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?

Answer:

1

Step-by-step explanation:

the gradient is a value that indicates how much the x value increases as the y value increases. It can be written as

rise/run

or

change in  y value/change in x value

or

(y1-y2)/(x1-x2), where we know two coordinates (x1,y1) and (x2,y2).

We have two coordinates (0,0) and (3,3)

Therefore,

x1 = 0, y1 = 0

x2 = 3, y2 = 3

If we plug these values into the formula, it is \(\frac{3-0}{3-0} = \frac{3}{3} = 1\)

The solution to the evaluation of the expression x(y² - z) x = 6, y = 4 and z = 1 is 90

Evaluate:

x(y² - z)

When

x = 6, y = 4 and z = 1

x(y² - z)

substitute the value of x, y and z

= 6(4² - 1)

Applying PEMDAS:

P = parenthesis

E = Exponential

M = Multiplication

D = Division

A = Addition

S = Subtraction

= 6(16 - 1)

= 96 - 6

= 90

In conclusion, the expression x(y² - z) when evaluated gives 90.

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Answer:

200

Step-by-step explanation:

72---->36%

x------> 100%

72×100

7200÷36=200

To check, let do it the other way round. 200×0.36=72.

There was total 200 multiple choice history question in Ximena's exam.

For the given question,

Total questions answered by the Ximena is 72.

The total percentage was 36%.

Let 'x' be the total number of the questions.

Then,

36% of x = 72

36x /100 = 72

x = 7200/36

x = 200

Thus, there was total 200 multiple choice history question in Ximena's exam.

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Answer:

x = 35

Step-by-step explanation:

12/7 = 60/x

60/12 = 5

7 x 5 = 35

x = 35

An element with mass 420 grams decays by 11.8% per minute. the amount of the element remaining after 16 minutes is 56.3 grams

This is a type of function that are of 3 main parts

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.

Considering the given problem,  

the starting = 420 grams

the base = 1 - r = 1 - 11.8% = 1 - 0.118 = 0.882

the exponents = 16

amount remaining = 420 (0.882)^16

= 56.330895

= 56.3 to the nearest tenths

the amount left is 56.3 g

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The tenth position is the one that goes after the decimal point.

To round a number, you have to take into account the following:

1. If the number that goes after the position we are going to round to is greater than 5, we round to the next number in that position.

2. If the number that goes after the position we are going to round to is less than 5, we round to the same number in that position.

In this case, the number that is on the tenth's position is 4. The number that is after this position is 1, which is less than 5, then we round the number in this positon to 4.

The rounded number would be:

Answer:

\( \frac{4}{4} > \frac{1}{4} \)

Step-by-step explanation:

1 is bigger than a quarter.

Answer:

Step-by-step explanation:

Scientific notation is a quick way to represent a number using powers of base ten. This notation is used to be able to express very large or very small numbers very easily.

The numbers are written as a product:

a * 10ⁿ

where:

Comparing what is equal to these two numbers when they are written in scientific notation you can see that the value of a is such that 1 ≤ a <10

Comparing what is different from these two numbers when they are written in scientific notation, you can see that the value of the exponent n in both numbers is different, one being positive, indicating that it is a very large number, and the other negative, indicating that it is It is a very small number that is between 0 and 1.

To change the chart style to style 42 (2nd column 6th row), follow these steps:

1. Select the chart you want to modify.
2. Right-click on the chart, and a menu will appear.
3. From the menu, choose "Chart Type" or "Change Chart Type," depending on the version of the software you are using.
4. A dialog box or a sidebar will open with a gallery of chart types.
5. In the gallery, find the style labeled as "Style 42." The styles are usually represented by small preview images.
6. Click on the style to select it.
7. After selecting the style, the chart will automatically update to reflect the new style.

Note: The position of the style in the gallery may vary depending on the software version, so the specific position of the 2nd column 6th row may differ. However, the process remains the same.

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The correct option of the given question is option(c) becomes narrower.

Based on the given information, when the confidence level is lowered from 98% to 97%, the confidence interval for the population mean μ becomes narrower. So, the correct answer is option c. becomes narrower.

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When the confidence level is lowered from 98% to 97%, the confidence interval for the population mean μ becomes wider.

This is because a higher confidence level implies a narrower interval to provide a higher level of certainty in capturing the true population mean. Conversely, when the confidence level is decreased, the interval needs to be wider to allow for a larger margin of error and account for the reduced confidence requirement.

