(The sum of 5 times a number and 6 equals 9)

Translate the sentence into an equation

use the variable c for the unknown number

does anyone know the answer to this ?

The median number of vehicles going through the bank drive-up line in a 15-minute period is 27 vehicles.

To find the median, we need to arrange the recorded number of vehicles in ascending order. The given data set is: 15, 20, 24, 25, 25, 25, 25, 27, 27, 27, 27, 28, 28, 29, 30, 31, 31, 31, 35. There are 19 values in the data set, so the middle value is the 10th value. In this case, the median is 27, as it is the value that separates the lower half of the data set from the upper half.

To calculate the median, we arrange the data set in ascending order: 15, 20, 24, 25, 25, 25, 25, 27, 27, 27, 27, 28, 28, 29, 30, 31, 31, 31, 35. The middle value is the 10th value, which is 27. Therefore, the median number of vehicles going through the bank drive-up line in a 15-minute period is 27 vehicles.

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To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

The domain of the function f(x) = ln(x-3) is x > 3, since the natural logarithm is undefined for non-positive values. The x-intercept occurs when f(x) = 0, so ln(x-3) = 0, which implies x - 3 = 1. Solving for x gives x = 4 as the x-intercept.

There are no vertical asymptotes for the function f(x) = ln(x-3) since the natural logarithm is defined for all positive values. However, the graph approaches negative infinity as x approaches 3 from the right, indicating a vertical asymptote at x = 3.

To sketch the graph of f(x) = ln(x-3), we start with the x-intercept at (4, 0). We can plot a few more points by choosing values of x greater than 4 and evaluating f(x) using a calculator.

As x approaches 3 from the right, the graph approaches the vertical asymptote at x = 3. The graph will have a horizontal shape, increasing slowly as x increases. Remember to label the axes and indicate the asymptote on the graph.

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Answer:

For this case, the first thing we must do is define variables:

x: number of hammers

y: number of wrenches

We write the system of inequations:

10x + 6y <= 120

x + y> = 14

Step-by-step explanation:

Answer:

A and B both have an input that has multiple outputs so the answer is C and D.

Someone gave me the question,Evaluate | ,15 C + 15% da. Note that the constant of integration has been added for you a ab va al sin(a) IT bCan you write just two words to say which specific  sub-topic from this question belongs to? Do not use more than 2 words.

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The evaluated expression, where "K" represents the constant of integration.

To evaluate the given expression | ,15 C + 15% da, first, we need to clarify the terms and the context in which they are being used. It appears that there might be an integral involved, as you mentioned the constant of integration.

Assuming the integral is ∫(15 C + 15% da), where "C" is a constant, we can proceed as follows:

1. Integrate the constant term: ∫(15 C) = 15 C * a
2. Integrate the variable term: ∫(15% da) = 0.15 * (a^2 / 2)

Now, add the two integrated terms and the constant of integration:
15 C * a + 0.15 * (a^2 / 2) + K

This is the evaluated expression, where "K" represents the constant of integration.

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(a)True

According to the law of supply, p = s(x) is an increasing function. This is true because as the price of a good increases, producers are more willing and able to supply more of that good to the market.

(b)False

The Total Revenue is not minimized when the demand is unitary. In fact, the Total Revenue is maximized when the demand is unitary. When the demand is unitary, the increase in revenue due to a price increase is exactly offset by the decrease in revenue due to the decrease in the number of units sold. As a result, Total Revenue is maximized.

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Answer:

Step-by-step explanation:

The value of the given expression 105 times 3 is equal to 315.

Calculation of the expression 105 times 3 is equal to :

  1

1 0 5

×    3

3 1 5

Therefore, the calculated value of the expression 105 times 3 is equal to 315.

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Answer:

273 - 153.94 = 119.1 \(in^{2}\)

Step-by-step explanation:

area of a trapezoid - area of a circle = shaded area

Answer:

8/3

Step-by-step explanation:

Answer:

8/3

Step-by-step explanation:

K is the only factor that will change if the customer asks for a more expensive brand of paint.

The correct option is C.

The figures used to represent geometric shapes in mathematics are those that show how commonplace items are shaped. Shapes are the outlines of objects in geometry that have surfaces, angles, and boundary lines.

n = number of walls

K = units of $/ft²

L = length of each wall in feet

h = height of each wall in feet

This equation shows that A and h will be used to determine the area of each wall.

The variable n is the number of walls,

n times the area of the walls will give the amount of area that will need to be painted.

The only remaining variable is K.

This  represents the cost per square foot and is determined by the painter’s time and the price of paint.

K is the only factor that will change if the customer asks for a more expensive brand of paint

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Answer:

Todd's

Step-by-step explanation:

Given the expression x^2+6x+5=8, we are to determine which whether Imani or Todd method will work

Imani method might not work because he hasn't written the equation in standard form before factorizing. He should have equated the expression to zero first before factorizing and finding the zeros of the expression. The equation should have been written in the form ax²+bx+c = 0 first.

For Todd, his method will work because he used the completing the square method. The value at the right hand may not necessarily be zero before applying the rule. The idea is to make the quadratic equation complete and a perfect square.

This is achieved by adding the half of coefficient of x to both sides of the expression before simplifying.

From the expression x²+6x+5 = 8 we can see that adding 4 to both sides will make the quadratic equation on the left a perfect square.

x²+6x+5= 8

x²+6x+5+4= 8 +4

x²+6x+9 = 12

x²+3x+3x+9 = 12

x(x+3)+3(x+3) = 12

(x+3)(x+3) = 12

(x+3)² = 12

We can see that the expression at the left hand is now a perfect square. Hence Todd solution strategy will work

Answer:

only todd i got it from khan

Step-by-step explanation:

If you are filling traffic cones with sand to keep them from blowing over and the cone has a radius of 7 inches and a height of 28 inches, then 1436 cubic inches of sand can fit inside the cone.

The volume of the cone can be described as the measure of a 3-D space occupied by matter.

The volume of sand in cubic inches that can fit inside the traffic cone can be calculated by the formula,

v = πr²h / 3

As the radius of the cone = 7 inches

Height of the cone = 28 inches

v = π(7)²28 / 3

v = (π)(49)(28) / 3

v = (π)(1372) / 3

As π = 3.14

v = (3.14)(1372) / 3

v = 4308.08 / 3

v = 1436.02 ≈ 1436 cubic inches

Hence, 1436 cubic inches of sand is calculated to fit inside the cone.

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Answer:

$1.85

Step-by-step explanation:

2.15

-1.30

--------

1.85

The given information states that a sample of 40 shortbread cookies was taken for research purposes. The average weight of these 40 cookies was found to be 6400 mg, with a standard deviation of 312 mg.

The average weight of 6400 mg represents the mean weight of the 40 shortbread cookies in the sample. This indicates that, on average, each cookie weighs approximately 6400 mg. The standard deviation of 312 mg reflects the variability or spread of the weights within the sample of 40 shortbread cookies.

A higher standard deviation indicates greater variation in the weights, suggesting that the weights of the cookies in the sample may vary from the mean weight of 6400 mg by approximately 312 mg. These statistics provide valuable insights into the weight distribution of the sampled shortbread cookies and are useful for understanding the characteristics of the cookies in the given research context.

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Answer:

Sila put a wrong number in her calculator when multiplying the numerators.

Step-by-step explanation:

StartFraction 12 kilometers Over 1 EndFraction times StartFraction 0.62 miles Over 1 kilometer EndFraction times StartFraction 5280 feet Over 1 mile EndFraction = 392,832 feet

Correct calculation:

12 km/ 1 * 0.6miles / 1km * 5280 feet / 1 mile

= (12km * 0.62 miles * 5280 feet) / (1 * 1 km * 1 mile)

= 39,283.2 feet

Sila's calculation:

12 km/ 1 * 0.6miles / 1km * 5280 feet / 1 mile

= 392,832 feet

When Jim's model car ownership is compared to Terrence's model car ownership, the ratio is 8:6, Jim possesses 48 model vehicles.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, according to the definition given by the term in its most basic form.  When two terms are placed on each side of an equal sign, a simple equation is used to show their relationship. The four mathematical operations of addition, subtraction, multiplication, and division may be used singly or in combination in simple equations.

given

You are aware that Jim and Terrence both own four model automobiles in comparison to three owned by Jim.

Let's assume that Jim owns Jim has the following number of model cars, then you can answer the task as follows:

4/3 = x/36

x = (4* 36)/ 3

x = 48

Therefore, Jims owns 48 model cars.

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We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

Option B

Step-by-step explanation:

Slope = Change in y / Change in x

Slope = (8 - 2) / {6 - (-4)}

Slope = 6 / (6 + 4)

Slope = 6 / 10

Slope = 3 / 5

So option B is your answer

The average rate of change of f is less than the average rate of change of g.

The symmetry axis for the functions f and g is either the same or different.The line that passes through the vertex's x value is known as an axis of symmetry. It is the line of symmetry, but for a quadratic equation, and it divides the equation in half.

By examining function f, we can determine the vertex's location by either the lowest point, or (-3, -10). This is so that the numbers before and after (-3, -10), which increase by the same amount, have the same interval as the x values. (For instance, the symmetric pairs x = -5 and x = -1 have y values of -2 and x = -4 and x = -2, respectively, have y values of -8.)

Consequently, x = -3 is the axis of symmetry for function F.because the vertex's x value is -3.The graph demonstrates that x = -3 is also the axis of symmetry for function g because an illustrative vertical line drawn through this value bisects the quadratic.As a result, the symmetry axis for the functions f and g is the same.

The relationship between f's and g's y-intercepts is (less than, equal to, greater than) Where an equation crosses the y axis is known as the y intercept. As x = 0 is the y axis, it always has a value of 0.Looking at function f, the y-intercept of the function is equal to 8 when x = 0.We can observe the y value of when the function g returns aOn the graph, the quadratic intercepts the y axis. It is y = -2.As a result, f's y-intercept is larger than g's y-intercept.The average rate of change of f is (equal to, less than, or greater than) the average rate of change of g across the range [-6, -3].The amount that the y value rises for each unit of x that passes is the rate of change.

For function f, we can see that the function declines by 18 between x = -6 and x = -3. The sum of the rate of change (the amount the y changed / difference between the x values of points) is therefore -18 / 3 = -6.For function g, we can see that the function grows between x = -6 and x = -3. In this instance y value, but we may calculate that it rises by around 9. 9 / 3 = 3.

The average rate of change of f is therefore lower than the average rate of change of g.

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Answer:

< EFG

< GFE

Step-by-step explanation:

The letter for the vertex must be in the middle

< EFG

< GFE

<F

Answer:

\(a_n=1.04\cdot a_{n-1}\ \ ,\ \ a_1=35,000\)

Step-by-step explanation:

The salary is dependent upon the number of years you have worked.

Your salary increases by 1.04 times every year.

So, your salary over the years can be expressed as a Geometric Progression

35000, 35000*(1.04)², 35000*(1.04)³, ...

=> Common Ratio (r) = 1.04

∴ \(a_n=1.04\cdot a_{n-1}\ \ ,\ \ a_1=35,000\)

13 weeks.

Our equation is \(y=-24x + 379\).
x is the amount of weeks that has passed. x is being multiplied by -24. The +379 is our y-intercept. This means that per week, the account loses $24. The y-intercept also means that the account started with having $379 in it.

Finally, y is the output of the equation. This means that when you plug in the number of weeks, we see how much money is in the bank account with the y-value.

For example, if we solve for 2 weeks;

\(y=-24(2)+379=-48+379=331\). So after 2 weeks, the account will have $331 left.

Now to find the answer. We can plug in the final amount that we are given ($67) and then solve from there.

\(67=-24x+379\)

Next we isolate x and its coefficient:

\(67-379=-24x+379-379\)

\(-312=-24x\)

Multiply both by -1 to get positive numbers:

\(-312*-1=-24x*-1\)

\(312=24x\)

Now divide both sides by 24 to completely isolate x.

\(\frac{312}{24}=\frac{24x}{24}\)

\(13=x\)

OR

\(x=13\).

This means that when x = 13, y = 67. When 13 weeks pass, the amount of money in the account is equal to $67.

Therefore, the amount of time it takes for the account to be depleted to $67 is 13 weeks.

An example of an asymmetric relation on the set of all people is the "is taller than" relation.

In the "is taller than" relation, if person A is taller than person B, it implies that person B is not taller than person A. The relation is one-way and does not hold in the opposite direction. For example, if John is taller than Sarah, it does not mean that Sarah is taller than John. This relationship is asymmetric because it does not have a symmetric counterpart where both individuals are taller than each other. It is important to note that the "is taller than" relation is subjective and may vary based on individual comparisons and measurements.

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Answer: Number of sociology books sold = 143 books

              Number of physics books sold = 143 + 45 = 188 books

Step-by-step explanation:

Let us take the number of sociology books sold = x

Number of physics books sold = x+45

So now we can form an equation

x+x+45 = 331

2x+45 = 331

2x = 331-45

2x = 286

x = 286 ÷ 2

x = 143

Given a linear system of equations in unknowns x, y, and z with the following augmented matrix:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}Use Gauss-Jordan elimination to solve the system for x, y, and z.Solution:Step 1. The first step in solving this linear system of equations is to write the matrix in the form of an augmented matrix. In the following, we list the system of equations associated with the augmented matrix: 1x−1y=−72x+3y=24z−y=1  We begin by focusing on the first equation, which is:1x−1y=−7.

To get rid of the x-coefficient, we add one time the first equation to the second equation. This operation is written as follows:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}We add row1 to row2. -2r1 + r2 = r2{-2, 2, 0, 0, 14}r3 = r3This gives us the new augmented matrix.{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}Step 2Next, we focus on the second equation:0x+1y=−5.

The y-variable is isolated, and we now look at the third equation.4z−2y=1We can isolate the variable z by dividing the entire equation by 4 as follows:z−0.5y=0.25In order to eliminate y in the third row, we add 0.5 times the second row to the third row. This operation is written as follows:{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}We add 0.5 r2 to r3. r3 + 0.5r2 = r3{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -1, -1]}Step 3We can now solve for z using the third equation:4z−1y=−1z = (-1 + y) / 4.

Substituting this into the second equation gives:-2((1 - y) / 4) + 3y = 2y - 1 = 2y - 1Thus, y = 1/2.Substituting the value of y = 1/2 into the first equation gives:x - (1/2) = -7, so x = -13/2.Finally, we can substitute the values of x and y into the third equation to get the value of z: 4z - 1(1/2) = -1, so z = -3/2.The solution to the system of linear equations is: x = -13/2, y = 1/2, and z = -3/2.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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