A circle has a diameter whose end points are at (-3, -1) and (7, 7). What is the equation of the circle?

The probability that William does his homework is 25/44

Let A be the event that William walks the dog after school, and let B be the event that he does his homework.

We are given:

P(A) = 8/11

P(B|A) = 1/2 (the probability of doing homework given that he walks the dog)

P(B|A') = 3/4 (the probability of doing homework given that he doesn't walk the dog)

We want to find P(B), the probability that William does his homework. We can use the law of total probability, which states that:

P(B) = P(A)×P(B|A) + P(A') × P(B|A')

Substituting the values we have, we get:

P(B) = (8/11) × (1/2) + (3/11) × (3/4)

= 4/11 + 9/44

=16+9/44

= 25/44

Therefore, the probability that William does his homework is 25/44

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Sample Response: Bobby’s interquartile range is 113, while Amelia’s is 179. A lower interquartile range means Bobby’s scores are closer to the median.

I cannot agree or disagree with personal beliefs. However, based on statistical principles, if the range of Bobby's scores is narrower than Amelia's range, then it is likely that Bobby's scores are closer to his median. Alternatively, if Amelia's scores are spread out more, her median may not be a good representation of the typical score, and her scores may not cluster closely around it. Ultimately, without more information on the distribution of the scores, it is impossible to determine who has scores clustered closer to their median.

The altitude of the plane is approximately 21.65 miles.

An altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).

We have an observer on the ground (you) and a plane flying towards you. Let's call the distance between the observer and the point directly below the plane "x", and let's call the altitude of the plane "h".

At the first moment, the angle between the ground and your line of sight to the plane is 45 degrees. This means that the angle between the plane's altitude and the ground is also 45 degrees (since the plane is flying horizontally towards you). We can use trigonometry to find the value of "x" in terms of "h".

In the right triangle formed by the observer, the point directly below the plane, and the plane's altitude, we have:

tan(45) = h/x

Since tan(45) = 1, we can simplify this to:

h/x = 1

h = x

So the distance between the observer and the point directly below the plane is equal to the altitude of the plane.

One minute later, the angle between the ground and your line of sight to the plane is 60 degrees. We can use the same approach to find the new value of "x" in terms of "h".

In the right triangle formed by the observer, the point directly below the plane, and the plane's altitude, we have:

tan(60) = h/(x + 450/60)

Simplifying this, we get:

h = (x + 7.5h) * sqrt(3)

Solving for "x", we get:

x = (h / sqrt(3)) - 7.5h

Now we can substitute the value of "x" from the first moment (which is equal to the altitude of the plane) into this equation to find the altitude of the plane:

h = (h / sqrt(3)) - 7.5h

h = h(1 / sqrt(3) - 7.5)

h = 21.65 miles (rounded to two decimal places)

Therefore, the altitude of the plane is approximately 21.65 miles.

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Answer:

We need to subtract 41/6 from 53/6 to get 8. Alternatively, we can say that 8 is 41/6 less than 53/6.

Step-by-step explanation:

To determine how much to subtract from 53/6 to make 8, we need to perform the following calculation:

53/6 - x = 8

where x is the amount we need to subtract.

To isolate x, we need to isolate it on one side of the equation. We can do this by subtracting 53/6 from both sides:

53/6 - x - 53/6 = 8 - 53/6

Simplifying the left-hand side gives:

-x = 8 - 53/6 + 53/6

Simplifying the right-hand side gives:

-x = 41/6

Multiplying both sides by -1 gives:

x = -41/6

Therefore, we need to subtract 41/6 from 53/6 to get 8. Alternatively, we can say that 8 is 41/6 less than 53/6.

The principal money her  grandfather originally invested is R= 50000/1.08¹²

What is compound interest?

Compound interest is a type of financial phenomenon in which interest you earn in a savings or investment account earns interest of its own over time. It is also said that Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest

the given parameters to help solve the question are

Amount = R50,000

Interest rate = 8%

Time = 25years compounded quarterly

The formula for compound interest compounded quarterly is

A= P × (1 + R/(4 × 100))⁴ⁿ,

where P is the principal and R is the interest rate

50000 = R[1+0.08]⁴*³

50000 = R[1.08)¹²

R= 50000/1.08¹²

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The change referred to in the headline is an absolute change. An absolute change is a difference or increase in a quantity that is measured without reference to the original or initial value.

In this case, the headline states that enrollments at Northeastern University are expected to increase by 1,700 students. This means that the actual number of students is expected to increase by 1,700 from its current or previous level, without any reference to the original number of students enrolled at Northeastern University.

An absolute change is usually expressed in units of the quantity being measured, such as students, dollars, or meters. In contrast, a relative change is expressed as a percentage or ratio of the original or initial value. A relative change indicates how much a quantity has changed in proportion to its initial value.

For example, if enrollments at Northeastern University were expected to increase by 10%, this would be a relative change because it represents a percentage of the current or previous level of enrollment. However, the headline specifies an absolute increase of 1,700 students, which does not depend on the current or previous level of enrollment.

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D x = 7.8

√7.82

E y = 11.1

√11.12

F x = 5.1

√5.12

G y = 24.3

√24.32

H x = 9.1

√9.12

I y = 15.4

√15.42

J x = 13.7

√13.72

K y = 20.2

√20.22

L x = 11.9

√11.92

M y = 18.3

√18.32

N x = 21

√21

O y = 17.5

√17.52

The function f(x) = -0.05(x²-18x -40) represents the "height" of the projectile fired from the cannon at a "horizontal-distance" of x.

The function which represents the path, coming out of the cannon is f(x) = -0.05(x²-18x -40);

The term inside the bracket is : (x²-18x -40) is a quadratic expression that represents the shape of the projectile's path.

Now, let us consider the "negative-coefficient" (-0.05) in front of the quadratic expression.

This means that the function will be reflected about the x-axis, which  means that the height of the projectile will be measured downwards from a reference point.

Therefore, f(x) represents the height of the projectile.

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The angle of elevation from Jazmin to the top of the tree is 14°.

We are given that;

Top of tree= 24ft

String= 100ft

Now,

We can use any trigonometric ratio that involves opposite and hypotenuse sides, such as sine or cosine. Let’s use sine for this example.

sin θ = opposite / hypotenuse

sin θ = 24 / 100

sin θ = 0.24

θ = sin^-1 (0.24)

θ = 13.9° (rounded to the nearest degree)

Therefore, by the angle the answer will be 14°.

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If the  high temperature is 74° and the low temperature is have that of the high temperature then low temperature is 37°

Given that New center 13 has just released tomorrow’s weather forecast high temperature is 74°

High temperature = 74°

The low temperature is have that of the high temperature

Low temperature =1/2× High temperature

=1/2×74

=37

Hence, If the high temperature is 74° and the low temperature is have that of the high temperature then low temperature is 37°

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rest, Using the simple interest formula, P x R x T, the total interest that Victoria will earn in 8 years on an initial deposit of $250 at 2¹/₂% simple interest is $50.

Simple interest is a system of interest that charges interest only on the principal at the end of each period.

Unlike compound interest, the simple interest system does not accumulated interest in order to charge interest on accumulated interest.

The initial deposit = $250

Simple interest rate = 2¹/₂%

Investment period = 8 years.

Simple interest = $50 ($250 x 2¹/₂% x 8)

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The vertex of g(x) is translated left by 2 units and down by 5 units compared to the vertex of f(x).

The shape of the parabola for g(x) is the same as the shape of the parabola for f(x).

The axis of symmetry for g(x) is the same as the axis of symmetry for f(x).

The minimum point of g(x) is lower than the minimum point of f(x).

Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It is also the comparison of two like or similar quantities.

How to determine this,

The ratio of the amount men spent on swimwear to the amount women spent on swimwear

When the amount men spent on swimwear = $500,000

Amount women spent on swimwear = $2,000,000

Ratio = 500,000 : 2,000,000

Ratio = 500,000/2,000,000

Ratio = 1/4

Ratio = 1 : 4

The ratio as a fraction = 1/4

b. To find the ratio of the amount men spent on swimwear to the total amount men and women spent on swimwear.

Amount men spent on swimwear = $500,000

Total amount men and women spent on swimwear

= $2,000,000 + $500,000

= $2,500,000

Ratio = $500,000 : $2,500,000

Ratio = 500,000/2,500,000

Ratio = 1/5

Ratio = 1 : 5

Ratio expressed as a fraction = 1/5

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The surface area of this cylinder is about 45,413.59 square yards.

In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):

SA = 2πrh + 2πr²

Where:

From the circumference of the outside of the cylinder, the radius can be calculated as follows;

Circumference = 2πr

512.49 = 2(3.14)r

Radius, r = 512.49/6.28 = 81.61 yards.

By substituting the given parameters into the surface area of a cylinder formula, we have;

Surface area (SA) of cylinder = (2 × 3.14 × 81.61 × 7) + 2 × 3.14 × 81.61²

Surface area (SA) of cylinder = 3,587.58 + 41,826.01

Surface area (SA) of cylinder = 45,413.59 square yards.

