The rate of change of the gender ratio for the United States during the twentieth century can be modeled as g(t) = (1. 68 · 10^−4)t^2 − 0. 02t − 0. 10


where output is measured in males/100 females per year and t is the number of years since 1900. In 1970, the gender ratio was 94. 8 males per 100 females.



(a) Write a specific antiderivative giving the gender ratio.


G(t) = _______________ males/100 females



(b) How is this specific antiderivative related to an accumulation function of g?


The specific antiderivative in part (a) is the formula for the accumulation function of g passing through (t, g) =

The number of possible ways in which we can select 3 elements from 7 elements are  given in option d. 35.

There are a total of 7 elements and we can to select 3 elements out of them.

We have to apply the permutation and combination here in order to find the answer,

The formula is ⁿCₐ

Where, C represents combination,

n is the total number of combination,

a is the number of selections that we have to do,

ⁿCₐ = n!/(n-a)!a!

Now, putting n = 7 and a = 3,

ⁿCₐ = 7!/(4)!3!

ⁿCₐ = 35

So, the total number of ways possible are 35.

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The relation that is not a function from B to U is option b.

To determine which relation is not a function from B to U, we need to check if each element in B is associated with exactly one element in U. If there is any element in B that is associated with more than one element in U, then it is not a function.

Let's analyze each of the options:

a. {(b, b), (e, c), (d, b), (c, a)} This relation is a function because each element in B is associated with exactly one element in U.

b. {(d, a), (c, e), (e, e), (c, a)} This relation is not a function because the element 'c' in B is associated with both 'e' and 'a' in U. The element 'c' should be associated with exactly one element in U for it to be a function.

c. {(e, a), (b, a), (d, a), (c, b)} This relation is a function because each element in B is associated with exactly one element in U.

d. {(e, e), (b, c), (d, a), (c, b)} This relation is a function because each element in B is associated with exactly one element in U.

Among the given options, option b is the relation that is not a function from B to U.

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The underlined number is a statistic.

In this scenario, the underlined number, 40%, represents the proportion of professors in a sample who own a television. A statistic is a numerical value that describes a characteristic of a sample. In contrast, a parameter is a numerical value that describes a characteristic of an entire population. Since the information provided is based on a sample of professors, the 40% is a statistic.

The distinction between statistics and parameters in statistical analysis. Statistics are used to make inferences about populations based on sample data. Parameters, on the other hand, provide information about the entire population. Understanding this distinction is crucial for accurate data interpretation and drawing meaningful conclusions.

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Answer:

Your correct answer is going to be the third option

Step-by-step explanation:

Answer: Type I error and Type II error are associated with hypothesis testing, where we test a hypothesis by collecting data and analyzing it.

For the given hypothesis, we can set up the null hypothesis as follows:

H0: The percentage of households with Internet access is less than or equal to 60%.

And the alternative hypothesis as:

Ha: The percentage of households with Internet access is greater than 60%.

Now, a Type I error occurs when we reject the null hypothesis (i.e., conclude that the percentage of households with Internet access is greater than 60%) when it is actually true. This means that we would be making a false claim that the percentage of households with Internet access is greater than 60%, when it is not.

On the other hand, a Type II error occurs when we fail to reject the null hypothesis (i.e., conclude that the percentage of households with Internet access is less than or equal to 60%) when it is actually false. This means that we would be missing the truth that the percentage of households with Internet access is greater than 60%.

So, in the context of the given hypothesis, a Type I error would be to conclude that the percentage of households with Internet access is greater than 60% when it is actually less than or equal to 60%, and a Type II error would be to fail to conclude that the percentage of households with Internet access is greater than 60% when it is actually greater than 60%.

(a) The polar curve is a cardioid. (b) The inner loop can be expressed as 1/2 times the integral of (r^2) dθ from θ = -π/6 to θ = π/6. (c) The formula for the length of the outer loop can be expressed as the integral of the square root of (r^2 + (dr/dθ)^2) dθ from θ = -π/3 to θ = π/3.

(a) The given polar equation r = 3 + 6sin(θ) represents a cardioid. A cardioid is a heart-shaped curve, and in this case, the center of the cardioid is at (3, 0).

(b) To find the formula for the area inside the inner loop, we can use the formula for the area bounded by a polar curve, which is 1/2 times the integral of (r^2) dθ over the desired interval. In this case, the interval is from θ = -π/6 to θ = π/6. Thus, the formula for the area inside the inner loop is 1/2 times the integral of (3 + 6sin(θ))^2 dθ from θ = -π/6 to θ = π/6.

(c) The length of the outer loop can be found using the arc length formula for polar curves. The formula is the integral of the square root of (r^2 + (dr/dθ)^2) dθ over the desired interval. In this case, the interval is from θ = -π/3 to θ = π/3. Therefore, the formula for the length of the outer loop is the integral of the square root of (3 + 6sin(θ))^2 + (6cos(θ))^2 dθ from θ = -π/3 to θ = π/3.

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Step-by-step explanation:

3.5cm===> 35mm===> 3.5e–6 lit

4.0cm===> 40mm===> 4.0e–6 lit

8.0cm===> 80mm===> 8.0e–6 lit

V(mm)=35×40×80=112000mm³

V(lit)=(3.5×4.0×8.0)×e–6=112e–6lit³

y=14

have a good day

The given expression is

First, we express the first number in scientific notation. We have to make sure that both scientific notations have the same exponent.

Then, we subtract the coefficients.

Answer:

y = 2x + 5 (answer d)

Step-by-step explanation:

Parallel lines have the same slope, and thus, if we're given y = 2x + 7, we know that the slope of the 'new' line is 2.  This 'new line' passes through (3, 11).  Begin with the point-slope formula y - k = m(x - h) and substitute 3 for h, 11 for k and 2 for m:

y - 11 = 2(x - 3)

Rewriting this in slope-intercept form, we get:

y = 2x - 6 + 11. or y = 2x + 5 (answer d)

The solution is \(X = 122.0\), and the proportion in the equation is, \(X / 6 = 61x / 18\).

The notion of an equation in algebra is a theoretical statement that demonstrates the equality of two formalisms. For instance, the expression 3x + 5 = 14 consists of the two solutions 3x + 5 and 14, that are separated by the 'equal' sign.

Every utterance can be composed of a numerical value, a constants, or a mixture of numerals, constants, or operation signs. Two expressions joined by an equation form an equation.

We can cross-multiply,

18 * X = 61x * 6

Simplifying the right-hand side,

\(18 * X = 366x\)

Dividing both sides by \(18x\),

\(X / 6 = 366x / 18x\)

Simplifying:

\(X / 6 = 61 / 3\)

\(X / 6 = 20.3333\)

Multiplying both sides by \(6\):

\(X = 122.0\)

Therefore, the solution is \(X = 122.0\), and the proportion is:

\(X / 6 = 61x / 18\)

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The solution is x = 3.5633 of 18 / x = 61x / 6.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.

To set up the proportion, we need to equate the ratios of the corresponding terms in the two fractions, which gives:

18 / x = 61x / 6

Simplifying the right-hand side by dividing both the numerator and denominator by 6 gives:

18 / x = 61x / 6

18 / x = 10.1667x

Now we can cross-multiply to get:

18 * 10.1667x = x * 6

Simplifying and dividing both sides by 6:

(18 * 10.1667) * x = 6 * x

x = 3.5633

Therefore, the solution is x = 3.5633.

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Answer: -4.8, -4.08, -3.9, 0, 3, 3.1

Step-by-step explanation:

Think of these numbers on a number line. Starting at zero number to the right all positive numbers ex: 0,1,2,3,4

Then, starting at zero moving left number negative numbers ex: -4,-3,-2,-1,0

The evaluated probabilities for the given question are 0.20 for the men who asked for promotion, 0.59 for the men who received the promotion when asked, and  0.118 for men who asked for promotion and received.under the condition that from the men interviewed  20% had asked for a promotion and 59% of the men who had asked for a promotion and  received.
Then,
P(man asked for a promotion)
= 20/100
= 0.20

P(man received promotion, given he asked for one)
= 59/100
= 0.59

P(man asked for promotion and received )
= P(man asked for a promotion) x P(man received promotion, given he asked for one)
= 0.20 x 0.59
= 0.118
Probability is considered as  the percentage of an event taking place in a specific time frame, in a given place. It is said to be a great aid in the horizons of science and mathematics.


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A function in the mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as function's domain and codomain, respectively. Here f(x)= 60.

A function in the mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as function's domain and codomain, respectively.

Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest documented treatment of the concept of function. Initially, the functions represented the idealized relationship between two changing quantities. A planet's position, for the instance, depends on time. In the past, idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity). The realms of application of the concept of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.

The most common letters used to represent functions are f, g, and h. A function's value at an element of its domain x is denoted by the symbol f(x), and the numerical value obtained by evaluating the function at a specific input value is denoted by replacing x with that value. For example, the value of f at x = 4 is denoted by the symbol f(x) (4). The value of the function at, say, x = 4 may be denoted by E|x=4 when the function has no name and is represented by the expression E.

if, f(x)= (-8),

f(-8)= (-9)*(-8)-12 = 60

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To write 28/25 as a percentage we need to multiply the fraction by 100 as follows:

Answer:

7xy + 2x²t

Explanation:

5xy - x²t + 2xy + 3x²t

= (5xy + 2xy) + (3x²t - x²t)

= 7xy + 2x²t

Given:

The function is

\(f(x)=2x^3-x^2-13x-6\)

To find:

The linear factors of the given function.

Solution:

We have,

\(f(x)=2x^3-x^2-13x-6\)

Splitting the middle terms, it can be rewritten as

\(f(x)=2x^3-(6-5)x^2-(15-2)x-6\)

\(f(x)=2x^3-6x^2+5x^2-15x+2x-6\)

\(f(x)=2x^2(x-3)+5x(x-3)+2(x-3)\)

\(f(x)=(x-3)(2x^2+5x+2)\)

Now, Splitting the middle term, we get

\(f(x)=(x-3)(2x^2+4x+x+2)\)

\(f(x)=(x-3)(2x(x+2)+1(x+2))\)

\(f(x)=(x-3)(x+2)(2x+1)\)

Therefore, the three linear factors of given function are (x-3), (x+2) and (2x+1). Hence, option 4, 5 and 6 are correct.

The linear factors of the given function f(x) = 2x³ - x² - 13x - 6 are;

(x - 3), (x + 2) and (2x + 1)

We are given the function;

f(x) = 2x³ - x² - 13x - 6

Let us start by splitting the terms at the middle. Since last term is 6, we can write 1 before x² as (6 - 5)

Also, we can write 13 as (15 - 2). Thus;

f(x) = 2x³ - (6 - 5)x² - (15 - 2)x - 6

Expanding gives us;

f(x) = 2x³ - 6x² + 5x² - 15x + 2x - 6

Factorizing gives us;

f(x) = 2x²(x - 3) + 5x(x - 3) + 2(x - 3)

(x - 3) is common and so we factorize it out to get;

f(x) = (x - 3)(2x² + 5x + 2)

Let us split (2x² + 5x + 2); 5 can be expressed as 4 + 1.Thus;

f(x) = (x - 3)(2x² + (4 + 1)x + 2)

f(x) = (x - 3)(2x² + 4x + x + 2)

Factorizing again gives;

f(x) = (x - 3)(2x(x + 2) + 1(x +2))

f(x) = (x - 3)(x + 2)(2x + 1)

In conclusion, the linear factors of the given function f(x) = 2x³ - x² - 13x - 6 are; (x - 3), (x + 2) and (2x + 1)

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A study conducted in 2004 examined the usage of cable television and radio among 10 individuals to determine if there was a significant difference in the average hours spent on each medium. Using a significance level of 0.05, statistical analysis was performed to test for a disparity between the population mean usage of cable television and radio.

The researchers collected data on the number of hours per week spent watching cable television and listening to the radio from a sample of 10 individuals. The objective was to determine if there was a significant difference in the average usage between cable television and radio, considering the increasing competition among various entertainment options.

To test for a difference between the population mean usage for cable television and radio, a statistical hypothesis test was conducted. The significance level (α) of 0.05 was chosen, which means that the results would be considered statistically significant if the probability of obtaining such extreme results by chance alone was less than 5%.

The test compared the means of the two samples, namely the average hours spent watching cable television and listening to the radio. By analyzing the data using appropriate statistical techniques, such as a two-sample t-test, the researchers determined whether the observed difference in means was statistically significant or could be attributed to random variation.

After conducting the hypothesis test, if the p-value associated with the test statistic was less than 0.05, it would indicate that there was a significant difference between the population mean usage of cable television and radio. Conversely, if the p-value was greater than 0.05, there would be insufficient evidence to conclude a significant disparity.

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The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

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Answer:

3. Linear: f(x) = 1320(1.20)^2

Step-by-step explanation:

Exponential Growth Formula: f(x) = \(x_{0}\) × (1 + r)^x

f(x) is the value at time t.

x0 is the initial value at time t=0.

x0 = 1320

r = 20% = 0.2

Solve:

f(x) = \(x_{0}\) × (1 + r)^x

f(x) = 1320 × (1 + 0.2)^2

f(x) = 1320(1.2)^2

Answer: 3rd answer

Step-by-step explanation:

Because Purdue starts with 1320 employees, and then multiplies that by 1.2 each year. If x represents 3 years, Purdue has:

 1320(1.2)^3

=1320(1.728)

=2280.96

el pozole se descompone porque tiene más azucares

Answer: -6x^7

Step-by-step explanation:

 2x^3 × (-3x^4)

=(2×-3) · (x^3 × x^4) ⇔ multiply the like terms

=-6 × [x^(3+4)] ⇔ the multiplication of exponents works as addition if same base

=-6x^7

Answer:

\(-6x^7\)

Step-by-step explanation:

So when doing this equation, you multiply the numbers, which is 2 × -3, and add the exponents, which is 3 + 4, so then you get the answer, and that is \(-6x^7\).

Answer: 1st 173 2nd 396

Step-by-step explanation: I hope this helps!

Answer:

c=l/--a^2+b^2=l/--45^2+20^2≈49.24429

Step-by-step explanation:

l/-- mean square root

^ means squared/ exponent

Answer:

Since they're asking you to find the missing sides "y" and "x" here's what you need to do....

Step-by-step explanation:

1) This is the 45-45-90 Triangle.

2) y = 20 becasue this is an isocelese triangle - meaning a triangle that has 2 sides of equal lengths!

3) in order to find x (which is the hyptoneus) you have to do

       \(\sqrt{2}\) * leg (use on of the legs)

    =  \(20\sqrt{2}\)

also I think 45 degrees is there just to throw you off. And I'm pretty positive this is the correct answer, and i'm 100% sure that y = 20 is correct!