Phillip added 15 pencils to his collection. He then gave 30 pencils to a friend.

Write and then evaluate an expression that shows Phillip’s net gain or loss.

Ms. Summers will give each child 1/16 gallon of milk.

Beginning with a quarter gallon of milk, Ms. Summers. She consumes a quarter of a gallon of milk, leaving her with:

1/8 gallon divided by 2/8 gallon is equal to 1/8 gallon.

Mrs. Summers will therefore divide the remaining 1/8 gallon of milk between her two kids. She needs to divide it by 2 to distribute it equally amongst the two kids.

Hence, each kid will get:

(1/8 gallon x 2) yields 1/16 gallon

Ms. Summers will thus provide each youngster with 1/16 of a gallon of milk.

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The model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2

The Body Mass Index (BMI) of a person can be calculated using the formula:
BMI = (weight in pounds)/(height in inches)^2

In this case, the BMI varies directly as a person's weight in pounds and inversely as the square of the person's height in inches. This means that as the weight increases, the BMI increases and as the height increases, the BMI decreases.

To find a model for the BMI of a person, we can use the formula:
BMI = k(weight in pounds)/(height in inches)^2

Where k is a constant of proportionality. To find the value of k, we can use the given information that a 6ft 6in tall person has a BMI of 25.

First, we need to convert the height from feet and inches to inches. 6ft 6in is equivalent to 78 inches. Then, we can plug in the values into the formula and solve for k:

25 = k(weight in pounds)/(78 inches)^2
25(78 inches)^2 = k(weight in pounds)
152100 = k(weight in pounds)

Therefore, the model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2

This model can be used to calculate the BMI of a person given their weight in pounds and height in inches.

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The required side length of the variable "x" is 12.8 units for the given figure.

When a line parallel to one side of a triangle intersects the other two sides in distinct spots, the other two sides are separated in the same ratio.

As we can see that both are similar quadrilaterals,

According to Thales's Theorem,

5:8 = 8:x

So, 5/8 = 8/x

Apply the cross-multiplication, and we get

5x = 8 × 8

x = 64/5

Apply the division operation, and we get

x = 12.8

Thus, the required side length of the variable "x" is 12.8 units.

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Answer:

5

Step-by-step explanation:

The average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is 94.6.

The average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is calculated by taking the change in the y-value (h(10) - h(5)) and dividing it by the change in the x-value (10-5):

Average rate of change = (h(10)-h(5))/(10-5)

= (3(10)2+6(10)-7 - (3(5)2+6(5)-7))/(10-5)

= (745-272)/5

= 473/5

= 94.6

Therefore, the average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is 94.6.

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The simplified expression after doing this calculation is -1/3. To perform the addition or subtraction and simplify the given expression, we need to find a common denominator for the two fractions. The common denominator for x and 3 is 3x.

Multiply each fraction by the necessary factor to get the common denominator. For the first fraction, we multiply by 3/3, and for the second fraction, we multiply by x/x.

3/3 * (x/x) - x/x * (4/3) = (3x - 4x)/3x = (-x)/3x. Now, we can simplify the expression by canceling out the common factor of x in the numerator and denominator. (-x)/3x = -1/3

The simplified expression is -1/3.

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Answer:

Step-by-step explanation:

As before, I'll put slope-intercept first:

5. y = 1/4x + 1 ; y-2 = 1/4(x-4)

6. y = -1/2x + 2 ; y-1 = -1/2(x-2)

7. y = 1/3x + 1 ; y-2 = 1/3(x-3)

8. y = -x ; y-1 = 1(-x+1)

9. y = 2/3x -1 ; y-1 = 2/3(x-3)

Hope this helps!

The answer of the given question based on the sum of the two angles is ,the answer is  5x + 25° degrees.

The distributive property is fundamental property of arithmetic and algebra that allows us to  multiply single term or sum by factor. The property states that:

a×(b+c)=a×b+a×c

In words, this means that the when number or variable (a) is multiplied by  sum of two other numbers or variables (b + c), it is  same as  multiplying a by each term of  sum (b and c) and then adding two products. The distributive property can  be used in reverse to factor out common factor from  sum of terms.

The sum of these two angles is:

2x° + (3x + 25)°

= 2x° + 3x° + 25° (using the distributive property of multiplication)

= 5x° + 25°

Therefore, the sum of the two angles is 5x + 25° degrees.

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Answer:

n ≤ 6.5

Step-by-step explanation:

43.5 + n ≤ 50

43.5 + n - 43.5 ≤ 50 - 43.5

n ≤ 6.5

Rogelio has watched 23/20 hours of the movie.

What is a fraction?

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

Movie duration = 1 3/4 = 7/4

Duration of movie watched = 3/5

Duration watched = 7/4 - 3/5

Duration watched = 23/20

Duration watched = 1 3/20 (mixed fraction)

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The probability of rolling a sum of 5 when rolling a 6-sided die twice is 1/9.

According to the Law of Large Numbers, a fundamental tenet of probability theory, the average of the results of an experiment approaches the predicted value of the random variable being measured as the number of trials in the experiment rises. In other words, the Law of Big Numbers states that the observed results will be closer to the predicted outcomes the more times an experiment is conducted.

The total number of outcomes when a die is rolled two times is 36.

The sum of 5 is obtained for the following outcomes:

(1,4), (2,3), (3,2), and (4,1)

Thus,

P(sum of 5) = 4/36 = 1/9

Hence, the probability of rolling a sum of 5 when rolling a 6-sided die twice is 1/9.

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Answer: Your welcome!

Step-by-step explanation:

The slope of the line represents the amount of money that is donated each day, which is 25. The y-intercept represents the amount of money donated on the first day, which is 50.

6 hairless chimpanzees should the biologist expect to find in the troop.

What is the percentage?

A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

The sample number is 150.

Given that 3% of the chimpanzees are hairless, another sample indicates that 5% are hairless, and a third sample indicates that 4% are hairless.

The average percentage of chimpanzees of hairless is

(3% + 5% + 4%)/3

= 12%/3

= 4%

Now calculate 4% of 150:

4% of 150

= (4/100) × 150

= 6

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Answer:

Let's first find the volume of the original cuboidal box:

Volume = Length x Width x Height = 3 x 3 x 2 = 18 cubic units

We can then set up an equation to relate the volume of the original box to the volume of the new cuboid:

Volume of new cuboid = Volume of original box

Let's call the length and height of the new cuboid "x" (since we know that the length and height are the same). We know that the width of the new cuboid is 15 units. Therefore, we can write:

Volume of new cuboid = Length x Width x Height = x x 15 x x = 15x^2

Now we can set up the equation:

15x^2 = 18

Dividing both sides of the equation by 15 gives:

x^2 = 18/15

Simplifying the right side of the equation gives:

x^2 = 1.2

Taking the square root of both sides of the equation gives:

x ≈ 1.095

Therefore, the length and height of the new cuboid are approximately 1.095 units.

Answer:

The answer is -3 because it passes through (0,0) and (2,-6).

P is rational number from the given equation P=2(2x+5)+2x.

Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).

The given equation is P=2(2x+5)+2x.

Here, P=2(2x+5)+2x

P=4x+10+2x

P=6x+10

Given that, x=1.5, 3 and 1.2

Substitute, x=1.5 in P=6x+10, we get

P=6×1.5+10

P=9+10

P=19

So, 19 is rational number

Substitute, x=3 in P=6x+10, we get

P=6×3+10

P=18+10

P=28

So, 28 is rational number

Substitute, x=1.2 in P=6x+10, we get

P=6×1.2+10

P=7.2+10

P=17.2

So, 17.2 is rational number

Therefore, P is rational number from the given equation P=2(2x+5)+2x.

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The vertex of this function would be (-1, -8).

The question seems to be incomplete and there are some typos in it. However, I will try to provide a general answer based on the given information.

When finding the vertex of a function, you can use the formula -b/2a to find the x-coordinate of the vertex. Once you have the x-coordinate, you can plug it back into the original function to find the y-coordinate of the vertex.

For example, if the function is y = 2x^2 + 4x - 6, the formula for the x-coordinate of the vertex would be -4/(2*2) = -1. The y-coordinate of the vertex would be 2(-1)^2 + 4(-1) - 6 = -8.

So the vertex of this function would be (-1, -8).

Remember to Round all answers to 3 decimal places, as instructed in the question.

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The value of an investment with $1000 as principal amount compounding annually for 3 years with interest rate 7.5% is $1242.29

The interest rate is the amount that the lender charges the borrower and is the principal - a percentage of the loan amount. Loan interest rates are usually quoted on an annual basis known as the annual rate (APR). 

Solution according to the given information in the question:

Given, Principal = $1000

           Time = 3 years

           Interest rate = 7.5%

∴ Amount = P×(1 + r/100)³

                 = 1000×(1 + 7.5/100)³

                 = 1000×(1 + 0.075)³

                 = 1000×(1.075)³

                 = 1000 × 1.24

Amount   = $1242.29

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The linear function that models the data is S = 3.8x - 14.506 and  the circumference of a finger with a ring size of 6 is 5.4 cm.

a. To find a linear function S that models the data, we need to find the slope and y-intercept of the line that best fits the data. The slope can be found by using the formula:

m = (y2 - y1) / (x2 - x1)

Using the first two data points, we can find the slope:

m = (7 - 4) / (5.66 - 4.87)

m = 3 / 0.79

m = 3.8

To find the y-intercept, we can use the formula:

y = mx + b

Substituting one of the data points and the slope into the formula and solving for b:

4 = (3.8)(4.87) + b

b = 4 - (3.8)(4.87)

b = -14.506

So the linear function that models the data is:

S = 3.8x - 14.506

b. To find the circumference of a finger with a ring size of 6, we can substitute S = 6 into the linear function and solve for x:

6 = 3.8x - 14.506

3.8x = 20.506

x = 5.4 cm

So the circumference of a finger with a ring size of 6 is 5.4 cm.

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A store scanner has a red laser wavelength of 650 nm. While a green laser pointer has a wavelength of 502 μm. The ratio of green to red wavelengths is 0.77.

To find this ratio, we need to divide the wavelength of the green laser by the wavelength of the red laser:

502 μm / 650 nm = 0.77

Note that we need to convert the units of the green laser wavelength from micrometers (μm) to nanometers (nm) in order to divide it by the red laser wavelength, which is already in nanometers. To do this, we multiply the green laser wavelength by 1000:

502 μm * 1000 = 502000 nm

So the ratio of green to red wavelengths is 502000 nm / 650 nm = 0.77.

This ratio indicates that the green laser has a shorter wavelength than the red laser. Generally, shorter wavelengths correspond to higher energy and higher frequency light. In the case of lasers, this means that the green laser is capable of producing a more intense and focused beam of light than the red laser.

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The local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.

Using a graphing Utility, we can approximate the local maximum value and local minimum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6.

1. The local maximum value occurs at the highest point on the graph within the given interval of -6. By observing the graph, we can see that the local maximum value is y=2.2 and it occurs at x=-1.2.

2. The local minimum value occurs at the lowest point on the graph within the given interval of -6. By observing the graph, we can see that the local minimum value is y=-4.6 and it occurs at x=-4.8.

It is important to note that these values are approximations and may not be exact. The graphing Utility is a useful tool for visualizing the function and finding approximate values, but it is not always precise.

the local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.

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Answer:

Either x/9 or 0.75 per cookie

Step-by-step explanation:

Let the number of cookies in a box be x.

The cost of x=9$

Then, the cost of one cookie= x/9

alternatively:

Considering one box contains 12 cookies,

The cost of a box of cookies= 9$

Then, the cost of one cookie= 9/12=0.75

The time taken for Ben's ball to land after Andrew's ball is 2.5 seconds.

To calculate the time taken for the Ben's ball to land after Andrews ball is calculated as follows;

Since the value of parameter a is -5 for both balls, the height of each ball follows the equation:

h(t) = -5t² + vt + h0

where;

Let's assume that Andrew's ball is hit with an initial velocity of v1, and Ben's ball is hit with an initial velocity of v₂. We also know that Ben's ball reaches a maximum height 50% greater than Andrew's, which means that:

h_max2 = 1.5h_max1

At the maximum height, the velocity of the ball is zero, so we can find the time it takes for each ball to reach the maximum height by setting v = 0 in the equation for h(t):

t_max1 = v₁ / (2 x 5)

t_max2 = v₂ / (2 x 5)

