Which proves that (x – 7) is a factor of the given polynomial function?
f(x) = x2 – 5x – 14

A. f(-7) = 0
B. f(0) = -7
C. f(1) = 7
D. f(7) = 0

Answer:

C

Step-by-step explanation:

using the sine ratio in the right triangle

sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{18}{40}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{18}{40}[/tex] ) ≈ 27° ( to the nearest degree )

The solution to the possible values of θ for the trigonometric equation is given by θ = 0.96255... + 2πn and θ = 2π - 0.96255... + 2πn

Given data ,

Let the trigonometric equation be represented as A

Now , the value of A is

4sec ( θ ) - 7 = 0

Adding 7 on both sides , we get

4sec ( θ ) = 7

Divide by 4 on both sides , we get

sec ( θ ) = 7/4

From the trigonometric relations , we get

sec θ = 1/cos θ

cos θ = 4/7

Taking inverse on both sides , we get

θ = 0.96255... + 2πn and θ = 2π - 0.96255... + 2πn

Hence , the solution to the equation is θ = 0.96255... + 2πn and θ = 2π - 0.96255... + 2πn

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There are 57 green cards in the deck.

We are given the ratio of green cards to blue cards in a deck as 3 to 2, and there are 38 blue cards in the deck. Our goal is to find the number of green cards in the deck.

Step 1: Write the given ratio as a fraction.
Green cards / Blue cards = 3/2

Step 2: Use the information provided to create an equation.
Since we know there are 38 blue cards, we can write the equation as:
Green cards / 38 = 3/2

Step 3: Solve for the number of green cards.
To find the number of green cards, we can cross-multiply the equation:
Green cards = (3/2) × 38

Step 4: Calculate the result.
Green cards = (3 × 38) / 2
Green cards = 114 / 2
Green cards = 57

So, there are 57 green cards in the deck.

In summary, to find the number of green cards in the deck, we first expressed the given ratio as a fraction, then used the information provided to create an equation.

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The mean is smaller for the houses owned by teachers, as we reject the null hypothesis to be assumed that the mean is similar for all the houses owned by teachers.

For this study, we should use t-test for a population mean because the population standard deviation is not known.

b. The null hypothesis and alternative hypotheses would be provided as:

H0: μ = 13 (the mean number of paintings for all teachers is 13)

H1: μ < 13 (the mean number of paintings for teachers is less than 13)

c. The test statistic is calculated as:

t = (X - μ) / (s / √n)

where:

X = sample mean,

μ = hypothesized population mean,

s = sample standard deviation, and

n = sample size.

Plugging in the values, we get:

t = (12.18 - 13) / (1.320 / √11) = -1.63

d.The p-value is the likelihood of seeing a t-value that is at least as extreme as -1.63, assuming that the null hypothesis is correct. The p-value is roughly 0.07, as determined using a t-table or a t-distribution calculator with 10 degrees of freedom (n-1).

The p-value above the significance level of 0.01, hence the null hypothesis cannot be rejected. We lack adequate data to draw the conclusion that the average number of artworks in homes owned by teachers is less than 13.  

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Complete question is:

The average house has 13 paintings on its walls. Is the mean smaller for houses owned by teachers? The data show the results of a survey of 11 teachers who were asked how many paintings they have in their houses. Assume that the distribution of the population is normal.

12, 11, 11, 11, 11, 14, 11, 13, 14, 10, 14

What can be concluded at the α = 0.01 level of significance?

a. For this study, we should use t-test for a population mean.

b. The null and alternative hypotheses would be: H0: 13 H1: 13

c. The test statistic (please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.)

d. The p-value =

Answer:

D: $1.75

Step-by-step explanation:

To calculate the expected value of the payout, we need to multiply each cash prize amount by the probability of winning that prize and then sum the results.

The probability of winning the $350 prize is 1/400, since there is only one $350 prize and 400 tickets sold. The probability of winning the $200 prize is 1/399, since there is only one $200 prize and one ticket has been removed from the pool of available tickets. Similarly, the probability of winning the $100 prize is 1/398 and the probability of winning the $50 prize is 1/397.

So, the expected value of the payout is:

(1/400) x $350 + (1/399) x $200 + (1/398) x $100 + (1/397) x $50 = $0.875 + $0.501 + $0.251 + $0.126 = $1.753

Therefore, the expected value of the payout is $1.75 (rounded to the nearest cent). So, the answer is D: $1.75.

Answer:

The value of the expected value of payout is $1.75.

What is expected value?

In probability theory, the idea of expected value denotes the typical result of a random event when the event is repeated a lot of times. It is determined by multiplying each potential result by its likelihood before adding together all of these numbers. The anticipated value can shed light on the possible risks and benefits associated with various options or scenarios, making it frequently used to estimate the long-term average of a random process or to make decisions under uncertainty.

To get the payout we need to determine the probability of winning each prize.

For first prize = 1/400

Second prize = 1/400.

Third prize = 1/400.

Fourth prize = 1/400.

The expected value is calculated as:

(1/400) * $350 + (1/400) * $200 + (1/400) * $100 + (1/400) * $50

= $0.875 + $0.50 + $0.25 + $0.125

= $1.75

Hence, the value of the expected value of payout is $1.75.

Step-by-step explanation:

The quadratic equation on the given graph can be written as:

y = (x + 2)*(x - 1)

Here we have the graph of a quadratic equation, we can see that the roots of the quadratic are:

x = -2 and x = 1.

Then if the leading coefficient is a, we can write the factorized form as:

y = a*(x + 2)*(x - 1)

We also know that the y-intercept is (0, -2), replacing these values we will get:

-2= a*(0 + 2)*(0 - 1)

-2 = a*-2

-2/-2 = a

1 = a

The quadratic equation is:

y = (x + 2)*(x - 1)

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Answer:

Step-by-step explanation:

Correct option is C)

Let α be the common root,

⇒α

2

+bα+c=0.....(i) and α

2

+cα+b=0.....(ii)

(i)−(ii)⇒(b−c)α+(c−b)=0⇒α=1, since b



=c

Hence from (i) or (ii), b+c+1=0

Answer:

x2 bx 1*2

Step-by-step explanation:

The scale factor used in the dilation of the function f(x) to g(x) is 4

From the question, we have the following parameters that can be used in our computation:

The function f(x) dilated to get g(x)

Both functions pass through the origin

So, we have

Center = origin

Next, we have

The scale factor is calculated as

Scale factor  = g(x)/f(x)

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = 4/1

Evaluate

Scale factor = 4

Hence, the scale factor is 4

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Answer:

1250 m²

Step-by-step explanation:

Area of rectangle = L x W

L = 50 meters

W = 25 meters

Let's solve

50 x 25 = 1250 m²

So, the area of the piece of land is 1250 m²

There are no sufficient evidence using hypothesis to conclude percentage of commercial truck drivers those who suffer from sleep apnea is different from population's percentage of 5.2%.

To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 5.2%,

Use a hypothesis test.

Let p be the true proportion of commercial truck drivers who suffer from sleep apnea.

The null hypothesis is that the proportion of commercial truck drivers who suffer from sleep apnea is equal to 5.2%, or p = 0.052.

The alternative hypothesis is that the proportion is not equal to 5.2%, or p ≠ 0.052.

Use a z-test for the proportion to test this hypothesis.

The test statistic is,

z = (p₁ - p) / √(p(1-p) / n)

where p₁ is the sample proportion, n is the sample size, and p is the hypothesized population proportion.

In this case, we have,

p₁ = 30/397

   = 0.0756

n = 397

p = 0.052

Plugging these values into the formula, we get,

z = (0.0756 - 0.052) / √(0.052(1-0.052) / 397)

 = 2.11

The critical value for a two-tailed test at a 0.02 level of significance is ±2.33.

Since our test statistic, 2.11, is less than the critical value of 2.33, we fail to reject the null hypothesis.

Therefore, as per hypothesis we do not have sufficient evidence to conclude percentage of commercial truck drivers who suffer from sleep apnea is different from population's percentage of 5.2%.

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Answer:

0.127 ft per min

Step-by-step explanation:

I used the ai app to verify my answer

The volume of water displaced by the unknown mass (x) rock is 331 ml

What is meant by displaced?

Displaced means to be moved or forced out of its original position or location. It can refer to a physical object or a person who has been forced to leave their home or community due to conflict, natural disaster, or other circumstances. Displacement can cause significant challenges and disruptions to individuals and communities.

According to the given information

The formula for water displacement is: Volume (object) = Volume (water + object). This formula is based on Archimedes’ Principle, which states that the weight of the displaced fluid is equal to the weight of the submerged object1.

So, we can calculate the volume of water displaced by the unknown mass (x) rock as follows:

Volume (water + object) = 471 ml Volume (water) = 140 ml Volume (object) = Volume (water + object) - Volume (water) Volume (object) = 471 ml - 140 ml Volume (object) = 331 ml

Therefore, the volume of water displaced by the unknown mass (x) rock is 331 ml

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Given: $f(x) = \log(3x + 3 - 2x - 2)$

We need to prove that: $\frac{(a+b)^2}{f(a)+f(b)} = -4$

First, we need to simplify $f(x)$:

$f(x) = \log(x+1)$ (by simplifying the expression inside the log)

Now, we can rewrite the expression we need to prove as:

$\frac{(a+b)^2}{\log(a+1) + \log(b+1)} = -4$

Using the property of logarithms, we can rewrite this as:

