Find a polynomial f(x) of degree 4 that has the following zeros.
0, -5, 8, -2

Answer:

the number is 33 and 35 respectively

Step-by-step explanation:

The computation is shown below:

Let us assume X and X + 2 are the two consecutive odd integers

Now the equation is

(X ÷ 3) = ((X + 2) ÷ 7) + 6

(X ÷ 3) = (X + 2 + 6 × 7) ÷ 7

(X ÷ 3) = (X + 2 + 42) ÷ 7

(X ÷ 3) =  (X + 44) ÷ 7

Now do the cross multiplication

7X  = 3(X + 44)

7X = 3X + 132

4X = 132

X = 33

And, X + 2 = 33 + 2 = 35

hence, the number is 33 and 35 respectively

Answer:

Therefore, The Boat is Approaching the Dock at a Rate of 2ft/sec When the point of attachment is:  14ft from the dock.

Make a plan:

Let  X be the Distance between the Boat and the Dock

Y  be the Length of the Rope

We will use the Pythagorean Theorem to relate X  and Y

Then Differentiate with respect to Time to find the Rate at which the Boat is Approaching the Dock.

1 - Write the Pythagorean Theorem equation:

X^2  + 1^2 = Y^2

2 - Differentiate Both Sides with respect to Time (t):

2x dx/dt  =  2y dy/dt

3 - Given dy/dt  =  -2ft/sec, and  y = 14ft

Solve for,  dx/dt, When  X = 14ft

2(14)dx/dt  =  2(14)( -2 )

4 - Solve For:

dx/dt

dx/dt  =  -2ft/sec

Draw the conclusion:

Therefore, The Boat is Approaching the Dock at a Rate of 2ft/sec When the point of attachment is:  14ft from the dock.

I hope this helps you!

The area of the sector with a central angle of 60 degree and radius of 8 units is approximately 33.5 sqaure units.

A sector of a circle is simply part of a circle made up of an arc and two radii.

The area of a sector of a circle can be expressed as:

Area = (θ/360º) × πr²

Where θ is the sector angle in degrees, and r is the radius of the circle.

From the image:

Measure of central angle θ = 60 degrees

Radius r = 8 units

Plug these values into the above formula and solve for the area:

Area = (θ/360º) × πr²

Area = (60°/360°) × π × 8²

Area = 1/6 × π × 64

Area = 1/6 × π × 64

Area = 33.5 sqaure units.

Therefore, the area is approximately 33.5 sqaure units.

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Answer:

Step-by-step explanation:

j represents the amount of juice

2 : 3 :: j : 18        proportion

3j = (2)(18)

Answer:

72

Step-by-step explanation:

If he reads 24 pages in 1/3 of an hour, he reads 3 times as many pages in 1 hour.

3 × 24 pages = 72 pages

Answer: 72

Answer:

21u-26

Remember to add like terms

Answer:

Deepti has 6 boxes of crayons

Step-by-step explanation:

they have 8 boxes together. Mani has two more than her so 8-2=6

Answer:

Hello, we see that deepti has some boxes of crayons we dont know exactly how much so well name that a variable"x"  Than we see that mani has 2 more boxes than deepti together they have 8 boxes.

Lets make the equation!

x+2=8

We have to solve for x all you have to do here is subtract 8 from 2 the answer is 6.

So 6+2=8

Hope i explained that right :)

Answer:

54 Minutes

Step-by-step explanation:

The formula for the matrix of the projection onto Null(A) can be found using the concept of orthogonal projection. It is given by P = I - A(A^T A)^(-1) A^T, where A^T represents the transpose of matrix A,

To find the matrix of the projection onto Null(A), we can use the concept of orthogonal projection. The projection matrix P projects vectors onto the null space of A.

The formula for the projection matrix is P = I - A(A^T A)^(-1) A^T, where A^T represents the transpose of matrix A, I is the identity matrix, and (A^T A)^(-1) denotes the inverse of the matrix product A^T A.

The matrix A has independent rows, which implies that its columns are linearly independent. This means that the matrix A^T A is invertible.

Using the formula for the projection matrix P, we can find the matrix that projects vectors onto the null space of A. By subtracting the projection matrix from the identity matrix I, we obtain the desired matrix.

Therefore, the formula for the matrix of the projection onto Null(A) is P = I - A(A^T A)^(-1) A^T.

