table:
x c(x)
(days) (dollars)
1. 25
2. 45
3. 60
4. 70

Answer:

[tex]\frac{3\pi}{2}[/tex]  units to the right

Step-by-step explanation:

If we have a parent function y = Sin(x), the function

The function given is [tex]y=Sin(x-\frac{3\pi}{2})[/tex]

So from the rules, we can clearly say that it is parent function shifted RIGHT by  [tex]\frac{3\pi}{2}[/tex] units.

2nd answer choice is correct.

Answer:

f(x)=x^3-3x^2+25x-75

Step-by-step explanation:

Solve for x:

x^3 - 3 x^2 + 25 x - 75 = 0

The left hand side factors into a product with two terms:

(x - 3) (x^2 + 25) = 0

Split into two equations:

x - 3 = 0 or x^2 + 25 = 0

Add 3 to both sides:

x = 3 or x^2 + 25 = 0

Subtract 25 from both sides:

x = 3 or x^2 = -25

Take the square root of both sides:

Answer:  x = 3 or x = 5 i or x = -5 i

(0,0) satisfies y > 2x - 1 but does not satisfy y ≤ x^2 - 4. C

(0,0) satisfies both inequalities.

Answer:

x = 7.5

Step-by-step explanation:

Given

- 15 = [tex]\frac{x}{-0.5}[/tex]

Multiply both sides by - 0.5

- 0.5 × - 15 = x, hence

x = 7.5

Answer:

7.5.

Step-by-step explanation:

-15 = x / -0.5

Cross multiplying:

x =  -15 * -0.5

= 7.5.

Multiply the bracket by 5

I used PEMDAS

P= parenthesis

E= exponents

M=multiplication

D= division

A= addition

S= subtraction

7r+2= 5(r-4)

7r+2= 5r-20

Move 5r to the left hand side . Positive 5r changes to negative 5r

7r-5r+2= 5r-5r-20

2r+2=- 20

2r+2-2= -20-2

Move positive 2 to the right hand side. Changes to negative -2

2r+2-2= -20-2

2r= -22

Divide by 2 for 2r and -22

2r/2= -22/2

r= -11

Answer is r= -11

Answer:

r = (-11)

Step-by-step explanation:

7r + 2 = 5(r – 4) ​

7r + 2 = 5r – 4 * 5

7r + 2 = 5r – 20

7r - 5r = -20 - 2

     2r = -22

       r = -22/2 = (-11)

Answer:

z = 5

Step-by-step explanation:

Given

- 0.25z = - 1.25 ( divide both sides by - 0.25

z = [tex]\frac{-1.25}{-0.25}[/tex] = 5

z = 5

Answer:

z = 5.

Step-by-step explanation:

-0.25 z = -1.25

z = -1.25 / -0.25

z = 5.

Yes. You should add commas next time to make it easier to read.

Answer:

Yes this is a function..

Step-by-step explanation:

We have to see the inputs and outputs for the function.

Here x represents input and y represents output.

For a relation to be a function there should be no repition in domain or input of the function i.e. every element in domain should be unique.

The domain for given relation is:

{1,-1,3,5}

All the inputs are only once mapped to the output so this relation is a function ..

Answer:

F

Step-by-step explanation:

∠C is opposite ( or across from ) side AB

In the same way

∠A is opposite side BC and

∠B is opposite side AC

Answer:

2.25

Step-by-step explanation:

Answer:

x = 2.25

Step-by-step explanation

using process of elimination the only viable answer is 2.25

Answer:

see explanation

Step-by-step explanation:

81[tex]a^{6}[/tex] - 100 ← is a difference of squares which factors in general as

a² - b² = (a - b)(a + b)

81[tex]a^{6}[/tex] = (9a³ )² ⇒ a = 9a³ and 100 = 10² ⇒ b = 10

Hence

81[tex]a^{6}[/tex] - 100

= (9a³)² - 10²

= (9a³ - 10)(9a³ + 10)

Answer:

C

Step-by-step explanation:

Unit Test Is a pain I know

Answer:

28

Step-by-step explanation:

So this means to replace the r you see in 4r^2-8 with 3.

Let's do that:

4(3)^2-8

Now to simplify this just use pemdas or a calculator:

4(9)-8     since 3^2 means 3*3=9

36-8

28

Answer:

28.

Step-by-step explanation:

Put r =- 3 and work it out:

That would be 4(3)^2 - 8

=  4 * 9 - 8

= 36 - 8

= 28.

Answer:

11/16

Step-by-step explanation:

You could list all the possible fractions you will get:

Here are the's with 4 as the numerator:

4/4

4/5

4/6

4/7

Here are the one's with 5 as the numerator:

5/4

5/5

5/6

5/7

Here are the one's with 6 as the numerator:

6/4

6/5

6/6

6/7

Here are the one's with 7 as the numerator:

7/4

7/5

7/6

7/7

There are 4(4) different numerator-denominator combinations we can get.

