there are 6 different types of tasks in a department. in how many possible ways can 6 workers pick up the 6 tasks?

Answer:

To find the area break up the shapes:

The rectangle is A = bh which is 7*3 which is 21.

Triangle: A = 1/2(bh)

A=1/2(3*7)

A=1/2(21)

A=10.5

Now add up the areas:

21+10.5

=

31.5

The answer is 31.5 units.

Answer:

Step-by-step explanation:

Mr. Ernest can travel 65 miles with his motorcycle for each gallon of gas.

The unit rate = 64 miles per gallon.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

The values are given in the attached table.

From the table;

Motorcycle travels 640 miles on 10 gallons of gasoline.

To find the unit rate:

Divide the total distance in miles by the number of gallons of gasoline.

We get,

The unit rate = 640 / 10

The unit rate = 64 miles per gallon.

Therefore, the unit rate = 64 miles per gallon.

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The complete question;

Mr. Ernest wants to know how many miles, he can travel with his motorcycle for each gallon of gas.

The table is given in the image below.

What is the unit rate in miles per gallon?

Answer:

its 0.8

Step-by-step explanation:

Answer:

The answer is G

Step-by-step explanation:

The total cost of the truck, including tax, can be calculated by adding the standard vehicle price, extra options package price, freight and PDI, and then applying the 15% tax rate.

Total Cost = (Standard Vehicle Price + Extra Options Package + Freight and PDI) * (1 + Tax Rate)

= ($22,999 + $500 + $1,450) * (1 + 0.15)

= $24,949 * 1.15

= $28,691.35

Therefore, the total cost of the truck, including tax, is $28,691.35.

b) i) To determine the monthly payment for financing at 1.9% for 48 months, we can use a financial calculator or spreadsheet functions such as PMT (Payment). The formula to calculate the monthly payment is:

Monthly Payment = PV * (r / (1 - (1 + r)^(-n)))

Where PV is the present value (total cost of the truck), r is the monthly interest rate (1.9% divided by 12), and n is the total number of months (48).

ii) The total amount he will have to pay for the truck when it is paid off can be calculated by multiplying the monthly payment by the number of months. Total Amount = Monthly Payment * Number of Months

iii) The cost to finance the truck can be calculated by subtracting the total cost of the truck (including tax) from the total amount paid when it is paid off. Cost to Finance = Total Amount - Total Cost

c) i) To calculate how much money Robert will need to finance, we can subtract his down payment of $2000 from the total cost of the truck.  Amount to Finance = Total Cost - Down Payment

ii) To calculate the monthly payment in this case, we can use the same formula as in (b)i) with the updated present value (Amount to Finance) and the same interest rate and number of months. Monthly Payment = PV * (r / (1 - (1 + r)^(-n)))

By plugging in the values, we can determine the monthly payment using technology such as financial calculators or spreadsheet functions.

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Answer:

\(x=y-22\)

Step 1:

In order to solve this equation, we must subtract the y on both sides so the y could be cancelled out on the left and could move to the right side of the equation.

\(y=3x+22-2x\\=-y+3x+22-2x\)

Step 2:

Then, we add 2x on the right side of the equation to cancel out the -2x and bring it to the left of the equation, where the y was before.

\(=-y+3x+22-2x\\2x=-y+3x+22\)

Step 3:

Then, we do the same thing with 3x: subtract it from the right side and add it to the 2x, which becomes -x.  

\(2x=-y+3x+22\\2x-3x=-y+22\\-x=-y+22\)

Step 4:

Finally, we divide all the numbers by -1 to get our final answer! Reminder: we are doing all this because we have to isolate the x, since we are solving for x.

\(-x=-y+22\\\frac{-x}{-1} =\frac{-y}{-1}+\frac{22}{-1} \\x=y-22\)

Our answer is x = y - 22. Hope this helps!

Answer:

answer: x=y-22

Step-by-step explanation:

first subtract y from both sides. then, add -2x on both sides and subtract 3x from the right so the 2x will be -x. divide everything by a - and the answers x=y-22

99% Confidence Interval for the Population Percentage of Defective Disks = (0.1004, 0.1196).

Rules for Decimals. Align up the decimal points. To ensure that every one of the values have the same number of places following the decimal, add 0s. Add the same way you would with complete numbers.

