Help lol: Determine the missing side length:

Any height below the ground level is usually considered to be negative while any one above the ground level is usually considered to be positive.

Depth of first level of parking garage = 21.4 ft

149.8/7 = 21.4 ft

Height of each floor = 21.4 ft

This will also be the same depth of the first floor.

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Answer:

21.4 ft

Step-by-step explanation:

its the answer no need to explain

The average speed on the winding road was 45 mph.

The bus traveled for 3 hours on the winding road, so the distance covered can be calculated using the formula: Distance = Speed × Time. Let's assume the average speed on the winding road as 'x' mph. Therefore, the distance covered on the winding road is 3x miles.

On the straight road, the bus traveled for 3 hours at an average speed that was 12 mph faster than its average speed on the winding road. So the average speed on the straight road can be expressed as 'x + 12' mph. The distance covered on the straight road can be calculated as 3(x + 12) miles.

The total distance covered in the entire trip is given as 210 miles. Therefore, we can write the equation:

3x + 3(x + 12) = 210

Simplifying the equation:

3x + 3x + 36 = 210

6x + 36 = 210

6x = 174

x = 29

So the average speed on the winding road was 29 mph.

The problem states that the bus traveled for 3 hours on both the winding road and the straight road. Let's assume the average speed on the winding road as 'x' mph. Since the bus traveled for 3 hours on the winding road, the distance covered can be calculated as 3x miles.

On the straight road, the average speed was 12 mph faster than on the winding road. Therefore, the average speed on the straight road can be expressed as 'x + 12' mph. The distance covered on the straight road can be calculated as 3(x + 12) miles.

The total distance covered in the entire trip is given as 210 miles. This allows us to set up the equation 3x + 3(x + 12) = 210 to solve for 'x'. Simplifying the equation leads to 6x + 36 = 210. Solving for 'x', we find that the average speed on the winding road was 29 mph.

In summary, the average speed on the winding road was 29 mph.

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Answer:

Step-by-step explanation:

Slope-intercept form: y = mx + b

Isolate the y. Note the equal sign, what you do to one side, you do to the other.

First, subtract 4x from both sides:

4x (-4x) - 5y = 2 (-4x)

-5y = -4x + 2

Next, divide -5 from both sides:

(-5y)/-5 = (-4x + 2)/-5

y = (4/5)x - (2/5)

\(y = \frac{4}{5}x - \frac{2}{5}\) is your answer.

~

The 44th term of the arithmetic sequence with a first term of 3510 and a common difference of -15 is 2850.

To find the term of the arithmetic sequence that corresponds to the value 2850, we can use the formula for the nth term of an arithmetic sequence:

nth term = first term + (n - 1) * common difference

In this case, the first term is 3510 and the common difference is -15. Let's substitute these values into the formula and solve for n:

2850 = 3510 + (n - 1) * (-15)

Now we can simplify the equation:

2850 = 3510 - 15n + 15

Subtract 3510 from both sides:

-660 = -15n

To solve for n, divide both sides of the equation by -15:

n = -660 / -15

Simplifying further:

n = 44

Therefore, the 44th term of the arithmetic sequence with a first term of 3510 and a common difference of -15 is 2850.

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The partial sum of the given sequence, 1 + 10 + 19 + ... + 199, can be found by identifying the pattern and using the formula for the sum of an arithmetic series.  Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

To find the partial sum of the given sequence, we can observe the pattern in the terms. Each term is obtained by adding 9 to the previous term. This indicates that the common difference between consecutive terms is 9.

The formula for the sum of an arithmetic series is Sₙ = (n/2)(a + l), where Sₙ is the sum of the first n terms, a is the first term, and l is the last term.

In this case, the first term a is 1, and we need to find the value of l. Since each term is obtained by adding 9 to the previous term, we can determine l by solving the equation 1 + (n-1) * 9 = 199.

By solving this equation, we find that n = 23, and the last term l = 199.

Substituting the values into the formula for the partial sum, we have:

S₂₃ = (23/2)(1 + 199),

= 23 * 200,

= 4600.

However, this sum includes the terms beyond 199. Since we are interested in the partial sum up to 199, we need to subtract the excess terms.

The excess terms can be calculated by finding the sum of the terms beyond 199, which is (23/2)(9) = 103.5.

Therefore, the partial sum of the given sequence is 4600 - 103.5 = 4496.5, or approximately 4497 when rounded.

Hence, the partial sum of the sequence 1 + 10 + 19 + ... + 199 equals 4497.

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Answer

The height of the plane at that time is 1.1 miles

The distance of the plane's path is 10.1 miles

Explanation

The situation models a right angle triangle as shown below

Using trigonometric ratio,

tan 6° = opposite / adjacent

The opposite side of the triangle is the height of the plane. The distance traveled horizontally is the adjacent side. Therefore,

The height of the plane at that time ≈ 1.1 miles

The hypotenuse of the triangle formed is the distance of the plane path.

