The table shows the favourite type of film of 20 people.
Action
Horror
Comedy

Convert it to a decimal and multiply is the best way to describe rate in simple interest formula.

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number. An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.

Given

The r in the simple interest formula stands for rate.

Convert it to a decimal and multiply is the best way to describe rate in formula.

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Answer:

It is 6%, as 360 is earned each year.

Step-by-step explanation:

The simple interest earned on $6,000 at an interest rate of 4.25% in 4.5 years is $1,282.50.

percentage, a relative value indicating hundredth parts of any quantity.

To calculate the simple interest earned on $6,000 at an interest rate of 4.25% in 4.5 years, we can use the formula:

Simple Interest = Principal × Rate × Time

Where:

Principal = $6,000

Rate = 4.25% per year (expressed as a decimal, 0.0425)

Time = 4.5 years

Plugging in these values, we get:

Simple Interest = $6,000 × 0.0425 × 4.5

Simple Interest = $1,282.50

Therefore, the simple interest earned on $6,000 at an interest rate of 4.25% in 4.5 years is $1,282.50.

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The rate of change of the area of circle with respect to radius is: 8π.

The rate at which one quantity changes in relation to another quantity is known as the rate of change of a function.

Now,

Area of a circle having radius (=r) is given by: A = πr²

The rate of change of area of the circle will then be given by:

\(\frac{dA}{dr}=\pi \frac{d}{dr}(r^{2})=2\pi(r)\)​

For r = 4, \(\frac{dA}{dr}=2\pi(4)=8\pi\)

Hence, the rate of change of area of the circle when the radius is 8π.

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(i)  Standard deviation = 1.5 / sqrt(3) = 0.866 metric tons (rounded to three (ii) Approximately 2.28% of selected car models will be rejected.

(iii) The sampling distribution of the sample mean impact force will be normal.

(i) The standard deviation for a sample of size n can be calculated using the formula:

standard deviation = standard deviation of population / square root of sample size

In this case, the standard deviation of the population is 1.5 metric tons and the sample size is 3. Therefore,

standard deviation = 1.5 / sqrt(3) = 0.866 metric tons (rounded to three decimal places)

(ii) To find the percentage of selected car models that will be rejected, we need to calculate the probability that a car model has an impact force higher than 33 metric tons, given a normal distribution with mean 30 metric tons and standard deviation 1.5 metric tons. Using a standard normal distribution table or a calculator with the appropriate functions, we can find this probability to be:

P(X > 33) = P(Z > (33-30)/1.5) = P(Z > 2) = 0.0228 (rounded to four decimal places)

Therefore, approximately 2.28% of selected car models will be rejected.

(iii) The central limit theorem states that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution, even if the population distribution is not normal. In this case, the population distribution of impact forces is assumed to be normal, so the sampling distribution of the sample mean will also be normal regardless of sample size.

This is because the sample mean is an average of the underlying individual impacts, which by the law of large numbers converges to a normal distribution as the sample size increases. Therefore, the sampling distribution of the sample mean impact force will be normal.

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It's important to provide counterexamples to disprove these statements, as they are not universally true for all rings.

To show that the statement "In any ring which contains more than six elements, the left cancellation law holds" is false, we can consider the ring of 2x2 matrices over the real numbers (denoted as M(2, R)). In this ring, the left cancellation law does not hold.

For example, let A and B be two different matrices such that AB = 0. Even though A ≠ 0 and B ≠ 0, we have A × 0 = AB = 0, which violates the left cancellation law.

To show that the statement "If D is an integral domain, then D × D is an integral domain" is false, we can consider the ring of integers (Z) as an example. Z is an integral domain, but Z × Z is not.

In Z × Z, we have elements like (1, 0) and (0, 1) where their product is (0, 0), which violates the zero-divisor property of integral domains.

To show that the statement "The sum of two idempotent elements in a commutative ring with unity is idempotent" is false, we can consider the ring of integers modulo 4 (Z/4Z). In this ring, let a = 2 and b = 3.

Both a and b are idempotent since a²  = 2²  = 4 ≡ 0 (mod 4) and b²  = 3²  = 9 ≡ 1 (mod 4). However, the sum of a and b is 2 + 3 = 5 ≡ 1 (mod 4), which is not idempotent.

To show that the statement "If a is a unit in a commutative ring with unity, then a is an idempotent" is false, we can consider the ring of integers (Z). In Z, the only units are 1 and -1.

Neither of them is idempotent since 1^2 = 1 and (-1)^2 = 1, which is not equal to 1 or -1.

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Answer:

134

Step-by-step explanation:

The cost per second to power such a circuit during the peak usage period is approximately \(2.376 x 10^-6\)$/s. The cost per second to power the circuit during the peak usage period can be calculated using the following steps:

Calculate the power consumption of the device-The power consumption of the device can be calculated using the formula: Power = Voltage x Current. P = V x I, Substituting the given values:

P = 110V x 0.12A

= 13.2 W

Calculate the cost per second-The cost per second can be calculated using the formula:

Cost per second = Power x Cost per Joule

C = P x CC

= 13.2 W x 1.8 x \(10^-7\) $/J

≈ 2.376 x 10^-6 $/s

Therefore, the cost per second to power such a circuit during the peak usage period is approximately 2.376 x\(10^-6\) $/s.

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Answer:

0, 5%, 1/5, 5

5% is equal to 5÷100=0,05

1/5 is equal to 1÷5=0,2

Answer:500

explanchion: 1000/50=500

Answer:

\(90^{\circ}\)

Step-by-step explanation:

The interior angles of all triangles sum up to \(180^{\circ}\). Therefore, we can write the following equation:

\(4x+5x+9x=180\), where \(x\) is some constant.

Combining like terms, we have \(18x=180,\: x=10\).

Therefore, the angles of this triangle are \(4(10)=40^{\circ}, \: 5(10)=50^{\circ}, \: 9(10)=90^{\circ}\), the largest of them being \(\fbox{$90^{\circ}$}\).

Answer:

im pretty sure she began with 14 because if she sold half of them and then bought 7 more and then has 14 then she began with 14

Step-by-step explanation:

Answer:

14, Melanie began with 14 books.

Step-by-step explanation:

If we think the answer is 14, and she gets rid of half she has 7 left. If she buys 7 more she has 14 again. So the answer is 14 not 7, so sorry!

If you want I can try again with a different example.

I had to re-think that sorry!

Hope that helps though!

The independent variable is time on the x axis and the dependent variable is distance on the y-axis.

When making a time graph, the independent variable is the variable that is shown by the x-axis. Time will usually be the independent variable because we cannot change time so we watch for the changes in other things as time goes on.

In this case therefore, the independent variable is time which will be shown as the x-values. The dependent variables would then be the distance which would be the y-values.

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Answer:

\(\dfrac{c}{2}\)

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

\(\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2\)

Applying this logic to the given expression:

\(\dfrac{a}{2b} \cdot \dfrac{bc}{a}\)

↓ simplify multiplication of fractions

\(\dfrac{a \cdot bc}{2b \cdot a}\)

↓ rewrite to align like variables

\(\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}\)

↓ separate out variables that are divided by each other

\(\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}\)

↓ represent them as 1

\(1 \cdot 1 \cdot \dfrac{c}{2}\)

↓ rewrite without unnecessary 1's

\(\dfrac{c}{2}\)

The slope of the line that passes through the points (1,6) and (1,31) is infinity (∞).

According to the question,

We have the following information:

A line is passing through the two points: (1,6) and (1,31).

We know that the following formula is used to find the slope of the line where slope is denoted by m:

m = (y2-y1)/(x2-x1)

In this case, we have the following values:

x1 = 1 and y1 = 6

x2 = 1 and y2 = 31

Putting these values in the above formula:

m = (31-6)/(1-1)

m = 25/0

m = ∞ (infinity)

Hence, the slope of the line that passes through the points (1,6) and (1,31) is infinity (∞).

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The law of large numbers is a fundamental concept in probability theory that describes the behavior of the average of a large number of independent random variables.

It states that as the sample size increases, the sample mean will converge to the true population mean, and the sample proportion will converge to the true population proportion.

In other words, the larger the sample size, the more reliable the sample mean and proportion will be as an estimate of the true population mean and proportion. This is because the variation in the sample mean and proportion decreases as the sample size increases, and the sample becomes more representative of the population. This principle is widely used in statistics, and it underpins many statistical methods and techniques.

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Each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.

Let the cost of an adult-fare bus pass be A student-fare bus pass costs half as much as an adult-fare pass, hence, the cost of a student pass will be $129 - A.

Mathematically, this is represented as:A = 2($129 - A) $A = $258 - 2A 3A = $258 A = $86Therefore, the cost of an adult-fare bus pass is $86.A student pass costs half as much as an adult-fare pass.

Since the cost of an adult-fare pass is $86, therefore the cost of a student pass will be half of $86. Mathematically, this can be represented as:Cost of student pass = 1/2 x $86 = $43

Therefore, each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.

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Answer:

A.

Step-by-step explanation:

The slope increases from left to right.

Answer: Positive Slope

Step-by-step explanation:

If it’s from left to right in an upwards direction, it’s positive, if it’s left to right in a downwards directio, it’s negative

Answer:

g(x-3) = 2x^2 - 16x + 30

Step-by-step explanation:

To find g(x-3), we need to substitute x-3 wherever x appears in the expression for g(x), so we have:

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

Now we need to simplify this expression using algebraic rules.

First, we can expand the square by multiplying (x-3) by itself:

g(x-3) = 2(x^2 - 6x + 9) - 4(x-3)

Next, we can distribute the 2 and the -4:

g(x-3) = 2x^2 - 12x + 18 - 4x + 12

Simplifying further, we can combine like terms:

g(x-3) = 2x^2 - 16x + 30

Therefore, g(x-3) = 2(x-3)^2 - 4(x-3) simplifies to g(x-3) = 2x^2 - 16x + 30.

Answer:

g(x - 3) = 2x² - 16x + 30

Explanation:

To evaluate this function, I plug in (x-3):

\(\sf{g(x)=2x^2-4x}\)

\(\sf{g(x-3)=2(x-3)^2-4(x-3)}\)

\(\sf{g(x-3)=2(x-3)(x-3)-4(x-3)}\)

\(\sf{g(x-3)=2(x^2-3x-3x+9)-4(x-3)}\)

\(\sf{g(x-3)=2(x^2-6x+9)-4(x-3)}\)

\(\sf{g(x-3)=2x^2-12x+18-4(x-3)}\)

\(\sf{g(x-3)=2x^2-12x+18-4x+12}\)

\(\sf{g(x-3)=2x^2-12x-4x+12+18}\)

\(\sf{g(x-3)=2x^2-16x+12+18}\)

\(\sf{g(x-3)=2x^2-16x+30}\)

∴ answer = g(x - 3) = 2x² - 16x + 30

Answer:

A

Step-by-step explanation:

side opposite to smallest angle is smallest=1

Hypotenuse=2

sin 30=1/2

Answer:

Since the decoration is in the shape of a triangle, we can use the formula for the area of a triangle to solve for its height. The area of a triangle is given by:

Area = (1/2) x base x height

Let's call the height of the decoration h. We know that the base after firing is 9 inches, so we can plug in the given values and solve for h:

Area = (1/2) x 9 x h

Area = 4.5h

We don't know the exact area of the decoration, but we do know that the decoration maintains its shape after firing. This means that the ratio of the areas before and after firing is the same, and so is the ratio of the heights and bases. Since the height and base are proportional, we can write:

h / 15 = 9 / 10

Simplifying the equation, we get:

h = (9/10) x 15

h = 13.5

Therefore, the height of the finished decoration is 13.5 inches.

This questions is testing the knowledge on place value and total value.

The two to the left of the 2 in the tens place is 100 times larger than the 2 in the 100ths place in the value.

The total value of the 2 in the tens position is 20.

The total value of the 2 in the tenth position is 0.2.

To obtain the difference, divide the 20 in the tens position to the 2 in the tenths position.

20/0.2 = 100

the 2 in the tens place represents 100 times what the 2 to its left represents.

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Hello there! :)

The Distributive property states:

a(b+c)=ab+ac

So, we know what a is. It's 5.

b=3

c=0.4

5(3+0.4)

5*3+5*0.4

15+0.2

15.2

Hope it helps!

\(GraceRosalia\)

Setting x1 to zero in the equation 2x1 + 1x2 = 30 results in the value of x2 being 30.

The given equation is 2x1 + 1x2 = 30, where x1 and x2 represent variables. To find the value of x2 when x1 is set to zero, we substitute x1 with zero in the equation.

By replacing x1 with zero, we have 2(0) + 1x2 = 30. Simplifying further, we get 0 + 1x2 = 30, which simplifies to x2 = 30.

When x1 is set to zero, the equation reduces to a simple linear equation of the form 1x2 = 30. Therefore, the value of x2 in this scenario is 30.

Setting x1 to zero effectively eliminates the contribution of x1 in the equation, allowing us to focus solely on the value of x2. In this case, when x1 is removed from the equation, x2 becomes the sole variable responsible for fulfilling the equation's requirement of equaling 30. Thus, x2 is determined to be 30.

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Using the given average cost, standard deviation, and assuming a normal distribution, we can determine the probability that the cost for a randomly selected college is more than a certain value.

The average cost of tuition and fees at private nonprofit four-year colleges is $26,640 per year, with a standard deviation of $6,617. Assuming a normal distribution, let x represent the cost for a randomly selected college.
To find the probability that x is more than a certain value, we can use the Z-score formula: Z = (x - mean) / standard deviation.
To find the probability that x is more than a certain value, we can use the Z-score formula: Z = (x - mean) / standard deviation.
Let's say we want to find the probability that x is more than $30,000.
Z = (30000 - 26640) / 6617
Z = 0.051
Using a Z-table or calculator, we can find the corresponding probability to be approximately 0.4801. This means that there is a 48.01% chance that the cost for a randomly selected college is more than $30,000.
In conclusion, using the given average cost, standard deviation, and assuming a normal distribution, we can determine the probability that the cost for a randomly selected college is more than a certain value.

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2x^2 - 12x - 32

= 2 (x^2 - 6x - 16)
= 2 (x^2 + 2x - 8x - 16)
= 2 [x(x+2) - 8(x+2)]
= 2 (x+2)(x-8)

you don't necessarily have to randomly search for this, remember that in a quadratic equation ax^2 + bx + c and you need to factor a polynomial, find 2 numbers that add up to b and have the product of a x c.

We have the following:

factoring:

Therefore, the answer is:

Answer:

∠s=15.0 *

Step-by-step explanation:

Answer:

-5 hours

Step-by-step explanation:

Downsizing refers to the process of reducing the size and workforce of a company to cut costs, increase efficiency, or adapt to changing market conditions. It involves eliminating positions, reducing staff numbers, or even closing down certain business units or branches.

Downsizing can occur for various reasons, such as financial difficulties, mergers and acquisitions, technological advancements, or strategic reorganization. Companies often assess their operational costs and decide to downsize to improve their financial performance.

During the downsizing process, companies may calculate the potential cost savings by considering factors such as salaries, benefits, severance packages, and operational expenses. For example, if a company decides to eliminate 100 positions with an average salary of $50,000 per year, it could result in annual savings of $5 million.

While downsizing can help companies achieve short-term cost reductions, it often has significant implications for the affected employees, including layoffs, reduced morale, and increased workload for remaining staff. It is crucial for organizations to handle the downsizing process with sensitivity and transparency, providing support to affected employees and communicating the rationale behind the decisions.

It is important to note that downsizing should not be seen as a long-term solution, but rather as a strategic measure to address specific challenges. Companies should also explore alternatives to downsizing, such as retraining and redeploying employees, implementing productivity improvements, or seeking new business opportunities, to ensure sustainable growth and success in the long run.

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