If you’re are doing a gift exchange, and everyone has to spend at least 10 dollars but less than 20 dollars, what inequality represents the situation?


A. 10 > x > 20

B. 10 ≤ x < 20

C. 10 ≥ x ≥ 20

D. 10 < x < 20

Answer:

x = 10

Step-by-step explanation:

\(\frac{x-4}{4}\) = \(\frac{15}{x}\)  ( x > 0 )

x(x - 4) = 15(4)

x² - 4x - 60 = 0

( x + 6 )( x - 10 ) = 0

x = 10

Answer:

A) 24

Step-by-step explanation:

Answer:

m = 24

Step-by-step explanation:

Answer: 68 minutes or 1 hour and 8 minutes spent in all putting up the fence

Step-by-step explanation:

(4/5) x 60 = 48 minutes

4/5 is the same as 0.8, which is what you get when you divide four by 5

So, 0.8 x 60 = 48 is also acceptable

Then,

(1/3) x 60 = 20 minutes

1/3 is the same as 0.333333333333, which is what you get when you divided 1 by 3

So, 0.33333(and so on) x 60 = 20

- Typically, you can round 0.3333333 down to something like 0.333 which should give you a similar answer

Then, as it asks you for how much time he spent in all, you add those two together

48 minutes + 20 minutes = 68 minutes  OR 1 hour and 8 minutes (There is sixty minutes in 1 hour, so subtract the 60 from 68 and then you have 8 minutes left, thus 1 hour and 60 minutes)

Answer:

The mortgage chosen is option A;

15-year mortgage term with a 3% interest rate because it has the lowest total amount paid over the loan term of $270,470

Step-by-step explanation:

The details of the home purchase are;

The price of the home = $275,000

The mode of purchase of the home = Mortgage

The percentage of the loan amount payed as down payment = 20%

The amount used as down payment for the loan = $55,000

The principal of the mortgage borrowed, P = The price of the house - The down payment

∴ P = $275,000 - 20/100 × $275,000 = $275,000 - $55,000 = $220,000

The principal of the mortgage, P = $220,000

The formula for the total amount paid which is the cost of the loan is given as follows;

\(Outstanding \ Loan \ Balance = \dfrac{P \cdot \left[\left(1+\dfrac{r}{12} \right)^n - \left(1+\dfrac{r}{12} \right)^m \right] }{1 - \left(1+\dfrac{r}{12} \right)^n }\)

The formula for monthly payment on a mortgage, 'M', is given as follows;

\(M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}\)

A. When the mortgage term, t = 15-years,

The interest rate, r = 3%

The number of months over which the loan is payed, n = 12·t

∴ n = 12 months/year × 15 years = 180 months

n = 180 months

The monthly payment, 'M', is given as follows;

M =

The total amount paid over the loan term = Cost of the mortgage

Therefore, we have;

220,000*0.05/12*((1 + 0.05/12)^360/( (1 + 0.05/12)^(360) - 1)

\(M = \dfrac{220,000 \cdot \left(\dfrac{0.03}{12} \right) \cdot \left(1+\dfrac{0.03}{12} \right)^{180} }{\left(1+\dfrac{0.03}{12} \right)^{180} - 1} \approx 1,519.28\)

The minimum monthly payment for the loan, M ≈ $1,519.28

The total amount paid over loan term, A = n × M

∴ A ≈ 180 × $1,519.28 = $273,470

The total amount paid over loan term, A ≈ $270,470

B. When t = 20 year and r = 6%, we have;

n = 12 × 20 = 240

\(\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.06}{12} \right) \cdot \left(1+\dfrac{0.06}{12} \right)^{240} }{\left(1+\dfrac{0.06}{12} \right)^{240} - 1} \approx 1,576.15\)

The total amount paid over loan term, A = 240 × $1,576.15 ≈ $378.276

The monthly payment, M = $1,576.15

C. When t = 30 year and r = 5%, we have;

n = 12 × 30 = 360

\(\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.05}{12} \right) \cdot \left(1+\dfrac{0.05}{12} \right)^{360} }{\left(1+\dfrac{0.05}{12} \right)^{360} - 1} \approx 1,181.01\)

The total amount paid over loan term, A = 360 × $1,181.01 ≈ $425,163

The monthly payment, M ≈ $1,181.01

The mortgage to be chosen is the mortgage with the least total amount paid over the loan term so as to reduce the liability

Therefore;

The mortgage chosen is option A which is a 15-year mortgage term with a 3% interest rate;

The total amount paid over the loan term = $270,470

The probability that Team A wins the series in 3 games is 0.2745 (rounded to four decimal places).

To calculate the probability that Team A wins the series in 3 games, we need to consider the different possible scenarios. In order for Team A to win in 3 games, they must win the first three games of the series.

Since each game is independent and Team A has a probability of winning any given game with 0.65, the probability of Team A winning the first game is 0.65. If they win the first game, the probability of winning the second game is also 0.65. Similarly, if they win the second game, the probability of winning the third game is 0.65.

To find the probability of all these events occurring together (Team A winning the first, second, and third game), we multiply the individual probabilities. So the probability of Team A winning the series in 3 games is 0.65 * 0.65 * 0.65 = 0.2745.

Therefore, there is approximately a 27.45% chance that Team A will win the series in 3 games.

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We are prove the theorems by contradiction firstly we assume x to be irrational and prove that it is rational. our assumption must be false, and so the statement that if x * y > 50, then either x < 8 or y < 8 must be true.

a) Prove by contrapositive: If x - y is irrational, then x is rational.
Proof: Assume that x - y is irrational. Then, by definition, x - y cannot be expressed as the ratio of two integers.
Now, to prove that x is rational, let us assume that x is irrational. That implies that x cannot be expressed as the ratio of two integers either.

However, since x + y is rational, x + y must be expressible as the ratio of two integers. This would imply that both x and y must be expressible as the ratio of two integers, which is a contradiction of our initial assumption that x is irrational.

Therefore, our assumption that x is irrational must be false. Hence, x must be rational.
Therefore, we have proven by contrapositive that if x - y is irrational, then x is rational.

b) Prove by contradiction: Assume that for any positive two real numbers, x and y, if x * y > 50, then neither x < 8 nor y < 8. Now, to prove the contrary statement, let us consider the two real numbers x = 5 and y = 11. The product of these two numbers is 55, which is greater than 50.

However, 5 is less than 8, and 11 is also less than 8. Hence, this is a contradiction of our initial assumption. Therefore, our assumption must be false, and so the statement that if x * y > 50, then either x < 8 or y < 8 must be true.

Therefore, we have proven by contradiction that for any positive two real numbers, x and y, if x * y > 50, then either x < 8 or y < 8.

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Use the formula:

Radio= r, Height= h

V= 3.14xrx2h

r =25, h=31

V= 3.14 x 25 x 2 (31) =. 4867

V= 4867 cubic inches

Step-by-step explanation:

Answer:

It will take them 7.89 days

Answer:

A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to.

Step-by-step explanation:

A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to.

To maintain the height and width proportion of a shape while dragging, you would typically hold down the Shift key on your keyboard.

When you select and drag a shape, holding down the Shift key constrains the proportions of the shape and ensures that the height and width change proportionally.

This technique is commonly used in graphic design and image editing software, as well as in various drawing and design applications. By holding down the Shift key while dragging a shape, you can prevent it from being distorted or skewed, preserving its original aspect ratio.

This feature is especially useful when you want to maintain the shape's original proportions or when you need consistency in the size and dimensions of multiple shapes. It helps ensure that the height and width remain in the same ratio as the original shape, regardless of how you adjust its size.

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Answer:

The answer to your problem is, C. \(-\frac{4}{3}\)

Step-by-step explanation:

Given that, the green line has a slope of \(\frac{3}{4}\)

We would need to find the slope of the red line.

The formula for the slope of perpendicular lines is m1.m2 = -1. The productof the slopes of perpendicular lines is equal to -1.

Since, m1=\(\frac{3}{4}\)

Now, \(\frac{3}{4}\). M2 = -1

⇒m2 = \(-\frac{4}{3}\)

Thus the answer to your problem is, \(C. -\frac{4}{3}\)

The rule of inference being used here is Modus Tollens. Modus Tollens is a valid deductive argument form that states if a conditional statement "If P, then Q" is true and the consequent Q is false, then the antecedent P must also be false.

In the given scenario, the conditional statement is "If the guard dog doesn't know a person, then it barks."

The observation that the dog didn't bark (Q is false) leads to the conclusion that the dog must have known the person (the antecedent P is false).

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The speed of the sound is 0.3296 km per second

From the question, we have the following parameters that can be used in our computation:

Distance = 8.24 km

Time taken = 25 seconds

Using the above as a guide, we have the following:

Speed = Distance/Time taken

Substitute the known values in the above equation, so, we have the following representation

Speed = 8.24/25

Evaluate

Speed = 0.3296 km per second

Hence, the speed of the sound is 0.3296 km per second

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Answer:

Step-by-step explanation:

You had the first part of the first question correct. The answer is 100:64

The sides of the squares

Area of e = 69% more than area of area of f

e^2: f^2 = ( 1 + 69/100 ) / 1

e^2 : f^2 = (1.69)/1            Take the square root of both sides

e:f  = 1.3:1

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

The amount of Cashew nuts is 0.205

The amoun of Peanuts is 0.295

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Amount of Cashew nuts = x

Amoun of Peanuts = y

Now,

We can make two equations.

x + y = 1/2 ____(1)

x = 1/2 - y  _____(20

Substituting (2) in (3)

6.25x + 2.10y = 1.90 _____(3)

6.25 (1/2 - y) + 2.10y = 1.90

3.125 - 6.25y + 2.10y = 1.90

3.125 - 4.15y = 1.90

3.125 - 1.90 = 4.15y

y = 1.225/4.15

y = 0.295

And,

x = 1/2 - y

x = 1/2 - 0.295

x = 0.205

Thus,

Amount of Cashew nuts = 0.205

Amoun of Peanuts = 0.295

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Answer:

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

Answer:

2πrh+2πr2

Step-by-step explanation:

I'm a genius...

Answer:

Closed= 2πrh+2πr²

Open= 2πrh+πr²

Answer:

I think it's C

Step-by-step explanation:

Sorry if I'm wrong

Answer:

Step-by-step explanation:tan A = sin A / cos A

Given tan A = 4/3, we can set up the following equation:

4/3 = sin A / cos A

To find sin A and cos A, we can use the Pythagorean identity:

sin^2 A + cos^2 A = 1

Since we know tan A = 4/3, we can rewrite the equation as:

(4/3)^2 + cos^2 A = 1

16/9 + cos^2 A = 1

cos^2 A = 1 - 16/9

cos^2 A = 9/9 - 16/9

cos^2 A = -7/9

Answer:

Step-by-step explanation:

3/4 + 3/4 + 3/4 + 3/4 = 12/4 = 3. She will walk 3 miles in an hour.

The distance that Anusha covered in one hour is 3 miles

If Anusha is walking on a hiking trail at a rate of three-fourths miles in One-fourth hour, this is expressed as:

3/4 miles = 1/4 hours

We need to get the rate of Aisha that is the distance traveled in an hour

x = 1 hour

Divide both expressions

3/4x = 1/4

Cross multiply

4x = 3 * 4

4x = 12

x = 12/4

x = 3

Hence the distance that Anusha covered in one hour is 3 miles

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We can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.

Based on the line of best fit for the data, we can estimate the number of servings of kakigori Cho will sell on a day when the high temperature is 29° Celsius.

From the scatter plot, we can see that the line of best fit is increasing as the temperature increases.

By estimating the value on the line of best fit for the temperature of 29° Celsius, we can approximate the number of servings sold. Based on the scatter plot, it appears that the number of servings sold is around 100 when the temperature is 29° Celsius.

Therefore, we can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.

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The square of the length of the chord that is a common external tangent of the other two circles with radii of 3 and 6 is 45.

Given that circles of radii 3 and 6 are externally tangent to each other and internally tangent to a circle of radius 9. The circle of radius 9 has a chord that serves as a common external tangent for the other two circles. The task is to find the square of the length of this chord.

The distance between the centers of the circles of radii 3 and 6 can be found by adding their radii: d1 = 3 + 6 = 9 units.

Since the circles are internally tangent to the circle of radius 9, the distance between their centers can be found by subtracting their radii from the radius of the larger circle: d2 = 9 - 3 - 6 = 0 units.

The chord is a common external tangent of the circles, and its length can be found by doubling the distance between the center of the circle of radius 9 and the chord: Chord length = 2 × h.

To find the height (h) of the triangle formed by the chord and the center of the circle of radius 9, we can use the formula h = (r1 + r2 - R) / 2, where r1 and r2 are the radii of the smaller circles, and R is the radius of the larger circle. In this case, h = (3 + 6 - 9) / 2 = 0.
Since h is zero, it means that the chord passes through the center of the circle of radius 9. Therefore, its length will be the diameter of the circle of radius 9.

The square of the length of the chord can be found using the Pythagorean theorem. Let's denote the length of the chord as d.

- We know that r1 + h = R, so h = R - r1 = 9 - 3 = 6.

- Using the Pythagorean theorem: d = sqrt(R² - h²) = √(9² - 6²) = √(81 - 36) = √(45).

Therefore, the square of the length of the chord is d^2 = 45.

In summary, the square of the length of the chord that serves as a common external tangent for the circles of radii 3 and 6, and is internally tangent to a circle of radius 9, is 45.

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P(A) = (4/36) * (3/6) = 1/18. Rounded to four decimal places, P(A) is 0.0556.  P(B) is 0.1111.  A and B are mutually exclusive because they cannot occur at the same time. If event A occurs (rolling a 4 or 5 first followed by an even number), then the sum of the two dice will be either 6 or 8. A and B are mutually exclusive because they cannot occur at the same time.  the lowest possible sum for event A is 6. Therefore, the two events are not independent.

a. To calculate P(A), we need to find the probability of rolling 4 or 5 first (which can occur in 4 out of 36 ways) and then rolling an even number (which can occur in 3 out of 6 ways). The probability of both events occurring is the product of their probabilities: P(A) = (4/36) * (3/6) = 1/18. Rounded to four decimal places, P(A) is 0.0556.

b. There are only 4 ways to get a sum of 5 or less: (1,1), (1,2), (2,1), and (1,3). There are a total of 36 possible outcomes when rolling two dice, so P(B) = 4/36 = 1/9. Rounded to four decimal places, P(B) is 0.1111.

c. A and B are mutually exclusive because they cannot occur at the same time. If event A occurs (rolling a 4 or 5 first followed by an even number), then the sum of the two dice will be either 6 or 8. But if event B occurs (the sum of the two dice is at most 5), then the sum of the two dice will be either 2, 3, 4, or 5. These two events cannot occur together because their outcomes are mutually exclusive.

d. A and B are not independent events. The occurrence of one event affects the probability of the other event. For example, if we know that event A has occurred (rolling a 4 or 5 first followed by an even number), then the probability of event B (the sum of the two dice is at most 5) is zero, since the sum of the two dice will be either 6 or 8. Similarly, if we know that event B has occurred (the sum of the two dice is at most 5), then the probability of event A (rolling a 4 or 5 first followed by an even number) is zero, since the lowest possible sum for event A is 6. Therefore, the two events are not independent.

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the equation to find the slope between 2 points is

name the points

1=(11,9)

2=(12,9)

apply the formula

the slope between the points is 0.

Answer:

37.5%

Step-by-step explanation:

Area = (b1 + b2) * h / 2

Area = (1 + 2) * 0.4 / 2 = 0.6

Total area = 0.8 * 2 = 1.6

Percentage of observations between 0.4 and 0.8 = Area of trapezoid / Total area * 100%

= 0.6 / 1.6 * 100%

= 37.5%

Therefore, approximately 37.5% of observations fall between 0.4 and 0.8 on this density curve.

Answer:

the square foot is 5

Step-by-step explanation:

The square root of 5 is 5^(1/2)the cube root of 5 is 5^(1/3)so square root of five times cube root of five= 5^(1/2)*5^(1/3)=5^(1/2+1/3

Answer: x=57

Step-by-step explanation:

Let's take our equation

\(x=5(t)-3\\x=5(12)-3\\x=60-3\\x=57\)

The volume of the cone is 64π

From the question, we have the following parameters that can be used in our computation:

Height, h = 12 m

Radius, r = 4 m

The volume is calculated s

V = 1/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 1/3π * 4² * 12

Evaluate

V = 64π

Hence, the volume is 64π

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Answer:

Step-by-step explanation:

domain = x

range = y

when the domain is -1

y = 2(-1) - 3

y = -2 - 3

y = -5

range is -5

When the domain is 0

y = 2(0) - 3

y = 0 - 3

y = -3

range is -3

when the domain is 5

y = 2(5) - 3

y = 10 - 3

y = 7

range is 7

The range is { -5, -3, 7 }