What is the surface area? how did you find it(filled-in formula)?​

Answer:

9.09

Step-by-step explanation:

Pythagorean Theorem: a² + b²  =  c²

When looking at the triangle we see that we have the hypotenuse and the opposite side.

a = opposite

b = adjacent

c = hypotenuse (always)

So if we plug those numbers into the equation we can get the missing side length

1) a² + b²  =  c²

2) 9.7² + b² = 13.3²

3) b² = 13.3² - 9.7²

4) b² = 176.89 - 94.09

5) b = \(\sqrt{176.89 - 94.09}\)

6) b = 9.093954036

Now we round to nearest hundredth

To find the nearest hundredth we have to look at the thousandth place in the thousandth place we have 3 (9.093) that rounds down so,

b = 9.09

Answer:

4000

Step-by-step explanation:

V=4/3(3)(10)^3

V= 4/3 (3)(1000)

V=4/3 (3000)

V=4000

Answer:

\(x + 2y= 2\)

Step-by-step explanation:

Given

Points:

\(F = (4,9)\)

\(G = (1,3)\)

Required

Determine the equation of line that is perpendicular to the given points and that pass through \((2,0)\)

First, we need to determine the slope, m of FG

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where

\(F = (4,9)\) --- \((x_1,y_1)\)

\(G = (1,3)\) --- \((x_2,y_2)\)

\(m = \frac{3 - 9}{1 - 4}\)

\(m = \frac{- 6}{- 3}\)

\(m =2\)

The question says the line is perpendicular to FG.

Next, we determine the slope (m2) of the perpendicular line using:

\(m_2 = -\frac{1}{m}\)

\(m_2 = -\frac{1}{2}\)

The equation of the line is then calculated as:

\(y - y_1 = m_2(x - x_1)\)

Where

\(m_2 = -\frac{1}{2}\)

\((x_1,y_1) = (2,0)\)

\(y - 0 = -\frac{1}{2}(x - 2)\)

\(y = -\frac{1}{2}(x - 2)\)

\(y = -\frac{1}{2}x + 1\)

Multiply through by 2

\(2y = -x + 2\)

Add x to both sides

\(x + 2y= -x +x+ 2\)

\(x + 2y= 2\)

Hence, the line of the equation is \(x + 2y= 2\)

Answer:

X+2y=2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The pigeonhole principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. We can apply this principle to prove the following statements:

(a) Given any seven integers, there will be two that have a difference divisible by 6.

We can divide the integers into six pigeonholes based on their remainders when divided by 6: {0}, {1}, {2}, {3}, {4}, and {5}. Since there are seven integers, by the pigeonhole principle, at least two integers must belong to the same pigeonhole. If two integers belong to the same pigeonhole, then their difference will be divisible by 6.

(b) Given any five integers, there will be two that have a sum or difference divisible by 7.

We can divide the integers into six pigeonholes based on their remainders when divided by 7: {0}, {1}, {2}, {3}, {4}, {5}, and {6}. Since there are five integers, by the pigeonhole principle, at least two integers must belong to the same pigeonhole. If two integers belong to the same pigeonhole, then their sum or difference will be divisible by 7.

Note that if the two integers have the same remainder when divided by 7, then their difference will be divisible by 7. If they have different remainders, then their sum will be divisible by 7.

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The area of the football pitch is 3076 square meters larger than the area of the rugby pitch. To calculate the area of the football pitch, we can multiply its length by its width:

112 meters × 82 meters = 9184 square meters

To find out how much larger the football pitch is than the rugby pitch, we can subtract the area of the rugby pitch from the area of the football pitch:

9184 square meters - 6108 square meters = 3076 square meters

Therefore, the area of the football pitch is 3076 square meters larger than the area of the rugby pitch.

It's worth noting that rugby pitches can vary in size, but the International Rugby Board (IRB) suggests a minimum length of 100 meters and a maximum length of 144 meters, and a minimum width of 64 meters and a maximum width of 70 meters. On the other hand, football pitches must measure between 100-130 meters in length and 50-100 meters in width.

Both sports require a large, open playing area for athletes to run, pass, and kick the ball, but the dimensions of each pitch are tailored to the specific needs and rules of the sport. Overall, the football pitch is larger than the rugby pitch, which reflects the differences in the two sports' playing styles and strategies.

