A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is ý = 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements must be true? (a) For each one-point increase in performance rating, the raise will increase on average by S1400. (b) The actual relationship between salary raises and performance rating is linear. (c) The residuals for half the observations in the dataset will be positive.(d) The correlation between salary raise and performance rating is negative. (e) If the mean performance rating is 1.2, then the mean raise is $3800

The two numbers are 12 and 26.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Let x and y be the 2 numbers

x+y=38........(1)

8+2x=5y.......(2)

(1) => x=38-y

8+2(38-y)=5y

8+76-2y=5y

84=5y+2y=7y

y=84/7 = 12

when y=12, x=38-y = 38 - 12 = 26

So, the two numbers are 12 and 26.

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Answer:

C

Step-by-step explanation:

Denominator can't be 0

Therefore, [tex]x-7\neq 0[/tex]

Adding 7 to both sides gives [tex]x\neq 7[/tex]

Only C corresponds to our answer.

No , they do not form a proportion because 77 and 60 are not equal

Hence , not form proportion

Set up a proportion as 4/7 = 11/15

Cross multiply:

7×11

4×15

You should get 77 and 60 for the products. Since the products don't equal each other, they are not proportional.

complete question is

use cross products to determine whether the ratios 4/7 and 11/15 form a proportion. Do they form a proportion? Explain your steps and your conclusion

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The matching terms and processes are;

1. The nervous system's ability to acquire, retain, and retrieve information- memory

2. Remembering stored information- retrieval

3. Processing information for storage- encoding

4. Retention of information- storage

Given,

The nervous system's capacity for information acquisition, storage, and retrieval is known as memory. Information is processed for storage by encoding, whereas information is remembered from storage through retrieval. Information is retained through storage.

Memory is the process of storing and recalling previously acquired information. The act of storing involves adding new information to the memory, which the brain alters for improved storage. It is easier for the brain to access and bring into conscious mind information that has been encoded.

Information is stored so that it will last throughout time. Modern memory psychology distinguishes between two basic types of memory storage: short-term memory and long-term memory.

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Given question is incomplete. Completed question is here;

Match the terms with their corresponding processes.

a. memory

b. encoding

c. retrieval

d. storage

1. the nervous system's ability to acquire, retain, and retrieve information

2. remembering stored information

3. processing information for storage

4. retention of information

Mitochondria use proteins to break down sugars and produce cellular energy in the form of ATP.

Answer:

x = 1

Step-by-step explanation:

2(x - 2)= -2

2x - 4 = -2

2x = 2

x = 1

Answer:

x = 1

Step-by-step explanation:

2(x - 2) = -2

Solve for x

Divide each side by 2

2/2(x - 2) = -2/2

x-2 = -1

Add 2 to each side

x - 2+2 = -1+2

x = 1

The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.

A histogram is a bar graph-like representation of data that groups a range of classes into columns along the horizontal x-axis. The vertical y-axis represents the number count or percentage of occurrences in the data for each column. Columns can be used to visualized as patterns of data distributions.

Lesser the value of n larger the variablity.

Arranging from the least value of n to the naximum value, the order is A, C, B

Therefore, The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.

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5 types of cubical are: dedicated, Private office, L-shaped, circular, High walled cubicles

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Answer:

[tex]\huge\boxed{\sf r = 1/4}[/tex]

Step-by-step explanation:

y = rx -------------------(1)

From the table,

x = 8 when y = 2

Put in the above equation.

2 = r(8)

Divide 8 to both sides

2/8 = r

r = 2/8

r = 1/4

[tex]\rule[225]{225}{2}[/tex]

The value of the car after 10 years is 4668.9 dollars

Depreciation is the reduction in the value of an asset or commodity over time and such valued reductions are reflected in the balance sheet at the year ended.

According to the given information:

Prize of the new car purchased P = 23700 dollars

the rate at which the value of a car depreciates R = 15% per year

Now, the value of the car after 10 years could be determined by the formula

Amount        =    P[tex](1-r)^{t}[/tex]

P = 23700 dollars        R = 15% per year           t = 10 years

Substituting all the values in the above formula:

Amount       =   [tex]23700(1-0.15)^{10}[/tex]

                    =    [tex]23700(0.85)^{10}[/tex]

                    =    23700×0.197

                    =     4668.9 dollars

The value of the car after 10 years is 4668.9 dollars

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The solution of equation is y = -15, x = 1 .The equation used to obtain the value of y and x is y = -15x.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right   sides.

We have LHS = RHS (left hand side = right hand side) in every   mathematical equation. To determine the value of an unknown variable  that represents an unknown quantity, equations can be solved. A   statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.

The given equation is: y= -5x3

or        y= -15x

or      y\x=-15

Divide with 1 both side

    y/x = -15/1

Then  y = -15 , x = 1

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Answer: (5,28)

Step-by-step explanation:

A roster of twenty-four players divided into four teams can be represented by the expression 24/4.

Given

24 players total

(4) teams total.

This can be expression as = 24 / 4.

