9. Divide the polynomials using synthetic division.
(2y² + 10y + 17) ÷ (y + 3)

Answer: Susie is correct.

Step-by-step explanation:

Susie is correct, because the Pythagorean theorem does not work on this triangle. Since the Pythagorean theorem only works on right triangles, we can conclude that Susie is correct, and that this triangle is NOT a right triangle.

a²+b² = c²

a = 9

b = 12

c = 17

9² + 12² = 17²

==> 81 + 144 = 289

==> 225 = 289, This is not true

Therefore this triangle is not a right triangle.

Answer:

x1,y16 is the rate of change

Step-by-step explanatI subtracted 13-32 which gives me 16, then I added 16 to 32 to be sure and it gave me 48 so the change on the Y axis is going up by 16 and x axis is going up by 1

Answer: x = 9/10 - 7/10

Step-by-step explanation:

The adding property of equality should be used to satisfy the given equation.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

-15 + x/3 = 18

Add 15 on both sides of the equation

So, we have

45 + x = 18 × 3

x = 54 + 45

x = 99

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Answer:

Your answer is 416 + 13 [tex]\sqrt{5}[/tex].

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

m = k l^3    <=======given

when m  = 90 kg  and l = 20 cm

 90 = k (20^3)       shows k = .01125   kg/cm^3

sooooo :    m = .01125 l^3

        when m = 1700:

                  1700 = .01125 l^3

                      l = cubrt ( 1700/.01125) = 53.26 cm

The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

Now, According to the question:

The given sphere is of radius R.

Let h be the height and r be the radius of the cylinder inscribed in the sphere.

We know that:

Volume of cylinder

V = [tex]\pi R^2h[/tex]    .....(1)

In right Triangle OBA

[tex]AB^2 + OB^2 = OA^2[/tex]

[tex]R^2 + \frac{h^2}{4} = r^2[/tex]

So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]

Putting the value of [tex]R^2[/tex] in equation (1), We get

V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]

V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex]   ....(2)

dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)

For, Stationary point, dV/dh = 0

[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0

[tex](r^2 - \frac{3h}{4} )[/tex]   => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]

Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]

[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex]   = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0

Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]

Maximum volume is :

[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]

[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

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The probability that someone is in the right job and the test is then wrong is 0.195.

The probability that the employee is in the wrong job and the test predicts that he is in the right job is 0.105.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In

The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3.  Thus, the probability that someone is in the right job and the test is then wrong is:

= 0.65*0.3

= 0.195

The probability that someone is in the wrong job and the test is right is:

= 0.35 × 0.3

= 0.105.

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The graph of the equation y = (1/3)x + 2 is passing through points  

(3, 3) and ( -3, 1).

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A linear equation y = (1/3)x + 2.

Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.

When x = 3, y = 3 ⇒ (3, 3).

When x = - 3, y = 1 ⇒( -3, 1).

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The required probability is P(X≥3) =0.3234

The average number of winning tickets that the woman buys each month is 2.

The binomial probability distribution is a discrete type of probability distribution with two parameters, n, and p. The probability mass function of the distribution is used to get the required probability. The average value of the winning number is the expected value of the binomial distribution.

The probability mass function of the binomial distribution is defined as:

[tex]P(X=x)=\frac{n}{x} p^{x} (1-p)^{n-x} , x =0,1,2,3,....,n.[/tex]

Given that,

n = 20

p = 0.10

The required probability is P(X≥3)

P(X≥3) = 1-P(X<3)

P(X≥3)= 1-P(X=0)-P(X=1)-P(X=2)

P(X≥3)= 1- 0.1216- 0.270- 0.285

P(X≥3) = 0.3234

The mean of the distribution is defined as μ=n*p= 20*0.10= 2

The average number of winning tickets that the woman buys each month is 2.

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If 1+3+5+7+…+49 =625, then the value of 2+4+6+8+…+50 = 650.

What is arithmetic series?

A series of numbers called an arithmetic progression or sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Here, we have

Given:  1+3+5+7+…+49 =625

We have to find the value of 2+4+6+8+…+50.

Here, we calculate the sum of all even numbers and we get

2+4+6+8+…+50 = 650

Hence, if 1+3+5+7+…+49 =625, the value of 2+4+6+8+…+50 = 650.

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Answer:

y = - 0.4x -6

Step-by-step explanation:

The slope-intercept form of a line equation is

y = mx + b

where m is the slope and b the y-intercept where the line crosses the y axis.

From the figure it is clear that the line passes through (0, -6) and therefore the y-intercept is -6

To compute the slope, find another  convenient point on the line. Compute the ratio of change in y values(called rise) to the change in x values(called run). This will be the slope

We see that point (10, -10) has been identified on the graph.(Any of the 4 identified points will do, I just chose this)

So two points to consider are (0, -6) and (10, -10)

Change in y values = rise = -10 - (-6) = 1- + 6 = -4

Change in x values = run = 10 - 0 = 10

So slope m = -4/10 = -0.4

Equation of line is y = -0.4x -6

$10.12 will Cassie pay in all for the pair of binoculars after sales tax is included.

What is sales tax?

A sales tax is a fee that is paid to the government when specified products and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are often used to describe taxes on goods and services that consumers pay directly to a governing authority.

given data

we are told that the cost of binoculars is $155.75

and also the sales tax is 7%

Step two:

We want to first solve for the sales tax which is 7% of  $155.75

=7/100* 155.75

=0.070*155.75

=10.12

Cassie will pay a tax of $10.12

Also Cassie will pay a total amount of

= 155.75+10.12

=$165.87

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a) A discrete random variable is a variable that can take only a countable number of distinct values, such as 0, 1, 2, 3, 4, and so on.

b) Examples of discrete random variables are the number of children in a family, the number of people who go to the cinema on Friday nights, etc.

c) E(x) = 1/p

Discrete Random Variable:

A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.

Discrete random variables are used to quantify the results of random experiments. A discrete random variable takes on an infinite number of possible outcomes. In general, discrete random variables can be counted as 0, 1, 2, 3, 4, ...

Geometric Distribution :

The geometric variate is the variate that specifies the number of consecutive failures before the first success in Bernoulli trials. The probability of success of a Bernoulli trial is given by p and the probability of failure is 1 - p.

The Geometric Random Variable can be written as X ~ G(p).

The probability mass function is P(X = x) = (1  - p)ˣ⁻¹ p

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The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.

As per the given data,

we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.

We know that,

Probability(Event) =Number of Favorable Outcomes/Total number of

                                Outcomes = x/n.    

Total number of Outcomes is 52 (given)

So,  we will calculate Number of Favorable Outcomes as follows:

The total no. of King in deck of card is 4

The total no. of queen in deck of card is 4.

The total no. of ace in  deck of card is 4.

The total no. of jack in deck of card is 4.

Therefore, the number of favorable outcomes is 4+4+4+4= 16

Now, putting values in the above stated formula of probability, we get:

Probability= 16/52=4/13

Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.

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Answer:

0.25 − 3

=0.25 + −3

= −2.75

( a number line to help to)

Step-by-step explanation:

Answer: -433.15

Step-by-step explanation:

he's id debt and has to pay off the 433.15 later on.

Answer:

The McQuires' account is currently overdrawn by $483.15.

Step-by-step explanation:

If the McQuires' account balance was $750 on Friday and they wrote a check for $1,183.15 on Saturday, then the balance would be 750 - 1,183.15 = -$433.15 after the check cleared. Since the bank charges a $50 overdraft fee, the final balance in the McQuires' account would be -$433.15 - $50 = -$483.15. The McQuires' account is currently overdrawn by $483.15.

A. The top cycle in this case is a -> b -> c -> a.

B. The agenda that wins the candidate is:

First vote:

a vs b -> a wins

Second voice:

versus. c -> a wins

The agenda that Candidate B wins is:

First vote:

b vs c -> b wins

Second Voice:

b vs a -> b wins

The agenda that Candidate C wins is:

First vote:

c vs a -> c wins

Second Voice:

c vs b -> c wins

C. Using the Borda count system, the candidates' scores are as follows:

a:

18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)

b:

18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)

c:

18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)

d:

12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)

e:

12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)

f:

12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)

g:

6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)

Therefore, candidates a, b, and c tie for first place with 18 points each.

D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.

E. The candidate with the worst score in the Borda count is  g of 6 points.

F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:

a:

15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)

b:

15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)

c:

15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)

Day:

10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)

e:

10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)

f:

10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)

In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.

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The price of a ticket to the homecoming dance to maximize the council's profit is 4830.

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Answer:

$2 each ticket

Step-by-step explanation:

I don't really know how it's 2, but it's in the vertex of the graph. I just got my test back which the answer was 2. I'm sorry if you expected reasoning but I only got an answer. You can make a table for the equation and then see that 2 results in the highest profit though. 2 being substituted for t equates to the greatest profit.

Answer:

70

Step-by-step explanation:

The answers to find are 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30

When two triangles having congruent corresponding angles and the corresponding sides are in equal ratio, then the triangles are said to be similar triangles.

Given are the similar triangles,

1) Δ HJG ~ Δ CAB

Scale factor = 3:1

2) Δ NPM ~ Δ ABC

Scale factor = 1:2

3) KJML ~ CDAB

Scale factor = 1:2

4) 40/x = 20/5

x = 10

5) 18/x = 21/7

x = 6

6) 6/3 = x/15

x = 30

Hence, the answers are: 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30

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The probability of drawing 2 marbles of different colors would be 0.317.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:

Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81

Total number of ways to draw 2 marbles: 16 (4 marbles of each color)

Probability of drawing 2 marbles of different colors: 81/256 = 0.317

Hence, the probability of drawing 2 marbles of different colors would be 0.317.

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The probability of drawing 2 marbles of different colors would be 0.317.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:

Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81

Total number of ways to draw 2 marbles: 16 (4 marbles of each color)

Probability of drawing 2 marbles of different colors: 81/256 = 0.317

Hence, the probability of drawing 2 marbles of different colors would be 0.317.

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a) The event E, that the sum of the numbers showing face up is equal to 6, can be written as the set:

E = {11, 15, 24, 33, 42, 51}

b) The probability of E is 6/36 = 1/6.

c) The event F, that the sum of the numbers showing face up is at most 4, can be written as the set:

F = {11, 15, 22, 31, 33, 42, 44, 51}

d) The probability of F is 2/9.

Probability is a measure of the likelihood of an event occurring in a statistical experiment. It is a number between 0 and 1, where 0 indicates that the event will never happen and 1 indicates that the event will always happen. Probability can be used to make predictions about the outcome of statistical experiments, and it is a useful tool in many fields, including economics, finance, and science. It is also used in gambling and games of chance to determine the odds of winning.

The probability of event E is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 6 outcomes in the event E and 36 outcomes in the sample space.

So, the probability of E is 6/36 = 1/6.

The probability of event F is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 8 outcomes in the event F and 36 outcomes in the sample space.

So, the probability of F is 8/36 = 2/9.

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It takes about 120 years for the graph to reach 100 million barrels per day whereas it takes 50 years to go from 100 million to 200 million.

As per the question the left axis indicates the amount of oil in the earth in trillions of barrels.

The right axis indicates the global consumption rate of oil in millions of barrels per day.

To the left of the red vertical line are model results that approximate reality whereas to the right are model-based predictions of the future.

The bottom axis is time in years.

The graph attached at the end of the solution.

Let the number of years of transition from using no oil to consuming 100 million barrels per day be a.

Let the number of years of transition from using 100 million to 200 million barrels per day be b.

From the given graph, we can see that initial consumption rate is low, and it takes 120 years for the graph to reach 100 million barrels.

But it takes 50 years to go from 100 million to 200 million.

This is known as exponential growth.

Therefore, the value of a is 120 and the value of b is 50.

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Answer:

---------------------------

Given:

Find the missing sides:

Perimeter is:

Answer:

add one black and one white marble

Step-by-step explanation:

you have to make bag b equivalent to a 2:3 ratio.

add 1 to 5 to make it divisible by 2

divide 6 by 2

=3

multiply 3 by 3 to get a 2:3 ratio

=9

subtract initial marbles

9-8=1

The given triangles are congruent to each other by the rule of (AAS) Angle Angle side.

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the given figure in the question,

There are two given triangles in the question,

Δ ABC and Δ MNO

As we can see that,

∠ C = ∠ M

∠ B = ∠ N and,

The side, AC = OM

So, Δ ABC ≅ Δ MNO

So, by using AAS (Angle Angle Side) rule, triangle ABC and triangle MNO are congruent to each other.

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Answer: 0.06

Step-by-step explanation:

The length of the building on the scale drawing is found as 16 centimeters.

For the given data in the question-

Dimensions of the building;

Dimensions of the drawing of the building;

Thus, taking ratios of Height to length

125/80 = 25/x

On simplification;

x = 80 x 25 / 125

x = 16

Thus, the length of building on the scale drawing is found as 16 centimeters.

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