Knowledge Understanding Determine the slope of the normal to the function below at x = 2 1 point f (x) X-2 x + 2 1 -4 O Option 1 Option 2 4 1 2 Option 4 Option 3

Answer:

2(3 + 8k)

Step-by-step explanation:

GCF of 6 and 16 is 2.

6 + 16k = 2(3 + 8k)

Answer:

29

Step-by-step explanation:

The value of b by assuming that the two lines are parallel will be equal to 29°.

When two lines converge at a point, they produce an angle. The word "angle" refers to the length of the "gap" between these two rays. The symbol is used to denote it.

Radians, a unit of roundness or rotation, and degrees are the 2 most common units used to measure angles. In daily life, angles are present.

As per the given information provided by the given figure,

The angle is corresponding in nature,

So, the equation will be,

3b + 5 = 92

3b = 92 - 5

3b = 87

b = 87/3

b = 29°.

Therefore, the angle b is 29°.

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Answer:

   A=312m

Step-by-step explanation:

View image attached

(subtract is where you take something away from something else)

A. Squared (multiplication)

B. Product (multiplication)

C. Minus (subtraction)

D. Quotient (division)

E. Difference (subtraction)

Your answers are

C. Minus and E. Difference

The p-value is 0.0688.

It is given that null hypothesis, it is tested if the mean is the same as the national average of 3, that is:

H₀:μ=3

It is given that  alternative hypothesis, it is tested if the mean is different of the national average of 3, that is:

\(H_a\):μ ≠ 3  

Item b:

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is solved by the below formula

t=(X-μ)/(s/√n)

where,

Now, we have some values from the question that are

X=3.6,μ=3,s=2,n=39

So, on putting the above values in formula, we get

t=(3.6-3)/(2/√39)

=>t=1.873

We have a two-tailed test(test if the mean is different from a value), with t = 1.873 and 39 - 1 = 38 df.

Using a t-distribution calculator, we get that  the p-value is  0.0688.

Hence, we can conclude that p-value after conduction of hypothesis test  is 0.0688.

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(Complete question) is:

According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Suppose data for the sale of 39 randomly selected homes sold in Greene County, Ohio, in 2017 showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in 2017.Find the p-value. (Round your answer to four decimal places.)

Answer:

● 23.55 units

Step-by-step explanation:

Arc length = 5( 270 π/ 180)

= 7.5 π units

= 7.5 (3.14)

= 23.55 units

OAmalOHopeO.

============================================================

Explanation:

For now, we'll just find the perimeter of the full circle. The term "circumference" is the same as the perimeter of the circle.

Use the circumference formula to get

C = 2*pi*r

C = 2*3.14*5

C = 31.4

The distance around the full circle is approximately 31.4 units. It's approximate because pi = 3.14 is approximate.

We don't want the full distance around the circle. Instead, we want just the length of the green arc shown in the drawing. This is exactly 3/4 of the full circle, aka 3/4 = 0.75 = 75% of the full perimeter.

The length of the green arc is about 0.75*C = 0.75*31.4 = 23.55 units long. Imagine using a cloth ruler (used in tailoring clothes) as one way to confirm that this arc length is roughly 23.55 units long. Or you could imagine unwrapping this curved portion to lay it completely straight and flat against a ruler.

Answer:

8/50

Step-by-step explanation:

2/10 x 4/5 = 8/50

Hope that helps!

the second one √72= 8.48 and the square root of √83=9.11 pi^2 = 9.86

when you put this in order by the decimal you get

8.48, 8.7, 9.11, 9.25, 9.86 which is really √72, 8.7, √83, 9.25, pi^2

Expression in terms of y: (12y + 36) / 4.The expression (12y + 36) / 4 represents the side length of the square in terms of y.

The perimeter of a square is equal to four times the length of its side. In this case, the perimeter is given as 12y + 36 units. To find the side length, we divide the perimeter by 4. Thus, the expression (12y + 36) / 4 represents the side length of the square in terms of y.

Let's calculate it:

Side length = (12y + 36) / 4

             = 3y + 9

Therefore, the side length of the square in terms of y is 3y + 9 units.

The expression (12y + 36) / 4 represents the side length of the square in terms of y. By simplifying the expression, we find that the side length is equal to 3y + 9 units.

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Answer:q

Step-by-step explanation:

To find the base in the equation, divide the total number of lab tests (171) by the percentage value (47.5%), resulting in a base value of approximately 360.

To solve for the base in the given equation, divide the total number of lab tests (171) by the percentage value (47.5%).

Let's denote the base in the equation as "x." According to the given information, 171 lab tests represent 47.5% of the total lab tests. To determine the value of the base, we divide 171 by the decimal equivalent of 47.5%, which is 0.475.

Using the equation x = 171 / 0.475, we can calculate the base as follows:

x ≈ 360

Hence, the base in the equation is approximately 360.

By dividing the given quantity by the decimal equivalent of the percentage, we can find the base value in equations involving percentages.

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Answer:

Domain:

-∞ < x > ∞

Range:

-∞ < y > ∞

Step-by-step explanation:

The required circumference of the circle with a diameter of 97 cm is 304 cm.

The circumference of a circle can be calculated using the formula:

C = πd

Where 'd' is the diameter of the circle, and 'π' is a mathematical constant approximately equal to 3.14159.

In this case, the diameter of the circle is given as 97 cm. So we can substitute this value into the formula to get:

C = πd

C = π(97 cm)

C ≈ 304.35 cm

Rounding this answer to 3 significant figures gives:

C ≈ 304 cm

Therefore, the circumference of the circle with a diameter of 97 cm is 304 cm.

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a) The motion is in the positive direction on the interval (5.7, 7] and in the negative direction on the interval [0, 5.7].

b) The displacement over the interval [0, 7] is 213.1667 units

c) The distance traveled over the interval [0, 7] is also 213.1667 units.

To determine when the motion is in the positive or negative direction, we need to consider the sign of the velocity function v(t) = t^3 - 8t^2 + 15t.

a) Positive and negative direction:

We can find the critical points by setting v(t) = 0 and solving for t. Factoring the equation, we get (t - 3)(t - 1)(t - 5) = 0. Therefore, the critical points are t = 3, t = 1, and t = 5.

Checking the sign of v(t) in the intervals [0, 1], [1, 3], [3, 5], and [5, 7], we find that v(t) is positive on the interval (5.7, 7] and negative on the interval [0, 5.7].

b) Displacement over the given interval:

To find the displacement, we need to calculate the change in position between the endpoints of the interval. The displacement is given by the antiderivative of the velocity function v(t) over the interval [0, 7]. Integrating v(t), we get the displacement function s(t) = (1/4)t^4 - (8/3)t^3 + (15/2)t^2 + C.

Evaluating s(t) at t = 7 and t = 0, we find s(7) = 213.1667 and s(0) = 0. Therefore, the displacement over the interval [0, 7] is 213.1667 units.

c) Distance traveled over the given interval:

To find the distance traveled, we consider the absolute value of the velocity function v(t) over the interval [0, 7]. Taking the absolute value of v(t), we get |v(t)| = |t^3 - 8t^2 + 15t|.

Integrating |v(t)| over the interval [0, 7], we get the distance function D(t) = (1/4)t^4 - (8/3)t^3 + (15/2)t^2 + C'.

Evaluating D(t) at t = 7 and t = 0, we find D(7) = 213.1667 and D(0) = 0. Therefore, the distance traveled over the interval [0, 7] is 213.1667 units.

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Answer:

-300

just do inverse operation, and multiply both sides of the equation by -15 to cancel out the -15 from the denominator and you get V=20(-15)

solve for 20(-15) and you get -300

Answer:

6.4166

Step-by-step explanation:

77/12 = 6.41666666667

Answer:

I believe it’s 14400 people

Answer:

x-3+2x+3+2x = 5x

x+8+4x-3x-4 = 2x+4

4x+x-11-5X+25+4x = 4x+14

3x+5-2x-5x+9+8x = 4x+14

5+9x-7-4X-3x+6 = 2x+4

6x-9-5x+4-x+5x+5 = 5x

Step-by-step explanation:

Simplified by adding like terms

Answer:

Minimum at x=4

Hey I saw your new question.... If you just point about the points A and B in the graph I will gladly help you.

Answer:

7.3

Step-by-step explanation:

I think

The solution to this system of equations is (3,1,-2) which are represented by matrix.

This system of equations can be represented by the augmented matrix:

\(\begin{bmatrix}100 & -3 & 0 \\010 & 0 & 1 \\001 & 0 & -2\end{bmatrix}\)

The augmented matrix can be transformed into an upper triangular matrix using row operations:

\(\begin{bmatrix}100 & -3 & 0 \\000 & 3 & 1 \\000 & 0 & -2\end{bmatrix}\)

Now, we can use back substitution to solve for the unknowns.

From the bottom row, we can see that z = -2.

From the second row, we can see that y = 1.

Using the top row and the values for y and z, we can solve for x:

100x - 3(1) + 0(-2) = 0

100x - 3 + 0 = 0

100x = 3

x = 3

Thus, the solution to this system of equations is (3,1,-2).

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The confidence interval to find the margin of error and the sample mean:

(0.256,0.380) The sample mean is the average value obtained from the sample data.

To find the margin of error and the sample mean, we need more information.

The confidence interval (0.256, 0.380) provides the range of possible values for the true population mean.

However, without knowing the sample size or the level of confidence associated with the interval, we cannot calculate the margin of error or the sample mean.

The margin of error is typically calculated by multiplying the standard error by the appropriate critical value, based on the desired level of confidence. The sample mean is the average value obtained from the sample data.