Step 1:

Sample Size: n=7002

Number of non-defective disks =6232

Number of defective disks: x = 7002-6232=770

Sample proportion \(\widehat{p}\) = x/n = 770/ 7002 = 0.110

Estimated proportion of disks which are defective: Sample proportion: \(\widehat{p}\) = 0.110

Step 2:

Range of confidence for the population proportion:

\(=\widehat{p}\pm z_{\alpha /2}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

\(\alpha = (100-99)/100 = 0.01; \alpha/2 = 0.005\)

99% Confidence interval =

\(=\widehat{p}\pm z_{0.005}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

from standard normal tables z0.005 = 2.58

99% Confidence Level for the Population Percentage of Defective Disks =

\(=\widehat{p}\pm z_{0.005}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

\(=0.11\pm 2.58\sqrt{(0.11(1-0.11))/7002}\)

\(=0.11\pm 2.58\sqrt{(0.110\times 0.89)/7002}=0.11\pm 2.58\sqrt{\frac{0.0979}{7002}}\)

\(=0.11\pm 2.58\times 0.0037 = 0.11\pm 0.0096 =(0.1004, 0.1196)\)

99% Confidence interval for population proportion of disks which are defective= (0.1004, 0.1196).

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Step-by-step explanation:

you simplify your answer and write it as proper fraction

Answer:

C=$7.38

Step-by-step explanation:

$18.62 + c = $26.00

$26-$18.62=$7.38

c=$7.38

The probabilityIna deck of 52 cards, there are 26 red cards and 4 cards numbered 4.

Thus,

Probability of an event is evaluated as

Thus,

Similarly,

The probability of selecting a red card or a 4 is evaluated as

Thus, the probability of selecting a red card or a 4 from a deck of 52 cards is

The correct option is B

Approximately 304,657,600 Americans were there in July 2009 based on the estimated 2008 growth rate of 0.88%.

To find the approximate US population in July 2009, we need to apply the growth rate of 0.88% to the initial population in July 2008.

Convert the growth rate from percentage to decimal:

0.88% = 0.0088
Calculate the number of people added to the population in 2008: 302,000,000 * 0.0088 = 2,657,600
Add this number to the initial population to find the population in July 2009:

302,000,000 + 2,657,600 = 304,657,600.

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It is true that the slope of the horizontal tangent line to the parametric curve at a point (x(t), y(t)) is given by dy/dx = (dy/dt)/(dx/dt).

The statement is saying that if f(g(t)) has a horizontal tangent at t = 1, then the curve has a well-defined tangent line at that point, which is also a horizontal tangent. Let's break this down step by step:

f(g'(1)) = 0: This means that the derivative of f with respect to its input g(t) is equal to zero at t = 1. In other words, the slope of the tangent line of f(g(t)) at t = 1 is zero.

dx/dt is not zero at t = 1: This means that the curve g(t) has a well-defined tangent line at t = 1, because the slope of the tangent line of g(t) is not infinite (i.e., the derivative dx/dt is defined and finite).

Setting dy/dx = 0 gives dy/dt / dx/dt = 0: This is using the chain rule of differentiation to relate the derivative of f with respect to t (i.e., dy/dt) to the derivative of f with respect to x (i.e., dy/dx) and the derivative of g with respect to t (i.e., dx/dt).

dy/dt = 0 when dx/dt is not zero: Since dy/dx = 0 and dx/dt is not zero, we can conclude that dy/dt must also be zero at t = 1. This means that the slope of the tangent line of f(g(t)) is also zero at t = 1.

Therefore, the curve has a horizontal tangent at t = 1: Since both g(t) and f(g(t)) have horizontal tangents at t = 1, we can conclude that the curve f(x) also has a horizontal tangent at x = g(1). This means that the tangent line to the curve at that point is horizontal.

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Answer:  y = 23x - 62

Step-by-step explanation:

Parallel lines have the same slope.

y = 23x + 4

  m=23   b=4

Input x = 3, y = 7, & m = 23 into the Point-Slope formula to find the equation or the Slope-Intercept formula to find b (you already have m).  I will choose the latter.

 y = mx + b

 7 = 23(3) + b

 7 = 69 + b

-62 = b

m = 23, b = -62  -->  y = 23x - 62

An angle of rotation is the measure of the amount that a figure is rotated about a fixed point called a point of rotation.

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Answer:

165

Step-by-step explanation:

first 1% of 500 is calculated and then multiplied by 33:

\(\frac{1}{100} (500)=5\)

5(33)=165

Hope this helps

The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).

The difference of two expressions is determined by subtracting one from the other.

Find the difference of each of the expressions given to determine which will give us 5.

-3 - (-8)

= -3 + 8

= 5

-2 - 3 = -5 [this is not the same as 5]

1 - (-4)

= 1 + 4

= 5

7 - (-2)

= 7 + 2

= 9

-3 - (-8) and 1 - (-4) will give us a difference of 5.

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Answer:

72° and 108°

Step-by-step explanation:

let one angle be x then the other angle is 1.5x

A linear pair sum to 180° , so

x + 1.5x = 180 , that is

2.5x = 180 ( divide both sides by 2.5 )

x = 72

1.5x = 1.5 × 72° = 108°

The two angles are 72° and 108°

Answer:

do you have wazapp I can send full pic of the answer here

Answer:

32.1m

Step-by-step explanation:

\(2\pi r*(\frac{x}{360})=\) arc length of sector of a circle

2 radii + arc length of a sector of a circle= perimeter of the sector

x=90 degrees

r=9

substitute values to find the arc length

\(2(9)*\pi *(\frac{90}{360} )= arc length\\arclength=14.1\\\)\(14.1+2(9)=32.1\)

Answer:

I would call them and ask for the manager lowkey!

Step-by-step explanation:

❤❤

Answer:

Of course today

Step-by-step explanation:

Answer: I only know the angles I am so sorry but for the questions with angles is 4. 90 degrees   5. 60 degrees   6. 60 degrees        

Step-by-step explanation:

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

x=-9ln(1/2)/[ln(4)-ln(1/2)]

Step-by-step explanation:

4^{x}=(1/2)^{x-9}

ln(4^{x})=ln((1/2)^{x-9})

xln(4)=(x-9)ln(1/2)

xln(4)=xln(1/2)-9ln(1/2)

xln(4)-xln(1/2)=-9ln(1/2)

x[ln(4)-ln(1/2)]=-9ln(1/2)

x=-9ln(1/2)/[ln(4)-ln(1/2)]

The correct statement is that F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).

Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.

This can be seen by looking at the function's minimum and maximum values and its points of intersection with the x- and y-axes. The minimum value of (1.9, negative 5.7) is to the left of the x-axis, indicating that the function is negative over the interval (-0.7, 0.76). The maximum value of (0, 2) is above the x-axis, indicating that the function is negative over the interval (2.5, ∞).

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When an inequality is multiplied or divided by a negative number, the inequality sign will flip, meaning it will change its direction. For example, if you have a > b and you multiply or divide both sides by a negative number, the inequality will become a < b. This is because the relationship between the values reverses when multiplied or divided by a negative number.

Explanation:

When an inequality is multiplied or divided by a negative number, the direction of the inequality sign is flipped. This is because multiplication or division by a negative number, results in a reversal of the order of the numbers on the number line.

To see why this happens, consider the following example:

Suppose we have the inequality x < 5. If we multiply both sides of this inequality by -1, we get -x > -5. Notice that we have flipped the inequality sign from "<" to ">". This is because multiplying by -1 changes the sign of x to its opposite, and also changes the sign of 5 to its opposite, resulting in a reversal of the order of the numbers on the number line.

Similarly, if we divide both sides of the inequality x > 3 by -2, we get (-1/2)x < (-3/2). Here, we have again flipped the inequality sign from ">" to "<". This is because dividing by a negative number also changes the order of the numbers on the number line.

In general, if we have an inequality of the form a < b or a > b, where a and b are real numbers, and we multiply or divide both sides by a negative number, we obtain:

If we multiply by a negative number, the inequality sign is flipped. For example, if a < b and c < 0, then ac > bc.

If we divide by a negative number, the inequality sign is also flipped. For example, if a > b and c < 0, then a/c < b/c.

Therefore, it is important to be mindful of the signs of the numbers involved when performing operations on inequalities. If we multiply or divide by a negative number, we must flip the direction of the inequality sign accordingly.

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Answer: $3.87

Step-by-step explanation:

3.10 increase 24.8% =

3.10 × (1 + 24.8%) = 3.10 × (1 + 0.248) = 3.8688

a)  k1(x) = log2(x-5)

b) k2(x) = log2(x-5) - 2

c) k3(x) = -log2(x-5) - 2

d) k4(x) = log2(x-5) - 2

A)  It takes approximately 6.931 minutes for the probability to reach 50%.

B) It takes approximately 17.329 minutes for the probability to reach 80%.

Consider the following transformations of the function k(x) = log2 (x)

a) Shift it to the right 5 units.

Denote the function that results from this transformation by k1.

The function k(x) = log2(x) shifted to the right 5 units can be represented as k1(x) = log2(x-5)

b) Shift k1 down 2 units.

Denote the function that results from this transformation by K2.

The function k1(x) = log2(x-5) shifted down 2 units can be represented as k2(x) = log2(x-5) - 2

c) Reflect K2 about the x-axis.

Denote the function that results from this transformation by k3.

The function k2(x) = log2(x-5) - 2 reflected about the x-axis can be represented as k3(x) = -log2(x-5) - 2

d) Reflect k3 about the y-axis.

Denote the function that results from this transformation by k4.

The function k3(x) = -log2(x-5) - 2 reflected about the y-axis can be represented as k4(x) = log2(x-5) - 2

e) Use Maple to Plot k4

The following is the graph for the function k4:

Therefore, the Maple command for k4 can be written as plot(log2(x-5) - 2, x = -100 .. 100);2.

Between 12:00pm and 1:00pm, cars arrive at Citibank's drive-thru at the rate of 6 cars per hour. (0.1 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 12:00pm

F(t)= 1-e0.1t

Use Maple command fsolve to solve for t.

a) Determine how many minutes are needed for the probability to reach 50%.

The probability of a car arriving within t minutes can be represented by F(t) = 1 - e^(-0.1t).

We need to find the value of t such that F(t) = 0.5.

Therefore, we have:0.5 = 1 - e^(-0.1t)⇒ e^(-0.1t) = 0.5⇒ -0.1t = ln(0.5)⇒ t = -(ln(0.5))/(-0.1) = 6.931 min

Therefore, it takes approximately 6.931 minutes for the probability to reach 50%.

b) Determine how many minutes are needed for the probability to reach 80%.

The probability of a car arriving within t minutes can be represented by F(t) = 1 - e^(-0.1t).

We need to find the value of t such that F(t) = 0.8.

Therefore, we have:0.8 = 1 - e^(-0.1t)⇒ e^(-0.1t) = 0.2⇒ -0.1t = ln(0.2)⇒ t = -(ln(0.2))/(-0.1) = 17.329 min

Therefore, it takes approximately 17.329 minutes for the probability to reach 80%.

c) No, it is not possible for the probability to equal 100% because F(t) approaches 1 as t approaches infinity, but never actually reaches 1.3. Roger places one thousand dollars in a bank account that pays 5.6 % compounded continuously.  Let A(t) represent the balance in the account after t years.

Find A(t).

The balance in the account after t years is given by the formula A(t) = A0e^(rt), where A0 is the initial amount, r is the interest rate, and t is the time in years.

The balance in the account after one year with continuous compounding is:

A(1) = 1000e^(0.056 * 1)≈ 1056.09

Since the balance in the account after one year is less than $1060, Roger does not have enough money to buy a computer system.

The balance in the account after t years with monthly compounding is:

A(t) = 1000(1 + 0.059/12)^(12t)≈ 1095.02

Therefore, the balance in the account after one year with monthly compounding is:

A(1) = 1000(1 + 0.059/12)^(12*1)≈ 1059.36

Since the balance in the account after one year with monthly compounding is greater than $1060, the other bank is a better deal.

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The data analyst should use a bar chart for the visualization that makes it easy to show which of the top ten most populous cities in North Carolina have a population below 250,000 people.

A bar chart is a graph that represents categorical data with rectangular bars.

The height or length of the bars is proportional to the values they represent.

The bars can be plotted either horizontally or vertically based on the data being presented.

They are frequently used to compare values across different categories by plotting the categories along the horizontal axis and the values along the vertical axis.

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Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

.Answer

Step-by-step .