use the graph for all 3 question
1) Henry, a 41-year-old male, bought a $100,000, 10-year life insurance policy through his employer. Henry is paid biweekly. what is his annual life insurance premium?
A)$455
B)$578
C)$1033
D)$1368

2) Karen, a 52-year-old female, bought a $75,000, 20-year life insurance policy though her employer. Karen is paid weekly. How much is deducted from her paycheck for life insurance?
A)$10.86
B)$25.33
C)$35.12
D)$50.65

3) Nikos, a 39-year-old male, bought a $300,000, 20-year life insurance policy.
What is the total amount he will pay for 20 year of coverage?
A)$13,650
B)$27,300
C)$30,990
D)$61,980

Answer:

1 1/2 hours

Step-by-step explanation:

Time spent by Antonio in driving = 3 1/4 = 13/4

Time spent in gardening = 1 3/4 = 7/4

In order to find how much he spend driving than gardening, we can subtract 13/4 and 7/4.

[tex]\frac{13}{4}-\frac{7}{4}[/tex]

Te denominator is same. So, we can directly subtract the numerators.

[tex]\frac{13-7}{4}\\\\=\frac{6}{4}\\\\=\frac{3}{2}=1\frac{1}{2}[/tex]

Therefore, Antonio spent 1 1/2 hours more in driving than gardening.

To determine the total cost including sales tax, first calculate the subtotal of the items, then apply the 7% tax rate to this subtotal. After adding the sales tax to the subtotal, the final cost comes to $90.23.

To calculate the total cost of your purchase including sales tax, first figure out the total cost of the items before tax. You bought one skirt at $18.27, two shirts at $15.78 each, and a pair of shoes at $34.50. The cost of the shirts needs to be doubled since you bought two. Then, apply the 7% sales tax to the subtotal to find the overall total.

Subtotal before tax: $18.27 + $31.56 + $34.50 = $84.33

To calculate the sales tax, convert the tax rate to a decimal (7% = 0.07) and multiply by the subtotal: $84.33 × 0.07 = $5.90 (rounded to the nearest cent).

Add the sales tax to the subtotal for the total cost: $84.33 + $5.90 = $90.23.

Therefore, the total cost of your purchase after including the 7% sales tax is $90.23.

The area of the base of the pyramid which is a hexagon with given parameters is; 96√3

We are told that the base of the pyramid is a hexagon.

Now, from the given image we can find the base length of the right angle triangle from trigonometric ratio which is;

x/8 = cos 60°

x = 8 cos 60°

x = 4

Thus, length of side of hexagon is;

s = 4 * 2

s = 8

Formula for area of hexagon is given by;

A = ((3√3) * s²)/2

Where;

s is length of a side of hexagon

A = ((3√3) * 8²)/2

A = 96√3

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Answer:

hello the answer is choice D

Step-by-step explanation:

Answer:

15cm

Step-by-step explanation:

i had the same question but difrent if you know what i mean. in mine you solved it for me in your picture of 6.

If  cost of annual tution at a university increased from $10,500 to $11,300.Then 7.61%  increase in tution to the nearest tenth of a percent

Percentage, a relative value indicating hundredth parts of any quantity.

Given,

The cost of annual tution at a university increased from $10,500 to $11,300.

We need to find what percentage increase in tution.

Firstly we have to check how much increased.

11300-10500

800

Hence 800 is increase.

We have to check what is 800 percentage in 10500

percent increase=change/original

origianal=10500

change=800

800/10500=8/105=0.0761

By the definition of percentage we know percent means parts out of 100

0.0761×100=7.61%

Hence 7.61% is the  increase in tution to the nearest tenth of a percent.

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The lateral surface area of the equilateral triangular prism shaped shipping tube is 252 square inches.

The question pertains to the calculation of the lateral surface area of a triangular prism shaped shipping tube, more specifically an

equilateral triangular prism

. The lateral area of a triangular prism can be calculated using the formula: Perimeter of the base x length of the prism. Here, the base of the prism is an equilateral triangle, so the perimeter of the base will be 3 x the length of one edge, which in this case is 3 x 6 inches = 18 inches. The length of the prism is given to be 14 inches. Hence, by substituting these values into the formula, the lateral surface area = 18 inches x 14 inches =

252 square inches.

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Answer:

The correct answer is:  6.5%

Step-by-step explanation:

Final answer:

The value of n, or the number of trials in a binomial experiment, affects the shape of the binomial probability histogram. As n increases, the histogram becomes more symmetric and bell-shaped, reflecting the Central Limit Theorem. The correct answer is (c): as n increases, the binomial distribution becomes more bell-shaped.

Explanation:

The shape of the binomial probability histogram is indeed influenced by the value of n, which stands for the number of trials in a binomial experiment. As the value of n increases, the distribution becomes more symmetrical and tends to resemble a normal distribution. Specifically, the correct statement regarding the effect of n on the shape of the histogram is: as n increases, the binomial distribution becomes more bell-shaped. Therefore, the correct answer to the student's question is (c).

When the sample size n is small, the histogram may appear skewed left or right, depending on the probability of success p. However, as n becomes larger (especially when both np and n(1-p) are greater than 5), the distribution's shape becomes more symmetric due to the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases.

Answer:

Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4 . Add the resulting equations together.

Step-by-step explanation:

Given the simultaneous equation below:

4x+3y=−1 ...(1) × 3

3x−5y=4 ...(2) × -4

Using elimination method to solve the problem,

Before we can eliminate x, the coefficient of x in both equation must have similar whole number as coefficient.

To make the coefficient equal, we will multiply equation 1 by 3 and equation 2 by -4 as shown above

The equations will then become

12x+9y = -3

-12x+20y = -16

Then we will add the resulting simultaneous equations.

The steps that would allow her to eliminate the x terms in the system of equations is to "Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4 . Add the resulting equations together"

In this set, the points reflect across the indicated lines of symmetry. Matches are as follows: 3 corresponds to X, 5 to F, 6 to B, 4 to Y, 1 to Q, and 2 to S.

R_I

This means that the line of symmetry is line I

R_m

This means that the line of symmetry is line m.

1. R_I:T

This matches with Q.

In this number, the line of symmetry is I. If you reflect T across line I, you will get point Q. This is because they are right across from each other with line I between them, and they are both the same distance from line I.

2. R_I:S

This matches with S.

Point S lies on the line of symmetry; thus, S reflects itself.

3. R_I:Z

This is similar to number 1. If you reflect Z across line I, you will get point X because they are directly across each other with line I between them and they have the same distance from the line of symmetry.

4. R_m:S

This time, S isn't on the line of symmetry. The line of symmetry is the vertical line m. Point Y matches with point S because they are directly across each other with line m between them. They are also the same distance apart from line m.

5. R_I:B

This is very similar to number 1. This matches with F. The point directly across the line of symmetry is F.

6. R_I:F

This is the exact same as number 5! With the same line of symmetry, B matched with F. Thus, F must match with B!

Here are the matches:

3-X

5-F

6-B

4-Y

1-Q

2-S

The recursive formula for a geometric sequence is a₁=-4 and [tex]a_n}=6.a_{n-1}[/tex]. Therefore, option D is the correct answer.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

The given geometric sequence is -4, -24, -144, -864.

A recursive formula for a geometric sequence with common ratio r is given by [tex]a_n}=ra_{n-1}[/tex] for n≥2.

Here, a=-4 and r=-24/(-4) =6

So, recursive formula is [tex]a_n}=6.a_{n-1}[/tex]

Therefore, option D is the correct answer.

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The dimension of the rectangle will be 6 inches by 3 inches.

Assume L is the length and W is the width. Then the area is given as,

A = L × W

And the perimeter is given as,

P = 2(L + W)

A rectangular note card has an area of 18 square inches. Its perimeter is 18 inches. Then the equations are given as,

18 = 2(L + W)

9 = L + W             ...1

L x W = 18           ...2

From equations 1 and 2, then we have

L x (9 - L) = 18

L² - 9L + 18 = 0

L² - 6L - 3L + 18 = 0

L(L - 6) - 3(L - 6) = 0

(L - 6)(L - 3) = 0

L = 3, 6

Then the width of the rectangle will be calculated as,

W = 9 - 3 = 6

W = 9 - 6 = 3

Then the dimension of the rectangle will be 6 inches by 3 inches.

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To solve this problem, you have to determine the value of the number 3 in both numbers:

6,300 – the number 3 is in the hundreds place so its value is 300

530 – the number 3 is in the tens place so its value is 30

To answer the question, the value of 3 in 6,300 is 10 times the value of 3 in 530.

Answer:

11. Equation of hyperbola having  vertices at (0, ±6) and foci at (0, ±9).

is given by [tex]\frac{y^2}{a^2}- \frac{x^2}{b^2}=1[/tex]

also b²= c²-a²

 b²=81-36

b²=45

So, Equation becomes , [tex]\frac{y^2}{36}- \frac{x^2}{45}=1[/tex]

Option (D) is correct.

12.Vertices (0,  ± 4), Asymptotes = ±1/4.x

equation of asymptote is given by, [tex]x = \pm y \frac{b}{a}[/tex]

[tex]\frac{4}{b}=\frac{1}{4}[/tex]

So a=4 and b=16,

So , equation becomes [tex]\frac{y^2}{16}- \frac{x^2}{256}=1[/tex]

Option (B) is correct.

13.  x= t-3, and y = t²+ 5

Replace t by x+3, we get

y= (x+3)² +5

y=x²+ 6x +14

Option (A) is correct.

14. Polar coordinates is given by (r,∅)

Polar coordinates of point is (3, 2π/3)

So, r =3, ∅ =2π/3

x= r cos∅ and y = r sin∅

x=3 Cos (2π/3) and y= 3 Sin (2π/3)

x= -3/2 and y=3√3/2

Option (A) is correct.

14. Polar coordinate is given by (r,∅)

Here , r=1, and ∅ = -π/6

x= r Cos ∅ and y =r Sin∅

x= 1 Cos (-π/6) and  y= 1 Sin (-π/6)

x =√3/2 and y =1/2

Option (B) which is B) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ) is correct.

16. Two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.

is  option (B) which is B) (4 square root 2 , 45°), (-4 square root 2 , 225°).

17. A circular graph with inner loop on the left of a limacon curve is given by

r = a + b Cos∅.

In this case a> b.

So , Option (D) r = 4 + cos θ as well as (A) r = 3 + 2 cos θ looks correct.

18. Equation of limacon curve is given by r = -2 + 3 cos θ, here , a<b

So it is symmetric about y-axis only.Option (B) is correct.