ella’s cat climbed up onto the roof of her house and can’t get down. the roof of the house is 24 feet above ground. the fire department set up a 28 foot ladder to climb to rescue the cat, the base of the ladder is resting on the ground. and the top of the ladder extends 2 feet beyond the edge of the roof. how far away from the base of the house is the base of the ladder??

Answer:

I think C

Step-by-step explanation:

The order of the product ab in the abelian group is lcm(m, n).

In an abelian group, the order of the product of two elements can be determined using the concept of the least common multiple (LCM) of their individual orders.

Let a and b be elements of an abelian group, where the order of a is m and the order of b is n. The order of an element in a group is defined as the smallest positive integer k such that the element raised to the power of k yields the identity element.

In this case, the order of the product ab can be determined by considering the LCM of m and n, denoted as lcm(m, n). The LCM is the smallest positive integer that is divisible by both m and n.

Therefore, the order of the product ab in the abelian group is lcm(m, n).

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Answer:

The correct answer is:

The graph will be the same width as the parent graph f(x) = x², but the vertex has been shifted to (1, 2).

Step-by-step explanation:

Since the value of a, the coefficient of x², is 1, this means the graph has not been stretched or shrunk. However, since the function is different than f(x)=x², we know that the vertex is not at (0, 0). We can write the function in vertex form to find the new vertex.

To write the function in vertex form, we find the value of b/2. The value of b in this function is -2; -2/2 = -1. We then square this: (-1)² = 1. This is what we add and subtract to the function (we must do both to preserve equality), giving us:

f(x) = x²-2x+1+3-1

The first three terms of this function can be written as the square (x+(b/2))²; this is (x-1)², and gives us f(x) = (x-1)²+3-1. Combining like terms, we have:

f(x) = (x-1)²+2

This is vertex form, f(x) = a(x-h)²+k, where (h, k) is the vertex. This means the vertex is at (1, 2) instead of (0, 0).

Answer:

It's the first graph :D

Step-by-step explanation: hope it helps ^w^

Answer:

\(\frac{b+1}{a} , \frac{6}{a}+\frac{b}{4}, a+\frac{1}{4}b, ab-17, \frac{b}{2} +4, 5a-6\)

Step-by-step explanation:
1) When b=8,

\(\frac{b}{2}+4=\frac{8}{2}= 4+4= 8\)

2) When a=3,

    5a-6= 5(3)-6

            = 15-6

            = 9

3) When a=3 and b=8,

\(\frac{b+1}{a} = \frac{8+1}{3} = \frac{9}{3} = 3\)

4) When a=3 and b=8,

    ab-17= (3)(8)-17

             = 24-17

             = 7

5) When a=3 and b=8,

\(a+\frac{1}{4} b= 3+\frac{1}{4} (8)= 3+2=5\)

6) When a=3 and b=8,

\(\frac{6}{a}+\frac{b}{4}= \frac{6}{3}+\frac{8}{4}= 2+2= 4\)

Answer:

C) $130

Step-by-step explanation:

simplify the equation:

p = 210 - (20 * 4)

p = 210 - (80)

p = 130

Answer:

3

Step-by-step explanation:

$25×6.50=152.5

50÷13=0.26

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

The gradient vector field of function f(x,y) is given as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

Suppose that we have a function defined as follows:

f(x,y).

The gradient function is defined considering the partial derivatives of function f(x,y), as follows:

grad(f(x,y)) = fx(x,y) i + fy(x,y) j.

In which:

The function in this problem is defined as follows:

f(x,y) = xe^(3xy).

Applying the product rule, the partial derivative relative to x is given as follows:

fx(x,y) = e^(3xy) + 3xye^(3xy) = (1 + 3xy)e^(3xy).

Applying the chain rule, the partial derivative relative to y is given as follows:

fy(x,y) = 3x²e^(3xy).

Hence the gradient vector field of the function is defined as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

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Answer:

send the complete question . there are some missing signs .

According to the problem the product of (X —6)(3X + 4) is 3X² - 18X - 24.

Product is any item or service that is offered to the public for sale. It can be a physical product such as a car, a piece of clothing, or a computer, or it can be a service such as a haircut, a massage, or a restaurant meal. Products are typically developed to meet a customer's need or to solve a problem, and they are usually sold in exchange for money.

The product of (X —6)(3X + 4) can be found by using the distributive property and multiplying each term of the first binomial (X —6) by each term of the second binomial (3X + 4). This can be done by creating a table with the two binomials written out in two columns.
|  X  |  -6  |
| 3X  |  4   |
Then, multiply each term in the first column by each term in the second column and add the products together.
X*3X = 3X²
X*4 = 4X
-6*3X = -18X
-6*4 = -24
Therefore, the product of (X —6)(3X + 4) is 3X² - 18X - 24.

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Step-by-step explanation:

\( - 5n - 8(1 + 7n) = - 8 \\ 5n - 8 - 56n = - 8 \\ collecting \: like \: terms \: \\ 5n - 56n = - 8 + 8 \\ - 51n = 1 \\ n = \frac{1}{ - 51} \\ as \: 1 \: is \: consider \: as \: 0 \: \\ so \: answer \: is \: \\ n = - 51\)

Using the Fundamental Counting Theorem, it is found that you have 16 choices in building your bike.

It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

In this problem:

Thus, the total number of choices is given by:

N = 4 x 2 x 2 = 16.

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The first step is to Prepare. Heidi wants to make a 30 pounds of molasses solution. She mixes and solution together. How much mixture does she make?

The value of the arc length and area are 11. 2ft and 44.2 ft² respectively

To determine the arc length, we use the formula;

s = 2πr(θ/360)

Such that the parameters of the formula are expressed as;

Substitute the values, we get;

s = 2 × 3.14 × 8 × (80/360)

Divide the values, we get;

s = 50. 24(0. 22)

Multiply the values, we have;

s = 11. 2ft

The area of the sector is expressed as;

(θ/360º) × πr2

Substitute the values

80/360 × 3.14 ×8²

Find the square and multiply

0. 22 × 200. 96

Multiply

44.2 ft²

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Answer:

Solution.

Step-by-step explanation:

if to substitute x=5; y=2 into the both equation:

5+2=7; 5-2=3, then the answer is: Solution.

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

In contrast to mass media, interactive media messages converge, which means that they can be sent one to one, one to many, or many to many. The statement is true. Interactive media refers to media that allows active participation from the user, rather than one-way communication.

Interactive media messages converge, which means that they can be sent one to one, one to many, or many to many. This refers to the flexibility that is available for interactive media messages compared to mass media.In the case of interactive media, feedback is not only encouraged but also acknowledged and included in the ongoing communication process. In addition, as opposed to mass media, interactive media allows for one-on-one conversations between participants as well as between a sender and many recipients. The sender is not the only one conveying the message. The recipients can also send messages back, resulting in a more interactive experience.

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Answer:

PART A

The amount of snowfall and number of trucks is proportional.

Because the increase in snowfall, increases the number of trucks sent out as read from the table.

PART B

\( let \: the \: number \: of \: tracks \: be \: x\\ by \: linear \: extrapolation \\ \binom{inches \: \: \: \: 12 \: \: 18 \: \: 23}{trucks \: \: \: \: 30 \: \: 45 \: \: x} \\ \frac{23 - 12}{x - 30} = \frac{18 - 12}{45 - 30} \\ \frac{11}{x - 30} = \frac{6}{15} \\ 11 \times 15 = 6(x - 30) \\ 165 = 6x - 180 \\ 6x = 165 + 180 \\ 6x = 345 \\ x = 57.5 \\ x = 58 \: trucks \\ hence \: 58 \: trucks \: were \: sent \: out\)

Answer:

PART A

The amount of snowfall and number of trucks is proportional.

Because the increase in snowfall, increases the number of trucks sent out as read from the table.

PART B

Let the number of tracks be x

By linear extrapolation, we get

inches | 12 | 18 | 23

trucks | 30 | 45 | x

(23 - 12)/(x - 30) = (18 - 12)/(45 - 30)

(11)/(x - 30)=6/15

11×15 = 6(x - 30)

165 = 6x - 180

6x = 165 + 180

6x = 345

x = 57.5

x = 58 trucks

Hence, 58 trucks were sent out.

Answer:

mean = 24

Step-by-step explanation:

From inspection, there are 7 values.

The values are 12, 13, 15, 28, 28, 30, 42

To find the mean, sum the numbers: 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

Divide by the number of values:  168 ÷ 7 = 24

Therefore, mean = 24

√18

The closest perfect square to 18 are 16 and 25. Hence the closest integers to √18 are 4 and 5.

ii. √360

The closest perfect squares to 360 are 324 and 361. Hence the closest integers to √360 are 18 and 19.

-√195

The closest integers to 196 and 169. Hence the closest integers to -√195 are -14 and -13.

Range of a function are the output values of the function:

since the domain is (-3, 0, 4), then we have to substite x with this values:

f(x)=2(-3)-4

f(x)=-6-4

f(x)=-10

f(x)=2(0)-4

f(x)=-4

f(x)=2(4)-4

f(x)=4

Range of the function is (-10, -4, 4)

Answer:

B

Step-by-step explanation:

44/77

=0.55

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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Answer:

18/8= 9/4

Step-by-step explanation:

3x6=18 the denominator is 8 so 8x1 is 8 simplified by 2

hope this helped!

Answer:2 1/4

Step-by-step explanation:

Because I know what it is

Therefore, the numerical value of the sample statistic (sample proportion) in this case is 0.36 or 36%.

The sample statistic in this case is the proportion of people in the sample who preferred candidate A.

Given:

Sample size (n) = 600

Number of people who preferred candidate A in the sample (x) = 216

The sample statistic, which represents the proportion of people who preferred candidate A in the sample, can be calculated as:

Sample proportion (p-hat) = x / n

Substituting the given values:

Sample proportion (p-hat) = 216 / 600

= 0.36

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Always use alpha=0.05 since it's the most commonly used one. Use a smaller alpha when the consequences of mistakenly rejecting the null hypothesis are more serious.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H0.

When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a smaller alpha. Generally speaking, you should reject the null hypothesis less frequently when there is a greater risk of doing so, which happens as you lower the significance level.

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The numerical or verbal descriptions that usually result from measurements are called data or observations.

When measurements are conducted, whether in scientific experiments, surveys, or other data collection processes, the outcome is typically a set of data or observations.

These measurements can be represented numerically, such as numerical values or quantities, or verbally, using descriptive terms or categories.

Numerical descriptions provide precise quantitative information, such as measurements of length, weight, temperature, time, or any other measurable attribute. These measurements are often expressed using numbers or units of measurement.

Verbal descriptions, on the other hand, use words or qualitative descriptions to convey information about the observations.

For example, when conducting a survey, respondents might provide verbal responses that describe their opinions, preferences, or experiences.

Both numerical and verbal descriptions play important roles in data analysis and interpretation.

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Answer:

49-9i²

Step-by-step explanation:

(7+3i)(7-3i)

expand the brackets

49-21i +21i -9i²

49-9i²

Answer:

6,11,17

Step-by-step explanation:

One of the properties of a triangle is that the sum of two sides must be greater than the third side

Therefore adding 6 +11=17,which does not hold for the properties of the triangle.