F(x) =∣x∣ g(x)=∣x+2∣ ​ we can think of g as a translated (shifted) version of f. complete the description of the transformation.

From the situation described in the problem, we have that:

a) The sinusoidal function that models the depth of the water is given by: D(t) = 2sin(π/6x) + 3.

b) After 4 hours, the depth is of 4.732 meters.

The sine function is defined as follows:

g(x) = a sin(bx+c)+d.

The coefficients are defined as follows:

For this problem, the minimum value is of 1 and the maximum value is of 5, having a difference of 4, hence the amplitude is found as follows:

2a = 4 -> a = 2.

A standard sine function with an amplitude of 2 varies between -2 and 2, while this varies between 1 and 5, meaning that it had a vertical shift up 3 units, and d = 3.

The period is of 12 hours, hence:

2π/B = 12

12B = 2π

B = π/6.

The function has no phase shift, hence c = 0 and the function is given by:

D(t) = 2sin(π/6x) + 3.

From point (4, 4.732) on the graph of the function, after 4 hours, the depth is of 4.732 meters.

More can be learned about sinusoidal functions at brainly.com/question/21558626

#SPJ1

Answer:

the first one is correct

Step-by-step explanation:

The angle of elevation from P to Q is 14.8°

The angle of elevation of point P from point Q can be discovered by using the concept of similar triangles. Let's consider the right triangles QSR and QTP.

In triangle QSR, we have:

QS = 25m (given)

SR = 5m (given)

Utilizing the Pythagorean hypothesis, able to discover QR:

QR = sqrt(QS^2 + SR^2) = sqrt(25^2 + 5^2) = sqrt(650) ≈ 25.5m

Presently, in triangle QTP, we have:

QT = QR + RT = 25.5m + 9m = 34.5m (since SR and TP are in line)

We are given that the angle of elevation of P from R is 30°. This implies that point PRT is 30°.

Utilizing trigonometry in triangle QTP, able to discover the angle of elevation of P from Q:

tan(angle PQT) = TP / QT

tan(angle PQT) = 9m / 34.5m

point PQT = arctan(9m / 34.5m) ≈ 14.8°

Hence, the angle of elevation of P from Q is  14.8°, redress to one decimal place.

Learn more about an angle of elevation here:

https://brainly.com/question/27243378

#SPJ1

The second derivative of v with respect to t, denoted as d²v/dt², is equal to 4

The second derivative of v with respect to t, we will differentiate v twice.

v = 2t² + 7t + 11

First, let's find the first derivative of v with respect to t (dv/dt):

dv/dt = d/dt (2t² + 7t + 11)

Using the power rule of differentiation, we differentiate each term separately:

dv/dt = 2(2t) + 7(1) + 0

dv/dt = 4t + 7

Now, let's find the second derivative of v with respect to t (d²v/dt²):

d²v/dt² = d/dt (4t + 7)

Again, using the power rule of differentiation, we differentiate each term separately:

d²v/dt² = 4(1) + 0

d²v/dt² = 4

Therefore, the second derivative of v with respect to t, denoted as d²v/dt², is equal to 4.

To know more about second derivative click here :

https://brainly.com/question/29090070

#SPJ4

Answer:The two true statements are:

A. The reflection point across the y-axis is (2, 6).

D. The reflection point across the x-axis is (¯2, ¯6).

Step-by-step explanation:

Answer:

The two true statements are:

A. The reflection point across the y-axis is (2, 6).

D. The reflection point across the x-axis is (¯2, ¯6).

Step-by-step explanation:

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

Explanation:

The square marker in the top left corner tells us we have a 90 degree angle. The 8x+10 must also be 90 degrees for lines u and v to be parallel. Refer to the alternate exterior angle theorem. Ignore the diagonal lines. Your teacher likely put them there as a distraction.

8x+10 = 90

8x = 90-10

8x = 80

x = 80/8

x = 10

The correct answer is option 2. The radius of the balloon after 9 minutes is approximately 0.7889 centimeters.

To find the radius of the balloon after 9 minutes, we substitute t = 9 into the equation r(t) = 3√t + 6:

r(9) = 3√9 + 6

r(9) = 3 * 3 + 6

r(9) = 9 + 6

r(9) = 15

Therefore, the radius of the balloon after 9 minutes is 15 centimeters.

However, none of the given options match the value of 15 centimeters. It is possible that there was an error in the options provided or in the calculations. If we assume that option 2 corresponds to the radius after 9 minutes, the value of 0.7889 centimeters does not align with the equation r(9) = 15. Therefore, there may be a discrepancy in the options or in the calculations provided.

