7)A point is chosen randomly inside rectangle ABCD with vertices A(4, 8), B(4, -3), C(-5, -3), and
D(-5, 8). whats the probability The point does not lie in circle P with center P(-2, 5) and radius 3.

The circumference of the circle is 18.84.

We have,

Radius = 3

Now,

The circumference of a circle.

= 2πr

Substituting r and π = 3.14.

= 2 x 3.14 x 3

= 18.84

Thus,

The circumference of the circle is 18.84.

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The volume of the composite figure is 228 ft³.

To calculate the volume of a composite figure, we need to break it down into its individual components and then sum up the volumes of each component.

From the given dimensions, it seems that the composite figure consists of multiple rectangular prisms. Let's calculate the volume of each prism and then add them together.

First prism:

Length = 8 ft, Width = 4 ft, Height = 6 ft

Volume = Length * Width * Height = 8 ft * 4 ft * 6 ft = 192 ft³

Second prism:

Length = 3 ft, Width = 2 ft, Height = 6 ft

Volume = Length * Width * Height = 3 ft * 2 ft * 6 ft = 36 ft³

Now, let's add the volumes of both prisms:

192 ft³ + 36 ft³ = 228 ft³

Therefore, the volume of the composite figure is 228 ft³.

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What is the volume of the composite figure? 8 ft 4 ft 6 ft 3 ft 2 ft

Answers 96 ft³3 76 ft³ 228 ft³ 192 ft³ ​

On the 10th day, Jennifer and Elena will have the same number of tickets left to sell.

We have,

To determine the day when Jennifer and Elena will have the same number of tickets left to sell, we can set up an equation to represent the situation.

Let's assume x represents the number of days that have passed since they started selling tickets.

For Jennifer, the number of tickets she has left to sell after x days can be represented as:

Tickets left for Jennifer = 50 - 2x

For Elena, the number of tickets she has left to sell after x days can be represented as:

Tickets left for Elena = 70 - 4x

To find the day when they have the same number of tickets left to sell, we set the two equations equal to each other and solve for x:

50 - 2x = 70 - 4x

Simplifying the equation:

2x - 4x = 70 - 50

-2x = 20

x = -10

Since we can't have a negative number of days, it means that they will have the same number of tickets left to sell after 10 days.

Therefore,

On the 10th day, Jennifer and Elena will have the same number of tickets left to sell.

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Answer:

C. dilation with a scale factor of 3

Step-by-step explanation:

If triangle RST is congruent to triangle WXY by the Angle-Side-Angle Theorem, then a **dilation with a scale factor of 3** would not map triangle RST to triangle WXY. Congruent triangles have the same shape and size, meaning that their corresponding sides and angles are equal. A dilation changes the size of a figure but not its shape, so it would not preserve congruence between the two triangles.

The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.  

To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.

The factor corresponding to x = 3 is (x - 3).

The factor corresponding to x = -4 is (x + 4).

The factor corresponding to x = 5 is (x - 5).

To obtain the polynomial, we multiply these factors together:

P(x) = (x - 3)(x + 4)(x - 5)

Expanding this expression gives us:

[tex]P(x) = (x^2 - 3x + 4x - 12)(x - 5)[/tex]

[tex]= (x^2 + x - 12)(x - 5)[/tex]

[tex]= x^3 - 5x^2 + x^2 - 5x - 12x + 60[/tex]

[tex]= x^3 - 4x^2 - 17x + 60[/tex].

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(a) The expected profit of the game is $0. (b) The variance of the profit is 0. (c) The probability of gaining $20 in 10 plays is 0.

To solve the given problem, we'll calculate the expected profit, variance of the profit, and the probability of gaining $20 in 10 game plays.

(a) Expected Profit:

To calculate the expected profit, we need to multiply the potential profit or loss with its corresponding probability and sum them up.

Profit (X) = Gain - Loss = $10 - $10 = $0

Probability of gaining: P(X = $0) = P(Z > 5) = 0 (since Z is only defined up to 5)

Expected Profit (E(X)) = $0 * P(X = $0) = $0

(b) Variance of the Profit:

The variance can be calculated using the formula: Var(X) = E(X^2) - (E(X))^2.

In this case, since the profit is always zero, the variance will also be zero.

Variance of the Profit (Var(X)) = 0 - (0)^2 = 0

(c) Probability of Gaining $20 in 10 plays:

Since each play is independent, the probability of gaining $20 in a single play is 0. Since the probability of gaining is 0 for each play, the probability of gaining $20 in 10 plays will also be 0.

Probability of gaining $20 in 10 plays = 0

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Answer:

m∠J is approximately equal to m∠H and m∠I, so it is also approximately 40 degrees.

Step-by-step explanation:

To find the measures of angles H, I, and J, we can use the fact that HI is approximately equal to IJ. Let's denote the measures of angles H, I, and J as m∠H, m∠I, and m∠J, respectively.

Given that HI is approximately equal to IJ, we can say that m∠H is approximately equal to m∠J.

So, m∠H ≈ m∠J.

We're also given that m∠H = 3x + 10 and m∠I = 6x - 20.

Since m∠H ≈ m∠J, we can equate their expressions:

3x + 10 ≈ 6x - 20.

To solve for x, we can subtract 3x from both sides and add 20 to both sides:

10 + 20 ≈ 6x - 3x.

30 ≈ 3x.

Dividing both sides by 3, we find:

10 ≈ x.

Now that we have the value of x, we can substitute it back into the expressions for m∠H and m∠I:

m∠H = 3x + 10 = 3(10) + 10 = 30 + 10 = 40.

m∠I = 6x - 20 = 6(10) - 20 = 60 - 20 = 40.

Therefore, the measures of angles H, I, and J are:

m∠H = 40 degrees,

m∠I = 40 degrees,

m∠J is approximately equal to m∠H and m∠I, so it is also approximately 40 degrees.

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Answer:

(a) 4

Step-by-step explanation:

Let's start with the equation:

8x-4y

Since we already have the values of x and y, we can solve out equation.

8(2)-4(3)

16-12=4

The answer is (a)4

(a) the function which has the graph with greatest slope is function 3.

(b) The function which has the graph with a y intercept closest to 0 is function 2.

(c) The functions which have graphs with y intercepts greater than 4 is function 4.

Given are 4 functions.

For function 1, consider two points (1, -3) and (0, -4).

Slope = (-4 - -3) / (0 - 1) = 1

For function 2, consider two points (1, -6) and (0, -1).

Slope = (-1 - -6) / (0 - 1) = -5

For function 3,

Slope = 4

For function 4,

Slope = -3

Greatest slope is for function 3.

y intercept is the point where the graph touches the Y axis. x coordinate will be 0 at that point.

For function 1,

y intercept = -4

For function 2,

y intercept = -1

For function 3,

y intercept = 3

For function 4,

y intercept = 5

The graph which has y intercept closest to 0 is function 2.

The functions which have graphs with y intercepts greater than 4 is function 4.

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One would pay $5,232.96 in interest over the 5-year loan term.

To get interest paid on the loan, we will the formula for compound interest [tex]Interest = Principal * (1 + Annual Interest Rate)^{Number of Years} - Principal[/tex]

The principal is the loan amount which is $9,000.

The annual interest rate is 9.6%

The number of years is 5.

Interest = $9,000 * (1 + 0.096)^(5) - $9,000

Interest = $9,000 * 1.58144018701 - $9,000

Interest = $5,232.96168

Interest = $5,232.96.

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The Surface Area of Prism is 17.6 ft².

We have,

Sides of triangle = 2 ft, 1 ft and 2.2 ft.

and, l = 3 ft, b = 1 ft and h= 2 ft

So, Surface Area of Prism

= (2 + 1 + 2.2)3 + 2 x 1

= 5.2 x 3 + 2

= 17.6 ft²

Thus, Surface Area of Prism is 17.6 ft².

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Total cost (in rands) = R300 + (Number of minutes - 500) * R0.50

To calculate the total cost (in rands) for Call Package 2, we can use the following formula:

Total cost (in rands) = Monthly rental + (Number of minutes - Free minutes) * Cost per minute

Let's break down the formula:

Monthly rental: This is a fixed cost that MaNdlovu pays every month for the call package. In this case, the monthly rental for Package 2 is R300.

Number of minutes: This refers to the total number of minutes MaNdlovu uses for her calls.

Free minutes: The first 500 minutes are free, meaning MaNdlovu does not have to pay for them.

Cost per minute: This is the cost per minute for the calls that are not covered by the free minutes. In this case, the cost per minute is R0.50.

By substituting the values into the formula, we get:

Total cost (in rands) = R300 + (Number of minutes - 500) * R0.50

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The expression represents the subtraction of two Complex numbers, resulting in a new complex number with a real part of 10 and an imaginary part of -3i.

The expression (4 + 1i) - (-6 + 4i),the subtraction of complex numbers by distributing the negative sign across the terms in the parentheses.

(4 + 1i) - (-6 + 4i) can be rewritten as:

4 + 1i + 6 - 4i

Next, we can combine like terms by adding the real parts (the numbers without the "i" term) and the imaginary parts (the numbers multiplied by "i") separately.

For the real parts, we have 4 + 6 = 10.

For the imaginary parts, we have 1i - 4i = -3i.

Therefore, the expression (4 + 1i) - (-6 + 4i) simplifies to:

10 - 3i

So the result of the expression is 10 - 3i.

It is important to note that "i" represents the imaginary unit, which is defined as the square root of -1. In complex numbers, the real part represents the real number component, and the imaginary part represents the multiple of the imaginary unit.

the expression represents the subtraction of two complex numbers, resulting in a new complex number with a real part of 10 and an imaginary part of -3i.

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Using a system of equations, the rental cost for a movie and a video game is as follows:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations is also described as simultaneous equations.

                                  Movies   Video     Total

                                                Games    Cost

First month rental           3          5          $32

Second month rental    12          2          $29

Let the rental cost per movie = x

Let the rental cost per video game = y

3x + 5y = 32 ... Equation 1

12x + 2y = 29 ... Equation 2

Multiply Equation 1 by 4:

12x + 20y = 128 ... Equation 3

Subtract Equation 2 from Equation 3:

12x + 20y = 128

-

12x + 2y = 29

18y = 99

y = 5.5

Substitute y = 5.5 in Equation 1 or 2:

12x + 2y = 29

12x + 2(5.5) = 29

12x + 11 = 29

12x = 18

x = 1.5

Thus, based on simultaneous equations, the rental cost for a movie is $1.50 while a video game's is $5.50.

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The sale price is $5.44 while the discount is $0.96

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

The list price of a goods is $6.40 and the discount rate is 15%, hence:

Discount = 15% of list price = 0.15 * $6.40 = $0.96

Sale price = List price - Discount = $6.40 - $0.96 = $5.44

The sale price is $5.44

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Answer: 0,1

Step-by-step explanation:

Answer:

The remainder is always smaller than the divisor.

For example, if we divide 12 by 5, we get 2 with a remainder of 2. The remainder is 2, which is smaller than the divisor, which is 5.

This is because the remainder is the part of the dividend that is not divisible by the divisor. In this case, 12 is not divisible by 5, so the remainder is 2.

The remainder can also be zero if the dividend is divisible by the divisor. For example, if we divide 10 by 5, we get 2 with a remainder of 0. This is because 10 is divisible by 5, so the remainder is 0.

In general, the remainder is always smaller than the divisor.

To find the values of x and y in the system of equations:

Equation 1: [tex]x + 2y = 3[/tex]

Equation 2: [tex]3x + 4y = 1[/tex]

We can solve the system using the method of substitution or elimination. Here, I will demonstrate the method of substitution:

Step 1: Solve Equation 1 for x:

[tex]x = 3 - 2y[/tex]

Step 2: Substitute the value of x from Step 1 into Equation 2:

[tex]3(3 - 2y) + 4y = 1[/tex]

Step 3: Simplify and solve for y:

[tex]9 - 6y + 4y = 1[/tex]

[tex]-2y = 1 - 9[/tex]

[tex]-2y = -8[/tex]

[tex]y = \frac{-8}{-2}[/tex]

[tex]y = 4[/tex]

Step 4: Substitute the value of y back into Equation 1 to find x:

[tex]x + 2(4) = 3[/tex]

[tex]x + 8 = 3[/tex]

[tex]x = 3 - 8[/tex]

[tex]x = -5[/tex]

Therefore, the solution to the system of equations is:

[tex]x = -5[/tex]

[tex]y = 4[/tex]

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer: X=-2 & Y=5/2

Step-by-step explanation:

STEP 1: Find the given equations

            x+2y=3 and 3x+4y=1

STEP 2: Try to equate any of the terms by multiplying either of the equations.

