Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86. The cost of the call and the length of the call are related. What is the cost y of a call of x minutes duration? (Assume this is a constant-increase situation) and How long can you talk on the phone if you have $12 to spend? *
Your answer

The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.

To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.

Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.

The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.

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Answer:

The shaded region in all of the answers are equal.

Step-by-step explanation:

Since squares have equal sides, the area of each square is 12 squared or 144.

The area of the circle in A is pi*radius squared. The diameter is 12, because that is the side length of the square. This means the radius is 6 because the radius of a circle is always half the diameter. So, the area equals 36pi.

The area of the shaded region of A is 144-36pi.

In B, the diameter of each circle is half of what it was in the circles in answer A. So, the diameter is 6 and the radius is 3. The area of each circle is 9pi, and 9 pi * 4 circles is 36pi.

The area of the shaded region of B is 144-36pi.

In C, the diameter of each circle is a third of what it was in the circles in answer A. So, the diameter is 4, and the radius is 2. The area of each circle is 4pi, and 4pi * 9 circles is 36pi.

The area of the shaded region of C is 144-36pi.

Answer:

176degrees

Step-by-step explanation:

Find the diagram attached. From the diagram;

arcGC  = = arc BG

5x + 28 = 9x - 20

5x - 9x = -20  28

-4x = -48

x = -48/-4

x = 12

Get <AB

Since <AB = <BC

<BC = arcGC +arc BG

<AB = arcGC+ arc BG

<AB = 5x + 28 + 9x - 20

<AB = 14x + 8

<AB = 14(12) + 8

<AB = 168 + 8

<AB = 176degrees

Hence the arc AB is 176degrees

Answer:

Pi: 3.141592653589793238

3.142 I believe.

Step-by-step explanation:

The solution to the equation -2(x + 3) = -6 is x = 0.

To simplify the expression 5t + 7 + 8b, we can combine like terms.

There are two like terms in the expression: 5t and 8b.

Combining the like terms gives us:

5t + 8b + 7

Therefore, the simplified form of the expression 5t + 7 + 8b is 5t + 8b + 7.

Regarding the equation -2(x + 3) = -6:

To solve this equation, we can follow these steps:

Distribute the -2 to the terms inside the parentheses:

-2 * x + (-2) * 3 = -6

This simplifies to:

-2x - 6 = -6

Move the constant term to the right side by adding 6 to both sides of the equation:

-2x = 0

Divide both sides of the equation by -2 to isolate the variable x:

x = 0 / -2

Simplifying the right side of the equation gives us:

x = 0

The solution to the equation -2(x + 3) = -6 is x = 0.

The simplified expression 5t + 7 + 8b remains as 5t + 8b + 7, and the solution to the equation -2(x + 3) = -6 is x = 0.

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It would take 3.43 hours to paint living room working together.

In this question, we have been given Fran were to paint her living room alone, it would take her 5 hours. Her sister Wanda could do the job in 8 hours.

We need to find the amount of time required them working together.

Let they need 'x' hours to paint living room together.

So, we get an equation,

1/6 + 1/8 = 1/x

We need to find the value of x.

1/x = (8 + 6) / 48

1/x = 14/48

x = 48 / 14

x = 3.43 hours

Therefore, it would take 3.43 hours to paint living room working together.

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Connor has 4/5 hours more to play the game he played 3 times, and each time he takes 2/5 hours to finish the game.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have: Connor has 2 hours to play a game that takes 2/5 hour each time. He plays the game 3 times.

Let's suppose he will have x hours after playing the 3 times

Each time he will, he takes 2/5 hours.

(2×3)/5 + x = 2

6/5 + x = 2

x = 2 – 6/5

x = 4/5 hours

Thus, Connor has 4/5 hours more to play the game he played 3 times, and each time he takes 2/5 hours to finish the game.

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Answer:

Step-by-step explanation:

We can start by setting up an inequality based on the given information:

54 / (x + 3) ≥ 6

We can simplify this inequality by multiplying both sides by (x + 3):

54 ≥ 6(x + 3)

Next, we can simplify further by distributing the 6 on the right side of the inequality:

54 ≥ 6x + 18

Subtracting 18 from both sides, we get:

36 ≥ 6x

Dividing both sides by 6, we get:

6 ≥ x

Therefore, the range of values of x that satisfy the given conditions is:

x ≤ 6

So any value of x that is less than or equal to 6 will result in a quotient of 54 divided by a sum that is at least 6, which is greater than or equal to 6.

Answer:

Cost of each hoodies = $25.5

Cost of each t-shirt = $12.75

Step-by-step explanation:

Given:

Cost of 2 t-shirt and 2 hoodies = $76.50

Cost of 5 t-shirt and 3 hoodies = $140.25

Find:

Cost of each t-shirt

Computation:

Assume;

Cost of each t-shirt = t

Cost of each hoodies = h

So,

2t + 2h = 76.50..........eq1

5t + 3h = 140.25..........eq2

Eq 1 x 2.5

5t + 5h = 191.25.............eq3

Eq3 - Eq2

2h = 51

h = 25.5

Cost of each hoodies = $25.5

2t + 2h = 76.50

2t + 2(25.5) = 76.50

t = 12.75

Cost of each t-shirt = $12.75

To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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The number of tiles in figure 70 and figure 93 are 142 and 188.

Figure 2 = 6

Figure 3 = 8

The common difference = 8 - 6

= 2

figure 2 = a + (n - 1)d

Where,

a = first term

figure 2 = a + (n - 1)d

6 = a + (2 - 1)2

6 = a + (1)2

6 = a + 2

6 - 2 = a

a = 4

Figure 70 = a + (n -1)d

= 4 + (70-1)2

= 4 + (69)2

= 4 + 138

Figure 70 = 142

Figure 93 = a + (n -1)d

= 4 + (93 - 1)2

= 4 + (92)2

= 4 + 184

Figure 93 = 188

Therefore, figure 70 and 93 have 142 and 188 tiles respectively.

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Answer:

The function that represents the graph is:

Explanation:

The graph represents a parabola with 2 as the horizontal coordinate of the vertex, and 4 as the vertical coordinate of the vertex.

It is written as:

Answer:

1/16,807 chance that they all will be born on Friday

Probably 5/7, but don't take my word for it.

Step-by-step explanation:

There are 7 days of the week.

There is a 1/7 chance for one kid to be born on a certain day of the week.

We can attach an exponent of 5 since the 1/7 is a constant, and I'm not going to bother typing the same thing over and over again.

(1/7)^5 = 1/16,807.

The probability of all of them being born on Friday or anyday is 1/16,807.

The probability of each person being born on a different day of the week is  probabily going to be 5/7, but it could be different, because you need to factor in the requirement that they are not born on the same day.

I can guarantee that the first question is probably correct, but not the second.

Answer:

So, if you need to convert the fraction into a decimal, 3/4=0.75. So, I think it's 19-0.75 I'm not sure if I'm correct.

Step-by-step explanation:

Answer:

let no be x

293+x=326

x=326-293=33

33 is needed to add.

Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

Answer:

1/5 of your money is = 30

Step-by-step explanation:

2/5 of your money is equal to 60, so if you divide 60 by 2 you will get 30, which is 1/5 of your money. A way to check if it is right is by multiplying 30 by 5, which is 150, and divide it by 5, to see if it matches (150 : 5 = 30).

hope this helps!

answer:30

explanation:

2/5×X=60

X=150

means your money is 150

so 1/5 of your money is 1/5×150=30

Answer:

The quotient is 2

I don't think this needs solution

Answer:

the quotient is 2

Step-by-step explanation:

1/2÷1/4

1/2×4/1

=2

we will need at least 96 bags of sand to cover the base of the circular pool.

what is circle?

A circle is a two-dimensional geometric shape consisting of all the points that are equidistant from a given point, called the center.

The area of a circular pool with a diameter of 22 feet can be calculated using the formula:

A = πr^2

where A is the area of the circle, π is a constant (approximately equal to 3.14), and r is the radius of the circle (which is half the diameter).

In this case, the diameter is 22 feet, so the radius is:

r = d/2 = 22/2 = 11 feet

Now we can calculate the area of the circle:

A = πr^2 = 3.14 x 11^2 = 379.94 square feet (rounded to 2 decimal places)

To cover this area with sand, we need to know how many bags of sand are required. We are told that one bag of sand covers about 4 square feet, so we can calculate the number of bags of sand required as follows:

Number of bags = Area of pool / Area covered by one bag

Number of bags = 379.94 square feet / 4 square feet per bag

Number of bags ≈ 95 bags

Since we need to round up to a whole number of bags, we will need at least 96 bags of sand to cover the base of the circular pool.

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Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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Answer:

\(x=5\)

Step-by-step explanation:

From the question we are told that

The logarithmic function \(y= 398-73 lnx\)

Price p= $275

Generally we solve mathematically for the equation \(y= 398-73 lnx\)

\(y= 398-73 lnx\)

\(275= 398-73 lnx\)

\(73 lnx=123\)

\(lnx=\frac{123}{73}\)

Therefore

\(x=e^(^\frac{123}{73}^)\)

\(x=5.4\)

Nearest whole number

\(x=5\)

The number of required hand-held electric organizers would be 5, option b. Understand the step-by-step calculations below.

The logarithm is an exponent or power to which a base must be raised to obtain a given number.

Mathematically, logarithms are expressed as, m is the logarithm of n to the base b if \(bm = n\), which can also be written as \(m = log_nb\).

Given function is,

\(y=398-73 lnx\)

Also, the cost is $275 then from the given equation,

\(398-73 lnx=275\)

Now, solving the above equation we get,

\(398-73 lnx=275\\73ln=398-275\\lnx=\frac{123}{73}\)

Now, shifting the algorithm into another side we get the exponential equation as,

\(\\x=e^{\frac{123}{73} }\\x=5.39\\x\approx5\)

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Therefore, the matrix equation represents the system of equations

4x - 2y = -7

0x + 3y = 5 is given by

\(\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-7\\5\end{array}\right]\).

Three easy steps must be taken in order to express any system of linear equations in matrix form:

1. First, create a single matrix with all the coefficients. An acronym for this is a coefficient matrix.

2. Multiply this matrix by the system setup variables in a different matrix. The variable matrix is another name for this.

3. In another matrix, place the solutions on the other side of the equal sign. The answer matrix is another name for this.

Given system of linear equations:

4x - 2y = -7

0x + 3y = 5

The coefficient matrix is \(\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right]\).

The variable matrix is \(\left[\begin{array}{ccc}x\\y\end{array}\right]\).

[ Since \(\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4x-2y\\0x+3y\end{array}\right]\) ]

The answer matrix is \(\left[\begin{array}{ccc}-7\\5\end{array}\right]\).

Therefore, the matrix equation represents the system of equations

4x - 2y = -7

0x + 3y = 5 is given by

\(\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-7\\5\end{array}\right]\). So, the last option is correct.

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To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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Answer:

33 + p = 43 is the answer

Answer:

$242.82

Step-by-step explanation: