If KL=12 and LM=7, what is JL? Write your answer as a whole number or as a decimal rounded to the nearest hundredth. JL =

Any counting number can be written as the sum of distinct powers of 2.(proved).

What is counting number?

Counting numbers are nothing but  the natural numbers that can be used for counting. The numbers start from 1 and the series continues as 1, 2, 3, 4, 5, 6,-- and so on. Zero can not be included in counting numbers because we cannot count 0.

To prove this statement we have to consider two cases.

Let, n be any counting number or natural number. Then the power of 2 can be written as 2ⁿ.

n can be even or odd.

n=1:

If n=1 then it can be written as 2⁰

Let us assume that for n≤ k that n can be written as the sum of distinct powers of 2.

Now let us take, n= k+1.

Here one case is n is odd.

Then n≤ k+1

   so, n-1≤ k

By the induction hypothesis n-1 can be written as distinct power of 2.

n is the sum of these distinct powers of 2 as well 2⁰, which is not among them. as n-1 is even.

Now if n is even,

so n=2m (say) for m≤ k

Thus, by the induction hypothesis m can be written as distinct power of 2.

If for each power of 2 in this sum , increment the exponent by 1 then the resulting sum of distinct powers of 2 equals n= 2m

Hence, the statement is true.

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The solution set for this equation S^2-11s can be expressed as 0, 11.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on. The purpose of an equation is to find the value(s) of the variable(s) that make the equation true.

Given that S^2-11s, which can be written as S^2-11s = 0 We can factor the expression on the left-hand side to get:

S(S-11) = 0

Then this  equation is satisfied when either S = 0 or S-11 = 0. Thus, the solution set is: S = {0, 11}

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Naya earns a total of $98538.30 in the 5th year

Naya starts with a salary of $85,000 per year, and her salary increases by 3% each year.

So, her salary in year 5 will be:

Salary = Initial salary * (1 + rate)^5

So, we have

Salary = 85000* (1 + 3%)^5

Evaluate

Salary = 98538.30

Hence, the 5th year earnings is 98538.30

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To save on shipping costs, Camile should choose a box that is lightweight and has a small volume.

This is because she has realized that she is charged based on the volume of the box and not the weight.

Therefore, a smaller volume box would cost her less than a larger volume box of the same weight.

For example, if Camile needs to ship a 5-pound item, she should choose a smaller box with a volume that is just enough to fit the item, rather than a larger box with more empty space. This is because the larger box would have a greater volume, and therefore, incur a higher shipping cost even though it weighs the same as the smaller box.

In summary, when selecting a box to save on shipping costs, it is important to consider both weight and volume. Camile should choose a box that is lightweight and has a smaller volume to reduce her shipping costs.

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The volume of the solid figure bis 1465. 33 in³

The formula for the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters are;

From the information given, we have;

Volume = 3.14 × 4² × 18

Multiply the values

Volume = 904. 32 in²

Volume of the smaller cylinder

Volume = 3.1 4 × 4 × 18

Volume = 226. 08 in³

Volume of a cone = πr²h/3 = 3.14 × 8² × 5/3

Multiply the values

Volume = 334. 93 in³

Then, the volume of the solid = 904. 32 + 226. 08 + 334. 93 = 1465. 33 in³

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The probability of not getting a purple after turning the spinner would be = 0.75

To calculate the probability of the given sample;

= possible outcome/sample space

where;

possible outcome = 3

sample space = 4

Probability = 3/4 = 0.75

Therefore, the probability of not getting a purple colour would be = 0.75

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The surface area of cylinder M is approximately 184.85 square feet, and the surface area of cylinder N is approximately 401.92 square feet.

Let r_N and h_N be the radius and height of cylinder N, and r_M and h_M be the radius and height of cylinder M. We are given that the radius of cylinder N is equal to its height (rN = hN), and the ratio of the height of cylinder N to the height of cylinder M is 5 : 3.