Learn more about radius here:

https://brainly.com/question/13449316

#SPJ11

The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

For more such information on: significant figures

https://brainly.com/question/30169

#SPJ8

Given that the particle moves along the curve y=e^(2x) and the magnitude of its velocity is v=5ft/s.A particle moving along a curve is given by:y = e^(2x)Taking the derivative of this function with respect to time t will give the velocity function as follows;dy/dt = 2e^(2x) dx/dt ............................... (1)We know that the magnitude of velocity is constant v = 5ft/s.

Therefore, we can use the velocity function to solve for dx/dt and dy/dt as shown below;dx/dt = v/√(4e^(4x)) = v/(2e^(2x)) ................ (2)Substituting equation (2) into (1), we get;dy/dt = 2e^(2x) dx/dt = 2e^(2x) * v/(2e^(2x))=v = 5 ft/sHence, the y-component of velocity when the particle is at y = 8 ft is 5 ft/s.

Therefore, we can use the slope of the curve at point y = 8 ft to find the angle of the slope, then use trigonometry to solve for the x-component of velocity.

To know more about particle visit:

https://brainly.com/question/13874021

#SPJ11

Values of x and y will be 12 and 5 respectively.

It's given in the question,

Since, expression for the coordinates of a point (h, k) which divides the segment joining points \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio of m : n is given by,

h = \(\frac{mx_2+nx_1}{m+n}\)

k = \(\frac{my_2+my_1}{m+n}\)

Since, R is a point on segment QS dividing in the ratio of 3 : 2, coordinates of R will be,

\(8=\frac{3x+2\times 2}{3+2}\)

\(8=\frac{3x+4}{5}\)

\(3x+4=40\)

\(3x=36\)

\(x=12\)

Similarly, \(3=\frac{3y+2\times 0}{3+2}\)

\(3=\frac{3y}{5}\)

\(3y=15\)

\(y=5\)

       Therefore, values of x and y will be 12 and 5 respectively.

Learn more,

https://brainly.com/question/8061114

a. There are three independent variables in a 4 x 2 x 3 factorial design.

b. There are four possible main effects in a 4 x 2 x 3 factorial design, one for each independent variable.

c. There are 24 different conditions in a 4 x 2 x 3 factorial design, which is the product of the levels of each independent variable (4 x 2 x 3 = 24).

d. There are several possible interactions in a 4 x 2 x 3 factorial design, including two-way and three-way interactions between the independent variables.

a). In a factorial design, the independent variables are systematically manipulated in all possible combinations. In a 4 x 2 x 3 factorial design, there are three independent variables, each with a different number of levels.

The first independent variable has four levels, the second independent variable has two levels, and the third independent variable has three levels.

Therefore, there are three independent variables in this design.

b). A main effect is the effect of a single independent variable on the dependent variable, averaged across all levels of the other independent variables.

In a 4 x 2 x 3 factorial design, there are three independent variables, each of which can have a main effect. Therefore, there are three possible main effects in this design.

Additionally, there can be two-way and three-way interactions between the independent variables, which can also affect the dependent variable. However, a main effect is distinct from an interaction effect and is not dependent on any other independent variables.

c).The number of different conditions in a 4 x 2 x 3 factorial design is calculated by multiplying the number of levels for each independent variable.

In this case, the first independent variable has four levels, the second independent variable has two levels, and the third independent variable has three levels.

Therefore, the total number of different conditions is obtained by multiplying these three numbers (4 x 2 x 3 = 24). Each condition represents a unique combination of the levels of the three independent variables.

d). Interactions in factorial designs occur when the effect of one independent variable on the dependent variable depends on the level of another independent variable. In a 4 x 2 x 3 factorial design, there are several possible interactions between the independent variables.

For example, there may be a two-way interaction between the first and second independent variables, meaning that the effect of the first independent variable on the dependent variable depends on the level of the second independent variable.

Similarly, there may be a two-way interaction between the second and third independent variables, or between the first and third independent variables.

Learn more about Factorial design

brainly.com/question/29490374

#SPJ11

Answer:

Step-by-step explanation:

For the first half of the Marathon, we need to find the time.

t = d/r

r = 7 mph

d = 13.1

t = 13.1 / 7

t = 1.87 hours.

For the second half of the Marathon we need the time as well.

t = d/r

r = 2 mph

d = 13.1

t = 13.1 / 2

t = 6.55 hours.

Now to find the average speed, you will need the total time and the total distance

Total distance = 13.1 + 13.1 = 26.2 miles

Total time = t1 + t2

Total time = 1.87 hours + 6.55 hours.

Total time =  8.42

average speed = Total Distance / total time

average speed = 26.2 / 8.42 = 3.11 miles per hour

Answer:

False

Step-by-step explanation:

Please mark me as brainliest

Answer:

false

Step-by-step explanation:

just took test

The conclusion after conducting one sample z-test for z value 5.7 is not possible the correct answer is option c. None of the above.

To determine the conclusion of a one-sample Z test based on the Z-value,

We need to compare the Z-value with the critical value of Z at the chosen level of significance (alpha) and with the corresponding p-value.

If the Z-value is greater than the critical value of Z or if the p-value is less than the chosen level of significance (alpha).

Then we reject the null hypothesis.

Otherwise, we fail to reject the null hypothesis.

Without knowing the level of significance and the corresponding critical value.

We cannot determine the conclusion of the test based solely on the Z-value of 5.7.

However, if we assume a standard significance level of 0.05.

We can use a Z-table or statistical software to find the corresponding critical value of Z, which is 1.96 for a two-tailed test.

If the Z-value of 5.7 is greater than the critical value of Z of 1.96, then we reject the null hypothesis.

Otherwise, we fail to reject the null hypothesis.

Therefore, for the one-sample Z test with given information it is not possible to conclude the correct answer is option c. none of the above.

learn more about Z test here

brainly.com/question/15937859

#SPJ4

The total fluid force exerted on each vertically oriented porthole with a 3 ft diameter and a center located 50 ft underwater is approximately 28,274 pounds. The fluid force on a horizontally oriented porthole under 50 ft of water is also approximately 28,274 pounds.

The pressure at a given depth in a fluid is given by the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth.

In this case, the depth of the vertically oriented porthole is 50 ft. We assume the density of water to be approximately 62.4 pounds per cubic foot, and the acceleration due to gravity is approximately 32.2 ft/s². Plugging these values into the equation, we can calculate the pressure at the depth of the porthole:

P = (62.4 lb/ft³) * (32.2 ft/s²) * (50 ft) = 100,080 lb/ft²

To find the fluid force exerted on the porthole, we need to multiply the pressure by the area of the porthole. The area of circle is given by the formula A = πr², where r is the radius of the circle. In this case, the radius is half the diameter, which is 1.5 ft. Thus, the area of the porthole is:

A = π * (1.5 ft)² = 7.07 ft²

Now, we can calculate the fluid force:

Fluid Force = Pressure * Area = 100,080 lb/ft² * 7.07 ft² ≈ 28,274 lb

Therefore, the total fluid force exerted on each vertically oriented porthole is approximately 28,274 pounds.

For the horizontally oriented porthole under 50 ft of water, the fluid force would be the same as the vertically oriented porthole.  Hence, the fluid force on the horizontally oriented porthole is also approximately 28,274 pounds.

Learn more about area of circle here:

https://brainly.com/question/28642423

#SPJ11

A'B'C' is the image of triangle ABC under rotation about 120° CCW about point Q. This is true.

It should be noted that triangle A'B'C' appears to be congruent to triangle ABC and about the same distance from point Q.

Here, the angle of rotation from ABC to A'B'C' appears to be about 120° counterclockwise when measured using a geometry program.

Therefore, triangle A'B'C' is the image of triangle ABC under rotation about 120° CCW about point Q.

Learn more about triangles on:

https://brainly.com/question/1058720

#SPJ1

Answer:

1/13

Step-by-step explanation:

Knowing that:

In a deck of card half of the deck of card are red: 1/2  

Also means 52/2 = 26

There are 2 red 10 in a deck of card.

Solve:

Since there are 2 red 10 in a deck of card and half of the deck of 52 card are red also known as 26.

Thus, the probability of getting a red 10 is 2/26. As you can see that not a answer choice. That because 2/26 is a even number as well as it means that it can be simplify.

GCD (or HCF) of 2 and 26 is 2.

Therefore, divide both by 2.

2/2 = 1

26/2 = 13

Hence, we can see that the simplify form is 1/13.

As a result, the probability of getting a red 10 is 1/13.

~lenvy~

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
To learn more about : equity

https://brainly.com/question/27821130

#SPJ8

Answer:

  see attached

Step-by-step explanation:

The attachment is my effort to complete the proof. It appears to me the idea is to show that B=3+1 and that 1=3+C. Then you substitute (3+C) for 1 and you've got the proof you want.

_____

The given statements and reasons are intended to give you enough clues that you can figure out the logic that is being used. Once you have done that, you fill in the missing details.

Answer:

1. a-b

2. a-d

3. c-e

4. g-f

5. a-h

6. e-j

Hilbert axioms changed Euclid's theorem by identifying and explaining the concept of undefined terms

These were the sets of axioms that were proposed by the man David Hilbert in the 1899. They are a set of 20 assumptions that he made. He made these assumptions as a treatment to the geometry of Euclid.

These helped to create a form of formalistic foundation in the field of mathematics. They are regarded as his axiom of completeness.

Hilbert’s axioms are divided into 5 distinct groups.  He named the first two of his axioms to be the axioms of incidence and the axioms of completeness. His third axiom is what he called the axiom of congruence  for line segments. The forth and the fifth are the axioms of congruence for angles respectively.

Hence we can conclude by saying that Hilbert axioms changed Euclid's theorem by identifying and explaining the concept of undefined terms.

Read more on Euclid's geometry here: https://brainly.com/question/1833716

#SPJ1

complete question

Hilbert’s axiom’s changed Euclid’s geometry by _____.

1 disproving Euclid’s postulates

2 utilizing 3-dimensional geometry instead of 2-dimensional geometry

3 describing the relationships of shapes

4 identifying and explaining the concept of undefined terms

Answer:

2 1/3

1 4/3

2.333...

233.3...%

Step-by-step explanation:

There is sufficient evidence to believe that the number of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.

To determine if there's sufficient evidence,

Let us define the null and alternative hypotheses for this test as follows:

Null hypothesis (H0): The proportion of household pets leaving the shelter over the weekend is the same as the proportion of wildlife animals leaving the shelter over the weekend.

Alternative hypothesis (Ha): The proportion of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.

The test statistic for two sample test is given by:

z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))

where

p1 and p2 are the proportions of household pets and wildlife animals leaving the shelter over the weekend, respectively,

p is the pooled proportion,

n1 and n2 are the sample sizes for household pets and wildlife animals, respectively.

Pooled proportion is

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of household pets and wildlife animals leaving the shelter over the weekend, respectively.

Given

-n1 = 376, n2 = 52, x1 = 29, x2 = 10

p = (29 + 10) / (376 + 52) = 0.091

The observed proportions are:

p1 = x1 / n1 = 29 / 376 = 0.0771

p2 = x2 / n2 = 10 / 52 = 0.1923

The test statistic value

z = (0.0771 - 0.1923) / sqrt(0.091 * (1 - 0.091) * (1/376 + 1/52)) = -3.04

By using a standard normal distribution table,

The p-value is 0.00238.

Since the p-value (0.00238) is less than the level of significance (0.01), we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the number of animals leaving the shelter over the weekend for household pets and wildlife animals.

Learn more on t test onhttps://brainly.com/question/6589776

#SPJ1

By using the variable Mr. Leppold can do 18 pull-ups, Mr. Will can do 15 pull-ups, and Mrs. Crump can do 23 pull-ups. Mr. Leppold can do 3 more pull-ups than Mr. Will and Mrs. Crump can do 5 more than Mr. Leppold.

To solve this problem, we need to set up equations using the given information. Mr. Leppold claims he can do 3 more pull-ups than Mr. Will, so we can express that as l = w + 3. Mrs. Crump says she can do 5 more than Mr. Leppold, so we can write c = l + 5. We can then substitute l = w + 3 into c = l + 5 to get c = w + 8. This gives us the equations l = w + 3, c = l + 5, and c = w + 8. We can then substitute in a number for l (18) to solve for the other two variables. When l = 18, we get w = 15 and c = 23. Therefore, Mr. Leppold can do 18 pull-ups, Mr. Will can do 15 pull-ups, and Mrs. Crump can do 23 pull-ups.

Learn more about variable here

brainly.com/question/29583350

#SPJ4

Answer:

m^3 + 3m, I simplified.

Answer:

\( m\angle EFG =69\degree \)

Step-by-step explanation:

\( m\angle EFG =\frac{1}{2}(191- 53)\degree \)

\( m\angle EFG =\frac{1}{2}\times 138\degree \)

\( m\angle EFG =69\degree \)

Answer:

Shown below.

Step-by-step explanation:

Test Marks          Tally          Frequency          Percentage

1                                                    8                   8/60 = 0.133

2                                                   6                   6/60 = 0.100

3                                                   5                   5/60 = 0.083

4                                                   5                   5/60 = 0.083

5                                                   5                   5/60 = 0.083

6                                                   8                   8/60 = 0.133

7                                                   6                   6/60 = 0.100

8                                                   7                   7/60 = 0.116

9                                                   4                   4/60 = 0.066

10                                                 5                   5/60 = 0.083

Total                                            59                 59/60 = 0.983

For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.

An "unbiased-statistic" is preferred over "biased-statistic" for estimating population because it provides more accurate estimate of true population parameter.

A "biased-statistic" systematically overestimates or underestimates the population parameter, which leads to incorrect conclusions about the population. Biases can arise in many ways, such as through sampling methods or measurement errors.

Whereas, an "unbiased-statistic" is not systematically too high or too low, but rather it is an estimate that is equal on average to the true population parameter.

The "Unbiased-estimates" have a smaller "sampling-error" and are more accurate and more reliable for making inferences about the population.

Learn more about Estimator here

https://brainly.com/question/15840694

#SPJ4