Hello I need help with this

The composition of functions evaluated in x = 3 is equal to -8.

t(3) = -8.

Here we have the two functions g(x) and f(x), and the composition:

(g°f)(x) = t(x).

This is equal to:

t(x) = g(f(x))

Then:

t(3)  = g( f(3) )

Evaluating f(x) in 3 we get:

f(3) = 4*3-  6 = 12 - 6 = 6

Then:

t(3) = g( f(3))  =g(6)

And we know that g(6) = -8, then:

t(3) = -8.

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The zeroes of the function k(x)=15x³-48x²-48x are 0, 4 and -4/5.

The function provided is a cubic polynomial.

There will be three zeroes in total for the function k(x).

K(x) = 15x³-48x²-48x

If we put x = 0,

We can see that k(x) becomes zero,

So we can say that 0 is a solutions for this function,

Now,

K(x) = x(15x²-48x-48)

Solving 15x²-48x-48 seperately using quadratic formula,

a = 15

b = -48

c = -48

x = (-b+√D)/D and (-b-√D)/D

D = b²-4ac.

D = (-48)²-4(15)(-48)

D= 5184.

√D = 72

putting all the values to find x,

x = (-(-48)+72)/30 and (-(-48)+72)/30

x = 4 and -4/5.

our function becomes,

k(x) = x(x-4)(x+4/5)

so the zeroes are 0, 4, -4/5.

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Given the sample table below:

Total number of teenagers that get less than 8 hours of sleep each school night

Sample #1:

The number of teenagers that get less than 8 hours of sleep each night include the sum of teenagers that get less than 4 hours, teenagers that get between 4 and 6 hours, teenagers that get between 6 and 8 hours.

Thus, we have

Sample #2:

Thus, we have

Percentage of teenagers that get between 4 and 10 hours of sleep each school night

ample #1:

The total number of teenagers that get between 4 and 10 hours of sleep is evaluated to be

Thus, the percentage becomes

Sample #2:

Hence, based on the result of the survey,

About half of the teenagers get less than 8 hours of sleep each school night,

More than 90% of teenagers get between 4 and 10 hours of sleep each school night.

Answer:

1/6th chance

Step-by-step explanation:

Since there are 6 possible outcomes that will be the denominator, now count the number you want to roll, in this case 1 since you only want to find the probably of getting a 3. So the probably is 1/6

Point (C) C closely approximates the given mathematical operation that is the difference between B and A (B - A).

So, when we add up 2 numbers let's say A and B, the result is always a 3rd number which is C.

Similarly, when we subtract a number from another number (B - A), the result is always a third number C.

So, (C) C closely approximates the difference between B and A (B - A).

Therefore, point (C) C closely approximates the given mathematical operation that is the difference between B and A (B - A).

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The only quantities that will be directly proportional are; A) distance and time traveled if speed is a constant 77 mph

Direct proportionality means the change of a similar kind.

For example, as pressure increases, density also increases, which means both the parameters (pressure and density) are experiencing a similar kind of change i.e. increment in their magnitude.

Looking at the given options;

A) Distance and time traveled if speed is a constant 77 mph.

Now, formula for speed is;

Speed = Distance/Time

Thus, if speed is constant, then it means that distance varies  directly with the time because as distance increases, then time also increases.

B) We are told that the distance traveled is 110 miles.

Distance = Speed * time.

Thus, speed and time vary indirectly with the time because as one increases, the other decreases

C) Since the amount of money spent is constant, then it means that;

Amount spent = Price per item * number of items

The price per item and the number of items bought will vary indirectly

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The equation that calculates the time taken to get to Springfield is x = 926/57

Rate is used to establish the relationship between two quantities of different units. one of the quantity is usually expressed to unity in order to estimate the change in the other quantity.

If Hillwood and Springfield are 926 mile apart, and the speed taken to get to Springfield is 57miles per hour.

Let the time taken to get to Spring field be x.

Then if 57 miles is covered in an hour and it takes x hours to get to the destination

It means total distance covered is 57 × x

This distance is equal to the distance from Hillwood to Springfield which is 926 miles.

Equating both equations.

57x = 926

In conclusion, 57x = 926 is the equation that can be used to find out the time taken.

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The members and non-members who pay the equal cost after 5 visits for the local zoo.

For the given question;

The cost of membership of local zoo is $135 for members.

The parking cost is $3 for members.

Non-member admission cost is $25 for the zoo and $5 for the parking.

Let the number of number of visits paid the same amount be 'x'.

Then, the equation becomes.

Members: m = 135 + 3x

Non-Members: n = 25x + 5x

As, members and non-members are equal.

m = n

Put the values;

135 + 3x =  25x + 5x

135 + 3x = 30x

27x = 135

x = 5

Thus, members and non-members who pay the equal cost after 5 visits.

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The factor that is the least important thing for Lelia to consider right now is D. Average cost of Uber, Lyft, or taxi fare.

It should be noted that Leila just graduated from college and is comparing a few different cities to move to.

It's important for her to consider the average rent for an apartment, food and grocery store options in the area, and employment opportunities.

In this case, the. oat of Uber isn't necessary. The correct option is D.

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Leila just graduated from college and is comparing a few different cities to move to. Which of these factors is the LEAST important thing for her to consider right now?

Average rent for an apartment

Food and grocery store options in the area

Employment opportunities

Average cost of Uber, Lyft, or taxi fare

The insurance company will pay $10000 while Roger's share will be $4800 and therefore he must pay $4,800 in the insurance claim.

From the information, Roger Laut, who lives in Territory 5, carries 10/20/5 compulsory liability insurance along with optional collision that has a $1,000 deductible.

An insurance claim is a formal request for payment for losses protected by your insurance policy. A contract between you and your insurer is known as an insurance policy. You must pay a predetermined premium. With a $5,000 maximum limit on property damage, the insurance provider will pay losses up to $10,000 for one injured or killed person and up to $20,000 for several persons. This slab is for any accident.

Roger's share will be $4800 because the cost of repairing the other car is only expected to be around $4800. He's got $4,800 to pay.

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The ratios of y/x are the same for the graph of y = 3x

and the ratios of y/x are NOT the same for the graph of  y = 3x + 4

In this question, we have been given the graphs of lines y = 3x and y = 3x + 4.

Consider the ratios of y/x for the graph y = 3x

6/2 = 3

3/1 = 3

(-6)/(-2) = 3

Consider the ratios of y/x for the graph y = 3x + 4.

7/1 = 7

(1)/(-1) = -1

(-2)/(-2) = 1

We can observe that the ratios of y/x are the same for the graph of y = 3x

and the ratios of y/x are different for the graph of  y = 3x + 4.

Therefore, the ratios of y/x are the same for the graph of y = 3x

and the ratios of y/x are NOT the same for the graph of  y = 3x + 4

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Answer:

The number is 5.

Step-by-step explanation:

Let x be the number.

[tex]3x - 8 = x + 2[/tex]

[tex]2x = 10[/tex]

[tex]x = 5[/tex]

Trigonometric functions using the ratio of two sides of a triangle can be used to solve D.right triangles.

To solve for a missing side of a right angle, one can use trigonometric functions that will use the ratio of the other two known sides of the triangle in question.

For instance, using the trigonometric function of Sin can allow for the use of the opposite side and the hypotenuse to find the adjacent side. The Cos and Tan can also be used for the other sides.

This means that either of two sides (including the hypotenuse) can be used to find the other.

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The answer to your question is =

0.583333333

I believe the answer is 0.58333333333. I think it would be 0.583 if you rounded it up. Hope this helps:)

Answer:

1/8

Step-by-step explanation:

First Pick P(red card) = 26/52 = 1/2

Second Pick after replacement P(heart) = 13/52 = 1/4

P(red on first pick and heart on second pick

= 1/2 x 1/4 = 1/8

The graph of the linear function w(x) = 0.6x+2 has been plotted

The given linear function is

w(x) = 0.6x+2

The domain is the set of all possible inputs of the functions.

The range is the set of  all possible outputs of the functions

Here we will substitute some values of x that is the domain of the function and the result will be the range of the function

w(-3) = 0.6×-3+2

= 0.2

w(-2) = 0.6×-2+2

= 0.8

w(-1) = 0.6×-1+2

= 1.4

w(0)  = 0.6×0+2

= 2

w(1) = 0.6×1+2

= 2.6

w(2) = 0.6×2+2

= 3.2

w(3) = 0.6×3+2

= 3.8

Plot the graph using the domain and range

Hence, the graph of the linear function w(x) = 0.6x+2 has been plotted

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Answer:

y = (7/4)x + 2

Step-by-step explanation:

(-4, -5) and (0, 2)

(x₁, y₁) (x₂, y₂)

y₂ - y₁ 2 - (-5) 2 + 5 7

m = ------------- = ------------- = ------------- = --------

x₂ - x₁ 0 - (-4) 0 + 4 4

(it doesn't matter which points you put)

y - y₁ = m(x - x₁)

y - 2 = (7/4)(x - 0)

y - 2 = (7/4)x - 0

+2 +2

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

y = (7/4)x + 2

I hope this helps!

Answer:

1 × 10^-4

Step-by-step explanation:

This is because after the decimal point there are 4 numbers so u have to put -4, and the 1 is there because of the last number

Answer:

1 × 10^-4

Step-by-step explanation:

The required inequality is k > -8.48. Option A is correct.

Given that,

To determine the equivalent expression to the k / -1.6 > -5.3

What is inequality?

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

As per the given condition, we have to simplify the given expression to get the equivalent expression,

k / -1.6 > -5.3

k > -1.6 (-5.3)

k >- 8.48.

Thus, the required inequality is k > -8.48. Option A is correct.

Applying the side splitter theorem

we have that

PT/TS=PQ/QR

so

substitute the given values

7/21=PQ/27

solve for PQ

PQ=27*7/21

PQ=9

Find the value of PR

PR=PQ+QR

PR=9+27

The function y =|x|+3 has been plotted in the graph and

Domain =  {-4, -3, -2, -1, 0, 1, 2, 3, 4}

Range =  {7,6,5,4,3}

The function y =|x|+3

The some values of x = -4, -3, -2, -1, 0, 1, 2, 3  and 4

Substitute the values in the function

y=|-4|+3 =7

y=|-3|+3 = 6

y=|-2|+3 = 5

y=|-1|+3 = 4

y=|0|+3 = 3

y=|1|+3 = 4

y=|2|+3 =5

y=|3|+3 = 6

y=|4|+3 = 7

Using the values complete the graph

The domain is the set of all possible inputs of the function

Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}

The range is the set of all possible outputs of the function

Range = {7,6,5,4,3}

Hence, the function y =|x|+3 has been plotted in the graph and, the Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}

Range = {7,6,5,4,3}

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[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+3} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(1)}~~~~ ,~~~~ 3-\cfrac{ (6)^2}{4(1)}\right) \implies \left( - \cfrac{ 6 }{ 2 }~~,~~3 - \cfrac{ 36 }{ 4 } \right)\implies (\stackrel{x}{-3}~~,~~-6)[/tex]

Answer:

D

Step-by-step explanation:

[tex]-3(3+p)<-66 \\ \\ 3+p>22 \\ \\ p>19[/tex]

The total cost of the metal needed to cover the tank shaped like a metal is $5,099.36.

In order to determine the total metal cost, we are to first calculate the total surface area of the tank. Since the tank is a closed cylinder, we are to determine the total surface area of a cylinder.

The total surface area of a closed cylinder can be determined by adding the area of all its faces.

Total surface area of the closed cylinder = 2πr(r + h)

Where:

r = radius = diameter / 2 = 8/2 = 4ft

h = height

π = pi = 3.14

(2 x 3.14 x 4)(4 + 3)

25.12 x 7 = 175.84 ft²

Total cost of the metal = $29 x 175.84 = $5,099.36

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1.Consider a 5-degree-of-freedom t distribution. P (t≤1.05)=0.829.

2. Think about a t distribution with 26 possible degree. P(t>c)=0.05 and c=1.7056

Given that,

We have 2 question

1. Consider a 5-degree-of-freedom t distribution.

We have to find P (t≤1.05) at least three decimal places, round your response.

From t- value cumulative distribution function

Given a t-value and the degrees of freedom, locate the area under the t-distribution from -t to t.

P(t≤1.05)=0.829.

Therefore, P(t≤1.05) is 0.829.

2. Think about a t distribution with 26 possible degree. P(t>c)=0.05.

We have to find c at least three decimal places.

From inverse t-value distribution function

t=invT(0.95,26)=1.7056

Therefore, c is 1.7056

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The sample proportion saying that the food is delicious will be approximately normal.

In this question, we have been given that 87% of the people who sampled their food said that it was delicious

so, the Population proportion = 87%

A random sample of 144 people is obtained from a population of 5,000. The 144 people are asked to sample the caterer's food.

The sample size of 144 from 5000 will have proportion p cap which will follow a normal distribution with mean= p = 87%

and variance = npq

Since the mean of the sampling distribution of p hat, mean is 0.87 the sample proportion saying that the food is delicious will be approximately normal.

Therefore, the sample proportion saying that the food is delicious will be approximately normal.

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From the given vectors, we have that:

a) The vectorial products are given as follows:

b) The angle between vectors a and c is of 6.84º.

A vectorial product between two vectors A and B is found from the determinant of a matrix, in which:

Then for the vectorial product b x a, the matrix is:

[tex]\left[\begin{array}{ccc}i&j&k\\3&-1&2\\-2&2&1\end{array}\right][/tex]

Using a calculator, the determinant, which is the vectorial product, is given by:

b x a  = -3i - j + 4z.

For the vectorial product a x c, the matrix is:

[tex]\left[\begin{array}{ccc}i&j&k\\-2&2&-1\\-2&3&-1\end{array}\right][/tex]

a x c  = 1i - 2z.

The angle is found as follows:

sin(θ) = |a x c|/(|a| x |c|)

The norms are given as follows:

Hence:

[tex]\sin{\theta} = \frac{\sqrt{5}}{3\sqrt{14}}[/tex]

[tex]\theta = \sin^{-1}{\left(\frac{\sqrt{5}}{3\sqrt{14}}\right)}[/tex]

θ = 6.84º.

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Taking into account the definition of a system of linear equations, the  local hamburger shop sold 199 hamburgers on Thursday.

A system of linear equations is a set of equations in which every equation is linear., in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

h + c= 449

h= c - 51

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

c - 51 + c= 449

c+ c= 449 + 51

2c= 500

c= 500÷2

c= 250

Remembering that h= c - 51, you get:

h= 250 - 51

h= 199

Finally, 199 hamburgers were sold on Thursday.

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The elements that are neither in set A nor set B are: {10}

Answer: 10