$\log((a+1)(b+1)) = \log(e^{-4})$

Simplifying further:

$(a+1)(b+1) = e^{-4}$

Expanding the left side and simplifying:

$ab + a + b + 1 = e^{-4}$

Now, we can use the identity $(a+b)^2 = a^2 + 2ab + b^2$:

$(a+b)^2 = a^2 + 2ab + b^2$

Dividing both sides by $f(a)+f(b)$, which is $\log(a+1) + \log(b+1)$:

$\frac{(a+b)^2}{\log(a+1) + \log(b+1)} = \frac{a^2 + 2ab + b^2}{\log(a+1) + \log(b+1)}$

Using the property of logarithms again, we can simplify the denominator:

$\frac{(a+b)^2}{\log((a+1)(b+1))} = \frac{a^2 + 2ab + b^2}{\log((a+1)(b+1))}$

Substituting the value we derived earlier for $(a+1)(b+1)$:

$\frac{(a+b)^2}{\log(e^{-4})} = \frac{a^2 + 2ab + b^2}{\log(e^{-4})}$

Simplifying:

$(a+b)^2 = a^2 + 2ab + b^2$

$4ab = -4$

Dividing both sides by 4:

$ab = -1$

Therefore, we have shown that $\frac{(a+b)^2}{f(a)+f(b)} = -4$ if $f(x) = \log(3x+3-2x-2)$.

Answer:

D) 48

Step-by-step explanation:

area = length x width x height

8 x 2 x 3

16 x 3 = 48

The experimental probability of selecting a black marble is 0.4, which is found by dividing the frequency of selecting a black marble (6) by the total number of marbles (15). The correct answer is C).

To determine the experimental probability of selecting a black marble, we need to divide the frequency of selecting a black marble by the total number of marbles.

The table shows that Michael has a bag of marbles with a total frequency of 4 + 6 + 5 = 15 marbles. The frequency of selecting a black marble is 6, so the experimental probability of selecting a black marble is:

6/15 = 0.4

Therefore, the answer is option (C), 0.40.

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The Coordinates of B (0, -2), C(0, -1) and D(-2, -1).

We have, the vertices of quadrilateral of A(1, -2).

Since AB = -1 which means that B is located 1 unit left then coordinates of B are

= (1 -1 , -2)

= (0, -2)

Now, C must have the same y coordinate as B. Also CB is vertical length 1 which moved above by 1 unit the coordinates of C

C (0, -2+1) = (0, -1)

and the coordinates of D are (0 -2, -1) = (-2, -1)

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The number of chairs that Mr. Carter can paint in 3 hours is (60/t) chairs and he would use (15/t) litres of paint to paint them.

We know that Mr. Carter can paint 20 chairs in t hours. Therefore, we can say that he can paint:

(20 chairs) / (t hours) = (20/t) chairs per hour

Using this rate, we can find the number of chairs that he can paint in 3 hours as:

(20/t chairs per hour) x (3 hours) = (60/t) chairs in 3 hours

Now we can use the information that Mr. Carter uses 3 litres of paint for every 12 chairs that he painted. This means he uses 1 litre of paint for every 4 chairs painted. Therefore, he would use:

(60/t) chairs / 4 chairs per litre = (15/t) litres of paint

So, in terms of t, the number of chairs that Mr. Carter can paint in 3 hours is (60/t) chairs and he would use (15/t) litres of paint to paint them.

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The surface area of the given right rectangular prism will be 592 square inches.

The formula for a right rectangular prism's surface area is:

SA = 2lh + 2lw + 2lh

where l denotes the prism's length, w its width, and h its height.

Here, l is equal to 12 feet, w to 8 feet, and h to 10 feet. When these values are added to the formula, we obtain:

SA = 2(12)(8) + 2(12)(10) + 2(8)(10) (10)

SA = 192 + 240 + 160

SA = 592

Hence, the right rectangular prism has a surface area of 592 square feet.

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We can choose different fruits in 252 ways.

Given that, a smoothie shop offers 10 different kinds of fruit. we need to select 5 kinds of fruits, we need to find the in how many ways can we do so,

Using the concept of combination,

ⁿCₓ = n! / r!(n-r)!

Therefore,

¹⁰C₅ = 10! / 5!(10-5)!

¹⁰C₅ = 10! / 5!·5!

¹⁰C₅ = 10·9·8·7·6·5! / 5!·5!

¹⁰C₅ = 10·9·8·7·6 / 5!

¹⁰C₅ = 252

Hence, we can choose different fruits in 252 ways.

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The CPI for year 2 is 108. 78 and the rate of inflation from year 1 to year 2 is 8. 78 %.

The Consumer Price Index is a gauge of the mean fluctuation in costs of commodities and amenities that consumers procure across durations. It is measured by assessing the cost of a collection of provisions and utilities that symbolizes what an ordinary family acquires, then equating it to the price of the identical set during some antecedent period.

The CPI would be:

= Total cost of basket in year 2 / Total cost of basket in year 1

= ( (1. 65  x 3 bread ) + 3. 10 ) / ( ( 1.50 x 3 ) + 2. 90 )

= 108. 78

The inflation would then be :

= (CPI of year 2 - 100 base year CPI) x 100 %

= (108. 78 - 100) x 100 %

= 8. 78 %

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Answer:

Set your calculator to Degree mode.

55^2 = 90^2 + 50^2 - 2(90)(50)cos(C)

3,025 = 10,600 - 9,000cos(C)

-7,575 = -9,000cos(C)

cos(C) = 101/120

C = cos^-1 (101/120) = 32.7°

The radian solutions of the equation are θ = 2.71 and θ = 0.43 radians

From the question, we have the following parameters that can be used in our computation:

-sin² (θ) - 2sin (θ) + 1 = 0

Divide through by -1

So, we have

sin² (θ) + 2sin(θ) - 1 = 0

Let y = sin(θ)

So, we have

y² + 2y - 1 = 0

When solved graphically, we have

y = 0.414 and -2.414

This means that

sin(θ) = 0.414 and sin(θ) = -2.414

Take the arcsin of both sides

θ = 2.71 and θ = 0.43

Hence, the angles are θ = 2.71 and θ = 0.43

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Answer:

50° 54' 55"

Step-by-step explanation:

To convert decimal degrees to degrees, minutes, and seconds, we can use the following conversion factors:

1 degree = 60 minutes

1 minute = 60 seconds

To convert 350.9154° to degrees, minutes, and seconds, we can follow these steps:

Therefore, 350.9154° is equivalent to 350° 54' 55".

The linear equation that passes through the two given points is

3y - 2x = 22

Remember that a linear equation that passes through the points (x₁, y₁) and (x₂, y₂) has a slope:

a = (y₂ - y₁)/(x₂ - x₁)

In this case the points are  (-5,4) and (10,14), then the slope is:

a = (14 - 4)/(10 + 5) = 10/15 = 2/3

Then the line is something like:

y = (2/3)*x + b

To find the value of b, you can replace the values of one of the points there.

14 = (2/3)*10 + b

14 - 20/3 = b

22/3 = b

Then the line is:

y = (2/3)*x + 22/3

3y = 2x + 22

3y - 2x = 22

That is the line that passes through the two points.

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a) 18.80% probability that among 18 randomly observed individuals exactly 4 do not cover their mouth when sneezing

b) 10.4 probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when​ sneezing.

c) It would not be surprising if fewer than half covered their mouth when​ sneezing.

Using the formula,

P(X= x) = C( n, x)[tex]p^x q^{1-x[/tex]

Here n= 18, p= 0.267

a) P(X= 4)

= C( 18, 4) [tex]0.267^{18} 0.733^{14[/tex]

= 3060 x 4.755 x [tex]10^{-11[/tex] x 0.01292574681

= 188.073 x [tex]10^{-11[/tex]

b) The probability is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

P(X= 0) =0.0037

P(X= 1)= 0.0245

P(X= 2)= 0.0758

So, P(X < 3) = 0.0037 + 0.0245 + 0.0758 = 0.104

c) E(X) = np = 18 x 0.267 = 4.81.

and, standard deviation

= √18 (0.267)(0.733)

= 1.88

Thus, it would not be surprising if fewer than half covered their mouth when​ sneezing.

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Answer:

The population of the town will be 1771.44663 in 6 years.

Here is the calculation:

1400 * (1.04)^6 = 1771.44663

The formula for calculating the population of a town after a certain number of years is:

Population after n years = Initial population * (1 + growth rate)^n

In this case, the initial population is 1400, the growth rate is 4%, and the number of years is 6.

Plugging these values into the formula, we get:

Population after 6 years = 1400 * (1 + 0.04)^6 = 1771.44663

Step-by-step explanation:

The Use of  python programming language to find the differentiation of y= e^2x sin2x/cos 4x. is given in the image attached.

This programming code given in the image is one that uses SymPy's symbolic mathematics abilities to create a function, calculates its derivative, and then utilizes the lambdify feature to generate NumPy functions that can be applied to evaluate the function and its derivative at particular locations.

Therefore, through the use of matplotlib, a variety of x values are generated and the function and its derivative are plotted.

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Answer:

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

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation of line

Answer:

y= -0.5x + 2 (I think)

Step-by-step explanation:

y =mx + c

gradient is -0.5 because society

m = -0.5

y intercept is 2 because 2

so that means answer swag