Equations and Functions

Answer:

n = 32

Step-by-step explanation:

an = a1 + (n - 1)d

a4 = a1 + 3d = 16

a8 = a1 + 7d = 32

7d - 3d = 32 - 16

4d = 16

d = 4

a4 = a1 + 3d = 16

a1 + 3(4) = 16

a1 + 12 = 16

a1 = 4

an = 4 + (n - 1)4 = 128

4 + 4n - 4 = 128

4n = 128

n = 32

Answer:

See below.

Step-by-step explanation:

Recall the volume of a sphere: [tex]V=\frac{4}{3}\pi r^3[/tex]

We know that the diameter is 14, so the radius is 7.

Plug it into the equation:

[tex]V=\frac{4}{3}(3.14)(7^3)\approx 1436.03cm^3[/tex]

Answer:

66

Step-by-step explanation:

30+25+5+6 = 66.

There are 66 students in the class.

Answer:

75%

Step-by-step explanation:

There are 6 numbers that fit the rule, 1, 2, 3, 4, 6, 8. Since there are a total of 8 numbers, there is a 6/8 chance picking one or 75% chance.

Answer:

50%

Step-by-step explanation:

so the original fraction is 4/8 or 1/2 so it is 50%.

Answer:

$25.00 + $10x = $115.00

Step-by-step explanation:

We know that the initial charge of joining is $25. Each class costs $10 each. She spent a total of $115. What we don't know is how many classes she took. With this equation, we can easily find out how many classes she took.

Answer:

Step-by-step explanation:

Mean is defined as the ratio of the total sum of all the given datas to the total number of data present. It is expressed mathematically as;

[tex]\overline x = \frac{ \sum Xi}{N}[/tex] where;

[tex]\overline x = mean\\Xi= individual \ data\\N = total\ amount\ of \ data[/tex]

Given N = 7

[tex]\overline x = \frac{15+12+5+14+4+4+6}{7}[/tex]

[tex]\overline x= \frac{60}{7} \\\overline x = 8.57[/tex]

The mean number of cousins is 8.57

Answer:

1/13 chance or roughly 7.7% chance.

Step-by-step explanation:

There are 4 Kings in a standard 52-card deck. If one King was to be pulled out, you'd get a probability of 4/52 chance of pulling a king. Simplified, 4/52 is  1/13 chance.

Answer:

Option (2)

Step-by-step explanation:

In the figure attached,

ΔA'B'C' is a dilation image of ΔABC or both the triangle are similar.

Therefore, by the property of similarity of two similar triangles, corresponding sides these similar triangles will be proportional.

Scale factor = [tex]\frac{\text{Side of image triangle}}{\text{Side of the pre-image}}[/tex]

                    = [tex]\frac{\text{B'A'}}{\text{B'A}}[/tex]

                    = [tex]\frac{\text{(B'A+AA')}}{\text{B'A}}[/tex]

                    = [tex]\frac{(6+12)}{6}[/tex]

                    = 3

Therefore, scale factor is 3 when center of dilation is B.

Option (2) will be the answer.

Answer:

  [tex]\dfrac{6^2-3^2}{2}=\dfrac{27}{2}[/tex]

Step-by-step explanation:

You can go to the trouble to integrate y = x from 3 to 6, or you can figure the area geometrically.

  [tex]\displaystyle\int_3^6{x}\,dx=\left.\dfrac{x^2}{2}\right|_3^6=\dfrac{6^2-3^2}{2}\quad\text{using integration}\\\\A=\dfrac{1}{2}(b_1+b_2)h=\dfrac{1}{2}(6+3)(6-3)=\dfrac{6^2-3^2}{2}\quad\text{using geometry}[/tex]

Answer:

∠2 = 75° because of alternate interior angles. Since ∠1 and ∠2 form a linear pair, they are also supplementary which means that ∠1 = 180 - ∠2 = 180 - 75 = 105°.

The value of angles are,

⇒ ∠1 = 105°

⇒ ∠2 = 75°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Now, We get;

∠2 = 75°

Because of alternate interior angles.

