Find the volume of the triangular prism.


4 cm
6 cm
5 cm

Answer:

$677.25

Step-by-step explanation:

Money deposited: $375.45 + 614.20 + $187.60 = $1177.25

Money withdrawn: $500.00

Total deposit: $1177.25 - $500.00 = $677.25

Answer: $677.25

To obtain 15 gallons of 24% alcohol, you would need to mix 14 gallons of 25% alcohol and 1 gallon of 10% alcohol.

To determine the amounts of 25% alcohol and 10% alcohol needed to obtain 15 gallons of 24% alcohol, we can set up an equation based on the principle of the mixture:

Let x represent the number of gallons of 25% alcohol.

Let y represent the number of gallons of 10% alcohol.

The equation can be set up as follows:

0.25x + 0.10y = 0.24  (15)

0.25x + 0.10y = 3.6

To solve this equation, we need another equation. Since we know that the total volume of the mixture is 15 gallons, we can add a second equation:

x + y = 15

Now we have a system of equations:

0.25x + 0.10y = 3.6

x + y = 15

Now, solving

x = 15 - y

Substituting this value of x into the first equation:

0.25(15 - y) + 0.10y = 3.6

3.75 - 0.25y + 0.10y = 3.6

-0.15y = -0.15

y = 1

and, x + 1 = 15

x = 14

Therefore, to obtain 15 gallons of 24% alcohol, you would need to mix 14 gallons of 25% alcohol and 1 gallon of 10% alcohol.

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To solve the inequality 2x < 12, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides by 2:

2x < 12

x < 6

Therefore, the solution to the inequality is x < 6. This means that all values of x that are less than 6 satisfy the inequality. We can represent this graphically on a number line:

<=======()------6-------------->

The open circle () indicates that x cannot be equal to 6, but can be any value less than 6. The arrow indicates that the inequality is true for all values of x to the left of the open circle.

In summary, the solution to the inequality 2x < 12 is x < 6.

I'm 15 BTW

Using this fact, we can find the measure of arc MN. Since angle MSN has a measure of 129 degrees, arc MN must have a measure of 2*129 = 258 degrees.



. Let's call the point where the circle intersects with the line that passes through the center point M.

We also know that the measure of angle MSN (where N is the point where the circle intersects with the line opposite to M) is 129 degrees.

Now, there are a few things we can deduce from this information. First of all, we know that angle MSN is an inscribed angle, since it intercepts an arc of the circle.

We also know that the measure of an inscribed angle is equal to half the measure of the intercepted arc.

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The concentration of the drug after 8 hours is equal to 24 mg/L.

The interval over which the concentration increases is 0 < t < 2.

The interval over which the concentration decreases is 2 < t < ∞.

The drug is at its maximum concentration when t = 2 hours and the maximum concentration is 64 mg/L.

After the drug reaches its maximum concentration, the number of hours that are required for the concentration to decrease to 16 mg/L is 8 hours.

After 1 week and 1 month, we can predict that the concentration of the drug kept decreasing after reaching 20 hours.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of the given function, we can reasonably infer and logically deduce the following:

The function is increasing over the interval [0, 2] or 0 < t < 2.

The function is decreasing over the interval [2, ∞] or 2 < t < ∞.

In conclusion, the vertex (2, 64) of the graph represent the point where the drug is at its maximum concentration, which is time (t) = 2 hours and the maximum concentration is y = 64 mg/L.

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Step-by-step explanation:

To determine which point is a solution of the linear inequality 92 + 3y < 6, we can substitute the values of each point into the inequality and check if the inequality holds true.

Let's evaluate the inequality for each point:

1. Point (1, -1):

92 + 3(-1) < 6

92 - 3 < 6

89 < 6

The inequality is not true for this point.

2. Point (2, -2):

92 + 3(-2) < 6

92 - 6 < 6

86 < 6

The inequality is not true for this point.

3. Point (1, 1):

92 + 3(1) < 6

92 + 3 < 6

95 < 6

The inequality is not true for this point.

