I'll MARK THE BRAINLIEST!
The line plots show the results of a survey of 10 boys and 10 girls about how many hours they spent reading for pleasure the previous week. A) Which statement is true about the range? B) Which statement is true about the mean?
A} The range is greater for the girls, B) The mean is less for the girls
B} The range is greater for the girls, B) The mean is greater for the girls
C} The range is greater for the boys, B) The mean is greater for the girls
D}The range is greater for the boys, B) The mean is greater for the boys
Answers
The range is greater for the girls and the mean is greater for the girls. So, correct option is B.
A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.
Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.
B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:
(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours
To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:
(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours
Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".
So, correct option is B.
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Related Questions
Three balls toll at an intervals of
10 minutes, 15 minutes and 20 minutes.
If they toll together all 11:00am.
When next do they toll again?
Answers
Next all three balls toll after 60 minutes, that is 12:00 PM.
Given that, Three balls toll at an intervals of 10 minutes, 15 minutes and 20 minutes.
They toll together all 11:00 am.
Take LCM of three different intervals. That is,
10= 2×5
15=3×5
20=2×2×5
So, the LCM is 2×2×3×5= 60
Means all three balls toll after 60 minutes, which is 12:00 PM.
Therefore, next all three balls toll after 60 minutes, that is 12:00 PM.
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Which expression are equivalent to the expression X minus Y times 5÷8-1÷4 X plus Y
Answers
The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to
(20X² - 20Y² - 1) / (4X + 4Y)
We have,
We can simplify the given expression as follows:
(X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y)
= (5X - 5Y) ÷ 8 - 1 ÷ (4X + 4Y)
[distributing the factors]
= (5X - 5Y) /8 - 1/(4X + 4Y)
[finding a common denominator]
= ((5X - 5Y)(4X + 4Y) - 1)/(4X + 4Y)
= (20X² + 20XY - 20XY - 20Y² - 1) / (4X + 4Y)
= (20X² - 20Y² - 1) / (4X + 4Y)
Therefore,
The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to
(20X² - 20Y² - 1) / (4X + 4Y)
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The ratio of the corresponding linear measures of two similar cans of fruit is 4 to 7. The smaller can has a surface area of 220 square centimeters. Find the surface area of the larger can. Write your answer as a decimal or mixed number.
The surface area is
square centimeters.
Answers
The surface area of the larger can is approximately 674.375 square centimeters.
We have,
The ratio of the corresponding linear measures of two similar cans is 4 to 7.
The ratio of their surface areas will be the square of this ratio, which is (4/7)² = 16/49.
Let A be the surface area of the larger can.
(220 cm²) / A = 16/49
220 cm² x 49 = A x 16
10780 cm² = A x 16
A = 10780 cm² / 16
A = 674.375 cm²
Therefore,
The surface area of the larger can is approximately 674.375 square centimeters.
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Please calculate this...
Answers
The evaluation of the equation by expressing the terms as improper fractions indicates that the value of y is 14 2/3
y = 14 2/3What is a fraction?A fraction is an expression of a part of a whole, using two numbers, one located in the numerator, and the other in the denominator in the expression of the fraction separated by a line, known as the fraction bar.
The equation can be expressed as follows;
4 2/9 + (16 5/9 - y) = 15 1/9 - 8 7/9
The above equation comprising of fractions can be expressed using improper fractions as follows;
4 2/9 + (16 5/9 - y) = 15 1/9 - 8 7/9
38/9 + (149/9 - y) = 136/9 - 79/9 = 57/9
38/9 + 149/9 - 57/9 = y
130/9 = y
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A rectangular prisms has a length of 2 1/2 centimeters a width of 2 1/2 centimeters and a height of 5 centimeters Justin has a storage container for the prism that has a volume of 35 cubic centimeters
Answers
It could be feasible to accommodate the prism diagonally or by orienting it in a certain way, depending on the geometry of the container.
Given that:
Length, L = 2 and 1/2 = 2.5 cm
Width, W = 2 and 1/2 = 2.5 cm
Height, H = 5 cm
The volume of the rectangular prism is calculated as,
Volume = 2.5 x 2.5 x 5
Volume = 31.25 cubic centimeters
Therefore, the volume of the rectangular prism is 31.25 cubic centimeters.