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The solution of Unit Problem is Solution of first part is As the contribution margin is positive, accepting the special sales order would be profitable for Hobby-Cardz,and second part is  total profit is negative

Contribution margin is the difference between a product's revenue and its variable costs. It represents the amount of money that is available to cover fixed costs and contribute to profit.

1)Incremental Analysis without special order:

Revenue from 51,000 packs at $0.43 per pack = $21,930

Total variable costs for 51,000 packs = 51,000 x $0.33 = $16,830

Contribution margin = $21,930 - $16,830 = $5,100

As the contribution margin is positive, accepting the special sales order would be profitable for Hobby-Cardz.

2)Incremental Analysis with special hologram baseball cards:

In addition to the incremental analysis performed in Part 1, we need to consider the additional cost of $5,300 to develop the hologram.

Revenue from 51,000 packs at $0.43 per pack = $21,930

Total variable costs for 51,000 packs = 51,000 x $0.33 = $16,830

Contribution margin = $21,930 - $16,830 = $5,100

Less: Additional cost of hologram development = $5,300

Total profit/loss = $5,100 - $5,300 = ($200)

As the total profit is negative, accepting the special sales order with the hologram development cost would result in a loss of $200. Therefore, Hobby-Cardz should not accept the special order under these circumstances.

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To find the volume of an irregular 3D shape like Myron's pool, he needs to determine:

1. The length

2. The width

3. The depth

With those three measurements, he can plug them into the formula for volume of a rectangular prism:

Volume = Length x Width x Depth

So if the pool is:

Length = 20 ft

Width = 10 ft

Depth = 5 ft

Then the volume would be:

20 ft x 10 ft x 5 ft = 1000 cubic feet

Does this make sense? Let me know if Myron has any other questions!

The system of linear equations has no solutions.

Here we want to solve the system of linear equations:

2x-  2y = 7

-x + y = -2

One could easily identify that the two lines are parallel, but let's prove it. To do so, we can multiply the second equation by -2.

Then we will get:

-2*(-x + y) = -2*-2

2x - 2y = 4

Then the system of equations is:

2x-  2y = 7

2x - 2y = 4

The coefficients in the left side are the same ones and the constants in the right side are different. Thus, the lines are parallel, and thus, the system has no solutions.

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According to the given information, the one angle on the straight line inside a circle is 135 then the value of the x = 4 as both angles are supplementary angles.

Supplementary angles are two angles whose sum is 180 degrees. In other words, if we add the measures of two supplementary angles, the result is always 180 degrees.

When two lines intersect, they form four angles at the intersection point. If two of these angles are supplementary, they are called adjacent supplementary angles. In this case, they share a common side and a common vertex, and their non-shared sides form a straight line.

For example, if angle A and angle B are adjacent angles, and angle A measures 120 degrees, then angle B must measure 60 degrees, since 120 + 60 = 180.

If the two angles are on a straight line, then they are supplementary, meaning their sum is 180 degrees. Therefore, we can set up the equation:

135 + (11x + 1) = 180

Simplifying the left side, we get:

136 + 11x = 180

Subtracting 136 from both sides, we get:

11x = 44

Dividing both sides by 11, we get:

x = 4

Therefore, the value of x is 4.

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Answer:C is your answer

Step-by-step explanation:This is not a 90 degree angle or 360 degree shape

The correct option that indicates the quadrant that contains the translation of the shaded figure is the option B

B. III

A translation is a transformation in which the size, relative position of the points on the pre-image, are preserved but the location of the pre-image changes to obtain the image.

The shape of the shaded figure is an L-shape

The geometric figure in quadrant II and IV are a reflection of the shaded figure, across the y-axis and across the x-axis, respectively which is not a translation transformation.

The geometric figure in quadrant III can be obtained from the shaded figure by a translation 4 units to the left and 5 units downwards, which can be expressed as <-4, -5>, which is a translation transformation, therefore;

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Yes, this represents an exponential function.

The exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function.

Because the growth rate is inversely correlated with the function's present value, this function is exponential. Regardless of how many cells were present the previous hour the number of cells is multiplied by the same factor of 4 every hour.

Therefore, One can estimate the number of cells for every hour x by evaluating the function at a specific value of x. The function f(x) = 4x implies exponential growth.

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The derivative of the function y =  ((2x - 1)³)/√(3x + 1)​ is dy/dx = (2x - 1)²[3x + 6]/(2[√(3x + 1)]³)

The derivative of a function is the limit as the change in x tnds to zero of the change in y over the change in x.

To find the derivative of the function y =  ((2x - 1)³)/√(3x + 1)​, we use the quotient rule.

dy/dx = (vdu/dx - udv/dx)/v²

where u = (2x - 1)³ and v = √(3x + 1)

So, du/dx = 3(2x - 1)² and dv/dx = 3/[2√(3x + 1)]

Substituting the values of the variables into the equation, we have that

dy/dx = (vdu/dx - udv/dx)/v²

dy/dx = (√(3x + 1) × 3(2x - 1)²  -  (2x - 1)³ × 3/[2√(3x + 1)])/[√(3x + 1)]²

dy/dx = (3√(3x + 1)(2x - 1)²  -  3(2x - 1)³/[2√(3x + 1)])/[√(3x + 1)]²

= (3√(3x + 1)√(3x + 1)(2x - 1)²  -  3(2x - 1)³/[2√(3x + 1)])(3x + 1)²

= [3(3x + 1)(2x - 1)²  -  3(2x - 1)³/[2√(3x + 1)])(3x + 1)²

= (2x - 1)²[3(3x + 1)  -  3(2x - 1)/[2√(3x + 1)])(3x + 1)²

= (2x - 1)²[9x + 3  -  6x + 3]/[2√(3x + 1)])(3x + 1)²

= (2x - 1)²[3x + 6]/(2[√(3x + 1)]³)

So, dy/dx = (2x - 1)²[3x + 6]/(2[√(3x + 1)]³)

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8.7 kilometers is longer than 8.005 kilometers.

Answer:

8.7 is longer than 8.005

Step-by-step explanation:

An equation to match the graph include the following: f(x) = |x + 1| + 1.

In Mathematics and Geometry, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Since the parent function is f(x) = |x|, g(x) would be created by translating f(x) the parent function one unit to the left and one unit upward as follows;

f(x) = |x|

g(x) = |x + 1| + 1

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The 2 people from the 9 people can sit on the aisle in 72 ways

from the question, we have the following parameters that can be used in our computation:

Number of peiple = 9

Number of seats = 2

Using the above as a guide, we have the following:

n = 9 and r = 2

The can arrange themselves in nPr ways.

Where

nPr = n!/(n - r)!

Substitute the known values in the above equation, so, we have the following representation

9P2 = 9!/(9 - 2)!

Evaluate the expression

9P2 = 72

Hence, the number of ways they can arrange themselves is 72

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The rectangle have length = 4, breath = 16, perimeter = 40, and area = 64.

The perimeter of a rectangle is the sum of length of its four sides or the sum of its length and breadth, multiplied by two. While the area is the length multiplied by the breadth.

Perimeter = 2(L + B)

Area = L × B

From the question;

2(L + B) = 2LB

32L = 2L(L²)...(1) {since B = L²}

from equation (1), L = 4 by solving for L

so;

B = 4² = 16

perimeter of the rectangle = 2(4 + 16) = 40

area of the rectangle = 4 × 16 = 64

Therefore, the rectangle have length = 4, breath = 16, perimeter = 40, and area = 64.

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Answer:

115 meters

Step-by-step explanation:

Think of this like a ratio    [tex]\frac{3.2}{1.3} =\frac{x}{46.75}[/tex]

Then solve for x    [tex](\frac{3.2}{1.3} )*46.75 = 115.08[/tex]

Answer:

The dimensions of the rectangle are approximately 8.54 units by 3.54 units.

Step-by-step explanation:

Let's start by using algebra to represent the information given in the problem.

Let L be the length of the rectangle.

Then, the width of the rectangle is 5 units less than the length, which means the width can be expressed as L - 5.

The area of a rectangle is given by the formula A = L * W, where A is the area, L is the length, and W is the width. In this case, we are given that the area is 36 square units. So we can write:

A = L * (L - 5)

36 = L * (L - 5)

Expanding the right-hand side of the equation, we get:

36 = L^2 - 5L

Moving all the terms to the left-hand side of the equation, we get:

L^2 - 5L - 36 = 0

Now we can use the quadratic formula to solve for L:

L = (-(-5) ± sqrt((-5)^2 - 4(1)(-36))) / (2(1))

Simplifying this expression, we get:

L = (5 ± sqrt(229)) / 2

We can discard the negative solution since the length of a rectangle cannot be negative.

So, the length of the rectangle is approximately 8.54 units (rounded to two decimal places).

To find the width, we can substitute this value of L into the expression we derived earlier for the width:

W = L - 5

W = 8.54 - 5

W ≈ 3.54 units (rounded to two decimal places)

Therefore, the dimensions of the rectangle are approximately 8.54 units by 3.54 units.