Heights of adult women in the united states are normally distributed with a population mean of μ = 63.5 inches and a population standard deviation of σ = 2.5. a medical researcher is planning to select a large random sample of adult women to participate in a future study. what is the standard value, or z-value, for an adult woman who has a height of 50.4 inches? (calculate to 1 decimal)

Answers

Answer 1

For an adult woman with a height of 50.4 inches in the United States, the standard value (z-value) is approximately -5.2, calculated based on a normal distribution with a mean of 63.5 inches and a standard deviation of 2.5 inches.

To find the standard value or z-value for a given height in a normal distribution, you can use the formula:

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

where:

- Z is the z-value,

- X is the individual data point (height in this case),

- [tex]$ \mu $[/tex] is the population mean,

- [tex]$ \sigma $[/tex] is the population standard deviation.

For the given problem:

- [tex]$ \mu = 63.5 $[/tex] inches,

- [tex]$ \sigma = 2.5 $[/tex] inches,

- X = 50.4 inches.

[tex]\[ Z = \frac{{50.4 - 63.5}}{{2.5}} \]\[ Z \approx -5.24 \][/tex]

Rounded to one decimal place, the z-value for an adult woman with a height of 50.4 inches is approximately -5.2.

Related Questions

Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. But then, the price of bagels falls to $1 per bagel.

Answers

60 divided by 2 = 30
40 divided by 2 =20
and thats all i got xD

60/2=30
40/2=20
with a new price of that bagel drop is 50%
(40/40+60=80
and 20$ is the money that Deborah income reducing

Identify the type of correlation shown in the scatter plot
A. Positive Correlation
B. Negative Correlation
C. No correlation.

Answers

I think it is no correlation because we can't exactly draw a line through this scatter plot

If f(x)=7+4x and g(x)=1/2x What is the value of (f/g)(5)?

Answers

If im not mistaken the answer is D 270

Answer:

[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 270[/tex]

Step-by-step explanation:

We are given the following information in the question:

[tex]f(x) = 7 +4x\\\\g(x) = \displaystyle\frac{1}{2x}[/tex]

We have to find the values of [tex]\displaystyle\frac{f}{g}(x)[/tex]

[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = \frac{f(x)}{g(x)} = \frac{7 + 4x}{\frac{1}{2x}} = 2x(7+4x)[/tex]

Putting x = 5, we have:

[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = 2x(7+4x)\\\\\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 2(5)(7+20)=270[/tex]

270 is the required value of [tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5)[/tex].

△ABC is reflected to form △A′B′C′ . The vertices of △ABC are A(3, 1) , B(1, 5) , and C(6, 9) . The vertices of △A′B′C′ are A′(−1, −3) , B′(−5, −1) , and C′(−9, −6) . Which reflection results in the transformation of △ABC to △A′B′C′ ?

Answers

The reflection of the triangle across y = -x is the new triangle.

Answer:

that would be a reflection across the y axis resulting in a -x

Step-by-step explanation:

What is the solution to 2log9(x)=log^9(8)+log9(x-2)

Answers

2log9(x)=log^9(8)+log9(x-2)

Log₉x² = log₉8 + log₉(x-2)

Log₉x² = log₉(8×(x-2))

Log₉x² = log₉8x-16

Log₉x² - log₉8x-16 = 0

Log₉(x²/(8x-16)) = 0

x²/(8x-16) = 9°

x² = 1 × 8x-16

x²-8x+16 = 0

x²-4x-4x+16 = 0

x(x-4)-4(x-4) = 0

(x-4)(x-4) =0

Therefore x = 4.....

Answer:

C. x=4

Step-by-step explanation:

Solve 4y - 8 -2y + 5 = 0

Answers

The answer to your problem is 3/2.

The scale on a map is 1 cm for every 400 km. If Maine and Japan are 22 cm apart on the map, what is the distance between Maine and Japan?

Answers

Essentially, you must multiply 22 by 400. You get 8800 km apart for your answer.

Which statement best compares -1/2 and -2 1/2

Answers

From the Iready New York CCLS Question 18, The answer is B. If you count the spaces between -1 1/2 and -2 1/2 you get -2.

The Comparison between -1/2 and -2 1/2 is -1/2 is -2 more than -5/2.

What are fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

-1/2 and -2 1/2

So, -1/2 and -5/2.

So, the quantity -1/2 > -5/2

Also, -1/2 is -2 more than -5/2.

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The sum between two numbers is 170 and their difference is 110, what is the larger of the two numbers

Answers

x + y = 170
x - y = 110 Add these two equations.
2x = 280 Divide by 2
x = 280/2
x = 140

A rectangular prism has a length of 4 1/2 millimeters, a width of 4 1/2 millimeters, and a height of 6 millimeters.

Sally has a storage container for the prism that has a volume of 143 cubic millimeters.

What is the difference between the volume of the prism and the volume of the storage container?

Help Please?

Answers

Volume of a rectangular prism is found by multiplying the length by the width by the height. The volume of our given prism would be
V = (4 1/2)(4 1/2)(6)
Converting the fractions to mixed numbers we have
V = (9/2)(9/2)(6/1) = 486/4 = 121.5

The storage container has a volume of 143, so the difference is 143 - 121.5 = 21.5 cubic mm.

Answer:

21 1/2

Step-by-step explanation:

The measure of angle E, the angle of elevation from point A to point B, is 5(x-2). The measure of angle D, the angle of depression from point B to point A, is (x+14). Find the measure of each angle.

Answers

The angle of elevation and the angle of depression are the same. (They are alternate interior angles between the parallel lines of the ground and "horizontal.")
5(x -2) = x +14
5x -10 = x +14 . . . . . . . eliminate parentheses
4x = 24 . . . . . . . . . . . . add 10-x
x = 6

The angles of elevation and depression are both (6+14)° = 20°.

Answer:

measure of angle E equals 20 degrees, measure of angle D equals 20 degrees

what is the solution to -9×<63

Answers

Hey there! :D

I'm assuming that the multiplication sign is x.

When you are multiply something by x, you divide -9 on both sides. When you divide a negative number in an equality, you switch the signs.

x>-7 <== solution

I hope this helps!
~kaikers

amy is building a house. the basement floor is at -15 feet. the roof of the house is above the ground 25 feet. write an inequality to compare the heights. explain the meaning of the inequality.

BONUS: what is an inequality.

Answers

An inequation is a mathematical expression that is used to make constraints given a problem.
For example, this is a problem of heights.
There is a minimum height and a maximum height.
We can use the following inequation to describe the problem:
Let
x = height in feet.
The inequation is:
-15 <= x <= 25
answer:
-15 <= x <= 25

What is 1/4 as a whole number?

Answers

the answer is 1÷4=0.25

i think the answer is = .25

how to solve -2x+y=7, 3y=6x+4

Answers

Consider, pls, this option.
To the additional, see the attached graph for this system.

Do you know the answer???????? Help!!!!!

Answers

To find the area of the shaded region we need to divide it into one triangle and two rectangles like you can see in the picture.
The area of a triangle is [tex]A _{t} = \frac{1}{2} (base)(height)[/tex], and we know from our figure that our triangle has base=10 feet and height=5 feet, so:
[tex]A_{t} = \frac{1}{2} (10feet)(5feet)[/tex]
[tex]A_{t} = 25feet^{2} [/tex]
The area of a rectangle is [tex]A_{r} =(length)(width)[/tex]. We have tow rectangles in our figure, so for our first one:
[tex]A _{r1} =(10feet)(1feet)[/tex]
[tex]A_{r1}=10feet^{2} [/tex]
for our second one:
[tex]A_{r2} =(8feet)(2feet)[/tex]
[tex]A_{r2} =16feet^{2} [/tex]

Now that we have the areas of all out figures, lets add them to find the area of the shaded region:
[tex]A _{total} =25feet^{2} +10feet^{2} +16feet^{2} [/tex]
[tex]A _{total} =51feet^{2} [/tex]

We can conclude that the area of the shaded region is 51 square feet.

Which is a disadvantage of withdrawing more money than is available in a checking account?

Answers

One disadvantage is most banks charge an overdraft fee once you take out more money than what is available.

A disadvantage of withdrawing more than you have in your account is you will be charged an overdraft fee.

What is an Overdraft Fee?

An overdraft fee can be described as the fee your bank charges you when you make a withdrawal from your account beyond what you have in it.

An overdraft fee is one of the disadvantages of withdrawing more money than you have in your account..

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HELP ME PLEASE! How is the graph of mc027-1.jpg related to its parent function, mc027-2.jpg?

Answers

We will try to approach it generally. If we have a function y=f(x) and we have then y=f(2x), then the graph of the function will be horizontally compressed. If we take f(x/2), the graph of the function will be dilated. (To get horizontal shifts, we need f(x+a), which is not the case here; for example [tex] \sqrt{x+4} [/tex] is horizontally shifted relative to its parent function). If we consider -y=f(x), then the graph of this new function is the graph of the parent function flipped along the x-axis. If we consider y=f(-x) (which is the case here, since [tex] \sqrt{-x} = \sqrt{(-x)} [/tex]) we have that the graph of the new function is the same as the old graph, just flipped along the y-axis. Each of those transformations is independent; combining our observations we see that the last answer is the correct one.

The graph of [tex]y = \sqrt{-2x[/tex] relates to its parent function as a result of (d) horizontal compression by a factor of 2, and a reflection across the y-axis

What is a function transformation?

A function transformation involves changing the form or equation of a function to another through reflection, dilation, translation or rotation

How to determine the function transformation

The parent function is given as:

[tex]y = \sqrt x[/tex]

Compress the function horizontally by a factor of 2, using the following rule

[tex](x,y) \to (2x,y)[/tex]

So, we have:

[tex]y = \sqrt {2x[/tex]

Next, reflect the function over the y-axis, using the following rule

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]y = \sqrt {-2x[/tex]

Hence, the function transformation is (d)

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In matrix T, what is the value of element t13?

Answers

we know that
in the matrix T the element t(13) refers to the element in row 1 and column 3

therefore
the answer is 7

Answer:

[tex]t_{13} =7[/tex]

Step-by-step explanation:

[tex]t_{13}[/tex] here 1 represents that it is in 1st row whereas 3 represents that it is in 3rd column so the element placed in 1st row and 3rd column is 7

therefore answer is

[tex]t_{13} =7[/tex]

a kittens heartbeat can be as fast as 240 beats per minute . to find the number of times a kittens heart beats in 30 seconds , Aiden says divide 240 ny 30 . do you agree with him why or why not

Answers

I do not agree. If you divide 240 by 30, it would be 8 heartbeats, which is absurd. It's impossible for something to survive with 8 heartbeats per 30 seconds.
In order to get the CORRECT answer, divide 240 by 60 seconds.
This would give you 4 heartbeats per second.
Then, multiply it by 30 seconds, which would give you 120 heartbeats.

CORRECT answer: 120

A radar gun used to determine the speed of passing cars must be within 7 mph of the actual speed of a selected car. If a highway patrol officer reads a speed of 59 mph for a car, does he have irrefutable evidence that the car was speeding in a 55 mph zone?

Answers

No. if it has a 7mph range the highest and lowest possible values would be 66mph to 52mph. The radar gun would have to measure 63 to cover the 14mph range for accuracy to claim the person was speeding.

Patrick ate 2/3 of a fruit bar write an equivalent fraction for the amount of fruit bar Patrick ate

Answers

To get an equivalent fraction, multiply the fraction by a whole number. For example, you can do 2/3 times 2 to both sides which is 4/6.

Translated these questions to a equation:
6 more than 9 times a number x is -12
the quotient of a number t and 7, plus 2, is -4

Answers

6 more than 9 times a number x is -12...
6 + 9x = -12

the quotient of a number t and 7, plus 2, is -4 ...
(t/7)+ 2 = -4

Hope this helps :)

which is equivalent to (9y2 – 4x)(9y2 + 4x), and what type of special product is it?
81y4 – 16x2, a perfect square trinomial
81y4 – 16x2, the difference of squares
81y4 – 72xy2 – 16x2, a perfect square trinomial
81y4 – 72xy2 – 16x2, the difference of squares

Answers

81y4 -16x, the difference of squares.

Final answer:

The expression (9y2 – 4x)(9y2 + 4x) is equivalent to 81y4 – 16x2, a difference of squares in mathematical terms.

Explanation:

The expression you are asking about is equivalent to

81y4 – 16x2

, which is a special product known as

the difference of squares

. In mathematics, a difference of squares is a term that describes an expression of the form a^2 - b^2. It can be factored into the multiplication of two binomials: (a+b)(a-b). In your example, (9y2)^2 is 81y4 and (-2x)^2 is 16x2, so the final expression is 81y4 – 16x2.

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The diameter of the base of a cylinder cookies is 8 inches. The volume of the cookie jar is 160 cubic inches. What is the height of the cookie jar?

Answers

Hello!

To calculate the height of the cookie jar, we must use this formula.

FORMULA FOR HEIGHT:

H = V ÷ 3.14 × r × r

First, let's fine the radius. The radius of a circle is always half of the diameter. This means we must divide the diameter by 2.

r = d ÷ 2

r = 8 ÷ 2

r = 4 inches

The radius is 4 inches. Now, let's use the formula and find that height!

FORMULA:

H = V ÷ 3.14 × r × r

V = 160 cubic inches

Pi = 3.14

r = 4 inches

h = ?

First, square the radius.

160 = (3.14(4 × 4))h

160 = (3.14 (16))h

Now multiply that by pi.

160 = 50.24h

Finally, divide this by the volume:

160 ÷ 50.24 = 3.18 (Repeating Decimal)

Just round the repeating decimal to 3.2

A N S W E R:

The height of the cookie jar is about 3.2 inches.

Rearrange the formula A = P + Prt for t.

Answers

Given that:
A=P+Prt
Solving for t.
Factor out P from the right side of the equation.
A=P(1+rt)
Divide both sides by P.
A/P= 1+rt
Subtract 1 from both sides
A/P-1=rt
Divide both sides by r.
(A/P) / r - 1/r= t
or
t= (A/P) / r - 1/r
t= A/Pr - 1/r
t= (A-P)/r

Answer: t= (A-P)/rP

Divide both side by p+pr . And T should be t= A over p+pr

Find the sum of the geometric series with a1 = 7, r = 2, And n = 14

Answers

Final answer:

The sum of the geometric series with a1 = 7, r = 2, and n = 14 is -327661.

Explanation:

The question is asking for the sum of a geometric series. In mathematics, the sum (S) of a geometric series is determined using the formula S = a1 * (1 - r^n) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.

In the provided geometric series, a1 = 7, r = 2, and n = 14. Substituting these values into the formula gives us S = 7 * (1 - 2^14) / (1 - 2). After performing the calculations, the sum of the geometric series is -327661.

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Final answer:

The sum of the first 14 terms of the geometric series with the first term (a1) = 7, common ratio (r) = 2, is 114,691.

Explanation:

Given the first term of the geometric series (a1) = 7, the common ratio (r) = 2, and the number of terms (n) = 14, we would like to find the sum of this series. Using the formula for the sum of a geometric series, S = a1 * (1 - r^n) / (1 - r), substituting the given values, we get:

S = 7 * (1 - 2^14) / (1 - 2)

This simplifies to S = 7 * ( -16383) / -1, which results in S = 114,691. So, the sum of the first 14 terms of this geometric series is 114,691.

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Which expression represents the sixth term in the binomial expansion of (5y+3)^10

Answers

[tex]\bf \textit{the coefficient and values of an expanded term}\\\\ (5y-3)^{10} \qquad \qquad \begin{array}{llll} expansion\\ for\\ 6^{th}~term \end{array} \quad \begin{cases} \stackrel{term}{k}=0..10\\ \stackrel{exponent}{10}\\ -----\\ k=\stackrel{6^{th}~term}{5}\\ n=10 \end{cases}[/tex]

[tex]\bf \stackrel{coefficient}{\left(\frac{n!}{k!(n-k)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( a^{n-k} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( b^k \right)}[/tex]

[tex]\bf \stackrel{coefficient}{\left(\frac{10!}{5!(10-5)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( (5y)^{10-5} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( (-3)^5 \right)} \\\\\\ 252(5y)^5(-3)^5\implies 252(5^5y^5)(-3)^5\implies -252(3125y^5)(243) \\\\\\ -191362500y^5[/tex]

Answer:

Step-by-step explanation:

what is the square root of 4 multiplied by 16

Answers

it is 32, 2x2 is 4 so 2x16 is 32

the square root of 4 is 2, 2 x 16 is 32.

the answer is 32.

What is the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months?
a. $25.47
b. $202.55
c. $611.20
d. $4,861.20

Answers

Answer: Option c. $ 611.20 will be correct.

Explanation:

Since, the total amount of finance charge is [tex]A=P\frac{r(1+r)^n}{(1+r)^n-1}[/tex]

Where P is the principle, r is the rate, n is the times of compound interest (monthly or quarterly etc.) .

Here P=$4250 r=13.25%, and n=24.

So according to the formula So, the finance charge= [tex]4250\frac{13.25(1+13.25)^{24}}{(1+13.25)^{24}-1}[/tex] = $ 611.20

The total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months is c) $611.20.

To calculate the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months, we can use the following formula:

Total finance charge = Principal * (1 + Monthly interest rate)^Number of months - Principal

Where:

Principal is the amount of the loan ($4,250)

Monthly interest rate is the annual interest rate divided by 12 (13.25% / 12 = 1.1042%)

Number of months is the term of the loan in months (24)

Total finance charge = 4250 * (1 + 0.011042)^24 - 4250

Total finance charge = 611.20

Therefore, the answer is c. $611.20.

Note that this formula is for calculating the total finance charge over the entire term of the loan. If you want to calculate the monthly finance charge, you can simply divide the total finance charge by the number of months in the loan term. For example, the monthly finance charge for this loan would be $611.20 / 24 = $25.47.

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