Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths.
Base 3 1/2 feet, altitude 3/4 feet.

Answer:

Step-by-step explanation:

I am going to assume that you are doing this on your calculator using the stat button as opposed to having to find it by hand which is so extremely long and drawn out, you'd be dead by the time we found the equation...

The equation of the line of best fit is

y = 1.383x - 1.526

I would explain to you how to do that, but it's a very involved process on your calculator. Find out how to do it and it's the easiest thing in the world!!!

The required equation of the line is y = 0.667x + 2.334

From the table given equation of the line is determined.
x = 4  7  10  12  13
y = 5  7  12  14  18

A line is a curve showing the shortest distance between 2 points.

Standard equation of line, y =mx + c
The slope of equation m = \(\frac{y_2-y_1}{x_2-x_1}\) and c is y intercept.
                                m  = 7-5/7-4
                                m = 2/3
Now put m in the standard equation
y = 2x/3 + c  - - - - -(1)
to find the value of c we will put a point  (7, 7) in the equation.

7 = 7*2/3 + c
c = 7 - 14/3
c = (21-14)/3
c = 7/3
Put c in equation 1
y = 2x/3 + 7/3
y = 0.667 x +2.334

Thus, The required equation of the line is y = 0.667 x +2.334

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We have the following:

Answer:

Im not sure about a but, b= 38

Step-by-step explanation

b: 90 - 52 = 38

*90 because it is a right angle

The work required can be calculated by multiplying the weight of the water by the distance it needs to be lifted. Given that the density of water is 1000 kg/m³.

The work required to pump the water out of the pool can be calculated using the formula:

Work = Force × Distance

In this case, the force is the weight of the water and the distance is the height the water needs to be lifted.

First, we need to calculate the volume of water in the pool. The volume of a rectangular box is given by:

Volume = Length × Width × Depth

Substituting the given values, we have:

Volume = 28 m × 12 m × 2.4 m = 806.4 m³

Next, we calculate the weight of the water using the formula:

Weight = Density × Volume × Gravity

Given that the density of water is 1000 kg/m³ and the acceleration due to gravity is approximately 9.8 m/s², we have:

Weight = 1000 kg/m³ × 806.4 m³ × 9.8 m/s² ≈ 7,913,920 N

Finally, we calculate the work required to pump the water out of the pool by multiplying the weight of the water by the distance it needs to be lifted. Since the pool is full, the water needs to be lifted by its depth, which is 2.4 m:

Work = 7,913,920 N × 2.4 m = 18,913,408 joules

Therefore, approximately 18,913,408 joules of work are required to pump the water out of the pool when it is full.

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Answer: 9c+12

Step-by-step explanation:

To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer:

1. 24

2. 4 with power 5 (4⁵)

Number 1 is going to be 24

So, here we have the following.

\((2)(3)(4)\)

The equation in a simpler form is the following.

\(2x3x4\)

So, \(2x3x4=24\).

Number 2 is going to be 4⁵ (4 to the 5th power.)

So, we have the equation \(4x4x4x4x4\).

If we were to simplify that into an exponent we would do the following.

Count how many 4s there are and if you counted right then there is 5 4s.

So that means it is 4 to the 5th power.

If this helped could i get brainliest?

The probability that a randomly selected member of the US labor force was unemployed in 2011 was approximately 0.087 or 8.7%.

This can be calculated by dividing the number of unemployed individuals in the labor force by the total number of individuals in the labor force. According to the US Bureau of Labor Statistics, there were 13.9 million unemployed individuals in the US labor force in 2011, out of a total labor force of 159.7 million. Dividing 13.9 million by 159.7 million gives a probability of approximately 0.087, or 8.7%.

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The probability is 0.9772. The average age of professors at a certain university is normally distributed with an average of 45.0 years and a standard deviation of 6.0 years.

If 16 professors are chosen at random for a committee, find the probability that the average age of those professors is greater than 42.0 years. We are required to find the probability that the average age of the 16 professors is greater than 42 years. Let us consider the mean of sample means as mu_x = 45 years. The standard error of the mean can be calculated as;  standard error = standard deviation/sqrt(n)`where n = sample size.

Standard error = 6.0/sqrt(16) = 1.5. Therefore, z-score is calculated as; z-score = (sample mean - population mean)/standard error = (42-45)/1.5 = -2. Now, the probability of Z being less than -2 can be found from the z-table as P(Z < -2) = 0.0228. So, the probability that the average age of those professors is greater than 42 years is 1- P(Z < -2) = 1- 0.0228 = 0.9772.

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Answer:

3 hours and 30 minutes

Step-by-step explanation:

8:15+3=11:15

11:15+30=11:45

Answer:

15 hr 30 min

Step-by-step explanation:

8:15 - 9 am = 45 min

9 am to 11 pm = 14 hours

11pm - 11:45 pm = 45 min

90 min = 1 hr 30 min

14 hr + 1 hr 30 min = 15 hr 30 min

We use the t-distribution instead of the normal distribution to construct confidence intervals for a population means, u, when Population Standard Deviation 0 is known.

When we use the T distribution instead of the normal distribution to construct a confidence interval for the population mean, if you have the population standard deviation sigma, you are using the standard normal distribution.

The t-distribution, also known as the Student's t-distribution, is a probability distribution similar to the normal bell-shaped distribution, but with heavier tails. It is used to estimate population parameters with small samples or unknown variance. The T distribution is more prone to outliers than the normal distribution and therefore has fatter tails. The t-distribution is the basis for calculating t-tests in statistics.

The normal distribution is used when the population distribution is assumed to be normal. The t-distribution is similar to the normal distribution, except with thicker tails. Both assume that the population is normally distributed. Therefore, the T distribution has higher kurtosis than the normal distribution. The t-distribution is more likely to give values ​​far from the mean than the normal distribution.

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The sun would more frequently be reaching the ground at a high angle at latitude 0° (the equator). Option A is correct.

What is latitude?

Latitude is the angle north or south of the equator and extends horizontally over the globe. Longitude, on the other hand, runs from east to east and runs vertically across the globe.

On any given day, only points on Earth's surface that are located along a single line of latitude can experience sunlight at a 90-degree angle. Lower levels of sunshine are present everywhere else. The sun's beams are typically strongest at the equator and weakest at the poles.

Option A is correct,0° (the equator).

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The limit of function \($\lim_{x\to 0} \frac{10-17x}{1-x}$\) is 10. The limit \($\lim_{x\to 0} \frac{-0.0419x+17}{20}$\) of is evaluated to be \($\frac{17}{20}$\). The limit of the function is \($\frac{11}{5}$\).

Limit evaluation is a fundamental concept in calculus that involves determining the behavior of a function as the input variable approaches a specific value or infinity. The concept is used extensively in various branches of mathematics, physics, and engineering. A limit is defined as the value that a function approaches as its input variable gets closer and closer to a specific value, without necessarily reaching that value.

Using direct substitution, we get \($\frac{10-17\cdot0}{1-0} = 10$\). Therefore, the limit exists and equals 10.

Using direct substitution, we get \($\frac{-0.0419\cdot0+17}{20} = \frac{17}{20}$\). Therefore, the limit exists and equals \($\frac{17}{20}$\).

Using direct substitution, we get \($\frac{6\cdot3-7}{4\cdot3-19} = \frac{11}{5}$\). Therefore, the limit exists and equals \($\frac{11}{5}$\).

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--The complete question is, Evaluate the following limits:

1. \($\lim_{x\to 0} \frac{10-17x}{1-x}$\)

2. \($\lim_{x\to 0} \frac{-0.0419x+17}{20}$\)

3. \($\lim_{x\to 3} \frac{6x-7}{4x-19}$\)

For each of the above limits, provide the final answer if it exists or show that it diverges if applicable.--

As per the details given, the equation of the plane passing through the point (−2, 7, 10) and perpendicular to the line x = 3t, y = 4t, z = 3 − 4t is 3x + 4y - 4z + 18 = 0.

We require a point on the plane and the normal vector to the plane in order to find the equation of the plane. On the plane, the specified point (2, 7, 10) is located. We must now locate the normal vector.

The parametric form of the line x = 3t, y = 4t, and z = 3 4t. This line's direction vector is [3, 4, -4]. Use the direction vector of the line as the normal vector in order to get the normal vector to the plane.

3(x + 2) + 4(y - 7) - 4(z - 10) = 0

3x + 6 + 4y - 28 - 4z + 40 = 0

3x + 4y - 4z + 18 = 0

Thus, the equation of the plane passing through the point (−2, 7, 10) and perpendicular to the line x = 3t, y = 4t, z = 3 − 4t is 3x + 4y - 4z + 18 = 0.

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Answer:  165,24

Step-by-step explanation: do 17 x 1.35 then get the answer for it and times it by 7.2 hope this helps

The measurement of angle DBC is equal to 33°, here we have to know the meaning of angle.

Angle is the measurement distance between two straight line or ray when they meet and it can also say that their one part is opening and other part is joint.

We have given that, ∠ABD = 4x, ∠DBC = 3x and measure of angle ABC is equal to 77°.

So ∠ABD + ∠DBC = ∠ ABC

⇒  4x + 3x = 77°

⇒ 7x = 77°

⇒ x = 11°

So, ∠ ABD = 4x = 4 * 11 = 44°

and, ∠DBC = 3x = 3 * 11 = 33°

Therefore, angle DBC is equal to 33°.

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Complete Question:

What is the measure of angle DBC if the measure of angle ABD is represented by 4x, the measure of angle DBC is represented by 3x and the measure of angle ABC is 77° ?

The critical value for the \(X^{2}\) goodness-of-fit test with 4 categories and α = 0.05 is approximately 7.815.

In a chi-square goodness-of-fit test, we compare the observed frequencies of a nominal variable across different categories with the expected frequencies under the null hypothesis. The test statistic, \(X^{2}\), measures the discrepancy between the observed and expected frequencies.

To determine if the observed frequencies significantly differ from the expected frequencies, we compare the test statistic with the critical value at the specified significance level (α). The critical value is determined based on the degrees of freedom, which is the number of categories minus 1.

In this scenario, the nominal variable has 4 categories. Degrees of freedom is (4 - 1) = 3. Using the degrees of freedom and the significance level of α = 0.05, we can consult the chi-square distribution table or use statistical software to find the critical value.

The critical value for the \(X^{2}\) goodness-of-fit test with 4 categories and α = 0.05 is approximately 7.815.

Since the test statistic \(X^{2}\) = 6.432 is less than the critical value of 7.815, we fail to reject the null hypothesis. This means that there is not enough evidence to suggest a significant difference between the observed and expected frequencies.

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The area and the perimeter of the room having rectangular shaped base are respectively,   121 feet² & 44 feet

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Given that,

2 of the walls are 11 and 11,

The room is into rectangle shape,

Base area of room = length x width

                               =  11 x 11

                               =   121 feet²

Perimeter of base of the room = Sum of lengths and widths

                                                   = 11 + 11 + 11 + 11

                                                   =   44 feet

Hence, the area and perimeter are respectively 121 feet² & 44 feet

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\(~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}}\\ \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount} \\ pymnt=\textit{periodic payments}\dotfill &\$5000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}\)

\(A=5000\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1\cdot 12}-1}{\frac{0.04}{1}} \right]\implies A=5000\left( \cfrac{1.04^{12}~~ - ~~1}{0.04} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 75129.03~\hfill\)

The marginal pdf of X is fX(x) = (2πσxσy√(1-ρ²))⁻¹ exp⁡[(-1/(2(1-ρ²))) (zx² - 2ρzx . zy + zy²)] dy

The conditional distribution of Y given X = x is Y ∼ N(1.5x - 15, 175).

(a) To derive the marginal pdf of X, we integrate the joint pdf fX,Y(x, y) with respect to y over the entire range of y:

fX(x) = ∫fX,Y(x, y) dy

Given the joint pdf fX,Y(x, y) = (2πσxσy√(1-ρ²))⁻¹ exp⁡[(-1/(2(1-ρ²))) (zx² - 2ρzx . zy + zy²)],

Now, fX(x) = (2πσxσy√(1-ρ²))⁻¹ exp⁡[(-1/(2(1-ρ²))) (zx² - 2ρzx . zy + zy²)] dy

(b) To find the mean and variance of the conditional distribution of Y given X, we use the conditional expectation and conditional variance formulas.

The conditional mean of Y given X = x, E[Y|X = x], is given by:

E[Y|X = x] = μy + (ρσy/σx)(x - μx)

The conditional variance of Y given X = x, Var[Y|X = x], is given by:

Var[Y|X = x] = σy²(1 - ρ²)

(c) Given X ∼ N(50, 100), Y ∼ N(60, 400), and ρ = 0.75, we can use the formulas from part

The conditional mean of Y given X = x is:

E[Y|X = x] = μy + (ρσy/σx)(x - μx)

           = 60 + (0.75 x√400/√100)(x - 50)

           = 60 + (0.75 )( 2)(x - 50)

           = 60 + 1.5(x - 50)

           = 60 + 1.5x - 75

           = 1.5x - 15

The conditional variance of Y given X = x is:

Var[Y|X = x] = σy²(1 - ρ²)

            = 400(1 - 0.75²)

            = 400(1 - 0.5625)

            = 400(0.4375)

            = 175

Therefore, the conditional distribution of Y given X = x is Y ∼ N(1.5x - 15, 175).

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Answer:

245

Step-by-step explanation:

Answer:

678.32 feet

Step-by-step explanation:

Circumference=2π(radius)=2·π·50≈314.15927
314.15927·2=628.31854
628.31854+50=678.31854

Answer:

678 ft (nearest foot)

Step-by-step explanation:

The distance from the center of a circle its edge is its radius.

Given that the distance from the center of a circular tent to the tent’s edge is 50 ft then:

⇒ radius (r) = 50

The edge of a circle is its circumference

Circumference of a circle = \(2\pi r\) (where r is the radius)

Therefore, the circumference of the tent is:

\(\implies 2 \cdot \pi \cdot 50=100\pi\) ft

If Kelly walked around the edge of the tent twice, then walked straight to the center:

⇒ total distance walked = 2 × circumference + radius

                                        = 2 × \(100\pi\) + 50

                                       = 678.3185307...

                                       = 678 ft (nearest foot)

Answer:

Step-by-step explanation:

choices:

W c Z

R c W

0 E Z

∅ c R

{0, 1, 2, ...} c_ W

-2 E W

Answer:

156

Step-by-step explanation:

s8 = n/2 [2t + (n-1)(d)]

= 8/2 [2(2) + (8-1)(5)]

= 4 [4 + (7)(5)]

= 4 (4 + 35)

= 4 (39)

= 156

The probability best prediction for the number of times that Ellen will draw a blue marble is 200.

Number of blue marbles: 222

Number of red marbles: 333

Total number of marbles: 555

Probability of drawing a blue marble:

222/555

= 0.4

Number of times drawing a blue marble:

300300300 x 0.4

= 120,120,120

Rounded to nearest whole number:

120,120

Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. The best prediction for the number of times that Ellen will draw a blue marble is 200. This prediction is based on the fact that there are more red marbles than blue marbles in the bag. To calculate this, we first need to determine the probability of drawing a blue marble; there are 222 blue marbles out of 555 total marbles, so the probability is

222/555

= 0.4.

Multiplying this by the total number of draws (300300300) gives us 120,120,120. Rounding this to the nearest whole number gives us our prediction of 200 times.

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Answer: 1/6 of an hour

Step-by-step explanation: multiply the numerator and denominator by 3 of 1/2 and 1/3 to get 3/6 and 2/6. There is 1/6 more

If a pilot elects to proceed to the selected alternate, the landing minimums used at that airport should be equal to or higher than the minimums required for the original destination airport.

When a pilot chooses to proceed to the selected alternate airport, they must consider the weather conditions at that airport, particularly the landing minimums. The landing minimums are the lowest weather conditions in which an aircraft can safely land at an airport. They are determined by various factors, such as the visibility range and the height of the cloud ceiling.

Therefore, if a pilot decides to go to the alternate airport, they should use the landing minimums for that airport to ensure a safe landing. The landing minimums for the alternate airport should be equal to or higher than the minimums required for the original destination airport.

It's important to note that the pilot must have knowledge of the landing minimums for the alternate airport before deciding to proceed there. If they don't have the necessary information, they should consider other options, such as returning to the departure airport or diverting to a different airport with suitable weather conditions.

In summary, when a pilot chooses to proceed to an alternate airport, they should use the landing minimums for that airport to ensure a safe landing. The pilot must have knowledge of the minimums before proceeding to the alternate airport.

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Possible values of y depend on the value of x. From the given options, we would need to know the specific values of x to determine the corresponding values of y. Without knowing the specific value of x, we cannot identify a specific value of y.

The given equation is y = x^(x-1).

To determine possible values of y, we need to evaluate the expression for different values of x, considering that x > 1.

Let's calculate some values of y for different values of x:

For x = 2:

y = 2^(2-1) = 2^1 = 2

For x = 3:

y = 3^(3-1) = 3^2 = 9

For x = 4:

y = 4^(4-1) = 4^3 = 64

For x = 5:

y = 5^(5-1) = 5^4 = 625

As we can see, possible values of y depend on the value of x. From the given options, we would need to know the specific values of x to determine the corresponding value of y. Without knowing the specific value of x, we cannot identify a specific value of y.

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