Last year the depth of the river was 4.2 feet deep. This year it dropped 24%. Find the depth of the river this year to cross it.

Answer:

3x+13 units

Step-by-step explanation:

square perimeter of 12x +52 units

perimeter= 12x +52

12x + 52= 4(sides)

divide both sides by 4 = 12x/4 + 52/4= 3x+13

which give you 3x +13 units

Answer:

3.0000

Step-by-step explanation:

Answer:

i'm assuming you mean tenth so 3

Step-by-step explanation:

you start by looking at just 2.97, the seven will round the 9 up to a ten so you will add one to the 2 and end up with 3 as your answer

Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)

\(F(x)=4cos(x)-6sin(x)+4x+8\)

1. Write the expression.

\(f'(x)=-4sin(x)-6cos(x)+4\)

2. Write the expression for the integral.

\(\int\((-4sin(x)-6cos(x)+4) \, dx\)

3. Separate into multiple integrals.

\(\int\((-4sin(x)) \, dx+\int\((-6cos(x)) \, dx+\int\((4) \, dx\)

4. Solve each integral.

• Check the attached image for a better understanding of these results.

\(\int\((-4sin(x)) \, dx=\\ \\-4\int\((sin(x)) \, dx=\\ \\-4(-cos(x))+C=\\ \\4cos(x)+C\)

---------------------------------------------------------------------------------------------------------

\(\int\((-6cos(x)) \, dx=\\ \\-6\int\((cos(x)) \, dx=\\\\-6(sin(x))+C=\\ \\-6sin(x)+C\)

---------------------------------------------------------------------------------------------------------

\(\int\((4) \, dx=\\ \\4x+C\)

5. Sum up all the integrals.

\((4cos(x))+(-6sin(x))+(4x)+C\\ \\4cos(x)-6sin(x)+4x+C\)

6. Write in standard form (solved for y).

\(y=4cos(x)-6sin(x)+4x+C\)

7. Substitute the given values and solve for C.

\(12=4cos(0)-6sin(0)+4(0)+C\\ \\4cos(0)-6sin(0)+4(0)+C=12\\ \\C=12-4cos(0)+6sin(0)-4(0)\\ \\C=12-4(1)+6(0)-4(0)\\ \\C=12-4\\ \\C=8\)

8. Express your result.

\(F(x)=4cos(x)-6sin(x)+4x+8\)

---------------------------------------------------------------------------------------------------------

How to verify the result?

If the result is correct, then F(0)=12. Let's test it!

\(F(0)=4cos(0)-6sin(0)+4(0)+8=12\). Hence, the answer is correct.

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The graph.

I want to share the graph of this function, it looks pretty interesting. Check it out in attached image 2.

Answer:

\(\text{f}(x)=4\cos(x)-6\sin(x)+4x+8\)

Step-by-step explanation:

Given:

Fundamental Theorem of Calculus

\(\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))\)

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

To find the function f(x), integrate f'(x) and use f(0) = 12 to find the value of the constant.

\(\begin{aligned}\displaystyle \int (-4 \sin(x)-6 \cos (x)+4)\:\:\text{d}x & = \int -4 \sin(x)\:\:\text{d}x -\int 6 \cos(x)\:\:\text{d}x+\int 4\:\:\text{d}x \\\\& =-4 \int \sin(x)\:\:\text{d}x -6\int \cos(x)\:\:\text{d}x +\int 4\:\:\text{d}x\\\\& = -4 \cdot -\cos(x)-6 \cdot \sin(x)+4x+\text{C}\\\\& = 4\cos(x)-6\sin(x)+4x+\text{C}\end{aligned}\)

To find the value of C, substitute x = 0 into the function and set it to 12:

\(\begin{aligned}\text{f}(0) & =12\\\implies 4 \cos(0)-6\sin(0)+4(0)+\text{C} & =12\\4-0+0+\text{C} & =12\\4+\text{C} & = 12\\\text{C} & =8\end{aligned}\)

Finally, substitute the found value of C into the equation:

\(\text{f}(x)=4\cos(x)-6\sin(x)+4x+8\)

Rules of Integration

\(\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}\)

If the terms are multiplied by constants, take them outside the integral.

\(\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}\)

Just add an x to the constant.

\(\boxed{\begin{minipage}{6 cm}\underline{Integrating Trigonometric functions}\\\\$\displaystyle \int \sin(x)\:\text{d}x=- \cos (x)+\text{C}\\\\ \int \cos (x)\:\text{d}x=\sin(x)+\text{C}$\\\end{minipage}}\)

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Answer:

49.6

Step-by-step explanation:

Answer:

Please mark as brainliest;)

Hey there! :)

Answer:

A. x - 5

B. x + 4

Step-by-step explanation:

Starting with:

x² - x - 20

Find two numbers that add up to -1 and multiply to form -20. We get:

-5, and 4. Use these numbers when writing this equation in factored form:

(x - 5) (x + 4) is the trinomial in factored form. The two binomials that are factors are:

A. x - 5

B. x + 4.

Answer:

(x-5) (x+4)

Step-by-step explanation:

x^2 - X-20

Factor

What two numbers multiply to -20 and add to -1

-5*4 = -20

-5+4 = -1

(x-5) (x+4)

This amount of money which is received by Ginger weekly represents Ginger's net pay.

Net pay is defined as the amount of money an individual such as Ginger receive at the end of a week or a month after other payroll deductions such as insurance and tax has been removed.

The amount of money received by Ginger at the end of a week as a worker = $560

Therefore at the end of a year his total net pay would be = 560×12

= $6,720

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Answer:

seriously??

have you heard of calculators lol

the answer is 3.45

Given:

a.) Acme Movers charges $245 plus $30 per hour.

b.) Hank's Movers charges $65 per hour.

First, let's generate the equation that represents the different price offers.

Let,

x = the number of hours of service

y = total cost

a.) Acme Movers charges $245 plus $30 per hour.

b.) Hank's Movers charges $65 per hour.

Next, let's determine x (the number of hours) where the price of the two will be the same.

Applying the Substitution Method, substitute equation b to equation a.

y = 245 + 30x

65x = 245 + 30x

65x - 30x = 245

35x = 245

35x/35 = 245/35

x = 7

The cost of the two service providers will be the same in a 7 hours service.

Let's now determine at

Answer:

80:280

Step-by-step explanation:

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer:it would be 88 because of the co efficient due to the process of mingus in china which made it a law to not pursue dreams within country borders

Step-by-step explanation:

The numbered spot at which all the runners will be next to one another is spot 19.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Starting with the runner on the outside track, the provided parameters are;

The runner covered n₁ = 5 places on the outside track, which is the number of spaces.

Next, the inner runner will traverse n₂ spaces, which equals one space.

The following inner runner will cover n₃ = 3 spaces.

The subsequent runner will traverse n₄ = 2 spaces.

The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.

LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.

Time = 30/ = 6

Consequently, when the first runner has covered 30 places, we have;

Six time units have been expended.

The runner comes to a stop at position 30- (30 -19) = Position 19.

First runner's new destination is Spot 19.

The distance covered simultaneously by runner 2 is 6 x 1 = 6.

The distance covered by two runners running simultaneously equals six spaces.

Second runner's new position: 6 spaces plus spot 13 equals spot 19.

The combined distance covered by the three runners is 6 x 3 = 18.

The distance runner 3 covers 18 spaces simultaneously.

Third runner's new position: 18 spaces + Spot 1 = 19 spaces

Runner 4 covers a distance of 6 x 2 = 12 at the same time.

Distance runner 4 journeys equals 12 spaces

Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.

Therefore, all the runners will be next to one another is spot 19.

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Answer:

Step-by-step explanation:

Whenever a problem asks for f(x+n) or really anything, you just plug it into the OG function

f(x+2) = 3(x+2) - 5

= 3x + 6 - 5

=3x + 1

When factoring a polynomial in the form ax2 + bx + c, where a, b, and c are positive real numbers, the signs in the binomials should be both positive

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The form of the polynomial is given as:

ax2 + bx + c

Where a, b, and c are positive real numbers.

Since a, b, and c are positive real numbers. then the form of the expansion would be:

ax2 + bx + c = (dx + e)(fx + g)

Take for instance, we have the following quadratic equation

x^2 + 6x +  8

Expand the equation

x^2 + 6x +  8 = x^2 + 4x + 2x +  8

Factorize the equation

x^2 + 6x +  8 = (x + 2)(x + 4)

Hence, the signs in the binomials should be both positive

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Answer:

D

Might be the Right Answer

Answer:

16π

Step-by-step explanation:

2 * π * 8

16π

Answer:

16π

Hope this helps out!

Answer:

.

1) 0.35 x 24 =8.4

2) 0.59 x 29 =17.11

3) 2.45 x 5 =12.25

4) 0.84 x 3 =2.52

5) 0.45 ×63=28.35

6) 3.54 x 0.59=2.0886

7) 5.28 x 1.18 =6.2304

8) 4.37 x 0.58 =2.5346

9) 7.05 * 0.52 =3.666

10) 2.36 x 1.28=3.0208

\(0.35 \times 24 = \)=8.4

Answer:

1) 8.4

2) 17.11

3) 12.25

4) 2.52

5) 28.35 (if numbers are multiplied)

6) 2.0886

7) 6.2304

8) 2.5346

9) 3.666

10) 3.0208

Answer:

-4

Step-by-step explanation:

Answer:

\( = \frac{10}{0.2} = \frac{100}{2} = 50 \\ = \frac{10}{0.02} = \frac{1000}{2} = 500 \\ = \frac{10}{0.002} = \frac{10000}{2} = 5000 \\ \\ \)

hopefully that will help u

Answer:

10.5 mph

Step-by-step explanation:

To find the constant of proportionality in miles per hour, we need to divide the distance (in miles) by the time (in hours) for each of the two runs, and then take the average of the two rates.

For Monday's run:

Rate = Distance / Time = 21 miles / 3 hours = 7 miles per hourFor Wednesday's run:Rate = Distance / Time = 10 1/2 miles / 1 1/2 hours = (21/2) miles / (3/2) hours = 14 miles per hour

To find the average rate, we add the two rates and divide by 2:Average rate = (7 miles per hour + 14 miles per hour) / 2 = 10.5 miles per hour

Therefore, the constant of proportionality in miles per hour is 10.5. This means that Ashley runs at an average rate of 10.5 miles per hour during her training.

Answer:

the probability of passing the exam if a student does not use ADAPT is 0.3584

Step-by-step explanation:

Given the data in the question;

Probability a student will pass = 38% = 0.38

Probability a student have used ADAPT = 5% = 0.05

P(passed  | used ADAPT) = 79% = 0.79

Now lets use table

                          Used ADAPT                        Not use ADAPT                 Total

Passed            [0.05×0.79] = 0.0395           [0.38 - 0.0395] = 0.3405     0.38

Not Passed     [0.05-0.0395] = 0.0105        [0.62 - 0.0105] = 0.6095     0.62

Total                             0.05                                      0.95

Now, the probability of passing the exam if a student does not use ADAPT will be;

⇒ P(passed and Not used ADAPT) / P( did not use ADAPT)

⇒ 0.3405 / 0.95

⇒ 0.3584

Therefore, the probability of passing the exam if a student does not use ADAPT is 0.3584

Answer:

\(\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})\)

And replacing we got:

\(\mu_{\bar X}= 2.2\)

\(\sigma_{\bar X}= \frac{6}{\sqrt{100}}= 0.6\)

Step-by-step explanation:

For this case we have the following info given:

\( \mu = 2.2\) represent the mean

\(\sigma = 6\) represent the deviation

We select a sample size of n=100. This sample is >30 so then we can use the central limit theorem. And we want to find the distribution for the sample mean and we know that the distribution is given by:

\(\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})\)

And replacing we got:

\(\mu_{\bar X}= 2.2\)

\(\sigma_{\bar X}= \frac{6}{\sqrt{100}}= 0.6\)

An angle of 1,600 mils is equivalent to 90 degrees.

To solve this problem, we can set up a proportion to find the relationship between degrees and mils.

We know that 360 degrees is equivalent to 6,400 mils.

Let's set up the proportion:

360 degrees / 6,400 mils = x degrees / 1,600 mils

For value of x, we can cross-multiply:

360 degrees * 1,600 mils = 6,400 mils * x degrees

Dividing both sides by 6,400 mils gives us:

(360 degrees * 1,600 mils) / 6,400 mils = x degrees

Simplifying the expression on the left side:

(360 * 1,600) / 6,400 = x degrees

Calculating the numerator:

360 * 1,600 = 576,000

Dividing the numerator by the denominator:

576,000 / 6,400 = x degrees

Simplifying the expression on the right side:

x = 90 degrees

Therefore, an angle of 1,600 mils is equivalent to 90 degrees.

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The average is 40 and  the margin of error is 10.95.

What is margin of error?

The margin of error is a statistic expressing the amount of random sampling in the result of a survey.

Average (A) = sum of all the value/ given set.

A = (51+ 41 + 28)/3 = 40

margin of error = 100/square root of 120 = 10.95.

Therefore, the average is 40 and  the margin of error is 10.95.

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