Complete the squares in order to write the equation of
the circle.
Then identify the coordinates of the center, and find the
radius.
x2 + y2 - 28% -10y + 220 = 0

Answer:

The actual speed = 27.12 mi/h

Direction = 36.5° in NE(north of east)

Step-by-step explanation:

As given , A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E.

⇒θ = 36°

Let v₀ be the constant speed, then v₀ = 20

Let vₓ be the speed in East direction

     \(v_{y}\) be the speed in North direction

So,

vₓ  = v₀ sin(θ) = 20 sin(36°) + 10 ( As given, There is a 10mi/h cross wind blowing due east.)

⇒vₓ  = 20(0.588) + 10 = 11.76 + 10 = 21.76 mi/h

and   \(v_{y}\)  = v₀ cos(θ) = 20 cos(36°) = 20(0.809) = 16.18 mi/h

Now,

the actual speed = √(vₓ)² + (\(v_{y}\))²

                            = √(21.76)² + (16.18)²

                            = √473.498 + 261.792

                            = √735.29 =  27.12

⇒The actual speed = 27.12 mi/h

Now,

Direction = θ = \(tan^{-1}(\frac{v_{y} }{v_{x} } ) = tan^{-1}(\frac{16.18 }{21.76 } ) = tan^{-1}(0.74) = 36.5\)

⇒ Direction = 36.5° in NE(north of east)

Answer:

27.1 mi / h; N 53° E

Step-by-step explanation

The area of the smaller sector or minor sector is  125.66 yd².

The area of the larger sector or major sector is  326.73 yd².

The areas of the minor and major sectors is calculated by applying the following formulas follow;

Area of sector is given as;

A = (θ/360) x πr²

where;

The area of the smaller sector or minor sector is calculated as follows;

A = ( 100 / 360 ) x π ( 12 yd)²

A = 125.66 yd²

The area of the larger sector or major sector is calculated as follows;

θ = 360 - 100

θ = 260⁰

A =  ( 260 / 360 ) x π ( 12 yd)²

A = 326.73 yd²

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Answer:

true

Step-by-step explanation:

\(3x - 4(2x - 5) = \\ 3x - 8x + 20 = \\ - 5x + 20 = \\ 20 - 5x = > \: true\)

Answer:

true

Step-by-step explanation:

3x -4(2x-5)

3x-8x+20

5x+20

Answer:

2; 1.6; 1.57; 1.568

Step-by-step explanation:

the first one is to the whole number

it is 5 to round up and below 4 to stay the same

so whole number is 2

tenth is 1.6

hundredth is 1.57

thousandth is 1.568

add it and you will get 24 so pick D

To find the volume of the solid generated by revolving the plane region about the line x using the shell method, we need more specific information about the given plane region and the boundaries of integration.

The shell method is a technique used to calculate volumes of solids of revolution. It involves integrating cylindrical shells along the axis of rotation. However, in order to apply the shell method, we require additional details regarding the given plane region and the boundaries of integration.

Typically, the plane region is defined by a function or an equation. For example, if the plane region is bounded by the curves y = f(x), y = g(x), and the line x = a, x = b (where f(x) > g(x) for all x in the interval [a,b]), we can proceed with the shell method.

To calculate the volume using the shell method, we integrate the circumference of each cylindrical shell multiplied by its height. The differential height is given by Δh = f(x) - g(x), and the differential circumference is 2πx.

The integral expression for calculating the volume using the shell method is:

V = ∫[a,b] 2πx * (f(x) - g(x)) dx

By evaluating this integral over the appropriate interval [a,b], we obtain the volume of the solid generated by revolving the given plane region about the line x.

However, without specific information about the plane region, the equations or functions defining it, and the boundaries of integration, it is not possible to provide a numerical value for the volume. If you can provide more details or specify the plane region, I would be happy to assist you further in using the shell method to determine the volume.

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Answer:

The question is incomplete, here is the complete question.

Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below. Children in 50 Households Number of Children Number of Households 0 5 1 11 2 13 3 10 4 9 5 2 Using a proportion, what can you infer about the number of households in her town that have more than three children?

A) About 242 households have more than three children.

B) About 269 households have more than three children.

C) About 296 households have more than three children.

D) About 565 households have more than three children.

Step-by-step explanation:

The given sample size is 50

The number of households with more than three children = 9+2

= 11

The proportion of household where more than three children are present is calculated by:

Household with a greater number of children/sample size

= 11/50

The original household size= 1,346

Therefore, the amount of household with children greater than 3 is:

= 1346×11/50

= 1346× 0.22

= 296.12

= 296

Thus, about 296 households have more than three children.

The critical value that should be used in constructing the confidence interval is ( 1.592, 1.807 ).

Given that;

Number of residents, n = 7

Z*- value of 90% confidence level equals z* = 0.79

Mean x = 1.7 and deviation σ = 0.36

What is the standard deviation?

Standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean.

Now,

Number of residents, n = 7

Z*- value of 90% confidence level equals z* = 0.79

Mean x = 1.7 and deviation σ = 0.36

The confidence interval for mean waste recycled per person is

\((x-z^{*} \frac{sigma}{\sqrt{n} } ; x+z^{*} \frac{sigma}{\sqrt{n} } )\)

\((1.7 - 0.79*\frac{0.36}{\sqrt{7} } ; 1.7 + 0.79*\frac{0.36}{\sqrt{7} })\)

\((1.592, 1.807)\)

Hence, the critical value that should be used in constructing the confidence interval is ( 1.592, 1.807 ).

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Answer:

c)2:1..................

Answer:

C

Step-by-step explanation:

Find the distance of AB:

Distance formula: \(\sqrt{[(-8)-(-2)]^2+(9-1)^2}\)

\(\sqrt{(-6)^2+(8)^2}=\sqrt{36+64}=\sqrt{100}=10 units\)

Find the distance of BC:

Distance formula: \(\sqrt{[(-2)-1]^2+[1-(-3)]^2}\)

\(\sqrt{(-3)^2+4^2}=\sqrt{9+16} =\sqrt{25} =5 units\)

AB=10 units

BC=5 units

AB:BC = 10:5=2:1

b=48

1) Solving for b, we'll proceed this way:

b/4 = 12 Multiply both sides by 4, to eliminate the fraction

b= 48

2) So the answer is b=48

Answer:

add 18 to both sides, giving you 3x = 96

a preliminary sample of at least 30 members is already available, it is likely that the required sample size of 92 is achievable.

The formula for the minimum sample size n needed to estimate the population mean μ with a confidence level of c and a margin of error of E, when the population standard deviation σ is known, is given by:

n = [(z_c/2 * σ)/E]^2

where z_c/2 is the z-score corresponding to the confidence level c.

For a 95% confidence level, c = 0.95, the corresponding z-score is:

z_c/2 = 1.96

Substituting the given values of c, σ, and E into the formula, we get:

n = [(1.96 * 5.7)/1]^2 = 91.69

Rounding up to the nearest integer, the minimum sample size required is n = 92.

what is standard deviation?

In statistics, the standard deviation is a measure of the spread or variability of a set of data values. It measures how much the individual data points differ from the mean or average value of the data set.

The formula for calculating the standard deviation is as follows:

s = sqrt((1/n) * Σ(xi - x)^2)

where s is the standard deviation, n is the number of data points, xi is the ith data point, x is the mean of the data set, and Σ denotes the sum of the terms.

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Answer:

V = 672 cm³ (Option 3)

Step-by-step explanation:

Volume of Rectangular Prism = \(Length * Width * Height\)

Where L = 14 cm, W = 6 cm and H = 8 cm

V = 14 * 6 * 8

V = 672 cm³

Answer:

x = 3.32

y = 2.11

Step-by-Step Explanation:

Answer:

(5,-1)

Step-by-step explanation:

Since one of the equations gives x in terms of y , ie x = 1 - 4y

Then this can be substituted directly into the other equation.