4. Point (1, 3):

92 + 3(3) < 6

92 + 9 < 6

101 < 6

The inequality is not true for this point.

None of the given points satisfy the inequality. Therefore, none of the points (1, -1), (2, -2), (1, 1), or (1, 3) are solutions to the linear inequality 92 + 3y < 6.

There are [tex]4[/tex] students in total who went down the slide during recess after counting the sequence.

To determine the total number of students who went down the slide during recess, we need to count the number of times the slide was used and consider that each use represents one student. By analyzing the given data, we can count the occurrences of the letter 'X' in the provided sequence:

[tex]\[ x \quad x \quad xx \quad xx \quad x \quad x \quad xx \quad xx \quad xx \quad xx \quad 0 \quad 1 \quad X \quad XXX \quad xx45 \quad xxxxx \quad X \][/tex]

Counting the 'X's, we find that there are [tex]4[/tex] occurrences. Since each 'X' represents one student going down the slide, the total number of students is [tex]4[/tex].

Therefore, there are [tex]4[/tex] students in total who went down the slide during recess.

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The correct option of system of equations that can be used to find the temperature at which the degrees Celsius and the degrees Fahrenheit would be equivalent is the option;

5·F - 9·C = 160

F - C = 0

A system of equation, is a set of equation that have common variables.

The equation for conversion of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is; 9·C = 5·F - 160

When the temperature in degrees Celsius is equivalent to the temperature in degrees Fahrenheit, we get;

F = C

Therefore;

F - C = 0

Similarly, from the specified equation, we get;

9·C = 5·F - 160

5·F - 9·C = 160

The system of equation that would give the temperature where the degrees Celsius and degrees Fahrenheit are equivalent is therefore;

5·F - 9·C = 160

F - C = 0

(Which yields a temperature of 40°)

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The equation of the circle given at the end of the image is:

(x - 2)² + y² = 16.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.

The center of the circle given at the end of the image has the coordinates given as follows:

(2,0).

The center is at (2,0), while one x-intercept of the circumference is at x = 6, that is, point (6,0), hence the radius is given as follows:

r = 6 - 2

r = 4.

Thus the equation of the circle is given as follows:

(x - 2)² + y² = 16.

The circle is given by the image presented at the end of the answer.

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Answer: tan(O) = 3/4

Step-by-step explanation:

The following triangle is a right triangle so we can use the pythagorean theorem to find side QP.

4^2 + b^2 = 5^2

16 + b^2 = 25

b^2 = 9

b = 3

tangent is equal to opposite over adjacent.

The side opposite O is QP which we found to be 3

The side adjacent to O is OP which is given to be 4

tan(o) = 3/4

a. The interest that would accrue at Bank A is $1484.32.

b. Kathy would owe $5984.32 at Bank A.

c. The interest that would accrue at Bank B is $201.82.

d. Kathy would owe $4776.82 at Bank B.

e. Kathy would save $1213.03 by using Bank B.

a. The annual interest at Bank A is 21.99%. The simple interest for 18 months can be calculated as:

I = Prt = 4500 x 0.2199 x (18/12) = $1484.32.

Therefore, the interest that would accrue at Bank A is $1484.32.

b. The total amount that Kathy would owe at Bank A is the sum of the principal and interest:

Total = Principal + Interest = $4500 + $1484.32. = $5984.32.

Therefore, Kathy would owe $5984.32 at Bank A.

c. The annual interest rate at Bank B is 2.99%, but there is also a one-time service fee of $75. The interest for 18 months can be calculated as:

I = Prt = 4500 x 0.0299 x (18/12) = $201.82.

Therefore, the interest that would accrue at Bank B is $201.82.

d. The total amount that Kathy would owe at Bank B is the sum of the principal, interest, and service fee:

Total = Principal + Interest + Service fee = $4500 + $201.82 + $75 = $4776.82

Therefore, Kathy would owe $4776.82 at Bank B.

e. By using Bank B, Kathy would save the difference between the total amount owed at Bank A and the total amount owed at Bank B:

Savings = Total at Bank A - Total at Bank B = $5989.85 - $4776.82 = $1213.03.

Therefore, Kathy would save $1213.03 by using Bank B.

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Looking at these angles, we can see that they are alternate interior angles. Alternate interior angles are congruent. This means that to solve we will simply need to set the given expressions equal to each other and solve for x.

4x - 23 = 3x + 18

x - 23 = 18

x = 41

Answer: x = 41

Hope this helps!

The probability of getting 14 successes out of 19 trials with a probability of success of 0.8 is approximately 0.0572.

Using the binomial probability formula, we have:

P(X=14) = (n choose x) * pˣ . (1-p)⁽ⁿ⁻ˣ⁾

Plugging in the values, we get:

P(X=14) = (19 choose 14) x 0.8¹⁴ x 0.2⁵

P(X=14) ≈ 0.0572

Therefore, the probability of getting 14 successes out of 19 trials with a probability of success of 0.8 is approximately 0.0572.

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Answer: Since there is no amount of texts given we will have to replace it with a variable, and 0.48 as the co-efficient. So the equation will be 0.48x+3, this is as far as you can get.

This function relationship is linear because it increases at a constant rate

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 10.5x

where the slope of the line is m = 10.5

So , function relationship is linear because it increases at a constant rate

Hence , the function is f ( x ) = 10.5x is linear

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The standard deviation of this sample of shopping time is equal to 50.

In order to calculate the standard deviation of this sample of shopping time, we would have to first determine the mean of the data set.

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

For the total sum of data, we have:

F(x) = 42 + 27 + 22 + 37 + 32

F(x) = 132.1.

Mean = 160/5

Mean = 32

Now, we can calculate the standard deviation by using this formula:

Standard deviation, S = √(1/n × ∑(xi - u₁)²)

Standard deviation, S = √(1/5 × ∑(42 - 32)² + 1/5 × ∑(27 - 32)² + 1/6 × ∑(22 - 32)² + 1/5 × ∑(37 - 32)² + 1/5 × ∑(32 - 32)²

Standard deviation, S = 250/5

Standard deviation, S = 50.

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The nearest Whole number, the coordinator should use a sample size of 753.

To find the sample size needed when the population proportion is known, we can use the formula:

n = (z^2 * p * q) / E^2

where:

n= sample size

z = z-score for the desired level of confidence (we'll use 1.96 for 95% confidence)

p = population proportion

q = 1 - p (the proportion of the population that does not have the characteristic)

E = margin of error (we'll use 0.03 for 3% margin of error)

Substituting the values given in the problem:

n = (1.96^2 * 0.3 * 0.7) / 0.03^2

n ≈ 752.9

Rounding up to the nearest whole number, the coordinator should use a sample size of 753.

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The proof is shown in the solution.

Given is an expression (2k + x)", we need to expand and prove,

Expand the binomials and cancel the 2k's:

n(n−1) / 2 (2k) = n(n−1)(n−2) / 6

Solving,

3(2k) = n−2

n = 6k+2

Hence proved.

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Answer:

y = 6x²+15x-2x-5

dy/dx = 6*2(x) ²-¹ +15*1(x)¹-¹ -5*1¹-⁰

dy/dx = 12x + 15

Answer: (0, 5)

Step-by-step explanation:

       To find the y-intercept, we will substitute 0 for x into the equation given. This means we will find (0, y), which is the y-intercept.

Given:

       f(x) = x² + 3x + 5

Substiute:

       f(0) = (0)² + 3(0) + 5

Multiply:

       f(0) = 5

       Based on this, the y-intercept is (0, 5). We can also see this when we graph the function. See attached.

The measure of angle x of the intersecting lines is x = 7.4°

Given data ,

Let the measure of angle be x

Now , the measure of angle ∠PON = 105.3°

And , the measure of angle ∠NOR = 153.1°

Now , the measure of angle ∠QOR = 94.2°

So , the intersecting lines are solved and

The measure of x = 360° - ( 153.1° + 105.3° + 94.2° )

On simplifying , we get

x = 7.4°

Hence , the measure of angle x = 7.4°

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The value of y for the ordered pair (9, y) is -5

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

A(-6,1), B(4,1), and C(4,-3)

The line AC would form a linear equation. when extended

A linear equation is represented as

y = mx + c

Using the points A and C, we have

-6m + c = 1

4m + c = -3

When evaluated, we have

-10m = 4

This gives

m = -0.4

So, we have

-6(-0.4) + c = 1

Evaluate

c = 1 + 6(-0.4)

c = -1.4

So, the equation is

y = -0.4x - 1.4

When x = 9, we have

y = -0.4 * 9 - 1.4

Evaluate

y = -5

So, the ordered pair is (9, -5) and y = -5

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Answer:

b. Low balance alert

Step-by-step explanation:

Because if you know that you have a low balance, you will presumably stop withdrawing money from the account so that you don't have an overdraft (which is when you withdraw more money than you have).

Answer:

Step-by-step explanation:

41 + 85 + 180 - x = 180

x = 126

There are distance of 1.3 miles does Lucy walk before stopping.

Given that;

A hiking trail is 2 3/5 miles long. Lucy walks 1/2 of the trail before stopping for water break.

Hence, Number of miles does Lucy walk before stopping is,

⇒ 1/2 of (2 3/5)

⇒ 1/2 × 13/5

⇒ 13/10

⇒ 1.3 miles

Thus, Number of miles does Lucy walk before stopping is, 1.3 miles

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1) The mean of the number of children is ≈ 1.5

2) the median is 1

3) the 5 number summary is

4) See the box plot attached.

A) Mean = sum of all the children reported by the adults/ number of adults

(0 × 5) + (1 × 3) + (2 × 4) + (3 × 2) + (4 × 0) + (5 × 1) = 22

number of adults
5 + 3 + 4 + 2 + 0 + 1 = 15

Mean = 22/15 ≈ 1.5

B)  to find the median we must arrange all the number in ascending order

0, 0, 0, 0, 0, 1, 1, 1, 2,  2, 2, 2, 3,  3, 5

Thus, 1 is the median when we select the number in the middle.

C) the 5 number summary is

D) See the box plot attached.

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Answer:

0.225

Step-by-step explanation:

5 + 7 + 8 = 20 crayons.

we want 4 blue crayons from 15 draws. p(blue) = 5/20.

p(4 from 15 draws) = 0.225

Answer: 32 ounces

Step-by-step explanation:

1 pint = 16 ounces, 16 x 2 = 32 ounces.

(a) The Goran's monthly payment is  605.9.

(b) His total amount to repay the loan is 50,895.6.

(c) The amount of interest he will pay is 10,395.6.

The Goran's monthly payment, is calculated using the following formula;

P = r(PV) / (1 - (1 + r)⁻ⁿ)

where;

r = 6.7% / 12 = 0.00558

PV = 40,500

n = 7 years x 12 months/year = 84 months

P = 0.00558(40,500) / (1 - (1 + 0.00558)⁻⁸⁴)

P  = 605.9

Total amount = 84 x 605.9 = 50,895.6

The total interest paid on the loan is the difference between the total amount repaid and the amount borrowed.

= 50,895.6 - 40,500

= 10,395.6

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(26) The length FE in the intersecting chords is 6.

(27) The length of arc AE is 64⁰.

The length FE is calculated by applying intersecting chord theorem as follows;

The intersecting chord theorem, also known as the power of a point theorem, states that:

If two chords of a circle intersect inside the circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

FE ≅ AB = 6

The length of arc AE is calculated as follows;

arc AE + arc AB + arc ED = 180 (sum of angles of a semi circle)

arc AE + 58 + 58 = 180

arc AE + 116 = 180

arc AE = 64

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