Tyrone spends $2 on ingredients for every $7 of revenue he collects selling
sandwiches at his shop. Tyrone collects $2100 selling sandwiches in a day. What
is Tyrone's PROFIT for the day?*
Cost ($)
Revenue ($)
2
7
2100

Given:

In a given figure,

The length of the sides of the triangle is 4, 13, and 15.

The dimensions of one rectangle are 4 by 6.

The dimensions of one rectangle are 13 by 6.

The dimensions of one rectangle are 15 by 6.

To find:

The total surface area and volume.

Explanation:

The total surface area of the figure is,

Using the heron's formula,

The area of the triangle will be,

Therefore, the total surface area of the figure becomes,

Thus, the total surface area of the figure is 240 square units.

The volume formula is,

Thus, the volume of the figure is 144 cubic units.

Final answer:

• The total surface area of the figure is 240 square units.

• The volume of the figure is 144 cubic units.

Answer:

-6,-1

-6,2

-3,2

-3,-1

Step-by-step explanation:

imagine the coordinates on a graph

moving right adds

moving left subtracts

moving down subtracts

moving up adds

____________________________________________________________________________________________________________________________________________________________________________________

If you chose to compute a mode for a variable, the measure of variability you would most likely want to report is the a) range .

The mode represents the most frequently occurring value in a dataset, which provides information about the central tendency and the characteristic value in the data. It helps identify the value or values that are most common or dominant in the dataset.

On the other hand, the range measures the spread or variability in the dataset. It gives you the difference between the maximum and minimum values in the dataset, providing insight into the extent of the dispersion of values.

The standard deviation (option b) is another measure of variability, but it quantifies the dispersion of values around the mean. It is not directly related to the mode and provides a different aspect of variability compared to the mode.

Therefore, if you are specifically interested in the measure of variability to report when computing the mode, the range (option a) would be more relevant than the standard deviation (option b).

Correct Question:

If you chose to compute a mode for a variable, which measure of variability would you most likely want to report?

a) Range

b) Standard Deviation

c) Neither of these

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Answer:

Step-by-step explanation:

D?

Latisha needs to pay first month's rent ($675), last month's rent ($675), and the security deposit ($325), which totals $1,325.

Latisha needs to pay a total of $1,325 to move into her new apartment. This includes the first month's rent of $675, the last month's rent of $675, and the security deposit of $325. This total amount must be paid before Latisha can move in and enjoy her new place. In addition to the up-front costs for move-in, Latisha will also need to be prepared to pay her rent each month and maintain her security deposit in case there are any damages to the apartment. Paying the move-in costs is the first step to ensure that Latisha can enjoy her new home.

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Given, the   Probability   Density Function: f(x)=(6/27)x(3−x) for 0≤x≤3

To determine the Expected Value of demand, E(x), we use the formula; E(x) = ∫x f(x)dx

For the probability Density function given ;f(x)=(6/27)x(3−x) for 0≤x≤3E(x) = ∫x f(x)dx= ∫[0,3] x (6/27)x(3−x) dx= (6/27) ∫[0,3] x²(3−x) dx= (6/27) [∫[0,3] 3x² dx - ∫[0,3] x³ dx]= (6/27) [(3x³/3) - (x⁴/4)] [0,3]= (6/27) [(27-81/4)]= (6/27) [(108-81)/4]= (6/27) (27/4)= 1/4

Therefore, the expected value of demand is 1/4To determine the Standard Deviation of demand,

We use the formula; SD(x) = √Var(x) where, Var(x) = ∫(x - E(x))² f(x) dx SD(x) = √[∫(x - E(x))² f(x)dx]Var(x) = ∫(x - E(x))² f(x)dxVar(x) = ∫[0,3] (x - 1/4)² (6/27)x(3−x) dx= (6/27) ∫[0,3] (x - 1/4)² (3−x) dx= (6/27) [∫[0,3] (x - 1/4)² (3) dx - ∫[0,3] (x - 1/4)² x dx]= (6/27) [9∫[0,3] (x² - 1/2x + 1/16) dx - ∫[0,3] (x³ - 1/2x² + 1/16x) dx]= (6/27) [9(27/4 - 1/2(3)/2 + 1/16(3)) - (81/4 - 1/2(3²)/2 + 1/16(3²)/2)]= (6/27) [(243/4 - 9/2 + 3/16) - (81/4 - 9/4 + 9/32)]= (6/27) [(243/4 - 9/2 + 3/16) - (81/4 - 9/4 + 9/32)]= (6/27) (24.53)= 1.46

Therefore, the standard deviation of demand is 1.46

To determine the probability that x is within one standard deviation of the mean,

We use the formula P(μ - σ < X < μ + σ) = ∫f(x)dx

Where,μ = E(x) = 1/4σ = SD(x) = 1.46P(μ - σ < X < μ + σ) = ∫[μ - σ, μ + σ] f(x)dx= ∫[1/4 - 1.46, 1/4 + 1.46] (6/27)x(3−x) dx= (6/27) ∫[-1.21, 1.96] x(3−x) dx= (6/27) [(3x²/2 - x³/3)] [-1.21, 1.96]= (6/27) [(3(1.96)²/2 - 1.96³/3) - (3(-1.21)²/2 - (-1.21)³/3)]= (6/27) (3.56 + 1.17)= 1.06

Therefore, the probability that x is within one standard deviation of the mean is 1.06.

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Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

Vertical Angles are the angles opposite each other when two lines cross.

In our question, we have to opposite angles. For this reason the answer is letter B.

Tanner needs a total of 146.5 square inches of construction paper for his project.

The area of rectangle is calculated by multiplying its length by its width.

For the first rectangle, with dimensions 15 inches by 1/3 inches, the area is:

Area = Length x Width = 15 inches x 1/3 inches = 5 square inches

For the second rectangle, with dimensions 10 1/4 inches by 10 1/3 inches, we can first convert the mixed numbers to improper fractions:

Length = 10 1/4 inches = 41/4 inches

Width = 10 1/3 inches = 31/3 inches

Then, we can calculate the area:

Area = Length x Width = (41/4 inches) x (31/3 inches)

To multiply these fractions, we can first simplify them by finding common factors. Both 4 and 3 are factors of 12, so we can convert the fractions to have a denominator of 12:

(41/4 inches) x (31/3 inches) = (41/4 inches) x (31/3 inches) x (3/3) x (4/4)

= (41 x 31 x 3 x 4) / (4 x 3 x 3) square inches

= (5094 / 36) square inches

= 141.5 square inches (rounded to one decimal place)

Therefore, the total square inches of construction paper that Tanner needs for his project is:

Total Area = Area of first rectangle + Area of second rectangle

Total Area = 5 square inches + 141.5 square inches

Total Area = 146.5 square inches

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Answer: 35, 63

Step-by-step explanation: sorry if wrong

An expression that represents the measure of the third side is 4x.

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Given:

The perimeter of the triangle is 3x² - 7x + 2.

And the measures of the two sides are x² - x - 4 and 2x² - 10x + 6.

The measure of the third side = the perimeter of the triangle - (the total measure of the two sides)

The measure of the third side = 3x² - 7x + 2 - (x² - x - 4 + 2x² - 10x + 6)

The measure of the third side = 3x² - 7x + 2 - (3x² - 11x +2)

The measure of the third side = 4x

Therefore, the measure of the third side = 4x.

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1/10 of all take 2/5 time

10/10=10 times 1/10

so 10 times 2/5 time=20/5=4 days to finish 1 order

4 days

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Answer:

5a + 8 = a - 8

Step-by-step explanation:

five times a number = 5 X a = 5a

plus 8 = 5a + 8

is equal to eight less than the number = a - 8

5a + 8 = a - 8

Answer:

$61.50

Step-by-step explanation:

14.25(4) + 4.50

= 57.00 + 4.50

= 61.50

Answer:

I believethe answers are (x-1)(x+3)

Step-by-step explanation:

x^2 + 2x - 3 can be simplified to

(x+3)(x-1)

The factors of this expression are therefore (x+3) and (x-1)

The binomial of each dimension is:

x+3

x-1

Answer:

The square root of 4096 is 64. The cube root of 4096 is 16. The fourth root of 4096 is 8 and the fifth root is 5.2780316430916.

Step-by-step explanation:

The real fourth roots of 4096 are 8 and -8, as these values satisfy the equation \(x^4 = 4096\).

To find all the real fourth roots of 4096, we need to determine all the real values of x that satisfy the equation \(x^4 = 4096\).

The equation we need to solve is \(x^4 = 4096\).

To find the fourth root of 4096, take the positive and negative square roots of the positive value 4096.

Fourth root of 4096:

x = ±√4096

Simplify the square root.

√4096 = √(64 * 64) = √64 * √64 = 8 * 8 = 8

so, we get,

x = ±8

So, the real fourth roots of 4096 are 8 and -8, as these values satisfy the equation \(x^4 = 4096\).

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Answer:(-6.5,-5)

Step-by-step explanation:

 P = (3A +1B)/(3+1)

 P = (3(-7, -9) +(-5, 7))/4 = (-21-5, -27+7)/4 = (-6.5, -5)

Answer:

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

According to the diagram we have:

1) Angles w and 138° form a linear pair, hence:

2) Angles 19°, x and w form a right angle, hence:

Answer:

1a7

Step-by-step explanation:

26+-25=1

The relative price is a useful measure for comparing the prices of different products or services, especially in the context of consumer preferences and demand.

Relative price refers to the price of a particular product or service in relation to other goods or services in the market.

It is calculated as the ratio of the price of a given product or service to the price of a reference product or service, commonly referred to as a base good or service.

Let the price of a pair of shoes be $5 and the price of a box of tea be $3.

Then the relative price of a pair of shoes is given by:

Relative price of shoes = Price of shoes / Price of tea

= $5 / $3

= 1.67

Thus, the relative price of a pair of shoes is 1.67.

Similarly,

The relative price of a box of tea can be calculated as follows:

Relative price of tea = Price of tea / Price of shoes

= $3 / $5

= 0.6

Therefore, the relative price of a box of tea is 0.6.

This means that the price of tea is relatively cheaper than that of shoes, as its relative price is less than one.

The relative price of shoes is greater than one, which indicates that shoes are relatively more expensive than tea.

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a. Total revenue R(x) = 190x - 4x^2

b. Price-demand equation: p(x) = 190 - 4x

c. The price of 100 compact discs is -210 dollars.

a. To find the total revenue R(x), we need to integrate the marginal revenue function R'(x) with respect to x.

Integrating R'(x), we get:

R(x) = ∫(190 - 8x) dx

      = 190x - 4x^2 + C

Given that R(0) = 0, we can substitute x = 0 into the equation to find the constant C:

0 = 190(0) - 4(0^2) + C

C = 0

Therefore, the total revenue function is:

R(x) = 190x - 4x^2

b. The price-demand equation represents the relationship between the price (p) and the quantity demanded (x). In this case, the price-demand equation can be derived from the total revenue function.

To find the price-demand equation, we need to express price (p) in terms of quantity demanded (x):

Total Revenue = Price × Quantity Demanded

R(x) = p(x) × x

From the total revenue function R(x) = 190x - 4x^2, we can divide both sides by x to isolate p(x):

p(x) = (190x - 4x^2) / x

p(x) = 190 - 4x

Therefore, the price-demand equation is:

p(x) = 190 - 4x

c. To find the price of 100 compact discs, we can substitute x = 100 into the price-demand equation:

p(100) = 190 - 4(100)

p(100) = 190 - 400

p(100) = -210

The price of 100 compact discs is -210 dollars.

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2. (10 points) Price- demand Function The marginal revenue from the sale of compact discs is given by R′ (x)=190−8x and R(0)=0 where R(x) is the revenue in dollars. a. Find the total revenue R(x) a. Find the price-demand equation ( the equation of the price in terms of x ) c. Find the price of 100 compact discs.

Answer:

undefined

Step-by-step explanation:

To find the slope

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

   = ( 6-5)/( -2 - -2)

   = (6-5) /(-2+2)

    = 1/0

We cannot divide by zero, so the slope is undefined

Answer:

13/7

Step-by-step explanation:

Method 1 :

1/2*3/7-5/7*1/2+2​ = (3/14)- (5/14) + 2

                            = -2/14 + 2            

                            = -2/14 + 28/14

                            = 26/14

                            = 13/7

Method 2 :

1/2*3/7-5/7*1/2+2​ = (1/2) [3/7 - 5/7] + 2

                            = (1/2)(-2/7) + 2            

                            = (-1/7) + 14/7

                            = 13/7

The component form of a vector refers to breaking the vector into components with unit vectors denoting the direction of each component. The general component form angled vectors in a two-dimensional space is given by:

\(\vec v=|v|cos\theta\hat{x}+|v|sin\theta\hat{y}\)

where |v| is the magnitude of the vector component and theta is the angle of the vector.

Using the magnitude and angle given for vector u we can write its component form :

\(\vec u=|u|cos\theta_u \hat{x}+|u|sin\theta_u \hat{y}\\\vec u=|5|cos(9)\hat{x}+|5|sin\(9) \hat{y}\\\vec v=5cos9_u\hat{x}+5sin9_u\hat{y}\)

Doing the same for v

\(\vec v=|v|cos\theta_u \hat{x}+|v|sin\theta_u \hat{y}\\\vec v=|1|cos5_u \hat{x}+|1|sin5_u \hat{y}\\\vec v=1cos5_u\hat{x}+sin5_u\hat{y}\)

Now adding both vector together

\(\vec u+\vec v=(5cos9_u\hat{x}+5sin9_u\hat{y})+(cos5_u\hat{x}+sin5_u\hat{x})\\\vec u+\vec v=(5cos9_u\hat{x}+cos5_u\hat{x})+(5sin9_u\hat{y}+sin5_u\hat{y})\)

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Answer:

  A dilation with a scale factor of 2

Step-by-step explanation:

Each image coordinate is double the corresponding pre-image coordinate. That means the figure was dilated by a factor of 2.

Answer:

4

3

+

5

9

2

−

8

0

Step-by-step explanation:

Answer:

New dimensions are; Width = 12m and Length = 12m

Step-by-step explanation:

Let length of rectangle be L

Let width be W

Area of rectangle has a formula;

Area = Length x Width = LW

We are given the area = 144 m²

So,

LW = 144 - - - (eq1)

Now, we are told that width is doubled and length is decreased by 12m but area remains the same.

Thus, we have;

Width as 2W and Length as L - 12.

Area = 2W(L - 12)

So,

2W(L - 12) = 144 - - - (eq2)

Equating eq 1 and 2,we have;

LW = 2W(L - 12)

W will cancel out to give;

L = 2(L - 12)

L = 2L - 24

2L - L = 24

L = 24m

From equation 1, LW = 144

Thus; W = 144/L = 144/24

W = 6m

So new design of rectangle now has a dimension of;

Width = 2W = 2 × 6 = 12m

Length = L - 12 = 24 - 12 = 12m

So, new dimensions are; Width = 12m and Length = 12m