There are only 2.1 x 10^8 metric tonnes of usable fossil fuels existing on Earth.

Assuming an estimated rate of fossil fuel use of 1 x 10^5 metric tonnes per year, calculate an order of magnitude estimation of the time left before the fossil fuel reserves run out.

Give your answer to one significant figure.

The answer is 2000 but I cannot figure out how they got it.

Answer:

Yes. There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

Step-by-step explanation:

We want to test the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

To perform this test we have a sample of 500 students which have paid their balance in full each month. The sample mean is $825 and the estimated sample deviation is considered $200.

Then, the null and alternative hypothesis are:

\(H_0: \mu=905\\\\H_a:\mu< 905\)

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=825.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{200}{\sqrt{500}}=8.94\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{825-905}{8.94}=\dfrac{-80}{8.94}=-8.94\)

The degrees of freedom for this sample size are:

\(df=n-1=500-1=499\)

This test is a left-tailed test, with 499 degrees of freedom and t=-8.94, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t<-8.94)=0\)

As the P-value (0) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

Answer:

675 devided bye 9 = 75

Step-by-step explanation:

Answer: 75 words per minute

Step-by-step explanation:

We can set this problem up similar to a ratio
675:9
Knowing that this is for 9 minutes, dividing by 9 will give you the amount per one minute
675/9   9/9
75:1 or 75 words per minute

Answer:

1. 38.95= 3 p+11.98

2. 38.95-11.98=3p

3. 26.97/3.=p

4. $8.99= p

Step-by-step explanation:

done

Answer:

The inequality is 25+8.50w≥122

The size of a matrix is typically described using the number of rows and columns, such as a 3x4 matrix, where there are 3 rows and 4 columns.

Matrices are commonly used in mathematics, engineering, physics, and computer science to represent data, perform calculations, and solve problems. The size of a matrix is an important factor in determining its properties and the operations that can be performed on it.

For instance, if T refers to a transformation matrix used in computer graphics, it could be a 4x4 matrix that describes the translation, rotation, and scaling of a 3D object in space. If T refers to a transition matrix used in Markov chains, it could be a square matrix with dimensions equal to the number of states in the chain.

In summary, the size of a matrix T depends on the context in which it is used, and without additional information, it is not possible to determine its dimensions or properties.

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James owns on owns only 5 percent of the business capital.

We should know that percentage deals with number of ratios as a fraction of 100

James = $10,000

One partner = $10,000

Other two partners = ($90,000+90,000)=$180,000

Total capital invested = $)10000+10000+90000+90000)

Total investment = $200,000

James proportion= \(\frac{10,000}{200,000} *\frac{100}{1}\)

Simplifying this to have James percentage of investment as 5 percent

James =5%

In conclusion James has only 5% of the business investment

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Answer:

D. y = 2x - 10

Step-by-step explanation:

y + 4 = 2(x – 3)

y + 4 = 2x - 6

Subtract 4 from both sides

y = 2x - 6 - 4

y = 2x - 10

The correct answer is D. y = 2x - 10

Answer:

HIIHFIIFJF

Step-by-step explanation:

it will be y

Answer: 0.18

Step-by-step explanation:I had a nearpod with the same questions and got this answer it was the correct one

Answer:

x = 1/2.

Step-by-step explanation:

x/x+1 = 1/3

3x = x + 1

2x = 1

x = 1/2.

There are 4 hundred billions in the number 432,845,979,484.

To determine how many hundred billions are in the number 432,845,979,484, we need to consider the place value of the hundred billions digit.

The number 432,845,979,484 has 12 digits, and we count the digits from right to left, starting with the units place. The digit in the hundred billions place is the seventh digit from the right.

Let's break down the number:

4 hundred billions (4 x 100,000,000,000)

3 ten billions (3 x 10,000,000,000)

2 billions (2 x 1,000,000,000)

8 hundred millions (8 x 100,000,000)

4 ten millions (4 x 10,000,000)

5 millions (5 x 1,000,000)

9 hundred thousands (9 x 100,000)

7 ten thousands (7 x 10,000)

9 thousands (9 x 1,000)

4 hundreds (4 x 100)

8 tens (8 x 10)

4 units (4 x 1)

As we can see, there are 4 hundred billions in the number 432,845,979,484.

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Answer:

True,

Step-by-step explanation:

In math we prove the theorem using known axioms in Math.

Answer: True

Step-by-step explanation:

Answer:

80 degrees

Step-by-step explanation:

Sum of the interior angles of a triangle = 180

a + 50 + 50 = 180

a = 80

The possible exact values of the trigonometric functions of θ are:

sin θ = -1/√3,  cos θ = √3/3, sec θ = √3

The law of sines, also known as the sine rule, is a mathematical principle that relates the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle.

Trigonometric functions are mathematical functions that relate angles to the ratios of the sides of a right triangle. The six primary trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Each function represents a different ratio of two sides of a right triangle and can be used to solve problems in geometry, physics, engineering, and other fields that involve angles and triangles.

According to the given information,

Given that tan θ = -√(1/3) and 0 < θ < 180°, we can use the trigonometric identities to find the values of the other trigonometric functions of θ.

First, we can use the definition of the tangent function:

tan θ = opposite/adjacent

Since tan θ = -√(1/3), we can assign opposite = -1 and adjacent = √3 as their ratio equals -√(1/3). This means that the terminal side of the angle θ will lie in the fourth quadrant of the unit circle since the opposite is negative and the adjacent is positive.

Next, we can use the Pythagorean identity:

sin²θ + cos²θ = 1

to find the value of sin θ. Since we know that θ is in the fourth quadrant, we can assign sin θ = -1/√3, since sin θ is negative in the fourth quadrant and the ratio of opposite/hypotenuse of a 30-60-90 triangle is √3/2, which means the ratio of hypotenuse/opposite is 2/√3 = √3/3.

Then, we can use the definition of the cosine function:

cos θ = adjacent/hypotenuse

to find the value of cos θ. We know that adjacent = √3 and the hypotenuse is positive (since it is a length), so we can assign cos θ = √3/3.

Finally, we can use the reciprocal identity:

sec θ = 1/cos θ

to find the value of sec θ. We know that cos θ = √3/3, so we can assign sec θ = √3.

Therefore, the possible exact values of the trigonometric functions of θ are:

sin θ = -1/√3

cos θ = √3/3

tan θ = -√(1/3)

sec θ = √3

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Draw a figure representing that situation:

Since the angle A and the angle of 68° are supplementary angles, then:

Substract 68 from both sides of the equation to find A:

Since the sum of the interior angles of a triangle is always 180, then:

Substitute for A=112:

Substract 112 from both sides of the equation:

Divide both sides of the equation by 2:

Therefore, the measure of both remote angles is 34°.

(Both have the same measure, since it is an isosceles triangle).

The circumference of the pool is 26.38 meters

The radius, r is given as:

r = 4.2

The circumference, C is calculated using:

\(C =2\pi r\)

This gives

C =2 * 3.14 * 4.2

Evaluate

C = 26.38

Hence, the circumference of the pool is 26.38 meters

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Answer:

1 +1 = 2

Step-by-step explanation:

Answer:

x<4

Step-by-step explanation:

3x<12

x<12/3

x<4

I hope this helps

Answer:x<4

Step-by-step explanation:

3x/3 < 12/3

a. T(n) = O(n^4) and Ω(n^4): For the upper bound, we can use the substitution method to prove that T(n) is O(n^4). Let S(n) = cn^4, where c is a constant. We can then substitute S(n) into the recurrence to prove that T(n) is O(n^4):

T(n) = 2T(n/2) + n^4 <= 2S(n/2) + n^4 <= 2cn^4/2 + n^4 <= cn^4 + n^4 = (c + 1)n^4

Since (c + 1) is a constant, this expression is equal to O(n^4).

For the lower bound, we can use the recurrence tree method to prove that T(n) is Ω(n^4). Let k be the number of levels in the tree. We can then calculate the total cost of the tree:

Total Cost = 2^k * n^4 = n^4 * (2^k/n^4) = n^4 * (2/n)^k

Since 2/n is a constant and k is a function of n, this expression is equal to Ω(n^4).

b. For the upper bound, we can use the substitution method to prove that T(n) is O(n log n). Let S(n) = cn log n, where c is a constant. We can then substitute S(n) into the recurrence to prove that T(n) is O(n log n):

T(n) = T(7n/10) + n <= S(7n/10) + n <= c(7n/10) log (7n/10) + n = c(7/10)n log n + n = (c(7/10) + 1)n log n

Since (c(7/10) + 1) is a constant, this expression is equal to O(n log n).

For the lower bound, we can use the recurrence tree method to prove that T(n) is Ω(n). Let k be the number of levels in the tree. We can then calculate the total cost of the tree:

Total Cost = 7^k * n = n * (7^k/n) = n * (7/n)^k

Since 7/n is a constant and k is a function of n, this expression is equal to Ω(n).

c. For the upper bound, we can use the substitution method to prove that T(n) is O(n^2). Let S(n) = cn^2, where c is a constant. We can then substitute S(n) into the recurrence to prove that T(n) is O(n^2):

T(n) = 16T(n/4) + n^2 <= 16S(n/4) + n^2 <= 16cn^2/4 + n^2 <= 4cn^2 + n^2 = (4c + 1)n^2

Since (4c + 1) is a constant, this expression is equal to O(n^2).

For the lower bound, we can use the recurrence tree method to prove that T(n) is Ω(n^2). Let k be the number of levels in the tree. We can then calculate the total cost of the tree:

Total Cost = 16^k * n^2 = n^2 * (16^k/n^2) = n^2 * (16/n^2)^k

Since 16/n^2 is a constant and k is a function of n, this expression is equal to Ω(n^2).

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Answer:

I think it would be 2/6 or 33.33%

Answer:

with the X you now know you will have to multiply then you need to figure out what the other side of the = sign is with X and you should get your answer!

Step-by-step explanation:

That's all I know Sorry

Answer:

372

Step-by-step explanation:

We know that a ratio of 3 : 2 has 5 people, so figuring out how many times that ratio goes into our total number helps us find the value of the total number of adults.

930 / 5 = 186

This means that there are 186 groups of 3 children to 2 adults

So, in each of the 186 groups, there are 2 adults.

Therefore, we can multiply (186)(2)

to find the total number of adults: 372

The number of the children and adult will be 558 and 372.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

At a swimming pool, the ratio of children to adults was 3 : 2.

C / A = 3 / 2

Then solve the equation for C, then the equation will be

C = (3/2)A

The total number of the people is 930. Then the equation will be

C + A = 930

Substitute the value of C in the above equation. Then the equation will be

(3/2)A + A = 930

     (5/2)A = 930

            A = 930 x (2/5)

            A = 372

The number of the adult will be 372.

Then the number of the children will be

C + 372 = 930

         C = 930 – 372

         C = 558

The number of the children will be 558.

Thus, the number of the children and adult will be 558 and 372.

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Answer:

5.4, -5, -9/10

Step-by-step explanation:

Answer:

1711

Step-by-step explanation:

\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)

Make sure to follow order of operations!

Answer:

It will take Jerome 1 1/2 (one and a half) minutes to write a full page.

Step-by-step explanation:

Answer:

1 1/2

Step-by-step explanation:

1/2 x 3=1 1/2

The quadrant in which the point (-11, -22) lies is the third (3rd) quadrant.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate in a graph.

This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:

Generally speaking, the coordinates of the third (3rd) quadrant are all negative, which simply means that both the x-values and y-values are negative e.g (-11, -22).

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Keep in mind that without the population standard deviation, it is impossible to provide an exact sample size. However, this formula will give you a good starting point.

To find the sample size needed for a 99.5% confidence interval with a margin of error of 1.5, we can use the formula:

n = (Z * σ / E)^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the margin of error.

For a 99.5% confidence interval, the Z-score is approximately 2.807 (from a standard normal distribution table). Since we do not have the population standard deviation (σ), we will need to estimate it using a sample standard deviation or use a conservative approach by assuming the maximum possible value. For now, let's assume we have an estimated standard deviation.

n = (2.807 * σ / 1.5)^2

Solve for n by plugging in the estimated standard deviation (σ) and then round up to the nearest whole number, as you cannot have a fraction of a sample.
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Answer: A: 31

Step-by-step explanation:

2m+9p-11
(plug in m=3, p=4)
2(3)+ 9(4)-11
6+36-11

42-11

31