Each student in a school was asked, "What is your favorite color?" The circle graph below shows how they answered

Which color was chosen by approximately one fourth of the students?

Approximately what percentage of the students chose purple or green?

Answer:

A

Step-by-step explanation:

(f+g)(x)=f(x) + g(x)=(x/2)-3+3x^2+x-6=3x^2+(3/2)x-9

Parameterize this surface (call it S) by

[tex]\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+u^2\,\mathbf k[/tex]

with [tex]0\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex].

The normal vector to S is

[tex]\mathbf n=\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}=-2u^2\cos v\,\mathbf i-2u^2\sin v\,\mathbf j+u\,\mathbf k[/tex]

Compute the curl of F :

[tex]\nabla\times\mathbf F=-2\,\mathbf i+3\,\mathbf j+5\,\mathbf k[/tex]

So the flux of curl(F) is

[tex]\displaystyle\iint_S(\nabla\times\mathbf F)\cdot\mathrm d\mathbf S=\int_0^{2\pi}\int_0^2(\nabla\times\mathbf F)\cdot\mathbf n\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle\int_0^{2\pi}\int_0^2(5u+4u^2\cos v-6u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{20\pi}[/tex]

Alternatively, you can apply Stokes' theorem, which reduces the surface integral of the curl of F to the line integral of F along the intersection of the paraboloid with the plane z = 4. Parameterize this curve (call it C) by

[tex]\mathbf r(t)=2\cos t\,\mathbf i+2\sin t\,\mathbf j+3\,\mathbf k[/tex]

with [tex]0\le t\le2\pi[/tex]. Then

[tex]\displaystyle\iint_S(\nabla\times\mathbf F)\cdot\mathrm d\mathbf S=\int_0^{2\pi}\mathbf F\cdot\mathrm d\mathbf r[/tex]

[tex]=\displaystyle\int_0^{2\pi}(20\cos^2t-24\sin t)\,\mathrm dt=\boxed{20\pi}[/tex]

Answer:

17

Step-by-step explanation:

We are adding the previous two terms

1+5 = 6

5+6 = 11

6+11 = 17

11+17 = 28

The missing term is 17

Answer:

Standard deviation = 2.2360679774998

Step-by-step explanation:

We are asked to find the Standard deviation of a samples of speeches as an awards.

The formula for sample standard deviation is given as:

√[(x - μ)²/N - 1 ]

Step 1

We find the mean (μ)

The mean of the sample =>

= Sum of term/ Number of terms

= (3 + 7 + 5 + 4 + 1)/5

= 20/5

= 4

Step 2

Find the Standard deviation of the sample

√[(x - μ)²/N - 1 ]

N = number of samples or terms = 5

= √[(3 - 4) ² + (7 - 4)² + (5 - 4)² +(4 - 4)² +(1 - 4)²/ 4]

= √ (1 ² + 3² + -1² + 0² + -3²/4)

= √( 1 + 9 + 1 + 0 + 9/4)

= √20/5 - 1

= √5

= 2.2360679774998

The standard deviation of the sample = 2.2360679774998

Answer:

subtract the 6.99 from 50 and you get your answer

Step-by-step explanation:

Answer:

8.06

Step-by-step explanation:

Take the cost of a cd and multiply by 6

6.99 *6

41.94

Subtract this from 50.00

50.00 - 41.94

8.06

You will get 8.06 back

Answer:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

Solutions: x = 6, y = 5   or   x = -2, y = 5

Step-by-step explanation:

Use a graph.

Plot point (-2, 5). That will be a point on a circle with radius 5.

From point (-2, 5), go right 4 and down 3 to point (2, 2). (2, 2) is the center of the circle.

You now need the equation of a circle with center (2, 2) and radius 5.

Use the standard equation of a circle:

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

where (h, k) is the center and 5 is the radius.

The circle has equation:

[tex] (x - 2)^2 + (y - 2)^2 = 25 [/tex]

To have a single solution, you need the equation of the line tangent to the circle at (-2, 5), but since you want more than one solution, you need the equation of a secant to the circle. For example, use the equation of the horizontal line through point (2, 5) which is y = 5.

System:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

To solve, let y = 5 in the equation of the circle.

(x - 2)^2 + (5 - 2)^2 = 25

(x - 2)^2 + 9 = 25

(x - 2)^2 = 16

x - 2 = 4  or x - 2 = -4

x = 6 or x = -2

Solutions: x = 6, y = 5   or   x = -2, y = 5

An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, This system by starting with the equation of a circle centered at the origin with radius sqrt(29), which is,

⇒ x² + y² = 29.

Then, Added a linear equation that intersects the circle at (-2,5) to create a system with two solutions.

The entire solution set for this system is: (-2, 5) and (7/5, -19/10)

Thus, An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

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Answer:

Distributive property, addition property

Answer:

additive identity

associative property of addition

distributive property

Step-by-step explanation:

Hey there! I'm happy to help!

An equation with infinite solutions has a solution of x=x. You can plug in any x-value and it will equal x, so there are infinitely many solutions.

ANSWER A

10x-10=-10x+10

We add 10 to both sides.

10x=-10x+20

We add 10x to both sides.

20x=20

We divide both sides by 20.

x=1

We have a solution of 1, so this is not an equation with infinitely many solutions.

Answer B

-10x-10=-10x+10

We add 10 to both sides.

-10x=-10x+20

We add 10 x to both sides.

0=20

This has no solutions because the x is gone, so there cannot be a solution.

Answer C

-10x-10=-10x-10

We add 10 to both sides.

-10x=-10x

We divide both sides by -10.

x=x

This has infinitely many solutions.

Answer D

10x-10= -10x-10

We add 10x to both sides.

20x-10=-10

We add 20 to both sides.

20x=0

We divide both sides by 20.

x=0

There is a single solution here, not infinitely many.

Therefore, the answer is C. -10x-10=-10x-10.

Have a wonderful day! :D

Answer:

federal loans = $29,000

private loans = $14,000

Step-by-step explanation:

x + y = 43000

.045x + .02y = 1585

x = 29,000

y = 14,000

Answer:

Amount of loan from federal : $ 29,000

Amount of loan from private bank : $ 14,000

Step-by-step explanation:

We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.

If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -

x + y = 43,000

At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -

0.045x + 0.02y = 1585

Let's solve the following system for x and y, the amount of each loan,

[tex]\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}[/tex] ( Substitute x = 43000 - y )

[tex]0.045\left(43000-y\right)+0.02y=1585[/tex] ( Simplify )

[tex]1935-0.025y=1585[/tex],

[tex]1935000-25y=1585000[/tex],

[tex]-25y=-350000[/tex],

[tex]y=14000[/tex],

[tex]x=29000[/tex]

Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.

Answer:

15 dollars

Step-by-step explanation:

12 inches = 1 ft

so 12 inch by 12 inches  is 1 ft * 1 ft

1 ft* 1 ft

1 ft^2

This is smaller than 3 ft^2 so they will get charged for 3 ft^2

3 ft^2 = 3 ft^2 * $5 / ft^2 = 15 dollars

Answer:

C and E

Step-by-step explanation:

C and E are the correct answer

Answer:

$14

Step-by-step explanation:

80% of $70 is $14, saving him $56

The other person has a great answer. Here's another approach.

If the discount is 80%, then you have to pay the remaining 20% (the two percentages add to 100%)

20% of 70 = 0.20*70 = 14

The sale price is $14 which is the amount Keiko pays

We see that Keiko saves 70-14 = 56 dollars.

Answer:

Step-by-step explanation:

The sequence of the problem above is an arithmetic sequence

For an nth term in an arithmetic sequence

F(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

To find the equation first find the common difference

0.65 - 0.5 = 0.15 or 0.80 - 0.65 = 0.15

The first term is 0.5

Substitute the values into the above formula

That's

f(n) = 0.5 + (n - 1)0.15

f(n) = 0.5 + 0.15n - 0.15

The final answer is

Hope this helps you

Answer:

Step-by-step explanation:

Took the math test on edge

Answer:

174 cm²

Step-by-step explanation:

The figure given is a prism with isosceles trapezoid as base.

Its surface area can be calculating the area of each face that makes up the prism, and summing all together.

There are 6 faces. Their dimensions and areas can be calculated as follows:

2 isosceles trapezium:

It has 2 parallel bases, (a and b), of 4cm and 6cm,

Height (h) = 2.8cm

Area = ½(a+b)*h

Area = ½(4+6)*2.8

Area = ½(10)*2.8 = 5*2.8 = 14 cm²

4 rectangles of different dimensions:

Rectangle 1 (down face): l = 10cm, b = 4cm

Area = 10*4 = 40 cm²

Rectangle 2 and 3 (side faces): l = 10cm, b = 3cm

Area = 2(l*b) = 2(10*3) = 60cm²

Rectangle 4 (top face) = l = 10cm, b = 6cm

Area = 10*6 = 60cm²

Surface area of the figure = 14 + 40 + 60 + 60 = 174 cm²

Answer:

[tex]\boxed{4x + 3y}[/tex]

Step-by-step explanation:

Hey there!

Well 4x + 3y cannot be added together because they are 2 different variables.

4x + 3y = 4x + 3y

So 4x + 3y simplified is,

Hope this helps :)

Answer:

A) Reject H0 if F > 5.417

B) we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms

Step-by-step explanation:

A) From the table, we can see that we have df1 = 3 and df2 = 15. And we are given a significance level of α = 0.01

We are also given f-value of 1.75

Thus,from the f-distribution table attached at significance level of α = 0.01 and df1 = 3 and df2 = 15, we have;

F-critical = 5.417

Normally, we reject H0 if F > 5.417

But in this case, F is 1.75 < 5.417 and so we conclude that we do not reject H0 at the 0.01 level of significance

B) for 0.05 level of significance, df1 = 3 and df2 = 15, from the 2nd table attached, we have;

F-critical = 3.2874

Again the f-value is less than this critical one.

Thus, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms

Answer:

Quantitative

Step-by-step explanation: Quantitative or numerical variable are statistical or measured variables which involves numbers. Numerical variables allows for mathematical operations such as addition, subtraction and so on to be performed in them. Quantitative variables include height, age, weight, population and other measured variable with have numerical attributes. They can be measured on either ordinal, ratio or interval scales. Hence, since Julien is trying to determine height, the variable is a quantitative or numeric variable.

Answer:

The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Step-by-step explanation:

The complete question is:

Salaries of 42 college graduates who took a statistics course in college have a​ mean, [tex]\bar x[/tex] of, $64, 100. Assuming a standard​ deviation, σ of ​$10​,016 construct a ​99% confidence interval for estimating the population mean μ.

Solution:

The (1 - α)% confidence interval for estimating the population mean μ is:

[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

The critical value of z for 99% confidence interval is:

[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57[/tex]

Compute the 99% confidence interval for estimating the population mean μ as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)[/tex]

Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Answer:

-10

Step-by-step explanation:

y : x

= 5 : 4

4z = -8

= -8 / 4 = -2 = z

y : x

= 5 * -2 : 4 * -2

= -10 : -8

Answer:

800×200= 8 × 200 hundreds= 1600 Hundreds = 160000

Answer:

V = 1071.79 yd^3

Step-by-step explanation:

The volume of a cone is

V = 1/3 pi r^2 h  where r is the radius and h is the height

We are given a diameter of 16 so the radius is 1/2 of the diameter or 8

The height is 16

V = 1/3 ( 3.14) (8)^2 ( 16)

V = 1071.78666 yd^3

Rounding to the nearest hundredth

V = 1071.79 yd^3

[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: of \: Cone \: = \: \pi \: {r}^{2} \: \frac{h}{3} }}}}}\end{gathered}[/tex]

[tex] \bf{\red{ \longrightarrow}} \tt \: r \: = \: \frac{Diameter}{2} \\ [/tex]

[tex]\bf{\red{ \longrightarrow}} \tt \: r \: = \: \frac{16 \: yd}{2} \\ [/tex]

[tex]\bf{\red{ \longrightarrow}} \tt \: r \: = \: \frac{ \cancel{16 \: yd} \: \: ^{8} }{ \cancel{2}} \\ [/tex]

[tex]\bf{\red{ \longrightarrow}} \tt \: \large{\bf{{{\color{navy}{r \: = \: 8 \: yd}}}}}[/tex]

[tex]\bf{\red{ \longrightarrow}} \tt \: \: \large{\bf{{{\color{navy}{h \: = \: 16 \: yd}}}}}[/tex]

[tex] \bf \large \longrightarrow \: \: 3.14 \: \times \: {8}^{2} \: \times \: \frac{16}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \:3.14 \: \times \: 64 \: \times \: \frac{16}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \:3.14 \: \times \: 64 \: \times \: \frac{ \cancel{16} \: \: ^{5.33} }{ \cancel{3}} \\ [/tex]

[tex]\bf \large \longrightarrow \: \:3.14 \: \times \: 64 \: \times \: 5.33[/tex]

[tex]\bf \large \longrightarrow \: \:200.96 \: \times \: 5.3[/tex]

[tex]\bf \large \longrightarrow \: \:1071.79[/tex]

Option (A) is the correct answer

Answer:

The percentage increase in the production cost of the printer is 3%.

Step-by-step explanation:

We are given that the production of a printer consists of the cost of raw material at 100 dollars the cost of overheads at 80$ and wages at 120$.

Also, the cost of raw materials and overheads are increased by 11% and 20% respectively while wages are decreased by 15%.

Cost of raw material = $100

Cost of overheads = $80

Cost of wages = $120

So, the total cost of the printer = $100 + $80 + $120

                                                   = $300

Now, the increase in the cost of raw material = $100 + 11% of $100

                                                                           = [tex]\$100 + (\frac{11}{100} \times \$100)[/tex]

                                                                           = $100 + $11 = $111

The increase in the cost of overheads = $80 + 20% of $80

                                                                = [tex]\$80 + (\frac{20}{100} \times \$80)[/tex]

                                                                = $80 + $16 = $96

The decrease in the cost of wages = $120 - 15% of $120

                                                          = [tex]\$120 - (\frac{15}{100} \times \$120)[/tex]

                                                          = $120 - $18 = $102

So, the new cost of a printer = $111 + $96 + $102 = $309

Now, the percentage increase in the production cost of the printer is given by;

      % increase =  [tex]\frac{\text{Net increase in the cost of printer}}{\text{Original cost of printer}} \times 100[/tex]

                         =  [tex]\frac{\$309- \$300}{\$300} \times 100[/tex]

                         =  3%

Hence, the percentage increase in the production cost of the printer is 3%.

Answer:

please mark my answer brainliest

Step-by-step explanation:

question is unclear to give u correct answer

Answer:

Step-by-step explanation:

Let the speed of Frank be x and speed of Gregory be y. If Gregory drives 22 miles per hour faster than Frank, then y = 22+x. SInce they they are 216miles apart after 2.25 hours,

Speed = Distance/Time

Total time travelled by them = 2.25hours

Total distance = 216 hours

Total speed = x+y = x+22+x

Substituting this parameters into the formula given to get x we will have;

x+22+x = 216/2.25

2x+22 = 96

2x = 96-22

2x = 74

x = 74/2

x = 37

Hence the speed of Frank is 37miles per hour while that of gregory is 37+22 = 59miles/hour

Answer:

x = 11/10

Step-by-step explanation:

5(2x - 1) = 6

Distribute

10x -5 = 6

Add 5 to each side

10x-5+5 = 6+5

10x = 11

Divide each side by 10

10x/10 = 11/10

x = 11/10

Answer:

ok as we know 15 is a whole number by itself and 3/8 is the decimal part

so we know it is 15. something

that something is 3/8 to find decimal you do 3/8

3/8 is = .375

so 15.375 is the answer

hope it helps

brainliest give me pls

Answer:

Step-by-step explanation:

If the larger of 2 consecutive integers is 324, then 324-(2-1) = 323 is the smaller.

If the largest of 89 consecutive integers is 324, then 324 - (89-1) = 236 is the smallest.

Hence, the smallest consecutive integer is [tex]237[/tex].

What is the smallest consecutive integer?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Here given that,

The largest of [tex]89[/tex] consecutive integers is [tex]324[/tex]

So, it is of the form

[tex]324-89=237[/tex]

Hence, the smallest consecutive integer is [tex]237[/tex].

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Answer:

[tex]{ \underline{ \sf{equation \: is : \: y = - \frac{5}{4} x + 2 }}}[/tex]

Step-by-step explanation:

[tex]y = mx + c \\ 4y = - 5x + 18 \\ y = - \frac{5}{4} x + \frac{9}{2} [/tex]

since it is parallel, the gradients are the same; m = -5/4

[tex]y = - \frac{5}{4} x + 2[/tex]

Answer:

y=-5x+2

Step-by-step explanation:

x intercept=2

points will be (2,0)

slope of given line:

4y=-5x+18

y=mx+c

comparing equation:

m=-5

lines are parallel so given slope is equal to required slope.

using point slope form:

y-0=-5(x-2)

y=-5x+2

Answer:

X+9=24

Or,x=24-9

:.x=15

Step-by-step explanation:

Answer:

B. x=15

Step-by-step explanation:

To find the solution to the equation, we must get x by itself on one side of the equation.

[tex]x+9=24[/tex]

9 is being added to x. The inverse of addition is subtraction. Subtract 9 from both sides of the equation.

[tex]x+9-9=24-9[/tex]

[tex]x=24-9[/tex]

[tex]x=15[/tex]

Let's check our solution. Plug 15 in for x.

[tex]x+9=24 (x=15)[/tex]

[tex]15+9=24[/tex]

[tex]24=24[/tex]

This checks out, so we know our solution is correct. The answer is B. x=15