Use a ratio box to solve this problem. The cost of a 10-minute call to Boise decreased by 20%. If the cost before the decrease was $3.40, what was the cost after the decrease?

Answer:

Step-by-step explanation:

Given a table of values (x, y) = {(5, 6.5), (7, 9.1), (9, 11.7)}, you want to know (a) if the quantities are proportional, and (b) the equation for the relation.

A proportion is a relation that can be described by the equation ...

  y = kx

where k is the constant of proportionality.

To see if the table describes a proportional relationship, we can compute k for each of the ordered pairs.

  k = y/x = 6.5/5 = 9.1/7 = 11.7/9 = 1.3

The value of k is the same for all of the given table values, so ...

  the quantities are proportional.

As we saw above, the equation y = kx can be used with the value k = 1.3 for this relationship:

  y = 1.3x

Answer:

a is not equivalent to b and c.

Step-by-step explanation:

a.

\(50( {2}^{x + 2} ) = 25 \times 2( {2}^{x + 2} ) = 25( {2}^{x + 3} )\)

b.

\(25( {2}^{2x + 1} ) \)

c.

\(50( {4}^{x} ) = 50( { {2}^{x} )}^{2} = 50( {2}^{2x} ) = 25 \times 2( {2}^{2x} ) = 25( {2}^{2x + 1} )\)

The dimensions of the field should be 125m by 100m to enclose the maximum area.

To solve this problem, we can use the fact that the area of a rectangle is given by A = lw, where l and w are the length and width of the rectangle, respectively. Since the field is to be subdivided into four congruent plots, we can express the width in terms of the length as w = (1/4)(l).

We can then use the fact that the total length of fencing available is 6000m to set up an equation for the perimeter of the rectangle, which is given by P = 2l + 5w. Substituting w with (1/4)(l), we get P = 2l + 5((1/4)(l)) = (9/2)l.

Solving for l in terms of P, we get l = (2/9)P. Substituting this expression for l into the equation for the area, we get A = (1/4)(l)(w) = (1/4)(l)((1/4)(l)) = (1/16)l^2.

We can now express the area in terms of P as A = (1/16)((2/9)P)^2 = (4/81)(P^2). To find the maximum area, we can take the derivative of A with respect to P and set it equal to zero, which gives dA/dP = (8/81)P = 0. This implies that P = 0 or P = 81/8. Since P cannot be zero, we have P = 81/8.

Substituting this value of P back into the equation for l, we get l = (2/9)(81/8) = 18.75. Finally, substituting l and w = (1/4)(l) into the equation for A, we get A = (1/16)(18.75)(4.6875) = 117.1875. Therefore, the dimensions of the field should be 125m by 100m to enclose the maximum area.

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Based on the diagram, the point of tangency is Point Z. Therefore, the answer is B.

A point of tangency is a point at which a straight line, called a tangent line, touches a curve or a circle at only one point.

At the point of tangency, the tangent line is perpendicular to the radius of the circle that intersects the point of tangency.

The point of tangency is the point where a tangent line to the circle touches the circle at only one point.

In the given diagram, the line segment XZ appears to be a tangent to the circle.

Therefore, the point of tangency is the point where the line segment XZ touches the circle.

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Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

Marshall is wondering whether he can participate in the LLP again next year. The statement that is true is "He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000.

The Lifelong Learning Plan is a program that helps Canadian residents finance their post-secondary education through their registered retirement savings plans (RRSP). If an individual is attending school full-time, they can withdraw up to $10,000 a year from their RRSP under the program, or up to $20,000 in total. There are certain rules that must be followed by an individual participating in the LLP. For example, withdrawals must be made within four years of enrolling in an eligible educational program, and repayments must begin within the same period.

Here are the statements: Provided he repays his LLP balance in full by the end of this year, Marshall can participate in the LLP again next year.Marshall can only participate in the LLP once over his lifetime. However, his wife can make a LLP withdrawal from her RRSP on his behalf. He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000. He can only participate in the LLP a second time if he repays his LLP balance in full and waits 5 years before he returns to school.The correct statement is: He can participate in the LLP again, but only to the extent that his existing LLP balance is less than $20,000.

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The property that allows the statement, 3 = x, to be written as x = 3, is: symmetric property of equality.

The symmetric property of equality states that for any real numbers, for example, a and b, if a = b, then, b = a. This means that, if the value of a equals b, then symmetrically, the value of b will also be equal to the value of a.

Thus, given the statement that, 3 = x, based on the symmetric property of equality, we can also state that the value of x, also equals 3. Mathematically, we can state that x = 3.

therefore, the property that allows the statement, 3 = x, to be written as x = 3, is: symmetric property of equality.

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What happens to the mean: It increases by 22.

What happens to the median: It stays the same.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data, we have;

Total, F(x) = 365 + 471 + 496 + 526 + 542 + 552 + 589 + 595

Total, F(x) = 4,136

Mean = 4,136/8

Mean = 517.

When the number 365 from this list changes to 541, the mean is given by;

Total, F(x) = 541 + 471 + 496 + 526 + 542 + 552 + 589 + 595

Total, F(x) = 4,312

Mean = 4,312/8

Mean = 539.

Difference = 539 - 517 = 22 (It increases by 22).

However, the median stays the same.

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Answer:

(a) What happens to the mean?

Zero....stays the same

(b) What happens to the median?

Zero...stays the same

Answer:

B which is b=4

Step-by-step explanation:

POSITIVE FOUR, just to be clear

Answer:

the answer is b

Step-by-step explanation:

Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

Answer:

6

Step-by-step explanation:

Plug the values of a and b into the equation.

4(3) + 5(-1.2)

12 + (-6)

Adding negatives basically means subtracting, so...

12-6 = 6

Therefore your answer is 6

Hope this helps!

Answer:

6

Step-by-step explanation:

4 a + 5 b

a=3 and b= -1.2

4(3) +5(-1.2)

12 +-6

6

To simplify the following equation, f(x + h) - f(x) = h.

Using the definition of the difference quotient:

f(x + h) - f(x) / h = [2(x + h)² - 5(x + h) + 10] - [2x² - 5x + 10] / h

= [2(x² + 2xh + h²) - 5x - 5h + 10] - [2x² - 5x + 10] / h

= [2x² + 4xh + 2h² - 5x - 5h + 10] - [2x² - 5x + 10] / h

= 2x² + 4xh + 2h² - 5x - 5h + 10 - 2x² + 5x - 10 / h

= (4xh + 2h² - 5h) / h

= 4x + 2h - 5.

Therefore, f(x + h) - f(x) = 4x + 2h - 5h

= 4x - 3h.

So, f(x + h) - f(x) / h = (4x - 3h) / h

= 4 - 3(h/h)

= 4 - 3

= 1.

Therefore, f(x + h) - f(x) = h.

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Working

Q=k÷p

0•25=k÷2(cross multiply)

0•50=k or k=0•50

Answer

Q=0•50÷2

The optimal point values for x1, x2, λ, and μ (Lagrange multipliers) in the given problem are:

x1 = 1

x2 = 1

λ = -4

μ = 2

To solve the optimization problem using the Lagrange multipliers technique, we first construct the Lagrangian function L(x1, x2, λ) by incorporating the equality constraint:

L(x1, x2, λ) = f(x1, x2) - λ(g(x1, x2))

Where f(x1, x2) is the objective function, g(x1, x2) is the equality constraint, and λ is the Lagrange multiplier.

In this case, the objective function is f(x1, x2) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6, and the equality constraint is g(x1, x2) = x1 + x2 - 2.

The Lagrangian function becomes:

L(x1, x2, λ) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6 - λ(x1 + x2 - 2)

To find the optimal values, we need to find the critical points by taking partial derivatives of L with respect to x1, x2, and λ and setting them equal to zero. Solving these equations simultaneously, we get:

∂L/∂x1 = 4x1 - 2x2 - 6 - λ = 0

∂L/∂x2 = -2x1 + 2 + λ = 0

∂L/∂λ = -(x1 + x2 - 2) = 0

Solving these equations, we find x1 = 1, x2 = 1, and λ = -4. Substituting these values into the equality constraint, we can solve for μ:

x1 + x2 - 2 = 1 + 1 - 2 = 0

Therefore, μ = 2.

The optimal point values for the variables in the optimization problem are x1 = 1, x2 = 1, λ = -4, and μ = 2. The Lagrange multipliers λ and μ represent the rates of change of the objective function and the equality constraint, respectively, with respect to the variables. They provide insights into the sensitivity of the objective function to changes in the constraints and can indicate the impact of relaxing or tightening the constraints on the optimal solution. In this case, the Lagrange multiplier λ of -4 indicates that a small increase in the equality constraint (x1 + x2 - 2) would result in a decrease in the objective function value. The Lagrange multiplier μ of 2 indicates the shadow price or the marginal cost of satisfying the equality constraint.

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Answer:  Choice A)  x = 45 degrees

==========================================================

Explanation:

We're given △ABC≅△EFG

The order of the letters is important. This is because we have these pairings:

Because of these pairings, and because of the triangles are congruent, we then can say

Then recall that for any triangle, the three inside angles add to 180

A+B+C = 180

50+x+85 = 180

x+135 = 180

x = 180-135

x = 45

You chose the correct answer.

Answer:

7

Step-by-step explanation:

Sure, I can definitely help you out with your question. To calculate the equation for an investment of $500 earning an interest rate of 13 percent, we need to use the following formula:
Interest = Principal x Rate x Time
Here, the principal is the initial amount of the investment, which is $500. The rate is the interest rate, which is 13 percent or 0.13 as a decimal. And, the time is the duration of the investment, which we'll assume is one year.
So, plugging in these values into the formula, we get:
Interest = $500 x 0.13 x 1
Simplifying this equation, we get:
Interest = $65
Therefore, the interest earned on a $500 investment with a 13 percent interest rate for one year is $65. This means that the total value of the investment after one year would be $565 ($500 initial investment + $65 interest earned).:
Future Value = Principal * (1 + Interest Rate)^n
In this case, the principal is $500, the interest rate is 13% (0.13 as a decimal), and n represents the number of years.

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The day the athlete spent the longest total amount of time training is Friday

Monday:

Tuesday:

Wednesday:

Thursday:

Friday:

The day the athlete spent the longest total amount of time training is Friday

The median total number of minutes the athlete spent training each day = (30 + 70 + 35 + 80 + 85) / 5

= 300 / 5

= 60 minutes

Percent of the total number of minutes the athlete spent training for the 5 days was spent on strength training = (20 + 10 + 15 + 30 + 45) / 300 × 100

= 120/300 × 100

= 0.4 × 100

= 40%

(Mean of aerobic + mean of strength training) = Mean of total training

(10 + 60 + 20 + 50 + 40) /5 + (20 + 10 + 15 + 30 + 45) / 5 = (30 + 70 + 35 + 80 + 85) / 5

(180/5 + 120/5) = 300/5

36 + 24 = 60 minutes

Therefore, the sum of the mean number of minutes spent on aerobic training and the mean number of minutes spent on strength training is equal to the mean total number of minutes spent training

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Answer:

Step-by-step explanation:

The function \(g(x) =|x + 1| - 7\) decreases at interval \((-\infty, -1)\)

The parent function is given as:

\(f(x) =|x|\)

The transformed function is given as:

\(g(x) =|x + 1| - 7\)

Both functions are absolute value functions, and an absolute value function is represented as:

\(y=a| x-h |+k\)

Where, the vertex of the function is:

\(Vertex = (h,k)\)

By comparing \(y=a| x-h |+k\) and \(g(x) =|x + 1| - 7\), we have:

\((h,k) = (-1,-7)\)

\(a= 1\)

Because (a) has a positive value (i.e. 1) and (h) is negative, then the vertex represents a minimum.

This also means that, the function will decrease from infinity, till it gets to the x-coordinate of the vertex.

Hence, the function \(g(x) =|x + 1| - 7\) decreases at interval \((-\infty, -1)\)

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Answer:

5 men and 2 women = 7 people with no restriction

a) Two women must sit next to each other:

b) The two women must not sit next to each other:

3 men and 5 women with no restriction:

Answer:

Simplest form of radical √245c³ = 7c√5c

Step-by-step explanation:

Given radical value:

√245c³

Find:

Simplest form of radical √245c³

Computation:

Given value

√245c³

Step 1 :

Prime factorisation of given radical value

Simplest form of radical √245c³ = √5 × 7 × 7 × c × c × c

By taking 7 and c from out of root

Simplest form of radical √245c³ = 7 × c √ 5 × c

Simplest form of radical √245c³ = 7c√5c

The function that models the cone's height as a function of its volume is; h = 3V/28²π.

Since Volume, V is given by the formula;

To determine a function that models the cone's height as a function of its volume; we must evaluate as follows;

As such, when the volume of the cone is 5488π cm3;

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Step-by-step explanation:

\(midpoint = ( \frac{ \frac{1}{3} - \frac{7}{3} }{2} , \frac{ \frac{5}{12} + \frac{7}{12} }{2} )\)

\( = ( \frac{ \frac{ - 6}{3} }{2} , \frac{ \frac{12}{12} }{2} )\)

\( = ( \frac{ - 2}{2} , \frac{1}{2} )\)

\( = ( - 1,0.5)\)

The principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

What is continuous compounding?

There is no cap on how frequently interest can accumulate thanks to continuous compounding. A balance can compound continuously an unlimited number of times, which means interest is earned on it constantly.

We have,

9 years in an account with a 3.9% annual interest rate compounded continuously,

an investment is worth a total of $17,757.16.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.9/100

r = 0.039 per year,

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Hence, the principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

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Answer:

$12,500.75

Step-by-step explanation:

I got it right.

Answer: The interest earned on a principal of $646 invested at an interest rate of 5% for three years is $96.9

The simple formula for interest is:

Simple Interest = Principal * Interest Rate * Time in years

          ?               =     646      *       5/100       *            3

          ?               =   9690/100

          ?               =  $96.9

The interest earned is $96.9

Brainliest pwease if the answer is correct!

The quadrilateral ABCD is a trapezium is proved.

To show that quadrilateral ABCD is a trapezium (or trapezoid), we need to prove that one pair of opposite sides is parallel.

Given:

- Diagonals AC and BD intersect at point O.

- The ratio of AO to BO is equal to the ratio of CO to DO,

i.e., AO/BO = CO/DO.

Proof:

1. Consider triangle AOB and triangle COD.

2. By the property of intersecting lines,

<AOC = <BOD {vertically opposite angles}.

3. Similarly, angles COA and DOB are equal.

4. From the given ratio

AO/BO = CO/DO, we can write

AO/CO = BO/DO.

(Dividing numerator and denominator of both sides by CO)

5. By the Angle-Angle (AA) similarity criterion,

Triangles AOC and BOD are similar.

6. If triangles are similar, their corresponding angles are equal.

7. Therefore, angles ACO and BDO are equal.

8. Since angles AOC and BOD are equal, and angles ACO and BDO are equal, we have:

  ∠AOC = ∠BOD and ∠ACO = ∠BDO.

9. By the Alternate Interior Angles Theorem, since ∠ACO and ∠BDO are equal, lines AB and CD are parallel.

10. Hence, quadrilateral ABCD is a trapezium.

Therefore, by showing that one pair of opposite sides (AB and CD) is parallel, we have proved that quadrilateral ABCD is a trapezium.

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Answer:

y = 3x - 10

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

68% falls between the first standard deviation from the mean.

plus minus two would fall under 95%