Simplify 2.54 + 1.5 × 4

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Answer:

Percentage Calculator: 100. is what percent of 500.? = 20.

Step-by-step explanation:

Area of Hexagon having six sides = \(\frac{3\sqrt{3}s^{2} }{2}\)

Hexagons are polygons with six sides and six angles.

Six equilateral triangles make up a regular hexagon, which has six equal sides and six angles. Whether you're dealing with an irregular hexagon or a standard hexagon, there are numerous approaches to figure out the area of a hexagon.

The area of hexagon formula can be calculated in a number of different ways. The various techniques primarily depend on the hexagon's spitting motion.

It can be split into two triangles and one rectangle, or six equilateral triangles. We shall examine numerous approaches to calculating the hexagon's surface area in this post.

According to the given information

Area of Hexagon having six sides = \(\frac{3\sqrt{3}s^{2} }{2}\)

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Answer:

x = 216

Step-by-step explanation:

2 + 5\(\sqrt[3]{x}\) = 32

Subtract 2 from both sides of the equation

i.e. 2 + 5\(\sqrt[3]{x}\) - 2 = 32 - 2

5\(\sqrt[3]{x}\) = 30

Take the cube of both sides of the equation

i.e. (5\(\sqrt[3]{x}\))³ = (30)³

(5)³(\(\sqrt[3]{x}\))³ = (30)³

(5 × 5 × 5)(\(\sqrt[3]{x}\))³ = (30 × 30 ×30)

125x = 27,000

Divide both sides of the equation by the coefficient of x(which is 125)

\(\frac{125x}{125} = \frac{27000}{125}\)

x = 216

Check

Substituting 216 for x in 2 + 5∛x = 32,

2 + 5 \(\sqrt[3]{216}\) = 32 (\(\sqrt[3]{216}\) = 6)

2 + (5 × 6) = 32

2 + 30 = 32

∴ x = 216

Hope this helps :))

The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

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Answer:

\(\alpha^3-\beta^3 = \frac{28}{3}\sqrt{\frac{5}{3}}\)

Step-by-step explanation:

The value of a³-B³ from the given quadratic equation is 12.05.

The roots to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, a and B are the roots of the equation 3x²+6x-2=0

By comparing 3x²+6x-2=0 with ax²+bx+c=0, we get a=3, b=6 and c=-2

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

Now, substitute a=3, b=6 and c=-2 in quadratic formula

That is, x = [-6 ±√(6² - 4×3×(-2))]/2×3

= [-6 ±√60]/6

= (-6±2√15)/6

= (-3±√15)/3

So, a=(-3+√15)/3 and B=(-3-√15)/3

Now, a³-B³ = [(-3+√15)/3]³- [(-3-√15)/3]³

= 12.05

Therefore, the value of a³-B³ from the given quadratic equation is 12.05.

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Answer:

1. 33 foot

2. 6.2 foot

Step-by-step explanation:

1.

Let's denote the height of the tree by "h". We can use the tangent function to solve the problem:

tangent of the angle of elevation = opposite / adjacent

In this case, the opposite side is the height of the tree, and the adjacent side is the distance from the tree to the point on the ground where the angle of elevation is measured. So we have:

tan(35) = h / 47

To solve for "h", we can multiply both sides by 47:

h = 47 tan(35)

Using a calculator, we get:

h ≈ 32.9 feet

So the height of the tree to the nearest foot is 33 feet.

2.

Let's call the distance we're trying to find "x". We can use trigonometry to relate the angle and the length of the guy wire to the distance "x". Specifically, we can use the sine function:

sine of the angle = opposite / hypotenuse

In this case, the opposite side is the distance "x", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:

sin(51) = x / 8

To solve for "x", we can multiply both sides by 8:

x = 8 sin(51)

Using a calculator, we get:

x ≈ 6.2 feet

So the stake is about 6.2 feet from the foot of the stop sign, to the nearest tenth of a foot.

Answer:

The answer is C 10

Step-by-step explanation:

When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include

A. 27, 22, 17, 12, 7

D. 100, 95, 90, 85, 80

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.

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Complete question

Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.

27, 22, 17, 12, 7

5, 10, 15, 20, 25

55, 50, 35, 30, 25

100, 95, 90, 85, 80

75, 65, 55, 45, 35

Based on the given information and adjustments, the adjusted bank balance for ABC Company on July 31 would be Br. 5,169.42.

Based on the provided information, let's analyze the various transactions and their impact on the bank reconciliation for ABC Company:

1. The deposit of Br. 410.90 made after banking hours: This deposit does not appear in the bank statement, so it should be added to the bank balance. After including this deposit, the adjusted bank balance would be Br. 5,375.37 (Br. 4,964.47 + Br. 410.90).

2. The erroneously charged check of Br. 79: This check should be deducted from the bank balance as it was charged in error by the bank. After deducting this amount, the adjusted bank balance would be Br. 5,296.37 (Br. 5,375.37 - Br. 79).

3. Outstanding checks: The outstanding checks that haven't been paid by the bank need to be deducted from the adjusted bank balance. The total amount of outstanding checks is Br. 610.75 (Br. 100 + Br. 10.25 + Br. 294.50 + Br. 205). After deducting this amount, the adjusted bank balance would be Br. 4,685.62 (Br. 5,296.37 - Br. 610.75).

4. Incorrectly charged check of Br. 210 as Br. 120: This error made by the bank needs to be corrected. The bank balance should be increased by the difference, which is Br. 90. Therefore, the adjusted bank balance would be Br. 4,775.62 (Br. 4,685.62 + Br. 90).

5. Proceeds from collection of an interest-bearing note receivable: The face amount of the note was Br. 500. Since the note was left with the bank's collection department, the amount collected should be added to the bank balance. Therefore, the adjusted bank balance would be Br. 5,275.62 (Br. 4,775.62 + Br. 500).

6. Interest earned on the average account balance: The interest earned of Br. 24.75 should be added to the bank balance. After including this amount, the adjusted bank balance would be Br. 5,300.37 (Br. 5,275.62 + Br. 24.75).

7. The returned check of Br. 10: This check was recorded in the check register as Br. 100 but was returned for Br. 10. The difference of Br. 90 should be deducted from the bank balance. Therefore, the adjusted bank balance would be Br. 5,210.37 (Br. 5,300.37 - Br. 90).

8. Fee charged by the bank for handling the collection of the note receivable: The fee of Br. 5.00 should be deducted from the bank balance. After deducting this fee, the adjusted bank balance would be Br. 5,205.37 (Br. 5,210.37 - Br. 5.00).

9. Check from customer John charged as Non-sufficient funds (NSF): The check of Br. 50.25 should be deducted from the bank balance. After deducting this amount, the adjusted bank balance would be Br. 5,155.12 (Br. 5,205.37 - Br. 50.25).

10. Service charge by the bank for the month of July: The service charge of Br. 12.70 should be deducted from the bank balance. After deducting this charge, the adjusted bank balance would be Br. 5,142.42 (Br. 5,155.12 - Br. 12.70).

11. Erroneously recorded check of Br. 85 as Br. 58: This error in the cash payment journal needs to be corrected. The bank balance should be increased by the difference, which is Br. 27. Therefore, the adjusted bank balance would be Br. 5,169.42 (Br. 5,142.42 + Br. 27).

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According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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The product of two linear functions having same variables will be a quadratic function where as the The product of two linear functions having different variables will be a linear function.

Linear function is the function whose degree is 1.

Degree of a function is the highest power of the variable of the function.

Let us take two examples.

1. Suppose the two linear functions are -

f(x) = 2x + 3 and g (x) = x + 5

The product of f(x) and g(x) will be

(2x + 3)(x + 5)

=2x (x + 5) + 3 (x + 5)

= 2x² + 10x + 3x + 15

= 2x² + 13x + 15

Here, f(x) and g(x) are the functions having same variables so there product is a quadratic function.

2. Suppose the two linear functions are -

f(x) = 2x + 3 and g (y) = y + 5

The product of f(x) and g(y) will be

(2x + 3)(y + 5)

=2x (y + 5) + 3 (y + 5)

= 2xy + 10x + 3y + 15

Here, f(x) and g(y) are the functions having different variables so there product is a linear function.

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Answer:

f = (N² - H) / 6

Step-by-step explanation:

N² = 6f + H,

N² - H = 6f,

(N² - H) / 6 = f

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

πr^2 h

π(11)^2 (15)

= 1815π or = 5701

Answer:

B

Step-by-step explanation:

You could solve this and verify with a system of equations, but b is correct! :) have a good day!

Answer:

2m+5s=60

Step-by-step explanation:

2m+5s=60

Since each multiple choice is 2 points, we have 2m and since every short answer is 5 points we have 5s. The total number of points is 60 so we have that equal to 60.

Answer:

\(y=-x+1\)

Step-by-step explanation:

It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:

\(-7x-7y=7\)

add 7x to both sides:

\(-7y=7x+7\)

Divide both sides by -7

\(y=-x-1\)

Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:

\(y=-x+b\text{ where b }\ne -1\)

We're given the point (-1, 2) and we can use it to solve for that "b" value.

We plug in -1 as x and 2 as y

\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)

Now we just plug this into the general equation to get: \(y=-x+1\)

The value of y on the diagram of the image is given as follows:

23 + 5y.

The value of y on the context of the given problem is obtained applying the proportions of the problem.

The bars represent an addition operation, with 23 added to 5 times y being equals to 38, hence the expression is given as follows:

23 + 5y = 38.

The value of y is then obtained isolating the variable y as follows:

5y = 15

y = 3.

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Answer:

-2.053 to  2.053  is ± .48 from z=0

Step-by-step explanation:

Answer:

The answer would be two feet.

Step-by-step explanation:

Step 1. Do 10-6 (10 being the total space and 6 being the painting)
Step 2. Get the answer of 4.
Step 3. Divide four by 2 because it needs to be centered.
Step 4. Get the answer of two feet on each side.
I hope this helps! :)

Answer and Step-by-step explanation:

According to the situation the solution is shown below:-

The expected value is

\(\mu = 5\)

The standard deviation is

= $3

The sample distribution of the sample standard deviation is

\(\sigma_x = \frac{\sigma}{\sqrt{n} } \\\\ = \frac{3}{\sqrt{36} } \\\\ = \frac{3}{6}\)

After solving the above equation  we will get

= 0.5

Basically we applied the applied formula so that each part could be determined

Answer:

8u + 7z + 15

Step-by-step explanation:

Let's solve the problem,

→ 3z + 6 + 4z + 9 + 8u

→ 8u + (3z + 4z) + (6 + 9)

→ 8u + 7z + 15

Thus, solution is 8u + 7z + 15.

Answer:

8u±7z±15

Step-by-step explanation:

3z±6±4z±9±8u

8u±3z±4z±9±6

8u±7z±15

Hope its helpful for you

Answer:

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Step-by-step explanation:

For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.

To find the probability of damage on a parachute, the normal distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Probability of a parachute having damage.

The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that \(\mu = 185, \sigma = 32\)

Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of  Z when X = 100. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{100 - 185}{32}\)

\(Z = -2.66\)

\(Z = -2.66\) has a p-value of 0.0039.

What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

0.0039 probability of a parachute having damage, which means that \(p = 0.0039\)

5 parachutes, which means that \(n = 5\)

This probability is:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807\)

Then

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193\)

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Answer:

5

Step-by-step explanation:

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Answer

Let x = the number of ounces of Solution A

Let y = the number of ounces of Solution B

x + y = 180        y = 180 - x

.60x + .85y = .75(180)

.60x + .85y = 135      Multiply both sides of the equation by 100 to remove the decimal points.

60x + 85y = 13500

60x + 85(180 - x) = 13500

60x + 15300 - 85x = 13500

-25x = -1800

x = 72ounces

y = 180 - 72

y = 108 ounces          

Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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