please help! asap!!!

Area of the given figure composed of a rectangle and semicircle is 218.6 sq units.

If for a rectangle if the length is L and breadth is B then its area will be :

Area of a rectangle = L * B

For a circle if the radius of the circle is r then area of the circle = \(\pi r^{2}\)

Area of semicircle = area of circle/2 = \(\frac{\pi r^{2} }{2}\)

For given figure composed of a rectangle and  a semicircle.

The length and breadth of the  rectangle part is 14 and 30 respectively

Then Area = L * B = 14 * 10 = 140 square units

From the figure the diameter of the semicircle part = breadth of  rectangle , Diameter  = 10

Radius of the semicircle =   diameter/ 2 = 10 /2 = 5

therefore area of the given semicircle part =  \(\frac{\pi 5^{2} }{2}\) = (44*25)/(7*2) =78.6

Area of the given figure = area of rectangle + area of semicircle = 78.6+140 =218 .6 square units

Therefore, Area of the figure composed of a rectangle and semicircle =218.6 sq units

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Solution

- The solution steps are given below:

Final Answer

Answer:

there is one line of symmetry if you look closely at the shape

Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

We have,

To find the mean and variance of the return series, we can substitute the given model into the equation and calculate:

Mean of rt:

E(rt) = E(0.02 + 0.5rt-2 + et)

= 0.02 + 0.5E(rt-2) + E(et)

= 0.02 + 0.5 * 0 + 0

= 0.02

The variance of rt:

Var(rt) = Var(0.02 + 0.5rt-2 + et)

= Var(et) (since the term 0.5rt-2 does not contribute to the variance)

= 0.02

The mean of the return series rt is 0.02, and the variance is 0.02.

To compute the lag-1 and lag-2 autocorrelations of rt, we need to determine the correlation between rt and rt-1, and between rt and rt-2:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

Since we are given r100 = -0.01 and r99 = 0.02, we can substitute these values into the equations:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

= Cov(r100, r99) / (σ(r100) * σ(r99))

= Cov(-0.01, 0.02) / (σ(r100) * σ(r99))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

= Cov(r100, r98) / (σ(r100) * σ(r98))

To compute the 1- and 2-step-ahead forecasts of the return series at

t = 100, we use the given model:

1-step ahead forecast:

E(rt+1 | r100, r99) = E(0.02 + 0.5rt-1 + et+1 | r100, r99)

= 0.02 + 0.5r100

2-step ahead forecast:

E(rt+2 | r100, r99) = E(0.02 + 0.5rt | r100, r99)

= 0.02 + 0.5E(rt | r100, r99)

= 0.02 + 0.5(0.02 + 0.5r100)

The associated standard deviation of the forecast errors can be calculated as the square root of the variance of the return series, which is given as 0.02.

Thus,

Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

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Infinitely many position vectors with length 2 in xyz-space are orthogonal to the nonzero position vector v. (D)

A position vector in xyz-space is a vector that starts at the origin and ends at a point in xyz-space. The length of a position vector is the distance from the origin to the point it ends at.

If we want to find position vectors with length 2 that are orthogonal (perpendicular) to a given nonzero position vector v, we can use the dot product.

Let w be a position vector with length 2 that is orthogonal to v. Then, the dot product of v and w must be zero, since they are orthogonal. That is, v · w = 0. Since the length of w is 2, we can write w as 2u for some unit vector u. Thus, v · w = v · (2u) = 2(v · u) = 0.

This means that v and u are orthogonal as well, since the dot product of two vectors is zero if and only if they are orthogonal.

There are infinitely many unit vectors u that are orthogonal to v, and therefore, there are infinitely many position vectors with length 2 that are orthogonal to v. Therefore, the answer is (d) infinitely many.

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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Davis wants to pour 5 gallons of punch into ½ gallon jugs How many jugs will he need?

A. 2½

B. 5½

C. 10

D. 15

Answer:

Number of jugs = 10

Davis will need 10 jugs to pour 5 gallons of punch into ½ gallon jugs.

Step-by-step explanation:

David has 5 gallons of punch that he wants to pour into jugs.

The capacity of 1 jug is ½ gallon.

The required number of jugs may be found as

Number of jugs = gallons of punch/capacity of jug

For the given case, we have

Gallons of punch = 5

capacity of jug (in gallons) = ½ = 0.5

So, the required number of jugs is,

Number of jugs = 5/½

Number of jugs = 5/0.5

Number of jugs = 10

Therefore, Davis will need 10 jugs to pour 5 gallons of punch into ½ gallon jugs.

