A restaurant owner is buying new tableware for her restaurant. She wants the new pieces to be proportionate, and needs to know the measurements of the different pieces she is buying. The circle-shaped part of the bottom of the glass above has an area of 12.56 in2. What is the radius? Use = 3.14. A. 4 in B. 5 in C. 1 in D. 2 in Reset Submit

Te surface area of the smaller figure based on the ratio is 1600m²

The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding sides.

Let x be the scale factor between the smaller and larger figures.

Then we have:

(x³)/(4000) = 6912

x³ = 6912/4000

x³ = 1.728

Taking the cube root of both sides, we get:

x = 1.2

So the scale factor from the larger figure to the smaller figure is 1:1.2.

The surface area of a similar figure is proportional to the square of the scale factor.

So we can use the scale factor to find the ratio of the surface areas:

SA(smaller) / SA(larger) = 1/(1.2)²

We know that the surface area of the larger figure is 2304m^2, so we can solve for the surface area of the smaller figure:

SA(smaller) = 2304 * 1/(1.2)²

SA(smaller) = 1600m²

Therefore, the surface area of the smaller figure is 1600m²

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Answer:

A.

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

4. shift the boundary line up 1

Answer:

Second choice
∠BCA ≅ ∠DCA

Step-by-step explanation:

This logically follows from the fact that both ∠BCA and ∠DCA are right angles from the previous step. And the reason given is "All right angles are ≅)

So they are congruent

Answer:

x = 24 and y = 24

Step-by-step explanation:

Let's use algebra to solve this optimization problem.

Let x be the first number, and y be the second number. Then we have the following two equations based on the problem statement:

x + y = 48 (sum of the two numbers is 48)

xy = ? (product of the two numbers, which we want to maximize)

To solve for x and y in terms of each other, we can use the fact that:

(x + y)^2 = x^2 + 2xy + y^2

Expanding the left side of the equation gives:

x^2 + 2xy + y^2 = 2304

And substituting xy for its value in terms of x and y gives:

x^2 + 2xy + y^2 = x^2 + 2(48 - x)y + y^2 = 2304

Simplifying this equation gives:

2y^2 - 96y + x^2 - 2304 = 0

To maximize the product xy, we need to maximize the value of xy = x(48 - x) = 48x - x^2. This function is a quadratic that opens downwards, and therefore, its maximum value occurs at the vertex of the parabola, which is located at x = -b/2a = -48/(2*-1) = 24.

Thus, the two positive real numbers that sum up to 48 and their product is a maximum are x = 24 and y = 24.

The percent markup is 25%.

Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus it's cost to make or purchase for resale) by the cost of that unit.

Given that, A department store buys 300 shirts for a total cost of $7,200 and sells them for $30 each.

Cost of one shirt [tex]= 7200 \div 300 = \$24[/tex]

And they sold at $30 each,

Percent markup [tex]= 30-24 \div 24 \times 100[/tex]

[tex]= 25\%[/tex]

Hence, the percent markup is 25%.

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The product of two random variables that follows the normal distribution with mean 0 and variance 1 is expected 0.

To compute the product of two random variables that are normal distributed with a mean of 0 and a variance of 1, the following procedure can be employed:

Thus, we can write the probability density function of the normal distribution as:

f(x) = (1/√2π) * e^(-x^2/2)

E[X] = ∫x * f(x) dx, where the integral is taken over the entire range of X.

E[Y] = ∫y * f(y) dy, where the integral is taken over the entire range of Y.

E[XY] = E[X] * E[Y]

E[X] = ∫x * f(x) dx = ∫x * (1/√2π) * e^(-x^2/2) dx = 0

E[Y] = ∫y * f(y) dy = ∫y * (1/√2π) * e^(-y^2/2) dy = 0

E[XY] = E[X] * E[Y]

= 0 * 0 ⇒ 0

Therefore, the product of two random variables that follow a normal distribution with mean 0 and variance 1 has an expected value of 0.

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Answer:

Step-by-step explanation:

The area of given circle is 28.27 sq.m. The circumference of given circle is 18.85 m (rounded to the nearest hundredth).

