Guadalupe and Roberto plan to send their daughter to university. To pay for this they will contribute 8 equal yearly payments to an account bearing interest at the APR of 3%, compounded annually. Six years after their last contribution, they will begin the first of five, yearly, withdrawals of $55,200 to pay the university's bills. How large must their yearly contributions be?

Answer:

For company A, y = 24x + 42

For company B, y = 28x + 25

Step-by-step explanation:

x is the number of containers

y is the total cost

For company A, y = 24x + 42

For company B, y = 28x + 25

For the cost of both companies to be the same, then

24x + 42 = 28x + 25

28x - 24x = 42 - 25

4x = 17

x = 4.25

Mr Lycan would have to order about 4 containers so the cost would be the same from each company

The inequality in both inequality expressions is the less than or equal to sign

Inequality 1

The inequality is given as:

\(-1 \le \frac x2\)

Multiply both sides by 2

\(-2 \le x\)

Rewrite as:

\(x \ge - 2\)

The above means that the correct values of x are at least -2.

See attachment for the complete table is as follows:

Inequality 2

The inequality is given as:

\(1 \le \frac {-x}2\)

Multiply both sides by 2

\(2 \le -x\)

Rewrite as:

\(-x \ge 2\)

Multiply both sides by -1

\(x \le -2\)

The above means that the correct values of x are at most -2.

See attachment for the complete table is as follows:

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Answer:

Hello, I think your answer is D, Third Move

Step-by-step explanation:

Here, x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.

Let's start by integrating f'(x) to get f(x). We have:

f'(x) = 16(x+2)(6-x)³ - 32(x+6)

Integrating both sides with respect to x:

f(x) = ∫[16(x+2)(6-x)³ - 32(x+6)] dx

Simplifying the integral, we get:

f(x) = -2(x+2)²(6-x)⁴ + 16(x+6) + C

where C is the constant of integration.

Next, we can find the critical points of f(x) by setting f'(x) = 0:

f'(x) = 16(x+2)(6-x)³ - 32(x+6) = 0

Solving for x, we get x = -2 and x = 6 as critical points.

Now, we can use the second derivative f''(x) to determine the concavity of the function. We have:

f''(x) = (6x-x)⁴ = x⁴

Since the second derivative is always positive for x > 0, the function is concave up on the interval (6, ∞).

Similarly, since the second derivative is always negative for x < 0, the function is concave down on the interval (-∞, -2).

At x = -2 and x = 6, the function has an inflection point.

Finally, we know that x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.

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The inequality that describes the allowable temperature in a greenhouse is T ≥ 65, where T represents the temperature of the greenhouse.

To describe the allowable temperature in a greenhouse, we will make use of inequality. Let's write an inequality for the given information; the temperature in a greenhouse should be 65 degrees or higher. An inequality is a mathematical sentence containing symbols of inequality (<, >, ≤, ≥).When the temperature in a greenhouse should be 65 degrees or higher, we can write it in the form of inequality as: T ≥ 65 (where T represents the temperature in the greenhouse)This inequality states that the temperature (T) should be greater than or equal to 65 degrees. Hence, this inequality can be used to describe the allowable temperature in the greenhouse.

In conclusion, the inequality that describes the allowable temperature in a greenhouse is T ≥ 65, where T represents the temperature of the greenhouse.

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Answer:

factors

Step-by-step explanation:

To find the roots of a polynomial, it is often useful to find the Factors of the polynomial.

\(7 - 4(2w + 1) = 9w - 49 + w \\ 7 - 8w - 4 = 10w - 49 \\ 10w + 8w = 7 - 4 + 49 \\ 18w = 52 \\ w = \frac{52}{18} \\ w= 2.88\)

I hope I helped you^_^

Answer:

Fifth graders= 93 shirts

Sixth graders= 156 shirts

Teachers= 51 shirts

Step-by-step explanation:

31% of 300 is 93

52% of 300 is 156

The total number of shirts sold to fifth graders and sixth graders is:

156+93= 249

The number of shirts sold to teachers is:

300-249= 51

The wave equation Δu = 0 is a second-order partial differential equation that describes the behavior of waves in space and time.

In this case, the equation Δu = 0 indicates that there are no external sources or sinks of waves present, resulting in a homogeneous wave equation. The solution to the wave equation Δu = 0 with initial conditions u(x, 0) = 0 and ∂u/∂t(x, 0) = 1 is given by u(x, t) = 0. This implies that there are no waves propagating in the system, and the function u remains constant and equal to zero for all values of x and t. The initial condition u(x, 0) = 0 ensures that the system starts with zero displacement, and the condition ∂u/∂t(x, 0) = 1 indicates an initial velocity of 1. However, due to the nature of the wave equation, no wave-like behavior is observed, and the solution remains trivial.

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If the current dispatch rate is one bus every 1 minute and the average traveling time is currently 5 minutes, dispatching buses every 0.5 minute will actually increase the average traveling time to 10 minutes, not reduce it to 4.5 minutes as suggested by the branch manager.

Assuming that the current dispatch rate is one bus every 1 minute, and the average traveling time (a round trip) is currently 5 minutes, we can use the following formula to estimate the average traveling time with the proposed dispatch rate:

new average traveling time = current average traveling time / (new dispatch rate / current dispatch rate)

Plugging in the values, we get:

new average traveling time = 5 / (0.5 / 1) = 10 minutes

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Answer:

It's the first and last one

Step-by-step explanation:

I just did it

Answer:

A) The population density for Montana can be found using the ratio 1,005,141:145,552.

E)The state with the smallest population density is Montana.

Step-by-step explanation:

Answer:

−

344064

x

3

Explanation:

There's a quick way to answering questions like this without the need to go through the whole process of finding the terms before the  

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Using the  

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Step-by-step explanation:

Answer:

14 weeks

Step-by-step explanation:

In the 2012 Gallup survey, a random sample of 474,195 U.S. adults was interviewed by phone to gather information about their work status, height, and weight.

The objective was to determine the prevalence of obesity (defined as having a body mass index greater than 30) among different work status groups. The survey found that 24.9% of the participants who were employed (either full-time or part-time by choice) were classified as obese. In contrast, 28.6% of the participants who were unemployed and actively seeking work were also found to be obese. This indicates that there may be a relationship between employment status and obesity rates in the U.S. adult population.

However, it is important to note that correlation does not necessarily imply causation, and various factors could contribute to these findings. Further research may be necessary to determine the underlying causes behind the differences in obesity rates among employed and unemployed individuals.

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(a) The interpret the p-value in context of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower.

(b) The conclusion would make if a 0.05 is rejected because the p-value (0.0016) is less than the significance level.

If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01.

(a) The p-value of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower, assuming that the true population mean is 12 g/dl (or higher), is only 0.0016. This suggests that the observed difference between the sample mean and the hypothesized population mean is statistically significant and unlikely to be due to chance alone.

(b) If using a significance level of 0.05, the null hypothesis (that the true population mean is 12 g/dl or higher) would be rejected because the p-value (0.0016) is less than the significance level. Therefore, it can be concluded that the sample provides evidence that the true population mean hemoglobin level is lower than 12 g/dl.

If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01. In this case, the evidence is even stronger, and the conclusion that the true population mean is lower than 12 g/dl would be even more robust.

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Answer:

like:-

1/9x20 = 2 2/9

1/9-20 = 19 8/9

Step-by-step explanation:

Answer: The constant rate change would be \(\frac{1}{9}\).

Step-by-step explanation: The general rate of change can be found by using the difference quotient formula. To find the average rate of change over an interval, enter a function with an interval: f (x) = \(x^{2}\) , [2,3]

Write y = \(\frac{1}{9}\)x - 20 as a function which is f (x) = \(\frac{1}{9}\)x - 20

Consider the difference quotient formula which is \(\frac{f (x +h) - f (x) }{h}\).

Find the components of the definition. \(\frac{f (x+h) = \frac{h}{9} + \frac{x}{9} - 20}\)simplify then it would be \(\frac{f (x) = \frac{x}{9} - 20 }\).

Lastly plug in all the components.

\(\frac{f (x + h) - f (x)}{h} = \frac{\frac{h}{9} +\frac{x}{9} - 20 - (\frac{x}{9} - 20) }{h}\)

After solving all this the answer would be \(\frac{1}{9}\)

Answer:

240

Step-by-step explanation:

The top triangle has an area of 40 while the bottom rectangle has an area of 200. Add them together and you get 240

Answer:

0.000000001

Step-by-step explanation:

Let's convert this :

0.000000001

  tHT      M    B

t=tenths

H=Hundredths

T=Thousandths

M=millionths

B=Billionths

Answer:

The correct option - Figure A

Step-by-step explanation:

The exact question is as follows :

Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

To find - Which box plot shows this data set?

Solution -

Given the data is -

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

Firstly,

Arrange the data from smallest to largest

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7

Now,

Find the median

Median is the middle value - i.e. (15 + 1)/2 = 8th value

So, we get Median = 2

Now,

Find the Quartile -

The first quartile is the median of the data points to the left of the median.

i.e. Median of 0, 0, 0, 0, 0, 1, 1

so, we get

Q1 = 0

The third quartile is the median of the data points to the right of the median.

i.e. Median of 2, 2, 2, 3, 3, 5, 7

so, we get

Q3 = 3

Now,

Compute the min and the max

Minimum value = 0

Maximum value - 7

So,

five number summary is -

0, 0, 2, 3, 7

And we draw the box as follows -

So,

The correct option - Figure A

Answer:D. (5,0)

Step-by-step explanation:

The point which is a solution to the system of inequalities graphed here is (0, 5)

Hence the point which is a solution to the system of inequalities graphed here is (0, 5)

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Answer:

Step-by-step explanation:

1. height serves as the y-value and shoes as the x-value. because domain is the values of x we take in consideration the units x represents. shoe sizes tend to come in sizes 10, 11,12

2. for this one I relied on process of elimination, 2 & 4 include negative numbers and height, at least here, cannot be negative. (3) is representing the y-value or height. so the only one left is 1

this also makes sense because time is positive and the distance would be too.

Answer:

f(x) = 3.33x - 7

Step-by-step explanation:

We are suppposed to write the slope intercept form of the line . The slope intercept form of the line is ,

\(\rm\implies y = mx + c \)

where ,

Here we can see that the line is passing through (0,-7) . Therefore ,

\(\rm\implies y- intercept = -7\)

Also we can see that the line is passing through (2.1,0) . Therefore we can find the slope as ,

\(\rm\implies Slope =\dfrac{y_2-y_1}{x_2-x_1}\\\\\rm\implies Slope =\dfrac{ -7-0}{0-2.1}\\\\\rm\implies \bf Slope = 3.33 \)

Using Slope Intercept Form :-

\(\rm\implies y = mx + c \\\\\rm\implies y = 3.33x + (-7) \\\\\rm\implies\underline{\boxed{\rm\blue{f(x) = 3.33x - 7 }}}\)

Answer:

you would place it right after -1 about a forth the way to -2

The unit tangent vector T and the principal unit normal vector N can be computed for the given vector-valued function r(t) = (sin(t) + 2, cos(t) + 10, 6t). The unit tangent vector T represents the direction of the curve at each point, while the principal unit normal vector N is perpendicular to the tangent vector and points towards the center of curvature.

To find the unit tangent vector T, we differentiate r(t) with respect to t and divide by its magnitude:

r'(t) = (cos(t), -sin(t), 6)

||r'(t)|| = sqrt((cos(t))^2 + (-sin(t))^2 + 6^2) = sqrt(1 + 1 + 36) = sqrt(38)

Therefore, the unit tangent vector T is given by:

T = r'(t) / ||r'(t)|| = (cos(t)/sqrt(38), -sin(t)/sqrt(38), 6/sqrt(38))

To find the principal unit normal vector N, we differentiate T with respect to t and divide by its magnitude:

T'(t) = (-sin(t)/sqrt(38), -cos(t)/sqrt(38), 0)

||T'(t)|| = sqrt((sin(t)/sqrt(38))^2 + (-cos(t)/sqrt(38))^2) = sqrt(1/38 + 1/38) = sqrt(2/38) = sqrt(1/19)

Therefore, the principal unit normal vector N is given by:

N = T'(t) / ||T'(t)|| = (-sin(t)/sqrt(19), -cos(t)/sqrt(19), 0)

In summary, the unit tangent vector T for the given vector-valued function is (cos(t)/sqrt(38), -sin(t)/sqrt(38), 6/sqrt(38)), and the principal unit normal vector N is (-sin(t)/sqrt(19), -cos(t)/sqrt(19), 0). These vectors represent the direction and perpendicular direction to the curve defined by r(t).

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The number 459 in the citation 319 N.W. 2d 459 represents the page number where the case or legal opinion can be found in the North Western Reporter, Second Series. The North Western Reporter is a series of case reporters that includes court decisions from various states in the northwestern region of the United States.

In legal citations, the number before the "N.W." indicates the volume number of the reporter. So in this case, "319" refers to the specific volume where the case is located. The abbreviation "N.W." stands for North Western Reporter, which is the name of the reporter series. The number "2d" after "N.W." indicates that this is the second series of the North Western Reporter.

To locate the case within the volume, the number "459" refers to the page number where the case begins. This allows readers, such as lawyers, judges, or researchers, to easily find and reference the specific case within the reporter.

In summary, the number "459" in the citation 319 N.W. 2d 459 represents the page number where the case can be found in the North Western Reporter, Second Series.

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Answer:

..........................