What is the solution set for −4x−38<2

Answer:

They need to survey 4145 residents.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a p-value of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).

At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.02 of the true proportion?

This is n for which \(M = 0.02\). As we have no estimate for the proportion, we use \(\pi = 0.5\). So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.02 = 2.575\sqrt{\frac{0.5*0.5}{n}}\)

\(0.02\sqrt{n} = 2.575*0.5\)

\(\sqrt{n} = \frac{2.575*0.5}{0.02}\)

\((\sqrt{n})^2 = (\frac{2.575*0.5}{0.02})^2\)

\(n = 4144.1\)

Rounding up:

They need to survey 4145 residents.

Answer:

42

Step-by-step explanation:

[ ( 7 - 3 ) * 2 + 6 ] * 3

= [ 4 * 2 + 6 ] * 3

= [ 8 + 6 ] * 3

= 14 * 3

= 42

Answer:

D. 144km

Step-by-step explanation:

If the vehicle travels 72km every hour, in two hours, it will drive 144km. (72x2=144)

Answer:

You need to add a picture

Step-by-step explanation:

But to find the vectr you basically need to count the squares from each of the shapes going up or down

For example:

- squares going down would be -x

- squares going up would be x

- squares going left would be -x

- squares goinf right would be x

Then you put it in the form of a fraction

Answer:

b

Step-by-step explanation:

pls give brainliest hope helpful

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2

How to solve a function?

If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:

g(x) = a(4) raise to the power x-k/2

where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:

f(x) = g(x)/2

Substituting the expression for g(x) into this equation and simplifying, we get:

4raise to the power x - 6 = a(4)raise to the power x-k/2

To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:

f(0) = 4 - 6 = -5

f(1) = 4- 6 = -2

Using the equation g(x)/2 = f(x), we can write:

g(0)/2 = -5

g(1)/2 = -2

Substituting the expression for g(x) into these equations, we get:

a(4) raise to the power -k/2 = -10

a(4) raise to the power 1-k/2 = -4

Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":

(4)raise to the power -k/2 / (4)  raise to the power 1-k/2 = -10 / -4

Simplifying this equation, we get:

4.raise to the power(1-k/2) = 5

Taking the logarithm of both sides (with base 4), we get:

1-k/2 = log4(5)

Solving for "k", we get:

k = 2 - 2 log4(5)

Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":

a = -10 / (4)   raise to the power  -k/2

Substituting the numerical value of "k", we get:

k = 2 - 2 log4(5) ≈ 0.872

a = -10 / (4) raise ti the power  -k/2 ≈ 2.323

Therefore, the equation for the transformed function g(x) is:

g(x) = 2.323 (4)raise to the power x-0.872/2

or equivalently:

g(x) = 1.1615 (4) raise to the power -x0.872

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Answer:

g(x) = 1/2 (4)^x - 3

Step-by-step explanation:

A vertical compression by a factor of 1/2

means that the entire function f is multiplied by 1/2:

1/2 f (x) = 1/2 (4^x - 6)

= 1/2 (4)^x - 3

Answer:

can u show pictures?

Step-by-step explanation:

The rule of the arc of a circle is

x is the subtended angle of the arc

r is the radius of the circle

Since the arc subtended an angle of measure 85 degrees, then

x = 85

Since the radius of the circle is 23 inches, then

r = 23

Substitute them in the rule above

The length of the arc is 34.1 inches to the nearest tenth

The answer is 34.1 inches

The output value of (f∘g)(x) is:  \((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)

The domain of (f∘g)(x) is (-∞, -3) U (-3, ∞).

In this scenario, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations (multiplication) in simplified form as follows;

\(f(x) = \frac{x-6}{x +3}\)

g(x) = 4x - 15

Next, we would write the numerators and denominators in factored form as follows;

(x - 6)(4x - 15)

4x² - 15x - 24x + 60

4x² - 29x + 60

Now, we can derive the corresponding composite function of f(x) and g(x);

\((f \circ g)(x) = \frac{4x^2-29x+60}{x +3}\)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

x + 3 ≠ 0

x ≠ -3

Domain = (-∞, -3) U (-3, ∞).

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Answer:

3

Step-by-step explanation:

The answer is three because u need to simply the fractions

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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Answer:

Step-by-step explanation:

\(x+7\frac{1}{3}=18\ frac{2}{3}\\ \\ x+\frac{22}{3}=\ frac{56}{3}\\ \\ x=\frac{56-22}{3}\\ \\ x=\frac{34}{3}\\ \\ x=11\frac{1}{3}\)

Answer:

11 1/3

Step-by-step explanation:

<CAB= 56°

(DC= 78°

(DB= 78+56=134°

<DAB=134°

(BED=360-134= 226°

(BEC=226+78=304°

(CED= 360-78=282°

hey:) I hope this was correct and helpful

Answer:

>>   \(6\frac{5}{18}\)

Step-by-step explanation:

1) Add the whole numbers first.

\(5+\frac{5}{6} +\frac{4}{9}\)

2) Find the Least Common Denominator (LCD) of \(\frac{5}{6} ,\frac{4}{9}\) . In other words, find the Least Common Multiple (LCM) of \(6,9\).

Method 1: By Listing Multiples

1. List the multiples of each number.

Multiples of 6 : 6, 12, 18, ...

Multiples of 9 : 9, 18, ...

2. Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 18

3. Make the denominators the same as the LCD.

\(5+\frac{5\times 3}{6\times 3}+\frac{4\times 2}{9\times 2}\)

4. Simplify. Denominators are now the same.

\(5+\frac{15}{18}+\frac{8}{18}\)

5.  Join the denominators.

\(5+\frac{15+8}{18}\)

6. Simplify.

\(5+\frac{23}{18}\)

7. Convert \(\frac{23}{18}\) to mixed fraction.

\(5+1\frac{5}{18}\)

8. Simplify.

\(6\frac{5}{18}\)

Decimal Form: 6.277778

Cheers.

The addition of 3 5/6 + 2 4/9  is 113/18

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

3 5/6 + 2 4/9

Now, writing it into normal fraction

3 5/6 + 2 4/9

= 23/ 6 + 22/9

= 23/6 x 3/3 + 22/9 x 2/2

= 69/ 18 + 44/18

= 113/18

Hence, the addition is 113/18

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Answer:

8+8=0 because it equals 16

ANSWER

The relationship between the number of turkey subs delivered and the amount charged is proportional

STEP-BY-STEP EXPLANATION:

Given information

The total amount charged by a sandwich store to deliver 3 turkey subs is $20

The total amount charged by a sandwich store to deliver 4 turkey subs is $26

To determine whether the relationship is proportional, we need to determine the amount to deliver one turkey sub

Let r represents the rate for delivering a turkey sub

To calculate the rate, we will need to apply the below formula

Since the rate of delivering a turkey sub is $6.667/turkey sub, then, we can now find the amount in dollars to deliver 4 turkey subs

From the above calculation, you will see that it will take $26.68 to deliver 4 turkey subs and not $26.

Therefore, the relationship between the number of turkey subs delivered and the amount charged is proportional

Answer:

790

Step-by-step explanation:

7098uuilu4645

All thre functions share the same y intercept

We can analyze the characteristics of the given functions based on the information provided in the table.

We cannot determine which function has the greatest maximum based on the table alone, as we do not have the complete graph of any of the functions.

We can see from the table that h(x) has an x-intercept of 0, which is the smallest among the three functions. Therefore, we can say that h(x) has the smallest x-intercept.

We can see from the table that g(x) has a minimum value of -204, which is the smallest among the three functions. Therefore, we can say that g(x) has the smallest minimum value.

We cannot determine if all three functions share the same domain based on the table alone. We can only see that all three functions have been evaluated at the same set of input values.

We can see from the table that the y-intercept of f(x) is 2, the y-intercept of g(x) is 3, and the y-intercept of h(x) is 4. Therefore, we can say that all three functions have different y-intercepts.

Therefore, the statements that can be used to compare the characteristics of the functions are:

h(x) has the smallest x-intercept.

g(x) has the smallest minimum value.

All three functions have different y-intercepts.

Answer: The same as

Step-by-step explanation:

Hope this helps

Answer:

Same as

Step-by-step explanation:

Answer:

-6,-2 is the answer!!

Step-by-step explanation:

The coordinate of A' would be (-6, -2)

Dilation is a transformation technique that changes the size of an object by a scale factor "k"

From the diagram shown, the measure of the coordinate point is given as (-3, -1).

If the coordinate A is dilated by a factor of 2, the resulting coordinate A' will be given as:

A' = (2(-3), 2(-1)) = (-6, -2)

Hence the  coordinate of A' would be (-6, -2)

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Answer:

7

As calculated in the photo above

a)Since this scenario is about winning or losing an election, i.e., failure or success. Thus, this experiment has a Bernoulli distribution.

b)Also notice that since the elections are performed 12 times, the distribution of the whole experiment has a Binomial distribution. In this case, let p be the probability that the Democrats win. Then, we have the following:

then, the mean and the standard deviation are:

c)To find the probability that the democrats will win the 7th race, we have to use the binomial probability function:

in this case, x = 7, then we have:

then, the probability that they win the 7th race is 23%

d) Finally, for the probability that the democrats win the 12 races, we can calculate with x = 12 to get:

therefore, the probability that they win all the races is 0.2%

Answer

C. 86 times larger

Step-by-step explanation

To compare the mass of the Earth with respect to the mass of the Moon we need to divide both masses and simplify as follows:

Answer:

300 dollars

Step-by-step explanation:

each month you get paid 100 and march is the 3rd month and 100x3 is 300

Answer:

  x -5y = -6

Step-by-step explanation:

A plot of the given points shows the hypotenuse is QR, and the vertex through which the altitude line goes is point P. We want a line through P that is perpendicular to QR.

__

The equation for a line perpendicular to the one through (x1, y1) and (x2, y2) can be written in the general form ...

  (x2 -x1)(x -h) +(y2 -y1)(y -k) = 0

where (x, y) = (h, k) is a point on the line.

Using points Q(3, 5) and R(5, -5) for the two points, and (h, k) = P(-1, 1), we have ...

  (5 -3)(x -(-1)) +(-5-5)(y -1) = 0

  2x +2 -10y +10 = 0 . . . . . . . . . eliminate parentheses

The standard-form equation will have mutually-prime coefficients and the constant on the right. Dividing by 2 and subtracting 6 gives ...

  x -5y = -6