How to slove this proof ?

Answer:

207.345

Step-by-step explanation:

Formula: A=2πrh+2πr2

Work : 2·π·3·8+2·π·32≈207.34512

Answer:  207.351 [tex]m^{2}[/tex]

Step-by-step explanation:

Surface Area is = Lateral Area + 2(Base Area)

LA = Ph       P, perimeter = C= 2[tex]\pi r[/tex]    r = 3m

                                           P= 2[tex]\pi 3[/tex]

                                            P= 18.849

                     h=8

LA = 18.849(8)

   =150.7964  This is the lateral area

B= [tex]\pi r^{2}[/tex]   Trying to find the Base area from original formula

=[tex]\pi 3^{2}[/tex]

=28.274

Put it all together

SA = LA+2B

=150.345+2(28.274)

=207.351 [tex]m^{2}[/tex]

The area of the composite figure is equal to 294.491 square meters.

In this problem we find the representation of a composite figure formed by a circular sector and an isosceles triangle. The area formulas for each case are shown below:

Circular sector

A = π · (α / 360) · r²

Triangle

A = 0.5 · (2 · r · sin 0.5α) · (r · cos 0.5α)

A = r² · sin 0.5α · cos 0.5α

Where:

A = π · (230 / 360) · (11.1 m)² + (11.1 m)² · sin 65° · cos 65°

A = 294.491 m²

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The modulus of rupture (MOR) can be calculated by dividing the maximum load by the section modulus. The section modulus for a rectangular cross-section is (width * height^2)/6.

In this case, the width is 2 inches and the height is 4 inches, so the section modulus is (2 * 4^2)/6 = 5.33 in^3. Therefore, the MOR = 240 kips / 5.33 in^3 = 45 kpsi.

The apparent modulus of elasticity (MOE) can be calculated using the formula MOE = (F * L^3) / (4 * h * d^3 * delta), where F is the maximum load, L is the span length, h is the height of the wood, d is the depth of the wood, and delta is the deflection at mid-span. Plugging in the values given, we get MOE = (240 kips * 4^3) / (4 * 4 * 2^3 * 2.4 in) = 1,333 kpsi. Therefore, the apparent MOE for the 2 * 4 wood lumber is 1,333 kpsi.

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Answer:

5, 6, 7

Step-by-step explanation:

This question deals with linear equetion.

Let the first no. x , the 2nd one x + 1 and the 3rd no. will be x + 2 .

we have given that 3 consucetive sum are 18 so we write this equetion as

x + x + 1 + x + 2 = 18

3x + 3 = 18

3x = 18 - 3

3x = 15

3x/3 = 15/3

x = 5

so the 1st no. is 5

the 2nd no. is 5 + 1 = 6

the 3rd no. is 5 + 2 = 7

and the no. is 5, 6, 7

The correct generalization about the height of the trees is given as follows:

The IQR is 160 feet. The middle half of cedar trees have heights that vary by 160 feet at most.

The ordered heights of the trees are given as follows:

16, 40, 49, 130, 200, 210.

The data-set is divided into two halves, as follows:

The quartiles are given as follows:

The interquartile range represents how much the middle 50% of elements vary, and is the difference of the third quartile by the first quartile, hence:

IQR = 200 - 40 = 60.

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The parallelogram is a rhombus because all it's angle and sides are equal.

A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. The properties of rhombus include;

1. All sides are equal in length.

2. Opposite angles are equal in a rhombus.

3. The diagonals bisect each other at 90 degrees.

4. Adjacent angles add up to 180 degrees.

Therefore since angle DCE = angle FCE

this means that angle FEC = DEC and thus angle D = angle F.

Therefore, we can say that the parallelogram is a rhombus because al it's sides and angles are equal.

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The number of ways we can pick five students for a student council if we have twelve people running would be 792 ways.

The formula needed to calculate the number of possible ways for a student council consisting of five individuals, from a pool of twelve candidates, is the combination equation.

n choose k = n! / (k! x (n - k)!)

= 12 ! / ( 5 ! ( 12 ! - 5 ) !)

= 12 ! / ( 5 ! x 7 !)

= 792 ways

Thus, it has been determined that there exist 792 feasible options for selecting members for this student council out of the aforementioned dozen contestants.

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Answer:

17550

Step-by-step explanation:

I am pretty sure you multiply them all together. If not sorry.

Answer:  344 yd²

Step-by-step explanation:

You can find the Area of the full block and then subtract the portion on the top right thats cut out

A(full block)=LA+2B          P= 9+9+16+16=50    h=10     B=(9)(16)

= Ph+2B              P, perimeter of Base;   h, height    B, area of base

=(50)(10)+2(144)

=788 yd²

A(cut out) = LA +2B         P=13+13+4+4=34     h=10   B=(13)(4)=52

=Ph +2B

=34(10)+2(52)

=444 yd²

Now subtract the 2 areas and that will give you your shape

A(shape)=A(full block)-A(cut out)

A(shape)= 788-444=344 yd²

To generate 25 random variates from this distribution using VLOOKUP, you can follow these steps:

1. Create a table with two columns - "Cumulative Probability" and "Demand".
2. In the "Cumulative Probability" column, list the cumulative probabilities for each demand value. To do this, add up the probabilities for all demand values up to and including the current demand value. For example, for demand value 1, the cumulative probability would be 0.4 (0.2 + 0.2).
3. In the "Demand" column, list the demand values.
4. Use the VLOOKUP function to generate the random variates. For each variate, use the RAND() function to generate a random number between 0 and 1, and then use VLOOKUP to find the corresponding demand value based on the cumulative probability. For example, if the random number is 0.3, and the cumulative probability for demand value 2 is 0.7, then the VLOOKUP function would return a demand value of 2.

Here's an example of how the table and VLOOKUP formula would look:

| Cumulative Probability | Demand |
|-----------------------|--------|
| 0.4                   | 1      |
| 0.7                   | 2      |
| 1.0                   | 3      |
| 1.0                   | 4 or more |

Assuming the table is in cells A1:B4, the VLOOKUP formula for the first variate would be:

=VLOOKUP(RAND(), A1:B4, 2, TRUE)

This will generate a random variate from the distribution. Copy and paste the formula into 24 more cells to generate a total of 25 variates.

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Answer:

  (c)  Reflection across x = -2

Step-by-step explanation:

You want to know the line of reflection that causes VWYZ to be mapped to V'W'Y'Z' as shown in the attached figure.

The line of reflection is the perpendicular bisector of the segment joining a point and its image.

The midpoint of VV' is ((-11, 2) +(7, 2))/2 = (-4, 4)/2 = (-2, 2). The line VV' has the same y-coordinate at both ends, so is a horizontal line. Its perpendicular bisector is the vertical line through (-2, 2), which is the line ...

  x = -2 . . . . . choice C

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To organize the information about summer jobs available for college students in my area, I could use a spreadsheet as my data set.

(a) The cases would be each job opportunity available for college students in the area.

(b) The variables would include:
- Job Title
- Company Name
- Job Description
- Pay Rate
- Location
- Required Skills/Qualifications

The possible values for each variable would depend on the specific jobs available.

(c) The variables "Job Title," "Company Name," "Location," and "Required Skills/Qualifications" would be categorical variables, as they involve categories or labels. The variables "Job Description" and "Pay Rate" would be quantitative variables, as they involve numerical values.

(d) I would label this data set as "Summer Jobs for College Students in [Name of Area]." I chose this label to clearly indicate the focus of the data set.

(e) The key characteristics of this data set would include the job title, company name, job description, pay rate, location, and required skills/qualifications for each summer job available for college students in the area. By organizing this information, students can compare and contrast job opportunities to find the best fit for their skills and needs.

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Answer:

516.99

Step-by-step explanation:

i just answered it and it told me the correct answer after i did it

Therefore, there are 45 different combinations of meals that Yann and Camille can order if they refuse to order the same dish.

This problem involves counting the number of ways two people can choose different dishes from a menu of 10 items, without repeating any dish. To solve this problem, we can use the formula for combinations, which is given by:

C(n, k) = n!/[(n-k)! k!]

where n is the total number of items, and k is the number of items we want to choose. In this case, we want to choose 2 items from a menu of 10, so we have:

C(10, 2) = 10!/[(10-2)! 2!]

= (10 x 9)/2

= 45

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The generalization about cedar trees is that the height of cedar trees varies from the mean by an average of 107.5

Average is the quotient obtained by dividing the sum total of a set of figures by the number of figures.

