Find the z value to the right of the mean such that 85% of the total area under the standard normal distribution curve lies to the left of it

We can determine the value of the computer for the year 2023 by subtracting the depreciation for 8 years from the current value.Value in 2023 = Current value - Depreciation for 8 years = $9,500.00 - $6,800.00

To determine the value of the computer for the year 2023, we need to calculate the annual depreciation and subtract it from the current value.

Given:

- Cost of the computer in 2015: $17,000.00

- Current value: $9,500.00

- Depreciation assumed to be straight-line

To calculate the annual depreciation, we need to determine the depreciation rate per year. The depreciation rate can be calculated as the difference in value divided by the number of years.

Depreciation rate per year = (Cost - Current value) / Number of years

Number of years = 2023 - 2015 = 8 years

Depreciation rate per year = ($17,000.00 - $9,500.00) / 8 = $850.00 per year

Now, we can calculate the depreciation for the remaining years until 2023. Since the depreciation is assumed to be straight-line, the depreciation per year remains constant.

Depreciation for 8 years = Depreciation rate per year * Number of years = $850.00 * 8 = $6,800.00

Finally, we can determine the value of the computer for the year 2023 by subtracting the depreciation for 8 years from the current value.

Value in 2023 = Current value - Depreciation for 8 years = $9,500.00 - $6,800.00

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Area of the parallelogram equals to a*h, where a is the length of its side and h is the length of a height drawn to that side. In this case, we know all its sides, but we don't know height to the side 23.2, so we can't use it.

S = 18 * 21 = 378 (in²).

To solve this problem, we can use the binomial probability formula. Let's break it down:

Given information:

Total number of people surveyed (n) = 1369

Number of people who said they voted (x) = 912

Probability of an eligible voter actually voting (p) = 0.64

(a) To find the probability that at least 912 people actually voted, we need to calculate the probability of x being 912 or more. We can use the cumulative binomial probability for this.

P(X ≥ 912) = 1 - P(X < 912)

Using the binomial probability formula, we can calculate P(X < 912):

P(X < 912) = ∑[from k=0 to 911] (nCk) * p^k * (1-p)^(n-k)

Calculating this summation may be complex, but we can use statistical software or calculators to compute it. The result is:

P(X < 912) ≈ 0.0003

Therefore, to find P(X ≥ 912), we subtract this value from 1:

P(X ≥ 912) = 1 - P(X < 912) ≈ 1 - 0.0003 ≈ 0.9997

Rounded to four decimal places, the probability that among 1369 randomly selected voters, at least 912 actually voted is approximately 0.9997.

(b) The result from part (a) suggests that some people may not be honest about whether they actually voted. The probability of observing at least 912 people who said they voted, given the true voting rate of 64%, is extremely high (approximately 0.9997). This suggests that either the voting records are inaccurate or some individuals may have misrepresented their voting behavior in the survey. The high probability implies that the reported number of voters may not align with the actual voting participation. Therefore, option C is the most appropriate:

C. Some people are being less than honest because P(X) is less than 5%.

Please note that the interpretation and implications may vary depending on the context and additional factors involved.

The total take-home pay for the family is $4,000, and 15% of the budget is allocated for transportation.

1. Determine the total take-home pay: According to the figure, we can see that the income stated is $4,000. Hence, the total take-home pay for the family is $4,000.

2. Calculate the percentage allocated for transportation: Looking at the figure, we need to identify the portion of the budget allocated for transportation. By observing the diagram, we can see that the section labeled "Transportation" represents 15% of the total budget.

3. Calculate the percentage: To find the percentage, we divide the amount allocated for transportation by the total budget and then multiply by 100. In this case, the total budget is $4,000, and 15% of that is allocated for transportation.

  Percentage = (Amount allocated for transportation / Total budget) * 100

  Percentage = ($600 / $4,000) * 100

  Percentage = 0.15 * 100

  Percentage = 15%

Therefore, 15% of the family budget is allocated for transportation.

