Choose the best method for solving and solve. Show your work.
y=-2x+17
y=8-x

The number of ways of obtaining exactly one Democrat is 504

We are choosing 6 committee members, and exactly 1 of them must be a Democrat, which leaves 5 members to be selected from the Republicans. The number of ways to select 5 Republicans from 9 Republicans is 9 choose 5, which is 9! / (5! * (9-5)!).

Therefore, the total number of ways to form a committee with exactly 1 Democrat and 5 Republicans is 4 * (9 choose 5) = 4 * 126 = 504. or

There are a total of 13 members (4 Democrats and 9 Republicans), so the number of combinations that can be chosen is 13C6, or 1716. Since we are looking for a committee with exactly one Democrat, we need to subtract the total number of combinations with no Democrats (9C6, or 84) from the total number of combinations, giving us 1716-84 = 504 ways of obtaining exactly one Democrat.

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Your question is incomplete but probably the full question was:

A committee of six Congressmen will be selected from a group of four Democrats and nine Republicans. What is the number of ways of obtaining exactly one Democrat?

The car's value will exceed $10,000 during the interval of 6.97 years to  12.97 years.

To find the interval during which the car's value exceeds $10,000, we can use the following formula to calculate the value of the car after n years:

Value = $20,000 × [tex](1 - 0.15)^n[/tex]

We want to find the number of years, n, such that Value > $10,000. Rearranging the equation, we get:

n = (log(Value / $20,000)) / (log(1 - 0.15))

Substituting Value = $10,000, we find that n = approximately 6.97 years.

So, the car's value will exceed $10,000 from approximately 6.97 years after it was purchased until about 12.97 years after it was purchased.

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Answer:

Step-by-step explanation:

If Ben has 7 hours of lessons with Off Track Biking, we can find the total cost (C) using the formula:

C = 40h + 100

where h is the number of hours of lessons. Substituting h = 7, we get:

C = 40(7) + 100

C = 280 + 100

C = 380

Therefore, Ben pays $380 in total for his 7 hours of lessons with Off Track Biking.

Answer:

(2) whole numbers

Step-by-step explanation:

Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.

Step-by-step explanation:

let's say x stands for years.

FFR(x) is a function that calculates the number of fast food restaurant after x years.

FFR(x) = 2x + 13

they have 13 fast food restaurants right now (x = 0).

in 4 years (x = 4) they think they will have 21. that is 8 more than now. that means 2 more per year (2×4 = 8). therefore the factor 2 for every year (x).

FFR(4) = 2×4 + 13 = 8 + 13 = 21

The table represents the exponential function as f(x) = a(b)^3

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

Here we have the table:

Year       number of new college programs

2005     3

2006     22

2007     27

2008     66

2009     100

Few things that are useful to identify this as an exponential equation are:

f(x) = a(b)^3

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The perimeter of the rectangle is (23.5y + 1) feet.

The perimeter of the rectangle formula:

The perimeter = the width + the length + the width + the length

The perimeter = 2 × (the width + the length)

The perimeter = 2 × ((4.25y - 7.5) + (7.5y + 8))

The perimeter = 2 × ((4.25y + 7.5y) + (- 7.5 + 8)

The perimeter = 2 × (11.75y + 0.5)

The perimeter = 23.5y + 1

So, the perimeter of the rectangle is (23.5y + 1) feet.

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Based on the information, it can be inferred that the correct fraction is 8/8 - 3/8 (option B).

To select the correct fraction we must perform the following procedure:

Analyze the fraction that we have as reference. Once we know its elements (numerator and denominator) we can identify any fracture that is related to it.

We analyze the options and identify the one that is related to the reference fraction. In this case the correct fraction would be 8/8 - 3/8 because we leave the same denominator and do the subtraction with the numerators.

So it would be 8 - 3 = 5. So the correct fraction is option B.

Note: This question is incomplete. Here is the complete information:

Question: Which expression has a value of 8/8 - 3/8?

Options:

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The initial value is 20000 and it is a growth function

The rate is 14%

From the question, we have the following parameters that can be used in our computation:

v(t) = 20000(1.14)^t

A function represented as

v(t) =ab^t has teh following features

Initial value = a

Growth/Decay factor = b

This means that

Initial value = 20000

Also, we have

Growth factor = 1.14

This means that

Percentage rate = 1.14 - 1

Percentage rate = .14

So, we have

Percentage rate = 14%

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Answer:

see below

Step-by-step explanation:

the figure shows that GF = FH

so 5x+26 = ∠H

because sum of all angles in a triangle =180 (memorize this)

so then you have 2*(5x+26) + 3x+37 =180

solve for x

10x + 52 +3x +37 =180

13x = 91

x=7

so 5x+26 = 35+26 = 61

3x+37 =21+37 =58

The fence surrounds a square yard with an area of 64 square meters. We first have to find length of fence and then multiply it by itself.

Given that it took 48 square meters of lumber to build the fence, and the fence is 1.5 meters tall, we can calculate the area of the yard inside the fence. To do this, we need to determine the total length of the fence. If we assume that the fence is built around a square yard, then the length of each side of the yard will be equal to the total length of the fence divided by 4.

Let's call the length of each side of the yard x. Then, the area of the yard inside the fence is x * x, or x^2. The total length of the fence is 4 * x. Since the fence is 1.5 meters tall, the total area of the lumber used to build the fence is 4 * x * 1.5, or 6x. This is equal to 48 square meters, so we have the equation:

6x = 48.

Solving for x,

x = 8.

Therefore, each side of the yard is 8 meters long.

Area of the yard inside the fence = 8 * 8 = 64 square meters.

This means that the fence surrounds a square yard with an area of 64 square meters.

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Answer:

$79.82 (to 2 d.p.)

Step-by-step explanation:

100%=$74.95

1%=$74.95÷100

=$0.7495

100%+6.5%=106.5%

106.5%=$0.7495×106.5

=$79.82 (to 2 d.p.)

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line that passes through the point (-1, 3) and has a slope of -3, we can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

Substituting the given values, we get: y - 3 = -3(x - (-1))

Expanding the right side, we get: y - 3 = -3x + 3

Adding 3 to both sides, we get: y = -3x + 6

So the equation of the line that passes through the point (-1, 3) and has a slope of -3 is y = -3x + 6.

Hope this helps,

- Jeron :- )

Answer: y=-3x+6

Step-by-step explanation:

The equation for slope intercept form is y=mx+b, and since you are given your y and x values from the point (-1, 3), you can plug those values into it. You are also given your slope of -3, and since m is your slope value, you would plug the -3 in as your m.

After you plug in your given values from the problem, you should should get 3 = -1 (3) + b.

Then, you isolate the b. Multiply the -1 and 3 to get -3.

3 = -1 (3) + b

3 = -3 + b

Next, add the 3 to both sides of the equation, and you should be left with b=6.

3 = -3 + b

+3  +3

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

6 =  0 + b

6 = b

Finally, you re-write the slope intercept equation with the y-intercept (b value) you just found along with the slope of -3 given by the problem to get y=-3+6.

The correct order for the exponent expression is,

A-3, B-1, C-4, and D-2.

The formula for an exponential function is f (x) = aˣ, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given functions to match,

for the functions using property,

aⁿ.aᵇ = aⁿ⁺ᵇ

A; x¹⁸.x¹⁴

x¹⁸.x¹⁴ = x¹⁸⁺¹⁴ = x³²

B: x⁸.x⁵ = x⁸⁺⁵

x⁸.x⁵ = x¹³

C: x³⁵.x⁴⁰  = x³⁵⁺⁴⁰

x³⁵.x⁴⁰  = x⁷⁵

D: x⁴⁵.x² = x⁴⁵⁺²

x⁴⁵.x² = x⁴⁷

Hence correct order is, A-3, B-1, C-4, and D-2.

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On solving the provided question, we can say that the speed of the boat in still water is 11 miles per hour, and equation  the speed of the current is 9 miles per hour.

A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.

distance = rate × time

to set up two equations using the given information:

Equation 1: 140 = (b + c) × 7 (downstream trip)

Equation 2: 140 = (b - c) × 70 (upstream trip)

b + c = 20 (dividing both sides by 7)

b - c = 2 (dividing both sides by 70)

Now we have two equations with two variables. We can solve for "b" and "c" by adding the two equations together:

[tex](b + c) + (b - c) = 20 + 2\\2b = 22\\b = 11\\[/tex]

So the speed of the boat in still water is 11 miles per hour.

We can then use either Equation 1 or Equation 2 to solve for the speed of the current. Let's use Equation 1:

[tex]140 = (11 + c) × 7\\20 = 11 + c\\c = 9[/tex]

So the speed of the current is 9 miles per hour.

Therefore, the speed of the boat in still water is 11 miles per hour, and the speed of the current is 9 miles per hour.

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The variable x shows fish with common features.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.

Given:

G(x) =  -10x² + 100x +44

Now solving the Quadratic Equation we have

D = √(100)² - 4(-10)(44)

D = √10000 + 1760

D = √11760

D= 108.44

Now, x= -b ± D/2a

x= -100 ± 108.44 /2(-10)

x= -100 ± 108.44 / (-20)

x = -100 + 108.44 / (-20)  or x= -100- 108.44 / (-20)

x= -0.422 or x= 10.422

Here x represents the fish with common features.

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The equation of circle is,

⇒ x² + y² = 100

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

Here is a point (6, 8) on a circle centered (0,0) at.

Now, Distance between the point (6, 8) and (0, 0) is,

⇒ D = √(6 - 0)² + (8 - 0)²

⇒ D = √36 + 64

⇒ D = √100

⇒ D = 10

We know that;

Distance between the point (6, 8) and (0, 0) is the radius of circle.

And, The equation of circle is,

⇒ (x - a)² + (y - b)² = r²

Where, (a, b) is center of circle and r is radius of circle.

Here, Center of circle = (0, 0)

And, Radius of circle = 10

So, We get;

The equation of circle is,

⇒ (x - a)² + (y - b)² = r²

⇒ (x - 0)² + (y - 0)² = 10²

⇒ x² + y² = 100

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Answer:

Your answer is: 6 wpm

Step-by-step explanation:

If Tyler types twice as fast as Kyla, you multiply the amount of wpm Kyla writes by 2. 3 multiplied by 2 equals 6. Therefore, Tyler writes 6 wpm.

The area of the combined figure is  98.64 sq cm and the perimeter of the combined figure is 91.88 cm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

What are the area and perimeter of a rectangle?

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know, The area of a triangle is (1/2)×base ×height and the area of the semicircle is (1/2)πr².

Also, the perimeter of a triangle is the sum of the lengths of all the sides and the perimeter of a semicircle is πr.

From the given figure The right angle triangle is an isosceles therefore, The length of the side BC is also 12 units.

Hence the area is = (1/2)×12×12 = 72 sq cm.

And The area of the semicircle is,

(1/2)×π×(√12² + 12²) sq cm.

= (1/2)×3.14×√(288) sq cm.

= 26.64 sq cm.

Therefore, The total area is (72 + 26.64) sq cm.

= 98.64 sq cm.

And the perimeter is,

= (12 + 12 + 16.97) + (3.14×16.97) cm.

= 91.88 cm.

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Answer:

approximately 33.2%

Step-by-step explanation:

Find Zachary's commission by subtracting his basic salary from total monthly earnings.

Commission = 4236 - 700

                     =  $ 3536

[tex]\sf rate \ of \ commission = \dfrac{commission}{total \ sales}*100[/tex]

                             [tex]\sf = \dfrac{3536}{10654}*100\\\\ = 33.19 \%\\ = 33.2 \%[/tex]

5 persons are to be selected to form a committee so that at least 3 men are there on the committee, in 3192 ways the committee can be formed.

Combinations are decisions that are made by choosing some or all of a group of objects, regardless of how they are arranged. the variety of n distinct combinations, each taken r at a time,

We may have four males and one lady or three men and two women (5 men only).

∴ Required number of ways = (⁸C₃ x ⁷C₂) + (⁸C₄ x ⁷C₁) + ⁸C₅

= [tex]\frac{8*7*6}{3*2*1} *\frac{7*6}{2*1} + \frac{8*7*6*5*4}{4*3*2} *\frac{7}{1} + \frac{8*7*6}{3*2}[/tex]

= 1176 + 1960 + 56

= 3192

Therefore, at least 3 men are there on the committee can be formed 3192 times.

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Answer:

-4050

Step-by-step explanation:

you have to do inverse operation

so divide by 10 and times by 100

you can test it out by taking 10 percent of -4050

by dividing it by 100 and times by 10.

the answer comes out as -405

When multiplying fractions, multiply the numerator (top number), then the denominator (bottom number), and finally reduce to the lowest term if necessary.

Fractions are subsets of wholes. They are made up of a numerator (the number on top) and a denominator (the number on the bottom). The numerator represents the number of parts, while the denominator represents the total number of available parts.

To multiply two fractions, follow these three simple steps:

Step 1: Multiply the numerators of each fraction by themselves (the numbers on top). The answer's numerator is the result.

Step 2: Add the denominators of each fraction together (the numbers on the bottom). The answer's denominator is the result.

Step 3: Simplify or reduce your response.

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Using a system of equations and assuming neither pizza nor cake has changed in price, the cost of a pizza in dollars is $10.56.

A system of equations is two or more equations solved at the same time or concurrently.

A system of equations is also called simultaneous equations.

                  Pizzas   Cakes    Total Cost

Last week      12          6             $186

Today           29        24            $554

Let the cost per pizza = x

Let the cost per cake = y

12x + 6y = 186 ... Equation 1

29x + 24y = 554 ... Equation 2

Multiply Equation 1 by 4:

48x + 24y = 744 ... Equation 3:

Subtract Equation 2 from Equation 3:

48x + 24y = 744

-

29x + 24y = 554

18x = 190

x = 10.56

= $10.56

Substitute x = $10.56 in Equation 1:

12x + 6y = 186

12(10.56) + 6y = 186

126.72 + 6y = 186

6y = 59.28

y = 9.88

= $9.88

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Answer:

i wish i knew but try just posting the pictures on the math page and boom

Answer: it should just be (x, -y)

Step-by-step explanation:

Answer:

62 degrees

Step-by-step explanation:

To find the answer simply add both measures of angles 1 and 2 (29 + 33) to get 62 degrees.

To select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys , there are 1260 ways.

To find the number of ways to select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys, you can use the formula for combinations:

C(n, k) = n! / (k! * (n - k)!)

where n is the total number of items (9 girls and 5 boys), k is the number of items to be selected (3 boys and 4 girls), and ! represents the factorial function.

So, the number of ways to select 3 boys out of 5 boys is:

C(5, 3) = 5! / (3! * (5 - 3)!) = 5! / (3! * 2!) = 10

And the number of ways to select 4 girls out of 9 girls is:

C(9, 4) = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!) = 126

Finally, the number of ways to select a team of 7 members consisting of 3 boys and 4 girls is:

C(14, 7) = 10 * 126 = 1260

So, there are 1260 ways to select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys.

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This system of equations has the ordered pair (4, -6) as its only solution, as the two lines intersect only at that point.

What is the system of equations?

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

To create a system of equations that has one solution, we can write a second equation that intersects with the first equation in exactly one point.

One way to do this is to solve the first equation for y, then substitute the expression for y into a second equation. For example:

3x + y = 6

y = -3x + 6

This system of equations has one solution, as the two lines intersect at exactly one point.

To create a system of equations that has an infinite number of solutions, we can write a second equation that is identical to the first equation:=

3x + y = 6

3x + y = 6

This system of equations has an infinite number of solutions, as the two lines are coincident and overlap exactly.

To create a system of equations that has no solution, we can write a second equation that is parallel to the first equation:

3x + y = 6

3x + y = 8

This system of equations has no solution, as the two lines are parallel and do not intersect.

To create a system of equations that has (4, -6) as its only solution, we can write a second equation that passes through the point (4, -6):

3x + y = 6

y = -3x - 6 + 12

y = -3x + 6

Hence, This system of equations has the ordered pair (4, -6) as its only solution, as the two lines intersect only at that point.

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The unit of analysis that supposed to use when researcher describes the age, race, and gender distributions for people who are charged with shoplifting is called individuals.

The entity that frames what is being investigated in a study, or the entity being studied as a whole is known as the unit of analysis. At the macro level of social science study, the state is the most frequently used analytical unit that is regarded as a society. Groups, organizations, and institutions are frequent observational units at the meso level, while individuals are the unit of observation at the micro level.

The individual unit of analysis could be either a human or an animal. A group might be made up of a single person or a number of people who communicate with one another. For instance, if we are interested in examining people's shopping behaviors, their learning outcomes, or their views about new technology, then the individual is the unit of analysis that we should use.

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