So, we can write:

hN = rN

hN / hM = 5 / 3

The surface area formulas for cylinders M and N:

Surface Area (M) = 2πr_MhM + 2πr_M^2

Surface Area (N) = 2πrNhN + 2πrN^2

If Surface Area (N) = Surface Area (M) + 256

∴ 2πrNhN + 2πrN^2 = 2πrMhM + 2πrM^2 + 256

Combine like terms:

4πrN^2 = 2πrMhM + 2πrM^2 + 256

Divide both sides by 2π:

2rN^2 = rMhM + rM^2 + 128/π

Since hN = rN, we can write:

hM = (3/5)rN

Now substitute hM into equation

2rN^2 = rM((3/5)rN) + rM^2 + 128/π

2rN^2 = (3/5)rN x ((3/5)rN) + ((3/5)rN)^2 + 128/π

= 2rN^2 = (9/25)rN^2 + (9/25)rN^2 + 128/π

= 2rN^2 = (18/25)rN^2 + 128/π

rN = 5.64, hN = 5.64,

rM = 5.64 x (3/5) = 3.38

rM = 3.38.

let's calculate the surface areas:

Surface Area (M) = 2π(3.38)(3.38) + 2π(3.38)^2 ≈ 71.15 + 113.70 ≈ 184.85 square feet

Surface Area (N) = 2π(5.64)(5.64) + 2π(5.64)^2 ≈ 200.96 + 200.96 ≈ 401.92 square feet

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A good prediction for the number of times a 5 will be rolled out of 50 rolls of a 6-sided number cube is 8 times.

Assuming the number cube is fair and each outcome has an equal probability of occurring, we can use the concept of probability to make a prediction for the number of times a 5 will be rolled.

Since there are six possible outcomes, each with a probability of 1/6, the expected frequency of rolling a 5 in one roll is:

1/6 x 50 = 8.33

This means that if the number cube is rolled 50 times, we would expect to see a 5 appear approximately 8.33 times. However, since we cannot roll a fraction of a time, we need to round this number to the nearest whole number.

Rounding 8.33 to the nearest whole number, we get:

8

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Complete question is:

A 6-sided number cube with sides labeled 1,2,3,4,5, and 6 is rolled 50 times. What is a good prediction for the number of times a 5 will be rolled?

a group of 237 campers would require 40 campsites (since we cannot have half of a campsite).

How to solve the question?

To determine the number of camp sites required for a group of 237 campers, we can divide the total number of campers by the maximum number of campers allowed per site.

237 campers ÷ 6 campers per site = 39.5

Since we cannot have a fraction of a campsite, we need to round up to the nearest whole number. This is because we need to ensure that there is enough space for all of the campers, and rounding up will ensure that we have enough sites to accommodate them.

Therefore, a group of 237 campers would require 40 campsites (since we cannot have half of a campsite).

It is important to note that while this calculation is a good starting point, it is always a good idea to check with the campground to ensure that they can accommodate a group of this size. Additionally, the campground may have specific policies or procedures in place for reserving campsites for large groups.

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Answer: Profit = .95 or 95 cents

Step-by-step explanation:

What is the question here?

If it is profit then the answer is 3.79-2.84

Answer:

3 + 7 = 10

Step-by-step explanation:

I hope this answers your question. :)

Answer: 3+7=10

Step-by-step explanation:

maybe this is it but this question is really unclear

To construct a confidence interval for the proportion of defectives, we should use the plus four method.

Since the sample size is 20, which is not very large, the large-sample interval is not appropriate. Instep, we ought to utilize a strategy that's suitable for little test sizes. 

The plus four method is one such method that is commonly used when the sample size is small. Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

The plus four strategies may be a strategy for building a certainty interim for an extent when the test estimate is little.

To utilize this strategy, we to begin with include four fanciful perceptions to our test, two of which are flawed and two of which are not imperfect.

This increments the test estimate to 24, which permits us to utilize the typical guess to the binomial dispersion to build the certainty interim.

The equation for the certainty interim utilizing the also four strategies is:

p ± zα/2 √((p + 2) (1 - p + 2) / n + 4)

where:

p is the test extent (number of defectives/test estimate)

zα/2 is the basic esteem from the standard typical dissemination at the level of importance α/2

n is the test estimate (counting the included four nonexistent perceptions)

Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

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Answer:

A byte is 8 bits.

WX must be positive because it measures the width of a trapezoid's side. WX thus equals 16.

A parallelogram with at least two pair of parallel sides is known as a trapezium in geometry (or a parallelogram in American English). The legs of a trapezium are the non-parallel sides, whereas the parallel sides are referred to as the bases. The legs of a zygomatic arch might be equal in length (isosceles) or varied in length (non-isosceles). By averaging the widths of the two bases and multiplying by the height, a trapezium's area can be determined (the perpendicular distance between the two bases). that is Area equals (a + b)*h / 2. where h is the trapezium's height and a and b are the lengths of the base's two parallel sides (the bases).

given

MN can be used in place of XV2 in the equation, and the result is simplified to:

XV² = (1/4) (WX + 18)² + h²

Now, we can add the following expression for XV2 to the equation for WX2:

WX² = 18² + XV²

WX² = 18² + (1/4) (WX + 18)² + h²

Adding and subtracting:

3WX² - 218WX - 18² = 4h²

We can now resolve WX:

WX is equal to (218 sqrt((218)2 - 43(-182))). / (2*3)

WX = 16 or -27

WX must be positive because it measures the width of a trapezoid's side. WX thus equals 16.

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The graph of the solution would be a number line with an open circle at 48 and an arrow extending to the right, indicating all values greater than 48 are solutions to the inequality. The solution would be (48, ∞).

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

Part A:

We can solve the inequality as follows:

1/4x - 3 - 5 > 4

1/4x - 8 > 4

1/4x > 12

x > 48

Therefore, the solution to the inequality is x > 48.

Part B:

Since the inequality is stringent, the graph of the solution would be a number line with an open circle at 48 and an arrow pointing to the right, signifying that all numbers greater than 48 are solutions to the inequality. The answer would be (48, ) in interval notation.

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The measure of Arc AU is 50⁰. Hence, the correct option is B.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.

arc QU = 88 and <QUA = 111

QDA = 2 <QUA

= 2 X 111

= 222⁰

Now, QUA = 360- 222 = 138

arc AU = QUA - arc QU

= 138- 58

= 50⁰

Hence, the measure of AU is 50⁰.

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-- The given question is incomplete, the complete question is attached below. --

Answer:

50⁰

Step-by-step explanation:

The measure of Arc AU is 50⁰. Hence, the correct option is B.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.

Edge 2023

Answer: 49/60 of corn

Step-by-step explanation:

How I got this answer was I basically paid attention to the wording. 1/6 as much meaning x 1/6. So, I converted 4 9/10 to a fraction and got 49/10. Then, I multiplied 49/10 by 1/6 and got 49/60. The fraction can't be simplified any lower, so it is supposed to be left as is. Hope this helped!

Answer:

x = -8 + sqrt(10) and x = -8 - sqrt(10)

Step-by-step explanation:

The quadratic equation to be solved is:

2(x + 8)² + 9 = 29

First, we need to simplify the left-hand side of the equation by expanding the squared term:

2(x + 8)(x + 8) + 9 = 29

Simplifying further, we get:

2(x² + 16x + 64) + 9 = 29

Distributing the 2, we get:

2x² + 32x + 128 + 9 = 29

Combining like terms, we get:

2x² + 32x + 137 = 29

Subtracting 29 from both sides, we get:

2x² + 32x + 108 = 0

Dividing both sides by 2, we get:

x² + 16x + 54 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula :

The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).

Answer:

We can start by using the tangent formula:

tan(P) = sin(P) / cos(P)

We are not given the values of sin(P) and cos(P) directly, but we can use the Pythagorean identity to relate them:

sin^2(P) + cos^2(P) = 1

We can rearrange this expression to solve for sin(P) in terms of cos(P):

sin^2(P) = 1 - cos^2(P)

sin(P) = ±√(1 - cos^2(P))

Now we can substitute this expression into the tangent formula:

tan(P) = ±√(1 - cos^2(P)) / cos(P)

Substituting the given values and simplifying:

tan(P) = ±√(1 - (2/√85)^2) / (1/√89)

tan(P) = ±√(1 - 4/85) * √89

tan(P) = ±√(81/85) * √89 / 1

We want to express tan P in simplest radical form, so we can simplify the square root by factoring out the greatest perfect square factor of the numerator:

tan(P) = ±(√9/√85) * (√89/1)

tan(P) = ±(3/√85) * (√89/1)

Therefore, the exact value of tan P in simplest radical form is ±(3/√85) * (√89/1).

Answer: Part A is (-9, 13) Part B is (9, 13)

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

[tex]-4x-5-11x=40\\-15x=40+5[/tex]

[tex]x=\frac{45}{-15}[/tex]

[tex]x=-3[/tex]

Hope this helps.

The measure of the angle MSP, m∠MSP, obtained using the relationship between linear pair angles is 80°

Linear pair angles are angles that have a sum of 180°. Linear pair angles come together to form a straight line.

The specified measure of the angle NSM is m∠NSM = 100°

The angles ∠NSM and ∠MSP are linear pair angles therefore;

m∠NSM + m∠MSP = 180°

Plugging in the known value of the angle NSM, we get;

100° + m∠MSP = 180°

Therefore; m∠MSP = 180° - 100° = 80°

The measure of the angle MSP, m∠MSP is 80°

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Method of predicting a continuous dependent variable on the basis of two or more independent variables. The correct answer is (b)

Multiple regression is a statistical technique used to examine the relationship between a single dependent variable and multiple independent variables.

It is a type of regression analysis that can help to identify which independent variables are related to the dependent variable and to what extent.

The goal of multiple regression is to create a model that can be used to predict the value of the dependent variable based on the values of the independent variables.

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Before doing calculations we can predict rectangular prism A has greater surface area to volume ratio than that of rectangular prism B.

The surface area of rectangular prism A is 136 square inches and that of B is 170 square inches. And  the ratio of surface area to volume of rectangular prism A is 1.4167 square inches/ cubic inches (approximately) and that of B is 1.1334 square inches/ cubic inches (approximately).

Rectangular prism A has dimension as,

length = 3 inches , breadth = 4 inches and height = 8 inches

Rectangular prism B has dimension as,

length = 5 inches , breadth = 5 inches and height = 6 inches

The surface area of rectangular prism can be calculated using the formula = 2( length*breadth + length*height + height*breadth)

Therefore, surface area of rectangular prism A = 2{ (3*4) + (3*8) + (4*8)} square inches =136 square inches (that is, 136 [tex]inches^{2}[/tex])

Surface area of rectangular prism B = 2{ (5*5) + (5*6) + (5*6)} square inches =170 square inches (that is, 170 [tex]inches^{2}[/tex])

The volume of rectangular prism can be calculated using the formula = length * breadth * height (in cubic unit)

Therefore, volume of rectangular prism A = (3)(4)(8) cubic inches =96 cubic inches (that is, 96 [tex]inches^{3}[/tex] )

Volume of rectangular prism B = (5)(5)(6) cubic inches =150 cubic inches (that is, 150 [tex]inches^{3}\\[/tex] )

Therefore, ratio of surface area to volume of rectangular prism A = (136/96) square inches/ cubic inches = 1.4167 square inches/ cubic inches (approximately)

Ratio of surface area to volume of rectangular prism B = (170/150) square inches/ cubic inches = 1.1334 square inches/ cubic inches (approximately)

Thus,  ratio of surface area to volume of rectangular prism A is greater than that of rectangular prism B.

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Answer: 81mi^2

Step-by-step explanation:

Area Formula for Square: side * side

9*9 = 81

a. Angle 1 and angle 2 are equal because they are alternate to each other

b. since angle 1 and angle 2 are equal, arc AC and BD will be equal too

c. Parallel lines will intercept congruent arcs.

When any two parallel lines are cut by a transversal, there are various pairs of angles that are formed.

These angles are corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.

Therefore , angle 1 and 2are alternate to each other, this means that they are equal.

Since the two angles are equal , the corresponding arc formed by the two angles are also equal.

This means parallel lines will intercept congruent arcs

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The appropriate measure of center for the data on the tickets sold is C. The median is the best measure of center, and it equals 19.

In a box plot, the median is represented by the horizontal line that divides the box into two equal parts. The median is the middle value of the dataset when it is ordered from smallest to largest.

The median is the best measure of center for a box plot. The median is represented by the line inside the box, which in this case is at 19 on the number line.

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Answer:

ccccccccccccccccccccccccc

Step-by-step explanation: