what is the solution

The car drives a distance of 210 kilometers.

To find the distance the car drives, we can use the formula:

Distance = Speed × Time

The given speed is 90 km/h. However, we need to convert the time of 2 hours and 20 minutes into hours.

Since there are 60 minutes in an hour, 20 minutes is equal to 20/60 = 1/3 hours. Therefore, the total time is 2 hours + 1/3 hours = 2 1/3 hours.

Now we can calculate the distance:

Distance = 90 km/h × 2 1/3 hours

To multiply a whole number by a mixed fraction, we convert the whole number to a fraction with the same denominator as the mixed fraction:

Distance = 90 km/h × 7/3 hours

Simplifying:

Distance = (90 × 7) km / (3 hours)

Distance = 630 km / 3

Distance = 210 km

Therefore, the car drives a distance of 210 kilometers.

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We do not have enough evidence to conclude that the proportion of students being bullied at school has decreased at a 5% level of significance.

Hypothesis testing is a statistical method used to determine whether a hypothesis about a population parameter is supported by the data. In this case, the hypothesis is that the proportion of students being bullied at school has decreased.

The one-sample proportion test is a type of hypothesis test used to determine whether a proportion in a sample is significantly different from a known population proportion.

In this case, we are testing whether the proportion of students who reported being bullied in the sample of 75 sixth grade students is significantly different from the population proportion of 43%.

To test whether the proportion of students being bullied at school has decreased, we can use a hypothesis test with the null hypothesis that the proportion is still 0.43 and the alternative hypothesis that the proportion is less than 0.43.

Let p be the true proportion of students being bullied at school, then we have:

H₀ : p = 0.43

Hₐ : p < 0.43 (one-tailed test)

Using the sample data, we can calculate the sample proportion of students who reported being bullied at school:

=> \(\hat{p}\) = 30/75 = 0.4

We can use this to calculate the test statistic:

=> z = ( \(\hat{p}\)  - p) / √(p×(1 - p)/n) = (0.4 - 0.43) /√(0.43×0.57/75) = -0.81

At the 5% level of significance with a one-tailed test, the critical z-value is -1.645. Since our calculated test statistic (-0.81) is greater than the critical value, we fail to reject the null hypothesis.

Therefore,

We do not have enough evidence to conclude that the proportion of students being bullied at school has decreased at a 5% level of significance.

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The value of the given integrals can be evaluated as follows:

∫₁⁹ f(x) dx = 11, ∫₁⁹ g(x) dx = 7, ∫₄⁹ f(x) dx = 6, and ∫₁⁴ g(x) dx = 4.

How can we evaluate the given integrals based on the provided information?

To evaluate the integrals, we can use the properties of definite integrals. Since the intervals of integration for the given functions f and g are disjoint, we can split the integrals into smaller intervals and combine the results.

By applying the properties of definite integrals, we can determine the values of the integrals.

Therefore, the answer is:

∫₁⁴ f(x) dx = ∫₁⁹ f(x) dx - ∫₄⁹ f(x) dx = 11 - 6 = 5, and

∫₁⁴ g(x) dx = ∫₁⁹ g(x) dx - ∫₄⁹ g(x) dx = 7 - 4 = 3.

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When the bottom of the 6-foot ladder is 2 feet from the wall, the bottom is moving along the ground at 1 foot per second.

To find the rate at which the bottom of the ladder moves along the ground, we can use the Pythagorean theorem and related rates. Let x be the distance from the bottom of the ladder to the wall, and y be the height of the ladder on the wall. The Pythagorean theorem is x² + y² = 36.

Differentiating both sides with respect to time (t) gives 2x(dx/dt) + 2y(dy/dt) = 0. We are given that dy/dt = -2 ft/s, and we need to find dx/dt when x = 2 feet.

To find y, we can use the Pythagorean theorem: 2² + y² = 36, so y² = 32, and y = 4√2. Plugging these values into the differentiated equation, we get 2(2)(dx/dt) + 2(4√2)(-2) = 0. Solving for dx/dt, we find that dx/dt = 1 ft/s.

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The expression 17n+11 represents the perimeter of a triangle, which is the sum of the lengths of the three sides of the triangle. Therefore, we can use this expression to determine the length of the third side of the triangle.

Since the perimeter of the triangle is equal to 17n+11, we know that the sum of the lengths of the three sides is equal to 17n+11. We can write this as:

a + b + c = 17n+11

where a, b, and c are the lengths of the three sides of the triangle.

To determine the length of the third side, we need to know the lengths of the other two sides. However, since the question does not provide this information, we cannot determine the length of the third side with certainty. In general, there are many different triangles that could have a perimeter of 17n+11, and the length of the third side could vary depending on the specific lengths of the other two sides.

Without additional information about the lengths of the other two sides, it is not possible to determine the length of the third side of the triangle.

Answer:

the answer is 18x-23

Step-by-step explanation:

Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations (I use it all the time).

The slope of the tangent line to the given polar curve at θ = π/3 is √3/5.

Given the polar curve r = 5 + 4cosθ and the point θ = π/3, we'll follow these steps:

1. Convert polar coordinates to rectangular coordinates: x = rcosθ and y = rsinθ
2. Differentiate x and y with respect to θ
3. Find the slope dy/dx

Step 1: Convert polar coordinates to rectangular coordinates:
x = rcosθ = (5 + 4cosθ)cosθ
y = rsinθ = (5 + 4cosθ)sinθ

Step 2: Differentiate x and y with respect to θ:
dx/dθ = -4cosθ(sinθ + cosθ)
dy/dθ = 4cos^2θ - 4sin^2θ - 5sinθ

Step 3: Find the slope dy/dx at θ = π/3:
dy/dx = (dy/dθ) / (dx/dθ) at θ = π/3
= (-4cos(π/3)(sin(π/3) + cos(π/3))) / (4cos^2(π/3) - 4sin^2(π/3) - 5sin(π/3))
= -√3 / -5

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Answer:

D all real numbers

Step-by-step explanation:

Hope this helped

To determine the dimension of the subspace spanned by the given vectors, you would need to provide the specific vectors in question.

Generally, you would check for linear independence among the vectors and count the number of linearly independent vectors. The number of linearly independent vectors will give you the dimension of the subspace in R3.

The given question is: In each of the following, determine the dimension of the subspace of r3 spanned by the given vectors. The dimensions of the subspace of R³ spanned by the given vectors are given as follows:1. $\begin{bmatrix}1 \\ 2 \\ -3 \end{bmatrix}$, $\begin{bmatrix}2 \\ 4 \\ -6 \end{bmatrix}$, $\begin{bmatrix}-1 \\ -2 \\ 3 \end{bmatrix}$.

If we take the row echelon form of the matrix composed of the given vectors, it turns out that there are 2 pivots in the matrix, so there are 2 basis vectors which means that the dimension is equal to 2.2.

$\begin{bmatrix}2 \\ 4 \\ -2 \end{bmatrix}$, $\begin{bmatrix}3 \\ 6 \\ -3 \end{bmatrix}$, $\begin{bmatrix}-1 \\ -2 \\ 1 \end{bmatrix}$The given vectors have a dependent vector, and so, one of the basis vectors can be omitted, and we are left with two basis vectors only.

Thus, the dimension is 2.3. $\begin{bmatrix}1 \\ -3 \\ 0 \end{bmatrix}$, $\begin{bmatrix}-2 \\ 6 \\ 0 \end{bmatrix}$Since the given vectors lie in a plane, there is only one free variable, hence the basis has only one vector, which means the dimension is equal to 1.4. $\begin{bmatrix}1 \\ -1 \\ 1 \end{bmatrix}$, $\begin{bmatrix}2 \\ -2 \\ 2 \end{bmatrix}$,

$\begin{bmatrix}1 \\ 1 \\ 2 \end{bmatrix}$Since the given vectors lie in a plane, there is only one free variable, hence the basis has only one vector, which means the dimension is equal to 1.Thus, the dimensions of the subspace of R³ spanned by the given vectors are as follows:1. 2. 2.3. 1.4. 1.

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Answer:

(-1, 1 1/4) or (-1, 1.25)

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

Note that the perpendicular bisector to line PQ is constructed and attached accordingly. Here is how to do it.

Note that the first stage is to draw a line PQ. But this has already been done.

Next is to place the compass on P as shown in the image above. If you allow you compass (locked at the same degree) to rotate about point P, you will get a circle. However, that is not the objective.

If you also place your compass on point Q, locked to the same degree as when it was on P, and take a rotation around point Q, you will also get a circle.

At some point, you will notice that both circles intersect at two point, which we can call AB₁ and AB₂.

Now you are done with the compass. Take up your ruler, and place it such that it meet both AB₁ and AB₂ but allowing you space to mark a line connecting both points.

Next, using your live or online pencil tool, draw the line from AB₁ to AB₂. Now you have the Perpendicular bisector which you can call AB₁₂.

Note that a perpendicular bisector is a line or plane that intersects a line segment at its midpoint, forming a right angle and dividing the segment into two equal parts.

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To calculate the value of X that Ellen should deposit in the bank, we need to determine the present value of the future payments that will accumulate to $50,000 in six years.

Using the formula for compound interest, the present value can be calculated as follows:

PV = X/(1 + r)^1 + X/(1 + r)^2 + X/(1 + r)^3,

where r is the annual interest rate (5%) expressed as a decimal.

To find the value of X, we set the present value equal to $50,000 and solve for X:

50,000 = X/(1 + 0.05)^1 + X/(1 + 0.05)^2 + X/(1 + 0.05)^3.

Once we determine the value of X, we can proceed to the next step.

For the second part of the question, after four years, the bank raises the interest rate to 6%.

From year four to year six, Ellen's money will continue to accumulate interest.

To find the amount donated, we calculate the future value of the remaining amount after deducting the down payment of $50,000:

Remaining amount = X/(1 + 0.06)^2 + X/(1 + 0.06)^3 + X/(1 + 0.06)^4.

The donated amount is then the difference between the remaining amount and the total accumulated after six years.

By evaluating these expressions, we can determine the value of X and the amount donated by Ellen.

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The best description about the sampling distribution of means for the student's sample is mu x = 45, sigma x = 3.75, shape of distribution unknown.

Sampling distribution is defined as the probability distribution of a statistical measure which is got by the repeated sampling of a specific population.

Given that,

μ = 45 minutes and σ = 15 minutes

Sampling distribution of means for the student's sample is :

μₓ = μ = 45

σₓ = σ / √n, where n is the sample size.

σₓ = 15 / √(16) = 15 / 4 = 3.75

Now since the sample size 16 which is less than 30, shape of the distribution is unknown.

Hence the sampling distribution is, μₓ = 45, σₓ = 3.75, and the shape of distribution is unknown.

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Answer:

3 buses are needed.

Step-by-step explanation:

If there are only 2 buses, it would be full, but there would still be 12 students without a bus. To take all students, you'd need 3 buses. 2 buses will be full, and the other bus would only have 12 students.

Answer:3 buses

Step-by-step explanation:

Because 50+50 is 100 which is two buses

But there are 12 students left so you need 1 more buses

To determine the annual energy output of the small grid-connected wind turbine, additional information is needed, such as the average wind speed at the location and the power curve of the turbine. Without these details, it is not possible to provide a direct answer.

The annual energy output of a wind turbine depends on various factors, including the wind resource available at the site. The wind speed distribution and the power curve of the specific turbine model are crucial in estimating the energy production.

To calculate the annual energy output, the following steps can be taken:

Without the specific wind speed data and power curve of the wind turbine, it is not possible to calculate the annual energy output accurately. These details are crucial in estimating the energy production of the small grid-connected wind turbine.

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The height of the cube brick is 7 units and the volume is equal to 343 unit³

The volume of a cube is defined as the total number of cubic units occupied by the cube. The formula is given as V = a³ where "a" is the length of edge or sides.

The length of an edge for the cube brick is 7 units which implies the height represented by h is also 7 units and the volume is calculated as follows:

volume of cube brick = 7 units × 7 units × 7 units

volume of cube brick = 343 units ³

Therefore, the height of the cube brick is 7 units and the volume is equal to 343 unit³

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Explanation

We are given a triangle

and then asked to determine the value of x

To do so, we know that the total angles in a triangle are 180 degrees

Thus

The value of x is 41 degrees

Answer:

Step-by-step explanation:

1st use the two points to find the slope of the line that passes thru those two points

m = y2 - y1 / x2  - x1    

where point1 = ( x1, y1 )  and point2 = (x2, y2 )

your are given P1 = ( -2,10)  and P2 = (1,1)

find the slope

m = 1-(-2) / 1-10

m = 1+2 / -9

m = 3 / -9

m = - 1/3

then use the point-slope formula [y-y1 = m(x-x1)] with either of the two points, I'll use P2 b/c it seems easier (1,1) , you get the same results with either point and work the problem to the slope-intercept form [y = mx +b ]

y -y1 = m(x-x1)

y-1 = -1/3(x-1)

y-1 = -1/3x + 1/3

y = -1/3x + 1/3 + 1

y = -1/3x + 4/3

:)   got it ?

The probability of getting 2 the same color is 9/11.

What is probability?

  According to the probability formula, the probability of an event occurring, or P(E), is equal to the proportion of positive outcomes to all outcomes. P(E) is defined mathematically as favorable outcomes divided by total outcomes. Mathematical branch known as probability deals with determining the possibility of an event occurring. Here using probability we can also calculate combination .