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The volume of a cylinder is 171 pi cubic inches and the radius of the cylinder is 3 inches. What is the height of the cylinder?
Answers
The value of the height of the cylinder is,
⇒ h = 19 inches
We have to given that;
The volume of a cylinder is 171 pi cubic inches and the radius of the cylinder is 3 inches.
We know that;
Volume of cylinder = πr²h
Hence, We get;
⇒ 171π = π × 3² × h
⇒ 171 = 9h
⇒ h = 171 / 9
⇒ h = 19 inches
Thus,
The value of the height of the cylinder is,
⇒ h = 19 inches
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#7 What is the area of a rectangle with a length of 5 inches and a width of 2 inches? 9 #8 of
Answers
The area of the rectangle is 10 in².
We have,
Given,
Length = 5 inches
Width = 2 inches
Now,
Area of a rectangle.
= length x width
= 5 x 2
= 10 in²
Thus,
The area of the rectangle is 10 in².
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Help me read the picture
Answers
Answer:
C
Step-by-step explanation:
Answer:
B x ≤ 0
Step-by-step explanation:
A solid dot on zero means that zero is included.
The line to the left of zero with an arrowhead means that all numbers less than zero are all included.
The graph represents zero and all numbers less than zero.
The correct inequality is
B x ≤ 0
Find the median and mean of the data set below: 38 , 24 , 31 , 24 , 3 , 33 , 8
Answers
The median of the data set is 24 and the mean is 23.
To find the median of the data set, we need to first put the values in order from least to greatest:
3, 8, 24, 24, 31, 33, 38
There are 7 values in the data set, so the median is the middle value. Since there are an odd number of values, the median is the fourth value, which is 24.
To find the mean of the data set, we add up all the values and divide by the number of values:
Mean = (3 + 8 + 24 + 24 + 31 + 33 + 38) / 7
Mean = 161 / 7
Mean = 23
Therefore, the median of the data set is 24 and the mean is 23.
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For her end of the year party Adriana mixed 6 L of Brand A juice with 9 L of Brand B juice. Brand A contains 52% fruit juice and Brand B contains 12% fruit juice. What percent of the mixture is fruit juice?
A. 28%
B. 20%
c. 30%
Answers
A. 28% is the percent of the mixture is fruit juice.
First, we need to find the total amount of fruit juice in the mixture.
For Brand A juice: 6 L x 52% = 3.12 L of fruit juice
For Brand B juice: 9 L x 12% = 1.08 L of fruit juice
Total fruit juice in the mixture: 3.12 L + 1.08 L = 4.2 L
The total amount of the mixture is 6 L + 9 L = 15 L
The percent of the mixture that is fruit juice is:
(4.2 L / 15 L) x 100% = 28%
Therefore, the answer is A. 28%.
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Sadie and Andres are making fruit salads for a picnic. Sadie mixes 4 cups of melon and 3 cups of apple and Andres mixes 7 cups of melon and 5 cups of apple. Use Sadie and Andres’s proportions of melon to determine whose fruit salad will taste more melony.
Answers
Based on the percentage of melons, Andres' fruit salad will taste more Melony than Sadie's.
What is the percentage?The percentage is the quotient of the numerator and denominator.
Like ratios, percentages show the relative size of a value compared to another.
Percentages are expressed as the quotient multiplied by 100.
Sadie Andres
Cups of melon 4 7
Cups of apple 3 5
Ratios 4:3 7:5
The sum of ratios 7 12
Percentages of melon to apple:
Sadie Andres
57.14% (4/7 x 100) 58.33% (7/12 x 100)
Thus, using the percentage of melon to apple, we can conclude that Andres' fruit salads tastes 58.33% more Melony than Sadie's.
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ہfind the unknown length in the right triangle.
Pleas
Answers
Applying the Pythagorean theorem, the length of the unknown side in the right triangle is: a ≈ 13.2.
