the volume of a cylinder is 540 pi ft^3 the height is 15 ft. what is the diameter
a. 6
b.12
c.24
d.36​

Answer:

5.94×10^6

Step-by-step explanation:

you have to move the decimal 6 times before reaching the next number then you have to mutiply it by 10 and put the 6

Answer:

fast bike speed = 41/3= 17mph

slower bike speed = 37/3 =12.33 mph

Final answer:

The slower biker's speed is 12 mph and the faster biker's speed is 14 mph, determined by setting up an equation with their combined distances equating to 78 miles after 3 hours.

Explanation:

To resolve the puzzle of the two bikers departing from the same location and traveling in opposite directions, we can apply concepts of rate, time, and distance. We are given that the two bikers are 78 miles apart after 3 hours and that one biker is traveling at a speed that is 2 mph faster than the other.

Let's denote the speed of the slower biker as $x$ mph. Consequently, the speed of the faster biker would be $x + 2$ mph. Considering that they have been traveling for 3 hours, the slower biker would have covered 3$x$ miles and the faster biker 3($x + 2$) miles. The sum of these distances is the total distance between the bikers after 3 hours, which is 78 miles.

Mathematically, we can represent the situation as:

3$x$ + 3($x + 2$) = 78

Simplifying the equation:

3$x$ + 3$x$ + 6 = 78

6$x$ + 6 = 78

6$x$ = 72

$x$ = 12

Thus, the slower biker's speed is 12 mph and the faster biker's speed is 12 mph + 2 mph = 14 mph.

Answer: The faster biker travels at 14 mph and the slower biker travels at 12 mph

If the quotient of two numbers is negative, it means that the result of dividing one number by the other is negative.

This situation can only occur if the two numbers have opposite signs. In other words, one number must be positive, and the other must be negative.

When we divide a positive number by a negative number or a negative number by a positive number, the resulting quotient will always be negative. So, to satisfy the given condition, the two numbers must have opposite signs—one positive and one negative.

Therefore, If the quotient of two numbers is negative, it means that the result of dividing one number by the other is negative.

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Final answer:

For the quotient of two numbers to be negative, one of the numbers must be positive and the other must be negative. This principle follows the general rules for multiplication and division involving signed numbers.

Explanation:

For a quotient of two numbers to be negative, one number must be positive and the other negative. This rule aligns with the multiplication and division rules for signs, whereby the product or quotient of two numbers with opposite signs results in a negative outcome.

Essentially, this can be understood by considering examples of multiplication, such as (-3) x 2 = -6 and 4 x (-4) = -16, which similarly apply to division. The same principle holds when dividing two numbers; if their signs are opposite, the result is negative.

This mathematical rule is fundamental and applies universally across mathematics, ensuring consistency in the calculation and understanding of operations involving signed numbers.

Answer:

there is no graph

Step-by-step explanation:

Answer:

Option The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above

the line

Step-by-step explanation:

we have

[tex]y>3x-8[/tex]

The solution of the inequality is the shaded area above the dashed line The equation of the dashed line is [tex]y=3x-8[/tex]

The slope of the dashed line is positive [tex]m=3[/tex]

The y-intercept of the dashed line is -8

see the attached figure to better understand the problem

Answer:

D is the correct answer

Step-by-step explanation:

Final answer:

A linear equation represents a straight line and is written in the form y = mx + b. A quadratic equation represents a parabolic curve and is written in the form y = ax² + bx + c.

Explanation:

A linear equation is an equation that represents a straight line when graphed. It is typically written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope describes the rate of change between the independent and dependent variables, while the y-intercept is the point where the graph crosses the y-axis.

On the other hand, a quadratic equation is an equation that represents a parabolic curve when graphed. It is typically written in the form y = ax² + bx + c, where a, b, and c are constants. The graph of a quadratic equation is symmetric around a vertical line called the axis of symmetry, and it has either a maximum point or a minimum point.

Answer:

D

Step-by-step explanation:

There are infinitely many possible parallelograms.  The angles are fixed at 50° and 130°, and two parallel sides are fixed at 10 cm, but the other two sides can have any length (except 10 cm).

