Translate 12y + 3 into an english expression

Answer:

$51,750

Step-by-step explanation: We are going to make x = 3 and we will use the  i=prt equation meaning

Step 1: (45,000)(0.05)(3)= 6750

Step 2: 45,000+ 6750= 51,750

Solution: $ 51,750

Answer:

25 dollars is the ANSWER

Step-by-step explanation:

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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To solve this problem, you will need to know the formula to find the circumference of a circle given the diameter of a circle. After calculating the circumference, you will then divide this result by 5 to obtain the final answer needed for this problem.

The circumference of a circle is found using the formula C = 2πr.

\(C = 2\pi r\)

We are given the diameter. The radius can be found using r = D/2.

\(\displaystyle r=\frac{D}{2}\)

\(\displaystyle r=\frac{14}{2}\)

\(r=7\)

Plug in the radius to the formula for a circle's circumference: C = 2πr.

\(C = 2 \pi (7)\)

Rearrange the equation to distribute the 7 into the 2π.

\(C = 7(2\pi)\)

Distribute the 7.

\(C=14\pi\)

To find one-fifth of the distance (formally termed the circumference) around the circle, divide the circumference by 5.

\(\displaystyle \frac{14\pi}{5}\)

If you are looking for a simplified answer in terms of π, this will suffice. If you need an exact answer that does not reference π, continue reading.

For a solution not in terms of π, first, multiply 14 by π.

\(14\times\pi = 43.98229715\)

Divide this value by 5.

\(\displaystyle \frac{43.98229715}{5} = 8.7964594\)

To make this easier to present, round to the hundredths place.

\(8.7964594 \approx 8.80\)

The final answer, dependent on the value you are asked to provide, is:

\({\boxed{\displaystyle \frac{14\pi}{5} \ \text{inches}}\)

\(\boxed{\text{approximately} \ 8.8 \ \text{inches}}\)

Benny (B) would win the election using the plurality method.

To determine the winner using the plurality method, we need to calculate the total number of first-place votes for each candidate and see which candidate receives the most votes.

According to the given preference schedule, the number of first-place votes for each candidate is as follows:

Abe (A): 1st - 20 votes, 3rd - 2 votes (from the 2nd preference of voter 1)

Benny (B): 1st - 19 votes, 2nd - 5 votes

Chloe (C): 1st - 5 votes, 2nd - 19 votes, 3rd - 3 votes (from the 1st and 2nd preferences of voter 1)

Now, let's calculate the total number of first-place votes for each candidate:

Abe (A): 20 + 2 = 22 votes

Benny (B): 19 + 5 = 24 votes

Chloe (C): 5 + 0 + 3 = 8 votes

Based on the plurality method, the candidate with the highest number of first-place votes wins.

In this case, Benny (B) received the most first-place votes with a total of 24 votes.

Therefore, Benny (B) would win the election using the plurality method.

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

A 1.5 standard deviations above the mean IQ score is 122.5.

An expression that depicts the relationship between two or more numbers and variables is called an equation.

A dependent variable is one that depends on another variable, whereas an independent variable does not depend on any other variable for its value.

Giving the z score are:

z is calculated as (raw score - mean) / standard deviation.

with a standard deviation of 15 and a mean of 100. The z-score of 1.5 is equal to the IQ score that is 1.5 standard deviations above the mean, so:

1.5 = (x - 100)/15

x = 122.5

A 1.5 standard deviations above the mean IQ score is 122.5.

The Complete Question is IQ score.

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The unknown angle in the cyclic quadrilateral is as follows:

m∠CML = 109 degrees

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's find m∠CML as follows:

Using the arc angle and opposite angle of a quadrilateral theorem,

6x + 25 = 1 / 2 (7x + 14 + 106)

6x + 25 = 1 / 2(7x + 120)

6x + 25 = 7 / 2 x + 60

6x - 7 / 2 x  = 60 - 25

6x - 3.5x = 35

2.5x = 35

divide both sides by 2.5

x = 35 / 2.5

x = 14

Therefore,

m∠CML = 6x + 25 = 6(14) + 25 = 84 + 25 = 109 degrees

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The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

To calculate the total value of the annuity in 16 years, 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 yearly payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.

Let's substitute these values into the formula and calculate the total value of the annuity:

FV = 693 * ((1 + 0.053)^16 - 1) / 0.053

FV = 693 * (1.053^16 - 1) / 0.053

Using a calculator, we can evaluate the expression inside the parentheses:

1.053^16 ≈ 1.9738

Substituting this value back into the formula:

FV = 693 * (1.9738 - 1) / 0.053

FV = 693 * 0.9738 / 0.053

FV ≈ 12739.62

Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

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A graph that shows the relationship between the number of days and the total amount of sunglasses is shown in the image attached below.

What is a scatter plot?

This is the term that is used to refer to the graphical description that is used to show the relationship that would exists between two various variables. These variables would be on the y and the x coordinates of the scatter plot.

From the scatter plot (see attachment) which models the relationship between the number of days and the total amount of sunglasses, a linear equation for the line of best fit is given:

y = -2x + 62

Hence, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days and the total amount of sunglasses.

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In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

At mile 3 company A will start charging less.

Step-by-step explanation:

I came to this conclusion by realizing that no matter what company A will always charge $107 so, in theory all we needed to do was get company eight to $108. So having this mind set I created the equation, 65 + .70x  . I continuously kept on changing what was in x until the price was just above Company A's. And the number that got me there was 3.

Answer:

a) no

b) yes

c) 0.75(37 + c) ≥ 45

Step-by-step explanation:

lemonade = $0.75 per cup

Saturday sales = 37 cups

Let c = number of cups sold on Sunday

⇒ Total weekend sales = 0.75(37 + c)

a)  No, they will not reach their goal of making at least $45

If c = 12:

Total weekend sales = 0.75(37 + 12)= 0.75 x 49 = $36.75

$36.75 < $45

b) Yes, they will reach their goal of making at least $45

If c = 25:

Total weekend sales = 0.75(37 + 25)= 0.75 x 62 = $46.50

$46.50 > $45

c)

0.75(37 + c) ≥ 45

Answer:

9 Part-time employees

36 full-time employee

Step-by-step explanation:

20% multiply by 45 = 9

80% multioly by 45 =36

therefore to check if your answers are correct add 9 + 36 which gives you 45, the total number of employees in each company's four department.

Answer:

The company has 144 full-time employees and 36 part-time employees.

Step-by-step explanation:

The company has 144 full-time employees and 36 part-time employees because you have to do .20*45 to get 9 part-time employees per department. Then you can do 45-9 to get 36 full-time employees per department or you can do .8*45, either way is fine. Then you have to multiply 36 by 4 and 9 by 4 to get 144 full-time employees and 36 part-time employees.

If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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Answer:

\(\huge\boxed{No \ solutions}\)

Step-by-step explanation:

Our first goal is to transform these words into numbers for an expression.

Let's break it down.

-7 times a number

We'll assume that the number is \(n\). -7 times a number can be represented as \(-7n\).

8 times the sum of the number and 1

We can break this complex statement down.

8 times the sum of the number and 1

The sum of the number and 1 will be \(n+1\). 8 times that will be \(8(n+1)\). Since it says at the beginning the sum of, we add \(8(n+1)\) to \(-7n\).

\(-7n + 8(n+1)\)

Is the same as the number minus 7.

"Is the same" means we use an equal sign. The number minus 7 will be \(n-7\). So we get \(-7n + 8(n+1)=n-7\)

Now we can solve for n by reversing the equation until we have n isolated on one side.

\(-7n + 8n + 8 = n-7\)

\(n + 8 = n-7\)

\(8 = -7\)

We end up with 8 = -7. This is not possible. Therefore, there are no real values of x that satisfy this equation.

Hope this helped!

Part A: The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5

Part B: The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

Part C: the length of each of the five pieces of wood cut by Warren is 3.8 feet.

It is made up of two mathematical objects, with an equals sign (=) between them. Equations are used to represent relationships between unknown variables and can be solved to find their values.

Part A:

The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5, where x is the length of each piece of wood.

Part B:

The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

This equation can be used to calculate how much wood Warren has cut off from the original 4.5 feet of wood, which is the length of each of the five pieces of wood.

Part C:

Solving the equation from Part A:

x + 0.7 = 4.5

Subtract 0.7 from both sides:

x + 0.7 - 0.7 = 4.5 - 0.7

x = 3.8

Therefore, the length of each of the five pieces of wood cut by Warren is 3.8 feet.

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Answer:

x = 19/22

Step-by-step explanation:

8x-12+36x = 26

44x - 12 = 26

44x = 38 (add 12 on both sides)

x = 19/22 (divide bot sides by 44 and simplify)

Answer: Let 5/9=□/54

Clearly shows 54=(9×6)

Now multiply the numerator by 6 also

∴5 / 9 = (5 \times 6) / (9 \times 6) = 30 /54$$

Hence, 30/54 is the equivalent fraction of 5/9 having denominator 54

(ii) Let 5/9=35/□

Clearly shows 35=(5×7)

Now multiply the denominator by 7 also

∴5/9=(5×7)/(9×8)=35/63

Hence, 35/63 is the equivalent fraction of 5/9 having numerator 35

Step-by-step explanation:

Answer:

The circumference of the drive wheel is 10 feet * 3.14 = 31.4 feet.

The circumference of the vat is 18 feet * 3.14 = 56.52 feet.

The total length of belt needed to go around the drive wheel and the vat is 31.4 + 56.52 = 87.92 feet.

Answer: To calculate the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

20Y1:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share

Common Stock: $6,000 / 50,000 shares = $0.12 per share

20Y2:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share (cumulative preferred stock means that if the company misses a dividend, they still have to pay it in the future, so the dividends per share remain the same)

Common Stock: $45,000 / 50,000 shares = $0.90 per share

20Y3:

Preferred Stock: $30,000 / 15,000 shares = $2.00 per share

Common Stock: $0 (there is no information about dividends for the common stock in 20Y3)

So, the dividends per share for each year would be:

20Y1:

Preferred Stock: $2.00 per share

Common Stock: $0.12 per share

20Y2:

Preferred Stock: $2.00 per share

Common Stock: $0.90 per share

20Y3:

Preferred Stock: $2.00 per share

Common Stock: $0.00 per share

Step-by-step explanation:

The given number is 7.

The half of 7 is 7 divided by 2.

Hence there are 3.5 or 3 1/2 half's are in 7.

Given:

-10 is an integer.

When a particle is moving so that its position at time t is given by the parametric equations x = 5*sin(-2t) and y = 5*cos(2t), the speed of the particle is 10.

Speed is the rate of change of position of a particle with respect to time.

Here we are given the parametric equations of positions of particle, in order to obtain the rate of change with respect to time we have to differentiate the equation with respect to time.

Speed of particle in x-direction can be obtained by

Vx = dx/ dt

= -2 × 5 × cos(-2t)

= -10cos(-2t)

= -10cos(2t)

Speed of particle in y-direction can be obtained by

Vy = dy/ dt

= 2 × 5 × (-sin(2t))

= -10sin(2t)

Therefore speed of particle can be obtained by

speed = √( (-10cos(2t))² + (-10sin(2t))² )

= 10√( cos(2t))² + (sin(2t))² )

= 10

-- The question is incomplete, answering to the question given below--

"A particle is moving so that its position at time t is given by the parametric equations : x = 5*sin(-2t) and y = 5*cos(2t). What is the speed of the particle?"

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After the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

Before the 2:30 stop, the bus let off 15 people and let on 9 people. The total change in the number of people at that stop is -15 (let off) + 9 (let on) = -6.

Therefore, there are 6 fewer people on the bus after the 2:30 stop compared to before that stop.

Ten minutes later, the bus makes another stop and lets off 4 more people. This additional change needs to be considered.

Since the previous calculation only accounted for the changes up until the 2:30 stop, we need to adjust the total change by including the subsequent stop.

Adding the change of -4 (let off) to the previous total change of -6, we get a new total change of -10.

Therefore, after the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

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