Therefore, this distance can be calculated using Pythagoras rule as follows:

The distance of the plane's path = 10.1 miles

Answer:

24,024 different ways

Step-by-step explanation:

There are 9 boys and 13 girls competing for the medals. The number of ways to choose 3 boys out of 9 is C(9,3) = 84. The number of ways to choose 3 girls out of 13 is C(13,3) = 286. The total number of ways to choose 6 medals is the product of these two numbers: 84 * 286 = 24024.

Answer:

\(f(x)=-3x^2\)

Step-by-step explanation:

A quadratic function is a function in which its degree (Highest power of the variable) is 2.

\(f(x)=-3x^2\) is the function that has a degree of 2.

Answer:

7pq

Step-by-step explanation:

because we are subtracting a negative we add the coefficients

Answer:

8pq

Step-by-step explanation:

5pq-(-3pq), 3pq turns into a positive because two negatives create a positive, so 5pq+3pq. That is just simple math, so 5pq+3pq=8pq.

Answer:

325 divided by 5= 65

Step-by-step explanation:

Answer:

325/5= 65mph

.........

Answer:

Step-by-step explanation:

The trace of the matrix a−1 can be found by summing the diagonal elements of a−1.

To provide an explanation, the trace of a matrix is defined as the sum of its diagonal elements. In this case, a−1 is the inverse of a, which means that aa−1 = I, where I is the identity matrix.

Using the definition of matrix multiplication, we can write this as:

∑k=1naikbkj=δij

where δij is the Kronecker delta function, which equals 1 if i=j and 0 otherwise.

If we multiply both sides of this equation by a−1, we get:

∑k=1naik∑j=1nbkj[bij]=∑k=1naikδik=aii

where we used the fact that the product of a matrix and its inverse is the identity matrix, so we can substitute bjk for δjk.

Therefore, the diagonal elements of a−1 are the reciprocal of the diagonal elements of a, and the trace of a−1 is the sum of these reciprocals.

to find the trace of the matrix a−1, we simply need to sum the diagonal elements of a−1, which are the reciprocals of the diagonal elements of a.

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To prove the statement "For all integers n ≥ 0, 7 divides \(8^{n-1}\)" by mathematical induction, we need to show that the statement holds for the base case (n = 0) and then establish the inductive step to show that if the statement holds for some arbitrary integer k, it also holds for k + 1.

Base Case (n = 0):

When n = 0, the statement becomes 7 divides \(8^0 - 1\), which simplifies to 7 divides 0. This is true since any number divides 0.

Inductive Step:

Assume that for some arbitrary integer k ≥ 0, 7 divides \(8^k - 1\). This is our induction hypothesis (IH).

We need to show that the statement holds for k + 1, which means we need to prove that 7 divides \(8^{k+1} - 1\).

Starting with \(8^{k+1} - 1\), we can rewrite it as \(8 * 8^k - 1\).

By using the distributive property, we get \((7 + 1) * 8^k - 1\).

Expanding this expression, we have \(7 * 8^k + 8^k - 1.\)

Using the induction hypothesis (IH), we know that 7 divides \(8^k - 1\). Therefore, we can write \(8^k - 1\)as 7m for some integer m.

Substituting this value into the expression, we have \(7 * 8^k + 7m\).

Factoring out 7, we get \(7(8^k + m)\).

Since \(8^k + m\) is an integer, let's call it n (an arbitrary integer).

Thus, we have 7n, which shows that 7 divides \(8^{k+1} - 1\).

Therefore, by mathematical induction, we have proved that for all integers n ≥ 0, 7 divides \(8^n - 1\).

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The probability of a random variable x being greater than 43 if it is normally distributed with a mean of 50 and a standard deviation of 7 is 0.22662735237686885.

The formula for the normal distribution is:

P(x) = 1/(sqrt(2*pi*o^2)) * e^(-(x-u)^2/(2*o^2))

where u is the mean and o is the standard deviation.

For the first part, we have u = 50 and o = 7.

So, P(x>43) = 1/(sqrt(2*pi*7^2)) * e^(-(43-50)^2/(2*7^2)) = 0.22662735237686885

For the second part, we have u = 81 and o = 4.

So, P(x<76) = 1/(sqrt(2*pi*4^2)) * e^(-(76-81)^2/(2*4^2)) = 0.8413447460685429

The probability of a random variable x being greater than 43 if it is normally distributed with a mean of 50 and a standard deviation of 7 is 0.22662735237686885. Similarly, the probability of a random variable x being less than 76 if it is normally distributed with a mean of 81 and a standard deviation of 4 is 0.8413447460685429. This can be calculated using the formula for the normal distribution, which is P(x) = 1/(sqrt(2*pi*o^2)) * e^(-(x-u)^2/(2*o^2)), where u is the mean and o is the standard deviation.

the complete question is : Assume the random variable x is normally distributed with mean u = 50 and standard deviation o = 7.

