Which will form a composite function?

Answer:

[tex]6.25x+7.50=26.25[/tex]

Clara played 3 rounds of golf.

Step-by-step explanation:

The admission fee is = $7.50

Let the number of rounds be = x

Each round costs = $6.25

Total money Clara paid = $26.25

We can denote this in equation form as:

[tex]6.25x+7.50=26.25[/tex]

Now we will solve for x

[tex]6.25x=26.25-7.50[/tex]

=> [tex]6.25x=18.75[/tex]

=> x = 3

Hence, Clara played 3 rounds of golf.

The equation used to determine the number of rounds, x, that Clara golfs is 6.25x + 7.50 = 26.25

An equation is an expression that is used to show the relationship between two or more variables and numbers.

Let x represent the number of rounds that Clara golfs.

The total amount Clara pays for admission and the number of rounds she golfs is $26.25, hence this is given by:

The equation used to determine the number of rounds, x, that Clara golfs is 6.25x + 7.50 = 26.25

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Answer:

B

Step-by-step explanation:

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]

Given m = - [tex]\frac{5}{6}[/tex], then

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{-\frac{5}{6} }[/tex] = [tex]\frac{6}{5}[/tex]

Since m > 0 then lines LM and No are the 2 possible lines

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = L(- 5, - 3) and (x₂, y₂ ) = M(0, 3)

m = [tex]\frac{3+3}{0+5}[/tex] = [tex]\frac{6}{5}[/tex]

Hence the required line is LM

Answer:

Line LM

Step-by-step explanation:

ANSWER

all real numbers

EXPLANATION

The given absolute value function is

[tex]f(x) = |x + 2| [/tex]

This function is obtained by shifting the graph of

[tex]y = |x| [/tex]

to the left by 2 units.

Since the domain of the parent function is all real numbers, the domain of the transformed function is also all real numbers because the shifting the parent function horizontally or vertically does not affect the domain.

Konichiwa~! My name is Zalgo and I am here to help you out on this beautiful day. The answer is -7x-1. When you input it into the equation, you should get f (-7x-1) = -8.

Answer:

9%

Step-by-step explanation:

To find the percentage of Team B's mean absolute deviation difference in the means, you have to subtract the two means, 59.32-59.1.

After this, divide your answer the the mean absolute deviation of Team B, or you could put it all in the calculator or paper like this:

[tex]\frac{59.32-59.1}{2.4}[/tex]

You'd then end with the decimal: .0916, which you would multiply by 100 to get about 9%

Answer:

A

Step-by-step explanation:

Answer:

[tex]x^{5/12}[/tex]

Step-by-step explanation:

Having a power to a power means that you multiply them:

[tex]x^{5/8 * 2/3} = x^{(5 * 2)/ (8 * 3)} = x^{10/24} = x^{5/12}[/tex]

The simplified expression is  [tex]x^{(\frac{5}{12} )[/tex].

Given that an expression [tex](x^{\frac{5}{8}} )^\frac{2}{3}[/tex], we need to simply it.

To simplify the expression, first, we raise the fraction to the power of 2/3:

Step 1: [tex](x^{\frac{5}{8}} )^\frac{2}{3}[/tex]

Now, when raising a power to another power, we multiply the exponents:

Step 2: [tex]x^{\frac{5}{8} \times \frac{2}{3}[/tex]

To simplify further, we multiply the fractions:

Step 3: [tex]x^{\frac{10}{24}[/tex]

Now, we can simplify the exponent by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2 in this case:

Step 4: [tex]x^{(\frac{5}{12} )[/tex]

So, the simplified expression is  [tex]x^{(\frac{5}{12} )[/tex].

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Answer:

Answer will be: Jeremy is looking at the rate for renting a bike for 2 hours. To find the rate for one hour divide 7 by 2. The rate for renting a bike for one hour is $3.50.

The mistake that jeremy made is that the cost renting is not $7.00 for hour, it is $7.00 for two hours.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value

Given:

The table is attached below

Jeremy said the cost bike renting for an hour is $7.00. But looking at the table the difference between two consecutive cost is $7.00 not in the gap of 1 hour in fact in gap of 2 hours.

It means that the the cost of bike renting $7.00 is for 2 hours.

For an hour the cost for renting bike will be,

=7/2

=3.5 hours.

Hence, the cost of bike renting is 3.5 hours per hour.

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Final answer:

The total number of roots in the function H(x) = x³ - 7x² - x + 7 is 3, with 2 real roots and 1 complex root.

