Please help quick
In ΔPQR, sin P = 0.4, sin R = 0.5 and r = 14. Find the length of p.

The relationship between the height of the pole and the shadow cast by the pole is a proportional relationship, from which the height of the pole can be calculated

The height of the pole is 11.\(\overline 6\) feet

A proportional relationship is one in which the ratio between the elements of an ordered pair is a constant.

The example values for the lengths of the shadows and Sam's height are as follows;

Let the length of the shadow cast by the pole = 3.5 feet

Let the shadow cast by Sam = 1.5 feet

Let Sam's height = 5 feet

Sam's height and the height of the pole and their shadows have proportional relationship.

The constant of proportionality is therefore;

\(K = \dfrac{1.5}{5} =\dfrac{3.5 }{Height \, of \, the \, pole}\)

Therefore;

Height of the pole = 5 × 3.5 ÷ 1.5 = 11.\(\overline 6\)

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The value of the integral (9x + 9y) da over the region r is approximately 14.0625.

To evaluate the given integral using a transformation, we can use the concept of a double integral over a region in the xy-plane.

First, let's define the transformation T from the uv-plane to the xy-plane, where x = 9u and y = 9v. This transformation scales the coordinates by a factor of 9.

Next, let's find the Jacobian determinant of the transformation. The Jacobian determinant of T is given by the absolute value of the determinant of the matrix of partial derivatives of x and y with respect to u and v. In this case, the matrix is:

J(T) = |[∂x/∂u  ∂x/∂v]|
           |[∂y/∂u  ∂y/∂v]|

Taking the partial derivatives, we have:

∂x/∂u = 9   and   ∂x/∂v = 0
∂y/∂u = 0   and   ∂y/∂v = 9

Therefore, the Jacobian determinant is:

J(T) = |[9  0]|
           |[0  9]|

Taking the determinant, we have:

J(T) = (9)(9) - (0)(0) = 81

Now, we can evaluate the integral by transforming it into the uv-plane. The integral becomes:

∬(9x + 9y) dA = ∬(9(9u) + 9(9v))(J(T)) dA

Since x = 9u and y = 9v, we can substitute these expressions into the integral:

∬(9(9u) + 9(9v))(J(T)) dA = ∬(81u + 81v)(81) dA

Now, we need to find the limits of integration in the uv-plane. The region r in the xy-plane corresponds to a parallelogram in the uv-plane with vertices (-1/9, 2/9), (1/9, -2/9), (3/9, 0), and (1/9, 4/9).

Using these vertices, we can determine the limits of integration for u and v:

u ranges from -1/9 to 1/9
v ranges from 2/9 to 4/9

Therefore, the integral becomes:

∬(81u + 81v)(81) dA = ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv

Now, we can evaluate this double integral:

∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv = (81)(81) ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (u + v) dudv

Evaluating the inner integral with respect to u, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + vu [v=2/9 to 4/9] dv

Simplifying further, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(2/9) dv

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (4/81)u^2 du

Combining like terms, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2 + 4/81)u^2 du

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du

Now, we can evaluate the integral:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du = (81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du

Integrating u^2 with respect to u, we get:

(81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du = (81)(81)(85/162) [u^3/3] from -1/9 to 1/9

Plugging in the limits of integration, we have:

(81)(81)(85/162) [(1/9)^3/3 - (-1/9)^3/3]

Simplifying further, we get:

(81)(81)(85/162) [(1/729)/3 - (-1/729)/3] = (81)(81)(85/162) [2/729]/3

Now, we can simplify this expression:

(81)(81)(85/162) [2/729]/3 = (81)(81)(85/162) (2/729)(1/3)

Finally, evaluating this expression, we get:

(81)(81)(85/162) (2/729)(1/3) ≈ 14.0625

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Answer:

  m = 1, b = 0

Step-by-step explanation:

You want to know the values of m and b and where to find them on a graph of y = x.

The variables m and b are used for the slope and y-intercept, respectively, when the slope-intercept equation for a line is written generically as ...

  y = mx + b . . . . . . . . equation for line with slope m and y-intercept b

The equation for the line y = x can be written in the slope-intercept form by recognizing the identity elements involved:

  y = x

  y = 1x + 0 . . . . . . . . identity elements shown

Comparing this to ...

  y = mx + b

we see that m = 1 and b = 0.

The attachment shows where these are found on the graph.

__

Additional comment

You may recall that 1 is the multiplicative identity element. Anything multiplied by 1 is itself.

Zero is the additive identity element. Anything added to zero is itself.

Answer:

Step-by-step explanation:

answer is c

Answer:

The answer is B, the second one on your screen. I hope I wasn't too late! :)

Using relations in a right triangle, it is found that the approximate angle made by the stairway with the ground is given by:

D. 43.76.

The relations in a right triangle are given as follows:

This situation can be modeled by a right triangle described as follows:

Hence the angle is found as follows:

\(\cos{\theta} = \frac{13}{18}\)

\(\theta = \arccos{\left(\frac{13}{18}\right)}\)

\(\theta = 43.76^\circ\)

Hence option D is correct.

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Answer:

46.24

Step-by-step explanation:

:)

3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

The probability of seeing exactly 5 hearts out of 10 cards is\((13/52)^5 × (39/52)^5.\)

The probability of seeing exactly 5 hearts out of 10 cards can be calculated as follows: The total number of cards in a deck is 52. The number of hearts in a deck is 13. Since no card has been removed from the deck, the probability of seeing a heart is 13/52. The probability of seeing a non-heart is 39/52. Since we are looking at 10 cards, the probability of seeing exactly 5 hearts,

p(h)= 13/52

p(nh) = 39/52

hence, \((13/52)^5 × (39/52)^5\)

This means that the probability of seeing exactly 5 hearts out of 10 cards is \((13/52)^5 × (39/52)^5.\)

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

The area of a circle is 28.26 yd 2

Answer:

In the select box put negative, the first blank box put 9, and the second blank box put -27

Step-by-step explanation:

The solution fo the equation by completing the square is x = 12.544 or -4.544

Completing the square method is a method of solving quadratic equations in which the equation is converted into a perfect square binomial.

Given (x - 12)(x + 4) = 9

Expanding the brackets, we have

x² - 12x + 4x - 48 = 9

x² - 8x - 48 = 9

x² - 8x - 48 - 9 = 0

x² - 8x - 57 = 0

To complete the square, we add half the square of the coefficient of x to both sides. so,

x² - 8x - 57 = 0

x² - 8x - 57 + (-8/2)² = 0 + (-8/2)²

x² - 8x - 57 + (-4)² = 0 + (-4)²

x² - 8x + (-4)² - 57  = 0 + (-4)²

(x - 4)² - 57 = 16

(x - 4)² = 16 + 57

(x - 4)² = 73

Taking square roots, we have

x - 4 = ±√73

x - 4 = ±8.544

x = 4 ± 8.544

x = 4 + 8.544 or x = 4 - 8.544

x = 12.544 or -4.544

So, the solution fo the quadratic equation by completing the square is x = 12.544 or -4.544

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Answer:

Step-by-step explanation:

x=+/-square root 73

Answer:

5

Step-by-step explanation:

23 - 10 = 13

13 - 8 = 5

Answer:

5

Step-by-step explanation:

p = a + b + c

23 = 8 + 10 + c

23 = 18 + c

5 = c

Answer:

-9xy (xy+xy)-3

Step-by-step explanation:

What is the equation of the line that passes through the point (-3, 6) and has a

slope of -1

Answer:

y=-x+3

Answer:

24 (A)

Step-by-step explanation:

So we know 20%=20/100, reduced to 1/5.

1/5 of 30 is 6, meaning 6 students answered it incorrectly.

Therefore, 24 students answered correctly

Hope this helps :)

Answer:

a)10

b)-12

c)3.6

Step-by-step explanation:

a. 5, 25, 25, 125, 625 (Growth factor: 5)

b. -1, 6, -36, 216, -1296 (Growth factor: -6)

c. 10, 5, 2.5, 1.25, 0.625 (Growth factor: 0.5)

d. -9, 27, 36, -108, -324 (Growth factor: -3)

e. 9, 12, 18, 27, 40.5 (Growth factor: 1.5)

In a geometric sequence, each term is obtained by multiplying the previous term by a constant called the growth factor.

For sequence a, the growth factor is 5 since each term is obtained by multiplying the previous term by 5.

For sequence b, the growth factor is -6 since each term is obtained by multiplying the previous term by -6.

For sequence c, the growth factor is 0.5 since each term is obtained by multiplying the previous term by 0.5.

For sequence d, the growth factor is -3 since each term is obtained by multiplying the previous term by -3.

For sequence e, the growth factor is 1.5 since each term is obtained by multiplying the previous term by 1.5.

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Answer:

40%

Step-by-step explanation:

Well, if 4/10 work part time, 4/10 converted to percentages is 40%.

The correct answer is (d) +-3.707. the population standard deviation is unknown and the sample size is less than 30, we use the t-distribution.

To find the critical value for a hypothesis test of the population mean when the population standard deviation is unknown and the sample size is less than 30, we use the t-distribution.

In this case, we have a sample size of 7, so the degrees of freedom are n-1=6. We want to test the null hypothesis that the population mean weight of newborn infants is 1011 pounds. The alternative hypothesis can be either one-tailed or two-tailed, but since the question does not specify, we will assume a two-tailed test with a significance level of 0.010.

Using a t-distribution table with 6 degrees of freedom and a significance level of 0.010, we find that the critical values are approximately +-3.707.

Therefore, the correct answer is (d) +-3.707.

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Based on the given information, a journalist conducted a survey of a random sample of 900 adults in the United States, and 60 percent of them are in favor of increasing the minimum hourly wage.

The margin of error is given as 2.7 percentage points.
To determine the level of confidence, we need to use the margin of error and the sample size. The formula for margin of error is:
Margin of error = z * (standard deviation / sqrt(sample size))
where z is the z-score for the desired level of confidence, standard deviation is the estimated standard deviation of the population (which we don't know), and sqrt(sample size) is the square root of the sample size.
Since we don't know the standard deviation of the population, we can use the conservative estimate of 0.5 as the estimated proportion (since we don't know if the true proportion is closer to 0 or 1).
Using this information, we can solve for the z-score:
2.7 = z * (0.5 / sqrt(900))
2.7 = z * 0.0167
z = 2.7 / 0.0167
z = 161.68
Looking up this z-score in a standard normal distribution table, we can see that it corresponds to a level of confidence of 99.0%. Therefore, the closest answer choice is 99.0%.

Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. With a margin of error of 2.7 percentage points, the closest level of confidence is approximately 95.0%.
To determine this, you can use the following steps:
1. Identify the sample proportion (p) and sample size (n): p = 0.60, n = 900.
2. Calculate the standard error (SE): SE = sqrt[p(1-p)/n] = sqrt[0.60(0.40)/900] ≈ 0.016.
3. Determine the margin of error (MOE): MOE = 2.7% = 0.027.
4. Divide the MOE by the SE: 0.027/0.016 ≈ 1.69.
5. Look up the value in a Z-table or use a calculator to find the corresponding confidence level: Z = 1.69 corresponds to approximately 95.0% confidence level.

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Answer:

Anything from 0.31 - 0.34 rounds to 0.3

Answer:yes?

Step-by-step explanation:

it has #s in it lol

Answer:

no it isnt

Step-by-step explanation:

The time taken for the trip if the return trip was 9 hours is 17 hours.

The outward journey used 432 mph. The return journey was 480 mph and this was for 9 hours.

Let the time taken for the initial trip be x. This will be:

x/9 = 432 / 48

Cross multiply

480x = 432 × 9

x = (432 × 9) / 480

x = 8

Therefore, the initial trip was 8 hours.

The time taken for the whole trip will be:

= Outward trip + Return trip

= 8 hours + 9 hours

= 17 hours.

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Answer:

y = -2x^2 + 8

Step-by-step explanation:

It is clear from the information that (-2, 0) and (2, 0) are the zeros of the quadratic equation, while (0,8) is the vertex.

Thus, we can find the equation of the quadratic function using the vertex form which is

\(y = a(x-h)^2+k\), where y and x are any x and y coordinate on the parabola, and h and k are the coordinate of the vertex.

We can plug in (-2, 0) for x and y and (0, 8) for h and k.  This means we simply need to solve for a:

\(0=a(-2-0)^2+8\\0=a(-2)^2+8\\0=4a+8\\-8=4a\\-2=a\\\)

Thus, our equation is y = -2x^2 + 8

The triple integral evaluates to a value of 25/6, which represents the volume under the surface z = 1 within the solid bounded by the region x^2 + y^2 ≤ 25, x ≥ 0, y ≥ 0, and z between 0 and 1.

To evaluate the triple integral ∭e f(x, y, z) dv over the solid e, where f(x, y, z) = z, we need to find the volume under the surface z = 1 within the given solid. The solid e is defined as the region bounded by x^2 + y^2 ≤ 25, x ≥ 0, y ≥ 0, and z between 0 and 1.

Using cylindrical coordinates, we can express the region as 0 ≤ θ ≤ π/2, 0 ≤ r ≤ 5, and 0 ≤ z ≤ 1. The integral becomes:

∭e f(x, y, z) dv = ∫(0 to π/2) ∫(0 to 5) ∫(0 to 1) z * r dz dr dθ.

The innermost integral evaluates to [\(z^2\)/2] from 0 to 1, resulting in ∫(0 to π/2) ∫(0 to 5) (1/2) * r dr dθ. The second integral becomes  \([(r^2)/4]\)from 0 to 5, leading to ∫(0 to π/2) \((5^2)/4\)dθ. Finally, the outermost integral evaluates to (25/4) * (π/2), which simplifies to 25π/8 or approximately 9.82.

Therefore, the triple integral evaluates to 25/6, representing the volume under the surface z = 1 within the solid bounded by\(x^2 + y^2 < =25\), x ≥ 0, y ≥ 0, and z between 0 and 1.

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Answer:

To convert inches to feet, we divide the number of inches by the number of inches per foot. One foot is equal to 12 inches.

So, to convert 5 inches to feet:

5 inches / 12 inches/foot = 5/12 feet

The answer can be simplified as a proper fraction.

5 inches = 5/12 feet