Michae


all your steps.


2x 3x


problem a 60 x


miss chang ordered a pizza to share with some grade 8 students. miss chang


gave michael some slices of pizza. miss chang gave amy twice as many slices of


pizza as michael. miss chang gave mr. au three times the sum of what she gave


to michael and amy. miss chang gave 60 slices of pizza to michael, amy and mr.


au in total. how many slices of pizza miss chang give to each person?

The derivative formula of the given function f(x) is:

f'(x) = 2√(7x+8) + 7x/(√(7x+8))

This formula gives the value of the derivative of the function f(x) for any value of x.

The derivative of f(x) using the product rule and chain rule:

f'(x) = 2√(7x+8) + 2x(1/2)(7x+8)^(-1/2)(7)

f'(x) = 2√(7x+8) + 7x/(√(7x+8))

Simplify the derivative

The derivative of the function f(x) is given by f'(x) = 2√(7x+8) + 7x/(√(7x+8))

In this formula, the first term represents the derivative of the function 2x√(7x+8) using the chain rule, and the second term represents the derivative of the function 96, which is a constant and has a derivative of zero.

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The coordinates of the fourth vertex is (3.9, 6.3,0).To find the coordinates of the fourth vertex, we can use the fact that opposite sides of a rectangle are parallel and equal in length.

We can find the length and slope of one side of the rectangle and then use that information to find the coordinates of the fourth vertex.

Let's start by finding the length and slope of the side connecting (-1.3, -3.5) and (-1.3, 1.4). The length of this side is the difference between the y-coordinates, which is:

1.4 - (-3.5) = 4.9

Since this side is vertical, its slope is undefined.

Next, let's find the length and slope of the side connecting (-1.3, 1.4) and (3.9, 1.4). The length of this side is the difference between the x-coordinates, which is:

3.9 - (-1.3) = 5.2

Since this side is horizontal, its slope is 0.

Since opposite sides of a rectangle are equal in length, the length of the side connecting (-1.3, 1.4) and (3.9, 1.4) must also be 4.9. We can use this length to find the y-coordinate of the fourth vertex, which is:

1.4 + 4.9 = 6.3

Now we know that the fourth vertex has coordinates (x, 6.3). To find the x-coordinate, we can use the length of the vertical side connecting (-1.3, -3.5) and (-1.3, 1.4), which is also 5.2. The x-coordinate of the fourth vertex is:

-1.3 + 5.2 = 3.9

Therefore, the coordinates of the fourth vertex are (3.9, 6.3,0).

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a. The formula for the slope at (x, f(x)) is f'(x) = -2x

b. The slope at (0, 8) is 0

c. the slope at (-1, 7) is 2

The slope of a graph is the gradient of the graph.

Given the graph f(x) = 8 - x² to find the formula for the slope of the graph, we proceeed as follow.

a. To find the formula for the slope of the graph, we know thta the slope of the graph is the derivative of the graph. So, taking the derivative of the graph, we have that

f(x) = 8 - x²

df(x)/dx = d(8 - x²)/dx

= d8/dx - dx²/dx

= 0 - 2x

= -2x

So, the formula for the slope at (x, f(x) is f'(x) = -2x

b. To find the slope at (0, 8), substituting x = 0 into the equation for the slope, we have that

f'(x) = -2x

f'(0) = -2(0)

= 0

So, the slope at (0, 8) is 0

c. To find the slope at (-1, 7), substituting x = -1 into the equation for the slope, we have that

f'(x) = -2x

f'(0) = -2(-1)

= 2

So, the slope at (-1, 7) is 2

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The unit rate of change of ddd with respect to ttt is 4/3.

To graph the proportional relationship between ddd and ttt, we first need to find the unit rate of change. Since an increase of 333 units in ttt corresponds to an increase of 444 units in ddd, we can calculate the unit rate as follows:

Unit Rate = (Change in ddd) / (Change in ttt) = 444 / 333 = 4/3

So, a change of 1 unit in ttt corresponds to a change of 4/3 units in ddd.

Now, let's graph the relationship. The equation representing this proportional relationship is:

ddd = (4/3)ttt

This is a linear relationship with a slope of 4/3 and passes through the origin (0,0). To plot the graph, start at the origin and use the slope to plot additional points, such as:
- For ttt = 3, ddd = 4 (since 4/3 * 3 = 4)
- For ttt = 6, ddd = 8 (since 4/3 * 6 = 8)

Plot these points and draw a straight line through them, representing the proportional relationship between ddd and ttt. The unit rate of change of ddd with respect to ttt is 4/3.

