Questions 5 to 8: Finding probabilities for the t-distribution Question 5: Find P(X<2.262) where X follows a t-distribution with 9 df. Question 6: Find P(X>-2.262) where X follows a t-distribution with 9 df. Question 7: Find P(Y< -1.325) where Y follows a t-distribution with 20 df. Question 8: What Excel command/formula can be used to find P(2.179

Answer:

C

Step-by-step explanation:

Using Parts Whole Postulate we can write:

∠LQP = ∠LQR + ∠PQR

We know that ∠LQP = 77° and ∠LQR = 35° so we can write:

77° = 35° + ∠PQR

Therefore the answer is 77 - 35 = 42°.

a = 4 and b = 5 are the answers to the system of equations.

Let's square both sides of the first equation to eliminate the square root:

√a + b = 7

(√a + b)² = 7²

a + 2√ab + b² = 49

a + b² = 49 - 2√ab ---(1)

Now, let's square both sides of the second equation:

√b + a = 11

(√b + a)² = 11²

b + 2√ab + a² = 121

a² + b + 2√ab = 121 ---(2)

We can use equation (1) to substitute for √ab in equation (2):

a + b² = 49 - 2√ab

√ab = (49 - a - b²)/2

Substituting for √ab in equation (2), we get:

a² + b + 2(49 - a - b²)/2 = 121

Simplifying and rearranging, we get:

a² - a + b² - b - 36 = 0

(a - 1/2)² + (b - 1/2)² = 37.25

This is the equation of a circle centered at (1/2, 1/2) with a radius √37.25. We need to find the points where this circle intersects the line defined by equation (1).

Substituting b = 49 - a - 2√(a(49 - a))/2 into equation (1), we get:

a + (49 - a - 2√(a(49 - a)))² = 49 - 2√a(49 - a)

Simplifying and rearranging, we get:

4a³ - 294a² + 2421a - 5929 = 0

Using a numerical solver or the rational root theorem, we can find that one solution of this cubic equation is a = 4.

Substituting this value back into equation (1), we can solve for b:

4 + b² = 49 - 2√(4b)

b² + 2√(4b) - 45 = 0

Using the quadratic formula, we get:

b = 5

Therefore, the solutions of the system of equations are a = 4 and b = 5.

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Complete question:

√a+b=7 and √b +a = 11 If a and b are real numbers that satisfy the equation above, what is the value of a and b respectively?

Answer:

\(\huge\boxed{S_8=3,280}\)

Step-by-step explanation:

The formula:

\(S_n=\dfrac{a_1(1-r^n)}{1-r}\)

Substitute:

\(n=8;\ r=3;\ a_1=1\\\\S_8=\dfrac{1\cdot(1-3^8)}{1-3}=\dfrac{1-6,561}{-2}=\dfrac{6,560}{2}=3,280\)

Answer:

JK = 24

Step-by-step explanation:

Δ BKJ and Δ BCA are similar and ratios of corresponding sides are equal, that is

\(\frac{JK}{AC}\) = \(\frac{BK}{BC}\) , substitute values

\(\frac{JK}{40}\) = \(\frac{3}{5}\) ( cross- multiply )

5JK = 120 ( divide both sides by 5 )

JK = 24

Formula used to calculate the grades to a student is as follows:

F=G−((1−w)×C))/w.

You may determine the grade you need on the final exam to get your desired course grade if you know your present grade and the final test's weight.

The explanation for the given formula, F = Final exam grade

G = Grade you want for the class

w = Weight of the final exam, divided by 100 (put weight in decimal form vs. percentage form)

C = Your current grade.

Being able to keep track of your class grades is a really valuable ability. You may keep track of your progress and see whether you need to work more to achieve the grade you want. In order to figure out how much you need to raise your grade with a point system. Compare that number against the point count for the work you have not yet done. Thus this is the way to calculate grades.

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Answer:

20

Step-by-step explanation:

36➗4=9

20➗4=5

Answer:

rotation

Step-by-step explanation:

because the earth rotates

Answer:

-4

Step-by-step explanation:

8+4(-3)

first solve 4(-3)

4(-3)

4*-3=-12

8+(-12)

8-12

-4

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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Answer:

\(4x + 5 \: if \: x = 9 \\ 4(9) + 5 \\ = 41 \\ \\ 3x = 3(9) \\ = 27\)

\(41 + 27 \\ = 68\)

Answer:

I think it's qualitative

Step-by-step explanation:

My best guess

Answer:

i think it would be d? im not sure

Step-by-step explanation:

Answer: No, the statement "if f(x)= x² (x≠2), then lim f(x) =4" is not correct. The limit of a function is a value that the function approaches as the input (in this case, x) gets closer and closer to some specific number. In this case, the limit of f(x) as x approaches 2 would be 4, since f(x)=x² for all values of x other than 2. However, if you ignore the x≠2 restriction and consider all values of x, then the limit of f(x) as x approaches 2 would be undefined, since f(x)=4 for x=2.

Step-by-step explanation:

The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Answer:

2

Step-by-step explanation:

Answer:

The Answers Are:

B. The variable h is the independent variable.

C. The number of hours worked causes a change in the number of dollars earned.

D. The variable d is the dependent variable.

Step-by-step explanation:

As you can see on the picture, the more hours you work, the more dollars you get.

d=19h

The statement,B. The variable h is the independent variable. The number of hours worked causes a change in the number of dollars earned. The variable d is the dependent variable are correct.

We have the given options,

A.The variable d is the independent variable.

B. The variable h is the independent variable.

C. The number of hours worked causes a change in the number of dollars earned.

D. The variable d is the dependent variable.

Here d is dependent on hours,

In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an independent variable.

As you can see below, the more hours you work, the more dollars you get.

Hours        Dollars

1                   19

2                  38

3                  57

4                  76

5                  95

d=19h.

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83+34+99+79= 295

Step-by-step explanation:

yes Answer:

Step-by-step explanation: yes

For the given inequality 14 - 3f > 2 the option that comes out be correct is

f < 4 i.e option 2.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.The majority of the time, size comparisons between two numbers on the number line are made.

Here, "Less than" and "Greater than" have new meanings.

Less-than sign is the symbol for such phrase.

14 - 3f > 2

adding 3f on both sides:

14 - 3f + 3f > 2 + 3f

14 > 2 + 3f

subtracting 2 on both sides:

14 - 2 > 2 + 3f - 2

12 > 3f

dividing 3 on both sides:

(12)/3 > (3f)/3

4 > f

which means f < 4

Therefore, option 2 is correct.

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Using the normal distribution, it is found that 1234 pairs of jeans produced separates the lowest 33% of the means of jean production from the highest 67% in a sampling distribution of 12 factories.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For this problem, the parameters are given by:

\(\mu = 1250, \sigma = 125, n = 12, s = \frac{125}{\sqrt{12}} = 36.08\)

The desired amount is the 33rd percentile, which is X when Z = -0.44, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

-0.44 = (X - 1250)/36.08

X - 1250 = -0.44 x 36.08

X = 1234.

1234 pairs of jeans produced separates the lowest 33% of the means of jean production from the highest 67% in a sampling distribution of 12 factories.

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The equations represents that 5 less than 10 times a number is 15 is option A) 10n - 5 = 15

Equation with polynomials on both sides is known as an algebraic equation or polynomial equation (see also system of polynomial equations). They are further divided into levels: linear formula for level one.

The statement "5 less than 10 times a number is 15" is one that can be translated into an equation.

For example, Let's use the variable 'n' to stand for the unknown number.

The phrase "10 times a number" can be shown as 10n.

The statement "5 less than 10 times a number" implies subtracting 5 from 10n, and that gives us 10n - 5.

So, one have the equation 10n - 5 = 15.

This equation implies that "10 times a number, reduced by 5, is equal to 15." It stands for the relationship shown in the original statement.

Therefore, option A) 10n - 5 = 15 is the correct equation that stand for the given scenario.

To simplify it:

10n - 5 = 15

10n= 15 +5

10n =20

n = 20/10

n = 2

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Answer: X=8

Step-by-step explanation:

Remove parenthesis: X+2=10

Subtract 2 from both sides: X=10-2

Simplify 10-2 to 8

Your answer is X=8

The given statement " When the film is placed into the XCP (extension cone paralleling) holder with the smooth side of the film towards the throat, after processing, it will appear darker" is false because it will  lighter, not darker.

The smooth side of the film is the side that interacts with the X-ray radiation and receives the image, while the emulsion side contains the light-sensitive crystals that react to the radiation.

Placing the smooth side towards the throat ensures that the image is sharp and clear, as the X-ray beam travels through the teeth and soft tissues before reaching the film.

After processing, the exposed areas of the film turn dark, representing the captured X-ray image, while the unexposed areas remain light or clear.

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Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

The term which is used for describing the number of voters who casted their votes using the ballots is called as voter turnout.

The process of selecting a candidate for a suitable post who takes care of the policies which will be framed for the people is called as voting. In this process, the members/ citizens casts their vote in the favor of their suitable candidate. Many times voters are not valid and their votes are considered as null and void.

The voter turnout is either the percentage of registered voters, eligible voters, or all voting-age people ( this varies from place to place depending upon the minimum voting age required). The voter turnout is also referred to the number of people who go to it or take part in it. High voter turnout is generally considered a sign of a healthy democracy.

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B= (3,6) and D= (18,9)

Step-by-step explanation:

To find the midpoint of two given points add X1 and X2 together, then divide by 2 to get the X value of the midpoint and do the same thing for the Y value. That will get you B. From there you can see to get from point A to point C you add 10 to the x value and add 2 to the y value. Because C is the midpoint just double what you had to add to get point D (add 20 to x and add 4 to y)

To estimate the area under the graph of f(x) = 20x from x = 0 to x = 4, we can use the concept of numerical integration, specifically the trapezoidal rule.

The trapezoidal rule approximates the area under a curve by dividing the interval into small trapezoids and summing up their areas.

Here's how we can estimate the area using the trapezoidal rule:

Since we don't know the specific value of n, let's assume we divide the interval into 4 subintervals, resulting in Δx = (4 - 0) / 4 = 1.

Now, let's calculate the estimated area using the trapezoidal rule:

Area ≈ [(f(0) + f(1)) * Δx / 2] + [(f(1) + f(2)) * Δx / 2] + [(f(2) + f(3)) * Δx / 2] + [(f(3) + f(4)) * Δx / 2]

Substituting the values of f(x) = 20x:

Area ≈ [(20(0) + 20(1)) * 1 / 2] + [(20(1) + 20(2)) * 1 / 2] + [(20(2) + 20(3)) * 1 / 2] + [(20(3) + 20(4)) * 1 / 2]

= [(0 + 20) * 1 / 2] + [(20 + 40) * 1 / 2] + [(40 + 60) * 1 / 2] + [(60 + 80) * 1 / 2]

= [10] + [30] + [50] + [70]

= 160

Therefore, the estimated area under the graph of f(x) = 20x from x = 0 to x = 4 is approximately 160 square units.

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The perimeter of the playground is 92 meters

The figure is added as an attachment

To calculate the perimeter, we simply add the side lengths of the playground

i.e. Perimeter = Sum of side lengths

Using the above as a guide, we have the following:

Perimeter = 10 + 14 + 10 + 10 + 6 + 6 + 6 + 14 + 6 + 10

Evaluate the like terms

Perimeter = 92

Hence, the perimeter is 92 meters

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Answer: 4597

Step-by-step explanation:

Answer:

The answer is 4,597

Step-by-step explanation:

\((32+47)*(83-24)-4x^{3}\)

add the numbers

\(79(83-24)-4x^{3}\)

subtract the numbers

\(79*59-4x^{3}\)

evaluate the power

\(79*59-64\)

multiply the numbers

\(4661-64\)

subtract the numbers

\(4597\)

Answer:

limo is c = 0.20m + 25

taxi is c = 1.20m

Step-by-step explanation: