Find g-¹(3):
g(x) =
2x+2
4
Type your numerical answer below.

Answer:

Step-by-step explanation:

Describe a functiDescribe a function that takes an input, adds 2, and then multiplies by 4on that takes aDescribe a function that takes an input, adds 2, and then multiplies by 4n inpDescribe a function that takes an input, adds 2, and then multiplies by 4ut, adds 2, and then multiplies by 4

Answer:

HIK and GFD,

Step-by-step explanation:

Answer:

pay him after 3 years with and interest of 5% compounded annually. On the 3rd year, exact date of his payment, Ben requested to extend his deadline for another 2 years. Glenn being a considerate man, agreed but under the new condition that from then on, the interest shall be 6% compounded semi-annually. Two years later, on exact deadline, Ben asked Glenn, again, for 1 more year.

Step-by-step explanation:

Answer:

12345678901234567890

The equation that shows the point-slope form of the line passing through (3, 2) with a slope of (1/2) is:

y - 2 = (1/2)(x - 3)

In the point-slope form of a linear equation, the formula is y - y1 = m(x - x1), where (x1, y1) represents a point on the line, and m represents the slope of the line. By substituting the given values into the formula, we can determine the correct equation.

In this case, the given point is (3, 2) and the slope is (1/2). Plugging these values into the formula, we get:

y - 2 = (1/2)(x - 3)

This equation represents the line passing through the point (3, 2) with a slope of (1/2). It is in the point-slope form, which allows us to easily determine the equation of a line based on a given point and slope.

Therefore, the correct equation is y - 2 = (1/2)(x - 3).

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Answer: B

Step-by-step explanation:

Answer:

11/12

Step-by-step explanation:

simplify 5500/6000

I first divided by 100 and got

55/60

Then divide by 5 to get

11/12

Answer:

\(\huge\boxed{\sf r = 5}\)

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

\(\rule[225]{225}{2}\)

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

The travelled distance of the traveller is equal to 195 kilometers.

According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:

x = d / 3

x + 65 = d / 2

Where:

Now we proceed to determine the travelled distance:

d / 3 + 65 = d / 2

d / 2 - d / 3 = 65

3 · d - d = 390

2 · d = 390

d = 195

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Answer:

Step-by-step explanation:

Let the smaller of two consecutive integer be x therefore other integer is x+ 1

As per statement the sum of two consecutive integers is 41. To find out the integers.

x + (x + 1) = 41

x + x + 1 = 41

2x + 1 = 41

2x = 41 - 1

2x = 40

x = 40/2

x = 20

The smaller of two consecutive integers is 20, thus other integer is x + 1 = 20 + 1 = 21

The two consecutive integers are 20 and 21

Answer the two consecutive integers are 20 and 21

The value of m<RQS as required to be determined in the task content is; 70°.

It follows from the task content that the measure of angle RQS is to be determined as required.

Recall, the measure of the central angle subtended by an arc is twice that which it subtends at any point on the circumference.

Therefore, m<RPS = 2 • m<RQS.

m<RQS = 140°/2

m<RQS = 70°.

Ultimately, the measure of angle RQS are; 70°.

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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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The expression JK||GI implies line JK and GI are parallel lines

The ratio of HK : KI is 3 : 1

A ratio is used to show the relationship between two related quantities

The given parameter is:

HJ : JG = 3 : 1

Given that JK||GI , then it means that:

HJ : JG = HK : KI

This gives

HK : KI = 3 : 1

Hence, the ratio of HK : KI is 3 : 1

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You have the following algebraic expression:

+4x² - 4x²

In order to simplfy the previous expression you take into account that you can sum or subtract terms with variables with same exponents. In this case you have two term with x², then, you can subtract them. To do that you simply subtract the coefficients of the terms:

+4x² - 4x² = 0

The answer is zero, because the terms have the same coefficients but opposites sings.

The maximum value of the original data set is 109.

To determine the maximum value of the original data set from the given stemplot, we need to look at the rightmost digits in each stem and identify the highest value.

Looking at the stemplot:

O 10 | 0 0 8 9 8 9 0 0 0

0 20 | 5 4 7 9 6

0 30 | 1 4 6 7 7 9 7

0 40 | 0 0 2 5 5 7 7 9 9 8

0 50 | 1 2 2 2 3 4 5 5 7 8 9 9

0 60 | 0 0 0 3 3 3 3 6 8

The rightmost digits in each stem represent the original data values. We can see that the highest value occurs in the stem "10" with a rightmost digit of "9".

Therefore, the maximum value of the original data set is 109.

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domain of (f.g)(x) is {x l x ≠ 13} i.e option (c) where f(x) = x+7 and g(x) = 1/(x-13)

Domain of a function is defined as all those values of x that can be substituted in function for which function is defined.

Given: f(x) = x+7

g(x) = 1/(x-13)

First we need to find (f.g)(x) i.e multiplication of  f(x) and g(x)

(f.g)(x) = (x+7) ×1/(x-13) = \(\frac{x+7}{x-13}\)

Domain of function is values of x over which function is defined

For (f.g)(x) it is defined at all values of x except when x-13=0 as at this point denominator will be zero and function will become infinite that is not defined.

So,  x - 13 ≠ 0

Adding 13 on both sides, we get

x ≠ 13

So domain of  (f.g)(x) is x∈R - {13} i.e {x | x≠ 13}

Hence, option (c) is correct answer.

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Answer:

C

Step-by-step explanation:

Glad I could help!

Answer:

c

Step-by-step explanation:

rise/run

-20/2=-10 for the slope

Nope, I don't. LOL, if you don't agree with me, please don't start the fifth shinobi war. Also, may I ask how it's relates to a school assignment? LOLOL

Answer:

Yes and no

Step-by-step explanation:

I say yes and no because I think that their relationship throughout the show could spread to a romance rather than a bromance. I love this ship, although I do also love the cannon ships. Hinata x Naruto and Sakura x Sasuke. And I know a lot of people hate Sasuke and Sakura ship but you know that song that goes, "I hate everything about you! Why do I love you?!?" That is what I think of that ship and I love it.

Now I'm ranting lol. But yeah that is my opinion on Naruto x Sasuke! <3

If we try to use L'Hopital's Rule to find the limit we cannot apply L’Hopital’s Rule because the denominator equals zero for some value x = a, the correct option is D.

We are given that;

Function \(x/√x^2 +6\)

Now,

The limit of the function as x approaches infinity is an indeterminate form of type ∞/∞.

However, L’Hopital’s Rule can only be applied when the limit is in the form 0/0 or ∞/∞.

So, L’Hopital’s Rule cannot be applied in this case

Therefore, by L’Hopital’s rule answer will be  You cannot apply L’Hopital’s Rule because the denominator equals zero for some value x = a.

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The freighter is approximately 164.33 miles from the city.

We can use the Law of Cosines to solve this problem. Let's label the distances as follows:

d: distance between the city and the freighter

x: distance between the city and the island

y: distance between the island and the freighter

First, we need to find x using the given coordinates:

N23°38'W is equivalent to S23°38'E, so we have:

cos(23°38') = x/48

x = 48cos(23°38') ≈ 42.67 miles

Next, we can use the coordinates of the freighter to find y:

N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:

23°38' + 11°26' + 12°16' = 47°20'

cos(47°20') = y/d

We can rearrange this equation to solve for y:

y = dcos(47°20')

Now we can use the Law of Cosines to solve for d:

d² = x² + y² - 2xy cos(90° - 47°20')

d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')

d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')

d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')

d ≈ 164.33 miles

Therefore, the freighter is approximately 164.33 miles from the city.

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Answer:

(X'U'Y) + (XUY')

Step-by-step explanation:

Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:

[Xn(X'nY)]' = (Xn)' + (X'nY)'

Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:

(Xn)' + (X'nY)' = (X'U'Y) + (XUY')

where U represents the logical operator "or".

Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').

Answer:

x+3+10x^2-2.4x^3

Step-by-step explanation:

Answer:

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Apartment:

38 out of 78, so:

\(p_A = \frac{38}{78} = 0.4872\)

\(s_A = \sqrt{\frac{0.4872*0.5128}{78}} = 0.0566\)

Home:

46 out of 84, so:

\(p_H = \frac{46}{84} = 0.5476\)

\(s_H = \sqrt{\frac{0.5476*0.4524}{84}} = 0.0543\)

Test if the there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees:

At the null hypothesis, we test if there is no difference, that is, the subtraction of the proportions is equal to 0, so:

\(H_0: p_A - p_H = 0\)

At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0, so:

\(H_1: p_A - p_H \neq 0\)

The test statistic is:

\(z = \frac{X - \mu}{s}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that \(\mu = 0\)

From the samples:

\(X = p_A - p_H = 0.4872 - 0.5476 = -0.0604\)

\(s = \sqrt{s_A^2 + s_H^2} = \sqrt{0.0566^2 + 0.0543^2} = 0.0784\)

Value of the test statistic:

\(z = \frac{X - \mu}{s}\)

\(z = \frac{-0.0604 - 0}{0.0784}\)

\(z = -0.77\)

P-value of the test and decision:

The p-value of the test is the probability of the difference being of at least 0.0604, to either side, plus or minus, which is P(|z| > 0.77), given by 2 multiplied by the p-value of z = -0.77.