Since Ben's ball reaches a maximum height that is 50% greater than Andrew's, we can write:

h_max2 = 1.5h_max1

-5(t_max2)² + v₂t_max2 + h0 = 1.5(-5(t_max1)² + v1 * t_max1 + h0)

Simplifying this equation, we get:

-5(t_max2)² + v₂t_max2 = -7.5(t_max1)² + 1.5v₁t_max1

We also know that Andrew's ball lands after 4 seconds, which means that h(4) = 0:

h(4) = -5(4)² + v1 * 4 = 0

-80 + 4v1 = 0

v1 = 80/4

v1 = 20 m/s

Solving these equations for t_max2 and v2, we get:

t_max1 = v1 / (2 x 5)

t_max1 = 20 / (2 x 5)  = 2 s

t_max2 = 1.5t_max1 = 3 s

v2 = 1.5v1 = 30 m/s

To find the time it takes for Ben's ball to land, we need to find the time t2 when h(t2) = 0.

We can use the equation for h(t) with v = v2, h0 = 0, and solve for t:

-5t² + v₂t = 0

-5t² + 30 = 0

5t² = 30

t² = 30/5

t² = 6

t = √6

t = 2.5 s

Therefore, Ben's ball lands approximately 2.5 seconds after Andrew's ball.

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The set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.

(a) The set W is closed under standard scalar multiplication in the plane. This is because for any scalar c and any vector u = (x,y) in W, the product of the components of cu = (cx,cy) is (cx)(cy) = c2(xy) = c2(0) = 0, so cu is also in W.

(b) The set W is not closed under standard vector addition in the plane. For example, the vectors u = (1,0) and v = (0,1) are both in W, but their sum u + v = (1,1) is not in W because the product of its components is 1(1) = 1, which does not satisfy the equation x⋅y = 0.

Since the set W is not closed under standard vector addition, it does not form a vector space. A set must be closed under both scalar multiplication and vector addition in order to be a vector space.

Geometrically, the set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.

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The midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).

To find the exact distance between the points (9.6,-19.7) and (6.6,-23.7), we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given values:

distance = sqrt((6.6 - 9.6)^2 + (-23.7 - (-19.7))^2)

Simplifying:

distance = sqrt((-3)^2 + (-4)^2)

distance = sqrt(9 + 16)

distance = sqrt(25)

distance = 5

Therefore, the exact distance between the points is 5.

To find the midpoint of the line segment whose endpoints are the given points, we can use the midpoint formula:

midpoint = ((x1 + x2)/2 , (y1 + y2)/2)

Substituting the given values:

midpoint = ((9.6 + 6.6)/2 , (-19.7 + (-23.7))/2)

Simplifying:

midpoint = (16.2/2 , -43.4/2)

midpoint = (8.1 , -21.7)

Therefore, the midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).

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Therefore , the solution of the given problem of coordinates comes out to be B' = (-2, 1)  and  C' = (4, 6) .

A coordinate system is a method that employs one or more values or coordinates to accurately locate points or even other mathematical objects on a space, such as Euclidean space. Coordinates, that are pairs of numbers, are used to locate a point or object on a double plane. The y and x vectors are two integers that specify where a point is situated on a two - dimensional plane. a group of numerals designating particular places. Usually, the number has two numbers.

Here,

By adding 1 to the x-coordinate and 3 to the y-coordinate, we can determine that position A is translated to point A'. As a result, we can determine the values of B' and C' using the same translation vector.

We increase the x-coordinate for position B by one

=> (-3 + 1 = -2) and

the y-coordinate by three

=> (-2 + 3 = 1). Consequently, B"s values are (-2, 1).

We increase the x-coordinate for position C by one

=> (3 + 1 = 4) and

the y-coordinate by three

=>(3 + 3 = 6). Consequently, C"s dimensions are (4, 6).

Consequently, the translated locations' coordinates are as follows:

=> B' = (-2, 1)

=> C' = (4, 6)

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|The events X and Y are marginally dependent in the roulette example.

Two events X and Y are marginally dependent when the probability of one event occurring affects the probability of the other event occurring. In the roulette example, the events X and Y are marginally dependent because the probability of X = red depends on the probability of Y = 15, and vice versa.

The probabilities can be calculated as follows:

P[X = red | Y = 15] = 1, since all odd numbers are red and 15 is an odd number.

P[Y = 15 | X = red] = 1/18, since there are 18 red numbers and only one of them is 15.

P[X = Red, Y = 15] = P[X = red | Y = 15] * P[Y = 15] = 1 * 1/36 = 1/36, since there are 36 numbers in total and only one of them is both red and 15.

P[Y = 15] = 1/36, since there are 36 numbers in total and only one of them is 15.

P[X = Red] = 18/36 = 1/2, since there are 18 red numbers and 36 numbers in total.

Therefore, the events X and Y are marginally dependent in the roulette example.

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a) The simple interest earned is $704,

b) The interest earned when compounded daily is $975.19,

c) The difference between the two is $271.19.

To solve this problem, we will use the formulas for simple interest and compound interest.

Simple Interest = Principal x Interest Rate x Time

Compound Interest = Principal x (1 + Interest Rate / Number of Compounding Periods) ^ (Number of Compounding Periods x Time) - Principal

(a) Calculate the simple interest earned.

Simple Interest = $1100 x 0.08 x 8

Simple Interest = $704

(b) Calculate the interest earned if interest is compounded daily.

Compound Interest = $1100 x (1 + 0.08 / 365) ^ (365 x 8) - $1100

Compound Interest = $1100 x (1.000219178) ^ 2920 - $1100

Compound Interest = $1100 x 1.886533 - $1100

Compound Interest = $2075.19 - $1100

Compound Interest = $975.19

(c) How much more interest is earned on the account when the interest is compounded daily?

Difference = Compound Interest - Simple Interest

Difference = $975.19 - $704

Difference = $271.19

Therefore, the simple interest earned is $704, the interest earned when compounded daily is $975.19, and the difference between the two is $271.19.

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Answer:

If repetition of letter A is allowed and letter B cannot be repeated, then there are two cases to consider when constructing a 3-digit number:

Case 1: The first digit is letter A. In this case, there are 6 options for the first digit (since any of the 6 digits can be used), and there are 5 options for each of the remaining digits (since letter B cannot be repeated). Therefore, the total number of 3-digit numbers that can be formed in this case is:

6 x 5 x 5 = 150

Case 2: The first digit is not letter A. In this case, there are 5 options for the first digit (since letter A cannot be repeated), and there are 5 options for each of the remaining digits (since letter B cannot be repeated). Therefore, the total number of 3-digit numbers that can be formed in this case is:

5 x 5 x 4 = 100

To get the total number of 3-digit numbers that can be made from 1, 2, 3, 4, 5, and 6 with letter A repetition allowed and letter B repetition not allowed, we add the number of possibilities from Case 1 and Case 2:

Total = 150 + 100 = 250

Therefore, there are 250 different 3-digit numbers that can be made from 1, 2, 3, 4, 5, and 6 with letter A repetition allowed and letter B repetition not allowed.

There are 720 numbers consisting of 3 digits that can be made from 1, 2, 3, 4, 5, and 6 if letter A repetition is allowed and letter B repetition is not allowed.

This can be calculated by taking the number of possible combinations for each digit (6 for A, 5 for B, 4 for C) and multiplying them together: 6 x 5 x 4 = 120. Since there are 6 possible numbers for each digit, there are 120 combinations for a 3-digit number. Then, multiplying 120 by 6 (since repetition is allowed) yields 720 possible 3-digit numbers.

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The wind generator will produce 2744W of power in a 35mph wind.

To find the power generated by the wind generator in a 35mph wind, we can use the formula P = kV³, where P is the power generated, k is a constant, and V is the wind's speed.

First, we need to find the value of k. We can do this by plugging in the given values of P and V into the formula and solving for k:

1000W = k(25mph)³ 1000W = k(15625mph³)

k = 1000W/15625mph³

k = 0.064W/mph³

Now that we have the value of k, we can plug it back into the formula along with the new wind speed of 35mph to find the power generated:

P = (0.064W/mph³)(35mph)³

P = (0.064W/mph³)(42875mph³)

P = 2744W

Therefore, the wind generator will produce 2744W of power in a 35mph wind.

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