Find the value of each variable

a) z score corresponding to x = 27 is -1

b) z score corresponding to x = 43 is 2.2

c)  Raw score corresponding to z = -3 is 17.

d) Raw score corresponding to z = 1.1 is 37.5

Given,

Normal distribution with μ = 32 and σ = 5

a) z score corresponding to x = 27

z = (x - μ) / σ

Then,

z = (27 - 32) / 5 = -5/5 = -1

That is, z score corresponding to x = 27 is -1.

b) z score corresponding to x = 43

z = (x - μ) / σ

Then,

z = (43 - 32) / 5 = 11/5 = 2.2

That is, z score corresponding to x = 43 is 2.2

c) Raw score corresponding to z = -3

z = (x - μ) / σ

Then,

-3 = (x - 32) / 5

-3 × 5 = x - 32

-15 = x - 32

x = 32 - 15 = 17

That is, raw score corresponding to z = -3 is 17.

d) Raw score corresponding to z = 1.1

z = (x - μ) / σ

1.1 = (x - 32) / 5

1.1 × 5 = x - 32

x = 32 + 5.5 = 37.5

That is, raw score corresponding to z = 1.1 is 37.5

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Answer:

Go ahead and color the nose red!

The solution is
[tex]y = \dfrac{n-9}{x}[/tex]

Step-by-step explanation:

[tex]\text{We have: }\\\\[/tex]

[tex]\rightarrow\; \dfrac{x}{y} + 9 = n\\\\\\\text{Subtract 9 from both sides:}\\\\\rightarrow\;\dfrac{x}{y} + 9 - 9 = n - 9\\\\[/tex]

[tex]\rightarrow\;\dfrac{x}{y} = n - 9\\\\[/tex]

Multiply both sides by y:

[tex]\rightarrow\; y \cdot \dfrac{x}{y} = y (n-9)\\\\\rightarrow\; x = y(n-9)\\\\\\[/tex]

[tex]\text{Divide both sides by (n-9)}:\\\\\\\rightarrow\; \dfrac{x}{n-9} = \dfrac{y (n-9)}{n-9}\\\\\\\rightarrow\; \dfrac{x}{n-9} = y\\\\\\[/tex]

By switching sides without changing the meaning, this can be re-written as :

[tex]y = \dfrac{x}{n-9} \\\\[/tex]

which of course means you can color the nose red

:)

Answer:

(10 x 9) + (2 x 9) = 90 + 18 = 108

Step-by-step explanation:

This is the answer because you break 12 into different parts, multiply them separately multiply them with nine. You can check the answer by doing 12*9 = 108 which matches what we need.

Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:

We had 21 dollars and we spent 5x on the notebooks, this can be express as:

Finally we know that this is equal to the six dollars we had at the end, then we have the equations:

Solving for x we have:

Therefore each notebook cost $3

SOLUTION:

Case: Transformation:

To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Method:

1,

Transformation features:

Horizontal: None

Shift: None

Stretch/Compression: None

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5

2.

Transformation features:

Horizontal:

Shift: left by 9 units

Stretch/Compression: None

Vertical:

Shift: None

Stretch/Compression: Stretches by a factor of 7.

Final answer:

1.

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5.

2.

Horizontal:

Shift: left by 9 units

Vertical:

Stretch/Compression: Stretches by a factor of 7.

The state income tax owed on a $90,000 per year salary is $5,175.

Tax is a compulsory amount that is levied by the government on the income of individuals or on certain goods and services. Progressive tax is when the amount of tax paid by individuals increases as the amount of income earned increases. The amount paid as tax can be determined by multiplying the appropriate tax rate by the total income.

Tax paid = income x tax rate

$90,000 x 5.75%

$90,000 x 0.0575 = $5,175

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The state income tax owed on an $90,000 per year salary is  $5,175.

Taxes are mandatory contributions levied on individuals or corporations by a government entity

Given,

A certain state uses the following progressive tax rate for calculating individual income tax: Income Progressive Range ($) Tax Rate 0 - 3000 2% 3001 - 5000 3% 5001 - 17,000 5% 17,001 and up 5.75%

We need to find the state income tax owed on an $90,000 per year salary.

Tax paid = income x tax rate

$90,000 x 5.75%

5.75% should be converted to decimal by dividing with 100.

5.75/100=0.0575

So $90,000 x 0.0575 = $5,175

Hence the state income tax owed on an $90,000 per year salary is  $5,175.

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The equation of u when it is the subject is u = 9/t - 12at

From the question, the original equation is given as

9 = 12at2 + ut

Next, we rewrite the equation to show the exponents

This is represented as

9 = 12at² + ut

To solve further, we simply isolate the variable term ut

This is done by subtracting 12at²  from both sides of the equation

So, we have the following equation

9 - 12at² = 12at² - 12at² ut

Evaluate the like terms in the equation

So, we have

9 - 12at² = ut

Lastly, divide both sides of the equation by t

So, we have

(9 - 12at²)/t = ut/t

Evaluate the quotients

9/t - 12at = u

Make us the subject

u = 9/t - 12at

Hence, the solution for the equation for u is u = 9/t - 12at

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Answer 3(6 + x) = -18 is 3

-18 = 3(6 + x)

-18 = 18 + 3x

3x = 18 - 18

x = 0 + 3

x = 3

____________________

Class: High School

Lesson: Equation

[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]

The mean, median and mode are as follows:

1. 11.75

2. 11.5

3. 11 and 14

4. 16.75

5. 13 and 16

6. 23

7. 32

8.  79

9.  35

10.  14

11.  2

The three measures of central tendency used in statistics are mean, median, and mode. While describing a set of data, we always specify the focal point of any data set. The measure of central tendency is this. Every day, data are presented to us. We discover them in books, articles, bank statements, phone and utility bills, as well as in newspapers. There are so many; they are all around us. The challenge now is if we can identify some key characteristics of the data by focusing on only a few data points. The means, medians, and modes—measures of central tendency or averages—can be used to do this. When describing a set of data, a measure of central tendency locates the set's center.

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Answer:

The probability that exactly 4 of them favour the new building project is 0.0768

what is Probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Step-by-step explanation:

We would assume a binomial distribution for the number of people that are in favour of a new building project. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represents the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or samples.

From the information given,

p = 40% = 40/100 = 0.4

q = 1 - p = 1 - 0.4

q = 0.6

n = 5

x = r = 4

Therefore,

P(x = 4) = 5C4 × 0.4^4 × 0.6^(5 - 4)

P(x = 4) = 5 × 0.0256 × 0.6

P(x = 4) = 0.0768

Hence, The probability that exactly 4 of them favour the new building project is 0.0768.

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By application of the combination formula, there are 210 ways for distributing 10 indistinguishable candies among 4 children.

Combination is the arrangement of objects in which order is not taken into account.

The applicable formula is:

n combination r = n!/[(n - r)!r!]

where n is the number of indistinguishable items (10 candies), and r is the possible number of recipients (4 kids).

Hence;

10 combination 4 = 10!/[(10 - 4)!4!] ways

10 combination 4 = 10!/(6! × 4!) ways

10 combination 4 = (10 × 9 × 8 × 7 × 6!)/(6! × 4 × 3 × 2 × 1) ways

10 combination 4 = 10 × 3 × 7 ways

10 combination 4 = 210 ways

Therefore, there are 210 ways for the 10 indistinguishable candies to be distributed among the 4 children by with the application of combination formula.

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The expression to simplify is

We will simplify by combining like terms.

• There are FIVE x's and TWENTY-SIX more x's. We add.

5x + 26x = 31 x

• There is 1 constant, NEGATIVE THIRTEEN. No combining required so leave it as is.

•

• There is 1 term with y, which is SEVEN y. No combining required, so we leave it as is.

The final expression is

The chances that radio transmissions from Earth or messages sent on distant space probes will ever be received by living beings are very low.

In radio transmission, a radio transmitter's antenna couples electromagnetic energy into the atmosphere or other open space. Electromagnetic radio waves are caught by a receiving antenna during radio reception and coupled into a receiver for detection.

Radio waves have a low frequency, which limits their ability to deliver large amounts of data at once.

There are extremely slim odds that radio signals from Earth or messages placed on far-off space probes will ever be received by living things, it is acceptable to the state. Remember that some scientists have held this belief about the existence of extraterrestrial life for years without any convincing evidence.

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we have the vector

u=-8i+5j

see the attached figure to better understand the problem

tan(x)=5/8

x=tan^-1(5/8)

x=32 degrees

Find out the angle theta

148 degrees

the answer is 148 degrees

1) For this question, all we need to do is to plug it in the value for x.

So,

2/3x -8 =0 Plugging into x the value x=12

2/3(12) -8 =0

8 -8 =0

0

So when x=12, then the equation is equal to zero. This leads us to conclude that 12 is the root or the solution of this equation.

SOLUTION:

Questions involving arrangement is permutation, while questions involving selection is combination.

Since the given question involves arrangement, so the correct option is PERMUTATION.

The number of possible arrangements for the top five finishers from the 13 horses is 13 permutation 5.

Answer:

50:30

Step-by-step explanation:

The length of the guy wire, to the nearest foot is 1548 ft.

The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized

After sketching the information given, we have two similar right triangles, ΔABE and ΔCDE.

CD = 6 ft

DE = 1 ft

BD = 12 ft

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

Plug in the values

AB/6 = (12 + 1)/2

AB/6 = 13/2

Cross multiply

AB = 13(3)

AB = 39 ft

AE = √(AB² + BE²)

AE = √(39² + 12²)

AE = 1548 ft (nearest foot)

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Answer: The length of the guy wire, to the nearest foot is 1548 ft.

Step-by-step explanation:

Answer:

[tex]-2\sqrt{} 6x^{8}[/tex]

Step-by-step explanation:

Answer: $95.76

Explantion: Spencer spend $95.76 dollars at the copy center.

Then your done

Answer:8% started saving at or before 21

30% believe their children or grandchildren should start saving at or before 21

Step-by-step explanation: on the graph, the ones in lighter color start saving for requirements

That is 3%+5%=8%

The second solution goes thus

13%+17%= 30%

the ones in dark colors believe their children or grandchildren should start saving before 21

Answer:

I don't know men iam grade 7 student

The given function F(x) is,

Take the limit of the function when x ix close to 2.

Hence, the function diverges.

The scale factor which takes circle m to circle n as depicted in the attached image is; 3.

It follows from the task content that the scale factor which takes circle m and transforms it to circle n is to be determined.

Hence, since both circles have the same center, the center can be taken as a point of reference.

Therefore, the distances between the center of the circles m and n to any point on their circumferences are; 3 units and 9 units respectively.

On this note, since circle n is; 9/3 = 3 times as large as circle m, it follows that the required scale factor is; 3.

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Answer:

option a as x=8 hope you understand my writing , if got some problem comment down

I would use weight of the rice after it has been fully cooked as a response variable.

The response variable I would use would be weight of the rice after it has been fully cooked. Different studies have depicted that when different types of rice are cooked, they absorb the water and the ingredients in which they are being cooked, and they concluded having different weights after being fully cooked. So, the suitable response variable would be the final weight of the rice after they are fully cooked. This response can be measured by comparing it to the initial weight of rice before cooking.

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Answer:

m∠1 = 151°

m∠2 = 29°

m∠3 = 151°

Step-by-step explanation:

        We can use knowledge of vertical angles and supplementary angles.

➜ Vertical angles are congruent

➜ Supplementary angles are equal to 180° when added together

Answer:

m∠1 = 151, m∠2 = 29, m∠3 = 151.

Step-by-step explanation:

We know m∠4 is equal to 29. We know m∠4 and m∠2 are equal because they are vertical angles. That means m∠2 is 29. Now, m∠4 and m∠3 equal 180, and m∠2 and m∠1 also equal 180. Since we know m∠4 is 29, you can do 29 + m∠3 = 180. You get m∠3 = 151. Now, m∠1 and m∠3 are also equal because they are vertical angles. That means m∠1 is equal to 151 as well. So your final answers are m∠1 = 151, m∠2 = 29, and m∠3 = 151.