1) Uma sala tem o formato de um trapézio, determine a área dessa sala.(a) 10,4 m² (b) 25,6 m² (c) 12,8 m² (d) 15,2 m²

Answer: Pythagorean triples are given by the formula:- AC² = AB² + BC²

The third side in the right triangle measures 23 units

Step-by-step explanation: The Pythagoras theorem as stated in the answer above is used in mathematics to solve for an unknown side(s) in any right angled triangle.

Pythagorean triples are so named because it refers to a right angled triangle in which the values of all three sides are always the same set of three numbers, and changing one of them changes everything completely. A very common Pythagorean triple is given as 3, 4 and 5. This means, the right angled triangle has sides measuring 3, 4 and 5. Hence to solve a right angled triangle with two sides given as 3 and 4 with the Pythagoras theorem is already half solved as the answer would always be 5.

Therefore, in a right triangle with leg lengths of 16, the first thing to note is that this a right isosceles triangle. We know this because a triangle with two legs having the same length is an isosceles triangle. That leaves us with the third side which is the hypotenuse. The Pythagoras formula just as stated above is given as follows;

AC² = AB² + BC²

Where AC is the hypotenuse (longest side), and AB and BC are the other two sides.

AC² = 16² + 16²

AC² = 256 + 256

AC² = 512

Add the square root sign to both sides of the equation

√AC² = √512

AC = 22.62741699...

AC ≈ 23

Therefore the Pythagorean triple as required by the question is given as

16, 16 and 23

On the last day, $675 will be given away.

To find out how much money will be given away on the last day, we need to determine the pattern of the prize amounts given away each day.

Based on the information provided, we can observe that the prize amounts given away each day are increasing in a particular pattern.

On the first day, $25 is given away.

On the second day, $75 is given away.

On the third day, $225 is given away.

Looking at the pattern, we can see that the prize amounts are increasing by a factor of 3 each day. So, we can calculate the prize amount for the last day by continuing this pattern.

To find the prize amount for the last day, we need to calculate $225 multiplied by 3.

$225 * 3 = $675

Therefore, on the last day, $675 will be given away.

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Answer:

10%

Step-by-step explanation:

30/300 people like hip-hop

So, 1/10 or 10% like hip-hop

Answer: 10%

Step-by-step explanation: 30% out of 300% is like 10% out 100%

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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Answer:

C: The graph is not a function of x because the line y = 0 intersects the graph at two points.

Step-by-step explanation:

The line y = 0 will intersect the ellipse at the points, (-4 , 0) , (4 , 0)

Answer:

sqrt(216) = 6×sqrt(6) ≈ 14.6969

Step-by-step explanation:

Pythagoras :

c² = a² + b²

with c being the Hypotenuse.

so, we have

15² = a² + 3²

225 = a² + 9

a² = 225 - 9 = 216

a = sqrt(216) = sqrt(4×54) = sqrt(4×9×6) = 2×3×sqrt(6) =

= 6×sqrt(6)

Answer:

The length of the other leg is 14.697

Step-by-step explanation:

a^2 +b^2= c^2

fractions with the same denominator added together

You must add the numerators and keep the same denominator when adding fractions with the same denominator. Since the denominators of the two fractions are the same, we must add the numerators while maintaining the same denominator, which is 4.

What are the parts of fraction?

A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.

The number below the bar is called the denominator . It tells the number of equal parts into which the whole has been divided. The number above the bar is called the numerator. It tells how many of the equal parts are being considered.

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Answer:

SSS

Step-by-step explanation:

We can see that 2 sides are equal already, and because they share a side, that side is also equal. So, side side side.

Answer:

3×2+2x-5

6-5+2x

1+2x

-4+7×2

-4+14

10

Answer:

7x + 13

Step-by-step explanation:

because the correct answer is 7x+13

Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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Answer:

781250

Step-by-step explanation:

We first need to find the common ratio

-10 /2 = -5

50 / -10 = -5

The common ratio is -5

an = a (r) ^ (n-1)

a9 = 2 ( -5) ^(9-1)

     = 2 (-5)^8

      =781250

The direct variation equation between x and y is 4x = y.

Here, we are given that x and y are in direct variation. In other words, this means that x and y are directly proportional to each other.

Thus, if k is a constant term, then the relation between x and y can be represented as-

x = ky

Now, we are given that if y = 12, x = 3

⇒ 3 = 12k

12k = 3

k= 3/12

k= 1/4

Thus, we found the value of k, the relation will become-

x = y/4

or 4x = y

Thus, the direct variation equation between x and y is 4x = y.

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Answer:

Step-by-step explanation:

Answer:

-1.8

Step-by-step explanation:

I think that is what it is

Answer:

-1.8

Step-by-step explanation:

Just took the Unit Test

No, the plan will not work because tan B = 8/5; B ≈ 58°

There are three primary trigonometric ratios for a right angle triangle and they are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

To get angle B, we will make use of trigonometric ratios to get:

tan B = 8/5

tan B = 1.6

B = tan⁻¹1.6

B = 58°

From the ramp, we can see that the angle is greater than what Gael wants to build and as such we can say it will not work.

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The table with the scale measurements is given by the image shown at the end of the answer.

The measurements are obtained applying the proportion given for each table.

The symbols are given as follows:

For the first table, we have that every inch on the table represents one feet in real life, hence:

For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:

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Answer:

7x = 6

Step-by-step explanation:

  2x - 3y = 10

+ 5x + 3y = -4

------------------------

  7x         = 6

Answer:

c)  1 foot per 2 hours

Step-by-step explanation:

1/6 of a foot (which is 12 inches) is 2 inches

1/3 of an hour (which is 60 minutes) is 20 minutes

2 inches in 20 minutes is the same as 12 inches (which is 1 foot) in 120 minutes (which is 2 hours)

Answer:

Cheapest in london

Step-by-step explanation:

London : £699

Paris : € 799 ÷ 1.13 = £ 707.08 ( approximate)

New York : $ 1,099 ÷ 1.37 = £ 802.19 ( approximate)

Answer:

42

Step-by-step explanation:

a = 2, b = 5, and c = 1

Answer:

The answer is 42 .

Step-by-step explanation:

Here,

a = 2

b = 5

c = 1

Now,

 \(a(4b+c^{2} )\)

\(= 2(4 * 5 +1^{2} )\)

= 2( 20 + 1 )

= 2 x 21

=42

Based on the provided information, a) there is good evidence that coached students gained more on the average than uncoached students. (b) The 99% confidence interval for the difference between the mean gains of the coached and uncoached students is (3.07, 12.93) (c) Based on the work,  it may depend on the individual student and how much they are willing to pay for a small increase in their test scores.

(a) To determine whether there is good evidence that coached students gained more on the average than uncoached students, we can conduct a hypothesis test. The null hypothesis is that the mean gain of coached students is equal to the mean gain of uncoached students, and the alternative hypothesis is that the mean gain of coached students is greater than the mean gain of uncoached students. We can use a t-test to compare the means of the two groups.

The t-value is calculated as follows:

t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^0.5

where x1 and x2 are the mean gains of the coached and uncoached students, respectively, s1 and s2 are the standard deviations of the gains of the coached and uncoached students, respectively, and n1 and n2 are the sample sizes of the coached and uncoached students, respectively.

Plugging in the values from the table, we get:

t = (29 - 21) / (59^2/427 + 52^2/2733)^0.5 = 2.56

Using a t-distribution table with degrees of freedom = n1 + n2 - 2 = 427 + 2733 - 2 = 3158, we find that the p-value for a one-tailed test is 0.005. Since the p-value is less than the significance level of 0.01, we can reject the null hypothesis and conclude that there is good evidence that coached students gained more on the average than uncoached students.

(b) To find the 99% confidence interval for the difference between the mean gains of the coached and uncoached students, we can use the following formula:

(x1 - x2) ± t* (s1^2/n1 + s2^2/n2)^0.5

where t* is the critical value for the t-distribution with degrees of freedom = n1 + n2 - 2 at the 99% confidence level.

Using a t-distribution table, we find that t* = 2.576 for degrees of freedom = 3158 at the 99% confidence level. Plugging in the values from the table, we get:

(29 - 21) ± 2.576 * (59^2/427 + 52^2/2733)^0.5 = 8 ± 4.93

The 99% confidence interval for the difference between the mean gains of the coached and uncoached students is (3.07, 12.93).

(c) Based on the results of the hypothesis test and the confidence interval, it appears that coached students do gain more on the average than uncoached students. However, the difference is not very large, and the confidence interval is fairly wide. Therefore, it is difficult to say for certain whether coaching courses are worth paying for. It may depend on the individual student and how much they are willing to pay for a small increase in their test scores.

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(a) Yes, there is good evidence that coached students gained more on average than uncoached students. The coached students had a mean score of 427, compared to a mean score of 2733 for the uncoached students, suggesting that coaching can have an advantage.
(b) The 99% confidence interval for the difference between coached and uncoached students is 45.5 to 120.5. This suggests that coached students can gain between 45.5 and 120.5 more than uncoached students.
(c) Based on the results of this study, it can be concluded that coaching courses may be worth paying for, as they seem to have an advantage over uncoached students.

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The original price of the bracelet, before tax $0.68

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

Amount = $0.72

Sales tax = 6%

Using the above as a guide, we have the following:

Amount = Original amount * (1 + Sales tax)

Substitute the known values in the above equation, so, we have the following representation

0.72 = Original amount * (1.06)

So, we have

Original amount = 0.68

Hence, the original amount = 0.68

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Answer: 6.75 or 6 3/4

Step-by-step explanation: 3 3/8 x 2 = 6.75 Brainliest please?

Answer:

18p

Step-by-step explanation:

6x3=18

add the p

18p

Answer:

18p

Step-by-step explanation:

you can simply multiply the numbers and add p to the end

Answer: Quadrant III

Step-by-step explanation:

The slope is negative and the y-intercept is positive.

This means that it is impossible for both x and y to be negative, and thus it does not pass through Quadrant III

17.7 gallons of gas would she require to travel 413 miles at this rate when Jenny used 9 gallons of gas to travel 210 miles.

Given that,

Jenny used 9 gallons of gas to travel 210 miles.

We have to find how many gallons of gas would she require to travel 413 miles at this rate.

We know that,

Jenny used 9 gallons of gas to travel 210 miles.

Then

Rate = 210 miles/9 gallons

= 23.3 miles/gallon.

So,

Nicole can achieve a fuel efficiency of 23.3 miles per gallon.

He has a 413-mile drive ahead of him.

So,

413/23.3 = 17.7 gallons needed.

Therefore, 17.7 gallons of gas would she require to travel 413 miles at this rate when Jenny used 9 gallons of gas to travel 210 miles.

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The official poverty line of the United States, developed by Mollie Orshansky, is a measure used to determine the number and percentage of people living in poverty in the country. It sets a threshold income level below which individuals or families are considered to be in poverty.

The official poverty line of the United States was established by Mollie Orshansky in the 1960s. It is calculated based on a threshold income level that varies depending on the size and composition of a household. If a household's income falls below the threshold, they are considered to be living in poverty.

One reason the official poverty line is considered a good way to measure poverty is that it provides a standardized and consistent measure that allows for comparisons over time and across different regions. By using a specific income threshold, it allows policymakers, researchers, and organizations to track changes in poverty rates and develop targeted interventions to address poverty-related issues. It also enables the assessment of poverty trends and the evaluation of the effectiveness of anti-poverty programs.

While the official poverty line has its limitations, such as not accounting for regional variations in the cost of living or considering other factors like access to healthcare or education, it remains an important tool in understanding and addressing poverty in the United States.

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