find the surface area of the triangular prism.

The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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The revenue function is R = 25q, the cost function is C = 2000 + 20q, and the profit function is P = 5q - 2000.

The revenue function in terms of quantity can be calculated as follows:

Revenue (R) = q x p

Where: "q" is the quantity of units sold

"p" is the price per unit

At the break even point:

10,000 = 400p

p = 25 birr per unit

At the break even point, the total cost is equal to the total revenue:

Total cost = Total revenue = 10,000 birr

Fixed cost = 2000 birr

Variable cost (VC) = Total cost - Fixed cost

VC = 10,000 - 2000 = 8000 birr

The cost function in terms of quantity can be expressed as:

Cost (C) = FC + VC x q

C = 2000 + 20q

The profit function can be calculated as the difference between revenue and cost:

Profit (P) = R - C

P = 25q - (2000 + 20q)

P = 5q - 2000

Therefore, the revenue function is R = 25q,

the cost function is C = 2000 + 20q, and

the profit function is P = 5q - 2000.

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Answer:

Step-by-step explanation:

The perimeter is 28".

The total length of three sides of the square = 28-5-5 = 18", so the side length of the square is 18/3 = 6".

The area of the triangle is ½(6)(4) = 12 square inches.

The area of the square is 6² = 36 square inches.

Total area = 12+36 = 48 square inches.

Answer:

First triangle x=9

Second triangle x=20

Step-by-step explanation:

Using Pythagorean theorem

40^2+x=41^2

1600+x^2=1681

-1600        -1600

x^2=81

To find x we do the opposite of powers and find the squared

x=9

Second triangle

21^2+x^2=29^2

441+x^2=841

-441        -441

x^2=400

x=20

1. The velocity at time t , v(t) = (18t² + 3 ) m/s

2. The velocity at time t = 3 seconds = 165 m/s

3. The acceleration at time t, a(t) =( 36t )m/s²

4. The acceleration at time t = 3 seconds = 108 m/s²

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.

1. s(t) = 6t³ + 3t +9

to find the velocity at time t, we differentiate s(t)

= 18t² + 3

2. at t = 3s

= 18(3)² +3

= 165 m/s²

3. v(t) = 18t² + 3

to get the acceleration at time t, we differentiate v(t)

= 36t

4. when t = 3

a = 36 × 3

= 108 m/s²

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Answer:

the answer is b, c, d, a, respectively

Answer:

8.8 pounds

Step-by-step explanation:

Given the following :

Combined weight loss which occurred within a week = 28 kg

Number of days in a week = 7 days

1 kilogram (kg) = 2.2 pounds

Combined weight loss in pounds that occurs within a week:

Weight loss in kg × 2.2

28kg * 2.2 = 61.6 pounds

Assume weight loss occurred at a constant rate :

Weight lost by the group per day :

(Total weight loss / number of days in a week)

(61.6 pounds / 7)

= 8.8 pounds daily

Answer:

88

Step-by-step explanation:

Found the answer and I am doing the quiz rn lel

Answer:

$61.76

Step-by-step explanation:

So I can't answer how much do you have left or did you make enough money, but I can calculate the money you made. Since it's $9.15 per hour and you worked 6.75, you simply multiply the numbers together. The money you made was $61.76.

Answer:

the answer would be 3,3,7

Step-by-step explanation:

because to of the sides will be the same and one will be different

Answer:

Step-by-step explanation:

{3,3,7}

The appropriate notation to calculate conditional probabilities is

[P(C|D) = {P(C∩D)}/P(D)]

As per the question statement, we are provided with the term of "Conditional probability".

We are required to determine the the appropriate notation to calculate conditional probabilities from among the four options provided in the question statement itself.

To solve this question, first we need to know the concept of Conditional probability. According to probability theory, conditional probability is a measure of the probability, or extent of an event occurring, provided that  another event has already occurred, i.e., conditional probability can be expressed in the case of two events, say "C" and "D" as,

\(P(C|D)=\frac{P(CND)}{P(D)}\)

Which is the second option.

Hence, The appropriate notation to calculate conditional probabilities is Option (B) [P(C|D) = {P(C∩D)}/P(D)].

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Using the power reducing formulas the expression \(5cos^4(x) = 5(1 + cos(2x))^{2/4}\).

We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.

The given function is 5cos^4(x).

Now, the power reducing formulas are given by:

\(cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2\)

Substituting the value of second equation in 1 we have:

cos(2x) = 2(1 + cos(2x))/4 - 1

\(cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)\)

Now we have:

\(cos^2(x) = (1 + cos(2x))/2\)

Thus,

\(cos^4(x) = (1 + cos(2x))/2)^2\)

Now multiplying by 5:

\(5cos^4(x) = 5(1 + cos(2x))^{2/4}\)

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Answer:

Step-by-step explanation:

Let's get inverse of g(x) and compare it with f(x):

g'(x) and f(x) are different so the answer is No

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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The equation is correct, and the value on both sides of the equation is 40.

