-2x^2(3x - 6)
options to choose from
6x^3 + 12x^2
6x^3 - 12x^2
-6x^3 + 12x^2
-6x^3 - 12x^2

The equation of the graph is y = -| x | + 1

Given data ,

The graph of y = -|x| + 1 is a V-shaped graph with the vertex at the origin (0, 1), and it opens downwards along the y-axis. The negative sign in front of the absolute value function reflects the graph of y = |x| across the x-axis, flipping it upside down.

When x is greater than or equal to 0, the expression |x| becomes x, and the graph of y = -|x| + 1 will be y = -x + 1 for x ≥ 0.

When x is less than 0, the expression |x| becomes -x, and the graph of y = -|x| + 1 will be y = x + 1 for x < 0.

Thus, the graph of y = -|x| + 1 consists of two linear segments with slopes of -1, intersecting at the point (0, 1), and extends indefinitely in both directions along the x-axis.

Hence , the equation of graph is y = -| x | + 1

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The remainder when x³ - 1 is divided by (x + 3) is  -28

The functions are given as

x 3 1 is divided by x 3

Rewrite them as

f(x) = x³ - 1 is divided by (x + 3)

Set the divisor to 0

So, we have

x + 3 = 0

Determine the value of x

This gives

x = -3

By the remainder theorem

Substitute x = -3 in the function f(x)

So, we have

f(-3) = (-3)³ - 1

Evaluate the expression

f(-3) = -28

By the remainder theorem, this represents the remainder

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The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Answer:

\(\left\{\begin{matrix}3x+4y+8z=36.65\\ 5x+3y+10z=37.50\\ 4x+5y+6z=43.35\end{matrix}\right.\)

Step-by-step explanation:

System of equations

Let's set the following variables:

x=Price of chocolate pumpkins

y=Price of masks

z=Price of candy witches

We'll establish the system of equations needed to know the prices of all the Halloween treats.

Cory bought 3 chocolate pumpkins, 4 masks, and 8 candy witches and he spent $36.65. This leads to the following equation:

\(3x+4y+8z=36.65\qquad\qquad [1]\)

Josh bought 5 chocolate pumpkins, 3 masks, and 10 candy witches and he spent $37.50. This leads to the following equation:

\(5x+3y+10z=37.50\qquad\qquad [2]\)

Dan bought 4 chocolate pumpkins, 5 masks, and 6 candy witches and he spent $43.45. This leads to the following equation:

\(4x+5y+6z=43.35\qquad\qquad [3]\)

Collecting the equations [1] [2] [3], we form the system of equations to represent this problem:

\(\left\{\begin{matrix}3x+4y+8z=36.65\\ 5x+3y+10z=37.50\\ 4x+5y+6z=43.35\end{matrix}\right.\)

Answer:

How much did she start with tho???

Step-by-step explanation:

Answer:

 x-intercept = 6/4 = 3/2 = 1.50000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*x+13*y-(6)=0

Step 1: Equation of a Straight Line

Solve   4x+13y-6  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  4x+13y-6  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 6/13 so this line "cuts" the y axis at y= 0.46154

 y-intercept = 6/13  =  0.46154  

Calculate the X-Intercept :

When y = 0 the value of x is 3/2 Our line therefore "cuts" the x axis at x= 1.50000

 x-intercept = 6/4 = 3/2  =  1.50000  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.462 and for x=2.000, the value of y is -0.154. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.154 - 0.462 = -0.615 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -0.615/2.000 = -0.308  

Geometric figure: Straight Line

 Slope = -0.615/2.000 = -0.308

 x-intercept = 6/4 = 3/2 = 1.50000

 y-intercept = 6/13 = 0.46154

Answer:

50

Step-by-step explanation:

m3 and m4 are going to be equaivalent due to some law I don't remember the name of.

So, 3x-16 = x+84

(do some rearranging)

2x=100

x=50

The probability that sample is greater than 418 will be is 6.533.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.

Here we have

\(\mu=397.64,n=40,\sigma=20\)

According to central limit theorem, the sampling distribution of mean will be normal with mean

\(\mu_{\bar{x}}=\mu=397.64\)

and standard deviation

\(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{40}}=3.1623\)

The z-score for\(\bar{x}=418\) is

\(z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{418-397.34}{3.1623}=6.533\)

Therefore, the probability that sample is greater than 418 will be

\(P(\bar{x} > 418)=P(z > 6.533)\)

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Incomplete Question

Carbon dioxide (CO2) is one of the primary gases contributing to the greenhouse effect and global warming. The mean amount of CO2 in the atmosphere for March 2013 was 397.34 parts per million (ppm). Suppose 40 atmospheric samples are selected at random in May 2013 and the standard deviation for CO2 in the atmosphere is σ = 20 ppm. (1 pt.)

c) Suppose the sample mean CO2 level is 400. Is there any evidence to suggest that the population mean CO2 level has increased?

Answer:

\(8(156 \times 1.1) + 12(156 \times 1.2) \)

Answer:

35 minutes

Step-by-step explanation:

this requires us to find out how long it took and because both times given to figure this out are within the same hour it is easy to figure out in this case, 50 - 15 = 35. This is not as simple with all problems like this but because of the times given in this problem its much easier.

Answer:

∠ 1 = 60°

Step-by-step explanation:

the angle on the circle is half the measure of the central angle , subtended on the same arc , then

∠ 1 = \(\frac{1}{2}\) × 120° = 60°

Answer:

96%

Step-by-step explanation:

48 ÷ 50 × 100

The estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

To estimate the monthly average daily radiation on a horizontal surface H in June in Amman, we can use the following equation:

\([H = S \times H_s \times \frac{\sin(\phi)\sin(\delta)+\cos(\phi)\cos(\delta)\cos(H_a)}{\pi}]\)

where:

S is the solar constant, which is approximately equal to 1367 W/m(^2);

\(H(_s)\) is the average number of sunshine hours per day in Amman in June, which is given as 10 hours;

(\(\phi\)) is the latitude of the location, which for Amman is approximately 31.9 degrees North;

(\(\delta\)) is the solar declination angle, which is a function of the day of the year and can be calculated using various methods such as the one given in the answer to Q1;

\(H(_a)\) is the hour angle, which is the difference between the local solar time and solar noon, and can also be calculated using various methods such as the one given in the answer to Q1.

Substituting the given values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(\delta)+\cos(31.9)\cos(\delta)\cos(H_a)}{\pi}]\)

Since we are only interested in the monthly average daily radiation, we can assume an average value for the solar declination angle and the hour angle over the month of June. For simplicity, we can assume that the solar declination angle (\(\delta\)) is constant at the value it has on June 21, which is approximately 23.5 degrees North. We can also assume that the hour angle \(H(_a)\) varies linearly from -15 degrees at sunrise to +15 degrees at sunset, with an average value of 0 degrees over the day.

Substituting these values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(23.5)+\cos(31.9)\cos(23.5)\cos(0)}{\pi}]\)

Simplifying the equation, we get:

\([H \approx 7.35 \text{ kWh/m}^2\text{/day}]\)

Therefore, the estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

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Answer:

Step-by-step explanation:

$270 in total

The speed of the first bus is 60 km/h while the speed of the second bus is 80 km/h.

Speed is the rate of change of distance with time. It is given by:

Speed = distance / time

Let a represent the speed of the first bus, and b represent the speed of the second bus.

b = a + 20

At 12:00, t = 3 hours, hence:

a = d/3

d = 3a

Also:

b = d/2.25

d = 2.25b

3a = 2.25b

3a = 2.25(a + 20)

a = 60

b = 60 + 20 = 80

The speed of the first bus is 60 km/h while the speed of the second bus is 80 km/h.

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Answer:

??

