3kx + 24 = 9kx solve for X

A: -2/k B: 4/k C: -4/k D:2/k

Answer:

500π in^3

Step-by-step explanation:

The radius is half the diameter, so the radius is 5 in. Since the height is four times that, the height is 20 in.

The equation for the volume of a cylinder is:

\(V = \pi r^{2}h\)

We can plug in the radius and height:

\(V = \pi \times (5)^{2} \times 20\\V = \pi \times 25 \times 20\\V = 500\pi in^{3}\)

Explanation:

Label the slots A,B,C for first through third place.

There are 8 choices for slot A, 7 for slot B, and 6 for slot C. We start with 8 and count our way down until we get to the final slot. Then we multiply out those values

8*7*6 = 336

There are 336 ways to select three people from a pool of eight overall.

-----------------

If you want to use the permutation formula, then your steps might look like this

\(_n P _r = \frac{n!}{(n-r)!}\\\\_8 P _3 = \frac{8!}{(8-3)!}\\\\_8 P _3 = \frac{8!}{5!}\\\\_8 P _3 = \frac{8*7*6*5!}{5!}\\\\_8 P _3 = 8*7*6\\\\_8 P _3 = 336\\\\\)

Note how the 5! terms cancel out on the second to last step, leaving behind the expression 8*7*6 which was found earlier.

Answer:

He needs 8

Step-by-step explanation:

40 - 20 = 20

2.5 x 8 - 20

aaden needs to visit the movies 8 more times

Answer:

8

Step-by-step explanation:

20+2.5x=40

x equal the number of visits adam need to make to earn a free movie ticket

2.5x=40-20

2.5x=20

x= 20/2.5

x=8

The example regarding the values of digits is also true for decimal numbers, as we showed with 0.52.

For example, for the decimal 0.52.

.52 = 5 x 0.1 + 2 x 0.01 = 0.52.

Hence, moving a digit one place to the left, the value is 10 times as much, as we saw with digits 5 and 2 in the number 0.52.

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Answer:

32, 39, 46

Step-by-step explanation:

Given sequence:

Work out the differences between the terms:

\(4 \underset{+7}{\longrightarrow} 11 \underset{+7}{\longrightarrow} 18 \underset{+7}{\longrightarrow} 25\)

As the difference between each term in the sequence is constant, the sequence is an arithmetic sequence with common difference of 7.

To find the next three terms in the given sequence, simply add 7 to the previous term:

\(\implies 25 + 7 = 32\)

\(\implies 32 + 7 = 39\)

\(\implies 39 + 7 = 46\)

Answer:

Step-by-step explanation:

Next three terms are 32, 39, 46

As the different in all of them is of 7 so we add 7 with each term to get the next terms :)

Step-by-step explanation:

Use PEMDAS

\(\begin{array}{ccc}214.8-(4^2+3)\times4&\\214.8-(16+3)\times4&Evaluate\\214.8-19\times4&Add\\214.8-76&Multiply\\138.8&Subtract\end{array}\)

Answer:

Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.

Step-by-step explanation:

The given linear regression equation is y=0.775x+950.25, where x represents the square footage of the apartment and y represents the monthly rental price. To find the size of the apartment Grace can expect to rent for $1,500 per month, we can substitute y with 1,500 in the equation and solve for x:

1,500 = 0.775x + 950.25

0.775x = 1,500 - 950.25

0.775x = 549.75

x = 710.32

Therefore, Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.

Answer: 1735259

Step-by-step explanation:

I think I did this before.

The Divisor is 100 billion / M.

A value-weighted index is a stock market index in which stocks are weighted according to the market capitalization of the corporation. To answer the given question, we need to understand what a value-weighted index is and what divisor to be considered to get an initial value of 100 billion.

A value-weighted index is a stock market index in which stocks are weighted according to the market capitalization of the corporation. Large corporations have a greater influence on the index’s value than small corporations. The index is computed by dividing the total market value of the stocks in the index by a divisor to arrive at an index value. The divisor is constantly changing since changes in market value alter it. 

The devisor is calculated by dividing the initial value of the index by the sum of the market capitalizations of the stocks in the index, that is,If V is the initial value of the index andM1, M2, ……, Mn are the market capitalizations of the n stocks in the index, then the divisor D is given by:

D=V / (M1 + M2 + ... + Mn)

For the given problem, the divisor can be computed as follows:

Assuming the total market value of stocks to be M,

where, V = 100 billion.

Then,

Divisor = 100 billion / M.

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A nurse should empty a Hemovac wound suction device when it is half full to ensure proper functioning and prevent discomfort or injury to the patient due to the device becoming too heavy.

The rationale for a nurse to empty a Hemovac wound suction device when it is half full is to ensure the device is functioning correctly and to prevent it from becoming too heavy and potentially causing discomfort or injury to the patient.

When a Hemovac wound suction device is half full, it may start to lose suction, which can result in less efficient drainage of fluid from the wound site. By emptying the device, the nurse can ensure that the device is functioning correctly and that the suction pressure is maintained.

Additionally, allowing the device to become too full can make it heavy and uncomfortable for the patient, potentially causing discomfort or injury to the wound site. Therefore, emptying the device when it is half full can help prevent these complications and ensure that the patient remains comfortable throughout the healing process.

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Option c) is true, which states that the standard deviation of a sample is 9.56 and the variance is 3.09.

Simply taking the square root of the sum of all the squared variances yields the standard deviation. A zone containing 68 percent of the data points would be defined by one standard deviation, or one sigma, drawn above or below the average value on that normal distribution curve.

We are given that

X ~U (0,20

Size of sample,n=100

E(X)=\(\frac{a+b}{2}\)=\(\frac{0+20}{2}\)=10

Var(x)=\(\frac{(b-a)^2}{12}\)=\(\frac{(20-0)^2}{12}\)=33.33

Using normality approximation

X\(\sim N(\mu,Var(X)/n)\)=N(10,33.33/100)

X ~ N(10,0.333)

Hence, option b is true.

Therefore, option c) is true, which states that the standard deviation of a sample is 9.56 and the variance is 3.09.

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Answer:

7q - 21 (can also be written as 7(q - 3))

Step-by-step explanation:

\(4(q-12) + 3(q + 9)\\4q - 48 + 3q + 27\\7q - 21\)

The given statement is true.

If f and g are polynomials of degree n, then f + g is a polynomial of degree n as well.

Explanation:

Let the degree of polynomial f(x) be n, and let the degree of polynomial g(x) be m.Then we can express f(x) and g(x) as follows:f(x) = anxn + an-1xn-1 + ... + a1x + a0g(x) = bmxm + bm-1xm-1 + ... + b1x + b0When we add the two polynomials, we get:f(x) + g(x) = anxn + an-1xn-1 + ... + a1x + a0 + bmxm + bm-1xm-1 + ... + b1x + b0Since the degree of a polynomial is determined by the highest power of x that appears, the degree of f(x) + g(x) is max(n, m). Since f(x) and g(x) both have degree n, we can say that f(x) + g(x) has degree n as well.

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Answer:

Step-by-step explanation: Answer c the -1 is equivalent to the -0 and -* to the third power equaled the equation mathematics of it being c

Thus, the answer c

The volume of cylindrical tin is 1584 \(cm^3\). The depth of the oil in the tin is 9cm.

\(V_1 =\) VOLUME OF CYLINDRICAL TIN

   \(= \pi r^2 h\)

  \(=\frac{22}{7}\) x 6 x 6 x 14

  = 44 x 36

  = 1584 \(cm^3\)

\(V_2 =\) VOLUME OF RECTANGULAR TIN

    = lbh = 1584

    = (16)(11)(h) = 1584

    = 176h =1584

    = h = 1584 / 176

    = h = 9 cm

A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that extends upward to meet at a point known as the apex. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula V = πr²h, Once we have calculated the area of the circular base, we can multiply it by the height of the cylinder to get the volume.

To calculate the volume of a cylinder, we need to know its dimensions, which are the radius and height. The radius is the distance from the center of the circular base to the edge, while the height is the distance between the two circular bases.

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The equation of function for the given problem is y = 3x + 12.

What is point slope form of the line?

For linear equations, the general form is y - y1 = m(x - x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Given:

A bathtub has some water in it. Mia turns on the faucet to add more water.

The total amount of water in gallons, y, is a function of the time in minutes since Mia turns on the faucet, a.

The graph of the linear function passes through the points (4, 24) and

(6, 30).

We have to find the equation of function.

Let the linear function passes through the points (4, 24) and (6, 30).

First to find the slope of equation using given points.

\(m = \frac{y_2-y_1}{x_2-x_1} = \frac{30-24}{6-4} = \frac{6}{2} = 3\)

Now to find the equation of function.