The IQR is the inter quartile range of a data. This means 50% of the data is the inter quartile range.

This means 50/100 × 492

= 246

The range is the difference between the largest and smallest

Range = 210 -16

= 194

Average = sum of height/ number of trees

= 210+16+40+130+49+200

= 107.5

therefore the average height of cedar tree is 107.5

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Probability is a measure of the likelihood of an event occurring.

A. To find how many foreclosures to expect, we can use the expected value formula: E(X) = np, where X is the number of foreclosures, n is the number of loans, and p is the foreclosure rate. Substituting the given values, we have E(X) = (300)(1/136) ≈ 2.21. Therefore, we can expect about 2 foreclosures last month.

B. To find the probability of exactly two foreclosures, we can use the Poisson distribution with parameter λ = E(X) = 2.21. The probability mass function of the Poisson distribution is given by P(X = k) = (e^(-λ) * λ^k) / k!, where k is the number of foreclosures. Substituting k = 2 and λ = 2.21, we have P(X = 2) = (e^(-2.21) * 2.21^2) / 2! ≈ 0.244. Therefore, the probability of exactly two foreclosures is about 0.244.

C. To find the probability of at least one foreclosure, we can use the complement rule: P(X ≥ 1) = 1 - P(X = 0). Since the foreclosure rate is one out of every 136 loans, the probability of not having a foreclosure in a single loan is (135/136). Therefore, the probability of not having a foreclosure in 300 loans is (135/136)^300 ≈ 0.427. Substituting this value into the complement rule, we have P(X ≥ 1) = 1 - 0.427 ≈ 0.573. Therefore, the probability of at least one foreclosure is about 0.573.

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The probability of getting a large or blueberry smoothie is 7/15.

The probability is calculated based on the following assumptions:

Probability of getting a large smoothie = 1/3

Probability of getting a blueberry smoothie = 1/5

P(large and blueberry) = P(large) * P(blueberry)

P(large and blueberry) = (1/3) * (1/5)

P(large and blueberry) = 1/15

P(large or blueberry) = P(large) + P(blueberry) - P(large and blueberry)

P(large or blueberry) = 1/3 + 1/5 - 1/15

P(large or blueberry)  = 7/15

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Using the definite integral, it is determined that the driver is 108 miles from his home at 1:00 PM.

We need to find the distance travelled by the driver between 11:00 AM and 1:00 PM.

The velocity of the driver is given by v(t) = 54t − 24t^2.

We can find the distance travelled by finding the definite integral of v(t) with respect to t, between 0 and 2 (since the driver leaves at 11:00 AM and we need to find the distance travelled by 1:00 PM, which is 2 hours later).

[tex]\int\limits^0_2[/tex]v(t) dt   =    [tex]\int\limits^0_2[/tex](54t − 24t²) dt

= [27t² - 8t³] between 0 and 2

= [27(2)² - 8(2)³] - [27(0)² - 8(0)³]

= 108 - 0

= 108 miles

Therefore, the driver is 108 miles away from his home at 1:00 PM.

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The sample standard deviation of the heights (in inches) of 10 adult males is approximately 1.464 inches.

To find the sample standard deviation of the heights of the 10 adult males, follow these steps:

1. Calculate the mean (average) height:

(70+72+71+70+69+73+69+68+70+71) / 10 = 703 / 10 = 70.3 inches.

2. Subtract the mean from each height and square the result:

[tex][(70-70.3)^2, (72-70.3)^2, ... (71-70.3)^2].[/tex]

3. Calculate the sum of these squared differences:

0.09+2.89+0.49+0.09+1.69+7.29+1.69+5.29+0.09+0.49 = 19.31.

4. Divide the sum by (n-1), where n is the sample size: [tex]19.31 / (10-1) = 19.31 / 9 = 2.145.[/tex]
5. Take the square root of the result: √2.145 = 1.464 (rounded to 3 decimal places).

The sample standard deviation of the heights of the 10 adult males is approximately 1.464 inches.

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Answer:

ANSWER: 59/ 60

Step-by-step explanation:

What should be subtracted to get 1 / 2 ?( 3 / 4 + 1 / 3 + 2 / 5 )

to get 1 / 2A.3 / 4 = 3.00 ÷ 4 = .75 *.1 / 3 = 1.000 ÷ 3 = .333 * .2 / 5 = 2.0 ÷ 5 = .4 * ..75 + .33 + .4 = 1.48…75+.33.40 == 1.48 *OR3 / 4 = 45 / 60+1 /3 = 20 / 602 / 5 = 24 / 60 ======== 89 / 60 = 1 29/601 29 /60 = 1 29/60 === 0 89/60—0 1/2 ==== 0 30/ 60=—0 30/60 =====================0 59/ 60

The slope of the line is -3. The equation of the line is expressed as: y = -3x + 7.

The equation, y = mx + b, if the slope-intercept form of any straight line, where:

m is the slope = change in y / change in x = rise / run

b is the y-intercept or the point on the y-axis that the line cuts across.

From the graph, we know that:

b = 7 (y-intercept)

Slope (m) = rise/run = -3/1

Slope (m) = -3

Therefore, the equation of the line would be:

y = -3x + 7

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The area of the figure attached is 15 square meters

The figure is a parallelogram and area of a parallelogram is solved using the formula

= base x height

Information given in the problem includes:

base = 5 m

height = 3 m

plugging in the values in to the formula for area for area of a parallelogram will result to

= 5 m x 3 m

= 15 square meters

Hence the area of the parallelogram  attached is 15 square meters

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[A] This is likely because bedrooms, bathrooms, and the living area are all roughly measuring the same thing: the size of the property.

The most likely explanation for the negative coefficient for BEDROOMS is option A - a multicollinearity problem with the model. This means that the variables included in the model (bedrooms, bathrooms, and living area) are highly correlated with each other, making it difficult to distinguish their individual effects on the selling price. As a result, the coefficient for BEDROOMS may be affected and appear counterintuitive.

[A] This is likely because bedrooms, bathrooms, and living area are all roughly measuring the same thing: The size of the property.

The negative coefficient for bedrooms could be a result of multicollinearity, where the predictor variables (bedrooms, bathrooms, and living area) are highly correlated. In this case, they are all related to the property's size, making it difficult for the model to distinguish their individual effects on the selling price.

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The width of the original piece of sheet metal is (w^2 - l^2)/(3w + 3l), and the length is (l^2 - w^2)/(3w + 3l).

To solve this problem, we can use the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.

First, let's find the height of the box. Since we cut squares from each corner, the height of the box is the length of the square that was cut out. Let's call this length x.

The width of the box is the original width minus the lengths of the two squares that were cut out, which is w - 2x.

Similarly, the length of the box is the original length minus the lengths of the two squares that were cut out, which is l - 2x.

Now we can write the volume of the box in terms of x, w, and l:

V = (w - 2x)(l - 2x)(x)

Expanding this expression, we get:

V = x(4wl - 4wx - 4lx + 8x^2)

Simplifying further:

V = 4x^3 - 4wx^2 - 4lx^2 + 4wlx

To find the dimensions of the original piece of sheet metal, we need to maximize this volume. We can do this by taking the derivative of the volume with respect to x and setting it equal to zero:

dV/dx = 12x^2 - 8wx - 8lx + 4wl = 0

Solving for x, we get:

x = (2wl)/(3w + 3l)

Now we can use this value of x to find the width and length of the original piece of sheet metal:

w - 2x = w - 2(2wl)/(3w + 3l) = (w^2 - l^2)/(3w + 3l)

l - 2x = l - 2(2wl)/(3w + 3l) = (l^2 - w^2)/(3w + 3l)

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Hey ⊂hcpsibekweou⊃

Answer:

( 6 , 2 )

Step-by-step explanation:

Based on the image we can see that P' is in quadrant 4.

Coordinate plane:

As you may know reflection is known as a flip.

For example: (-5, 4) in quadrant 1  reflects to ( -5, -4 ) quadrant 3.

From the given we can see that P' is (6, -2 ),    Therefore the reflection of             ( 6, - 2) is ( 6 , 2 ).

xcookiex12

4/19/2023

The values of angle N in the triangle is 71.3 degrees

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

l = 6.9 cm, m = 8.1 cm and n=8.8

Using the law of cosine, we have

n^2 = l^2 + m^2 - 2lmCos(N)

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

8.8^2 = 6.9^2 + 8.1^2 - 2 * 6.9 * 8.1Cos(N)

So, we have

- 2 * 6.9 * 8.1Cos(N) = -35.78

This gives

Cos(N) = 0.32

Evaluate and take the arc cos

N = 71.3 degrees

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Therefore, the 90% confidence interval for μ1 - μ2 is -1 ± 1.74 years, which means that we are 90% confident that the true difference in mean ages between registered Republicans and Democrats is between -2.74 years and 0.74 years.

To find the confidence interval for the difference of means, we can use the following formula:

(X1 - X2) ± t*√(s1²/n1 + s2²/n2)

where X1 and X2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and t is the critical value from the t-distribution with (n1 + n2 - 2) degrees of freedom and the desired level of confidence.

We are given:

X1 = 39 years

s1 = 8 years

n1 = 128

X2 = 40 years

s2 = 10 years

n2 = 200

90% confidence level

First, we need to calculate the pooled standard deviation:

sp = √(((n1-1)*s1² + (n2-1)*s2²) / (n1+n2-2))

sp = √(((128-1)*8² + (200-1)*10²) / (128+200-2))

sp = 9.29

Next, we calculate the t-value:

t = invT(0.05, 327)

t = 1.66

where invT is the inverse t-distribution function with (n1+n2-2) degrees of freedom and a one-tailed area of 0.05 (since we want a 90% confidence interval, which corresponds to a one-tailed area of 0.05).

Finally, we can calculate the confidence interval:

(X1 - X2) ± T√(s1²/n1 + s2²/n2)

(39 - 40) ± 1.66√(8²/128 + 10²/200)

-1 ± 1.74

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Complete question:

A political analyst was curious if younger adults were becoming more conservative. He decided to see if the mean age of registered Republicans was lower than that of registered Democrats. He selected an SRS of 128 registered Republicans from a list of registered Republicans and determined the mean age to be = 39 years, with a standard deviation s1 = 8 years. He also selected an independent SRS of 200 registered Democrats from a list of registered Democrats and determined the mean age to be = 40 years, with a standard deviation s2 = 10 years. Let μ1 and μ2 represent the mean ages of the populations of all registered Republicans and Democrats, respectively. Suppose that the distributions of age in the populations of registered Republicans and of registered Democrats have the same standard deviation. Assume the pooled two-sample t procedures are safe to use. A 90% confidence interval for μ1 – μ2 is: –1 ± 1.66 years. 1 ± 2.76 years. –1 ± 1.74 years. –1 ± 1.98 years.

Answer:

4. 8.25

Step-by-step explanation:

x/5.25=6.6/4.2

Cross Multiply
4.2x=34.65

Divide

8.25

To compute Paasche's index for 2018 using 2010 as the base period, we need to use the formula:

Paasche's index = (current year prices * current year quantities) / (base year prices * current year quantities)

Using the given information, we have:

For Margarine:
- Current year prices: $2.00
- Current year quantities: 26
- Base year prices: $0.81
- Base year quantities: 20

Paasche's index for Margarine = (2.00 * 26) / (0.81 * 20) = 2.54

For Shortening:
- Current year prices: $1.88
- Current year quantities: 8
- Base year prices: $0.84
- Base year quantities: 1

Paasche's index for Shortening = (1.88 * 8) / (0.84 * 1) = 17.71

For Milk:
- Current year prices: $2.89
- Current year quantities: 63
- Base year prices: $1.44
- Base year quantities: 74

Paasche's index for Milk = (2.89 * 63) / (1.44 * 74) = 2.26

For Potato chips:
- Current year prices: $3.99
- Current year quantities: 34
- Base year prices: $2.91
- Base year quantities: 28

Paasche's index for Potato chips = (3.99 * 34) / (2.91 * 28) = 1.87

Therefore, the Paasche's index for 2018 using 2010 as the base period is:

Paasche's index = (2.54 + 17.71 + 2.26 + 1.87) / 4 = 6.34 (rounded to 2 decimal places)

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The requried arc length of DF is given as 66°.

A circle with tangent and secant pair is shown, we have to determine the arc  DF.

The angle between the tangent and secant of the circle is given as:

∠E= DG - DF/2

Substitute the value in the above expression,
24 = 114 - x/2
48 = 114 - x
x = 114 - 48
x = 66°

Thus, the requried arc length of DF is given as 66°.

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