Step-by-step explanation:

Can't see that clear

Answer: -5/6

Step-by-step explanation:

(1 + -2) + (2/3+ -1/2)

-1 + 2 x 2 / 3 x 2 + -1 x 3 / 2 x 3

Simplify:

-1 + 4/6 + -3/6

Turn into a simpler fraction:

1 + 4 + (-3) / 6

Combine like terms:

-1 + 1/6

Add together:

- 5/6

Hope this helps!

Answer:

m<R = 106°

Step-by-step explanation:

Given,

m<R = (6x+10)°

m<S = (2x+5)°

m<T = (3x-11)°

Now,

6x+10°+2x+5°+3x-11° = 180°{the sum of angles of triangle is 180°}

or, 11x+4° = 180°

or, 11x = 180°-4

or, x = 176°/11

or, x = 16°

therefore, x = 16°

m<R = (6x+10)°

= 6×16°+10°

= 96°+10°

= 106°

Answer:

man can u send the pic of the diagram I will solve it

The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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An integer between 1 and 1200 leaves remainders of 1, 2, and 6 when divided by 9, 11, and 13, respectively. By finding the least common multiple of these divisors, we can determine the integer. In this case, the integer is 361.

To find the integer that satisfies the given conditions, we need to determine the least common multiple (LCM) of 9, 11, and 13.

First, let's consider the remainders: 1, 2, and 6. These are one less than the respective divisors. We can rewrite them as 9 - 8, 11 - 9, and 13 - 7, respectively.

Next, we calculate the LCM of the divisors: LCM(9, 11, 13) = 9 * 11 * 13 = 1287.

Now, we need to find the remainder when 1287 is divided by 9, 11, and 13. This can be done by subtracting the respective remainders we calculated earlier: 1287 - 8 = 1279 (remainder 1), 1287 - 9 = 1278 (remainder 2), 1287 - 7 = 1280 (remainder 6).

Therefore, the integer that satisfies the conditions is 1287 - (1 + 2 + 6) = 1287 - 9 = 1278.

However, we need to ensure that the integer is within the given range of 1 to 1200. Since 1278 is greater than 1200, we need to subtract the LCM (1287) to get the integer within the range.

1278 - 1287 = -9.

Thus, the integer that satisfies all the given conditions is 1287 - 9 = 1278.

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The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1295, 1317).

To find the critical value for a 90% confidence interval, we need to determine the value of tc. Since the sample size is small (n < 30) and the population standard deviation is unknown, we can use the t-distribution.

The critical value can be found using a t-table or a statistical calculator. For a 90% confidence level with 8 degrees of freedom (n - 1), the critical value is approximately 1.860.

tc = 1.860

To find the maximal margin of error, we can use the formula:

E = tc * (s / √n)

where s is the sample standard deviation and n is the sample size. Given that the sample size is 9 and we don't have the sample standard deviation, we can estimate it using the sample standard deviation formula.

After calculating the sample standard deviation, let's assume it is s = 18.45 (rounded to two decimal places).

E = 1.860 * (18.45 / √9) = 11.079

The maximal margin of error is approximately 11.

To find the confidence interval, we use the formula:

lower limit = sample mean - E

upper limit = sample mean + E

Given that the sample mean is 1306 (rounded to the nearest whole number):

lower limit = 1306 - 11 = 1295

upper limit = 1306 + 11 = 1317

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The dot product of two free vectors is independent of the choice of frames, as it relies only on the inner product of their transposed coordinate vectors.

The dot product of two free vectors, v1 and v2, can be expressed as the inner product of their transposed coordinate vectors, v1t and v2. This inner product is invariant under changes of frames, i.e. the same result will be obtained regardless of the choice of frames in which the coordinates are defined. This is because the transpose of a vector only changes the order of the coordinates, and the inner product of two vectors is unaffected by this reordering. Therefore, the dot product of two free vectors does not depend on the choice of frames in which their coordinates are defined.

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Answer:

1/3 of the 342 seats which would be 267 of the seats are used by the Students

Step-by-step explanation:

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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