Consider the point slope form of the line,

\(y-y_1=m(x-x_1)\)

Plug the values of m = 3 and \((x_1,, y_1) = (4, 24)\)

⇒

\(y-24=3(x-4)\\y-24=3x-12\\y=3x-12+24\\y=3x+12\)

Hence, the equation of function for the given problem is y = 3x + 12.

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Answer: $67.50

Step-by-step explanation:

\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)

Answer:

A positive number

I hope this helps!

Answer:

The difference between any two even number is even.

Step-by-step explanation:

2-4 is -2

-2 is an even number

now let's say 190-20 that is 170

and 170 is even

a) The rate of change of temperature at point P(4, -1, 5) in the direction towards the point (6, -3, 6) is approximately -3000e⁻²⁴⁶ °C/m.

b) The direction in which the temperature increases fastest is the direction of the gradient vector at point P.

c) The maximum rate of increase at point P is approximately 3262.656 *e⁻²⁴⁶ °C/m.

Here, we have,

To find the rate of change of temperature at point P(4, -1, 5) in the direction towards the point (6, -3, 6), we need to find the directional derivative of the temperature function T(x, y, z) = 400\(e^{(-x^{2}-5y^{2}-9z^{2}) }\) in the direction of the vector from P to the given point.

(a) Rate of change of temperature:

The directional derivative of T(x, y, z) in the direction of a vector v = <v1, v2, v3> is given by the dot product of the gradient of T with the unit vector in the direction of v.

First, let's find the gradient of T(x, y, z):

∇T(x, y, z) = <∂T/∂x, ∂T/∂y, ∂T/∂z>

Taking the partial derivatives:

∂T/∂x = -800x\(e^{(-x^{2}-5y^{2}-9z^{2}) }\)

∂T/∂y = -400y\(e^{(-x^{2}-5y^{2}-9z^{2}) }\)

∂T/∂z = -360z\(e^{(-x^{2}-5y^{2}-9z^{2}) }\)

Now, we can calculate the gradient at point P(4, -1, 5):

∇T(4, -1, 5)

= <-3200e⁻²⁴⁶, 400e⁻²⁴⁶, -1800e⁻²⁴⁶>

Next, let's find the unit vector in the direction from P to (6, -3, 6):

v = <6 - 4, -3 - (-1), 6 - 5>

= <2, -2, 1>

To find the unit vector, we need to normalize v:

||v|| = √(2² + (-2)² + 1²)

= √(4 + 4 + 1)

= √9

= 3

The unit vector in the direction of v is:

u = v/||v|

= <2/3, -2/3, 1/3>

Now, let's calculate the dot product of the gradient and the unit vector:

∇T(4, -1, 5) · u = <-3200e⁻²⁴⁶, 400e⁻²⁴⁶, -1800e⁻²⁴⁶> · <2/3, -2/3, 1/3>

Calculating the dot product:

∇T(4, -1, 5) · u = (-3200e⁻²⁴⁶)(2/3) + (400e⁻²⁴⁶)(-2/3) + (-1800e⁻²⁴⁶)(1/3)

Simplifying:

∇T(4, -1, 5) · u = (-6400/3)e⁻²⁴⁶+ (-800/3)e⁻²⁴⁶ - (1800/3)e⁻²⁴⁶

= (-9000/3)e⁻²⁴⁶

= -3000e⁻²⁴⁶

Therefore, the rate of change of temperature at point P(4, -1, 5) in the direction towards the point (6, -3, 6) is approximately -3000e⁻²⁴⁶ °C/m.

(b) The direction in which the temperature increases fastest at point P is opposite to the direction of the negative gradient vector. Therefore, the direction in which the temperature increases fastest is the direction of the gradient vector at point P.

(c) To find the maximum rate of increase at point P, we need to find the magnitude of the gradient vector at point P:

||∇T(4, -1, 5)|| = ||<-3200e⁻²⁴⁶, 400e⁻²⁴⁶, -1800e⁻²⁴⁶>||

= √((-3200e⁻²⁴⁶)² + (400e⁻²⁴⁶)² + (-1800e⁻²⁴⁶)²)

Calculating the magnitude:

||∇T(4, -1, 5)|| = √(10240000e⁻⁴⁹² + 160000e⁻⁴⁹² + 3240000e⁻⁴⁹²)

= √(10624000e⁻⁴⁹²)

= √10624000 * √e⁻⁴⁹²

= √10624000 * e⁻²⁴⁶

≈ 3262.656 *e⁻²⁴⁶

Therefore, the maximum rate of increase at point P is approximately 3262.656 *e⁻²⁴⁶ °C/m.

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Answer:

y = x² -8x + 16

Step-by-step explanation:

y = (x -4)^2

y = (x -4) * (x -4)

use the FOIL method

y = x*x -4x -4x +16

y = x² -8x + 16

The percentile rank represents the percentage of values that are less than or equal to a particular value. the percentile rank of a rating of 7 is 80%.

To determine the percentile rank of a rating of 7, we need to calculate the percentage of ratings that are less than or equal to 7 out of the total number of ratings.

Given that there are 10 movie ratings in total and 8 of them are less than or equal to 7, we can calculate the percentile rank as follows: Percentile Rank = (Number of ratings ≤ 7 / Total number of ratings) * 100, Percentile Rank = (8 / 10) * 100, Percentile Rank = 80

Therefore, the percentile rank of a rating of 7 is 80%.

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According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. The correct option is A. 34% and 26%.

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. This indicates that women are still underrepresented in STEM fields, despite the fact that there has been an effort to attract more women to STEM fields.

In both Canada and the United States, women have made significant progress in breaking down gender barriers in STEM fields. However, there is still work to be done to close the gender gap and increase representation of women in STEM fields.

Women's representation in STEM fields has increased in both Canada and the United States in recent years, but the percentage of women in STEM fields is still significantly lower than the percentage of men. More efforts are needed to close the gender gap in STEM fields and encourage more women to pursue STEM careers.

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Answer: a. x<3 and x<1

The radius of the circle centered at N is 11/2.

Assuming that J, K, L, and M lie on the circle centered at N, we can use the fact that the radius of a circle is perpendicular to any tangent line drawn to the circle at the point of tangency.

Since JK and LM are chords of the circle, they each intersect the radius at a right angle.

Let P and Q be the points where JK and LM intersect the radius, respectively. Then we have NP = NQ = 5 and JP = PK = 5x - 1 and LQ = QM = 7x - 11.

Using the Pythagorean theorem, we can find the length of NP in terms of x:

\(NP^2 = JP^2 - JN^2\)

\(5^2 = (5x - 1)^2 - N^2\)

\(25 = 25x^2 - 10x + 1 - N^2\)

\(N^2 = 25x^2 - 10x - 24\)

Similarly, we can find the length of NQ in terms of x:

\(NQ^2 = LQ^2 - LN^2\)

\(5^2 = (7x - 11)^2 - N^2\)

\(25 = 49x^2 - 154x + 122 - N^2\)

\(N^2 = 49x^2 - 154x + 97\)

Setting the expressions for \(N^2\) equal to each other, we get:

\(25x^2 - 10x - 24 = 49x^2 - 154x + 97\)

\(24x^2 - 144x + 121 = 0\)

\((2x - 11)^2 = 0\)

Therefore, x = 11/2.

Substituting this value of x into the expression for \(NP^2 \:or\: NQ^2\), we get:

\(N^2\) = 25\((11/2)^2\) - 10(11/2) - 24 = 121/4

Taking the square root of \(N^2\), we get the radius

NP = NQ = \(\sqrt{(121/4)}\) = 11/2.

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Factorial notation is used to represent the product of a series of descending positive integers, and is denoted by an exclamation mark.

For example, 5! represents 5 x 4 x 3 x 2 x 1, which equals 120. If the study involves counting the number of ways a certain group of items can be arranged, factorial notation may be used to express the total number of possible arrangements. However, without knowing the specifics of Dr. Elder's study, it is impossible to provide the correct factorial notation. Therefore, I would recommend providing more details about the study in order to receive a more accurate answer.

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Answer:

huh okay well hi

Step-by-step explanation:

may the force be with u :)

Answer: 140 degrees

A straight line is 180 degrees. Since we know one of the angles in the line is 40, we just subtract 40 from 180. So, the measure of angle 1 plus the measure of angle 2 is 140 degrees.

:)

The solution of (3,13) means you need to create two lines that satisfy x = 3 and y = 13

The two lines can be anything as long as they give this solution

For example, if you wrote x + y = 16 (you know their values already)

Then write another y - x = 10

From here you have your equations, turn them into the f(x) form.

x + y = 16 can be turned into y = 16 - x which is f(x)=16-x

y-x = 10 can be turned into y = 10 + x which is g(x)=10 + x

Answer:

-26-8i does this help?

Step-by-step explanation:

I took what was in the parenthesis and put them together coming out with -10 and -4i. Then I took what was next and started putting the variables together and the numbers together.