a play starts at 7:30pm, first act last 46 minutes, interval lasts 20 minutes. second act lasts 53 minutes, what time does the second act end?

Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

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If circle has a diameter of 20 cm, the area of the circle is 100π square centimeters.

The area of a circle can be calculated using the formula:

A = πr²

where A is the area, π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter (approximately 3.14), and r is the radius of the circle.

In this case, we are given the diameter of the circle, which is 20 cm. To find the radius, we can divide the diameter by 2:

r = d/2 = 20/2 = 10 cm

Now that we know the radius, we can substitute it into the formula for the area:

A = πr² = π(10)² = 100π

We leave π in the answer since the question specifies to do so.

It's important to include units in our answer to indicate the quantity being measured. In this case, the area is measured in square centimeters (cm²), which is a unit of area.

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The statement that is NOT true in a Chi-Square test is "Small values of the chi squared test statistic would lead to a decision to reject the null hypothesis."

This is because if the test statistic is small, it means that the observed values are close to the expected values, and there is no significant difference between the populations. Therefore, a small test statistic would lead to a failure to reject the null hypothesis. In a Chi-Square test, we compare the proportions of specified characteristics in different populations, and we wish to determine whether they are the same or not. If the test statistic is large, it means that the observed values are significantly different from the expected values, and we have evidence to reject the null hypothesis. Finally, the P-value will be small if the test statistic is large, indicating strong evidence against the null hypothesis.

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To obtain a margin of error of 0.5 days with 95% confidence, a sample size of 738 would be required. To obtain a margin of error of 2 days with 90% confidence, a sample size of 127 would be required.

a. The required sample size for a given margin of error, we can use the formula:

n = (Z * σ / E)^2

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, 95% confidence corresponds to a Z-score of approximately 1.96)

σ = population standard deviation

E = margin of error

Given:

Population standard deviation (σ) = 6.87 days

Margin of error (E) = 0.5 days

Confidence level = 95% (Z-score ≈ 1.96)

Substituting these values into the formula, we can solve for n:

n = (1.96 * 6.87 / 0.5)^2

n = 27.143^2

n ≈ 737.742

Rounding up to the nearest whole number, the required sample size is approximately 738.

b. Similarly, for a 90% confidence level, the Z-score is approximately 1.645. We can use the same formula to calculate the required sample size:

n = (Z * σ / E)^2

Given:

Population standard deviation (σ) = 6.87 days

Margin of error (E) = 2 days

Confidence level = 90% (Z-score ≈ 1.645)

Substituting these values into the formula, we can solve for n:

n = (1.645 * 6.87 / 2)^2

n = 11.256^2

n ≈ 126.485

Rounding up to the nearest whole number, the required sample size is approximately 127.

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The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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Answer:

X<5

Step-by-step explanation:

Divide by 2

Answer=5

Step-by-step explanation:

You can solve this question step by step as follows;

here

2x<10

place 2 to another side and you know it divides 10

or, x<10/2

or,x<5

therefore the answer is 5

Answer:

Step-by-step explanation:

7+m>5

Answer:

m = -2

Step-by-step explanation:

yes.

Therefore , the solution of the given problem of parallelograms comes out to be NM and OL both equal 37.

In Euclidean mathematics, a parallelogram is actually a simple hexagon with two distinct groups and equal distances. A specific kind of quadrilateral called a parallelogram is formed when both sets of sides equally share a horizontal path. Parallelograms come in four different varieties, three of which are mutually exclusive.

Here,

Since LMNO is a parallelogram, we know that the lengths of the opposing sides are identical. Therefore, we can equalize the NM and OL formulas, then solve for x:

=> OL = 4x + 9 and

=>  NM = x + 30

=>  OL = x + 30

=> 4x + 9 = NM

=>  3x = 21

=>  x = 7

We have thus established that x = 7. In order to discover the values for NM and OL, we can put this value back into the expressions for those variables:

=> NM = x + 30 = 7 + 30 = 37

=>  OL = 4x + 9 = 4(7) + 9 = 37

As a result, NM and OL both equal 37.

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The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

Given equation:  y = x² + 2x - 3

If you wish to find the values of y when x = -2 and x = -5:

When x = -2:

⇒ y = (-2)² + 2(-2) - 3

⇒ y = 4 - 4 - 3

⇒ y = -3

When x = -5:

⇒ y = (-5)² + 2(-5) - 3

⇒ y = 25 - 10 - 3

⇒ y = 12

If you wish to find the value of y when x = -2-5:

When x = -2-5 ⇒ x = -7

⇒ y = (-7)² + 2(-7) - 3

⇒ y = 49 - 14 - 3

⇒ y = 32

Answer:

y = 32

Step-by-step explanation:

Given :-

y = x² + 2x - 3

x = -2-5 = -7

To Find :-

y

Inputting the value of x :

y = (-7)² + 2(-7) - 3

y = 49 - 17

Solution :-

y = 32

The G.P. of a term is 256/243.

To find out the G.P. for the 3rd term:

Let us consider the 1st term to be 'a'.

So, \(ar^{2}=18\) ....... Equation (1)

Also \(ar^{6} = \frac{32}{9}\) .....  Equation (2)

Dividing (2) by (1), we get,

\(\frac{ar^{6}}{ar^{2}} = \frac{32}{162}\)

\(r^{4}\) = 16/81.

r = 2/3.

Putting r in equation (1) than we will get

a = 81/2.

So, 10th term = \(ar^{9}\)

= (81/2) ×(512/19683)

= 256/243.

Hence the answer is the G.P. of a term is 256/243.

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Thanks for the points hope you'll understand

Answer:

a=72° b = 6°

Step-by-step explanation:

answer is in pic

Answer:

\(\sf\fbox\red{Answer:-}\)

The answer in the attachment may help uh

\(\small\fbox{\blue{\underline{mαrk \; mє \; вrαínlíєѕt \; plєαѕє ♥}}}\)

\(\sf \bold{\:y\:=\:4\:cos\:3x\:+\:7}\)

graph attached below:

[ fieryanswererft ]

Answer:

d. All of the above are true

Step-by-step explanation:

All of the following statements,

a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.

b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.

C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.

are true

Answer: .14

Step-by-step explanation: Khan Academy

Answer:

0.14

Step-by-step explanation:

First off, please read clearly.

This problem is asking for the probability that (M = 3).

The correct answer for this P(M = 3) problem is 0.14 through Khan Academy.

Even when you solve it, it is 0.14. The equation would be zero point twenty-five multiplied by parenthesis one minus zero point twenty-five closed parenthesis to the power of two. Written out the equation would be the following:

0.25x(1-0.25)^2

*** DO NOT MIX THIS UP WITH A VERY SIMILAR PROBLEM TO THIS. ***

There is a problem using this same Jeremiah situation but it asks for P(M < 4).

If you want the answer for P(M < 4) it is 0.58 so

P(M < 4) = 0.58

And another Jeremiah problem that asks for P(M > 6).

If you want the answer for P(M > 6) it is 0.18 so

P(M > 6) = 0.18

Have a nice day :)

Answer:

a is the correct answer

Step-by-step explanation:

\( \binom{8 \: \: \: - 4 \: \: \: 3}{ - 9 \: \: \: 5 \: \: \: - 4} \)

The number of different social security numbers that can be formed is 3628800.

Given that :

A social security number contains nine digits, such as 914-47-2245.

There are digits 0,1,2,....,9.

So there are 10 numbers in total.

So we can select 9 numbers from a total of 10 numbers.

Using permutation, total numbers is :

P(10, 9) = 10! / (10 - 9)!

            = 10!

            = 3628800

Hence the total number of security numbers that can be formed is 3628800.

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The number of minutes of practice in two weeks is 658.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total minutes of practice in one week = 329.

Total minutes of practice in two weeks.

= 2 x 329

= 658 minutes.

Thus,

658 minutes was the practice in two weeks.

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Answer:

The value of x is 20.

Step-by-step explanation:

The steps are :

0.75x - 13 = 2

0.75x = 2 + 13

0.75x = 15

x = 15 ÷ 0.75

x = 20

Among the 4,229,138 residents of Indiana aged 25 and older, the percentage of the residents aged 25 and older that have a degree is 31 %.

Percentage, which was adapted from the Latin word "per centum", which means "by the hundred", is a fraction or a ratio in which the value of whole is always 100. It is represented by the symbol "%".

The formula to get the percentage is:

Percentage = (Value / Total Value) × 100

Getting first the total value of the degree holders: 326,036 have an associate's degree, 623,200 have a bachelor's degree, and 348,807 have either a graduate or professional degree

residents with degree = 326,036 + 623,200 + 348,807

residents with degree = 1,298,043

If the total value of the residents aged 25 and older is 4,229,138 and among them, 1,298,043 have a degree, getting its percentage using the formula:

Percentage = (Value / Total Value) × 100

Percentage = (1,298,043 / 4,229,138) × 100

Percentage = (0.3069285041) × 100

Percentage = 30.69 %

Rounding off to the nearest whole number,

Percentage = 31 %

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Answer:

E

Step-by-step explanation:

=√9pr / (pr)^-3/2

=3√(pr) × (pr)^3/2

= 3p²r²

Answer:

E. 3p²r²

Step-by-step explanation:

√9pr / (pr)^-3/2=

3(pr)^1/2*(pr)^3/2=

3(pr)^(1/2+3/2)=

3(pr)^2=3p^2r^2

Answer:

12.5

Step-by-step explanation:

150 / 12 = 12.5

     (I'm not the best at explaining-)

A 2% solution of Minoxidil has been moderately effective for about 50% of men who have used it. Minoxidil is a vasodilator that was initially developed to manage hypertension.

Minoxidil, a medication that is applied topically, is used to cure hair loss in males and females, although it is more often used in men. It works by stimulating hair growth and slowing down hair loss.Minoxidil, a vasodilator, increases blood flow to the hair follicles, allowing them to produce thicker and longer hair. It is sold under various brand names, including Rogaine, Regaine, and Avacor Physician's Formulation, and is available in various strengths, including 2% and 5%.Minoxidil is more effective in treating androgenetic alopecia, also known.

As male pattern baldness, than other types of hair loss. It is believed that minoxidil promotes hair growth by increasing the diameter of the hair shaft, resulting in thicker and longer hair growth.Minoxidil is used to treat male and female pattern baldness (androgenetic alopecia) by applying it topically to the scalp. However, like any medication, there may be side effects, such as skin irritation, burning, or itching. As a result, it is recommended that people use it under the supervision of a physician.

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Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Step 1

Remove full rotations of 360 degrees until the angle is between 0 and 360 degrees

Step 2

Hence, we find sin 120 using reference angles in the first quadrant

Therefore,

Answer sin 480 =(√3)/2

According to the question For a) This statement is correct. For b) statement is incorrect. For c) statement is correct. For d) statement is incorrect and For e) This statement is correct.

a. A linear transformation is a special type of function.

This statement is correct. A linear transformation is a function between vector spaces that preserves the vector addition and scalar multiplication operations. In other words, it satisfies two properties: preservation of addition

\(\[T(u + v) = T(u) + T(v)\]\)

and preservation of scalar multiplication

\(\[T(cu) = cT(u)\]\)

where \(\(T\)\) is the linear transformation, \(\(u\)\) and \(\(v\)\) are vectors, and \(\(c\)\) is a scalar.

b. If \(\(A\)\) is a \(\(3 \times 5\)\) matrix and \(\(T\)\) is a transformation defined by  \(\(T(x) = Ax\),\) then the domain of \(\(T\)\) is \(\(\mathbb{R}^5\).\)

This statement is incorrect. The domain of the transformation \(\(T\)\) is determined by the size of the input vectors, which in this case is determined by the number of columns of matrix \(\(A\)\). Since \(\(A\)\) is a \(\(3 \times 5\)\) matrix, the domain of \(\(T\)\) is \(\(\mathbb{R}^5\), not \(\mathbb{R}\).\)

c. If \(\(A\)\) is an \(\(m \times n\)\) matrix, then the range of the transformation \(\(x \rightarrow Ax\)\) is \(\(\mathbb{R}^m\).\)

This statement is correct. The range of the transformation \(\(x \rightarrow Ax\)\) is the set of all possible outputs obtained by multiplying the matrix \(A\)\) with the input vectors \(\(x\).\) Since \(\(A\)\) is an \(\(m \times n\)\) matrix, the resulting vectors will have \(\(m\)\) dimensions. Therefore, the range of the transformation is \(\(\mathbb{R}^m\).\)

d. Every linear transformation is a matrix transformation.

This statement is incorrect. While every matrix transformation is a linear transformation (since matrix multiplication satisfies the properties of linearity), not every linear transformation can be represented by a matrix. Linear transformations can have various forms and may not always be expressible as matrix multiplication.

e. A transformation \(\(T\)\) is linear if and only if \(\(T(cv + c_2v_2) = cT(v_1) + c_2T(v_2)\)\) for all \(\(v_1\)\) and \(\(v_2\)\) in the domain of \(\(T\)\) and for all scalars \(\(c\)\) and \(\(c_2\).\)

This statement is correct. This equation represents the linearity property of a transformation. A transformation \(\(T\)\) is linear if and only if it satisfies this equation, which states that the transformation of a linear combination of two vectors is equal to the linear combination of the transformed vectors.

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Answer:

x=2

Step-by-step explanation:

2x - 3 = 1

Add 3 to each side

2x - 3+3 = 1+3

2x = 4

Divide by 2

2x/2 = 4/2

x = 2

Answer:

2=x

Step-by-step explanation:

2x-3=1

    +3  +3

2x=4

4/2=2

2=x

Step-by-step explanation:

2X-Y=4 ---------(1)

x=4-y---------(2)

since x = 4 – y just substitute for eqn 1

2(4–y) – y = 4

8 – 2y –y=4

8 –3y = 4

–3y=4–8

–3y=–4

y=–4/–3

y= 4/3

since y = 4/3 just substitute for y in eqn (2)

x=4–4/3

multiply both sides by 3

3x=12–4

3x=8

x=8/3 or 2 2/3