find the equation of the line using the point-slope formula. write the final equation using the slope-intercept form. (1,2) with a slope of -5/6

Answer: true

Step-by-step explanation:

6:8 = 12:16

12:16 less than 14:16

Answer:

As per the given information, Paul's profit from selling b bottles of water is given by the formula:

P(b) = 1.05b - 279

Here, b represents the number of bottles sold, and P(b) represents the profit made by Paul in dollars.

We can find the profit made by Paul by substituting the given value of b in the above equation. For example, if Paul sells 100 bottles of water, then his profit can be calculated as follows:

P(100) = 1.05(100) - 279

= 105 - 279

= -174

So, if Paul sells 100 bottles of water, he will make a profit of $174.

Note that the profit is negative in the above example, which means that Paul will incur a loss if he sells only 100 bottles of water. To make a profit, he needs to sell more than 265 bottles of water. We can find this by setting P(b) equal to zero and solving for b as follows:

P(b) = 1.05b - 279 = 0

1.05b = 279

b = 265.71

Therefore, Paul needs to sell more than 265 bottles of water to make a profit.

Paul's profit from selling bottled water is described by the formula P(b)=1.05b-279. This suggests he makes $1.05 per bottle minus an initial cost of $279. To break even, Paul must sell approximately 266 bottles.

The question involves understanding of linear functions in the context of a real-world problem. Paul is planning to sell bottled water at the local carnival. His profit function, P(b), represented by the formula P(b)=1.05b-279, describes how his profit changes based on the number of bottles, b, he sells. This formula suggests that for every bottle Paul sells, he makes a profit of $1.05 with the subtraction of $279, which probably represents his initial costs. To break even, Paul has to sell enough water such that his profit, P(b), is zero. Solving the equation P(b)=0 gives b=279/1.05. This means Paul needs to sell approximately 266 bottles of water to break even. Any sales beyond this would generate profit.

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Answer:

Step-by-step explanation:

a, YES,  x is a solution as 4 + 2 = 6.

b. looks like there's a missing symbol here.

When 1. 384 is divided by 0. 4, the quotient would be 3. 46.

One way to divide 1. 384 by 0. 4 is to use the fact that division is the same as multiplying by the reciprocal of the divisor. The reciprocal of 0. 4 is 1 / 0. 4 or 2. 5. Therefore, we can rewrite the division as:

1. 384 / 0. 4 = 1. 384 x 2.5

We can then use multiplication to get the result:

1. 384 × 2. 5 = 3. 46

Therefore, 1. 384 divided by 0. 4 equals 3. 46.

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Answer:

To find the 9th term of a geometric sequence, we can use the formula:

an = a1 * r^(n-1)

where:

an = the nth term of the sequence

a1 = the first term of the sequence

r = the common ratio of the sequence

n = the term number we want to find

In this case, we are given that the common ratio is 2/3, the first term is 6, and we want to find the 9th term. So we can plug in those values and get:

a9 = 6 * (2/3)^(9-1)

Simplifying the exponent, we get:

a9 = 6 * (2/3)^8

Using a calculator, we can evaluate the exponent:

a9 = 6 * 0.015625

Multiplying, we get:

a9 = 0.09375

Therefore, the 9th term of the geometric sequence is 0.09375.

Step-by-step explanation:

here's a step-by-step explanation:

We are given the first term of the geometric sequence, a1 = 6, and the common ratio, r = 2/3. We need to find the 9th term, which we can do using the formula:

an = a1 * r^(n-1)

where n is the term number we want to find.

Step 1: Substitute the given values into the formula

a9 = 6 * (2/3)^(9-1)

Step 2: Simplify the exponent

a9 = 6 * (2/3)^8

The exponent 9-1 simplifies to 8.

Step 3: Evaluate the exponent

a9 = 6 * 0.015625

We can use a calculator to evaluate (2/3)^8, which is 0.015625.

Step 4: Multiply to find the 9th term

a9 = 0.09375

Multiplying 6 by 0.015625 gives us the 9th term of the geometric sequence, which is 0.09375.

Therefore, the 9th term of the geometric sequence whose common ratio is 2/3 and whose first term is 6 is 0.09375.

Answer:

To solve the problem, we need to determine the number of ways to choose 2 girls out of 8 and 2 boys out of 4, and then multiply those numbers together to get the total number of arrangements.

The number of ways to choose 2 girls out of 8 is given by the combination formula:

C(8,2) = 8! / (2! * 6!) = 28

Similarly, the number of ways to choose 2 boys out of 4 is:

C(4,2) = 4! / (2! * 2!) = 6

Therefore, the total number of different arrangements of 2 girls and 2 boys that can be chosen from the 12 students is:

28 x 6 = 168

So there are 168 different arrangements possible.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the number of different arrangements, we can use combinations.

The number of ways to choose 2 girls out of 8 is C(8,2) = 28.

The number of ways to choose 2 boys out of 4 is C(4,2) = 6.

So, the total number of ways to choose 2 girls and 2 boys from 8 girls and 4 boys is:

C(8,2) * C(4,2) = 28 * 6 = 168

Therefore, there are 168 different arrangements for the piano teacher to take 4 of her 12 students to the concert.

The data modelling function is Price required to recoup printing expenses is equal to 0.1 * (numbers of yearbooks sold) + 45.

A yearbook is a collection of images and text that is issued by an organisation once a year to remember and highlight the happenings at a particular school during the previous academic year. Yearbooks were used in elementary, middle, high, and college and university settings throughout the 20th century.

Using the information in the table,

[tex]n = 5[/tex]

Σ[tex]x = 1175[/tex]

Σ[tex]y = 145[/tex]

Σ[tex](xy) = 41000[/tex]

Σ[tex](x^2) = 287500[/tex]

When these values are inserted into the formula,

[tex]m = (541000 - 1175145) / (5*287500 - 1175^2)[/tex]

[tex]= -0.1[/tex]

Therefore, the slope of the linear function is [tex]-0.1[/tex].

[tex]b = y - mx[/tex]

where we can use any of the data points. Let's use[tex](250, 20)[/tex]

[tex]b = 20 - (-0.1*250)[/tex]

[tex]= 45[/tex]

Therefore, the y-intercept of the linear function is [tex]45[/tex].

[tex]y = -0.1x + 45[/tex]

Therefore,

Price needed to cover the costs of printing [tex]= -0.1*[/tex](number of yearbooks sold) [tex]+ 45[/tex].

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[tex]4x^2+20x-24 = 4x^2-4x+24x-24 = 4x(x-1)+24(x-1) = (4x + 24)(x-1)\\[/tex]

[tex]= 4(x+6)(x-1)[/tex]

Answer:

Step-by-step explanation:1.) Each person receives 5/6 of a cake.

To see why, we can think of dividing the 5 cakes into 6 equal parts. This would give us 30 equal parts, and each person would receive 5 of these parts. So, the fraction of a cake each person receives is:

5/30 = 1/6

2.) Each person receives 3/8 of a pizza.

To see why, we can think of dividing the 3 pizzas into 8 equal parts. This would give us 24 equal parts, and each person would receive 3 of these parts. So, the fraction of a pizza each person receives is:

3/24 = 1/8

3.) Each person receives 1/2 of a granola bar.

To see why, we can think of dividing the 4 granola bars into 8 equal parts. This would give us 32 equal parts, and each person would receive 4 of these parts. So, the fraction of a granola bar each person receives is:

4/32 = 1/8

1/8 ÷ 2 = 1/16

So, each person receives 1/2 of a granola bar, which is equal to 1/8 ÷ 2 = 1/16.

4.) Each pie has 2.4 pounds of blueberries.

To see why, we can divide the 12 pounds of blueberries by the 5 pies:

12 ÷ 5 = 2.4

So, each pie has 2.4 pounds of blueberries.

5.)

4 ÷ 5 = 4/5

5 ÷ 4 = 1 1/4

12 ÷ 30 = 2/5

30 ÷ 12 = 2 1/2

Answer: 1) 5/6

              2) 3/8

              3) 4/8 OR 1/2

              4) 12/5lb OR 2 2/5lb OR 2.4lb

              5) 4/5

                  5/4 OR 1 1/4

                  12/30 OR 2/5

                  30/12 OR 5/2 OR 2 1/2

Step-by-step explanation:

The average number of siblings for the group is 1.3.

We must compute the total number of siblings and divide it by the total number of children in the group to determine the average number of siblings for the group.

There are a total of: siblings in the bunch.

3 + 8 + 9 = 20 (1 sibling times 3 children) + (2 siblings times 4 children) + (3 siblings times 3 children)

The total number of kids in the group is: 5 + 3 + 4 + 3 = 15

As a result, the group as a whole has an average of:

20/15 = 1.33 (rounded to the nearest tenth) (rounded to the nearest tenth)

So, the group as a whole has 1.3 siblings on average.

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Answer:

3

Step-by-step explanation:

the coordinates are the answers for X and Y.

x+3y=20

n+3n=20

n=5

y=ax-10

5=5a-10

a=3

The Scotch Bonnet seashell is 3/4 inches shorter than the combined lengths of the two Alphabet Cone seashells.

What is length ?

Length is a physical quantity that describes the size or distance of an object in one dimension. It is typically measured in units such as meters, feet, inches, or centimeters, and can refer to the distance between two points or the size of an object in one direction. In geometry, length is a fundamental concept that is used to define other geometrical properties such as area, volume, and perimeter. In general, length can be defined as the extent of something along its longest dimension, and it is a crucial parameter in many fields, including physics, engineering, architecture, and mathematics.

According to the question:

The combined length of two Alphabet Cone seashells is:

1(3/4) inches + 1(3/4) inches = 3(1/2) inches

The length of the Scotch Bonnet seashell is:

2(1/8) inches

To find the difference in length, we can subtract the length of the Scotch Bonnet seashell from the combined length of the two Alphabet Cone seashells:

3(1/2) inches - 2(1/8) inches = 3(4/8) inches - 2(1/8) inches

Simplifying the expression, we get:

3(4/8) inches - 2(1/8) inches = 3(2/8) inches = 3/4 inches

Therefore, the Scotch Bonnet seashell is 3/4 inches shorter than the combined lengths of the two Alphabet Cone seashells.

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Answer: The answer is B!

Step-by-step explanation:

If you multiply 22.2 by 8.3, you get 84.36 (if you move the decimal point one space, otherwise you'd get 843.6.) Then if you estimate it, you would get 84.58.

Answer: To find the height of the ramp, we need to use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ramp, porch, and ground form a right triangle, with the height of the ramp being the missing side.

We know that the ramp begins 96 centimeters from the porch and is 100 centimeters long. Let's represent the height of the ramp with the variable "h". Then, we can write the Pythagorean theorem equation:

h^2 + 96^2 = 100^2

Simplifying this equation, we get:

h^2 + 9216 = 10000

Subtracting 9216 from both sides, we get:

h^2 = 784

Taking the square root of both sides, we get:

h = 28

Therefore, the height of the ramp is 28 centimeters.

Step-by-step explanation:

Answer: 5 Miles and 1,241 Yards and 2 Feet

Step-by-step explanation: There are 5,280 ft in a mile. To convert to miles, you can do 30,125/5,280. This will give you 5 miles with a remainder of 3,725 ft.

Next, we convert to yards. There are 3 yards in a foot. For this you can do 3,725/3. This will give you 1,241 yd. with a remainder of 2 feet.

Combine these and it will give you 5 miles and 1,241 yd. and 2 ft.

To check your work, you can do (5*5,280)+(3,725*3)+2=30,125.

Please reply back if you have any question.

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The volume of the Cylinder formed  approximately 16.37 cubic units.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two parallel circular bases, connected by a curved lateral surface. It is similar to a prism, but instead of having polygons as its bases, it has circles. The lateral surface of a cylinder is formed by the set of all straight lines connecting the points on the edge of one base to the corresponding points on the edge of the other base.

Now,

To find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x⁸about the y-axis, we can use the method of cylindrical shells.

First, we need to express the equation y=5+x⁸ in terms of x, so we can integrate with respect to x:

y = 5 + x⁸

y - 5 = x⁸

x = (y - 5)¹/⁸

Next, we need to determine the limits of integration. The region is bounded by x=0 and x=1, so we integrate from x=0 to x=1.

Volume of a cylindrical shell is

V = 2πrhΔx

In this case, the radius r is simply x, the height h is y, and Δx is dx. So, we have:

V = 2πxy dx

V = 2πx(5+x^8) dx

V = 10πx dx + 2πx⁸ dx

Integrating with respect to x from x=0 to x=1, we get:

V = [5π + 2π/10] - [0 + 0]

V = 5.2π

Therefore, the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x⁸ about the y-axis is approximately 16.37 cubic units.

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The mean of the data-set represented by the frequency table is given as follows:

d) 13.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

We have a frequency distribution, hence each observation is considered to be the midpoint of each interval, and thus the sum of the observations is given as follows:

5 x 4 + 10 x 7 + 15 x 9 + 20 x 5 = 325.

The number of observations is given as follows:

4 + 7 + 9 + 5 = 25.

Hence the mean is given as follows:

325/25 = 13.

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Answer:

x = 45

Step-by-step explanation:

since the lines are congruent, then the opposite angles will be the same.

2x+90=180

Hope this helps

Therefore , the solution of the given problem of volume comes out to be  1.5 centimetres is the appropriate height measurement option A.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two instances of cubic units are the numbers cm3 and in3. However, an object's bulk can be used to determine its dimensions. Typically, an object's weight is transformed into mass units like kilogrammes and kilos.

Here,

The technique used by the classmate made a mistake by rearranging the measurements in the formula. The right equation to use to determine a rectangle prism's volume is:

=> V = lwh

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

The colleague in this instance applied the formula:

=>  h = 1.5(1.2)(2.5)

which, rather than the height, is the method for calculating the volume.

We must rewrite the volume formula to determine the height:

=>  V = lwh

=>  h = V/lw

Now that we know the numbers to substitute, we can determine the height:

=>  h = 1.5(1.2)(2.5) / (1.2)(2.5)

=>  h = 1.5 cm

Consequently, 1.5 centimetres is the appropriate height measurement (option A).

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Answer:

[tex]y=-\frac{2}{3}x+2[/tex]

Step-by-step explanation:

The formula for equation of a line is [tex]y=mx+b[/tex] where m is the slope, b is the y-intercept, and (x,y) can represent any point on the line. We calculate the slope using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. We are subtracting the y-coordinates in the numerator and the x-coordinates in the denominator.

[tex]\frac{0-2}{3-0} = -\frac{2}{3}[/tex]

You can subtract the coordinates of your second point from your first point and you will get the same slope. Just be sure not to mix up the order.

Now that we have our slope, we can either pull the y-intercept off the graph; the line crosses the y-axis as y = 2, or we can solve our equation for the value of b.

We can pick any point on the line to solve for b. It is recommended to use one of the intercepts because either the x or y component will be zeroed out. I will use the point (0,2)

[tex]y = mx + b\\y = -\frac{2}{3}x +b\\2 = (-\frac{2}{3})(0) + b\\b = 2[/tex]

Now we have all the parts of our equation in slope-intercept form.

[tex]y = -\frac{2}{3}x +2[/tex]

A) the annual rate of change between 1991 and 2000 is -$3,000.

