The number of sticks of gum varies directly as the number of packages. There are 36 sticks of gum in 2 packages. Suppose you have 5 packages of gum. The direct variation equation to determine how many sticks you have is ________giving you _______sticks of gum

The z score that corresponds to the 90th percentile is 1.28. Option D

A z-score (also called a standard score) gives you an idea of how far from the mean a data point is. But more technically it’s a measure of how many standard deviations below or above the population mean a raw score is.

The 90th percentile refers to the value above 90 percent of the data. This is illustrated in the figure.

Therefore, using a z-table (also attached) or a technology, we can solve that  getting the  z=1.28.

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Answer:

arithmetic sequence

Step-by-step explanation:

there is a common difference d between consecutive terms , that is

d = 6 - 11 = 1 - 6 = - 5

therefore the sequence is arithmetic.

The area of the triangle is approximately 56.08 square units having the measurements as C = 55°43', a = 6. 5, and b = 14.

The formula for finding the area of a triangle is given by:

Area of triangle = (1/2) × base × height

Here, base of the triangle is b, and the corresponding height is h.

We know that sin C = (h/b)

sin 55°43' = (h/14)

h = 14 sin 55°43'

Using the law of cosines, we can find the value of c (the other side of the triangle).

We have a² = b² + c² - 2bc cos A

Therefore,c² = a² + b² - 2ab cos C

c² = 6.5² + 14² - 2(6.5)(14)cos 55°43'c²

≈ 141.37c

≈ 11.89

Now we can use the formula to find the area of the triangle:

Area of triangle = (1/2) × base × height

Area of triangle = (1/2) × 14 × 14 sin 55°43'

Area of triangle ≈ 56.08 square units

Therefore, the area of the triangle is approximately 56.08 square units.

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The amount you would pay altogether if you borrow $500 for  5 years at

an annual interest rate of 7% is $945.

The amount you would pay altogether is the sum of the amount borrowed and the interest.

Total value of the debt = interest + amount borrowed

Interest = $700 x 7% x 5 = $245

Total value of the debt = $245 + $700 = $945

Answer:

D

Step-by-step explanation:

You have to multiply the functions

so (x+4)(3x^2-7)

Use the FOIL method to multiply them

3x^3+12x-7x-28 which is d

Multiply the number of students (10) by the percentage that say that they use credit cards because of the rewards program (32%)

First, write the percentage in decimal form, by dividing it by 100:

32/100 = 0.32

Now multiply:

10 x 0.32 = 3.2 students

More than 2

So just use Cyclander formula. That’s how you solve!

Answer:

Part A)

\(\displaystyle V=\frac{1}{12}\pi h^3\)

Part B)

\(\displaystyle \frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}\)

Part C)

\(\displaystyle \frac{dh}{dt}\approx0.4\text{ feet per second}\)

Step-by-step explanation:

Please refer to the attachment.

We know that the conical tank has a height of 10 feet and a radius of 5 feet.

The rate at which water is being drained through a hole in the vertex is 5 cubic feet per second.

Part A)

Recall the volume formula for a cone:

\(\displaystyle V=\frac{1}{3}\pi r^2h\)

Since this is a cone, we can draw two similar triangles (refer to the attachment). Then, by properties of similar triangles, we can write:

\(\displaystyle \frac{10}{5}=\frac{h}{r}\)

Therefore:

\(\displaystyle 2=\frac{h}{r}\)

So:

\(\displaystyle r=\frac{h}{2}\)

Substituting this into our formula yields:

\(\displaystyle V=\frac{1}{3}\pi \big( \frac{h}{2} \big)^2h\)

Simplify:

\(\displaystyle V=\frac{1}{12}\pi h^3\)

Part B)

Let’s take the derivative of both sides with respect to t. So:

\(\displaystyle\frac{d}{dt}\big[V\big]=\frac{d}{dt}\big[\frac{1}{12}\pi h^3}\big]\)

The left will simply be dV/dt. We can move the coefficient from the right:

\(\displaystyle \frac{dV}{dt}=\frac{1}{12}\pi\frac{d}{dt}\big[h^3\big]\)

Implicitly differentiate:

\(\displaystyle \frac{dV}{dt}=\frac{1}{12}\pi(3h^2\frac{dh}{dt})\)

Simplify. So, our derivative is:

\(\displaystyle \frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}\)

Part C)

We want to find the rate of change of the water depth (in other words, dh/dt) when h=4.

Since our water is being drained at a rate of 5 cubic feet per second, this means that dV/dt=5.

So, substituting, we get:

\(\displaystyle 5=\frac{1}{4}\pi(4)^2\frac{dh}{dt}\)

Simplify:

\(\displaystyle 5=4\pi\frac{dh}{dt}\)

Therefore:

\(\displaystyle \frac{dh}{dt}=\frac{5}{4\pi}\approx0.3978\approx 0.40\)

So, the change of the water depth is about 0.4 feet per second.

Answer:

A im pretty sure

Step-by-step explanation:

mark me brainliest please lol

The annual income of Juan Vance is $12,955.17.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

In order to pay for Social Security and Medicare, the Federal Insurance Contributions Act(FICA) mandates payroll deductions from both employers and employees.

Given, Juan Vance's Weekly salary is $231.67.

∴ Annually Juan earns $(52×231.67) = $12,046.84.

FICA deducts 7.51% from it and then combines another 7.51% with the employee,

∴ The net annual income of Juan Vence is

= [{12046.84 - (7.51/100)×12046.84 + {(7.51 + 7.51)/100}×12046.84}]

= (12046.84 - 904.71 + 1813.04}.

= $12,955.17

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Answer:

the answer is graph 1

Step-by-step explanation:

Answer:

n = 5

Step-by-step explanation:

180(n − 2) = s

180(n − 2) = 540

180n - 360 = 540

180n - 360 + 360 = 540 + 360

180n = 900

(1/180) 180n = 900 (1/180)

n = 5

Answer and Step-by-step explanation:

The sum of 20 and 8 would look like

20 + 8

Then we have to subtract the product of 3 and 5 from the sum of 20 and 8.

(20 + 8) - 3(5)

^That is the expression^

The answer, when you evaluate the expression, is:

28 - 15 = 13

#teamtrees #PAW (Plant And Water)

Answer:

No.

Step-by-step explanation:

The ratios 12:7 and 2:1 are not equivalent.

If you divide 2/1, the result would be 2.

12/7 would give you 1.71 which does not equal 2.

To make this pair of ratios equivalent, just simply change the first ratio to 12:6.

\( \sf \: No. \: of \: touch \: downs \: \div \: No. \: of \: games\)

\( \tt45 \div 16 = > \frac{45}{16} = > 2.8125 \: \: \\ \tt \: or \\ \tt \: 3 \: when \: rounded \: off\)

Based on the information given the unit rate is: 2.81.

In order to determine the unit rate we will have to divide the touch down by the number of games.

Using this formula

Unit rate=Number of touch down/Number of games

Where:

Number of touch down=45

Number of games=16

Let plug in the formula

Unit rate=45/16

Unit rate=2.81

Inconclusion the unit rate is: 2.81.

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Answer:

\(0\leq x<\infty\)

Step-by-step explanation:

The function \(y=\sqrt{x}\) is not defined for negative numbers in the domain as they produce non-real results. Therefore, all positive numbers including 0 are included in the domain, so the domain of the function would be \(0\leq x<\infty\).

I've attached a diagram to help you visualize the domain.

Answer:

Step-by-step explanation:

Joshua wants to buy a flat-screen TV that costs $625. He saves $62.50 each week to buy the TV. In how many weeks will he have enough money to make his purchase?

A. 8

B. 9

C. 10

D. 11

cost of television divided by weekly savings = number of weeks

625 : 62.50 = 10 weeks

We cannot definitively say which of them is more likely to be accepted based solely on their exam scores. We can use z-scores to compare the performance of Kyle and Ryan.

For Kyle:

z-score = (x - mean) / standard deviation = (489 - 400) / 67 = 1.33

For Ryan:

z-score = (x - mean) / standard deviation = (39 - 35) / 2 = 2

Comparing the z-scores, we see that Ryan performed better relative to his peers than Kyle did. This is because Ryan's z-score of 2 is larger than Kyle's z-score of 1.33.

However, it's important to note that acceptance into a university is based on multiple factors, not just exam scores. Therefore, we cannot definitively say which of them is more likely to be accepted based solely on their exam scores.

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It will be valued about £886 after 10 years

The art piece originally costs £600.

And it appreciates at a rate of 3.97% each year.

And we want to find the value of the art after 10 years.

We can write an exponential function to model the situation. The standard exponential function is given by:

Where t is the time in years.

Since it appreciates at a rate of 3.97% each year, the value after each year will be (100% + 3.97%) or 103.97%.

103.97% = 1.0397. So, r = 1.0397:

Our a is the initial value. Therefore:

Then the value of the piece of art after 10 years is:

It will be valued about £885.59 after 10 years

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Answer:

C

Step-by-step explanation:

Graph it and you will see it is a function and since you are adding them it is also a relation. Good luck.

Answer:

it represents both a relation and a function.

Step-by-step explanation:

To find the 4th order Newton's divided-difference interpolating polynomial for f(x)=ln(x) with x=1,4,5,6,8, we first need to calculate the divided differences:

A. (a) The 4th order Newton's divided-difference interpolating polynomial for the function f(x) = ln(x) using the given data points is:

P(x) = ln(1) + (x - 1)[(ln(4) - ln(1))/(4 - 1)] + (x - 1)(x - 4)[(ln(5) - ln(4))/(5 - 4)(5 - 1)] + (x - 1)(x - 4)(x - 5)[(ln(6) - ln(5))/(6 - 5)(6 - 1)] + (x - 1)(x - 4)(x - 5)(x - 6)[(ln(8) - ln(6))/(8 - 6)(8 - 1)]

B. (a) To find f(x) at x = 7 and x = 9 using the interpolating polynomial, substitute the respective values into the polynomial expression P(x) obtained in the previous part.

