What is X equal to if 1X+30=6X+20?

Answer:

The point of estimate for the true difference would be:

\( 186-171= 15\)

And the confidence interval is given by:

\( (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753\)

\( (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753\)

Step-by-step explanation:

For this case we have the following info given:

\( \bar X_1 = 186\) the sample mean for the first sample

\( \bar X_2 = 171\) the sample mean for the second sample

\(s_1 =33\) the sample deviation for the first sample

\(s_2 =23\) the sample deviation for the second sample

\(n_1 = 8\) the sample size for the first group

\(n_2 = 7\) the sample size for the second group

The confidence interval for the true difference is given by:

\( (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}\)

We can find the degrees of freedom are given:

\( df = n_1 +n_2 -2 =8+7-2= 13\)

The confidence level is given by 90% so then the significance would be \(\alpha=1-0.9=0.1\) and \(\alpha/2=0.05\) we can find the critical value with the degrees of freedom given and we got:

\( t_{\alpha/2}= \pm 1.77\)

The point of estimate for the true difference would be:

\( 186-171= 15\)

And replacing into the formula for the confidence interval we got:

\( (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753\)

\( (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753\)

Answer:

\(\chi^2 =\frac{20-1}{2500} 68^2 =35.14\)

The degrees of freedom are given by:

\( df = n-1=20-1=19\)

And the p value would be given by:

\(p_v =2*P(\chi^2 >35.14)=0.0268\)

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true variance for this case is different from 2500

Step-by-step explanation:

Information given

\(n=20\) represent the sample size

\(\alpha=0.05\) represent the confidence level  

\(s^2 =68^2=4624 \) represent the sample variance obtained

\(\sigma^2_0 =2500\) represent the value that we want to test

Null and alternative hypothesis

We want to test if the true variance is 2500, so the system of hypothesis would be:

Null Hypothesis: \(\sigma^2 = 2500\)

Alternative hypothesis: \(\sigma^2 \neq 2500\)

Calculate the statistic  

The statistic would be given by:

\(\chi^2 =\frac{n-1}{\sigma^2_0} s^2\)

Repalcing we got:

\(\chi^2 =\frac{20-1}{2500} 68^2 =35.14\)

The degrees of freedom are given by:

\( df = n-1=20-1=19\)

And the p value would be given by:

\(p_v =2*P(\chi^2 >35.14)=0.0268\)

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true variance for this case is different from 2500

Answer:

7/10 or 70%

Step-by-step explanation:

Add the number of each color of balls together to get the total

5 + 2 + 3 = 10

Add the number of all the balls that aren't black

5 + 2 = 7

Then divide how many balls that aren't black by the total. This gives us the probability the ball you choose is not black

7/10 = 0.7 or 70%

The value of n(AUB) i.e. union of A and B is 53.

What are Intersections and Unions in Probablity?

The union of two sets results in a new set that contains all of the items from both sets. The union is abbreviated as A∪B or "A or B." The intersection of two sets yields a new set containing all of the members from both sets. The junction is denoted by the letters A∩B or "A and B."

Solution:

Given that,

n(A) = 14

n(B) = 51

n(A∩B) = 12

We know that thee formula is n(AUB) = n(A) + n(B) - n(A∩B)

Putting the values,

n(AUB) = 14 + 51 - 12 = 53

So, the answer for the value of n(AUB) = 53

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The slope of a linear demand curve is negative

The demand curve's negative slope indicates that there is an inverse link between price and demand.

It is true that the demand curve's negative slope indicates an inverse link between price and quantity desired. According to the demand curve, demand declines as prices increase and rises as prices decrease.

This statement is false since it only applies to Giffen products, where the demand curve has a positive slope and a direct correlation between price and quantity desired.

Because unit requests rise when prices decrease and decline when prices rise, the demand curve often slopes downward (i.e., is negative). Demand increases when prices are low, but demand decreases when prices are high.

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Answer:

Yds Ft

99 -> 297

120 -> 369

144 -> 432

162 -> 486

174 -> 522

192 -> 576

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

Answer:

IJ = 13

Step-by-step explanation:

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Given:

So JK · IJK = LK · MLK

If MK = 15 and ML = 9, then LK = 15 - 9 = 6

Given JK = 5

⇒ JK · IJK = LK · MLK

⇒ 5 · IJK = 6 · 15

⇒ 5 · IJK = 90

⇒ IJK = 90 ÷ 5 = 18

IJ = IJK - JK

⇒  IJ = 18 - 5 = 13

9514 1404 393

Answer:

  (a)  -10d^4 +17d^2s -6s^2

Step-by-step explanation:

Use the distributive property to eliminate parentheses, then collect terms.

  \((-2d^2+s)(5d^2-6s)=-2d^2(5d^2-6s)+s(5d^2-6s)\\\\=(-2d^2)(5d^2) +(-2d^2)(-6s)+s(5d^2)+s(-6s)\\\\=-10d^4+12d^2s+5d^2s-6s^2\\\\=\boxed{-10d^4+17d^2s-6s^2}\)

The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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6 WEEKS

2x + 28 = 4x + 16

x = 6

Answer:

250

Step-by-step explanation:

everything u need is in the picture

Answer:

2.34

Step-by-step explanation:

A pharmacy purchased 550 products over a period of 3 months

The average inventory was 235 products during the period of 3 months

Therefore, the inventory turnover rate for this period can be calculated as follows

= 550/235

= 2.34

Hence the inventory turnover rate for this period is 2.34

Answer:

A) Each of the smaller donations is $20.

B) The larger donation is greater than the smaller donations by $15.

Step-by-step explanation:

4+4+7 is equal to 15, and divide 75 by 15 to get $5 per part. Multiply 4 by 5 to get $20 for a smaller donation, and 7 by 5 to get $35 for the larger donation. Hope this helped :)

Answer:

Smaller donations each cost $20

The bigger donation is $15 more than the smaller ones.

Step-by-step explanation:

Let 4x be defined as the amount of the smaller donation, and let 7x be defined as the larger amount of the donation. We can then set up an equation:

4x+4x+7x = 75

15x = 75

x = 5

We can now plugin 5 for x to solve for the smaller donation and the larger donation:

Smaller donation = 4*5 = 20

Bigger donation = 7*5 = 35

Now, to find how much greater the bigger donation is, we just subtract 35 from 20, which is 15.

I hope this helped.

Answer:

I am pretty sure it is J

Step-by-step explanation:

128 divided by 16 equals 8

Answer:

F

8 ounce per serving

Step-by-step explanation:

128 ounce jug of iced tea.

label says = serves 16 people

therefore, the number of ounces per serving = 128 ounce / 16 serving

= 8 ounce per serving

so the answer is option F

Q5 is 115. Hope this helps! :) ✨

I can't see the numbers on Q6 sorry :((

Based on the description provided, the section of the chart that represents the point where a bill is first debated in subcommittees is: C and D

In the given chart, the parallel lines represent the progression of a bill through various stages in the legislative process. The boxes on the top line represent one set of actions or steps, while the boxes on the bottom line represent another set of actions or steps.

Moving from left to right on the chart, the boxes A and B are paired, representing a particular stage in the process. Similarly, the boxes C and D are paired, indicating another stage in the process.

In the context of the question, the stage where a bill is first debated in subcommittees is represented by the boxes C and D.

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9514 1404 393

Answer:

  x^2/1024 -y^2/7744 = 1

Step-by-step explanation:

The parent hyperbola relation is ...

  x^2 -y^2 = 1

This has asymptotes of y = ±x and x-intercepts of ±1.

For the given hyperbola, we want to scale x by a factor of 32, and y by a factor that is 2.75 times that, or 88. Then the equation could be written as ...

  (x/32)^2 -(y/88)^2 = 1

More conventionally, the denominator is shown at full value:

  x^2/1024 -y^2/7744 = 1

Answer:

Step-by-step explanation:

Volume = Bh

Turn the shape so the trapezoid is on the bottom/base

h=18   for overall shape

B = area of base, trapezoid

B = 1/2 (b₁ + b₂) h  

b₁ = 11

b₂ = 25

h = 24   for trapezoid

B = 1/2 (11 + 25)(24)

B = 432

V = Bh

V = (432)(18)

V= 7776 in³

Yes, cropping a picture and then using a scale factor to resize it is a two-step process.

The image is first cropped by subtracting 2 inches from the right side, altering the image's proportions.

The image is then enlarged using a scale factor of 1.5, which increases the image's dimensions by 1.5.

The final measurements of the image would be its original measurements less 2 inches (for cropping), then multiplied by 1.5. (for the resizing).

It's vital to keep in mind that both picture cropping and image scaling change the size of the final product.

Yes, cropping a photo, then resizing it with a scale factor, is a two-step process.

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Answer:

2000*(1.08)^t where t is years after deposit

Step-by-step explanation:

(a)1/2 * (a + a^T) is symmetric.

(b)1/2 * (a - a^T) is skew-symmetric.

(c)a = 1/2 * (a + a^T) + 1/2 * (a - a^T). The first term is symmetric, and the second is skew-symmetric.

(a) If a is any square matrix, then 1/2 * (a + a^T) is symmetric. To show this, we need to prove that it is equal to its transpose.

(a + a^T)^T = a^T + (a^T)^T = a + a^T

Therefore, 1/2 * (a + a^T) is symmetric.

(b) If a is any square matrix, then 1/2 * (a - a^T) is skew-symmetric. To show this, we need to prove that it equals the negative of its transpose.

(a - a^T)^T = a^T - (a^T)^T = a - a^T

Therefore, 1/2 * (a - a^T) is skew-symmetric.

(c) Any square matrix can always be written as the sum of a symmetric and skew-symmetric matrix.

a = 1/2 * (a + a^T) + 1/2 * (a - a^T)

The first term is symmetric, and the second term is skew-symmetric.

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Distance traveled after toll payment is 1.2 miles on highway 40.

The distance may be calculated using a curved route. Displacement measurements can only be made along straight lines. Distance is path-dependent, meaning it varies depending on the direction followed. Displacement simply depends on the body's beginning and ending positions; it is independent of the route.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The entire length of the journey taken between two points is known as the distance traveled. Travel distance is not a vector.

Distance traveled before toll payment =3/5 miles on highway 40

Distance traveled after toll payment =2*3/5  = 6/5 =

1.2 miles on highway 40.

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From the box-and-whisker plot, we have that:

a) City B had more noon temperatures above 76ºF.

b) City A had the largest IQR.

c) City B had the larger median temperature.

d) City A had the highest noon temperature.

For City A, the measures are given as follows:

Hence the interquartile range of temperatures is of:

75 - 67 = 8ºF.

For City B, the measures are given as follows:

Hence the interquartile range of temperatures is of:

80 - 73 = 7ºF.

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Answer:

\(s \ne \±2\)

\(x_1 = \frac{3s - 2}{3(s^2 -4)}\)

\(x_2 = \frac{2(s- 6)}{5(s^2 - 4)}\)

Step-by-step explanation:

Given

\(3sx_1 +5x_2 = 3\)

\(12x_1 + 5sx_2 =2\)

Required

Determine the value of s

Express the equations as a matrix

\(A =\left[\begin{array}{cc}3s&5\\12&5s\end{array}\right]\)

Calculate the determinant

\(|A|= (3s*5s -5 *12)\)

\(|A|= (15s^2 -60)\)

Factorize

\(|A|= 15(s^2 -4)\)

Apply difference of two squares

\(|A|= 15(s -2)(s + 2)\)

For the system to have a unique solution;

\(|A| =0\)

So, we have:

\(15(s -2)(s+2) = 0\)

Divide both sides by 15

\((s -2)(s+2) = 0\)

Solve for s

\(s -2 = 0\ or\ s +2 = 0\)

\(s = 2\ or\ s = -2\)

The result can be combined as:

\(s =\±2\)

Hence, the system has a unique solution when \(s \ne \±2\)

Next, we solve for s using Cramer's rule.

We have:

\(mat\ x_1 = \left[\begin{array}{cc}3&5\\2&5s\end{array}\right]\)

Calculate the determinant

\(|x_1| = (3 * 5s - 5 *2)\)

\(|x_1| = 15s - 10\)

So:

\(x_1 =\frac{|x_1|}{|A|}\)

\(x_1 = \frac{15s - 10}{15(s -2)(s+2)}\)

Factorize

\(x_1 = \frac{5(3s - 2)}{15(s -2)(s+2)}\)

Divide by 5

\(x_1 = \frac{3s - 2}{3(s -2)(s+2)}\)

\(x_1 = \frac{3s - 2}{3(s^2 -4)}\)

Similarly:

\(mat\ x_2 =\left[\begin{array}{cc}3s&3\\12&2\end{array}\right]\)

Calculate the determinant

\(|x_2| = 3s * 2 - 3 * 12\)

\(|x_2| = 6s- 36\)

So:

\(x_2 =\frac{|x_2|}{|A|}\)

\(x_2 = \frac{6s- 36}{15(s -2)(s+2)}\)

Factorize

\(x_2 = \frac{6(s- 6)}{15(s -2)(s+2)}\)

Divide by 3

\(x_2 = \frac{2(s- 6)}{5(s -2)(s+2)}\)

\(x_2 = \frac{2(s- 6)}{5(s^2 - 4)}\)

Answer:

Question:

Convert 291 dg to kg

Concept:

Using the conversion rate, we will have

By applying the conversion rate above, we will have that

Hence,

The final answer is

Answer:

\(x=\frac{z-y}{2y}\)

Step-by-step explanation:

The length of the wood necessary to frame the outside of the railing will be 48.167 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The length of the wood necessary to frame the outside of the railing will be given as,

l² = 32² + 36²

l² = 1,024 + 1,296

l² = 2,320

I = 48.167 inches

The length of the wood necessary to frame the outside of the railing will be 48.167 inches.

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