Let's see which of these are bigger than 5/6.

If you think it is easier to look at the decimals of all these you can.

5/6=0.8333333333

----

4/4 =1

4/5 =0.8

4/6  =0.6666666666

4/7  =0.5714 (approximately)

There is only 1 bigger than 5/6 in this section.

5/4 =1.25

5/5  =1

5/6  =0.83333333333

5/7  =0.714 (approximately)

There is 2 bigger than 5/6 in this section.

6/4  =1.5

6/5   =1.2

6/6   =1

6/7   =0.857 (approximately)

There is 4 bigger than 5/6 in this section.

7/4

7/5

7/6

7/7

All of these are 1 or bigger because the numerator is bigger than or equal to the denominator so all 4 of these are bigger than 5/6 in this section.

P(fraction being greater than 5/6)=[\tex]\frac{\text{ the numbers I listed bigger than } \frac{5}{6}}{\text{ all the fractions I listed }}[/tex]

P(fraction being greater than 5/6)=[\tex]\frac{4+4+2+1}{4(4)}=\frac{11}{16}{/tex]

11/16

Answer:

1/6 or 11/16

Step-by-step explanation:

If you spin a spinner with the first spin giving the numerator and the second spin giving the denominator of a fraction, the probability of the fraction will be greater is 1/6 or 11/16.

6 - 5/6 = 1/6

However, there are 4 possible spots you could land on so, it would change to 11/16.

Answer:

c

Step-by-step explanation:

3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. In actuality, 3^2 + 3^3 = 36, while 3^5 = 243.

No, 3 to the 2nd power plus 3 to the 3rd power does not equal 3 to the 5th power. This is a common misconception when dealing with exponents. To clear this up, let's look at what these expressions actually mean:

3 to the 2nd power (3^2) = 3*3 = 9

3 to the 3rd power (3^3) = 3*3*3 = 27

So, 3^2 + 3^3 = 9 + 27 = 36

However, 3 to the 5th power (3^5) = 3*3*3*3*3 = 243

So, as you can see, 36 does not equal 243.

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Answer:

1. 24

2. 30

3. 20

4. 12

5. 6

Answer:

Step-by-step explanation:

[tex]3x+1=4x+(-4)\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\3x-4x+1=4x-4x-4\\\\-x+1=-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=-4-1\\\\-x=-5\qquad\text{change the signs}\\\\x=5[/tex]

Answer:

The answer is B. In step one he should have added 3 negative x-tiles to both sides.

Step-by-step explanation:

Answer:

7.6 inches

Step-by-step explanation:

First of all we have to define range.

Range gives us the difference of two values between which the data is spread.

the formula for range is:

Range = Highest value - lowest value

By observing the diagram, we can see that

The highest value is = 8.5 inches

The lowest value is: 0.9 inches

So,

Range = 8.5 - 0.9

= 7.6 inches

So, the range is 7.6 inches ..

Answer:

see explanation

Step-by-step explanation:

These are the terms of an arithmetic sequence

The n th term ( explicit rule ) for an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

d = 9 - 2 = 16 - 9 = 23 - 16 = 30 - 23 = 7 and a₁ = 2, hence

[tex]a_{n}[/tex] = 2 + 7(n - 1) = 2 + 7n - 7 = 7n - 5

The explicit rule for the sequence 2,9,16,23,30... is 7n - 5

2,9,16,23,30

= 7

The explicit rule is defined by

nth term = a + (n - 1) d

= 2 + (n - 1)7

= 2 + 7n - 7

= 7n - 5

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Answer:

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below a line or to the left if is a vertical line

>, ≥ - shaded region above a line or to the right if is a vertical line

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

We have x ≥ 4:

solid vertical line x = 4

shaded region to the right

Step-by-step explanation:

pt C is (-4,-4)

pt D is (2,-4)

length of CD is 6 units

to form a rectangle AB must be parallel to CD, AC must be parallel to BD and AC and BD must be 6 units

Therefore...A =(-4, 2) and B = (2, 2)

[tex]\bf \cfrac{1+cot^2(\theta )}{1+csc(\theta )}=\cfrac{1}{sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\implies \cfrac{1+\frac{cos^2(\theta )}{sin^2(\theta )}}{1+\frac{1}{sin(\theta )}}\implies \cfrac{~~\frac{sin^2(\theta )+cos^2(\theta )}{sin^2(\theta )}~~}{\frac{sin(\theta )+1}{sin(\theta )}}\implies \cfrac{~~\frac{1}{sin^2(\theta )}~~}{\frac{sin(\theta )+1}{sin(\theta )}}[/tex]

[tex]\bf \cfrac{1}{\underset{sin(\theta )}{~~\begin{matrix} sin^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }}\cdot \cfrac{~~\begin{matrix} sin(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{sin(\theta )+1}\implies \cfrac{1}{sin^2(\theta )+sin(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{1+cot^2(\theta )}{1+csc(\theta )}\ne \cfrac{1}{sin(\theta )}~\hfill[/tex]

Answer:

Option A (Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance).