Looking at the z-table, z = -0.77 has a p-value of 0.2207.

2*0.2207 = 0.4414

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Complete Question

The  complete question is shown on the first uploaded image  

Answer:

The interval is  \(-0.0037 < p_1-p_2<-0.0023\)

Step-by-step explanation:

From the question we are told that

   The first  sample size is  \(n _1 = 1068000\)

    The  first sample proportion is \(\r p_1 = 0.089\)

    The  second sample  size is  \(n_2 = 1476000\)

    The  second sample proportion is  \(\r p_2 = 0.092\)

Given that the confidence level is  95% then the level of significance is mathematically evaluated as

             \(\alpha = (100 - 95 )\%\)

              \(\alpha = 0.05\)

Next we obtain the critical value  of  \(\frac{\alpha }{2}\)  from the normal distribution table  

The value is  

               \(Z_{\frac{\alpha }{2} } =z_c= 1.96\)

Generally the 95% confidence interval is mathematically represented as

       \((\r p_1 - \r p_2 ) -z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}} < (p_1 - p_2 ) < (\r p_1 - \r p_2 ) +z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2}}\)

Here  \(\r q_1\) is mathematically evaluated as \(\r q_1 = (1 - \r p_1)= 1-0.089 =0.911\)

and  \(\r q_2\)  is mathematically evaluated as  \(\r q_2 = (1 - \r p_2) = 1- 0.092 = 0.908\)

So

       \((0.089 - 0.092 ) -1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}} < (p_1 - p_2 ) < (0.089 - 0.092 ) +1.96 \sqrt{ \frac{0.089* 0.911 }{1068000} + \frac{0.092* 0.908 }{1476000}}\)

\(-0.0037 < p_1-p_2<-0.0023\)

Answer:

20

Step-by-step explanation:

19-44=25

45-64=19 25+19=44 44-64=20

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

According the question,

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

Where x represents the quantity of additional tours that the tourist wants to add to their travel package.

The function f(x) represents the total cost of the travel package plus the additional cost of the extra tours.

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Answer:

-2a⁴ b⁶ c³

Step-by-step explanation:

2a² b c³ (-a² b⁵)

determine the signs for multiplication or division

-2a²bc³a²b⁵

multiply the monomials

-2a⁴b⁶c³

(then done)

You'll first Cross multiply: 5× 3x

that'll give you 15x.

15x=12(12 is a numerical constant).

Divide both sides by the the coefficient of X .That is 15x/15= 12/15

Therefore the answer is 12/15= x

\(\huge\textbf{Hey there!}\)

\(\mathsf{5 = 1 \dfrac{2}{3}x}\)

\(\mathsf{1 \dfrac{2}{3}x = 5}\)

\(\mathsf{\dfrac{1\times3 + 2}{3}x= 5}\)

\(\mathsf{\dfrac{3 + 2}{3}x = 5}\)

\(\mathsf{\dfrac{5}{3}x = 5}\)

\(\large\text{MULTIPLY }\rm{\dfrac{3}{5}}\large\text{ to BOTH SIDES}\)

\(\mathsf{\dfrac{3}{5}\times\dfrac{5}{3}x = \dfrac{3}{5}\times5}\)

\(\large\text{SIMPLIFY IT!}\)

\(\mathsf{x = \dfrac{3}{5}\times5}\)

\(\mathsf{x = \dfrac{3}{5}\times\dfrac{5}{1}}\)

\(\mathsf{x = \dfrac{3\times5}{5\times1}}\)

\(\mathsf{x = \dfrac{15}{5}}\)

\(\mathsf{x = \dfrac{15\div5}{5\div5}}\)

\(\mathsf{x = \dfrac{3}{1}}\)

\(\mathsf{x = 3\div1}\)

\(\mathsf{x = 3}\)

\(\huge\text{Therefore, your answer: \boxed{\mathsf{x = 3}}}\huge\checkmark\)

The given numbers, 24.3 ,2 ,7 ,25 are all rational numbers.