The rate of consumption of oil in the United States during the 1980s (in billions of barrels per year) is modeled by the function C(t) = 27.08e', where t is the number of years after January 1, 1980. Find the total consumption of oil in the United States from January 1, 1980 to January 1, 1990.

Answer:

ok

Step-by-step explanation:

Answer:

ok is that it I will try to join

You will need a graduated scale and you measure.. it will be something like x ≈ 5.2 or 5.3 approximately

You can see in the picture below what you need to find. It is the red point in the picture

Good luck

Answer:

-5x+(- 15 ) = 20

x=-7

Step by Step

-5x+(-15)= 20 becomes

-5-15=20 add 15 tp (15 and 20)

-5x=35 ( divide by 51

x=-7

Answer:

5+1=6,2+3=5 6times 5is equal 30

Answer:

7+17i

Step-by-step explanation:

(5+i)(2+3i)

Multiply complex numbers 5+i and 2+3i like you multiply binomials.

By definition, \(i^{2}\) is -1.

5×2+5×(3i)+2i+3(−1)

Do the multiplications.

10+15i+2i−3

Combine the real and imaginary parts.

10−3+(15+2)i

Do the additions.

7+17i

Comparing a census of a large population to a sample drawn from it, we expect that the sample is usually a more practical method of obtaining the desired information.

This is because a census involves collecting data from every individual in the population, which can be time-consuming, expensive, and logistically challenging, especially for large populations. In contrast, a sample is a smaller, more manageable subset of the population, making it easier to gather and analyze data.

However, it's essential to note that the accuracy of the observations in the census is generally higher than in the sample, as the census covers the entire population, eliminating any sampling error. In comparison, a sample may be subject to various biases or inaccuracies, depending on the sampling technique used and the sample size.

To ensure that the sample accurately represents the population, it is crucial to select a sample that is both random and of an appropriate size. While the sample doesn't need to be a large fraction of the population, it should be sufficiently large to provide reliable estimates and minimize sampling error. Overall, sampling is a practical and efficient approach to obtaining information about a population when properly conducted, balancing the need for accuracy with resource constraints.

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To use the chain rule and find the derivative of the given expression, we need the functions g(u) = sin(u) and h(x) = 4x^2 + 3x.

To use the chain rule, we need to identify two functions within the given expression, one serving as the outer function and the other as the inner function.

Let's rewrite the expression in the required form:

f(x) = g(h(x))

In this case, we can choose the functions as follows:

g(u) = sin(u)

h(x) = 4x^2 + 3x

Now, we can rewrite the original expression using these functions:

f(x) = g(h(x)) = sin(4x^2 + 3x)

Here, g(u) represents the outer function, which is the sine function, and h(x) represents the inner function, which is the polynomial 4x^2 + 3x.

By using the chain rule, we can differentiate the composite function f(x) by taking the derivative of the outer function with respect to the inner function multiplied by the derivative of the inner function with respect to x:

f'(x) = g'(h(x)) * h'(x)

In this case, g'(u) represents the derivative of the sine function, which is cos(u), and h'(x) represents the derivative of the polynomial 4x^2 + 3x.

Therefore, to use the chain rule and find the derivative of the given expression, we need the functions g(u) = sin(u) and h(x) = 4x^2 + 3x.

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answer

624/10000 or 39/625

Answer:

The answer is 1

:D

Step-by-step explanation:

1/4 ÷ 1/4 =  1/4 ÷ 4/1 (flip the recipocal) = 1

The width of rectangle is 5 feet.

Let us assume the length of rectangle to be x. So, the width of rectangle will be (x - 3).

Now, as per the known fact, perimeter, length and width of rectangle are related by the formula -

Perimeter = 2 × (length + width)

Keep the values in formula to find the value of width

26 = 2 × (x + x - 3)

Performing addition of variables inside the bracket

26 = 2 × (2x - 3)

Shifting 2 to other side of equation to find the value of x

2x - 3 = \(\frac{26}{2}\)

Performing division to find the value of x

2x - 3 = 13

Shifting 3 to other side of equation to find the value of x

2x = 13 + 3

Performing addition to find the value of x

2x = 16

Shifting 2 as denominator to other side of equation to find the value of x

x = \(\frac{16}{2}\)

Performing division to find the value of x

x = 8

So, length of rectangle is 8 feet

Width of rectangle = x - 3

Width of rectangle = 8 - 3

Width of rectangle = 5 feet

Hence, the width of rectangle is 5 feet.

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The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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Answer:

The 9th term is 1/64.

I hope it is correct ✌️

The mathematical procedure for decomposing a complex waveform into simpler waveforms is known as Fourier analysis. It allows for the identification of the individual frequency components that contribute to the overall pattern.

Fourier analysis, named after the French mathematician Jean-Baptiste Joseph Fourier, is a fundamental technique used in many fields, including signal processing, physics, and engineering. It is based on the concept that any complex waveform can be represented as a combination of simpler sinusoidal waveforms. These simpler waveforms are characterized by their frequency, amplitude, and phase.

The procedure involves decomposing a complex waveform into its constituent frequencies by applying the Fourier transform. The Fourier transform converts the waveform from the time domain to the frequency domain, revealing the underlying frequency components. By analyzing the resulting spectrum, which shows the amplitude and phase of each frequency component, one can determine the simpler waveforms that make up the original complex pattern.

Fourier analysis has numerous applications, such as analyzing sound waves, image processing, and data compression. It enables us to better understand and manipulate complex signals by breaking them down into their fundamental building blocks.

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The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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Answer:

I believe the answer is 52,080 numbers.

Step-by-step explanation:

Don't be mad if i'm wrong.

The answer is:

Work/explanation:

Let's find something that 48 and 60 have in common.

In other words, we find their GCF (greatest common factor).

The GCF of 48 and 60 is 12.

So I factor it out :

12(4 + 5)

which is A.

The correct answer is (b) divide the sum of the cross-products of Z scores by the sample size.

When calculating the correlation coefficient, also known as Pearson's correlation coefficient, the last step involves dividing the sum of the cross-products of Z scores by the sample size. The correlation coefficient measures the strength and direction of the linear relationship between two variables.

To calculate the correlation coefficient, we follow these steps:

Standardize the variables: Convert the raw scores of each variable into Z-scores. The Z-score represents the number of standard deviations a particular score is from the mean. This step is done to put both variables on the same scale and make them comparable.

Calculate the cross-products: Multiply the Z-scores of the corresponding pairs of observations. This step gives us the cross-products of Z-scores for each pair of observations.

Sum the cross-products: Add up all the cross-products of Z-scores.

Divide by the sample size: Divide the sum of the cross-products of Z-scores by the sample size. The sample size represents the number of paired observations used in the analysis.

By dividing the sum of the cross-products by the sample size, we obtain the covariance of the variables. The covariance measures the extent to which the variables vary together. However, the covariance itself is not sufficient to determine the strength and direction of the relationship.

The final step involves dividing the covariance by the product of the standard deviations of the variables. This step normalizes the covariance and results in the correlation coefficient, which is a value between -1 and 1. The correlation coefficient indicates the strength and direction of the linear relationship between the variables. A positive correlation coefficient indicates a positive linear relationship, a negative correlation coefficient indicates a negative linear relationship, and a correlation coefficient close to zero indicates a weak or no linear relationship.

Therefore, the last step in calculating the correlation coefficient is to divide the sum of the cross-products of Z-scores by the sample size.

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Answer:  x=16

Step-by-step explanation:

28= 8x + 12-7x

28= 8x-7x +12

28= x + 12

-12       -12

16= x

An equation of a line can be written by using the standard form of the equation of line y = mx + b,

What is the equation of a line?

The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis.

An equation of a line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of a line that is perpendicular to another line, you will need to find the negative reciprocal of the slope of the original line.

For example, suppose you have a line with the equation y = 3x + 2.

The slope of this line is 3, so the slope of a line that is perpendicular to it would be the negative reciprocal of 3, which is -1/3.

The equation of the perpendicular line would be y = -1/3x + b, where b is the y-intercept.

To find the y-intercept of the perpendicular line, you can plug in the coordinates of a point on the original line into the equation of the perpendicular line.

For example, if you know that the original line passes through the point (4, 14), you can substitute these values into the equation y = -1/3x + b to find the value of b.

This gives you the equation -1/3x + b = 14, so b = 14 + 1/3x.

Substituting x = 4 gives you b = 14 + 1/3(4) = 14 + 4/3 = 18/3, so the equation of the perpendicular line is y = -1/3x + 18/3.

Hence, An equation of a line can be written by using the standard form of the equation of line y = mx + b,

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Given:

Polynomial = P(x) = 3x² + kx + 6

Factor of the ablove polynomial = (x+3)

To Find:

Value of K, for which (x+3) become the factor of P(x) = 3x² + kx + 6

Solution :

Now,

x + 3 = 0

⇒x = (-3)

So,

As (x+3) is a factor so x = (-3) is one root of the polynomial.

Therefore,

P(-3) = 0

→ P(-3) = 3(-3)² + k(-3) + 6 = 0

→ 3(9) - 3k + 6 = 0

→ 27 - 3k + 6 = 0

→ 27 + 6 - 3k = 0

→ 33 - 3k = 0

→ - 3k = -33

→ k = -33 ÷ -3

→ k = 11

3x²+ kx + 6, by putting the value of k = 11 and taking -3 as root the remainder should be zero

→ 3x²+ 11x + 6

→ 3(-3)² + 11(-3) + 6

→ 3(9) - 33 + 6

→ 27 - 33 + 6

→ 27 + 6 - 33

→ 33 - 33

→ 0

Hence verified !

Answer:

10 dollars

Step-by-step explanation:

Answer:

i don no

Step-by-step explanation:

The correct measure of center for the data-set of the bands who have played at a single music venue over the past five years is given by:

Mode.

The three measures of center are listed and explained as follows:

The cases in which each of them are used are given as follows:

The variable in this problem is given as follows:

Bands.

Which is a qualitative variable, as it assumes names, and hence the mode is the measure of center that should be used.

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The amount of Type A coffee that was used is 40 pounds.

From the given information;

Type A coffee costs Miguel $5.95 per pound

Type B coffee costs $4.65 per pound.

For this month, the equation can be expressed as:

A + 3A

Thus;

5.95A + 3(4.65)A = 796.00

5.95A +13.95A = 796.00

19.9A = 796.00

A = 796.00/19.9

A = 40

Therefore, we can conclude that the amount of pounds of type A coffee that was used is 40 pounds.

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Answer: 83 on the dot

Step-by-step explanation:83x4.50=373.50

The value of b in the quadratic function affects the position of the axis of symmetry by determining the position of the vertex of the graph and the direction in which the graph opens.

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Answer:

value of b

Step-by-step explanation:

Answer:

a the answer for angle 1 is also 52

b the answer for angle 3 is 180- 112= 68

Answer:

A) 27

Step-by-step explanation:

\( \frac{16}{16 + 12} = \frac{63 - ?}{63} \)

➡️ \( \frac{4}{7} = \frac{63-? }{63}\)

➡️ \(63 - ? = 36\)

➡️ \(? = 27\)

Answer:

The common factor of all the terms of the polynomial 16x² - 14x is:

2x

Step-by-step explanation:

We are given a polynomial:

16x²-14x

We have to find the common factor of all terms.

First we factorize each term separately and then see the common factor.

16x²=2×2×2×2×x×x

14x=2×7×x

We observe that the common factor is:

2x

Hence,  the common factor of all the terms of the polynomial 16x² - 14x is:

2x

Answer:

2x

Step-by-step explanation:

16 = 2^4

14 = 2 × 7

Common factor of 16 and 14 is 2.

x² = x × x

x = x

Common factor of x² and x is x

The common factor of the two terms is 2x.

Answer:

h(t) = 40,000 - 1,500t

Step-by-step explanation:

Let h(t) be the height of the airplane after t minutes.

h(t) = 40,000 - 1,500t