→ 2(1 - 4y) + 7y = 3 → 2 - 8y + 7y = 3 → -y = 1 → y = -1

now, substitute y = -1 into x = 1 - 4y , to obtain x

→ x = 1 - 4(-1) = 1 + 4 = 5

Thus solution is (5 , -1 )

The total square footage (area) of the apartment is 337 square feet.

It is given in the question that, In a small apartment:-

Dimensions of the bedroom = 10 ft by 10ft

Dimensions of the bathroom = 5 ft by 5 ft

Dimensions of the living room/kitchen = 14 ft by 18 ft

We have to find the total square footage (area) of the apartment.

We know that,

Area of square = \(side^2\)

Hence,

Area of the bedroom = 100 square feet

Area of the bathroom = 25 square feet

Area of the living room/ kitchen = 212 square feet

Hence,

Total square footage of the apartment = 100 + 25 + 212 = 337 square feet.

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The profit increases from 0 to 5 and decreases from 5 to 10

The x intercept is the point where the graph crosses the x-axis.

From the graph, we have:

x-intercept = 0 and 10

This represents the initial and the final prices of the pencil

The vertex of the graph is (5, 160)

And it represents the maximum of the graph

This means that the company makes a maximum profit of $160 when they sell the pencil for $5

From the graph, we have:

Increasing interval = [0, 5]

Decreasing interval = [5, 10]

This means that the profit increases from 0 to 5 and decreases from 5 to 10

From the graph, we have

f(2) = 90

f(5) = 160

The average rate of change of the graph from x = 2 to x = 5 is

Rate = (f(5) - f(2))/(5 - 2)

This gives

Rate = (160 - 90)/(5 - 2)

Evaluate

Rate = 23

This means that the company makes a profit of $23 per $1 increment in price

The domain is the range of the x-intercept

Hence, the domain of the function is [0, 10]

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Answer:

Supplementary

Step-by-step explanation:

The system that is represented by the graph is inequality 3

What is system of inequalities?

A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem requires a variety of solutions and those solutions must satisfy multiple constraints, systems of inequalities are used.

We are given the graph of inequalities and given 4 choices out which 1 is the correction representation of the inequalities given in the graph

Now As you  can see one the parabolas open downwards that means the term x^2 is negative in that case where as the other parabola opens upwards hence the term x^2 is positive.

So second and third options are the options which satisfies this criteria

if we put x = 0 in the second equation of both the inequalities we get y= 4

This criteria is satisfied by only inequality 3 hence the correct system of inequality is inequality 3

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Answer:y ≥ x2 – 2x + 4

y < –x2 + 4

Step-by-step explanation:

The series converges because it is a geometric series with |r| < 1. The sum of the series is 1/(1 - e⁻³) ≈ 0.9502.

The series ∑ⁿ₌₀ e⁻³ⁿ can be analyzed using the ratio test.

The ratio of successive terms is given by e⁻³⁽ⁿ⁺¹⁾/e⁻³ⁿ = e⁻³. Since the limit of the ratio as n goes to infinity is less than 1, the series converges by the ratio test. The sum of the series can be found using the formula for the sum of an infinite geometric series: S = a/(1 - r), where a is the first term and r is the common ratio.

In this case, a = e^0 = 1 and r = e⁻³. Thus, the sum of the series is S = 1/(1 - e⁻³) ≈ 0.9502. Therefore, the correct answer is E. The series converges because it is a geometric series with |r| < 1. The sum of the series is 1/(1 - e⁻³) ≈ 0.9502.

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Complete complete:

Determine whether the series sigma^infinity_ n = 0 e^-3n converges or diverges. If it converges, find its sum. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. The series diverges because lim_n rightarrow infinity e^-3n notequalto 0 or fails to exist.

B. The series converges because lim_k rightarrow infinity sigma^k_n = 0 e^-3n fails to exist.

The series converges because lim_n rightarrow infinity e^-3n = 0.

The sum of the series is (Type an exact answer.)

D. The series diverges because it is a geometric series with |r| greaterthanorequalto 1.

E. The series converges because it is a geometric series with |r| < 1. The sum of the series is (Type an exact answer.)

No, The range of r contains points that are not in the domain of f.

Calculus is a branch of mathematics that deals with the study of rates of change, accumulation, and mathematical modeling of continuous quantities.

The correct answer is: No. The range of r contains points that are not in the domain of f.

In order for a function to be integrable along a curve, the curve must lie entirely within the domain of the function. The domain of a function is the set of all possible input values for which the function is defined.

In this case, the function f(x, y, z) = x ln(yz) has a domain that depends on the values of x, y, and z. However, the curve C, parametrized by r(t) = et², ln(t) + 1/2, t³ - 2, where 0 ≤ t ≤ e, may contain points that fall outside the domain of f.

Hence, f may not be integrable along C because the range of r (i.e., the set of all possible points traced by C) contains points that are not in the domain of f.

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Answer:

I think you need to add them.

Answer:

0.24

Step-by-step explanation:

Miles he drives: x

55.96+0.12x=49.96+0.16x

0.04x=6

x=0.24mi

Answer:

12 dollars an hour

Step-by-step explanation:

Just divide 54 by 4.5 which equals 12.

Answer:

12 dollars an hour

Step-by-step explanation:

Just divide 54 by 4.5 which equals 12

70 percentage of the meeting attendees were managers. The solution has been obtained by using the percentage.

What is a percentage?

A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. A portion per hundred is what the percentage denotes. Percentage refers to one in a hundred.

We are given that 49 out of the 70 people in a company meeting were managers.

Now, in order to find the percentage of the managers attending the meeting, we will do as follows:

49/70 * 100 = 70%

Hence, 70 percentage of the meeting attendees were managers.

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Answer:

Indirect variation

Step-by-step explanation:

If two variables change in inverse proportion, then it is called indirect variation.

xy = k where k is a constant.

5*2 = 10

10*1 =10

\(15*\dfrac{2}{3}=5*2=10\\\\\\20*\dfrac{1}{2}=10\)

So, this is indirect variation.

There is no figure pic above

Step-by-step explanation:

The null and alternative hypotheses to describe the given  situation are;

Null Hypothesis; H₀: μ = 0.3

Alternative Hypothesis; Hₐ: μ < 0.3

Null and alternative hypotheses are basically parameters utilized in statistical hypothesis testing. The null hypothesis of a test is defined as one that is used to predict no effect or no relationship between variables. Meanwhile, the alternative hypothesis of a test is one that states the research prediction of an effect or relationship.

Now, we are told that the known mean weight is 0.3 lbs. However, after looking through an orchard, we see that the farmer believes that the apples might weigh less on average.

Thus, the hypotheses are defined as;

Null Hypothesis; H₀: μ = 0.3

Alternative Hypothesis; Hₐ: μ < 0.3

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The player's distance from home plate changing at that instant is 37.42 feet per second.

The distance covered by an object in unit time.

First, let's define a few variables.

t = time

x = Distance the player is from third base = 20 feet

dx/dt = Velocity the player is running towards third base = -30 fps

y = Distance between the player and home plate

dy/dt = Rate of change between the player's distance from home plate (This is the answer to our problem)

By Pythagorean theorem

y² = x² + 90²...(*)

Put x = 20

y² = 20² + 90²

y = 92.2 feet

Apply  differentiation to (*)

2ydy/dt = 2xdx/dt + 90²

And let's plug in x, y, and dx/dt to solve for dy/dt.

2(92.2)dy/dt = 2×20×-30 + 90²

dy/dt = 37.42 feet per second

Hence 37.42 feet per second  is the player's distance from home plate changing at that instant

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