From a horizontal distance of 80.0 m, the angle to the top of a flagpole is 18°. Calculate the height of the flagpole to the nearest tenth of a meter.

1. 24.7 meters
2. 76.1 meters
3. 26.0 meters
4. 25.3 meters ​

So the radius and diameter for each plate are:

Plate 1: radius ≈ 7 in., diameter ≈ 14 in.

Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.

Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.

Circumference is the distance around the edge of a circle. It is the total length of the boundary of a circle. It is also referred to as the perimeter of a circle. The circumference of a circle can be calculated using the formula: C = 2πr where C is the circumference, r is the radius of the circle, and π is a mathematical constant with an approximate value of 3.14. The circumference of a circle is directly proportional to its radius; that is, as the radius of a circle increases, the circumference also increases.

Here,

Part A:

To find the radius and diameter of each plate, we can use the formula for the circumference of a circle:

C = 2πr

where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:

r = C / 2π

Using the given circumferences and the value of π as 3.14, we can find the radius for each plate:

Plate 1:

C = 43.96 in.

r = 43.96 / (2 x 3.14) ≈ 7 in.

d = 2r ≈ 14 in.

Plate 2:

C = 28.26 in.

r = 28.26 / (2 x 3.14) ≈ 4.5 in.

d = 2r ≈ 9 in.

Plate 3:

C = 21.98 in.

r = 21.98 / (2 x 3.14) ≈ 3.5 in.

d = 2r ≈ 7 in.

So the radius and diameter for each plate are:

Plate 1: radius ≈ 7 in., diameter ≈ 14 in.

Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.

Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.

Part B:

To find the radius and diameter of each plate, we used the formula for the circumference of a circle and rearranged it to solve for the radius. We then used the formula for the diameter of a circle, which is simply twice the radius, to find the diameter. We also used the value of π as 3.14 in our calculations.

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We need at least 3.465 gallons of paint to paint the walls of this room.

The area of the two rectangular faces on either end of the prism is:

length x height = 17 x 12 = 204 square feet

The area of the two rectangular faces on the sides of the prism is:

width x height = 15 x 12 = 180 square feet

The area of the top and bottom faces of the prism is:

length x width = 17 x 15 = 255 square feet

The total surface area of the prism is:

2(204) + 2(180) + 2(255) = 1386 square feet

Now, we divide surface area by coverage of one gallon of paint:

1386 / 400 = 3.465

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Answer:

1 student wears glasses

Step-by-step explanation:

If out of people who were chosen 3 out of 8 were chosen-again, then the ratio of people who were chosen twice is 3:10.

The "Ratio" is defined as a way of expressing the quantitative relationship between two or more quantities.

We know that, 40 people were selected and out of those 40 selected, 4 out of 5 were chosen, and

Out of the chosen people, 3 out of 8 were chosen again,

Now, we calculate the total-number of people who were chosen,

⇒ 40 selected × (4/5 chosen) = 32 people were chosen in the first round,

⇒ 32 chosen × (3/8 chosen again) = 12 people were chosen again in the second round.

So, the total number of people who were chosen twice is 12,

Now, we find ratio of people who were "chosen-twice" to "total-number-of-people" who were selected,

⇒ Ratio of people chosen twice to total people selected = 12/40,

On simplifying the ratio "12/40",

We get,

⇒ 12/40 = 3/10,

Therefore, the required ratio is 3:10.

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The base, lateral area and surface area is B = 96 cm², L = 499.2 cm²,S = 691.2 cm²

The lateral area for the triangular prism is the sum of all three areas. Thus, the formula for lateral area of triangular prism, Lateral surface area of triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h.

To find the lateral area (L) of this solid, we need to calculate the area of the four rectangles that make up the sides of the solid. Since each rectangle has a height of 10.4 cm and a width of 12 cm, the area of one rectangle is:

A = 10.4 cm * 12 cm = 124.8 cm²

Since there are four rectangles, the total lateral area is:

L = 4 * A = 4 * 124.8 cm² = 499.2 cm²

To find the surface area (S) of the solid, we need to add the lateral area to the area of the two circular bases. The base area is given as 96 cm², so the area of both bases is:

A = 2 * 96 cm² = 192 cm²

Therefore, the total surface area is:

S = L + A = 499.2 cm² + 192 cm² = 691.2 cm²

Rounding to the nearest tenth, we have:

B = 96 cm²

L = 499.2 cm²

S = 691.2 cm²

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The resulting two-dimensional shape is a square with an area of 72 square units.