How to Find the Unknown Side by Applying the Pythagorean Theorem?The Pythagorean theorem is expressed as:
c² = a² + b², given that a and b are small legs of the right triangle and c is the longest leg or hypotenuse facing the right angle in the triangle.
Given the following:
c = 16
b = 9
a = ?
Plug in the values:
16² = a² + 9²
a² = 16² - 9²
a = √(16² - 9²)
a ≈ 13.2
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Stephanie Fox is a 28-year-old management trainee at a large chemical company. She is single, has an annual salary of $75,000 (placing her in the 22 percent tax bracket), and her monthly expenditures come to approximately $3,500. During the past year or so, Stephanie has managed to save around $11,000, and she expects to continue saving at least that amount each year for the foreseeable future. Her company pays the premium on her $100,000 life insurance policy. Because Stephanie's entire education was financed by scholarships, she was able to save money from the summer and
part-time jobs she held as a student. Altogether, she has a nest egg of nearly $38,000, out of which she'd like to invest about $30,000. She'll keep the remaining $8,000 in a bank CD that pays 3 percent interest and will use this money only in an emergency. Stephanie can afford to take more risks than someone with family obligations can, but she doesn't wish to be a speculator; she simply wants to earn an attractive rate of return on her investments.
Critical Thinking Questions
1. What investment options are open to Stephanie?
2. What chance does she have of earning a satisfactory return if she invests her $30,000 in (a) blue-chip stocks, (b) growth stocks, (c) speculative stocks, (d) corporate bonds, or (e) municipal bonds?
3. Discuss the factors you would consider when analyzing these alternate investment vehicles.
4. What recommendations would you make to Stephanie regarding investment alternatives? Explain.
Answers
The solution is, she have in her retirement account 25 years from now is $261172.09.
Here, we have,
given data
contribute principal P = $250
employer = 50 %
employer add = $125
interest rate = 0.5 % = 0.005
time = 25 year = 300 months
to find out
how much will she have in her retirement account 25 years from now
solution
here monthly payment = 250 + 125 = $375
we will apply here amount formula that is
amount = P × (1+r)^t -1 /r × ( 1 + rate )
put here value
amount = 375 × (1+0.05)^300 -1 /0.05 × ( 1 + 0.005 )
amount = 261172.09
Hence, she have in her retirement account 25 years from now is $261172.09.
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complete question:
Stephanie is going to contribute $250 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will add $125 to the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly interest rate of .5 percent, how much will she have in her retirement account 25 years from now?
When h=4 , j=5 , and k=−1 , the expression jkh+hj−jk equals?
Answers
When h = 4, j = 5, and k = -1, the expression jkh + hj - jk equals 5.
To solve the expression we have to substitute the value of each variable in the expression. Then simplify the expression according to mathematic rule. After solving we get the solution of the expression.
An expression is a combination of numbers, variables, and/or operations that can be evaluated or simplified to obtain a numerical or algebraic result.
The given expression is:
jkh + hj - jk
Substituting the given values of h, j, and k, we get:
jkh + hj - jk = (5 x (-1) x 4) + (5 x 4) - (5 x (-1))
Now simplify the expression
jkh + hj - jk = (-20) + 20 + 5
jkh + hj - jk = 5
Therefore, the value of jkh + hj - jk equals 5.
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3. Study Hours (Based on Exercise 8.7) Babcock and Marks (2010) reviewed survey data from 2003–2005 and obtained an average of µ = 14 hours per week spent studying by full-time students at 4-year colleges in the United States. To determine whether this average changed over the 10 subsequent years, a researcher selected a sample of = 64 of college students. The data file hours.csv has data consistent with what the researcher found. In this question, you will use the data to if this sample indicates a significant change in the number of hours spent studying.
a. Which of the following are the hypotheses to test if this sample indicates a significant change in the average number of hours spent studying?
i. 0: µ = 14 and 1: µ < 14
ii. 0: µ = 14 and 1: µ ≠ 14
iii. 0: µ = 14 and 1: µ > 14
Answers
The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:
0: µ = 14 (null hypothesis)
1: µ ≠ 14 (alternative hypothesis)
Option B is the correct answer.
We have,
The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,
while the alternative hypothesis states that it is different from 14 hours per week.
By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.
Thus,
The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:
0: µ = 14 (null hypothesis)
1: µ ≠ 14 (alternative hypothesis)
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Question 6 of 25
A population has a mean of 37 with a standard deviation of 9. A sample of 50
items from that population has a mean of 35.5 with a standard deviation of
11.
Which equation describes the point estimate?
Ο Α. μ = 37
B. = 37
OC.
OD.
= 35.5
= 35.5
SUBMIT
Answers
The equation that describes the point estimate of the population mean is x = 35.5
Which equation describes the point estimate?From the question, we have the following parameters that can be used in our computation:
A population has a mean of 37 with a standard deviation of 9.A sample of 50 items has a mean of 35.5 with a standard deviation of 11.As a general rule
The point estimate of the mean equals the sample mean
This means that
Point estimate = 35.5
Hence, the equation is x = 35.5
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The radius of the circle below is 19 mm. Calculate the area of the circle. Give your answer in mm² to 1 d.p. area= 19 mm mm² Not drawn accurately
Answers
Substituting the given value of the radius, we have:
A = π(19 mm)²
A = π(361 mm²)
A ≈ 1134.11 mm²
Rounding to 1 decimal place, the area of the circle is approximately 1134.1 mm².
If PQRS is a Rectangle, PR = 4x - 15, and QS = 3x + 5, what is the value of x?
Answers
The value of x is 20.
Given that a rectangle PQRS has diagonals PR = 4x - 15, and QS = 3x + 5, we need to find the value of x,
Since, we know that the diagonals of a rectangle are equal,
So,
PR = QS
4x-15 = 3x+5
x = 20
Hence the value of x is 20.
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Suppose Δ JCD ΣΔ MAY.
Which other congruency statements are correct?
Select each correct answer.
Ο ΔDJC ΣΔΥAM
Ο ΔCJD_Δ ΑΜΥ
Ο
Ο ΔJDC ΣΔΥΜΑ
ΔDCJΔΥΑΜ
Answers
Answer:
The correct statement is: ΔJDC ≅ ΔYAM.
This is because the given statement ΔJCD ΣΔMAY tells us that ΔJCD is congruent to ΔMAY by the SAS (side-angle-side) postulate.
We can use this information to conclude that ΔJDC is congruent to ΔYAM by the CPCTC (corresponding parts of congruent triangles are congruent) theorem. Specifically, the corresponding parts that are congruent are:
Side JD of ΔJDC is congruent to side YA of ΔYAM (corresponding sides in the congruent triangles ΔJCD and ΔMAY)Side JC of ΔJDC is congruent to side YM of ΔYAM (corresponding sides in the congruent triangles ΔJCD and ΔMAY)Side DC of ΔJDC is congruent to side AM of ΔYAM (given in the statement ΔJCD ΣΔMAY)Therefore, the correct congruency statement is ΔJDC ≅ ΔYAM. The other statements are not correct.
A ladder of length (2x+6) feet is positioned x feet from a wall. If the ladder reaches a height of (2x+4) feet along the wall. Find the longest leg.
A. 10ft
B. 24ft
C. 26ft
D. 13cm
Answers
Using the Pythagoras theorem, the longest leg has the length of 24 feet.
Given that,
A ladder of length (2x+6) feet is positioned x feet from a wall.
Height of the ladder = (2x + 6) feet
Distance of ladder from the wall = x feet
Height of the wall that the ladder is placed = (2x + 4) feet
These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.
Longest leg is (2x + 4) feet
Using the Pythagoras theorem,
(2x + 6)² = (2x + 4)² + x²
4x² + 24x + 36 = 4x² + 16x + 16 + x²
4x² + 24x + 36 = 5x² + 16x + 16
x² - 8x - 20 = 0
(x - 10) (x + 2) = 0
x = 10 or x = -2
x = 2 is not possible.
So x = 10
Longest leg = 2x + 4 = 20 + 4 = 24 feet
Hence the length of the longest leg is 24 feet.
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100pts!! A flower garden is composed of 1/2 tulips and 3/10 of the tulips are pick.
How many pink tulips are in the garden? Type your answer like this: 1/2
Answers
There are 3/20 pink tulips in the garden
How to determine how many pink tulips are in the gardenBy determining the percentage of the garden that is made up of pink tulips.
If 3/10 of the tulips are pink and tulips account for half of the garden, the percentage of the garden that is pink tulips is:
(3/10) x (1/2) = 3/20
So, 3/20 of the garden is pink tulips.
Hence, the answer is 3/20.
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onsider the incomplete paragraph proof. Given: P is a point on the perpendicular bisector, l, of MN. Prove: PM = PN Line l is a perpendicular bisector of line segment M N. It intersects line segment M N at point Q. Line l also contains point P. Because of the unique line postulate, we can draw unique line segment PM. Using the definition of reflection, PM can be reflected over line l. By the definition of reflection, point P is the image of itself and point N is the image of ________. Because reflections preserve length, PM = PN. point M point Q segment PM segment QM
Answers
As we have proved that PM = PN and Line l is a perpendicular bisector of line segment M N.
A perpendicular bisector is a line that is perpendicular to another line segment and passes through the midpoint of that line segment. In this context, we will prove that if point P is on the perpendicular bisector of line segment MN, then PM = PN.
To prove this, we need to use the properties of perpendicular bisectors. Let l be the perpendicular bisector of line segment MN, passing through its midpoint O. By definition, the line l intersects MN at right angles, and so angle POM and angle PON are both right angles.
Now, since point P lies on the perpendicular bisector l, it is equidistant from the endpoints of the line segment MN, which means that PM = PO and PN = PO. Therefore, PM = PO = PN, and we have proven that if P lies on the perpendicular bisector of MN, then PM = PN.
In summary, we have used the properties of a perpendicular bisector to show that if a point P lies on the perpendicular bisector of line segment MN, then it is equidistant from the endpoints of that segment.
Hence, PM = PN.
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Please help studying for next grade.
93+48÷(12-42)x17
Answers
Answer:
65.8
Step-by-step explanation:
to solve such equations u should use (PEMDAS)
parenthesis, exponents, multiplication, division, addition, subtraction
note that multiplication doesn't become always before division if the division is before in the equation we divide then multiply
same with addition and subtraction we add or subtract depnding on what first
other than that we follow the steps i mentioned before
parenthesis, exponents, multiplication, division, addition, subtraction
so solve the parantheses first
then the exponents (you may have not learned this yet)
then multiplication and division together start with the one that comes first
the addition and subtraction start with the one that comes first
so for example :5×5÷5×5
=25÷5×5
=5×5
=25
i started with the first multiplication cuz it came first then division cuz it was before the other multiplication
and then the other multiplication
now here is the answer for your equation 93+48÷(12-42)x17
using PEMDAS(don't write this it's just for explaining)
parantheses first
93+48÷-30×17
we don't have exponents so just skip it
now division and multiplication
93+(-1.6)×17
finally addition amd subtraction
because we don't have subtraction we won't use it too
93 +(-27.2)
=65.8
Terrence has a balance of $4000 on his credit cards with a 20% APR. he has decided that he will not make any other purchases on his card until he pays off the debt. he can pay $300 per month. after five months how much will he have paid in interest so far in how large will the remaining balance be?
Answers
The interest is $293.88 in interest
The remaining balance is approximately $2793.88.
