PLEASE HURRY!!

Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:

A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 9 feet.
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer stating the theorem you used. Show all your work. (5 points)

Part B: The length of rod PR is adjusted to 18 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)

Answer:

2 dp 19.35

1dp 19.4

nearest integer 19

Step-by-step explanation:

\(\frac{6.3}{(\cos71)}\\\)

19.35078697

dp= decimal point

The area of the triangle with a base of 15 yards and height 6 yards is 45 sqaure yards.

A triangle is simply three-sided polygon having three edges and three vertices.

The area of a triangle can be expressed as:

Area = 1/2 × base × height.

From the image:

Base = 15 yards

Height = 6 yards

Area A = ?

To solve for the area of the triangle, plug the given values into the above formula:

Area = 1/2 × base × height

Area = 1/2 × 15 yd × 6 yd

Area = 15 yd × 3 yd

Area = 45 yd²

Therefore, the area is 45 sqaure yards.

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The only value of x in the interval [-3, 3] for which the function equals its average value is approximately x = 2.984.

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

To find the average value of the function f(x) = 6e^x over the interval [-3, 3], we need to evaluate the definite integral of f(x) over that interval and divide the result by the length of the interval:

Average value = (1/(3-(-3))) * ∫[−3, 3] 6e^x dx

= (1/6) * [\(6e^x\)] from -3 to 3

= (1/6) * (\(6e^3\) - \(6e^{(-3)}\))

≈ 118.936

Therefore, the average value of the function over the given interval is approximately 118.936.

To find all values of x in the interval [-3, 3] for which the function equals its average value, we need to solve the equation f(x) = 118.936, which means:

\(6e^x\) = 118.936

Dividing both sides by 6, we get:

\(e^x\) = 19.823666...

Taking the natural logarithm of both sides, we get:

x = ln(19.823666...)

≈ 2.984

Therefore, the only value of x in the interval [-3, 3] for which the function equals its average value is approximately x = 2.984.

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Answer:

18€

Step-by-step explanation:

Given data

Selling price= €30

increase= 12%

Cost price= ???

We know that

% increase= selling price- cost price/cost price*100

let the cost price be x

12= 30- x/x*100

cross multiply

12*100= (30- x)100

1200= 3000-100x

1200-3000=-100x

-1800=-100x

x= 1800/100

x= 18

Hence the price before the increase is 18€

Answer:

A (0,6)  B (6, 1)  C (2,2)

Step-by-step explanation:

A (4, 4)

  [-4, 2]

Subtract 4 - 4 = 0 and then add 4+2 since both of them are positive. Do it for all of the coordinates

Image Coordinates:

A----->A¹(0,6)

B----->B¹(2,3)

C----->C¹(-2,4)

Answer:

the domain of the function is all real numbers less than or equal to 0

In order to find the sample size, we can use the following formula that relates the population and sample standard deviations:

For a confidence interval of 95%, we have z = 1.96.

Then, using the values of the standard deviations, we have:

Rounding to the next whole number, we have a sample size of 139.

Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

In an actual business, the following is an inventory accounting issue that frequently arises:

When a business holds a high amount of inventory, a significant amount of its funds are tied up in stock, which can have a significant impact on its cash flow. When sales are slow or inventory takes longer to sell than expected, a company's cash flow may be impacted, making it difficult for the business to meet its obligations. Therefore, inventory management is one of the most crucial factors that a business must consider.

If a company's inventory management system isn't optimized, it may face stockout costs. It means that the company runs out of inventory or can't meet customer demands due to insufficient inventory. This leads to a loss of sales and clients, resulting in a significant loss to the company.

Inventory accounting is the accounting method used to calculate the value of a company's inventory. The calculation is completed at the end of each accounting period and is utilized to identify the cost of goods sold and to determine the inventory's ending balance. Businesses utilize several inventory accounting methods, including FIFO (First-In, First-Out), LIFO (Last-In, First-Out), and weighted average. All these methods help to calculate the cost of inventory, including production expenses, shipping costs, and storage costs.

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The mean of the given frequency distribution is 587.12.

What is frequency distribution?

In frequency tables or charts, frequency distributions are displayed. The actual number of observations that fall into each range can be seen in frequency distributions, as well as the proportion of observations that do.

We are given a frequency distribution table.

We know that the mean is the average of sum of all the values.

So, we first get the values as :

⇒ 610 * 12 = 7320

⇒ 537 * 6 = 3222

⇒ 597 * 10 = 5970

⇒ 572 * 14 = 8008

⇒ 590 * 9 = 5310

⇒ 606 * 6 = 3636

Now, on adding all the values, we get

⇒ 7320 + 3222 + 5970 + 8008 + 5310 + 3636

⇒ 33466

So,

⇒ Mean =  33466 ÷ 57

⇒ Mean = 587.12

Hence, the mean of the given frequency distribution is 587.12.

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Answer:

Hello,

Step-by-step explanation:

a)

\(y=a^x*b+c\\\\if\ x- > -\infty,\ y- > -1 \ \Longrightarrow\ c=-1\\if\ x=0\ y=1\ \Longrightarrow\ 1=b-1\ \Longrightarrow\ b=2\\if\ x=1\ y=5 \ \Longrightarrow\ a*2-1=5\ \Longrightarrow\ a=3\\\\\boxed{y=2*3^x-1}\\\)

b)

\(f(x,y)=(x-a)(y-b)-k=0\ since\ hyperbola\ "\' equilat\`ere\ in\ French"\\\\\dfrac{\partial{f}}{\partial{x}} =y-b=0\ \Longrightarrow\ y=b\\\\\dfrac{\partial{f}}{\partial{y}} =x-b=0\ \Longrightarrow\ x=a\\\\Here\ center\ is\ (0,2)\ so (x-0)(y-2)=k\\\\(-3,3)\ is \ a\ point\ of \ the\ hyperbola:\\-3*(3-2)=k\ \Longrightarrow\ k=-3\\\\\boxed{x(y-2)=-3}\\\)

c)

It is parabola

y=k*(x-3)(x+3)

(1,24) is a point of the parabola:

24=k*(1²-9) => k=-3

\(\boxed{y=-3(x^2-9)}\\\)

The values of x make the quadratic equation (x-2)² =2 is 2 + √2.

To find the values of x that make the quadratic equation (x-2)² = 2 true, we need to solve for x.

First, we can take the square root of both sides of the equation:

x - 2 = ±√2

Next, we can add 2 to both sides of the equation:

x = 2 ± √2

Therefore, the two solutions for x are:

x = 2 + √2

x = 2 - √2

These are the two values of x that make the quadratic equation (x-2)^2 = 2 true.

To check these solutions, we can substitute each value back into the original equation:

[(2 + √2) - 2]² = 2

Simplifying:

√2² = 2

2 = 2

This solution works. Now let's check the other solution:

[(2 - √2) - 2]² = 2

Simplifying:

-√2² = 2

-2 = 2

This solution does not work, so we discard it. Therefore, the only value of x that makes the quadratic equation (x-2)² = 2 true is: x = 2 + √2.

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A stochastic process X(t) is called a martingale if the expected value of X(t) given all information available up to and including time s is equal to the value of X(s).

Thus, to show that the process X(t):=e^(t/2)cos(W(t)), 0 ≤ t ≤ T is a martingale w.r.t. any filtration for Brownian motion, we need to prove that E(X(t)|F_s) = X(s), where F_s is the sigma-algebra of all events up to time s.

As X(t) is of the form e^(t/2)cos(W(t)), we can use Itô's lemma to obtain the differential form:dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt

Taking the expectation on both sides of this equation gives:E(dX) = E(e^(t/2)cos(W(t))dW) - 1/2 E(e^(t/2)sin(W(t))dt)Now, as E(dW) = 0 and E(dW^2) = dt, the first term of the right-hand side vanishes.

For the second term, we can use the fact that sin(W(t)) is independent of F_s and therefore can be taken outside the conditional expectation:

E(dX) = - 1/2 E(e^(t/2)sin(W(t)))dt = 0Since dX is zero-mean, it follows that X(t) is a martingale w.r.t. any filtration for Brownian motion.

Now, let's represent X(t) as an Itô process on the interval [0,T]. Applying Itô's lemma to X(t) gives:

dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt= dM + 1/2 e^(t/2)sin(W(t))dt

where M is a martingale with M(0) = 0.

Thus, X(t) can be represented as an Itô process on [0,T] of the form:

X(t) = M(t) + ∫₀ᵗ 1/2 e^(s/2)sin(W(s))ds

Hence, we have shown that X(t) is a martingale w.r.t. any filtration for Brownian motion and represented it as an Itô process on any time interval [0,T], T > 0.

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There are no x-coordinate(s) to be found for this particular scenario.

To find the x-coordinate(s) of the point(s) on the graph of the function f(x) where the tangent line is perpendicular to the line 5y - x = 0, we need to solve two conditions:

Find the point(s) on the graph of f(x) where the slope of the tangent line is equal to the negative reciprocal of the slope of the line 5y - x = 0.

Determine the x-coordinate(s) of the point(s) obtained from the first condition.

Let's start by finding the slope of the line 5y - x = 0. We can rewrite the equation in slope-intercept form:

5y = x

y = (1/5)x

The slope of this line is 1/5. Since we want the tangent line to be perpendicular, the slope of the tangent line will be -5 (negative reciprocal of 1/5).

Next, we differentiate the function f(x) to find its derivative, which will give us the slope of the tangent line at any point on the graph.

f(x) = (9²) * (1³)²

f(x) = 81 * 1²

f(x) = 81

The derivative of f(x) is zero since it is a constant function:

f'(x) = 0

Now, we equate the derivative to -5 (the negative reciprocal of the slope of the line) and solve for x:

0 = -5 Since the equation has no solution, it means there are no points on the graph of f(x) where the tangent line is perpendicular to the line 5y - x = 0.

Therefore, there are no x-coordinate(s) to be found for this particular scenario.

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The correct factor is (2x - 3) and (2x + 3).

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

Given

4x² -9 = 0 is a quadratic equation.

The factor of the given equation.

4x² -9 = 0 is a quadratic equation.

According to factorization,

                 4x² - 9 = 0

             (2x)² - 3² = 0

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

Thus the correct factor is (2x - 3) and (2x + 3).

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Answer:

The answer is C or the third option.

Step-by-step explanation:

Looking at the tiles for the third option, there are the same amount of negative and positive x-tiles. This means that they cancel each other out. What's left are the 4 x^2 tiles and 9 negative tiles. When put together the equation is 4x^2 - 9. This option represents the factors of 4x^2 - 9 accurately.

Answer:

300

Step-by-step explanation:

do 15 times 20 and that should make 300.

hope this helps

The directional derivative of the function f(x, y) = cos(x + y) at point P(0, π) in the direction of Q(π/2, 0) is 0.

The directional derivative measures the rate of change of a function in a particular direction. In this case, we are asked to find the directional derivative of the function f(x, y) = cos(x + y) at point P(0, π) in the direction of Q(π/2, 0).

According to Theorem 13.9, the directional derivative DQf(P) can be calculated using the formula DQf(P) = ∇f(P) · uQ, where ∇f(P) represents the gradient of f at point P and uQ is the unit vector in the direction of Q.

First, we find the gradient of f at point P:

∇f(P) = (-sin(0 + π), -sin(0 + π)) = (0, 0)

Next, we determine the unit vector uQ in the direction of Q:

uQ = (π/2 - 0, 0 - π) = (π/2, -π)

Finally, we compute the directional derivative:

DQf(P) = ∇f(P) · uQ = (0, 0) · (π/2, -π) = 0

Therefore, the directional derivative of the function at point P in the direction of Q is 0.

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Answer:

She take 20 cookies to her students.

Step-by-step explanation:

Because 120÷6 is 20

and 20×6 is 120

Answer:

20

Step-by-step explanation:

She baked 120 cookies.

To solve this, use the equation: 120/1/6

In this equation, the 1 is useless. The real equation is 120/6 or 120 divided by 6.

12/6=2

After evaluating 12 divided by 6, add a zero to the end of the answer since you're trying to find 120 divided by 6.

The answer should be 20

By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.

To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.

First, let's examine the given figure and information.

We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.

To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.

Supplementary angles are defined as two angles whose measures sum up to 180 degrees.

We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.

Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.

Now, let's assume that segments HI and JK are not parallel.

In this case, if we extend lines HA and JA, they will eventually intersect at point P.

Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.

However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.

Therefore, our assumption that segments HI and JK are not parallel must be incorrect.

Consequently, we can conclude that segment HI is indeed parallel to segment JK.

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A 95% confidence interval for percent of american adults who believe in aliens:  (0.6578, 0.7822)

In this question we have been given that in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens

We need to find the 95% confidence interval for percent of american adults who believe in aliens.

95% confidence interval = (p ± z√[p(1 - p)/n])

Here, n = 200

p = 72%

p = 0.72

And the z-score for 95% confidence interval is 1.960

The upper limit of interval would be,

(p + z√[p(1 - p)/n])

= 0.72 + 1.960 √[0.72(1 - 0.72)/200]

= 0.72 + 1.960 √[(0.72 * 0.28)/200]

= 0.72 + 1.960 √0.001008

= 0.72 + 0.0622

= 0.7822

The lower limit of interval would be,

(p - z√[p(1 - p)/n])

= 0.72 - 1.960 √[0.72(1 - 0.72)/200]

= 0.72 - 1.960 √[(0.72 * 0.28)/200]

= 0.72 - 1.960 √0.001008

= 0.72 - 0.0622

= 0.6578

Therefore, a 95% confidence interval = (0.6578, 0.7822)

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Let's start by substituting the right-hand side of the equation into the left-hand side:

What does the math equation mean?

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

4y - 3 = 4(y + 1)

4y - 3 = 4y + 4

Now, we can isolate y by subtracting 4y from both sides:

0 = y + 4

-4 = y

So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.

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Answer:

D

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

4x+5y=8

-4x+5y=6

0=2

no solutions

Given:

The regression equation for change in temperature, y, to amount of rain, r, is given by

\(\hat{y}=0.2-1.4r\)

The observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees.

To find:

The residual and interpret it.

Solution:

According to the question, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees.

So, the actual value is 2.3 degrees.

Put r=0.4 in the given equation, to find the predicted value.

\(\hat{y}=0.2-1.4(0.4)\)

\(\hat{y}=0.2-0.56\)

\(\hat{y}=-0.36\)

We know that,

Residual = Actual value - Predicted value

\(Residual=2.3-(-0.36)\)

\(Residual=2.3+0.36\)

\(Residual=2.66\)

Residual is positive because predicated value is less than the actual value.

So, the regression line underpredicts the temperature change.

Therefore, the correct option is B.

Answer:

168 miles total

Step-by-step explanation:

42 miles x 4 hours = 168

Answer:

168 miles in 4 hours

Step-by-step explanation:

42x4=168, meaning that in 4 hours, the car travels at a constant speed of 42mph and travels a total of 168 miles in 4 hours

The probability of obtaining a royalty card = 3/13

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes

We know that:

The number of cards in a pack = 52

and, Royalty cards contain is 12

We have to find the probability of obtaining a royalty card.

Now, According to the question:

The probability of obtaining a royalty card = Number of royalty cards/ total no. of cards

Plug the values in the probability formula:

The probability of obtaining a royalty card = 12/52 = 6/26 = 3/13

Hence, The probability of obtaining a royalty card = 3/13

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False. It is not generally suggested that the sample size in developing a multiple regression model should be at least four times the number of independent variables.

There is no specific rule or guideline that states the sample size in developing a multiple regression model should be at least four times the number of independent variables. The appropriate sample size for a multiple regression model depends on various factors, such as the desired level of statistical power, the effect size, and the level of significance. In general, a larger sample size is preferred as it can increase the statistical power and reliability of the results.

However, the relationship between sample size and the number of independent variables is not fixed at a specific ratio like four times. It is important to consider the specific context of the study and the research question when determining the appropriate sample size for a multiple regression model.

Therefore, it is not accurate to suggest that the sample size should be at least four times the number of independent variables.

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Answer: It is linear

Step-by-step explanation:

When you graph the equation, it is a straight line, meaning it is linear.

If you graphed the equation and it wasn't a straight line, it would be nonlinear.