pls help me ask you can
value of x​

Answer:

x=3

Step-by-step explanation:

f(x) = -3x – 1

Let f(x) = -10

-10 = -3x-1

Add 1 to each side

-10+1= -3x-1+1

-9 = -3x

Divide each side by -3

-9/-3 = -3x/-3

3 = x

Given that the original sample had a variance of 4, variance of the transformed sample is 36.

Given the data in the question;

Now, Lets represent the original random variable by X  

So, Variance of X will be 4

Var(X) = 4

The Variance of the transformation is;

\(Y = 3X + 10\)

By using property of variance [ derived from its definition]

\(Var(Y) = a^2Var(X)\)

Here, X is the variable and "a" is the constant

We substitute

\(Var(Y) = 3^2\ * \ 4\)

\(Var(Y) = 9\ *\ 4\\\)

\(Var(Y) = 36\)

Therefore, given that the original sample had a variance of 4, variance of the transformed sample is 36.

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Answer:

F=ma

F=1250*40

F=50000N

Step-by-step explanation:

\(a {b}^{2} = \frac{27}{5} \\ \\ {a}^{2} b = 135 \\ \)

\( {b}^{2} = \frac{5.4}{a} \\ {a}^{2} = \frac{135}{b} \)

\(b = \sqrt{ \frac{5.4}{a} } \)

\(b = { ( \frac{5.4}{a} ) }^{0.5 } \\ \\ b = \frac{2.32}{ {a}^{0.5} } \\ \)

\( {a}^{2} = \frac{135}{ \frac{2.32}{ {a}^{0.5} } } \\ {a}^{2} = \frac{135 {a}^{0.5} }{2.32} \\ \)

\( {a}^{2} = 58.19 {a}^{0.5} \)

\( {a}^{1.5} = 58.19\)

a =15.018(approximately)

\(b = \frac{2.32}{ {a}^{0.5} } \\ b = \frac{2.32}{3.875} \\ b = 0.598\)

b= 0.598 (approximately)

a+5b =18

The number of valid ways to construct the cube is \(4096 - 48 = 4048\)

Each corner of the cube is formed by three wires coming together. Since the wires are soldered together at the ends, each corner must have either 3 silver wires or 3 copper wires coming together.

There are two choices for each wire: it can be silver or copper. Since there are 12 edges in a cube, there are 2 choices for each edge, giving a total of \(2^12 = 4096\) possible arrangements of the edges.

However, not all of these arrangements are valid. We must eliminate the arrangements where at least one corner has two silver wires and one copper wire

There are 8 corners in a cube, and for each corner, there are 3 ways to choose which wire is different from the other two. Once we choose which wire is different, there are 2 choices for its color (silver or copper). Thus, there are \(8 x 3 x 2 = 48\) invalid arrangements.

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The transformation of the function f(x) = log2(x) involves shifting 2 units up and vertically compressing by a factor of 0.4.

Which function represents the transformation g(x)?

The following equation can be used to represent the transformation:

g(x) = 0.4*log2(x) + 2

Therefore, the function that represents the transformation g(x) is:

g(x) = 0.4*log2(x) + 2

To understand the transformation of the function f(x) = log2(x) into g(x), we need to first understand the individual transformations involved.

Vertical compression: When a function is vertically compressed by a factor 'a', its output values get multiplied by 'a'. This means that the function's range gets compressed by a factor of 'a'. In this case, the function f(x) = log2(x) is vertically compressed by a factor of 0.4. So, the output values of f(x) get multiplied by 0.4, which compresses the range of the function by a factor of 0.4.

Vertical shift: When a function is shifted 'b' units up or down, its output values get increased or decreased by 'b'. This means that the function's range gets shifted up or down by 'b'. In this case, the function f(x) = log2(x) is shifted 2 units up. So, the output values of f(x) get increased by 2, which shifts the range of the function 2 units up.

Putting these two transformations together, we get the transformation of the function f(x) = log2(x) into g(x) as follows:

g(x) = 0.4*log2(x) + 2

This equation represents a vertical compression of the function f(x) by a factor of 0.4, followed by a vertical shift of 2 units up.

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Complete question:

Answer:

In order of the questions asked, the answers are, C, D, A, C

Step-by-step explanation:

After three half-lives have elapsed, 12.5% of the original nuclide remains, so the answer is C.

if 17 % is daughter nuclide, then 83% is parent nuclide, so , the answer is D

the isotope for dating organic remains is A. carbon-14

for 25% of original, 2 half-lives must have passed, so we get (2)(5730) = 11460

so the answer is C

The population must be normally distributed or the sample size must be large (n>30). The sampling distribution of x is normal with mean 61 and standard deviation 4.

The central limit theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution, as long as the sample size is large enough. In this case, the sample size is 41, which is large enough to assume that the sampling distribution of the sample mean is approximately normally distributed.

The mean of the sampling distribution of the sample mean is equal to the population mean, which is 61. The standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size, which is 16/sqrt(41) = 4.

Therefore, the sampling distribution of the sample mean is normal with mean 61 and standard deviation 4.

(b)P(X<64.5) = P(Z<(64.5-61)/4) = P(Z<0.875) = 0.8088

(c)P(X>67.9) = P(Z>(67.9-61)/4) = P(Z>1.725) = 0.0427

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Percentage of data within 2 population standard deviations of the mean is 68%.

To calculate the percentage of data within two population standard deviations of the mean, we need to first find the mean and standard deviation of the data set.

The mean can be found by summing all the values and dividing by the total number of values:

Mean = (20*2 + 22*8 + 28*9 + 34*13 + 38*16 + 39*11 + 41*7 + 48*0)/(2+8+9+13+16+11+7) = 32.68

To calculate standard deviation, we need to calculate the variance first. Variance is the average of the squared differences from the mean.

Variance = [(20-32.68)^2*2 + (22-32.68)^2*8 + (28-32.68)^2*9 + (34-32.68)^2*13 + (38-32.68)^2*16 + (39-32.68)^2*11 + (41-32.68)^2*7]/(2+8+9+13+16+11+7-1) = 139.98

Standard Deviation = sqrt(139.98) = 11.83

Now we can calculate the range within two population standard deviations of the mean. Two population standard deviations of the mean can be found by multiplying the standard deviation by 2.

Range = 2*11.83 = 23.66

The minimum value within two population standard deviations of the mean can be found by subtracting the range from the mean and the maximum value can be found by adding the range to the mean:

Minimum Value = 32.68 - 23.66 = 9.02 Maximum Value = 32.68 + 23.66 = 56.34

Now we can count the number of data points within this range, which are 45 out of 66 data points. To find the percentage, we divide 45 by 66 and multiply by 100:

Percentage of data within 2 population standard deviations of the mean = (45/66)*100 = 68% (rounded to the nearest percent).

Therefore, approximately 68% of the data falls within two population standard deviations of the mean.

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- 2.5 i

Dividing complex numbers is actually simpler than it seems. We don't start by dividing, rather we multiply the top and the bottom by the complex conjugate of the denominator. Remember that a complex number times its complex conjugate gives an entirely real number. Also, a fraction multiplied by anything in both the numerator and denominator is unchanged.

Answer:

The true statements are:

* The Corresponding Angles Congruent ⇒ B

* Same Side Interior Angles are supplementary ⇒ C

* Alternate Interior Angles are congruent ⇒ F

Step-by-step explanation:

∵ Lines m and l are parallel

∵ Line t intersects them

∵ Corresponding angles are equal in measures

∴ ∠1 = ∠5 ⇒ corresponding angles

∴ ∠3 = ∠7 ⇒ corresponding angles

∴ ∠2 = ∠6 ⇒ corresponding angles

∴ ∠4 = ∠8 ⇒ corresponding angles

∵ The alternate interior angles are equal in measures

∴ ∠3 = ∠6 ⇒ alternate interior angles

∴ ∠4 = ∠5 ⇒ alternate interior angles

∵ The same side interior angles are supplementary

∴ m∠3 + m∠ 5 = 180° ⇒ same side interior angles

∴ ∠3 and ∠5 are interior supplementary angles

∴ m∠4 + m∠ 6 = 180° ⇒ same side interior angles

∴ ∠4 and ∠6 are interior supplementary angles

The true statements are:

* The Corresponding Angles Congruent ⇒ B

* Same Side Interior Angles are supplementary ⇒ C

* Alternate Interior Angles are congruent ⇒ F

If there are 100 black cars in the parking lot, then 50.66% of the cars are green and 49.34% of the cars are black.

percentage, a relative value indicating hundredth parts of any quantity.

Let's x be the number of black cars in the parking lot.

Then, there are x + 27 green cars in the parking lot, according to the problem statement.

The total number of cars in the parking lot is the sum of black and green cars, which is:

Total cars = x + (x + 27) = 2x + 27

To find the percentage of green cars, we need to divide the number of green cars by the total number of cars and multiply by 100:

% of green cars = (x + 27) / (2x + 27) * 100

To find the percentage of black cars, we can subtract the percentage of green cars from 100%:

% of black cars = 100% - % of green cars

Substituting x with any value, we can find the specific percentage of green and black cars. For example, let's assume there are 100 black cars in the parking lot:

Total cars = 2x + 27 = 2(100) + 27 = 227 cars

% of green cars = (100 + 27) / 227 * 100 = 50.66%

% of black cars = 100% - 50.66% = 49.34%

Therefore, if there are 100 black cars in the parking lot, then 50.66% of the cars are green and 49.34% of the cars are black.

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Step-by-step explanation:

To determine the intercepts of a function, you need to follow the following steps:

For the x-intercept, set y = 0 and solve for x.

For the y-intercept, set x = 0 and solve for y.

Therefore, to determine the intercepts of a function, you need to know the equation of the function. Suppose you have the function equation f(x) = 2x + 3. To find the intercepts, you can follow the steps below:

To find the x-intercept, set y = 0, so you have:

0 = 2x + 3

Then, solve for x:

-3/2 = x

Therefore, the x-intercept is -3/2.

To find the y-intercept, set x = 0, so you have:

y = 2(0) + 3

Then, solve for y:

y = 3

Therefore, the y-intercept is 3.

Answer:

Step-by-step explanation:

Umm

Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.

Here are the details for the given frequency distribution:

Lower class limits are the least number among the pair

Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.

Upper class limits are the greater number among the pair

Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.

Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).

Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.

Class boundaries are the extreme points of the classes which are  [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.

Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1

                                     = 76

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The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

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Answer:

a = 3 \(\frac{1}{3}\)

Step-by-step explanation:

Given

a + 5 \(\frac{2}{3}\) = 9 ← change mixed number to improper fraction

a + \(\frac{17}{3}\) = 9 ( multiply through by 3 to clear the fraction )

3a + 17 = 27 ( subtract 17 from both sides )

3a = 10 ( divide both sides by 3 )

a = \(\frac{10}{3}\) = 3 \(\frac{1}{3}\)

The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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a) To find a regression model predicting the 2010 index from the index in 2007 for the sample of 43 countries, we can perform a linear regression analysis. The regression model can be expressed as:

2010 index = β0 + β1 * 2007 index

Using statistical software or calculators, we can estimate the regression coefficients β0 and β1. These coefficients represent the intercept and slope of the regression line, respectively, and indicate the relationship between the two variables.

b) To determine if a linear regression is appropriate, we can examine the scatter plot of the data points and assess the linearity of the relationship. Additionally, we can calculate the correlation coefficient (r) to measure the strength and direction of the linear relationship between the 2007 index and the 2010 index. If the correlation coefficient is close to 1 or -1, it suggests a strong linear relationship.

c) To construct a plot of the residuals against x, we need to calculate the residuals by subtracting the predicted values (based on the regression model) from the actual 2010 index values. The residuals represent the differences between the observed and predicted values and help assess the accuracy of the regression model. Plotting the residuals against the 2007 index allows us to examine if there are any patterns or deviations from randomness, which can indicate potential issues with the model.

d) Based on the provided options, it is not clear which graph (A, B, or C) corresponds to plotting the residuals against x. However, in a typical linear regression analysis, the correct graph choice would be graph B, where the residuals are plotted against the x-axis (2007 index). This plot helps identify any systematic patterns or heteroscedasticity (unequal spread) in the residuals.

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Answer: its A have a good day

There is not enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To find the standardized test statistic (Z-score), we need to first calculate the sample mean and standard error of the mean.

Sample mean:

x = (17.8 + 21.1 + 19.7 + 9.5 + 18.5 + 13.2 + 13.6 + 10.7 + 19.1 + 7.5 + 11.3 + 7.6 + 21.8 + 9.2 + 21.6 + 9.8 + 19.3 + 21.9 + 22.6 + 15.5 + 12.4 + 9.5 + 14.9 + 7.7 + 12.9 + 17.6 + 14.1 + 19.4 + 17.1 + 17.3 + 15.4 + 22.5) / 32

x = 15.91875

Standard error of the mean:

SE = σ /√(n)

SE = 6.1 / √(32)

SE = 1.0823

Now we can calculate the Z-score:

Z = (x - μ) / SE

Z = (15.91875 - 13) / 1.0823

Z = 2.5707

we can find that the p-value associated with a Z-score of 2.5707 is approximately 0.0051.

Since the significance level (α) is 0.06, which is larger than the p-value, we fail to reject the null hypothesis.

Therefore, there is not enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.

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Answer:

220

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

3x=6x-2

6x-3x=2

3x=2

x=2/3

Answer:

1. 18

2. 16

3. 45

4. 72

5. 32

6. 42

7. 20

8. 9

9. 78

10. 4

The number of square units that a figure covers is its area.

The height of a triangle is the length of the perpendicular line segment from a vertex to the opposite side.

The volume of a solid figure is the number of cubic units needed to fill it.

Any line segment that connects the center of a circle to a point on the circle is called a radius.

The area of a figure refers to the number of square units that the figure covers.

It is a measure of the surface enclosed by the figure.

In the context of a triangle, the height refers to the length of the perpendicular line segment drawn from a vertex of the triangle to the opposite side or the line containing the opposite side.

The volume of a solid figure measures the amount of space occupied by the figure in three dimensions.

The radius of a circle is any line segment that connects the center of the circle to a point on the circle's circumference.

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Answer:

2.82

Step-by-step explanation: