14. C=226.08 in
r_ and d≈
1'

Answer:

x > 9 cm

Explanation:

Let the length of the base = x cm

One side of a triangle is 2 cm shorter than the base.

Length = (x-2)cm

The other side is 4 cm than the base, therefore:

Length of the other side = (x+4)cm

Perimeter = x+(x-2)+(x+4)

If the perimeter is greater than 29, then:

x+(x-2)+(x+4)>29

3x-2+4>29

3x+2>29

3x>29-2

3x>27

x>27/3

x>9

The length of the base greater than 9cm will allow the perimeter to be more than 29 cm.

Answer:

The line is super close to 15 or 20. So one of those for sure

Step-by-step explanation:

Answer: its got to be 15 because the line isn't on 20

Step-by-step explanation:

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

1/3 is the fraction form of 33.3% or 0.333

Answer:

(1/6) of the students did not pass.

Ans: (1/6)30 = 5 of the students did not pass

To solve this question, we need to first figure out, in fractional form, the number of students who did not pass. The problem tells us that 5/6 of the students passed. Therefore, we know that 1/6 of the students did not pass, because 5/6 + 1/6 = 1. So, all we need to do is multiply 1/6 by the total number of students:

1/6 * 36 = 6

So, 6 students did not pass.

It is 130 beats per minute.

Step-by-step explanation:

Just divide 1560 by 12.

Answer:

x = 58.03°

Step-by-step explanation:

Given:

Solve for x:

1. \(x=cos^{-1}(\frac{9}{17})=58.03\)

Answer:

So, the measure of angle x is equal to 58.03.

Answer:

1) -0.016 pounds per square inch per cubic inch.

2) \(\displaystyle V'(P)=-\frac{800}{P^2}\)

Step-by-step explanation:

We are given the equation \(PV=800\).

Part A)

We want to determine the average rate of change of P as V increases from 200 cubic inches to 250 cubic inches.

To find the average rate of change between two points, we find the slope between them.

Rewrite the given equation as a function of V:

\(\displaystyle P(V)=\frac{800}{V}\)

Hence, the average rate of change for V = 200 and V = 250 is:

\(\displaystyle \begin{aligned} m &= \frac{P(250) - P(200)}{250 - 200} \\ \\ & = \frac{3.2 - 4}{250 - 200} \\ \\ & = -0.016\end{aligned}\)

Therefore, the average rate of change is -0.016 pounds per square inch per cubic inch.

Part B)

We want to express V as a function of P. This can be done through simple division:

\(\displaystyle V(P)=\frac{800}{P}\)

We want to show that the instantaneous change of V with respect to P is inversely proportional to the square of P. So, let's take the derivative of both sides with respect to P:  

\(\displaystyle \frac{d}{dP}\left[V(P)\right]=\frac{d}{dP}\left[\frac{800}{P}\right]\)

Differentiate. Note that 1/P is equivalent to P⁻¹. This allows for a simple Power Rule:

\(\displaystyle \begin{aligned} V'(P) & = 800\frac{d}{dP}\left[ P^{-1}\right] \\ \\ & = -800(P^{-2}) \\ \\ & = -\frac{800}{P^2}\end{aligned}\)

Therefore, the instantaneous change of V is indeed inversely proportional to the square of P.

\(\sf \dashrightarrow t = 6r^2 + 12t\)

\(\sf \dashrightarrow -6r^2 = 12t-t\)

\(\sf \dashrightarrow -6r^2 = 11t\)

\(\sf \dashrightarrow 6r^2 = -11t\)

\(\sf \dashrightarrow r^2 = -\dfrac{11t}{6}\)

\(\sf \dashrightarrow r = \pm \sqrt{-\dfrac{11t}{6} }\)

\(\dashrightarrow \sf r=\pm i\sqrt{\dfrac{11t}{6}}\)

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:

8( b - 4 )

Step-by-step explanation:

8 x ( b - 4 )

8( b - 4 )

I hope this helps!

The Probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

To find the probability that a randomly selected senior is both in the band and on the honor roll, we need to divide the number of seniors who are in both categories by the total number of seniors.

