Find the Greatest Common Factor of each pair of Numbers.
60 and 72; GCF
45 and 81: GCF:

Answer:

what's the problem i know that "tickets for the school play cost 6 dollars for the adults and 3.50 for the students" but you didn't say how many people are going

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1/4 - ( - 3/4)

{Multiplying two negative signs gives us positive sign}

1/4 + 3/4

Add both of them:

1/4 + 3/4 = 1

Answer:

1

Step-by-step explanation:

note that - (- ) = +

\(\frac{1}{4}\) - (- \(\frac{3}{4}\) )

= \(\frac{1}{4}\) + \(\frac{3}{4}\)

= 1

The area of the semi-circle with a diameter of 18 cm will be 127.17 square cm.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let 'd' be the diameter of the circle. Then the area of the circle will be

A = (π/4)d² square units

The diameter is 18 cm. Then the area of the circle is given as,

A = (π/4) x 18²

A = (3.14 / 4) x 324

A = 254.34 square cm

Then the area of the semicircle is the area of the half of the circle, then we have

Semicircle area = 254.34 / 2

Semicircle area = 127.17 square cm

The area of the semi-circle with a diameter of 18 cm will be 127.17 square cm.

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Answer:

False

Step-by-step explanation:

It is not proportional because the distance does increase with the same amount with time.

if Proportional , this would be the tabel

Time distance

1 4

2 5.5

3 7

4 8.5

5 10

9.75 ft is the answer

\(By \: Pythagoras \: Theorem, \\ \boxed{ {hyotenuse}^{2} = {base}^{2} + {height}^{2} } \\ \\ here \\ hypotenuse = 12ft \\ base = 7 ft\\ height = x\ \\ \\ \ {12}^{2} = {7}^{2} + {x}^{2} \\ \implies144 = 49 + {x}^{2} \\ \implies {x}^{2} = 144 - 49 \\ =95 \\ x = \sqrt{95 } \\ = 9.75 ft\\ \\ \\ \)

Answer

O False

Step-by-step explanation

Let's plug in each co-ordinate into the inequality:

\(\sf{3x+2y\leqslant2}\)

I plug in 2 for x and 1 for y:

\(\sf{3(2)+2(1)\leqslant2}\)

Simplify

\(\sf{6+2\leqslant2}\)

\(\sf{8\leqslant2}\)

Hence, the (2,1) doesn't make the inequality true, so the statement is false.

Answer:

the expression to find the shaded region : 14x+21

Step-by-step explanation:

(x+5)² - (x-2)² solve by distribution

7(2x+3)

14x+21

Answer:

14x+21

Step-by-step explanation:

(x+5)² - (x-2)²

7(2x+3)

14x+21

In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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James will be flying a total of 85,680 miles in the next year.

To find out how many miles James will be flying in the next year, we need to multiply the distance of one round trip by the number of round trips he will make in a year.

The distance of one round trip is twice the one-way distance, so:

2 x 2,856 miles = 5,712 miles per round trip

Since James will make 15 round trips in a year, we can multiply the distance of one round trip by 15:

5,712 miles/round trip x 15 round trips = 85,680 miles

Therefore, James will be flying a total of 85,680 miles in the next year.
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The Taylor polynomial T3(x) for the function f centered at the number a is 1, -1.

To find the slope of the tangent line to the curve at a given point, we need to find the derivative of the curve and evaluate it at that point. So, let's find the derivative of the curve x(t) = cos^3(4t), y(t) = sin^3(4t):

x'(t) = 3cos^2(4t) * (-sin(4t)) * 4 = -12cos^2(4t)sin(4t)

y'(t) = 3sin^2(4t) * cos(4t) * 4 = 12sin^2(4t)cos(4t)

Now, let's evaluate these derivatives at t = pi/6:

x'(pi/6) = -12cos^2(2pi/3)sin(2pi/3) = -6sqrt(3)

y'(pi/6) = 12sin^2(2pi/3)cos(2pi/3) = 6sqrt(3)

So, the slope of the tangent line at t = pi/6 is:

y'(pi/6) / x'(pi/6) = (6sqrt(3)) / (-6sqrt(3)) = -1

Therefore, the answer is option 1, -1.

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Answer

this is a tough one, but if I had to guess... it would be 55 muffins.

Step-by-step explanation:

Answer:

I would say 55

Step-by-step explanation:

Given the exponential expression

Give the general exponential equation

The equivalent logarithmic functions is given as:

Compared with the exponential function:

• a = 8

• b = 2/3

• y = 4

Substitute into the logarithm equivalent:

To verify the generalized Stokes's theorem for the given region M and vector field w, we need to evaluate the surface integral of the curl of w over M and compare it to the line integral of w over the boundary of M.

First, let's find the curl of w:
curl(w) = (d/dy)(x + y + z) - (d/dz)(z) dx + (d/dz)(zdx) + (d/dx)(x) dy
= (1 - 0) dx + (0 - 1) dy + (0 - 1) dz
= dx - dy - dz

Next, let's parametrize the surface M. We can use cylindrical coordinates:
x = cos(theta)
y = y
z = sin(theta)

The unit normal vector N = (x, 0, z) becomes N = (cos(theta), 0, sin(theta)).

The bounds for theta will be from 0 to 2*pi, and for y, it will be from -∞ to 3.

Now, let's evaluate the surface integral of curl(w) over M:
∫∫_M curl(w) · dS
= ∫_0^(2pi) ∫_-∞^3 (cos(theta), 0, sin(theta)) · (dx - dy - dz) dy d(theta)
= ∫_0^(2pi) ∫_-∞^3 (cos(theta) - sin(theta)) dy d(theta)
= ∫_0^(2pi) (3 - (-∞)) (cos(theta) - sin(theta)) d(theta)
= ∫_0^(2pi) 3(cos(theta) - sin(theta)) d(theta)
= 3[ sin(theta) + cos(theta) ] |_0^(2pi)
= 3[ sin(2pi) + cos(2*pi) - (sin(0) + cos(0)) ]
= 3(0 + 1 - 0 - 1)
= 3(0)
= 0

Now, let's calculate the line integral of w over the boundary of M. The boundary curve consists of two parts: the upper circle and the lower circle.

For the upper circle (y = 3):
r = (cos(theta), 3, sin(theta)), theta ∈ [0, 2*pi]
dr = (-sin(theta), 0, cos(theta)) d(theta)

∫_C1 w · dr = ∫_0^(2pi) (sin(theta) d(theta) + (cos(theta) + 3) d(theta) + 0)
= ∫_0^(2pi) (sin(theta) + cos(theta) + 3) d(theta)
= [ -cos(theta) + sin(theta) + 3theta ] |_0^(2pi)
= [-1 + 1 + 6pi - (-1 + 0)] = 6pi

For the lower circle (y = -∞):
r = (cos(theta), -∞, sin(theta)), theta ∈ [0, 2*pi]
dr = (-sin(theta), 0, cos(theta)) d(theta)

∫_C2 w · dr = ∫_0^(2pi) (sin(theta) d(theta) + (cos(theta) + (-∞) + 0)
= ∫_0^(2pi) (sin(theta) + cos(theta) - ∞) d(theta)
= [-cos(theta) + sin(theta) - ∞theta ] |_0^(2pi)
= [-1 + 1 - ∞2pi

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The probability that Luisa gets 2 diamonds and 2 hearts (in any order) is:

P = 0.022

The probability of getting a particular type of card, is given by the quotient between the number of cards of that type and the total number of cards.

Here, let's assume that the 4 draws are:

diamond-diamond-heart-heart.

In that order.

First, the probability of drawing a diamond card is equal to:

p₁ = 13/52

Because there are 13 diamond cards and 52 cards in total.

Bt after that draw, there will be 12 diamond cards and 51 cards in total, so the probability of getting the second diamond card is:

p₂ = 12/51.

Now, there are 13 heart cards and 50 cards in the deck, so the probability of getting the first heart card is:

p₃ = 13/50

And the probability of getting the second one is:

p₄ = 12/49.

The joint probability will be the product of the 4 individual probabilities, but we also need to take in account the possible permutations, these are:

(using D for diamond and H for heart).

D - D - H - H

D - H - D - H

D - H - H - D

H - D - D - H

H - D - H - D

H - H - D - D

So there are 6 permutations, this means that the probability is:

P = 6*p₁*p₂*p₃*p₄ = 6*(13/52)*(12/51)*(13/50)*(12/49) = 0.022

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Answer:

c. Real, rational and unequal

Answer:

well it asking for a vowel I think and the only vowel that is on there that is not (Y) is (A) so I would think it would be 1

The measurement that is closest to the value of x, in centimeters, is given as follows:

14.3.

In this problem, we have a right triangle, in which the legs, which are the sides between the angle of 90º, are of 11.9 cm and 7.9 cm.

Then the hypotenuse x, which is the segment connecting both legs, is obtained using the Pythagorean Theorem.

The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.

Then the length of x is calculated as follows:

x² = 11.9² + 7.9²

x = square root of (11.9² + 7.9²)

x = 14.28.

Closest to 14.3, rounding to the nearest tenth, meaning that the third option is correct.  

We suppose that 11.9 cm and 7.9 cm are the measures of the legs.

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Step-by-step explanation:

y varies inversely as x=

y= k/xz

-5= k(-5)/6

k= 6

y=6/xz

y=6/5×-8

y= -3/20

1. To determine the number of tubs John must sell per show to break even, we need to consider the fixed costs and the contribution margin per tub. The contribution margin is the difference between the selling price and the variable cost per tub.

In this case, the variable cost is the wholesale cost of $30 per tub. The contribution margin per tub is $80 - $30 = $50.  To calculate the break-even point, we divide the fixed costs by the contribution margin per tub:

Break-even point = Fixed costs / Contribution margin per tub

Break-even point = $900 / $50 = 18 tubs

Therefore, John must sell at least 18 tubs per show to break even.

2a. To earn a profit of $1,100 per show, we need to determine the sales volume in units necessary. The desired profit is considered an additional fixed cost in this case. We add the desired profit to the fixed costs and divide by the contribution margin per tub:

Sales volume for desired profit = (Fixed costs + Desired profit) / Contribution margin per tub

Sales volume for desired profit = ($900 + $1,100) / $50 = 40 tubs

Therefore, John needs to sell 40 tubs per show to earn a profit of $1,100.

2b. To determine the sales volume in dollars necessary to earn the desired profit, we multiply the sales volume in units (40 tubs) by the selling price per tub ($80):

Sales volume in dollars for desired profit = Sales volume for desired profit * Selling price per tub

Sales volume in dollars for desired profit = 40 tubs * $80 = $3,200

Therefore, John needs to achieve sales of $3,200 to earn a profit of $1,100 per show.

c. Income Statement (condensed version):

Sales Revene: 40 tubs * $80 = $3,200

Variable Costs: 40 tubs * $30 = $1,200

Contribution Margin: Sales Revenue - Variable Costs = $3,200 - $1,200 = $2,000

Fixed Costs: $900

Operating Income: Contribution Margin - Fixed Costs = $2,000 - $900 = $1,100

The condensed income statement confirms the answers from parts a and b, showing that the desired profit of $1,100 is achieved by selling 40 tubs and generating sales of $3,200.

3. The margin of safety represents the difference between the actual sales volume and the breakeven sales volume.

Margin of safety in sales dollars = Actual Sales - Breakeven Sales = $3,200 - ($50 * 18) = $2,300

Margin of safety in units = Actual Sales Volume - Breakeven Sales Volume = 40 tubs - 18 tubs = 22 tubs

Margin of safety as a percentage = (Margin of Safety in Sales Dollars / Actual Sales) * 100

Margin of safety as a percentage = ($2,300 / $3,200) * 100 ≈ 71.88%

Therefore, the margin of safety is $2,300 in sales dollars, 22 tubs in units, and approximately 71.88% as a percentage.

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The probability that a randomly selected sample mean will be more than $100 = 0.14082.

We are given that according to a research​ institution, the average hotel price in a certain year was $97.00.

Assume the population standard deviation is $18.00 and that a random sample of 40 hotels was selected.

Here, Mean = μ = $97.00  and  Standard deviation = σ = $18 and  n = 40

(a) Standard error of the mean = σ/\(\sqrt{n}\) = 18/\(\sqrt{40}\) = 2.74

(b) Let X bar = Sample Mean

The z score probability distribution for sample mean is ;

          Z = Xbar-μ/ σ/\(\sqrt{n}\) ~ N(0,1)

So, Probability that the sample mean will be less than $102 = P(X bar < $102)

P(X bar < 102) = P(Xbar-μ/ σ/\(\sqrt{n}\) < 102 - 97.00/ 18/\(\sqrt{40}\)) = P(Z < 0.74) = 0.7704

(c) Probability that the sample mean will be more than $104 =P(X bar > $104)

=  P(X bar > 104) = P(Xbar-μ/ σ/\(\sqrt{n}\) < 104 - 97.00/ 18/\(\sqrt{40}\)) = P(Z > 1.47) = 1 - P(Z <= 1.47)

= 1 - 0.92922 = 0.0708

(d) Probability that the sample mean will be between $99 and $100 is given by = P($99 < X bar < $100) = P(X bar < $100) - P(X bar <= $99)

= P(X bar < 100) = P(Xbar-μ/ σ/\(\sqrt{n}\) < 100 - 97.00/ 18/\(\sqrt{40}\)) = P(Z < 0.01) = 0.50399

= P(X bar <= 99) = P(Xbar-μ/ σ/\(\sqrt{n}\) <= 99 - 97.00/ 18/\(\sqrt{40}\)) = P(Z <= -0.35) = 1 - P(Z <= 0.35)

= 1 - 0.63683 = 0.36317

Therefore, P($99 < X bar < $100) = 0.50399 - 0.36317 = 0.14082 .

Hence the answer is the probability that a randomly selected sample mean will be more than $100 = 0.14082.

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A rule that makes a particular cell is highlighted in yellow only if the value it contains is less than $5000 is an example of conditional formatting.

