What is the value of x?

Answer:  4/21

Step-by-step explanation:

1/7 = 6/42

2/3 = 28/42

28+6=34        

42-34=8        

8/42=4/21

Answer:

B. PK = 15, RJ = 9

Step-by-step explanation:

RQ = 3

PQ = 5

✔️In ∆JKL, Q is the centroid. According to the centroid theorem, thus:

⅓(RJ) = RQ

⅓(RJ) = 3

Multiply both sides by 3

RJ = 3*3

RJ = 9

✔️Also, based on the centroid theorem,

⅓(PK) = PQ

⅓(PK) = 5

Multiply both sides by 3

PK = 5*3

PK = 15

Answer:

(1) let pen = x

let pencil= y

i) y ≤ 5x

ii) 5x + 2y ≤ 40

Step-by-step explanation:

at most = maximum

Answer:

20x-13

Step-by-step explanation:

The correct answer to the question is option d) 75 PCF.

To calculate the expected vertical load, we need to consider the weight of the concrete slab and the additional load due to the concrete's temperature and pouring rate. The weight of the slab can be calculated by multiplying the density of the concrete (150 PCF) by the depth (6 inches) and the area (1 square foot). This gives us a weight of 75 pounds per square foot (PSF).

The temperature and pouring rate do not directly affect the vertical load. The temperature and pouring rate are factors that may affect the structural integrity of the slab or the time it takes for the concrete to fully cure. However, they do not contribute to the actual load borne by the slab itself. Therefore, the correct answer is 75 PCF, as it represents the weight of the concrete slab alone.

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Answer:

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Heron's formula states that the area of a triangle with side lengths a, b, and c is:

We have a triangle with side lengths:

We can first find the semi-perimeter:

Then we can plug this into Heron's formula to find the area:

So the area of the triangle is approximately 82.41 square units.

In the multiple regression model with k regressors, the variance of the stochastic errors in the population can be estimated by the residual mean square (MSE).

         Multiple regression is a statistical tool that allows the researcher to estimate the relationship between multiple independent variables and a dependent variable. It measures the impact of a given independent variable on the dependent variable after controlling for the other independent variables.

        In simple linear regression, there is only one independent variable, whereas, in multiple linear regression, there is more than one independent variable.

         Residual mean square (MSE) is the variance of the error term (the difference between the predicted and observed values). It represents the average variance of the errors or the average deviation of the dependent variable from its predicted value.

         The MSE can be used to estimate the variance of the stochastic errors in the population. It is calculated by dividing the sum of squared residuals by the degrees of freedom (n-k-1)

           Where n is the sample size and k is the number of regressors.

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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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Answer:

112 guests

Step-by-step explanation:

I. If her total cost is 773$

When Total = DJ + Cake + Guest

            773 = 250 + 75 + 4(x)

            773 = 325 + 4(x)

            773 - 325 = 4(x)

            448 = 4x

               x = 448/4

               x = 112

That makes guests are 112

The percent change in the cookies sales from Tuesday to Wednesday equals -18.2%.

Number of cookies sold on Tuesday = 132

Number of cookies sold on Wednesday = 108

Percent change between Tuesday and Wednesday sales

= Difference between the two amounts divide by the original amount Tuesday sales and then multiply by 100 to express the change as a percentage.

The difference between the two amounts is,

= 108 - 132

= -24

Negative result because the Wednesday sales were less than Tuesday sales.

Percent change from Tuesday to Wednesday is

= (-24/132) x 100%

= -18.2%

Rounding to the nearest tenth of a percent, we get,

Percent change = -18.2%

Therefore, there was a 18.2 percent decrease in sales from Tuesday to Wednesday.

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To calculate the 97% confidence interval, we can use the following formula:

CI = (mean - (critical value) * (standard deviation / square root of sample size), mean + (critical value) * (standard deviation / square root of sample size))

Where critical value is the t-value that corresponds to 97% confidence level and degrees of freedom (df) equal to n-1.

Using a t-distribution table with df = 103, the critical value is 1.98.

Putting  in the numbers:

CI = (12.05 - (1.98) * (0.08 / sqrt(104)), 12.05 + (1.98) * (0.08 / sqrt(104)))

CI = (12.05 - (1.98) * (0.08 / 10.197), 12.05 + (1.98) * (0.08 / 10.197))

CI = (12.05 - 0.0177, 12.05 + 0.0177)

CI = (12.0323, 12.0677)

So the 97% confidence interval for the mean amount of soda in a can is (12.0323, 12.0677) ounces.

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To find the interquartile range (IQR), we need to first find the first quartile (Q1) and the third quartile (Q3).

Then, the IQR can be calculated as the difference between Q3 and Q1.

Here's how to find the IQR for the given data set:

Step 1:Arrange the data set in ascending order.60, 62, 64, 66, 70, 70, 72, 75, 75, 76, 77

Step 2: Find the median (middle value) of the data set. If the data set has an odd number of values, then the median is the middle value. If the data set has an even number of values, then the median is the average of the middle two values. In this case, the data set has 11 values, which is odd. Therefore, the median is the middle value, which is 70.

Step 3: Divide the data set into two halves: the lower half and the upper half. The median separates the data set into two halves. The lower half consists of values less than or equal to the median, while the upper half consists of values greater than or equal to the median. Lower half: 60, 62, 64, 66, 70, 70Upper half: 72, 75, 75, 76, 77

Step 4: Find the median of the lower half. This is the first quartile (Q1).

Q1 = median of lower half = (64 + 66) / 2 = 65

Step 5: Find the median of the upper half.

This is the third quartile (Q3).

Q3 = median of upper half = (75 + 76) / 2 = 75.5

Step 6: Calculate the IQR.IQR = Q3 - Q1 = 75.5 - 65 = 10.5

Therefore, the IQR for the given data set is 10.5

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Answer:

P = 9x

Step-by-step explanation:

Given that,

→ a = 2x

→ b = 3x

→ c = 4x

The formula we use,

→ P = a + b + c

Then the perimeter of triangle will be,

→ P = 2x + 3x + 4x

→ [ P = 9x ]

Therefore, the perimeter is 9x.

Answer:

The answer is 63+7k. :))

Answer:

7k+63

Step-by-step explanation:

Distribute the 7 into the expression 9+k

so 7*9=63

and 7*k=7K

Answer:

x=25

Step-by-step explanation:

25 degree angle is the same as x

If each driver’s distance (miles) is shown for the same elapsed time (hours) of the trip. The person that had a head start is: Rita had a 28-mile head start.

Slope for speed = (y² - y1) / (x² - x1)

Slope for speed = (130 - 65) / (2 - 1)

Slope for speed= 65 / 1

Slope for speed= 65 mph

Determining Roger's starting position if Roger distance is 65.

Hence,

Mile of head start = Slope of speed - Roger distance

Mile of head start = 65 mph - 65 miles

Mile of head start = 0 miles

Rita  starting position if Rita distance is 93

Slope for speed = (y² - y1) / (x² - x1)

Slope for speed = (158 - 93) / (2 - 1)

Slope for speed = 65 / 1

Slope for speed = 65 mph  

Mile of head start = Slope of speed - Rita distance

Mile of head start =  93 - 65

Mile of head start= 28 miles

Therefore we can conclude that Rita has a head start of 28 miles.

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Answer:

Rita had a 28-mile head start.

Step-by-step explanation:

EDGE

The ordered pair that is the solution to the equation -x + 5y = 3 is (-3,0) and (0, 0.6)

Ordered pair:

Ordered pairs refers a set of 2 numbers that exist in a particular order. The first one represents the x value and the second one refer the y value.

Given,

Here we need to find the ordered pair (x, y) that is a solution to the equation -x + 5y = 3

In order to find the solution ordered pair we have to plot this equation on the graph.

To plot this equation, we have to use the graphing calculator, and then input the given equation as the function, then we get the graph like the following.

While we looking into the graph, we have identified that the solution ordered pairs are (-3,0) and (0, 0.6)

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Answer:

it will take 6 minutes, just keep adding 1.4 to -8.4 until you reach 0

Step-by-step explanation:

Answer: It will take 6 minutes because all you need is to divide 8.4 and 1.4 (don't put the negative sign or ignore it)!

The phasor form of a sinusoid represents the amplitude and phase angle of the sinusoid in complex number notation. In this case, the phasor form of \(8 sin(20t 57)\) would be 8 ∠57°. The amplitude, 8, is the magnitude of the complex number, and the phase angle, 57°, is the angle of the complex number in the complex plane.

In terms of amplitude and phase angle, a sinusoidal waveform is mathematically represented in phasor form. Electrical engineering frequently employs it to depict AC (alternating current) circuits and signals. A complex number that depicts the magnitude and phase of a sinusoidal waveform is called a phasor. The phase angle is represented by the imaginary component of the phasor, whereas the real part of the phasor represents the waveform's amplitude. Complex algebra can be used to analyse AC circuits using the phasor form, which makes computations simpler and makes it simpler to see how the circuit behaves.

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Answer:

The lowest common denominator is 8

Step-by-step explanation:

To find the lowest common denominator, we look at the multiples

Multiples of 4: 4,8,12,16,20

Multiples of 8: 8,16,24

The 1st common multiple is 8

The lowest common denominator is 8

The annual maintenance collected in 2014 will be $1,750,000.

To calculate the annual maintenance collected in 2014, we need to find the number of customers who will renew their maintenance contract and the number of customers who will pay for maintenance as a percentage of product sales in 2013.

Number of customers renewing maintenance in 2014 = 80% of $2,000,000 = $1,600,000

Number of customers paying for maintenance in 2014 = 75% of $2,000,000 = $1,500,000

So, the total annual maintenance collected in 2014 will be:

$1,600,000 + $1,500,000*10% = $1,750,000

Therefore, the annual maintenance collected in 2014 will be $1,750,000.

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Answer:

$11.33

Step-by-step explanation:

Keisha will own 307 shares after the split. and the amount of check is 11 dollar.

Given that, NoteQuest Inc. instituted a 3-for-2 split. At that time Keisha owned 205 shares of that stock. The price per share was

$33.99.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, 3+ 2 = 5

Now, let x be the number of shares post split

Then;

3/2 = x/205

x = 3/2 (205)

x = 615/2 = 307.5

Therefore, Keisha will own 307 shares after the split.

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If the incenter, circumcenter, centroid, and orthocenter are always inside the triangle, the correct answer is an acute triangle (option B).

In an acute triangle, all three angles are less than 90 degrees. The incenter, which is the center of the inscribed circle, lies inside the triangle. The circumcenter, which is the center of the circumscribed circle, also lies inside the triangle.

The centroid, which is the point of intersection of the medians, is located inside the triangle as well. Finally, the orthocenter, which is the point of intersection of the altitudes, is inside the triangle in an acute triangle.

In contrast, a right triangle has one angle measuring 90 degrees, an obtuse triangle has one angle greater than 90 degrees, and an isosceles triangle has two equal side lengths. These types of triangles may have some of the points (incenter, circumcenter, centroid, orthocenter) located outside the triangle.

Therefore, the correct answer is option B, acute triangle.

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Answer:

1/x-1

Step-by-step explanation:

(a) There are 81 different sequences of sandwiches are possible

(b) The total number of different (unordered) collections of sandwiches is 3.

First, we need to determine the number of ways the four tuna fish sandwiches can be ordered. Since all four sandwiches are the same, there is only one way to order them. Similarly, there is only one way to order the two chicken sandwiches and the two roast beef sandwiches. For the two people who can choose any sandwich, there are three options for each person, giving a total of 3 x 3 = 9 possible sandwich combinations.

Therefore, the total number of different sequences of sandwiches is:

1 (tuna fish) x 1 (chicken) x 1 (roast beef) x 9 (any sandwich) x 9 (any sandwich) = 81

For part (b), we need to determine the number of different (unordered) collections of sandwiches. We can use combinations to solve this problem. We need to select 10 sandwiches from the total of 10 sandwiches available. Since there are four tuna fish sandwiches, we need to select four of them.

Similarly, we need to select two chicken sandwiches and two roast beef sandwiches. Finally, we need to select two more sandwiches from the remaining three (since two people can choose any sandwich). The number of ways to select these sandwiches is:

combination(4,4) x combination(2,2) x combination(2,2) x combination(3,2) = 3

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The answer of the given question is y = 7x – 48. This is the result of the equation of the line through (6,−6) (6,−6) left parenthesis, 6, comma, minus, 6, right parenthesis and (8,8) (8,8) left parenthesis, 8, comma, 8, right parenthesis. This result is generated by using point-slope formula.

What is slope formula?

Slope formula is required to calculate the inclination of a line. For calculating the slope of a line, x and y coordinates of the points on the line are required. Ratio of change in y coordinates and change in x coordinates is called the slope of a line.

Slope (m) = change in y / change in x = Δy / Δx

Thus, in this case, the calculation as follows:

m = Δy / Δx

= 8 – (–6) / 8 – 6

= 14 / 2

= 7

Now, use the point-slope formula:

y – y1 = m (x – x1)

y – 8 = 7 (x – 8)

y = 7x – 56 + 8

y = 7x – 48

Hence, the result is y = 7x – 48.

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Answer:

y = 13/4x-21

Step-by-step explanation:

Khan Academy

a) The total amount of money earned is 7.30 dollars.

b) Max is wrong, it is possible to divide the money equally between Gwen and Max, even though the total amount is an odd number.

a) To find the total amount of money earned, we need to convert the number of quarters and dimes to dollars.

6 quarters = 6 * 0.25 = 1.50 dollars

8 dimes = 8 * 0.10 = 0.80 dollars

The total amount of money earned is:

5 dollars + 1.50 dollars + 0.80 dollars = 7.30 dollars

b) Max is incorrect. The total amount of money earned is an odd number ($7.30), which means it is impossible to divide it equally between two people in whole dollar amounts. However, it is possible to divide the total amount equally if we allow for fractions of a dollar.

For example, if we split the money equally, Gwen and Max would each get $3.65. This means that Gwen would get 3 dollars and 65 cents, while Max would also get 3 dollars and 65 cents.

Therefore, it is possible to divide the money equally between Gwen and Max, even though the total amount is an odd number.

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To calculate the probabilities, we need to use the concept of binomial probability.

For a fair coin being tossed 5 times:

(a) Probability of getting five heads:

The probability of getting a head in a single toss is 1/2.

Since each toss is independent, we multiply the probabilities together.

P(Head) = 1/2

P(Tails) = 1/2

P(Five Heads) = P(Head) * P(Head) * P(Head) * P(Head) * P(Head) = \((1/2)^5\) = 1/32 ≈ 0.03125

So, the probability of obtaining five heads is approximately 0.03125 or 3.125%.

(b) Probability of getting four heads:

There are five possible positions for the four heads.

P(Four Heads) = (5C4) * P(Head) * P(Head) * P(Head) * P(Head) * P(Tails) = 5 * \((1/2)^4\) * (1/2) = 5/32 ≈ 0.15625

So, the probability of obtaining four heads is approximately 0.15625 or 15.625%.

(c) Probability of getting one head:

There are five possible positions for the one head.

P(One Head) = (5C1) * P(Head) * P(Tails) * P(Tails) * P(Tails) * P(Tails) = 5 * (1/2) * \((1/2)^4\) = 5/32 ≈ 0.15625

So, the probability of obtaining one head is approximately 0.15625 or 15.625%.

For a fair die being thrown eight times:

(a) Probability of a 6 occurring six times:

The probability of rolling a 6 on a fair die is 1/6.

Since each roll is independent, we multiply the probabilities together.

P(6) = 1/6

P(Not 6) = 1 - P(6) = 5/6

P(Six 6s) = P(6) * P(6) * P(6) * P(6) * P(6) * P(6) * P(Not 6) * P(Not 6) = \((1/6)^6 * (5/6)^2\) ≈ 0.000021433

So, the probability of rolling a 6 six times is approximately 0.000021433 or 0.0021433%.

(b) Probability of a 6 never happening:

P(No 6) = P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) * P(Not 6) = \((5/6)^8\) ≈ 0.23256

So, the probability of not rolling a 6 at all is approximately 0.23256 or 23.256%.

(c) Probability of an odd number of 6s:

To have an odd number of 6s, we can either have 1, 3, 5, or 7 6s.

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

\(P(One 6) = (8C1) * P(6) * P(Not 6)^7 = 8 * (1/6) * (5/6)^7P(Three 6s) = (8C3) * P(6)^3 * P(Not 6)^5 = 56 * (1/6)^3 * (5/6)^5P(Five 6s) = (8C5) * P(6)^5 * P(Not 6)^3 = 56 * (1/6)^5 * (5/6)^3P(Seven 6s) = (8C7) * P(6)^7 * P(Not 6) = 8 * (1/6)^7 * (5/6)\)

P(Odd 6s) = P(One 6) + P(Three 6s) + P(Five 6s) + P(Seven 6s)

Calculate each term and sum them up to find the final probability.

After performing the calculations, we find that P(Odd 6s) is approximately 0.28806 or 28.806%.

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