I am 41 years old. I am 24 years older than double my elder son's age. How old is my elder son?

Answer: The length of the base of the ramp is approximately 27 inches when rounded to the nearest inch.

Step-by-step explanation:

We can use trigonometry to solve this problem.

Let's call the length of the base of the ramp "x". Then, we can use the tangent function to find x:

tan(22) = 11/x

To solve for x, we can multiply both sides by x and divide by tan(22):

x = 11 / tan(22)

Using a calculator, we can find that:

x ≈ 27 inches

Therefore, the length of the base of the ramp is approximately 27 inches when rounded to the nearest inch.

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The amount invested at 4% interest rate that is $3900 and

the amount invested at 3% interest rate is $4300.

Last year Sarah invested money in two accounts. The first account had an interest rate of 3% and the second account had an interest rate of 4%. If she invested $400 more in the first account than the second and her total interest income was $285,

the equations are:

       s= f + 400  (1)

      0.03s + 0.04f = 285   (2)

modifying (1) and (2) for simpler calculations

      3s - 3f = 3 * 400 (3)

      3s + 4f = 100 * 285  (4)

by solving eqns (3) and (4) we get

  we get f=3900 and s=4300

Here, f is the amount invested at 4% interest rate that is $3900 and

   s refers to the amount invested at 3% interest rate is $4300.

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The percentage of buyers who paid between $150,000 and $156,000 if the standard deviation is $2000 is 49.9%

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

Mean = 150000

Standard deviation = 2000

Scores = from $150,000 and $156,000

So, we have

z = (150000 - 150000)/2000 = 0

z = (156000 - 150000)/2000 = 3

This means that it is between a z-score of 0 and a z-score of 3

This is represented as

Probability = (0 < z < 3)

Using a graphing calculator, we have

Probability =  0.49865

Express as percentage

Probability =  49.9%

Hence, the probability is 49.9%

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Answer:

its the third please mark me as a brainliest

Answer:

y = 4

Step-by-step explanation:

given equation of line is

y = - 3x - 2 and (- 2, y ) is a point on the line, then substitute x = - 2 into the equation for y , that is

y = - 3(- 2) - 2 = 6 - 2 = 4

ABCD is square, AC = 6, AO = 3√2, BO = 3√2, BO = 4, DC = 6, OC = 2√13 and area is  36 square units.

To solve the problems, we can use the following properties of squares:

The diagonals of a square bisect each other and are equal in length.

The diagonals of a square form two congruent right triangles.

The center of a square is equidistant from all four vertices of the square.

Since ABCD is a square, we have AC = AB = 6.

Since O is the center of the square, AO is half the length of the diagonal of the square. Using the Pythagorean theorem, we can find the diagonal of the square:

diagonal² = AB² + BC²

= 6² + 6²

= 72

diagonal = √72 = 6√2

Therefore, AO = (1/2) diagonal = 3√2

Since O is the center of the square, BO is equal in length to AO, which we found in part (18). Therefore, BO = 3√2.

If AO = 4 and BO = AO, then BO = 4.

The area of ΔAOB is half the area of the square ABCD. The area of a square is given by side², so the area of ABCD is 6² = 36. Therefore, the area of ΔAOB is (1/2) × 36 = 18 square units.

The area of a square is given by side², so the area of ABCD is 6² = 36 square units.

Since the diagonals of a square bisect each other, DO is half the length of the diagonal of the square. Using the Pythagorean theorem, we can find the diagonal of the square:

diagonal² = AB² + BC²

= 6² + 6²

= 72

diagonal = √72 = 6√2

Therefore, DO = (1/2) diagonal = 3√2

Since ABCD is a square, DC = AB = 6.

The area of ΔDOC is half the area of the square ABCD. Using the Pythagorean theorem, we can find the length of OC:

OC² = AO² + AC²

= 4² + 6²

= 52

OC = √52 = 2√13

Therefore, the area of ΔDOC is (1/2) × 6 × 2√13 = 6√13 square units.

The area of a square is given by side², so the area of ABCD is 6² = 36 square units.

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Answer:

45 Minutes

Step-by-step explanation:

1.5 Hours = 90 Minutes (1.5*60)

90/2 = 45

45 Minutes on the trampoline.

The completely factored form of the expression 4x² + 28x + 49 is (x + 7)(4x + 7) (option a).

In this case, we need to factor the expression 4x² + 28x + 49. One way to do this is by using the quadratic formula, which is a formula used to find the roots or solutions of a quadratic equation.

However, since we are only looking for the completely factored form, we can use a simpler method known as "factoring by grouping." This method involves grouping terms with common factors and factoring them separately.

Starting with the given expression:

4x² + 28x + 49

We notice that the first two terms have a common factor of 4x:

4x(x + 7) + 49

Now, we can factor out the common factor of (x + 7) from the first two terms:

4x(x + 7) + 49 = (x + 7)(4x + 49/7)

Simplifying the expression in the second set of parentheses:

4x + 49/7 = 4x + 7

Hence the correct option is (a).

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Complete Question:

Which is the completely factored form of 4x2 + 28x + 49?

a) (x + 7)(4x + 7)

b) 4(x + 7)(x + 7)

c) (2x + 7)(2x + 7)

d) 2(x+7)(x + 7)

Answer:

Step-by-step explanation:

The three true statements about circle Q are:

1. The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth.

2. The area of the shaded sector is 4 units 2.

3. The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the circumference of the circle.

The True statements are:

The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.

The area of the shaded sector depends on the length of the radius.

The area of the shaded sector depends on the area of the circle.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.  

First, The measure of the central angle is 45°.  

So, ratio of the central angle to the entire circle

= 45/360

= 9/72

= 1/8

Now, area of shaded sector

A = πr² = π(6²) = 36π

or, 1/8(36π)

= 36π/8

= 18π/4

= 9π/2

= 4.5π square units.  

Since, we use the circle's radius to determine area, the shaded sector's area is dependent on the circle's radius.

Given that the sector is a portion of the circle, its size is also influenced by the size of the circle.

and, The ratio of the shaded sector's area to the circle's area wouldn't be the same as the ratio of the arc's length to the circle's area.

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Answer:

Yes, Melanie's statement that the basketball season starts in 15 weeks is reasonable.

To see why, we can estimate the number of days in 15 weeks. Since 1 week is equal to 7 days, 15 weeks would be approximately equal to:

15 weeks x 7 days/week = 105 days

The surface area of the cylinder is 471 mm².

Given is a cylinder of height 5 mm and radius 10 mm, we need to find the surface area of the cylinder,

So, the surface area of the cylinder is = 2π × r (h+r)

= 2 × 3.14 × 5 (5+10)

= 2 × 3.14 × 75

= 471 mm²

Hence, the surface area of the cylinder is 471 mm².

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The meter reading, in ccf, indicated by each of the gas meters would be  8.83 ccf.

Required to find the meter reading in ccf

Let x be [tex]m^{2}[/tex] - meter readings.

The readings in ccf is:

Reading = x/ 2.832

Now, Assume the value of x is 25; The readings will be:

Reading = 25/ 2.832 ccf

Reading = 8.83 ccf

The complete question is

Manuel works for the water company as a meter reader. The meter below is the Jansen's water meter. What is the reading, in ccf, on the meter shown?

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Answer:

The temperature in 5 hours will be -25°C.

The temperature 8 hours ago was 14°C.

Step-by-step explanation:

To find the temperature, y, in degrees Celsius at any given number of hours, x, from the current time, we can create a linear equation in the form y = mx + b, where m is the rate of change and b is the current temperature.

Given the current temperature is -10°C, then b = -10.

Given the temperature falls at a constant rate of 3°C per hour, then m = -3.

Substitute the values of m and b into the formula:

[tex]\boxed{y = -3x - 10}[/tex]

where:

To calculate the temperature in 5 hours time, substitute x = 5 into the equation:

[tex]\begin{aligned}\implies y&=-3(5)-10\\&=-15-10\\&=-25^{\circ}\text{C}\end{aligned}[/tex]

Therefore, the temperature in 5 hours will be -25°C.

To calculate the temperature 8 hours ago, substitute x = -8 into the equation. The value of x is negative since we want to find the temperature 8 hours before the current time.

[tex]\begin{aligned}\implies y&=-3(-8)-10\\&=24-10\\&=14^{\circ}\text{C}\end{aligned}[/tex]

Therefore, the temperature 8 hours ago was 14°C.

Answer:

77

Step-by-step explanation:

First, let's simplify the expression inside the innermost parentheses:

5x12 = 60

60/2 = 30

-14 + 30 - 6 = 10

Now, we have:

[64 + {23 - 10}] = [64 + 13] = 77

Answer:

V = 5747.02 ft^3

Step-by-step explanation:

Therefore, to solve for volume, we plug in 14 for r in the general formula:

[tex]V=2/3\pi (14)^3\\V=2/3\pi (14)(14)(14)\\V=2/3\pi *2744\\V=5747.020161\\V=5747.02[/tex]

Lastly, volume is always in units cubed (e.g., ft^3 or mi^3 since volume deals with the three-dimensional space of an object

The 95% confidence interval of the mean body temperature of adults in the town is (97.584, 98.876)°F (open-interval notation), accurate to 3 decimal places.

To find the 95% confidence interval (C.I.) of the mean body temperature, we need to use the formula:

C.I. = x ± z*(σ/√n)

Where:

x is the sample mean

σ is the population standard deviation (unknown, but we can estimate it using the sample standard deviation)

n is the sample size

z is the critical value for the desired confidence level (95% in this case)

First, we need to calculate the sample mean, sample standard deviation, and sample size:

x = (98 + 97.9 + 99 + 97.3 + 98.9 + 99.6 + 97.8 + 99.8 + 99.1 + 98.4 + 98.7 + 97.6 + 96.5) / 13 = 98.23

s = √((1/(n-1)) * Σ(xi - x)²)

s = 1.339

n = 13

Next, we need to find the critical value, z, for a 95% confidence level. We can look this up in a standard normal distribution table or use a calculator. For a 95% confidence level, z = 1.96.

Now we can plug in the values into the formula to get the 95% confidence interval:

C.I. = 98.23 ± 1.96*(1.339/√13) = (97.584, 98.876)

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Answer:

  C  86

Step-by-step explanation:

You want the measure of the angle marked x° where chords cross. The angle marked x° intercepts an arc of 104° and one that is unmarked. The remaining arcs of the circle are marked 111° and 77°.

The measure of angle x is half the sum of the arcs it intercepts. One of those is given as 104°. The other will be ...

  360° -111° -104° -77° = 68°

Then the value of x is ...

  (104 +68)/2 = 172/2 = 86

The value of x is 86, choice C.

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The probability of selecting a mystery book, then without replacing it, selecting a nonfiction book is approximately 0.1462.

On the bookcase, there are 24 + 12 + 4 = 40 volumes.

The odds of picking a mystery book on the first draw are 24/40.

There are 39 books remaining after the first is drawn, including 12 nonfiction works. Because the initial book was never replaced, there are currently only 11 nonfiction volumes left.

Given that a mystery book was chosen without replacement in the first draw, the probability of selecting a nonfiction book in the second draw is 12/39.

When we multiply these probability together, we get:

P(nonfiction after mystery, not replacing) * P(mystery, not replacing) = (24/40) * (12/39) = 0.14615...

P(nonfiction after mystery, not replacing) * P(mystery, not replacing) = 0.1462

So, the probability of selecting a mystery book, followed by a nonfiction book without replacing it is roughly 0.1462.

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Answer:

50 in

Step-by-step explanation:

Split into 4 shapes. One on each side with 5 in x 2 in, one on the top with 12 in x 2 in, and one in the middle with 3 in x 2 in. We add all together:

2(5×2)+(12×2)+(3×2) = 50 in

well, we know the sphere's "great circle" has a circumference of 13mm, so

[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=13 \end{cases}\implies 13=2\pi r\implies \cfrac{13}{2\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{13}{2\pi } \end{cases}\implies SA=4\pi \left( \cfrac{13}{2\pi } \right)^2 \\\\\\ SA=\cfrac{169}{\pi } \implies SA\approx 53.79~mm^2[/tex]

The strategy that could be used to eliminate a variable is:

Multiply the first equation by 2 and multiply the second equation by 5. Then, add the resulting equations

From the question, we are to determine a strategy that could be used to eliminate a variable in the given system of equations

From the given information,

The system of linear equations is

5x + 3y = 4

-2x - 8y = 6

To eliminate the variable x, we can multiply the first equation by 2 and then multiply the second equation by 5. After that, we will add the resulting equations

2 × [ 5x + 3y = 4

5 × [-2x - 8y = 6

10x + 6y = 8

-10x - 40y = 30

Add the resulting equations

   10x + 6y = 8

+ (-10x - 40y = 30

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

-34y = 38

This way we have eliminated x

Hence,

The above strategy can be used to eliminate a variable

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The total interest that will accrue on the principal amount of $44,000 over a period of 2 years at a simple interest rate of 6% is $5,280.

The given problem involves calculating the amount of interest that will accrue on a principal amount of $44,000, which is invested at a simple interest rate of 6% for a period of 2 years.

