1. Maryann is tracking the change in her vertical jump over 6 months. Use the table to write a linear function that models her jump distance.



Month Vertical Jump in inches
0 16
2 17
4 18
6 19


A.f of x equals one half times x plus 16

B.f of x equals one half times x plus 19

C.f(x) = 2x + 16

D.f(x) = 2x + 19



2. What is the equation of a line that contains the points (5, 0) and (5, −2)?



A.x = 5

B.x = 0

C.y = 0

D.y = 5

3. Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).





A.4x − y = −6

B.x + 4y = 7

C.x − 4y = −9

D.4x + y = 2

4Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario.



 A. The number of rides is the independent variable, and the total cost is the dependent variable.

B. The total cost is the independent variable, and the number of rides is the dependent variable.

C. The number of rides and the total cost are both independent variables.

D. The number of rides and the total cost are both dependent variables.

Answer:

Number of cats in the kennel = 8

Step-by-step explanation:

Let

c denote the number of cats and

d be the number of dogs

Given that the ratio of dogs to cats is 3 to 2

So,

d:c=3:2

Sum of ratio is 5.

And the total number of cats and dogs is 20.

So in order to find the number of cats, following formula will be used:

[tex]Numbr\ of\ cats=\frac{ratio\ of\ cats}{sum\ of\ ratio}*Total\ number\ of\ animals\\ =\frac{2}{5}*20\\ =2*4\\=8[/tex]

So, there are 8 cats in the kennel ..

The number of cats in the kennel can be found using the given ratio of dogs to cats, 3 to 2. Each part in this ratio represents 4, since the total number of animals is 20. Therefore, since the number of cats is represented by 2 parts in the ratio, there are 2 * 4, or 8 cats.

This question can be solved using the concepts of ratios and proportions. In this case, the ratio of the number of dogs to the number of cats at the kennel is given as 3 to 2. This means for every 3 dogs, there are 2 cats.

The total number of dogs and cats at the kennel is given as 20. We need to find out how many of these are cats.

To find the number of cats, we first find the total parts of the ratio by adding 3 (for dogs) and 2 (for cats), which equals 5 parts. Since the total number of animals is 20, each part in the ratio represents 20 divided by 5, which is 4. Therefore, since the number of cats is represented by 2 parts in the ratio, the number of cats is 2 multiplied by 4, which equals 8.

Therefore, there are 8 cats in the kennel.

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Answer:

52

Step-by-step explanation:

you divide 60 by 3120

[tex]\bf (b^4)^2\implies b^{4\cdot 2}\implies b^8[/tex]

Answer:

(h.g)(x) = 4x^2 + 5x - 6

Step-by-step explanation:

Given the following: f(a) = x^2 - 8x + 4; g(x) = 4x – 3; and h(x) = x + 2.

(h.g)(x) = (4x – 3)(x + 2)

(h.g)(x) = 4x^2 + 8x - 3x - 6

(h.g)(x) = 4x^2 + 5x - 6

The value of (h . g)(x) is 4x² + 5x - 6.

A function whose values are found from two given functions by applying one function to an independent variable and then applying the second function to the result and whose domain consists of those values of the independent variable for which the result yielded by the first function lies in the domain of the second.

Given:

f(x) = x² - 8x + 4; g(x) = 4x – 3; and h(x) = x + 2.

Now,

(h . g)(x) = (4x – 3)(x + 2)

(h . g)(x) = 4x² + 8x - 3x - 6

(h . g)(x) = 4x² + 5x - 6

Hence, (h . g)(x)=  4x² + 5x - 6.

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Answer:

[tex]\frac{57}{16}[/tex] lb

Step-by-step explanation:

[tex]\frac{7}{8} +1\frac{3}{4} +\frac{15}{16}[/tex]

Change the mixed fraction into an improper fraction,

[tex]\frac{7}{8} +\frac{7}{4} +\frac{15}{16}[/tex]

Now convert the denominator to 16 (since 8 and 4 are factors of 16)

And remember that what you do to the denominator, you must do the same to the numerator!

[tex]\frac{14}{16} +\frac{28}{16} +\frac{15}{16}[/tex]

Now that we have all fractions with the same denominator, we can simply add all the numerators together,

= [tex]\frac{57}{16}[/tex]

It cannot be simplified any further, so this is your answer!

Hope this helped!!

Answer:

[tex] \log_2 16 = 4 ~~\Longleftrightarrow ~~ 2^4 = 16 [/tex]

Step-by-step explanation:

[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]

[tex] \log_2 16 = 4 ~~\Longleftrightarrow ~~ 2^4 = 16 [/tex]

Keep in mind that a log is an exponent.

When you are asked for the log base 2 of 16, you are being asked for the exponent you need to raise 2 to, to get 16. The base in the log is the same base as in the exponential form.

In other words, the question "what is log base 2 of 16?" is the same as the question "what exponent do you raise the base 2 to to get 16?"

Answer:

This is the answer

SORRY IF CAM QUALITY ISNT GOOD ENOUGH...PLZ TRY TO FIGURE OUT...

PLZ MARK BRAINLISEST

Step-by-step explanation:

Answer:

Im not this sure but i think its 25/40 so its 62.5%

Step-by-step explanation:

23 Take psychology but 8 takes both so 23-8=15

18-8=10

7 dont take any

this is where im not sure, im not sure if i add the 8 who take both of the classes. I Didnt so its

15+10=25

25/40

Hope this help??

Answer:

Step-by-step explanation:

This is a Venn Diagram problem.

23 - 8 = 15 take just AP Psychology

18 - 8 = 10 take just AP Calculus

I think this question is likely done by adding all three areas together to get 33

15 + 10 + 8

33

The probability is therefore 33/40 = 0.825

Answer:

right 3 units and down 1 unit

Step-by-step explanation:

we know that

[tex]f(x)=x^{2}[/tex]

Is the equation of a vertical parabola open upward with vertex at (0,0)

and

[tex]f(x)=(x-3)^{2}-1[/tex]

Is the equation of a vertical parabola open upward with vertex at (3,-1)

so

The rule of the translation of

(0,0) -----> (3,-1)

is equal to

(x,y) -----> (x+3,y-1)

That means ----> the translation is right 3 units and down 1 unit

Answer:

C.right 3 units and down 1 unit

Step-by-step explanation:

Answer: I think the correct answer is B

Step-by-step explanation:

Answer:

The correct option is A.

Step-by-step explanation:

The given expression is

[tex](4x^2+3x-7)(x-2)[/tex]

If a ,b, c are three real number, then by distributive property,

[tex]a(b+c)\Leftrightarrow ab+ac[/tex]

Using distributive property, then given expression can be written as

[tex](4x^2+3x-7)(x)+(4x^2+3x-7)(-2)[/tex]

Option A is not a correct way to rewrite the given expression and option C represents a correct way to rewrite the given expression.

Using distributive property, then given expression can be written as

[tex](4x^2)(x-2)+(3x)(x-2)+(-7)(x-2)[/tex]

Option D represents a correct way to rewrite the given expression.

Again using distributive property in the above expression, we get

[tex](4x^2)(x)+(4x^2)(-2)+(3x)(x)+(3x)(-2)+(-7)(x)+(-7)(-2)[/tex]

Option B represents a correct way to rewrite the given expression.

Therefore the correct option is A.

Let the point (1,3) be (x1, y1)

Let the point (5,2) be (x2, y2)

The distance between the two points would be √((x2-x1)²+(y2-y1)²)

Substitute the numbers into the  points

distance: √((5-1)²+(2-3)²)

=√(4²+(-1)²)

=√(16+1)

=√17

Answer:5 but its probaly not right bc im just looking for points

Step-by-step explanation:

Answer:

19 inches each I believe but I'll stand corrected if Im wrong.

Step-by-step explanation:

Answer:

Scale factor is [tex]\frac{1}{2}[/tex]

Dimension for each channel is 46 in × 38 in

Step-by-step explanation:

Given,

The original dimension of television = 92 in × 76 in

Let A represents the area of the television,

So, after splitting the screen of television into 4 channels,

The area of each channel = [tex]\frac{A}{4}[/tex]

We know that, the scale factor is equal to the square root of the ratio of areas of the figures ( new over old ),

If x represents the scale factor,

[tex]\implies x=\sqrt{\frac{A/4}{A}}=\sqrt{\frac{1}{4}}=\frac{1}{2}[/tex]

Hence, scale factor in the given situation is [tex]\frac{1}{2}[/tex]

Also, the dimension of each channel will get after multiplying each dimension of the TV by the scale factor ( i.e. 1/2 ),

Therefore, the dimension of each channel would be 46 in × 38 in

Given two sets X and Y, a relation between X and Y freely associates elements of X with elements of Y, with no restrictions.

A function is a relation with some restrictions: there must be exactly one element of Y connected with each element of X.

The set X is called the domain of the function, and it represents all the possible inputs that we can feed the function with. As we just said, every element of the domain must have a correlated element in Y.

The set Y is called the range of the function, and it represents all the possible outputs that the function can return.

The difference between function and relation and the relationship between the domain and the range of a function is discussed below

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

Let there be an X set and a Y set. An ordered pair (x,y) is called a relation in x and y. The first element in an ordered pair is called the domain, and the set of second elements is called the range of the relation.

A function is a particular kind of relation between sets. A function takes every element x in a starting set, called the domain, and tells us how to assign it to exactly one element y in an ending set, called the range.

For example, each person is in the following table is paired with a number representing his or her height:

Alex → 180 Claudia → 165 Gilbert → 204 Judith → 165

The given relation {(Alex, 180), (Claudia, 165), (Gilbert, 204), (Judith, 165)} is a function as every person is pairs with exactly one number, their height. The domain is (Alex, Claudia, Gilbert, Judith). The range is (165, 180, 204).

The domain is the input, the independent value—it's what goes into a function. The range is the output, the dependent value—it's what comes out. Domain and range may be limited to a few discrete values, or they may include all numbers everywhere, to infinity and beyond.

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Answer:  (f·g)(x) = -5x³ - 31x² + 62x + 18

               (f·g)(1) = 44

Step-by-step explanation:

f(x) = x² + 8x + 2          g(x) = -5x + 9

(f·g)(x) = (x² + 8x + 2)(-5x + 9)

          = -5x³ + 9x²

                    - 40x² + 72x

                                - 10x + 18

          = -5x³ - 31x² + 62x + 18

(f·g)(1)= -5(1)³ - 31(1)² + 62(1) + 18

         =  -5     -   31    + 62   + 18

         =  44

Answer:

The first choice is the one you want

Step-by-step explanation:

Use geometric means to solve for a first. The formula is

[tex]8^2=15a[/tex] and 64 = 15a and a = 64/15

That one was quite easy.  Finding b is a bit more difficult.

The formula for finding b is

[tex]\frac{a}{b}=\frac{b}{15+a}[/tex]

Solving for b:

[tex]b^2=a(15+a)[/tex]

Filling in we have

[tex]b^2=15(\frac{64}{15})+(\frac{64}{15})^2[/tex] and

[tex]b^2=64+\frac{4096}{225}[/tex] and

[tex]b^2=\frac{18496}{225}[/tex] so b = 136/15

Answer:

  1. C, E, G

  2. A, D, H

Step-by-step explanation:

Compare each equation to the form ...

  f(x) = 1/(4p)(x -h)^2 +k

In this form, p is the distance from the vertex to the focus (positive is up), and (h, k) is the location of the vertex. The focus is (h, k+p); the directrix is y=k-p.

1. The equation tells us ...

  (h, k) = (1, 4)

  1/(4p) = (-1) . . . ⇒ . . . p = -1/4

So, we have ...

--

2. The equation tells us ...

  (h, k) = (-1, 4)

  1/(4p) = 2 . . . ⇒ . . . p = 1/8

So, we have ...

Answer:

Step-by-step explanation:

Answer:

m= 4, -2

Step-by-step explanation:

move everything to one side.

m^2-2m-8=0

then factor

(m-4)(m+2)

then

m= 4, -2

hope this helps!

Answer:

Step-by-step explanation:

Answer:

C. increases rapidly.

Step-by-step explanation:

tan(θ) =  sin(θ)/cos(θ)

Now, when sin 90 = 1

and cos 90 = 0

so, tan(90) = 1/0 = not defined.

(1/0 is infinity and its value is not defined)

So, when angle θ increases to 90°, then the value of tan(θ) increases rapidly, as shown in the figure below.

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Answer:

Step-by-step explanation:

D

Answer:

The sample should be a random sample from the entire set of students and should include enough students to be reliable. Small samples have more variation, which leads to less reliable inferences.

To find out how many sixth through eighth grade students are interested in joining a running club, you can conduct a survey among these students. Choose a sample by randomly selecting a certain number of students from the list, ensuring diversity. Contact the selected students to ask about their interest in joining the club and calculate the percentage of interested students.

To find out how many sixth through eighth grade students are interested in joining a running club, you would need to conduct a survey or questionnaire among the students in these grades. Here's how you can choose a sample that will give you a good representation of the whole population:

Answer:

f(x) = 7 sin 8x + 3 ⇒ 1st answer

Step-by-step explanation:

* Lets revise the trigonometry translation  

- If the equation is y = A sin (B x + C) + D  

* A is the amplitude  

- The amplitude is the height from highest to lowest points and  

  divide the answer by 2  

* The period is 2π/B  

- The period is the distance from one peak to the next peak

* C is the horizontal shift  

- The horizontal shift is how far the function is shifted to left  

  (C is positive) or to right (C is negative) from the original position.  

* D is the vertical shift  

- The vertical shift is how far the function is shifted vertically up

  (D is positive) or down (D is negative) from the original position.  

- The equation of the mid-line is y = D

* Now lets solve the problem

∵ f(x) = A sin(Bx + C) + D

∵ The amplitude is 7

∴ A = 7

∵ The period is 2π/B

∵ The period is π/4

∴ 2π/B = π/4 ⇒ divide both sides by π

∴ 2/B = 1/4 ⇒ Use cross multiplication

∴ B × 1 = 2 × 4

∴ B = 8

∵ The equation of the mid-line is y = D

∵ The equation of the mid-line is y = 3

∴ D = 3

- There is no mention for C

∴ C = 0

∴ f(x) = 7 sin 8x + 3

Answer:

6

Step-by-step explanation:

I think you mean |v|... you wouldn't need dot product for that...

It is just sqrt(6^2)=6

Answer:

d

Step-by-step explanation:

You cannot use the dot product on a single vector

To find the magnitude of v = - 6i, then

| v | = [tex]\sqrt{(-6)^2}[/tex] = [tex]\sqrt{36}[/tex] = 6 → d

Answer:

  7.  B) 26–35

  8.  C) 31/77

Step-by-step explanation:

7. It's a matter of writing the fractions in a way that lets you compare their values. It is usually convenient to convert them to decimal:

(age group, healthy fraction)

(18–25, 9/48 = 0.1875)

(26–35, 16/98 ≈ 0.1633)

(36–45, 19/94 ≈ 0.2021)

(> 45, 12/60 = 0.2000)

The group with the smallest percentage of healthy blood sugar is 26–35.

__

8. There are 94+60 = 154 study participants who are at least 36. Of those, 35+27 = 62 are at risk for diabetes. That ratio is ...

  62/154 = 31/77

A = (-3, 2) → (-3 + 2, 2 - 4) → (-1, - 2)

B = (1, 5) → (1 + 2, 5 - 4) → (3, 1)

C = (2, -3) → (2 + 2, -3 - 4) → (4, -7)

A’ = (-1, -2)

B’ = (3, 1)

C’ = (4, -7)

Answer:

Table C

Step-by-step explanation:

we have

[tex]y=-4x^{2}[/tex]

The quadratic equation in standard form is equal to

[tex]ax^{2}+bx+c=0[/tex]

so

In this problem

[tex]a=-4, b=0,c=0[/tex]

The y-intercept is the value of y when the value of x is equal to zero

[tex]y=-4(0)^{2}=0[/tex]

The y-intercept is the point (0,0)

The coefficient a is negative, therefore the parabola open down

Answer:

C

Step-by-step explanation:

Edge2021

Answer:

  230

Step-by-step explanation:

The function simplifies to ...

  f(t) = 230

This will be the value for any value of t, so ...

  f(2) = 230

For this case we have that by definition:

Two angles are complementary if their sum is 90 degrees.

Then, assuming that the variable "x" represents the complement of 22, we have:

[tex]x + 22 = 90\\x = 90-22\\x = 68[/tex]

Thus, the complement of 22 degrees is 68 degrees.

Answer:

Option A

Angles 8 and 7 are adjacent angles, meaning that their sum is 180 degrees. Knowing this you can make a formula like so...

2x + 15 + 3x = 180

Now you must combine like terms. Like terms are numbers that have matching variables OR are numbers with out variables. In this case the like terms are 2x and 3x, since they both have the variables "x" attached.

2x + 3x = 5x

so...

5x + 15 = 180

Now bring 15 to the left side by subtracting 15 to both sides (what you do on one side you must do to the other). Since 15 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

5x + 15 - 15 = 180 - 15

5x + 0 = 165

5x = 165

Next divide 5 to both sides to finish isolating x. Since 5 is being multiplied by x, division (the opposite of multiplication) will cancel 5 out (in this case it will make 5 one) from the left side and bring it over to the right side.

5x / 5 = 165 / 5

x = 33

x is 33.

To find measure of angle 7, plug in 33 for x in 2x + 15 and solve

2(33) + 15

66 + 15

81

Measure of angle 7 is 81 degrees

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

0

y = -2

Step-by-step explanation:

The formula for the slope is (in general) Δy / Δx Since the value of y does not change (I'm assuming we are talking about AB), the slope is (-2 - - 2) / (2 - -2) = 0/4 = 0

So the equation of the line is

y = mx + b

m = 0

y = 0*x - 2

y = - 2  <<<< Equation

Answer:

Slope = 0

Equation:

[tex]y = -2[/tex]

Step-by-step explanation:

Note that the diagonal AB is a horizontal line parallel to the x axis. The Slope m of a line is a measure of how the function f(x) changes when x increases or decreases.

Note, however, that horizontal lines such as segment AB do not change and their value of y does not depend on the value of x. Therefore all horizontal lines have slope m = 0.

Finally, the equation of line AB is

[tex]y = -2[/tex]

Answer:

[tex]19.22\:<\:\mu\:<\:44.78[/tex]

Step-by-step explanation:

Tthe population is normally distributed and the sample size is [tex]n=22\:<\:30[/tex].

Since the population standard deviation [tex]\sigma[/tex] is unknown and the sample standard deviation [tex]s[/tex], must replace it, the t distribution must be used for the confidence interval.

Hence with degrees of freedom of 21, [tex]t_{\frac{\alpha}{2} }=3.527[/tex].(Read from the t distribution table)

The 98% confidence interval can be constructed  using the formula:

[tex]\bar X-t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )\:<\:\mu\:<\:\bar X+t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )[/tex].

From the question the sample mean is [tex]\bar X=32[/tex]dollars and the sample standard deviation is [tex]s=17[/tex] dollars.

We substitute the values into the formula to get

[tex]32-3.527(\frac{17}{\sqrt{22} } )\:<\:\mu \:<\:32+3.527(\frac{17}{\sqrt{22} } )[/tex]

[tex]19.22\:<\:\mu\:<\:44.78[/tex]

Therefore, we can be 98% confident that the population mean is between is between 19.22 and 44.78 dollars.