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Step-by-step explanation:

the quotient of a number and 3 is 6

Solution,

Let the number be x, then

\( \frac{x}{3} = 6 \\ x = 6 \times 3 \\ x = 18\)

Answer:

The quotient of a number and 3 is 6

Let the required number be x

According to the above problem,

\(→ x \div 3 = 6 \\ \frac{x}{3} = 6 \\ x = 6 \times 3 \\ \boxed{x = 18}✓\)

From the right angled triangle given,

To find the missing side, x, of the triangle, Pythagorean theorem is applied

The Pythagorean theorem formula is

The dimensions of the triangle are

Substituting the values into the Pythagorean theorem formula above,

The missing side, x is 1mi

Answer is D

The price of rolls of film is $2.50 and the price camera batteries is $1.50.

of Two equations can be derived from the  question:

8f + 2b = 23 equation 1

6f + 2b = 18 equation 2

Where:

f = rolls of film

b = camera batteries

In order to determine the value of f, subtract equation 2 from 1

2f = 5

Divide both sides of the equation by 2

f = 2.50

In order to determine the value of b, substitute for f in equation 1:

8(2.50) + 2b = 23

20 + 2b = 23

2b = 23 - 20

2b = 3

b = 1.50

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Answer:

-60

Step-by-step explanation:

s=-105+45

=-60

hope it helps

Answer: 13 saltos en total, 6 de los saltos de 3 metros, 7 de los saltos de 2 metros

Step-by-step explanation:

Si sumas 2+3, suma 5 y 5 cabe en 32 6 veces con un resto 2. (2+3)6 +2 = 30 +2 = 32 metros.

So the question is just asking for you to simplify the inequality until you get an answer.

1. Open the bracket on the left side. If you open it, you get 4x+8 > 8x - 3

2. Know - 4x from both side so you dont have x on 1 side. So 8 > 4x - 3

3. Get rid of the -3 from the right side by adding 3 onto both side. So 11>4x

4. Now you can divide by 4 on each side. x<2.75

= x < 2.75 (x is smaller than 2.75) .

You can write 2.75 > x. It is the same thing but I like writing my x first :)

Answer:

x=12

Step-by-step explanation:

Just use some algebra to collect the like terms from each side

Answer:

x = 12

Step-by-step explanation:

1/3x+10=3/4x+5

make 1/3 & 3/4 have the same denominator

4/12 & 9/12

4/12x+10=9/12x+5

-4/12x+10=9/12x-5

5 = 5/12x

60 = 5x

12 = x

Calculating this expression, we find that the length of the image of the rectangle is 36 in.

To find the length of the image of the rectangle after dilation, we can use the property of similar triangles. Since the width of the image is known to be 21 in., we can set up a proportion:

(image width) / (original width) = (image length) / (original length)

Substituting the known values, we have:

21 in. / 14 in. = (image length) / 24 in.

Solving for the image length, we get:

(image length) = (21 in. / 14 in.) * 24 in.

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The correct decision in a hypothesis test when the data produces a t-statistic that is in the critical region is to reject the null hypothesis.

This is because a t-statics in the critical region indicates that the differences between the sample mean and the population mean are statistically significant. This means that the data indicates that the null hypothesis is wrong and that the alternative hypothesis is true. In a hypothesis test, the null hypothesis is what the researcher is trying to disprove. It is the general statement that suggests that there is no difference between the sample mean and the population mean. The alternative hypothesis is what the researcher is attempting to prove. It suggests that there is a difference between the sample mean and the population mean. Therefore, when the data produces a t-statistic that is in the critical region, it indicates that the alternative hypothesis is true. When a t-statistic is in the critical region, it means that the result is statistically significant. This means that the differences between the sample mean and the population mean are unlikely to have occurred by chance and that the alternative hypothesis is likely to be true. Therefore, when the data produces a t-statistic that is in the critical region, the correct decision is to reject the null hypothesis and accept the alternative hypothesis.

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Answer:

+2 ، +3 ، - 2 ، - 3

Step-by-step explanation:

-12.2÷-6.1=+2

(3(3/7))÷((1(1/7))=+3

16/-8=-2

(-2(2/5))÷(4/5)=-3

Answer:

3 --> 3 3/7 ÷  1 1/7

-2 --> 16 ÷ (-8)

-3 --> -2 2/5 ÷ 4/5

2 -->  -12.2 ÷ (-6.1)

Solution:

Simply plug these numbers into the calculator and receive your answer.

We are given two plots of normal distributions A and B.

The mean of a normal distribution is located at the center of the plot.

Since the centers of both of the normal distributions A and B seems to be aligned, therefore, they both seems to have equal means.

The standard deviation basically determines the shape of the distribution.

As you can see, the normal distribution A is more spread out and thus has a larger standard deviation than normal distribution B.

Therefore, the two correct options are

• The means of A and B are equal.

• A has larger standard deviation.

The null hypothesis (H0) states that the average age is equal to or greater than 30.8 years, while the alternative hypothesis (Ha) states that the average age is less than 30.8 years.

In hypothesis testing, we set up the null hypothesis (H0) and the alternative hypothesis (Ha) to investigate a claim or conjecture. In this case, the conjecture is that the average age of a senior surgical resident in the United States is less than 30.8 years old.

The null hypothesis (H0) assumes that the average age is equal to or greater than 30.8 years, and any difference observed in the sample is due to random chance or sampling variability. Therefore, the null hypothesis can be stated as:

H0: The average age of senior surgical residents in the United States is greater than or equal to 30.8 years.

The alternative hypothesis (Ha) represents the claim or the opposite of the null hypothesis. In this case, the alternative hypothesis states that the average age is less than 30.8 years, indicating that there is a significant difference or evidence against the null hypothesis. Therefore, the alternative hypothesis can be stated as:

Ha: The average age of senior surgical residents in the United States is less than 30.8 years.

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The exponential model for the data on Hispanic-owned businesses is N(t) =\(1.16 e^{(0.084t)\), where t represents the number of years since 1999 and N(t) is the number of businesses in millions.

To find an exponential model for the data, we need to fit it into the general form of an exponential function: N(t) = ae^(kt).

Let's assign t = 0 to correspond to the year 1999 and N(t) represents the number of businesses in millions. We are given two data points: (t=0, N=1.16) and (t=4, N=1.53).

Plugging in the first data point, we have:

1.16 = ae^(k*0) => 1.16 = a.

Next, plugging in the second data point, we get:

1.53 = ae^(4k).

Now, we can substitute a = 1.16 into the second equation:

1.53 = 1.16  e^(4k).

Dividing both sides of the equation by 1.16:

1.32 = e^(4k).

Taking the natural logarithm (ln) of both sides:

ln(1.32) = 4k.

Solving for k:

k = ln(1.32)/4.

Now, we have the values of a = 1.16 and k = ln(1.32)/4. Therefore, the exponential model for the data is:

N(t) = 1.16 * e^((ln(1.32)/4) * t), where t represents the number of years since 1999, and N(t) is the number of businesses in millions.

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The given statement "if you’re comparing the test scores between two groups, you should use a one-sample z-test." is False because you should use two-sample t-test.

If you are comparing the test scores between two groups, you should use a two-sample t-test. A one-sample z-test is used to compare a sample mean to a known population mean when the population standard deviation is known.

However, in most cases, the population standard deviation is unknown, and the sample size is typically small, so a t-test is preferred. The two-sample t-test is used to compare the means of two independent groups. The test assumes that the samples are normally distributed and have equal variances.

If the variances are unequal, a modified version of the t-test called the Welch's t-test should be used. In summary, the appropriate test to use depends on the nature of the comparison being made, the sample size, the distribution of the data, and whether the variances of the two groups are equal or not.

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none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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The nonresponse caused the results of the survey to be biased as C. Those who did not respond caused a violation of the assumption of independence.

It should be noted that each person in a simple random sample of 1,200 received a survey, and 325 people returned their survey. How could nonresponse cause the results of the survey to be biased?

In this case, the nonresponse caused rhe results of the survey to be biased as those who did not respond caused a violation of the assumption of independence. Those who did not respond may differ in some important way from those who did respond

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The probability that the sum of the two selected numbers is even is 1/2.

The parity of the two chosen numbers must match for the sum to be even.

Given this information, we can divide the larger problem into smaller ones. First, we may determine the likelihood that the first spinner will land on an even number.

Exists a \($\frac{1}{2}$\) chance that this happens, and a \($\frac{1}{3}\) there is a chance that the second spinner will also land on an even number, hence

\($\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$\)

There is a win if both the first and second spinners land on an odd number.

\($\frac{1}{2} \cdot \frac{2}{3} = \frac{2}{6}$\)

chance of this happening. Adding these two probabilities together, we get

\(\frac{1}{6} +\frac{2}{6} =\frac{3}{6} =\frac{1}{2}\)

Therefore, The probability that the sum of the two selected numbers is even is 1/2.

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The height of the drop tower is 140 feet

From the image shown, the opposite side of the triangle measures 84 feet, we are to determine the adjacent side of the angle which is thus, the height of the drop tower.

Let's solve to determine the angle from the shadow which is similar to the tower

cos θ = opposite/ adjacent

cos θ = 3/ 6

cos θ = 0. 6

θ = \(cos^-^1(0. 6)\)

θ = 53. 1 degrees

To determine the height of the tower, we use the trigonometric identity cosine

cos θ = 84/ x

cross multiply

cos 53. 1 × x = 84

0. 600 × x = 84

Make 'x' the subject

x = 84/ 0. 600

x = 140 feet

The height of the tower is 140 feet

Thus, the height of the drop tower is 140 feet

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Answer:

The answer is B. 8 miles

Step-by-step explanation:

First you take the original route length and subtract the shortcut route length from that. Next, since the problem has the key word, Approximately, we would find the closest answer to our difference.

28.3 - 19.7 = 8.6

8.6 = 8

8 miles