Let = 160 and = 16. find the z-score for the score, x = 150.

Let μ = 160 and σ = 16. find the z-score for the score, x = 150.

Answers

Answer 1

Put the given values in the formula
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
and evaluate.
z = (150 -160)/16 = -10/16
z = -5/8

The z-score for the score x=150 is -5/8 = -0.625.

Related Questions

In 2012 the population of a city 6.16 was find the exponential growth function estimate the population

Answers

y=aXb^x
that would be your starting equation

how long will it take to triple the amount of $500 if you invest it at a rate of 6% compound annually

Answers

It will take you 18.85 years.

Find the measure of each angle indicated.

Answers

All of these angles are either corresponding or supplementary, so it looks like I haven't answered them, but I have.

(11). 110 degree (12).84 degree (13).80 degree (14).111 degree (15).125 degree (16).47 degree.

What is angle theorem?

The relation between the angles which is formed by intersecting two lines , described by Geometry called angle theorem. Some common angle theorem are Alternate interior angle , Alternate exterior angle etc.

Given,

(11) One angle of 110 degree is given and other angle which is asked is

also 110 degree by alternate exterior angle theorem.

(12) One angle of 84 degree is given and other angle which is asked is

also 84 degree by alternate interior angle theorem.

(13) The angle formed by straight line is 180 degree .So one angle is

given which is 100 degree and other will be 80 degree. Now asked

also 80 degree by alternate interior angle theorem.

(14) One angle of 111 degree is given and other angle which is asked is

also 111 degree by alternate interior angle theorem.

(15) One angle of 125 degree is given and other angle which is asked is

also 125 degree by alternate interior angle theorem.

(16) One angle of 47 degree is given and other angle which is asked is

also 47 degree by alternate exterior angle theorem.

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What's a parabola? What's a hyperbola?

Answers

Parabola: is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram below, but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape.

Hyperbola:
In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows

Hope this Helps

Both parabolas and hyperbolas are an open curve which means that the arms or branches of the curves continue to infinity; they are not closed curves like a circle or an ellipse.

The length of a rectangle is five times the width.

The area of the rectangle is 1620cm squared.

Work out the width of the rectangle

Answers

Hi there!

Let's use x for the width because we know the width is only 1. Next, we'll use 5x for the length because the length is 5 times the width. Now, we can set up an equation to solve for x.

WORK:
x * 5x = 1620
5x^2 = 1620
x^2 = 324
x = 18

ANSWER:
The width of the rectangle is 18 centimeters

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

Write the expression as a single natural logarithm.3 ln x – 5 ln c

Answers

The rules are ...
[tex]\Longrightarrow \ln(\frac{a}{b})=\ln(a)-\ln(b)[/tex]
[tex]\Longrightarrow \ln(a^{b})=b\ln(a)[/tex]

Your expression makes use of both these rules.
[tex]3\ln(x)-5\ln(c)=\ln(x^{3})-\ln(c^{5})=\ln \left( \dfrac{x^{3}}{c^{5}} \right)[/tex]

Your single logarithm is ...
[tex]\ln \left( \dfrac{x^{3}}{c^{5}} \right)[/tex]

In order to accumulate enough money for a down payment on a house, a couple deposits $300/month into an account paying 6% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 5 years? What formula is required to complete this problem?

Answers

[tex]\bf ~~~~~~~~~~~~\textit{Future Value of an ordinary annuity}\\ ~~~~~~~~~~~~(\textit{payments at the end of the period}) \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right][/tex]

[tex]\bf \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array}\\ pymnt=\textit{periodic payments}\to &300\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to &5 \end{cases}[/tex]

[tex]\bf A=300\left[ \cfrac{\left( 1+\frac{0.06}{12} \right)^{12\cdot 5}-1}{\frac{0.06}{12}} \right]\implies A=300\left[ \cfrac{(1.005)^{60}-1}{0.005} \right] \\\\\\ A=300(\stackrel{\approx}{69.770030509863214)}\implies A\approx 20931.009152958964[/tex]

A sales associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in commission for selling 3 suits and a pair of shoes. The next week, she earned $107 in commission for selling 7 suits and 2 pairs of shoes. How much commission does she earn for selling each suit and each pair of shoes? Solve by substitution.

Answers

let h shoes and s suit:

3s+h=47

7s+2h=107

substitution property:

3s=47-h

s=(47-h)/3

plug it into the other equation and solve for h:

7((47-h)/3)+2h=107

distribute 7 and multiply 3 on both sides:

329-7h+6h = 321

329-h=321

-h=-8

h=8 pair of shoes

s=(47-8)/3=13 suits

median mode mean and range on 84 45 10 28 75 63 16 55

Answers

PUT THIS SET IN ORDER FROM LEAST TO GREATEST:

10, 16, 28, 45, 55, 63, 75, 84
__________________
MEDIAN: Find the number in the middle of the set.
10, 16, 28, 45, 55, 63, 75, 84
There cannot be two medians, so you find the number between 45 & 55.
MEDIAN = 50
_________________
MEAN: Find the average by adding up all of the numbers and dividing them by how many numbers there are.
10 + 16 + 28 + 45 + 55 + 63 + 75 + 84 = 376
376/8 = 47
MEAN = 47
________________
MODE: The number that occurs most often. If no number repeats, there's no mode.
THERE IS NO MODE
________________
RANGE: The difference between the largest and smallest value in the set. Subtract the largest (84) and smallest (10) value.
84 - 10 = 74
RANGE = 74

Mean: 47. Mean is when you add up all the numbers, then divide by how many numbers you added (adding them together you get 376, which you divide by 8).

Median: 50. Median is when you sort every number numerically and find which number is in the middle. Since there are 8 numbers, there are 2 numbers you'd find the number equally in between each of those 2 numbers. That number being 50.

Mode: There is no mode. Mode is the number that is "most frequent" or is repeated the most in the number sequence.

Range: 74. Range is when you subtract the smallest number of the sequence from the largest number.

I hope this helps!

Which type of study contains a treatment?

Sample.
Experiment.
Survey.
Observational study.

Answers

Typically, in an experiment there are two groups. One group is called the control group. The other group is the experimental group. This second group receives some sort of treatment. The control group does not. The idea is to see if the treatment has an effect on those who receive it by comparing them to a comparable group that does not receive the treatment.

So the answer is experiment.

The type of study that contains a treatment is called EXPERIMENTAL STUDY.
An experimental set up usually involved random assignment of variables into different group and manipulation of a particular variable while others are controlled. This type of study is usually done to determine the effect of one variable on the outcome of another variable. The experimental set up is usually made up of control and treatment groups.

Find the inverse of the function r(t) = 5^t. I WILL make you BRAINLIEST

Answers

(log5 t)

hope it helps if not say something ill change it :P

hey can you please help me posted picture of question

Answers

G(x) is obtained from F(x) after both horizontal and vertical translation.

Following translations occur in F(x) to obtain G(x)
a) 2 units to Right
b) 4 units down

Translation towards right can be expressed as:

F(x - 2)

Vertically down translation can be expressed as:

F(x-2) - 4

So,

G(x) = (x-2)² - 4

Thus, option A is the correct answer.

cylinder A has a volume of 360 cm3. Cylinder B has a base and height identical to that of cylinder B, but leans to the right in such a way that its slant is greater than 4 cm. what is the volume of cylinder B

Answers

If the height is measured between the parallel ends of the cylinder, the volume is identical:
360 cm³.

_____
If the "height" is measured along the central axis of the cylinder, there is insufficient information to determine the volume.

The slant length of a prism (even a cylindrical one) is immaterial. What matters to the volume is the area of the base and the distance between the planes of the bases (height).

hey user

360

is the answer

A basketball is thrown with an initial upward velocity of 30 feet per second from a height of 6 feet above the ground. The equation h=-16t^(2)+30t+6 models the height in feet t seconds after the basketball is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?

Answers

For this case we have the following equation:
h = -16t ^ (2) + 30t + 6
We substitute the value of h = 10 in the equation:
10 = -16t ^ (2) + 30t + 6
Rewriting we have:
0 = -16t ^ (2) + 30t + 6-10
0 = - 16t ^ (2) + 30t - 4
We look for the roots of the polynomial:
t1 = 0.144463904
t2 = 1.730536096
"the ball passes its maximum height, it comes down and then goes into the hoop". Therefore, the correct root is:
t = 1.730536096
Answer:
It goes into the hoop after:
t = 1.73 seconds

Find the value of x for which M//N. PLEASE EXPLAIN HOW TO SOLVE ALSO

A.
38
B.
62
C.
102
D.
150

Answers

The answer is A, 38.

The two angles are complementary so 3x-36+2x+26=180

Just simplify from there.

If m//n the external conjugated angles must be complementary:
(3x-36)°+(2x+26)°=180°
(3x-36+2x+26)°=180°
3x-36+2x+26=180
5x-10=180
5x-10+10=180+10
5x=190
5x/5=190/5
x=38

Answer: Option A. 38

Choose any numbers for he first column that will correctly complete the table.

Answers

1. Can be any number between 1,765 - 1,769
2. Any number between 9,425 - 9,429

Number: 7,760

Number: 9,440

The ratio of the lengths of corresponding sides of two similar octagons is 8:9. what is the ratio of their perimeters? *

Answers

The ratio of perimeters is the same as the ratio of the corresponding sides: 8:9.

_____
Any corresponding length measures of the similar figures will have the same ratio.

The ratio of the perimeters of the two similar octagons is the same as the ratio of the lengths of their corresponding sides, which is 8:9.

When dealing with similar polygons, such as octagons in this case, the ratio of the lengths of corresponding sides directly determines the ratio of their perimeters. Since the sides of the octagons are proportional, with a specific ratio of 8:9, we can infer that the perimeters of the octagons will also have the same ratio. This is due to the perimeter being the sum of the lengths of all sides of the polygon.

Therefore, if one side of the first octagon is scaled up by a factor of 8, the entire perimeter will be scaled by the same factor. Correspondingly, if one side of the second octagon is scaled up by a factor of 9, its entire perimeter will also reflect that scaling. Given that the ratio of the lengths of corresponding sides is 8:9, the ratio of their perimeters will also be 8:9.

PLEASE HELP!!!!!! WHICH OF THE FOLLOWING IS A CORRECT EQUATION FOR THE LINE PASSING THROUGH THE POINT (-2 1) AND HAVING SLOPE M = 1/2

Answers

The answer for this equation is A and B.

Answer choice A is in slope-intercept (y = mx+b) form. The slope of the line is the number in front of the x, so in this case it's [tex] \frac{1}{2} [/tex]. Now, just plug in the given point to see if the equation is satisfied:

[tex]1= \frac{1}{2} (-2)+2[/tex]
[tex]1= -1+2[/tex]
[tex]1= 1[/tex]

It works, so answer choice A works.

Answer choice B is in slope-intercept (y = mx+b) form. The slope of the line is the number in front of the x, so in this case it's -2. Answer choice B has the wrong slope, so eliminate B.

Answer choice C is in standard form. Rearrange it to slope-intercept form:

[tex]x-2y=-4[/tex]
[tex]-2y=-x-4[/tex]
[tex]y= \frac{1}{2} x+2[/tex]

Same as A, so answer choice C works.

Answer choice D is in point-slope form: y - y1 = m(x - x1). If you know this form well, you should be able to see that the given equation satisfies both the slope and point requirement. If you don't know the form well, try putting it into slope-intercept:

[tex]y-1= \frac{1}{2} (x+2) [/tex]
[tex]y-1= \frac{1}{2} x+1 [/tex]
[tex]y= \frac{1}{2} x+2 [/tex]

Same as A, so answer choice D works.

Indicate the general rule for this sequence. Find a 1 and the common difference. a 4 = 18 a 7 = 9

Answers

Final answer:

The general rule for the sequence is an = -9 + (n-1)(9). The first term (a1) is -9 and the common difference is 9.

Explanation:

Sequence Analysis:

To find the general rule for a sequence, we need to determine the pattern or relationship between the terms. In this case, we are given a4 = 18 and a7 = 9. To find the common difference, we subtract the two terms: 18 - 9 = 9. So, the common difference is 9. To find a1, we can use the formula: an = a1 + (n-1)d, where n is the term number and d is the common difference. Substituting n = 4, a4 = 18, and d = 9, we can solve for a1. 18 = a1 + (4-1)(9), which gives us a1 = 18 - 3(9) = 18 - 27 = -9. Therefore, the general rule for this sequence is an = -9 + (n-1)(9). The first term (a1) is -9 and the common difference is 9.

a^1 = 27

d = -3

Step-by-step explanation:

Because your friends stayed in bed instead of helping you with the breakfast, you agree to split the £248 hostel bill to the ratio of: 3:3:2 with you paying the least. How much will you have to pay?

Answers

Final answer:

The question posed is about the concept of ratio, you are required to divide £248 according to the ratio 3:3:2. Each part of the ratio is worth £31, thus you will have to pay for two parts, hence, your total responsibility is £62.

Explanation:

The subject of this question is ratio. In the given problem, you need to distribute £248 hostel bill into the ratio of 3:3:2. Firstly, you add the three parts of the ratio which equals to 8 (3+3+2). Now, to find out how much each part is worth you need to divide the total sum, which is £248, by the total number of parts, which is 8. This gives you the value for one part, which is £31 (248 ÷ 8).

Given that you have to pay the least, which corresponds to 2 parts, you multiply £31 by 2, thus you have to pay £62 (31 * 2).

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An equilateral triangle's perimeter and a rectangle's perimeter have the same numerical value. The length of the rectangle is the same as the side of the triangle. The width of the rectangle is 12. What is the length of the rectangle?

Answers

just set the perimeter equation equal to each other and put the values in that you know and solve

A basket is filled with 8 white eggs and 10 brown eggs. Half of the white eggs are cracked. An egg is randomly selected from the basket. What is the probability that it is a cracked, white egg?Write the answer in a fraction in simplest form

Answers

Number of white eggs = 8
Number of brown eggs = 10
Total sample = 8+10 = 18

Number of broken eggs = 4 white

P(broken egg) = 4/18 = 2/9

Event A is a subset of event B. P(A)=.15 and P(B)=.53 Find P(A|B). Round the answer to the nearest hundredth.

Answers

If [tex]A\subseteq B[/tex], then [tex]A\cap B=A[/tex]. So

[tex]\mathbb P(A\mid B)=\dfrac{\mathbb P(A\cap B)}{\mathbb P(B)}=\dfrac{\mathbb P(A)}{\mathbb P(B)}=\dfrac{0.15}{0.53}\approx0.28[/tex]

Answer:

Step-by-step explanation:

Good Treads and Speed Tracks manufacture tires. Good Treads claims that their tires last longer than Speed Tracks tires. A car company decided to test Good Tread's claim. They purchased 20 sets of Good Tread's tires and 20 sets of Speed Track's tires. They tested the lifetime of each tire by simulating 1,000 miles of driving conditions for each set of tires each day. At the end of each day, they measured the tread on each of the tires. Once the tire tread drops below minimum safe tread depth, the tire is considered to have passed its lifetime.

After observing the lifetime of each tire, the car company reported that the average lifetime of a Good Treads tire is 55,000 miles and the average lifetime of a Speed Tracks tire is 65,000 miles.

Given the car company's report, what conclusion can be made regarding the average lifetime of Good Treads and Speed Tracks tires?
There is not enough information to make any conclusions from the car company's report.

Good Treads' claim is false; therefore, it can be concluded that Speed Tracks tires last longer than Good Treads tires.

Good Treads' claim is false; therefore, it can be concluded that Good Treads tires last longer than Speed Tracks tires.

Good Treads' claim is true; therefore, it can be concluded that Good Treads tires last longer than Speed Tracks tires.

Answers

Good Treads' claim is false; therefore, it can be concluded that Speed Tracks tires last longer than Good Treads tires.

The car company's report provides evidence that Speed Tracks tires have a longer average lifetime compared to Good Treads tires. Therefore, we can conclude that Good Treads' claim that their tires last longer is false.

Based on the car company's report, we can conclude that Good Treads' claim that their tires last longer than Speed Tracks' tires is false. The average lifetime of a Good Treads tire is reported to be 55,000 miles, while the average lifetime of a Speed Tracks tire is reported to be 65,000 miles.

To reach this conclusion, we compare the average lifetimes of the two tire brands. Since the car company tested 20 sets of each brand's tires and measured the tread on each tire after simulating 1,000 miles of driving conditions, we can assume that these results are representative.

By comparing the average lifetimes, we see that the average lifetime of Speed Tracks tires is greater than the average lifetime of Good Treads tires. Therefore, we can conclude that Speed Tracks tires last longer than Good Treads tires, contradicting Good Treads' claim.

In conclusion, the car company's report provides evidence that Speed Tracks tires have a longer average lifetime compared to Good Treads tires. Therefore, we can conclude that Good Treads' claim that their tires last longer is false.

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Maggie ebought 52 ounces of swordfish selling for $6.92 per pund. What was the total cost?

Answers

The total cost was $22.49

PLZ HELP ASAP CIRCLES

Answers

From the figure we are given that the measure of angle U is equal to 85°. With this, we can conclude that the arc intercepted by the angle which is the arc DKC will have a measure that is twice its value.

m(DKC) = 2(85°) = 170°

The total measure of the arc in a circle is equal to 360°. Hence,

m(DKC) + m(DUC) = 360°

Substituting the known value,
170° + m(DUC) = 360°

The value of m(DUC) is equal to 190°. The measure of the angle K is half this value.
m∠K = 190°/2 = 95°

Answer: 95°

To finance her community college education, Sarah takes out a loan for $3700. After a year Sarah decides to pay off the interest, which is 5% of $3700. How much will she pay?

Answers

So, to solve this, we use this equation:
3700 + 0.05(3700)
But, if we want to make it shorter:
1.05(3700)
Now you just multiply(you may want to use a calculator)
1.05(3700) = 3885
She will pay $3885

Choose the single logarithmic expression that is equivalent to the one shown 5 log x + 3 log x^2

Answers

5 log x+3 log x^2
=log x^5+log x^(2×3)
=log x^5+ log x^6
=log (x^5×x^6)
=log x^(5+6)
=log x^11

Answer: log x^11

a $1600 principal earns 7% annual interest, compounded semiannually. What is the balance after 33 years?

Answers

Use the future value formula.
FV = P(1 +r/n)^(nt)
FV = 1600*(1 +.07/2)^(2*33)
FV = 1600*1.035^66 ≈ 15,494.70

The balance after 33 years will be $15,494.70

Given a slope of and the points left-parenthesis 220 comma 500 right-parenthesis and left-parenthesis 140 comma 350 right-parenthesis, which is the correct equation in point-slope form?

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 220 &,& 500~) % (c,d) &&(~ 140 &,& 350~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{350-500}{140-220}\implies \cfrac{-150}{-80}\implies \cfrac{15}{8} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-500=\cfrac{15}{8}(x-220)[/tex]

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