To solve the problem, we can use the formula for simple interest, which is:

Interest = Principal x Rate x Time

In this case, the principal amount is $44,000, the rate of interest is 6%, and the time period is 2 years. So, plugging in these values, we get:

Interest = $44,000 x 0.06 x 2

Interest = $5,280

Unlike compound interest, simple interest is calculated only on the principal amount, and not on the accumulated interest. This means that the interest earned each year remains constant, which can make it easier to calculate and understand compared to compound interest.

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Answer:

A = $1853.96

Step-by-step explanation:

The formula for compound interest is

[tex]A(t)=P(1+r/n)^n^t[/tex], where A(t) is the amount, P is the principal (amount invested or deposited), r is the interest rate, n is the number of compound periods per year, and t is the time in years.

[tex]A(t)=1600(1+0.037/4)^(^4^*^4^)\\A(t)=1600(1.00925)^1^6\\A(t)=1853.958942\\A(t)=1853.96[/tex]

The output value of h(-7) in the function h(x) = 2x² - 7x + 4 is 151.

A function is simply a relationship that maps one input to one output.

Given the function in the question

h(x) = 2x² - 7x + 4,

Find h(-7)

To find h(-7), we substitute -7 for x in the equation of h(x) and simplify:

h(x) = 2x² - 7x + 4

Plug in x = -7

h(-7) = 2(-7)² - 7(-7) + 4

h(-7) = 2(49) + 49 + 4

h(-7) = 98 + 49 + 4

h(-7) = 151

Therefore,the output value of h(-7) is equal to 151.

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g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}. And the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.

How to solve the problem?

(i) To determine the range of a function, we need to find all the possible output values of the function. In other words, we need to find the set of all second elements in the ordered pairs of the function. For the function f, the set of all second elements is {3, 5, 1, 2}. For the function g, the set of all second elements is {4, 1, 2, 3}. Therefore, the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.

(ii) To find the composition functions f ∘ g and g ∘ f, we need to apply the functions in the correct order. The composition function f ∘ g means that we first apply g and then apply f to the result. The composition function g ∘ f means that we first apply f and then apply g to the result.

For f ∘ g:

First, we apply g to the domain of f.

(1,3) is mapped to (4,2) by g

(2,5) is mapped to (1,4) by g

(3,3) is mapped to (1,4) by g

(4,1) is mapped to (2,1) by g

(5,2) is mapped to (3,1) by g

Now we apply f to the result of g.

(4,2) is mapped to 2 by f

(1,4) is mapped to 4 by f

Therefore, f ∘ g is the function {(1,4), (4,2)}.

For g ∘ f:

First, we apply f to the domain of g.

(1,4) is mapped to 3 by f

(2,1) is mapped to 5 by f

(3,1) is mapped to 3 by f

(4,2) is mapped to 1 by f

(5,3) is mapped to 2 by f

Now we apply g to the result of f.

3 is mapped to (1,2) by g

5 is mapped to (2,1) by g

1 is mapped to (4,2) by g

2 is mapped to (5,3) by g

Therefore, g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}.

Note that the composition functions f ∘ g and g ∘ f are not the same. In general, composition of functions is not commutative, i.e., f ∘ g is not equal to g ∘ f.

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As the tree is 4/5 meters tall the unit rate in meters per year is 8/45 or approximately 0.177 meters per year.

To find the unit rate in meters per year, we need to divide the height of the tree by the time it took to grow.

Height of the tree = 4/5 meters

Time taken to grow = 4 1/2 years = 9/2 years

Unit rate = Height/Time = (4/5)/(9/2) meters per year

To divide by a fraction, we can multiply by its reciprocal:

Unit rate = (4/5) * (2/9) meters per year

Unit rate = 8/45 meters per year

Therefore, the unit rate of the tree in meters per year is 8/45 or approximately 0.177 meters per year.

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Answer: You will pay £1,912.54 each month.

Step-by-step explanation:

We can use the formula for the monthly payment of a loan with compound interest:

monthly payment = (principal * monthly interest rate) / (1 - (1 + monthly interest rate)^(-n))

where principal is the amount borrowed, monthly interest rate is the annual interest rate divided by 12, and n is the total number of monthly payments.

In this case, the principal is £64,950, the annual interest rate is 4%, so the monthly interest rate is 4%/12 = 0.00333, and the number of monthly payments is 36.

Plugging in these values, we get:

monthly payment = (64950 * 0.00333) / (1 - (1 + 0.00333)^(-36)) = £1,912.54

Therefore, you will pay £1,912.54 each month.