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The equation could be used to solve for charles' rate if it is represented by x is 2x=54.

In the given question wehave to find the equation could be used to solve for charles' rate if it is represented by x.

Bill riding a bicycle at an average rate of 9 mph.

Charles' rate is x.

So the relative rate = x−9 mph

Distance traveled by Bill in 4 hours = 9*4 =36 mph

Charles' overtook Bill in 2 hours. So

Relative Rate = Distance/Time

x−9=36/2

Multiply by 2 on both side. We get

2(x−9)=36

Simplifying

2x−18=36

Add 18 on both side, we get

2x=36+18

2x=54

Hence, the equation could be used to solve for charles' rate if it is represented by x is 2x=54.

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Answer:

the first one for sure.

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

65x2=130

185-130=155'

hope this helps :)

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A parallelogram possesses rotational symmetry of order 2, but no line symmetry.

The rotational symmetry of a parallelogram:

Therefore, a parallelogram possesses rotational symmetry of order 2, but no line symmetry.

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Answer:

in picture ....

Step-by-step explanation:

The research is a one-tailed test because the company won't be sued if many minorities were hired.

In the context, the type I error will be deciding the company is discriminating or not. The type II error will be deciding the company is not discriminating when it is.

The power of the test is the probability of correctly detecting actual discrimination. The type of error that the company consider to be more serious is the type I error.

In conclusion, the type of error that job applicants might consider to be more serious is type II error.

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Answer:

answers is 26.3%.

Step-by-step explanation:

you will say ( NEW price-OLD price)

95.99-75.99=20

20/75.99*100%

=26.3%

Answer:

x = 1

Step-by-step explanation:

1 + 24x + 105 + 51x - 1 = 180

75x = 75

x = 1

Answer:

b

Step-by-step explanation:

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

The correct formula for the margin of error in the interval estimation of p is Za/2 √p(1-p)/n.

Interval estimation:

Interval estimation refers the evaluation of a parameter—for example, the mean (average)—of a population by computing an interval, or range of values, within which the parameter is most likely to be located.

Given,

Here we need to find the correct formula for the margin of error in the interval estimation of p.

In order to find the correct formula for the margin of error, we have to know the definition of the margin of error,

Margin of error states that "a statistical measurement that accounts for the difference between actual and projected results in a random survey sample."

According to this definition, we have identified that the correct formula, for the margin of error in the interval estimation P is written as,

=> Za/2 √p(1-p)/n.

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Answer:  35,000

Step-by-step explanation:

The distance traveled in 150 rotations by Calvin is 16014.0 in

Let the diameter be= d

Let the radius be= r

Let the circumference be= c

Then,

          d=38in (Given in question)

Formula,

              radius=diameter/2

          r=38/2

          r=17in -(i)

The distance traveled in one rotation is equal to the circumference of the wheel.

Then,

          The distance traveled in one rotation = c

The formula of the circumference of a circle= 2π r

c= 2x 3.14xr

 = 6.28x r

putting values from (i)

 =6.28x17

 = 106.76                            

Distance traveled in one rotation= 1xc

then,

The distance traveled by Calvin in 150 rotations is= 150x106.76

                                                                                    =16014.0    

The distance traveled in 150 rotations by Calvin is 16014.0 in

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Answer:

12

Step-by-step explanation:

48/4=12

perimeter of squre is 4l so the length of a squre side is 12 (4*12=48)

Answer:

\(18x^3y\)

Step-by-step explanation:

The area of a trapezium is \(\frac{a+b}{2}h\) (where \(a,b\) are the parallel sides and \(h\) is the perpendicular height)

Area of trapezoid \(= \frac{4xy+8xy}{2}3x^2\)

\(=6xy(3x^2)\)

\(=18x^3y\)

∴ The area of the trapezoid is \(18x^3y\)

Hope this helps :)

The equation for the plane tangent to each surface - -10x + 6y + z - 5 = 0

What is Plane Tangent?

a tangent is a line that touches a curve at exactly one point without intersecting it. Similarly, a plane tangent is a plane that touches a surface at only one point without intersecting it further. This concept is commonly used in calculus and differential geometry to study the behavior of curves and surfaces.

We usually use partial derivatives of the equation of the surface to find the equation of the plane tangent to the surface at a point. The normal vector to the surface at that point is obtained by taking the cross product of the partial derivatives evaluated at that point. Then, using the coordinates of the point and the normal vector, we can determine the equation of the plane using the point-normal form or the general form of the plane equation.

It is important to note that the tangent plane equation depends on the specific point on the surface where the tangent plane is desired. Different points on the surface will have different tangent planes associated with them.

To find the equation for the plane tangent to the surface z = f(x, y) at a point (a, b, c), we need to use the partial derivatives of f with respect to x and y at the point (a, b) to find the normal vector to the plane.

Then we can use the point-normal form of the equation of a plane to write the equation.

First, we need to find the partial derivatives of f(x, y) = x^2 + y^3 - 6xy with respect to x and y:

fx = 2x - 6y

fy = 3y^2 - 6x

Then we can evaluate these partial derivatives at the point (1, 2) to get the normal vector:

n = <fx(1, 2), fy(1, 2)> = <2(1) - 6(2), 3(2)^2 - 6(1)> = <-10, 6>

So the equation of the plane tangent to the surface z = f(x, y) = x^2 + y^3 - 6xy at the point (1, 2, 3) is:

-10(x - 1) + 6(y - 2) + (z - 3) = 0

Simplifying, we get:

-10x + 6y + z - 5 = 0

So the equation of the plane tangent to the surface z = x^2 + y^3 - 6xy at the point (1, 2, 3) is -10x + 6y + z - 5 = 0

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).

With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.

We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).

The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).

The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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Answer:

B im pretty sure

Step-by-step explanation:

Answer:

1 to 20 that have the same mean, median, and range. ... The set {3,3,5,6,8} contains 5 whole numbers whose mean, median, and range are 5

The length of the arc is approximately 5.51 meters when a circle with a radius of 21 meters is subtended by a central angle of 15 degrees.

The length of an arc of a circle with radius 21m that subtends a central angle of 15° can be calculated using the formula:

Arc length = (central angle/360°) x 2πr

where r is the radius of the circle, and π is the mathematical constant pi.

Substituting the given values, we get:

Arc length = (15/360) x 2π x 21

Arc length = (1/24) x 2 x 3.14 x 21

Arc length = (1/12) x 3.14 x 21

Arc length = 5.51 meters (rounded to two decimal places).

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We need to apply the  formula to determine the length of a circle's arc: (Central angle / 360°) x (2 x x radius) is the formula for arc length. the radius is  distance from the circle center to any point on its perimeter,

and the central angle is the angle subtended by the arc at its center. The radius in this instance is stated as 21 meters, while the arc's center angle is provided as 15 degrees. When these values are added to the formula, we obtain: arc length is equal to (15°/360°) x (2x x 21m) 3.68 m. As a result, the arc measures around 3.68 meters in length. As a result, the radius is the distance from the circle's center to any point on its perimeter, if we were to sketch an arc of The arc's length would be around 3.68 meters for a circle with a radius of 21 meters and a center angle of 15 degrees.

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The solutions are;

The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.

The critical value with a level of significance ‘of 0.01’ and degrees of freedom ‘of 3’ is 3.747.

The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.

Given;

Let's say you randomly choose n = 4 measurements from a normal distribution. If you were constructing the following confidence intervals, compare the standard normal z values with the appropriate t values.

(a) 80% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 1.2 and the column value is 08.

The critical value with a level of significance is 1.28.

α = 1 - 0.80 = 0.20

α/2 = 0.10

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.

(b) 98% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 2.3 and the column value is 03.

The critical value with a level of significance is 2.33.

α = 1 - 0.98 = 0.02

α/2 = 0.01

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with level of significance ‘0.01’ and degrees of freedom ‘3’ is 3.747

(C) 90% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 1.6 and the column value is 04.

The critical value with a level of significance is 1.64.

α = 1 - 0.90 = 0.10

α/2 = 0.05

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.

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The correct answer is Beta. In this case, it is more important to make the Beta error as low as possible.

This is due to the Beta error being a false negative, which would suggest that the lead levels did not go above the permitted limit even though they did.

As a result, the park would continue to be open and the general public would be exposed to a potentially dangerous situation.

On the other side, a false positive (also known as an Alpha error) would cause the park to be closed without a need and would prevent the public from accessing a secure park.

Making the Beta error as small as feasible is therefore more crucial in order to protect the public from unwarranted dangers.

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Answer:

a = 6, b = 12, c = 18, d = 12

Step-by-step explanation:

Jordan and RayAnn will have saved the same amount of money at 5 weeks.

An equation is an expression that shows the relationship between two or more numbers and variables.

We have been given that Jordan saved $225 and continues to save $45 each week. RayAnn saved $150 and continues to save $60 each week.

Jordan: 225 + 45x

RayAnn: 150 + 60x

Therefore, 225 + 45x = 150 + 60x

225 - 150 = 60x - 45x

15x = 75

x = 5 weeks

Thus At 5 weeks, Jordan and RayAnn will have saved the same amount of money.

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As Kenisha packs three crates of merchandise having masses of 65kg , 72 kg and 42 kg, he or she packs total of 179 kg of merchandise.

Kenisha has 3 crates of merchandise.

Each of the crates have different masses, those  are as : first crate has mass 65 kg, second has mass of72 kg and third case has mass of 42 kg.

By simple addition rule we get,

The total masses of three crates is =  (65 + 72 + 42) kg

=179 kg

Thus, Kenisha has packed 179 kg of merchandise as he or she has packed three crates having masses 65 kg, 72kg and  42kg.

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Answer

= 6x3

Step-by-step explanation:

= (2 × 3) × (x2 × x)

= 6 × x2+1

= 6x3

Answer:

1=y

Step-by-step explanation:

Lets solve first:

6=2y+4

-4    -4

______________

4=4y

÷4   ÷4

______________---

1=y

Hope this helps :3

Answer:

tan a = perpendicular \ base

cos a = base \ hypotenuse

cos a = 5\13

using Pythagoras

perpendicular will be 12

and tan a will be 12\5

Answer: y=3/4x

Step-by-step explanation:

1. Find slope using slope formula

2. Find b value by plugging a point to solve for b with

The completed statement for the congruence of triangles is ΔXYZ ≅ ΔABC, the correct option is (d).

The Congruence of triangles is a term used in geometry which refers to the equality of shape and size of two triangles. The "Two-triangles" are  congruent if their "corresponding-sides" and angles are equal.

On observing both the triangles, we can say that,

The first triangle is right-angled at "X", and the second triangle is right-angled at "A",

the hypotnuse of first triangle is "ZY" and the hypotnuse of second triangle is "CB",

So, the "vertex X" similar to "vertex A", "vertex Z" similar to "vertex C", and "vertex Y" similar to "vertex B",

Therefore, triangle XYZ is congruent to triangle ABC, Option (d) is correct.

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Answer:

ACB

Step-by-step explanation:

Trust me