The diagram shows a star made by surrounding a
regular octagon with triangles.
Explain why angle a must be 135°.
a

Answer:

m∠x = 98°

Step-by-step explanation:

Step 1: Find the supplementary angle in the triangle

180 - (53 + 45) = 82

Step 2: Use Supplementary Angles to solve for x

180 - 82 = 98°

The adjusted forecast for the year 2022, Period 1 is $318.92. The adjusted forecast for future periods can be obtained by dividing the forecast of the future period by the seasonal index of the corresponding period.

Given the linear regression trend line equation for the de-seasonalized data (Unadjusted) and Seasonality Index table as:

1. Ft = 160+4t (The linear regression trend line equation for the de-seasonalized data (Unadjusted))

2. The Seasonality Index table Year

Period2021

period 12021

period 22021

period 316171818

Seasonality Index (SI) 0.741.420.920

The formula to calculate the adjusted forecast for future periods: Adjusted Forecast (Ft) = Ft / SI

The adjusted forecast for future periods can be obtained by dividing the forecast of the future period by the seasonal index of the corresponding period. Therefore, the adjusted forecast in year 2022 for Period 1 can be calculated as follows:

Ft = 160 + 4t

Ft for the year 2022 = 160 + 4 x 19 (t = 19 for the year 2022),

Ft for the year 2022 = 160 + 76 = 236

Adjusted Forecast (Ft) = Ft / SI

Ft for the year 2022 = 236

Seasonality Index for period 1 = 0.74

Adjusted Forecast (Ft) = 236 / 0.74 = 318.92.

The adjusted forecast for the year 2022, Period 1 is $318.92.

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Answer: 8x + 48y - 40

Step-by-step explanation:

Rearrange The Terms

-8(-6y - x + 5)

-8(-x - 6y + 5)

Distribute Them

-8(-x - 6y + 5)

=8x + 48y - 40

The answer of the given question based on the Voltage drop the answer is , the voltage dropped across R3 is 277.11 V.

Ohm's law is  fundamental principle in electrical engineering and physics that describes  relationship between voltage, current, and resistance in  electrical circuit. It states that current through conductor between two points is directly proportional to voltage across  two points, and inversely proportional to resistance between them.

To determine the voltage dropped across R3, we need to use Ohm's law and Kirchhoff's circuit laws. First, we can calculate the total resistance in the circuit:

Rtotal = R1 + R2 || R3

R2 || R3 = (R2 * R3) / (R2 + R3) (parallel resistance formula)

Rtotal = R1 + (R2 || R3)

Rtotal = 152 + ((18 * 362) / (18 + 362))

Rtotal = 149.89 Ω (rounded to 2 decimal places)

Next, we can use Ohm's law to calculate the current flowing through the circuit:

I = ET / Rtotal

I = 120 / 149.89

I = 0.8004 A (rounded to 4 decimal places)

Finally, we can use Kirchhoff's voltage law to determine the voltage dropped across R3:

ET = IR1 + IR2 || IR3 + IR3

ET = I(R1 + R2 || R3) + IR3

ET - I(R1 + R2 || R3) = IR3

R3 = (ET - I(R1 + R2 || R3)) / I

R3 = (120 - (0.8004 * (152 + ((18 * 362) / (18 + 362))))) / 0.8004

R3 = 277.11 V (rounded to 2 decimal places)

Therefore, the voltage dropped across R3 is 277.11 V.

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Answer: 4²

Step-by-step explanation:

There is some rule but just remember:

1. parenthesis

2. exponents

3. division/multiplication

4. subtraction/addition

Answer:

18 units

Step-by-step explanation:

A picture of what it would look like is at the bottom.

You know that the legs are equal because it's isosceles, so AB = AC. This means:

\(4x - 14 = x + 10\\3x - 14 = 10\\3x = 24\\x = 8\)

using the rules of solving an equation.

The length of one leg is:

\(x + 10\\8 + 10\\18\)

Answer:

12 nickels

21 dimes

16 quarters

Step-by-step explanation:

9 extra dimes : 9 x 10 = 90

4 extra quarters : 4 x 25 = 100

total of the extras : 100 + 90 = 190

remaining amount: 670 - 190 = 480

remaining amount are made up of equal number of nickel, dimes and quarters, thus

5 + 10 + 25 = 40 ( 1 set of each type)

480 / 40 = 12 sets

therefore there are

12 nickels

12 + 9 = 21 dimes

12 + 4 = 16 quarters

An example of a pyramid and a prism that have the same base and volume is a triangular pyramid and a triangular prism with congruent bases and heights.

Let's consider a triangular pyramid and a triangular prism with congruent bases and heights. Both shapes have a triangular base, meaning their base area is the same. The volume of a pyramid is given by the formula V = (1/3) * base area * height, whereas the volume of a prism is calculated as V = base area * height.

Since the bases of the pyramid and prism are congruent, their base areas are equal. In order for the pyramid and prism to have the same volume, the height of the pyramid must be three times the height of the prism. This is because the volume of a pyramid is one-third of the volume of a prism with the same base and height.

By choosing a triangular pyramid and a triangular prism with congruent bases and heights, we ensure that the base area and the height are the same for both shapes. Therefore, their volumes will also be equal.

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Answer:

16.5

Step-by-step explanation:

Answer:

33/2

Step-by-step explanation:

The length of the path described by the parametric equations

 is 3/2units.

We can find the length of the path described by the parametric equations x=cos³t and y=sin³t by using the arc length formula.

The arc length formula for a parametric curve given by:

x=f(t) and y=g(t) is given by:

L = ∫[a,b] √[f'(t)² + g'(t)²] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t), respectively.

In this case, we have:

x = cos³t, so x' = -3cos²t sin t

y = sin³t, so y' = 3sin²t cos t

Therefore,

f'(t)² + g'(t)² = (-3cos²t sin t)² + (3sin²t cos t)²

= 9(cos⁴t sin²t + sin⁴t cos²t)

= 9(cos²t sin²t)(cos²t + sin²t)

= 9(cos²t sin²t)

Thus, we have:

L = ∫[0,2π] √[f'(t)² + g'(t)²] dt

= ∫[0,2π] √[9(cos²t sin²t)] dt

= 3∫[0,2π] sin t cos t dt

Using the identity sin 2t = 2sin t cos t, we can rewrite the integral as:

L = 3/2 ∫[0,2π] sin 2t dt

Integrating, we get:

L = 3/2 [-1/2 cos 2t] from 0 to 2π

= 3/4 (cos 0 - cos 4π)

= 3/2

Therefore, the length of the path described by the parametric equations x=cos³t and y=sin³t is 3/2 units.

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The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is given as follows:

(1.9, 2.3).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 80% confidence interval, with 18 - 1 = 17 df, is t = 1.33.

The parameters are given as follows:

\(\overline{x} = 2.1, s = 0.74, n = 18\)

The lower bound of the interval is given as follows:

2.1 - 1.33 x 0.74/sqrt(18) = 1.9.

The upper bound of the interval is given as follows:

2.1 + 1.33 x 0.74/sqrt(18) = 2.3.

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Answer:

Step-by-step explanation:

Pls check

(Is this question not too complex)

Ask the questions one-by-one.

If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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a) The sample mean height of the 10 randomly selected students is 69.8 inches.

b) The margin of error at 90% confidence level is approximately 4.26 inches.

c) The 90% confidence interval is approximately (65.54 inches, 74.06 inches), meaning we are 90% confident that the true population mean height of all 9th grade students at the high school lies within this range.

a) The sample mean can be calculated by adding up all the heights and dividing by the sample size

x¯ = (72+71+65+73+65+71+74+63+73+65) / 10

= 698 / 10

= 69.8 inches

Therefore, the sample mean height of the 10 randomly selected students is 69.8 inches.

b) The margin of error at 90% confidence level can be calculated using the formula:

Margin of error = z× (σ/√n)

where z* is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

For a 90% confidence level, the z-score is 1.645 (from standard normal distribution table). Plugging in the values:

Margin of error = 1.645 × (6 / √10)

≈ 4.26 inches

Therefore, the margin of error at 90% confidence level is approximately 4.26 inches.

c) The 90% confidence interval can be calculated as

x¯ ± margin of error

Substituting the values obtained in (a) and (b)

Lower limit = 69.8 - 4.26

≈ 65.54 inches

Upper limit = 69.8 + 4.26

≈ 74.06 inches

Therefore, the 90% confidence interval is approximately (65.54 inches, 74.06 inches). This means we are 90% confident that the true population mean height of all 9th grade students at the high school lies within this range.

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Answer:

Mark:

x + y + z = 10

Jessica:

5x + 2y + 3z = 28

Nate:

3x + 3y + z = 20

Step-by-step explanation:

Let

x = number of pop song downloaded by Mike

y = number of rock song downloaded by Mike

z = number of hip song downloaded by Mike

Mark downloaded 10 songs in total consisting of pop, rock, and hip hop

Mark:

x + y + z = 10

Jessica downloaded five times as many pop songs, twice as many rock schgs, and three times as many hip hop songs as Mark. She downloaded 28 songs total.

Jessica:

5x + 2y + 3z = 28

Nate downloaded 20 songs total with three times as many pop songs, three times as many rock songs, and the same number of hip hop songs as Mark.

Nate:

3x + 3y + z = 20

The following system of equations represents their music choices

Mark:

x + y + z = 10

Jessica:

5x + 2y + 3z = 28

Nate:

3x + 3y + z = 20

Answer:

Mark:

x + y + z = 10

Jessica:

5x + 2y + 3z = 28

Nate:

3x + 3y + z = 20

Step-by-step explanation:

Let

x = number of pop song downloaded by Mike

y = number of rock song downloaded by Mike

z = number of hip song downloaded by Mike

Mark downloaded 10 songs in total consisting of pop, rock, and hip hop

Mark:

x + y + z = 10

Jessica downloaded five times as many pop songs, twice as many rock schgs, and three times as many hip hop songs as Mark. She downloaded 28 songs total.

Jessica:

5x + 2y + 3z = 28

Nate downloaded 20 songs total with three times as many pop songs, three times as many rock songs, and the same number of hip hop songs as Mark.

Nate:

3x + 3y + z = 20

The following system of equations represents their music choices

Mark:

x + y + z = 10

Jessica:

5x + 2y + 3z = 28

Nate:

3x + 3y + z = 20

Step-by-step explanation:

Answer:

A- 95.53 $         B- 47.35 $     C- 48.18 $

Step-by-step explanation:

45.00+35.75=80.75 (The money Sergio Pappas earned by working.)

80.75+14.78=95.53 (Sergio Pappas money earned by working + initial money.)

25.23+22.12=47.35 (Total money lost by Sergio Pappas.)

95.53-47.35=48.18 (Total money left by Sergio Pappas over the weekend.)

a higher percentage of males (48.4%) favor decriminalization compared to females (46.1%). Thus, males are more likely to favor the decriminalization of prostitution based on the given data.

BasedBased on the percentages calculated, males are more likely to favor the decriminalization of prostitution compared to females.

For males, out of the total sample size of 62, 30 individuals favor decriminalization, which represents approximately 48.4% of male respondents.

For females, out of the total sample size of 76, 35 individuals favor decriminalization, which represents approximately 46.1% of female respondents.

Therefore, a higher percentage of males (48.4%) favor decriminalization compared to females (46.1%). Thus, males are more likely to favor the decriminalization of prostitution based on the given data.

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Answer:

what do you mean

Step-by-step explanation:

Answer:

6 - 2t < -4

Step-by-step explanation:

:)

Answer:

\(-33c+22d\)

Step-by-step explanation:

\(-11(3c-2d)\\\\(-11)(3c)+(-11)(-2d)\\\\-33c+22d\)

The value of the dependent variable a is always one-half the value of the independent variable c.

A variable that is dependent will always change when the independent variable changes.

On the other hand, the variable that brings changes to the dependent variable and is called the independent variable.

Given that the relation between the number of children, c and the number of adults, a, is represented by the table, we can see that:

k = a/e = 1/2 = 3/6 = 5/10 = 7/14 = 9/18 = 1/2.

Thus, the equation of the relationship can be modelled as a = 1/2(c).

This therefore means that, a is always one-half of the value of c.

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Answer:

40 m

Step-by-step explanation:

A rhombus is a quadrilateral whose four sides all have the same length.

The perimeter of the rhombus will be the total addition of the lengths of the four  sides or rather, since a rhombus has all its four sides equal, then its perimeter will be 4 times the length of one of the sides.

side length = 10 m

perimeter =  10 x 4 = 40 m

Answer:

9 times larger and 9 times smaller (it changes by the square of the change factor of the radius).

Step-by-step explanation:

the reason :

the formula of the volume of a cone is base area times height divided by 3.

and the base area is the area of a circle with radius r.

=> Vc = pi×r²×height / 3

now, when we multiply r by a factor, like in our examples here by 3 and also by 1/3, then this factor also gets squared in the calculation of that formula.

so, if the new radius is 3×r, then the formula looks like

Vc = pi×(3r)²×height / 3 = pi×9r²×height / 3

so, as you can see, when we triple the radius, we introduce the factor 9 (square of 3) into the volume, and therefore the volume increases by the factor 9.

similar, when we divide the radius by 3

Vc = pi×(r/3)²×height / 3 = pi×(r²/9)×height / 3

we introduce the factor 1/9 into the volume, and it decreases to 1/9th of its original size.

Answer:

--------------------

The scale is given:

The length of the actual building is 120 feet, it is 60 times the 2 in, hence the length of the building in the drawing will be 60 times greater than the  corresponding part of the scale:

Answer:

B

Step-by-step explanation:

The answer would be B because your reflecting across the x-axis and you can clearly see that from the fact that both PQRS and P'Q'R'S' are perfectly opposite each other except for R because its on the X-axis

P(1,5) become (-1,5)

Q(2,5) become (-2,5)

Only the x-axis should change.

Answer:

B

Step-by-step explanation:

Reflects across x axis so it would be b

The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/4.A spinner is a gambling tool used for games and competitions. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result.

When it stops, a pointer will land on one of many different numbered segments of the spinner, each of which corresponds to a particular reward or consequence. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result. Probability is the study of the likelihood of events taking place.

Probability is expressed as a fraction, decimal, or percentage and is always between 0 and 1. The probability of an event can be calculated using the following formula: Probability = number of favorable outcomes / total number of possible outcomes. Given the spinner has a polka-dot section, 2 white sections, and 1 shaded section, it has a total of 4 sections.

Therefore, the probability of the spinner stopping at a polka-dot section is 1/4.Also, after the first spin, the spinner still has 2 white sections. Therefore, the probability of stopping at a solid white section is 2/4 or 1/2 (since there are only 2 possible outcomes after the first spin).

To determine the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section, we must multiply the probability of each event.1/4 × 1/2 = 1/8

Hence, the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

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Yes, the probability of drawing a heart and then a diamond from a standard deck of 52 cards is indeed (13/52) x (13/52).

To calculate the probability of two independent events occurring, we multiply their individual probabilities. In this case, the probability of drawing a heart on the first card is 13 out of 52 because there are 13 hearts in a standard deck of 52 cards. The probability of drawing a diamond on the second card is also 13 out of 52 since there are 13 diamonds in the deck.

Therefore, the probability of drawing a heart and then a diamond is:

(13/52) x (13/52) = (169/2704) = 1/16 ≈ 0.0625 ≈ 6.25%

So, the probability of drawing a heart and then a diamond from a standard deck is 13/52 multiplied by 13/52.

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After set s1.retainAll(s2), s1 is [2].

After performing the operation s1.retainAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become [2].
To determine the value of s1, the following steps has to be taken:

1. Start with sets s1 [1, 2, 5] and s2 [2, 3, 6].
2. Perform the retainAll() operation on s1 with s2.
3. The retainAll() operation keeps only the elements that are common in both sets.
4. The common element in both sets is 2.
5. Therefore, suppose if set s1 is [1, 2, 5] and set s2 is [2, 3, 6] then, after s1.retainAll(s2), the set s1 becomes [2].

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Answer:

Step-by-step explanation:

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