Explanation:

The function H(x) = x³ - 7x² - x + 7 is a cubic function, meaning it is a polynomial of degree 3. The total number of roots for a cubic function is always 3. This is because the highest power of x in the function is 3.

To determine the number of real roots, we can use the rule of signs. We count the number of sign changes in the coefficients of the function. In this case, we have two sign changes from positive to negative. Therefore, there are either 2 or 0 real roots.

To find the number of complex roots, we subtract the number of real roots from the total number of roots. So, in this case, there must be 3 - 2 = 1 complex root.

The number of roots that the function H(x) has is: a total of 3 roots

What is the number of roots of the Polynomial?

The function H(x) = x³ - 7x² - x + 7 is a polynomial of degree 3.

According to the fundamental theorem of algebra, a polynomial of degree n has exactly n roots, counting multiplicities.

In this case, the function has 3 roots, which may be real or complex, taking into account their multiplicities. The number of roots is determined by the degree of the polynomial, and the roots are the values of x for which the polynomial is equal to zero. Therefore, the function H(x) has a total of 3 roots

Answer:

Step-by-step explanation:

Point slope form is y-y1=m(x-x1)

(x1,y1) is (-9,-3)

m is -6

Plug in!

y-(-3)=(-6)(x-(-9)) The answer could look like this.

y+3=-6(x+9)    Or this.

y=-6(x+9)-3     Or this

y=-6x-54-3     Even this but unlikely...

y=-6x-57         Or this.

I will change my answer after choices are posted.

Answer:

y+3 = -6(x+9)  point slope form

y = -6x-57  slope intercept form

Step-by-step explanation:

We can use the point slope equation of a line

y-y1 = m(x-x1)

y--3 = -6(x--9)

y+3 = -6(x+9)

If we want the equation in point slope form

Distribute the -6

y+3 = -6x -54

Subtract 3 from each side

y+3-3 = -5x-54 -3

y = -6x-57

Answer:

this is the diagram

Step-by-step explanation:

Answer:

11 has 85° because it is opposite to 9

Step-by-step explanation:

If x is 12 units away from 20 it is either 20-12 or 20+12 so the two possibilities would be 8 or 32

Hope this helps!!

The equation is x = 20 + 12 or x = 32 if "x is 12 units from 20" into an equation here x is the real number.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Translate "x is 12 units from 20" into an equation.

Here x is a real number.

The linear equation can be framed as follows:

x = 20 + 12

x = 32

Thus, the equation is x = 20 + 12 or x = 32 if "x is 12 units from 20" into an equation here x is the real number.

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Answer:

a) y=1/3 sqrt(x+1)

b) 2/3

c) 224

Step-by-step explanation:

a) y varies directly to sqrt(x+1)

means there is some constant k such that y=ksqrt(x+1)

y=1 when x=8  (plug this in and find k)    1=ksqrt(8+1)

                                                                 1=ksqrt(9)

                                                                 1=k(3)

                                                                 1/3=k

So the equation is y=1/3 * sqrt(x+1)

a)  y=1/3 *sqrt(x+1)

b) what is y when x=3 if you have y=1/3 * sqrt(x+1)

Plug in 3 for x            

y=1/3 *sqrt(3+1)

y=1/3 *sqrt(4)

y=1/3 *2

y=2/3

b) 2/3

c) what is x when y=5

Plug in 5 for y

5=1/3 *sqrt(x+1)

multiply both sides by 3

15=sqrt(x+1)

square both sides

225=x+1

subtract 1 on both sides

224=x

c) 224

Answer:

ED = 5π/6

Step-by-step explanation:

First convert angles into radians by using formula 1° = π/180 rad

So, 50° becomes 5π/18.

Now using formula,

angle = length of arc / radius of circle

we get,

5π/18 = length of arc / 3

Hence , length of arc = 5π/6

Answer:

ED ≈ 2.62 in

Step-by-step explanation:

The length of the arc ED is calculated as

ED = circumference × fraction of circle

     = 2πr × [tex]\frac{50}{360}[/tex]

     = 2π × 3 × [tex]\frac{5}{36}[/tex]

     = 6π × [tex]\frac{5}{36}[/tex]

     = [tex]\frac{5\pi }{6}[/tex] ≈ 2.62 in ( to 2 dec. places )

Answer:

