Determine whether f has an inverse function. If it does, find the inverse function and state any restrictions on its domain:

f(x) =\(\frac{x - 7}{x + 4}\)

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

The trigonometric rations of the sine functions are:

Sin α = opposite side / hypotenuse. Cos α = adjacent side / hypotenuse.

Tan α =  opposite side / adjacent side.

From the given figure, ∠P=90° and ∠R+∠Q=90°.

According to the Pythagoras's Theorem,

(PQ)² = √(50)² - (14)²

(PQ)² = 2500-196= 2304

PQ = √(2304)

PQ= 48 units

Blank 1: Sin Q = opposite side / hypotenuse

Sin Q = 14/50

Sin Q = 0.28

Blank 2: Cos Q = adjacent side / hypotenuse

Cos Q = 48/50

Cos Q = 0.96

Blank 3: Tan Q = opposite side / adjacent side

Tan Q = 14/48

Tan Q = 0.29

Blank 4: Sin R = opposite side / hypotenuse

Sin R = 48/50

Sin R = 0.96

Blank 5: Cos R = adjacent side / hypotenuse

Cos R = 14/50

Cos R = 0.28

Blank 6: Tan R = opposite side / adjacent side

Tan R = 48/14

Tan R = 3.42

Therefore, these are the trigonometric ratios that are given in the sum.

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Answer:

Step-by-step explanation:

When x =3 y=-1

X =2 y =0

X=0 y =3

X = -1 y=6

So c g d f true

Answer:

F

Step-by-step explanation:

Answer:

Length is 7 units

Step by Step explanation:

Assuming you mean the Area is 28 square units

Then

L = w + 3

A = w(w + 3)

28 = w2 + 3w

We can subtract 28 from both sides of the equation to obtain the Quadratic

w2 + 3w - 28 = 0

Factoring to give

(w + 7)(w - 4) = 0

The width cannot be -7

w = 4

L = w + 3

L = 4 + 3 = 7

The width of the rectangle is 4 units and the length of the rectangle is 7 unites.

Answer:

1) gradient  (00) (-2 4) = y2-y1 / 2-1 = 4/-2 = -2  m = -2/1  means = m = -2  (negative slope)   2)  gradient  y2-y1 / x2-x1 = 3-0 / 2-0  = 3/2 = (1 1/2)/1   m = 1 1/2  (positive slope) we use the formula y-values divided by the change in the x-values.    The equation of the gradient each goes like this 1) y = -2x   as y is at origin nothing else to add     The equation of the gradient each goes like this 2) y = 1  1/2x     The equation of the point formula  1) we take the y -y1 = m (x +x 1)  =  y-0 = -2x (x +0)  (as m = -2) y = -2(x +0)   and  The equation of the point formula  2)  y - 0 = m ( x +x1)     y - 0 = 1 1/2( x +0)  = y = 1 1/2( x +0)

Answer:

este patruzece

Step-by-step explanation:

In a given study that the null hypothesis asserts the expected value of a phenomenon is 100 resulting in a 95% confidence interval reported as [98.76, 105.24], then we fail to reject the null hypothesis.

Therefore the answer is d) Fail to reject the null hypothesis.

A 95% confidence interval is a range of values that there is a 95% chance that the true value of a population parameter falls within. In this case, the 95% confidence interval is [98.76, 105.24], which includes the expected value of 100 that is stated in the null hypothesis.

Therefore, we fail to reject the null hypothesis because the data does not provide sufficient evidence to suggest that the true value of the population parameter is different from what is stated in the null hypothesis.

It's worth to mention that, Failing to reject the null hypothesis doesn't mean accepting it, it means that we don't have enough evidence to say that the parameter is different from the null hypothesis, it could be due the sample size, or other factors.

--The question is incomplete, complete question is as follows--

"Assume for a given study that the null hypothesis asserts the expected value of a phenomenon is 100. A research study results in a 95% confidence interval reported as [98.76, 105.24]. What decision would you make based on this confidence interval?

a) A decision cannot be made on a confidence interval; a hypothesis test is required.

b) Retain the null hypothesis.

c) Reject the null hypothesis.

d) Fail to reject the null hypothesis."

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Answer:

The answer is b

Step-by-step explanation:

The data in the Restaurant Line file contains 10 observations of the number of people in line ahead of a customer and the actual waiting time.

The owners of small restaurants in cities like Portland, Oregon, often choose not to take reservations due to the cost of no-shows and the desire to focus on customer service instead of maintaining a reservation system. However, it is important to provide customers with reasonable estimates of waiting time when they arrive and put their name on the waiting list. To address this, the data was used to estimate a regression equation, which can be used to predict waiting time based on the number of people in line ahead of a customer.

The estimated regression equation is -7.82+8.84% with a mean squared error (MSE) of 113.9197. This means that for every additional person in line ahead of a customer, the predicted waiting time increases by 8.84%. The negative intercept (-7.82) indicates that even when there are no people in line ahead of a customer, there is still an expected waiting time of approximately 8 minutes.

The MSE of 113.9197 indicates that the predictions from the regression equation may have some error, but overall it is a useful tool for estimating waiting times based on the number of people in line. By using this equation, small restaurants can provide customers with more accurate estimates of their wait time, leading to better customer satisfaction and improved overall experience.

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They are congruent, therefore both are 78°

Answer:

x=-3.5 and y=6.25

Step-by-step explanation:

x+2y=9

x=9-2y

-6(9-2y)+4y=46

-54+12y+4y=46

16y-54=46

16y = 100

y = 100/16 = 50/8 = 25/4 = 6.25

x+2(6.25)=9

x+12.5=9

x= -3.5

The expression shows the area of the shaded region in terms of A and B are 4A + B, 1.5B, and 12A.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

Given

The area of one of the small right triangles outlined in blue is A cm2, while the area of the square outlined in red is B.

There are 4 triangles with an area of 4 so that is 4A and since there is only one square the area of the whole thing is 4A+B.

Each triangle is also equal to 1/8 of the square.

This means A=B/8 or B=8A.

First replacing B in the previous equation you get 4A+8A which is 12A.

Then replacing A with B/8 you get 4(B/8)+B which is B/2+B which is 3B/2 and 3/2 is 1.5 so 3/2B is equal to 1.5B.

Hence, the expression shows the area of the shaded region in terms of A and B are 4A + B, 1.5B, and 12A.

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Answer: 60 Votes

Step-by-step explanation:

540 divded by 9 which equals 60 votes.

So Student B received 60 votes.

60 votes was received by student B.

540/9=60

If the price paid for a certain item is $40 and the consumer surplus is $4, then the maximum buying price for that item is $44 .

The Consumer's Surplus is defined as the difference between the maximum price a consumer is willing to pay for an item and the actual price paid for the item.

If the price paid for the item is $40 and the consumer's surplus is $4, then the maximum buying price for that item can be calculated as :

⇒ Maximum buying price = Price paid + Consumer's surplus

Substituting the values of Price paid and consumer surplus ,

we get ;

⇒ $40 + $4

⇒ $44

Therefore , the maximum buying price for that item is $44 .

The given question is incomplete , the complete question is

If the price paid for a certain item is $40 and the consumer surplus is $4, then what is the maximum buying price for that item ?

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Answer:

x + y = 5

Step-by-step explanation:

\( {4}^{x} . {4}^{y} = 1024 \\ \\ {4}^{x + y} = {4}^{5} \\ \\ x + y = 5\)

Answer:

x + y = 5

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{m+n}\) , then

\(4^{x}\) × \(4^{y}\) = \(4^{x+y}\) , so

\(4^{x+y}\) = 1024 = \(4^{5}\)

since the bases on both sides are equal, both 4 then equate exponents

x + y = 5

Answer:the quadratic function in f(x)= a(x-h)^2+k is f(x) = - (x - 2)² + 2.I think this is false";}

Step-by-step explanation:

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Answer: x = 9

Explanation:

17x = 153

x = 9

I hope this helped!

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- Zack Slocum

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Answer:

9

Step-by-step explanation:

153/17=9

Answer:

3,5?

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

joshua times 3 is basically derrick's amount

so 3j = d

Answer:

D

Step-by-step explanation:

Im smart trust me its this one

1. The sequence \(X_n = 8n^3/(2+n^3)\) converges to 8.

2. The sequence \(X_n = (2n-1)/(4n+1)\) converges to 1/2.

1) To prove that the sequence \(X_n = 8n^3/(2+n^3)\) converges to 8, we need to show that for any positive epsilon (ε), there exists a positive integer N such that for all n > N, the terms of the sequence \(X_n\) are within ε of the limit 8.

Let's proceed with the epsilon argument:

We want to find N such that for all n > N, \(|X_n - 8|\) < ε.

\(|X_n - 8| = |8n^3/(2+n^3) - 8|\)

Now, we can simplify the expression:

\(|8n^3/(2+n^3) - 8| = |8n^3/(2+n^3) - (8(2+n^3))/(2+n^3)|\)

\(= |(8n^3 - 16 - 8n^3)/(2+n^3)|\)

\(= |-16/(2+n^3)|\)

Since 16 is a positive constant, we can rewrite the expression as:

\(|-16/(2+n^3)| = 16/(2+n^3)\)

Now, we want to make this expression less than ε:

\(16/(2+n^3) < \epsilon\)

To find N, we can set the expression to ε and solve for n:

\(16/(2+n^3) = \epsilon\)

Simplifying further:

\(2+n^3\) = 16/ε

\(n^3\) = (16/ε) - 2

\(n = ((16/\epsilon) - 2)^{(1/3)\)

Let N be the ceiling of the value of n calculated above. Then, for all n > N, the terms of the sequence \(X_n\) will be within ε of the limit 8.

Therefore, the sequence \(X_n = 8n^3/(2+n^3)\) converges to 8.

2) To prove that the sequence \(X_n\) = (2n-1)/(4n+1) converges to 1/2, we need to show that for any positive epsilon (ε), there exists a positive integer N such that for all n > N, the terms of the sequence \(X_n\) are within ε of the limit 1/2.

Let's proceed with the epsilon argument:

We want to find N such that for all n > N, |\(X_n\) - 1/2| < ε.

|\(X_n\) - 1/2| = |(2n-1)/(4n+1) - 1/2|

Now, we can simplify the expression:

|(2n-1)/(4n+1) - 1/2| = |(2n-1 - (4n+1))/(4n+1)|

= |(2n-1 - 4n - 1)/(4n+1)|

= |-2n - 2)/(4n+1)|

= (2n+2)/(4n+1)

Now, we want to make this expression less than ε:

(2n+2)/(4n+1) < ε

To find N, we can set the expression to ε and solve for n:

(2n+2)/(4n+1) = ε

Simplifying further:

2n+2 = ε(4n+1)

2n+2 = 4εn + ε

2 - ε = (4ε - 2)n

n = (2 - ε)/(4ε - 2)

Let N be the ceiling of the value of n calculated above. Then, for all n > N, the terms of the sequence \(X_n\) will be within ε of the limit 1/2.

Therefore, the sequence \(X_n = (2n-1)/(4n+1)\) converges to 1/2.

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Answer:

\(x=8,\:x=-3\)

Step-by-step explanation:

\(x^2-5x-24=0\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-5,\:c=-24:\quad x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\left(-24\right)}}{2\cdot \:1}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=8,\:x=-3\)\(=\frac{5+\sqrt{\left(-5\right)^2+4\cdot \:1\cdot \:24}}{2\cdot \:1}\\5+\sqrt{\left(-5\right)^2+4\cdot \:1\cdot \:24}\\5+\sqrt{121}\\=\frac{5+\sqrt{121}}{2}\\=\frac{5+11}{2}\\=\frac{16}{2}\\=8\\\frac{-\left(-5\right)-\sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-24\right)}}{2\cdot \:1}\\=\frac{5-\sqrt{\left(-5\right)^2+4\cdot \:1\cdot \:24}}{2\cdot \:1}\\5-\sqrt{\left(-5\right)^2+4\cdot \:1\cdot \:24}\\\left(-5\right)^2\\=25\\4\cdot \:1\cdot \:24\\=96\\=5+\sqrt{25+96}\\\)

\(\frac{5-\sqrt{121}}{2\cdot \:1}\\\frac{5-11}{2}\\=-\frac{6}{2}\\=-3\\\)

Answer:

18

Step-by-step explanation:

for every one cup there are 3 one third servings so all you have to do is simply multiply 3 by 6.

Answer:

i think 18 because if it was 2 cups it will be 6 , cheack if 18 in ur choices

Step-by-step explanation:

Answer:

Step-by-step explanation:

the rest are incorrect

The required plant grew 9 centimeters in the sixth week.

Let x be the number of centimeters the plant grew in the sixth week.
To estimate x, we can use the formula for the mean (average) of a set of numbers:

mean = (sum of numbers) / (number of numbers)

We know the mean for 6 weeks is 9, so we can write:

9 = (13 + 6 + 10 + 5 + 11 + x) / 6

Multiplying both sides by 6, we get:

54 = 45 + x

Subtracting 45 from both sides, we get:

x = 9

Therefore, the plant grew 9 centimeters in the sixth week.

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Answer:

The formula for circumference of a circle is C = πd, where C is the circumference and d is the diameter.

We are given that the circumference is 48.984 feet, and we can use the approximation of π as 3.14.

Substituting into the formula, we have:

48.984 = 3.14d

To solve for d, we divide both sides by 3.14:

d = 48.984 / 3.14

d ≈ 15.6 feet

Therefore, the floor's diameter is approximately 15.6 feet.

Answer:

-100

Step-by-step explanation:

1/5 of -125 will be -25.

So, if she deposits 1/5 of what she owes, then she will deposit $25.

Her balance will then become -100 because she paid back 25.

Her new balance is -100