While on vacation in Lanberry, Grace went out for a dinner that cost $108.63. If sales tax in Lanberry is 3.75% and Grace left an 18% tip on $108.63, what was the total cost of her meal?

Answer: 24°

Step-by-step explanation:

You have the opposite, the height of the building and the adjacent, the distance from the base of the building. Opposite and adjacent mean you have to use tangent. SOHCAHTOA

Take the inverse tangent on both sides

tan(Ф) = 40/90

Ф = 24°

Answer:

Rounded to the nearest whole number, your answer is 70 feet.

Step-by-step explanation:

I found it pretty funny that the person was "The individual". Guess they ran out of names! :P

Anyways:

All you need to do for this problem is multiply the feet of fabric by the number of blankets.

7.75 x 9 = 69.75

Rounded to the nearest whole number, your answer is 70 feet.

hope this helped, brainliest would be epic

The expected value of playing a single game is given as follows:

-$0.499.

As the expected value is negative, it is not a wise investment to play the NC pick 3 in the long run.

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

You have to pick three digits in correct order. Considering that for each digit there are 10 possible outcomes, the probability of winning is given as follows:

1/10 x (1/10) x (1/10) = 1/1000 = 0.001.

The probability of losing is given as follows:

1 - 1/1000 = 1000/1000 - 1/1000 = 999/1000 = 0.999.

Considering that you get $500 winning, while you lose $1 losing, the distribution is given as follows:

Hence the expected value of the distribution is given as follows:

E(X) = 500 x 0.001 - 1 x 0.999

E(X) = -$0.499.

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Answer: We can conclude that at least one of the population means has a different value than the other population means.

Step-by-step explanation:

When the null hypothesis is rejected for an analysis of variance, we can then conclude that at least one of the population proportions has a different value.

For one-way analysis of variance, it should be noted that the null hypothesis is rejected when there is sufficient evidence which is used in making the conclusion that not all the means are equal and that there is a different value.

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The percentage error of Akira's measurement is 0.66

The difference between your guess and the actual number in comparison to the actual number expressed as a percent is the percentage error.

Given

Akira is redecorating her bedroom. She misread the markings on her ruler and misjudged the width of a picture frame she purchased. The width of the frame was 4.8 centimeters.

We have to find the percent error of Akira's measurement

Given original value = 4.8

Error value  = 5.2

Percentage error = (Error value  - original value)/original value

Percentage error = (5.2 – 4.8) / 4.8

= 1.6 / 4.8

= 1/3

= 0.66

Therefore the percentage error of Akira's measurement is 0.66

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Answer:8.3

Step-by-step explanation:

I got it right

The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

Greetings from Brasil...

F(V) = - 11V² - 8

F(a + h) - F(a)]/h

let's do it by steps

F(a + h) = - 11 · (a + h)² - 8

F(a + h) = - 11 · (a² + 2ah + h²) - 8

F(a + h) = - 11a² - 22ah - 11h² - 8

and

F(a) = - 11 · (a)² - 8

F(a) = - 11a² - 8

Then

F(a + h) - F(a)]/h

{- 11a² - 22ah - 11h² - 8 - [- 11a² - 8]}/h

[- 11a² - 22ah - 11h² - 8 + 11a² + 8]/h

[- 22ah - 11h²]/h

h · [- 22a - 11h]/h

Answer:

C -1

Step-by-step explanation:

in such a case the simplest way is to simply try the 4 numbers and see :

x² - 3x - 4 = |x + 3| - 2

x² - 3x - 2 = |x + 3|

A x = -4

(-4)² - 3×-4 - 2 = |-4 + 3|

16 + 12 - 2 = 1

26 = 1

wrong.

B x = -3

(-3)² - 3×-3 - 2 = |-3 + 3|

9 + 9 - 2 = 0

16 = 0

wrong.

C x = -1

(-1)² - 3×-1 - 2 = |-1 + 3|

1 + 3 - 2 = 2

2 = 2

correct.

D x = 4

4² - 3×4 - 2 = |4 + 3|

16 - 12 - 2 = 7

2 = 7

wrong.