Step-by-step explanation:

Correlation is a concept which explains a linear relationship between two variables. The correlation constant lies between -1 and 1. 0 lies in the center of the interval. A negative correlation means an inverse relationship, and a positive correlation means a direct relationship. 0 technically means no linear relation between the variables. Further the correlation constant lies from 0, more the strength of the relationship. It is important to note that correlation shows a relationship between the two variables but it cannot determine the causation i.e. it cannot be concluded that one variable caused the other variable to occur. Even though having a strong correlation does not mean causal relationship. Therefore, correlation does not prove causation. This is because there are several other lurking and unobserved variables which affect the observed variables. The former class of variables are not accounted for in the correlation. Therefore, the exact magnitude of the causal relationship cannot be determined. Therefore, Option A is the correct choice!!!

Answer:

OPTION A: Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance.

Step-by-step explanation: I got it right on the test.

Answer:

see explanation

Step-by-step explanation:

Using the exact values of the trigonometric ratios

sin30° = [tex]\frac{1}{2}[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

Then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{17}{y}[/tex] = [tex]\frac{1}{2}[/tex]

Cross- multiply

y = 2 × 17 = 34

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{y}[/tex] = [tex]\frac{x}{34}[/tex] and

[tex]\frac{x}{34}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 34[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 17[tex]\sqrt{3}[/tex]

Hence

x = 17[tex]\sqrt{3}[/tex] and y = 34

Answer:

[tex]\large\boxed{D.\ (x-4)^2=55}[/tex]

Step-by-step explanation:

[tex](a-b)^2=a^2-2ab+b^2\qquad(*)\\\\\\x^2-8x=39\\\\x^2-2(x)(4)=39\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\\underbrace{x^2-2(x)(4)+4^2}_{(*)}=39+16\\\\(x-4)^2=55[/tex]

Answer: the answer is D

Step-by-step explanation:

Answer: 50 degrees.

Step-by-step explanation:

To find the measure of the angle Q, you need to follow these steps:

- Knowing that:

[tex]-980= -(1,360)cos(Q)[/tex]

You can divide both sides of the equation by -1,360:

[tex]\frac{-980}{-1,360}=\frac{-1,360cos(Q)}{-1,360}\\\\\frac{49}{68}=cos(Q)[/tex]

- Finally, using  the inverse function of the cosine, Arccosine, we get:

[tex]Q=Arcos(\frac{49}{68})\\\\Q=49.89\°[/tex]

To the nearest whole degree, this is:

[tex]Q=50\°[/tex]

Answer:

2160

Step-by-step explanation:

36*20=720      720*3=2160

To find the number of square inches of paper needed, multiply the length and width of each drawer to get the area, and then multiply that area by 3.

To find the number of square inches of paper needed, we need to find the area of the bottom of each drawer and then add them together. The area of a rectangle is found by multiplying its length by its width. So, for each drawer, we multiply 36 inches by 20 inches to get an area of 720 square inches.

Since there are 3 drawers, we need to multiply the area of one drawer by 3. So, the total number of square inches of paper needed is 720 square inches times 3, which equals 2160 square inches.

Therefore, the correct answer is D) 2160.

Answer:

D. Linear decay.

Step-by-step explanation:

The data decays and lowers.

Answer with explanation:

If you will look at the graph of function, it is not a straight line.

Horizontal Asymptote is, y=0.

There is no vertical Asymptote.

Either it can be growth function or decay function.

But , if you will look at the graph of growth function, it begins from negative infinity and then starts increasing.

In this case graph is decreasing function.

So, The function represents

Option C:→ Exponential Decay

Answer:

x = -7 and x = 2

Step-by-step explanation:

Look for the points on the graph where if you draw a horizontal line at y=1, you will intersect the curve.

By observation, we can see that this happens at x = -7 and x = 2

x = -7 and x = 2

Here in the diagram, we can see that, a curve is present & 6 co-ordinates on that curve are given.

We have to find the values of x correspond with f(x) = 1

f(x) = 1 means y = 1

So, if we draw a horizontal line at y = 1, which is parallel to x-axis.

Then, we can able to observe the points which are on the line y = 1.

So, the points on line y = 1 are (-7, 1) & (2, 1).

Hence, we can say that, input values that correspond with f(x) = 1 are x= -7 & x = 2.

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