The army reports that the distribution of waist sizes among female soldiers is approximately normal, with a mean of 28.4 inches and a standard deviation of 1.2 inches.
Part A: A female soldier whose waist is 26.1 inches is at what percentile? Mathematically explain your reasoning and justify your work.

Part B: The army uniform supplier regularly stocks uniform pants between sizes 24 and 32. Anyone with a waist circumference outside that interval requires a customized order. Describe what this interval looks like if displayed visually. What percent of female soldiers requires custom uniform pants? Show your work and mathematically justify your reasoning.

Answer:

The correct ratio is 7:8, so no, Emma is not correct.

Hello cayleahm253!

\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)

There are 35 boys in 6th grade. The number of girls in 6th grade is 40. Emma says that means the ratio of the number of boys in 6th grade to the number of girls in 6th grade is 3:4. Is Emma correct? If not, what is the correct answer?

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

Okay, so we can see from the question that there are 35 boys & 40 girls in the 6th grade. So the ratio of boys is to girls will be 35:40.

__________________

Solving...

\(35 : 40 \\ = \frac{35}{40} \\ \\ \sf \: Cancel \: out \: 35 \: and \: 40 \: to \: get \: 7 \: and \: 8.\\ \\ = \frac{7}{8} \\ = \huge \boxed{\boxed{\bf \: 7 : 8}}\)

__________________

__________________

Hope it'll help you ッ

ℓucαzz

Answer:

1 /5

Step-by-step explanation:

The equivalent fractions for 2/3 is (3×2)/(3×3) = 6/9 and for  5/12 is (4×5)/(4×12) = 20/48.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

The equivalent fraction for 2/3 is (3×2)/(3×3) = 6/9.

The equivalent fraction for 5/12 is (4×5)/(4×12) = 20/48.

We have to multiply the same number to both the numerator and denominator to get equivalent fractions.

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Answer and explanation:

The domain would be [-11,10). -11 has a bracket because there is a closed circle for -11; while 10 only has a parenthesis because there is an open circle. You can use every number between -11 and 10, including -11 (because of the closed circle).

Answer:

x is greater than or equal to -11 and less than 10.

Step-by-step explanation:

On the left it is a solid filled in dot which includes the -11 and on the right the dot is open so 10 is not included.

The maximum probability that a photon with the polarization state will be transmitted through the A filter is 1/2

To solve this problem, we need to use Malus' law, which states that the intensity of light transmitted through a polarizer is proportional to the square of the cosine of the angle between the polarization direction of the incoming light and the axis of the polarizer.

To find the overall probability that a photon will be transmitted through all three filters, we need to multiply the probabilities of each filter

P = 1/2 × cos²(θ) × 1

We are not given the angle θ, so we cannot calculate the exact value of P. However, we can calculate the maximum value of P, which occurs when the rotated filter is aligned with the A filter (i.e., θ = 0). In this case, P = 1/2.

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The given question is incomplete, the complete question is:

H filter Rotated filter Rotated filter followed by A filter An unpolarized photon beam is incident on a linear polarizing filter. The incoming photon flux is is 2.34 x 101 photons/m' /sec.  What is the probability that a photo with the polarization state be transmitted through a subsequent filter, that is aligned with the direction?

Complete question :

Jelena has a piece of fabric in the shape of a parallelogram the height is 10 feet and its base is 16 feet because the fabric into four equal parallelograms by current base and the height in half what is the area of each new parallelogram?

Answer:

40 ft²

Step-by-step explanation:

Given that:

Height = 10 feets

Base = 16 feets

Area of parallelogram = height * base

Area of parallelogram = 10 * 16 = 160 ft²

Area of each new parallelogram :

Area of parallelogram / number of divisions

= 160ft² / 4

= 40 ft²

The simplified version of the equation 32x + 8 - 34x is   -2x +8

Given that,

The equation is 32x + 8 - 34x

To find : The simplified version of 32x + 8 - 34x ?

Since the terms involving x are "like" terms, when the terms are joined, their coefficients are added.

= 32x -34x +8

= (32 -34)x +8 . . . . . x is factored out according to the distributive property

= -2x +8

Therefore, the simplified version of 32x + 8 - 34x is given as  -2x +8

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Therefore, the work done in pulling the bucket to the top of the well is 4h lb.