And, Since ∠1 and ∠2 form a linear pair,

Hence,  they are also supplementary which means that;

⇒ ∠1 = 180 - ∠2

⇒ ∠1 = 180 - 75

⇒ ∠1 = 105°

Thus, The value of angles are,

⇒ ∠1 = 105°

⇒ ∠2 = 75°

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Answer:

see below

Step-by-step explanation:

Modified problem

(x)^2-3/x

Step 1: Find f(x+h)

(x+h)^2-3/(x+h)

x^2 +2hx + h^2 -3/(x+h)

Step 2: Find f(x + h) − f(x)

x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)

Distribute the minus sign

x^2 +2hx + h^2 -3/(x+h) -  x^2+3/x

Combine like terms and get a common denominator

2hx + h^2  -3x/(x(x+h)) +3(x+h)/(x(x+h)

2hx + h^2  +3h/(x(x+h))

Step 3: Find (f(x + h) − f(x))/h

(2hx + h^2+3h/(x(x+h)) )/h

2hx/h  + h^2/h+3h/(x(x+h)) /h

2x +h +3/(x(x+h))

Step 4: Find lim  h→0  (f(x + h) − f(x))/h

2x+0 +3/(x(x+0))

2x +3/x^2

Answer:

[tex] \angle B[/tex]

Step-by-step explanation:

[tex] \angle B[/tex] is included by AB and BC, because B is the common vertex in AB and BC,

Answer:

$10452958

Step-by-step explanation:

Initial profit = $11900848

Fall rate= $48263 per year

Equation:

where P(x)= profit at year of x, and 1990<x<2020

Answer:

2.24 s

Step-by-step explanation:

Given:

Δy = 80 ft

v₀ = 0 ft/s

a = 32 ft/s²

Find: t

Δy = v₀ t + ½ at²

80 ft = (0 ft/s) t + ½ (32 ft/s²) t²

t = 2.24 s

Answer:

2,973 in^3

Step-by-step explanation:

3000- large section

27- smaller center cut-out

Answer:

2973 in³

Step-by-step explanation:

volume of cuboid - volume of cube

20*15*10 - 3³

3000 - 27

= 2973

The volume of the aquarium is 2973 in³.

Hey there! :)

Answer:

y = 7/2x - 11

Step-by-step explanation:

Use the slope formula to calculate the slope:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates:

[tex]m = \frac{10-(-4)}{6-2}[/tex]

Simplify:

[tex]m= \frac{14}{4}[/tex]

[tex]m = \frac{7}{2}[/tex]

Slope-intercept form is y = mx + b. Plug in the slope, as well as the coordinates of a point given to solve for b:

10 = 7/2(6) + b

10 = 42/2 + b

10 = 21 + b

10 - 21 = b

b = -11.

Write the equation:

y = 7/2x - 11

Answer:

The expected value is also known as the expectation, mathematical expectation, mean, average, or first moment.

Answer:

x + (4x-85) = 90

Step-by-step explanation:

The two angles are complementary which means they add to 90 degrees

x + (4x-85) = 90

Answer: A

Step-by-step explanation:

Both angles are makes a right angle which adds up to 90 degrees so they both have to add up to 90 degrees.

Answer:

n > 1700

Step-by-step explanation:

n ÷ 4 – 125 > 300

Add 125 to both sides.

n ÷ 4 > 425

Multiply both sides by 4.

n > 1700

Answer:

n > 1700

Step-by-step explanation:

n ÷ 4 - 125 > 300

Add 125 to both parts.

n ÷ 4 > 300 + 125

n ÷ 4 > 425

Multiply both sides with 4.

n > 425 × 4

n > 1700

[tex]

6+5\sqrt{249}-2x=7 \\

-2x=7-6-5\sqrt{249} \\

-2x\approx-77.9 \\

x\approx\frac{-77.9}{2}\approx38.95

[/tex]

Hope this helps.

Answer:

Step-by-step explanation:

Hello!

(a) Which genre has the highest mean audience score? The lowest mean audience score?

1) Action [tex]\frac{}{X}_1[/tex]= 58.63

2) Comedy [tex]\frac{}{X}_2[/tex]= 59.11

3) Drama [tex]\frac{}{X} _3[/tex] = 72.10

4) Horror [tex]\frac{}{X}_4[/tex]= 48.65

The lowest mean score is  [tex]\frac{}{X}_4[/tex]= 48.65

The highest mean score is  [tex]\frac{}{X} _3[/tex] = 72.10

(b) Which genre has the highest median score? The lowest median score?

1) Action Me₁= 51.00

2) Comedy Me₂= 58.00

3) Drama Me₃= 72.00

4) Horror Me₄= 52.00

The Lowest median is Me₁= 51.00

The Highest median is Me₃= 72.00

(c) In which genre is the lowest score, and what is that score? In which genre is the highest score, and what is that score?

Lowest or minimum scores:

1) Action 32.00

2) Comedy 31.00

3) Drama 46.00

4) Horror 25.00

The genre with the lowest score is "Comedy"

Highest or maximum scores:

1) Action 93.00

2) Comedy 93.00

3) Drama 91.00

4) Horror 78.00

There are two genres with the highest score "Action" and "Comedy"

(d) Which genre has the largest number of movies in that category?

The number of movies for each category corresponds to the sample sizes:

1) Action n₁= 32

2) Comedy n₂= 27

3) Drama n₃= 21

4) Horror n₄= 17

The largest number of movies sampled was for the genre "Action"

(e) Calculate the difference in mean score between comedies and horror movies, and give notation with your answer, using i, for the mean comedy score and, for the mean horror score.

Comedy [tex]\frac{}{X}_C[/tex]= 59.11

Horror [tex]\frac{}{X}_H[/tex]= 48.65

[tex]\frac{}{X}_C[/tex] -  [tex]\frac{}{X}_H[/tex]= 59.11 - 48.65= 10.46

I hope this helps!

Answer:

6/5

Step-by-step explanation:

you have to flip the numerator and denominator. If it is 5/6 then it would be 6/5.

The reciprocal fraction that is required will be 31/26.

A fraction is a numerical number that is represented in the numerator and denominator form.

We have Two mixed fractions, the First fraction = 4(1/3) and the Second fraction =  5(1/6).

Now,First, convert mixed fractions into simple fractions,i.e.First fraction  = 4(1/3) = 13/3And,Second fraction = 5(1/6) = 31/6

Now, According to the question,

Divide First fraction by Second fraction;i.e.= (13/3) / (31/6)Now simplify,= ( 13 × 6) / (31 × 3)

Now, We get,= 26/31

So, the reciprocal fraction = 31/26.

Hence we can say that the reciprocal fraction that is required will be 31/26.

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Answer:

33.33%

Step-by-step explanation:

use a proportion

20/60 =10/30=1/3=33.333%

hope this helped!

Answer:

It is increasing and the x-intercept is (1,0) so F and E

Step-by-step explanation:

A P E X

The true statements are F and E

The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

We need to graph the log function. F(x) = log6x

Domain: x>0 All real number greater than 0.

Range: All real number.

y-intercept: Put x=0 and solve for y. (Does not exist)

y-intercept: Put y=0 and solve for x. (1,0)

Log function is increasing function.

F is true. (It is increasing)

D is False. (Because Range is all real number)

E is true. (x-intercept (1,0))

A is false. (It is decreasing.)

B is false. (The y-intercept is (0, 6))

C is false. (Domain is x>0)

Hence, F and E are true.

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Answereippcb.jrc.ec.europa.eu

Step-by-step explanation:

this I the wed go on it and you will get your answer

Answer:

Step-by-step explanation:

33.3%

19.4%

Hey there! :)

Answer:

Has one solution.

(Graphed below)

Step-by-step explanation:

***The equations are graphed below, but this can also be solved algebraically.***

Set each equation equal to each other:

-6x + 6 = -3x - 3

Add 6x to both sides:

6 = 3x - 3

Add 3 to both sides:

9 = 3x

x = 3.

Plug in the value of x into an equation to solve for y:

y = -6(3) + 6

y = -18 + 6

y = -12.

The system of equations only has ONE solution at (3, -12).

On the graph, as well, the point of intersection is at (3, -12). This is the solution.

Answer:

Two Portions!!!

Step-by-step explanation:

Answer:  A) ΔABD ≡ ΔECD

Step-by-step explanation:

Match up the letters of the congruent sides.

AD = ED      and    BD = CD

A D                        B D           →     ABD

E D                        C D           →     ECD

This can be written in any order as long as the letters are matched properly.   A & E,   D & D,   B & C

ADB          or        BDA       or     ...

EDC                      CDE

The only correct option provided is option A.

Answer:

Answer is option 1)

Answer is given below with explanations.

Step-by-step explanation:

[tex]triangle \: ABD \: and \: triangle \:ECD \: are \: congruent \\ length \: of \: BD \: = \: length \: of \: CD \\ \: and \: also \\ length \: of \: AD = length \: of \: ED \\ angle \: BDA \: = \: angle \: CDE \\ by \: \: side \: - angle - side \: postulate \\ triangle \: ABD \: and \: triangle \:ECD \: are \: congruent.[/tex]

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