1 point
Solve: 0.75 (x + 200) = 150.5 (2 – 28)
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The average rate of change of the function is of zero on the following interval:

d. From week 5 to week 6.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence, over an interval [a,b], the rate is calculated by the equation presented as follows:

\(r = \frac{f(b) - f(a)}{b - a}\)

The rate of change is of zero when:

f(b) - f(a) = 0.

That is, when the two outputs are the same at the endpoints of the interval.

From the relation in this problem, during weeks 5 and 6, the weight is the same, hence it is the interval in which the average rate of change is of zero, and option d is correct.

The input is:

Time (weeks)

0

1

2

3

4

5

6

7

8

The output is:

Weight (lb)

150

144

143

141

140

137

137

132

129

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Answer:

x^2 + 4x + 3

Step-by-step explanation:

divide everything by 3

Answer:

Step-by-step explanation:

This statement translates into the symbolic statement

ye + 6 ≥ 15

Circumference of Circle --> \(2\pi r\)

Now compute with the known information plugged into the equation

   --> \(2(3.14) * 10) = 6.28*10 = 62.8in^2\)

Thus the circumference of the circle is 62.8 square inches.

Hope that helps!

Answer:

x-int: (3, 0)

y-int: (0, -3)

General Formulas and Concepts:

Alg 1

Slope-Intercept Form: y = mx + b

The y-intercept is the y value when x = 0.

Another way to reword that is when the graph crosses the y-axis.

The x-intercept is the x value when y = 0.

Another way to reword that is when the graph crosses the x-axis.

Step-by-step explanation:

Step 1: Define equation

x - y = 3

Step 2: Convert to slope-intercept form

Step 3: Find x/y-intercepts

x-int

y-int

Answer:

x=3

y=-3

Step-by-step explanation:

find the length using the Pythagorean theorem.

Length = sqrt(20^2 - 12^2)

Length = 16 feet

area = 12 x 16 = 192 square feet

(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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Answer:

Step-by-step explanation:

Correct option is A)

Answer

x+y

Step-by-step explanation:

Answer:

175

Step-by-step explanation:

(a) The fundamental matrix for the given system of equations is Φ(t) = e^(At).

Let's denote the given coefficient matrix as A:

A = [ -1 -4

      1 -1 ]

The fundamental matrix Φ(t) for the system is given by the matrix exponential of the coefficient matrix A multiplied by t:

Φ(t) = e^(At)

(b) The fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix.

Finding the fundamental matrix φ(t) satisfying φ(0) = I:

To find the fundamental matrix φ(t) satisfying φ(0) = I, we substitute t = 0 into Φ(t):

φ(0) = Φ(0) = e^(A * 0) = e^(0) = I

So, the fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix.

In summary, for the given system:

(a) The fundamental matrix Φ(t) is e^(At).

(b) The fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix, denoted as φ(t) = I.

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Answer:

5. ABC and XYZ

Step-by-step explanation:

matching angle values

The equation is equivalent to the r = d/t.

There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

We have to find which equation is equivalent to the formula d = rt.

Formula given: d = rt

Divide both sides by t

d/t = rt / t

d/t = r

Thus, the equation is equivalent to the r = d/t.

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Answer:

a = 8

Step-by-step explanation:

a ÷ 2 - 8 + 8 = - 4 + 8

a ÷ 2 = 4

a ÷ 2 × 2 = 4 × 2

a = 8

Answer:

a = 8

Step-by-step explanation:

Given

\(\frac{a}{2}\) - 8 = - 4 ( add 8 to both sides )

\(\frac{a}{2}\) = 4 ( multiply both sides by 2 to clear the fraction )

a = 8

99999 ÷ 9999

using the calculator the answer will be 10.0009

Answer:

0.5km/h

Step-by-step explanation:

Assume lake has no current.

.

V=distance / time

V=39km / 3h

V=13km/h

In water Assume boat used same power travelling

V=35km / 2h

V= 12.5km/h

Current is the difference 0.5km/h

Ginny should reorder when the inventory level reaches 116.515 pounds to maintain a 95% service level

To calculate the reorder point, we need to consider two factors: the lead time (time between ordering and receiving the delivery) and the safety stock (the extra amount of flour kept in case of unexpected demand or delay in delivery).

Using the formula: Reorder point = (Average daily usage x Lead time) + Safety stock, we can calculate the reorder point.

Here, the average daily flour consumption is 35 pounds with a standard deviation of 7 pounds, and the average delivery time from the supplier is 3 days with a standard deviation of 0.5 days. She decides to order 72 pounds at a time.

The lead time is 3 days, and the safety stock can be calculated using the service level and standard deviation of demand during lead time. Assuming a 95% service level, we can use the z-score of 1.645 (from the standard normal distribution table) to calculate the safety stock.

Safety stock = (z-score x Standard deviation of demand during lead time) = (1.645 x 7) = 11.515 pounds

Now, we can calculate the reorder point:

Reorder point = (Average daily usage x Lead time) + Safety stock = (35 x 3) + 11.515 = 116.515 pounds

Therefore, Ginny should reorder when the inventory level reaches 116.515 pounds to maintain a 95% service level. This ensures that she has enough flour to cover her daily usage and also account for any unexpected demand or delivery delays.

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The subgame perfect Nash equilibrium involves Player 1 receiving a piece that is no less than 1/4 of the original cake, Player 2 receiving a piece that is no less than 1/2 of the cake, and Player 3 receiving a piece that is no less than 1/4 of the cake. Player 2 obtains the largest piece at 1/2 of the cake, while Player 1 gets a share that is no less than 1/4 of the cake, which is larger than Player 3's share of the remaining cake.

The subgame perfect Nash equilibrium and complete strategies are as follows:

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Answer:

1680

Step-by-step explanation:

subtract the 310 words and then multiply 524 by 2 then add the answer of the subtraction to what you got in the multiplication

Answer:

The second one

Step-by-step explanation:

ur welcome sire or madam which ever one you are

A statistical test that may be used to compare a sample proportion to a given population proportion is the one-sample proportion test.

The following is the calculation of the test statistic and p-value for a sample size of 411, 88 successes, and a population proportion of 0.16 for the null hypothesis. The calculation for the test statistic is given by:

$$z=\frac{\hat{p}-p_0}{\sqrt{p_0(1-p_0)/n}}$$

where $\hat{p}

=88/411

≈0.2144$,

and $p_0=0.16$.$$

z=\frac{0.2144-0.16}{\sqrt{0.16(1-0.16)/411}

≈2.803$$

Therefore, the test statistic for this sample is 2.803.The p-value is defined as the probability of obtaining the observed results or more extreme results assuming the null hypothesis is true.

Since this is a two-sided test, the p-value is equal to twice the area to the right of the absolute value of the test statistic in the standard normal distribution.

$$p=2P(Z≥2.803)

≈0.0050$$

Therefore, the p-value for this sample is approximately 0.0050.The p-value is less than the significance level α = 0.001.

Hence, we can reject the null hypothesis. Therefore, we can conclude that there is evidence that the proportion of women over 40 who regularly have mammograms is significantly different from 0.16.

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Answer:

Step-by-step explanation:

The first questions are answered on the attachment.

Answer:

x=(2z/5y-1)/6

Step-by-step explanation:

5y(6x+1)=2z

6x+1=2z/5y

6x=2z/5y-1

x=(2z/5y-1)/6

Answer:

96

Step-by-step explanation:

(2^22-2^20) (3^24-3^22) (4^26-4^24)

=[(2^2-1)2^20][(3^3-1)3^22][(4^2-1)4^24]

=3*2^20*8*3^22*15*4^24

=2^23*3^23*4^24*15

=2^23*3^23*2^48*3*5

=2^71*3^24*5.

∵(2^22-2^20) (3^24-3^22) (4^26-4^24)=2^x × 3^y × 5^z，

∴x=71, y=24, z=1,

∴x+y+z=71+24+1=96.

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of 32}}{\left( \cfrac{80}{100} \right)32}\implies 25.6~\hfill \underset{ marked~up }{\stackrel{ 32~~ + ~~25.6 }{\text{\LARGE 57.6}}}\)

The percent off the store should display is 27.0%

The percent off the store should display is the total percent off given to their product. That is, the addition of the first and second percent off.

The total percent off the store gave to Matt is calculated as;

= 20% + 7%

= 27%

To the nearest tenth of a percent = 27.0%

Thus, the percent off the store should display is 27.0%

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We are 90% confident that the true difference between the mean strengths of the two types lies between 0.015 and 0.105. The data does not show at the 0.05 level that the mean strengths are different, with a p-value of approximately 0.055. Therefore, we fail to reject the null hypothesis that the means are equal.

To find a 90% confidence interval for the difference in the mean strengths of the two types, we can use the two-sample t-test with pooled variance. The formula for the confidence interval is:

\($(\bar{x}_1 - \bar{x}2) \pm t{\alpha/2,\nu} \cdot s_p \cdot \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$\)

Plugging in the given values, we get:

\(\bar{x}1 = 3.18, \bar{x}2 = 3.24, n_1 = 5, n_2 = 7, s_p = \sqrt{\frac{ (n_1 - 1)s_1^2 + (n_2 - 1)s_2^2 }{ df }} = \sqrt{\frac{ (40.042^2 + 60.048^2) }{ 10 }} = 0.046, t{\alpha/2,\nu} = t{0.05/2,10} = 2.306$\)

Therefore, the 90% confidence interval for the difference between the mean strengths of the two types is:

\($(3.24 - 3.18) \pm 2.306 \cdot 0.046 \cdot \sqrt{\frac{1}{5}+\frac{1}{7}} = 0.06 \pm 0.045$\)

So the interval is (0.015, 0.105).

Thus, we are 90% confident that the true difference between the mean strengths of the two types lies between 0.015 and 0.105.

To test whether the mean strengths are different, we can use a two-tailed hypothesis test with a significance level of 0.05. The null hypothesis is that the means are equal, while the alternative hypothesis is that they are different. We can calculate the t-value as:

\($t = \frac{\bar{x}_1 - \bar{x}_2}{s_p \cdot \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} = \frac{3.18-3.24}{0.046 \cdot \sqrt{\frac{1}{5}+\frac{1}{7}}} = -2.13$\)

The degrees of freedom are the same as before, \($df = n_1 + n_2 - 2 = 10$\)

The p-value is the probability of getting a t-value at least as extreme as the observed one, assuming the null hypothesis is true. From a t-distribution table, we can find that the p-value for t = -2.13 with df = 10 is approximately 0.055. Since this is greater than the significance level of 0.05, we fail to reject the null hypothesis.

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Graphing calculators provide a variety of advantages to students. They are powerful tools that allow students to graph equations, visualize data, and explore mathematical concepts.

Graphing calculators also provide students with a comprehensive set of math functions, including trigonometric, exponential, and logarithmic functions. This means that students can use them to solve complex equations, or to develop and graph mathematical models.

With a graphing calculator, students can easily manipulate the graph to explore the effect of changing variables on the equation. This is particularly useful for understanding calculus concepts, and for visualizing the effects of different mathematical operations.

Overall, graphing calculators provide a variety of advantages and are an invaluable tool for students studying mathematics.

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