20+20+20+20+20-10-10/5

The probability of observing exactly two heads when a fair coin is flipped four times is found to the nearest percent to be 38%.

It is the ratio that shows the likelihood of an event occurring out of all the other possible events.

∴ P( Getting exactly two heads when a coin is flipped four times) = 6/16 = 0.375

0.375*100 = 37.5%

≈ 38%

Therefore, we have found the probability of observing exactly two heads when the coins are flipped four times to the nearest percent as 38%.

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The critical value, given the sample size of 5 and the confidence level of 99. 0 percent would be 16. 812.

The critical values for the chi-squared (χ^2) distribution depend on the degree of freedom and the level of significance.

The degree of freedom for a chi-squared distribution typically equals the sample size minus 1 so the degrees of freedom here is:

= 5 - 1

= 4

The level of significance would be:

= 1 - 99. 0 %

= 0. 01

The critical value of the sample would therefore be found on a chi -squared distribution table for df = 4 and α = 0.01 to be 16. 812.

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The question is not written correctly

Complete Question

The mean speed of vehicles on a stretch of I-84 is 69.5 mph, with a standard deviation of 4 mph. A random sample of 64 vehicles is selected. Find the probabilty that the mean speed is 70 mph

Answer:

0.84134

Step-by-step explanation:

When given a random number of samples when asked to find probability of that a mean is equal to, less than or greater than a given number, the z score formula we use is :

z = (x- μ)/Standard error, where

x is the raw score,

μ is the population mean

n = Random number of samples

Standard error = is the population standard deviation/square root of randy number of samples

= σ /√n

Standard error = σ /√n

σ = 4 mph, n = 64

= 4/√64

= 4/8 = 1/2

= 0.5

z = (x- μ)/Standard error

x = 69.5mph μ = 70mph ,Standard error = 0.5

z = 70 - 69.5/0.5

z = 1

Using the z score table for find the probability,

P(x = 70) = P(z = 1)

= 0.84134

Therefore, the probability that the mean is 70mph = 0.84134

Answer:

Step-by-step explanation:

i hope this helps

Answer:

0.5

Step-by-step explanation:

BODMAS

17-2*8+3/2

17-2*8+1.5

17-16+1.5

17-17.5

=0.5

Answer: The equation used to find the value of x is 5x - 4 = 3x + 10. The value of x is determined to be 7.

Step-by-step explanation:

Four less than the product of a number (x) and 5 = 5x - 4

8 more than 2 added to 3 times the number = 3x + 2 + 8 = 3x + 10

Four less than the product of a number (x) and 5 is equal to 8 more than 2 added to 3 times the number => 5x - 4 = 3x + 10

                                                         5x - 3x = 10 + 4

                                                         2x = 14

                                                         x = 14/2

                 therefore,                      x = 7

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Answer:

Step-by-step explanation:

Nicholas has purchased 1.8 pounds of pixie sticks.

Jane has purchased 3.0 pounds of Jolly ranchers.

Step-by-step explanation:

Cost of 1 pounds of pixie sticks = $4.50

Let the number of pixie sticks = x

Total  money spend on x pounds of pixie sticks = $8.10

Nicholas has purchased 1.8 pounds of pixie sticks.

Cost of 1 pounds of Jolly ranchers = $3.25

Let the number of Jolly ranchers = y

Total  money spend on y pounds of Jolly ranchers = $9.75

Jane has purchased 3.0 pounds of Jolly ranchers.

Answer:

C and E are correct

Step-by-step explanation:

We simply substitute the value of x to see if we can get y for each of the equations

A. y = -3x

2 is not -3(6)

This is wrong

B. y = -3/2x + 6

-3/2x + 6 = -3/12 + 6

This cannot be equal to 2 so this is wrong also

c. y = -1/6x + 3

y = -1/6(6) + 3

= -1 + 3 = 2

This is correct

d. y = 2/3x - 1

This is wrong

2/3(6) - 1 cannot be 2

e. y = 1/2x - 1

2 = 1/2(6) -1

This is correct

F. y = 4(6) - 2 = 24-2 = 22

"The correct answer is option A." The missing coordinates of point Q are (a, c/2).We are given the coordinates of points P and N as (0, c) and (2a, 0), respectively. We are also given that point Q lies on the same line as points P, Q, and N. We need to find the missing coordinates of point Q.

Since point Q lies on the same line as P, Q, and N, its x-coordinate must be halfway between the x-coordinates of points P and N. That is, the x-coordinate of Q is:

x-coordinate of Q = (x-coordinate of P + x-coordinate of N) / 2

x-coordinate of Q = (0 + 2a) / 2 = a

So, we know that the x-coordinate of point Q is a.

To find the y-coordinate of point Q, we can use the fact that point Q lies on the same line as point P, which has coordinates (0, c). The equation of the line passing through P and N is:

y - c = (0 - c) / (2a - 0) * (x - 0)

Simplifying this equation gives:

y - c = -c/2a * xy = -c/2a * x + c

Substituting x = a in this equation gives:

y = -c/2a * a + cy = -c/2 + cy = c/2

So, we know that the y-coordinate of point Q is c/2.

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According to the given question we can conclude that the probability that a student who majors in science is a female is approximately 0.375 and the probability that a student is male or majors in art is 0.78.

Probability is the research of probabilities, which also are based on the ratio of favourable events to likely circumstances. One of the areas of probability theory is the estimation of the chance of experiments occurring. With a probability, we can calculate any number of things, from the probability of obtaining a head or a tail when flipping a coin towards the likelihood of generating a research error, for example.

A.) To find the probability that a student who majors in science is a female, we need to use Bayes' theorem. Let F be the event that a randomly selected student is female, and S be the event that the student majors in science. Then we have:

P(F|S) = P(S|F) * P(F) / P(S)

We know that P(F) = 0.6 (since 60% of students are female), and P(S|F) = 0.1 (since 10% of female students major in science). To find P(S), we need to use the law of total probability:

P(S) = P(S|F) * P(F) + P(S|M) * P(M)

We know that P(S|M) = 0.4 (since 40% of male students major in science), and P(M) = 0.4 (since 40% of students are male). Therefore:

P(S) = 0.1 * 0.6 + 0.4 * 0.4 = 0.16

Now we can calculate P(F|S):

P(F|S) = 0.1 * 0.6 / 0.16 ≈ 0.375

Therefore, the probability that a student who majors in science is a female is approximately 0.375.

B.) To find the probability that a student is male or majors in art, we need to use the law of total probability again:

P(Male or Art) = P(Male) + P(Art) - P(Male and Art)

We know that P(Male) = 0.4 (since 40% of students are male), and P(Art|Male) = 0.5 (since 50% of male students major in art). We also know that P(Female) = 0.6 (since 60% of students are female), and P(Art|Female) = 0.7 (since 70% of female students major in art). Therefore:

P(Art) = P(Art|Male) * P(Male) + P(Art|Female) * P(Female)

= 0.5*0.4+0.7*0.6

= 0.58

To find P(Male and Art), we can multiply the probabilities of being male and majoring in art:

P(Male and Art) = P(Male) * P(Art|Male)

= 0.4 * 0.5

= 0.2

Now we can calculate P(Male or Art):

P(Male or Art) = 0.4 + 0.58 - 0.2

= 0.78

Therefore, the probability that a student is male or majors in art is 0.78.

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Your description of the surface is incomplete. But it looks like you're considering some subset of the paraboloid z = 1 - x ² - y ², so I'll go ahead and assume it's the part of said paraboloid above the x,y-plane, so that the boundary is a circle centered at the origin with radius 1.

By Stokes' theorem, the line integral of F along this boundary (∂S) is equal to the surface integral of curl(F ) over the surface itself (S). We have

F(x, y, z) = z ² i + 2x j + y ² k

which has curl

curl(F ) = (∂(y ²)/∂y - ∂(2x)/∂z) i - (∂(y ²)/∂x - ∂(z ²)/∂z) j + (∂(2x)/∂x - ∂(z ²)/∂y) k

curl(F ) = 2y i + 2z j + 2k

Parameterize S by the vector function,

r(u, v)  = u cos(v) i + u sin(v) j + (1 - u ²) k

with 0 ≤ u ≤ 1 and 0 ≤ v ≤ 2π.

Take the upward-pointing normal vector to S to be

n = ∂r/∂v × ∂r/∂u

n = (-u sin(v) i + u cos(v) j ) × (cos(v) i + sin(v) j - 2u k)

n = 2u ² cos(v) i + 2u ² sin(v) j + u k

Then the integral of curl(F ) over S - and hence the line integral of F over ∂S - is

\(\displaystyle \iint_S \mathrm{curl}(\mathbf F(x,y,z))\cdot\mathbf S \\\\ = \iint_S \mathrm{curl}(\mathbf F(\mathbf r(u,v)))\cdot\mathbf n\,\mathrm du\,\mathrm dv \\\\ = \int_0^{2\pi}\int_0^1 \left(2u\sin(v)\,\mathbf i + 2(1-u^2)\,\mathbf j + 2\,\mathbf k\right)\cdot\left(2u^2\cos(v)\,\mathbf i+2u^2\sin(v)\,\mathbf j+u\,\mathbf k\right)\,\mathrm du\,\mathrm dv \\\\ = \int_0^{2\pi}\int_0^1 \left(4u^3\sin(v)\cos(v)+4(1-u^2)u^2\sin(v)+2u\right)\,\mathrm du\,\mathrm dv \\\\ = \int_0^{2\pi}\left(\sin(v)\cos(v)+\frac8{15}\sin(v)+1\right)\,\mathrm dv \\\\ = \boxed{2\pi}\)

Just to confirm this result, we can compute the line integral directly, since it's not so difficult to deal with. Parameterize ∂S by the vector function

r(t) = cos(t ) i + sin(t ) j

with 0 ≤ t ≤ 2π. (Note that there is a k component, but its coefficient is 0.) Then

dr/dt = -sin(t ) i + cos(t ) j

and the line integral is again

\(\displaystyle \int_{\partial S}\mathbf F(x,y,z)\cdot\mathrm d\mathbf r \\\\ = \int_{\partial S} \mathbf F(\mathbf r(t))\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt \\\\= \int_0^{2\pi} (\cos(t)\,\mathbf i+\sin(t)\,\mathbf j)\cdot(-\sin(t)\,\mathbf i+\cos(t)\,\mathbf j)\,\mathrm dt \\\\ = \int_0^{2\pi}2\cos^2(t)\,\mathrm dt \\\\ = \boxed{2\pi}\)

Answer:

No. It is not proportional.

Answer:

\(Area = 153.938040026m^2\)

\(Circumference= 43.9822971503m\)

Step-by-step explanation:

Area

\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)

Circumference

\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)

Answer:

false

Step-by-step explanation:

Answer:

false because the absolute value of -9 would be 9 not negativ 9

Answer:

1. Compound Interest

2. Simple Interest

Step-by-step explanation:

Simple Interest multiplies the interest rate on the principal rate by the number of days.

Compound Interest multiplies the interest rate on the principal rate and existing rate by periods. 

Answer:

:)

Step-by-step explanation:

Answer:  6 * 24 = 144 ways.

Step-by-step explanation:

Solution:

Given word => DANGER.

The condition is that vowels can't occupy odd places so, we will let them occupy even places.

A total number of arrangements will be = 6 * 24 = 144 ways.

Answer: 6x24 = 144 ways.

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

Total Questions = 20

Total Points = 28

Correct Answers = +2 points

Incorrect Answers = -1 point

The viewer represents the correct answers with x and the incorrect ones with y.

x+y = 20

for every correct answers 2 points;

and for every incorrect answers, -1 point

This can be written as

2x-y = 28

The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;

now

2x-y = 28

x+y = 20

On adding the equations

]3x = 48

x = 16

y = 4

This means that the contestant answered 16 questions correctly and 4 questions incorrectly

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.

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Answer:

Sum

Step-by-step explanation:

Remember that the plus sign (+) always means to add.

Answer:

It would be the sum of a number and eight.

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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Answer:

P-value = 0.0455

Step-by-step explanation:

In this question, we are concerned with calculating the P- value in a test.

Mathematically we know that;

P-value = 2 * P(Z > |z|)

Please check attachment for complete solution and by step explanation

Answer:

9 Pizzas

Step-by-step explanation:

The general solution to the given differential equation is:

y = (x/12) - (1/288)

How to solve the Differential Equation?

We want to solve the differential equation given as: y' - 24xy = -2x

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -24x. Therefore, the integrating factor is e^(-24x).

Multiplying the entire equation by the integrating factor, we get:

e^(-24x)y' - 24xe^(-24x)y = -2xe^(-24x)

The left side of the equation is the derivative of (e^(-24x)y) with respect to x:

(d/dx)(e^(-24x)y) = -2xe^(-24x)

Integrating both sides with respect to x, we have:

e^(-24x)y = ∫(-2xe^(-24x))dx

Integrating the right side, we get:

e^(-24x)y = -∫(2xe^(-24x))dx

To evaluate the integral on the right side, we can use integration by parts. Let's differentiate -2x and integrate e^(-24x):

u = -2x (differential of u = -2dx)

dv = e^(-24x) (integral of dv = -1/24e^(-24x)dx)

Using the integration by parts formula:

∫uv dx = uv - ∫v du

We can compute the integral as follows:

-∫(2xe^(-24x))dx = -[(-2x)(-1/24e^(-24x)) - ∫(-1/24e^(-24x))(-2dx)]

= -[x/12e^(-24x) + 1/12∫e^(-24x)dx]

= -[x/12e^(-24x) + 1/12(-1/24)e^(-24x)]

= -[x/12e^(-24x) - 1/(12*24)e^(-24x)]

= -[x/12e^(-24x) - 1/(288e^(-24x))]

= -[x/12 - 1/288]e^(-24x)

Substituting this back into the previous equation, we have:

e^(-24x)y = -[-(x/12 - 1/288)e^(-24x)]

Simplifying further:

e^(-24x)y = (x/12 - 1/288)e^(-24x)

Canceling out e^(-24x) on both sides:

y = x/12 - 1/288

Therefore, the general solution to the given differential equation is:

y = x/12 - 1/288

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Based on the information given, it should be noted that the length of other leg 12.

Based on the information, the owner of the course asks you to provide a scale drawing of the green section he requested that you use the length of the legs of the right triangle.

Based on the information, 1/2ab = 54

1/2 × 4/3b² = 54

b² = 81

b = ✓81

b = 9

a will be

= 4/3 × 9

= 12 feet.

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Answer:

b

Step-by-step explanation:

Answer:

B)miles per hour

Step-by-step explanation:

Answer:

Step-by-step explanation:

The smallest perfect square that has three different prime numbers as factor is 900

900 = 30 * 30

Factors = 2² * 3² * 5² = 900

Using a calculator, the value of  csc (203°) is -1.086

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Since csc (203°) = 1/[sin (203°)]

Press 1/ [sin (203°)] and then the equal to button on your calculator. We have:

1/[sin (203°)] = -1.086

Note: If you calculator have "cosec" or "csc" button, you can simply press cosec (203°) or csc (203°) to get the answer.

Thus, the value of  csc (203°) is -1.086

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Step-by-step explanation:

hope you can send the questions again because your question is to long to answer everything. I answered 1,2,3,4