The probability of event E2
​occurring, given that event E1
has happened is called​ a(n) _______ probability.

The magnitude of the bird's displacement is 3.6 km, which corresponds to option (C).

We can use the Pythagorean theorem to find the magnitude of the bird's displacement, which is the length of the straight line between the bird's starting point and ending point (i.e., the distance between the two points).

If we draw a diagram, we can see that the bird's displacement forms the hypotenuse of a right triangle with legs of length 3.0 km (the distance traveled due west) and 2.0 km (the distance traveled due north).

So, we can use the Pythagorean theorem to find the length of the hypotenuse:

displacement = √[(3.0 km)² + (2.0 km)²] ≈ 3.6 km

Thus, the magnitude of the bird's displacement is 3.6 km.

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Answer:

2 4/5

Step-by-step explanation:

Answer:

26/3 cup of rice

Step-by-step explanation:

We Know

1 serving of stir fry uses 2/3 cup of rice.

How many cups are in 13 servings?

We Take

2/3 x 13 = 26/3 cup of rice

So, there are 26/3 cups of rice are in 13 servings.

Answer:

26/3 (8 2/3) cups

Step-by-step explanation:

If one serving of stir fry uses 2/3 cups of rice,

1:2/3

If there are 13 servings,

13: 2/3 * 13

13: 26/3

So 26/3 cups of rice

The difference in heights of their stacks of books is 15 1/4 inches.

Trevor’s stack of books is 7 7/4 inches tall. Rick's stack of books is 3 times as tall as Trevor's stack, which means:

Height of Rick's stack = 3 × Height of Trevor's stack

= 3 × 7 7/4 inches

= 22 3/4 inches

The difference in height between their stacks of books can be found by subtracting the height of Trevor's stack from the height of Rick's stack:

Height of Rick's stack - Height of Trevor's stack

= 22 3/4 inches - 7 7/4 inches

= (22 - 7) + (3/4 - 7/4) inches

= 15 + 0.25 inches

= 15 1/4 inches

Therefore, the difference in heights of their stacks of books is 15 1/4 inches.

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Answer: Let the number of tomato plants Nelson planted last year be x.

According to the problem, he planted 6 more than one-fifth of the tomato plants he planted last year.

So, the number of tomato plants he planted this year is:

(1/5)x + 6

Therefore, the expression that represents the number of tomato plants he planted this year is (1/5)x + 6.

The measure of the angles is 22°.

Given is figure with two parallel lines we need to find the measures of the asked angles,

∠1 + ∠2 = 180° [linear pair]

∠1 = 180° - 158°

∠1 = 22°

Now angles 1 and 3 are alternate exterior angles between parallel lines,

Hence are equal,

Therefore,

∠3 = 22°

Hence the measure of the angles is 22°.

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The answer to the set (Z ∪ X')' ∩ Y = {a}.

-Since U = {a, f, j, m, p, s, v} and X = {a, j, p, v}, the complement of X, denoted as X', is the set of all elements in U that are not in X. Therefore, X' = {f, m, s}.

-Now, find the union of Z and X'. Z = {f, j, m, p, s} and X' = {f, m, s}. The union of Z and X', denoted as Z ∪ X', is the set of all elements in either Z or X' or both. Thus, Z ∪ X' = {f, j, m, p, s}.

-To find the complement of Z ∪ X', denoted as (Z ∪ X')', we need to find all elements in U that are not in Z ∪ X'. Since Z ∪ X' = {f, j, m, p, s} and U = {a, f, j, m, p, s, v}, (Z ∪ X')' = {a, v}.

-Finally, find the intersection of (Z ∪ X')' and Y. (Z ∪ X')' = {a, v} and Y = {a, f, j}. The intersection of (Z ∪ X')' and Y, denoted as (Z ∪ X')' ∩ Y, is the set of all elements that are in both (Z ∪ X')' and Y. Therefore, (Z ∪ X')' ∩ Y = {a}.

So, the answer is (Z ∪ X')' ∩ Y = {a}.

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Answer:0.096

Step-by-step explanation:

1/6 = 0.16

3/5 = 0.6

0.16 times 0.6 = 0.096

hope that helps

To determine how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis, we need to first establish a hypothesis test. A hypothesis test is a statistical procedure that helps us determine if there is enough evidence to support a particular hypothesis.

In a hypothesis test, we start with a null hypothesis (H0) which is a statement that there is no significant difference between two groups or variables. The alternative hypothesis (Ha) is the statement that there is a significant difference between the two groups or variables.

Once we have established our null and alternative hypotheses, we need to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The test statistic is the numerical value that we obtain from our statistical test, which we compare to a critical value to determine if we can reject the null hypothesis.

The critical value is determined by the level of significance (α) we have chosen for our test, which is the probability of making a type I error (rejecting the null hypothesis when it is actually true). Typically, the level of significance is set at 0.05 or 0.01.

So, to answer the question, how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis depends on the level of significance we have chosen, as well as the degrees of freedom and distribution of the test statistic. The critical value for a given level of significance and degrees of freedom can be found in statistical tables or calculated using software. If the test statistic is larger than the critical value, we can reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

Probability of Zach wearing a solid shirt, blue pants, and a bow tie is 1/12.

Step-by-step explanation:

The probability of Zach wearing a solid shirt, blue pants, and a bow tie is equal to the product of the probabilities of each event happening independently.

The probability of Zach wearing a solid shirt is 1/3, since he has 3 shirts and only one of them is solid.

The probability of him wearing blue pants is 1/2, since he has 2 pairs of pants and only one of them is blue.

The probability of him wearing a bow tie is 1/2, since he has 2 ties and only one of them is a bow tie.

Therefore, the probability of Zach wearing a solid shirt, blue pants, and a bow tie is:

P(solid shirt) * P(blue pants) * P(bow tie) = 1/3 * 1/2 * 1/2 = 1/12

So the probability of Zach wearing a solid shirt, blue pants, and a bow tie is 1/12.

Whenever possible, research should be designed so that the data can be anlyzed using option (a) statistics

-This includes both parametric tests (which assume that the data is normally distributed and meet certain assumptions) and non-parametric tests (which do not make these assumptions and are useful for non-normal data). SPSS is a software program commonly used for statistical analysis, but it is not necessary for conducting statistical analyses.

a. statistics

Research should be designed so that the data can be analyzed using statistics. Statistics provide a set of methods and tools for analyzing and interpreting data, which can help researchers draw meaningful conclusions from their findings. Statistical analysis can be used to identify patterns, trends, and relationships in data, as well as to test hypothesis and make predictions.

Depending on the research question, data type, and sample size, different types of statistical tests may be appropriate. Both parametric and non-parametric tests can be used to analyze data, depending on the assumptions made about the underlying distribution of the data and the level of measurement of the variables. SPSS is a statistical software program that can be used to perform statistical analysis, but it is not necessary for designing research studies or analyzing data.

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Answer:

Step-by-step explanation:

12y - 15x = 84     you want to make the equation look like y=mx+b

12y=15x+84       bring over the x term

y=5/4 x +7         divide both sides by 12

Answer:

Using the Pythagorean theorem we can first put the points into x and y

x1 = 7

y1 = 9

x2 = 1

y2 = 1

The distance between the two points can be found as follows:

d = √((x2 - x1)² + (y2 - y1)²)

= √((1 - 7)² + (1 - 9)²)

= √((-6)² + (-8)²)

= √(36 + 64)

= √100

= 10

Therefore, the distance between the points (7, 9) and (1, 1) is 10 units.

The area of triangle be 312.4 m²

In the given figure,

Angle B = 140 degree

AB = 25 m = c (say)

BC = 40 m = a (say)

Since Area of triangle = (1/2) ac sin(B)

Therefore,

Area = (1/2)x25x40 sin 140

        =  (1000 x 0.6428)/2

        =  312.4

Hence area = 312.4 m²

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The complete question is:

Find the area of triangle shown below?

The area of the triangle JHI is 8.75 square units.

From the given figure,

Area of a ΔJHI = Area of a rectangle - (Area of 3 triangles)

= 5×4 - (1/2 ×3×4 + 1/2 ×2×3 + 1/2 ×1×5)

= 20 - (6+3+2.5)

= 20 - 11.25

= 8.75 square units

Therefore, the area of the triangle JHI is 8.75 square units.

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The perimeter of the rectangular frame is 2.5 feet.

Perimeter is the measurement of the distance around an object.

To calculate the perimeter of the frame, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation  1

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Part A: Based on the image, Zachary used systematic sampling method, and he  must have recorded the color of every fifth car that  was known to traveled north.

Part B: To know the percentage of red cars and black cars from all of  sample, we have to calculate the total number of cars in all  sample first and it is done below:

Sample 1:

Total cars = 3 + 5 + 3 + 6 + 3  

                    = 20

The Percentage of red cars = (3/20) x 100%

                                            = 15%

The Percentage of black cars = (6/20) x 100%

                                              = 30%

Sample 2:

Total cars = 4 + 7 + 3 + 4 + 2

                  = 20

The percentage of red cars = (4/20) x 100%

                                        = 20%

The percentage  of black cars = (4/20) x 100%

                                          = 20%

Sample 3:

Total cars = 2 + 6 + 3 + 4 + 5

                   = 20

The percentage of red cars = (2/20) x 100%

                                        = 10%

The percentage of black cars = (4/20) x 100%

                                        = 20%

Sample 4:

Total cars = 3 + 4 + 4 + 5 + 4  

                = 20

The percentage of red cars  = (3/20) x 100%

                                                  = 15%

The percentage  of black cars = (5/20) x 100%

                                                   = 25%

Sample 5:

Total cars = 2 + 4 + 3 + 5 + 6

                   = 20

The percentage of red cars = (2/20) x 100%

                                              = 10%

The percentage  of black cars = (5/20) x 100%

                                                    = 25%

Part C:

The Two conclusions that I have drawn are:

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See text below



All changes saved Zachary took five random samples of cars that passed through the intersection near his school. He recorded the color of every fifth car that traveled north, and the results of his samples are organized in the table below.

                  Sample1   Sample2   Sample3    Sample4  Sample5

  red                3             4                   2                3                   2

white              5              7                    6                4                  4

blue                3               3                    3                 4                3

black              6              4                    4                 5                  5

gray                3              2                    5                 4                   6

Part A: What sampling method did Zachary use to gather his data?

Part B: Determine the percentage of red cars from each sample and the percentage of black cars from each sample.

Part C: Draw two conclusions about your findings from Part B.

Answer: 24 feet of ribbon needed in total

Step-by-step explanation:

Nonlinear programming involves optimizing a nonlinear objective function subject to nonlinear constraints. Excel Solver uses the Generalized Reduced Gradient (GRG) algorithm to solve nonlinear programming problems. This algorithm is a variant of the more well-known Newton's method for optimization, but with modifications to handle nonlinear constraints.

Solving nonlinear problems with local optimal solutions can be performed using various optimization techniques, including gradient descent, Newton's method, and simulated annealing, among others. However, in Excel Solver, which is a widely used optimization tool, local optimal solutions are typically found using the more classical optimization technique of nonlinear programming.

The GRG algorithm iteratively computes the gradient and Hessian of the objective function, and then uses this information to update the decision variable values. The algorithm then checks whether the updated solution satisfies the nonlinear constraints. If it does, the algorithm terminates. Otherwise, the algorithm modifies the constraints and repeats the process until a feasible solution is found.

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30.54 units is the measurement of the side JG.

It is given that, quadrilateral CDEF and the quadrilateral GHIJ are similar,

in a similar figure, the ratio of the adjacent sides is equal,

Thus in the given figure,

FE/JI =  FC/JG

11/42 = 8/JG

JG = 42*8/11

JG =30.54

Therefore, the measurement of the side JG is 30.54 units.

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Answer:

-------------------------

Simplify the given expression:

Simplify the answer choices and compare with the given:

The exponential expression is not equal to given expression is (5⁻²)¹.

Given is an exponential expression 5⁴·5⁻²,

So, when solving this,

5⁴·5⁻² = 5(⁴⁺⁽⁻²⁾)

= 5²

So, from the given options,

A) 5⁻³·5⁵ = 5² [equivalent]

B) 1/5⁻² = 5² [equivalent]

C) (5⁻²)⁻¹ = 1/(5⁻²) = 5² [equivalent]

D) (5⁻²)¹ = 5⁻² [non-equivalent]

Hence exponential expression is not equal to given expression is (5⁻²)¹.

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Answer:

X= 5

Step-by-step explanation:

If 2 triangles are similar then their corresponding side ratio are proportional

∆ABC ~∆DEF

Then

AB/DE = BC/EF = AC/DF

AB/DE = BC/EF = AC/DF6/4 = 21/2x+4 = 4x-2/12 when we simplify them

3/2 = 21/2x+4 = 2x-1/6

3/2 = 21/2x+4 = 2x-1/63/2 = 21/2x+4 .............. criss cross

3(2x+4) = 42

3(2x+4) = 422x+4 = 14

3(2x+4) = 422x+4 = 142x=14 - 4 = 10

3(2x+4) = 422x+4 = 142x=14 - 4 = 102x/2 = 10/2

3(2x+4) = 422x+4 = 142x=14 - 4 = 102x/2 = 10/2x = 5 ........we solve the value of x

In order to take x = 5 we must check it by inserting to the other proportion

6/4 = 4x-2/12 ........ when we simplify it

3/2 = 2x-1/6 ........ then we will insert 5 in place of x

3/2 = 9/6....... when we simplify it by 3

3/2 = 3/2 ..... so the are proportional ( equal )

so the value of x is 5

Answer:

you move the decimal point three times

The surface area of the rectangular prism is 108 square units.

To sketch each face of the rectangular prism, we need to identify the dimensions of each face. Let's assume the rectangular prism has length (L), width (W), and height (H).

Face 1: Front Face

Dimensions: L x H

Face 2: Back Face

Dimensions: L x H

Face 3: Top Face

Dimensions: L x W

Face 4: Bottom Face

Dimensions: L x W

Face 5: Right Side Face

Dimensions: W x H

Face 6: Left Side Face

Dimensions: W x H

Now, to find the surface area, we calculate the area of each face and sum them up.

Surface Area = 2(L x H) + 2(L x W) + 2(W x H)

Let's assume the dimensions of the rectangular prism are:

Length (L) = 6 units

Width (W) = 4 units

Height (H) = 3 units

Substituting these values into the surface area formula:

Surface Area = 2(6 x 3) + 2(6 x 4) + 2(4 x 3)

= 2(18) + 2(24) + 2(12)

= 36 + 48 + 24

= 108

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Step-by-step explanation:

if a triangle is in the form ∆ABC,

then, According to Pythagoras Theorem,

AB²+BC² = AC²

4²+8² = AC²

√80 = AC or 8.944 cm = AC

hope this helps.

The ratio of the area of a base ball diamond to the area of a softball diamond is 9/4

From the question, we have the following parameters that can be used in our computation:

This means that

d1 = 90

d2 = 60

So, the ratio of the side lengths are

r = d1/d2

This gives

r = 90/60

Simplify

r = 3/2

For the area ratio, we have

r^2 = 9/4

Hence, the ratio is 9/4

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A quadratic equation with opposite solutions can be found when D > 0.

In a quadratic equation, the discriminant D describes the nature of the roots which is also called the solutions of the equation.

For a quadratic equation ax²+bx+c = 0, the discriminant D is given by =

D = [-b ± √(b² – 4ac)]/2a

Nature of roots:

D > 0, roots are real and distinct.

D = 0, roots are real and equal.

D < 0, roots are imaginary and unequal.

Hence, the quadratic equation with opposite solutions can be found when D > 0.

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1. The parts of the circle identified are as explained below.

2. Area = 153.94 m²;

Circumference = 43.98 m;

3. Area= 706.86 ft²;

Circumference =94.25 ft;

4. Area =  326.85 in.;

Circumference = 64.09 in.

A circle is described as a closed two-dimensional shape that consists of points that are equidistant from a central point called the center.

The  example of each part using the diagram of the circle given is shown below:

a. a center= K

b. One radius = JK

c. A chord = JL

d. Diameter = JI

e. Secant = GI

f. Tangent = GJ

g. Point of tangency= J

h. A minor arc = IL

i. A major arc = HIL

j. Semicircle = JLI

k. A central angle is less than JKL

l. An inscribed angle is less than HIJ

2. we then apply the area and circumference formula to find  each required measure for each circle.

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Complete question is attached in diagram:

The t-value is less than or equal to the critical value, you would fail to reject the null hypothesis, indicating that the sample mean is not significantly different from the population mean.

If the population is normal, the sample is large, and the standard deviation is not known, the appropriate test to use would be the one-sample t-test.
The t-test is a statistical test that allows us to compare the means of two groups to determine if there is a significant difference between them.

In this case, we are interested in testing if a sample mean is significantly different from the population mean.
Since we do not know the standard deviation of the population, we use the standard deviation of the sample to estimate it.

The t-test takes into account the sample size, the sample mean, and the sample standard deviation to determine the probability of obtaining the observed sample mean if the population mean is the same as the sample mean.
If the calculated t-value is greater than the critical t-value at a given significance level, we can reject the null hypothesis that the sample mean is equal to the population mean and conclude that there is a significant difference between the two means.
In summary, the one-sample t-test is the appropriate test to use when dealing with a normal population, a large sample, and an unknown population standard deviation.

It allows us to test whether a sample mean is significantly different from the population mean and provides us with a measure of the probability of obtaining the observed sample mean by chance.

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