The sugar sweet company is going to transfer its sugar to market. It will cost $4500 to rent trucks, and it will cost an additional $225 for each ton of sugar transported.

Let C Represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find a total cost to transport 14 tons of sugar.

Answer:

It is D

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The endpoints of a line segment graphed on the coordinate system are (−7, 3) and (2, 5). What is the range of the graph? the x values are the domains which are the first numbers so in this case the domains would be -7 and 2 but this question is talking about range which is the y in other words its the second numbers which is 3 and 5

Answer:

The perimeter of the quadrilateral is the sum of the four side lengths. If the perimeter is 92 feet, then we can write the equation $x + (x+2) + (x+4) + (x+6) = 92$, where $x$ is the length of the shortest side. Solving this equation, we find that $x = 20$. This means that the side lengths are 20 feet, 22 feet, 24 feet, and 26 feet, so the longest side is 26 feet.

The amount of money, less that one would contribute if they began investing at 18 as opposed to 45 is $ 238, 920

First, find the total amount that the person who started saving at 18 would pay :

= Monthly investment x Months till retirement

= 65 x 588

= $ 38, 220

The total amount that would be invested by a person who starts at 45 :

= 264 x 1, 050

= $ 277, 200

The amount less that you would contribute if you started at 18 is:

= 277, 200 - 38, 220

= $ 238, 920

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Investment B provides a higher value in comparison to Investment A.

Given that Investment A: A monthly investment of $200 starting now and lasting for 40 years at a 9% annual interest rate, compounded monthly.

Investment B: A monthly investment of $400 starting in 20 years and lasting for 20 years at a 9% annual interest rate, compounded monthly.

To Find Investment A (The present value of annuity due)

PVAD=PMT*(((1-(1+r)^-n)/r)*(1+r))

Here, PMT=$200,

r=0.75%

= (9/12)% monthly interest rate,

n=40*12

months=480P

VAD=$200*(((1-(1+0.75%)^-480)/(0.75%))*(1+0.75%))

= $67,933.50

Investment B (The present value of annuity)

PVA= PMT*(((1-(1+r)^-n)/r))

Here, PMT=$400,

r=0.75%

= (9/12)% monthly interest rate,

n=20*12

=240 months

PVA=$400*(((1-(1+0.75%)^-240)/(0.75%)))

= $69,354.54

∴ Investment B provides a higher value in comparison to Investment A.

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Answer:

Answer:

3x+1

Step-by-step explanation:

Answer:

1. -5/3x+4

2. -7x+2

3. -2/5x-4

Step-by-step explanation:

The way you calculate slope is rise over run. This will determine your x. Your y-intercept is determined by the point the y-intercept connects with. So if the line crosses (0,-4), the -4 is the whole y-intercept. If that makes sense?

Answer:

a

Step-by-step explanation:

if its the same one i saw, the answer is a :)

Box 2 containing 1.2 kg of paperclips has the greatest mass, and thus the greatest inertia among the three boxes.

Inertia is a property of a body due to which it resists any change in its state of rest or motion.

When we talk about the greatest inertia among three boxes of the exact same size and shape, it is important to know that inertia is directly proportional to mass.

So, the box that has the greatest mass will have the greatest inertia.

Now, we have to find the box that has the greatest mass.

The mass of the boxes are as follows:

Box 1 containing 1.0 kg of pencils

Box 2 containing 1.2 kg of paperclips

Box 3 containing 0.5 kg of rubber bands

Therefore, Box 2 containing 1.2 kg of paperclips has the greatest mass, and thus the greatest inertia among the three boxes.

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The width of the driveway in terms of x is 5x - 2.

To find the width of the driveway in terms of x, we need to divide the area of the driveway by its length.

The area of the driveway is given as 5x² + 43x - 18, and the length is x + 9.

Therefore, the width (W) can be calculated by dividing the area by the length:

W = (5x² + 43x - 18) / (x + 9)

We can simplify this expression further by performing polynomial long division. However, since the length of the driveway is x + 9, we can deduce that x + 9 is a factor of the area polynomial (5x² + 43x - 18) based on the factor theorem.

Using synthetic division or factoring, we can divide the polynomial 5x² + 43x - 18 by x + 9 to find the quotient, which will represent the width of the driveway:

       -9 |   5    43    -18

            -----------------

              5    -2     0

From the synthetic division, we obtain a quotient of 5x - 2.

Therefore, the width of the driveway in terms of x is 5x - 2.

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Answer:

Step-by-step explanation:

You didn't mark your graph but I'm assuming the point is (1,2)

You notice how the function stops at the point? x and y can not be above that point because there is no line above it.

The domain of the function means what can x possibly be.

The maximum value of x in this function is 1 because that's the x value of the point where the function ended. This means x can at most be one or x≤1. So the domain is x≤1.

The range of the function means what can y possibly be.

The maximum value of y in this function is 2 because that's the y value of the point where the function ended. This means y can at most be two or y≤2. So the range is y≤2.

Answer. I think is A

Step-by-step explanation:

The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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Answer:

i would say the answer is 20 + 6i but thats not an answer

-1 + 21 = 20

and

i + 5i = 6i

so

20 + 6i

hope this helped!

The probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days is null or 0.

We need to use the central limit theorem and assume that the distribution of the average amount of paid time lost during a three-month period for the 100 blue-collar workers is approximately normal with a mean of 1.8 days and a standard error of 0.2 days.

To find the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days, we need to find the corresponding z-score and look up the probability in a standard normal distribution table or use a calculator.

The z-score can be calculated using the z score formula,

Putting the values in the calculator given in the problem, we get:

z = (1.5 - 1.8) / (0.2 / √(100)) = -7.5

Looking up the probability corresponding to a z-score of -7.5 in a standard normal distribution table or using a calculator, we get a probability of approximately 0.

Therefore, the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days is approximately 0.

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The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;

a) a = 2

b = -2

c = 4

The general equation of a circle is; (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The coordinates of the radius of the circle

The specified equation of a circle is; x² + y² = 9

The coordinates of the center of the circle, is therefore, O = (0, 0)

a) The coordinates of the points P  and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)

((3·√3)/4)/(3/2) = (√3)/2

The specified form of the gradient is; (√3)/a, therefore;

(√3)/a = (√3)/2

a = 2

The value of a is 2

b) The gradient of the tangent to a line that has a gradient of m is -1/m

The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)

The form of the gradient of the tangent at P is b/(√3), therefore;

-2/(√3) = b/(√3)

b = -2

The value of b is; -2

c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates

Slope of the tangent = -2/(√3)

((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)

((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3

(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4

Therefore; c = 4

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The 90% confidence interval for the mean household usage of electricity by non-commercial customers is (17.3, 17.7) kWh per day, given a population, standard deviation of 2.1 kWh and a sample mean of 17.5 kWh per day for a sample size of 877 families.

Given that n = 877, X = 17.5 kWh, σ = 2.1 kWh, and to find the 90% confidence interval of the mean µ.

To find the 90% confidence interval, we need to calculate the z-value for the given confidence level.

α = 1 - 0.90 = 0.10 (as the level of significance is 10%)α/2 = 0.10/2 = 0.05 (as we are looking for a two-tailed test)

From the Z-tables, we find that the z-value for 0.05 is 1.645.

Hence the confidence interval is given by,

\(\[\Large CI=\left( X\pm \frac {z\sigma }{\sqrt {n}} \right)\]Substitute the values,\[\Large CI=\left( 17.5\pm \frac {1.645\times 2.1}{\sqrt {877}} \right)\]\)

On simplification, the confidence interval is (17.3, 17.7).

Hence the required 90% confidence interval is (17.3, 17.7).

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The interest amount (simple interest ) on the loan amount $5315 at 5% from 10th aug to 23rd dec. of same year is $105.50

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

\(I = \dfrac{P \times R \times T}{100}\)

For this case, we're specified that:

Converting this time in terms of year, we get:

Aug has 31 days, Sept has 30 days, Oct. has 31 days, Nov has 30 days.

From 10th aug, till its last, there went 22 days.

Whole sept and oct and nov. was spent (30+31+30 = 91 days)

And then there were 22 days of december(23rd day not covered assumingly)

So, total days = 22+22+91 = 145 days.

Assuming averagely 365.25 days in an year, we get the average time for which the interest will be calculated as:

\(\dfrac{145}{365.25} \approx 0.397 \: \rm years\)

Thus, we get: the amount of interest as:

\(I = \dfrac{P \times R \times T}{100}\\\\I \approx \dfrac{5315 \times 5\times 0.397}{100} \approx 105.50 \: \rm dollars\)

Thus, the interest amount (simple interest ) on the loan amount $5315 at 5% from 10th aug to 23rd dec. of same year is $105.50

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The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.

Given: y = -0.8x + 0.4

As we know that the slop-intercept form of the equation of a line is given by: y = mx + c, where

On comparing the given equation of line with the above form of equation of line, we get: m = -0.8 and c = 0.4.

Hence, The slope of the given equation of the line is -0.8 and the y-intercept = 0.4.

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The answer is:

Nth term=200n-238

The rectangle has equal dimensions, and the area of the rectangle is 44944 square units

The given parameters are:

Length = 212 units

Width = 212 units

The area of the rectangle is:
Area = Length * Width

So, we have:

Area = 212 * 212

Evaluate

Area = 44944

Hence, the area of the rectangle is 44944 square units

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The correct option D; models the depth of the submarine.

When a submarine is x miles out of its launch place, we need to figure out which table best represents the depth of the submarine using the function d, wherein d(x) is the depth, in meters.

Both x = 5 as well as x = 40 have zeros.

Since it's a parabola,

D(x) = a(x-5)(x-40)

vertex = (22.5, -146)

Thus,

-146 = a(22.5-5)(22.5-40)

a = -146/(22.5-5)(22.5-40)

a = 0.4767

Put value of a in equation.

D(x) = a(x-5)(x-40)

D(x) = 0.4767(x-5)(x-40)

The equation above is quadratic function model.

We can see from the graph that:

(5) and (0), respectively, are points on the graph (40,0).

Consequently, if x = 5 when y = 0, then.

y(min) > -160.

Additionally, the table in option (D) represents the submarine's depth.

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The graph of the question with the options are attached.

An example of a linear function table is y=3x

A linear function is used to relate an independent variable and a dependent variable by introducing a rate of change(function) of which the independent variable is equated to find the dependent variable. Linear functions are those whose graph is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

for example:

y=3x hence is the dependent variable as it depends on the change of x and 3 is the rate of change which is a constant and is determined by the division of the values of y/x hence to make a table of y over x of which y is determined by the rate of change the unrelated variable x, 3.

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Answer:

X= -12

Step-by-step explanation:

So just combine like terms and isolate the variable

5x+2=6x+14

2=x+14

-12=x

So x is negative twelve

Answer:

x = -12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

7x - 2x + 2 = 6x + 14

Step 2: Solve for x

The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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We are asked that how could we determine the number of feet per second a squirrel can run?

Recall that rate (also known as speed) is given by

Where d is the distance in feet.

t is

Answer:

0

Step-by-step explanation:

54m² - 54m² = 0

Water is 0

Given that a consumer with u(x,y)=x^3 y^2 pays

px=3,

py =4. Utility is maximized when

y=2We have to determine the consumer's income.

Let I be the income of the consumer. Then the consumer's budget constraint can be represented aspx x+py y=I, where px=3 and

py=4. Hence we have3x+4y

=I ................

(1)From the utility function, the consumer's marginal rate of substitution is given byMRS = (∂u/∂x)/(∂u/∂y)

= 2x^2/3y^2Setting this equal to the price ratio py/px

= 4/3, we get2x^2/3y^2

= 4/3or x^2/y^2

= 2Substituting y

=2 (since utility is maximized when y

=2), we getx^2/4

= 2or x^2

= 8Hence, x

= ±2√2.

Substituting this in equation (1), we get3(±2√2)+4(2) = Ior I

= 14 ± 6√2Since I is the income, it cannot be negative. Hence the income is given byI

= 14 + 6√2.

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Answer:

3 3/4 hours

Step-by-step explanation:

1 1/2 + 1 1/2(1 1/2) = 3 3/4 hours

Therefore , the solution of the given problem of quadrilateral comes out to be it is isosceles.

In geometry, a quadrilateral is an object with four sides and four corners. The term is derived either the Latin quadri or inventive portfolio (meaning "side"). A rectangle has three dimensions: four states, four corners, and four states. There are fundamentally two types of concave and convex surfaces. Trapezoids, parallelograms, triangles, rhombuses, plus rectangles are further subclasses of convex quadrilaterals. Rectangles essentially two-dimensional objects because they have four straight sides.

Here,
Given :

=> W(1,4) , X (1,8)

=> Y(-3,9) and Z (-3,3)

The distance length formula:

=> √(x2 -x1)² + (y2 -y1)²

=> WX =  √(1-1)² + (8 -4)² = √4² = 4

=> XY = √(1-(-3))² + (8 -9 )² = √16+1 =√17

=> YZ = √(-3 - (-3))² + (3 - 9)² = √36 = 6

=> WZ =  √(1-(-3))² + (4 -3)² = √16+1 = √17

Hence it is an isosceles.

Therefore , the solution of the given problem of quadrilateral comes out to be it is isosceles.

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