How to solve for the interestMonthly Interest Rate = 0.2 / 12
Monthly Interest Rate ≈ 0.01667 (rounded)
Month 1:
Interest: $4000 * 0.01667 ≈ $66.68 (rounded)
New Balance: $4000 + $66.68 = $4066.68
Payment: $300
Remaining Balance: $4066.68 - $300 = $3766.68
Month 2:
Interest: $3766.68 * 0.01667 ≈ $62.82 (rounded)
New Balance: $3766.68 + $62.82 = $3829.50
Payment: $300
Remaining Balance: $3829.50 - $300 = $3529.50
Month 3:
Interest: $3529.50 * 0.01667 ≈ $58.86 (rounded)
New Balance: $3529.50 + $58.86 = $3588.36
Payment: $300
Remaining Balance: $3588.36 - $300 = $3288.36
Month 4:
Interest: $3288.36 * 0.01667 ≈ $54.80 (rounded)
New Balance: $3288.36 + $54.80 = $3343.16
Payment: $300
Remaining Balance: $3343.16 - $300 = $3043.16
Interest: $3043.16 * 0.01667 ≈ $50.72 (rounded)
New Balance: $3043.16 + $50.72 = $3093.88
Payment: $300
Remaining Balance: $3093.88 - $300 = $2793.88
Total = $66.68 + $62.82 + $58.86 + $54.80 + $50.72
≈ $293.88 in interest
The remaining balance is approximately $2793.88.
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What number is a common denominator for 5/6 and 8/9
Answers
Answer:
Step-by-step explanation:
18
18 is a mulitple of both 6 and 18
GARDENING Saurabh is designing a rectangular vegetable garden with a stone path around it. The total area of the path is 296 square feet. Use the diagram to determine the value of x.
Answers
The total area of the path is 296 square feet, and the value of x is,
⇒ 64.2 feet.
Now, We know that;
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Based on the screenshot provided, the rectangular vegetable garden has dimensions of (x+2) feet by (x+10) feet, and there is a stone path around the garden that is 3 feet wide on all sides.
To find the value of x, we need to set up an equation using the information given.
Hence, The total area of the garden and the path is equal to the area of the outer rectangle minus the area of the inner rectangle, which is:
(x+2+2) × (x+10+2) = (x+2) × (x+10) + 296
Simplifying and solving for x, we get:
x² + 16x + 48 = x² + 12x + 20 + 296
4x = 268
x = 67
Therefore, the value of x is, 67 feet.
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A single filer had a taxable income of $90,725. Base on table, what is is the tax?
Answers
The amount that the taxpayer is owing in taxes is $2,691.05.
We have,
Income tax payable refers to a business organization's tax liability to the government in the jurisdiction in which it operates. The amount of liability will be determined by the company's profitability over a given time period and the applicable tax rates. Tax payable is considered a current liability rather than a long-term liability because it must be settled within the next 12 months.
Based on the table, we are using the tax rate of 15% for the taxable income of $11,757.
The tax payable will equals to:
= 15%*$11,757 + $927.50
= $1,763.55 + $927.50
= $2,691.05
Hence, The amount that the taxpayer is owing in taxes is $2,691.05.
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complete question:
Based on this table, if someone had a taxable income of $11,757, how much would they owe in taxes?
A triangular portion of a baseball field is marked as shown below. To the
nearest tenth, what is the length of the side labeled c?
B
A
36°
A. 2.4 yds
B. 3.6 yds
b
C. 2.8 yds
D. 3.2 yds
3 yds
Triangle not drawn to scale
28°
C
Answers
Answer: 2.4
Step-by-step explanation: obviously not anywhere close to 3 trust
A state lotto has a prize that pays $900 each week for 20 years.
Find the total value of the prize: $
If the state can earn 5% interest on investments, how much money will they need to put into an account
now to cover the weekly prize payments?
Reminder: There are 52 weeks in a year.
Answers
The total value of the prize is $936,000.
The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.
What is the total value of the prize?The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:
= $900/week x 52 weeks/year x 20 years
= $936,000.
How much money is needed to put into the account?We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r
Plugging in the values:
PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154
PV = $900 x 657.221075423
PV = $591,498.968.
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Help please, view attachment below
Answers
The required, in a reflection of triangle AB ≡ A'B' and ΔABC ≡ ΔABC are true.
AB ≡ A'B': True, because a reflection conserves length, so corresponding segments are congruent.
BC < B'C': False, in general, the length of conserves is preserved under a reflection, so BC = B'C'.
Triangle BACE = triangle B'A'C': True, because a reflection also conserves shape and size, so corresponding angles and sides are congruent.
∠BCA > ∠B'C'A': False, because the measure of an angle is not preserved under a reflection.
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