Here the total number of marbles are,

=>Total marbles = Blue + Red + Green

=>Total marbles = 5 + 4 + 3

=>Total marbles = 12

Then, Probability of a green = 3/12

=> Probability of not green = 1 - 3/12 = 9/12=3/4

To get exactly one green in two draws, we either get a green, not green, or a not green, green

=>First Draw Green, Second Draw Not Green

=> 1st draw: Probability of a green = 3/12

In 2nd draw: Probability of not green = 9/11 <-- 11 since we did not replace the first marble

To get the probability of the event, since each draw is independent, we multiply both probabilities

=> Probability of the event is (5/12) * (9/11) = 45/132

First Draw Not Green, Second Draw Not Green

=>1st draw: Probability of not a green = 9/12

=>2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble

To get the probability of the event, since each draw is independent, we multiply both probabilities

=>Probability of the event is (9/12) * (7/11) = 63/132

To get the probability of exactly one green, we add both of the events:

First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green

=> 45/132 + 63/132 = 108/132=9/11.

Hence the probability of getting 2 the same color is 9/11.

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Answer:

The area of the figure is 80 ft^2.

Step-by-step explanation:

Answer:48

Step-by-step explanation:

Answer:

The light blue/greenish one that says T=PV/K or Greeland

Step-by-step explanation:

We can make the equation more simplier by multiplying both sides by P to remove fractions.

It would become VP=KT

The only answer with VP or PV is B, or the T=PV/K

also, to isolate T, divide the VP=KT by K on both sides to isolate T.

VP/K=T

Answer:

I think the  answer is D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

??

Step-by-step explanation:

The normally distributed process has specifications of LSL = 75 and USL = 85 has a Cp of 2.22 , this process is capable and 0.08 defective parts can be expected per day.

To obtain the estimate of Cp, we first need to calculate the process capability index (Cpk) using the formula:

Cpk = min[(USL - mean) / (3 * standard deviation), (mean - LSL) / (3 * standard deviation)]

In this case, the sample mean is 80 and the sample standard deviation is 1.5, so:

Cpk = min[(85 - 80) / (3 * 1.5), (80 - 75) / (3 * 1.5)]
   = min[1.11, 1.11]
   = 1.11

To obtain Cp, we simply multiply Cpk by 2, since Cp = 2 * Cpk when the process is centered:

Cp = 2 * Cpk
  = 2 * 1.11
  = 2.22

Since Cp is greater than 1.0, this process is capable.

To calculate the expected number of defective parts per day, we need to know the proportion of parts that are defective.

Assuming that the process is centered, the proportion of parts that are defective can be estimated using the area under the normal distribution curve beyond the specification limits.

Since the process is normally distributed with mean 80 and standard deviation 1.5, we can use a standard normal distribution table to find the area beyond the limits:

Area beyond USL = P(Z > (USL - mean) / standard deviation) = P(Z > (85 - 80) / 1.5) = P(Z > 3.33) = 0.0004

Area beyond LSL = P(Z < (LSL - mean) / standard deviation) = P(Z < (75 - 80) / 1.5) = P(Z < -3.33) = 0.0004

So the proportion of parts that are defective is:

Proportion defective = 0.0004 + 0.0004 = 0.0008

To find the expected number of defective parts per day, we multiply this proportion by the number of parts produced per day:

Expected number of defective parts per day = 0.0008 * 100 = 0.08

So we would expect to see approximately 0.08 defective parts per day.

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It would cost approximately $1.10 to use the clothes washer.

To calculate the cost of using the clothes washer, you'll need to multiply the energy usage (in kilowatts) by the duration (in hours) and the cost per kilowatt-hour. In this case, the clothes washer used 2.6 kilowatts for 0.9 hours and the electricity cost is $0.47 per kilowatt-hour.

To find the total cost, use the following formula:

Total cost = Energy usage (kilowatts) × Duration (hours) × Cost per kilowatt-hour

Plug in the given values:

Total cost = 2.6 kilowatts × 0.9 hours × $0.47 per kilowatt-hour

Total cost = $1.1046

To find the cost to the nearest penny, round the result to two decimal places:

Total cost = $1.10

So, it cost approximately $1.10 to use the clothes washer.

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Answer:

21

Step-by-step explanation:

I set it up as a table and found the equation. With increasing student counting it increases by six. So 6 times the number of students of counting gives you your output (y).

Input | Output                                                       Equation: 6x = y

1              6                                                            

2             12            

3             18                

4             24                    

5             30    

....             .....    

19             114

20            120

21             126

Hope this makes sense

Answer:

I think it's 34%

Step-by-step explanation:

hope this helps love you <3

The table of values that represents exponential decay is (c)

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

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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