B)  the correct answer to part A in percentage form is -6.67%.
C) where n is the number of years from 2000 to 2003, which is 3, $8,450. approximately.

A) The total change in value between 1991 and 2000 is $45,000 - $12,000 = $33,000. The number of years between 1991 and 2000 is 9. Therefore, the annual rate of change is:

r = (final value - initial value) / (number of years)

r = ($12,000 - $45,000) / 9

r = -$3,000 per year

Thus, the annual rate of change between 1991 and 2000 is -$3,000.

B) To convert the rate of change to percentage form, we need to divide it by the initial value and multiply by 100:

r = (-$3,000 / $45,000) * 100%

r = -6.67%

Therefore, the correct answer to part A in percentage form is -6.67%.

C) If the value continues to drop by the same percentage, we can use the following formula to find the value in 2003:

value = initial value * (1 + r)^n

where n is the number of years from 2000 to 2003, which is 3. Plugging in the values, we get:

value = $12,000 * (1 - 0.0667)^3

value = $8,454.58

Rounding to the nearest $50, we get the value in 2003 to be $8,450.

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Answer:

Step-by-step explanation:

The equation would be

f(x) = (x - 1)^2 + 1

Answer:

1.49 minutes

Step-by-step explanation:

Let the number of minutes be x.

Deandre paid $17.43 for $7 to start  and 7 cents per minute.

Mathematically,

7x+7=17.43

7x= 17.43-7

7x = 10.43

∴ x = 10.43/7

x = 1.49 minutes.

Hope this helps! :)

The quotient gives (f/g)(4) = -16/3 and the value that is not in the domain is x = 1.

Here we know that:

f(x) = (x + 4)(x - 6)

g(x) = x - 1

And we want to find the quotient between these functions:

(f/g)(4)

So first let's find the values of the functions when x = 4.

f(4) = (4 + 4)*(4 - 6) = 8*-2 = -16

g(4) = 4 - 1 = 3

Then the quotient is:

(f/g)(4) = -16/3

Now, the values that are not in the domain of f/g are the values that make the denominator equal to zero, because we can't divide by zero.

g(x) = 0 = x - 1

         1  =x

The denominator is zero for x = 1, so that value is not in the domain.

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Answer:

Hmm.. not quite sure why you multiplied A with 10 yds. I am going to assume M=meters.

A.) You can convert to whatever units you like, but I am going to convert into meters.

0.89/yd * 0.9144yd/m = $0.97 > $0.94.. So.. A Lumber yard is selling the same rope for less expensive.

B.) You convert feet until you get to the correct units. like this....

550 ft * 1yd/3ft * .9144m/yd * $.97/m = $162.62

550 ft * 1yd/3ft * .9144m/yd * $.94/m = $157.58

taking the difference would be $5.03.

I believe for answer A, you forgot to convert...or converted differently. Hope this helps.

Step-by-step explanation:

Answer:

Since $0.973/m is greater than $0.94/m, the lumber yard sells the rope for a lower price

So Jim would save $6.19 if he purchased 650 ft of the less expensive rope before taxes.

Step-by-step explanation:

Answer:

7.111 per pound of seed.

Step-by-step explanation:

64/9 = 7.111

Step-by-step explanation:

The parent square root function is given by f(x) = √x. The function g(x) is obtained by applying the following transformations to the parent function:

Shift the graph 3 units to the left: f(x+3)

Shift the graph 4 units down: f(x+3)-4

Add a constant 3: f(x+3)-4+3 = f(x+3)-1

Take the square root: g(x) = √(f(x+3)-1) = √(√(x+3)-1)

Therefore, the graph of f is translated 3 units to the left and 1 unit down to obtain the graph of g. None of the given options accurately describe the transformation, so the correct answer is option E: None of the above.

Answer: 87

Step-by-step explanation:

(74+85+x)/3  = 82

3(82)=74+85+x

246 = 74+85 + x

246-74-85=x

x= 87