At the beginning of the year office supplies of $1200 for on hand. During the year, boat air conditioning service paid $6000 for more office supplies. At the end of the year a boat has $800 of office supplies on hand

The standard error of this measurement is 6.32

The standard error of measurement is simply the estimate of how repeated measures of an entity on the same instrument tend to be distributed around the entity' “true” score.

In this case, we have the following parameters

Standard deviation = 20

Reliability = 0.90

The standard error of measurement from the standard deviation and the reliability is calculated using the following formula

Standard error of measurement = Standard deviation * √1 - reliability

Substitute the known values in the above equation, so, we have the following representation

Standard error of measurement = 20 * √1 - 0.90

This gives

Standard error of measurement = 20 * √0.10

Evaluate

Standard error of measurement = 6.32

Hence, the standard error in this case is 6.32

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Answer:

5r³ - 34r² + 44r - 16

Step-by-step explanation:

use the distributive property

5r × (r² − 6r + 4) - 4× (r² − 6r + 4)

5r³ - 30r² + 20r - 4r² + 24r - 16

combine like terms

5r³ - 30r² - 4r² + 20r + 24r - 16

5r³ - 34r² + 44r - 16

Hope this helped!!

Answer:

A. 5r3 − 34r2 + 44r − 16

Step-by-step explanation:

The given system of equations have infinitely many solutions.

Given is the system of equations as -

3x - 2y = 4

9x - 6y = 12

We can write the system of equations as -

3x - 2y = 4

9x - 6y = 12

We can write (9x - 6y = 12) as -

3(3x - 2y) = 3(4)

3x - 2y = 4

So both the lines coincide. We can say that the given system of equations have infinitely many solutions.

Therefore, the given system of equations have infinitely many solutions.

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Answer:

The answer is D which is 330

Answer:

330 degrees

Step-by-step explanation:

\(\pi = 180 so \pi /6 = 30 \\30 x 11 = 330\)

The equation of a line y=2x+8.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis

Looking at the given line,

y = 2x + 7

Compared with the slope-intercept equation,

Slope, m = 2

If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2

Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes

4 = 2 × - 2 + c

4 = - 4 + c

c = 4 + 4 = 8

The equation becomes y=2x+8.

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The answer is -2 1/13

Answer:

-3 / 8 is the correct answer

hope this answer will help you

The values for x, y, and z are 95, -9, and -21, respectively, resulting in a three-digit number: 95-9-21 = 95921.

To solve the system of equations:

x + 3y - 2z = 1

2x + y + 3z = 20

2x - 2y + z = 6

By the use of the method of Gaussian elimination or matrix algebra. Here, the Gaussian elimination:

1. Multiply equation 1 by 2 and subtract equation 3:

2(x + 3y - 2z) - (2x - 2y + z) = 2 - 6

2x + 6y - 4z - 2x + 2y - z = -4

8y - 5z = -4

2. Multiply equation 1 by 2 and subtract equation 2:

2(x + 3y - 2z) - (2x + y + 3z) = 2 - 20

2x + 6y - 4z - 2x - y - 3z = -18

5y + z = -18

3. Rearrange equation 2:

2x + y + 3z = 20

2x + 2y + 6z = 40

4. Subtract equation 3 from equation 2:

(2x + 2y + 6z) - (5y + z) = 40 - (-18)

2x + y + 5y + 6z - z = 58

2x + 6y + 5z = 58

Now we have a new system of equations:

8y - 5z = -4

5y + z = -18

2x + 6y + 5z = 58

We can solve this system using any method of our choice. In this case, solving the system yields:

x = 95

y = -9

z = -21

Therefore, the values for x, y, and z are 95, -9, and -21, respectively, resulting in a three-digit number: 95-9-21 = 95921.

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The correct option is A, The area of triangle RST (8 ∙ 4) - 1/2 (10 + 12 + 16)

We begin by using drawing a rectangle across the triangle as shown inside the diagram under

Area of RST = region of the rectangle - (location of triangle A + area of triangle B + place of triangle C)

Area of RST = \((8*4) - [ (\frac{1}{2}*8*2) + (\frac{1}{2}*4*3) + (\frac{1}{2}*5*2) ]\) ⇒ we factorize the 1/2 out of the expression for the place of triangles A, B, and C

Area of RST = \((8*4)\) - \(\frac{1}{2}\) \((16+12+10)\)

A triangle is a closed -dimensional shape with 3 immediately facets and 3 angles. The sum of the inner angles of a triangle is continually 180 levels. Triangles are one of the basic shapes studied in geometry, and that they have many exciting properties and packages.

There are several methods to categorise triangles, based totally on their sides and angles. in line with their aspects, triangles may be categorised as equilateral, isosceles, or scalene. An equilateral triangle has three identical facets, an isosceles triangle has the same facets, and a scalene triangle has no same facets. according to their angles, triangles may be labeled as acute, right, or obtuse. An acute triangle has all angles less than ninety levels, a right triangle has one angle same to ninety degrees, and an obtuse triangle has one perspective greater than 90 ranges.

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Complete Question:

Which expression can be used to discover the place of triangle RST?

A). (8 ∙ 4) - 1/2 (10 + 12 + 16)

B). (8 ∙ 4) - (10 + 12 + 16)

C). (8 ∙ 4) - 1/2 (5 + 6 + 8)

D). (8 ∙ 4) - (5 - 6 - 8)

Answer:

Domain: 3, 6, 12, 18

Range: 5, 7, 9, 10

This is not a function.

Step-by-step explanation:

In a function there is a single y value for each x value. In this case, when x = 6, y can be both 5 and 10.  If you were to plot all these points and graph them, you would see that the result would fail the "vertical line test" for a function.

Answer:

9.4

Explanation:

Solve for perimeter to find how long the label is

2(3.14)(1.5)

Answer:

First number:15

Second number: 7

Step-by-step explanation:

To find the 2 numbers, we can use system of equations.

Let's use x for the first number and y for the second number. Our first equation would be:

x-y=8

This equation comes from the first sentence: the difference of the 2 numbers is 8. The second equation would be

2x+3y=51

This equation comes from the second part of the question.

We can use elimination method to find x and y.

x-y=8

2x+3y=51

Let's eliminate x. To do so, the x in both equations must be equal to each other. Since one is x and another is 2x, we must multiply the first equation by 2 to get the same x.

2x-2y=16

2x+3y=51

Now that the x are the same, we can subtract the equations.

-5y=-35

y=7

With our y value, we can find x by plugging y into any of the equations.

x-7=8

x=15

Since we found our x and y, the first number is 15 and the second number is 7.

x=-3

x=-11

because

x(x+14)=-33

so if x = -11 it will be 3*-11

and if x= -3 it will be -3*11

Answer:

x = -3, -11

Step-by-step explanation:

First, factor

Get all the terms on one side by adding 33 to both sides:

\(x^2 + 14x + 33 = 0\)

now, you want to find two numbers that add up to 14 and multiply to 33.

those numbers would be 3 and 11.

so you can then make it:

\((x + 3)(x+11)=0\)

you know that either x + 3 or x + 11 = 0,

so you can say:

x + 3 = 0

x = -3

ork

x + 11 = 0

x = -11

so x = -3, -11.

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Answer:

6 hours.

Step-by-step explanation:

since that is true we can use trial and error. if every km took an hour it would take six hours up and 4 hours down but they said they were twice as fast going down so that means it would take 2 hours going down. 6 add 2 is 8 which is our total meaning that 6 hours is the right answer

Answer:

19.20

Step-by-step explanation:

P.S im not a genius

Answer:

-1

Step-by-step explanation:

Substitute the x in.

y = -2(2)+3

y = -4+3

y = -1

Answer:

70%

Step-by-step explanation:

\(42\div60\)

Calculate

\(\frac{42}{60}\)

Cross out the common factor

\(\frac{7}{10}\)

Multiply a number to both the numerator and the denominator

\(\frac{7}{10}\times\frac{10}{10}\)

Write as a single fraction

\(\frac{7\times10}{10\times10}\)

Calculate the product or quotient

\(\frac{70}{10\times10}\)

Calculate the product or quotient

\(\frac{70}{100}\)

Rewrite a fraction with denominator equals 100 to a percentage

\(70\)%

I hope this helps you

:)

Answer:

50%

Step-by-step explanation:

The distribution is symmetrical about  the y-axis.

The probability that z is greater than zero in a standard normal distribution is 0.5 or 50%.

The branch which deals with the occurrence of a random event is known as probability.

The area under the curve to the right of z = 0 is equal to the area under the curve to the left of z = 0. So the standard normal distribution is symmetric about the mean of zero

As the total area under the curve is equal to 1, each of these areas must be 0.5 or 50%.

In a standard normal distribution, the probability that z is greater than zero is 0.5, or 50%.

Therefore, the probability that z is greater than zero in a standard normal distribution is 0.5 or 50%.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer:

1. 219.571428571

2. 150.314285714

The function that describes the fund that was raised is 0.05³ - 30x - 12425

The revenue is  R (z) = 0.05x³ + 75

the cost = C(z) = 30x + 12,500.

Please note that the equation for revenue missed a sign in the question so I made use of the plus sign

We would have revenue - cost

Hence ( 0.05x³ + 75) - (30x + 12,500)

We would open the bracket

0.05x³ + 75 -30x -12500

We would take the like term to

0.05³ - 30x -12500 + 75

0.05³ - 30x - 12425

The function that describes the fund that was raised is 0.05³ - 30x - 12425

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Answer: F(x)=0.05x^3-30x-12,575

Step-by-step explanation:

Correct on test.

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

3

Step-by-step explanation:

Subtract (inverse opperations):

18-15=3

Answer:

\(\sqrt{\frac{15}{2} }\) or 2.738

Step-by-step explanation:

Let’s just look at the triangle on the top with the \(\sqrt{10}\) on the top and x on the bottom. (Basically the top half to the equilateral triangle)

There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem: \(a^{2} +b^{2} =c^{2}\)

We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b=\(\frac{1}{2}(\sqrt{10})\) or \(\frac{\sqrt{10} }{2}\)

Plugging these values into the equation:

x^2+ (\frac{\sqrt{10} }{2})^{2}=\sqrt{10} ^{2}

\(x^{2}=\sqrt{10} ^{2}-\frac{\sqrt{10} }{2} ^{2}\)

\(x^{2} =10-\frac{10}{4}\)

\(x^{2} =\frac{15}{2}\)

\(x=\sqrt{\frac{15}{2} }\)

This approximately equals 2.738

Answer:

\(x=\sqrt{\frac{15}{2} }\). Another form of this answer is \(x=\frac{\sqrt{15} }{\sqrt{2} }\)(it's the same thing)

Step-by-step explanation:

Because the triangle is equilateral, all other sides of the triangle are also \(\sqrt{10}\). Also, x is the altitude of this triangle as it forms a right angle with the base and is therefore perpendicular. We know that this triangle is equilateral and in any triangle that has at least two sides that are equal(in other words isosceles), the altitude is also the median and angle bisector. A median would cut the side it reaches into half. So, x would cut the base into two equal parts. Since the base is \(\sqrt{10}\), divide it by two and both halves are \(\frac{\sqrt{10}}{2}\). What we are left with is two right triangles, both with legs \(\frac{\sqrt{10} }{2}\) and x. Using the Pythagorean Theorem, we know that \(a^{2}+b^{2}=c^{2}\), with \(a\) and \(b\) being the legs and \(c\) being the hypotenuse. So, we plug in the values and get \(\frac{\sqrt{10} }{2} ^{2}\)\(+x^{2}=\sqrt{10}^{2}\). Squaring, we get \(\frac{10}{4}+x^{2}=10\). This becomes \(x^{2}=10-\frac{10}{4}\) which equals \(x^{2}=\frac{40}{4}-\frac{10}{4}\). Finally, \(x^{2}=\frac{30}{4}\). This is \(x^{2}=\frac{15}{2}\). Square rooting this we get \(x=\sqrt{\frac{15}{2} }\). Another form of this answer is \(x=\frac{\sqrt{15} }{\sqrt{2} }\)

Answer:

1) The function is monotonically increasing

2) The end behavior of the function is x tends to infinity as t(x) tends infinity

3) The x and y -intercept is (0, 0)

4) The endpoint is (0, 0)

5) The domain is 0 ≤ x ≤ +∞

The range is 0 ≤ t(x) ≤ +∞

Step-by-step explanation:

1) The given function of the time for the object to hit the ground is t(x) = 1/4·√x

Where;

x = The distance from the ground

t = The time it takes for the object to hit the ground

Monotonically increasing function, we have;

A function that is continuous on [a, b] and it can be differentiated in the domain, (a, b) is monotonically increasing when df(x)/dx > 0 for all values of x in (a, b)

However, where df(x)/dx < 0 for all values of x in (a, b), the function is decreasing

Therefore, using an online tool, we have;

dt(x)/dx = d(1/4·√x)/dx = 1/8 × 1/√x

Therefore, the dt(x)/dx > 0, for 0 < x < +∞ and the function is monotonically increasing

2) The end behavior of the function as x tends to infinity, t(x) = 1/4·√x approaches infinity

3) From the end behavior, and the nature, of the function t(x) = 1/4·√x, where both variables are directly proportional, we have that the x and y -intercept =  (0, 0)

4) The endpoint is (0, 0) given that as t(x) tends to 0, x tends to 0

5) The domain is 0 ≤ x ≤ +∞

The range is 0 ≤ t(x) ≤ +∞.

Answer:

The function is monotonically increasing since the output values are continually getting larger. This also tells us that the end behavior of the function is infinity.

The x-intercept is (0,0), the y-intercept is (0,0), and the endpoint too is (0,0).

The domain of the graph is all values greater than or equal to 0, and the range is all positive output values.

Step-by-step explanation:

Answer:

a) 53%

b) 12%

Step-by-step explanation:

you need to use the equation given

y = -6.83x + 108

x is the rank

y is the probability of winning 1st game

a) for rank 8th or x=8

y = -6.83(8) + 108 = 53.36 or 53%

b) for rank 14th or x=14

y = -6.83(14) + 108 = 12.38 or 12%

Recursive algorithm for minimum number of bills needed to make an amount, given n and k denominations:Calculate the minimum number of bills by considering each denomination and recursively reducing the remaining amount

Here's a description and analysis of a recursive algorithm that computes the minimum number of bills needed to make an amount n using a system of k denominations:

Algorithm: MinimumBills(n, denominations)

If n is zero, return 0 (no bills needed).

If n is negative, return infinity (impossible to make the amount).

If n is a value that has already been computed and stored, return the stored value.

Set minBills to infinity.

For each denomination d in the k denominations:

a. If n is greater than or equal to d, recursively call MinimumBills(n - d, denominations) and store the result in numBills.

b. If numBills is less than minBills, update minBills to numBills.

Store minBills for the value of n.

Return minBills.

Analysis:

The recursive algorithm computes the minimum number of bills needed to make the amount n using the given denominations. The algorithm explores all possible combinations of denominations to find the optimal solution.

Time Complexity: The time complexity of the algorithm depends on the values of n and k denominations. Since the algorithm explores all possible combinations, the worst-case time complexity is exponential, \(O(k^n)\).

However, if the denominations are limited and n is relatively small, the algorithm can run in polynomial time.

Space Complexity: The space complexity of the algorithm is determined by the recursion depth, which is equal to n. Therefore, the space complexity is \(O(n).\)

Note: To optimize the algorithm and avoid redundant calculations, you can use memoization by storing the results for previously computed values of n in a lookup table. This can significantly reduce the number of recursive calls and improve the overall performance.

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Answer:

20

Step-by-step explanation:

320 = 16x

Our objective here is to isolate the variable (x) using inverse operations

First we want to get rid of 16

16x is the same as 16 times x( which is multiplication)

The inverse of multiplication is division so to get rid of the 16 we divide by 16 ( but note: whatever you do to one side you must do to the other ) so we divide both sides by 16

320/16=20

16x/16 = x

We would be left with x = 20

This meaning that they would need 20 first grade classes

Answer:

The school will need 20 first grade classes

Step-by-step explanation:

So think about it. There are 320 first grade students and each class can have 16 students which represents the equation 16x=320

All you need to do is solve the equation 16x=320

The equation is multplication. To undo multiplication you need to do division

So, x=320/16

x=20

So overall, your awnser is 20.

Answer:

10x=1/2(x+3)

Step-by-step explanation:

option b is the answer