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Answer:

to find the y intercept 6x20=120 220-120=100   so the pool started at 100cm

i think the equation is this

Y=6x+100

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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Answer:

B.56

Step-by-step explanation:

80x0.70 is 56

The mean number of garage stalls per home in the sample of 200 homes is 1.09.

The mean is a measure of central tendency in statistics that represents the average value of a set of numerical data. It is calculated by summing up all the values and dividing by the total number of values.

According to the given information:

To find the mean number of garage stalls per home in the sample of 200 homes, we need to calculate the expected value or the average value of X, which is the number of garage stalls per home. We are given the probabilities of X taking the values 0, 1, and 2, which are P(X=0) = 0.06, P(X=1) = 0.45, and P(X=2) = 0.32.

The formula for calculating the expected value of X is:

E(X) = Σ [ x × P(X=x) ]

where Σ represents the sum of all values of x, and P(X=x) is the probability of X taking the value x.

Using this formula, we can calculate the expected value of X as follows:

\(E(X) = (0 * 0.06) + (1 * 0.45) + (2 * 0.32)\)

\(= 0 + 0.45 + 0.64\)

= 1.09

Therefore, the mean number of garage stalls per home in the sample of 200 homes is 1.09. Hence, the correct option is (a) 1.09.

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The mean number of garage stalls per home in the sample of 200 homes is 1.09.

What is mean?

The mean is a measure of central tendency in statistics that represents the average value of a set of numerical data. It is calculated by summing up all the values and dividing by the total number of values.

According to the given information:

To find the mean number of garage stalls per home in the sample of 200 homes, we need to calculate the expected value or the average value of X, which is the number of garage stalls per home. We are given the probabilities of X taking the values 0, 1, and 2, which are P(X=0) = 0.06, P(X=1) = 0.45, and P(X=2) = 0.32.

The formula for calculating the expected value of X is:

E(X) = Σ [ x × P(X=x) ]

where Σ represents the sum of all values of x, and P(X=x) is the probability of X taking the value x.

Using this formula, we can calculate the expected value of X as follows:

E(x) = (0.06*0)+(1*0.45)+(2*0.32)

= 1.09

Therefore, the mean number of garage stalls per home in the sample of 200 homes is 1.09. Hence, the correct option is (a) 1.09.

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The statement that best describes the depth of the fish, given this equation, is this: C. From a starting position of 3 meters below sea level, the fish is descending 7 meters per second.

The first description of this statement should indicate the depth from which the fish descends. From the equation, y is equal to -7x -3. The minus in this case is indicative of descent.

7 is the rate at which the fish travels with respect to time and 3 is indicative of the distance from sea level and the starting point from which the fish moves.

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Answer:

x = 5

Step-by-step explanation:

4x = 20

x is called a 'variable' and we fine the value of this variable.

Now, Given that

=> 4x = 20

To get the value of x, we divide the equation on the left hand side and right hand side by 4

=> 4x/4 = 20/4

In the left hand side 4/4 becomes 1 and in the right hand side 20/4 becomes 5.

=> x = 5

We get x = 5.

Hope it helps!

Answer:9.75

Step-by-step explanation:12x12 =144 and 7x7= 49 subtract 144-49 and get 95 the square root of 95 is approximately 9.747 rounded to the nearest hundredths place is 9.75

Answer:

9.75

Step-by-step explanation:

To do this problem, use the Pythagorean Theorem, \(a^2 + b^2 = c^2\). Right now, you have that a = 7 and c = 12, so it would be

\(7^2 + b^2 = 12^2\\49 + b^2 = 144\\b^2 = 95\\b = \sqrt{95}\)

Rounding to the nearest hundredth, you get: 9.75

By the solving equation we get 570 adult tickets and 215 child tickets were sold on that Saturday at the movie theater.

To find the number of each type of tickets sold, we can use a system of equations. Let's assume that the number of adult tickets sold is represented by 'a', and the number of child tickets sold is represented by 'c'.

From the given information, we know that the movie theater charges $5 for an adult ticket and $2 for a child's ticket. We also know that the theater sold 785 tickets for a total revenue of $3,280.

Based on this information, we can write two equations:

1. The total number of tickets sold: a + c = 785 (Equation 1)
2. The total revenue from ticket sales: 5a + 2c = 3280 (Equation 2)

Now, let's solve this system of equations to find the values of 'a' and 'c'.

First, let's isolate 'a' in Equation 1 by subtracting 'c' from both sides:
a = 785 - c

Next, substitute the value of 'a' in Equation 2:
5(785 - c) + 2c = 3280

Simplify the equation:
3925 - 5c + 2c = 3280
3925 - 3c = 3280

Now, isolate 'c' by subtracting 3925 from both sides:
-3c = 3280 - 3925
-3c = -645

Divide both sides of the equation by -3 to solve for 'c':
c = -645 / -3
c = 215

Now, substitute the value of 'c' back into Equation 1 to solve for 'a':
a + 215 = 785
a = 785 - 215
a = 570

Therefore, 570 adult tickets and 215 child tickets were sold on that Saturday at the movie theater.

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