Answer:

B

Step-by-step explanation:

To evaluate (f ￮ f)(2) substitute x = 2 into f(x) and evaluate. Then substitute this value into f(x)

f(2) = 15 - 2 = 13, then

f(13) = 15 - 13 = 2

Hence (f ￮ f)(2) = 2

Answer:

14 yds

Step-by-step explanation:

To find the perimeter, we add up all the sides

P = s1 + s2+ s3 + s4

38 = 5.8+7+11.2 + s4

Combine like terms

38 = 24+s4

Subtract 24 from each side

38-24 = 24-24 +s4

14 = s4

The 4th side is 14 yds

Answer:

14yd

Step-by-step explanation:

Answer:

x= 42/5

alternative forms:

x=8 2/5

x=8.4

Step-by-step explanation:

Start with x-1/6x=7

Multiply both sides by 6 to get 6x-x=42

combine like terms (the Xs) to get 5x (6x-x is 5x)

5x=42

divide both sides by 5 to get x=42/5

Answer:

x = 42/5

Step-by-step explanation:

x -1/6x=7

Get a common denominator

6/6x - 1/6 x = 7

5/6x = 7

Multiply each side by 6/5 to isolate x

6/5 * 5/6x = 6/5*7

x = 42/5

The origin O appears rotated by 180° about ’( -2,0), (-4,0), (-5,2) , ’(-1,2).

Coordinate geometry (or analytic geometry) is described as the examination of geometry and the use of coordinate factors. using coordinate geometry.

Coordinate using the horizontal and vertical distances from the two reference axes. generally represented by way of (x,y) the x-price and y-cost.

Coordinate geometry is used to control and regulate air visitors. The coordinates of the flight are used to describe the plane's modern location. despite the fact that a plane actions a tiny distance (up, down, forward, or backward), the machine updates the coordinates of flight for each small change in its role.

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Answer:

1. G IS A DEPENDENT VARIABLE

2.U IS THE INDEPENDENT VARIABLE

Step-by-step explanation:

G is a dependent variable because its values will rely on the values of U multiplied by 748. A dependent variable in most cases is isolated on one side of an equation ( mostly the left-hand side) and it value is affected by the values selected on the other side of the equation.

U is an independent variable because it stands on its own such that it does not rely on the behavior of another variable to determine its value/characteristic.Characteristic here i mean , U is freely selected without considering the behavior of other variable, thus it does not face any restrictions as compared to G.

Answer:

C. (3, 2)

Step-by-step explanation:

(3, 2) is the solutions to the inequality y ≤ 2x − 4 shaded region.

Answer:

A.) 1/81

Step-by-step explanation:

This is your equation:

f(x) = 9^x

They want you to solve for x = -2, so substitute -2 in for x.

f(-2) = 9^-2

When you solve this, you get, 1/81.

So, the answer is A.)

I hope this helps! :)

Working and answer in the photo above. Hope this helps

Answer:

15% of 38= 5.7

Round up to 6

Answer: b) $6

Step-by-step explanation:

Please mark brainliest and have a great day!

The conjugate of the complex number a+bi is a-bi

you just reverse the sign of the imaginary part of the number; so it is 4 -51i

The complex conjugate of the complex number is Option C. 4-51i

To simplify this fraction we multiply the numerator and the denominator by the complex conjugate of the denominator. When we change the sign of the imaginary part, we have the complex conjugate. Another way to think of this is to return all the i with -i. As we can see here, the complex conjugate of 3 - 4i is 3 + 4i.

You find the complex conjugate simply by reversing the sign of the imaginary part of the complex number. To find the complex conjugate of 4+7i we change the sign of the imaginary part. Thus the complex conjugate of 4+7i is 4 - 7i.

Complex conjugate is when "Each of two complex numbers having their real parts equal and their imaginary parts of equal magnitude but opposite sign."

The notation for the complex conjugate of z is either ˉz or z∗. The complex conjugate has the exact real part as z and the same imaginary part but with the opposite sign.

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Answer:

Option C is correct.

Step-by-step explanation:

We are given the expression:

[tex](\frac{3^2a^{-2}}{3a^{-1}})^k[/tex]

The value of a =5 and k = -2

Putting the values and solving

[tex]=(\frac{3^2*5^{-2}}{3*5^{-1}})^-2\\=(\frac{3^{2-1}}{5^{-1+2}})^-2\\=(\frac{3^{1}}{5^{1}})^-2\\\\=(\frac{3}{5})^-2\\if \,\,a^{-1} \,\,then\,\, 1/a\\=\frac{(3)^{-2}}{(5)^{-2}}\\ Can\,\,be\,\,written\,\,as\\\\=\frac{(5)^{2}}{(3)^{2}} \\=\frac{25}{9}[/tex]

Option C is correct.

Answer:

543.7

Step-by-step explanation:

.67 is closer to .7 than to .6

Answer:

543.7

Step-by-step explanation:

The 7 rounds up to a 6 in the tenth place.

Answer:

x = 10000

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

log x = 4 ( noting that log x has base 10 ), then

x = [tex]10^{4}[/tex] = 10000

Answer:

x=30

Step-by-step explanation:

The two angles form a straight line

4x+2x = 180

6x= 180

Divide each side by 6

6x/6 = 180/6

x = 30

Answer:

X=30

Step-by-step explanation:

the degree of a straight line is 180

Add 2x and 4x together = 6x

Then divide 6x = 180 by 6 to get the x value.

The answer is 30

Gradient is the slope of the line.

Use two points of the graphed line to find the slope, which is the change in Y over the change in x.

I'll use the points (4,0) and (6,8)

Slope = (8-0) / 6/4) = 8/2 = 4

The gradient is 4

Answer:

The correct answer option is B. 60%.

Step-by-step explanation:

We are given the results of a survey which asked the students whether they have any siblings and pets.

We are to determine the likelihood that student has a pet, given that he or she does not have a sibling.

Assuming A to be the event showing that a student does not have a sibling and B to be the event that a students has a pet.

Then P(B|A) is:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

Substituting the given values, P(A)=0.25 and P(A∩B)=0.15:

[tex]P(B|A)=\dfrac{0.15}{0.25}\\\\P(B|A)=\dfrac{3}{5}\\\\P(B|A)=0.6[/tex]

So the percentage will be:

[tex]0.6\times 100 = [/tex] 60%

For this case we have the following equation:

[tex]81x = x ^ 2[/tex]

Rewriting we have:

[tex]x ^ 2-81x = 0[/tex]

We take common factor "x" from both terms:

[tex]x (x-81) = 0[/tex]

It is observed that equality is fulfilled when x = 0 and when x = 81

So, the roots are:

[tex]x_ {1} = 0\\x_ {2} = 81[/tex]

Answer:

[tex]x_ {1} = 0\\x_ {2} = 81[/tex]

Answer:

Step-by-step explanation:

Without brackets, we are not exactly sure what is under the root sign. There are 3 choices.

sqrt(x) + 2 - 15 = - 3

sqrt(x + 2) - 15 = - 3

sqrt(x + 2 - 15) = - 3

I think the middle one is what you intend. If not leave a note.

sqrt(x + 2) - 15 = - 3                Add 15 to both sides.

sqrt(x + 2) - 15+15 = - 3+15     Combine

sqrt(x + 2) = 12                        Square both sides

x + 2 = 12^2                             Do the right

x + 2 = 144                               Subtract 2 from both sides.

x + 2-2 = 144-2

x = 142

Answer:

142

Step-by-step explanation:

Answer:

The answer is (2,-2)

You just distribute the 2 into (1,1) and same with the -4 into (0,1) and add them together ‍

Step-by-step explanation:

ANSWER

[tex]\binom{2 }{ - 2}[/tex]

EXPLANATION

We were given the vector equation:

[tex]2 \binom{1}{1} ) - 4 \binom{0}{1} [/tex]

We perform the scalar multiplications first to get:

[tex]\binom{2 \times 1}{2 \times 1} ) - \binom{4 \times 0}{4 \times 1}[/tex]

Simplify the components of each vector

[tex]\binom{2 }{2} - \binom{0}{4}[/tex]

We subtract the corresponding components of the vector to get:

[tex]\binom{2 - 0}{2 - 4} [/tex]

This simplifies to

[tex]\binom{2 }{ - 2}[/tex]

[tex]\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{y}{xy}+\dfrac{x}{xy}=\dfrac{x+y}{xy}=\dfrac{12}{-5}=-\dfrac{12}{5}=-2,4[/tex]

Answer:

3

Step-by-step explanation:

Range is the largest number minus the smallest number

4-1 = 3

The range is 3

Answer:

3

Step-by-step explanation:

The range of a set of data is the difference between the highest and lowest values in the set.

Sort your data from lowest to highest. You get

1, 2, 3, 4, 4, 4, 4, 4

Highest value = 4

Lowest value = 1

           Range = 3  chocolate chips

Answer:

(2,-4) And (3,-2)

Step-by-step explanation:

Here we have to solve one linear equation and a quadratic equation.

First we find the value of y in terms of x from linear equation and then substitute this value in our quadratic equation to solve it for x , Let us see how :

we have y-2x=8

y=2x-8

Now we substitute this in [tex]x^2-3x-y=2[/tex]

Hence we have

[tex]x^2-3x-(2x-8)=2\\x^2-3x-2x+8=2\\x^2-5x+8=2\\x^2-5x+8-2=0\\x^2-5x+6=0\\x^2-2x-3x+6=0\\x(x-2)-3(x-6)=0\\(x-2)(x-3)=0\\[/tex]

Thus we have

either (x-2)= 0 or (x-3)=0

or  x=2 or x=3

Now let us find the value of y by substituting them in y=2x-8 one by one.

y=2(2)-8= 4-8=-4

y+2((3)-8=6-8=-2

Hence our coordinates are

(2,-4) and (3,-2)

Answer:

(2, - 4), (3, - 2)

Step-by-step explanation:

Given the 2 equations

y - 2x = - 8 → (1)

x² - 3x - y = 2 → (2)

Rearrange (1) expressing y in terms of x

y = 2x - 8 → (3)

Substitute y = 2x - 8 in (2)

x² - 3x - 2x + 8 = 2

x² - 5x + 6 = 0 ← in standard form

(x - 2)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 3 = 0 ⇒ x = 3

Substitute these values into (3) for corresponding values of y

x = 2 : y = (2 × 2) - 8 = 4 - 8 = - 4 ⇒ (2, - 4)

x = 3 : y = (2 × 3) - 8 = 6 - 8 = - 2 ⇒ (3, - 2)

Answer:

The 99.7% confidence interval for the mean here is

[tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].

Step-by-step explanation:

The data in this question comes from random samples. In other words, the true population data are not known. Assume that both the sample average and the sample stdev are unbiased estimates for the population mean and stdev.  

The sample size 196 is sufficient large, such that the central limit theorem will apply. By the central limit theorem, the distribution of the mean (as well as the sum) of a sufficiently large samples resembles normal distributions. However, since stdev is only an estimate, the confidence interval can only be found using the Student's t-distribution.

What is the confidence interval for the mean of a random variable that follows the t-distribution?

[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex],

where

What is not given is

Start by determining the degree of freedom [tex]df[/tex] of [tex]t[/tex]. The degree of freedom for a one-variable estimate is usually equal to [tex]n -1[/tex] (that is: sample size minus one.) For this question, [tex]n = 196[/tex] so [tex]df = 196 - 1 = 195[/tex].

If [tex]T[/tex] represent a random variable that follows the [tex]t_{195}[/tex]-distribution, the value of t shall ensure that

[tex]P(-t \le T \le t) = \text{Confidence Interval} = 0.997[/tex].

The t-distribution is symmetric. As a result,

[tex]\displaystyle P(T > t) = 0.997 + \frac{1}{2}\times (1 - 0.997) = 0.9985[/tex].

Find the value of [tex]t[/tex] either with a t-distribution table or with technology. Keep in mind that for this question, [tex]df = n - 1 = 195[/tex].

[tex]t \approx 3.00549[/tex].

Apply the formula for the confidence interval:

[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex].

Lower bound:

[tex]\displaystyle \bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 - 3.00549\times \frac{3.5}{\sqrt{196}}\approx 11.2[/tex].

Upper bound:

[tex]\displaystyle \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 + 3.00549\times \frac{3.5}{\sqrt{196}}\approx 12.8[/tex].

In other words, the 99.7% confidence interval for the actual concentration is [tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].