1. P(5 U 6) =2/3

2. P(2 U 5 U 6) = 5/6

3. P(1 U 2) = 1/3

4. P(4) = 0

Step-by-step explanation:

As the number cube has 6 sides,

So,

Total outcomes = {1,2,5,5,6,6}

n(S) = 6

Now,

1. P(5U6) = P(5) + P(6)

P(5)=2/6=1/3

P(6)=2/6=1/3

P(5U6)= 1/3 + 1/3 = 2/3

2. P(2 U 5 U 6) = P(2) + P(5) + P(6)

P(2)=1/6

P(5)=2/6

P(6)=2/6

P(2 U 5 U 6) = 1/6 + 2/6 + 2/6

= 5/6

3. P(1 U 2) = P(1) + P(2)

P(1) = 1/6

P(2)= 1/6

P(1 U 2) = 1/6 + 1/6

= 2/6 = 1/3

4. P(4) = 0

As 4 is not in the outcomes, it's probability will be zero ..

Answer: We need a picture or a description of how we need to find the value ok k.

Step-by-step explanation:

Answer:

600 feet

Step-by-step explanation:

I am assuming that the park is rectangular, and the together, the length, with and diagonal form a right triangle.

In this case, we are given

Diagonal = 750 ft = hypotenuse

Width = 450 feet

Find length L

Using the Pythagorean theorem,

L² + 450² = 750²

L² = 750² - 450² = 360,000

L= √360,000 = 600 feet

Answer:

C, 600 ft.

Step-by-step explanation:

a^2+b^2=c^2

C is always the hypotenuse/diagonal. Let A represent length and B represent width.

A^2+450^2=750^2

A^2+202500=562500

562500-202500=360000=A^2

take the square root of both sides to solve for A and the value of A is 600.

Answer:

D. y - 5 =3(x + 1)

Step-by-step explanation:

y = -1/3x -6

The slope is -1/3

Take the negative reciprocal to find the slope of the line that is perpendicular

- (-3) = 3

The slope would be 3

We have the slope and a point

Using point slope form

y-y1 = m(x-x21)

y-5 = 3(x--1)

y-5 = 3(x+1)

Answer:

D. y - 5 =3(x + 1)

Step-by-step explanation:

Given equation of line:

[tex]y = -\frac{1}{3}x-6[/tex]

Comparing it with the standard form of equation of line

y=mx+b

m = -1/3

Let m1 be the slope of line perpendicular to the given line.

We know that the product of slopes of two perpendicular lines is -1.

[tex]m*m_1 = -1\\-\frac{1}{3} * m_1 = -1\\ m_1 = -1 * -\frac{3}{1}\\ m_1 = 3[/tex]

The equation of line in point slope form is:

[tex]y-y_1 = m(x-x_1)[/tex]

where x_1 and y_1 is the point from which the line passes.

So, putting the values of slope and point,

[tex]y-5 = 3[x-(-1)]\\y-5=3(x+1)[/tex]

Option D is correct ..

Answer:

Option B and C  are correct.

Step-by-step explanation:

We need to find the pattern of the values in the table and find the values of a and b.

6³ = 216

216/6 = 36

6² = 36

36/6 = 6

6¹ = 6

6/6 = 1

6⁰ = 1

1/6 = 1/6

6⁻¹ = 1/6

1/6*1/6 = 1/36

6⁻² = 1/36

So, value of a = 1/6

and value of b = 1/36

And we have seen as the exponent is decreasing, each previous value is divided by 6.

So, Option B and C  are correct.

Answer:  The correct options are

(B) the value of b is [tex]\dfrac{1}{36}.[/tex]

(C) As the value of the exponent decreases, each previous value is divided by 6.

Step-by-step explanation:  We are given that Tori examined the pattern of exponents in the following table :

[tex]\textup{power of 6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{value}\\\\6^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~216\\\\6^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~36\\\\6^1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6\\\\6^0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1\\\\6^{-1}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a\\\\6^{-2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~b[/tex]

We are to select the true statements based on the above pattern.

We will be using the following property of exponents :

[tex]x^{-y}=\dfrac{1}{x^y}.[/tex]

Therefore, we get

[tex]a=6^{-1}=\dfrac{1}{6^1}=\dfrac{1}{6}.[/tex]

and

[tex]b=6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}.[/tex]

Also, the value of the exponent is decreasing and we see that

[tex]\dfrac{216}{36}=\dfrac{36}{6}=\dfrac{6}{1}=\dfrac{1}{\frac{1}{6}}=\dfrac{\frac{1}{6}}{\frac{1}{36}}=6.[/tex]

So, each previous value is divided by 6.

Thus, the correct options are

(B) the value of b is [tex]\dfrac{1}{36}.[/tex]

(C) As the value of the exponent decreases, each previous value is divided by 6.

Answer:

Mean Absolute Deviation (MAD): 8.5

Step-by-step explanation:

Xmean = (28 + 32 + 47 + 16 + 40 + 35 + 38 + 54)/8  = 290/8

Xmean = 36.25

MAD =

(28 - 36.25) + (32 - 36.25) + (47 - 36.25) + (16 - 36.25) + (40 - 36.25) + (35 - 36.25) + (38 - 36.25) + (54 - 36.25)  divided by 8

a break down of each ( )

(8.25) + (4.25) + (10.75) + (20.25) + (3.75) + (1.25) + (1.75) + (17.75)  divided by 8  =  68

then you take 68/8 = Mean Absolute Deviation  8.5

Answer:

Mean Absolute Deviation (M.A.D): 8.5

Step-by-step explanation:

1. To find the mean absolute deviation of the data, start by finding the mean of the data set.

2. Find the sum of the data values, and divide the sum by the number of data values.

3. Find the absolute value of the difference between each data value and the mean: |data value – mean|.

4. Find the sum of the absolute values of the differences.

5. Divide the sum of the absolute values of the differences by the number of data values.

Hope that helped! :)

Answer:

A.  

The model is not a good fit.

Step-by-step explanation:

The correlation coefficient is a measure of the degree of association between two quantitative variables , such as weight and height.

On the other hand, the quantity R-squared is an indicator of the predictive power of a model. It is an indicator of how well the model fits the data. R-squared is the coefficient of determination.

R-squared = the square of the correlation coefficient

                  = 0.6 * 0.6

                  = 0.36

Therefore, only 36% of the variations in the dependent variable can be explained by the model. More than 50% can thus not be explained by the model. The model is thus not a good fit.

Answer:

A the model is not good

Step-by-step explanation:

Final answer:

The domain of the pancake mix function N(p) is 0 <= p <= 4 and the range is 0 <= N(p) <= 480, assuming the school has 4 packages and each package feeds 120 people.

Explanation:

The high school pancake breakfast fundraiser question deals with writing the domain and range for a given function. Our function is N(p) = 120p, where N(p) represents the number of people fed by p packages of pancake mix, and each package feeds 120 people. Since the school has 4 packages of pancake mix, the domain, which is the set of all possible values of p (packages), would be 0 <= p <= 4, as they cannot use negative packages and have only 4 packages available. The corresponding range would be the number of people that can be fed, which is from 0 to 4 times 120, so 0 <= N(p) <= 480.

Answer:

B. 24

Step-by-step explanation:

it takes 60 minutes for one and 40 for another. since you don't know the time. the denominator is going to be x. The equation to solve this problem will be x/60 + x/40 = 1. Since you're adding, you want to have the same denominator. ( i chose to do 120) this will change the problem to 2x/120 + 3x/120 = 1. which will simplify to 5x/120=1. Multiply each side by 120 to get 5x=120 and divide each side by 5 to get x=24.

Answer: Third option.

Step-by-step explanation:

Given the expression [tex]\frac{2x+4}{x+1}+\frac{-x+5}{x+1}[/tex] you need to make the addition indicated.

First, it is important to remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Therefore, since both fractions have equal denominator, you can rewrite the same denominator and add the numerators. Then you get that the sum is:

 [tex]\frac{2x+4}{x+1}+\frac{-x+5}{x+1}=[/tex][tex]\frac{(2x+4)+(-x+5)}{x+1}=\frac{2x+4-x+5}{x+1}=\frac{x+9}{x+1}[/tex]  

Answer:

The correct answer is third option

(x + 9)/(x + 1)

Step-by-step explanation:

It is given an expression,

(2x + 4)/(x + 1)  + (-x + 5)/(x + 1)

To find the sum

The given expression shows the sum of two fractions,

The denominators are same

(2x + 4)/(x + 1)  + (-x + 5)/(x + 1)

 = [2x + 4 + -x + 5]/(x + 1)

 = (x + 9)/(x + 1)

Therefore the correct answer is third option

(x + 9)/(x + 1)

Answer:

-1/2 b

Step-by-step explanation:

Answer:

The measure of the arc it creates from the central angle is 124°

Step-by-step explanation:

Remember that a central angle's vertex is located on the center of the circle. The measure of the arc, is the same as the measure of the central angle. If it's an inscribed angle, the measure of the arc is two times the measure of the inscribed angle.

