The oblique circular cone has an altitude and a diameter of base that are each of length 12 cm. The line segment joining the vertex to the center of the base is the axis of the cone.What is the length (in centimeters) of the axis?

Answer:

Sales tax: $2.10

■ Cost/Price before ST: $30.00

■ Total Cost/Price including ST: $32.10

The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

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Answer:

x = 6

Step-by-step explanation:

First, we need to cross multiply on both sides, which gives us:

9 * (5x - 6) = 27 * (2 + x)

45x - 54 = 54 + 27x

Now, we want to isolate x on either side.

We can substract 54 from both sides:

(45x - 54 = 54 + 27x) - 54

45x - 108 = 27x

We then subtract 45 from both sides:

(45x - 108 = 27x) - 45

-108 = -18x

Finally, we divide both sides by -18:

(-108 = -18x) / -18

6 = x

Answer:

7.722 cm^2

Step-by-step explanation:

To find the area of the shaded area, you need to subtract the area of the circle from the area of the square. The area of the square is easy: just the square of the side length. In this case, the area is 6^2=36 square centimeters. The area of the circle is:

\(\pi r^2 = \pi (3)^2 = 9\pi \approx 28.278\)

Thus, the area of the shaded region is 36-28.278 = 7.722 square centimeters.

Answer:

D.

Step-by-step explanation:

We know that each centimeter is equal to 2.5 feet. The way I solved it was this.

We start with the 4cm. We can multiply 4×2.5, and that gives us 10 feet. We can do 8.5×2.5, and that will equal 21.25 feet. So the final and correct answer is D. 10 feet by 21.25 feet

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Polar coordinates describe the position of a point P in the plane by its separation from the origin, r, and the angle formed between the positive x-axis and the line segment leading to P.

To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

Polar coordinates can also be extended into three dimensions using the coordinates (ρ, φ, θ), where ρ is the distance from the pole, φ is the angle from the z-axis ( called the co-latitude or zenith and measured from 0 to 180° ) and θ is the angle from the x-axis ( as in the polar coordinates ).

Given data ,

Let the polar curve be represented as A

Now , the polar coordinates is given as

r = -4 sin ( 3θ )

And , To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

So , on simplifying , we get

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Hence , the polar curve is r = -4 sin ( 3θ )

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Answer:

D

Step-by-step explanation:

Answer:

899

Step-by-step explanation:

+

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

What sequence of transformation are we applying

11

Step-by-step explanation:

first you have 6 colors, then you have 22 inches, now multiple 22 × 6=132÷12=11

Answer:

(9,16)

Step-by-step explanation:

We Know

The equation y = 3x - 2

Find the y coordinate (9, ?)

We just simply put 9 in for x and solve for y

y = 3(9) - 2

y = 18 - 2

y = 16

So, the coordinate are (9,16)

The length of the arc intercepted by a central angle of 3 radians in a circle of radius 76 is 228 and the length of the arc intercepted by a central angle of 2 radians in a circle of radius 15 is 30.

Explain:

The following formula determines the length of an arc that a circle's central angle intercepts:

Arc length is equal to (central angle / 2) 2r r r

where r denotes the circle's radius. We can determine the length of the two arcs using the following formula:

For the first circle, with a radius of 76 and a center angle of 3 radians:

Arc length = 3 x 76 = 228

Therefore, in a circle with a radius of 76, the length of the arc that is intercepted by a central angle of 3 radians is 228.

For the second circle, whose radius is 15, and whose center angle is 2 radians:

Arc length = 2 x 15 = 30

As a result, the length of the arc in a circle with a radius of 15 is 30 when it is intercepted by a central angle of 2 radians.

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The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Answer:

False. The product of two negative integers is a positive integer.

this question is non linear

Answer: (A), (B) and (E).

Step-by-step explanation: Given that ΔA’B’C’ with coordinates of A(-6,2),B’(-4,2), and C’(-6,-2) is the image of ΔABC after a translation of (x-3,y+2). We are to find the possible coordinates for the original vertices of ΔABC.

For vertex A, we have

So, the coordinates of vertex A are (-3, 0).

For vertex B, we have

So, the coordinates of vertex B are (-1, 0).

For vertex C, we have

So, the coordinates of vertex C are (-3, -4).

The final answer for the surface area of the prism is 32 m^2 + 16h m^2.

To find the surface area of the prism, we need to calculate the area of each face and sum them up.

The prism has two identical square faces and four rectangular faces. The square face has a side length of 4 m. The area of one square face is given by:

Area of square face = side length^2 = 4^2 = 16 m^2

Since there are two square faces, the total area of the square faces is:

Total area of square faces = \(2 * 16 = 32 m^2\)

The rectangular faces have a length equal to the side length of the square face (4 m) and a width equal to the height of the prism. Let's assume the height of the prism is h. The area of one rectangular face is given by:

Area of rectangular face = length * width = \(4 * h = 4h m^2\)

Since there are four rectangular faces, the total area of the rectangular faces is:

Total area of rectangular faces = \(4 * 4h = 16h m^2\)

Therefore, the surface area of the prism is the sum of the areas of the square and rectangular faces:

Surface area of prism = Total area of square faces + Total area of rectangular faces

                          = \(32 m^2 + 16h m^2\)

                          = \(32 m^2 + 16h m^2\)

The answer for the surface area of the prism is 32 m^2 + 16h m^2.

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#A

We have to find 3% of 120000 and then final cost.

\(\\ \sf\longmapsto 3\%\:of\:120000\)

\(\\ \sf\longmapsto 0.03(120000)\)

\(\\ \sf\longmapsto 3600\)

Now

Final cost=Cost-discount

Final cost=120000-3600=116400

#B

Final price=Cost-Rebate

Final price=120000-1500=118500

a. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division 1 basketball (to 2 decimals). b. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches (to 4 decimals). c. What is the 95% confidence interval for the population variance (to 2 decimals)

Answer:

A) x¯ = $1.33 million

B) σ = $0.9508 million

C) CI = ($0.74 million, $1.92 million)

Step-by-step explanation:

We are given the salary data as;

$2.2 million, $1.5 million, $0.5 million, $0.2 million, $2.4 million, $1.5 million, $2.7 million, $0.1 million, $2 million, $0.2 million

A) Population mean annual salary = $(2.2 + 1.5 + 0.5 + 0.2 + 2.4 + 1.5 + 2.7 + 0.1 + 2 + 0.2)/10 in millions

x¯ = $1.33 million

B) Formula for the standard deviation is;

√(Σ(x - x¯)²/n)

Thus, let's first find (x - x¯)² all in millions

>> (2.7 - 1.33)² = 1.37² = 1.8769

>> (2.4 - 1.33)² = 1.07² = 1.1449

>> (2.2 - 1.33)² = 0.87² = 0.7569

>> (2 - 1.33)² = 0.67² = 0.4489

>> (1.5 - 1.33)² = 0.17² = 0.0289

>> (1.5 - 1.33)² = 0.17² = 0.0289

>> (0.5 - 1.33)² = (-0.83)² = 0.6889

>> (0.2 - 1.33)² = (-1.13)² = 1.2769

>> (0.2 - 1.33)² = (-1.13)² = 1.2769

>> (0.1 - 1.33)² = (-1.23)² = 1.5129

Σ(x - x¯)² = 1.8769 + 1.1449 + 0.7569 + 0.4489 + 0.0289 + 0.0289 + 0.6889 + 1.2769 + 1.2769 + 1.5129

Σ(x - x¯)² = $9.041 million

Σ(x - x¯)²/n = $9.041/10 = $0.9041 million

standard deviation = √0.9041

σ = $0.9508 million

C) Critical value at a Confidence level of 95% is z = 1.96

Thus,formula for critical interval is;

CI = x¯ ± z(σ/√n)

CI = 1.33 ± 1.96(0.9508/√10)

CI = ($0.74 million, $1.92 million)

Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer:\(\frac{15}{8}\) or \(2 \frac{7}{8}\)

Step-by-step explanation:

Adding,

\(\frac{1}{2}+\frac{3}{4}+\frac{5}{8} =\frac{4+6+5}{8} =\frac{15}{8}\)\(=2\frac{7}{8}\)

Step-by-step explanation:

7

1 ---

18

hope it helps !

Answer:

Step-by-step explanation:

So in this example we'll be using the difference of squares which essentially states that: \((a-b)(a+b)=a^2-b^2\) or another way to think of it would be: \(a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})\). So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:

\(x^8-16 = (x^4-4)(x^4+4)\)

Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:

\(x^4-4 = (x^2-2)(x^2+2)\)

So completely factored form is: \((x^2-2)(x^2+4)(x^4+4)\)

I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because \(x^2+4 = x^2-(-4)\). and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: \(x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i)\) just something that might be useful in some cases.

We can factor this into \((x^{4}+4)(x^{4} -4)\).

This is because we use  difference of two squares where \(x^{2} -y^{2} = (x+y)(x-y)\)

So we rewrite x^8-16 to x^8-4^2.

This can then be written to the equation I put at the start.

p.s. The reason its \(x^{4}\) is because \(x^{4} * x^{4} = x^{8}\)
(P.S.S I just found that the other helper did it fully so I stopped here, read his, its correct)

Answer:

I'm not 100% on the interoperation of this question...

are the two red cars out of a 52 card deck and you can try all the combinations of two red and black cards ????

for this answer i will assume that you have 4 coins two nickels and 2 quarters

and the question is " how many ways can you arrange the four coins given that the nickels can not be next to the quarters"

in that case I think the answer is 8

Step-by-step explanation:

1- N1 Q1 N2 Q2

2- N1 Q2 N2 Q1

3- N2 Q1 N1 Q2

4- N2 Q2 N1 Q1

5- Q1 N2 Q2 N1

6- Q2 N2 Q1 N1

7- Q1 N1 Q2 N2

8- Q2 N1 Q1 N2

\(2\cdot \left(\left(2\:choose\:1\right)\:\cdot \:\left(2\:choose\:1\right)\right)\)

Answer:

C and E

Step-by-step explanation:

Factor it so you get

(x-2)(x+5)=0

Then find x

x=-5

x=2

5 and 2 are the solutions of quadratic equation which answer are option C and E.

The quadratic equation is defined as an equation conataining the highest power of a variable is two.

The quadratic equation

x² + 3x - 10 = 0

x² + 5x - 2x - 10 = 0

x(x+5)-2(x+5)

(x-2)(x+5)=0

x = -5, x = 2

Hence, 5 and 2 are the solutions of quadratic equation.

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Answer:

You can calculate for x by

Step-by-step explanation:

7.5 - 2.8 = 4.7

Hope this helps.