Given:

Total number of seniors = 200

Number of seniors in the band = 32

Number of seniors in the band or on the honor roll = 64

Let's calculate the probability using these values:

Probability = Number of seniors in both categories / Total number of seniors

Probability = 64 / 200

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:

Probability = (64 ÷ 8) / (200 ÷ 8)

Probability = 8 / 25

Therefore, the probability that a randomly selected senior is both in the band and on the honor roll is 8/25.

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The total amount Derek repaid after 5 years of quarterly payments at 10% per annum is $12,829.40.

The quarterly payments represent periodic payments made every three months to offset the credit.

The periodic payments can be computed using an online finance calculator.

Where the periodic payment is given, the total payment made can be determined as the product of the periodic payments and the number of periods involved.

N (# of periods) = 20 quarters (5 years x 4)

I/Y (Interest per year) = 10%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $-641.47

Results:

FV = $-0.03

Sum of all periodic payments = $-12,829.40

Total Interest = $2,829.43

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Derek borrowed $10,000 at 10% per annum compounded quarterly and repays $641.47 quarterly.  How much money did he repay after 5 years?

The equivalent expression to 0.2(3x-4) is 0.6x - 0.8.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Expression: 0.2(3x-4)

Now, using the distributive property we have

= 0.2(3x-4)

= 0.2(3x)- 0.2(4)

= 0.6x - 0.8

Hence, the equivalent expression is 0.6x - 0.8.

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Answer:

I think its 6.25  (6 and 1/4) but I'm not a teacher or anything so it may be incorrect.

Answer:

x-10

Step-by-step explanation:

ten is less than x

follow me for more answer

The completion of the following table under different depreciation methods is as follows:

Method                           Year 1                     Year 2

Straight line                   $18,000                 $18,000

Units of production      $54,000                 $13,500

Declining balance        $37,600                $22,560

MACRS (5-year class)   $18,800                $30,080

Cost of machine = $94,000

Residual value = $4,000

Depreciable value = $90,000 ($94,000 - $4,000)

Estimated useful life = 5 years

Depreciation expense:

Straight-line method = $18,000 ($90,000/5)

Estimated units of produciton = 100,000

Unit depreciation rate = $0.90

Actual production   Depreciation

Year 1 = 60,000      $54,000 ($0.90 x 60,000)

Year 2 = 15,000      $13,500 ($0.90 x 15,000)

Declining Balance:

Year 1 = $37,600 ($94,000 x 40%)

Year 2 = $22,560 ($94,000 - $37,600) x 40%

MACRS:

Year 1 = $18,800 ($94,000 x 20%)

Year 2 = $30,080 ($94,000 x 32%)

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Answer:

19.4 g (rounded to the nearest tenth)

Step-by-step explanation:

Convert the percentage to a decimal by dividing by 100:

29% = 29/100 = 0.29

To find 29% of 67, multiply the decimal percentage by the total amount:

0.29 x 67 = 19.43

= 19.4 g (rounded to the nearest tenth)

Answer:

60

Step-by-step explanation:

To begin, we can look at combinations and permutations. A permutation or combination is when we need to find how many possibilities there are to choose a certain amount of objects (in this case, candidates) given an array of options (members on the board)

Combinations are when the order doesn't matter, and permutations are when the order does matter. Here, we know that we care whether someone is chairperson or secretary. If we were to just choose three for an "elite" board, and there were no specific positions in the board, then order would not matter. However, because it does matter which person gets which role, order does matter.

Assuming that someone cannot have more than one role, we know that this is a permutation without repetition. The formula for this is

(n!) / (n-r)!, where we have to choose from n number of people and choose r number of people. We have 5 members to choose from, and 3 people to choose, making our equation

(5!) / (5-3)! = 120 / 2! = 120/2 = 60

Answer:

For the equation 75x+30y=1500,  x is (100 - 2y) / 5 and y is (100 - 5x) / 2.

An equation is a mathematical statement that uses symbols and numbers to express a relationship between two or more variables. It states that two expressions are equal to each other.

We can solve for x and y in the equation 75x + 30y = 1500 by using algebraic manipulation.

First, we can simplify the equation by dividing both sides by the greatest common factor of 75 and 30, which is 15:

(75x + 30y) / 15 = 1500 / 15

Simplifying the left side gives:

5x + 2y = 100

Next, we can isolate one of the variables. Let's isolate y by subtracting 5x from both sides:

5x + 2y - 5x = 100 - 5x

Simplifying the left side gives:

2y = 100 - 5x

by dividing both sides by 2:

y = (100 - 5x) / 2

This is the equation for y in terms of x. We can use this equation to solve for y given a value of x, or we can substitute it back into the original equation to solve for x in terms of y.

Let's solve for x in terms of y by isolating x in the equation 5x + 2y = 100:

5x = 100 - 2y

Dividing both sides by 5 gives:

x = (100 - 2y) / 5

This is the equation for x in terms of y. We can use this equation to solve for x given a value of y, or we can substitute it back into the original equation to solve for y in terms of x.

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The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.

The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?

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Applying the necessary circle theorem, the measures of the missing angles are: 12. m<KJL = 115 degrees.         14. 76 degrees.

12. The circle theorem to apply is the angle of intersecting chords theorem, which states that:

m<KJL = 1/2(measure of arc KL + measure of arc MT)

Plug in the values:

m<KJL = 1/2(160 + 70)

m<KJL = 115 degrees.

14. The circle theorem to apply is the tangent theorem:

this means that the tangents form right angles with the radii of the circle, therefore:

Measure of the indicated angle = 360 - 90 - 90 - 104 = 76 degrees.

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Answer:

The weight of an object is the force of gravity exerted on that object. The mass of an object is the amount of matter it has, and it stays the same wherever you are, regardless of gravity.[1] That's why an object that has 20 kilograms of mass on earth also has 20 kilograms of mass while on the moon, even though it would only weigh 1/6 as much. It weighs 1/6 as much on the moon because the force of gravity on the moon is 1/6 of what it is on Earth.

Step-by-step explanation:

Answer:

your mother

Step-by-step explanation:

The logical answer would be your mother because 9.8m/s^2 x 55 would equal your mother weight,  539 squared pounds.

Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.

Answer:

1/12

Step-by-step explanation:

Answer:

1/12

Just multiple 1×1 and 3×4

1. The initial population size will be 2,996.

2. The function represent the exponential growth.

3. The change in percent of the population size in each hour will be 7%.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The population size P (t) after t hours is given by the exponential function,

⇒ \(P (t) = 2800 (1.07)^t\)

Now,

Since, The population size P (t) after t hours is given by the exponential function,

⇒ \(P (t) = 2800 (1.07)^t\)

Hence, The initial population size = 2800 x (1.07)¹

                                                      = 2,996

And, Here the number 1.07 > 1.

So, The function represent the exponential growth.

Here, e population size P (t) after t hours is given by the exponential function,

⇒ \(P (t) = 2800 (1.07)^t\)

And, The initial population size = 2,996

And, Put t = 2,

⇒ P (t) = 2800 × 1.07²

          = 3,205.72

So, The change in percent of the population size in each hour will be;

= (3205.7 -  2,996) / 2996 x 100

= 7%

Thus, The change in percent of the population size in each hour will be 7%.

Therefore,

1. The initial population size will be 2996.

2. The function represent the exponential growth.

3. The change in percent of the population size in each hour will be 7%.

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The probability that a randomly selected product will last longer than 166 days is approximately 0.1492, οr 14.92%.

The probability οf an event οccurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn οut.

We can use the standard normal distribution to answer this question.

z = (x - μ) / σ

For x = 166, μ = 146, and σ = 19.5, we have:

z = (166 - 146) / 19.5

z = 1.03

Using a standard normal distribution table, we can find that the area to the right οf z = 1.03 is approximately 0.1492.

Therefore, the probability that a randomly selected product will last longer than 166 days is approximately 0.1492, οr 14.92%.

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Use the combination formula.

5 C2 = 5!/5!3! = 10

The answer is 10

Answer:

10

Step-by-step explanation: