Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 86. 53 inches and forms a 56. 31° angle with the bottom of the frame, what is its height? Round your answer to the nearest inch. 48 inches 56 inches 72 inches 131 inches.

Answer:

Domain: All Real Numbers (ℝ)

Range: y ≥ -4

Step-by-step explanation:

The area of the graph that is between points of x

Technically where the graph falls from left to right

The area of the graph that is between points of y

Technically where the graph falls from top to bottom

Domain: We can see that the graph will extend forever left and right, so the Domain is All Real Numbers ( ℝ )

Range: The graph never goes below the value -4, so the Range is y ≥ -4

-Chetan K

The 95% confidence interval estimate of the population mean the difference between μ1 and μ2 with the provided values is (4.34, 9.66) (rounded to two decimal places as needed).

To find the 95% confidence interval estimate of the population mean the difference between μ1 and μ2 with the provided values, use the formula below: 95% confidence interval estimate:

(X1 - X2) ± t(α/2, n-1) (Sp²/ n₁ + Sp²/ n₂)½

Where X1 is the sample mean of population 1, X2 is the sample mean of population 2, Sp² is the pooled variance, n1 is the sample size of population 1, n2 is the sample size of population 2, and t(α/2, n-1) is the t-distribution value with n-1 degrees of freedom and an area of α/2 to the right of it.

So, we have; n1 = 7, X1 = 41, and S1 = 4, n2 = 12, X2 = 34, and S2 = 8

Firstly, we'll compute the pooled variance:

SP² = [(n₁ - 1) S₁² + (n₂ - 1) S₂²] / (n₁ + n₂ - 2) = [(7 - 1)4² + (12 - 1)8²] / (7 + 12 - 2) = 75.50

Secondly, we'll have the value of t(α/2, n-1):

Using a t-distribution table with 17 degrees of freedom (7 + 12 - 2), and a level of significance of 0.05,

t(0.025, 17) = 2.110.

The 95% confidence interval estimate is:

(X1 - X2) ± t(α/2, n-1) (Sp²/ n₁ + Sp²/ n₂)½= (41 - 34) ± 2.110(75.50/7 + 75.50/12)½

= 7 ± 2.6565

= (7 - 2.6565, 7 + 2.6565)

= (4.3435, 9.6565)

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On calculating, the 40% of 84 is found to be 33.6.

Given is that to find the 40% of 84.

Assume that the 40% of 84 is equivalent to [x]. Then, we can write -

x = (40/100) x 84

x = 4/10 x 84

x = 8.4 x 4

x = 33.6

Therefore, on calculation, the 40% of 84 is equivalent to 33.6.

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The probability that Sue will sit next to Bob is 96/24 = 4. So, the odds are 4:1.

We need to find out the odds that Sue will sit next to Bob. There is a round table with five different people. Therefore, the total number of ways that five different people can be seated at a round table is (5 - 1)! = 4!.

Thus, there are 24 ways that these five different people can be seated around the table. Now, let's say Sue and Bob are sitting next to each other. Thus, there are 4! = 24 ways in which they can be seated around the table. Now, Sue and Bob can be treated as a single unit since they are sitting together. So, there are a total of 48 + 48 = 96 possible ways that Sue will sit next to Bob in a 5 person round table. There are 24 possible ways that 5 people can be seated around the table.

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Answer:

Below!

Step-by-step explanation:

X intercept

y = 5x - 6

0 = 5x - 6

-5x = -6

divide both sides by -5

x = 6/5 or 1.2  

(1.2, 0)

Y intercept

y = 5x - 6

y = 5(0) - 6

y = -6

(0, -6)

Hope this helps! Best of luck <3

The number of degrees in the measure of inscribed angle C is 90°.

Given a circle O.

AB is the diameter.

Triangle ABC is inscribed in the circle.

Inscribed Angle Theorem states that the angle inscribed in a circle has a measure of half of the central angle which forms the same arc.

Since AB is the diameter,

m ∠AB = 180°

Measure of ∠C = half of the measure of ∠AB

                         = 180 / 2

                         = 90°

Hence the measure of angle C is 90°.

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Answer:

4.7

Step-by-step explanation:

6.5-1.8= 4.7

Answer:

4.7

Step-by-step explanation:

substitute:

6.5 - 1.8

solve:

4.7

have a wonderful day <3

Answer

224 over 567

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

the greatest possible length that the two ribbons would be when the ribbons are divided by their lowest common multiple.

The lowest common multiple of 63 is 3. 63/3 = 21

The lowest common multiple of 42 is 2 = 42/2 = 21

The series \(\sum n=17^{[\infty]} ln(n)/n^3\) is a convergent series.

To determine whether the improper integral

\(\int [\infty,17] ln(x)/x^3 dx\)

converges or diverges, we can use the Limit Comparison Test.

Let's compare it to the convergent p-series \(\int [\infty] 1/x^2 dx:\)

lim x→∞ ln(x)/\((x^3 * 1/x^2)\) = lim x→∞ ln(x)/x = 0

Since the limit is finite and positive, and the integral ∫[infinity] \(1/x^2\) dx converges, by the Limit Comparison Test, we can conclude that the integral \(\int [\infty,17] ln(x)/x^3 dx\) converges.

To find its value, we can integrate by parts:

Let u = ln(x) and dv = 1/x^3 dx, then du = 1/x dx and v = -1/(2x^2)

Using the formula for integration by parts, we get:

\(\int [\infty,17] ln(x)/x^3 dx = [-ln(x)/(2x^2)] [\infty,17] + ∫[\infty,17] 1/(x^2 \times 2x) dx\)

The first term evaluates to:

-lim x→∞ \(ln(x)/(2x^2) + ln(17)/(217^2) = 0 + ln(17)/(217^2)\)

The second term simplifies to:

\(\int [\infty,17] 1/(x^3 \times 2) dx = [-1/(4x^2)] [\infty,17] = 1/(4\times 17^2)\)

Adding the two terms, we get:

\(\int [\infty,17] ln(x)/x^3 dx = ln(17)/(217^2) + 1/(417^2)\)

\(\int [\infty,17] ln(x)/x^3 dx \approx 0.000198\)

Now, we can use the Integral Test to determine whether the series

\(\sum n=17^{[\infty]} ln(n)/n^3\)

converges or diverges.

Since the function\(f(x) = ln(x)/x^3\) is continuous, positive, and decreasing for x > 17, we can apply the Integral Test:

\(\int [n,\infty] ln(x)/x^3 dx ≤ \sum k=n^{[\infty]} ln(k)/k^3 ≤ ln(n)/n^3 + \int [n,\infty] ln(x)/x^3 dx\)

By the comparison we have just shown, the improper integral \(\int [\infty,17] ln(x)/x^3 dx\) converges.

Thus, by the Integral Test, the series also converges.

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Using the Integral Test, we can now determine whether the series ∑(from n=1 to infinity) (ln(n)/n^3) converges. Since the improper integral of the same function converges and the function is positive, continuous, and decreasing, the series also converges.

To determine whether the improper integral ∫[infinity]17ln(x)x3dx converges or diverges, we can use the integral test. Let's first find the antiderivative of ln(x):

∫ln(x)dx = xln(x) - x + C

Now, we can use integration by parts with u = ln(x) and dv = x^3dx:

∫ln(x)x^3dx = x^3ln(x) - ∫x^2dx
             = x^3ln(x) - (1/3)x^3 + C

Now, we can evaluate the improper integral:

∫[infinity]17ln(x)x^3dx = lim as b->infinity [∫b17ln(x)x^3dx]
                                 = lim as b->infinity [(b^3ln(b) - (1/3)b^3) - (17^3ln(17) - (1/3)17^3)]
                                 = infinity

Since the improper integral diverges, we can conclude that the series [infinity]∑n=17ln(n)n^3 also diverges by the integral test.

Therefore, the improper integral ∫[infinity]17ln(x)x^3dx diverges and the series [infinity]∑n=17ln(n)n^3 also diverges.

To determine whether the improper integral ∫(from 1 to infinity) (ln(x)/x^3) dx converges or diverges, we can use integration by parts. Let u = ln(x) and dv = 1/x^3 dx. Then, du = (1/x) dx and v = -1/(2x^2).

Now, integrate by parts:
∫(ln(x)/x^3) dx = uv - ∫(v*du)
= (-ln(x)/(2x^2)) - ∫(-1/(2x^3) dx)
= (-ln(x)/(2x^2)) + (1/(4x^2)) evaluated from 1 to infinity.

As x approaches infinity, both terms in the sum approach 0:
(-ln(x)/(2x^2)) -> 0 and (1/(4x^2)) -> 0.

Thus, the improper integral converges, and its value is:
((-ln(x)/(2x^2)) + (1/(4x^2))) evaluated from 1 to infinity
= (0 + 0) - ((-ln(1)/(2*1^2)) + (1/(4*1^2)))
= 1/4.

Using the Integral Test, we can now determine whether the series ∑(from n=1 to infinity) (ln(n)/n^3) converges. Since the improper integral of the same function converges and the function is positive, continuous, and decreasing, the series also converges.

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To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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The measure of angle KJM in the parallelogram is given as follows:

m < KJM = 129º.

In a parallelogram, the angle measures are obtained as follows:

Angle KJM is opposite to angle MLK, hence:

m < KJM = m < MLK.

By the angle addition postulate, the measure of angle MLK is given as follows:

m < MLK = m < KLO + m < MLO = 68º + 61º = 129º.

Hence the measure of angle KJM is obtained as follows:

m < KJM = m < MLK = 129º.

The problem is given by the image shown at the end of the answer.

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Answer:

An equation that represents the line is:

y = 3/4x - 9/2

Step-by-step explanation:

The slope-intercept form of the line equation

\(y = mx+b\)

where

Given the attached graph of a line.

Taking two points from the line, such as

Determining the slope between (2, -3) and (0, 6)

\(\left(x_1,\:y_1\right)=\left(2,\:-3\right),\:\left(x_2,\:y_2\right)=\left(6,\:0\right)\)

\(m=\frac{0-\left(-3\right)}{6-2}\)

refine

\(m=\frac{3}{4}\)

substituting m = 3/4 and the point (2, -3) in the slope-intercept form of the line equation

y = mx + b

\(\left(-3\right)=\frac{3}{4}\left(2\right)+b\)

\(\frac{3}{2}+b=-3\)

subtract 3/2 from both sides

\(\frac{3}{2}+b-\frac{3}{2}=-3-\frac{3}{2}\)

\(b=-\frac{9}{2}\)

now substituting b = -9/2 and m = 3/4 in the slope-intercept form of the line equation

y = mx + b

y = 3/4x + (-9/2)

Therefore, an equation that represents the line is:

y = 3/4x - 9/2

Answer:

64=x

Step-by-step explanation:

128= 2x

128÷2= 64

x=64

Step-by-step explanation:

4x+2=8+6x

-2x=6

x=-3

Hope it helps

Answer:

That is 133 yds.

Step-by-step explanation:

To find area you just multiply the two numbers.

The 2 actions would result in a smaller confidence interval is d) Increase n and increase the confidence level.

Here, we are given a fixed sample size of n = 8 and a confidence level of 90%. Increasing the sample size and decreasing the confidence level will increase the critical value, which will increase the margin of error, leading to a wider confidence interval. So, this option is (a) not correct.

Decreasing the sample size decreasing the confidence level will increase the critical value and further increase the margin of error, leading to a wider confidence interval. So, (b) option is not correct.

Decreasing the sample size, increasing the confidence level will decrease the critical value, which will decrease the margin of error, leading to a narrower confidence interval. So, (c) option is not correct.

Increasing the sample size will decrease the standard error and hence decrease the margin of error, resulting in a narrower confidence interval. Also, increasing the confidence level will increase the critical value, but the decrease in the standard error will be more significant, leading to a narrower confidence interval. Therefore, (d) option is correct.

So, the answer is d) Increase n and increase the confidence level.

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Answer:

La mayor tiene 61 años.

Step-by-step explanation:

Sea x,y,z la edad de la mayor, intermedio y la menor respectivamente.

Tenemos las siguientes ecuaciones:

\(x+y+z=127\) (la suma de las edades es 127)

\(x = z+30\) (la mayor tiene 30 años más que la menor)

La frase "y la del intermedio 26 menos que la menor" no tiene sentido, puesto que esto implicaría que la del intermedio es menor que la menor. Luego se asume que la frase ha de ser "y la del intermedio 26 menos que la mayor"

\(x-26 = y\) (la del intermedio tiene 26 menos que la mayor).

La segunda ecuación se traduce a x-30 =z. Si reemplazamos todo en la primera ecuación obtenemos

\(x+(x-26)+(x-30) = 127\)

Obtenemos la ecuación

\(3x-56 = 127\)

Sumando 56 a ambos lados y dividiendo por 3, obtenemos

\( x = \frac{127+56}{3} = 61\)

Es decir la mayor tiene 61 años.

Answer: 73.7

5 rounds up so you add 1 to the 6

An inequality that expresses the interval of values that n may have is (B) \((5 < n < 17)\)

The sides of a triangle are 5, 12, and n.

To write an inequality that expresses the interval of values that n may have, we use the Triangle Inequality Theorem.

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So for this question, the inequality that expresses the interval of values that n may have is given as:\(5 + 12 > n12 + n > 5n + 5 > 12\)

Simplifying the above inequality: \(n > -7n > 7\)

The interval for n will be \([7,∞)\), where n has to be greater than 7.

Option D \((7 < n < 12\)) is not the correct answer.

Hence, the correct answer is option B\((5 < n < 17).\)

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The first three terms of the sequence Tₙ = n^2 - 2n - 6 are -7, -8, and 0, and the sequence is a quadratic sequence with a parabolic graph that opens upward.

To find the first three terms of the sequence Tₙ = n^2 - 2n - 6, we simply need to substitute the first three positive integers for n, which gives us:

T₁ = 1^2 - 2(1) - 6 = -7

T₂ = 2^2 - 2(2) - 6 = -8

T₃ = 3^2 - 2(3) - 6 = 0

Therefore, the first three terms of the sequence are -7, -8, and 0.

The sequence Tₙ is a quadratic sequence, which means that it has a second-order difference. In other words, the differences between the terms of the sequence form a linear sequence.

Specifically, the first differences are 2, 4, 6, 8, and so on, which form an arithmetic sequence with a common difference of 2. The second differences are all equal to 2, which confirms that the sequence is quadratic.

The graph of the sequence Tₙ is a parabola that opens upward, with a vertex at (1, -7). This means that the sequence starts with a negative term, then decreases until it reaches a minimum at n = 1, and then increases indefinitely.

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Answer:

B

Step-by-step explanation:

285 × .30 = 85.50

285 - 85.50 = 199.50

The joint density function represents the probabilities of events related to Y1 and Y2 within the given conditions.

(a) F(1/2, 1/2) = 5/32.

(b) F(1/2, 3) = 5/32.

(c) P(Y1 > Y2) = 5/6.

The joint density function of Y1 and Y2 is given by f(y1, y2) = 30y1y2^2, y1 − 1 ≤ y2 ≤ 1 − y1, 0 ≤ y1 ≤ 1, 0, elsewhere.

(a) To find F(1/2, 1/2), we need to calculate the cumulative distribution function (CDF) at the point (1/2, 1/2). The CDF is defined as the integral of the joint density function over the appropriate region.

F(y1, y2) = ∫∫f(u, v) du dv

Since we want to find F(1/2, 1/2), the integral limits will be from y1 = 0 to 1/2 and y2 = 0 to 1/2.

F(1/2, 1/2) = ∫[0 to 1/2] ∫[0 to 1/2] f(u, v) du dv

Substituting the joint density function, f(y1, y2) = 30y1y2^2, into the integral, we have:

F(1/2, 1/2) = ∫[0 to 1/2] ∫[0 to 1/2] 30u(v^2) du dv

Integrating the inner integral with respect to u, we get:

F(1/2, 1/2) = ∫[0 to 1/2] 15v^2 [u^2]  dv

= ∫[0 to 1/2] 15v^2 (1/4) dv

= (15/4) ∫[0 to 1/2] v^2 dv

= (15/4) [(v^3)/3] [0 to 1/2]

= (15/4) [(1/2)^3/3]

= 5/32

Therefore, F(1/2, 1/2) = 5/32.

(b) To find F(1/2, 3), The integral limits will be from y1 = 0 to 1/2 and y2 = 0 to 3.

F(1/2, 3) = ∫[0 to 1/2] ∫[0 to 3] f(u, v) du dv

Substituting the joint density function, f(y1, y2) = 30y1y2^2, into the integral, we have:

F(1/2, 3) = ∫[0 to 1/2] ∫[0 to 3] 30u(v^2) du dv

By evaluating,

F(1/2, 3) = 15/4

Therefore, F(1/2, 3) = 15/4.

(c) To find P(Y1 > Y2), we need to integrate the joint density function over the region where Y1 > Y2.

P(Y1 > Y2) = ∫∫f(u, v) du dv, with the condition y1 > y2

We need to set up the integral limits based on the given condition. The region where Y1 > Y2 lies below the line y1 = y2 and above the line y1 = 1 - y2.

P(Y1 > Y2) = ∫[0 to 1] ∫[y1-1 to 1-y1] f(u, v) dv du

Substituting the joint density function, f(y1, y2) = 30y1y2^2, into the integral, we have:

P(Y1 > Y2) = ∫[0 to 1] ∫[y1-1 to 1-y1] 30u(v^2) dv du

Evaluating the integral will give us the probability:

P(Y1 > Y2) = 5/6

Therefore, P(Y1 > Y2) = 5/6.

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Answer:

5x+4

Step-by-step explanation:

Answer:

u = 24, v = 92, and w = 184

Step-by-step explanation:

According to circle theorem, we have;

∠ACD = ∠ABD = 88° by angle inscribed in a circle and also subtending the same chord

∠DOA = 2 × ∠ABD by angle subtended at the center = 2 × Angle subtended at the circumference

∴ ∠DOA = 2 × ∠ABD = 2 × 88° = 176°

w° + ∠DOA = 360  by the sum of angles at a point

∴ w° = 360° - ∠DOA = 360° - 176° = 184°

w° = 184°

w° = 2 × v° by angle subtended at the center = 2 × Angle subtended at the circumference

∴ v° = w°/2 = 184°/2 = 92°

v° = 92°

In triangle ΔCDY and ΔABY, we have;

∠ABD = ∠ABY by reflexive property

∠ACD = ∠ACY by reflexive property

∠ACD = ∠ABD = 88°

∴ ∠ABY = 88°

∠CYD = ∠AYB  by vertically opposite angles are equal

∴ ∠CYD = 68° = ∠AYB

u° + ∠ABY + ∠AYB = 180° by angle sum property

∴ u° = 180° - (∠ABY + ∠AYB)

u° = 180° - (88° + 68°) = 24°

u° = 24°.

Answer:

J=16

Step-by-step explanation:

You have to move all the number to the opposite side of the variable.

j-12=4

j=4+12

j=16

Answer: C 28.47° latitude and -7.35° longitude

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

8-5=3

3/5=0.6 and 0.6 = 60%

so 3 is 60% or 5

so 5+3 is a 60% increase

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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The correct identification of the dependent variable and the independent variable for the experiment is valid experiment.

Independent variable: The variable that is being changed or manipulated in an experiment is called the independent variable. The experimenter modifies the independent variable to observe its effect on the dependent variable.

Dependent variable: The dependent variable is the variable that is being measured and observed in an experiment. It is dependent on the independent variable because it changes as a result of the manipulation of the independent variable.

Therefore, To carry out a valid experiment, it is crucial to accurately identify the dependent variable and independent variable.

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