when this polynomial is divided by (m+1), the remainder is 0. What is the value of the polynomial’s constant term?

From the statement we know that the triangle ABC has:

• angle A = 90°,

• angle C = 34°,

• side AC = 71.4.

We must compute the length of the side BC.

Given the data above, we draw the following graph of the triangle:

From the graph, we see that the side BC is the hypotenuse of the triangle, and the side AC is the adjacent cathetus with respect to angle C. From trigonometry we have the following identity:

Where:

• θ = angle = ,C = 34°,,

• ac = adjacent cathethus = ,AC = 71.4,,

• h = hyphotenuse = ,BC, (the unknown).

Replacing the data above in the equation, we have:

Solving the last equation for BC, we get:

Answer

Answer:

f(-4) = -5

Step-by-step explanation:

Step 1: Define

f(x) = 2x + 3

f(-4) is x = -4

Step 2: Substitute and Evaluate

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

f(-4) = -8 + 3

f(-4) = -5

Answer:f(-4) = -5

Step-by-step explanation:

Step 1: Define

f(x) = 2x + 3

f(-4) is x = -4

Step 2: Substitute and Evaluate

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

f(-4) = -8 + 3

f(-4) = -5

Answer:

b = $2.40

d = $5.70

Step-by-step explanation:

d = hot dog and b = hot dog buns

Equations:

2d + 5b = $23.40

3d + 2b = $21.90

-------------------------------subtract these two equations

-d + 3b = $1.50

3b - $1.50 = d

Substitute:

3d + 2b = $21.90

3(3b - $1.50) + 2b = $21.90

9b - $4.50 + 2= $21.90

11b = 26.40

b =  $2.40

Substitute again but this time with b:

3d + 2b = $21.90

3d + 2($2.40) = $21.90

3d + $4.80 = $21.90

3d = $21.90

d = $5.70

The probability that any particular shift being inspected has produced fewer than 50 bad bulbs is 0.2851.

The mean number of bad bulbs per shift is 6.0.

The probability mass function of Poisson distribution is:

P(X=x)=e^(−λ)λ^x/x!

The Poisson distribution is used to find the given probability.

The probability that any particular shift being inspected has produced fewer than 5 0 bad bulbs is:

P(x<5)=P(x≤4)

=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)

=\(e^{-6}\cdot\frac{6^0}{0!}+e^{-6}\cdot\frac{6^1}{1!}+e^{-6}\cdot\frac{6^2}{2!}+e^{-6}\cdot\frac{6^3}{3!}+e^{-6}\cdot\frac{6^4}{4!}\)

=0.0025+0.0149+0.0446+0.0892+0.1339

=0.2851

The required probability is obtained by substituting the values of mean and x in Poisson probability mass function.

The probability that any particular shift being inspected has produced fewer than 50 bad bulbs is 0.2851.

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The variables for this problem are classified as follows:

a) The number of songs on a randomly chosen ipod is discrete.

b) The number of people in line at the bank at a randomly chosen time is discrete.

c) The time it takes to drive to the airport is continuous.

d) The amount of rain during the next thunderstorm is continuous.

Variables are classified as continuous or discrete depending if they can assume decimal values, as follows:

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To solve the investment problem and determine how the retiree should invest her money to maximize expected earnings, we can set up a linear programming problem using the given data.

Let's define the decision variables as follows:

xM: Amount invested in municipal bonds (in dollars)

xR: Amount invested in real estate (in dollars)

xβ: Amount invested in blue chip stocks (in dollars)

xJ: Amount invested in junk bonds (in dollars)

xG: Amount invested in grain futures (in dollars)

The objective is to maximize expected earnings, which can be represented as:

0.06xM + 0.08xR + 0.1xβ + 0.12xJ + 0.15xG

Subject to the following constraints:

xM + xR + xβ + xJ + xG ≤ 250,000 (total investment cannot exceed $250,000)

xR / 100,000 + 1.5xβ / 100,000 + 2.5xJ / 100,000 + 5xG / 100,000 ≤ 5 (total management hours per week cannot exceed 5)

xM, xR, xβ, xJ, xG ≥ 0 (investment amounts cannot be negative)

Using Excel or any other linear programming software, we can input these constraints and the objective function to obtain the optimal solution. However, based on the provided information from Maple, the solution is as follows:

xM = $27,500

xR = $125,000

xβ = 0

xJ = 0

xG = 0

This means that the retiree should invest $27,500 in municipal bonds and $125,000 in real estate to maximize her expected earnings. No investment should be made in blue chip stocks, junk bonds, or grain futures according to this solution.