Answer:

124

Step-by-step explanation:

a. Your answer and reasoning are correct.

b. If O is the center of the circle, then angle ABO has measure 72º, so that by the law of cosines

[tex]AB^2=6^2+6^2-2\cdot6\cdot6\cos72^\circ\implies AB=3\sqrt{10-2\sqrt5}[/tex]

just to add to the superb reply above by @LammettHash

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=6\\ \theta =72 \end{cases}\implies s=\cfrac{\pi (72)(6)}{180}\implies s=\cfrac{12\pi }{5}\implies s\approx 7.54[/tex]

Answer:

2nd one

Step-by-step explanation:

I think I'm understanding your function to be f(x)=4(1.5)^x.

It goes through (0,4) becuase when x=0, you have y=4(1.5)^0=4(1)=4.

It also increases by a factor of 1.5 each time x goes up by 1.

Example: When x=1, you have 4(1.5)^1=4(1.5)

Another example: When x=2, you have 4(1.5)^2=4(1.5)(1.5).

Those are called factors because the operation is multiplication.

Answer:

b

Step-by-step explanation:

recall your d = rt, distance = rate * time.

s = Samantha's speed rate

one thing to bear in mind is that, when Samantha is going upstream, she's not really going "s" mph fast, because she's going against the current, and the current's rate is 4 mph and subtracting speed from her, then she's really going "s - 4" fast.

Likewise, when she's going downstream because she's going with the current, the current is adding speed to her, so she's going "s + 4" fast.

Now, let's say the distance she covered both ways was the same "d" miles.

Let's recall that since there are 60 minutes in 1 hour, 12 minutes is 12/60 = 1/5 of an hour.

[tex]\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&d&s-4&1\\ Downstream&d&s+4&\frac{1}{5} \end{array}\qquad \implies \begin{cases} d=(s-4)(1)\\ d=(s+4)\left( \frac{1}{5} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{from 1st equation}}{\boxed{d}=s-4}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}~\hfill }{\boxed{s-4}=\cfrac{s+4}{5}\implies 5s-20=s+4} \\\\\\ 4s-20=4\implies 4s=24\implies s=\cfrac{24}{4}\implies s=6[/tex]

Answer:

6 mph

Step-by-step explanation:

Let the the total distance is D and the speed of Samantha's speed in still water is x ( in mph ),

Here, speed of stream = 4 mph,

Thus, the speed in upstream = (x - 4) mph,

Speed in downstream = (x + 4) mph,

We know that,

[tex]Speed =\frac{Distance}{Time}\implies Time =\frac{Distance}{Speed}[/tex]

∴ Time taken in upstream = [tex]\frac{D}{x-4}[/tex]

And, time taken in downstream = [tex]\frac{D}{x+4}[/tex]

According to the question,

[tex]\frac{D}{x-4}=1\implies D = x-4-----(1)[/tex]

[tex]\frac{D}{x+4}=\frac{12}{60}\implies \frac{D}{x+4}=\frac{1}{5}\implies 5D=x+4----(2)[/tex]

Equation (1) - 5 equation (2),

0 = x + 4 - 5x + 20

0 = -4x + 24

4x = 24

⇒ x = 6 mph.

Hence, Samantha swims with the speed 6 mph.

Answer:

[tex]\large\boxed{x=-\dfrac{1}{11}}[/tex]

Step-by-step explanation:

[tex]34x+5-12x=3\qquad\text{subtraxct 5 from both sides}\\\\34x-12x=3-5\\\\22x=-2\qquad\text{divide both sides by 22}\\\\x=\dfrac{-2}{22}\\\\x=-\dfrac{2:2}{22:2}\\\\x=-\dfrac{1}{11}[/tex]

To solve the equation 34x+5−12x=3, we combine like terms to get 22x+5=3, then isolate x to find that x=-1/11.

The student's question, 34x+5−12x=3, presents a linear equation where we need to find the value of x.

To solve for x, we shall first consolidate like terms on the left side of the equation.

We have:

34x - 12x + 5 = 3

22x + 5 = 3

22x = 3 - 5

22x = -2

x = -2/22

x = -1/11

The value of x in this equation is -1/11.