The circumference of a circle is the distance around the edge or boundary of the circle. It is also the perimeter of the circle. The circumference is calculated using the formula:

C = 2πr

where "C" is the circumference, "π" is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the circle.

The circumference of a circle is proportional to its diameter, which is the distance across the circle passing through its center. Specifically, the circumference is equal to the diameter multiplied by π, or:

C = πd

where "d" is the diameter of the circle.

Given that the diameter of the circle is 6m.

We know that the radius (r) of the circle is half of the diameter (d), so:

r = d/2 = 6/2 = 3m

The area (A) of the circle is given by the formula:

A = πr²

Substituting the value of r, we get:

A = π(3)² = 9π ≈ 28.27 sq.m (rounded to the nearest hundredth)

The circumference (C) of the circle is given by the formula:

C = 2πr

Substituting the value of r, we get:

C = 2π(3) = 6π ≈ 18.85 m (rounded to the nearest hundredth)

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The complete question is:

The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.

Using the distance formula, we have:

d(P,Q) = √((x2-x1)² + (y2-y1)²)

= √((-4-(-12))² + (-9-7)²)

= √(8² + (-16)²)

= √(320)

= 8 √(5)

Since PR:QR is 3:5, we can set up the following equation:

d(P,R)/d(R,Q) = 3/5

Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.

Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)

Using the distance formula again, we can find the distance between P and R:

d(P,R) = (3/8) d(P,Q)

= (3/8) (8 √(5))

= 3 √(5)

Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:

d(R,Q) = (5/3) d(P,R)

= (5/3) (3 √(5))

= 5 √(5)

Finally, we can use the midpoint formula to find the coordinates of R:

x = (-12 + (3/8) (8))/2 = -8

y = (7 + (-1))/2 = 3

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Complete Question:

The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?

The expected value of x is 1.80, the variance is 0.72, and the standard deviation is 0.85.

Calculate the expected value, variance, and standard deviation of the random variable x as follows. Round all answers to two decimal places, and keep in mind that x is the number of red marbles that Suzan has in her hand after selecting three marbles from a bag containing three red marbles and two green ones.

Expected Value: Since there are 3 red marbles and 2 green marbles in the bag, the probability of drawing a red marble is: P(R) = 3/5The probability of drawing a green marble is P(G) = 2/5Therefore, the expected value of the random variable X is: E(X) = μ = np = 3/5 * 3 = 1.80

Variance can be calculated using the following formula: Var(X) = npq, where p is the probability of success and q is the probability of failure of the event. In this scenario, the probability of drawing a red marble is P(R) = 3/5, and the probability of drawing a green marble is P(G) = 2/5.

Therefore, Var(X) = npq Var(X) = (3/5)*(2/5)*3Var(X) = 1.80 * 0.4Var(X) = 0.72Standard Deviation: The square root of the variance is equal to the standard deviation. Hence, the formula for standard deviation is: S.D. = √Var(X)S.D. = √0.72S.D. = 0.85

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The probability density function (PDF) of Y can be determined by the transformation of the PDF of X. Using the transformation rule, we can calculate that fy(y) = fx(x) |dx/dy|, where x is a function of y, since y = Fx(x).

We can use the Chain Rule to determine the derivative of x with respect to y. Since Fx is a monotone increasing function, dx/dy = 1/F'x(x). Substituting this into the transformation rule, fy(y) = fx(x) / F'x(x).

Therefore, to find fy(y), we need to calculate F'x(x). Fx is the cumulative distribution function, which means that its derivative F'x(x) is the probability density function of X, or fx(x). Substituting this into the transformation rule, fy(y) = fx(x) / fx(x). Since fx(x) = fx(2) and fx(2) is a constant, fy(y) = 1/fx(2).

To summarize, the probability density function of Y is given by fy(y) = 1/fx(2).

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The quantity of  water are needed to fill the tank to the top is 960 cubic inches

The total volume of the tank is given by multiplying its length, width, and height

Volume of tank = 24 inches × 10 inches × 12 inches = 2,880 cubic inches

The volume of water in the tank is given by multiplying the filled height with the base area of the tank:

Volume of water = 8 inches × 24 inches × 10 inches = 1,920 cubic inches

To find how many more cubic inches of water are needed to fill the tank to the top, we need to subtract the volume of water in the tank from the total volume of the tank:

Volume of air space = Volume of tank - Volume of water

= 2,880 cubic inches - 1,920 cubic inches

= 960 cubic inches

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The given question is incomplete, the complete question is:

Julio bought a fish tank shaped like a rectangular prism. The inside of the tank measures

24 inches in length, 10 inches in width, and 12 inches in height. The tank is filled with water to a height of 8 inches. How many more cubic inches of water are needed to fill the tank to the top?

Answer: To solve the problem, we need to use the given time to find Michaela's swimming rate in meters per second, and then use that rate to calculate the distance she will swim in 10 minutes.

1 minute = 60 seconds

4 minutes and 50 seconds = 4 x 60 + 50 = 290 seconds

So, Michaela's rate is:

distance / time = x / 290 seconds

where x is the distance she can swim in 290 seconds.

Simplifying the equation:

x = distance = (time x distance) / time = (290 seconds x distance) / 290 seconds = distance

We know that Michaela can swim 500 meters in 290 seconds:

500 meters / 290 seconds = 1.724 meters per second

Therefore, in 10 minutes (600 seconds), she will swim:

distance = rate x time = 1.724 meters/second x 600 seconds = 1034.4 meters

So, Michaela will swim 1034.4 meters in 10 minutes.

Step-by-step explanation:

The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

To solve the system of equations:

1x + 0y + 60z = 1

1x + 10y + 0z = 0

0x + 0y + 0z = 0

The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:

From the first equation, we get x = 1 - 60z

From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z

Therefore, the solution to the system can be written as a point in terms of z as:

(x, y, z) = (1 - 60z, -10 + 600z, z)

Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:

(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

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Answer:

The skydiver has an initial height of 3600.

Step-by-step explanation:

3600 is the y-intercept in the form y=mx+b

In the point (0,3600) .Time is the x-axis and Height is the y-axis.

Replacing,

3600= m(0)+b

b=3600

Taking another point: (2, 3536)

We apply the formula to obtain the slope.

m= (y2-y1) / (x2-x1)

m= (3536 - 3600) / (2-0)

m= -64 / 2

m= -32

Joining all the terms:

y=-32x+3600

The Laplace transform is a mathematical technique used to solve differential equations and analyze signals and systems in engineering, physics, and other fields. It is named after the French mathematician Pierre-Simon Laplace.

The Laplace transform of the given initial value problem is given by:

Y(s) = (2s^2 + 16) / (s^2(s^2+16))

Inverting the Laplace transform to find y(t) gives us:

y(t) = e^(-8t) * (1-cos(4t)) + 2sin(4t) + u2(t)

Where u2(t) is the Heaviside function that turns on at t = 2.

To find the Laplace transform of y(t), we first take the Laplace transform of both sides of the differential equation:

L(y''(t)) + 16L(y(t)) = L(e^(-2t)u_2(t))

Using the property L(y''(t)) = s^2Y(s) - sy(0) - y'(0) and noting that y(0) = 0 and y'(0) = 0, we can simplify to get:

s^2Y(s) + 16Y(s) = L(e^(-2t)u_2(t))

Using the property L(e^(-at)u_c(t)) = 1/(s + a) * e^(-cs), we can substitute to get:

s^2Y(s) + 16Y(s) = 1/(s + 2)^2

Now we can solve for Y(s):

Y(s) = 1/(s^2 + 16) * 1/(s + 2)^2

To find y(t), we need to take the inverse Laplace transform of Y(s). We can use partial fraction decomposition to simplify the expression:

Y(s) = A/(s^2 + 16) + B/(s + 2) + C/(s + 2)^2

Multiplying both sides by the denominator and solving for A, B, and C, we get:

A = 1/8

B = -1/4

C = 1/8

Substituting these values, we get:

Y(s) = 1/8 * 1/(s^2 + 16) - 1/4 * 1/(s + 2) + 1/8 * 1/(s + 2)^2

Taking the inverse Laplace transform of each term, we get:

y(t) = (1/8)sin(4t) - (1/4)e^(-2t) + (1/4)te^(-2t)

Therefore, the solution to the initial value problem y'' + 16y = e^(-2t)u_2(t), y(0) = 0, y'(0) = 0 is y(t) = (1/8)sin(4t) - (1/4)e^(-2t) + (1/4)te^(-2t).

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There are two possible outcomes where a red counter and a vowel are spun: a)red, A and b) red, E.

To see why, we can make a table listing all the possible outcomes of flipping a red or yellow counter and spinning a spinner labeled A-E:

A B C D E

Red A B C D E

Yellow A B C D E

We can then circle the outcomes that satisfy the condition of spinning a red counter and a vowel: red, A and red, E.

Therefore, the selected outcomes are:

red, A

red, E

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Answer:

a) 44 children can safely play in the playground of area 154 m^2.

b) The smallest playground area in which 24 children can play is 84 m^2.

Step-by-step explanation:

We have the ratio 210m^2 : 60.

a) 154/210 is 11/15. Multiplying this scale factor gives the ratio 154 m^2 : 44.

44 is found by multiplying 11/15 by 60.

44 children can safely play in the playground of area 154 m^2.

b) 24/60 is 2/5. Multiplying this scale factor gives the ratio 84 m^2 : 24

84 is found by multiplying 2/5 by 210.

The smallest playground area in which 24 children can play is 84 m^2.

Hope this helps!

Step-by-step explanation:

x²-6x+9=0

using the almighty formula where a=1 , b=-6 , c=9

Statement d is also correct because it means the same thing as statement b, just using different phrasing.

It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equal sign (=). The equation represents a relationship between the expressions on both sides, indicating that they have the same value.

The two correct statements that describe the equation y = 4 × 18 are:

b. The value of y is 4 times as many as 18.

d. The value of y is 4 times as much as 18.

Statement b is correct because the equation y = 4 × 18 means that y is equal to 4 times the value of 18, or y = 4 × 18 = 72.

Statement d is also correct because it means the same thing as statement b, just using different phrasing. "As much as" and "many as" are interchangeable in this context, and both mean "multiplied by."

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Answer:

The system has one point because when the system is graphed the lines will intersect at exactly one point. Therefore, there is only one solution to this system of equations.

Answer: To determine if Marco has made a mistake, we would need to know the expected mass of the contents of the beaker before the reaction took place. If the expected mass was 247 g or close to it, then Marco may not have made a mistake.

However, if the expected mass was significantly different from 247 g, then it is possible that Marco made a mistake in his experiment. It could be a measurement error, a calculation error, or a procedural error.

There are several reasons why Marco may have obtained a mass of 247 g at the end of the reaction. One possibility is that the reaction produced a product that was relatively volatile, and some of it was lost during the experiment. Another possibility is that Marco did not completely dry the product before weighing it, which could result in a higher measured mass due to the presence of residual moisture.

To determine the exact reason why Marco obtained a mass of 247 g, further investigation and experimentation would be needed.

Step-by-step explanation:

Using trigonometry, the distance between the two vessels when the second boat enters the lighthouse's radius is 13.46 miles.

The relationships between angles and length ratios are investigated in the branch of mathematics known as trigonometry. The use of geometry in astronomical study led to the establishment of the field during the Hellenistic era in the third century BC.

The distance between the two boats when the second boat enters the radius of the lighthouse light is 13.46 miles using trigonometry.

A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the vertices A, B, and C is represented by the Δ ABC.

Any three points that are not collinear create a singular triangle and a singular plane in Euclidean geometry. (i.e. a two-dimensional Euclidean space). In other words, every triangle is a part of a plane, and that triangle is a part of only one plane. In the Euclidean plane, all triangles are contained within a single plane, but in higher-dimensional Euclidean spaces, this is no longer the case. This page covers triangles in Euclidean geometry, especially the Euclidean plane, unless otherwise specified.

In this question,

The side of the isosceles triangle is given by,

l=2a sin(θ/2)

where a= 18 miles

θ= 44°

l= 2*18*sin 22°

= 36*0.374

= 13.46 miles

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In the given diagram, ΔHIJ ≈ ΔFIG, the value of u in triangle FIG is calculated as: IG = 8 yd

A triangle is a geometric shape that is formed by three line segments that intersect at three non-collinear points. The three line segments are called the sides of the triangle, while the three points where they intersect are called the vertices of the triangle.

A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

∆HIJ similar to ∆FIG

HI/FI = IJ/IG

5/10 = 4/IG

IG = 8 yd

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In the given diagram, ΔHIJ ≈ ΔFIG, the value of u in triangle FIG is calculated as: IG = 8 yd

A triangle is a geometric shape that is formed by three line segments that intersect at three non-collinear points. The three line segments are called the sides of the triangle, while the three points where they intersect are called the vertices of the triangle.

A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

∆HIJ similar to ∆FIG
HI/FI = IJ/IG
5/10 = 4/IG
IG = 8 yd

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Step-by-step explanation:

The equation that represents how much will be in the account after 7 years is:

M = 7,600(1+0.06)^7

Here's the explanation:

The formula for calculating the future value (M) of a present value (P) invested at an annual interest rate (r) for a certain number of years (t) is M = P(1+r)^t.

In this case, the present value (P) is 7,600 dollars, the annual interest rate (r) is 6% or 0.06, and the number of years (t) is 7.

Substituting these values into the formula, we get M = 7,600(1+0.06)^7. This represents how much will be in the account after 7 years if no money is added or removed from the account.

Answer:

A=100

B= 80

C=80

D=100

E=80

F=80

G=100

Step-by-step explanation:

Answer:

The answer is letter D.

Step-by-step explanation:

Ye

Answer:

The answer is C

x -10 < -20

x < -20 + 10

x< -10

The sign won't change to the other side because the variable we were asked to find is in the positive form.

The soda can has an estimated volume of 1,026.72 cubic centimeters and an estimated surface area of 452.39 square centimeters.

To find the volume and surface area of a soda can with radius 6 cm and height 11 cm, we can use the formulas:

Volume of cylinder = πr²h

Surface area of cylinder = 2πrh + 2πr²

Substituting the given values, we get:

Volume = π × 6² × 11

Volume = 1,026.72 cubic centimeters (rounded to two decimal places)

Surface area = 2π × 6 × 11 + 2π × 6²

Surface area = 452.39 square centimeters (rounded to two decimal places)

Therefore, the volume of the soda can is approximately 1,026.72 cubic centimeters, and the surface area is approximately 452.39 square centimeters.

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You walked a total of 4576 yards to get to the basketball court.

In order to represent amounts in a more practical or acceptable unit of measurement, unit conversions are crucial for addressing mathematical issues. In this task, for instance, we were given distances in miles but had to translate them into yards to get the overall distance travelled. We wouldn't be able to compare or combine values that are stated in various units without unit conversions. When working with formulae or equations that contain physical quantities with multiple units, unit conversions are also crucial.

Given that, the distance walked is 1.5 miles and 1 1/10 miles.

Coverting into yards we have:

1.5 miles is equal to 1.5 x 1760 = 2640 yards

1 1/10 miles is equal to (1 + 1/10) x 1760 = 1936 yards

Total distance is:

2640 + 1936 = 4576 yards

Hence, you walked a total of 4576 yards to get to the basketball court.

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We are interested in the population proportion of drivers who claim they always buckle upa.i. x = 320 ii. n = 400 iii. p′ = 0.8

b. The random variable X represents the number of drivers out of the sample of 400 who claim they always buckle up, while P′ represents the sample proportion of drivers who claim they always buckle up.

c. The distribution to use for this problem is the normal distribution because the sample size is large enough (n=400) and the population proportion is not known.

d. i. The 95% confidence interval for the population proportion who claim they always buckle up is (0.7709, 0.8291).

ii. The graph is a normal distribution curve with mean p′ = 0.8 and standard deviation σ = sqrt[p′(1-p′)/n].

iii. The error bound is 0.0291.

e. Three difficulties the insurance companies might have in obtaining random results from a telephone survey are:

Selection bias: The survey might not be truly random if the telephone numbers selected are not representative of the population of interest.

Nonresponse bias: People may choose not to participate in the survey or may not be reached, which could bias the results.

Social desirability bias: Respondents may give socially desirable answers rather than their true opinions, which could also bias the results.

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