Duncan shares 20 percent of all of his sales commissions with his personal assistant. If Duncan earns x dollars in commissions and gives his assistant y dollars, which equation correctly models this situation? mc011-1.jpg

Answer: 5ab

Step-by-step explanation:

The given polynomial : [tex]5ab^2+10ab[/tex]

The prime factorization of [tex]5ab^2= 5\times a\times b\times b[/tex]

The prime factorization of [tex]10ab= 5\times2\times a\times b[/tex]

We can see that the greatest common factor of  [tex]5ab^2\text{ and }10ab[/tex] is  [tex]5\times a\times b[/tex]

Hence, the greatest common factor of  [tex]5ab^2+10ab[/tex] = 5ab

a + b = 88

ab = y

a = 88 - b

y = (88 - b)*b
y = -b^2 + 88b

Take the derivative and set equal to 0

y' = -2b + 88 = 0

2b = 88
b = 44

a=44

 both numbers are 44

To find two positive numbers a and b whose sum is 88 and whose product is maximized, we can use the concept of quadratic equations. By taking the derivative of the product function and setting it equal to zero, we can find the maximum value. Plugging that value back into the product function will give us the maximum product.

To find two positive numbers a and b whose sum is 88 and whose product is maximized, we need to use the concept of quadratic equations. Let's assume a as x and b as 88-x. The product of the two numbers can be expressed as the quadratic equation P(x) = x(88-x). To maximize the product, we need to find the maximum value of P(x). We can use calculus to find the maximum value by taking the derivative of P(x) and setting it equal to zero. Solving that equation will give us the value of x, and plugging it back into P(x) will give us the maximum product.

Let's go through the steps:

So, the two positive numbers a and b are 44 and 88-44, which is 44 as well. Their sum is 88 and their product is maximized at 1936.

there are 60 minutes marks on a clock

 360/60 = 6

 6 degree between every minute

 From 1:25 to 1:50 there are 25 minutes

25 x 6 = for a total of 150 degrees

150*pi/180 = 5pi/6 radians. ( 2.61799 radians)

Total distance the tip of minute hand has traveled in this time = 2pi*(4 in) * (5pi/6)/(2pi) = 10pi/3 inches (10.47 inches)

This is a negative linear association because when ever the x (top line) is increasing and the y (bottom line) is decreasing, that shows that you are going farther to the end of the  x axis and lower down the y axis.

Negative linear association is the type of association will the scatter plot for this data represent between the time, in hours, and the distance from the destination, in miles

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The scatter plot for this data will represent a negative linear association between the time, in hours, and the distance from the destination, in miles.

As the time in hours increases, the distance from the destination in miles decreases, and this relationship is a straight line that slopes downwards from left to right which indicates a negative linear association.

Therefore, Negative linear association is the type of association will the scatter plot for this data represent between the time, in hours, and the distance from the destination, in miles.

To learn more on Graph click:

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Answer:

b

Step-by-step explanation:

i took the test

1st Prism = 8*14 = 112

672/112 = 6

2nd prism = 8*12=96

96*6 = 576 cubic cm

 answer is 576 cubic centimeters

Answer:

The correct option is 1.

Step-by-step explanation:

The volume of a rectangular prism varies jointly with the length and width of the figure when the height remains constant.

Let the height of both rectangular prism be h cm.

The volume of a prism is

[tex]V=l\times b\times h[/tex]

Where, l is length, b is breadth or width and h is height.

The volume of a rectangular prism is 672 cubic centimeters. The figure has a length of 8 centimeters and a width of 14 centimeters.

[tex]672=8\times 14\times h[/tex]

[tex]672=112h[/tex]

Divide both sides by 112.

[tex]\frac{672}{112}=h[/tex]

[tex]6=h[/tex]

The value of h is 6 cm. It means the height of both prism is 6 cm.

A second prism has a length of 12 centimeters and a width of 8 centimeters.  So, the volume of second prism is

[tex]V=12 \times 8\times 6[/tex]

[tex]V=576[/tex]

The volume of second prism is 576 cubic centimeters. Therefore the correct option is 1.

5^2 +x^2 = 13^2

25 + x^2 = 169

x^2 = 144

x = sqrt(144) = 12

 they run west for 12 KM

 12+5 = 17 total km

need to divide 4 1/8 by 1 1/4

4 1/8 = 33/8

1 1/4 = 5/4

33/8 / 5/4 = 33/8 * 4/5 =  132/40 reduces to 33/10 = 3 3/10

100* 3 3/10 = 330 miles

Final answer:

Using the map scale of 1 1/4 inches equals 100 miles, and the measured map distance of 4 1/8 inches, the actual distance between the two cities is calculated to be 330 miles.

Explanation:

To find the actual distance between two cities on a map, we can set up a proportion based on the scale of the map. In this case, the scale is 1 1/4 inches = 100 miles. The measured distance on the map between the two cities is 4 1/8 inches.

We'll convert these measurements to an easier-to-calculate form by changing the mixed numbers to improper fractions.

First, we convert 1 1/4 inches to an improper fraction: 1 1/4 = 5/4 inches. Likewise, we convert 4 1/8 inches to an improper fraction: 4 1/8 = 33/8 inches. Now we set up the proportion using the scale.

(5/4 inches) / (100 miles) = (33/8 inches) / (x miles)

To solve for x, cross-multiply and divide:

(5/4) * x = (33/8) * 100
x = (33/8 * 100) / (5/4)
x = (33 * 100 * 4) / (8 * 5)
x = (33 * 4) / (2)
x = 66 miles

Therefore, the actual distance between the two cities is 330 miles.

Answer:

Part A: 12y^2+9y-21

Part B: 4y^2+6y^2+7y-5

Part C:  A set of numbers is closed, or has closure, under a given operation if the result of the operation on any two numbers in the set is also in the set. For example, the set of real numbers is closed under addition, because adding any two real numbers results in another real number. Likewise, the real numbers are closed under subtraction, multiplication and division (by a nonzero real number), because performing these operations on two real numbers always yields another real number. Polynomials are closed under the same operations as integers.

Step-by-step explanation:

Hope this helps!!

Answer: The answer is (C) 47.5.

Step-by-step explanation:  In the given figure, O is the centre of a circle, where AC is the diameter and OB is the radius. We are to find the measure of ∠BAC.

We have

[tex]m\angle AOB+m\angle BOC=180^\circ\\\\\Rightarrow m\angle BOC=180^\circ-85^\circ\\\\\Rightarrow m\angle BOC =95^\circ.[/tex]

∠BOC and ∠BAC are angles at the centre and at the circumference subtended by the arc BC, so

[tex]m\angle BAC=\dfrac{1}{2}\times m\angle BOC=\dfrac{1}{2}\times 95^\circ=47.5^\circ.[/tex]

Thus, (C) is the correct option.

To solve this problem, we must first imagine out that the sequence of the children is either 
GBGBGB.... or BGBGBG....

So there are 2 possible sequence all in all. Now to solve for the total arrangements per sequence, the girls can be arranged in n! ways in their alloted spots, and so can the boys n! in their alternate spots, therefore:
Total arrangements = 2 * n! * n!

If n = 55

Total arrangements = 2 * 55! * 55!

Total arrangements = (The answer is very big ~almost infinite)

If n = 5

Total arrangements = 2 * 5! * 5!

Total arrangements = 28,800

So I believe the correct given is 5 boys and 5 girls and there are a total of 28,800 arrangements.

total = 3000*(1-0.011)^10

1-0.011 = 0.989

total = 3000*(0.989)^10

0.989^10 = 0.895288314

3000* 0.895288314 = 2685.86

rounded to nearest whole number = 2686

 there will be 2686 people

This question can simply be answered directly. To solve this, we should recall that the formula of a circle is:

Area of circle = π r^2                       where r is the radius of the circle

Now we are given that segment OA is equivalent to 5 units. Segment OA is also the diameter of that circle therefore d = 5.

Now let us convert the formula knowing that radius is one half the diameter:

r = d / 2

Area of circle = π (d / 2)^2

Area of circle = π d^2 / 4

Substituting:

Area of circle = π (5)^2 / 4

Area of circle = 3.14 * 25 / 4

Area of circle = 19.625 = 19.6 square units

Answer:

The answer would be 19.6 for plato Users

Step-by-step explanation:

-the answer would be C: "x+y+z= 180 degrees"

-and here is proof so you know you won't get the answer wrong

- hope you do good on your test, have a good day :)

Answer:  The required simplified form is [tex]4\cos^2\theta.[/tex]

Step-by-step explanation:  We are given to simplify the following trigonometric expression :

[tex]T=(\cos \theta-\cos\theta)^2+(\cos \theta+\cos \theta)^2.[/tex]

To simplify, first we need to evaluate the terms within the brackets.

The simplification is as follows :

[tex]T\\\\=(\cos \theta-\cos\theta)^2+(\cos \theta+\cos \theta)^2\\\\=0^2+(2\cos\theta)^2\\\\=0+4\cos^2\theta\\\\=4\cos^2\theta.[/tex]

Thus, the required simplified form is [tex]4\cos^2\theta.[/tex]

since they both end with 5 divide each number by 5

4415 = 883

22245/5 = 4449

there is no number that can go into 883 evenly

 so the lowest term

 would be 883/4449

The correct ratio in lowest terms is [tex]\(\frac{883}{4449}\)[/tex].

To find the ratio in lowest terms, we first write the ratio of the two given lengths:

[tex]\[ \frac{4415 \text{ feet}}{22245 \text{ feet}} \][/tex]

Next, we divide both the numerator and the denominator by their greatest common divisor (GCD) to simplify the ratio. The GCD of 4415 and 22245 can be found by using the Euclidean algorithm or by inspection.

We can start by dividing both numbers by 5:

[tex]\[ \frac{4415 \div 5}{22245 \div 5} = \frac{883}{4449} \][/tex]

Now, we check if 883 and 4449 have any common divisors other than 1. Since 883 is a prime number and does not divide evenly into 4449, we have found the simplest form of the ratio.

Thus, the ratio of 4415 feet to 22245 feet in lowest terms is [tex]\(\frac{883}{4449}\)[/tex].

line QP =

11.5*(11.5 +24) = 11.5 * 35.5 = 408.25

SqRT(408.25) = 20.205

round answer to 20 units

Answer:  The required probability is 25%.

Step-by-step explanation:  Given that in an upcoming race, the top 3 finishers will be recognized with the same award and Ryan is one of 12 people entered in the race.

We are to find the probability that Ryan will be one of the top 3 racers, if all racers are equal in skills.

Let S denote the sample space of the experiment for selecting a racer and A denote the event of selecting the top 3 finishers.

Then, according to the given information, we have

n(S) = 12   and    n(A) = 3.

So, the probability of event A is given by

[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{3}{12}=\dfrac{1}{4}\times100\%=25\%.[/tex]

Thus, the required probability is 25%.

To use the standard deviation formula in a significance test, the sample must be random and the population standard deviation should typically be unknown, while approximation with a normal distribution requires a sufficiently large sample size and the success-failure condition for proportions. Choosing the correct distribution depends on whether the standard deviation is known and the sample size.

Conditions for Using the Standard Deviation Formula and Approximating with a Normal Distribution

For conducting a significance test using the standard deviation formula, certain conditions must be met:

To approximate the sample distribution with a normal distribution, particularly when conducting hypothesis testing:

The conditions for a hypothesis test often include:

Examples of Hypothesis Testing with Different Conditions

try it with a couple different numbers

 try 4:  1^2 +2^2 +3^2 +4^2 = 1 +4 +9 +16 =30

 formula: 4(4+1)(2*4+1)/6 = 4*5*9 = 180/6=30

 this one works

now try 5

1^2 + 2^2+3^2+4^2+5^2 = 55

formula: 5(5+1)(2*5+1)/6 = 5*6*11 = 330/6=55

I tried a larger number ( 14) as well and it worked

so you can say that this is true