Explain how you can use the Properties of Equality to solve the following equation:

72 = 5x + 2

Integral that would give the volume V generated by rotating the region bounded by the given curves will be 200 pi unit³

Finding the volume of rotation is similar to finding the area of the bounded region of the graphs of the functions. The only difference is the added component added due to the rotation of the bounded region. Now whether we are using disk method or cylindrical shell method to find the volume, we will first set up the integral and its limits of integration, then evaluate this integral.

To find the volume of the solid generated by rotating the region bounded by curves:

(y = x^3 and y = 0) around the y-axis

We use the Cylindrical Shells Method.

First, we need to set up the integral.

We have:

2π∫\(0^5\) x (\(x^3\)) dx.

To solve this integral, we use the power rule for integration.

This states that if we have an integral of \(x^n\), the antiderivative is

x^(n+1)/(n+1).

Therefore, the antiderivative of our integral is 2π∫\(0^5\) x (\(x^3\)) dx.. Now that we have the antiderivative, we can solve the integral by applying the fundamental theorem of calculus.

This states that the integral of a function is equal to the difference between the evaluated antiderivative at the upper and lower limits of the integral.

Therefore, the volume of the solid generated is

V = \([x^5/5]^5_0\) = 2π(\(5^5/5\)) = 200π\(unit^3\).

Learn more about integration here

https://brainly.com/question/2289273

#SPJ4

Answer:

0.56652

Step-by-step explanation:

Given that :

1 job takes 15 seconds

x jobs will take 60 seconds

15x = 60

x = 4

4 jobs take 60 seconds

μ = 4

Job is 4th in line :

Find the probability of ;

P(x ≥ 4) = 1 - [P(x ≥ 4) = 1 - [P(x < 3 ) + P(x < 2) + P(x < 1) + p(x < 0)]

P(μ, x) = [(e^-μ) * (μ^x)] ÷ x!

Using the poisson distribution calculator :

P(x< 3) = 0.19537

P(x< 2) = 0.14653

P(x< 1) = 0.07326

P(x< 0) = 0.01832

Hence,

P(x ≥ 4) = 1 - [P(x < 3 ) + P(x < 2) + P(x < 1) + p(x < 0)

= 1 - (0.19537 + 0.14653 + 0.07326 + 0.01832)

= 1 - 0.43348

= 0.56652

Answer:

68.9 degrees

Step-by-step explanation:

To find this we can use the rule of sines.

It states \(\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}\)

We will use 56 degrees and its complementary measurement, which is discovered by observing the opposite side from the angle, which is 4. Then, we will find the side that compliments x, which is 4.5. Then we can plug those values into the rule of sines.

\(\frac{sin56}{4}=\frac{Sinx}{4.5}\)

Then, we want to get Sin x by itself.

\(\frac{sin56}{4}*4.5=sinx\)

Then, we can solve for sin x.

\(0.932667269124=sinx\)

finally, we need to take the inverse of sin to find our solution.

\(sin^{-1} (0.932667269124)=sin^-^1(sinx)\\x=68.85\\\)

Which can be rounded to 68.9.

Answer:

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

It assumes the scores are normally distributed with a mean score of 75 and a standard deviation of 15.

This means that \(\mu = 75, \sigma = 15\)

How many students will score between 48 and 75?

First we find the proportion, which is the pvalue of Z when X = 75 subtracted by the pvalue of Z when X = 48. So

X = 75

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{75 - 75}{15}\)

\(Z = 0\)

\(Z = 0\) has a p-value of 0.5

X = 48

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{48 - 75}{15}\)

\(Z = -1.8\)

\(Z = -1.8\) has a p-value of 0.0359

1 - 0.0359 = 0.4641

Out of 1000:

0.4641*1000 = 464

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

We have the following sequence

We calculate the pattern of change like this:

Therefore, by knowing the pattern of change, we can know the explicit formula

can I have brainliest if I answer

Step-by-step explanation:

please do a brainliest to me

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

Learn more on trigonometric identity here;

https://brainly.com/question/24496175

#SPJ1

The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

Its geometric meaning is the slope of tangent of the function at a given point.

The given function is as below,

y = sec⁻¹(x³)

The given function is a composite function of sec⁻¹x and x³.

In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,

dx³/dx = 3x²

And, dsec⁻¹x /dx = 1/x√(x² - 1)

Now, differentiation of sec⁻¹(x³) is given as,

d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))

                      = 3x/√(x² - 1)

Hence, the differentiation of the given function is 3x/√(x² - 1).

To know more about differentiation click on,

https://brainly.com/question/24898810

#SPJ1

Answer:

(36 × $7) - $15 = $252 - $15 = $237

Answer: 3/10, 1/3, 8/9, 4/5

Answer:

True

Step-by-step explanation:

Hope this helped :)

Answer:ITS FALSE!!

Step-by-step explanation:

Answer:

Its C boys

Step-by-step explanation:

I graphed all of them and compared

The equation that could represent the graph of the parabola is (c) \(y = -2x^2 - 16x- 28\)

From the question, we have the following highlights

The second highlight above means that:

The x coordinate (h) of the vertex is negative, while the y-coordinate (k) is positive.

For a parabola: \(y = ax^2 + bx + c\), the vertex is:

\((h,k) = (-\frac{b}{2a},f(h))\)

Next, we test the options

(a) y = –2x2 + 3x – 5

We have:

\(h = -\frac{3}{-2 \times 2}\)

\(h = 0.75\)

The value of h is positive.

So, this cannot represent the parabola

(b) y = –2x2 – 4x – 2

We have:

\(h = -\frac{-4}{-2\times 2}\)

\(h = -1\)

Substitute -1 for x in the function

\(k = -2x^2 - 4x - 2\)

\(k = -2(-1)^2 - 4(-1) - 2\)

\(k = 0\)

The value of k cannot be 0

So, this cannot represent the parabola

(c) y = –2x2 – 16x– 28

We have:

\(h = -\frac{-16}{-2\times 2}\)

\(h = -4\)

Substitute -4 for x in the function

\(k = -2x^2 - 16x- 28\)

\(k = -2(-4)^2 - 16(-4)- 28\)

\(k=4\)

The x coordinate (h) of the vertex is negative, while the y-coordinate (k) is positive.

Hence, \(y = -2x^2 - 16x- 28\) could represent the parabola

Read more about parabola at:

https://brainly.com/question/17987697

Answer:

  (d)  (1, 2)

Step-by-step explanation:

You want to know which of the given points satisfies the inequality.

We find it easiest to plot the given points on a graph of the solution. This shows us that (1, 2) is a solution to the inequality. (It lies in the solution area.)

__

Additional comment

Another way to choose the answer is to try each of the points in the inequality.

If you can visualize the boundary line (without plotting it) as a line with positive slope and a y-intercept of 2, you can more readily reject the first choice and accept the last choice. (0, 3) is above the y-intercept, and (1, 2) is to the right of it (in the solution space).

You may also recognize the x-intercept will be -3, so the second choice lies above the boundary line.

Answer:

False

Step-by-step explanation:

4 cos^4 (4x)-3 = 0

Substitute into the equation

4 cos^4 (4pi/24)-3 = 0

4 cos^4 (pi/6)-3 = 0

Take the cos pi/6

4 ( sqrt(3)/2) ^4 -3 =0

Take it to the 4th power

4 ( 9/16) -3 =0

9/4 -3 =0

9/4 - 12/4 = 0

-3/4 =0

False

Answer:

THE ANSWER IS TRUE.

Step-by-step explanation:

I did this on my homework.

The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

A similar problem about the volume of rectangular prisms is presented at brainly.com/question/22070273

#SPJ1

Answer:

-8

Step-by-step explanation:

to isolate x you have to divide both sides by 5/4 and -10/(5/4) is -8

$92000 is the James’s current equity in the home.

Equity, also known as shareholders' equity or owners' equity for privately held businesses, is the sum of money that, in the event of a company's liquidation, would be distributed to its shareholders after all of the company's assets have been sold and its debt has been fully repaid.

In an acquisition scenario, it is equal to the sum of the company's sales less any liabilities that were not transferred to the new owner.

A company's book value can also be represented by shareholder equity. A payment-in-kind arrangement may occasionally include equity. Furthermore, it represents the proportionate ownership of a company's shares.

James’s current equity =  (180000 × 1.25) - ((180000 × 0.8) -11000)

                                       = 92000

To know more about equity check the link below

https://brainly.com/question/28148396

#SPJ1

Answer:343

Step-by-step explanation:3434343

Step-by-step explanation:

x. f(x)

-1. -3

1. 1

4. 7

now you can plot them in graph

Answer:

B

Step-by-step explanation:

given 2 secants from an external point to the circle, then the product of the external part of one secant and that entire secant is equal to the product of the other secant's external part and that entire secant, that is

3(3 + x) = 4(4 + 5)

3(3 + x) = 4 × 9 = 36 ( divide both sides by 3 )

3 + x = 12 ( subtract 3 from both sides )

x = 9

Answer:

35

Step-by-step explanation:

all are obeying a constant ratio

The solution for the given inequality is -6 < x < 9.

What is linear equality?

In mathematics a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

The given inequality is:

         -7 < x - 1 < 8

       −7 + 1 < x − 1 + 1 < 8 + 1 -------- (Add 1 to all parts)

             -6 < x < 9

Hence, the solution for the given inequality is -6 < x < 9.

To learn more about linear inequality, visit:

https://brainly.com/question/24372553

#SPJ1

If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

Learn more about averages at:

https://brainly.com/question/20118982

#SPJ1

I don't what form of measurement to use (like grams, cusp, etc.) but I'm pretty sure it'd be cups

I think it's 5/96 or .05208333

So, 5/8 is .625. Dividing that up in throwing it into 12 cupcakes.

Answer:

Width = 3

Length = 6

Step-by-step explanation:

width = x

length = x + 3

Perimeter = 2(length + width)

\(p = 2(x + (x + 3)) \\ 18 = 2(x + x + 3) \\ 18 = 2(2x + 3) \\ 18 = 4x + 6 \\ 18 - 6 = 4x \\ 12 = 4x \\ \frac{12}{4} = x \\ 3 = x\)

Therefore, out of the 24 students that Blake interviewed, 9 of them participate in sports.

An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value.

Here,

According to the table, Blake interviewed a total of 24 students. To find out how many of these students participate in sports, we need to add up the number of students who collect sports cards and participate in sports, as well as the number of students who do not collect sports cards and participate in sports. So:

Total students who participate in sports = Number of students who collect sports cards and participate in sports + Number of students who do not collect sports cards and participate in sports

Total students who participate in sports = 6 + 3

Total students who participate in sports = 9

To know more about equation,

https://brainly.com/question/28243079

#SPJ1

We get the following answers:

A) The least square regression line is:

yi = 88.73 - 2.827(xi)

B) The slope  is β₁ = -2.827 and The intercept is β₀ = 88.73.

C) e*₆ = -0.6964, final grade is below average grade.

E) It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

we have Xi = No of absences

Yi = Final grade

The regression model is

Yi = β₀ +  β₁Xi + i

β₀ = y -  β₁x

we have n = 10, x bar = 4.5 , y bar = 76.01

cov(x,y) = -23.325 and var(x) = 9.1667

therefore,  β₀ = 88.73 and  β₁ = -2.827

A) Least square regression line is given by:

yi =  β₀+ β₁Xi

yi = 88.73 - 2.827(xi)

B) The slope  β₁ = -2.827 which means when no of absence is increased by 1 duty then the final grade will decrease by 2.827

The intercept  β₀ = 88.73 when there are 0 days absence the average grade is 88.73

C) Predicted graph for student who misses five class periods is

x = 5

y*5 = 88.73 - 2.827(5) = 74.5964

Hence for corresponding residual is:

e*₆ = 73.9 - 74.5964

e*₆ = -0.6964, final grade is below average grade.

D) please see graph

E) when student miss 15 class periods the final grade will be

X = 5

y* = 88.73 - 2.827(15)

= 46

It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

Learn more about Least square regression here:

brainly.com/question/14563186

#SPJ4

Answer:

The correct option is A

Step-by-step explanation:

From the question we are told that

   The average  number of meetings  hours per week is \(\mu= 18 \ hours\)

    The standard deviation is  \(\sigma = 5.2 \ hours\)

     The sample size is  n=  35

     The sample average per week is  \(p = 16.8 \ hours\)

From each solution statement we can deduce that the confidence level is  

    \(t = 95\)%

Thus the significance level is  \(\alpha = 0.05\)= 5%

The z value for the significance level is gotten as 1.96 from the z-table

    The confidence level interval for the sample mean is mathematically evaluated as

            \(\= x = \mu \pm (1.96 * \frac{\sigma }{\sqrt{n} } )\)

 Sustituting values

           \(\= x = 18 \pm (1.96 * \frac{5.2 }{\sqrt{35} } )\)

             \(\= x = 18 \pm1.7\)

=>               \(18 - 1.7 < \= x < 18 +1.7\)

                  \(16.3 < \= x < 19.7\)