The formula f equals c over lambda, where f = frequency, c = wave speed, and λ = wavelength, is used to calculate frequency. Solve this formula for c.

Answer:

Step-by-step explanation:

Since the viewing angle between the star and Planet B is 19 degrees, we can use trigonometry to find the distances from Planet A to Planet B. Let's call these distances x and y, where x is the distance to the closer position of Planet B and y is the distance to the farther position of Planet B, as shown in the figure.

Using the Law of Cosines for the triangles with sides 65, x, and 45 (for the closer position) and 65, y, and 45 (for the farther position), we can write:

x^2 = 65^2 + 45^2 - 26545*cos(19) ≈ 2374.6

y^2 = 65^2 + 45^2 - 26545*cos(161) ≈ 10864.6

Taking the square roots of both sides, we get:

x ≈ 48.7 and y ≈ 104.2

Therefore, the possible distances from Planet A to Planet B are approximately 48.7 million miles (for the closer position of Planet B) and 104.2 million miles (for the farther position of Planet B), rounded to the nearest tenth.

From what I see in the problem, the expression is

\((\frac{3^a^2}{3a^-1} )^k\)

To solve, plug in a and k.

\((\frac{3^(5)^2}{3*5^-1} )^-2\)

3*5^2=75

(3*5)^-1 = 1/15

\(75 / \frac{1}{15} = 5\)

5^-2 = 1/25

The average rate of change of the function over the interval is -6

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = 2 to x = 4

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(2) = -3

f(4) = -15

Next, we have

Rate = (-15 + 3)/(4 - 2)

Evaluate

Rate = -6

Hence, the rate is -6

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Answer:

256x^8

Step-by-step explanation:

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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The distance from point A to point B is 582.83.

Given that,

A 141-foot-high lighthouse with a beacon is being approached by a boat. Before approaching the beacon, the boat's crew estimates the angle of elevation to it from point AA, 7°. Later, they take another measurement of the angle of elevation from point BB and find it to be 14°.

We have to find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Describe a slope.

The slope is calculated by dividing the vertical and horizontal changes.

Additionally, it is the tangent of the depression angle.

At point A:

The change in height is 141.

The position x base A that we are looking for is the horizontal change.

It is an 7° angle.

Tan7=\(\frac{141}{x_{A} }\)

\(x_{A}\)=141/Tan7

\(x_{A}\)=1148.35

At point B:

The change in height is 141.

The position x base B that we are looking for is the horizontal change.

It is an 14° angle.

Tan14=\(\frac{141}{x_{B} }\)

\(x_{B}\)=141/Tan14

\(x_{B}\)=565.52

The distance is

d=\(x_{A}-x_{B}\)=1148.35-565.52=582.83

Therefore, The distance from point A to point B is 582.83.

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Answer:

583

Step-by-step explanation:

I got this as a question and this is the correct answer!!

The equation is true, we have confirmed that x = 3 is the correct solution.

The equation shown in the image is:

4x + 12 = 24

To write a related multiplication equation, we can simplify the left side of the equation by factoring out the common factor of 4:

4(x + 3) = 24

By multiplying both sides of the equation by 4, we can now find x:

x + 3 = 6

x = 6 - 3

x = 3

Therefore, the solution to the original equation is x = 3. We can check this solution by substituting it back into the original equation:

4x + 12 = 24

4(3) + 12 = 24

12 + 12 = 24

24 = 24

Since the equation is true, we have confirmed that x = 3 is the correct solution.

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Answer:

x = 21

Step-by-step explanation:

corresponding sides in similar polygons are proportional:

set a proportion: BC/FK = CA/KJ => 18/6 = x/7 => x = 18 × 7 ÷ 6 = 21

Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let be \(f(x) = \frac{1}{8\cdot x}\cdot \ln(2\cdot x) -7\), the first and second derivatives of the function are, respectively:

\(f'(x) = \frac{\left(\frac{2}{2\cdot x}\right)\cdot 8\cdot x-8\cdot \ln (2\cdot x) }{64\cdot x^{2}}\)

\(f'(x) = \frac{8-8\cdot \ln (2\cdot x)}{64\cdot x^{2}}\)

\(f'(x) = \frac{1-\ln(2\cdot x)}{8\cdot x^{2}}\)

\(f''(x) = \frac{\left(-\frac{2}{2\cdot x} \right)\cdot (8\cdot x^{2})-[1-\ln(2\cdot x)]\cdot (16\cdot x)}{64\cdot x^{4}}\)

\(f''(x) = \frac{-8\cdot x-16\cdot x+16\cdot x\cdot \ln (2\cdot x)}{64\cdot x^{4}}\)

\(f''(x) = \frac{-24\cdot x+16\cdot x \cdot \ln (2\cdot x)}{64\cdot x^{4}}\)

\(f''(x) = -\frac{3}{8\cdot x^{3}}+\frac{\ln (2\cdot x)}{4\cdot x^{3}}\)

Now, let equalise the first derivative to zero and solve the resulting expression:

\(\frac{1-\ln(2\cdot x)}{8\cdot x^{2}} = 0\)

\(1-\ln(2\cdot x) = 0\)

\(\ln(2\cdot x) = 1\)

\(\ln 2 +\ln x = 1\)

\(\ln x = 1-\ln 2\)

\(x = e^{1-\ln 2}\)

\(x = \frac{e}{e^{\ln 2}}\)

\(x = \frac{e}{2}\)

\(x \approx 1.359\)

This result is evaluated at the second derivative expression:

\(f''(1.359) =-\frac{3}{8\cdot (1.359)^{3}}+\frac{\ln [2\cdot (1.359)]}{4\cdot (1.359)^{3}}\)

\(f''(1.359)\approx -0.050\)

The critical value leads to a critical maximum and there are two intervals:

\((0, 1.359)\) - Increasing

\((1.359,+\infty )\) - Decreasing

The graphic of the function is presented below as attachment.

The slope (m) is 1 and the y-intercept (b) is 33 for the equation y = x + 33.

The equation y = x + 33 represents a linear equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope (m) is the coefficient of x, which is 1. Therefore, the slope is 1.

The y-intercept (b) is the value of y when x is 0. In the given equation, y = x + 33, when x = 0, we can see that y = 0 + 33 = 33. Hence, the y-intercept is 33.

Therefore, the slope (m) is 1 and the y-intercept (b) is 33 for the equation y = x + 33.

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How to calculate force?

.Inorder to calculate force we will use Newton's second law of motion.

\(\\ \sf\longmapsto Force=Mass\times Acceleration \)

\(\\ \sf\longmapsto F=ma\)

Here we can observe

\(\\ \sf\longmapsto F\propto a\)

\(\\ \sf\longmapsto F\propto m\)

The expression is simplified to x = 10/ a

Subject of formula is defined as a variable which is expressed in terms of other variables involved in a given formula or expression.

Given the expression;

2 - ax = -8

Let's make 'x' the subject of formula

collect like terms

-ax = -8 - 2

Subtract like terms

-ax = - 10

Divide both sides by -a

-ax/ -a = - 10/-a

Find the ratio

x = 10/ a

Thus, the expression is simplified to x = 10/ a

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Answer:

-9

Step-by-step explanation:

because let's just say that 9 below 0 is -9, so it will be -9 degrees.

Comparison analysis is defined as describing the data in the sample with the use of percentages or averages. Hence, option A is the most suitable answer to this question.

Comparative analysis talks about the comparison of two or more data sets, or other objects. Comparing data becomes very easy when the data is consolidated with the help of average or mean, percentages, and rounding up of the decimals.

Comparison is a very important method to check the difference in the parameters of the two data sets. Not just comparing, summarization of this data is vital for understanding what that data actually means. Hence, we can say that comparison analysis is defined as describing the data in the sample with the use of percentages or averages.

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The complete question is -

Fill in the blanks -

________ analysis is defined as describing the data in the sample with the use of percentages or averages.

A) Comparison

B) Generalization

C) Relationship

D) Summarization

E) Confidence

The assumption in answering the question is that no student scored 0

From the question, we have the following parameters that can be used in our computation:

The bar chart

On the bar chart, we hae

Students that score more than 8 = 5

Students in the class = 33

The (b) is calculated by considering all students that score more than 0 from the histogram

This means that the assumption is that no student scored 0

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Answer:

  1/4 cup

Step-by-step explanation:

To make half a recipe, each of the quantities in the recipe must be multiplied by 1/2. Alvin will need ...

  (1/2) × (1/2 cup) = 1/4 cup

of bread crumbs.

The mean for the number of people with the genetic mutation in such groups of 600 is 18.

Given that,

About 3% of the population has a particular genetic mutation.

This means that for any group of people, 3% of the people has a particular genetic mutation.

This is a binomial distribution.

Probability that people having genetic mutation = 3% = 0.03

Random sample size = 600

Mean for a binomial distribution can be calculated as,

Mean = n × p

         = 600 × 0.03

         = 18

Hence the mean number of people having genetic mutation is 18.

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Subtract 229 and 164 its 65 so thats your answer .

Answer:

At 4:00 PM the distance between the two ships is 104.40 kilometers.

Step-by-step explanation:

Given that at noon, ship A is 150 km west of ship B, and ship A is sailing east at 30 km / h and ship B is sailing north at 25 km / h, to determine how fast is the distance between the ships changing at 4:00 PM the following calculation must be performed:

150 - (30 x 4) = 150 - 120 = 30

0 + (25 x 4) = 0 + 100 = 100

30 ^ 2 + 100 ^ 2 = X ^ 2

√ (900 + 10,000) = X

√10,900 = X

104.40 = X

Therefore, at 4:00 PM the distance between the two ships is 104.40 kilometers.

The z-score for the raw score of 39 is 1.The z-score for the raw score of 30 is -0.8.Z-scores measure the number of standard deviations a raw score is from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.

To find the z-scores, we need to use the formula:

z = (x - μ) / σ

where:

z is the z-score,x is the raw score,μ is the mean, andσ is the standard deviation.

Let's calculate the z-scores for the given mean of 34 and standard deviation of 5.For a raw score of 39:

z = (39 - 34) / 5

z = 5 / 5

z = 1

So, the z-score for the raw score of 39 is 1.For a raw score of 30:

z = (30 - 34) / 5

z = -4 / 5

z = -0.8

The z-score for the raw score of 30 is -0.8.

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Answer:

The actual dimensions of the floor are 12,5m by 1,8m.

Step-by-step explanation:

Scale problems are solved by proportions, using a rule of three.

Scale of 1:50

This means that each cm on the cupboard has a real dimension of 50 cm

25 cm on the cupboard:

So the real dimension is:

25*50 = 1250 cm = 12,5m

3.6 cm

The real dimension is:

3.6*50 = 160 cm = 1,8 m

The actual dimensions of the floor are 12,5m by 1,8m.

Answer:

  40 lb of Type A

Step-by-step explanation:

3 pounds of Type B and 1 pound of Type A will give 4 pounds of mix at a cost of ...

  3($4.65) +($5.95) = $19.90

Then $796 is the cost equivalent of 796/19.90 = 40 times that 4-lb mix. Since each instance of that 4-lb mix has 1 lb of Type A, $796 worth of blend has 40 lb of Type A coffee.

_____

Additional comment

If you'd like to do this using a variable, you can let 'a' represent the amount of Type A coffee used. Then (3a) is the amount of Type B, and the total cost is ...

  5.95a +4.65(3a) = 796

  19.90a = 796 . . . . . . . . simplify

  a = 796/19.90 = 40 . . . as above

___

There will be 120 lb of Type B coffee in that amount of blend.

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Answer:

Hence, the mean of the potato chips lie between the interval \((1.006, 1.194)\)

Given :

data is :

  \(1.1,1.2,1.0,0.9,1.1,1.3,1.2,1.1,1.0\)

Confidence level is \(95\%\).

To find :

Confidence interval.

Explanation :

Mean \(\bar{x}\) \(=\frac{\sum x}{n}\)

  \(\Rightarrow \bar{x}=\frac{1.1+1.2+1.0+0.9+1.1+1.3+1.2+1.1+1.0}{9}\)

  \(\Rightarrow \bar{x}=\frac{9.9}{9}\)

 \(\Rightarrow \bar{x}=1.1\)

Standard deviation \(\sigma\) \(=\sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}\)

   \(\Rightarrow \sigma=\sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}=0.122\)

here, \(\alpha=1-\;\text{confidence level}\)

     \(\Rightarrow \alpha=1-0.95=0.05\)

\(Z_{\frac{\alpha}{2}}=Z_{0.05}=2.306\) by the Z- table

\(95\%\) confidence interval is :

    \(\bar{x}\pm Z_{\frac{\alpha}{2}}\times \frac{\sigma}{\sqrt{n}}\)

\(\Rightarrow 1.1\pm 2.306\times \frac{0.122}{\sqrt{9}}\)

\(\Rightarrow 1.1\pm 2.306\times \frac{0.122}{3}\)

\(\Rightarrow 1.1\pm 0.094\)

\(\Rightarrow (1.006, 1.194)\)

Therefore, the mean of the potato chips lie between the interval \((1.006, 1.194)\)

Answer:

Number of year = 11.725 year (Approx.)

Step-by-step explanation:

Given:

Amount invested = $200

Interest rate = 6% (compounded semi annually)

Future value = 2 x Amount invested

Find:

Number of year

Commutation:

Future value = 2 x Amount invested

Future value = 2 x 200

Future value = $400

Number of year (Semi-annual) = 2n

Interest rate (Semi-annual) = 6% / 2 = 3%

So.

A = P[1+r]ⁿ

400 = 200[1+3%]²ⁿ

2 = [1.03]²ⁿ

n = 11.725 year

Number of year = 11.725 year (Approx.)