what is the answer to
-4x12

The value of x in the triangle is (a) 30√2

The complete question is in the attached image.

From the attached image of the triangle, we can see that the triangle is a right triangle, and x can be solved using the following sine function

\(\sin(45) = \frac{30}{x}\)

Evaluate sin(45)

\(\frac 1{\sqrt 2} = \frac{30}{x}\)

Solve for x

\(x = 30 * \sqrt 2\)

Evaluate

\(x = 30 \sqrt 2\)

Hence, the value of x in the triangle is (a) \(30 \sqrt 2\)

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Answer:

c 12.45

Step-by-step explanation:

The amount that is saved compared to the original price will be $12.45. Then the correct option is C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The original price of the one T-shirt and one pair of sandals will be

⇒ $15.95 + $12.99

⇒ $28.94

The price of one T-shirt and one pair of sandals at the sale will be

⇒ $8.99 + $7.50

⇒ $16.49

The amount that is saved compared to the original prices if you buy one T-shirt and one pair of sandals at the sale prices will be

⇒ $28.94 + $16.49

⇒ $12.45

Then the correct option is C.

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Answer:

$765

Step-by-step explanation:

\(interest \: = \frac{prt}{100} \\ = \frac{(450)(5)(14)}{100} \\ = 315 \\ total \: money \: = 315 + 450 \\ = 765\)

A(n) = 450 + (n – 1)(0.05 • 450); $765.00

The width of the new interval is about three times the width of the original interval. As the sample size decreases, the standard error of the estimate increases, resulting in a wider confidence interval. In fact, the width of a confidence interval is inversely proportional to the square root of the sample size.

The width of a confidence interval is affected by three factors: the sample size, the level of confidence, and the variability of the data. In this case, the sample size has decreased from 225 to 25, while the level of confidence and the variability of the data have remained constant.

As the sample size decreases, the standard error of the estimate increases, resulting in a wider confidence interval. In fact, the width of a confidence interval is inversely proportional to the square root of the sample size.

To be more specific, the formula for the width of a confidence interval for a population proportion is:

Width = 2 × zα/2 × SE

where zα/2 is the critical value of the standard normal distribution corresponding to the desired level of confidence, SE is the standard error of the estimate, and the factor of 2 is used to account for the two-sided nature of the interval.

Assuming a 95% level of confidence and a sample proportion of 0.5, the standard error of the estimate for the original sample size of 225 is:

SE = sqrt[(0.5 × 0.5) / 225] = 0.033

The critical value of zα/2 for a 95% level of confidence is approximately 1.96. Therefore, the width of the original confidence interval is:

Width = 2 × 1.96 × 0.033 = 0.13

For a new sample size of 25, the standard error of the estimate becomes:

SE = sqrt[(0.5 × 0.5) / 25] = 0.1

Using the same critical value of zα/2, the width of the new confidence interval is:

Width = 2 × 1.96 × 0.1 = 0.39

Therefore, the width of the new interval is about three times the width of the original interval.

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The answer would be 27/8.

Answer: The slope is 1/8

Step-by-step explanation:

The x values go up by 8. That gives the run.

the y values go up by 1. That gives the rise.

Slope is rise/run  SO

1/8 is the slope.

Graph attached.

Answer:

Slope = 4

Step-by-step explanation:

Answer:

wHOLE number

Step-by-step explanation:

IT is a whole number

Answer:

The answer is 6.64 I believe.

Answer:

The answer would be 6.64

Step-by-step explanation:

He will read 700 pages each day.He must be committed to reading this amount of pages each day in order to finish the book in two days.

1. There are 1400 pages in the book.

2. The book must be read in even days.

3. To find the number of pages read each day, divide 1400 by 2 (since it must be read in two days).

4. The answer is 700 pages read each day.

The book contains 1400 pages and must be read in two days. To find the answer, the number of pages must be divided by two. This means that each day, he must read 700 pages. This is the same amount each day, so he will read the same amount of pages for each day he reads it. He will have to read for two days in order to finish the book and will read 700 pages for each day. He must be committed to reading this amount of pages each day in order to finish the book in two days.

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Millimeter (mm) and inch are both units of measurement for length, but they are not equivalent. One inch is equal to 25.4 millimeters. To convert inches to millimeters you multiply the number of inches by 25.4, for example 2 inches is equal to 50.8 millimeters. It's important to note that you can also use a conversion calculator or a conversion table to convert inches to millimeters.

A millimeter (mm) and an inch are both units of measurement for length. However, they are not equivalent and cannot be directly compared.

A millimeter is a metric unit of length, commonly used in most countries around the world. It is a unit of the International System of Units (SI) and it is one of the most widely used units of length in science and engineering. An inch, on the other hand, is an imperial unit of length that is mainly used in the United States. It is part of the British Imperial system of measurements and it is one of the most widely used units of length in the United States.

To convert inches to millimeters, we use the conversion factor that 1 inch is equal to 25.4 millimeters. So to convert inches to millimeters you multiply the number of inches by 25.4. For example, if you want to convert 2 inches to millimeters, you would multiply 2 by 25.4 to get 50.8 millimeters. It's important to note that you can also use a conversion calculator or a conversion table to convert inches to millimeters.

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Answer:

1/2

Step-by-step explanation:

Cos 60 = \(\frac{adjacent}{hypotenuse}\)

1/2 = \(\frac{XZ}{4}\)

Multiplying both sides by 4

=> XZ = 2

Sin Y = \(\frac{opposite}{hypotenuse}\)

Sin Y = \(\frac{2}{4}\)

Sin Y = 1/2

Answer:

-1.

Step-by-step explanation:

The difference of -3 and a number is -2. Find the number:

-3 - x = -2

x = -2 + (-3)

x = -1

-1 is the answer.

Formula to calculate combinations is given by -

nCr=[n !]/[r ! * (n-r) !]

where,

nCr = number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

Now, according to given -

n = 10 people

r = 5 callers

Hence,

Number of possible combinations = nCr

= 10C5

= (10!)/[5! * (10-5)!]

= 252

Thus, 252 different people could have made successful calls to the radio station.

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The correct answer is 1.6. By solving the proportion, we determined that the value of k that satisfies the given equation is approximately 1.6.

To find the unknown value, k, in the proportion (k)/(1.2) = (4)/(3), we can cross-multiply and solve for k.

cross-multiplying the proportion, we have:

3k = 4 * 1.2

Multiplying the numbers:

3k = 4.8

To isolate k, we divide both sides of the equation by 3:

k = 4.8 / 3

Evaluating the division, we find:

k ≈ 1.6

Therefore, the correct answer is 1.6. By solving the proportion, we determined that the value of k that satisfies the given equation is approximately 1.6.

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Angie walked a total of 1.8 miles. These distances are assumptions and may vary depending on the actual length of each trail.

Angie walked from the parking lot along Oak Trail to the picnic area, and then to the Pine Trail before returning to the parking lot. To calculate the total distance she walked, we need to know the length of each trail.

Let's assume the distance from the parking lot to the picnic area along Oak Trail is 0.5 miles. From the picnic area to the Pine Trail, let's assume the distance is 0.7 miles. Finally, from the Pine Trail back to the parking lot, let's assume the distance is 0.6 miles.

To find the total distance Angie walked, we can add up the distances of each leg of her journey:

0.5 miles (parking lot to picnic area) + 0.7 miles (picnic area to Pine Trail) + 0.6 miles (Pine Trail back to parking lot) = 1.8 miles

Therefore, Angie walked a total of 1.8 miles.

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The author's opinion on the possibility of life on ten planets may differ from NASA scientists, as the author's perspective could be speculative while NASA scientists rely on scientific research and data.

According to the given information, there is no specific article mentioned to refer to. However, based on general knowledge, it can be stated that the author's opinion on the possibility of life on ten planets may vary from NASA scientists.

   The author's perspective might be subjective, speculative, or based on hypothetical scenarios, while NASA scientists' opinions are typically grounded in scientific research and data. NASA scientists would likely rely on concrete evidence, such as data from telescopes, space probes, and missions, to assess the potential for life on different planets.



Therefore, NASA scientists' opinions are more likely to be objective and scientifically supported, while the author's opinion may be more speculative or imaginative in nature.

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Answer:

The domain of a function is the set of all input values of the function. The range of a function is the set of all possible outputs of the function, given its domain.

Answer:

see explanation

Step-by-step explanation:

Firstly, dividing by zero is undefined.

given

f(x) = \(\frac{x}{x-1}\) , then

f(1) = \(\frac{1}{1-1}\) = \(\frac{1}{0}\) = undefined

About $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.

What is a graph ?

A graph is a visual representation of data that shows the relationship between two or more variables. It is a way of presenting information in a clear and concise manner that makes it easy to interpret and understand.

Graphs can be used to show trends over time, compare different groups or categories, or illustrate the relationship between two or more variables.

Since the graph shows the balance for two accounts with the same principal and annual interest rate, we can assume that one account is earning simple interest while the other is earning compound interest.

To estimate the amount of compound interest earned after 35 years, we can look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 35 years is approximately $4,000, while the balance for the compound interest account is approximately $10,000. Therefore, the amount of compound interest earned after 35 years is approximately:

$10,000 - $4,000 = $6,000

To estimate the amount of compound interest earned after 45 years, we can again look at the difference in balance between the two accounts at that time. From the graph, we can see that the balance for the simple interest account after 45 years is approximately $5,500, while the balance for the compound interest account is approximately $18,000. Therefore, the amount of compound interest earned after 45 years is approximately:

$18,000 - $5,500 = $12,500

Therefore,  about $6,000 more compound interest than simple interest is earned after 35 years, and about $12,500 more compound interest than simple interest is earned after 45 years.

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Answer:

t ≤ 2.8

Leo can travel no more than 2.8 hours or 2 hrs, 48 min

Step-by-step explanation:

50t ≤ 140

t ≤ 140/50

t ≤ 2.8

Answer:

\(y=c_1\cos(x)+c_2\+\sin(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}}}\)

Step-by-step explanation:

Given the second-order differential equation, \(y'' + y = cos2(x)\), solve it using variation of parameters.

(1) - Solve the DE as if it were homogenous and find the homogeneous solution\(y'' + y = cos2(x) \Longrightarrow y'' + y =0\\\\\text{The characteristic equation} \Rightarrow m^2+1=0\\\\m^2+1=0\\\\ \Longrightarrow m^2=-1\\\\\ \Longrightarrow m=\sqrt{-1} \\\\\Longrightarrow \boxed{m=\pm i} \\ \\\text{Solution is complex will be in the form} \ \boxed{y=c_1e^{\alpha t}\cos(\beta t)+c_2e^{\alpha t}\sin(\beta t)} \ \text{where} \ m=\alpha \pm \beta i\)

\(\therefore \text{homogeneous solution} \rightarrow \boxed{y_h=c_1\cos(x)+c_2\sin(x)}\)

(2) - Find the Wronskian determinant

\(|W|=\left|\begin{array}{ccc}y_1&y_2\\y'_1&y'_2\end{array}\right| \\\\\Longrightarrow |W|=\left|\begin{array}{ccc}\cos(x)&\sin(x)\\-sin(t)&cos(x)\end{array}\right|\\\\\Longrightarrow \cos^2(x)+\sin^2(x)\\\\\Longrightarrow \boxed{|W|=1}\)

(3) - Find W_1 and W_2

\(\boxed{W_1=\left|\begin{array}{ccc}0&y_2\\g(x)&y'_2\end{array}\right| and \ W_2=\left|\begin{array}{ccc}y_2&0\\y'_2&g(x)\end{array}\right|}\)

\(W_1=\left|\begin{array}{ccc}0&\sin(x)\\\cos^2(x)&\cos(x)\end{array}\right|\\\\\Longrightarrow \boxed{W_1= -\sin(x)\cos^2(x)}\\\\W_2=\left|\begin{array}{ccc}\cos(x)&0\\ -\sin(x)&\cos^2(x)\end{array}\right|\\\\\Longrightarrow \boxed{W_2= \cos^3(x)}\)

(4) - Find u_1 and u_2

\(\boxed{u_1=\int\frac{W_1}{|W|} \ and \ u_2=\int\frac{W_2}{|W|} }\)\

u_1:

