A group of friends were working on a student film. They spent all their budget on equipment and props. They spent $216 on equipment, and 73% of the total budget on props. What was the total budget for their student film?

The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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Answer:

false

Step-by-step explanation:

The angles of the triangles that measure 90° will be ABC and DEF.

The pairs of line segments that are formed by the triangle sides are line ED and AB.

It should be noted that parallel lines are the lines that maintains the same distance between them and never meet.

Also, the angle that has the same measurement as angle DEA will be BAC. This is based on alternate exterior angles.

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Explanation:

These two similar quadrilaterals could look like this:

We have to follow the same order of the letters for each vertex. We can see that the corresponding vertices are :

• R - J

• S - K

• T - L

• U -M

This means that their angles are congruent (the symbol you wrote means congruent)

We can see in the options that the only one that doesn't match what I wrote above is option C, because U and J are not corresponding vertices, so their angles are not congruent.

Answer:

The option that's NOT true is option C.

the answer is 4

Step-by-step explanation:

Answer:

The answer is 2/4

Step-by-step explanation:

Answer:

The value of x is 1

Step-by-step explanation:

Let us solve the question

∵ Δ PQR ≈ Δ FGH

→ From similarity, then their corresponding sides have an equal ratio

∴ \(\frac{PQ}{FG}\) = \(\frac{QR}{GH}\) = \(\frac{PR}{FH}\)

∵ PQ = 3, QR = x + 3, PR = 2

∵ FG = 6, GH = 6x + 2, FH = 4

→ Substitute them in the ratios above

∴ \(\frac{3}{6}\) = \(\frac{x+3}{6x+2}\) = \(\frac{2}{4}\)

→ By using cross multiplication between the first two ratios

∵ 3 × (6x + 2) = 6 × (x + 3)

∴ 3(6x + 2) = 6(x + 3)

∴ 3(6x) + 3(2) = 6(x) + 6(3)

∴ 18x + 6 = 6x + 18

→ Subtract 6x from both sides

∵ 18x - 6x + 6 = 6x - 6x + 18

∴ 12x + 6 = 18

→ Subtract 6 from both sides

∵ 12x + 6 - 6 = 18 - 6

∴ 12x = 12

→ Divide both sides by 12

∴ x = 1

Answer:

3

Step-by-step explanation:

3

Answer:

x = 4

Step-by-step explanation:

Given the equation:

\(\displaystyle{4^x - 4^0 - 255=0}\)

We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,

\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)

Add both sides by 256, so we have:

\(\displaystyle{4^x=256}\)

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

\(\displaystyle{4^x=2^8}\)

Convert to the same base:

\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)

When two sides have same base, solve the equation through exponents:

\(\displaystyle{2x=8}\)

Divide both sides by 2, so we have:

\(\displaystyle{x=4}\)

The diameter of the given circle with a circumference of 28.6 centimeters is approximately 9.11 cm.

The circumference of a circle is given by the simple formula: C = πd, where C is the circumference, π is the constant pi and d is the diameter of the circle.

Given that the circumference of the circle is 28.6 cm, we can use the formula to find the diameter:

28.6 = πd

d = 28.6/π

Using 3.14 as an approximation for π, we get:

d ≈ 28.6/3.14 ≈ 9.11

Therefore, the diameter of the circle is approximately 9.11 cm.

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Answer:

\(y = \frac{2x}{x - 1} \)

Step-by-step explanation:

find the inverse of the function

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables

\(y = \frac{x}{x - 2} \)

becomes

\(x = \frac{y}{y - 2} \)

Now, solve the equation 

\(x = \frac{y}{y - 2} \)

 for y.

\(y = \frac{2x}{x - 1} \)

Answer:

y = -2x + 9

Step-by-step explanation:

1) Use the equation y = mx + c (m being gradient and c being y-intercept)

2) Substitute all the values to get 7 = -2(1) + c

3) Solve to get c:

4) Final answer: y = -2x + 9

If C = 15 , then the values of A and B will be A = 3, B = 5  and equation in standard form is 3x + 5y = 15  .

In the question ,

the equation is given

the equation is Ax + By = C

also given that C = 15 ,

so , Ax + By = 15

From the graph we see that when x = 5 , y = 0

substituting , in Ax + By = 15  , we get

A(5) + B(0) = 15

5A = 15

A = 3 .

also when x = 0 , y = 3

Substituting in Ax + By = 15  , we get

A(0) + B(3) = 15

3B = 15

B = 5

so , the equation in standard form is 3x + 5y = 15   .

Therefore , If C = 15 , then the values of A and B will be A = 3, B = 5     .

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\(\\ \rm\bullet\rightarrowtail a^2=5^2-3^2\)

\(\\ \rm\bullet\rightarrowtail a^2=25-9\)

\(\\ \rm\bullet\rightarrowtail a^2=16\)

\(\\ \rm\bullet\rightarrowtail a=\sqrt{16}\)

\(\\ \rm\bullet\rightarrowtail a=4\)

As per the unitary method, there are 64.29 weeks does it take to empty the lake.

The term unitary method is known as a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here we have given that officials begin to release water from a full man-made lake at a rate that would empty the lake in 12 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time.

And we need to find the number of weeks does it take to empty the lake

While we looking into the given question, we have identified the following values,

=> Empty rate = 1/18 job/week

=> Fill rate = 1/25 job/week

Then together rate is written as 1/x

Then the equation of the given situation is written as,

=> rate - rate = together rate

When we apply the values, then we get,

=> 1/18 - 1/25 = 1/x

Now we have to multiply thru by 18*25x, then we get,

=> 25x - 18x = 18*25

=> 7x = 18*25

Therefore, x = 64.29 weeks.

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The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.

To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.

Let's denote:

P(R) as the probability of a student spending time reading (P(R) = 0.59),

P(E) as the probability of a student doing well on an exam (P(E)),

P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).

The formula for conditional probability is:

P(E|R) = P(E and R) / P(R).

Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:

P(E|R) = 0.58 / 0.59 = 0.983.

Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.

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The particular solution of the differential equation  y''-5y' 4y=8e^x is A*e^x form.

To find the form of the particular solution for the given differential equation, y'' - 5y' + 4y = 8e^x, we will first identify the terms involved and then determine an appropriate trial function for the particular solution.

Given differential equation: y'' - 5y' + 4y = 8e^x

Here, the left side represents a linear differential equation with constant coefficient and the right side is the non-homogeneous term (8e^x).

To find the form of the particular solution, we'll assume a trial function based on the non-homogeneous term. Since the non-homogeneous term is 8e^x, our trial function will have the form:

Trial function: Y_p(x) = A*e^x

Now, we need to find the derivatives of Y_p(x) and substitute them into the differential equation:

First derivative: Y_p'(x) = A*e^x
Second derivative: Y_p''(x) = A*e^x

Substituting these into the differential equation:

(A*e^x) - 5(A*e^x) + 4(A*e^x) = 8e^x

Simplifying the equation:

(A - 5A + 4A)e^x = 8e^x

Now, we compare the coefficients:

A = 8

So, the form of the particular solution for the given differential equation is Y_p(x) = 8e^x

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Answer:

which one 3 or 4. please tell me

6y + 4 I guess is the answer for the question

Step-by-step explanation:

tsa= total surface area

csa=curved surface area

answer is in the picture

Answer:

Tell me you address right now!!!

Step-by-step explanation:

I am gonna call police for help!

Answer:

bye

Step-by-step explanation:

hi and bye

Let the number of hours = h

Multiply the rate per hour by hours and add to the rental fee.

This at most can equal the amount you have.

Equation: 6h+ 13.50 <= 37.50

Solve for h:

6h + 13.50 <= 37.50

Subtract 13.50 from both sides:

6h <= 24.00

Divide both sides by 6:

H <= 4

You can rent the canoe for 4 hours maximum.

Answer:

The interest earned is $10.00

Step-by-step explanation:

Interest = principal x rate x time

I= 100(.01)(10)

I = 10

Answer:

48 square meters

Step-by-step explanation:

cause if u  4m x 12m =48

Answer:

48 square meters

Step-by-step explanation:

The equation used to solve this is a= wl (area equals length times width)

Therefore, all you have to do is multiply 12 and 4 to get the area of the rectangle.

12 times 4= 48

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Answer:

Give more points

Step-by-step explanation:

Answer:

the building is 38.4 feet tall

Step-by-step explanation:

because the ratio for the man is 6:2.5 and the building is x:16

so x = 38.4

the critical F-value when the sample size for the numerator is four and the sample size for the denominator is seven = Fα=9.78

The F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher-Snedecor distribution, is a continuous probability distribution that frequently appears as the null distribution of a test statistic, most notably in the analysis of variance and other F-tests.

The quantity of values in a statistic's final calculation that are subject to variation is known as the number of degrees of freedom. Various amounts of information or data can be used to estimate statistical parameters.

The sample size of the numerator = 4

The sample size of the denominator = 7

The degree of freedom for the numerator df = n -1

The degree of freedom for the numerator df = 4 - 1

The degree of freedom for the numerator df = 3

The degree of freedom for the denominator df = n - 1

The degree of freedom for the denominator df = 7 - 1

The degree of freedom for the denominator df = 6

the F distribution-table \alpha=0.01α=0.01

in the appendix :

F\(_\alpha\)=9.78

Fα=9.78

the critical F-value when the sample size for the numerator is four and the sample size for the denominator is seven = Fα=9.78

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The equation of the tangent line at the point (x(t), y(t)) can be written as:

y - sin t cos t = cot t(x - cos t sin t).

The equation of the line tangent to the curve is required to be determined at the given value of t, and the value of t also has to be found.

The curve is defined as x cos t, y sin t, t.

Therefore, the first step would be to differentiate the curve equation with respect to t. Let's differentiate it and then evaluate it at the given value of t:

dy/dt = (dy/dt)(sin t) = cos tdx/dt = (dx/dt)(cos t) = -sin t

Now, the slope of the tangent line can be calculated at the point t (given value of t) as follows:

m = dy/dx = (dy/dt)/(dx/dt) = (cos t)/(sin t) = cot t

Now, the point on the curve at t can be substituted into the equation of the curve to find the corresponding value of y, which is the value of f(x) at that point.

f(t) = y sin t = sin t cos t

Therefore, the equation of the tangent line at the point (x(t), y(t)) can be written as:

y - sin t cos t = cot t(x - cos t sin t).

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