if g (x) = 3x +5, for which value of x does g (x) =17?

The sample size will now have to be is 3200.

Given:

the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error (e) must be reduced to just 0.025. if the original calculation led to a sample size of 1000.

n = p(1-p)(z/E)^2

800 = 0.5(1-0.5)(z/0.05)^2

800 = 0.5*0.5* z^2/0.0025

800 = 0.25 * z^2/0.0025

800 = 25/100*10000*z^2/25

800 = 1*100*z^2

800/100 = z^2

8 = z^2

z = [tex]\sqrt{8}[/tex]

z = 2.8284

n = p(1-p)(z/E)^2

= 0.25(2.8284/0.025)^2

= 0.25*(113.136)^2

= 0.25*12799.754496

= 3199.938 ≈ 3200

Therefore the sample size will now have to be is 3200.

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The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .

In the question ,

Four equations are given , we need to find the equation that represents the identity property of multiplication .

we know that the identity property of multiplication states that the product of any number and 1 is the same given number .

For Example : the product of a number 'a' and 1 is = a , that is a×1 = a .

So , by the applying the definition of Identity property of multiplication we get that the equation that models the identity property is

(a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi)

Therefore , The equation that illustrates the identity property of multiplication is (a + bi) × 1 [tex]=[/tex] (a [tex]+[/tex] bi) , the correct option is (d) .

The given question is incomplete , the complete question is

Which equation illustrates the identity property of multiplication?

(a) (a + bi) × c = (ac + bci)

(b) (a + bi) × 0 = 0

(c) (a + bi) × (c + di) = (c + di) × (a + bi)

(d) (a + bi) × 1 = (a + bi)

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Answer:

  5.5%

Step-by-step explanation:

You want the interest rate that can be compounded continuously to give $1490 from an investment of $650 after 15 years.

The formula for account value with continuously compounded interest is ...

  A = Pe^(rt) . . . . P=principal, r=interest rate, t=years

Solving for r, we find ...

  ln(A/P)/t = r

  ln(1490/650)/15 = 0.0553...

The interest rate is about 5.5%.

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Answer:

90 liters

Step-by-step explanation:

It's given in the question!

Answer:

[tex]-2[/tex]

Step-by-step explanation:

The perpendicular slope is the opposite of the reciprocal of the original slope. So, let's find the slope of this line! I will put it in slope-intercept form (y = )

[tex]x-2y=-8\\-2y=-8-x\\y=4+\frac{1}{2} x\\y=\frac{1}{2} x+4[/tex]

Here, I see that the slope of the line is [tex]\frac{1}{2}[/tex]. The reciprocal of [tex]\frac{1}{2}[/tex] is 2. The opposite of 2 is [tex]-2[/tex]. The slope of the perpendicular line is [tex]-2[/tex]!

Answer:

The percentage of the distance Dominic is on the path is his distance

travelled as a fraction of the total distance when equivalent to 100.

The distance he has travelled on the path is 8.75 miles.

Reasons:

The given parameter are;

Length of Dominic's path = 12.5 miles

The length of the way Dominic is to

Step-by-step explanation:

Answer:

[tex](f+g)(x)=7x^2-3x-5[/tex]

Step-by-step explanation:

Step 1: What you are given & need to find

Step 2: Set up the problem

Step 3: Simplify

Answer:

l = 1

Step-by-step explanation:

v = lwh

8 = l(2)(4)

8 = l8  Divide both sides by 8

1 = l

Answer:

1st

Step-by-step explanation:

Explanation in the picture.

The initial size of the bacteria culture is 33

The count of the bacteria after 10 days = 200

The count of bacteria after 20 days = 1200

The difference in time = 20 - 10

= 10 days

Then the exponential growth equation will be

1200 = 200×[tex]e^{10k}[/tex]

[tex]e^{10k}[/tex] = 1200 / 200

Divide the terms

[tex]e^{10k}[/tex] = 6

10k = ln(6)

10k = 1.79

k = 1.79 / 10

Divide the terms

k = 0.179

Use the same equation to find the initial size of the bacteria culture

200 = x × [tex]e^{10(0.179)}[/tex]

x = 200 / [tex]e^{10(0.179)}[/tex]

x = 200 / 5.99

Divide the terms

x = 33.38

x ≈ 33

Hence, the initial size of the bacteria culture is 33

The complete question is:

The bacteria count in a certain culture was 200 after 10 days and 1200 after 20 days. assume the bacteria are growing exponentially. Find the initial size of the bacteria culture

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Answer:

The number of candy bars each friend will receive is 1.66.

Step-by-step explanation:

Given that Becky has 5 candy bars

She wants to share them with 3 friends.

To determine the number of candy bars each friend will receive

We need to determine the number of candy bars each friend will receive

So,  the number of candy bars would be

5/3 which would = to 1.66

and that's how much she will give each friend

Answer:

123.00

Step-by-step explanation:

Answer:

It is A. C. and D.

Step-by-step explanation.

The question is asking for the three different points to be moved, answer choice A is the answer for one point, answer C is for the second point, and answer D is for the third point.

Answer:

in the picture

Step-by-step explanation:

Hope this helped! Solve your problem: Use the quadratic formula to solve for x.

8x²-8x-1=0

The correct answer is  H0 : Living in Northern or southern California is not associated with watering habits and  Ha : Living Northern or southern California is associated with watering habits.

Given that,

H0 : Living in Northern or southern California is not associated with watering habits.

Ha : Living Northern or southern California is associated with watering habits.

In independent test in that test we Check the two variables are independent or not. The chi square can be used for any variable. Both the group (independent) and test variable(dependent)   can be nominal, ordinal, or grouped interval.

Therefore, The difference between living in Northern or Southern California and the difference between living in Northern or Southern California is that the former is related to watering practices.

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The value of g = 4π²l/T²

Operators are Mathematical operations that emphasize particular actions like summing up, dividing, and adding multiple times, etc.

In Mathematics, the basic arithmetic operations are Addition, Subtraction Division, and Multiplication.  

The symbols which are used for each operation are

Addition  - (+)

Subtraction  - (-)

Division  - (÷)

Multiplication  - (x)  

Given [tex]l = \frac{gT^{2} }{4 \pi ^{2} }[/tex]  

To get the 'g' value we will use Multiplication and Division

Multiply both sides with 4π²  

=> [tex]4 \pi ^{2} (l )= \frac{gT^{2} }{4 \pi ^{2} }(4 \pi ^{2} )[/tex]  

=> [tex]4 \pi ^{2} (l )= gT^{2}[/tex]  

Divide by T² on both sides

=> [tex]4 \pi ^{2} (l )\frac{1}{T^{2}} = g\frac{T^{2}}{T^{2}}[/tex]

=> [tex]\frac{ 4 \pi ^{2} l }{T^{2}} = g[/tex]

=> [tex]g = \frac{ 4 \pi ^{2} l }{T^{2}}[/tex]  

Therefore,

The value of g = 4π²l/T²

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Answer:

The average speed is 80km/h.

Step-by-step explanation:

In order to calculate the average speed you have to divide the total distance by the total elapsed time:

Let t represent time (in hours)

t=12:30-11:30=1

Let D represent distance (in kilometers)

D=80

Therefore, since t=/=0:

D/t=80/1=80km/h

And there you have it! Your answer is 80 km per hour.

The length of the side x on the right triangle is 41.06

A right triangle is a triangle that has one interior angle of 90°

The parameters in the right triangle are;

Acute angle = 47°

Leg length of side adjacent to 47° = 28

Length of the hypotenuse = x

From trigonometric ratios, we have;

[tex]cos(\theta) =\mathbf{ \dfrac{Length \, of \, adjacent \, side}{Length \, of \, Hypotenuse}}[/tex]

The cosine of the 47° angle is therefore;

[tex]cos(47^{\circ}) = \dfrac{28}{x}[/tex]

From which we have;

[tex]x= \dfrac{28}{cos(47^{\circ}) } \approx 41.06[/tex]

The length of the side, x ≈ 41.06

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Answer:

both

Step-by-step explanation:

because the first one, since the number 4 isn’t next to the parentheses then we are not multiplying so it’s actually adding so it still equals 7

74-126+329/2

-52+329/2

277/2

138.5

Answer:

[3, ∞]

Step-by-step explanation:

Answer:16.e+6.18

Step-by-step explanation:

Answer:

[tex]x=10^{\frac{4}{3}}=\sqrt[3]{10000}[/tex]

Step-by-step explanation:

Given equation:

[tex]9^{\log_3 (\log x)}= \log x-2\log^2x+4[/tex]

Rewrite 9 as 3²:

[tex]\implies (3^2)^{\log_3 (\log x)}= \log x-2\log^2x+4[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{2\log_3 (\log x)}= \log x-2\log^2x+4[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies 3^{\log_3 (\log x)^2}= \log x-2\log^2x+4[/tex]

[tex]\textsf{Apply log law}: \quad a^{\log_ab}=b[/tex]

[tex]\implies (\log x)^2= \log x-2\log^2x+4[/tex]

Simplify:

[tex]\implies\log ^2 x= \log x-2\log^2x+4[/tex]

[tex]\implies 3\log ^2 x- \log x-4=0[/tex]

Let log(x) = u:

[tex]\implies 3u^2-u-4=0[/tex]

Factor:

[tex]\implies 3u^2+3u-4u-4=0[/tex]

[tex]\implies 3u(u+1)-4(u+1)=0[/tex]

[tex]\implies (3u-4)(u+1)=0[/tex]

Apply the zero-product property:

[tex]\implies 3u-4=0 \implies u=\dfrac{4}{3}[/tex]

[tex]\implies u+1=0 \implies u=-1[/tex]

Substitute u=log(x) back in:

[tex]\implies \log x = -1[/tex]

[tex]\implies \log x= \dfrac{4}{3}[/tex]

On the left side of the original equation, we have log₃ (log x).  

As logs of negative numbers cannot be taken, log(x)=-1 is not a valid solution since this would give log₃(-1) which is undefined.

Therefore, the only valid solution is:

[tex]\implies \log x= \dfrac{4}{3}[/tex]

[tex]\implies x=10^{\frac{4}{3}}[/tex]

[tex]\implies x=\left(10^4\right)^{\frac{1}{3}}[/tex]

[tex]\implies x=10000^{\frac{1}{3}}[/tex]

[tex]\implies x=\sqrt[3]{10000}[/tex]

Note: If a log has no base, assume that the base is 10.

The standard error of the sample proportion bringing their own personal computers to campus is 0.045

The standard error of a sample proportion is calculated as:

[tex]SE=\sqrt{\frac{p(1-p)}{n} }[/tex]

with p=0.4 and n=120:

[tex]SE=\sqrt{\frac{0.4(1-0.4)} {120}}[/tex]

[tex]SE=\sqrt{0.002}[/tex]

[tex]SE=0.045[/tex]

The standard error of the sample proportion of students bringing their own computer is 0.045.

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Answer:

x = 5

Step-by-step explanation:

Let's say

x = #s of nickels Nina has (we are going to try to get X)

y = # of nickels Maurice has

5x + 9 < The amount Nina has

y = 2x < Amount that Maurice has

Add them both to the total, 84

5x + 9 + 5y = 84

Transfer the 9 to the other side

5x + 5y = 75

Substitute y with it's value

5x + 5(2x) = 75

5x + 10x  = 75

15x = 75

Divide

x = 5

Answer:

Person 2 jogs faster as compared to person 1.

The time taken by the faster jogger finish a five-kilometer race will be, 27.5 minutes.

Step-by-step explanation:

speed = distance/time

Under any circumstances, the imaginary number i = √-1. We use i to represent the square root of a negative number because negative numbers cannot have square roots (ex: 2^2 = 4, -2^2 = 4).

So, we have a complex number 2 + i. The absolue value? Simple.

[tex]|2 + i|\\2 + |\sqrt{-1} |\\2 + \sqrt{1} \\2 + 1\\3[/tex]

If you need an explanation, look at it this way. The number cannot exist. Yet let's assume it did exist for a moment. What would be the absolute value of a negative square root if they could exist? Well, it would be the same as the square root of that number's opposite, it's positive counterpart!

So, what is the positive counterpart of -1? That would be 1. What's the square root of 1? 1! So, why don't we eliminate these steps? Instead of assuming √-1 can exist and then finding the absolute value of that, just skip those steps and instead take √1, or just 1.

So finally: |√-1| = 1