Answer:

a > −6

Step-by-step explanation:

Step 1: Subtract a from both sides.

2a + 6 − a > a − a

a + 6 > 0

Step 2: Subtract 6 from both sides.

a + 6 − 6 > 0 − 6

a > −6

a) the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

a) To find the probability that a randomly selected Cobalt gets more than 34 MPG, we need to calculate the area under the normal distribution curve to the right of 34 MPG.

Using the z-score formula, we can convert the MPG value to a standard score (z-score) using the formula:

z = (x - μ) / σ,

where x is the given value (34 MPG), μ is the mean (32 MPG), and σ is the standard deviation (3.5 MPG).

Calculating the z-score:

z = (34 - 32) / 3.5 = 0.57

Using a standard normal distribution table or a statistical calculator, we can find the area to the right of the z-score 0.57.

Let's assume the standard normal distribution table gives us a value of 0.2851 for z = 0.57.

Since the total area under the normal curve is 1, the probability of getting more than 34 MPG is:

P(X > 34) = 1 - P(X ≤ 34) = 1 - 0.2851 = 0.7149

Therefore, the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) When selecting a sample of 10 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√10).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √10 ≈ 1.107

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 10 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

We can again convert the value of 34 MPG to a z-score:

z = (34 - 32) / 1.107 ≈ 1.805

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 1.805.

Let's assume the standard normal distribution table gives us a value of 0.035 for z = 1.805.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) When selecting a sample of 20 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√20).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √20 ≈ 0.78

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 20 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

Similarly, we can convert the value of 34 MPG to a z-score:

z = (34 - 32) / 0.78 ≈ 2.564

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 2.564.

Assuming the standard normal distribution table gives us a value of 0.005 for z = 2.564.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

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Answer:y=4x^2+5x+1

Step-by-step explanation:

Just did the quiz on big ideas math

The equation of the parabola which passes through the points  (-2, 7) , (1, 10) , and (2, 27) is  y = (25/6)x² -(17/6)b + (1/3)c.

A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

We know equation of a parabola is y = ax² + bx + c.

Given are three points  (-2, 7) , (1, 10) , and (2, 27).

If these points lie on the parabola it must verify that \(y_o = ax^2_o + bx_o + c.\)

Therefore,

7 = a(-2)² + b(-2) + c = 0

7 = 4a - 2b + c ...(i)

10 = a(1)² + b(1) + c = 0

10 = a + b + c ...(ii)

27 = a(2)² + b(2) + c

27 = 4a + 2b + c...(iii)

Now adding eqn(i) and eqn(ii) we get 8a + 2c = 34...(iv)

Now multiplying eq(ii) by 2 and adding it to eq(i) we get 6a + 3c = 27...(v).

Now multiplying eqn(iv) by 3 and (v) by 2 and subtracting them we get a = 25/6.

Putting the value of an in eqn(iv) we get c = 1/3.

Similarly substituting the value of a and c in eqn(ii) we get b = -17/6.

∴ The equation of the parabola is y = (25/6)x² -(17/6)b + (1/3)c.

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Answer:

43.3cm

Step-by-step explanation:

Circumference = PI * diameter.

Circumference = PI * 13.8

Circumference = 43.3cm

The value of x in the given equation i.e \(\frac{16x+12}{2}=100\) is 11.825

Given that equation  \(\frac{16x+12}{2}=100\)  and asked to evaluate the value of x in the given equation

⇒ \(\frac{16x+12}{2}=100\)(given equation)

To solve the given equation, need to use the various mathematical  operations i.e division and subtraction)

⇒8x+6=100 ( using the operation division)

⇒8x=100-6 (using the operation subtraction)

⇒8x=94

⇒x=\(\frac{94}{8}\)(using the operation division)

⇒x=11.825

By using the mathematical  operations i.e division and subtraction the value of x came as 11.825

⇒Therefore, The value of x in the given equation i.e \(\frac{16x+12}{2}=100\) is 11.825

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The marginal cost in month nine is also $35.

The derivative of the cost function in relation to time indicates the additional cost of using the network for an additional unit of time, which is referred to as the marginal cost.

The cost function C(x) = 50 + 35x gives the total cost C for using the telephone network for x months

Taking the derivative of C(x) with respect to x, we get:

C'(x) = 35

This indicates that regardless of the number of months, the marginal cost remains constant at 35. To put it another way, no matter how many months have passed, using the network for an additional month always costs $35.

Therefore, the marginal cost in month nine is also $35.

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The z-score for a man who is exactly 78 inches tall is 3.214. This indicates that his height is 3.214 standard deviations above the mean height for men in the United States, which is quite unusual.

To find the z-score for a man who is exactly 78 inches tall, we first need to calculate the man's height in terms of standard deviations from the mean.

The formula for calculating the z-score is:

z = (x - μ) / σ

where x is the value we want to convert to a z-score, μ is the mean, and σ is the standard deviation.

In this case, the man's height is x = 78 inches, and the mean and standard deviation for men's heights are μ = 69 inches and σ = 2.8 inches, respectively.

Plugging these values into the formula, we get:

z = (78 - 69) / 2.8 = 3.214

Therefore, the z-score for a man who is exactly 78 inches tall is 3.214. This means that the man's height is 3.214 standard deviations above the mean height for men in the United States.

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The probability of picking a red counter is therefore; 8/25.

Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;

x = (2/3)× 24 = 16 red.

The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.

The total number of counters is therefore; 40/0.8 = 50 counters.

The probability of picking a red counter is therefore; 16/50 = 8/25.

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Answer:

3

Step-by-step explanation:

Angle 1 is a supplement of angle 2, and m angle 1 is 123 degrees. Angle 2 is a complement of angle 3. Find m angle 3.

The probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States, is approximately 0.267 or 26.7%.

To find the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States, we need to consider the percentage distribution provided in the table.

From the table, we can see that the probability of selecting a restaurant from the southwestern United States (SW) is 3%. Within the southwestern region, the probability of selecting a restaurant in a city with a population over 100,000 is given as 8%.

To calculate the conditional probability, we use the formula:

Probability (A|B) = Probability (A ∩ B) / Probability (B),

where A is the event of selecting a restaurant in a city with a population over 100,000 and B is the event of selecting a restaurant from the southwestern United States.

Applying the formula, we have:

Probability (A|B) = (Probability of selecting a restaurant in the southwestern United States with a population over 100,000) / (Probability of selecting a restaurant from the southwestern United States).

Probability (A|B) = 8% / 3%.

Simplifying, we find:

Probability (A|B) ≈ 0.267.

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Note the full question is 1) A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich. Region <10,000 Population of City 10,000 - 100,000 >100,000 NE 6% 15% 20% SE 6% 1% 4% SW 3% 12% 8% NW 0% 5% 20% What is the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States?

Answer:

$2.98

Step-by-step explanation:

x is how many units of potato salad were sold and y represents the total earnings

The main condition for a setting to be considered binomial is that the probability of success remains the same for each trial, and the other conditions include having 3 possible outcomes for each observation, no variation in outcomes based on the first success, and independence of trials from one another.

A condition for a setting to be considered binomial is that the probability of success is the same for each trial.

In order for a setting to be considered binomial, there are certain conditions that need to be met. The first condition is that the probability of success remains constant for each trial or observation. This means that the likelihood of achieving the desired outcome remains unchanged throughout the entire process.

The second condition states that each observation or trial must have exactly 3 possible outcomes. This implies that there are only three options or choices for each trial, typically categorized as success, failure, or a neutral outcome.

The third condition is that the number of outcomes should not vary based on the occurrence of the first success. This means that the probability of success is not affected or altered by the outcome of previous trials.

Lastly, the fourth condition is that the trials or observations must be independent of one another. This implies that the outcome of one trial should not impact the outcome of subsequent trials.

Therefore, the main condition for a setting to be considered binomial is that the probability of success remains the same for each trial, and the other conditions include having 3 possible outcomes for each observation, no variation in outcomes based on the first success, and independence of trials from one another.

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Answer:

x = 125

Step-by-step explanation:

x<125

Step-by-step explanation:

Multiply to remove the fraction, then set equal to 00 and solve.

Answer:

Step-by-step explanation:

3245

Answer:

\(\displaystyle \cos(\alpha+\beta)=\frac{21}{221}\)

Step-by-step explanation:

First, we can draw two right triangles to represent the given information.

Please refer to the attachment.

We will ignore the negatives for now.

The triangle on the left represents the ratio:

\(\displaystyle \tan(\alpha)=\frac{15}{8}\)

And the triangle on the right represents the ratio:

\(\displaystyle \sin(\beta)=\frac{5}{13}\)

And the unknown side, c and d, were determined using the Pythagorean Theorem.

We want to find:

\(\displaystyle \cos(\alpha+\beta), \; \pi/2<\alpha<\pi, \; \pi/2<\beta<\pi\)

So, both α and β are in QII.

Using the Sum Identity, we can write our expression as:

\(\displaystyle\cos(\alpha+\beta) =\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)\)

Now, we will use our triangles and what we know about our angles and quadrants.

Since α and β are in QII, cosine is always negative, sine is always positive, and tangent is always negative.

Now, we can use our trig ratios. Recall SohCahToa.

According to the first triangle, cos(α) is 8/17.

However, since α is in QII, cos(α) must be -8/17.

Likewise, according to the second triangle, cos(β) is 12/13.

Since β is in QII, cos(β) is -12/13.

Now, we can determine our sine ratios.

According to the first triangle, sin(α) is 15/17.

And since α is in QII, this stays positive.

And, sin(β), as given to us, is 5/13.

Therefore, we will substitute this into our equation. So:

\(\displaystyle \cos(\alpha+\beta)=(-\frac{8}{17})(-\frac{12}{13})-(\frac{15}{17})(\frac{5}{13})\)

Evaluate:

\(\displaystyle \cos(\alpha+\beta)=\frac{96}{221}-\frac{75}{221}\)

Hence:

\(\displaystyle \cos(\alpha+\beta)=\frac{21}{221}\)

The height of the cone in discuss as required to be determined is; 16.38 cm.

Since the height of the cone is three times the length of the diameter of its base;

h = 3d;

d = h/3

Therefore, radius,

r = d/2

r = h/3 ÷ 2

multiply by the reciprocal of 2

r = h/3 × 1/2

r = h / 6.

Volume of a cone, V = (1/3) πr²h

128 = (1/3) × (22/7) × (h³/36)

h³ = 4398.55

h = 16.38 cm.

Ultimately, the height of the cone is; 16.38 cm.

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Answer:

C

Step-by-step explanation:

Variability refers to the spread or dispersion of the data points in a dot plot. The greater the variability, the wider the spread of the data points.

Here is the list of the four dot plots in order of variability from least to greatest:

1. Dot Plot A: This plot has the least variability, meaning the data points are closely clustered together. The range of the data is small, indicating a low spread.

2. Dot Plot B: This plot has slightly more variability than Dot Plot A. The data points are still relatively close, but the range is slightly wider.

3. Dot Plot C: This plot has a higher variability compared to Dot Plots A and B. The data points are spread out more, indicating a wider range.

4. Dot Plot D: This plot has the greatest variability among the four. The data points are widely dispersed, indicating a large range.

Remember, when comparing dot plots, it is important to consider the range and spread of the data points to determine the order of variability from least to greatest.

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Answer: Please see explanation column for answer.

x= -36

Step-by-step explanation:

Step 1

from the attachment, Mai's solving is given as

1/3 (1/2x- 9) = 1/2 (x+18)

1/6x-3= 1/2x+9

1/4x-3=9

1/4x=12

x=48

Mai's error started when he subtracted wrongly 1/2 x from 1/6x which gave him 1/4 x instead of - 1/3 x.

Solving correctly, we have that

1/3(1/2x-9) = 1/2(x+18)

1/6x -3= 1/2x+ 9

taking like terms to like terms

1/6x-1/2x= 9+3

(1-3)/6x= 12

-2/6x= 12

-1/3x= 12

multiplying both sides by -3

-1/3x X -3 = 12 X -3

x= -36

Answer: area of triangle = 1/2 base*height  = 1/2  * 2 x 10   = 10 ft2   each

then you are left with a rectangle   13 ft x 10 ft = 130 ft^2

130 + 10 + 10 = 150 ft2

Step-by-step explanation: Hope it helps

The equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

What is the rate?

A rate is a measure of the amount of change of one quantity with respect to another quantity. It is expressed as a ratio of two different units, and it indicates how fast or slow one quantity is changing in relation to another quantity.

If we assume that a person's height decreases by 0.06 cm per year starting at age 30,

we can use the following equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

where h(30) represents the person's height at age 30.

This equation assumes that the rate of height decrease is constant and linear over time.

Hence, the equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

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Answer:

32.

Step-by-step explanation:

39 - 7 = 32

32 + 7 = 39

Brielle scored 32 points.

I hope this helped! :) Have a nice day.

Note that the proof that ΔABC ≅ ΔEDC is given as follows:

According to the ASA rule, if any two angles and sides included between the angles of one triangle are comparable to the corresponding two angles and sides included between the angles of the second triangle, the two triangles are said to be congruent.

Thus, given the above statements, it is clear that ΔABC ≅ ΔEDC

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Full Question:

Angle BAC is congruent to Angle DEC: Given

C is the midpoint of AE: Given

Prove triangle ABC is congruent to triangle EDC

What are the statements and reasons for this proof?