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If the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)

The expression is given by

56 + 96

First we have to find the GCF of the numbers

Prime factorization

56 = 2×2×2×7

96 = 2×2×2×2×2×3

The GCF(56, 96) = 8

Write the expression using the GCF

56 + 96 = 8(7) + 8(12)

Here we have to apply the distributive property

AB + AC = A(B + C)

Then,

8(7) + 8(12) = 8 (7 + 12)

Hence, if the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)

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The kind of line is used when the inequality symbol is ≥ or ≤ is solid line

If the original inequality is ≤ or ≥, the boundary line is drawn as a solid line, since the points on the line will make the original inequality true.

The kind of line is used when the inequality symbol is ≥ or ≤ is solid line

But in case of < or > symbol, the line used is dotted line.

A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement.

Therefore, The kind of line is used when the inequality symbol is ≥ or ≤ is solid line

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Answer:

7/9

Step-by-step explanation:

total: 3+2+4

starbucks or crazy mocho: 3+4

(3+4)/(3+2+4)=7/9

Answer:

y = -1/3 x + 5

Step-by-step explanation:

To write the equation, you need the slope and the y-intercept to write the equation in the slope intercept form.  You did not state what form, so this is the form that I will use.

y = mx + b  M is the slope and b is the y intercept.

The slope is the change in y over the change in x.  For the two points we can find the change in y by using the numbers 6 and 7.  We can find the change in x by using the numbers - and -6,

[tex]\frac{6-7}{-3 - -3}[/tex] = [tex]\frac{-1}{-3+6}[/tex] = [tex]\frac{-1}{3}[/tex]  This is the slope.

To find the y intercept (b) we will use one point and the slope.  It does not matter which point that you use.  I am going to use the point (-3,6).

slope (m) = [tex]\frac{-1}{3}[/tex]

x = -3

y = 6  Plug these into the equation and solve for b.

y = mx + b

6 = ([tex]\frac{-1}{3}[/tex]) (-3) + b

6 = 1 + b  Subtract 1 from both sides.

5 = b

y = [tex]\frac{-1}{3}[/tex]x + 5

If the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).

Given that,

The area inside the circle where x² + y² = 18y and outside the circle where x² + y² = 81 is occupied by a lamina.

We have to find if the density at any place is inversely proportional to its distance from the origin, locate the center of mass.

We know that,

Take the equation

x² + y² = 18y

x² + y² - 18y=0

Adding and subtracting 9².

x² + y² - 18y+ 9²-9²=0

x² + y² - 18y+ 9²=9²

x² + (y-9)²=9²

Which is a circle of radius 9 and center (0,9), And now the second equation

Now,

x²+y²=81

Which is a circle with radius 9 and center (0,0).

We can plot the curves in the picture we can see.

The density will be evenly distributed around the lines x=0 and y=4.5, which are the lines of symmetry, in a more complicated scenario where we would need to utilize integration to identify the Center of Mass.

Therefore, if the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).

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The required height of given regular pentagonal prism is 19 millimeters.

We work out the volume of a pentagonal crystal utilizing the recipe is V = 5/2abh where this equation is additionally perceived as V = [1/2 × 5 × base length × apothem] × level of the crystal. The qualities are placed in the recipe and compose the response so got in cubic units.

We have,

Then

V = 5/2abh

2850 =( 5×12×h)×5/2

h = 19 millimeters

Thus, required height of the pentagonal prism is 19 millimeters.

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Answer:

19 millimeters

Step-by-step explanation:

i took the test and got right hope this helps :)

The probability of drawing two pink ones if the first marble was not put back before the 2nd drawing is 2/9.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that there are 10 marbles in the bag 2 yellow 3 pink and 5 blue.

First, we need to find the probability of drawing a blue marble on the first draw.

Since there are 5 blue marbles and 10 total, then the probability is;

5⁄10, or 1/2.

Now, we no longer have that blue marble, there are 4 blue marbles and 9 total.

The chances of drawing a blue marble are; 4/9.

Therefore, the chance that both marbles drawn are blue is the chance that the first one is blue times the chance that the second one is blue.

1/2 x  4/9 = 4/18 = 2/9

Hence, the probability of drawing two pink ones if the first marble was not put back before the 2nd drawing is 2/9.

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Sum of all positive integers having twice as many digits when written in base  $2$  as they have when written is base $3$ is 10.

This is because the only two integers which fits the constraint are 2 and 8,

2 in base 10 =10 in base 2 = 2 in base 3

8 in base 10 =1000 in base 2 = 22 in base 3.

The result of the expression $a+b$ is 11

This is because the LCM of [1!+2!, 2!+3!, 3!+4!, 4!+5!, 5!+6!, 6!+7!, 7!+8!, 8!+9!] =3,628,800

Which can be written as :  1. 10! = 1 + 10 = 11

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Answer:

i believe it is b)

the no. of days beginning with T (2)

the no. of days not starting with T (5)

The school cook ordered p packages of hot dog buns for the year-end picnic. Each package contains 8 buns. Write an expression that shows how many hot dog buns were ordered.

order = 8p

The probability density function f(x) represents the probability at a given value of x.

In a distribution, the notation f(x) is the equivalent to the probability of event x, that is:

[tex]f(x) = P(X = x)[/tex]

The area under the curve is given by the cumulative distribution, which is given by:

[tex]P(X\leq x) = \int\limits^x_0f(x)dx[/tex]

Thus it is not f(x).

And f(x) can also be the height of the relative frequency function, but not of the function itself.

Hence the answer is the probability density function f(x) represents the probability at a given value of x.

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Answer:

---------------------------

Find the area between x = 85 and x = 125.

The matching choice is A

Answer:

0.7938

Step-by-step explanation:

The given graph is a normal distribution curve.

If a continuous random variable X is normally distributed with mean μ and variance σ²:

[tex]\boxed{X \sim \textsf{N}(\mu,\sigma^2)}[/tex]

Given:

[tex]\text{If \; $X \sim \textsf{N}(100,15^2)$,\;\;find\;\;P$(85\leq X\leq 125)$\;\;to\;3\;s.f.}[/tex]

Therefore, we need to find the area to the left of x = 125 and subtract the area to the left of x = 85.

Method 1

Using a calculator:

[tex]\begin{aligned}\implies \text{P}(85\leq X\leq 125)&= \text{P}(X\leq 125)-\text{P}(X < 85)\\&=0.9522096477-0.1586552539 \\&=0.7935543938\\&\approx0.7938\end{aligned}[/tex]

Method 2

Converting to the z-distribution.

[tex]\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}[/tex]

[tex]x=85 \implies Z_1=\dfrac{85-100}{15}=-1[/tex]

[tex]x=125 \implies Z_2=\dfrac{125-100}{15}=1.67[/tex]

Using the z-tables to find the corresponding probabilities (see attachments).

[tex]\begin{aligned}\implies \text{P}(-1\leq Z\leq 1.67)&= \text{P}(Z\leq 1.67)-\text{P}(Z < -1)\\&=0.9525-0.1587\\&=0.7938\end{aligned}[/tex]

Answer: 32%

Step-by-step explanation:

Let's set the original dimensions of the rectangular patio as:

That'll set the original area(a) of the patio as a = w · l.

The new dimensions of the patio can be calculated as:

The new area can then be calculated as 1.1w · 1.2l = 1.32 · w · l = 1.32a

Using the two areas, the percent increase can be calculated as:

[tex]\frac{1.32a-a}{a}*100 =\frac{1.32-1}{1}*100 =0.32*100=32[/tex]

The central angle states the property of the center of the circle, So It is called the central angle.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.

An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.

Hence,

The central angle states the property of the center of the circle, So It is called the central angle.

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The required probability of a sum of 5 or sum of 7 and the first die shows a 3 or the sum of the result is 6 or 8 are 5/18 and 1/18 receptively.

Probability is just the way that logical something is to occur. Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions administered by likelihood is called statistics.

Two fair dice are thrown then the number of  possible way is 6×6 = 36

a) a sum of 5 or sum of 7 :-

The total possible way for dice occurs sum 5 or sum 7 is (1, 4), (2, 3), (3, 2), (4, 1), (1, 6), (2, 4), (3, 4), (4, 3), (5, 2), (6, 1).

So, the total number possible way for dice occurs sum 5 or sum 7 = 10.

Probability = 10/36 = 5/18

Hence, the probability is 5/18.

b) The first dice shows 3 or the sum of the result is 6 or 8 :-

As, first dice shows 3 we have fixed 3 in first dice or results sum is 6 or 8 then second dice possibilities only consist two number either 3 or 5,

So, total possible ways for first dice shows 3 or sum of result is 6 or 8 is (3, 3), (3, 5).

There are only two ways,

Therefore, probability = 2/36 = 1/18

Hence, the probability is 1/18.

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Answer:

The sale price is 39.99 % off

Step-by-step explanation:

To find the percentage off,

take 49.99 - 30.00 = 19.99

Then divide by 49.99

19.99/49.99

39.9879976

The sale price is 39.99 % off

The system of inequalities did not have any solution, but after reversing the  sign we will get a solution of the system of inequalities.

The inequalities are : y > 2x + 2/3 and y < 2x + 1/3

There is no intersection and no solution to the system since the region above the line y = 2x + 2/3 and the region below the line y = 2x + 1/3, respectively, are the solutions to the inequality y > 2x + 2/3 and y <2x + 1/3, respectively.

Now when the signs are changed we get:

y < 2x + 2/3 and y > 2x + 1/3

The region below the line y = 2x + 2/3 is the solution of the inequality

y= 2x + 2/3, and the region above the line y = 2x + 1/3 is the solution of the inequality y > 2x + 1/3. This implies that the area between the two lines is where the system's solution lies.

Disclaimer: The complete question is :

How will the solution of the system y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?

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Answer:

There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions. 

Step-by-step explanation:

Sample answer

Answer:

Multiple

Step-by-step explanation:

A multiple of 5 is anything that it can multiply into. For example: 5, 10, 15, 20, 25 and so on.

A factor is a number that divides into your number and leaves no remainder. An example of this is 2 is a factor of 4.  15 is not a factor of 5 because it cannot divide evenly. The only factors of 5 are 1 and 5.