This is a special feature that can be found in programs such as excel and allows users to automatically apply specific changes or formatting to cells that meet specific criteria.

There are four main types:

In the case of the formatting described, this can be classified as conditional formatting because all cells that meet the criteria (less than $5000) will be automatically highlighted in yellow. Moreover, the type of formatting is a change in the color of the cell.

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Answer:

Root( c square -9)

Step-by-step explanation:

The answer u have is the answer for a^2

Answer:

Root (c square -9)

Step-by-step explanation:

In Krystal's equation y = 4x + 2, y represents the number of toothpicks, and x represents the number of triangles. This is known because the equation relates the number of toothpicks (y) to the number of triangles (x) in the pattern.

In the equation y = 4x + 2, y represents the number of toothpicks in the pattern. This is evident from the fact that y is on the left side of the equation and is equal to a function of x. The equation states that the number of toothpicks (y) is equal to four times the number of triangles (x) plus two. Since toothpicks are being counted, y represents the dependent variable in this equation.

On the other hand, x represents the number of triangles in the pattern. This can be inferred from the fact that x is the independent variable in the equation. The equation relates the number of triangles (x) to the number of toothpicks (y), suggesting that x is the input variable that determines the number of triangles in the pattern.

Therefore, based on the given equation and the relationship it represents, we can conclude that y represents the number of toothpicks and x represents the number of triangles in Krystal's pattern of wooden toothpicks.

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It should be noted that an equilateral triangle simply means a triangle that has there equal sides.

1. Cut six desired measures of string to properly wrap and tied around each end of the three sticks

2. Once fastened, bring two of the sticks together making one the bottom (base) and the other a side (angle).

3. Cut a tiny piece of rope to interlock with the rope you already have tied on the ends.

4. Tie the ends together with the new cut of string and make your desired angle as you tighten it.

5. Mirror Step 4 for the other end of the bottom stick (base), while most importantly mirroring the desired angle of step 4.

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Answer:

This example is not a random example due to the fact that it is only questioning the eighth-graders. Random sample means that the sample is chosen simply randomly and everyone has an equal opportunity to be apart of the sampling.

Step-by-step explanation:

the region lies above the x -axis. f ( x )= x2 + x , x = −4, x = 2.The area of the region is (2^2 + 2) - (-4^2 + -4) = 26.

To determine the area of the region bounded by the given function, the x-axis, and the given vertical lines, we must first calculate the area of the region. To do this, we need to find the area of the region above the x-axis. To do this, we must calculate the area under the function between the given vertical lines. The area of the region is the area under the function f(x) = x2 + x between x = -4 and x = 2.

(2^2 + 2) - (-4^2 + -4)

= 26.

This can be calculated by solving the integral of the function from -4 to 2, which gives us the answer of 26.

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The perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6

What is perimeter of the rectangle?

The perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x+ 6

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2( l + w)

Given the following parameters

length l = 8x - 1

width w = 2x + 4

Substitute the expressions for the length and width into the formula;

P = 2(8x - 1 + 2x + 4)

P = 2(10x + 3)

Distribute 2 over each term in the parenthesis

P = 2(10x) + 2(3)

P = 20x + 6

Hence the perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6.

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The complete question is -

The perimeter formula for a rectangle is 2l + 2w, where l is the length and w is the width. Complete the steps to find an expression that represents the perimeter of the rectangle. Substitute the expressions for length and width into the formula 2l + 2w. Distribute 2 to each term in the parentheses. Combine like terms. inches

Marvin has to take 29 trips to the school to make in all to walk a total of 40 kilometers with the help of algebraic equation.

Marvin has already walked 11 kilometers this week, so he needs to walk an additional 29 kilometers (40 - 11) to reach his goal.

If he plans to walk 1 kilometer during each trip to school, we can use algebra to solve for the number of trips he needs to make:

Let's call the number of trips Marvin needs to make "x".

Then, the total distance he walks during these trips is 1 kilometer times "x".

So we can set up the following equation to solve for x:

1x + 11 = 40

Subtracting 11 from both sides:

1x = 29

Dividing both sides by 1:

x = 29

Therefore, Marvin needs to make 29 trips to school to walk a total of 40 kilometers.

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Answer: i would say 280.

Step-by-step explanation: because if you add 180 plus another set of it it would make 280

Answer:

180

Step-by-step explanation:

Since they are vertical angles, they are congruent to each other

m<1 = m<2

Here every 50th candy bar is tested . It is a sampling interval .

What does "systematic sampling" mean?

Systematic sampling is a probability sampling technique where researchers choose individuals from the population at regular intervals, such as every 15th person on a population list.

                       The advantages of simple random sampling can be imitated if the population is arranged randomly.

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.

Here every 50th candy bar is tested . It is a sampling interval .

Therefore he use systematic sampling plan.

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