Josie's office recycled a total of 10 kilograms of paper over 5 weeks. After 7 weeks, how many kilograms of paper will Josie's office have recycled? Assume the relationship is directly proportional.​

Answer:

\(\boxed {x=-36}\)

Step-by-step explanation:

\(\sf -13+x=23+2x\)

\(\sf -13+x+13=23+2x+13\)

\(\sf x=2x+36\)

\(\sf x-2x=2x+36-2x\)

\(\sf -x=36\)

\(\sf \cfrac{-x}{-1}=\cfrac{36}{-1}\)

\(\sf x=-36\)

The two triangles are said to be congruent by the SSS rule if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

Segments, or "triangles," are three-sided plane enclosed figures that can be classified according to their sides and angles. The typical variations include isosceles, equilateral, scalene, etc. So what exactly are congruent triangles? Triangles are said to be in congruence when all corresponding sides and interior angles are congruent (of the same length).

The triangles will be the same size and shape, but they will appear to be mirror images of one another. Simply put, objects that appear to be identical when placed over their opposites or that are Xerox copies of one another are said to be congruent.

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Answer:

Tony and his cousin will each have 42 points in 3 turns.

Step-by-step explanation:

10 x 3 = 30

30 + 12 = 42

14 x 3 = 42

The given statement "descriptive statistics uses the data to make inferences and predictions about a population based on a sample of data taken from the population in question" is FALSE.

How is this false?

Descriptive statistics is a branch of statistics that studies and summarizes a set of data's main features. It aids in the interpretation of data and drawing conclusions about the population based on sample data. Descriptive statistics are used to provide a quick summary of the data set's key characteristics.

An inference is a statistical method of estimating the characteristics of a population based on a sample's data. It is a method of predicting data in a population based on the observations made in a sample. The primary goal of inferential statistics is to make predictions about a population based on data from a sample of that population.

Predictions are projections or guesses about what might occur in the future. When used in statistics, prediction refers to the use of current data to estimate what might occur later. A statistical model is usually used to make a prediction.

A population is the entire collection of items or individuals about which you want to learn in statistics. A population is made up of all of the objects or people who possess the qualities that the researcher is interested in researching.

A sample is a subset of a population that is used to collect data and conduct statistical analyses. The sample size is typically less than the population size, and data collected from a sample is used to make inferences about the population as a whole.

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The distance between two raisins will increase by a factor of the square root of 2.

As the bread dough rises and doubles in size, each linear dimension of the dough, including the distance between the raisins, will also double. This means that the distance between two raisins will increase by a factor of 2.

However, since the change in distance is related to a change in the linear dimension, and not the area, the increase in distance is proportional to the square root of 2, not 2. This means that the distance between the two raisins will increase by a factor of the square root of 2, or approximately 1.41.

This increase in distance between the raisins is a result of the increase in the volume of the dough, as the yeast ferments the sugars in the dough, producing carbon dioxide and causing the dough to rise. The increase in volume causes the dough to stretch, resulting in the increased distance between the raisins.

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We have the following:

The first thing is to calculate the ratio between both paintings.

After finding the ratios, it can be calculated for any value using a proportionality rule.

for example, for 5 cups of blue paint, should be for yellow paint:

therefore, should be 25 cups of yellow paint

Answer:

Step-by-step explanation:

700.5

610 students must be randomly selected to estimate the mean weekly earnings of students at one college.

We have to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.

So: α = (1 - 0.95)/2

      α = 0.025

Now, we have to find z in the Z-table as such z has a p-value of 1 - α .

so, Z = 1.96

Now, find the margin of error M as such,

M = z(σ/√n)

In which  is the standard deviation of the population and n is the size of the sample.

The population standard deviation is known to be $63.

This means that σ = 63

ample mean within $5 of the population mean

This is n for which M = 5.

So, M = z(σ/√n)

5 = 1.96(63/√n)

2.55 = (63/√n)

√n = 24.70

n = 610.4

n ≈ 610

Therefore, 610 students must be randomly selected to estimate the mean weekly earnings of students at one college.

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So the acute angle of the rhombus is 90 degrees, and the obtuse angle is twice as large, or 180 degrees.

The Pythagorean theorem is a fundamental concept in geometry that describes the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's start by finding the length of one half of the longer diagonal. We can use the shorter diagonal (which we know is 10 cm) and the side length (which we know is 13 cm) to form a right triangle. The hypotenuse of this triangle is half of the longer diagonal, so we can solve for it using the Pythagorean theorem:

\(a^2+b^2 = c^2 \\(13/2)^2 + 10^2 = c^2\\169/4+100 =c^2 \\ 269/4= c^2 \\c = \sqrt{(269)}/2\\\)

Therefore, the length of one half of the longer diagonal is sqrt(269)/2 cm. To find the full length of the longer diagonal, we just need to double this value:

longer diagonal = \(2 \times \sqrt{(269)}/2 = \sqrt{(269)}cm\)

Now, we can use the fact that the sum of the angles in a rhombus is 360 degrees to solve for x:

2x + 2x = 360

4x = 360

x = 90

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Answer:

√99, 9.8 repeating, π2

Step-by-step explanation:

hope this helped!

a. The probability that he must stop at both signals is 0.2.b. The probability that he must stop at the first signal but not at the second one is 0.2.

c. The probability that he must stop at exactly one signal is 0.5.

a. The probability that he must stop at both signals is equal to the product of the individual probabilities of stopping at each signal, which is 0.4 x 0.5 = 0.2.

b. The probability that he must stop at the first signal but not at the second one is equal to the probability of stopping at the first signal only, which is 0.4.  

c. The probability that he must stop at exactly one signal is equal to the sum of the probability of stopping at the first signal and the probability of stopping at the second signal, which is 0.4 + 0.5 = 0.5.

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Step-by-step explanation:

the function is

d(n) = sqrt(1.49×n)

so,

85 = sqrt(1.49×n)

85² = 1.49×n

n = 85²/1.49 = 7225/1.49 = 4,848.993289... ft

≈ 4,849 ft

The polygon tool to graph the dilated figure will be drawn below.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

Graph the image of this figure after a dilation with a scale factor of 2 centered at the origin.

The polygon tool to graph the dilated figure will be drawn below.

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The length of the side of the smaller square is 7 inches.

Let x be the length of the side of the smaller square.

The length of each side of a square is 3 inches more than the length of each side of a smaller square. Thus the length of the side of the larger square is

(x + 3) inches.

The area of the smaller square is

x^2 square inches.

The area of the larger square is

(x + 3)^2 square inches.

We can set up the equation:

x^2 + (x + 3)^2 = 149

Expanding and simplifying the equation gives:

x^2 + x^2 + 6x + 9 = 149

Combining like terms:

2x^2 + 6x - 140 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

x = (-6 ± √(6^2 - 4 * 2 * (-140))) / 2 * 2

x = (-6 ± √(36 + 1120)) / 4

x = (-6 ± √(1156)) / 4

x = (-6 ± √(596)) / 4

x = (-6 ± 34) / 4

x = -10 or x = 7

The side length of the smaller square can't be negative, so x = 7 inches.

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When finding local maxima and minima from the graph of a derivative, we need to identify the points where the derivative changes sign. These points represent the locations of local maxima and minima on the original function.

When finding local maxima and minima from the graph of a derivative, we need to understand the relationship between the original function and its derivative. The derivative of a function represents the rate of change of the function at any given point. Local maxima and minima occur where the derivative changes sign from positive to negative or from negative to positive. At these points, the slope of the original function changes from increasing to decreasing or from decreasing to increasing.

By following these steps, we can identify the local maxima and minima from the graph of a derivative.

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Identify the critical points, Determine the intervals, Analyze the sign changes and Check the endpoints

To find the local maximum and minimum points from the graph of a derivative, you can follow these steps:

Identify the critical points: These are the points where the derivative is either zero or undefined. Find the values of x where f'(x) = 0 or f'(x) is undefined.

Determine the intervals: Divide the x-axis into intervals based on the critical points and any other points of interest. Each interval represents a section of the graph where the derivative is either positive or negative.

Analyze the sign changes: Within each interval, observe the sign of the derivative. If the derivative changes sign from positive to negative, there is a local maximum at that point. If the derivative changes sign from negative to positive, there is a local minimum at that point.

Check the endpoints: Also, check the derivative's sign at the endpoints of the graph. If the derivative is positive at the leftmost endpoint and negative at the rightmost endpoint, there is a local maximum at the left endpoint. Conversely, if the derivative is negative at the leftmost endpoint and positive at the rightmost endpoint, there is a local minimum at the left endpoint.

By following these steps and analyzing the sign changes of the derivative within intervals, as well as checking the endpoints, you can identify the local maximum and minimum points from the graph of the derivative.

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The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.

According to the statement

we have to explain about the function in which cryptography takes a string of any length as input and returns a string of any requested variable length.

So, For this purpose,

we know that the

A sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce an output bit stream of any desired length.

So from definition and its working process it is clear that for this purpose the sponge function is used.

this function returns the string of any variable length.

So, The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.

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Answer:

g(x) = x^2 - 4   (Answer #3)

Step-by-step explanation:

The graph of the parent function f(x) = x^2 is a parabola with vertex at (0, 0).  That of g(x) is the same, except that the first graph has been translated down by 4 units.

When this happens, the original function f(x) = x^2 + 0 changes to

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

Square

_________________

Answer:

Step-by-step explanation:

The measurement used to describe a television is the length of its diagonal. The relation between the width, height, and diagonal is described by the Pythagorean theorem.

The Pythagorean theorem tells us the relation between the sides of a right triangle and its hypotenuse. The diagonal of a rectangle is the hypotenuse of a right triangle whose sides are the width and height of the rectangle. If 'c' is the number of "ratio units" in the diagonal, we have ...

  4² +3² = c²

  c = √(16 +9) = 5

The diagonal of the screen is 5 ratio units, so the width is 4/5 of the length of the diagonal, and the height is 3/5 the length of the diagonal.

The width is ...

  (4/5)(47 in) = 37.6 in . . . width

The height is ...

  (3/5)(47 in) = 28.2 in . . . height

The area is the product of the width and height:

  A = WH = (37.6 in)(28.2 in) = 1060.32 in²

The area of the screen is 1060.32 square inches.

The probability of an earthquake in that magnitude range occurring in next 30 years is 3%.

The probability that the event will not occur for an exposure time of x years is:

\((1-\frac{1}{MRI} )^{x}\)

where, MRI = Mean Recurrence Interval = 1000

                x = Years = 30

Therefore, Probability of not occurring = \((1-\frac{1}{1000} )^{30}\)

                                                                 = \((\frac{999}{1000} )^{30}\)

                                                                 = \((0.999)^{30}\)

                                                                 = 0.97

Probability of occurring = 1 - 0.97

                                       = 0.3

Probability percent = 0.03 * 100

                                = 3 %

Hence, probability is 3%.

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The maximum number of hours for which Maria can rent the boat is 4 hours

The rental cost of boat = $60

The amount that have to pay for a water safety course = $10

The maximum amount that she can spend on = $280

The inequality is the mathematical statement that shows the relationship between two expression with an inequality sign.

Consider the number of hours as x

Then the inequality will be

60x + 10 ≤ 280

60x ≤ 280 -10

60x ≤ 270

x ≤ 270/60

Divide the terms

x  ≤ 4.5

Therefore, she can ride maximum of 4 hours in boat

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(a-1) The value of the population mean is unknown.

(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.

(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).

(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.

(e-2) It would be reasonable to conclude that the population mean is 18 eggs.

(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.

(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.

(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.

Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.

In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.

(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.

(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.

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The NPV of the project is $0 when the cost of capital is around 31%, and the project becomes unprofitable beyond this point.

Given data, The upfront cost of the project is $900,000Year 1 revenues

= $800,000Year

2 revenues = $1,500,000 Year

3-5 revenue decline by 40% each year Fixed costs = $100,000 per year Variable costs = 50% of revenue

Year-wise cash flows: Year 0: -$900,000 Year

1: $800,000 - 50%($800,000) - $100,000 = $300,000Year

2: $1,500,000 - 50%($1,500,000) - $100,000 = $550,000Year

3: $0.6(1 - 0.4)($1,500,000) - 50%($0.6(1 - 0.4)($1,500,000)) - $100,000

= $210,000Year

4: $0.6(1 - 0.4)2($1,500,000) - 50%($0.6(1 - 0.4)2($1,500,000)) - $100,000 = $126,000Year

5: $0.6(1 - 0.4)3($1,500,000) - 50%($0.6(1 - 0.4)3($1,500,000)) - $100,000 = $75,600

Net cash flow in years 0-5 = -$900,000 + $300,000 + $550,000 + $210,000 + $126,000 + $75,600

= $362,600.

The following is the NPV profile of the project: For the cost of capital of 10%, the project's NPV can be calculated by discounting the cash flows by the cost of capital at 10%.

NPV = -$900,000 + $300,000/(1 + 0.10) + $550,000/(1 + 0.10)2 + $210,000/(1 + 0.10)3 + $126,000/(1 + 0.10)4 + $75,600/(1 + 0.10)5

= -$900,000 + $272,727.27 + $452,892.56 + $152,979.17 + $80,362.63 + $42,429.59

= $101,392.22

The project's NPV is $101,392.22 when the cost of capital is 10%.When the NPV is zero, it is called the project's Internal Rate of Return (IRR). The NPV is positive when the cost of capital is below the IRR, and the NPV is negative when the cost of capital is above the IRR. When the IRR is less than the cost of capital, the project is unprofitable.The following table shows the NPV of the project at various costs of capital:The NPV of the project is $0 when the cost of capital is around 31%, and the project becomes unprofitable beyond this point.

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A z-score of 2.14 indicates that Katie's score on the test is quite high and unusual, and places her in the top 2% of the scores in the population.

Katie scored a 93 on a test and her calculated z score was 2.14, that means that her score is 2.14 standard deviations above the mean of the test scores.

A z score represents the number of standard deviations a data point is from the mean of the data set.

A positive z score means that the data point is above the mean, while a negative z score means that the data point is below the mean.

The mean of the test scores was, 80 with a standard deviation of 5, then Katie's z score would be calculated as:

z = (x - μ) / σ

= (93 - 80) / 5

= 2.6

Z scores are useful for comparing data points from different data sets or for comparing data points within the same data set that are measured on different scales.

Katie's score is 2.6 standard deviations above the mean.

A z score of 2.14 would mean that Katie's score is slightly below this value, but still significantly above the mean.

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The number that was coded is 45.

First, note that if you raise any integer between 1 and 76 to the power 17, the result will be an integer with many digits.

However, since we are reducing the result modulo 77, we only need to consider remainders when dividing this large number by 77.

To compute the remainder when raising a number to a power modulo 77, you can use the repeated squaring algorithm. Here's how it works:

Start with the base number, which is the secret digit you want to code (let's call it x).

Compute \(x^2\) modulo 77.

Compute\((x^2)^2\) modulo 77.

Repeat step 3 a total of 15 times. At this point, you have computed x^16 modulo 77.

Multiply \(x^{16}\) by x modulo 77 to get \(x^{17}\) modulo 77.

Alternatively, you can use a built-in function in most programming languages to compute modular exponentiation.

For example, in Python, you can use the pow() function with three arguments: the base, the exponent, and the modulus. Here's how you can use it:

x = 25  

for i in range(1, 77):

   if pow(i, 17, 77) == x:

       print(i)

       break

This code will print the secret digit that corresponds to the remainder of 25 when raised to the power of 17 and reduced modulo 77, which is 45.

Therefore, the number you coded is 45.

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Answer:

x = 28

Step-by-step explanation:

Let the total number of students = x

x/7 + 3x/7 + 2x/7 + 4 = x If that is all there is.  If it isn't the problem can't be done. Combine like terms.

x(1 + 3 + 2)/7 + 4 = x

x (6/7) + 4 = x                       Subtract 6x/7 from both sides

4 = x - 6x/7

4 = 7x/7 - 6x/7                     Combine

4 = 1/7x                                Multiply both sides by 7

4*7 = 7x / 7

x = 28

The most appropriate choice for expectation will be given by-

Expected value for someone who buys the ticket = $\((-1591.2)\)

What is expectation?

At first it is important to know about probability of an event.

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Suppose x is a random variable with the probability function f(x). suppose

\(x_1. x_2,........,x_n\) are the values corrosponding to the actual occurance of the event and \(p_1, p_2.,,,, p_n\) be the corrosponding probabilities.

Expectation is given by the formula \(p_1x_1+p_2x_2+...+p_nx_n\)

Here,

Total number of tickets = 832

Number of prized tickets = 1

Probability of winning a ticket = \(\frac{1}{832}\)

Probability of losing a ticket = \(\frac{831}{832}\)

Gain of winning = $(1600 - 5) = $1595

Loss of losing = $(5 - 1600) = -$1595

Expected value for someone who buys the ticket

\(1595 \times \frac{1}{832} + (-1595)\times \frac{831}{832}\)

\(1595\times(\frac{1-831}{832})\\-1595\times \frac{830}{832}\\\)

$\((-1591.2)\)

Expected value for someone who buys the ticket = $\((-1591.2)\)

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Answer:

Yes.

Step-by-step explanation:

Irrational numbers are number that cannot be represented by a fraction or numbers that have a non-terminating (never-ending) decimal.

Answer:

1 mile = 4 laps

3 miles = 12 laps

9/4 = x /1

9/4 = 2.25

he has run 2.25 miles = 9 laps

he needs to run 0.75 miles = 3 laps

Answer: The highest common factor of 91, 112 and 49 is 7

hope this helps :)