The height of a triangle is one-third of its base. If the area is 121.5ft^2, what is the height of the triangle?​

The magnitude of the given resultant vector is found as :C = 16.19 units. The direction is shown in figure.

For the stated question:

By using the cosine theory of the vectors:

C² = A² + B² - 2A.B cosФ

C² = 16.0² + 7.00² - 2(16.0)(7.00).B cosФ79°

On solving:

C = 16.19 units

Thus, the magnitude of the given resultant vector is found as :C = 16.19 units. The direction is shown in figure.

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The figure for the question is attached.

The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

His shadow changing at the instant when he is 24 feet from the pole Is \(\frac{95}{13}\)

What do triangles that are similar mean?

The related angle measurements and proportional side lengths of similar triangles are the same.

In this diagram, x represents the distance between the man and the pole, while y represents the distance between the shadow's tip and the pole. My assumption is that the man and the pole are both standing straight up, making the two triangles comparable.

by comparison, \(\frac{y-x}{y} = \frac{6}{19}\)

\(19(y-x)=6(y)\\19y-19x=6y\\19y-6y=19x\\13y=19x\\y=\frac{19}{13} y\)

differentiate both sides with respect to t or time.

\(\frac{dy}{dt}=\frac{19}{13}\frac{dx}{dt}\)

You know \(\frac{dx}{dt}\) = 5 ft/s because the man is edging away from the pole at that pace. Find out \(\frac{dy}{dt}\) how quickly the shadow's tip is moving.

That Means, \(\frac{dy}{dt}= \frac{19}{13} * 5 = \frac{95}{13}\)ft/s
Actually, it doesn't matter how far the man is from the pole because only his speed impacts how quickly his shadow moves.

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a) The area of the first circle is approximately 254.34 square inches

b) The area of the second circle is approximately 70650 square inches.

a) The area of a circle can be calculated using the formula A = πr², where π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

For the first circle with a diameter of 18 inches, we can find the radius by dividing the diameter by 2:

r = 18/2 = 9 inches

Now we can calculate the area using the formula:

A = πr² = 3.14 x 9² = 254.34 square inches

Therefore, the area of the first circle is approximately 254.34 square inches.

b) For the second circle with a diameter of 25 feet, we need to convert the diameter to inches, since our formula uses radius in inches:

25 feet = 25 x 12 inches = 300 inches

Then we can find the radius by dividing by 2:

r = 300/2 = 150 inches

Now we can calculate the area using the formula:

A = πr² = 3.14 x 150² = 70650 square inches

Therefore, the area of the second circle is approximately 70650 square inches.

Note that the units for the second calculation are in square inches, not square feet, because we used the formula that requires radius in inches.

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Answer:

E) Fill in "AT", "IN" or "ON":

My birthday is ... on ..... the 30th of July. Last year I had a great day, I got up ..Olur 8 o'clock ..at...... the morning and tidied the house. Thenthe afternoon I went into .town with my friend to buy food for the party. The party started.at....7 o'clock ..in..the evening and didn't stop until very late ....at..... night!the 31" of July I wasvery tired, so I went to bed early ....in......... the evening.

F) Fill in the spaces in the invitation with "IN", "ON" or "AT”,

I'm going to have a party! I hope you can come!!

It's going to start ...at...... 5 o'clock .in....... the afternoon.....on...... the secong Saturday .at........ August. We'regoing to have it in Tom's house on Wilton Avenue.There's a big garden and we're going to have the party inthe garden. Did you know that my birthday is ....on.... the eighth? Butas you can see, the party is going to be ....at...... the tenth.Why? Parties are better ...at....... the weekend!

BIRTHDAY PRESENTS WELCOME ANYDAY!!!!

Step-by-step explanation:

I have written answer is bold .

please mark me brainliest

  c

Step-by-step explanation:

The assumption for normality is correct.There is no strong evidence to indicate that the mean rod diameter is not 8.20 mm.

From the Histogram, the data appears to be roughly symmetric and bell-shaped, which is consistent with a normal distribution. Additionally, from the normal probability plot, the points appear to follow a roughly straight line, indicating that the data is also consistent with a normal distribution.

To test whether the mean rod diameter is not 8.20 mm using a fixed-level test with 0.05, we can perform a one-sample t-test. The null hypothesis is that the mean rod diameter is 8.20 mm, and the alternative hypothesis is that the mean rod diameter is not 8.20 mm.

Using a t-test calculator, we find that the test statistic is t = 1.432 and the corresponding two-tailed p-value is 0.178. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is no strong evidence to indicate that the mean rod diameter is not 8.20 mm.

To find a 95% two-sided confidence interval on the mean rod diameter, we can use a t-distribution with 11 degrees of freedom (n - 1). Using a confidence interval calculator, we find that the lower bound of the interval is 8.200 and the upper bound of the interval is 8.345.

Therefore, we can be 95% confident that the true mean rod diameter is between 8.200 mm and 8.345 mm. A practical interpretation of this interval is that if we were to take many random samples of 12 rods and calculate the mean diameter for each sample, we would expect about 95% of the resulting confidence intervals to contain the true mean diameter of all rods produced by the machine.

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Answer:

$4,230

Step-by-step explanation:

There are 846 puzzles sold and including tax, it is $5 per puzzle. Multiply the amount of puzzles by cost and you get the total cost of all puzzles sold including tax.

We can plot the vector r(t) and the vector N(T) at the given value of t = T.

To find the principal unit normal for the vector-valued function r(t) = sin(t)i + tcos(t)j + tk, we need to compute the derivative of r(t) with respect to t and then normalize it to obtain a unit vector.

First, let's find the derivative of r(t):

r'(t) = cos(t)i + (cos(t) - tsin(t))j + k

Next, we'll normalize the vector r'(t) to obtain the unit vector:

||r'(t)|| = sqrt((cos(t))^2 + (cos(t) - tsin(t))^2 + 1^2)

Now, we can find the principal unit normal vector by dividing r'(t) by its magnitude:

N(t) = r'(t) / ||r'(t)||

Let's evaluate the principal unit normal at t = T:

N(T) = (cos(T)i + (cos(T) - Tsin(T))j + k) / ||r'(T)||

To sketch the situation, we can plot the vector r(t) and the vector N(T) at the given value of t = T.

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Note that the the equation of the second line is y - 2 = (-1)(x - 0). The system of equations has no solutions, since the lines do not intersect.

One way to approach this problem is to find the slope of the line that passes through (0, -3) and (2, 0), which is:

slope = (0 - (-3))/(2 - 0) = 3/2

Then, we can use point-slope form to write the equation of this line:

y - (-3) = (3/2)(x - 0)

Simplifying, we get:

y = (3/2)x - 3

Now, we need to find a line that goes through (0, 2) and has a different slope than the first line. One way to do this is to choose a point that is not on the first line, say (1, 1), and use it to find the slope of the second line:

slope = (2 - 1)/(0 - 1) = -1

Then, we can use point-slope form again to write the equation of the second line:

y - 2 = (-1)(x - 0)

Simplifying, we get:

y = -x + 2

Now, we have two equations:

y = (3/2)x - 3

y = -x + 2

We can solve for the point of intersection by setting these two equations equal to each other:

(3/2)x - 3 = -x + 2

Simplifying and solving for x, we get:

x = 8/5

Substituting back into either equation, we get:

y = (3/2)(8/5) - 3 = -3/5

Therefore, the system of equations has no solutions, since the lines do not intersect.

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Divide the number of favorable outcomes by the total number of possible outcomes.

To calculate the probability of a spinner, you need to divide the number of favorable outcomes by the total number of possible outcomes. For example, if a spinner has 6 equal sections numbered 1 through 6, the probability of landing on any one particular number would be 1/6 or approximately 16.67%. If there were 2 sections labeled with a star and 4 sections labeled with a number, the probability of landing on a star would be 2/6 or 1/3, which is approximately 33.33%.

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One way to simplify variables with many levels (or decimal places) when creating a frequency distribution is to organize the data into class intervals (option B).

By grouping the data into intervals, the frequency distribution becomes more manageable and easier to interpret. This process involves dividing the range of values into distinct intervals or categories and then counting the number of observations falling within each interval. Class intervals provide a summary of the data by grouping similar values together, reducing the complexity of individual levels or decimal places.