This is normal question on Population growth.

Take the equation of population growth exponentially which is \(y=a(b)^x\)

Here, we have an exponential function of the form

\(y=a(b)^x\)

Parameters here are:

y, population of San Diego

x, number of years since 2012

So

Part a

2012 represents x=0, y=1,309,000

a=1,309,000

For the year 2016 ⇒ x=2016-2012=4 years

y=1,375,000

Therefore

\(1,375,000=1,309,000 (b)^4\)

Solving for b

b=1.0124

⇒Percentage, (b-1)×100=r=1.24%

Part b

2016-2020

Here

a=1,375,000

x is the number of years since 2016

For the year 2020 ⇒ x=2020-2016=4 years

y=1,386,000

After Substitution

\(1,38,600=1,375,000(b)^4\);

Solving for b

b=1.0020

Percentage= b-1=r=0.20%

Part c

Compare the growth rate each period

2012-2016 --> r=1.24%

2016-2020 --> r=0.20%

That means  in the second period the growth rate has decreased than the first period

Part d

The current growth rate is r=0.20%

\(y=1,375,000(1.002)^x\)

where

x is the number of years since 2016

For y=1,500,000

\(1,500,000=1,375,000(1.002)^x\)

Applying log on both sides

we get, x=43.5 years

Then the year is 2016+43.5=2059.5≅2060

This is normal question on Population growth.

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Answer:

false

Step-by-step explanation:

he needs at least 45.5 to fill his 13 gallon tank.

Answer: the slope of perpendicular lines are opposite and reciprocal.

First line slope is 3/2. The slope of the second line is - 2/3

First line slope is 2. The other line slope is -1/2

Step-by-step explanation:

Answer:

Barometer i think im not sure

Step-by-step explanation:

Pressure is a mechanical (non-electrical and non-magnetic) measure. All mechanical measures can be derived from just three basic mechanical units. Which three we use is actually arbitrary. This means that using three we can produce or define all other mechanical measures by multiplying or dividing some combination of the chosen three.

Most measuring systems use time, length, and mass as the basic three in which case pressure would be mass / (time * time * length * length). Compare that with kilogram per (meter*meter * second*second) which is also called a Pascal.

Another measuring system might use time, length, and force as the three basic measures. Here mass is omitted in place of force. Nothing is lost because mass and force can be written in terms of the other with the help of time and length. In this case pressure would be force / (length*length). Compare this with Newton per meter*meter which also defines a Pascal.

How pressure is measured in practice is another good question. The standard method is to use some device that employs a medium to compare the unknown pressure to some known familiar pressure. Mercury tubes illustrate this nicely and are still used in laboratories. They work because mercury is a very dense fluid. A lighter fluid can push upon and move a column of mercury but cannot pass through it.

Measuring the movement of mercury when a known pressure is applied to one end reveals the pressure at the other end. The persistence of millimeters of mercury (mmHg) as a unit for reporting pressure is testament to this method. Other pressure gages work by employing something like springs or strain sensors calibrated to mimic the readings that a mercury tube would report.

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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9514 1404 393

Answer:

  x = {-0.5-√1.25, -0.5+√1.25, 2, -0.5+i√0.75, -0.5-i√0.75}

Step-by-step explanation:

I like to use a graphing calculator to find clues as to the roots of higher-degree polynomials. Here, we see that x=2 is the only real rational root. Dividing that out by synthetic division, we see the remaining quartic factor is ...

  2x^5 -6x^3 -4x^2 -2x +4 = 0

  2(x -2)(x^4 +2x^3 +x^2 -1) = 0

We can recognize that the quartic factor is actually the difference of two squares:

  x^4 +2x^3 +x^2 -1 = (x^2 +x)^2 -1 = 0

So it resolves to two quadratic factors.

  (x^2 +x +1)(x^2 +x -1) = 0

One will have real roots, as shown by the graph. The other will have complex roots.

  x^2 +x + 1/4 = 1 +1/4 . . . . complete the square for the factor with real roots

  (x +1/2)^2 = 5/4

  x = -1/2 ± √(5/4) . . . . . . irrational real roots

__

  x^2 +x = -1 . . . . . . . . . . the quadratic factor with complex roots

  (x +1/2)^2 = -1 +1/4 . . . complete the square

  x = -1/2 ± i√(3/4) . . . . irrational complex roots

__

In summary, the values of x that satisfy the equation are ...

 x = 2

  x = -1/2 ± √(5/4)

  x = -1/2 ± i√(3/4)

Answer: 2 hours

Step-by-step explanation:

If they both walk 5 miles an hour combined, then it would take 2 hours for them to walk 10 miles.

hope this helps

Answer:

\(5 { \times 54}^{2} \)

An combined area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.

Every normally distributed random variable has a slightly different distribution shape, the only way to find areas using a table is to standardize the variable - transform our variable so it has a mean of 0 and a standard deviation of 1. How do we do that? Use the z-score!

Z = ( x - μ)/σ

if the random variable X has a mean μ and standard deviation σ,

then transforming X using the z-score creates a random variable with mean 0 and standard deviation 1!

With that in mind, we just need to learn how to find areas under the standard normal curve, which can then be applied to any normally distributed random variable.

An area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.

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Every normally distributed random variable has a slightly different distribution shape, the only way to find areas using a table is to standardize the variable - transform our variable so it has a mean of 0 and a standard deviation of 1. How do we do that? Use the z-score!

Z = ( x - μ)/σ

if the random variable X has a mean μ and standard deviation σ,

An area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.

Answer:

3

Step-by-step explanation:

Answer:

The smallest sample size required to obtain the desired margin of error is of 17.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.9}{2} = 0.05\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.05 = 0.95\), so \(z = 1.645\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

Which of these is the smallest approximate sample size required to obtain the desired margin of error?

The desired margin of error is 20, so \(M = 20\)

We have that \(\sigma = 50\).

The smallest sample size is n. So

\(M = z*\frac{\sigma}{\sqrt{n}}\)

\(20 = 1.645*\frac{50}{\sqrt{n}}\)

\(20\sqrt{n} = 50*1.645\)

\(\sqrt{n} = \frac{50*1.645}{20}\)

\((\sqrt{n})^2 = (\frac{50*1.645}{20})^2\)

\(n = 16.9\)

Rounding up

The smallest sample size required to obtain the desired margin of error is of 17.

9514 1404 393

Answer:

Step-by-step explanation:

In general, you solve equations like these by getting the function of the variable by itself on one side of the equal sign. Then you use the inverse function to find the argument of the function. As in problem 3, you may have to go another step or two to get from the value of the function argument to the value of the variable.

1. We need to find sin(θ), then use the arcsine function.

  sin(θ) -0.832 = 0 . . . . given

  sin(θ) = 0.832 . . . . . . add 0.832 to both sides

  θ = arcsin(0.832) ≈ 56.305° . . . . . . use the inverse sine function to find θ

  θ ≈ 56°

__

2. 1/2cos(θ) = 0.214 . . . . given

  cos(θ) = 0.428 . . . . . . multiply by 2

  θ = arccos(0.428) ≈ 64.659° . . . . use the inverse cosine function

  θ ≈ 65°

__

3. 3tan(θ -20°) = 1.43 . . . . given

  tan(θ -20°) = 0.47666... . . . divide by 3

  θ -20° = arctan(0.47666...) . . . . use the arctan function to find θ-20°

  θ -20° ≈ 25.486°

  θ = 45.486° . . . . . . . add 20°

  θ ≈ 45°

_____

Additional comments

Scientific and graphing calculators often require use of a 2nd or SHIFT key to access the inverse trig functions. The inverse function often uses the same key on the calculator. These are generally marked with a -1 superscript: a key might be marked with sin, for example, with sin⁻¹ as its alternate function.

The trig functions of a calculator will usually deal with angles in any of several units. The most common of these are degrees, grads, and radians. Usually, you are required to set the calculator mode to make use of one or the other of these angle measures. For this problem, you need to be sure the calculator is set to degrees mode.

6 cos(π/2 t) is the best model for the position of the weight.

The motion of the weight on the spring can be modeled by a sine or cosine function because it oscillates back and forth around its equilibrium position.

We know that, the weight is initially pulled down 6 inches from its equilibrium position, so the function should have an amplitude of 6.

The time it takes for the spring to complete one oscillation is 4 seconds, so the period of the function is 4 seconds.

The general form of a sine or cosine function with amplitude A and period T is:

f(t) = A sin(2πt/T) or f(t)

= A cos(2πt/T)

Substituting the given values,

we get:

f(t) = 6 sin(2πt/4) or f(t)

= 6 cos(2πt/4)

Simplifying, we get:

f(t) = 6 sin(π/2 t) or f(t)

= 6 cos(π/2 t)

Therefore,

the function that best models the position of the weight is

s(t) = 6 cos(π/2 t).

So, the answer is option (D).

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Answer:

Graph attached.

Step-by-step explanation:

The product of slope of line (i) and slope of line (ii) should be equal to -1 (product of slopes of two perpendicular lines = -1)

i.e

Slope of line (i) × 2 = -1

Slope of line (i) = \(-\frac{1}{2}\)

To find the equation of line (i), we need another point (x,y) on the line.

Slope (m) = change in y ÷ change in x = \(\frac{y - -3}{x - 0} = -\frac{1}{2}\)

y = \(-\frac{1}{2} x\) - 3

*The graph of this line is attached here below.

Jahna, this is the solution:

As you can see in the graph, the independent variable (Time) belongs on the x-axis and the dependent variable (Distance) belongs on the y-axis.

Therefore, the statement that is correct is:

B. The time values are the independent quantities and the distance values are the dependent quantities.

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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The conclusion hypothesis is to reject the null hypothesis and accept the alternative hypothesis. The z score of 0.14 is in the rejection area

What is hypothesis?

In statistics, hypothesis refers a testable statement about the relationship between two or more variables or a proposed variable.

Here we have given that two machines fill 32-oz cartons with cereal. the quality control manager believes the two machines are not filling the cartons with the same amount of cereal. samples from each line were taken and the following results were obtained. assume that the assumptions and conditions for inference with a two- sample t-test are met. at the 0.01 level of significance, test the claim that the population mean for machine 1 is different from the population mean for machine 2.

And we need to find the conclusion hypothesis.

While we looking into the given question, we have identified the following values,

Sample mean: Machine 1 25 31.8 oz 2.2 oz

Sample SD: Machine 2 36 30.9 OZ 1.98 oz

So, the hypothesis is calculated as, the claim is the population mean of cereal cartons from machine 1 is larger than that from the machine 2

Null hypothesis: H0 : The population mean of cereal cartons for machine 1 and machine 2 is same

Alternative hypothesis H1: The population defines the statistical inference experiment.

So, the conclusion of hypothesis is, the critical value (cutoff point) is 2.353. In left-tail hypothesis testing, any z score less than the critical value will be rejected. Since 0.14 is less than 2.353, we reject the null hypothesis. We accept the alternative hypothesis.

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In the given Quadrilateral, The measure of ∠x=110°.

what are quadrilaterals?

Quadrilaterals are four-sided polygons. They are two-dimensional shapes with four straight sides, four vertices, and four angles which have sum of 360°. Quadrilaterals can have parallel sides, opposite sides that are congruent, opposite angles that are congruent, and diagonals that bisect each other. Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.

Now,

For given Quadrilateral

three angles given are 128°, 82° and 40° and 4th angle=x°.

To find x

As we know

Sum of all interior angles of a quadrilateral=360°

128°+82° +40° +x°=360°

x=360-250

x=110°

hence,

          the measure of ∠x=110°.

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Answer:

f(2) = -5

Step-by-step explanation:

f(2) means that x = 2.

We are trying to find the y-value when x = 2.

When x = 2, we see from the graph that our y-values is equal to -5.

Therefore, f(2) = -5

Answer:

Y = - 5/3 x - 5

Step-by-step explanation: