Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten year term.

annual premium: $
quarterly premium: $

Answer:

A 123 and b 246 i think so these follow ratio table

Answer:

a) 0.4772 = 47.72% probability that the average is between 1,142 and 1,150.

b) 0.0228 = 2.28% probability that the average is greater than 1,158.

c) 0 = 0% probability that the average is less than 950.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days.

This means that [tex]\mu = 1150, \sigma = 40[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{40}{\sqrt{100}} = 4[/tex]

(a) The average is between 1,142 and 1,150.

This is the pvalue of Z when X = 1150 subtracted by the pvalue of Z when X = 1142. So

X = 1150

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1150 - 1150}{4}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

X = 1142

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1142 - 1150}{4}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.5 - 0.0228 = 0.4772

0.4772 = 47.72% probability that the average is between 1,142 and 1,150.

(b) The average is greater than 1,158.

This is 1 subtracted by the pvalue of Z when X = 1158. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1158 - 1150}{4}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the average is greater than 1,158.

(c) The average is less than 950.

This is the pvalue of Z when X = 950. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{950 - 1150}{4}[/tex]

[tex]Z = -50[/tex]

[tex]Z = -50[/tex] has a pvalue of 0

0 = 0% probability that the average is less than 950.

Step-by-step explanation:

the base is 5unit and the height is 9unit

Answer:

The base is 5 units the height is 9 units

Step-by-step explanation:

Just count the blocks in the diagram

base  = 5

Height = 9

Answer:

1/3[tex]\pi r[/tex]²[tex]h[/tex]

Step-by-step explanation:

Answer:

B. 30

Step-by-step explanation:

since Ann paid $400, you set the equation equal to 400

400=40+12d

Then you solve for d to find how many dozen of flowers Ann ordered.

400-40=12d

360=12d

360/12=d

d=30

Answer:

[tex]\rm\implies y = 4x + 3 [/tex]

Step-by-step explanation:

Given :-

And we need to find the equation of the line. On looking at the graph we see that , it cuts y axis at (0,3) .So the y Intercept of the equation is 3 .

Slope Intercept Form :-

[tex]\rm\implies y = mx + c[/tex]

Substituting the respective values :-

[tex]\rm\implies y = 4*x + 3 \\\\\rm\implies y = 4x + 3 [/tex]

Hence the equation of line is y = 4x + 3

Answer:

the equation will be

Step-by-step explanation:

2x+y+5=0

Answer:

2x + y + 5 = 0

Step-by-step explanation:

The equation of line is x-2y = 14 and we need to find the equⁿ of line which passes through (-1,-3) and is perpendicular to given line.

=> x - 2y = 14

=> 2y = x - 14

=> y = x-14/2

=> y = x/2 - 7

=> Slope (m) = 1/2 .

Now the slope of line perpendicular to it , will have a slope ,

=>[tex] m_{perp}[/tex] = -1/m

=>[tex] m_{perp}[/tex] = -1/½

=> [tex] m_{perp}[/tex] = -2

=> m = (y - y₁) / ( x - x₁)

=> -2 = { y - (-3) } / { x - (-1) }

=> -2 = y + 3/x + 1

=> -2(x + 1) = y + 3

=> -2x -2 = y + 3

=> y + 2x +3+2 = 0

=> 2x + y + 5 = 0

Answer:

According to the histogram, the data points from 15-29 would be 12.

Step-by-step explanation:

No explanation needed.

Answer:

12

Step-by-step explanation:

Add the number of data points that are greater or equal to 15 (4+2+6) = 12.

Answer:

105°

Step-by-step explanation:

The sum of all the interior angles of a triangle is equal to 180°. With that I. mind, we can write

(6x + 5) + (11x - 5) + x = 180

Collecting all similar terms, we get

18x = 180 or x = 10

They, the measure of angle Q is

Angle Q = 11x - 5 = 11(10) - 5

= 105°

Step-by-step explanation:

8(m + 2)= 16

8m + 16 = 16

8m = 0

m = 0

Answer:

I think the answer it b and a

Answer:

h = 4cm

b = 9cm

Step-by-step explanation:

Answer:

The answer is A. The product is greater than 12

Answer:

No, the 6 servings of soup is 1675 milliliters, which is greater than 1.5 liters.

Step-by-step explanation:

So we already know that 1 surving of soup is 275 milliliters.

We have 6 survings of this soup.

We need to see if these 6 servings will fit in a 1.5 liter jar.

To find the total amount of mililers, we must multipy this by 6:

275*6

=

1650

Remember that 1 liter is equal to 1000 mililiters. To find the 1650 mililliters in liters, we must divide by 1000:

1650/1000

=

1.65

This number is greater than 1.5 liters, which is how much soup the jar can store.

So the answer is no, the 6 servings of soup cannot fit in the jar.

Answer:54.9

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

Answer:

The coordinates for the point on a circle of radius at an angle of are At the radius of the unit circle, 1, serves as the hypotenuse of a 30-60-90 degree right triangle, as shown in (Figure).

Step-by-step explanation:

Answer:

here u go gurly

Step-by-step explanation:

Answer:

Step-by-step explanation:

The original angle of 30° is in a linear pair on a straight angle with ∠1. So since straight angles equal 180 subtract 30 from 180 to find m∠1, which is 150°.

The original angle of 30° is a vertical angle with ∠3, the same goes for ∠1 and ∠2. So those angles will be congruent. ∠1 = 30° and ∠2 = 150°

Lastly use corresponding angles to find out the values of ∠4, ∠5, ∠6, ∠7.

∠4 is corresponding to 30° so ∠4 is 30°

∠5 is corresponding to ∠1 so ∠5 is 150°

∠6 is corresponding to ∠2 so ∠6 is 150°

∠7 is corresponding to ∠3 so ∠7 is 30°

Hope this helps :)

Answer:

The original angle of 30° is in a linear pair on a straight angle with ∠1. So since straight angles equal 180 subtract 30 from 180 to find m∠1, which is 150°.

The original angle of 30° is a vertical angle with ∠3, the same goes for ∠1 and ∠2. So those angles will be congruent. ∠1 = 30° and ∠2 = 150°

Lastly use corresponding angles to find out the values of ∠4, ∠5, ∠6, ∠7.

∠4 is corresponding to 30° so ∠4 is 30°

∠5 is corresponding to ∠1 so ∠5 is 150°

∠6 is corresponding to ∠2 so ∠6 is 150°

∠7 is corresponding to ∠3 so ∠7 is 30°

Hope this helps :)

Step-by-step explanation:

Answer:

si

Step-by-step explanation:

si

Step-by-step explanation:

1)

7x+20°+3x=180°{straight angle}

10x=180-20

x=160/10

x=16°

again,

y=7x+20{vertically opposed angle r equal}

Answer:

1. x = 20

y = 120

2. x = 263

Step-by-step explanation:

•••

As AOB is a line,

( 7x - 20 ) + 3x = 180

7x - 20 + 3x = 180

10x - 20 = 180

10x = 180 + 20 = 200

10x = 200

x = 200/10 = 20

Then, as COD is a line,

y + 3x = 180

y + 3(20) = 180

y + 60 = 180

y = 180 - 60 = 120

•••

2. Draw a parallel line AB and CD.

Then,

Angle BAE + Angle y = 180 [Co-interior angles]

56 + y = 180

y = 180 - 56 = 124

Angle DCE + Angle z = 180

41 + z = 180

z = 180 - 41

z = 139

Now, z + y = 139 + 124 = 263

[tex][/tex]

9514 1404 393

Answer:

  A)  54.4

Step-by-step explanation:

The perimeter of a circumscribing quadrilateral is twice the sum of the lengths of opposite sides.

  P = 2(17.6 +(2.9 +6.7)) = 2(27.2)

  P = 54.4

Answer:

perimeter of each polygon

Answer:

B. 240 sq. ft

Step-by-step explanation:

I calculated it logically

Answer:

B. x = 0.14

Step-by-step explanation:

Inx = -2

x = e^(-2)

x = 0.135

x = 0.14 (to two d.p)

The solution of the equation ln x =-2 is 0.14

The correct option is (D)

Logarithms are the inverse of exponents.

Given that:

ln x =-2

Shifting the log on the right side, it will become exponential

x = [tex]e^{-2}[/tex]

x = 0.135

x = 0.14 (two decimal places)

Learn more about logarithm here:

https://brainly.com/question/20785664

#SPJ2

Answer:

i believe the answer is 03.028.68

Step-by-step explanation:

hope this helps

Answer:

D) y=-5/2x; y=-20

Step-by-step explanation:

If y varies directly with x, then y=kx where k is our proportionality constant

Therefore, since y=-5 when x=2, we have -5=k(2) where k=-5/2

This means that when x=8, y=(-5/2)(8)=-20, making choice D correct