\(\int(\frac{-\sin(x)\cos^2(x)}{1}) dx\\\\\Longrightarrow-\int(\sin(x)\cos^2(x)) dx\\\\\text{Let} \ u=\cos(x) \rightarrow du=-sin(x)dx\\\\\Longrightarrow\int u^2 du\\\\\Longrightarrow \frac{1}{3}u^3\\ \\\Longrightarrow \boxed{u_1=\frac{1}{3}\cos^3(x)}\)

u_2:

\(\int\frac{\cos^3(x)}{1}dx\\ \\\Longrightarrow \int \cos^3(x)dx\\\\ \Longrightarrow \int (\cos^2(x)\cos(x))dx \ \ \boxed{\text{Trig identity:} \cos^2(x)=1-\sin^2(x)}\\\\\Longrightarrow \int[(1-\sin^2(x)})\cos(x)]dx\\\\\Longrightarrow \int \cos(x)dx-\int (\sin^2(x)\cos(x))dx\\\\\Longrightarrow \sin(x)-\int (\sin^2(x)\cos(x))dx\\\\\text{Let} \ u=\sin(x) \rightarrow du=cos(x)dx\\\\\Longrightarrow \sin(x)-\int u^2du\\\\\Longrightarrow \sin(x)-\frac{1}{3} u^3\)\

\(\Longrightarrow \boxed{u_2=\sin(x)-\frac{1}{3} \sin^3(x)}\)

(5) - Generate the particular solution

\(\text{Particular solution} \rightarrow y_p=u_1y_1+u_2y_2\)

\(\Longrightarrow y_p=(\frac{1}{3}\cos(x))(\cos(x))+(\sin(x)-\frac{1}{3} \sin^3(x))(\sin(x))\\\\ \Longrightarrow y_p=\frac{1}{3}\cos^4(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)\\\\\Longrightarrow \boxed{y_p=\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}\)

(6) - Form the general solution

\(\text{General solution} \rightarrow y_{gen.}=y_h+y_p\)

\(\boxed{\boxed{y=c_1\cos(x)+c_2\+\sin(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}}}\)

Thus, the solution to the given DE is found where c_1 and c_2 are arbitrary constants that can be solved for given an initial condition. You can simplify the solution more if need be.

Answer:

Step-by-step explanation:

102

ml = 0 is valid so the sets of quantum numbers are validated or not validated as mentioned above.

Here are the given sets of quantum numbers for the hydrogen atom which need to be validated.

Set 1 (n=3, l=3, ml=0, ms=+1/2) - Valid or Not valid

Set 2 (n=2, l=1, ml=1, ms=-1/2) - Valid or Not valid

Set 3 (n=4, l=1, ml=0, ms=-1/2) - Valid or Not valid

The first step is to understand the set of quantum numbers. Each electron in an atom is assigned a set of four quantum numbers.

The four quantum numbers are: n, l, ml, and ms. The principal quantum number n, the angular momentum quantum number l, the magnetic quantum number ml, and the spin quantum number ms are the four quantum numbers that define the electron's state.

Set 1 (n=3, l=3, ml=0, ms=+1/2)

It is not valid because ml can be from -l to +l, and when l is 3, ml can be -3,-2,-1,0,1,2,3. So, the value of ml should be from -3 to +3.

Set 2 (n=2, l=1, ml=1, ms=-1/2)

It is valid because l = 1, so ml can be -1,0,1. Therefore, ml = 1 is valid.

Set 3 (n=4, l=1, ml=0, ms=-1/2)

It is valid because l = 1, so ml can be -1,0,1. Therefore, ml = 0 is valid.

Thus, the sets of quantum numbers are validated or not validated as mentioned above.

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Answer: 15v

Step-by-step explanation: we can combine all the terms since they all have “v” in them making 6+6+3 which is 15, just add “v” to get 15v

Answer:

b=34.2m

Step-by-step explanation:

equation for area of parallelogram

a=b×h

in which b is the base(length) and h is the height

\(690.84 = b \times 20.2\)

\(b = \frac{690.84}{20.2} \)

b=34.2m

Answer:

D

Step-by-step explanation:

Slope formula: m = (y2 - y1) / (x2 - x1)

First coordinate: (1, 3)

Second coordinate: (3, 9)

m = (9 - 3) / (3 - 1)

m = (6) / (2)

m = 3