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a. the horizontal sum of all individual firm supply schedules at this output level. b. output level, each firm will earn zero economic profit (normal profit).

a) In the long-run, each firm will produce 20 units of neckties. The industry supply schedule will be the horizontal sum of all individual firm supply schedules at this output level.

b) The long-run equilibrium price (P*) is $20 per unit, with a total industry output (Q*) of 1,000 units. Each firm will produce 20 units of neckties, and the number of firms in the industry will be 50. At this output level, each firm will earn zero economic profit (normal profit).

c) The short-run average cost curve can be found by dividing the short-run total cost by output. Thus, the short-run average cost curve is SAC = 0.5q - 10 + 200/q. The short-run marginal cost curve is SMC = q - 10. Short-run average cost reaches a minimum at an output level of 20 units.

d) The short-run supply curve for each firm is the portion of the marginal cost curve above the average variable cost curve. The industry short-run supply curve is the horizontal sum of all individual firm supply curves.

e) With the new demand curve, the short-run equilibrium price (P*) is $30 per unit. The total industry output (Q*) is 1,250 units, with each firm producing 25 units of neckties.

f) In the short run, the industry short-run supply curve will shift upwards, resulting in a higher equilibrium price and output level. The new short-run equilibrium price (P*) will be higher than $20 per unit and the new total industry output (Q*) will be higher than 1,000 units.

g) In the long run, new firms will enter the industry, causing the supply curve to shift to the right until price falls back to the minimum long-run average cost of $10 per unit. At the new long-run equilibrium, each firm will produce 20 units of neckties, the industry output (Q*) will increase, and the price (P*) will fall back to $20 per unit.

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The rate of reaction can be calculated by measuring the change in absorbance over time using the Beer-Lambert Law and applying the formula R = ΔA / Δt.

In order to calculate the rate of reaction from absorbance and time, we need to use the Beer-Lambert Law and measure the absorbance of the reaction mixture at different time intervals.

The Beer-Lambert Law states that the absorbance of a substance is directly proportional to its concentration and the path length of the light through the substance. Mathematically, it can be expressed as:

A = εcl

Where:

To calculate the rate of reaction, we need to measure the absorbance of the reaction mixture at different time intervals. Let's say we have absorbance values A1 and A2 at times t1 and t2 respectively.

The change in absorbance (ΔA) can be calculated as:

ΔA = A2 - A1

The change in time (Δt) can be calculated as:

Δt = t2 - t1

The rate of reaction (R) can then be calculated as:

R = ΔA / Δt

This gives us the rate of reaction in units of absorbance per time (e.g., absorbance per minute or absorbance per second).

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The required steps to calculate the rate of reaction from absorbance and time have been explained.

To calculate the rate of reaction from absorbance and time data, follow these steps: Obtain absorbance readings (A) at specific time intervals during the reaction.

Determine the change in absorbance (∆A) by subtracting the initial absorbance from the final absorbance. Determine the change in time (∆t) between the initial and final time points.

Calculate the rate of reaction using the formula:

Rate = ∆A / ∆t

Adjust the rate if necessary by considering the path length (l) of the cuvette and the molar absorptivity (ɛ) of the reacting species, using the Beer-Lambert Law equation, A = ɛcl.

It's important to note that the compact solution still requires the necessary measurements and calculations. However, the key steps are outlined succinctly for your reference.

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a) formula for the mass of the sample that remains after t years is k = -ln(1/2) / 1600

b) the mass after 500 years is \(100 * e^{(-(-ln(1/2) / 1600) * 500)\)

c) t = ln(30/100) / k will the mass be reduced to 30 mg.

What is sample?

In statistics, a sample refers to a subset of individuals, items, or elements selected from a larger population. It is a representative subset of the population that is used to gather information and draw inferences about the entire population.

a) The decay of radium-226 follows an exponential decay model, where the mass remaining after a certain time is given by the formula:

\(m(t) = m(0) * e^{(-kt)\)

where:

m(t) is the mass remaining after time t

m(0) is the initial mass

k is the decay constant

To find the decay constant, we can use the half-life of radium-226, which is approximately 1600 years. The half-life is the time it takes for half of the initial mass to decay.

Using the half-life formula:

\((1/2) = e^{(-k * 1600)\)

Taking the natural logarithm (ln) of both sides:

ln(1/2) = -k * 1600

Solving for k:

k = -ln(1/2) / 1600

Now, we can substitute the value of k into the formula to find the mass remaining after a given time.

b) After 500 years:

\(m(500) = 100 * e^{(-k * 500)\)

Substituting the value of k:

\(m(500) = 100 * e^{(-(-ln(1/2) / 1600) * 500)\)

Calculating the approximate value of m(500) to the nearest milligram will require a calculator or software. Let's denote the result as m_500.

c) To find when the mass is reduced to 30 mg, we can set up the equation:

\(30 = 100 * e^{(-k * t)\)

Solving for t:

\(e^{(-k * t)} = 30 / 100\\\\-e^{(-k * t)} = -ln(30/100)\)

k * t = ln(30/100)

t = ln(30/100) / k

Substituting the value of k and calculating the approximate value of t will give us the time it takes to reach a mass of 30 mg.

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The absolute value inequality that represents the number of hours spent on doing homework is 2 ≤ x ≤ 5

Let us assume that one spends x hours doing homework on a typical weekday. Then we can write

The inequality expression for a slow weekend is given as;

X ≥ 2

In the same vein, the inequality expression for a busy weekend is given as;

X ≤ 5

Pooling the two inequalities expression we have;

2 ≤ x ≤ 5

Two inequality expression could be written simultaneously if they can be expressed individually. They are commonly referred to as a “double” inequality and is often written in the form a ≤ f (x) ≤ b

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The equation of the circle (x + 6)^2 + y^2 = 121 has a radius of 11 and a center located at (-6 , 0).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle, (x + 6)^2 + y^2 = 121, is in standard form, then

h = -6

k = 0

r = 11

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Answer:

5

Explanation:

When we divide A by B, we are calculating how many Bs fit into A. So, if we want to know how many 2/5s fit into 2 yds, we need to divide 2 by 2/5. So:

So, 2 yds of rope can be divide into 5 ropes of 2/5 yd.

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

72

Explanation:

First, we can find the top and bottom smaller squares of the rectangular prism. Since we are working with a variety of rectangles, we only need to use the equation L×W.

To start with, let's multiply 2×3, which gives us 6, the surface area of both the bottom and top rectangles, so now we need to multiply it by 2 to account for both of them. 6×2=12

Now, we'll find the surface area of the bigger rectangles in the middle, which are 6 by 3, so again we will need to multiply length times width, then by 2 to count both rectangles. 6×3=18×2=36

Finally, we can find the surface area of the smaller rectangles in the middle, which are 6 by 2. 6×2=12, then multiply by 2 since there are 2 of those rectangles, 12×2=24

Now to find the total surface area, we need to add the gathered surface area from each shape, 12+36+24=72

Answer:

A = 2 1/2 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

A = 3 * 5/6

A = 5/2 ft^2

A = 2 1/2 ft^2

Answer:

A=2.5 ft^2

Step-by-step explanation:

A=3

A=3(5/6)

A=2.5 ft^2

Answer:

Total surface area of cube = 294 cm²

Step-by-step explanation:

Given:

Perimeter of cube = 84 cm

Find:

Total surface area of cube

Computation:

Perimeter of cube = 12 x side

84 = 12 x side

Side = 7 cm

Total surface area of cube = 6(a)²

Total surface area of cube = 6(7)²

Total surface area of cube = 294 cm²

Answer:

Sophia can drive 3672 miles using 18 gallons of gas.

Step-by-step explanation:

204 x 18 = 3672.

To determine which amounts of postage can be formed using just 4-cent and 11-cent stamps, we need to find all non-negative integer solutions to the equation 4x + 11y = z, where x and y are non-negative integers representing the number of 4-cent and 11-cent stamps used, respectively, and z is the total amount of postage. We can use a combination of trial and error and modular arithmetic to find all possible values of z.

(b) Proof by mathematical induction:

Base case: For z = 0, there are no stamps used, so the equation is satisfied. Thus, 0 can be formed using just 4-cent and 11-cent stamps.

Inductive step: Assume that all integers from 0 to k can be formed using just 4-cent and 11-cent stamps, where k is a non-negative integer. We want to show that k+1 can also be formed.

If k+1 is divisible by 4 or 11, then we can form it using only 4-cent or 11-cent stamps, respectively. Otherwise, we can use the inductive hypothesis to show that k-4 and k-11 can be formed using just 4-cent and 11-cent stamps, respectively. Then we can add one 4-cent or one 11-cent stamp to form k+1.

Therefore, by mathematical induction, all non-negative integers can be formed using just 4-cent and 11-cent stamps.

(c) Proof by strong induction:

Base case: For z = 0, there are no stamps used, so the equation is satisfied. Thus, 0 can be formed using just 4-cent and 11-cent stamps.

Inductive step: Assume that all integers from 0 to k can be formed using just 4-cent and 11-cent stamps, where k is a non-negative integer. We want to show that k+1 can also be formed.

If k+1 is divisible by 4 or 11, then we can form it using only 4-cent or 11-cent stamps, respectively. Otherwise, we can use the inductive hypothesis to show that all integers from k-10 to k-1 can be formed using just 4-cent and 11-cent stamps. Then we can add two 4-cent stamps and one 11-cent stamp to form k+1.

The inductive hypothesis in this proof differs from that in the proof using mathematical induction in that we assume that all integers from k-10 to k-1 can be formed, rather than just k-4 and k-11. This is because we need to show that all integers up to k+1 can be formed, and we may need to use more than one 4-cent or 11-cent stamp to form some of the intermediate values.

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Answer:

60 wpm

Step-by-step explanation:

The 95% confidence interval for the difference in population proportions of students who were consuming protein-rich food in 2000 and 2010 is (-0.111, -0.029).

What is confidence interval?

In statistics a confidence interval, usually refers to the probability that a population parameter may fall between a set of values for a certain proportion of times. The often use confidence intervals that contain either 95% or 99% of expected observations.

For constructing a 95% confidence interval for the difference in population proportions of students who were consuming protein-rich food in 2000 and 2010, can be determined by using the formula:

\(( p_{1} -p_{2} ) + z^{*} \sqrt{\frac{p_{1}(1-p_{1} ) }{n_{1} } +\frac{p_{2}(1-p_{2}) }{n_{2} }\)

and \(( p_{1} -p_{2} ) - z^{*} \sqrt{\frac{p_{1}(1-p_{1} ) }{n_{1} } +\frac{p_{2}(1-p_{2}) }{n_{2} }\)

where:

p₁ and p₂ implies that the sample proportions of students consuming protein-rich food in 2000 and 2010, respectively.

n₁ and n₂ = the sample sizes of the two years.

\(z^{*}\) is the critical value of the standard normal distribution corresponding to a 95% confidence level, which is  equals to 1.96.

Using the given data, we have:

p₁ = 0.75, n₁ = 700

p₂ = 0.82, n₂ = 850

Substituting these values into two formulae, we get:

\(( 0.75 -0.82) + 1.96\sqrt{\frac{0.75(1-0.75 ) }{700 } +\frac{0.82(1-0.82) }{850 }\)

\(( 0.75 -0.82) - 1.96\sqrt{\frac{0.75(1-0.75 ) }{700 } +\frac{0.82(1-0.82) }{850 }\)

Solving the above two expressions, we get:

-0.07 ± 0.041

Hence, rounded to three decimal places, the lower bound is -0.111 and the upper bound is -0.029.

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Answer:

The juice is 1 dollar

2+1= 3

2+2+2+1=7

hoped this helped

Answer:

The juice is worth $2.50

Step-by-step explanation:

7$- 3$ = 4$

1.50 *3 = 4.50

4.5 + 2.50 = 7

The apples are worth a $1.50

I hope this helps you!

Answer:

14 $1 coin

12 quarter coin

Step-by-step explanation:

Let :

x = $1 dollar coin

y = $0.25 (1 quarter) coin

x + y = 26 - - - (1)

1x + 0.25y = 17 - - - - (2)

From (1) :

x = 26 - y

Put x = 26 - y in (2)

1(26 - y) + 0.25y = 17

26 - y + 0.25y = 17

-y + 0.25y = 17 - 26

-0.75y = - 9

Divide both sides by - 0.75

-0.75y /- 0.75 = - 9 / - 0.75

y = 12

Put y = 12 in (1)

x = 26 - 12

x = 14

Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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We have the following coordinates given:

And we want to find US so we can use the following formula:

And using this formula we got:

And after solve we got:

and rounded to the nearest cent would be Us= 27.46

The three congruent triangles in this problem are given as follows:

LPN, MPL and PLN.

When triangles have the same side lengths, they are called congruent.

For a circle, we need to know that:

Hence, for this triangle, we have that:

The three triangles in this problem are given as follows:

LPN, MPL and PLN.

Since each triangle is composed by two segments that represent the radius of the circle and one segment representing the diameter, they have the same side lengths, hence they are congruent triangles.

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Answer:

2(x+7)+3(x+1)

2x+14+3x+3

5x+17

Answer:

Step-by-step explanation

2(x+7)+ 3(x+1)

2x+14+3x+3

5x+17 is the answer

Answer:

about 11.5

Step-by-step explanation: i think this is right

Answer:

11.538%

Step-by-step explanation:

290 - 260 /260  x 100% = 11.538