This simplification technique is particularly useful when dealing with large datasets or continuous variables that have numerous levels or decimal values, allowing for a clearer representation and analysis of the data.

Option B holds true.

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SONIC

Step-by-step explanation:

I looked up how fast each of them could run and sonic is the fastest, hold on, got it mixed up turns out flash is the fastest

Answer:

= $20.

Step-by-step explanation:

items pay now = x

40 : 100 = x : 50

40/100 = x/50

40× 5o = 100x

2000 = 100x

2000/100 = 100x/100

$20= x

therefore you pay $20 item that used to cost $50.

Answer:

I think its B)

Step-by-step explanation:

The harder you hit a baseball, the further the ball travels.

This is newton's first law of motion.

Option A is the correct answer.

It states that every object will remain in its state unless an external force acts on it.

Example:

Moving forward for a person sitting inside a moving car when it suddenly stops.

We have,

The harder you hit a baseball, the further the ball travels.

This is newton's first law of motion.

If it was about the fastest the ball travels it will be newtons second law of motion.

Thus,

The harder you hit a baseball, the further the ball travels is an example of Newton's first law of motion.

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Answer:

312x12 or \(2^{5} *3^{2}*13\)

is 3744

Step-by-step explanation:

The number line shows the value of 5 - (-8) = 13.

Addition:

Subtraction:

Here the given operation is subtraction. Where a subtrahend is a negative number i.e., -8.

Step1: Start from '5' on the number line.

Step2: Since the subtrahend is a negative number, move to the right side on the number line from '5'.

Step3: Thus, the number obtained on the line is 13.

Step4: Algebraically the result is 5 - (-8) = 5 + 8 = 13.

The number line for this operation is shown below.

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A value of 26 is 2.5 standard deviations away from the mean.

To find the number of standard deviations away from the mean, we can use the formula:

z = (x - μ) / σ

where x is the value we want to convert to a z-score, μ is the population mean, and σ is the population standard deviation.

In this case, the value we want to convert is x = 26, the population mean is μ = 16, and the population standard deviation is σ = 4. Substituting these values into the formula, we get:

z = (26 - 16) / 4 = 2.5

This means that the value of 26 is 2.5 standard deviations away from the mean. Since the z-score is positive, we know that the value of 26 is above the mean. Therefore, the answer is option D, 2.5.

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Answer: Around 67%

Step-by-step explanation:

92+70+41=203

203/3=67 2/3

Around 67%

Answer:

I think it's a 67.667

Step-by-step explanation:

1.Multiply each grade by the credits or weight attached to it

2. add all of the weighted grades together (or just the grades if there's no weighting)

3. divide the sum by the number of grades you added together

Answer: it A

Step-by-step explanation:

Halpert Corporation's overall equipment effectiveness (OEE) was approximately 0.51.

OEE is a measure of how effectively a machine or equipment is utilized in producing quality output. It takes into account three factors: availability, performance, and quality.
To calculate OEE, we need to consider the following formula:
OEE = Availability * Performance * Quality
Availability: This is the ratio of actual run time to machine time available. In this case, the availability is 2,500 minutes / 3,125 minutes = 0.8.
Performance: This is the ratio of actual run rate to ideal run rate. Here, the performance is 2.4 units per minute / 3.2 units per minute = 0.75.
Quality: This is the ratio of defect-free output to total output. In this case, the quality is 5,100 units / 6,000 units = 0.85.
Now, we can calculate the overall equipment effectiveness (OEE):
OEE = 0.8 * 0.75 * 0.85 = 0.51
Therefore, Halpert Corporation's OEE is approximately 0.51, indicating that their machine utilization is at 51% efficiency.

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Answer: 720

Step-by-step explanation: 1800 x 40%

Answer:

720 math books

Step-by-step explanation:

1800×40%= 720

there are 720 math books

An appropriate method for randomly assigning 60 participants to three groups, with each group having 20 participants, can be achieved using a randomized block design. Here's a suggested method:

Create a list of the 60 participants' names or ID numbers.

1. Randomly order the list of participants using a randomization method such as a random number generator or drawing names from a hat.

2.Divide the randomized list into three equal-sized blocks of 20 participants each. Each block represents one group.

3. Assign the participants in the first block to Group 1, the participants in the second block to Group 2, and the participants in the third block to Group 3.

By using this method, you ensure that the assignment of participants to groups is random and balanced, as each participant has an equal chance of being in any of the three groups.

Once the participants are assigned to their respective groups, you can proceed with conducting the visual search task before the assigned game and record the time to complete it. After the game is played, repeat the visual search task and record the time again. Calculate the mean improvement time (time before minus time after) for each group separately to analyze the impact of the game on task completion time.

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9514 1404 393

Answer:

  see below

Step-by-step explanation:

This question is easily answered using your calculator. You can also do some estimation.

√26 is a little more than 5, so 2/3 of 5 is 10/3 ≈ 3.3. A little more is 3.4.

__

3√5 is about 3 times 2.23 or 6.69. The value 6.71 is real close.

__

1.75π is about 7/4 × 22/7 = 22/4 = 5.5

__

√111 is √(100·(1 +0.11)) ≈ 10·(1 +0.11/2) ≈ 10.55. Half that is about 5.275, close to 5.27.

(With some experience, you learn that the percentage change in a root is about half the percentage change in the value being rooted. Here an 11% increase in the value being rooted results in approximately a 5.5% increase in the root. The smaller the percentage, the better this approximation is.)

Answer:

i think u missed out the missing variable

Step-by-step explanation:

The surface area of the figure is equal to 641.1 square inches.

The figure comprises of a smaller and a bigger cone, the sum of their surface area is the surface area of the figure.

Surface area of cone = πr[r + √(h² + r²)]

surface area of smaller cone = 22/7 × 6in[6in + √(8² + 6²)]

surface area of smaller cone = 301.7 square inches

Height of the bigger cone = √(12² - 6²) = 10.4in

surface area of bigger cone = 22/7 × 6in[6in + √(10.4² + 6²)]

surface area of bigger cone = 339.4 square inches

surface area of the shape = 301.7 + 339.4

surface area of the shape = 641.1 square inches.

Therefore, the surface area of the figure is equal to 641.1 square inches.

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The graph for the line that represents this equation: y+2=1/2(x+2) is attached.

1) Solve the equation for y

y + 2 = ½(x + 2)

y = ½(x + 2) - 2

Then, create a table containing a few values of x and y. I chose x = -2, 0, and 2.

Plot your points. Draw dots at the coordinates of each point.

Draw the graph. Draw a smooth line through the points. Extend the lines in both directions to the edges of the plot area.

In conclusion, the graph is attached.

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Graph the line that represents this equation:y+2=1/2(x+2)

There might be some non-linear pattern or other factors that the linear regression model fails to capture.

When a student fits a linear regression model for a class assignment, it is common practice to analyze the residuals to assess the model's performance. Residuals represent the differences between the observed values (yi) and the predicted values (yi head) obtained from the regression model.

In this case, the student plotted the residuals against the observed values (yi) and observed a positive relationship. This positive relationship indicates that the model tends to underestimate the values for some data points and overestimate them for others. In other words, the model's predictions tend to be consistently lower or higher than the actual observed values.

However, when the student plotted the residuals against the fitted values (yi head), they found no relationship. This means that the residuals are not systematically related to the predicted values. In other words, the model's performance is not influenced by the magnitude or direction of the predicted values.

This situation suggests that the linear regression model may not adequately capture the underlying relationship between the predictors and the response variable. It is possible that a linear model is not the best fit for the data, and a more complex model or a different regression approach may be required.

Alternatively, there might be some non-linear pattern or other factors that the linear regression model fails to capture. It would be advisable for the student to investigate further, possibly by exploring different model specifications, checking for influential data points, or considering additional predictors or transformations of the variables to improve the model's performance.

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Tim drove at a distance of 511 km in 7 h. His average driving speed in km/h is 73.

By computing Tim's average driving speed, we have to divide the total distance that he traveled by the time it takes him to complete the whole journey. In this respect, Tim drove a total distance of 511 km in 7 hours.

Average driving speed = Total distance/Total time taken

By putting the values in the equation we get :

Average driving speed =\(\frac{ 511 km}{7 h}\)

Now by computing  the average driving speed:

Average driving speed = 73 km

So, Tim's average driving speed was 73 km/h.

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Answer:

20

Step-by-step explanation: