3. A music store sells a guitar for $45. If the local sales tax is 6%, what is the total cost of the guitar, including tax? Do NOT use a dollar sign in your

Answer:

(1,0), (0,0),(-2<0)<(-1, -2)

Step-by-step explanation:

The probability that fewer than 135 did not use the top web browser is 0.0885 (rounded to four decimal places).

Given that the top web browser had 51.04% of the market.

Representing the probability of using top web browser P(T) = 0.5104

Probability of not using the top web browser is P(N) = 1 - 0.5104 = 0.4896

The sample size is n = 300 people.

We need to find the probability that fewer than 135 people did not use the top web browser.

Therefore, the required probability is given by;

P(X < 135)

Where X is the number of people who did not use the top web browser.

The number of people who did not use the top web browser follows a binomial distribution with parameters n = 300 and p = 0.4896.

The mean of the distribution is given by;

Mean = np= 300 × 0.4896 = 146.88

The variance of the distribution is given by;

Variance = np(1 - p)= 300 × 0.4896 × 0.5104 = 74.8473

The standard deviation of the distribution is;

Standard deviation = √variance= √74.8473= 8.6485z = (X - μ) / σ

Where μ is the mean and σ is the standard deviation of the distribution

Substitute the mean and standard deviation of the distribution; z = (X - μ) / σ = (135 - 146.88) / 8.6485= -1.3542

Using a standard normal distribution table, find the probability that Z < -1.3542P(Z < -1.3542) = 0.0885

The probability that fewer than 135 did not use the top web browser is 0.0885 (rounded to four decimal places).

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Answer:

Step-by-step explanation:

Slope =(x2-x1/y2-y1)

=(3-7/2+3)

-4/5

slope =-4/5

Answer:

Susan pays $2220 more interest than Robert

Step-by-step explanation:

Interest = principle times rate times the time

I = PRT

Robert:  I = 30000(.049)(4) = $5880  

Susan:   I = 30000(.045)(6) = $8100

8100 - 5880 = $2220

Answer:

\(\huge\boxed{\sqrt[3]{64}=4}\)

Step-by-step explanation:

We know:

\(\sqrt{a}=b\iff b^2=a\qquad\text{for}\ a\geq0\\\\\sqrt[3]{a}=b\iff b^3=a\)

We have:

\(\sqrt[3]{64}=4\ \text{because}\ 4^3=4\cdot4\cdot4=64\)

Answer:

x          y

10   →   6

4    →    0

8    →    4

Step-by-step explanation:

Using the given rule, plug in any known values:

\(y=x-4\\\\6=x-4\)

Solve for x. Add 4 to both sides of the equation to isolate the variable:

\(6+4=x-4+4\\\\x=10\)

Repeat:

\(y=x-4\\\\0=x-4\\\\0+4=x-4+4\\\\x=4\)

\(y=x-4\\\\4=x-4\\\\4+4=x-4+4\\\\x=8\)

:Done

Well, it's hard to really help because I can't draw a graph on here, but what you can do is make a list of a couple numbers (say -3, -2, -1, 0, 1, 2, and 3), and then use them as values of x to find y. Once you have found y, use those two values as your coordinate to plot your line:

x = -3, y = -3 + 4 = 1, so the coordinate would be (-3, 1).

x = -2, y = -2 + 4 = 2, so the coordinate would be (-2, 2).

]Hope that helps! Can you do the rest?

The convergence or divergence of a series is not provided, so it cannot be determined without knowing the specific series.

In order to determine whether a series is convergent or divergent, we need to know the terms of the series. The convergence or divergence of a series depends on the behavior of its terms as the series progresses. Different series have different convergence or divergence tests that can be applied to them.

Some common convergence tests for series include the comparison test, the ratio test, the root test, and the integral test, among others. These tests help determine whether the series converges or diverges based on the properties of the terms.

Without knowing the specific series or having any information about its terms, it is not possible to determine whether the series is convergent or divergent. Each series must be evaluated individually using the appropriate convergence test to reach a conclusion about its behavior.

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Answer:

-2y2 - 4y - 7

Step-by-step explanation:

2y2 + 2y2 - 6y2 - 4y - 5 - 3 + 1

4y2 - 6y2 - 4y - 8 + 1

-2y2 - 4y - 7

Answer:

Answer:

√3

√5

22/7.

16/4

Step-by-step explanation:

22/7 = 3.14

√3 = 1,73

16/4 = 4

√5 = 2.23

the least would have the smallest value. the greatest would have the largest value

The probability of there being exactly 13 earthquakes in a given month, assuming an average of 12 earthquakes, is 0.1008.

We can use the Poisson distribution, which is a probability distribution that can be used to calculate the probability of a certain number of events occurring in a given time period.

In this case, we can assume that the number of earthquakes in a month follows a Poisson distribution with a mean of 12. This means that the average number of earthquakes in a month is 12, but the actual number can vary.

To find the probability that there will be 13 earthquakes in a given month, we can use the Poisson probability formula:

P(x = k) = (e(-λ) * λk) / k!

Where:
- k is the number of events we're interested in (in this case, 13)
- λ is the mean or average number of events (in this case, 12)
- e is the mathematical constant e (approximately equal to 2.71828)
- k! is the factorial of k (i.e., k x (k-1) x (k-2) x ... x 2 x 1)

Plugging in the values for k and λ, we get:

P(x = 13) = (e-12) * 1213) / 13!

Simplifying this expression, we get:

P(x = 13) = 0.1008 (rounded to four decimal places)

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Based on this data, for every inch in height, the arm span increases by 1.1 inches.

Here, we have,

I put the height of people on the x-axis because this is what I am trying to correlate the arm span to. I put the arm span on the y-axis because it is dependent on height.

I used point (60,61) and (70,72) to draw the line of best fit and to get the equation. First, to get the slope I would use the slope formula of m = 72-61/70-60 or 11/10 to get a slope of approximately 1.1. Then I used (60,61) to get the rest of the equation by plugging it in: y-61 = 1.1(x -60). This becomes y-61 = 1.1x - 66. Add 61 to both sides and the final equation is y = 1.1x – 5.

The slope represents the rate of change arm span based on height. The y intercept is the arm span.

Using points (66,68) and points (70,72) I plug each into the equation y=1.1x-5 to figure each out based on the difference from the actual points and get .4 for (66,68) and 0 for point (70,72) so I would say, based on .4 and 0 for these two points that this is a good line of best fit.

Based on this data, for every inch in height, the arm span increases by 1.1 inches.

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complete question:

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement.

The probability to answer 5 questions correctly from 14 true or false questions is 0.1222

The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:

P(x)= nCx × p^x × q^(n-x)

Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.

n = 14 (total number of questions)

p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).

To find P(5), we substitute these values in the formula

P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222

Therefore, the answer is option D, 0.1222.

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Answer:

It's B, -2, v/5 4, and 3².

Answer:

-1 7/8

Step-by-step explanation:

First, you want to subtract 3/4 from both sides, leaving you with 3x=5x+9/4. Then, subtract 5x from each side and you get -2x=9/4. Divide 2 from each side and you get our answer, -1 and 7/8

Answer:

3/4+ 3x = 3 + 5x

3/4 - 3 = - 3x + 5x

3/4 - 12/4 = 2x

- 9/4 = 2x

-9/ 8 = x

what is the rate of increase of the function f(x) = 1/3(^3 √24)^2x

Juan can wear a total of 90 different outfits by choosing one tie, one shirt, and one pair of pants for each outfit.

To calculate the number of different outfits Juan can wear, we multiply the number of choices for each clothing item: ties, shirts, and pants.

Number of choices for ties: 3

Number of choices for shirts: 5

Number of choices for pants: 6

To find the total number of outfits, we multiply these numbers together:

3 (ties) × 5 (shirts) × 6 (pants) = 90

Therefore, Juan can wear a total of 90 different outfits by choosing one tie, one shirt, and one pair of pants for each outfit.

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Answer:

x = 20

Step-by-step explanation:

These angles are equal to each other because they are vertical angles.

Hence, we can equal the two measurements together to solve for x:

3x + 50 = 6x - 10

3x + 60 = 6x

60 = 3x

20 = x

Check your work:

3(20) + 50 = 6(20) - 10

60 + 50 = 120 - 10

110 = 110

Correct

Answer:

z=3m-2n

Step-by-step explanation:

\(\frac{1000^{m} }{100^{n} } = \frac{10^{3m} }{10^{2n} } = 10^{3m-2n}\)

Step-by-step explanation:

\( {5}^{3} \times {5}^{x} = {5}^{3 + x} = {5}^{7} \\ x = 4 \\ {( {q}^{2} )}^{y} = {q}^{6} = {q}^{2 \times y} = {q}^{6} \\ y = 3 \\ \frac{ {1000}^{m} }{ {100}^{n} } = {10}^{z} \\ z = m - n\)

Answer:

170 in²

Step-by-step explanation:

Given that :

Side, a = 14 in

Angle formed =? 60°

Take height, = l

The ratio of height to side = Sine of the angle formed

l /s = Sine 60°

Sin 60 = sqrt(3)/2

l/s = sqrt(3)/2

l = sqrt(3)/2 * s

s = 14

l = 14 * sqrt(3)/2

l = 7sqrt(3)

Area of rhombus :

l * s

7sqrt(3) * 14

= 169.74097

= 169.74 in²

= 170 (nearest square inch)

Answer:

Multiply by the inverse.

Answer: 45

Step-by-step explanation:

(15)/(1/3) is the same thing as multiplying the top (numerator), by the inverse of the bottom (denominator).

So we have the following: \(\frac{15/1}{1/3}\)

Taking the inverse means flipping the fraction. The inverse of \(\frac{1}{3}\) is \(\frac{3}{1}\). So we can keep the top, and multiply by the inverse.

\(\frac{15}{1}\) X \(\frac{3}{1}\) = 15 x 3 = 45.

Does this make sense?

The average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

Explanation:

The average acceleration of a body over a given time interval is defined as the change in velocity divided by the time interval. In this case, we are given the velocity function vA(t) for Train A, and we want to find its average acceleration over the interval 2 ≤ t ≤ 8.

To find the change in velocity over this interval, we can subtract the velocity at t=2 from the velocity at t=8:

Δv = vA(8) - vA(2) = (-120) - 100 = -220 meters per minute

To find the time interval, we can subtract 2 from 8:

Δt = 8 - 2 = 6 minutes

Now we can use the formula for average acceleration:

a = Δv/Δt = (-220)/6 = -40 meters per minute squared

Therefore, the average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

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To maximize profit, the factory should produce 2 checkers and 1 chess game, achieving a profit of 11.

The given problem involves the production planning of a wooden articles factory that specializes in checkers and chess games. The objective is to maximize the profit obtained from these games. The problem is subject to certain constraints that need to be taken into account.

The first constraint, x1 - 2x2 >= 3, represents the raw material availability for the production of the games. It states that the quantity of checkers produced (x1) minus twice the quantity of chess games produced (2x2) should be greater than or equal to 3. This constraint ensures that the raw material is efficiently utilized and does not exceed the available supply.

The second constraint, x1 + x2 <= 4, represents the production capacity limitation of the factory. It states that the sum of the quantities of checkers and chess games produced (x1 + x2) should be less than or equal to 4. This constraint ensures that the factory does not exceed its capacity to produce games.

The third constraint, x1, x2 >= 0, represents the non-negativity condition. It states that the quantities of checkers and chess games produced should be greater than or equal to zero. This constraint ensures that negative production quantities are not considered, as it is not feasible or meaningful in the context of the problem.

To determine the optimal production plan and profit, we need to solve the problem by maximizing the objective function: Z = 3x1 + 4x2. By applying mathematical techniques such as linear programming, we can find the values of x1 and x2 that satisfy all the constraints and yield the maximum profit. In this case, the optimal solution is to produce 2 checkers (x1 = 2) and 1 chess game (x2 = 1), resulting in a profit of 11 units.

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The surface area of the given shape above would be = 47.2

To determine the surface area of the solid shape above,the surface area of a cone and a cylinder is first determined and then added together.

The formula for the surface area (SA) of cone = πrs + πr²

where;

r = 1

s = 6

S.A = 3.14×1×6 + 3.14×1×1²

= 18.84+3.14

= 21.98

Formula for Surface area of cylinder = 2πr(r+h)

where;

r = 1

h = 3

SA = 2×3.14×1 (1+3)

= 25.12

Therefore, the surface area of the solid shape = 21.98+25.22 = 47.2

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Answer:

107 hamburgers

Step-by-step explanation:

Let's call hamburgers A and cheese burgers B.

We know that A + B = 321

And that the number of cheeseburgers sold was two times the number of hamburgers sold which means ->  B = 2A

So A + 2A = 321

3A = 321

Now you need to divide both sides of the equation by 3 and you get:

A= 107

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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Answer:

x = 69

Step-by-step explanation:

Knowns:

y = 69

Problem Workout

180 - z = 2y

180 - z = 2 (69)

180 - z = 138

-z = -42

z = 42

Since there is no picture, I am guessing x is the third angle.

x = 180 - (y + z)

x = 180 - (69 + 42)

x = 180 - 111

x = 69