numbers with the absolute value of -5

Answer:

y is 33 when x is 55

Step-by-step explanation:

set up using proportion and cross multiply to solve:

10/6 = 55/?

? = 33

Answer: m∠V = 28°

Step-by-step explanation:

     We know that a triangle's angles add up to 180. We will create an equation to solve for x. Then, we will substitute it back into the expression for angle V and simplify.

Given:

(9x - 8) + (2x + 2) + (3x + 4) = 180°

Simplify:

9x - 8 + 2x + 2 + 3x + 4 = 180°

Reorder:

9x + 2x + 3x - 8 + 2 + 4 = 180°

Combine like terms:

14x - 2 = 180°

Add 2 to both sides of the equation:

14x = 182°

Divide both sides of the equation by 13:

x = 13

---

m∠V = 2x + 2

m∠V = 2(13) + 2

m∠V = 28°

The equation to find the number of overtime hours worked on the second day is 19.5x = 87.75.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Earning of Lynette for one hour when she works overtime = $19.50

She worked overtime twice this week.

One day she worked 3 hours of overtime.

Earning on first day = 3 × $19.50 = $58.50

Total earnings for overtime = $146.25

Earnings on second day = $146.25 - $58.50 = $87.75

Let x be the number of hours worked overtime.

19.5x = 87.75

x = 4.5

Hence the required equation is 19.5x = 87.75.

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Step-by-step explanation:

8-3 = 5,

3-5 = -2 = the x coordinate of B

-2-4 =-6,

-2-6 =-8 = the y coordinate of B

(-2,-8) is the point B

A is 5 to the right of the midpoint, so B is 5 to the left of the midpoint

A is 6 up from the midpoint so B is 6 down from the midpoint

Answer:

5:3

Step-by-step explanation:

30/18 simplified is 5/3

So the simplified ratio is 5 girls for every 3 boys.

Answer:

5 girls to 3 boys

Step-by-step explanation:

Ratios can be written as:

a/b

a:b

a to b

We want to write the ratio of girls to boys in the Chess club. Therefore, "a" is girls and "b" is boys.

girls/boys

girls:boys

girls to boys

There are 30 girls and 18 boys.

30/18

30:18

30 to 18

The ratio can be simplified. Both 30 and 18 can be divided by 6.

(30/6) / (18/6)=5/3

(30/6) : (18/6)= 5:3

30/6 to 18/6= 5 to 3

a. The MRS is constant (not diminishing) at 1/3.

U(x,y) = 3x + y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / 3

The MRS is constant (not diminishing) at 1/3.

b. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

The MRS is diminishing because as y increases, the MRS decreases.

c. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.

d. The MRS depends on the ratio of y to x and can vary.

U(x,y) = x^2 - y^2

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x

The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.

e. The MRS depends on the values of x and y and can vary.

U(x,y) = x + y / (x * y)

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)

The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.

Now let's move on to the second part of the question:

For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.

To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.

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The cost function is composed of various pieces of information that relate to the costs of the production process.

Ashley's cost function includes the cost of her grandma's heat and cable TV and Yam price to make toys.The cost function of Ashley is the economic relationship between the costs incurred by Ashley and the production of her products. It is a mathematical function that helps her analyze the production process to make her product profitable. The cost function is composed of various pieces of information that relate to the costs of the production process.Here are the pieces of information included in Ashley's cost function:- The cost of her grandma's heat and cable TV- Yam price to make toysTherefore, the correct answer is B and E.

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Answer:

15 percent

Step-by-step explanation:

because add 2 adults =£110

2 children =£90

=£200

£170 = 15% off

The area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis is 2.08 square units.

We have been given parametric equations x = t^2 − 3t, y = √t

We need to find the area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

NWe know that the formula to find the area under the curve.

A = ∫[a to b] g(t)f'(t) dt

here, a = 0 and b = 3

so, A = ∫[0 to 3] √t (2t - 3) dt

A = ∫[0 to 3] (2t√t - 3√t) dt

A = ∫[0 to 3] (2t^(3/2) - 3t^(1/2)) dt

A = [4/5 t^(5/2) - 2 t^(3/2)]_[t = 0, t = 3]

A = 4/5 3^(5/2) - 2 3^(3/2) - 0 + 0

A = 4/5 3^(5/2) - 2 3^(3/2)

A = 6√3 /5

A = 2.08

Therefore,  the area of the curve is 2.08 square units.

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The domain of the function is all real numbers because there are no restrictions on the values of x. Therefore, the overall range of the function is {1} ∪ [3, ∞).

In mathematics, a function is a rule that assigns a unique output value to each input value. A function is typically denoted by a symbol, such as f(x), where f is the name of the function and x is the input variable. The output value of the function is denoted by f(x), which means "the value of the function f at x". A function takes input values from a set called the domain, and produces output values from a set called the range. The domain and range can be any set of numbers, such as the real numbers, integers, or even complex numbers.

Here,

The given function is:

f(x) =

1, x+2, x < -2

2, x²+2x+3, x > -2

To create a table of values, we can choose some values of x and plug them into the function to find the corresponding values of f(x):

x f(x)

-3 -1

-2 -2

-1 4

0 3

1 6

The domain of the function is all real numbers because there are no restrictions on the values of x.

The range of the function depends on the two cases:

For x < -2, the value of f(x) is always 1, so the range of f(x) in this case is {1}.

For x > -2, the value of f(x) is always greater than or equal to 3, so the range of f(x) in this case is [3, ∞).

To graph the function, we can plot the points from the table of values and connect them with lines:

          |

    20 ___|_____

       |   |     \

    15 |          \

       |           \

    10 |            \

       |             \

     5 |              \

       |               \

     0 |----------------\_____________

       -4 -3 -2 -1  0  1  2  3

The graph consists of two parts: a horizontal line at y = 1 for x < -2, and a parabolic curve opening upwards for x > -2. The graph is continuous at x = -2, since both the constant and quadratic functions agree at this point.

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In the short run, a decrease in market power (or monopolization) will decrease the price level. Hence option B is correct.

The ability of a corporation or group of enterprises to affect the price or quantity of goods or services in a market is referred to as market power. A company with market power has the ability to raise prices above the level of the market, which reduces consumer surplus and may result in inefficiencies. Market dominance can develop as a result of things like entry hurdles, brand awareness, or control over vital resources. In order to encourage competition and safeguard consumer welfare, governments may restrict or dissolve businesses that hold a large amount of market power. Market structure and performance are significantly impacted by market power, a major notion in industrial organisation.

This is because when a firm has market power, it can charge a higher price for its output due to its ability to restrict output and control the market. When this market power decreases, the firm loses the ability to control the price and must lower it to remain competitive. This decrease in price may also lead to an increase in output as the firm may seek to sell more units to make up for the lost revenue from lower prices.

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Answer:

TRUE

Step-by-step explanation:

Angle <A and angle <B are complementary, which means their sum must be = 90

Angle <B and angle <C are supplementary which means their sum must be = 180

Now let's see

m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1)

first find the sum of A and B

3x + 17 + 55 - x = 90 add like terms

2x + 72 = 90 subtract 72 from both sides

2x = 18 divide both sides by 2

x = 9

TRUE OR FALSE is asked for

m∠A=44, m∠B=46, and m∠C=134

to find that we just replace c with 9 with every expression given for angles

m<A = 3x + 17

m<A = 3*9 + 17 = 44

m<B =  55 - x

m<B = 55 - 9 = 46

m<C = 134, we don't really need to calculate one by one since the angle are complementary and supplementary.

The answer is TRUE

The statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

∠A and ∠B are complements, while ∠B and ∠C are supplements.

∠A + ∠B = 90 degree

3x + 17 + 55 - x = 90

2x = 18

x = 9

Angle ∠B and angle ∠C are supplementary:

∠B + ∠C = 180

55 -x + 67(x/3  - 1) = 180

x = 9

Put the value of x and find angles A, B, and C.

m∠A = 44

m∠B = 46

m∠C = 134

∠A + ∠B = 90

∠B + ∠C = 180

The above statement is true.

Thus, the statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

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Answer:

t = time in seconds after the ball was thrown

h(t) =  the height of the ball after t seconds.

h(t)=−16t2+64t+80

Question (1): What is the maximum height of the ball?

Remember that the graph of the function is a parabola open down because the leading coefficient is negative. Therefore, to get the maximum height we just have to find the vertex of this parabola. Since the function is in standard form h(t) = at2+bt+c, the formula for getting the vertex is:

V(h,k) = (-b/(2a), h(-b/(2a)))

-b/(2a) = -64/(2*(-16)) = 2 seconds (the time it reaches the highest point.)

h(-b/(2a)) = h(2) = -16(2)2 + 64(2) + 80 = 144 feet (Maximum height)

Question (2): How many seconds does it take until the ball hits the ground?

If it hits the ground, it means the height is zero. h(t)=0.

0= -16t2 + 64t + 80

Factor:

0 = -16(t2 - 4t - 5)

0 = -16(t - 5) (t + 1)

t-5 =0 or t+1=0

We eliminate t+1=0 because of the negative value of t. Time should always be positive in this case.

t = 5 seconds to hit the ground.

(a) After 5 years, there will be approximately $2,049.71 in Felipe's account if no withdrawals are made.

(b) The interest earned on Felipe's investment after 5 years will be approximately $149.71.

To calculate the amount of money in Felipe's account after 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A = the final amount in the account,

P = the principal amount (initial investment),

r = the annual interest rate (as a decimal),

n = the number of times the interest is compounded per year,

t = the number of years.

In this case, Felipe's principal amount is $1900, the annual interest rate is 1.48% (or 0.0148 as a decimal), the interest is compounded quarterly (n = 4), and the investment period is 5 years (t = 5).

(a) Plugging in these values into the formula, we have:

A = $1900(1 + 0.0148/4)^(4*5) ≈ $2,049.71.

Therefore, after 5 years, there will be approximately $2,049.71 in Felipe's account if no withdrawals are made.

(b) To calculate the interest earned on Felipe's investment, we subtract the initial investment from the final amount:

Interest = A - P = $2,049.71 - $1900 ≈ $149.71.

Therefore, the interest earned on Felipe's investment after 5 years will be approximately $149.71.

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Answer:

30 tenth

Step-by-step explanation:

Plotting 12 and 15 on a number line ;

The difference between the two values ; 12 and 15 is ;

15 - 12 = 3 units

Converting the difference in unit to tenth:

1 unit = 10 tenth

3 units = x tenth

x = 10 * 3

x = 30 tenth

Hence, approximate difference in tenth between 12 and 15 is 30 tenth

Hi there!

\(\large\boxed{f''(x) = 2 - \frac{4}{x^{3}}}\)

\(f(x) = x^2 - \frac{2}{x}\)

Recall the power rule:

\(\frac{dy}{dx} x^n = nx^{n-1}\)

Rewrite the function for ease of differentiation:

\(f(x) =x^2 - 2x^{-1}\)

Use the power rule:

\(f'(x) = 2x + 2x^{-2}\)

Take the derivative once more:

\(f''(x) = 2 - 4x^{-3}\)

Rewrite:

\(f''(x) = 2 - \frac{4}{x^{3}}\)

Answer:

Plot the -4 one point to the right of -5

Plot 7 two points to the right of 5

Plot 12 two points to the right of 10

Step-by-step explanation:

Have a nice day

Using it's formula, the distance between the points A(13,2) and B(7,10) is of 10 units.

Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

In this problem, the points are A(13,2) and B(7,10), hence the distance is given by:

\(D = \sqrt{(13 - 7)^2+(2 - 10)^2}\)

D = sqrt(100)

D = 10 units.

The distance between the points A(13,2) and B(7,10) is of 10 units.

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The expressions that show the number of students for each activity are;

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.

A set is a mathematical model for a collection of various things.

We are given;

Total number of students in the middle school = z

A) From the given table, we can deduce that;

B; Now, the expression to show the students that like either drama or dance is;

(1/7)z + 26 + (1/7)z + 22

>> (2/7)z + 48

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A middle school with z students ran a survey to determine the students' favorite activities. The table indicates the number of students who enjoy each activity. Answer parts A and B.

Table:

Activity:

Dance- 22 more than one-seventh of the students

Baseball- 24 fewer than four-sevenths of the students

Drama- 26 more than one-seventh of the students.

Answer: 15,600 different choices for initials

Step-by-step explanation:

26 choices for the first, 25 for the second, and 24 for the third. When multipled, this is 15600.

We must solve for x using the addition principle, the equation is as follows

In conclusion, the answer is x = -9

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

69

Step-by-step explanation:

Answer:

$54.68

Step-by-step explanation:

10.7 × 7 × $0.73 = $54.677

($54.68 to 2 decimal places)

Answer:

1a) h = 2

1b) "h" represents the amount of hours the electrician worked, so the electrician worked two hours. "60" represents the cost per hour. "20" represents the beginning service fee. "140" represents the total cost in the end.

2a) This impacts the meaning because instead of the equation, meaning that the customer of the electrician payed exactly $140, it is turned into an inequality, which means the customer payed $140 at most.

2b) The electrician charges a $20 service fee, plus $60 per hour for electrical repairs. The customer payed $140 at most. This is shown with the following equation: 60h + 20 < 140

Step-by-step explanation:

60h+20=140

60h=120

h=2

a) The average rate of change over the interval [−2,2] is 4.

b) The instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4).

A) To find the average rate of change of g(x) over the interval [-2,2], we need to calculate the slope of the line passing through the points (-2,g(-2)) and (2,g(2)).

g(-2) = (-2)³ - 6 = -8 - 6 = -14

g(2) = (2)³ - 6 = 8 - 6 = 2

Therefore, the slope of the line passing through these two points is:

(g(2) - g(-2))/(2 - (-2)) = (2 - (-14))/(2 - (-2)) = 16/4 = 4

B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivative of g(x):

g'(x) = 3x²

At x=-2, the instantaneous rate of change of g(x) is:

g'(-2) = 3(-2)² = 12

At x=2, the instantaneous rate of change of g(x) is:

g'(2) = 3(2)² = 12

We can see that the instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4). This is because the function g(x) is not a straight line and its rate of change varies across the interval.

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The mode of the survey results is 6 hours, as this was the most commonly reported number of hours of video games played in the previous week.

The mode of the survey results is the most frequently occurring number of hours of video games played in the previous week. In this survey, the most commonly reported number of hours played was 6. This is because 9 students reported playing 6 hours of video games in the previous week, which is the highest number of students reporting any single amount of hours played. The other numbers of hours played were reported less often, with 2 students reporting 5 hours, 4 students reporting 2 hours, 2 students reporting 1 hour, and 3 students reporting 0 hours. Therefore, the mode of the survey results is 6 hours.

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