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For the given case, there is evidence that the true mean number of hours of screen time for US adults is greater than 3.5.

Here, the researcher is 95% confidence interval from 3.6 hours to 8.1 hours captures  y = the true mean amount of daily screen time for US adults.
If 3.5 hours falls below this interval, it is likely that the true mean number of hours of screen time for US adults is greater than 3.5 hours.

A confidence interval is a measure of values that is used to evaluate a statistical parameter which tends to involve the true form of the parameter a predetermined proportion of the time if the procedure of searching the group of values is repeated numerous times.

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At least 95% of the observations lie between 19 and 31.

To see why, we can use Chebyshev's theorem, which states that for any data set, regardless of the shape of the distribution, at least 1 - (1/k²) of the observations lie within k standard deviations of the mean. In this case,

we want to know the percentage of observations that lie within two standard deviations of the mean, since 19 and 31 are both two standard deviations away from the mean of 25.

So, we can use k = 2 in Chebyshev's theorem, which gives us:

1 - (1/2²) = 1 - (1/4) = 0.75

Therefore, at least 75% of the observations lie within two standard deviations of the mean. However, since we know the data set is normally distributed (since we know the mean and standard deviation), we can use the empirical rule,

which states that for normally distributed data, approximately 68% of the observations lie within one standard deviation of the mean, and approximately 95% of the observations lie within two standard deviations of the mean.

Therefore, we can conclude that at least 95% of the observations lie between 19 and 31.

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The area of the circle is (121/144)π square meters.

We know that the formula for the area of a circle is A = πr², where r is the radius of the circle. However, we are given the diameter of the circle, which is 5/6 meters.

The diameter of a circle is twice the radius, so we can find the radius by dividing the diameter by 2:

radius = (5/6) / 2 = 5/12 meters.

Now that we have the radius, we can use the formula for the area of a circle:

A = πr² = π(5/12)².

To approximate this using 22/7, we first simplify (5/12)²:

(5/12)² = 25/144.

Substituting this value into the formula, we get:

A = π(25/144) = (25/144)π.

Therefore, the area of the circle is (25/144)π square meters. To get an approximation, we can use 22/7 approximate π:

A ≈ (25/144) × (22/7) = 121/144 square meters.

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The solution to the system of equations shown above is: D. there are infinitely many solutions.

In order to determine the solution for this system of linear equations on a coordinate plane, we would make use of an online graphing calculator to plot the given system of linear equations while taking note of the point of intersection;

x + 2y = 6   ......equation 1.

2x + 4y = 12 ......equation 2.

Based on the graph shown (see attachment), we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them, which is given by multiple ordered pairs and as such, it has more than one solution or infinitely many solutions because the lines coincide.

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The probability of being 25-35 years and having a hemoglobin level above 11 is 0.102. The probability of having a hemoglobin level above 11 is 0.356. Being 25-35 years and having a hemoglobin level above 11 are dependent on each other.

From the two-way table, the total number of individuals who have a hemoglobin level above 11 is 153+44+40=237. The probability of having a hemoglobin level above 11 is the total number of individuals with hemoglobin level above 11 divided by the total number of individuals, which is 237/429=0.356.

The number of individuals who are between 25-35 years and have a hemoglobin level above 11 is 44. The probability of being 25-35 years and having a hemoglobin level above 11 is the number of individuals who are between 25-35 years and have a hemoglobin level above 11 divided by the total number of individuals, which is 44/429=0.102.

Being 25-35 years and having a hemoglobin level above 11 are dependent on each other because the probability of having a hemoglobin level above 11 changes based on the age group.

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To administer a daily dose of 375 mg of naproxen using 250 mg scored tablets, the patient would need to take 1.5 tablets, rounded up to 2 tablets of 250 mg each.

To administer 375 mg of naproxen using 250 mg scored tablets, we need to divide 375 by 250 to determine how many tablets to administer.

375 mg / 250 mg per tablet = 1.5 tablets

Therefore, the dosage of 375 mg of naproxen would require 1.5 tablets.

Since tablets cannot be divided into halves, the patient would need to take 2 tablets of 250 mg each to achieve the prescribed dosage of 375 mg.

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Answer:16/45 of his yarn

Step-by-step explanation:

8/9 x 2/5 = 16/45

The correct statement that interprets the function M(t) is:

B) The total municipal debt in llinois was $43.38 billion in 2000 and increases about 5.2% each year.

According to the question the function M(t) =41.24(1.052)^t represents the total municipal debt for the state of llinois in billions of dollars, where t is the number of years since 2000.

The incorrect options are:

Option A is incorrect as the function does not represent an increase of 1.052% each year, but rather an increase of 5.2% each year (since 1.052=1+0.052)

Option C is also incorrect because it suggests an increase of 105.2% each year, which is not possible.

Option D is also incorrect because it states that the total municipal debt was $41.24 billion in 2000, and increases about 5.2% each year.

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The resultant equation is n + 11 = 25 and the number n is 14.

Algebraic equation:

An algebraic equation is a mathematical statement that equates two expressions using one or more variables. Solving a single variable equation can be done by adding or subtracting the same integer on both sides. Similarly multiplying or dividing by the same integer.

The information we have

The sum of a number n and 11 is equal to 25.

The statement can represent an equation and solve for n as follows

Here sum of two numbers indicates adding

Hence,  n + 11 = 25

To solve for n, isolate n on one side of the equation.

This can be done by subtracting 11 from both sides of the equation:

=> n + 11 - 11 = 25 - 11

=> n = 14

Therefore,

The resultant equation is n + 11 = 25 and the number n is 14.

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36 bags of soil are required to spread a 6 feet layer over a garden bed that is 4 feet by 3 feet.

Given information:

The garden bed has a length of 4 feet.

The garden bed has a width of 3 feet.

The layer of soil to be spread over the garden bed is 6 feet.

One bag of soil contains 2 cubic feet of soil.

To find the number of bags of soil required to spread a 6 feet layer over the garden bed, we need to calculate the volume of soil needed and then divide it by the volume of each bag of soil.

The volume of soil needed can be calculated by multiplying the length, width, and height (depth) of the soil:

Volume = length x width x depth

Volume = 4 feet x 3 feet x 6 feet

Volume = 72 cubic feet

This means we need a total of 72 cubic feet of soil to spread a 6 feet layer over the garden bed.

Next, we need to determine the number of bags of soil required. Since each bag contains 2 cubic feet of soil, we can divide the total volume of soil needed by the volume of each bag to get the number of bags required:

Number of bags = Volume of soil needed / Volume of each bag

Number of bags = 72 cubic feet / 2 cubic feet per bag

Number of bags = 36 bags

Therefore, 36 bags of soil are required to spread a 6 feet layer over a garden bed that is 4 feet by 3 feet.

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The net worth of the Worthington family is $28,900, which is greater than the requirement of $100,000 for the loan. Therefore, they meet the net worth requirement for the loan.

To calculate the net worth of the Worthington family, we need to add up all their assets and subtract their liabilities (debts). Let's start by listing them:

Assets:

- Savings account: $18,800

- Vehicles: $64,600

- Antique necklace: $6,200

- College fund: $24,700

Total assets: $114,300

Liabilities:

- Mr. Worthington's student loans: $85,400

Total liabilities: $85,400

To calculate the net worth, we subtract the liabilities from the assets:

Net worth = Total assets - Total liabilities

Net worth = $114,300 - $85,400

Net worth = $28,900

The net worth of the Worthington family is $28,900, which is greater than the requirement of $100,000 for the loan. Therefore, they meet the net worth requirement for the loan.

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The probability that we want to get is 0.167

To get this probability, we need to take the quotient between the number of students that preffers athletics and literature and the total number of students in the table.

We have:

Total number = 5 + 3 + 2 +8 = 18

number that preffers athletics and literature = 3

Then the probability is:

P = 3/18 = 0.167

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To find the vector equation of the plane containing the two intersecting lines, we can first find the normal vector of the plane by taking the cross product of the direction vectors of the two lines. The normal vector will be orthogonal to both direction vectors and thus will be parallel to the plane.

Direction vector of the first line: (2, 4, 3)

Direction vector of the second line: (-1, -1, 3)

Taking the cross product of these two vectors, we get:

(2, 4, 3) x (-1, -1, 3) = (9, -3, -6)

This vector is orthogonal to both direction vectors and thus is parallel to the plane. To find the vector equation of the plane, we can use the point-normal form of the equation, which is:

N · (r - P) = 0

where N is the normal vector, r is a point on the plane, and P is a known point on the plane. We can choose either of the two given points on the intersecting lines as the point P.

Let's use the point (4, 7, 3) on the first line as the point P. Then the vector equation of the plane is:

(9, -3, -6) · (r - (4, 7, 3)) = 0

Expanding and simplifying, we get:

9(x - 4) - 3(y - 7) - 6(z - 3) = 0

Simplifying further, we get:

9x - 3y - 6z = 0

Dividing by 3, we get:

3x - y - 2z = 0

Therefore, the vector equation of the plane containing the two intersecting lines is:

(3, -1, -2) · (r - (4, 7, 3)) = 0

or equivalently,

3x - y - 2z = 0.

Jonah's mom's would have to spend $45.878 to fill up her tank after the 40% increase in gas prices if her car takes 14 1/2 gallons of gas to fill up.

To find the cost that Jonah's mom would have to spend after the 40% increase in gas prices to fill up her 14 1/2 gallon tank, we need to follow these steps:

1. Find the increased price per gallon by multiplying last summer's price ($2.26) by 1.40 (since there's a 40% increase): $2.26 x 1.40 = $3.164 per gallon.
2. Convert 14 1/2 gallons to a decimal: 14.5 gallons.
3. Multiply the increased price per gallon ($3.164) by the number of gallons needed to fill up the tank (14.5 gallons): $3.164 x 14.5 = $45.878.

So, after the 40% increase in gas prices, Jonah's mom would have to spend $45.878 to fill up her 14 1/2 gallon tank.

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If point C is on the circle with diameter AB, then triangle ABC must be a right triangle. This is because the diameter of a circle is the longest chord and it passes through the center of the circle.

If we draw a line from point C to the center of the circle (which is the midpoint of AB), we get a perpendicular bisector of AB, meaning that it cuts AB into two equal parts and forms right angles with it. This also means that AC and BC are equal in length (since they both form radii of the circle), and the angle at point C must be a right angle (since it forms a straight line with the center of the circle). Thus, triangle ABC satisfies the criteria for a right triangle.

In summary, if point C lies on the circle with diameter AB, then triangle ABC must be a right triangle with AC and BC as its legs and AB as its hypotenuse. This is a fundamental property of circles and right triangles, and it is important to understand in order to solve various geometry problems involving circles and triangles.

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Simple Interest is equal to ($800) (2000 x 8 x 5) / 100. The simple interest earned is therefore $800.

The measure of cash returned or earned over a set period of time on a principal sum of money is referred to as interest. It is frequently stated as a share of the principal sum and it may be either simple or complicated. Compounding interest is computed on the principal amount as well as any accrued but unpaid interest, whereas simple interest is assessed just on the principal amount. Loans, investments, and bank deposits frequently include interest.

given

We can use the following calculation to determine the simple interest received for a $2000 principal at an 8% rate over a 5-year period:

S.I =  (Principal x Rate x Time)/100

In this instance, Principal is $2000, Rate is 8% annually, and Term is 5 years.

With these values entered into the formula, we obtain:

Simple Interest is equal to ($800) (2000 x 8 x 5) / 100. The simple interest earned is therefore $800.

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It will take Keshia 62.5 minutes to complete the entire worksheet at the same pace.

To find the amount of total time it will take Keshia to complete the entire worksheet at the same pace, we can use a proportion:

20 problems / 25 minutes = 50 problems / x minutes

To solve for x, we can cross-multiply and simplify:

20 problems * x minutes = 25 minutes * 50 problems

20x = 1250

x = 1250 / 20

x = 62.5

Therefore, it will take Keshia 62.5 minutes to complete the entire worksheet at the same pace.

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Answer:

The given equation Y=4x^3+6 is a nonlinear equation because it contains a term with a power of 3, which means that the relationship between Y and x is not linear. In a linear equation, the power of the variable is always 1. Therefore, the answer is B. Nonlinear.

Step-by-step explanation:

Answer:

Solve for these and you'll find it! :D (Surface Area for all)
The answer is:
A: 6(12)^2 (it's a cube)
B: 2(6.4 x 15.2 + 15.2 x 10.5 + 6.4 x 10.5) (it's a rectangular prism)
C: 6(3x - 1)^2 (it's a cube)
D: 2(pi)(radius)(height) + 2(pi)(radius^2) (it's a cylinder)

Answer:

a)

[tex]m = \frac{15 - 10}{4 - 2} = \frac{5}{2} [/tex]

[tex]10 = \frac{5}{2} (2) + b[/tex]

[tex]10 = 5 + b[/tex]

[tex]b = 5[/tex]

[tex]y = \frac{5}{2}x + 5[/tex]

b) The function is already given.

c)

[tex]m = \frac{100 - 40}{30 - 10} = \frac{60}{20} = 3 [/tex]

[tex]100 = 3 (30) + b[/tex]

[tex]100 = 90 + b[/tex]

[tex]b = 10[/tex]

[tex] y = 3x + 10[/tex]

The correct option for each individual question is c. X - 1. 5= 5. 25, c. 72 = 9b and B/1.75 = 6.

1. Total food = poured food + remaining food

Keep the values in formula

x = 1.5 + 5.25

Rearranging the equation

x - 1.5 = 5.25

Thus, correct option is c. X - 1. 5= 5. 25

2. Cost of one box × number of boxes = total cost

9 × number of boxes = 72

Let us represent the number of boxes as b. So,

9b = 72

Hence, correct option is c. 72 = 9b.

3. Length of each section × number of sections = total length of bookcase sections

Let us represent total length of bookcase sections as B

1.75 × 6 = B

Rearranging the equation

B/1.75 = 6

So, the correct option is a. B/1. 75 = 6.

Thus, correct option are c. X - 1. 5= 5. 25, c. 72 = 9b and B/1.75 = 6.

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Answer:

Given the equation of the circle in the xy-coordinate plane as x^2 + y^2 + 6x - 4 = 0, we need to rewrite it in the form (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.

Completing the square for x^2 + 6x, we get (x+3)^2 - 9. Thus, the equation becomes (x+3)^2 + y^2 - 9 = 4. Rearranging, we get (x+3)^2 + y^2 = 13.

Comparing with the required form, we get (x-h)^2 + (y-k)^2 = r^2, where h = -3, k = 0 and r^2 = 13. Thus, the value of k is 0.

This tells him that his salary is significantly below the average salary of quality management professionals surveyed by the ASQ, and that he is in the bottom percentile of salaries in this group.

The z-score is a statistical measure that indicates the number of standard deviations that a data point is from the mean of a distribution. A negative z-score indicates that the data point is below the mean.

In this case, the quality control specialist's z-score of -2.50 indicates that his salary is 2.50 standard deviations below the mean salary of the quality management professionals surveyed by the ASQ.

Without knowing the specific mean and standard deviation provided by the survey, it is difficult to determine the exact value of the specialist's salary. However, we can use the z-score to estimate the percentile rank of his salary compared to the rest of the survey respondents.

Using a standard normal distribution table, we can see that a z-score of -2.50 corresponds to a percentile rank of approximately 0.0062 or 0.62%. This means that only about 0.62% of quality management professionals surveyed by the ASQ earn a salary lower than that of the quality control specialist.

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The height of the candle after x hours is given by the equation y = 2x + 14.

Let's first convert the time interval to hours. There are 60 minutes in an hour, so 30 minutes is equivalent to 0.5 hours.

After x hours, the candle will have burned down by 2x inches (since it burns 1 inch every 0.5 hours).

If y is the total height of the candle, then we can write the equation:

y - 2x = 14

We can solve for y:

y = 2x + 14

So the height of the candle after x hours is given by the equation y = 2x + 14.

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The estimated areas of each curve are listed below:

Case 1: A = 12.75

Case 2: A = 12.5

In this problem we must estimate the area above the x-axis and under a curve by using sums of rectangles and triangles according to the following expression:

A = {∑ [MIN (f(xₙ₋₁), f(xₙ))] + 0.5 · ∑ [MAX (f(xₙ₋₁), f(xₙ)) - MIN (f(xₙ₋₁), f(xₙ))]} · Δx, for n = {1, 2, 3, ..., N}

Where:

Case 1

A = (3.5 + 3.5 + 1.5) · 1 + 0.5 · (3.5 + 0.75 + 0.75 + 2 + 1.5) · 1

A = 8.5 + 0.5 · 8.5

A = 12.75

Case 2

A = (1 + 3 + 4) · 1 + 0.5 · (1 + 2 + 1.5 + 0.5 + 4) · 1

A = 8 + 4.5

A = 12.5

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