Find the indicated probability. P(x >43) P(x>43)=

Assume the random variable x is normally distributed with mean u = 81 and standard deviation = 4.

Find the indicated probability. P(x <76) P(x<76)= 0.8413447460685429

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Answer:

$5 for a dog treat

$3 for a cat treat

Step-by-step explanation:

week 1: 6d + 4c = 42

week 2: 2d + 7c = 31

*used calculator & guessed what each treat costs*

WEEK 1:

6(5) + 4(3) = 42

30 + 12 = 42

42 = 42

WEEK 2:

2(5) + 7(3) = 31

10 + 21 = 31

31 = 31

Answer:

Eleventeen

Step-by-step explanation:

Answer:

THIRTEEN

Step-by-step explanation:

The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.

Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.

This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.

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The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.

Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.

This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.

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Complete questions as follows-
What value makes the expressions equivalent?
6(3x+5) and 15x+□+3x

A. 5
B.11
C.15
D.30

Hey there! I'm happy to help!

Let's flip the equation so m is on the left.

3m-16=-40

Let's isolate the m to see what it equals. We add 16 to both sides.

3m=-24

And we divide both sides by 3.

m=-8.

Have a wonderful day! :D

Answer:

Step-by-step explanation:

3m - 16 = -40

3m = -24

m = -8

Answer:

900 in a minute

Step-by-step explanation:

2700/3

=900

The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:

\(81x^6 - (y + 1)^2\)

Replacing U and V:

\(81(3x^3)^2 - (V)^2\)

Simplifying:

\(81 \times 9x^6 - V^2\)

\(729x^6 - V^2\)

Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)

In this way, we can represent the original expression in a simplified form using the assigned values for U and V.

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Consider the expression: \(81x^6 - (y + 1)^2\)

If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

Answer:

= Divide the 26 feet by 3.25 feet

26 ÷ 3.25 = 8

= then Multiply the 8 by 1.7 degrees

8 × 1.7 = 13.6

= Subtract 13.6 from 26 feet

26 - 13.6 = 12.4

= Round 12.4 to the nearest tenth

12.4 = 12

Answer: 12

Answer:

Answer on a graph

3.3 ÷ 0.3

3.3 = 33/10

0.3 = 3/10

33/10 ÷ 3/10 = 11

Answer: The mean is 24, and the median is 26.5 .

Step-by-step explanation: To find the mean, one must add all the numbers in a set of data and divide it by the amount of numbers added. To find the median, one must line the numbers in a set of data from biggest to smallest. The number in the middle is the median. If the amount of numbers in the set are even, resulting in no middle, the two numbers closest to the middle are added and then divided by two. The resulting number is the median. In this case I had to add and divide.

It is important for scientists to use all of their results because selective reporting can lead to biased or incomplete conclusions. Including all results helps ensure objectivity and transparency in scientific findings.

When the evidence neither supports nor contradicts the hypothesis, it is crucial for scientists to acknowledge and report this outcome. It indicates the need for further investigation and can contribute to the accumulation of knowledge. Scientists should explore alternative explanations, refine their hypotheses, or modify their experimental approaches to gain a deeper understanding of the phenomenon.

Scientists repeating each other's experiments serves as a vital aspect of the scientific process called replication. Replication helps validate or challenge previous findings, ensures the reliability of results, and identifies any potential errors or biases. It enhances the overall credibility and robustness of scientific knowledge by promoting consensus and reducing the likelihood of false or misleading conclusions.

Regarding whether there is any scientific knowledge that it would be better not to have, it is a complex question. Generally, scientific knowledge empowers humanity by expanding our understanding of the world and driving progress. However, ethical considerations may arise in certain areas, such as knowledge that could be weaponized or have harmful consequences if misused. Responsible dissemination and application of scientific knowledge, along with ethical frameworks, help ensure the benefits outweigh the potential risks.

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Answer:

x≤ 25.

Step-by-step explanation:

SO basically, the equation is x+-7≤ 18.  What you do is you use the equation to solve for x. So,  x+-7 is the same as x-7, so what you do is you add 7 from both sides to get x≤ 25.

Hope this helps:)

The graph which could represent an inequality which begins with y < .... is; Choice C; C.

It follows from the task content that the graph which could represent an inequality that begins with y < ..is required to be determined.

Since the inequality symbol is less; it follows that the boundary line for the inequality would be a broken line and the region shaded is the region below the line.

Ultimately, the graph that could represent the inequality is; Choice C; C.

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The values of the trig ratios is Sin X = a/c, Cos X = b/c and Tan X = a/b.

The value of each of the trig ratio is determined by applying a short formula known as SOH CAH TOA  as shown below;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

Let the opposite side of angle X = a

Let the adjacent side of angle X = b

Let the hypothenuse side of angle X =  c

The values of the trig ratios is calculated as follows;

Sin X = a/c

Cos X = b/c

Tan X = a/b

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