What is the volume, in cubic centimeters, of the cylinder? Round your
answer to the nearest hundredth
12.3 cm
4.5 cm
1
1
cm³

\(x=\textit{oz of solution at 10\%}\\\\ ~~~~~~ 10\%~of~x\implies \cfrac{10}{100}(x)\implies 0.1 (x) \\\\\\ y=\textit{oz of solution at 20\%}\\\\ ~~~~~~ 20\%~of~y\implies \cfrac{20}{100}(y)\implies 0.2 (y) \\\\\\ \textit{32 oz of solution at 12\%}\\\\ ~~~~~~ 12\%~of~32\implies \cfrac{12}{100}(32)\implies 0.12 (32)\implies 3.84 \\\\[-0.35em] ~\dotfill\)

\(\begin{array}{lcccl} &\stackrel{oz}{amount}&\stackrel{\textit{\% of oz that is}}{\textit{salt only}}&\stackrel{\textit{oz of}}{\textit{salt only}}\\ \cline{2-4}&\\ \textit{10\% salt water}&x&0.10&0.1x\\ \textit{20\% salt water}&y&0.20&0.2y\\ \cline{2-4}&\\ mixture&32&0.12&3.84 \end{array}~\hfill \begin{cases} x + y = 32\\\\ 0.1x+0.2y=3.84 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{x+y=32}\implies y=32-x \\\\\\ \stackrel{\textit{using the 2nd equation}}{0.1x+0.2y=3.84}\implies \stackrel{\textit{substituting from the 1st equation}}{0.1x+0.2(32-x)~~ = ~~3.84} \\\\\\ 0.1x+6.4-0.2x=3.84\implies 6.4-0.1x=3.84\implies 6.4=0.1x+3.84 \\\\\\ 2.56=0.1x\implies \cfrac{2.56}{0.1}=x\implies \boxed{25.6=x}\hspace{5em}\stackrel{ 32~~ - ~~25.6 }{\boxed{y=6.4}}\)

The values of sec x, csc x, and cot x are:

sec x = sqrt(61)/6

csc x = -sqrt(61)/5

cot x = -6/5

What is the Pythagoras Theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right-angled triangle.

We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the terminal side and the x- and y-axes. Then, we can use the definitions of the trigonometric ratios to find the values of sec x, csc x, and cot x.

Let r be the length of the hypotenuse:

r = sqrt(6^2 + (-5)^2) = sqrt(61)

Then, we have:

cos x = adjacent/hypotenuse = 6/sqrt(61)

sin x = opposite/hypotenuse = -5/sqrt(61)

From these, we can find:

sec x = hypotenuse/adjacent = sqrt(61)/6

csc x = hypotenuse/opposite = -sqrt(61)/5 (Note that csc x is negative because sin x is negative in the third quadrant)

cot x = adjacent/opposite = -6/5

Hence, the values of sec x, csc x, and cot x are:

sec x = sqrt(61)/6

csc x = -sqrt(61)/5

cot x = -6/5

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Answer: 5 cm

Step-by-step explanation:

We know that 3x + 2x makes up one side of the square. Recall that the formula for a square's perimeter is P = 4a. Thus:

(3x + 2x) * 4 = 100

5x * 4 = 100

20x = 100 (divide by 20)

x = 5 (cm)

Answer:

Hello! I just took the test not too long ago the answer is -3

Have a good day! please mark brainliest!

Answer:

x = 5

Step-by-step explanation:

\( \frac{15}{4x} = \frac{12}{3x + 1} \)

\(15(3x + 1) = 12(4x)\)

\(45x + 15 = 48x\)

\(3x = 15\)

\(x = 5\)

Answer:

\(x = 5\)

Step-by-step explanation:

We can solve for x using a proportion, since we are given that the two right triangles are similar. Here is the proportion modeled in an equation:

\(\dfrac{3x+1}{12} = \dfrac{4x}{12 + 3}\)

We can solve for x by algebraically manipulating this equation.

↓ simplifying the right fraction's denominator

\(\dfrac{3x+1}{12} = \dfrac{4x}{15}\)

↓ cross-multiplying

\(15(3x+1)= 12(4x)\)

↓ applying the distributive property

\(45x + 15 = 48x\)

↓ subtracting \(45x\) from both sides

\(15 = 3x\)

↓ dividing both sides by 3

\(5 = x\)

\(\boxed{x = 5}\)

The forest fires in southern Mexico and Guatemala consumed forest land at a rate of 28,600 acres per week.

During May 1998, forest fires in southern Mexico and Guatemala were burning at a significant rate, resulting in the spread of smoke all the way to Austin. The fires were consuming forest land at a rate of 28,600 acres per week. This indicates the amount of forest area that was destroyed or affected by the fires within a span of one week.

The figure of 28,600 acres per week provides an understanding of the magnitude and impact of the forest fires. It highlights the rapid rate at which the fires were spreading and consuming the forested areas. Forest fires are known to have severe ecological and environmental consequences, including loss of biodiversity, destruction of habitats, and degradation of air quality due to the smoke generated. The fact that the smoke from these fires reached Austin suggests the vast distance covered by the smoke plume, indicating the scale and intensity of the fires.

Forest fires are a significant concern as they pose risks to both human lives and natural ecosystems. They can have long-lasting effects on the affected regions, requiring extensive recovery and rehabilitation efforts. Monitoring and managing forest fires, along with implementing preventive measures, are crucial for minimizing their impact and protecting valuable forest resources.

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The value of 3 - x/4 is (12-x)/4

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

For example 5x+2 = 10 is an example of algebraic expression. Where x is the variable.

Also 10-y/6 is also an algebraic expression with fractions.

To solve 3 - x/4

using L.C.M method

(12- x)/4

therefore the value of 3 -x/4

=( 12-x)/4

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Answer:

His gross pay for the month is $4,509.50

Step-by-step explanation:

The commission Richard Klein earns for oil change = 3.00%

The commission he earns for tune ups = 5.00%

The commission he earns for auto parts sales = 6.25%

The minimum salary he is guaranteed = $2,450.00

The amount he brought in last month includes;

1) $2,500.00 in oil changes

2) $4,500 in tune ups

3) Sold $28,200.00 in parts

The amount he earns last month in commission are;

3/100 × 2,500 = 75 in oil changes

5/100 × 4,500 = 225 in tune ups

6.25/100 × 28,200 = 1762.5 in parts sold

The total commission = 72 + 225 + 1762.5 = 2,059.5

∴ The total commission = $2,059.5

The amount he makes as salary = $2,450.00

Richard Klein's gross pay for the month = His total pay for the month

Therefore;

Richard Klein's gross pay for the month = $2,059.5 + $2,450 = $4,509.5

The proper statistical technique to use in this scenario is "d. Two sample tests for means - independent."

In this study, the goal is to compare the mean ratings between two independent groups: men and women. The data consists of two samples, each representing ratings given by men and women.

To determine if there is sufficient evidence of a difference in mean ratings between the two groups, a two sample test for means - independent is appropriate.

This statistical technique, also known as an independent samples t-test, assesses whether the means of two independent groups are significantly different from each other. It compares the means of the two samples while taking into account the variability within each group.

By conducting this test, we can evaluate if there is a significant difference in the mean program ratings between men and women in the study.

Therefore, to analyze the difference in mean ratings between men and women in the study, the appropriate statistical technique is "d. Two sample tests for means - independent."

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To determine the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.

Although they are connected, confidence level and confidence interval are not the same thing.

Thus, to evaluate the accuracy of a "population parameter," a "sample statistic" is used to create a confidence interval.

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Answer:

Step-by-step explanation:

Diagonals of parallelogram bisect each other;

Substitute values:

11y + 33 = 14y - 12 ⇒ 14y - 11y = 33+12 ⇒ 3y = 45 ⇒ y = 15

3x + 5y = 6x + 3y ⇒ 6x - 3x = 5y - 3y ⇒ 3x = 2y ⇒ 3x = 30 ⇒ x = 10

Answer:

40

Step-by-step explanation:

you said it was 40.

Answer:

Step-by-step explanation:

Tom wanted to find the inverse of f(x)= 4x - 2 using the steps in the attached image.

Tom's first mistake was in Step 3.

To correct the mistake, he should not switch the variables.

The correct procedure is:

Step 1 : Given

f(x) = 4x - 2

Step 2 : Change f(x) to y

y = 4x - 2

Step 3 : Add 2 to both sides

\(4x=y+ 2\)

Step 4:  Divide each side by 4

\(x=\dfrac{y+2}{4}\)

Step 5: Change x to \(f^{-1}(x)\)

\(f^{-1}(x)=\dfrac{y+2}{4}\)

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

To find out how far she will have run in total after 16 days, we can use the formula for calculating compound interest:

A = P(1 + r/100)^n

Where:

A = Total distance run after n days

P = Initial distance (4.8 kilometers)

r = Rate of increase per day (6.9%)

n = Number of days (16)

Plugging in the given values, we can calculate the total distance:

A = 4.8(1 + 6.9/100)^16

Using a calculator or performing the calculations step by step, we get:

A ≈ 4.8(1.069)^16 ≈ 4.8(2.092473)^16 ≈ 4.8(2.628)

A ≈ 12.6144

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

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Answer:

17%

Step-by-step explanation:

5 out of 30 is 17%

5/30 = 5 ÷ 30 = .16.  rounds to .17 =17%

Answer:

( 2 4/5 * 1 3/10) * 1 1/2 = 5 23/50

Step-by-step explanation:

( 2 4/5 * 1 3/10) * 1 1/2 = 14/5 x 13/10 x 3/2 = 546/100 = 5 46/100 = 5 23/50

Answer:

The system of equation y=120+20x and y=30x

Step-by-step explanation:

Let the number of days be x and y be the total number minutes

Jamie has walked 120 mins. She will walk at a rate of 20 mins per day.

y=120+20x

Owen walks 30 mins a day. So

y = 30x

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9514 1404 393

Answer:

  (a)  x = (3 -ln(3))/5 ≈ 0.819722457734

  (b)  y = 10

Step-by-step explanation:

(a) Taking the natural log of both sides, we have ...

  2x +1 = ln(3) +4 -3x

  5x = ln(3) +3 . . . . . . . . add 3x-1

  x = (ln(3) +3)/5 ≈ 0.820

__

(b) Assuming "lg" means "log", the logarithm to base 10, we have ...

  log(y -6) +log(y +15) = 2

  (y -6)(y +15) = 100 . . . . . . . taking antilogs

  y^2 -9x -190 = 0 . . . . . . . . eliminate parentheses, subtract 100

  (y -19)(y +10) = 0 . . . . . . . . factor

The values of y that make these factors zero are -19 and 10. We know from the first term that (y-6) > 0, so y > 6. That means y = -19 is an extraneous solution.

The solution is ...

  y = 10

__

When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...

  f(x) = e^(2x+1) -3e^(4-3x)

Answer:

Step-by-step explanation:

e^(2x + 1) = 3e^(4 - 3x)

e^(2x + 1) = e^3(4-  3x)

lne^ (2x + 1) =ln e^3(4-  3x)

2x + 1 = 3*(4 - 3x)

2x + 1 = 12 - 9x

11x + 1 = 12

11x = 12 - 1

11x = 11

x = 1

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

I've never worked with binary logs but I'll give this my best shot. If someone comes along and gives you a different answer, use it.

lg(y-6) + lg(y + 15) = 2

lg (y - 6)(y + 15) = 2

inverse (y - 6)(y + 15) = 2^2

(y - 6)(y + 15) = 4

y^2 + 9y - 90 - 4 = 0

y^2 + 9y - 94 = 0

y = 6.19

y = -15,19

The correct option is D. y=60x + 200.To find the equation of the line that passes through the given points (4, 440) and (6, 560) on a coordinate grid, we use the point-slope formula.The point-slope formula is an equation used to find the straight line's slope and y-intercept with respect to an individual point, as well as the x and y-axis coordinates.

The point-slope formula for any line through two points (x1, y1) and (x2, y2) is given by:y − y1 = m(x − x1) where m is the slope of the line.Using the point-slope formula, we find the slope of the line that passes through the points (4, 440) and (6, 560) on a coordinate grid as follows:Slope, m = (y2 - y1) / (x2 - x1)

Putting the values of x1 = 4, y1 = 440, x2 = 6, y2 = 560.Slope, m = (560 - 440) / (6 - 4) = 120 / 2 = 60

Therefore, the slope of the line is 60.Using the point-slope formula,y − y1 = m(x − x1 ),where m = 60, x1 = 4, and y1 = 440.Substituting the values, we get:y - 440 = 60(x - 4).Simplifying the equation,y - 440 = 60x - 240y = 60x + 200.

Hence, the equation of the line is y = 60x + 200. Therefore, the correct option is D. y=60x + 200.

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The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).

Given by: The midpoint of the two points is:

M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)

The following vector runs between the two points:

V = (3 - 1, 4 - 0, 0 - (-2)) = (2, 4, 2) (2, 4, 2)

The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.

The normal vector is then provided by:

N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)

The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:

(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2

The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.

12(x - 2) = -8(y - 2) = 4(z + 1) + 2

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Answer:

Step-by-step explanation:

First, you will want to combine like terms. 5x and 2x, -4 and 8. After combining, you get 7x+4. Hope this helps!

The type of influence on wellness that this represents is given as follows:

A. Social.

An influence on wellness is an activity that improves the morale of certain aspect of our lives.

The aspect improved in this problem is the social aspect, along with the physical aspect, as follows:

Since this is an example of social bonding, option A gives the correct option regarding which type of influence on wellness this is an example of.

For example, reading a book would be intellectual influence, while recycling would be environmental influence.

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Answer:

21 quarters and 21 dimes

Step-by-step explanation:

21 quarters = 5 dollars and 25 cents

21 dimes = 2 dollars and 10 cents

add together and you get the total

21 quarters and 21 dimes

Answer:

36x+42 if you need it simplified

x=-7/6 if you set the equation equal to zero

Answer:

42+36w

Step-by-step explanation:

6(3w+5)+6(3w+2)?

18w+30+6(3w+2)?

18w+30+18w+12?

Combine like terms: 18w,18w and 30,12.

30+12=42

18w+18w=36w

Result/Answer= 42+36w

Underlined= (do)distributive property

Hope this helps!!

Answer:

\( 7.25 \: units\)

Step-by-step explanation:

\(d \bigg(5 \frac{1}{2}, \: \: - 1 \frac{3}{4} \bigg) \\ \\ = d \bigg( \frac{11}{2}, \: \: - \frac{7}{4} \bigg) \\ \\ = d \bigg( \frac{22}{4}, \: \: - \frac{7}{4} \bigg) \\ \\ = \frac{22}{4} - \bigg( - \frac{7}{4} \bigg) \\ \\ = \frac{22}{4} + \frac{7}{4} \\ \\ = \frac{22 + 7}{4} \\ \\ = \frac{29}{4} \\ \\ = 7. 25\: units\)

The definite integral ∫[0 to x] (f(t) + f(-t)) dt, where f(t) is an even function, can be evaluated using the properties of even and odd functions. The integral evaluates to zero.

s symmetric about the y-axis, which means f(t) = f(-t) for all values of t. In this case, we have f(t) + f(-t) = 2f(t). Therefore, the integral becomes ∫[0 to x] (2f(t)) dt.

When integrating an even function over a symmetric interval, such as from 0 to x, the positive and negative areas cancel each other out. For every positive area under the curve, there is an equal negative area. This cancellation is a result of the symmetry of the function.

Since the integrand 2f(t) is an even function, the integral ∫[0 to x] (2f(t)) dt will also be an even function. An even function integrated over a symmetric interval yields a result of zero. Therefore, the definite integral evaluates to zero:

∫[0 to x] (2f(t)) dt = 0.

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The height of the trapezoid is 98 units

The space enclosed by the boundary of a plane figure is called its area.

A trapeziod is a closed shape or a polygon, that has four sides, four corners/vertices and four angles

The area of a trapezoid is expressed as;

A = 1/2( a+b)h

where a and b are the bases length of the trapezoid.

245= 1/2 ( 14+21)h

490 = 35h

divide both sides by 35

h = 490/35

h = 98 units

Therefore the height of the trapezoid is 98 units

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Answer: 12 and 8

Step-by-step explanation:

Their difference is four while others aren't.