Short division
Long division
Dividing

Using the concepts of equation it is concluded that Theo was saving money from 6 weeks and he had $6 in savings when he started to save the money.

An equation is a mathematical expression comprised of two expressions linked by an equal sign.

Let Theo have x amount of money in the savings where 0 < x > 8.

He saves $8 per week until he has $52 including his savings.

Let y be the no. of weeks.

So, this given condition can be written as:

8y + x = 52

8y = 52 - x

As we know, y can't be negative or have decimal values, as here weeks can only be in natural numbers (y = 1, 2, 3...…).

From the obtained equation and above statement it is clear that the value of 52 - x must be a multiple of 8.

The closest multiples of 8 for the above condition are 48 or 56.

The value of x to obtain 48 is 4 and value of x to obtain 56 is - 4.

Since 0 < x > 8, we get that:

x = 6

Put the value of x = 6 in the equation 8y = 52 - x to obtain:

8y = 52 - 6

8y = 48

y = 6

Therefore, Theo was saving money from 6 weeks and he had $6 in savings when he started to save the money.

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The entomologist conducted a hypothesis test regarding the proportion of male fireflies unable to produce light due to a genetic mutation. After conducting the test, the null hypothesis was rejected.

Hypothesis testing is a statistical method used to evaluate claims or hypotheses based on sample data. In this case, the entomologist aimed to investigate the proportion of male fireflies affected by a genetic mutation that prevents them from producing light. The claim made in the journal was that the proportion is fewer than 17 in ten thousand.

The entomologist conducted the hypothesis test by formulating null and alternative hypotheses. The null hypothesis assumed that the proportion of affected male fireflies is equal to or greater than 17 in ten thousand, while the alternative hypothesis suggested that the proportion is indeed lower than 17 in ten thousand.

Using sample data, the entomologist analyzed the data and calculated the test statistic and its corresponding p-value. The p-value represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

If the p-value is smaller than the chosen significance level (α), typically 0.05 or 0.01, the null hypothesis is rejected in favor of the alternative hypothesis. In this scenario, the entomologist concluded that the null hypothesis should be rejected, providing evidence to support the claim made in the scientific journal.

Therefore, based on the hypothesis test results, the entomologist's conclusion in non-technical terms would be that there is sufficient evidence to suggest that fewer than 17 in ten thousand male fireflies are unable to produce light due to the genetic mutation.

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The percentage of increase in rate is 25%  

The percentage is a value that is expressed as a fraction of 100. In simple words, the percentage means, a part per hundred. To calculate the percent of a number, divide the number by the whole and multiply by 100. It is denoted by the symbol “%”.    

Here we have

The rate of petrol was Rs. 120  

After three months the rate of petrol was Rs.150

The increased rate = Rs.150 - Rs. 120 = 30

The percentage of increase = ( Increased rate/ initial rate) × 100

=  \(\frac{30}{120} \times 100\)  = 25%      

Therefore,

The percentage of increase in rate is 25%

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Answer:

25 cm^2

24 cm

Step-by-step explanation:

5*5 = 25 cm^2

Make sure not to forget the cm^2, otherwise you will get it wrong

10 + 14 = 24 cm

this is only perimeter so only cm

Answer:

25 cm²

24 cm

Step-by-step explanation:

Area of a Square: A = lw

Since the sides of a square are all the same, we have A = 5(5) = 25 cm²

Perimeter of a Rectangle: 2w + 2l

Simply plug it in:

P = 2(7) + 2(5)

P = 14 + 10

P = 24 cm

Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

Answer:

hi shaurya

Step-by-step explanation:

When the length and width of a rectangle change by a factor of 6, the area of the rectangle changes by a factor equal to the product of the changes in length and width. Since both the length and width are multiplied by 6, the area will be multiplied by 6 * 6, which is equal to 36.

This means that the area of the rectangle will increase by a factor of 36. In other words, the new area will be 36 times larger than the original area. This is because the area of a rectangle is calculated by multiplying the length by the width, so when both dimensions are multiplied by 6, the resulting area is the product of 6 * 6, which is 36 times larger than the original area.

For example, if the original area of the rectangle was 10 square units, after the change, the new area will be 10 * 36 = 360 square units. Therefore, the area of the rectangle is significantly increased when both the length and width are multiplied by the same factor.

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Answer:

A

Step-by-step explanation:

Just A!

Answer:

Step-by-step explanation:

Never capitalize the seasons

Answer:

7.14

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The number of ways to select a simple random sample of size 5 from a population of 7 children in a family is equal to 21ways.

As given in the question,

Number of children in the family 'n' = 7

Number of simple random sample of size  = 5  ( without replacement )

Number of ways to select the children defines a population

= ⁷C₅

= ( 7! ) / ( 7 - 5 )! ( 5! )

= ( 7 × 6 × 5! )/ ( 2! ) ( 5! )

= 7 × 3

= 21 ways

Therefore, the number of ways to select children of simple random sample of size 5 is equal to 21ways.

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The boundary lines are y > -3x + 4: dotted line and  y <= 8x + 1: solid line

From the question, we have the following parameters that can be used in our computation:

y > -3x + 4

y <= 8x + 1

The boundary line for the inequality "<" is a dotted line, which means that the endpoint is not included in the solution set.

The boundary line for the inequality ">=" is a solid line, which means that the endpoint is included in the solution set.

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The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Inequalities are used for the non equal comparison of numbers and variables.

Given the inequalities:

y ≥ (1/2)x - 1     (1)

and

x - y > 1     (2)

The graph of the inequality is attached. Shannon's graph is correct.

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The ordered pair that is a solution to the inequality:

y > (1/4)*x + 5

is (4, 7)

Here we have the inequality:

y > (1/4)*x + 5

To check if an ordered pair is a solution, we just need to replace the values of the ordered pair on the inequality and see if it is true.

For example, for (12, 8)

We will get:

8 > (1/4)*12 + 5

8 > 3 + 5

8 > 8

This is false, so (12, 8) is not a solution.

The pair that is a solution is:

(4, 7)

7 > (1/4)*4 + 5

7 > 1  + 5

7 > 6

This is true.

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Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Using trigonometric relations, it is found that option A is correct, that is:

\(\sin{x} = \frac{2}{\sqrt{13}}\)

---------------------

Tangent of an angle is sine of this angle divided by the cosine of this angle, thus:

\(\tan{x} = \frac{\sin{x}}{\cos{x}}\)

Another important relation is:

\(\sin^2{x} + \cos^2{x} = 1\)

Tangent is 2/3, that is:

\(\tan{x} = \frac{2}{3}\)

Which means that:

\(\frac{\sin{x}}{\cos{x}} = \frac{2}{3}\)

We want to find the sine, so we write the cosine as a function of the sine, that is:

\(2\cos{x} = 3\sin{x}\)

\(\cos{x} = \frac{3\sin{x}}{2}\)

Replacing in the equation for the relation:

\(\sin^2{x} + \cos^2{x} = 1\)

\(\sin^2{x} + (\frac{3\sin{x}}{2})^2 = 1\)

\(\sin^2{x} + \frac{9\sin^2{x}}{4} = 1\)

\(\frac{13\sin^{2}{x}}{4} = 1\)

\(\sin^2{x} = \frac{4}{13}\)

\(\sin{x} = \pm \sqrt{\frac{4}{13}}\)

First quadrant, thus positive:

\(\sin{x} = \frac{2}{\sqrt{13}}\)

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Answer: A

Step-by-step explanation:

The number of people are 72.

Highest Common Factor is the full name for HCF in mathematics.

According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.

Least Common Multiple is the full name for LCM in mathematics.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.

We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.

Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.

We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:

288 / x² = (16*18) / x² = 288 / x²

Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.

As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.

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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.

The total area of the cake is:

16 inches x 18 inches = 288 square inches

To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:

√(288 square inches) ≈ 16.97 inches

Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:

Each piece of cake will be approximately 16 inches by 16 inches.

To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:

288 square inches ÷ (16 inches x 16 inches) = 18

Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

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The probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

According to the given question.

A standard pair of dice is rolled.

So, the sample sapce for rolling a pair of dice = {(1,1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4),(5, 5),(5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

⇒ Total number of outcomes = 36

And, the outcomes for getting a sum of five on a sandard pair of six sided dice = {(2, 3), (3, 2), (4, 1), (1, 4)}

⇒ Total number of favorable outcomes = 4

As we know that " probability is the ratio of total number of favorable outcomes to the total number of outcomes".

Therefore,

The probability of rolling a sum of 5 on a standard pair of six-sided dice

= 4/36

= 1/9

Hence, the probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

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The area of the given vectors is 3√35

Given vectors are V = <1, 5, 0>

U = <2, 1, -3>

Calculating the cross product:

U x V = <u₂v₃ - u₃v₂, u₃v₁ - u₁v₃, u₁v₂ - u₂v₁>

U x V = <(1)(0) - (-3)(5), (-3)(1) - (2)(0), (2)(5) - (1)(1)>

= <15, -5, 9>

Area ||U x V||=√15²+25+81

=√315

=3√35

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Answer:

15

I HOPE IT WILL HELP YOU. .....

Answer:  5 2/5, or 5.4

Step-by-step explanation:

9/x = 5/3

5x = 27

x = 27/5, or 5 2/5

2/5 = 0.4

5.4

----

9/5.4 = 1.666 . . .

5/3 =  1.666 . . .

a.  You will pay 80% of the original price.

b. $14.40 is the discount price of the t-shirt.

c. The sale price of the gaming system is $288.

d. $22.50 is the regular price of the hat.

a. When a store offers a 20% discount, you will pay 80% of the original price. This is because the discount is taken off the original price, leaving you to pay the remaining percentage.

b. If the regular price of a t-shirt is $18, the discount price can be found by multiplying the regular price by the percentage you will pay after the discount, which is 80%.

Discount price = Regular price x (1 - Discount percentage)

Discount price = $18 x (1 - 0.20)

Discount price = $18 x 0.80

Discount price = $14.40

Therefore, $14.40 is the discount price of the t-shirt.

c. If the regular price of a gaming system is $360, the sale price can be found by multiplying the regular price by the percentage you will pay after the discount, which is 80%.

Sale price = Regular price x (1 - Discount percentage)

Sale price = $360 x (1 - 0.20)

Sale price = $360 x 0.80

Sale price = $288

Therefore, the sale price of the gaming system is $288.

d. If the discount price of a hat is $18 and the discount percentage is 20%, we can find the regular price by dividing the discount price by the percentage you will pay after the discount, which is 80%.

Regular price = Discount price / (1 - Discount percentage)

Regular price = $18 / (1 - 0.20)

Regular price = $18 / 0.80

Regular price = $22.50

Therefore, the regular price of the hat is $22.50.

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In a circle, when two diameters intersect, the angles formed at the intersection point are always right angles (90°).

Therefore, none of the given angle measures (50°, 80°, 100°, 130°) can represent the angle formed by diameters AC and BD.

The correct answer would be 90° since the intersection of diameters always creates right angles in a circle.

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Answer: A. 50°

Asked the AI

Answer:

Alternate exterior angles

Step-by-step explanation:

To find the volume of the parallelepiped determined by the vectors <1,3,7>, <2,1,5>, and <3,1,1>, we can use the determinant of a 3x3 matrix. The absolute value of the determinant represents the volume of the parallelepiped.

To calculate the volume, we arrange the vectors as columns of a matrix and compute the determinant. The determinant of a 3x3 matrix can be calculated using the formula: determinant = a(ei - fh) - b(di - fg) + c(dh - eg), where a, b, c, d, e, f, g, h, i are the corresponding elements of the matrix.

By plugging in the values from the given vectors, we construct the matrix and evaluate the determinant. The absolute value of the determinant will give us the volume of the parallelepiped.

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Answer:

Veronica:

d=5t

Chad:

d=4t

Step-by-step explanation

yes they do represent linear equations

Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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The sample size necessary for a 90% confidence interval about the mean height of a shrub with a margin of error of 0.5 inches and a population standard deviation of 1.3 inches is 18.

Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.

MOE = z x (SD / √n)

where MOE = margin of error = 0.5 inches

z = found by using a z-score table

SD = sample standard deviation = 1.3 inches

n = sample size

At 90% confidence interval, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.

(100 - 90) / 2 = 5

100 - 5 = 95

Find 0.95 in the z-table to get the value of z.

At p = 0.95, z = 1.647

Plug in the values to the formula and solve for the sample size, n.

MOE = z x (SD / √n)

0.5 = 1.647 x (1.3 / √n)

√n = 1.647(1.3) / 0.5

n = 18.34

n = 18

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