Melinda is decorating for her sister's birthday party. She is making a conical tent that will have a slant height of 9 feet and a radius of 6.5 feet. Approximately how much fabric will she need to cover the surface of the entire tent? Use 3.14 for pi, and round your answer to the nearest hundredth. Melinda will need ft2 of fabric.

Answer:

20, 24

Step-by-step explanation:

smaller:   x

  larger:  2x - 16

x + 2x - 16 = 44

3x -16 = 44

3x = 60

x = 20

smaller:   x = 20

  larger:  2x - 16 = 2(20) - 16 = 24

Answer:

15.2 cm, 130 m

Step-by-step explanation:

1. The sine of angle Z is XY/17.4; (opposite/hypotenuse);

sin(61) = XY/17.4; multiply both sides by 17.4 to find XY

17.4sin(61) = 15.2 cm

2.

This triangle is made by the anchor of the balloon to the ground, the balloon, and the area on the ground directly below the balloon.

The hypotenuse of the triangle is the 170 m string.

The angle of inclination is 50 degrees.

The height of the triangle will be opposite of the angle of inclination.

Therefore,

sin(50) = height/170 (opposite/hypotenuse)

170sin(50) = 130.2 meters

Answer: 1/4

Step-by-step explanation: In algebra, we use the word slope to describe how steep a line is and slope can be found using the ratio rise/run between any two points that are on that line.

So for the line you see here, let's use these two points to find its slope.

Let's go from left to right.

To get from the point that has the coordinates (0,1) to (4,2),

we rise 1 unit and run 4 units to the right and we end up the other point.

So the slope of this line is 1/4.

Answer:

-45

Step-by-step explanation:

add 10 to -25, then divide 1/3 to that answer, which is -15. and you get -45

Answer: N=-45

Step-by-step explanation: Solve for n by simplifying both sides of the equation, then isolating the variable.

The square footage of the rooftop of the clubhouse is 945 ft².

To determine the square footage of the rooftop of the clubhouse, we need to calculate the area of each component separately and then add them together.

Let's start with the parallelograms. Since the two parallelograms are congruent, we only need to calculate the area of one and then double it. The formula for the area of a parallelogram is base multiplied by height.

The base of the parallelogram is the shorter side, which measures 15 ft, and the height is the longer side, which measures 18 ft.

Area of one parallelogram = base × height = 15 ft × 18 ft = 270 ft²

Since there are two congruent parallelograms, the total area for both is:

Total area of parallelograms = 2 × 270 ft² = 540 ft²

Next, let's calculate the area of the rectangle. The rectangle's dimensions are 18 ft by 15 ft.

Area of rectangle = length × width = 18 ft × 15 ft = 270 ft²

Finally, let's calculate the area of the triangle. The triangle's dimensions are the same as the rectangle's width, which is 15 ft, and half of the rectangle's length, which is 18 ft/2 = 9 ft.

Area of triangle = (base × height) / 2 = (15 ft × 9 ft) / 2 = 135 ft²

Now, we can add up the areas of all the components to find the total square footage of the rooftop:

Total square footage of the rooftop = Total area of parallelograms + Area of rectangle + Area of triangle

= 540 ft² + 270 ft² + 135 ft²

= 945 ft²

Therefore, the square footage of the rooftop of the clubhouse is 945 ft².

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Answer:

x^36

Step-by-step explanation:

The number of marigold in the garden of Paula is 24.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of marigold be m.

In this case, the number of tulips in Paula's garden is 8 less than the number of marigolds. The number of marigold will be:

m - 8 = 16

m = 16 + 8.

m = 24

The number of marigold is 24.

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Answer:

0.96

Step-by-step explananation

stack the two numbers ontop of each other and it will be easier to do the multiplacation

The statements that are true regarding function S are:

What is function?

In mathematics, a function is a rule or a relationship between two sets of values, which associates each element of the first set (called the domain) with a unique element of the second set (called the range). The domain and range can be any sets, including numbers, letters, or other objects.

The statements that are true regarding function S are:

The other statements are not necessarily true:

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The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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Answer:

11

Step-by-step explanation:

Subtract:

-8 + x = 3

+8        +8

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

    x = 11

Hope this helped.

Answer:

x = 11

Step-by-step explanation:

−8 + x = 3

Add 8 to both sides

x = 11 ✓

Answer:

the area would be 10 i

Step-by-step explanation:

reason being the base is 4 and the height is 5 the answer was right for me

what i has highlighted in the picture is the answer

Answer:

6m/16 = 3m/8

Step-by-step explanation:

since the fractions have the same denominator, just take out the operation on the numerators of the 2 fractions. So, 7m +(-m).

7m +(-M) is the same as 7m - m, so that is 6,

when you put it back together, you get 6m/16, simplify it to 3m/8

The given integral expression is shown below:

$$\int_{3}^{12} \frac{12}{\sqrt{x+6}\sqrt{x}}\text{d}x$$

Substitute u as $\sqrt{x-3}$. Therefore,$$u^2=x-3$$$$x=u^2+3$$

Now differentiate both sides with respect to x,$$\frac{\text{d}}{\text{d}x}(x)=\frac{\text{d}}{\text{d}x}(u^2+3)$$$$1=2u\frac{\text{d}u}{\text{d}x}$$$$\frac{\text{d}x}{\text{d}u}=2u$$$$\text{d}x=2u\text{d}u$$

To evaluate the integral in terms of u, we need to convert the limits of integration from x to u.$$x=3$$$$u=\sqrt{x-3}=\sqrt{3-3}=0$$$$x=12$$$$u=\sqrt{x-3}=\sqrt{12-3}=3\sqrt{3}$$

The given integral expression becomes$$\int_{0}^{3\sqrt{3}} \frac{12}{\sqrt{(u^2+6)(u^2+3)}}\cdot 2u\text{d}u$$$$=24\int_{0}^{3\sqrt{3}} \frac{u}{\sqrt{(u^2+6)(u^2+3)}}\text{d}u$$

Using partial fraction, we can get$$\frac{1}{\sqrt{(u^2+6)(u^2+3)}}=\frac{1}{3\sqrt{2}}\left(\frac{1}{\sqrt{u^2+3}}-\frac{1}{\sqrt{u^2+6}}\right)$$Substituting the partial fraction back into the integral expression,$$=24\int_{0}^{3\sqrt{3}} \frac{u}{3\sqrt{2}}\left(\frac{1}{\sqrt{u^2+3}}-\frac{1}{\sqrt{u^2+6}}\right)\text{d}u$$$$=8\sqrt{2}\left[\sqrt{u^2+3}-\sqrt{u^2+6}\right]_0^{3\sqrt{3}}$$$$=8\sqrt{2}\left[\sqrt{(3\sqrt{3})^2+3}-\sqrt{(3\sqrt{3})^2+6}\right]-8\sqrt{2}\left[\sqrt{3}-\sqrt{6}\right]$$$$=\boxed{8\sqrt{54}-8\sqrt{21}+8\sqrt{6}-8\sqrt{3}}$$

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Step-by-step explanation:

Money = Rs 1800

Ratio = 2:3:4

1st Person = 2x

2nd Person = 3x

3rd Person = 4x

X = ?

2x + 3x + 4x = 1800

9x = 1800

X = 200

1st Person = 2x = 2×200 = Rs 400

2nd Person = 3x = 3×200 = Rs 600

3rd Person = 4x = 4×200 = Rs 800

Therefore, the equation of the line passing through (-3, -5) and parallel to the line 2x + 3y = 15, in slope-intercept form, is y = (-2/3)x - 7.

To find the equation of a line parallel to the line 2x + 3y = 15 and passing through the point (-3, -5), we need to determine the slope of the given line and use it to construct the equation in slope-intercept form (y = mx + b).

The given line is in the form Ax + By = C, where A = 2, B = 3, and C = 15. To find the slope of this line, we can rearrange the equation to isolate y:

2x + 3y = 15

3y = -2x + 15

y = (-2/3)x + 5

The slope of the given line is -2/3.

Since the line we want to find is parallel to this line, it will have the same slope. Therefore, the slope of the line passing through (-3, -5) will also be -2/3.

Now, we can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

Substituting the values of (-3, -5) and -2/3 for (x1, y1) and m, respectively:

y - (-5) = (-2/3)(x - (-3))

y + 5 = (-2/3)(x + 3)

To convert this equation into slope-intercept form, we can simplify and rearrange:

y + 5 = (-2/3)x - 2

y = (-2/3)x - 2 - 5

y = (-2/3)x - 7

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The shaded part is 3 column

There are 10 columnn in total.

The number of grids are 100 and shaded grids are 30

Thus the fraction of shaded portion is:

3/10.

The decimal form is 0.3.

Answer:

\(a = 2 \\ b = 11\)

Step-by-step explanation:

\( {x}^{2} + 4x + 4 - 4 - 7 = {(x + 2)}^{2} - 11\)

Answer:

Step-by-step explanation:

if we have 137 students, and out of this number 7 were in cars

137-7=130 students in buses

there are 5 buses

130/5=26

26 students in each bus

Answer:

As per above properties we have:

and

In then given right triangle, FH = 12, ∠F = 22.62° and ∠G = 67.38.

When οne οf the internal angles is 90 °, οr a right angle, the triangle is said tο be a right triangle. As a triangle's three internal angles sum up tο 180 degrees, a right triangle's three angles must always add tο a maximum οf 90 degrees since οne οf them is always 90 degrees.

Pieces that have any οf its sides οr tο be an acute angle οr larger than 90° are referred tο as οbtuse triangles οr οbstinate triangles. Only 180° is equivalent tο the internal angles οf an acute triangle.

Given:

Angle H is 90°

FG = 13

GH = 5

Using Pythagoras theorem:

FH = \(\rm \sqrt{FG^2 - GH^2}\)

FH = \(\rm \sqrt{13^2 - 5^2}\)

FH = 12

Sine: sin(θ) = Opposite / Hypotenuse

sin(F) = 5/13

sin(F) = 0.38

∠F = 22.62°

sin(G) = 12/13

sin(G) = 0.92

∠G = 67.38

Thus, in then given right triangle, FH = 12, ∠F = 22.62° and ∠G = 67.38.

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Complete question:

Find the measure of side and angle of each right triangle. Round the measures to the nearest degree.

8 miles is equal to 12.9 kilometers .

Given,

Convert 8 miles into kilometers  .

Now,

From the metric system of unit conversion table we see that;

1 kilometer = 1000 meters (m)

1 meter = 100 centimeters (cm)

1 centimeter = 10 millimeters (mm)

Here we need the conversion factor that includes miles,

So according to the table 1 mile is equal to 1.609 kilometers  .

Then,

8 miles will be equal to:
8*1.609

= 12.9 kilometers  .

Hence the value of 8 miles in km is equal to 12.9 kilometers .

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Answer:

r = 2

Step-by-step explanation:

Use cross products.

Set the cross products equal and solve for r.

r × 120 = 4 × 60

120r = 240

r = 2

Step-by-step explanation:

\( \frac{5gb}{110} = \frac{2.3gb}{x} \)

→ x = 2.3 ×110÷5 = 50.6 $ Aaron pay

→Brian = 1.1 × 110 ÷5=24.2$

Caleb = 110 - ( 24.2 + 50.6 ) = 110 -74.8 = 35.2$

Aaron should pay $50.60, Brian should pay $24.20, and Caleb should pay $35.20 to split the bill in proportion to the data they used.

To split the bill among the three brothers in proportion to the data they used, we need to calculate the fraction of the total data used by each brother and allocate the bill accordingly.

The total data used by the three brothers is 2.3gb + 1.1gb + 1.6gb = 5gb.

Now, let's calculate the fraction of the bill that each brother should pay based on their data usage:

Aaron's fraction = 2.3gb / 5gb = 0.46

Brian's fraction = 1.1gb / 5gb = 0.22

Caleb's fraction = 1.6gb / 5gb = 0.32

The sum of these fractions should equal 1, representing the entire bill.

To allocate the bill, we multiply each brother's fraction by the total bill amount:

Aaron's payment = 0.46 * $110 = $50.60

Brian's payment = 0.22 * $110 = $24.20

Caleb's payment = 0.32 * $110 = $35.20

Therefore, Aaron should pay $50.60, Brian should pay $24.20, and Caleb should pay $35.20 to split the bill in proportion to the data they used.

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7x - 2y = -4 (1)

-x - y = 7 (2)

To use the substitution method we will find y in the second equation

-x - y = 7 .......... add x to both sides

-x + x - y = 7 + x

-y = 7 + x ......... (3)

Substitute (3) in (1)

7x + 2(7 + x) = -4

7x + 2(7) + 2(x) = -4

7x + 14 + 2x = -4

Add the like terms

(7x + 2x) + 14 = - 4

9x + 14 = -4

Subtract 14 from both sides

9x + 14 - 14 = -4 - 14

9x

Sophie saves $11.25 when she buys the dress with a 15% discount.

To calculate the amount of money Sophie saves on the dress with a 15% discount, we need to find 15% of the original price and subtract that amount from the original price.

Original price of the dress: $75

Discount percentage: 15%

Calculate the discount amount

Discount amount = 15% of $75

Discount amount = (15/100) \(\times\) $75

Discount amount = $11.25

Calculate the final price after the discount

Final price = Original price - Discount amount

Final price = $75 - $11.25

Final price = $63.75

Calculate the amount saved

Amount saved = Original price - Final price

Amount saved = $75 - $63.75

Amount saved = $11.25

Therefore, Sophie saves $11.25 when she buys the dress with a 15% discount.

It's important to note that the discount amount may vary depending on the specific store policies and rounding methods used.

The above calculation assumes a straightforward 15% discount without any additional conditions or fees.

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It's important to note that correlation does not necessarily imply causation, and there may be other factors at play that contribute to the relationship between SAT scores and GPA.

The slope of 0.00362 represents the rate of change in the average GPA for every one-unit increase in the verbal SAT score. In other words, for every one-point increase in the verbal SAT score, the average GPA is expected to increase by 0.00362 points.

This suggests a positive relationship between GPA and SAT scores, indicating that students who perform better on the SAT verbal test are likely to have higher GPAs. However, it's important to note that correlation does not necessarily imply causation, and there may be other factors at play that contribute to the relationship between SAT scores and GPA.

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Answer:

9 pi

Step-by-step explanation:

First find the circumference of the circle

C =2 * pi *r

C = 2 * pi *9

C = 18 pi

This is a semicircle which is 1/2 of a circle

Take 1/2 of the circumference

1/2 C = 1/2 ( 18 pi)

1/2 C = 9 pi

The test that fits the description is called the Wechsler Preschool and Primary Scale of Intelligence (WPPSI).

The WPPSI is a standardized intelligence test designed for children aged 2½ to 7 years old. It assesses various cognitive abilities and provides separate levels for different age ranges, specifically ages 2½ to 4 and 4 to 7. The test measures both verbal and non-verbal (performance) abilities, and it also yields combined scores that provide an overall measure of intelligence.

The test consists of a series of subtests that evaluate different areas such as verbal comprehension, working memory, perceptual reasoning, and processing speed. These subtests assess the child's abilities in areas like vocabulary, comprehension, visual-spatial skills, problem-solving, and attention.

By providing separate levels for different age groups and assessing multiple cognitive domains, the WPPSI offers a comprehensive evaluation of a child's intellectual abilities during the preschool and primary school years.

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The area in square inches of triangle is 36.75.

Given,

∠A ≅ ∠P

Tan A = tan P

6/8 = x/14

X= 21/2

Area = 1/2 * 7*21/2

= 36.75 square

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base. Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

Hence, the area in square inches of triangle will be 36.75

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