A triangular prism is 18 yards long and has a triangular face with a base of 18 yards and a height of 12 yards. The other two sides of the triangle are each 15 yards. What is the surface area of the triangular prism?

Answer:

yes sir

Step-by-step explanation:

6.8py

a) The equation for Bueller's height above the ground as a function of time is: h(t) = 9 cos(πt/8) + 1.5

b) When Bueller has been on the ride for 1 minute and 30 seconds, his height above the ground is approximately 10.5 m.

In mathematics, a function is a rule that assigns a unique output value to each input value in a specified set. More precisely, a function is a set of ordered pairs (x, y) where each x-value (the input) corresponds to exactly one y-value (the output).

In mathematics, an equation is a statement that asserts the equality of two expressions, typically containing one or more variables. An equation consists of two sides, the left-hand side, and the right-hand side, separated by an equal sign (=).

According to the given information,

a) To determine an equation for Bueller's height above the ground as a function of time, we can use the equation for the height of a point on a Ferris wheel:

h(t) = r cos(ωt) + h0

where:

1) h(t) is the height of the point above the ground at time t

2) r is the radius of the Ferris wheel

3) ω is the angular velocity of the Ferris wheel (in radians per second)

4) t is the time elapsed since the point was at its lowest position

5) h0 is the initial height of the point above the ground

In this case, we know that Bueller boards the Ferris wheel at a height of 1.5 m off the ground, so h0 = 1.5 m. The radius of the Ferris wheel is 9 m, and it rotates once every 16 seconds, so the angular velocity is:

ω = 2π / T = 2π / 16 = π / 8 radians per second

Therefore, the equation for Bueller's height above the ground as a function of time is:

h(t) = 9 cos(πt/8) + 1.5

b) To find Bueller's height off the ground when he has been on the ride for 1 minute and 30 seconds (or 90 seconds), we can substitute t = 90 into the equation for h(t):

h(90) = 9 cos(π(90)/8) + 1.5

h(90) = 9 cos(11.25π) + 1.5

Using a calculator, we get:

h(90) ≈ -6.3 m

Note that the negative sign means that Bueller is below ground level, which is not physically possible. This occurs because we started counting time from the bottom of the wheel, so 90 seconds corresponds to the bottom position plus 5 and a half rotations. To fix this, we can add a multiple of the period T = 16 seconds to t to bring it back to the correct range:

h(t) = 9 cos(πt/8) + 1.5

h(90 + 5T/2) = 9 cos(π(90 + 5T/2)/8) + 1.5

h(90 + 5T/2) = 9 cos(π(2 + 5/16)) + 1.5

h(90 + 5T/2) ≈ 10.5 m

Therefore, when Bueller has been on the ride for 1 minute and 30 seconds, his height above the ground is approximately 10.5 m.

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Answer:

Linear

Step-by-step explanation:

y=x-5/4 is a linear equation.

The senior math contest ended at 10:40 pm on Sunday

If the senior math contest began at 6:00 am on a Sunday and ended 1000 minutes later, we can add 1000 minutes to the starting time to find the ending time.

To do this, we can first convert the starting time of 6:00 am into minutes. There are 60 minutes in one hour, so 6:00 am is equivalent to:

6 hours × 60 minutes/hour = 360 minutes

Now, we can add 1000 minutes to this starting time:

360 minutes + 1000 minutes = 1360 minutes

Finally, we can convert this total number of minutes back into hours and minutes.

Since there are 60 minutes in one hour, we can divide 1360 minutes by 60 to get:

1360 minutes ÷ 60 = 22 hours and 40 minutes

Therefore, the senior math contest ended at 10:40 pm on the day (Sunday).

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Answer:

Step-by-step explanation:

I'm guessing but I think you are asked to represent 40% of the circle graph. There are 5 equal slices in the circle. If you shade 2 of them, that will equal 40% because 1 slice represents 20% of the circle, so two slices must be 40%.

The triangle shown is a right triangle shown by the little square inside of it.

Area of a triangle is 1/2 x height x base

Rotating the shown triangle so the square is at a bottom corner the height is 6 and the base is 6

Area = 1/2 x 6 x 6 = 18 square cm

A. The total value of the loan with quarterly compounded interest is $52,400.

B. The total value of the loan with monthly compounded interest is $52,010.04

Part A: Total value of the loan with the quarterly compounded interest

To find the total value of the loan, we'll use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount (loan + interest)

P = principal amount (initial loan) = $20,000

r = interest rate = 7% = 0.07

n = number of times compounded per year = 4 (quarterly)

t = number of years = 10

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/4)^(4 * 10)

A = $20,000 * (1.0175)^40

A = $20,000 * 2.620075

A = $52,401.51

Rounding to the nearest hundred, the total value of the loan with quarterly compounded interest is $52,400.

Part B: Total value of the loan with the monthly compounded interest

To find the total value of the loan with monthly compounded interest, we'll use the same formula with a different value of n:

A = P * (1 + r/n)^(nt)

Where:

n = number of times compounded per year = 12 (monthly)

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/12)^(12 * 10)

A = $20,000 * (1.005833)^120

A = $20,000 * 2.600502

A = $52,010.04

Rounding to the nearest hundredth, the total value of the loan with monthly compounded interest is $52,010.04

The difference between the two loans is $52,401.51 - $52,010.04 = $391.47

The difference between the two loans is due to the higher frequency of compounding in the monthly compounded interest loan. The interest is compounded more times per year, so the interest is accumulating on the interest more quickly, leading to a higher overall interest charge.

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The mass of the drug in the organ at time t depends on the concentration of the drug in the blood entering the organ and the rate at which the blood is entering and leaving the organ. This can be calculated by multiplying the volume of the organ by the concentration of the drug in the blood.

At time t, since the rate at which the blood is entering and leaving the organ is 3 cm^3/sec, the amount of drug in the organ is equal to the amount of drug entering the organ plus the amount of drug that was initially in the organ. As there was no trace of the drug initially, the mass of the drug in the organ at time t is 3 cm^3/sec multiplied by the concentration of the drug in the blood (1/3 gm/cm3) multiplied by the volume of the organ (150 cm^3).

Therefore, the mass of the drug in the organ at time t is 150 gm.

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A.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Common Factors: 1, 2, 3, 4, 6, and 12

-----

B.

Factors of 16: 1, 2, 4, 8, and 16.

Factors of 56: 1, 2, 4, 7, 8, 14, 28, and 56

Common Factors: 1, 2, 4,  and 8

-----

C.

Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30.

Factors of 75: 1 , 3 , 5 , 15 , 25 and 75

Common Factors: 1, 3, 5, and 15.

-----

D.

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.

Common Factors: 1, 2, 3, 6, 9, and 18.

-----

E.

Whenever finding the greatest common factors of any pair of numbers it is necessary to list all the factors of each number. Then find the number that appears in both!

The domain of the step function f(x) is given as follows:

{x | -4 < x ≤ 4}.

For the function graphed at the end of the answer, we have that:

Hence the domain of the step function f(x) is given as follows:

{x | -4 < x ≤ 4}.

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

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103.08  is the total cost of the scooter including tax to the nearest cent .

Exactly what does a sales tax look like?

When you buy products and services, you must also pay sales tax, which is calculated as a percentage of the selling price.

                                For instance, you would pay $28 in sales tax if you spent $400 on a new television and resided in a region with a 7% sales tax. You want to know how much your purchase will cost after taxes before you check out at The Clothing Boutique. Your cart contains goods with a combined price of $100 after totaling up all the charges. You would calculate 9.5% of $100 since the sales tax in that county is 9.5%. (100 x 0.095).

 = 95 + 95 * 0.085

 = 95 + 8.075

 = 103.08

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1. The mean age of the team is 21 years.

2. The age of the new player is 34 years

1. From the information, the following can be deduced:

AGE (X) - - - - - - - 19 - -20 - - - 21 - - - 22 - - - 23

FREQUENCY (F) - 2 - - 3 - - - - 1 - - - - 4 - - - - 1

Mean = Age × Frequency / Sum of frequency

= [(19 * 2) + (20 * 3) + ( 21 * 1)+(22 * 4)+(23 * 1)]

= 38 + 60 +21 + 88 + 23 = 230

Sun of frequency = 2 + 3 + 1 + 4 + 1= 11

Mean(X) = 230 / 11

X = 21

The mean is 21 years.

2. A new player joins and raises it to 22 years. Let age of new player = y

Sum of Ages = 19 + 19 +20 + 20 + 20 + 21 + 22 + 22 + 22 + 22 + 23 + y

Number of players = 11 + 1 = 12

Mean(x) = sum of ages / number of players

New mean (x) = 22

x = (230 + y) / 12

22 = (230 + y) / 12

Cross multiply

264 = 230 + y

y = 264 - 230

y = 34 years

The age is 34 years.

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Complete question

The table shows the ages of players on a football team.

Age

Frequency

a) Work out the mean age of the team.

Round your answer to 1 decimal place.

19

2.

20

3

21

1

b) A new player joins the team and raises

the mean age to 22.

22

4

23

1

Work out the age of this new player

Answer:

im pretty sure the answer is a

Step-by-step explanation:

and follow me plz

The surface area of the backyard can be estimated using the measurements of y, taken every 3 feet for a 36 feet long yard, and using a mathematical formula such as the trapezoidal rule or numerical integration method.

The surface area of the backyard can be estimated by using a mathematical formula such as the trapezoidal rule or numerical integration method. To use the trapezoidal rule, the man would need to calculate the average height between each of the y measurements and use this average height as the height of a trapezoid with a base equal to the 3-foot increment.

The man would then sum up the areas of all the trapezoids to estimate the total surface area of the backyard. Numerical integration is a more complex method that uses more advanced mathematical concepts, such as calculus, to estimate the surface area. Both methods can provide an estimate of the surface area, but the accuracy of the estimate will depend on the accuracy of the y measurements.

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Answer:

•WHAT IS PERIMETER?

>> PERIMETER MEANS THE SUM OF ALL SIDES OF FIGURE

NOW,LET'S SEE YOUR GIVEN QUESTION.

THE FIGURES 2 SIDES DATA IS GIVEN

•6CM

•5.5CM

THEREFORE : 6 + 5.5

: 11.5 CM

THE PERIMETER OF FIGURE IS 11.5 CM

Answer:

Graph 4

Step-by-step explanation:

I have to put more words lol

Answer:

Step-by-step explanation:

To find the value of x we use sine

sin ∅ = opposite / hypotenuse

From the question

29 is the hypotenuse

9 is the opposite

sin x = 9/29

x = sin-¹ 9/29

x = 18.08°

Hope this helps you

Answer:

Angle=71.9°

using the trig inverse formula sec(angle)= hypotenuse/adjacent

Answer:

62.8 inches

Step-by-step explanation:

c = πd

c = 3.14 * 20

c = 62.8 inches

Answer:

18+x = -40

Step-by-step explanation:

The sum of 18 and a number x is translated to "18+x"
Equals means "="
Negative forty is "-40"
Put them all in order and you get 18+x = -40

Answer:

Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.

Step-by-step explanation:

Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables a, b, and c, respectively.

Since a total of 14 cups of coffee was served:

\(a+b+c=14\)

A total of 204 ounces of coffee was served. Therefore:

\(10a+14b+20c=204\)

A total of $16.70 was collected. Hence:

\(0.95a+1.15b+1.5c=16.7\)

This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.

From the first equation, let's subtract a and b from both sides:

\(c=14-a-b\)

Substitute this into both the second and third equations:

\(10a+14b+20(14-a-b)=204\)

And:

\(0.95a+1.15b+1.5(14-a-b)=16.7\)

In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:

For the Second Equation:

\(\displaystyle \begin{aligned} 10a+14b+280-20a-20b&=204\\ -10a-6b&=-76\\5a+3b&=38\end{aligned}\)

And for the Third:

\(\displaystyle \begin{aligned} 0.95a+1.15b+21-1.5a-1.5b&=16.7\\ -0.55a-0.35b&=-4.3\end{aligned}\)

We can solve this using substitution. From the second equation, isolate a:

\(\displaystyle a=\frac{1}{5}(38-3b)=7.6-0.6b\)

Substitute into the third:

\(-0.55(7.6-0.6b)-0.35b=-4.3\)

Distribute and simplify:

\(-4.18+0.33b-0.35b=-4.3\)

Therefore:

\(-0.02b=-0.12\Rightarrow b=6\)

Using the equation for a:

\(a=7.6-0.6(6)=4\)

And using the equation for c:

\(c=14-(4)-(6)=14-10=4\)

Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

The answer is ⁵√a²

Step-by-step explanation:

a⅖=⁵√a²

In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

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The solution that can be used to fill in location A is 45%.

In this case, Rena is trying to make a 45% solution. The alligation diagram shows two solutions with concentrations of 20% and 45%. The concentration at location A represents the concentration of the final mixture.

To determine the concentration at location A, we can visually observe the positioning of the concentrations on the diagram. The closer a concentration is to location A, the more it contributes to the final mixture.

In this case, the concentration of 45% is closer to location A than the concentration of 20%.

This means that more of the 45% solution should be used in the mixture to achieve a 45% concentration.

Therefore, the solution that can be used to fill in location A is 45%.

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The composite functions in this problem are given as follows:

a) (f ∘ g)(x) = x^4 + 18x² + 81.

b) (g ∘ f)(x) = x^4 + 9.

c) (f ∘ f)(x) = x^4.

d) (g ∘ g)(x) = x^4 + 18x² + 90.

All these functions have a domain of all real values.

For composite functions, the outer function is applied as the input to the inner function.

In the context of this problem, the functions are given as follows:

For item a, the composite function is given as follows:

(f ∘ g)(x) = f(x² + 9) = (x² + 9)² = x^4 + 18x² + 81.

For item b, the composite function is given as follows:

(g ∘ f)(x) = g(x²) = (x²)² + 9 = x^4 + 9.

For item c, the composite function is given as follows:

(f ∘ f)(x) = f(x²) = (x²)² = x^4.

For item d, the composite function is given as follows:

(g ∘ g)(x) = g(x² + 9) = (x² + 9)² + 9 = x^4 + 18x² + 90.

None of these functions have any restriction on the domain such as fractions or even roots, hence all of them have all real values as the domain.

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Figure 1:

We have that:

- The sum of the internal angles of a triangle is equal to 180°.

- A right angle measures 180°.

Therefore:

And

Answer: x = 117°

Figure 2:

And

Answer: x = 82°

Figure 3:

And

Answer: x = 10

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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The height of the largest photo is 16 inches.

Sydney's senior picture package includes several sizes of portraits. The smallest photo is a 1.5-inch wide and 2 inch tall rectangle.

The largest photo is 12 inches wide and is similar to the smallest photo.

Let's assume that the largest photo's height is h, then we can say the ratio of the largest photo to the smallest photo is given as:\[\frac{h}{2}=\frac{12}{1.5}\]

Simplify the ratio:\[\frac{h}{2}=8\]

Multiplying each side by 2:\[h = 16\]

Therefore, the height of the largest photo is 16 inches.

Hence, the answer is 16.

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