To find the work done in pulling the bucket to the top of the well, we need to consider the weight of the bucket and the work done against gravity. The work done against gravity can be calculated by multiplying the weight of the bucket by the height it is lifted.

Given:

Weight of the bucket = 4 lb

Rate of pulling the bucket = 0.2 lb/s

Let's assume the height of the well is h.

Since the bucket is lifted at a rate of 0.2 lb/s, the time taken to pull the bucket to the top is given by:

t = Weight of the bucket / Rate of pulling the bucket

t = 4 lb / 0.2 lb/s

t = 20 seconds

The work done against gravity is given by:

Work = Weight * Height

The weight of the bucket remains constant at 4 lb, and the height it is lifted is the height of the well, h. Therefore, the work done against gravity is:

Work = 4 lb * h

Since the weight of the bucket is constant, the work done against gravity is independent of time.

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A. The power of the two-tailed hypothesis test with α = .05 is 0.53.

B. The power of the one-tailed hypothesis test with α = .05 is 0.95.

A hypothesis test is used to make decisions about a population based on sample data. It involves specifying a null hypothesis, collecting data, and then assessing the data to either reject or accept the null hypothesis.

A. The power of the two-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- (1-α)\(^{1/2}\)

=1- (1-0.05)\(^{1/2}\)

=0.525

=0.53

This means that the researcher has an 53% chance of correctly rejecting the null hypothesis that there has been no change in the IQ over the past 10 years.

B. The power of the one-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- α

=1- 0.05

= 0.95

This means that the researcher has a 95% chance of correctly rejecting the null hypothesis that there has been no increase in the IQ over the past 10 years.

This is a higher power than the two-tailed test because the one-tailed test focuses on detecting an increase in the IQ, while the two-tailed test can detect both an increase or decrease in the IQ.

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Answer:

2^n

2^18= 262,144

Step-by-step explanation:

Answer:

h(t) = -3(t-8)(t+4). and 8 minutes

Step-by-step explanation:

The function can be written as: h(t) = - 3(t² - 4t - 32). As per quadratic equation, after take off, the drone will land on the ground after 8 minutes.

A quadratic equation is an equation that contains a variable with highest degree of 2.

Given, the height of the drone t minutes after take off is modeled by

h(t) = - 3t² + 12t + 96 = - 3(t² - 4t - 32)

Therefore, the function can be written as: h(t) = - 3(t² - 4t - 32)

Therefore, we can write the equation as:

t² - 4t - 32 = 0

⇒ t²- 8t + 4t - 32 = 0

⇒ t(t - 8) + 4(t - 8) = 0

⇒ (t + 4)(t - 8) = 0

Hence, (t + 4) = 0 and (t - 8) = 0

Therefore, t = -4, 8.

As 't' can't be negative, therefore, t = 8.

Therefore, after take off, the drone will land on the ground after 8 minutes.

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Answer:

67

Step-by-step explanation:

we have a gap between 1st and 2nd terms of 4. a gap between 2nd and 3rd of 8. 16 for next gap. the gap doubles every time.

so we expect gap between 4th and 5th terms to be 2 X 16 = 32.

35 + 32 = 67. that is the next number in the sequence.

The dimensions of the box that minimize the amount of material used are a square base with side length 4√2 cm and a height of 2√2 cm..

To minimize the amount of material used, we need to minimize the surface area of the box.
Let's call the height of the box "h" and the length of each side of the square base "x".
The volume of the box is given by V = x^2 * h = 32 cm^3.
We want to minimize the surface area, which consists of the area of the base (x^2) and the four sides (4xh). So the surface area is given by:
A = x^2 + 4xh
We can solve for h in terms of x using the volume equation:
h = 32 / x^2
Substituting this into the surface area equation, we get:
A = x^2 + 4x(32/x^2)
Simplifying this equation, we get:
A = x^2 + 128/x
To minimize the surface area, we need to find the value of x that makes the derivative of A with respect to x equal to zero:
dA/dx = 2x - 128/x^2 = 0
Solving for x, we get:
x = 4√2 cm
Substituting this value back into the equation for h, we get:
h = 2√2 cm
So the dimensions of the box that minimize the amount of material used are a square base with side length 4√2 cm and a height of 2√2 cm.

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\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\\ r=rate\to 47\%\to \frac{47}{100}\dotfill &0.47\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A = P(1 + 0.47)^{t} \implies A =P(1.47)^t\hspace{5em}\stackrel{ Growth~Factor }{\text{\LARGE 1.47}}\)

If one of the roots of the given quadratic equation is -7/5 then the value of k is -7.

Given: - We are having the quadratic equation 5m² + 2m + k = 0 and also one of the roots of the equation an given as -7/5

To find: - The value of K.

Now we find the value of k: -

∵ one root is given to us = -7/5

∴ m = -7/5 is one solution of the quadratic equation

i.e, m = -7/5 will satisfy the above equation

So, we put the value of m and we get,

5 (-7/5)² +2 (-7/5) + k = 0

49/5 - 14/5 + k = 0

∴ 35/5 +k = 0

⇒ 7 + k = 0

⇒ k = -7

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An equation of the line through the points (-6, 5) and (-3, -3) is y = -8x/3 - 11.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (-6, 5) and (-3, -3) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 5 = (-3 - 5)/(-3 + 6)(x + 6)

y - 5 = -8/3(x + 6)

y - 5 = -8x/3 - 16

y = -8x/3 - 16 + 5

y = -8x/3 - 11

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Step-by-step explanation:

This is a right triangle which means one of the angles is 90° and since the sum of interior angles in a triangle is equal to 180 then the sum of two other angles must be 90

7x + 6 + 6x - 7 = 90 add like terms

13x - 1 = 90 add 1 to both sides

13x = 91 now divide both sides by 13

x = 7 to find each angle replace x with 7

7x + 6 = 7×7 - 6 = 55° and

6x - 7 = 6×7 - 7 = 35°

The statements that are true about the function when graphed on a coordinate plane include the following:

C. The relative minimum of the function is (3, 0)

E. When t > 3, the function is increasing.

In order to determine the minimum and maximum of this function, we would have to determine the critical points where the derivative of the function is equal to zero or undefined, and then evaluate the function at these critical points and at the endpoints of the interval.

By taking the first derivative of the given function and factorizing, we have:

f(t) = t³ - 6t² + 9t

f'(t) = 3t² - 12t + 9  

3t² - 12t + 9 = 0

t² - 4t + 3 = 0

(t - 3)(t - 1) = 0

t = 3 and t = 1

Therefore, the critical points of the function are at t = 1 and t = 3.

By taking the second derivative of the given function and factorizing, we have:

f''(t) = 6t - 12

At point t = 1, we have:

f''(1) = 6(1) - 12 = -6 (it is less than zero).

Therefore, f(t) has a local maximum at t = 1.

At point t = 3, we have:

f''(3) = 18 - 12 = 6 (it is greater than zero).

Therefore, the function f(t) has a local minimum at t = 3.

At t = 4, f''(4) = 24 - 12 = 12

At t = 5, f''(5) = 30 - 12 = 18

In conclusion, the relative minimum of the function is (3, 0) and when t > 3, the function would increase.

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Answer:

i think its A sorry if im wrong

Step-by-step explanation:

Answer: \(\dfrac14\)

Step-by-step explanation:

Given: The factory produces equal quantities of four flavors cherry lemon orange and strawberry.

Let  orange candy= cherry = lemon = strawberry  = x

Total candies = x + x + x + x= 4x

The probability that a randomly selected candy is orange = \(\dfrac{x}{4x}=\dfrac14\)

Hence, the probability that a randomly selected candy is orange = \(\dfrac14\)

Answer:

In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 12 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter?

A. 15

B. 25

C. 30

D. 45

E. 60

Answer:

The correct answer is c.) 3/36.There are three favorable outcomes (2, 11, and 12) out of a total of 36 possible outcomes (assuming a fair six-sided number cube). Therefore, the probability of X being a 2, 11, or 12 is 3/36, which can be simplified to 1/12.

Step-by-step explanation:

The circumference of the circle with a radius of 6 feet would be approximately 37.7 feet.

The circumference of a circle is the distance around the outer edge of the circle. It is the perimeter of the circle, which is the total length of the boundary that encloses the area of the circle.

The formula for the circumference of a circle is

C = 2πr

Where C is the circumference, r is the radius, and π is approximately 3.14.

If a circle has a radius of 3 feet, the circumference would be

C = 2πr

C = 2π(3)

C ≈ 18.85 feet

When the radius doubles to 6 feet, the circumference would be

C = 2πr

C = 2π(6)

C ≈ 37.7 feet

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Answer:

double, and 36

Step-by-step explanation:

Mc graw hill

Q...

Answer:

a=16400 feet

Step-by-step explanation:

t = -0.0035 a +g

-17.40 = -0.0035 a+40

-17.40-40=-0.0035a+40-40

-57.40=-0.0035a

a = -57.40/-0.0035

a=16400 feet

The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

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The value of power is 27/64.

Rochelle used these steps to evaluate the power.

\( \left (\dfrac{3}{4}\right )^3\)

What is the value of power?

To determine the value of the power following all the steps given.

Expression; \( \left (\dfrac{3}{4}\right )^3\)

Then,

The value of power is,

\(= \dfrac{3}{4} \times \dfrac{3}{4} \times \dfrac{3}{4}\\ \\ = \dfrac{9}{16} \times \dfrac{3}{4}\\\\ = \dfrac{27}{64}\)

Hence, The value of power is 27/64.

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Answer:

-27/64

Step-by-step explanation:

Applying the midpoint formula, the coordinates of the other endpoint are: (-9, -13).

The midpoint formula, which can be used in determining the coordinates of the midpoint between two endpoints is usually expressed as: M[(x1 + x2)/2, (y1 + y2)/2].

Given the following coordinates:

Midpoint of GH --> m(-13/2,-6) = (x, y)

One endpoint ---> G(-4, 1) = (x1, y1)

The other endpoint ---> (x2, y2)

Plug in the values into the formula used in calculating the midpoint:

m(-13/2,-6) = [(-4 + x2)/2, (1 + y2)/2]

Solve for x2

-13/2 = (-4 + x2)/2

-13/2 × 2 = -4 + x2

-13 = -4 + x2

-13 + 4 = x2

-9 = x2

x2 = -9

Solve for y2

-6 = (1 + y2)/2

2(-6) = 1 + y2

-12 = 1 + y2

-12 - 1 = y2

-13 = y2

y2 = -13

Thus, using the midpoint formula, the coordinates of the other endpoint are: (-9, -13).

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Answer: x= 5 and y= -2

Step-by-step explanation:

The limit as (x, y) approaches (0, 0) along the x-axis is 1.

The limit as (x, y) approaches (0, 0) along the y-axis is 1.

The limit as (x, y) approaches (0, 0) along the line y = mx is also 1.

The overall limit is 1.

To find the limits as (x, y) approaches (0, 0), we substitute the given values into the expression and evaluate the result. Let's examine each case:

Along the x-axis, y = 0, so the expression becomes lim(x)→0 3x^2/(4x^2 + 1). By plugging in x = 0, we get 0/(0 + 1) = 0/1 = 0. Therefore, the limit along the x-axis is 0.

Along the y-axis, x = 0, so the expression becomes lim(y)→0 1/(5y^2 + 1). By plugging in y = 0, we get 1/(0 + 1) = 1/1 = 1. Therefore, the limit along the y-axis is 1.

Along the line y = mx, we substitute y = mx into the expression and simplify. The expression becomes lim(x)→0 3x^2/(4x^2 + 5m^2x^2 + 1). By factoring out x^2 from the denominator, we get lim(x)→0 3x^2/(x^2(4 + 5m^2) + 1). Canceling out x^2, we have 3/(4 + 5m^2 + 1/x^2). As x approaches 0, the term 1/x^2 becomes infinitely large, so the expression simplifies to 3/(4 + 5m^2). Therefore, the limit along the line y = mx is 3/(4 + 5m^2).

Since the limit along the x-axis, y-axis, and y = mx all yield the same value of 1, we can conclude that the overall limit as (x, y) approaches (0, 0) is 1.

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Answer:

PT = 17

Step-by-step explanation:

Since T is the midpoint of PQ, then

PT = TQ , substitute values

4x + 5 = 8x - 7 ( subtract 4x from both sides )

5 = 4x - 7 ( add 7 to both sides )

12 = 4x ( divide both sides by 4 )

3 = x

Thus

PT = 4x + 5 = 4(3) + 5 = 12 + 5 = 17

Answer:

17

Step-by-step explanation:

since T is mid point of PQ

PT=TQ

\(4x + 5 = 8x - 7 \\ 5 + 7 = 8x - 4x \\ 12 = 4x \\ x = 12 \div 4 \\ x = 3 \\ \)

so

\(pt = 4x + 5 \\ = 4(3) + 5 \\ = 12 + 5 \\ pt = 17\)