HERE, we can multiply the equation x+2y=3 by 2

WE GET, 2x+4y=6 and we can see that 4y terms is common in both te equations

STEP 3: cancel out the matching terms by simple addition or subtraction of the equations.

after solving we get, x=-2.

STEP 4: put the value of x in any of the two quations to get the value of y.

WE GET, the value of y as 5/2.

check the attached image for a better understanding.

Answer:

C. 2 units

Step-by-step explanation:

In right triangle ABD, BD is the hypotenuse and AB and AD are the legs of the right triangle each with a length of 1 unit

By the Pythagorean Thereom
hypotenuse² = sum of squares of each of the other sides

BD² = AB² + AD² = 1² + 1² = 1 + 1 = 2

In right triangle BCD, BC is the hypotenuse and we are given BD = DC

BC² = BD² + DC² = BD² + BD² =2 BD² = 2 · 2 = 4

BC = √4 = 2 units

Answer: 25

Step-by-step explanation:

bc

Answer:

622m²

Step-by-step explanation:

a right rectangular prism will have 6 sides and the parallel sides of the prism will be the same size

so we work out the given surface areas and multiply each by 2

7 x 11 = 77

times 2 is 154

11 x 13 = 143

times 2 is 286

7 x 13 = 91

times 2 is 182

then we add it all up

154 + 286 + 182 = 622m²

The box of pancake says that it makes 10 pancakes but sam is able to make 8 pancakes from the ingredient. Here the number 10 represents Theoretical yield.

Here,

Theoretical yield can be defined as the product received from the  complete conversion of the limiting reactant in a chemical process.

It is the amount of product resulting from a theoretical chemical reaction and it is not the same as the amount you'll actually get from a reaction in the lab.

Theoretical yield is commonly expressed in terms of grams or moles.  the actual yield is the amount of product actually produced by a reaction. Actual yield is usually a smaller quantity because few chemical reactions proceed with 100% efficiency because of loss recovering the product and because other reactions may be occurring that reduce the product.  so 10 here is a theoretical yield bot the actual yield.

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complete question:

Decide whether the following scenarios represent theoretical or actual yields. sam follows the directions on a box of pancake mix. the box says that it makes 10 pancakes, but he is able to make 8 pancakes from the ingredients. in this case, the number 10 represents which type of yield?

The minimum number of males over age 40 that the research company must include in their sample is 715.

To determine the minimum number of males over age 40 needed in the sample, we can use the formula for the sample size in a confidence interval:

n = (Z * σ / E)^2

Where:

n = sample size

Z = z-score corresponding to the desired confidence level (85% confidence interval corresponds to a z-score of approximately 1.44)

σ = standard deviation of the population

E = maximum error or margin of error

Given:

Z = 1.44

σ = 1.3 liters

E = 0.07 liters

Substituting these values into the formula, we have:

n = (1.44 * 1.3 / 0.07)^2

n = (1.872 / 0.07)^2

n = 26.742857^2

n ≈ 714.285714

Since we cannot have a fraction of a person in the sample, we need to round up the sample size to the next integer:

n = ceil(714.285714) = 715

Therefore, the minimum number of males over age 40 that the research company must include in their sample is 715.

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Answer:

see below

Step-by-step explanation:

b.

(x+2, y - 1) = (2, 3)

We have two equations:

x + 2 = 2

y - 1 = 3

Solving for x, we get:

x = 0

Solving for y, we get:

y = 4

Therefore, the values of x and y are 0 and 4, respectively.

To answer the original question, if Baez has 10 hits in 32 at-bats, he would have a total of 10 hits.

To answer this question, we first need to figure out how many at-bats Baez has had over the last seven games.

Since he hits 31.25% of the time he is at bat, we can assume that he has had 100/31.25 = 3.2 at-bats per hit. Therefore, he has had 32 at-bats over the last seven games (10 hits x 3.2 at-bats per hit).

Now that we know Baez has had 32 at-bats, we can calculate his batting average by dividing the number of hits he has (10) by the number of at-bats (32). This gives us a batting average of 0.3125, or 31.25%.

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Answer:

In an isosceles triangle, the sides opposite the equal angles are equal in length. Let's solve the given problem using the given information.

a) To find PQ, we need to find the length of the equal sides. Since QX = XR = 2.64 cm, we know that PQ = PR. Therefore, PQ = PR = 2.64 cm.

b) To find PX, we can use the concept of the Law of Cosines. In an isosceles triangle, the base angles are equal, so the angle at P is 65°, and the opposite side is PX.

Using the Law of Cosines formula:

c² = a² + b² - 2ab * cos(C)

Where c is the side opposite angle C, and a and b are the other two sides.

In our case, we have:

a = PQ = 2.64 cm

b = PR = 2.64 cm

C = 65°

We want to find PX, so c = PX.

Substituting the values into the formula:

PX² = (2.64)² + (2.64)² - 2(2.64)(2.64) * cos(65°)

PX² ≈ 6.9696 + 6.9696 - 2(2.64)(2.64) * 0.42262

PX² ≈ 13.9392 - 2(2.64)(2.64) * 0.42262

PX² ≈ 13.9392 - 2(2.64)(2.64) * 0.42262

PX² ≈ 13.9392 - 11.1197

PX² ≈ 2.8195

Taking the square root of both sides, we get:

PX ≈ √2.8195

PX ≈ 1.678 cm

Therefore, a) PQ = PR = 2.64 cm, and b) PX ≈ 1.678 cm.

Step-by-step explanation:

Answer:

  4π/3 ≈ 4.18879 cubic units

Step-by-step explanation:

You want the volume of revolution formed by revolving the 1st-quadrant area under y = 0.25 -(x -4)² around the y-axis.

There are several ways to find the volume of revolution. One can integrate a differential of volume, where that differential is a cylindrical shell or a washer. Alternatively, one can multiply the area under the curve by the centerline length of the path of revolution. We choose this latter approach.

The area in the first quadrant of the region being rotated can be found as the integral between its x-intercepts.

The x-intercepts are found by ...

  0 = 1/4 -(x -4)²

  x -4 = ±√(1/4) = ±1/2

  x = 4 ± 1/2 = {3.5, 4.5} . . . . . . x-intercepts

Then the area is ...

  [tex]\displaystyle\int_{3.5}^{4.5}(0.25-(x-4)^2)\,dx=\left[0.25x-\dfrac{1}{3}(x-4)^3\right]_{3.5}^{4.5}\\\\\\=0.25(1)-\dfrac{1}{3}(0.5^3-(-0.5)^3)=\dfrac{1}{6}\qquad\text{square units}[/tex]

The radius from the y-axis to the line of symmetry of the area is 4 units, so the length of the rotation path is

  C = 2πr = 2π(4) = 8π

The product of this path length and the area is ...

  V = C·A = (8π)(1/6) = 4π/3

The volume of the solid is 4π/3 cubic units.

__

Additional comment

The area under a symmetrical portion of a parabola is 2/3 of the area of the enclosing rectangle. The portion of the parabola in the 1st quadrant is 1 unit wide and 0.25 units high, so its area is (1)(1/4)(2/3) = 1/6 square unit, as we found above.

The second attachment shows the volume found using the cylindrical shell method.

<95141404393>

Answer:

2 . figures have a volume that is greater than 600 in3.

Step-by-step explanation:

The interquartile range of this data set is equal to 4.

In Mathematics and Statistics, IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.

Mathematically, interquartile range (IQR) of a data set is the difference between third quartile (Q₃) and the first quartile (Q₁):

Interquartile range (IQR) of data set = Q₃ - Q₁

Interquartile range (IQR) of data set = 6 - 2

Interquartile range (IQR) of data set = 4.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.