^2/n^2)(n/θ)
= θ^2/n
Since MSE(T2) < MSE(T1) for n > 1, T2 is the preferred estimator.
c)
Let Q(Y1, ..., Yn; θ) = 2nY(1)/θ. We have E[Q] = 2n/θ and V(Q) = 4n^2V(Y(1))/θ^2 = 4n^2/θ^2. To show that Q ~ Chi-squared(2), we need to show that Q has a gamma distribution with parameters k = 2 and θ = 1/2. We have,
fQ(q) = (1/θ^k)(q^(k-1) exp(-q/θ))/Γ(k) = (1/2^2)(q/2)exp(-q/2) = (1/4)q/2 exp(-q/2)
which is the pdf of a gamma distribution with k = 2 and θ = 1/2.
d)
To construct a two-sided 1 - α confidence interval for θ, we use the fact that 2nY(1)/Q(Y1, ..., Yn; θ) ~ F(2, 2n). Let Fα/2 be the (1 - α/2) quantile of the F distribution with 2 and 2n degrees of freedom. Then we have,
P(2nY(1)/(Fα/2) < θ < 2nY(1)/(F1-α/2)) = 1 - α
So the confidence interval is [2nY(1)/(Fα/2), 2nY(1)/(F1-α/2)].
Triple the sum of K and 2
"Triple the sum of K and 2" can be interpreted as a two-step procedure that involves adding K and 2 first, and then multiplying the result by 3.
What is multiplication?Multiplication is a fundamental arithmetic operation that involves combining two or more numbers to find their product. It is represented by the symbol "x" or "•" or sometimes simply by placing two numbers next to each other.
According to question:"Triple the sum of K and 2" can be expressed mathematically as:
3(K + 2)
This expression represents the value we get by adding K and 2, and then multiplying the sum by 3.
To evaluate this expression, we first add K and 2 together, giving us a sum of (K + 2). Then, we multiply that sum by 3, giving us a final result of 3(K + 2).
As a result, "triple the sum of K and 2" can be interpreted as a two-step procedure that involves adding K and 2 first, and then multiplying the result by 3.
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The full question is How do you write "triple the sum of K and 2" as an expression?
Find an equation of the line that passes through the pair of points (4,5) & (-1, -1). Write the equation in the form Ax+By=C
In response to the stated question, we may state that Hence the slope equation of the line passing through the points (4, 5) and (-1, -1) in the form Ax+By=C is: 6x - 5y = -1.
what is slope?Slope is just the curvature of a bend or line in mathematics. It is a measure of the manner in which the y-value of something like a function varies because when x-value changes. The slope of a line is commonly symbolized by the letter m and may be computed as follows: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) are any 2 options on the line. A bridge's slope might be negative, negative, zero, or unknown. A positive slope indicates that the line ascends to left to right, whereas a slope indicates that the line drops from left to right.
We must use the point-slope form of the equation of a line to obtain the equation of a line of the form Ax+By=C that goes through two points:
y - y1 = m(x - x1) (x - x1)
where (x1, y1) is the location of one of the points and m is the line's slope.
Then, we must determine the slope of the line.
[tex]m = (y2 - y1) / (x2 - x1) (x2 - x1)\\where (4, 5) = (x1, y1) and (x2, y2) = (-1, -1)m = (-1 - 5) / (-1 - 4) = -6 / (-5) = 6/5\\y - y1 = m(x - x1) (x - x1)\\y - 5 = (6/5)(x - 4) (x - 4)\\5y - 25 = 6x - 24\\6x - 5y = -1\\[/tex]
Hence the equation of the line passing through the points (4, 5) and (-1, -1) in the form Ax+By=C is: 6x - 5y = -1.
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Fionna, Anuar and Rizza had some cards. Fionna and Anuar had a total of 349 cards. Fionna had 145 cards. Anuar had 3 times as many cards as Rizza. How many cards did Fionna and Rizza have altogether? How do we draw model? I know question but how do we draw the model I need this asap
Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.
what is unitary method ?A mathematical concept known as the unitary approach entails calculating the value of a single unit in order to calculate the value of a given quantity. Finding the value of one unit and utilising that value to determine the value of a given quantity is an approach for solving problems. For instance, you can use the unitary technique to determine the price of 10 apples if you know that 5 apples cost $10. Now, divide $10 by 5, which equals $2, to determine the price of one apple. The cost of 10 apples is then determined by multiplying the price of one apple ($2) by 10, giving you a final cost of $20.
given
145 total cards with Fionna
349 total cards with Fionna and Aura
Card count with Anuar: 349 - 145
= 204
Rizza's number of cards equals 1/3 of 204.
= 204 / 3
= 68
Total number of cards: 68, 204, and 145
= 417
Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.
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Determine the intercepts of the line.
�
xx-intercept:
(
(left parenthesis
,
,comma
)
)right parenthesis
�
yy-intercept:
(
(left parenthesis
,
,comma
)
)right parenthesis
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points zero, negative ten and three, zero.
The intercepts of the line are:
x-intercept: (3, 0)
y-intercept: (0, 1)
What are the intercepts?
To find the x-intercept, we need to find the point where the line intersects the x-axis. This occurs when the y-coordinate of the point is zero. From the given information, we know that the line passes through the point (3, 0), so this point must be the x-intercept.
Therefore, the x-intercept is (3, 0).
To find the y-intercept, we need to find the point where the line intersects the y-axis. This occurs when the x-coordinate of the point is zero. We can find the equation of the line using the two given points (0, y) and (3, 0):
Slope of the line = (y2 - y1) / (x2 - x1)
= (0 - y) / (3 - 0)
= -y / 3
Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can write:
y - 0 = (-y/3)(x - 3)
Simplifying this equation, we get:
y = (-y/3)x + 1
Multiplying both sides by 3, we get:
3y = -yx + 3
Adding yx to both sides, we get:
yx + 3y = 3
This is the equation of the line in standard form. To find the y-intercept, we set x = 0:
0 + 3y = 3
Solving for y, we get:
y = 1
Therefore, the y-intercept is (0, 1).
Hence, the intercepts of the line are:
x-intercept: (3, 0)
y-intercept: (0, 1)
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HELP! triangle JKL is similar to triangle MNO. Find OM. round your answer to the nearest tenth if necessary
The length of OM, given that the triangles are similar to each other, is calculated as: 14.4.
What are Similar Triangles?Similar triangles are triangles that have the same shape but may have different sizes. They have the same angles, but the lengths of their sides are proportional. This means that corresponding sides of similar triangles are in proportion, and the ratio of their corresponding sides is constant.
Since triangle JKL is similar to triangle MNO, therefore:
JK/MN = JL/MO
Substitute:
5/24 = 3/x
Cross multiply:
5x = 72
5x/5 = 72/5
x = 14.4
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Brendon is building a clubhouse where 1 inch on the plans is equivalent to 8 inches on the actual clubhouse.
If the clubhouse is to be 126 inches wide, what will the width be on the plans?
Round answer to the nearest hundredth if necessary.
Answer:
To find the width of the clubhouse on the plans, we need to use the given scale of 1 inch on the plans being equivalent to 8 inches on the actual clubhouse. Let's assume that "x" inches on the plan correspond to the actual width of 126 inches of the clubhouse.
Using the proportionality of the scale, we can set up the following equation:
1 inch / 8 inches = x inches / 126 inches
Simplifying the equation, we can cross-multiply to get:
8 inches * x inches = 1 inch * 126 inches
8x = 126
x = 15.75
Therefore, the width of the clubhouse on the plans is 15.75 inches.
Math
Practice solving.
1. What is the sum of -5/7 and 3/7?
2. Find the different of 5/12 - 3/4
3. Find the difference of 1/8 - 13/2
4. Find the sim of 2/3 and 1/3
5. Find the difference of 3/4 and 1/3
6. What is 3/5 x 4/6
7. What is -8/9 x 3/4
8. What is 2 2/3 x 4/5
9. What is 3/4 of 120
10. What is 2/3 of 360
11. What is 1/3 of 180
12. Multiply 16/24 by 8/20
13. Multiply 1/7 by 4/1
14. What is 1/5 x 8/1
15. Multiply 4/7 x 6/1
16. Divide 3/8 and 2/5
17. Divide 16/21 and 24/14
18. What is 4/5 divided by 7/10
19. What is -4/15 divided by 8/12
20. What is 4/6 divided by -8
Answer:
1. -2/7
2. 7/6
3. 53/8
4. do u mean sum? if yes then the answer is 1
5. 5/12
6. 2/5
7. -2/3
8.
9.90
10.240
11.60
12. 4/15
13.4/7
14.8/5
15.24/7
16.15/16
17.4/9
18.8/7
19.-2/5
20.-1/12
Let f(x) = -3x - 5
What is the value of f(-5)?
Answer:
I think its 10Step-by-step explanation:
-16=(-4)-6x what does x mean
Answer: x=2 is the answer
Answer:
Step-by-step explanation
Rearrange terms
-16=(- 4)- 6 x
-16=-6x - 4
Add 4 to both sides
-16= - 6x - 4
-16 + 4= -6x - 4 + 4
Simplify the expression
-16+4=6x - 4+4
-12=6x
Divide both sides by the same factor
-12=6x
-12/-6= -6x/-6
so
x=2
If I get paid $12.50 an hour and I worked a total of 15 hours and 35 minutes how much did I make?
Answer: $194.79
Step-by-step explanation:
It is easiest to approach this question in two parts.
First part is simple - multiply the wage per hour times the number of whole number you have worked. ($12.50)(15) = $187.50
Next you need to find how much you make in 35 minutes at a wage rate of 12.50 an hour. You can set up a ratio to find this out -
($12.50) | (60 min) - (x dollars) | (35 min)
then cross multiply and divide - (12.5 * 35) / 60 = 7.291
This means you make $7.29 for 35 minutes of work.
$187.50 + $7.29 = $194.79 for 15 hours 35 minutes of work.
(this is based on a per minute/hour scale)
2 2/5 as an improper fraction in simplest form
Answer: 12/5
Step-by-step explanation:
Decide if each statement is true or false and explain.
All rectangles are quadrilaterals.
Answer: True
Step-by-step explanation:
They have four sides
Answer:true.
Step-by-step explanation: All Rectangles are indeed quadrilaterals because all rectangles have 4 sides and quadrilaterals are known as a four sided shape,
19 less than a number is 28
Answer: 47
Step-by-step explanation:
28+19=47
47-19=28
The table shows the results for spinning the spinner 75 times. What is the relative frequency for the event "spin a 4"?The table shows the results for spinning the spinner 75 times. What is the relative frequency for the event "spin a 4"?
Answer:
Answer: 6/25
======================================================
Explanation:
The table shows the spinner lands on "4" exactly 12 times out of the 50 total.
12/50 = (2*6)/(2*25) = 6/25
In decimal form that is 6/25 = 0.24 which converts to 24%
8 books cost 19.60 which equation would help determine the cost of 10 books?
Answer: $24.5
Step-by-step explanation:
8 Books = $19.60
1 Book = $19.60/8 = $2.45
10 Books = $2.45 X 10 = $24.5
Answer:
E none of the above
Step-by-step explanation:
a correct equation would be:
8/19.60 = 10/x
or
19.60/8 = x/10
DIRECTIONS: Use this information to answer Parts A, B, and C.
Each small square on this scale weighs 1 unit. Each larger square weighs 10 units. The weight of the triangle x is unknown. The scale is balanced. Look at the image.
A balanced scale. On one side there are four small squares and three large squares each labeled ten. On the other side there are two small squares, two large squares each labeled ten, and a triangle labeled x.
Question 1
Part A
Write an equation to represent relationship of the weights shown on the scale.
Enter the correct answer in the box.
An equation to represent relationship of the weights shown on the scale include the following: 22 + x = 34.
How to write an equation to represent relationship of the weights?Based on the information provided about the weights on this balanced scale, we can logically deduce the following parameters;
Each small square = 1 unit.
Each larger square = 10 units.
The variable x represent the weight of the triangle.
Since there are four small squares and three large squares each labeled ten on one side of this balanced scale, we have:
Total weight = 4(1) + 3(10)
Total weight = 34 units.
Similarly, there are two small squares, two large squares, and a triangle labeled x on the other side of this balanced scale, we have:
Total weight = 2(1) + 2(10) + x
Total weight = 22 + x
By equating the two equations, we have:
22 + x = 34
x = 34 - 22
x = 12
In conclusion, there are 34 units on each side of this balanced scale.
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A primary credit card holder's card has an APR of 11.99%. The current monthly balance, before interest, is $7,568.19. The cardholder makes a payment of $350 the first 11 months and then pays off the balance at the end of the 12th month. How much interest did the credit card holder pay?
$720.27
$156.34
$370.31
$679.70
The credit card holder paid $720.27 in interest over the 12 months. Answer choice A, $720.27, is the correct answer.
What is simple interest?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
First, let's calculate the monthly interest rate by dividing the APR by 12:
11.99% / 12 = 0.99917%
Next, let's calculate the interest paid on the monthly balance for each of the 11 months before the final payment:
Month 1:
Interest = $7,568.19 x 0.99917% = $75.59
Month 2:
Balance = $7,568.19 - $350 - $75.59 = $7,142.60
Interest = $7,142.60 x 0.99917% = $71.38
Month 3:
Balance = $7,142.60 - $350 - $71.38 = $6,721.82
Interest = $6,721.82 x 0.99917% = $67.11
Month 4-11: (follow the same process as above)
Interest for Month 4: $63.82
Interest for Month 5: $60.51
Interest for Month 6: $57.17
Interest for Month 7: $53.80
Interest for Month 8: $50.41
Interest for Month 9: $47.00
Interest for Month 10: $43.56
Interest for Month 11: $40.11
Now, at the end of month 11, the cardholder has a balance of:
$7,568.19 - ($350 x 11) - $75.59 - $71.38 - $67.11 - $63.82 - $60.51 - $57.17 - $53.80 - $50.41 - $47.00 - $43.56 - $40.11 = $1,225.74
Finally, the cardholder pays off the remaining balance of $1,225.74 at the end of month 12. The interest charged for this month would be:
Interest = $1,225.74 x 0.99917% = $12.25
So the total interest paid by the cardholder over the 12 months is:
$75.59 + $71.38 + $67.11 + $63.82 + $60.51 + $57.17 + $53.80 + $50.41 + $47.00 + $43.56 + $40.11 + $12.25 = $720.27
Therefore, the credit card holder paid $720.27 in interest over the 12 months. Answer choice A, $720.27, is the correct answer.
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A normal population has a mean of $76 and standard deviation of $6. You select random samples of 40.
1. What is the probability that a sample mean is less than $75? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
2. What is the probability that a sample mean is between $75 and $77? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
3. What is the probability that a sample mean is between $77 and $78? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
4. What is the probability that the sampling error ( x¯
− μ) would be $1.50 or less? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is used in various fields such as mathematics, statistics, science, and finance to make predictions and analyze data.
Here,
1. The z-score for a sample mean of $75 is calculated as:
z = (75 - 76) / (6 / √(40)) = -2.36
Using a z-table, the probability of a z-score less than -2.36 is 0.0099 (rounded to 4 decimal places).
2. The z-score for a sample mean of $75 is calculated as:
z1 = (75 - 76) / (6 / √(40))
= -2.36
The z-score for a sample mean of $77 is calculated as:
z2 = (77 - 76) / (6 / √(40))
= 0.79
Using a z-table, the probability of a z-score between -2.36 and 0.79 is 0.8669 (rounded to 4 decimal places).
3. The z-score for a sample mean of $77 is calculated as:
z1 = (77 - 76) / (6 / √(40))
= 0.79
The z-score for a sample mean of $78 is calculated as:
z2 = (78 - 76) / (6 / √(40))
= 1.57
Using a z-table, the probability of a z-score between 0.79 and 1.57 is 0.0823 (rounded to 4 decimal places).
4. The standard error of the mean (SEM) is calculated as:
SEM = standard deviation / sqrt(sample size)
SEM = 6 / √(40) = 0.9487
The z-score for a sampling error of $1.50 is calculated as:
z = 1.50 / 0.9487 = 1.58
Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).
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What is the ordered pair that represents the point (-8, 7) after a reflection over the y-axis?
A. (-8, -7)
B. (8,7)
C. (-7,8)
(7,-8) D.
PLEASE HELP ME
Given the following quadratic functions, complete the following:
1. Identify the zeros.
2. Identify the vertex.
3. Write the quadratic equation in factored form for the function that is graphed.
The zeros and vertex of each quadratic equation are:
Case 1: y = 4 · (x + 2) · (x - 2), Roots: - 2, 2, Vertex: (0, - 16)
Case 2: y = (1 / 2) · (x + 5) · (x - 3), Roots: - 5, 3, Vertex: (- 1, - 8)
Case 3: y = - 2 · (x + 4) · (x + 2), Roots: - 4, - 2, Vertex: (- 3, 2)
Case 4: y = - 2 · (x + 6) · (x + 2), Roots: - 6, - 2
Vertex: (- 4, 8)
How to analyze quadratic functions and derive their expressions
Graphically speaking, quadratic functions have the form of the parabola. The zeros are the points of parabola that are on the horizontal axis (x-axis) and the vertex is the only point of the parabola. The factor form of the parabola is:
y = C · (x - r₁) · (x - r₂)
Where:
C - Vertex constantr₁, r₂ - RootsNow we proceed to determine all the features of the quadratic function:
Case 1
Roots: r₁ = - 2, r₂ = 2
Vertex: (h, k) = (0, - 16)
C = y / [(x - r₁) · (x - r₂)]
C = - 16 / [2 · (- 2)]
C = - 16 / (- 4)
C = 4
Factor form: y = 4 · (x + 2) · (x - 2)
Case 2
Roots: r₁ = - 5, r₂ = 3
Vertex: (h, k) = (- 1, - 8)
C = y / [(x - r₁) · (x - r₂)]
C = - 8 / [(- 1 + 5) · (- 1 - 3)]
C = - 8 / [4 · (- 4)]
C = - 8 / (- 16)
C = 1 / 2
Factor form: y = (1 / 2) · (x + 5) · (x - 3)
Case 3
Roots: r₁ = - 4, r₂ = - 2
Vertex: (h, k) = (- 3, 2)
C = y / [(x - r₁) · (x - r₂)]
C = 2 / [(- 3 + 4) · (- 3 + 2)]
C = 2 / [1 · (- 1)]
C = - 2
Factor form: y = - 2 · (x + 4) · (x + 2)
Case 4
Roots: r₁ = - 6, r₂ = - 2
Vertex: (h, k) = (- 4, 8)
C = y / [(x - r₁) · (x - r₂)]
C = 8 / [(- 4 + 6) · (- 4 + 2)]
C = 8 / [2 · (- 2)]
C = 8 / (- 4)
C = - 2
Factor form: y = - 2 · (x + 6) · (x + 2)
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factor 4t+2rt+8st completly