Widening the interval ensures that the estimate is more conservative and includes a broader range of possible values for the population mean. Therefore, the confidence interval for μ becomes wider as the confidence level is lowered.

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Enlarged in 14 1.76 will be 0.95. Therefore, in order to provide you at least a 0.95 likelihood of being able to cover the transportation costs and other fees, I would need to visit the business with a minimum of 176 individuals.

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We want to find a system of inequalities that models the given situation.

We will find the system:

a + c ≤ 18

a ≥ 6

c ≤ 2*a

First we define the variables:

The given information is:

The manager needs one helper at a time for at most 18 hours.

From this we can write:

a + c ≤ 18

Axel wants to work at least 6 hours.

a ≥ 6

The manager wants carl to work no more than twice as many hours as Axel.

c ≤ 2*a

The system is then:

a + c ≤ 18

a ≥ 6

c ≤ 2*a

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Answer:

The equation in the polar form is;

\(r = \dfrac{6}{4 + 3 \cdot sin(\theta)}\)

Step-by-step explanation:

 e = 3/4  > 1, we have an hyperbola    

The polar equation of a conic is of the form;

For vertical directrix

\(r = \dfrac{k \cdot e}{1\pm e \cdot cos (\theta)}\)

For horizontal directrix

\(r = \dfrac{k \cdot e}{1\pm e \cdot sin(\theta)}\)

Where;

k = Distance from the focus to the directrix = 2

We have;

\(r = \dfrac{2 \cdot \dfrac{3}{4} }{1 + \dfrac{3}{4} \cdot sin(\theta)}\)

\(r = \dfrac{\dfrac{3}{2} }{1 + \dfrac{3}{4} \cdot sin(\theta)}\)

Which gives the equation in the polar form as follows;

\(r = \dfrac{6}{4 + 3 \cdot sin(\theta)}\).

By graphing the system of equations, we can see that the solution is (3, 5).

I assume we want to solve the following system of equations graphically:

x - 3y = -12

2x - y = 1

To do so we only need to graph both the lines on the same coordinate axis and find the point where the lines do intersect. The graph can be seen below.

There we can see that the intersection is at (3, 5), so that is the solution of the system of equations.

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Answer:

(2, 10)

Step-by-step explanation:

If you graph the line and all 3 points, you can tell that only (2, 10) lies on the point, therefore, it would make the equation true. You can also figure it out algebraically.

\(10 = 7(2) - 4\\\rule{150}{0.5}\\10 = 14 - 4\\\\\boxed{10=10}\)

Hope this helps.

The volume of the solid generated by revolving the triangle about the -axis is (8π/3).

The region enclosed by the -axis, the line y = 2, and the curve y = -x is a triangle with base 2 and height 2.

To find the volume of the solid generated by revolving this triangle about the -axis, we can use the method of cylindrical shells.

The volume of each shell is given by the formula:

V = 2πr * h * δr

where r is the distance from the -axis to the shell, h is the height of the shell, and δr is the thickness of the shell.

We can express r as a function of y, since each shell corresponds to a vertical slice of the triangle:

r = y

The height of each shell is given by the difference between the -axis and the curve y = -x:

h = 2 - (-x) = 2 + x

Finally, the thickness of each shell is δr = dy.

Therefore, the volume of the solid is:

V = ∫[0,2] 2πy * (2 + y) dy

= 2π ∫[0,2] (2y + y^2) dy

= 2π [y^2 + (1/3)y^3] |[0,2]

= (8π/3)

Therefore, the volume of the solid generated by revolving the triangle about the -axis is (8π/3).

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Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

The graph of the inequality y^2 > 0 represents all real numbers except y = 0.

The graph of the inequality y < 30 represents all real numbers less than 30.

The inequality y^2 > 0 represents all values of y where y squared is greater than 0. Since the square of any nonzero number is always positive, the solution is all real numbers except y = 0, which can be graphed as a number line with an open circle at y = 0.

The inequality y < 30 represents all values of y that are less than 30. This can be graphed as a horizontal line on the y-axis with an open circle at y = 30, indicating that 30 is not included in the solution set.

For the real-world applications, let's solve them step-by-step:

Two numbers add up to 144. One number is half the square of the other number.

Let's assume the two numbers are x and y. We have the following system of equations:

x + y = 144 (Equation 1)

x = (1/2)y^2 (Equation 2)

From Equation 1, we can solve for x in terms of y: x = 144 - y.

Substituting this into Equation 2, we get 144 - y = (1/2)y^2.

Rearranging the equation, we have: (1/2)y^2 + y - 144 = 0.

Now we can solve this quadratic equation for y. Once we find the value(s) of y, we can substitute them back into Equation 1 to find the corresponding values of x.

The squares of two numbers add to 1,156. The second number is the square root of three times the square of the first number.

Let's assume the two numbers are x and y. We have the following system of equations:

x^2 + y^2 = 1156 (Equation 1)

y = √(3x^2) (Equation 2)

Substituting Equation 2 into Equation 1, we get: x^2 + (√(3x^2))^2 = 1156.

Simplifying, we have x^2 + 3x^2 = 1156.

Combining like terms, we get 4x^2 = 1156.

Now we can solve this quadratic equation for x. Once we find the value(s) of x, we can substitute them back into Equation 2 to find the corresponding values of y.

Remember to leave a 1 line space between paragraphs in your answer.

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The resulting values for det(B) are 8, -8, 16

To determine the effect of each row operation on the determinant of the matrix, we can use the fact that the determinant is multilinear with respect to the rows. In other words, if we perform a row operation on a matrix, the determinant is multiplied by a scalar that depends on the row operation.

a) Interchanging rows 3 and 1 of A:

Let B be the matrix obtained by interchanging rows 3 and 1 of A. This row operation is equivalent to multiplying A by the permutation matrix P that interchanges rows 3 and 1. Since P is a permutation matrix, det(P) is either 1 or -1. In this case, interchanging rows 3 and 1 once is equivalent to applying P twice, so det(P) = 1. Therefore,

det(B) = det(PA) = det(P) det(A) = det(A) = 8

b) Adding -2 times row 3 to row 2 of A:

Let B be the matrix obtained by adding -2 times row 3 to row 2 of A. This row operation is equivalent to multiplying A by the matrix

I - 2 e_2 e_3^T,

where I is the 4x4 identity matrix, and e_2 and e_3 are the second and third standard basis vectors in R^4, respectively. The determinant of this matrix is -1 (it is a reflection matrix), so

det(B) = det((I - 2 e_2 e_3^T) A) = (-1) det(A) = -8.

c) Multiplying row 4 of A by 2:

Let B be the matrix obtained by multiplying row 4 of A by 2. This row operation is equivalent to multiplying A by the diagonal matrix D with diagonal entries 1, 1, 1, 2. The determinant of this matrix is 2, so

det(B) = det(DA) = 2 det(A) = 16.

Therefore, the resulting values for det(B) are:

a) det(B) = 8

b) det(B) = -8

c) det(B) = 16

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Answer:

put it on the dots for the x-axis and the y-axis

Step-by-step explanation:

if f has an absolute maximum value at c, then function f '(c) = 0 is True

This statement is true. This is because the first derivative of a function, f', is equal to 0 at the point of an absolute maximum. This is because the first derivative measures the rate of change of a function, and at a maximum, the rate of change of a function is 0. Therefore, if a function has an absolute maximum value at c, then f'(c) = 0.

The statement that if f has an absolute maximum value at c, then f '(c) = 0 is true. This is because the first derivative of a function measures the rate of change of a function. At an absolute maximum, the rate of change of a function is 0, so the first derivative of a function at that point must be 0. Therefore, if a function has an absolute maximum value at c, then f'(c) = 0.

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translating phrases and sentences into expressions, equations, and inequalities is an important skill in mathematics. It involves identifying key words and phrases that indicate mathematical operations and relationships. By understanding these key words, we can represent real-world problems using mathematical language and symbols, making it easier to solve and analyze them.

translating phrases and sentences into expressions, equations, and inequalities

When solving mathematical problems, it is often necessary to translate phrases and sentences into mathematical expressions, equations, and inequalities. This process involves identifying key words and phrases that indicate mathematical operations and relationships.

For example, let's consider the following sentence:

'The sum of a number and 5 is equal to 12.'

In this sentence, the key words 'sum,' 'number,' 'equal to,' and '12' indicate that we need to perform addition and find the value of the unknown number. We can represent this sentence as the following equation:

x + 5 = 12

Here, 'x' represents the unknown number.

Similarly, let's consider the following sentence:

'Twice a number decreased by 7 is greater than 15.'

In this sentence, the key words 'twice,' 'decreased by,' 'greater than,' and '15' indicate that we need to perform multiplication, subtraction, and comparison. We can represent this sentence as the following inequality:

2x - 7 > 15

Here, 'x' represents the unknown number.

By understanding key words and phrases, we can effectively translate real-world problems into mathematical language and solve them using expressions, equations, and inequalities.

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1) An inequality to represent the given phrase is 5q>30.

2) An equation to represent the given phrase is 2b²=8.

1) The given phrase is "The product of 5 and q is greater than 30."

Here, the product of 5 and q = 5×q

= 5q

Now, the product is greater than 30.

Thus, 5q>30

q>30/5

q>6

2) The given phrase is "Twice the square of b is equal to 8."

Here, the square of b = b×b

= b²

Twice the square of b = 2b²

So, the product is equal to 8.

That is. 2b²=8

b²=4

b=±2

Therefore,

1) An inequality to represent the given phrase is 5q>30.

2) An equation to represent the given phrase is 2b²=8.

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"Your question is incomplete, probably the complete question/missing part is:"

Translate phrases and sentences into expressions, equations and inequalities.

1) The product of 5 and q is greater than 30.

2) Twice the square of b is equal to 8.

The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

The coordinates of your position If we start at the origin, we are moving only along the x-axis  of  a distance of 7 units in positive direction and then only in the negative y-axis direction and  z-coordinate is zero are (7,-6,0).

The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.

The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).

The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).

Therefore, the coordinates of our position are (7, -6, 0)

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The given equations can be expressed in the form y = f(x) as y = 3x - 15.

To express the given equations, x = 2t + 6 and y = 6t + 3, in the form y = f(x), follow these steps:

1. Solve one of the equations for t. Let's choose the equation for x: x = 2t + 6.

2. Subtract 6 from both sides: x - 6 = 2t.

3. Divide by 2 to isolate t: t = (x - 6) / 2.

4. Now, substitute this expression for t into the equation for y: y = 6((x - 6) / 2) + 3.

5. Simplify the equation by multiplying 6 with the term inside the parenthesis: y = 6(x - 6) / 2 + 3.

6. Simplify further by dividing 6 by 2: y = 3(x - 6) + 3.

7. Distribute the 3 to both terms inside the parenthesis: y = 3x - 18 + 3.

8. Combine like terms: y = 3x - 15.

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The average height above the x-axis of a point in the region \(0\leq y\leq x^2\), for 0≤x≤25 using definite integral is 208.33 units.

To calculate the average height above the x-axis of a point in the region \(0\leq y\leq x^2\), for 0 ≤ x ≤ 25, we need to find the average value of y over this range.

The equation y = x² represents a parabola that opens upwards. To find the average height, we need to integrate the function y = x² over the given range and then divide by the length of the range.

Let's calculate it step by step:

Calculate the definite integral of y = x² with respect to x over the range 0 to 25:

∫[0,25] \(x^{2}\) dx = \([x^3/3]\) evaluated from 0 to 25

\(= (25^3/3) - (0^3/3)\\= (25^3/3)\\= 16666.67\)

Calculate the length of the range:

Length = 25 - 0 = 25

Divide the definite integral by the length of the range to find the average height:

\(Average height = (25^3/3) / 25\\= (25^2/3)\\= 208.33\)

Therefore, the average height above the x-axis of a point in the region \(0\leq y\leq x^2\), for 0 ≤ x ≤ 25, is approximately 208.33 units.

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The boolean expression that is true if the value of x is equal to zero is:

x == 0

Let's us first learn about Boolean expression.

A boolean expression is an expression that evaluates to either true or false. It can be created using comparison operators, such as == (equal to), != (not equal to), < (less than), > (greater than), <= (less than or equal to), and >= (greater than or equal to). These operators compare two values and return a boolean result.

In this question, the double equal sign (==) is the comparison operator for equality in many programming languages, and it returns true if the values on both sides are equal, and false otherwise.

So in this case, the expression "x == 0" would return true if x is equal to zero, and false otherwise.

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Answer:

\(y = 2\)

Step-by-step explanation:

1) Simplify 5y/9 - y/9 to 4y/9.

\( \frac{4y}{9} = \frac{8}{9} \)

2) Multiply both sides by 9.

\(4y = \frac{8}{9} \times 9\)

3) Cancle 9.

\(4y = 8\)

4) Divide both sides by 4.

\(y = \frac{8}{4} \)

4) Simplify 8/4 to 2.

\(y = 2\)

Hence, the answer is y = 2.