Find the CCF of 6 and 18

Answer:

The answer is 1x = 11. 5-4 = 1. 1*x = 1x

1x =11

Step-by-step explanation:

Answer:

that number would be 3

Step-by-step explanation:

5x−4=11

x=3

Answer:

\(-3(x+2)+5x=-9\\-3x-6+5x=-9\\-3x+5x=-9+6\\2x=-3\\x=-\frac{3}{2}\)

Answer: √177

Step-by-step explanation:

6²+9²=c²

36+81=c²

117=c²

√117=√c²

√177 = c

(√177 can also be watered down to ±3√13 but √177 is one of the answer choices so yeah)

Answer: In this graph, the y-intercept of the line is -2. The equation of the line is y=x-2.

Answer:

We can write this equation in slope-intercept form

y

=

m

x

+

b

where

m

is the slope and

b

is the

y

-intercept.

We know

m

=

−

4

and

b

=

6

, so we can insert these into the equation to get

y

=

−

4

x

+

6

Hope this helps!

The lower cost will occur at the extreme point, that is if the number of videos rented daily is 8 pieces and the cost will be $550.

The cost function is given by:

C(x) = 2x² - 32x + 678

The lowest cost happens at the extreme point. In this point the derivative of C(x) is equal to zero.

Take the derivative:

C'(x) = 4x - 32 = 0

4x = 32

x = 32/4 = 8

Hence, the lowest cost will occur if the number of video rented daily is 8 pcs.

Substitute x = 8 into the cost function:

C(8) = 2(8)² - 32.(8) + 678 =  550

Complete question:

The owner of a video store has determined that the cost c, C(x) = 2x² - 32x + 678 in dollars, of operating the store is approximately given by where x is the number of videos rented daily. find the lowest cost to the nearest dollar

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Answer:

-120 is a negative and 400 is a positive

Step-by-step explanation:

also there is a 520 difference

The division of the polynomial x^2 + 2*x - 6 by (x + 1), using the long division method of dividing polynomials is x + 1 - 7/(x + 1)

The long division method allows the division of large numbers (which is the dividend) into the number of groups of the divisor and a remainder which is a value less than the expressed value of the divisor.

The expression \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 can be presented as follows;

The long division showing the steps can be obtained using code found online as follows;

\(\begin{array}{*1r {\arraycolsep}{\arraycolsep} *{11}l} & && x + 1 \\\cline{4-3}& &x+1& \longdiv {) x^2 +2\cdot x - 6& & & & & \\ & & & x^2 +x \\\cline{4-} && &\ \ \ x -6& \\ & & \ \ \ & \ \ \ x +1 \\\cline{4-} & & & \ \ \ \ \ \ \ -7 & \\ \cline{4-} \end{array}\)

The remainder of the long division is -7, therefore, we get;

\(\dfrac{x^2+2\cdot x-6}{x + 1} = x + 1 - \dfrac{7}{x+1}\)

The value of the expression, \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 following the long division is; x + 1 - 7/(x + 1)

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the coefficient of correlation in this situation is 0.65.The coefficient of correlation (r) is a measure of the strength and direction of the linear relationship between two variables.
TheThe coefficient of determination (R-squared) is defined as the proportion of variance in the dependent variable that is explained by the independent variable(s) in a regression model. It ranges from 0 to 1, where 0 means that none of the variance in the dependent variable is explained by the independent variable(s), and 1 means that all of the variance in the dependent variable is explained by the independent variable(s).

The coefficient of correlation (r) is a measure of the strength and direction of the linear relationship between two variables. It also ranges from -1 to 1, where -1 means a perfect negative correlation, 0 means no correlation, and 1 means a perfect positive correlation.

Since the coefficient of determination is equal to the square of the coefficient of correlation, we can find the coefficient of correlation as the square root of the coefficient of determination:

r = sqrt(0.4225) = 0.65

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Answer:

y= 1/3x - 2

Step-by-step explanation:

Answer:

4q²+ 12q +9

Step-by-step explanation:

Chloe runs her air conditioner for a total of 4 months, or 120 days. Chloe spends $176.40 per year on utility bills for the air conditioner during the four hottest months.

The reason for this expense is the need for cooling during these months, and the cost associated with running the air conditioner for 7 hours per day at a rate of $0.21 per hour.

To calculate the annual cost of running Chloe's air conditioner, we need to consider the number of hours per day, the cost per hour, and the number of days the air conditioner is used.

1. First, let's determine the total number of hours the air conditioner runs during the four hottest months:
7 hours/day * 30 days/month * 4 months = 840 hours

2. Now, we can calculate the total cost by multiplying the number of hours by the cost per hour:
840 hours * $0.21/hour = $176.40

At 7 hours per day, that's a total of 840 hours of use. At a cost of 21 cents per hour, Chloe spends 0.21 x 840 = $176.40 per year on utility bills for her air conditioner.

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20 ounces

Step-by-step explanation:

no exceptions

Answer: F(x)=ax²+bx+c

If a=b=0 then F(X)= constant

If a=0 & b≠0 then F(X) is a linear function

If a≠0 then F (X) is a quadratic function

Step-by-step explanation:

Given:

Consider the tank that is filled with water drains at a rate of \(\dfrac{d^2}{16}+4d-100\) gallons per minute where d is the depth of the tank in feet.

Depth of tank = 120 feet.

To find:

The rate of water drain for that tank.

Solution:

We have, rate of water drain in gallons per minute.

\(r=\dfrac{d^2}{16}+4d-100\)

where, d is the depth of the tank in feet.

Put d=120, to get the rate of water drain for the tank.

\(r=\dfrac{120^2}{16}+4(120)-100\)

\(r=\dfrac{14400}{16}+480-100\)

\(r=900+380\)

\(r=1280\)

Therefore, the rate of water drain is 1280 gal/min. Hence, the correct option is B.

The solution to the initial value problem dx/dt = ax with x(0) = x0, where a = −5/2 or 3/2, and x0 = 1/4 is x(t) = (1/4) e^(-5/2t) or x(t) = (1/4) e^(3/2t), respectively.

The initial value problem dx/dt = ax with x(0) = x0, where a = −5/2 or 3/2, and x0 = 1/4 can be solved using the formula x(t) = x0 e^(at).
Substituting the given values, we get x(t) = (1/4) e^(-5/2t) or x(t) = (1/4) e^(3/2t).
To check the validity of these solutions, we can differentiate both sides of the equation x(t) = x0 e^(at) with respect to time t, which gives us dx/dt = ax0 e^(at).
Substituting the given value of a and x0, we get dx/dt = (-5/2)(1/4) e^(-5/2t) or dx/dt = (3/2)(1/4) e^(3/2t).
Comparing these with the given equation dx/dt = ax, we can see that they match, thus proving the validity of the initial solutions.
In summary, the solution to the initial value problem dx/dt = ax with x(0) = x0, where a = −5/2 or 3/2, and x0 = 1/4 is x(t) = (1/4) e^(-5/2t) or x(t) = (1/4) e^(3/2t), respectively.

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The calculated value of p in terms of m is (c) p = ±√m

from the question, we have the following parameters that can be used in our computation:

m/p = r

Multiply through by p

So, we have

m = rp

Divide both sides by r

p = m/r

Also, we have

r = p

Substitute the known values in the above equation, so, we have the following representation

p = m/p

So, we have

m = p²

Take the square root of both sides

p = ±√m

This means that the value of p is p = ±√m

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The total number of revolutions per minute tire makes when the car is traveling at a speed of 90 mi/hr and the tire has a diameter of 22 inches is equal to approximately 1375.09.

Diameter of a car tire = 22 inches

Speed of a car = 90mi/hr

Let us first convert the speed from miles per hour to inches per minute,

Since the diameter of the tire is given in inches.

90 mi/hr

= 90 × 5280 ft/hr

= 475200 ft/hr

= 475200 × 12 in/hr

= 5,702,400 in/hr

= 95,040 in/min

Number of revolutions the tire makes per minute,

Distance the tire travels in one revolution.

The circumference of a circle is given by,

C = πd

where C is the circumference and d is the diameter.

So the distance the tire travels in one revolution is,

d = π(22 in)

  = 69.115 in

Now, the number of revolutions per minute  is ,

=distance traveled per minute / distance traveled in one revolution

⇒ revolutions per minute = 95,040 in/min / 69.115 in/rev

⇒revolutions per minute ≈ 1375.09 rev/min

Therefore, the tire makes approximately 1375.09 revolutions per minute with tire of diameter of 22 inches.

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Answer:

Step-by-step explanation:

Answer:

. X^2+6x-3=0

x²+6x+9-9-3=0

(x+3)²=12

x+3=√12

x=√12-3=0.46410161513

Answer:

b

Step-by-step explanation:

The number which when substituted in a polynomial makes its value zero is called the zero of the polynomial.

The zero of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

In other words, The zeros of a polynomial p(x) are the values of x which satisfy the equation p(x) = 0

For example, the zero of the polynomial f(x) = x³- 12x²+ 20x is  x = 0 or x = 10 or x = 2.

This is because f(x) = o when we substitute those x values.

Therefore, the number which when substituted in a polynomial makes its value zero is called the zero of the polynomial.

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The growth of the population after .t. years would be \(y_t = 16000^{(1.06t)}\).

The formula for exponential growth is \(y = y_0e^{(kt)}.\)

The formula for exponential decay is \(y = y_0e^{(-kt)}.\).

Given, The number of students enrolled at a college is 16,000 and grows ​6% each year.

Now, 6% in terms of decimals is 0.06 hence k = 1 + 0.06 = 1.06.

The initial amount is 16000.

So, After t number of years, the population would be, \(y_t = 16000^{(1.06t)}\).

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The method to draw the Binomial table is:

What is the binomial table?

A binomial table is a mathematical table that lists the values of a binomial coefficient, which is a number that appears in the expansion of the powers of a binomial (a polynomial with two terms).

To draw a binomial table, you can start by writing the values of n in the left column of the table, and the values of k in the top row. Then, for each value of n and k, you can calculate the corresponding binomial coefficient using the formula above and write it in the corresponding cell of the table.

Hence, Using this method you can draw a Binomial table

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The height of the kite from the ground is approximately 114 feet.

Describe the Right Angled Triangle.

The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs or the adjacent and opposite sides.

The Pythagorean theorem, which states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides, is a fundamental principle of right-angled triangles. This theorem is often used to calculate the length of one side of a right-angled triangle when the lengths of the other two sides are known.

Here's the labeled triangle:

              /|

           /   |

    h  /      | 68°

      /        |

    /θ___ |

        d

where h is the height of the kite from the ground, d is the horizontal distance from Jaclyn to the kite, and θ is the angle of elevation of the kite.

Using trigonometry, we know that:

\(tan(68°) = h/d\)

We can rearrange this equation to solve for h:

\(h = d * tan(68°)\)

We're given that the length of the kite string is 125 feet, so we can use the Pythagorean theorem to find d:

\(d^2 + h^2 = 125^2\)

Substituting d * tan(68°) for h, we get:

\(d^2 + (d * tan(68°))^2 = 125^2\)

Simplifying and solving for d, we get:

\(d = 125 / sqrt(1 + tan(68°)^2)\)

Substituting this value of d into our expression for h, we get:

\(h = d * tan(68°) ≈ 114\)

Therefore, the height of the kite from the ground is approximately 114 feet.

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Answer: x=7 y=-8

Step-by-step explanation:

True. Parametric tests are a category of statistical tests that can only be applied to data that meets certain criteria.

They make use of normal distribution assumptions when analyzing data, which means that a significant proportion of the data must follow a normal distribution for the test to produce valid outcomes

.A sample is a subset of the population that is being examined. The size of the sample has an impact on the accuracy of the study. If the sample size is insufficient, it may not be representative of the entire population. In small sample sizes, the main assumptions of parametric tests may be violated, and the results of the test may be skewed.

A sample is a group of individuals or objects from a population that are chosen for a study. The size of the sample is critical since it has a direct impact on the statistical accuracy of the data. A small sample size can cause the primary assumptions of parametric tests to be broken.

Parametric tests are a type of statistical test that can only be used with specific kinds of data. When parametric tests are used to evaluate data, it is assumed that the data follows a normal distribution. In general, this means that the data should be symmetric around the mean, with the majority of the data values being near the mean and fewer outliers. However, when the sample size is small, the accuracy of these assumptions may be in doubt.

As a result, it's crucial to ensure that you choose the proper statistical test based on the size of your sample and the distribution of your data.

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Answer:

239 ft².

Step-by-step explanation:

Let P represent the price for tiling.

Let S represent the size of the room.

From the question,

Price (P) varies directly as the size (S) i.e

P & S

P = KS

Where K is the constant of proportionality.

Next, we shall determine the value of K as follow

Price (P) = $ 4224

Size (S) = 264 ft²

Constant of proportionality (K) =?

P = KS

4224 = K × 264

Divide both side by 264

K = 4224/264

K = 16

Finally, we shall determine the size of the kitchen that will cost $ 3824 for tiling.

This is illustrated below:

Price (P) = $ 3824

Constant of proportionality (K) = 16

Size (S) =?

P = KS

3824 = 16 × S

Divide both side by 16

S = 3824/16

S = 239 ft²

Therefore, the size of the kitchen is 239 ft².

Answer:

Option A

Step-by-step explanation:

\(4(6-2x)\\\rule{150}{0.5}\\\rightarrow ((6 * 4) ( -2x*4)) \leftarrow \text{Distribute the '4' into the content in the parenthesis.}\\\\\\\\\rightarrow 6 * 4 = 24\\\\\rightarrow -2x * 4 = -8x\\\\\\\\\rightarrow 4(6-2x) = \boxed{24 - 8x}\)

Hope this helps.

The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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