If r1 , r2 , and r3 represent rotations from Dn and f 1 , f 2 , and f 3 represent reflections from Dn , determine whether r1 r2 f 1 r3 f 2 f 3 r3 is a rotation or a reflection.

Answer:

Step-by-step explanation:

answer to Step 1

Households with unlisted numbers or without telephones.

answer to Step 2

2.People without the extra income to keep a phone line will largely comprise the population without a phone line.

3.Very busy people or those interested in maintaining privacy will largely comprise those with unlisted numbers.

Answer:

answer is AC^2

Step-by-step explanation:

Answer:

a. [tex]S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}[/tex] . Set S × T has 9 elements.

b. [tex]T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}[/tex]. Set T × S has 9 elements.  

c. [tex]S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}[/tex] . Set S × S has 9 elements.

d. [tex]T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}[/tex] . Set T × T has 9 elements.

Step-by-step explanation:

The given sets are S={2,4,6} and T={1,3,5}.

We need to find the set-roster notation to write each of the following sets, and the number of elements that are in each set.

a.

[tex]S\times T=\{(s,t)|s\in S and t\in T\}[/tex]

[tex]S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}[/tex]

Set S × T has 9 elements.

b.

[tex]T\times S=\{(t,s)|s\in S and t\in T\}[/tex]

[tex]T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}[/tex]

Set T × S has 9 elements.  

c.

[tex]S\times S=\{(s,s)|s\in S \}[/tex]

[tex]S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}[/tex]

Set S × S has 9 elements.

d.

[tex]T\times T=\{(t,t)|t\in T\}[/tex]

[tex]T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}[/tex]

Set T × T has 9 elements.

Using the set roster notation, the number of elements in each of the sets would be the product of the number of elements in each individual set, which is 9.

A.) S × T :

{2, 4, 6} × {1, 3, 5}

{(2, 1), (2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6, 5)}

Number is of elements = 9

B.) T × S :

{1, 3, 5} × {2, 4, 6}

{(1,2), (1,4), (1,6), (3,2), (3,4), (3, 6), (5, 2), (5,4), (5,6)}

Number is of elements = 9

C.) S × S :

{1, 3, 5} × {1, 3, 5}

{(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 3), (5, 1), (5, 3), (5, 5)}

Number is of elements = 9

D.) T × T :

{2, 4,6} × {2, 4, 6}

{(2,2), (2, 4), (2, 6), (4,2), (4, 4), (4, 6), (6,2), (6, 4), (6,6)}

Number is of elements = 9

Hence, the distribution of values of each set.

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Answer:

[tex]14\frac{1}{3}[/tex]

Step-by-step explanation:

Let's write this out as an equation. Let the unknown quantity be x:

[tex]x+\frac{2}{3} - \frac{1}{3} (x+\frac{2}{3}) = 10\\\\3x+2-x -\frac{2}{3} = 30\\\\9x+6-3x-2=90\\\\6x= 86\\\\x = \frac{86}{6} =\frac{43}{3} =14\frac{1}{3} \\[/tex]

Answer: the quantity is 9

Step-by-step explanation:

Let x represent the quantity.

A quantity and its 2/3 are added together. The 2/3 of the number is 2/3 × x = 2x/3

The sum of the quantity and its 2/3 would be

x + 2x/3 = (3x + 2x)/3 = 5x/3

From the sum, 1/3 of the sum is subtracted. 1/3 of the sum would be

1/3 × 5x/3 = 5x/9

Subtracting 1/3 of the sum from the sum, it becomes

5x/3 - 5x/9 = (15x - 5x)/9 = 10x/9

If the remainder is 10, it means that

10x/9 = 10

Crossmultiplying

10x = 9 × 10 = 90

x = 90/10

x = 9

Answer:

1) The production canister welds have consistently lower burst strengths than the test nozze welds.

2) The production canister weids have much more variable burst strengths.

3) The test nozzle welds data contain 2 outliers.

4) Test nozzle welds have much more variable burst strengths.

5) The production canister welds have much higher burst strengths.

6) The production canister welds data contain 2 outiers.

Step-by-step explanation:

Hello!

The boxplots summarize the information of test nozzle closure welds and production canister nozzle welds.

The boxplot for the test nozzle closure welds shows that the first quartile and second quartile are close to each other but the third quartile is more separated to them, meaning that the data contained in the box is asymmetric, the data seems to have less variability between C₁ and C₂ and more between C₂ and C₃, the box is right-skewed.

The left whisker is larger than the right one, there are no outliers in the sample, due to most of the data being comprehended below C₁, the overall distribution of the data set is left-skewed, with large variability.

The boxplot for production cannister nozzle welds shows that the box is small (the variability of the data set is low) and symmetric, with C₂ in the middle of it and C₁ and C₃ are equidistant to the second quartile.

The whiskers of the box are small but they have almost the same length, showing that there is the same amount of data in them, this adds to the overall symmetry of the data set.

Finally, this data set shows two outliers, these values are far from the box, meaning that they are relatively extreme unusual values in regards to the rest of the sample but their distance to the box seems to be equal wich adds to the conclusion of the symmetrical distribution, with low variability of the data set.

I hope it helps!

Final answer:

To create a histogram showing the probability distribution of the number of illiterate people out of eleven people in a sample, you can use the binomial probability formula. Calculate the probability for each possible number of illiterate people and represent it in a histogram.

Explanation:

This question is asking for a histogram showing the probability distribution of the number of illiterate people out of eleven people in a sample, based on the information that about 20% of all people in the United States are illiterate.

To create the histogram, we can use the binomial probability formula. The formula is P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where C(n, k) represents combinations, n is the number of trials, k is the number of successes, and p is the probability of success.

We can calculate the probability for each possible number of illiterate people out of the eleven, ranging from 0 to 11, and represent it in a histogram.

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

The slope is given as 1/2 and the line passes through (2, - 3)

To determine the intercept, we would substitute x = 2, y = - 3 and m= 1/2 into y = mx + c

y = mx + c. It becomes

- 3 = 1/2 × 2 + c = 1 + c

c = - 3 - 1 = - 4

The equation becomes

y = x/2 - 4

Answer:

a. is below in the explanation

b. 1/3e^(-y/3)

c.0.05882

d. 0.2231

e. 7     f.25

Step-by-step explanation:

Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3.

a can be solved as follows      [tex]\frac{1}{\alpha\beta } e^{\frac{-x-y}{\alpha\beta } }[/tex]

[tex]\frac{1}{6} e^{\frac{-\alpha }{2} -\beta/3 }[/tex]

1/6[tex]e^{\frac{-(3x+2y}{6 }[/tex]

b.

f(y/x)=f(x).f(y)/{f(y)}=f(y)

1/3e^(-y/3)

c. Find the probability that a Type A bulb lasts at least 300 hours and a Type B bulb lasts at least 400 hours.

[tex]\int\limits^\alpha _4 {1/6e^{-(3x+2y)/6} } \, dy[/tex]

1/2e^-(3x+8)/6

[tex]\int\limits^\alpha _3 {e^{-(3x+800)} } \, dx \\[/tex]

0.05882

Given that a type B fails at 300 hours . we find the probability that type A bulb lasts longer than 300hr

f(x>y|y=3)=f(x>3)

[tex]\int\limits^a_3 {1/2e^{-x/2} } \, dx[/tex]

0.2231

e.e) What is the expected total lifetime of two Type A bulbs and one Type B bulb?  

E(2A+B)

(2E(A)+E(y)

2*2+3

=7

f. variance of the total lifetime of two types A bulbs and one type B bulb

V(2x+y)=

4*4+9

=25

The joint pdf of X and Y is (1/6)e^(-x/2-y/3). The conditional pdf of Y given X = x is (1/2)e^(-y/3). The probability that a Type A bulb lasts at least 300 hours and a Type B bulb lasts at least 400 hours is 9/250. The probability that a Type A bulb lasts longer than 300 hours, given that a Type B bulb fails at 300 hours, is approximately 0.9999. The expected total lifetime of two Type A bulbs and one Type B bulb is 7 100 hours. The variance of the total lifetime of two Type A bulbs and one Type B bulb is 10 100 hours.

To find the joint pdf f(x|y) of X and Y, we need to find the product of the individual pdfs of X and Y since they are independent. Since X and Y follow exponential distributions with means of 2 and 3 respectively, their pdfs can be written as f(x) = (1/2)e^(-x/2) and f(y) = (1/3)e^(-y/3). Therefore, the joint pdf f(x|y) is given by:

f(x|y) = f(x)*f(y) = (1/2)e^(-x/2) * (1/3)e^(-y/3) = (1/6)e^(-x/2-y/3).

To find the conditional pdf f_2(y|x) of Y given X = x, we use Bayes' theorem:

f_2(y|x) = (f(x|y)*f(y))/f(x) = [(1/6)e^(-x/2-y/3) * (1/3)e^(-y/3)] / [(1/2)e^(-x/2)] = (1/2)e^(-y/3).

To find the probability that a Type A bulb lasts at least 300 hours and a Type B bulb lasts at least 400 hours, we integrate the joint pdf over the given range:

P(X >= 300, Y >= 400) = ∫∫(1/6)e^(-x/2-y/3)dxdy = ∫(3/2)e^(-x/2)dx * ∫e^(-y/3)dy. Solving the integrals, we get P(X >= 300, Y >= 400) = 9/250.

Given that a Type B bulb fails at 300 hours, we need to find the probability that a Type A bulb lasts longer than 300 hours. This is equivalent to finding P(X > 300 | Y = 300). Using the conditional pdf f_2(y|x) = (1/2)e^(-y/3), we integrate from 300 to infinity:

P(X > 300 | Y = 300) = ∫(1/2)e^(-y/3)dy = 1 - ∫(1/2)e^(-y/3)dy = 1 - (1/2)e^(-y/3) = 1 - (1/2)e^(-300/3) = 1 - e^(-100) ≈ 0.9999.

The expected total lifetime of two Type A bulbs and one Type B bulb is obtained by summing the means of X and Y twice and the mean of Y once:

E[Total Lifetime] = 2*E[X] + E[Y] = 2*2 + 3 = 7.

The variance of the total lifetime of two Type A bulbs and one Type B bulb is obtained by summing the variances of X and Y twice and the variance of Y once:

Var[Total Lifetime] = 2*Var[X] + Var[Y] = 2*(2^2) + 3^2 = 10.

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Answer:

$18

Step-by-step explanation:

The cost, c, of a ham sandwich at a deli varies directly with the number of sandwiches, n. c = $54 when n is 9

This means that to buy 9 sandwiches, it costs $54. So one sandwich costs 54/9 = $6.

What is the cost of the sandwiches when n is 3?

To buy three sandwiches, it costs $6*3 = $18.

So the correct answer is:

$18

Answer:A

Step-by-step explanation:

$18

Answer:

[tex]P = \left[\begin{array}{ccc}0&1&0\\0&0&1\\1&0&0\end{array}\right][/tex]

[tex]Q = \left[\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{array}\right][/tex]

Step-by-step explanation:

[tex]P*\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}0&1&0\\0&0&1\\1&0&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}y\\z\\x\end{array}\right][/tex]

[tex]Q*\left[\begin{array}{c}y\\z\\x\end{array}\right]=\left[\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{array}\right] \left[\begin{array}{c}y\\z\\x\end{array}\right] = \left[\begin{array}{c}x\\y\\z\end{array}\right][/tex]

Answer: lowering

Step-by-step explanation:

Statins are drugs that are administered in order to help reduce cholesterol level in the body. Statins achieves this by making it impossible for the body to have access to substances that helps to produce cholesterol. This drug reduces cholesterol up to 50% and are taken once every day. Examples includes rosuvastatin, pitavastatin, simvastatin.

SR =sin (angle) = opposite leg/ hypotenuse

sin(52) = SR/ 7.6

SR = 7.6 x sin(52)

SR = 5.988 ( round answer as needed.)

QR = cos(angle) = adjacent leg / hypotenuse

Cos(52) = QR/ 7.6

QR = 7.6 x cos(52)

QR = 4.679. ( round answer as needed).

Angle S = 180 - 90 -52 = 38 degrees

Answer:

A

Step-by-step explanation:

The relative frequency is calculated by dividing the frequency of that class to the sum of frequencies. It can be represented as

[tex]Relative frequency=\frac{f}{sum(f)}[/tex]

Hence, the relative frequency of class is the percentage or proportion of data lies in that class.

The cumulative frequency of a class is computed by adding the frequency of the respective class to the frequencies of all previous classes. The cumulative frequency of first class will always be equal to the frequency of first class.

Hence, the cumulative frequency  for a class is the sum of frequency for that class and the frequencies of all previous classes.

Relative frequency is the proportion of total data that falls into a class, while cumulative frequency is the sum of frequencies of that class and all previous classes. Therefore, relative frequency illustrates the percentage of data in a certain class, while cumulative frequency shows the accumulation of data up to that point.

The terms relative frequency and cumulative frequency both pertain to statistics; however, they represent different concepts. Relative frequency of a class is the percentage or proportion of the whole set of data that falls in that class. It's calculated by dividing the frequency of that class by the total number of data points.

On the other hand, cumulative frequency of a class is the sum of the frequencies of that class and all previous classes in a dataset. Essentially, it accumulates counts as you proceed through the dataset.

For instance, if you have five classes with frequencies of 1, 2, 3, 4 and 5, the relative frequencies would be 0.0667, 0.1333, 0.2, 0.2667, and 0.3333 respectively (assuming we divide each frequency by the total data points, which is 15 in this case). In contrast, the cumulative frequencies would be 1, 3, 6, 10 and 15, indicating the total count up to each class.

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Answer:

cos 38 = 17/c

Step-by-step explanation:

cos 38 = 17/c is the correct statement

Answer:

10 roses

Step-by-step explanation:

To find the number of roses in the blue vase, we double the number of roses in the red vase. Since the red vase has 5 roses, the blue vase contains 10 roses.

The student's question is about determining the number of roses in the blue vase given certain conditions about the number of flowers in vases. We know that each vase has 12 flowers, the red vase has 7 tulips, and thus 5 roses because the total is 12. The blue vase has twice as many roses as the red vase, so we need to double the number of roses in the red vase to find that number.

Since the red vase has 5 roses, the blue vase will have twice as many, which is 10 roses.

Here's the calculation step by step:

Answer:

4%

Step-by-step explanation:

A 20% solution with a total volume of 400 mL has 20% * 400 mL of solute.

20% * 400 mL = 80 mL

When you dilute the solution to 2 L, you introduce additional water, but no additional solute, so now you have the same 80 mL of solute in 2 L of total solution.

The concentration is:

(80 mL)/(2 L) = (80 mL)/(2000 mL) = 0.04

As a percent it is:

0.04 * 100% = 4%

"4" will be the final percentage strength.

According to the question,

20% solution with 400 mL has 20% × 400 mL of solute

then,

→ [tex]20 \ percent\times 400=80[/tex]

hence,

The concentration will be:

→ [tex]\frac{80 \ mL}{2 \ L} = \frac{80 \ mL}{2000 \ mL}[/tex]

            [tex]= 0.04[/tex]

or,

            [tex]= 0.04\times 100[/tex]

            [tex]= 4[/tex] (%)

Thus the answer above is right.

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Answer: 0.332 < p < 0.490

Step-by-step explanation:

We know that the confidence interval for population proportion is given by :-

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

, where n= sample size

[tex]\hat{p}[/tex] = sample proportion

z* = critical z-value.

As per given , we have

n= 258

Sample proportion of college students who own a car = [tex]\hat{p}=\dfrac{106}{258}\approx0.411[/tex]

Critical z-value for 99% confidence interval is 2.576. (By z-table)

Therefore , the  99% confidence interval for the true proportion(p) of all college students who own a car will be :[tex]0.411\pm (2.576)\sqrt{\dfrac{0.411(1-0.411)}{258}}\\\\=0.411\pm (2.576)\sqrt{0.00093829}\\\\= 0.411\pm (2.576)(0.0306315197142)\\\\=0.411\pm 0.0789=(0.411-0.0789,\ 0.411+0.0789)\\\\=(0.3321,\ 0.4899)\approx(0.332,\ 0.490)[/tex]

Hence, a 99% confidence interval for the true proportion of all college students who own a car : 0.332 < p < 0.490

Answer:

Step-by-step explanation:

Triangle QRS is a right angle triangle.

From the given right angle triangle

RS represents the hypotenuse of the right angle triangle.

With 30 degrees as the reference angle,

QR represents the adjacent side of the right angle triangle.

QS represents the opposite side of the right angle triangle.

To determine QR, we would apply trigonometric ratio

Cos θ = adjacent side/hypotenuse side. Therefore,

Cos 30 = QR/14

√3/2 = QR/14

QR = 14 × √3/2

QR = 14√3/2 = 7√3/2

Answer:

27m²

Step-by-step explanation:

surface area is area of all sides

these is two triangles and a rectangle

area of triangle = (base x height) /2 = (3 x 4)/2= 12/2 =6

area of rectangle = length x breadth = 5x3 = 15

surface area = area of triangle + area of triangle + area of rectangle

6 + 6 + 15 = 27m²

Answer:

$12,400

Step-by-step explanation:

Given:

Week earning + 9% commission = $1,916

Weekly Earning = $800

Commission for the Week = $1,916 - $800 = $1,116

Let total sales for the week = x

Therefore, x = ($1,116 * 100)/9

x = $12,400

Answer:

$12400

Step-by-step explanation:

Wages = Basic pay + Commission

1916 = 800 + 9%A

Let A be the total sales

9%A = 1916 - 800

9%A = 1116

A = $12400

Answer:

Solution of the system is (2,1).                                                          

Step-by-step explanation:

We are given the following system of equation:

[tex]3x+4y=10\\x - y = 1[/tex]

We would use the elimination method to solve the following system of equation.

Multiplying the second equation by 4 and adding the two equation we gwt:

[tex]3x + 4y = 10\\4\times (x-y = 1)\\\Rightarrow 4x - 4y = 4\\\text{Adding equations}\\3x + 4y + (4x-4y) = 10 + 4\\7x = 14\\\Rightarrow x = 2\\\text{Substituting value of x in second equation}\\2 - y = 1\\\Rightarrow y = 1[/tex]

Solution of the system is (2,1).

Answer: the solution is (2, 1)

Step-by-step explanation:

The given system of simultaneous equations is given as

3x+4y=10 - - - - - - - - - - - - -1

x−y=1 - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 1 an equation 2 by 3. It becomes

3x + 4y = 10

3x - 3y = 3

Subtracting, it becomes

7y = 7

Dividing the left hand side and the right hand side of the equation by 7, it becomes

7y/7 = 7/7

y = 1

Substituting y = 1 into equation 2, it becomes

x - 1 = 1

Adding 1 to the left hand side and the right hand side of the equation, it becomes

x - 1 + 1= 1 + 1

x = 2

Step-by-step explanation:

You need to find six combinations of a and b such that a² + b² = 7.

a = 1, b = √6

a = √2, b = √5

a = √3, b = 2

a = 2, b = √3

a = √5, b = √2

a = √6, b = 1

Answer:

a) Figure attached

b) For this case w have that A =(2.4 km)j, B= (-1.9 km) i , C= (-4.7 km)j

And the final position vector can be calculated adding the 3 vectors like this:

[tex] s = A +B+C[/tex]

[tex] s= (-1.9 km)i +(2.4 -4.7 km) j= (-1.9km)i + (-2.3 km)j[/tex]

We can find the magnitude of s like this:

[tex] |s| = \sqrt{(-1.9)^2 +(-2.3)^2}=2.983[/tex]

And then we can find the angle with this formula:

[tex] \theta = \tan^{-1} (\frac{-2.3 km}{-1.9 km})=50.44 [/tex]

The other possibility is [tex] \theta = 50.44+180 =230.44[/tex]

And since they want the angle measured from East the correct angle would be [tex] \theta = 230.44[/tex]

Step-by-step explanation:

Part a

On the figure attached we have the vectors for the pattern described.

Part b

For this case w have that A =(2.4 km)j, B= (-1.9 km) i , C= (-4.7 km)j

And the final position vector can be calculated adding the 3 vectors like this:

[tex] s = A +B+C[/tex]

[tex] s= (-1.9 km)i +(2.4 -4.7 km) j= (-1.9km)i + (-2.3 km)j[/tex]

We can find the magnitude of s like this:

[tex] |s| = \sqrt{(-1.9)^2 +(-2.3)^2}=2.983[/tex]

And then we can find the angle with this formula:

[tex] \theta = \tan^{-1} (\frac{-2.3 km}{-1.9 km})=50.44 [/tex]

The other possibility is [tex] \theta = 50.44+180 =230.44[/tex]

And since they want the angle measured from East the correct angle would be [tex] \theta = 230.44[/tex]

Answer:

Yes

Step-by-step explanation:

A system in echelon form can have more variables than equations. ... Every linear system with free variables has infinitely many solutions. True, a free variable can take any value, and so there are infinitely many solutions. Any linear system with more variables than equations cannot have a unique solution.

Answer:

Step-by-step explanation:

3x²-12x+7=0

        x = (-b ± √ b²-4ac) / 2a

  from these equation: a = 3 , b = 12 , c = 7

Accordingly, b²  -  4ac =   12²- 4 (3 x 7) = 144 - 4(21) = 144 - 84 =   60

                        2a= 2 x 3 = 6

Applying the quadratic formula :

             x =  (-12 ± √ 60 )/6

  √ 60 rounded to 2 decimal digit using calculator 7.75

x =  (-12 ± 7.75 )/6

(-12 ± 7.75 ) = (-12 + 7.75 ) = 5.75

                      (-12 - 7.75 )  = -19.75

x =  5.75/6 = 0.96

       -19.75/6 = 3.29

sum of the square of roots = 0.96² + 3.29²

                                                    0.9261 +   10.8241 = 11.75

The sum of the squares of its roots of the quadratic equation

3x² - 12x + 7 = 0 is p² + q² = 34/3.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We have a quadratic equation 3x² - 12x + 7 = 0.

We know a quadratic equation ax² - bx + c = 0 can be written as,

x² - (b/a)x + (c/a) = 0 ⇒ x² - (p + q)x + pq = 0 where p and q are the roots.

∴ 3x² - 12x + 7 = 0.

x² - (12/3)x + 7/3 = 0.

Hence (p + q) = 4 and pq = 7/3.

Now, (p + q)² = p² + q² + 2pq.

16 = p² + q² + 14/3.

p² + q² = 16 - 14/3.

p² + q² = (48 - 14)/3.

p² + q² = 34/3.

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Answer:

[tex]volume\ = \pi \frac{625^2}{6}[/tex]

Step-by-step explanation:

See the attached figure.

y₁ = 25x  and  y₂ =x²

The intersection between y₁ and y₂

25x = x²

x² - 25x = 0

x(x-25) = 0

x = 0 or x =25

y = 0 or y =25² = 625

The points of intersection (0,0) and (25,625)

To find the volume of the solid obtained by rotating about the y-axis the region bounded by y₁ and y₂

y₁ = 25x ⇒ x₁ = y/25 ⇒ x₁² = y²/625

y₂ =x² ⇒ x₂ = √y ⇒ x₂² = y

v = ∫A(y) dy = π ∫ (x₂² - x₁²) dy

∴ V =

[tex]\pi \int\limits^{625}_0 {y-\frac{y^2}{625} } \, dy =\pi( \frac{y^2}{2} -\frac{y^3}{3*625} ) =\pi (\frac{625^2}{2} -\frac{625^3}{3*625}) =\pi ( \frac{625^2}{2}-\frac{625^2}{3}) =\pi \frac{625^2}{6}[/tex]

To find the volume of the solid formed by rotating the region bounded by y = 25x and y = x²25 about the y-axis, one needs to calculate the area of a typical slice, then integrate this area over the range of x-values.

To find the volume V of the solid obtained by rotating the region bounded by y = 25x and y = x225 about the y-axis, we can apply the method of slicing.

First, we need to find the area A(x) of a typical slice perpendicular to the x-axis. Here we have two functions, finding the x- values where these functions intersect gives the bounds on the integral for the volume.

We can find the area A(x) = pi*(outer radius)2 - pi*(inner radius)2 = pi[(25x)ˆ2 - (xˆ2 * 25)ˆ2].

To find V, we integrate A(x) over the interval of x-values. This will give us the exact volume of the solid.

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The new net worth after a gain in stock value is $74.2 billion, or in the scientific notation it is $7.42×10¹0.

In this problem, we have a person with a starting net worth of $71.0 billion, or $7.10×1010 in scientific notation. This person's stock has increased by $3.20 billion, or 3.20×109 in scientific notation. To find the new net worth, these two amounts should be added together.

Step 1: Write the starting net worth and stock increase in standard form: $71.0×10⁹ + $3.2×10⁹. Step 2: Add these two amounts together to find the new net worth. $74.2×10⁹ This is the new net worth in standard form.

To express this amount in scientific notation, it becomes $7.42×10¹0, which is your final answer.

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The rate of change is A. constant, B. linear

Step-by-step explanation:

Rate of change is the ratio of change in value of y with corresponding value of x

Rate of change=Δy/Δx

Rate of change=5-2/4-1 =3/3=1

The rate of change is constant in the given interval and linear with a positive slope.

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Answer:

The accrued value after 5 years is $1,605.95.

The accrued value after 10 years is $1,672.9.

The accrued value after 15 years is $1,739.85.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex].

In this problem, we have that:

[tex]P = 1539, I = 0.01[/tex]

Accrued value after 5 years

This T when t = 5. So

[tex]E = P*I*t[/tex]

[tex]E = 1339*0.01*5 = 66.95[/tex]

The total is

[tex]T = E + P = 66.95 + 1539 = 1605.95[/tex]

The accrued value after 5 years is $1,605.95.

Accrued value after 10 years

This T when t = 10. So

[tex]E = P*I*t[/tex]

[tex]E = 1339*0.01*10 = 133.9[/tex]

The total is

[tex]T = E + P = 133.9 + 1539 = 1672.9[/tex]

The accrued value after 10 years is $1,672.9.

Accrued value after 15 years

This T when t = 15. So

[tex]E = P*I*t[/tex]

[tex]E = 1339*0.01*15 = 200.85[/tex]

The total is

[tex]T = E + P = 200.85 + 1539 = 1739.85[/tex]

The accrued value after 15 years is $1,739.85.