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Bank B has a basic fee of $9.95 per month and a bill paying fee of $5.95 per month. It has a limit of 20 checks written per month, with a cost of $1 per bill beyond the limit. The total annual cost for Bank B is $174.40.

To compare the cost of online banking, Tim Worker needs to consider various factors, including the basic monthly fee, bill paying monthly fee, limits on the number of checks written, and cost per bill beyond the limit. The basic fee is the amount charged by the bank for providing access to online banking services.

The bill paying fee is charged for each payment made through the online bill pay service. The limit on the number of checks written is the maximum number of checks that can be written in a given month without incurring additional charges. The cost per bill beyond the limit is the amount charged for each bill payment made beyond the specified limit.

Bank B has a basic fee of $9.95 per month and a bill paying fee of $5.95 per month. It has a limit of 20 checks written per month, with a cost of $1 per bill beyond the limit. To calculate the annual cost for Bank B, we can multiply the basic fee and bill paying fee by 12 and add the cost of any additional bills beyond the limit, multiplied by the cost per bill and the number of months in a year.

The total annual cost for Bank B is $174.40, calculated as follows:

Basic fee = $9.95 * 12 = $119.40

Bill paying fee = $5.95 * 12 = $71.40

Cost of bills beyond limit = $1 * (35 - 20) * 12 = $180

Total cost = $119.40 + $71.40 + $180 = $371.80

However, since the cost per bill beyond the limit is capped at $20 per month, the actual cost is $9.95 * 12 + $5.95 * 12 + $20 * 12 = $174.40.

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The `mean` function will give you the arithmetic mean of the variable. The `median` function will give you the median value of the variable. And the `mlv` function from the `modeest` package will give you the mode value of the variable.

To calculate mean, median and mode in R, you can use the following code.

Here, I have used the "mtcars" dataset which is a built-in dataset in R.

You can use any dataset of your own choosing.```
data(mtcars)  #loading the dataset
mtcars  #printing the entire data in the output

#finding mean
mean_mtcars <- mean(mtcars$mpg)
mean_mtcars

#finding median
median_mtcars <- median(mtcars$mpg)
median_mtcars

#finding mode
library(modeest)
mode_mtcars <- mlv(mtcars$mpg)
mode_mtcars$M

```The output of the above code will be the mean, median and mode of the "mpg" variable in the "mtcars" dataset.

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Answer:

11.25 miles

Step-by-step explanation:

To figure out how many miles John will travel in 1/2 an hour, we can use the following formula:

distance = rate x time

We know the rate, which is the number of miles John can travel per hour. We can find this by dividing the total distance by the total time:

rate = distance / time

rate = 45 miles / 2 hours

rate = 22.5 miles per hour

Now we can use this rate and the given time of 1/2 an hour to find the distance:

distance = rate x time

distance = 22.5 miles per hour x 1/2 hour

distance = 11.25 miles

Therefore, John will travel 11.25 miles in 1/2 an hour at this rate.

Answer:

x =-3

Step-by-step explanation:

5 + 6x = 2x - 7

Subtract 2x from each side

5 + 6x- 2x = 2x-2x - 7

5+4x = -7

Subtract 5 from each side

5+4x -5 = -7-5

4x = -12

Divide each side by 4

4x/4 = -12/4

x =-3

150 students scored between 42 and 56 on the district geometry test.

Box whisker plots are used to abstract a collection of data that has been approximated using an interval scale. Just a box plot is another name for it. They are mostly employed while interpreting data. It is one of the graphical approaches that shows how the dataset's data varies from one another. The histogram may be used to display the data as well. Yet a histogram offers a useful presentation. Box and whisker plots are preferable to histograms because they may exhibit numerous sets of data on a single graph, which adds more information.

From the box whisker plot we see that the lower quartile is 42 and the median is 56.

The median represents the 50th percentile whereas lower quartile is 75%.

The difference is:

75 - 50 = 25%.

Now, for 600 scores we have:

25% of 600

= 25/100 (600) = 150

Hence, 150 students scored between 42 and 56 on the district geometry test.

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Statistical considerations for the use of composite health-related quality-of-life scores in randomised trials

This is a research paper whose author is Andrew J. Vickers.

Abstract:

Conclusions:

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Answer:

-2

Step-by-step explanation:

You can see that when x goes up by 1, y goes down by 2. This means the rate of change is -2

Answer:

The rate of change is -2

Step-by-step explanation:

Take any two points from the graph. (0,-4) and (-2,0). Plug them into the equation y2-y1/x2-x1. In this case the equation would be 0--4/-2-0. Simplify this and get 0+4/-2-0. Simplify again and get 4/-2 which is -2

Therefore the rate of change is -2

Hope this helps

Answer:

2/5

Step-by-step explanation:

To convert a percentage to a fraction, we divide the percentage by 100 and simplify the resulting fraction. For example, to convert 40% to a fraction, we divide 40 by 100 to get 0.4 and then simplify the fraction 2/5. Therefore, 40% is equal to 2/5.

9514 1404 393

Answer:

  10b -40

Step-by-step explanation:

After giving away 4 of the b boxes she started with, she has (b-4) boxes remaining. Since there are 10 pencils in each box, the number of pencils she has left is ...

  10(b -4) = 10b -40

Answer:

hopefully u get the answer 9 squared answer

Step-by-step explanation:

Answer:

x=-1/4

Step-by-step explanation:

===============================================

Work Shown:

\(\text{x} = 0.\overline{63}\)

x = 0.63636363...

100x = 63.63636363...

100x - x = (63.63636363...) - (0.63636363...)

99x = 63

x = 63/99

x = (7*9)/(11*9)

x = 7/11

This table shows a few fractions equivalent to 7/11

\(\begin{array}{|c|c|} \cline{1-2}\text{Multiply top} & \\ \text{and bottom by} & \text{Equivalent fraction}\\\cline{1-2}2 & 14/22\\\cline{1-2}3 & \boldsymbol{21/33}\\\cline{1-2}4 & \boldsymbol{28/44}\\\cline{1-2}5 & 35/55\\\cline{1-2}6 & 42/66\\\cline{1-2}\end{array}\)

The terms in bold are the two answers

In other words, 7/11 = 21/33 when multiplying top and bottom by 3.

Also, 7/11 = 28/44 when multiplying top and bottom by 4.

To confirm those answers, use a calculator to find that

7/11 = 0.636363...

21/33 = 0.636363...

28/44 = 0.636363...

To rule out the non-answers, use the calculator to find that

14/21 = 0.667 approximately

7/12 = 0.5833 approximately

The solution to the given problem is

\(\[\int_{1}^{2} 2^{-\theta} d \theta= \frac{1}{\ln 2} \cdot \frac{1}{2}\].\)

The given integral is as follows:

\(\[\int_{1}^{2} 2^{-\theta} d \theta\]\)Using the formula of definite integral of power function,

\(\[\int_{a}^{b} x^{n} d x = \frac{b^{n+1} - a^{n+1}}{n+1}\]Thus \\\[\int_{1}^{2} 2^{-\theta} d \theta\]\)

can be written as,

\(\[\int_{1}^{2} (2)^{-\theta} d \theta = \frac{(2)^{-\theta + 1}}{-\ln2}\Big|_{1}^{2}\]\[=\frac{2^{-2+1}}{-\ln2} - \frac{2^{-1+1}}{-\ln2}\]\[= \frac{1}{\ln2} \bigg(\frac{1}{2} - 1\bigg)\]\)

Thus, \(\[\int_{1}^{2} 2^{-\theta} d \theta=\frac{1-\frac{1}{2}}{\ln 2}=\frac{1}{\ln 2} \cdot \frac{1}{2}\]\)

:n order to solve this question, we used the formula of definite integral of power function. The formula is given as

\(\[\int_{a}^{b} x^{n} d x = \frac{b^{n+1} - a^{n+1}}{n+1}\].\)

We followed these steps: First, we converted

\(\[\int_{1}^{2} 2^{-\theta} d \theta\]\)

into \(\[\int_{1}^{2} (2)^{-\theta} d \theta\].\)

We then applied the formula of definite integral of power function as shown:

\(\[\int_{1}^{2} (2)^{-\theta} d \theta = \frac{(2)^{-\theta + 1}}{-\ln2}\Big|_{1}^{2}\\) ]Finally,

we substituted the values to get our answer as

\(\[\frac{1}{\ln 2} \cdot \frac{1}{2}\]\)

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The charge q is ±7.46 × 10⁻⁷C.

Give:

Take a look at the charge on the left. The following forces are at work in response to this charge:

(Refer to the diagram below)

Because the charge is in equilibrium, the charge's vertical and horizontal forces must be zero.

We have the following in the vertical direction:

\(\begin{aligned}T \cos 20^{\circ} &=W \\\Rightarrow T &=\frac{m g}{\cos 20^{\circ}} \\&=\frac{3.0 \times 10^{-3} \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s}^2}{\cos 20^{\circ}} \\&=3.13 \times 10^{-2} \mathrm{~N}\end{aligned}\)

Coulomb's Law states that the electrostatic force between two point charges, q₁, and q₂, separated by r is given by the equation:

\(\begin{aligned}F &=\frac{q_1 q_2}{4 \pi \epsilon_0 r^2} \\&=\frac{K q_1 q_2}{r^2}\end{aligned}\)

Here,

Using trigonometric personalities, the distance between any two charges is:

\(\begin{aligned}r &=2 l \sin 20^{\circ} \\&=2 \times 1.0 \mathrm{~m} \times 0.342 \\&=0.684 \mathrm{~m}\end{aligned}\)

We have the following in the vertical direction:

\(\begin{aligned}F_e &=T \sin 20^{\circ} \\\Rightarrow \frac{K q_1 q_2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow \frac{K q^2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow q^2 &=\frac{r^2 T \sin 20^{\circ}}{K} \\&=\frac{(0.684 \mathrm{~m})^2 \times 3.13 \times 10^{-2} \mathrm{~N} \times \sin 20^{\circ}}{9 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2} \\&=55.65 \times 10^{-14} \mathrm{C}^2 \\\Rightarrow q &=\pm 7.46 \times 10^{-7} \mathrm{C}\end{aligned}\)

Therefore, the charge q is ±7.46 × 10⁻⁷C.

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The correct question is given below:
Two 3.0g point charges on 1.0m - long threads repel each other after being equally charged, as shown in the figure. What is the charge q?

Step-by-step explanation:

\(h(x) = a.6 \div 3 \\ \)

i hope its good

Answer: 1 and 1/20th. Don’t know if it’s in simplest form tho

Step-by-step explanation:

7/12 divided by 5/9, in its simplest form, is 21/20.

Given that we need to divide 7/12 by 5/9,

The reciprocal of a fraction is obtained by interchanging the numerator and the denominator.

So, to simplify 7/12 divided by 5/9, we multiply 7/12 by the reciprocal of 5/9:

7/12 ÷ 5/9 = 7/12 × 9/5

Next, we multiply the numerators and denominators:

(7 × 9) / (12 × 5) = 63/60

To simplify this fraction further, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3:

63/60 = (63 ÷ 3) / (60 ÷ 3) = 21/20

Therefore, 7/12 divided by 5/9, in its simplest form, is 21/20.

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Answer:

3x - 2y = 2

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, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line

m = \(\frac{5-2}{4-2}\) = \(\frac{3}{2}\) , 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 (2, 2 )

2 = \(\frac{3}{2}\) (2) + c = 3 + c ( subtract 3 from both sides )

- 1 = c

y = \(\frac{3}{2}\) x - 1 ← equation in slope- intercept form

multiply through by 2 to clear the fraction

2y = 3x - 2 ( subtract 3x from both sides )

- 3x + 2y = - 2 ( multiply through by - 1 )

3x - 2y = 2  ← in standard form

Answer:

             \(\bold{m=-\dfrac16}\)

Step-by-step explanation:

\(\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}\)

(1, 3)    ⇒   x₁ = 1,  y₁ = 3

(7, 2)    ⇒   x₂ = 7,  y₂ = 2

So the slope:

                    \(\bold{m=\dfrac{2-3}{7-1}=\dfrac{-1}6=-\dfrac16}\)