To verify if the equation 90 × 4/9 = 40 is true, we can perform the calculation on both sides and compare the results.

On the left side of the equation:

90 × 4/9 = (90 × 4) / 9 = 360 / 9 = 40

On the right side of the equation:

40

Both sides of the equation evaluate to 40, which means they are equal. Therefore, the equation 90 × 4/9 = 40 is indeed true.

In summary, the equation is correct, and the value on both sides of the equation is 40.

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The average change as a simplified mixed number would be,

⇒ 1 3/4

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The running back for the Bulldogs football team carried the ball 7 times for a total loss of 12 1/4 yards.

Now, The average change as a simplified mixed number would be,

⇒ (12 1/4) / 7

⇒ (49/4) / 7

⇒ (49 / 4×7)

⇒ 7/4

⇒ 1 3/4

Therefore, The average change is,

⇒ 1 3/4

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Answer:

8

Step-by-step explanation:

The answer is 8 multiple

Hope it helps

If the medication comes as tablets containing 5 mg. The order is for 1.5 tablets. the number of mg to be given is: 3 mg.

Using this formula to find the number of mg to be given

Number of mg = Mg of tablets/ Number of tablet order

Where:

Mg of tablets = 5mg

Number of tablets order = 1.5 tablets

Where:

Number of mg = 5mg /1.5 tablets

Number of mg =3 mg

Therefore the number of mg to be given is 3 mg.

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Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

Answer:

Step-by-step explanation:

Let Matt's age be x.

Then Pat is x + 2, Dave is x + 4 and Dan is x + 6.

Dan's age is 36 years less than twice Pat's age:

Solve it for x:

So Matt is 38, Pat is 40, Dave is 42 and Dan is 44.

The value of f⁻¹(3) is 6.

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

The inverse function of f(x) is denoted by f⁻¹(x). It is a function that reverses the action of f(x). That is:

if f(x) = y, then f⁻¹(y) = x.

In this case, we know that f(6) = 3. This means that if we input 6 into f(x), we will get 3 as the output.

Therefore, the inverse function of f(x) must take 3 as input and give 6 as output. This means that f⁻¹(3) = 6.

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Answer:

2

Step-by-step explanation:

tbh I just graphed it on desmos and used rise over run

Answer:$0.25

Step-by-step explanation:

To find the expected value of playing the game, we need to multiply the payoff for each possible outcome by its probability and then add up all the values.

Let's first find the probabilities of each outcome:

- Probability of spinning1:1/6

- Probability of spinning2:1/6

- Probability of spinning3:1/6

- Probability of spinning4:1/6

- Probability of spinning5 or6:2/6( or1/3)

Now let's calculate the expected value:

Expected value=(1/6*$1)+(1/6*$3)+(1/6*$5)+(1/6*$7)+(1/3*-$1.25)

Expected value=$0.25

So the expected value of playing the game is$0.25 per spin.

In the long run, Scott can expect to gain money since the expected value is positive. However, this doesn't guarantee that he will actually win money every time he plays the game, as there is still a certain degree of randomness involved in each spin.

Answer:

x ≥ 4

Step-by-step explanation:

Given the inequality 4x-1≥15

Add 1 to both sides

4x-1+1≥15+1

4x≥16

Divide both sides by 4

4x/4 ≥ 16/4

x ≥ 4

Hence the solution is x ≥ 4

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

Step-by-step explanation:

We need to find the value (f-g)(2), so we need first to substitute 2 into the given functions f(x) and g(x) and then subtract the result of g(2) from f(2).

Here, f(x) = 3x^2 + 1 and g(x) = 1 - x,

So, We will substitute 2 into these functions:

f(2) = 3(2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13

g(2) = 1 - 2 = -1

Now, we can subtract g(2) from f(2):

(f-g)(2) = f(2) - g(2) = 13 - (-1) = 13 + 1 = 14

Hence, the required value of (f-g)(2) is 14.

Answer:

The correct answer is 3. To solve for g(-2), we substitute -2 for x in the equation g(x) = 2x + 5. This gives us g(-2) = 2(-2) + 5, which simplifies to -4 + 5 = 1. Next, we substitute the value of g(-2) into the equation for f(g(x)) = 4 - x^2. Thus, f(g(-2)) = 4 - (1)^2, which equals 4 - 1 = 3.

Answer:

idk

Step-by-step explanation:

Answer:

130.8

Step-by-step explanation:

Use law of cosine

12^2=9^2+4^2-2*9*4cos

144=97-72cos

47=-72cos

(Use cosine inverse now)

Cos-1(47/-72)

Largest angle is 130.8 when rounded to the nearest then the