f(x)
9 - 4x
8x - 1
INVERSE??

Answer:

y+2=4(x-1)

y-6=4(x-3)

Step-by-step explanation:

Slope between (3, 6) and (1, -2)

6-(-2)/3-1

8/2

4

y+2=4(x-1)

y-6=4(x-3)

Answer:

[See Below]

Step-by-step explanation:

Point slope form is: [tex]y-y_1=m(x-x_1)[/tex]

'm' is the slope

(x1, y1) is a coordinate point.

Slope is rise over run. [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We are given the points (-1,5) and (3,-3).

[tex]\frac{-3-5}{3-(-1)}=\frac{-8}{4}= -2[/tex]

The slope of the line is -2.

I will use (-1,5) as the point:

[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y-5=-2(x+1)}[/tex]

Slope intercept is: [tex]y=mx+b[/tex]

'm' - Slope

'b' - y-intercept

We can use the point slope equation to convert it into slope intercept form:

[tex]y-5=-2(x+1)\\\\y-5=-2x-2\\\\y-5+5=-2x-2+5\\\\\boxed{y=-2x+3}[/tex]

Standard form is [tex]Ax+By=C[/tex]

Using out slope intercept form equation:

[tex]y=-2x+3\\\\y+2x=-2x+2x+3\\\\1y+2x=3\\\\\boxed{2x+1y=3}[/tex]

Answer:

980 intervals.

Step-by-step explanation:

For each interval, there are only two possible outcomes. Either it captures the population mean, or it does not. One interval is independent of other intervals. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

98% confidence interval

Has a 98% probability of capturing the population mean, so [tex]p = 0.98[/tex]

1000 intervals

This means that [tex]n = 1000[/tex]

How many of these 1000 intervals do you expect to capture the corresponding value of μ?

[tex]E(X) = np = 1000*0.98 = 980[/tex]

980 intervals.

Answer:

1 .angle S is 90 degree

2. 12

3. 155 degree

1. x = 3

hope it helps .....

Answer:

a. There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.

b. Test statistic z=-1.001

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion that correctly identifies the chip is significantly smaller than 50%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi<0.5[/tex]

The significance level is 0.01.

The sample has a size n=199.

The sample proportion is p=0.462.

[tex]p=X/n=92/199=0.462[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{199}}\\\\\\ \sigma_p=\sqrt{0.001256}=0.035[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.462-0.5+0.5/199}{0.035}=\dfrac{-0.035}{0.035}=-1.001[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.001)=0.16[/tex]

As the P-value (0.16) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.

Answer:

[tex]6cm^2[/tex]

Step-by-step explanation:

Let x and y be the sides of the rectangle.

Area of the Triangle, A(x,y)=xy

From the diagram, Triangle ABC is similar to Triangle AKL

AK=4-y

Therefore:

[tex]\dfrac{x}{6} =\dfrac{4-y}{4}[/tex]

[tex]4x=6(4-y)\\x=\dfrac{6(4-y)}{4} \\x=1.5(4-y)\\x=6-1.5y[/tex]

We substitute x into A(x,y)

[tex]A=y(6-1.5y)=6y-1.5y^2[/tex]

We are required to find the maximum area. This is done by finding

the derivative of Aand solving for the critical points.

Derivative of A:

[tex]A'(y)=6-3y\\$Set $A'=0\\6-3y=0\\3y=6\\y=2$ cm[/tex]

Recall that: x=6-1.5y

x=6-1.5(2)

x=6-3

x=3cm

Therefore, the maximum rectangle area is:

Area =3 X 2 =[tex]6cm^2[/tex]

Answer:

10 2/3π or 33.51

Step-by-step explanation:

the volume of a sphere is 4/3πr^3

if the sphere has a diameter of 4 the radius is half the diameter so it would be 2. 2^3 = 8 now multiply 8 by 4/3 to get 10 2/3. now multiply by pi to get 10 2/3 π or 33.5103 which rounds to 33.51

Answer:

32π/3 cubic cm

Step-by-step explanation:

Answer:

(fog)(x) means that we have the function f(x) evaluated in the function g(x), or f(g(x)).

So, if f(x) = x^3 + 1 and g(x) = x - 2.

we have:

a) (fog)(0) = f(g(0)) = (0 - 2)^3 + 1 = -8 + 1 = -7

b) (gof)(0) = g(f(0)) = (0^3 + 1) - 2 = -1

c)  (fof)(1) = f(f(1)) = (1^3 + 1)^3 + 1 = 2^3 + 1 = 8 + 1 = 9

d) (gog)(1) = g(g(1)) = (1 - 2) - 2 = -1 -2 = -3

Answer:

A

Step-by-step explanation:

We can use the trigonometric ratios. Recall that sine is the ratio of the opposite side to the hypotenuse:

[tex]\displaystyle \sin(C)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

The opposite side with respect to ∠C is 24 and the hypotenuse is 26.

Hence:

[tex]\displaystyle \sin(C)=\frac{24}{26}=\frac{12}{13}[/tex]

Our answer is A.

Answer: D. [tex]y+4=(x+2)[/tex]

Step-by-step explanation: Once you subtract [tex]4[/tex] from both sides, in order to solve for y (as the equation needs to be in the slope-intercept form, otherwise known as [tex]y=mx+b[/tex]), you end up with [tex]y=x-2[/tex], which is the right answer. It is the correct answer because the y-intecept shown in the equation matches what is on the graph, in addition to the fact that the slope is just [tex]x[/tex].

Answer:

Raspberry: 30%

Strawberry: 15%

Apple: 20%

Lemon: 35%

Step-by-step explanation:

18 + 9 + 12 + 21 = 60 (there are 60 gummy worms)

18 out of 60 = 30%

9 out of 60 = 15%

12 out of 60 = 20%

21 out of 60 = 35%

Please mark Brainliest

Hope this helps

Answer:

Raspberry Worms: 30%

Strawberry Worms: 15%

Apple Worms: 20%

Lemon Worms: 35%

Step-by-step explanation:

Raspberry Worms: [tex]\frac{18}{18+9+12+21}=\frac{18}{60}=\frac{30}{100}[/tex] or 30%

Strawberry Worms: [tex]\frac{9}{18+9+12+21}=\frac{9}{60} =\frac{15}{100}[/tex] or 15%

Apple Worms: [tex]\frac{12}{18+9+12+21} =\frac{12}{60} =\frac{20}{100}[/tex] or 20%

Lemon Worms: [tex]\frac{21}{18+9+12+21} =\frac{21}{60} =\frac{35}{100}[/tex] or 35%

Answer:

  9.233 ft, 23.233 ft

Step-by-step explanation:

If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...

  x^2 + (x +14)^2 = 25^2

  2x^2 +28x +196 = 625

  x^2 +14x = 214.5

  x^2 +14x +49 = 263.5

  (x +7)^2 = 263.5

  x = -7 +√263.5 ≈ 9.23268

The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.

Answer: 9 ft, 23 ft

Step-by-step explanation:

We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.

(x-14)²+x²=25²

(x²-28x+196)+x²=625

2x²-28x+196=625

2x²-28x-429=0

When we solve for x, we get [tex]x=\frac{14+\sqrt{1054} }{2}[/tex] and [tex]x=\frac{14-\sqrt{1054} }{2}[/tex].

Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.

Answer:

44.93% probability that the person will need to wait at least 7 minutes total

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional probability:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 5 minutes

This means that [tex]m = 5, \mu = \frac{1}{5} = 0.2[/tex]

Assume a person has waited for at least 3 minutes to be served. What is the probability that the person will need to wait at least 7 minutes total

Event A: Waits at least 3 minutes.

Event B: Waits at least 7 minutes.

Probability of waiting at least 3 minutes:

[tex]P(A) = P(X > 3) = e^{-0.2*3} = 0.5488[/tex]

Intersection:

The intersection between waiting at least 3 minutes and at least 7 minutes is waiting at least 7 minutes. So

[tex]P(A \cap B) = P(X > 7) = e^{-0.2*7} = 0.2466[/tex]

What is the probability that the person will need to wait at least 7 minutes total

[tex]P(B|A) = \frac{0.2466}{0.5488} = 0.4493[/tex]

44.93% probability that the person will need to wait at least 7 minutes total

Answer:

Minimum population of fish in lake = 2400 - 155 = 2245

Maximum population of fish in lake = 2400 + 155 = 2555

Step-by-step explanation:

population of fish in lake = 2400

Variation of fish = 155

it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.

For example

for increase

population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc

but it cannot be beyond 2400 + 155.

It cannot be 2400 + 156

similarly for decrease

population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc

but it cannot be less that 2400 - 155.

It cannot be 2400 - 156

Hence population can fish in lake can be between 2400 - 155 and 2400 + 155

minimum population of fish in lake = 2400 - 155 = 2245

maximum population of fish in lake = 2400 + 155 = 2555

Answer:

65

Step-by-step explanation:

We know that,

The Sum of all angles of the triangle is 180°.

As given in the question,

Triangle PQR is similar to Triangle WXY

Therefore ,

Let the third angle be 'x'.

35° + 80° + x = 180°

115 + x = 180°

x = 180° - 115°

x = 65°.

Hence, 65° is the appropriate answer to the question.

I hope my answer helped!!

Answer:

A: x= -1 or x=3

B: Since the quadratic equation has two real solutions, the graph of the quadratic equation intercepts the x axis at (-1,0) and (3,0)

Step-by-step explanation:

x^2 -2x -3 =0

Factor

(x-3 )(x+1) =0

Using the zero product property

x-3 =0   x+1 =0

x=3  x=-1

The zeros are

(3,0) (-1,0)

It intersects the x axis at (3,0) (-1,0)

Answer:

C. 2.75P

Step-by-step explanation:

The original value was P.

It increased by 275%. That means it increased by 275% of P.

275% of P = 2.75P

The increase in value is 2.75P.

Now we add the increase to the original value of P to find today's value.

2.75P + P = 3.75P

Answer: C. 2.75P

Complete Question:

A restaurant borrows $16,100 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. Assume each month is 1/12 of a year.

Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.

(a) Find the interest that will be owed after 4 months

(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months

Answer:

a) Interest that will be owed after 4 months , I = $131.48

b) Amount owed by the restaurant after 4 months = $16231.48

Step-by-step explanation:

Note that the question instructs not to round any intermediate computations except the final answer.

Annual rate = 2.45%

Monthly rate, [tex]R = \frac{2.45\%}{12}[/tex]

R = 0.20416666666%

Time, T = 4 months

Interest, [tex]I = \frac{PRT}{100}[/tex]

[tex]I = \frac{16100 * 0.20416666666 * 4}{100} \\I = 161 * 0.20416666666 * 4\\I = \$131.483333333\\I = \$131.48[/tex]

b) If the restaurant doesn't make any payments, that means after four months, they will be owing both the capital and the interest ( i.e the amount)

Amount owed by the restaurant after 4 months = (Amount borrowed + Interest)

Amount owed by the restaurant after 4 months = 16100 + 131.48

Amount owed by the restaurant after 4 months = $16231.48

Answer: 13 weeks

Step-by-step explanation:

y = -24x + 379

67 = -24x + 379

24x = 379 - 67

x = 312 / 24

x = 13

Answer:

the answer is 13 weeks

Step-by-step explanation:

y = amount left

y = 67

67 = -24x+379

-312 = -24x

x = -312 / -24

x = 13

Answer:

x = 3, -7

Step-by-step explanation:

Since you already have the factored form, all you need to do is set the equations equal to zero to find you roots:

x - 3 = 0

x + 7 = 0

x = 3, -7

Answer:

3 or -7

Step-by-step explanation:

For it to equal 0, x must be 3 or -7 because anything multiplied by 0 is 0. So you take each part, x-3 and see how you can make that a 0. x-3=0, therefore x must be 3. Other part x+7=0, x must be -7.

Answer:

25%

I cannot really describe how I did it but I am pretty sure it is correct.

Answer:

y-7=1/2(x-8)

y-4=1/2(x-2)

Step-by-step explanation:

Slope: 3/6, or 1/2

y-7=1/2(x-8)

y-4=1/2(x-2)

Answer:

[tex]-15.11[/tex]

Step-by-step explanation:

[tex]-12.48-(-2.99)-5.62=\\-12.48+2.99-5.62=\\-9.49-5.62=\\-15.11[/tex]

Answer:

-15.11

Step-by-step explanation:

-12.48+2.99-5.62=

-9.49 - 5.62= - (9.49+5.62)=-15.11

Answer:

  [tex]\dfrac{x^2+8x+16}{x-1}[/tex]

Step-by-step explanation:

In general, "over" and "divided by" are used to mean the same thing. Parentheses are helpful when you want to show fractions divided by fractions. Here, we will assume you intend ...

  [tex]\dfrac{\left(\dfrac{x^2+7x+12}{x+3}\right)}{\left(\dfrac{x-1}{x+4}\right)}=\dfrac{(x+3)(x+4)}{x+3}\cdot\dfrac{x+4}{x-1}=\dfrac{(x+4)^2}{x-1}\\\\=\boxed{\dfrac{x^2+8x+16}{x-1}}[/tex]

Answer:

Step-by-step explanation:

Answer:

its b on edge

Step-by-step explanation:

Step-by-step explanation:

[tex]( {n}^{3} )^{2} = {n}^{6} = n \times n \times n \times n \times n \times n [/tex]

Answer:

n x n x n x n x n x n

Step-by-step explanation:

(n^3)^2 = n^6 = n x n x n x n x n x n

Answer:

[tex]x\le \:9[/tex]

Step-by-step explanation:

[tex]5x\le 45[/tex]

[tex]\frac{5x}{5}\le \frac{45}{5}[/tex]

[tex]x\le \:9[/tex]

Answer:

B

Step-by-step explanation:

We divide the entire inequality by 5 to get rid of the coefficient of x. The ≤ stays the same so we get x ≤ 9.

Answer:

Your answer is 3.16227766

Step-by-step explanation:

Answer:

B, C and D

Step-by-step explanation:

Given:

Statement: "Every integer has an additive inverse"

To find: statement that is equivalent to the given statement

Solution:

For any integer x, if [tex]x+y=0[/tex] then y is the additive inverse of x.

Here, 0 is the additive identity.

Statements ''All integers have additive inverses '', '' If x is an integer, then x has an additive inverse'' and  ''Given an integer x, there exists a y such that y is the additive inverse of x'' are equivalent to the given statement "Every integer has an additive inverse".