The pyramid is a square right pyramid, the base is a square and the vertical height meets the base at its center. When the pyramid is sliced by a plane that passes vertically through the top vertex and is perpendicular to the base, the resulting two-dimensional shape is a square.

The plane section intersects the four triangular faces of the pyramid, creating four smaller triangles with the same shape and size. These four triangles can be rearranged to form a smaller square that is similar to the larger square base of the pyramid. The area of the plane section is equal to the area of the smaller square, which is proportional to the area of the larger square base. The proportionality constant is equal to the ratio of the height of the plane section to the height of the pyramid.

Let H be the height of the pyramid and h be the height of the plane section. Then, we have:

h/H = (side length of smaller square)/(side length of larger square)

= √(2)/2

Solving for h, we get:

h = (√(2)/2) * H

The area of the plane section is then:

A = (side length of smaller square)²

= (√2)/2 * side length of larger square)²

= (√(2)/2)² * (side length of larger square)²

= (1/2) * (side length of larger square)²

Since the side length of the larger square base is given, we can substitute it in and simplify to get:

A = (1/2) * (12)² = 72 square units

As a result, the resultant two-dimensional form is a square with 72 square units of area.

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The result of the expression in scientific notation is [tex]5.6 * 10^5.[/tex]

What is the basic arithmetic operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

Given:

[tex](8.4 * 10^8) / (1.5 * 10^3)[/tex]

Step 1: Divide the numerical parts:

8.4 ÷ 1.5 = 5.6

Step 2: Subtract the exponents:

[tex]10^8 / 10^3 = 10^{(8-3) }= 10^5[/tex]

Putting the numerical part and the exponent together, we get:

[tex]5.6 * 10^5[/tex]

Hence, the result of the expression in scientific notation is [tex]5.6 * 10^5.[/tex]

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Whether to use a histogram or a time plot depends on the specific objective of your analysis. A histogram

is suitable for analyzing the distribution of herbicide usage, while a time plot is better for analyzing trends over time.

It would be appropriate to display these data in a histogram without first plotting them in a time plot if you are looking

to analyze the distribution or frequency of herbicide usage across different amounts or categories.

A histogram can provide a clear visualization of the distribution and help identify any patterns or trends in the data.

However, if your goal is to analyze the trend of herbicide usage over time, then it would be more appropriate to use a

time plot.

A time plot will show changes in the usage of herbicides over a specific time period and help identify any seasonal

patterns or trends in the data.

In summary, whether to use a histogram or a time plot depends on the specific objective of your analysis. A histogram

is suitable for analyzing the distribution of herbicide usage, while a time plot is better for analyzing trends over time.

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Let x = width

Length = 3x

Area = 35

3x * x = 35

3x^2 = 35

x^2 = 35/3

x = √(35/3)

Width = √(35/3)

Length = 3√(35/3)

The p-value is 0.0001, indicating strong evidence that college students study more than 20 hours per week based on the sample data.

To test the hypothesis that the average number of hours that college students study per week is greater than 20, we can use a one-sample t-test.

The null hypothesis is that the population mean is equal to 20 hours per week, while the alternative hypothesis is that the population mean is greater than 20 hours per week.

Let's calculate the t-value:

t = (sample mean - hypothesized population mean) / (sample standard deviation / √(sample size))

t = (22.2 - 20) / (3.9 / √(33))

t = 4.49

The degrees of freedom for the t-test is 33 - 1 = 32.

Using a t-table or calculator, we can find the p-value associated with a t-value of 4.49 and 32 degrees of freedom. The p-value is less than 0.0001 (it is actually very close to 0), which means that there is very strong evidence to reject the null hypothesis and conclude that college students study more than 20 hours per week.

Therefore, the p-value is 0.0001 (rounded to 4 decimal places).

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Answer:

Step-by-step explanation:

25

=

a

b

−

2

10

=

a

b

1

Donna Mosier should use an Individuals control chart to set control limits for the data entry process.

An Individuals control chart is a type of process control chart used to monitor the process when the sample size is one. In this case, Mosier is examining 100 records entered by each of the 20 clerks, making the sample size one.

To set control limits that include 99.73% of the random variation in the data entry process, Mosier can use the following steps:

By using an Individuals control chart, Mosier can set control limits to monitor the data entry process and detect any issues before they become major problems.

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Therefore, the solution to the equation [tex]7x-1 / 5 = x[/tex].is[tex]x=1/30[/tex].

An equation is a mathematical statement that expresses the equality between two expressions or values, using mathematical symbols such as = (equals), < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

Equations can be used to solve problems in various fields such as mathematics, physics, chemistry, engineering, and economics. They can be simple or complex, and may involve variables, constants, and coefficients.

Some examples of equations are:

[tex]2x + 5 = 11[/tex] (an equation with one variable)

[tex]3x + 4y = 12[/tex] (an equation with two variables)

here's the step-by-step algebraic working to solve the equation 7x-1 ÷ 5 = x:

First, we need to simplify the left side of the equation by performing the division first:

[tex]7x - 1/5 = x[/tex]

Next, we want to isolate the variable x on one side of the equation by subtracting x from both sides:

[tex]7x - x - 1/5 = 0[/tex]

Simplify by combining like terms on the left side:

[tex]6x - 1/5 = 0[/tex]

Add 1/5 to both sides to eliminate the constant on the left side:

[tex]6x = 1/5[/tex]

Finally, divide both sides by 6 to solve for x:

[tex]x = 1/30[/tex]

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For 5 chairs, the machine needs 25 minutes.

A percentage in mathematics is an equation that connects two or more ratios and declares that they are equal. Two values are compared in a ratio, which is frequently stated as a fraction or the division of two integers. A percentage, which usually takes the form: expresses the equivalence of two or more ratios.

a/b = c/d

Given:

Rate of production = 2 chairs every 10 minutes

Time taken to make 5 chairs

2 chairs / 10 minutes = 5 chairs / x minutes

Cross-multiplying,

2 * x = 10 * 5

2x = 50

Dividing both sides by 2:

x = 50 / 2

x = 25

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Complete Question: a machine factory makes chairs at a rate 2 chair every 10 minutes how much time does machine take to make five chairs?

Answer:

C and D

Step-by-step explanation:

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{4}{5}[/tex] ⇒ C

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{5}[/tex] ⇒ D

Using the volume of the cylinder we know that 77% of the container B is full when the pumping is complete.

A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions.

In elementary geometry, it is regarded as a prism with a circle as its basis.

A cylinder can instead be described as an infinitely curved surface in a number of modern domains of geometry and topology.

The following is a list of the cylinder's attributes: It has two flat circular faces, two curved edges, and one curved surface.

Its uniform cross-section throughout makes it resemble a prism.

They feature two bases that are circular, flat, and arranged in a straight line.

So, the volume of cylinders A and B:

Formula: V=πr²h

Cylinder A:

V=πr²h

V=π10²20

V = 6283.18531

Rounding off: 6283 ft³

Cylinder B:

V=πr²h

V=π12²18

V=8143.00816

Rounding off: 8143 ft³

Then, contain A is what % of container B:

= 6283/8143 * 100

= 77.15

Rounding off: 77%

Therefore, using the volume of the cylinder we know that 77% of container B is full when the pumping is complete.

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So the two cars are approximately 13 kilometers apart.

The Pythagorean theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right-angled triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, the Pythagorean theorem can be expressed as:

c² = a² + b²

We can use the Pythagorean theorem to find the distance between the two cars, as they have traveled perpendicular to each other.

The horizontal distance between the two cars is 5 km, and the vertical distance is 12 km. Therefore, the distance between the two cars can be found using the Pythagorean theorem:

d² = 5² + 12²

d² = 25 + 144

d² = 169

d = √(169)

d = 13

So, the two cars are approximately 13 kilometers apart.

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The measure of the missing angle in the triangle is 30 degrees. Option 3

We have that there are six different trigonometric identities. they are;

Also note that the sum of the angles in a triangle is equal to 180 degrees.

The different trigonometric ratios of the identities are;

sin θ = opposite/hypotenuse

From the information given, we have;

Opposite = 15

Hypotenuse = 31

Substitute the values

sin x = 15/31

Divide the values

sin x = 0. 4839

Find the inverse sine

x = 30 degrees

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The tent with the assumed parameters is tall enough for the sisters to stand up inside.

Assuming a reasonable height for a typical tent, which is around 6 feet, it should be tall enough for both sisters to stand up inside if they are both over 5 feet tall.

In this case, we can imagine the tent as a triangular prism, with the sloping sides forming a right triangle.

Let's call the height of the tent "h," the length of the base "b," and the length of the sloping side "s."

Using the Pythagorean theorem, we can write:

s^2 = h^2 + (b/2)^2

Since we know that each sister is over 5 feet tall, we can set h = 5 feet. We also know that the base of the tent is usually wider than it is tall, so we can assume a reasonable value for b, such as 8 feet.

Substituting these values into the equation above, we get:

s^2 = 5^2 + (8/2)^2

s^2 = 25 + 16

s^2 = 41

Taking the square root of both sides, we get:

s ≈ 6.4 feet

Since this is greater than the height of both sisters (which is 5 feet), we can conclude that the tent is tall enough for them to stand up inside.

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Answer:

b = 93°

Step-by-step explanation:

We Know

A triangle is 180°

One angle of the triangle is 21.5°, and the other is 65.5°.

Find angle b, we take

180 - (21.5 + 65.5) = 93°

So, b = 93°

b) The power of the given problems is: Power = 30556 J/s

c) The Force is:  500 N

The power is:  625 J/s

Power is defined as the rate at which work is done. That is workdone over time taken.

b) The formula for power when given force and velocity is:

Power = Force * velocity

We are given:

Force = 1000 N

Velocity = 110 km/h = 30.556 m/s

Thus:

Power = 1000 * 30.556

= 30556 J/s

c) The formula for workdone is:

W = Force * distance

Thus:

Force = Work/distance

Force = 25000J/50 m

Force = 500 N

The power = wordkdone/time taken

= 25000/40

= 625 J/s

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The option that best describes the data is the option;

Dependent and independent data refers to the relationship between two sets of data.

The specified data in the table indicates;

The data obtained from an household in January is located directly on top the data obtained from the same household in June.

The heating bill depends on the amount of energy used in an household.

The amount of energy used in each household depends on the heating requirement of the household, such that the heating bill for an household in January is related to the heating bill for the same household in June

The correct option is therefore;

The data are related because the heating bills in January and June came from the same households.

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There are 3,628,800 different ways that Farmer Brown's animals can be arranged

Since there are only 5 stalls on the left and 6 stalls on the right, and Farmer Brown has 6 horses and 7 mules, some animals will have to stay outside.

We can start by considering the number of ways to arrange the horses in the stalls on the left side. Since there are 6 horses and 5 stalls, there are 6 choices for the first stall, 5 choices for the second stall, 4 choices for the third stall, and so on, giving a total of:

6 x 5 x 4 x 3 x 2 x 1 = 720

possible arrangements of horses in the stalls on the left.

Similarly, there are 7 mules and 6 stalls on the right side, so there are 7 choices for the first stall, 6 choices for the second stall, and so on, giving a total of:

7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

possible arrangements of mules in the stalls on the right.

To find the total number of ways to arrange all the animals, we can multiply the number of possible arrangements of horses on the left by the number of possible arrangements of mules on the right:

720 x 5,040 = 3,628,800

Therefore, there are 3,628,800 different ways that Farmer Brown's animals can be arranged under these circumstances, but some animals may have to stay outside.

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Answer:

[tex]3(6+x)=24[/tex]

[tex]3x+18=24[/tex]

[tex]3x=6[/tex]

[tex]x=2[/tex]

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The 95% lower confidence bound for the mean wall thickness is 4.023 millimeters.

We can be 95% confident that the true mean wall thickness of all glass 2-liter bottles is at least 4.023 millimeters.

95% lower confidence bound for the mean wall thickness.

One-tailed t-distribution since we are interested in finding the lower bound.

The formula for a one-tailed confidence interval for the population mean is:

Lower Bound =[tex]\bar x - (t\alpha,df \times s/\sqrt n)[/tex]

where:

[tex]\bar x = sample mean[/tex]

[tex]t\alpha ,df = t-value[/tex] for the desired level of confidence and degrees of freedom

s = sample standard deviation

n = sample size

Since we want a 95% confidence interval, the level of significance:

[tex]\alpha = 0.05[/tex], and the degrees of freedom [tex](df) = n-1 = 24.[/tex]

Using a t-table or calculator, we can find the t-value corresponding to a 95% confidence level with 24 degrees of freedom to be approximately 1.711.

Substituting the given values, we get:

[tex]Lower Bound = 4.05 - (1.711 \times 0.08/\sqrt25)[/tex]

[tex]Lower Bound = 4.05 - 0.027[/tex]

[tex]Lower Bound = 4.023 millimeters[/tex]

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To find the probability of drawing a face card or a red card, we first need to determine the total number of favorable outcomes and then divide it by the total number of possible outcomes (52 cards in a deck).

A face card can be a King, Queen, or Jack, and there are 12 face cards in a deck (3 face cards x 4 suits). There are 26 red cards in a deck (13 cards from hearts suit and 13 cards from diamonds suit). However, we must subtract the red face cards from the total, as they are already included in the 12 face cards. There are 6 red face cards (3 face cards x 2 red suits).

So, the total number of favorable outcomes is 12 face cards + 26 red cards - 6 red face cards = 32 cards.

The probability of drawing a face card or a red card is the number of favorable outcomes divided by the total number of possible outcomes: 32/52 ≈ 0.6154, or approximately 61.54%.

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Thus, the total surface area of cylinder is found to be 480π sq. cm.

A cylinder's surface area is made up of its two congruent, parallel circular sides added together with its curved surface area. You must determine the Base Area (B) and Curved Surface Area in order to determine the surface area of a cylinder (CSA).

As a result, the base area multiplied by two and the area of a curved surface add up to the surface area or total surface of a cylinder.

Given data:

radius r = 8 cm

Height h = 22 cm

Total surface area of cylinder = 2*area of circle + area of curved cylinder

TSA = 2πr² + 2πrh

TSA = 2π(8)² + 2π(8)(22)

TSA = 2π(64) + 2π(176)

TSA = 128π + 352π

TSA = 480π sq. cm.

Thus, the total surface area of cylinder is found to be 480π sq. cm.

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Complete question-

Find the surface area of the cylinder with radius of 8 cm and height of 22 cm. write the answer in terms of pi and round the answer to the nearest hundredths place.

The sample may not be representative of the population's preferences for frozen desserts.

Sampling technique that Keziah is using is convenience sampling. Convenience sampling is a non-probability sampling technique.

The researcher selects the easiest and most convenient individuals to participate in the study.

Keziah is simply surveying shoppers who are exiting a grocery store on the west side of her town without any predetermined criteria for selection.

As a result, the sample may not be representative of the population's preferences for frozen desserts.

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Answer:

m = 4

Y-intercept: 2

Step-by-step explanation:

8x + 4 = 2y

We rewrite the equation in slope-intercept form y = mx + b

m = the slope

b = y-intercept

8x + 4 = 2y

-2y + 8x + 4 = 0

-2y = -8x - 4

y = 4x + 2

m = 4

Y-intercept: 2

Rewriting the equation in slope-intercept form (y = mx + b) makes it easier to tell the slope and y-intercept. The rewritten form is y = 4x + 2. Since 'm' represents the slope, the slope of the equation is 4. 'b' represents the y-intercept, so the y-intercept is 2.

Answer: 320π or approximately 1005.31 mi

Step-by-step explanation:

The formula for the volume of a cylinder is

π r² h

we need to find the radius which is 16/2 = 8

plug in and solve

π 8² *5

π 64 *5

320π or approximately 1005.31 mi