Explanation:

A. (a) The 4th order Newton's divided-difference interpolating polynomial can be constructed using the divided-difference formula and the given data points. In this case, we have five data points: (1, ln(1)), (4, ln(4)), (5, ln(5)), (6, ln(6)), and (8, ln(8)). We apply the formula to calculate the polynomial.

B. (a) To find the value of f(x) at x = 7 and x = 9, we substitute these values into the polynomial P(x) obtained in the previous part. For x = 7, substitute 7 into P(x) and evaluate the expression. Similarly, for x = 9, substitute 9 into P(x) and evaluate the expression.

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Answer:

absolute value function

Step-by-step explanation:

hope this helps

Answer:

nice

Step-by-step explanation:

Answer:

The answer is 293.57.

Hope you do great!

Step-by-step explanation: The way you do it is by seeing the 100% of any number and subtracting the 30% off and then divide the number by 70% and then multiply that number by the original 100%!

A favor the right as shown at equilibrium the correct choice is C. Both 1 and 2.

The provided reaction and the \(pKax_{123}\) of \(hn3\), the factors that favour the reaction proceeding to the right at equilibrium.

\(NgBr\) + \(N3\)- ⇌ \(Ng\)+ + \(BrN3\)

\(BrOH\) + \(OH\)- ⇌ \(BrO\)- + \(H2O\)

To favor the right side of a reaction at equilibrium, factors such as stronger acids or bases, changes in temperature or pressure, and the relative stability of the reactants and products these factors for each reaction:

\(NgBr\) + \(N3\)- ⇌ \(Ng\)+ + \(BrN3\):

The \(PKa\) of \(HN3\) (around 5) that \(N3\)- is a stronger base than \(NgBr\), so it would favor the right side.

\(BrOH\) + \(OH\)- ⇌ \(BrO\)- + \(H2O\):

\(OH\)- is a stronger base than \(BrOH\), indicating that it would favor the right side.

Additionally, water (\(H2O\)) is a more stable compound than \(BrO\)-, further favoring the right side.

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Answer:

5^-18

Step-by-step explanation:

here is the answer please mark me as the brainliest

By substitution, the solution of the system of equations, x + 3y = 7 and 2x - 4y = 24, is (10 , -1).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

x + 3y = 7     (equation 1)

2x - 4y = 24     (equation 2)

Using the first equation, find the value of one variable, lets say x, in terms of the other.

x + 3y = 7     (equation 1)

x = 7 - 3y

Substitute the equation of x to the second equation.

2x - 4y = 24     (equation 2)

2(7 - 3y) - 4y = 24

14 - 6y - 4y = 24

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

14 - 6y - 4y = 24

-6y - 4y = 24 - 14

-10y = 10

y = -1

Substitute the value of y in the equation of x.

x = 7 - 3y

x = 7 - 3(-1)

x = 7 - (-3)

x = 10

Hence, the solution of the given system of equations is (10 , -1).

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The statement that could be true for the function g is: OA. g(-13) = 20.A is correct answer.

To determine which statement could be true for the function g, we need to examine the given information about the domain, range, and specific function values.

Given information:

Domain: -20 ≤ x ≤ 5

Range: -5 ≤ g(x) ≤ 45

g(0) = -2

g(-9) = 6

Let's analyze each statement:

OA. g(-13) = 20

Since the domain is -20 ≤ x ≤ 5, and -13 falls within this range, it is possible for g(-13) to be 20. This statement could be true.

OB. g(7) = -1

The domain is limited to -20 ≤ x ≤ 5, and 7 is outside this range. Therefore, g(7) is not defined within the given domain. This statement cannot be true.

OC. g(0) = 2

From the given information, we know that g(0) = -2. Therefore, g(0) cannot be 2. This statement cannot be true.

OD. g(-4) = -11

Since the domain is -20 ≤ x ≤ 5, and -4 falls within this range, it is possible for g(-4) to be -11. This statement could be true.

Based on the given information, the statement that could be true for the function g is:

OA. g(-13) = 20

Please note that there may be other statements that could be true for the function g, but based on the given options, option OA is the most plausible one. A is correct answer.

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Brock is at a distance of 621/40 miles away from home.

Here, we are given that Brock rides his bike 22 1/8 miles to the nature preserve.

This means that he is now 22 1/8 miles away from his home. Now, he starts on his way home and after 16 1/5 miles, he stops at a deli for lunch.

Thus, he is now 22 1/8 - 16 1/5 miles away from his home.

To subtract the fractions we need to convert the mixed fractions into improper fractions, which can be done as follows-

22 1/8 = (22*8 + 1)/8

= 177/8

and 16 1/5 = (16*5 + 1)/5

= 33/5

Thus, the expression becomes-

177/8 - 33/5

now, we need to make the denominators of each fraction so that we can subtract them.

= (177*5)/40 - (33*8)/40

= 885/40 - 264/40

= 621/40

Thus, Brock is at a distance of 621/40 miles away from home.

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