Find the surface area of the cone. Round your answer to the nearest hundredth.
A. 88.64 cm²
B. 99.53 cm
C. 100.23 cm²
D. 101.73 cm

Answer:

(-4, 3)

Step-by-step explanation:

There are coordinate rules for reflection that really help me with these:

Reflection over x-axis -- (x, y) -> (x, -y)

Reflection over y-axis -- (x, y) -> (-x, y)

Reflection over y = x -- (x, y) -> (y, x)

Reflection over y = -x -- (x, y) -> (-y, -x)

Hope this helps :]

Answer:

C. x = 3

Step-by-step explanation:

8x - 8 = 2x + 10

get the x on it's own

8x - 8 + 8 = 8x

2x + 10 + 8 = 2x + 18

8x = 2x + 18

8x - 2x = 6x

2x + 18 - 2x = 18

6x = 18

now divide each side by 6

6x / 6 = x

18 / 6 = 3

x = 3

X=3

Explanation

8x-8=2x+10

6x=18

x=3

The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

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There are 14 possible outcomes for the 7-question test.

Combinations are defined as the arrangement of objects or numbers in a way such that the order of the arrangement does not matter.

Given that the total number of questions is 7.

Each question has two possible outcomes, either true or false.

Given that, you randomly guess on all questions.

So you can guess either true or false for all questions.

That is, there are 2 possible options for each question.

And total number of questions = 7

Total number of possible outcomes = 2 × 7 = 14

Hence the total possible outcomes is 14.

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Answer:

y=\(\sqrt[3]{x-1}\)

Step-by-step explanation:

y=x^3-1

Switch y and x

x=y^3-1

Solve for y

x-1=y^3

y=\(\sqrt[3]{x-1}\)

Answer: C

Step-by-step explanation:

proportional relationship will have an equation that goes through the origin (0,0)  

The equation for C will not go through the origin because it has a y-intercept of -1  and the line will be going through (0,-1) instead of (0,0).

All the other equations will be going through the origin because they have no y intercepts.

The requried area of the larger triangle is 81 cm².

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not greater than 180°.

Here,
When two triangles are similar, the ratio of their corresponding sides is the same, and the ratio of their areas is equal to the square of this side ratio.

In this case, the ratio of the sides of the larger triangle to the sides of the smaller triangle is 3/2 (since it is given that the ratio of the sides is 2:3). Therefore, the ratio of the areas of the larger triangle to the area of the smaller triangle is (3/2)² = 9/4.

Given that the area of the smaller triangle is 36 cm^2, we can use the area ratio to find the area of the larger triangle:

Area of larger triangle = (9/4) × (Area of smaller triangle)

= (9/4) × 36 cm²

= 81 cm²

Therefore, the area of the larger triangle is 81 cm².

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Answer:

- 3 ( 2x+1 ) 20

8x+5

_____________

8x+5×20 -3 ( 2×12.5+1 )

8×=100 -3 ( 25+1 )

100÷8= 12.5 -3 ( 26 )

×= 12.5

-3 ( 26 )

-3×2 + -3×6 = -6+ -18 = -24

-24

Answer:

Step-by-step explanation:

we know that the total time of the show is 30 minutes.  

commercial part = 3x+2

entertainment part = y

also we know that   y = 3x +2

y + 3x+2 = 30

we can also say that

2(3(x) +2) = 30

so then

6x +4 = 30

6x = 26

x = 4\(\frac{1}{3}\)

4\(\frac{1}{3}\)  is the time in minutes for commercials

The given table represents the additive property of the relation.

What about additive property?

In mathematics, the additive property refers to the property that allows the addition of two or more numbers to produce a sum or total. It states that the order in which the numbers are added does not affect the result.

The additive property can be expressed mathematically as follows:

⇒ a + b = b + a

For example, the additive property of integers states that if you add any two integers, the order in which you add them does not matter. So, 3 + 4 is the same as 4 + 3, and both equal 7.

The additive property can be extended to other mathematical operations as well, such as addition of vectors, matrices, and complex numbers. In all cases, the order in which the elements are added does not affect the final result.

According to the given information:

When we check in case of (X) we have that ,

5 + 10 = 15 , 10 + 15 = 25 , 15 + 25 = 40 that follow additive property

In the same way for (Y)

1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8 that also follow additive property of the given condition.

So, the both condition follow additive property .

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The probability of a salesperson at Owl Realty selling 5 houses in a month is 0.05 or 5%.

The probability distribution provided gives the likelihood of a salesperson selling a specific number of houses (n) in a month. In this case, we are interested in finding the probability of a salesperson selling 5 houses in a month. From the given distribution, we can directly read the probability corresponding to n=5.

Unfortunately, it appears that the probability for selling 5 houses is missing in the information provided. However, we know that the total probability for all possible outcomes must equal 1. To find the missing probability, we can add up the probabilities for all other outcomes (0-4, 6-9) and then subtract that sum from 1.

0.05 (0 houses) + 0.10 (1 house) + 0.15 (2 houses) + 0.20 (3 houses) + 0.15 (4 houses) + 0.10 (6 houses) + 0.05 (7 houses) + 0.05 (8 houses) + 0.05 (9 houses) = 0.95

Now, subtract this sum from 1 to find the probability of selling 5 houses:

1 - 0.95 = 0.05

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Answer:

False

Step-by-step explanation:

First, you could add 16 to both sides, because the 16 is negative. 16 needs to be added to both sides to cancel it.

Then, you would divide by 6.

So, this is false because you would add 16 instead of subtracting 16.

The possible angles between two unit vectors u and v if ||u x v|| = √3/2 are 60 degree.

The magnitude of the cross product between two vectors u and v is equal to the area of the parallelogram formed by the two vectors. Since the magnitude of the cross product is ||u x v|| = √3/2, it means that the area of the parallelogram formed by u and v is √3/2.

The area of a parallelogram is given by the formula A = ||u|| ||v|| sin(theta), where theta is the angle between the two vectors. Since both u and v are unit vectors, their magnitudes are 1.

Thus, we can simplify the formula to A = sin(theta)/2.

Therefore, sin(theta) = √3/2, which implies that the value of sin theta is √3/2 when theta = 60°

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Answer:

A = 36 m²

Step-by-step explanation:

The area (A) of a kite is calculated as

A = \(\frac{1}{2}\) d₁ d₂ ( d₁, d₂ are the diagonals )

Here d₁ =  4 + 5 = 9 and d₂ = 4 + 4 = 8 , then

A = \(\frac{1}{2}\) × 9 × 8 = \(\frac{1}{2}\) × 72 = 36 m²

Answer: ME

Step-by-step explanation:

Answer:

280 kg

Step-by-step explanation:

279.98... so it rounds up to 280

Answer:

58kg

Step-by-step explanation:

127 pounds to kg is 57.606 kgs

divide pounds by 2.205

Answer:

$42.00

Step-by-step explanation:

So, something hasn't been subtracted from your bottom line. The bank is saying you only have $26.33. You think you have $68.33.

Let's look for the difference. This is one of those great times when the word in english and the word in math have the same meaning. Difference is telling us to subtract.

68.33 - 26.33

= 42.00

Check:

If you subtract the missing entry, $42.00 from your total,

68.33 - 42.00

you get $26.33, exactly the balance the bank says you have. Now your account is balanced!

The exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

from the question:

This is the shape of the exponential function:

f(x) = a *\(b^x\)

where a represents the starting point and b represents the exponential function's base.

We must solve the system of equations to determine the values of a and b that meet the requirements:

a * \(b^(-1)\) = 2/5 (equation 1) 

a *\(b^3\)= 250 (equation 2) 

We can solve for an in equation 1 by multiplying both sides by b:

a = (2/5) * b

Substituting this expression into equation 2, we get:

(2/5) * b *\(b^3\) = 250

Simplifying, we get:

\(b^4 = 3125\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

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The value of x from the expression 2x + 6 = 38 is 16.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2x + 6 = 38

Subtracting 6 on both sides.

2x = 38 - 6

2x = 32

Divide both sides by 2.

x = 16

Thus,

The value of x is 16.

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The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Answer:

y=-2x+-3

Step-by-step explanation:

y=mx+b

m=slope

b=y-intercept

-2 is our slope

-3 is our y-intercept

The area to the left of 25 is 0.6664, the area to the left of 17 is 0.2389, the area to the right of 22 is 0.5000, the area to the right of 27 is 0.2389, and the area between 17 and 30 is 0.6340.

μ = population mean = 22

σ = standard deviation = 7

The area from normal distribution can be calculated using z test or normal distribution formula.

a) The area to the left of 25 is

P(x ≤ 25) = P(z ≤ \(\frac{x-\mu}{\sigma}\))

= P(z ≤ \(\frac{25-22}{7}\))

= P(z ≤ 0.43)

using z table and we get,

= 0.6664

b) The area to the left of 17 is

P(x ≤ 17) = P(z ≤ \(\frac{x-\mu}{\sigma}\))

= P(z ≤ \(\frac{17-22}{7}\))

= P(z ≤ -0.71)

using z table and we get,

= 0.2389

c) The area to the right of 22 is

P(x > 22) = 1 - P(z ≤ \(\frac{x-\mu}{\sigma}\))

= 1 - P(z ≤ \(\frac{22-22}{7}\))

= 1 - P(z ≤ 0.00)

using z table and we get,

= 1 - 0.5

= 0.5000

d) The area to the right of 27 is

P(x > 22) = 1 - P(z ≤ \(\frac{x-\mu}{\sigma}\))

= 1 - P(z ≤ \(\frac{27-22}{7}\))

= 1 - P(z ≤ 0.71)

using z table and we get,

= 1 - 0.7611

= 0.2389

e) The area between 17 and 30 is

P(17 ≤ x ≤ 22) = P(\(\frac{x-\mu}{\sigma}\) ≤ z ≤ \(\frac{x-\mu}{\sigma}\))

= P(\(\frac{17-22}{7}\) ≤ z ≤ \(\frac{30-22}{7}\))

= P(-0.71 ≤ z ≤ 1.14)

= P(z ≤ 1.14) - P(z ≤ -0.71)

using z table and we get,

= 0.8729 - 0.2389

= 0.6340

Thus, the area is 0.6664 for area in the left of 25, the area is 0.2389 for area in the left of 17, the area is 0.5 for area in the right of 22, the area is 0.2389 for area in the right of 27, and the area is 0.634 for area between 17 and 30.

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Answer:

1

Step-by-step explanation:

Y=2x+3

Y=2×(-1)+3

Y=1

The given statement states that for all integers n ≥ 1, the product of the first n terms of the sequence 1 · 2 · 3 · ... · n is equal to n(n-1)(n-2)(n-3) · ... · 4. This can be proven using mathematical induction.

We will prove the given statement using mathematical induction.

Base case: For n = 1, the left-hand side of the equation is 1 and the right-hand side is also 1, so the statement holds true.

Inductive step: Assume the statement holds true for some integer k ≥ 1, i.e., 1 · 2 · 3 · ... · k = k(k-1)(k-2) · ... · 4. We need to prove that it holds for k+1 as well.

Consider the left-hand side of the equation for n = k+1:

1 · 2 · 3 · ... · k · (k+1)

Using the assumption, we can rewrite it as:

(k(k-1)(k-2) · ... · 4) · (k+1)

Expanding the right-hand side, we have:

(k+1)(k)(k-1)(k-2) · ... · 4

By comparing the two expressions, we see that they are equal.

Therefore, if the statement holds true for some integer k, it also holds true for k+1. Since it holds for n = 1, by mathematical induction, the statement holds for all integers n ≥ 1.

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Answer:

option 2

Step-by-step explanation:

its easier because you can transfer the y to the other side and it gets easier.

2x = -10y

x = 2/-10 y

x = -5y

Answer:

2x + y = -10

Step-by-step explanation:

2x + y = -10

y = -2x - 10

This can then be substituted for y, for the first equation.

Answer:

\(\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]\)

Step-by-step explanation:

The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9

\(\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]\)

To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.

\(A^{-1}\) = (1 / determinant of A) x Adjoint of A

the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2

Adjoint of A = \(\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]\)

\(A^{-1}\)= \(\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right]\) = \(\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]\)

=======================================================

Work Shown:

See below for the diagram.

(person height)/(person shadow) = (tree height)/(tree shadow)

x/3 = 6/4.5

x*4.5 = 3*6

4.5x = 18

x = 18/4.5 ...... dividing both sides by 4.5

x = 4

The boy is 4 feet tall.

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

Step-by-step explanation:

we will find all the factors of 36 and then go for their decimals

.2 * 1.8 = .36

.3 * 1.2 = .36

.4 * .9 = .36

.6 * .6 = .36