Answer to the question

9514 1404 393

Answer:

  $41,977.60

Step-by-step explanation:

Allison's average salary for the last 5 years is ...

  (70 +73.1 +75.2 +77.5 +79)/5 = 74.96 . . . . thousand dollars

Then her annual pension is ...

  1.75% × $74,960 × 32 = $41,997.60

============================================================

Explanation:

First we need the arithmetic mean

Add up the values to get 1+2+4+4+5+6+6 = 28

Divide this over the number of values (n = 7) to get 28/n = 28/7 = 4

The mean is 4.

Next, we subtract the mean from each data value and square the difference

Add up those results: 9+4+0+0+1+4+4 = 22

Lastly, we divide over the number of items (n = 7) to get the population variance: 22/n = 22/7 = 3.14 approximately

----------

Side note:

If you wanted the sample variance, then you divide over n-1 = 7-1 = 6

22/(n-1) = 22/6 = 3.67 is the approximate sample variance

Answer:

217

Step-by-step explanation:

Answer:

B) π

Step-by-step explanation:

y = sin 2 (x – π∕2)

y = sin (2x -π)

=> 2x = 2π

x = π

The period of function sin(2x−π) is π, which is correct option(B).

The period of the function is defined as the interval between repetitions of any function. A trigonometric function's period is the length of one one completed cycle.

The trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.

Given the function as :

y = sin 2 (x – π/2)

y = sin (2x − π)

Use the form asin(bx−c) + d to determine the variables used to find the amplitude, period, phase shift, and vertical shift.

a = 1

b = 2

c = π

d = 0

Determine the period of sin(2x−π).

y = sin (2x -π)

So, the period = c = π

Hence, the period of function sin(2x−π) is π.

Learn more about  period of the function here:

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Answer:

-1

Step-by-step explanation:

f(4) = 2.5(4) -11

f(4) = 10 -11

f(4) = -1

Answer:

A

Step-by-step explanation:

Did the quiz

Answer:

67 f

Step-by-step explanation:

Answer: -2 (b)

Step-by-step explanation:

So the slope of the line is the amount that the line changes as it goes along the x or y axis. Think of it like a ramp- goes up or down, steep or flat.

Take a pair of points like (-4, 11) and (2, -1)

{But you can use other points in the chart too. }

-4 to 2 is a distance of 6 --> that is the x

11 to -1 is a distance of -12 --> that is the y

We want the change in y over (or divided by) change in x.

-12 / 6 = -2

Answer:

B

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 11) and (x₂, y₂ ) = (2, - 1) ← 2 ordered pairs from the table

m = [tex]\frac{-1-11}{2-(-4)}[/tex] = [tex]\frac{-12}{2+4}[/tex] = [tex]\frac{-12}{6}[/tex] = - 2 → B

Answer:

[tex]x = - \frac{494}{3}[/tex] [tex]= - 164\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]75 + \frac{3}{8} x = 13\frac{1}{4}\\\\75 + \frac{3}{8} x = \frac{53}{4}\\\\\frac{3}{8}x = \frac{53}{ 4} - 75\\\\\frac{3}{8}x = \frac{53-300}{4}\\\\\frac{3}{8}x = - \frac{247}{4}\\\\x = -\frac{247 \times 8}{4 \times 3} \\\\x = -\frac{494}{3}[/tex]

Answer:

3/4

Step-by-step explanation:

because it is a linear function it means it has the same slope in every point

so you have to take 2 points and find the slope

I take points (0,1) and (4,4)

m = (y2-y1) / (x2-x1)

note that it does not matter which points you chose to be second or first

m = (4-1) / (4-0) = 3/4

you can solve it from the graph too 3/4 is y/x it means for every 4 unit right move 3 units up

Given:

The sequence is:

25,43,61,79,97

To find:

The recursive formula for the given sequence.

Solution:

We have,

25,43,61,79,97

Here, the first term is 25. Now, the differences between the two consecutive terms are:

[tex]43-25=18[/tex]

[tex]61-43=18[/tex]

[tex]79-61=18[/tex]

[tex]97-79=18[/tex]

The differences between the two consecutive terms is common, i.e., 18. So, the given sequence is an arithmetic sequence.

The recursive formula of an arithmetic sequence is:

[tex]F(n)=F(n-1)+d[/tex]

Where, d is the common difference and F(1) is the first term.

Putting [tex]d=18[/tex], we get

[tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex].

Therefore, the required recursive formula is [tex]F(n)=F(n-1)+18[/tex], where [tex]F(1)=25[/tex].

Answer:

[tex]2x^2y^3[/tex]

Step-by-step explanation:

The given expression is :

[tex]2x^2y^3+4x^2y^5[/tex]

We need to find the greatest common  factor of the expression.

The first term is [tex]2x^2y^3[/tex]

The other term is [tex]4x^2y^5[/tex]

[tex]2x^2y^3[/tex] is common in both terms. So,

[tex]2x^2y^3(1+2y^2)[/tex]

Hence, the greatest common factor of the expression is equal to [tex]2x^2y^3[/tex].

Answer:

A

Step-by-step explanation:

f(x)=-5x³+3x²+x-9

leading coefficient is negative and it is of odd degree.

so it starts from above onthe left  and ends at the bottom ont he right.

Answer:

23/26 is a greater percentage, it equals around 88% while 12/15 equals 80%

Step-by-step explanation:

Answer:

[tex]\cos(J) = 0.67[/tex]

Step-by-step explanation:

Given

[tex]\angle K = 90^o[/tex]

[tex]KJ = 65[/tex]

[tex]IK = 72[/tex]

[tex]JI = 97[/tex]

Required

[tex]\cos(J)[/tex]

The question is illustrated with the attached image.

From the image, we have:

[tex]\cos(J) = \frac{KJ}{JI}[/tex]

This gives:

[tex]\cos(J) = \frac{65}{97}[/tex]

[tex]\cos(J) = 0.67010309278[/tex]

[tex]\cos(J) = 0.67[/tex] --- approximated

Answer:

The relationship between the above two triangles is SAS and they are congruent

Answer:

inscribed

Step-by-step explanation:

For any given triangle, the circle inside of it is called the Inscribed circle

Answer:

The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to 0.248.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Of the 500 people sampled, 124 said that they would be interested in purchasing season tickets to a Six Flags in Ames.

This means that [tex]p = \frac{124}{500} = 0.248[/tex]

The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to

By the Central Limit Theorem, it is equal to the sample proportion of 0.248.

Answer:

x < 7

Step-by-step explanation:

the domain of a function defines the valid x values for the function.

as we go from left to right through all possible values of x, we see all values incl. x=-1 are creating a valid function result (y) for this function. until we reach x=7.

the empty ball indicates that there is no y value defined here. and for any value x>7 there is no y value defined.

so, x < 7 is the right one.

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the Base of the  △  be  x

Then the Height will be  2 x + 4

Area of △ = 1 2 b h

Where, b = b a s e , h = h e i g h t , A r e a = 35

(in this case)

Substitute the values into the equation → 35 = 1 2 ( 2 x + 4 ) ( x ) → 35 = ( 2 x + 4 ) 2 ( x ) →

35 = ( x + 2 ) ( x ) → 35 = x 2 + 2 x

Subtract  35  both sides

→ 0 = x ^2 + 2 x − 35

Rewrite the equation in the Standard form

x ^2 + 2 x − 35 = 0

Factor the equation

→ ( x + 7 ) ( x − 5 ) = 0

So we have  

x = − 7 , 5

numbers So  x = 5

They have asked us to find the Height

So, ⇒ H e i g h t = 2 x + 4 = 2

Answer:

7.5 is the difference

Step-by-step explanation:

basketball mean

(13+22+23+24+36+37+42+43+58+69) ÷10 = 36.7

tennis mean

(14+23+24+38+47+48+57+58+66+67) ÷10 = 44.2

tennis mean - basketball mean

44.2 - 36.7= 7.5

Answer:

[tex]\text{Dimensions: 25 x 50},\\\text{Area: }1,250\:\mathrm{m^2}[/tex]

Step-by-step explanation:

Let the one of the side lengths of the rectangle be [tex]x[/tex] and the other be [tex]y[/tex].

We can write the following equations, where [tex]x[/tex] will be the side opposite to the wall:

[tex]x+2y=100,\\xy=\text{Area}[/tex]

From the first equation, we can isolate [tex]x=100-2y[/tex] and substitute into the second equation:

[tex](100-2y)y=\text{Area},\\-2y^2+100=\text{Area}[/tex]

Therefore, the parabola [tex]-2y^2+100y[/tex] denotes the area of this rectangular enclosure. The maximum area possible will occur at the vertex of this parabola.

The x-coordinate of the vertex of a parabola in standard form [tex]ax^2+bx+c[/tex] is given by [tex]\frac{-b}{2a}[/tex].

Therefore, the vertex is:

[tex]\frac{-100}{2(-2)}=\frac{100}{4}=25[/tex]

Plug in [tex]x=25[/tex] to the equation to get the y-coordinate:

[tex]-2(25^2)+100(25)=\boxed{1,250}[/tex]

Thus the vertex of the parabola is at [tex](25, 1250)[/tex]. This tells us the following:

And therefore, the desired answers are:

[tex]\text{Dimensions: 25 x 50},\\\text{Area: }1,250\:\mathrm{m^2}[/tex]

Answer:-244

Step-by-step explanation:

I think you subtract -290 from -46.

Sorry If I am wrong.

========================================================

Explanation:

Imagine reflecting everything so that location A is above location B. Effectively all you're doing is erasing the negative signs.

That would place A at 290 feet and B would be at 46 feet. The difference in elevation is 290-46 = 244 feet

Instead of reflecting, you can turn the page upside down and just ignore the negative signs, and then subtract like normal.

This trick only works if both elevations A and B are below sea level.

--------

Or you could subtract like so:

|A-B| = |-290-(-46)| = |-290+46| = |-244| = 244

The absolute value is used to ensure the result is not negative. A negative difference makes no sense. In this case, "difference" and "distance" mean the same thing more or less.

Answer:

c 13 over 12

Step-by-step explanation:

it help I makeit

Answer:

yes it is

Step-by-step explanation:

hopefully that helps

195ft i think because 10 x 19.5

because 39 divided by 2 is 19.5

so then 19.5 x 10 = 195ft

Answer:

6

Step-by-step explanation:

The third digit to the right of decimal point is in the thousandths place. The fourth digit to the right of decimal point is in the ten thousandths place and so on.

In the decimal number 24.736, the digit which is at the thousandth place will be 6.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We know that the number starts from the tenths after the decimal.

....123.456..

The expansion of the number is given as,

... + 100 + 20 + 3 + 0.4 + 0.05 + 0.006 + ......

The expansion is written in form of words. Then

Hundreds + Tens + Ones + Tenths + Hundredths, Thousandths, and so on.

In the decimal number 24.736, the digit which is at the thousandth place will be 6.

More about the Algebra link is given below.

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Answer:

x = 40

Step-by-step explanation:

Two triangles are similar so we can use similarity ratio to find x

x/16 = 35/14 cross multiply expressions

14x = 560 divide both sides by 14

x = 40

Answer:

A: x ≤ −4

Step-by-step explanation:

Hi there!

We're given the two inequalities -8x + 3 ≥ 27 and  −13x + 5 ≥ 57

we need to find the set of solutions that make the two inequalities true (the intersection)

First, let's solve the two inequalities, starting with -8x + 3 ≥ 27

-8x + 3 ≥ 27

subtract 3 from both sides

-8x≥24

divide both sides by -8 and remember to FLIP the inequality sign, as we're dividing with a negative

x ≤ -3

now for the other inequality:

−13x + 5 ≥ 57

subtract 5 from both sides

-13x ≥ 52

divide both sides by -13 and remember to FLIP the sign

x ≤ -4

please see below for the graph to find the intersection, as well as the final answer

Hope this helps! :)