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Answer: 4(a+3) -3(a-2) => 12 +4a -3a +6 => a +18

When b is equal to 3/4, the following values are equivalent:

a) b to the power of 2:

(3/4)^2 = 9/16

b) 1 minus b:

1 - 3/4 = 1/4

c) 2b:

2 * (3/4) = 3/2 or 1.5

d) b divided by 2:

(3/4) / 2 = 3/8 or 0.375

After receiving both raises, Doug's annual salary amounts to $16,392.00.

Doug's monthly salary was initially $1250. After receiving a 5% raise, his new monthly salary can be calculated by multiplying his initial salary by 1 plus the raise percentage. Therefore, his new monthly salary is $1250 * (1 + 0.05) = $1312.50.

After six months, Doug receives another 4% raise. To calculate his new monthly salary, we can multiply his previous monthly salary by 1 plus the raise percentage. His new monthly salary is $1312.50 * (1 + 0.04) = $1366.00.

To determine Doug's annual salary after receiving both raises, we multiply his new monthly salary by 12 since there are 12 months in a year. Therefore, his annual salary is $1366.00 * 12 = $16,392.00.

As a result, Doug's annual income now stands at $16,392.00 after getting both raises.

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1a) To find the HCF (Highest Common Factor) and LCM (Least Common Multiple) of 224 and 336, we can use the prime factorization method.

Prime factorization of 224:

224 = 2 * 2 * 2 * 2 * 2 * 7 = 2^5 * 7

Prime factorization of 336:

336 = 2 * 2 * 2 * 2 * 3 * 7 = 2^4 * 3 * 7

HCF: We take the common prime factors with the lowest exponents, which are 2^4 and 7.

HCF of 224 and 336 = 2^4 * 7 = 112

LCM: We take all the prime factors with the highest exponents.

LCM of 224 and 336 = 2^5 * 3 * 7 = 672

Therefore, the HCF of 224 and 336 is 112, and the LCM is 672.

1b) Prime factorization of 18:

18 = 2 * 3 * 3 = 2 * 3^2

Prime factorization of 42:

42 = 2 * 3 * 7

HCF: The common prime factors are 2 and 3.

HCF of 18 and 42 = 2 * 3 = 6

LCM: We take all the prime factors with the highest exponents.

LCM of 18 and 42 = 2 * 3^2 * 7 = 126

Therefore, the HCF of 18 and 42 is 6, and the LCM is 126.

1c) Prime factorization of 45:

45 = 3 * 3 * 5 = 3^2 * 5

Prime factorization of 150:

150 = 2 * 3 * 5 * 5 = 2 * 3 * 5^2

HCF: The common prime factors are 3 and 5.

HCF of 45 and 150 = 3 * 5 = 15

LCM: We take all the prime factors with the highest exponents.

LCM of 45 and 150 = 2 * 3^2 * 5^2 = 450

Therefore, the HCF of 45 and 150 is 15, and the LCM is 450.

The interval at which the three patients visit the doctor can be found by taking the LCM of the intervals: 8, 15, and 24.

LCM of 8, 15, and 24 = 120

Therefore, they will next all go to the doctor on the same day after 120 days from 1 March. The date will be 29 June.

The bell rings every 15 minutes and the whistle is blown every 18 minutes. To find the time when they will be rung and blown at the same time again, we need to find the LCM of 15 and 18.

LCM of 15 and 18 = 90

Therefore, the bell will be rung and the whistle will be blown at the same time again after 90 minutes. The time will be 9:30 am.

To find the time when Anthony and Joseph will be at the same point on the circular track again, we need to find the LCM of their running times: 65 seconds and 75 seconds.

LCM of 65 and 75 = 975

Therefore, it will take 975 seconds for Anthony and Joseph to be at the same point on the circular track again.

swimmers question:

To find the time when the swimmers are side by side at one end of the pool again, we need to find the least common multiple (LCM) of their lap times.

The lap times of the three swimmers are 28 seconds, 44 seconds, and 68 seconds.

To find the LCM, we can list the multiples of each lap time until we find a common multiple:

Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, ...

Multiples of 44: 44, 88, 132, 176, 220, 264, 308, ...

Multiples of 68: 68, 136, 204, 272, 340, 408, ...

From the lists above, we can see that the least common multiple of 28, 44, and 68 is 308 seconds.

Therefore, it will take 308 seconds (or 5 minutes and 8 seconds) for the swimmers to be side by side at one end of the pool again.

Answer:

672

Step-by-step explanation:

Find the prime factorization of 224

224 = 2 × 2 × 2 × 2 × 2 × 7

Find the prime factorization of 336

336 = 2 × 2 × 2 × 2 × 3 × 7

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 2 × 2 × 2 × 2 × 3 × 7

LCM = 672

It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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Answer:

1)  x = 39

2)  x = 62

Step-by-step explanation:

The sum of all arc measures of a circle is 360°.

Therefore, to find the measure of the unlabelled intercepted arc, subtract the measures of the other two arcs from 360°:

[tex]360^{\circ}-160^{\circ}-122^{\circ}=78^{\circ}[/tex]

Therefore, the measure of the unlabelled intercepted arc is 78°.

To find the measure of the inscribed angle, x, we can use the Inscribed Angle Theorem. This theorem states that the measure of an inscribed angle is half the measure of the intercepted arc. Therefore, the inscribed angle x is half of 78°:

[tex]x^{\circ}=\dfrac{78^{\circ}}{2}=39^{\circ}[/tex]

Therefore, the value of x is 39.

[tex]\hrulefill[/tex]

To find the value of x, we can use the Intersecting Secants Theorem.

If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.

From inspection of the given diagram:

Therefore, according to the Intersecting Secants Theorem:

    [tex]42.5^{\circ}=\dfrac{1}{2}(147^{\circ}-x^{\circ})[/tex]

[tex]2 \cdot 42.5^{\circ}=2 \cdot \dfrac{1}{2}(147^{\circ}-x^{\circ})[/tex]

      [tex]85^{\circ}=147^{\circ}-x^{\circ}[/tex]

       [tex]x^{\circ}=147^{\circ}-85^{\circ}[/tex]

       [tex]x^{\circ}=62^{\circ}[/tex]

         [tex]x=62[/tex]

Therefore, the value of x is 62.

Answer: The bearing is below

N

|

|

|

S

Answer: 5, 10, and 12

Step-by-step explanation:

       Each square as been moved six units clockwise (or rotated 180 degrees). Using this knowledge there should be a dot in box 12, 10, and 5.

Answer:

Step-by-step explanation:

(10x⁵ - 2x⁴ +2)7x²                            > multiply 7x² by each term in

                                                          parenthesis

                                                       >Multiply number with number and

                                                         to multiply x's, add the exponents

=70x⁷- 14x⁶ + 14x²

a) The balance in Hazwan's account immediately after the withdrawal is RM1,674.61.

b) The value of X cannot be determined as the equation (1.07)^10 = (1.02667)^30 does not hold true. Pian should explore other investment options as neither Bank A nor Bank B can achieve the desired future value of RM50,000 in 10 years.

a) To find the balance in Hazwan's account immediately after the withdrawal, we need to calculate the interest earned during the five-year period and subtract the withdrawal amount from the final balance.

For the first two years, the interest is compounded quarterly at a rate of 4%. Using the formula for compound interest, we can calculate the balance after two years:

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

where:

A = final amount

P = principal (initial deposit)

r = interest rate per period

n = number of compounding periods per year

t = number of years

For the first two years:

P = RM6,000

r = 4% = 0.04

n = 4 (quarterly compounding)

t = 2

A = 6000(1 + 0.04/4)^(4*2)

A ≈ RM6,488.99

After two years, the interest rate changes to 5% compounded semiannually. Using the same formula, we can calculate the balance after the remaining three years:

For the next three years:

P = RM6,488.99

r = 5% = 0.05

n = 2 (semiannual compounding)

t = 3

A = 6488.99(1 + 0.05/2)^(2*3)

A ≈ RM7,674.61

After five years, the balance in Hazwan's account is RM7,674.61.

To find the balance immediately after the RM3,000 withdrawal, we subtract the withdrawal amount:

Balance = RM7,674.61 - RM3,000

Balance = RM4,674.61

Therefore, the balance in Hazwan's account immediately after the withdrawal is approximately RM4,674.61.

b) To find the value of X and determine which bank Pian should choose, we can compare the future values of the investments in Bank A and Bank B.

For Bank A, the investment is compounded annually at a rate of 7%. Using the formula for compound interest, we can calculate the future value:

FV_A = X(1 + 0.07)^10

FV_A = X(1.07)^10

For Bank B, the investment is compounded every four months at a rate of 8%. Using the same formula, we can calculate the future value:

FV_B = X(1 + 0.08/3)^(10*3)

FV_B = X(1.02667)^30

To determine the value of X, we equate the future values of the two investments:

X(1.07)^10 = X(1.02667)^30

Simplifying the equation, we can cancel out X:

(1.07)^10 = (1.02667)^30

Using a calculator, we find that (1.07)^10 ≈ 1.9672 and (1.02667)^30 ≈ 1.9443.

Therefore, the equation becomes:

1.9672 = 1.9443

This equation is not true, so there is no value of X that satisfies the equation. As a result, Pian cannot invest in either Bank A or Bank B to achieve a future value of RM50,000 in 10 years.

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Answer:

Step-by-step explanation:

The area of the bakery is given by:

Area = Length × Width

We know that the length of the bakery is (x + 6) and the area is 2x² + 12x - 12. We can use this information to find the width of the bakery.

Area = Length × Width

2x² + 12x - 12 = (x + 6) × Width

2x² + 12x - 12 = x × Width + 6 × Width

2x² + 12x - 12 = x × Width + 6 × Width

2x² + 12x - 12 = (x + 6) × Width

Width = (2x² + 12x - 12) / (x + 6)

Therefore, the width of the bakery is 2x - 4.

I hope this helps! Let me know if you have any other questions.

Answer: (-4,4), (-3,5),(-2,8),(-1,13),(0,20)

Step-by-step explanation: calculator and y-intersect is 20

To achieve a goal of $700,000 in 40 years with a 2.3% monthly compounded rate of return, you should invest approximately $554.95 per month.

To determine the monthly investment required to reach a goal of $700,000 in 40 years with a rate of return of 2.3% compounded monthly, we can use the formula for calculating the future value of an investment.

The formula for future value (FV) of a monthly investment is given by:

[tex]FV = P \times [(1 + r)^n - 1] / r[/tex]

Where:

P = monthly investment amount

r = monthly interest rate (2.3% = 0.023 divided by 12)

n = total number of compounding periods (40 years [tex]\times[/tex] 12 months/year = 480 months)

We want the future value (FV) to be $700,000.

Substituting the given values into the formula, we can solve for the monthly investment amount (P):

[tex]700,000 = P \times [(1 + 0.023/12)^480 - 1] / (0.023/12)[/tex]

Simplify the denominator:

(0.023/12) = 0.00191666667

Simplify the exponential term:

[tex](1 + 0.023/12)^{480} = (1.00191666667)^{480}[/tex]

Subtract 1 from the exponential term:

[tex](1.00191666667)^{480 - 1[/tex]

Multiply by the monthly investment amount (P):

[tex]P \times [(1.00191666667)^{480 - 1}][/tex]

Now, plugging in the simplified values, the equation becomes:

[tex]700,000 = P \times [(1.00191666667)^{480 - 1}] / 0.00191666667[/tex]

Simplifying this equation will give us the required monthly investment amount to reach the goal of $700,000 in 40 years with a 2.3% monthly compounded rate of return.

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Answer:

The correct interpretation of the confidence level is: If many random samples of size 100 are selected from all records of animals in shelters, approximately 95% of the intervals would capture the true proportion that were adopted. Therefore, the answer is option C.

Step-by-step explanation:

The radius of the base of the cone is approximately 8.86 inches, and the diameter is approximately 17.72 inches.

To find the radius and diameter of the cone's base, we can use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius, h is the height, and π is a constant (approximately 3.14). In this case, the volume is given as 1627 cubic inches and the height is 6 inches.

Rearranging the formula, we have r^2 = (3V)/(πh), where r is the radius. Substituting the given values, we get r^2 = (3 * 1627) / (π * 6). Solving this equation, we find that r^2 ≈ 271.17. Taking the square root of both sides, we get r ≈ 8.86 inches.

The diameter of the base is simply twice the radius, so the diameter is approximately 2 * 8.86 = 17.72 inches.

Therefore, the radius of the base of the cone is approximately 8.86 inches, and the diameter is approximately 17.72 inches.

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Answer: The obtained answer is 2.38.

Step-by-step explanation: By solving the first term and the second term separately and subsequently by dividing both the terms, we obtain the solution.

5/6 ÷ 7/20

5/6 = 5÷6 = 0.833

7/20= 7÷20 = 0.35

Therefore, 5/6  ÷ 7/20 = 0.833 ÷ 0.35

             => 5/6 ÷ 7/20 = 833 ÷ 350 =2.38

Answer:

Step-by-step explanation:

To derive a second-order equation from the sequence 1, 2, 4, 6, 10, 14, we can use the method of finite differences. The first differences are:

1, 2, 2, 4, 4

The second differences are:

1, 0, 2, 0

Since the second differences are not constant, we know that the sequence is not quadratic. However, we can still find a second-order equation that approximates the sequence.

One way to do this is to use the method of least squares to fit a curve to the data. We can assume that the curve has the form:

y = ax^2 + bx + c

where y is the nth term of the sequence and x is the index of the term (starting with x = 1 for the first term). We can then use the first six terms of the sequence to solve for a, b, and c.

Substituting x = 1, y = 1; x = 2, y = 2; and x = 3, y = 4 into the equation above gives us three equations:

a + b + c = 1

4a + 2b + c = 2

9a + 3b + c = 4

Solving these equations simultaneously gives us:

a = **1/2**

b = **-1/2**

c = **1/3**

Therefore, a second-order equation that approximates the sequence is:

y = **(1/2)x^2 - (1/2)x + (1/3)**

I hope this helps! Let me know if you have any other questions.

The Initial number of toads in the pond is 3x = 3 * 6 = 18.

Let's assume the initial number of toads in the pond is 3x, and the initial number of snails is 4x, where x is a positive integer representing the common factor of the ratio.

According to the problem, when 6 more snails enter the pond, the new ratio of toads to snails becomes 3:5. This means that the number of toads remains the same (3x), but the number of snails becomes 4x + 6.

Now we can set up an equation to solve for x:

(3x) / (4x + 6) = 3 / 5

To simplify the equation, we can cross-multiply:

5(3x) = 3(4x + 6)

15x = 12x + 18

15x - 12x = 18

3x = 18

x = 6

Therefore, the initial number of toads in the pond is 3x = 3 * 6 = 18.

So, there are 18 toads in the pond.

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To answer your question, let's examine each inequality separately and determine the corresponding regions on the diagram.

a) For the inequality ay > -x and x < -6:

The inequality ay > -x can be rewritten as y > (-1/a)x. Since a is a constant, we can assume that a is not equal to zero.

Given x < -6, we know that x is restricted to values less than -6.

Combining these conditions, we have the following:

1. If a > 0: The inequality y > (-1/a)x represents a line with a negative slope passing through the origin (0, 0). Since x is restricted to values less than -6, the line will be drawn up to x = -6 and extend indefinitely in the negative x direction. The region above this line represents the solution.

2. If a < 0: The inequality y > (-1/a)x represents a line with a positive slope passing through the origin (0, 0). Again, the line will be drawn up to x = -6 and extend indefinitely in the negative x direction. The region below this line represents the solution.

Therefore, the region on the diagram that represents ay > -x and x < -6 depends on the sign of a. If a > 0, it's the region above the line; if a < 0, it's the region below the line.

b) For the inequality y < -x and x > -6:

The inequality y < -x represents a line with a negative slope passing through the origin (0, 0).

Given x > -6, we know that x is restricted to values greater than -6.

Combining these conditions, we have the following:

The line y < -x will be drawn starting from the origin and extend indefinitely in the negative x and negative y directions. However, since x is restricted to values greater than -6, the line will not be drawn for x values less than -6. Therefore, the solution region for this inequality is the entire left side of the diagram (negative x-axis and negative y-axis), excluding the region beyond x = -6.

To summarize:

a) The region representing ay > -x and x < -6 depends on the sign of a. If a > 0, it's the region above the line; if a < 0, it's the region below the line.

b) The region representing y < -x and x > -6 is the entire left side of the diagram (negative x-axis and negative y-axis), excluding the region beyond x = -6.

The coordinates of point B are (12, 36). we need to examine the lengths of its sides and the angles between the sides.

To determine the coordinates of point B, we need to find the intersection of the line BD (given by the equation 3x - y = 0) and the line passing through points A and D.

We can find the equation of the line passing through points A and D using the slope-intercept form: y - y1 = m(x - x1), where m is the gradient and (x1, y1) is a point on the line. Given that point A is (-8, 6) and D is (3, 9), we can calculate the slope as:

m = (y2 - y1) / (x2 - x1)

 = (9 - 6) / (3 - (-8))

 = 3 / 11

Now, using the point-slope form with point A:

y - 6 = (3/11)(x + 8)

Simplifying the equation:

y = (3/11)x + 30/11 - 66/11

y = (3/11)x - 36/11

To find the coordinates of point B, we need to solve the system of equations formed by the lines BD and the line passing through A and D. Substituting the equation of line BD into the equation of the line passing through A and D:

3x - y = (3/11)x - 36/11

Multiplying both sides by 11 to eliminate fractions:

33x - 11y = 3x - 36

Simplifying the equation:

30x - 11y = -36

To find the intersection point (x, y), we can solve this equation along with the equation of line BD:

3x - y = 0

Solving the system of equations:

30x - 11y = -36

3x - y = 0

Multiplying the second equation by 11 to eliminate the y term:

33x - 11y = 0

Subtracting the second equation from the first:

30x - 33x = -36

-3x = -36

x = 12

Substituting the value of x back into the equation of line BD:

3(12) - y = 0

36 - y = 0

y = 36

Therefore, the coordinates of point B are (12, 36).

To determine whether ABCD is a square or not, we need to examine the lengths of its sides and the angles between the sides. Since we only have the coordinates of points A, B, and D, we cannot directly determine the lengths of all four sides or the angles. Therefore, additional information is required to determine if ABCD is a square.

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Based on the information provided, the numbers that are closest to -3/5 are -4/5 and -0.2 and the numbers that are closest to 4/5 are 2/5 and 0.6.

To understand this, we will simplify the fractions given by dividing the numbers:

-3/5 = -0.6

4/5 = 0.8

Now, let's evaluate if each number is closest to -3/5 or to 4/5. For this, we will simplify the numbers when it is possible.

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Answer:

2345.72 m³

Step-by-step explanation:

To find the volume of the shape, first find the volume of cylinder and then the volume of the cone. Then, add them.

Volume of the cylinder:

       h = height of the cylinder = 10 m

       d = 16 m

       r = 16 ÷ 2 = 8 m

[tex]\boxed{\text{\bf Volume of cylinder = $ \bf \pi r^2h$}}[/tex]

                                    = 3.14 * 8 * 8 * 10

                                    = 2010.62 m³

Volume of cone:

          H = height of cone = 5 m

          r = 8 m

          [tex]\boxed{\text{\bf Volume of cone = $\bf \dfrac{1}{3}*\pi r^2*H$}}[/tex]

                                       [tex]\sf =\dfrac{1}{3}*3.14*8*8*5\\\\ = 335.1 \ m^3[/tex]

Volume of the shape = 2010.62 + 335.1

                                   = 2345.72 m³

Answer:

x = 38.74

Step-by-step explanation:

Thus, we can find the bases of the two triangles and add them to find the base of the entire figure.

Finding the base of the first triangle

The sides of 30-60-90 triangles adhere to the following rules:

Since the side opposite the 60° angle is 30, we can find a by applying the rule for the side opposite the 60° angle in a 30-60-90 triangle:

Step 1:  Make an equation out of the fact that the side opposite the 60° equals a*√(3)

30 = a*√(3)

Step 2:  Divide both sides by √(3) to find a, the length of the base of triangle A:

(30 = a * √(3)) / √(3)

30 / √(3) = a

17.32050808 = a

Thus, the length of the base of triangle A is 17.32050808 units.

Finding the base of the second triangle:

tan(θ) = opposite / adjacent, where

Now we can plug in 35 for θ and 15 for the opposite side to find the adjacent side (aka the length of the base of triangle B):

Step 1:  Plug in 35 for θ and 15 for the opposite side:

tan(35) = 15 / adjacent

Step 2:  Multiply both sides by the adjacent side:

(tan(35) = 15 / adjajcent) * adjacent

adjacent * tan(35) = 15

Step 3:  Divide both sides by tan(35) to find the length of the adjacent side (i.e., the length of the base of triangle B):

(adjacent * tan(35) = 15) / tan(35)

adjacent = 15 / tan(35)

adjacent = 21.4222201

Thus, the length of the base of triangle B is 21.4222201 units.

Find the base(x) of the figure:

Now we can add the lengths of the bases of triangles A and B to find x, the base of the figure:

Length of triangle A's base + Length of triangle B's base = base of figure (x)

17.32050808 + 21.4222201 = x

38.74272818 = x

38.74 = x

Thus, the base of the figure built with 2 right triangles is 38.74.

Answer:

To find the angles, sine law can be used. The angles B and C are 38.23° and 53.82° respectively.

Step-by-step explanation:

Use sine law to find the remaining angles

[tex]\frac{sin B}{b} =\frac{sinA}{a} \\\frac{sinB}{16.1} = \frac{sin88}{26} \\sinB = \frac{16.1sin88}{26}\\ sinB = 0.6189\\B = Arcsin0.6189[/tex]

B = 38.23°

[tex]\frac{sinC}{c}=\frac{sinA}{a} \\\frac{sinC}{21} = \frac{sin88}{26} \\sinC = \frac{21sin88}{26}\\sinC= 0.8072\\ C = Arcsin0.8072[/tex]

C = 53.82°

The internal angles of a triangle is 180°

We can check if the sum of the three angles.

A + B + C = 180°

88° + 38.23° + 53.82° = 180°

180.05° ≈ 180°

The angles are approximately 180°.

Note that the slight difference is only because of the rounding off of the values.

Answer: Max is 13 years old now.

Step-by-step explanation:

Let x be Max's age now and y be Tom's age now.

We are given that,

=> x=y+10 and x+7=2(y+7).

Substituting the first equation into the second equation, we get

=> y+10+7=2y+14.

Solving for y, we get

=> y=3.

Substituting this value back into the first equation, we get

=> x=3+10=13.

Therefore, Max age is 13 years old now.

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