Find the length of the hypotenuse

Step-by-step explanation:

To mentally divide by 0.1, 0.01 and 0.001, you can use the following tips:

Dividing by 0.1 is equivalent to multiplying by 10.

Dividing by 0.01 is equivalent to multiplying by 100.

Dividing by 0.001 is equivalent to multiplying by 1000.

(a) Each xi in the vector (x1, x2, ..., xn) can be either 0 or 1.

Therefore, there are 2 possibilities for each xi.

The number of vectors that can be formed by combining these values is equal to the number of combinations of 2 possibilities, taken n times.

The number of vectors (x1, x2 . . ., xn) such that each xi is either 0 or 1 and n where k is a non-negative integer less than or equal to n is 2^n.

the same problem as before but under the condition thatx1 + x2 + · · · + xn ≥ k,

This is equivalent to 2^n. For example, if n = 2, then there are 2 possibilities for x1 (either 0 or 1) and 2 possibilities for x2 (either 0 or 1). The total number of vectors that can be formed is 2 * 2 = 2^2 = 4. In general, the number of vectors that can be formed is equal to 2^n.

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The complete question is :-

determine the number of vectors (x1, x2 . . ., xn) such that each xi is either 0 or 1 and n where k is a non-negative integer less than or equal to n.

The value of interior angle and the exterior angle will be 9, 140 degree.

Hence, option (a) is correct choice.

(a) 40, 140

An exterior angle of a regular polygon with 40 sides is equal to 360 divided by the number of sides, which is 360/40 = 9 degrees.

An interior angle of a regular polygon with 40 sides is equal to (180(n-2))/n,

where n is the number of sides,

which is (180(40-2))/40 = 140 degrees.

So the answer is: 9, 140.

(b) 140, 220

The exterior angle of a regular polygon with 40 sides is equal to 360 divided by the number of sides,

which is 360/40 = 9 degrees.

An interior angle of a regular polygon with 40 sides is equal to (180(n-2))/n,

where n is the number of sides, which is (180(40-2))/40 = 140 degrees.

So the answer is: 9, 140.

(c) 9, 171

The exterior angle of a regular polygon with 9 sides is equal to 360 divided by the number of sides, which is 360/9 = 40 degrees.

An interior angle of a regular polygon with 9 sides is equal to (180(n-2))/n,

where n is the number of sides, which is (180(9-2))/9 = 140 degrees.

So the answer is: 40, 140.

(d) 4.5, 175.5

This answer is incorrect.

The exterior angle of a regular polygon with 4.5 sides is not possible since the number of sides in a polygon must be a positive integer.

The interior angle of a regular polygon with 4.5 sides is not possible since the number of sides in a polygon must be a positive integer.

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The percent increase in the height of the seedling is, 23%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

A seedling Jeffery planted in 2009 was 5cm tall in 2010 it was 120 cm

i.e. increase in the height = 120-5

                                           =115 cm

now,

the percent increase in the height of the seedling is,

115/5*100

=23%

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The value of the principal investment is $21,597.30. The solution has been obtained by using the concept of compound interest.

What is compound interest?

When interest is calculated, both the principal and the interest that has accumulated over the previous period are used. Compound interest accounts for the principal when calculating the interest for the subsequent month, as opposed to simple interest, which does not. In algebra, the letter C.I. is frequently used to denote compound interest.

We are given that after 16 years in an account with a 6.2% annual interest rate compounded continuously, an investment is worth a total of $58,226.31.

This means that

P(t) = $58,226.31

t = 16 years

r = 6.2%

We know that formula for continuous compounding interest is

[tex]P(t) = P_{0} e^{rt}[/tex]

So, using this, we get

⇒58,226.31 = Pe^(0.062*16)

⇒58,226.31 = Pe^(0.992)

⇒58,226.31 = P*2.696

⇒P = $21,597.30

Hence, the value of the principal investment is $21,597.30.

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Answer:

[tex]\frac{2}{15}[/tex]

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] - [tex]\frac{1}{5}[/tex]

[tex]\frac{5}{15}[/tex] - [tex]\frac{3}{15}[/tex] = [tex]\frac{2}{15}[/tex]

Answer:

Jada's Coffee Shop used 1/3 of a carton of whole milk and 1/5 of a carton of nonfat milk on Saturday. Therefore, the amount of whole milk used was 2/3 of a carton, and the amount of nonfat milk used was 1/5 of a carton. The difference between the two is 2/3 - 1/5, which is equal to 7/15 of a carton. Therefore, Jada's Coffee Shop used 7/15 of a carton more whole milk than nonfat milk.

The parallel segments are MN & LK, MP & JK and NP & JL

The side lengths are listed below and the perimeter is 84 units

By definition, parallel segments are segments that extend indefinetely and do not meet

Using the above as a guide, we have the following:

The midsegments are given as

MP = 17, LK = 24 and PN = 13

This means that

JK = 2 * MP

JK = 2 * 17

JK = 34

Also, we have

MN = 1/2 * LK

MN = 1/2 * 24

MN = 12

Lastly, we have

JL = 2 * PN

JL = 2 * 13

JL = 26

For the perimeter, we have

Perimeter = JK + LK + JL

Perimeter = 34 + 24 + 26

Perimeter = 84

Hence, the perimeter is 84 units

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Luna received 9 dollar for each pair of sneakers. She got total 18 dollars for her 2 pairs of sneakers. The equation which we can use to find the amount of money x= total money spent+ money remained.

It is given that, total pair of jumper sneakers she sold at the secondhand market = 2 pairs.

So, total sneakers= 4

Let, she got total x dollar for her jumpy sneakers.

So, here, total money spent= 12 dollars

total money left with her= 6 dollars

Hence, x= 12+ 6 dollars = 18 dollars.

So, total money she got = 18 dollars.

Money for each pair of sneakers= 9 dollars.

Equation for x= total money spent+ money left with her.

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The performance score associated with the c grade is 157, and the performance score associated with the a grade is 355.

The z-score is a numerical measurement used in statistics to indicate how many standard deviations a particular value is from the mean of a dataset. It is calculated by subtracting the mean from the data point and dividing the result by the standard deviation. The resulting number is the z-score. The z-score is a useful tool for identifying outliers in a dataset, as values with z-scores that are too high or too low can be easily identified. Z-scores can also be used for comparing data points from different datasets, as z-scores are independent of the mean and standard deviation of the dataset. Z-scores can also be used for comparing data points from different datasets, as z-scores are independent of the mean and standard deviation of the dataset. This makes them ideal for normalizing data from different sources or for comparing data from different time periods or from different locations.

The z-score associated with the 9th percentile from the standard normal distribution is -1.28, and the z-score associated with the 91st percentile is 1.28.

b. (2 points) what are the performance scores associated with the c grade and the a grade?

The performance score associated with the c grade is 157, and the performance score associated with the a grade is 355.


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Answer:

2%

Step-by-step explanation:

we roll a red and a green die. let a = ""the red die shows a 2 or a 5"" and b = ""the sum of the two dice is at least 7."" are a and b independent.

Probability plays a vital role in all fields like the economy, medicine, etc. It intends to forecast the events that will be happening in the future. So its values never come in negative. It has two main rules.

Rule of multiplication

Rule of addition.

The green and red dice are rolling,

the sample space = {(1,1)(1,2)......(1,6) (2,1).....(2,6)(3,1)....(3,6).......(6,6)}

let A be the event of the red shown a 2or a or 5

let B be the event of the sum of the two dice is at most 7.

The probability of the red die shown as a 2 or a 5

total outcome =36

favorable case =24

the probablity=24/36=4/6=2/3

let B be the event of the sum of the two dice is at most 7.

p(B)=21/36=0.5833

p(AnB)=13/36=0.3611

P(A)P(B)=0.3888

Hence a and b are independent.

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1/8 is the 9th term in sequence .

What does sequence look like in math?

A sequence is a collection of numbers in a particular order. To go forward in the defined pattern, three dots are shown. A phrase is used to refer to each number in the series.

                            One is the first word, three is the second, five is the third, and so on, in the series 1, 3, 5, 7, 9,... There are groups of numbers called number sequences that adhere to a pattern or norm. Arithmetic sequences are those in which the rule is to add or remove a number each time. A geometric sequence is one where the rule is to multiply or divide by a specific amount each time. A word is used to describe each number in a sequence.

a₉ = 1/8

the general term through the pattern aₙ = 32(1/2)ⁿ⁻¹

  Substitute and calculate  aₙ = 1/8

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The correct option: C.) 3.75 x 10^6 m.  The size of other larger cell is found as the 3.75 x 10^6 m , written in the scientific notation.

The size of one smaller cell : 2.5 x 10^-9 m.

The size of other larger ball: 1.5 x 10^3 times larger than first ball.

For the size of other larger ball:

Size = 2.5 x 10^-9 x 1.5 x 10^3

Size = 2.5 x 1.5 x 10^(-9+3)

Size = 3.75 x 10^6 m

Thus, the size of other larger cell is found as the 3.75 x 10^6 m , written in the scientific notation.

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The correct question is-

The size of a certain cell is 2.5 x 10^-9 m. Another cell is 1.5 x 10^3 times larger. How large is the larger cell in scientific notation?

A.) 4 x 10^-27m

B.) 4 x 10^-12m

C.) 3.75 x 10^6m

D. 3.75 x 10^-6m

A kilogram is a unit of mass in the metric system and is often used to measure the weight of food items. One kilogram is equivalent to 35.27 ounces. To determine how many ounces of peanut butter you used for your sandwich, you need to convert the mass in kilograms to ounces.

In this case, the jar contains 1.41 kg of peanut butter. To find the amount of peanut butter you used, you multiply the total amount by the percentage of the peanut butter you used. In this case, 8.0% of 1.41 kg is 0.11 kg of peanut butter.

Finally, you convert the 0.11 kg of peanut butter to ounces using the conversion factor of 35.27 ounces per kilogram. So 0.11 kg * 35.27 oz/kg = 3.88 ounces of peanut butter.

This answer is expressed to two significant figures because the original mass of the peanut butter is given to two significant figures (1.41 kg) and the percentage of peanut butter used is also given to two significant figures (8.0%).

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Answer:(-2,4) (6,-2)

Step-by-step explanation: 1.We solve the equation with x = -2 and get y = 4 , (-2,4) which is a coordinate

2. we solve the equation with x=6 and gets y= -2 (6,-2) is a coordinate


Mark these two coordinates to get a line in the graph!

The measure of ∠XYZ is 130°. Option C is the correct option.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. Sometimes it is stated to have exactly two sides that are the same length, and other times it is stated to have at least two sides that are the same length, with the latter version including the equilateral triangle as an exception.

Given that the length of YZ = YX and ∠YZX = 25°.

There is an agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

According to the property of the isosceles triangle:

∠YXZ = ∠YZX = 25°

The sum of all angles of a triangle is 180°.

Therefore,

∠YXZ + ∠YZX + ∠XYZ = 180°

25° + 25° +  ∠XYZ = 180°

50° +  ∠XYZ = 180°

∠XYZ = 180° - 50°

∠XYZ = 130°

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The equation using the identity rule is a^3 - 3a^2b + 3ab^2 - b^3

The equation (a-b)^3 can be expanded using the binomial theorem, where the variables are the two numbers (a and b),

From the question, we have the following parameters that can be used in our computation:

(a-b)^3

When expanded, we have

a^3 - 3a^2b + 3ab^2 - b^3

Hence, the expansion is a^3 - 3a^2b + 3ab^2 - b^3

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The benefit of using a curve over a histogram is that, it is a useful tool for visualizing data distributions, curves provide a more detailed and flexible representation of the data and offer additional advantages in terms of resolution, flexibility, parametric modeling, and comparison.

Visualizing data is an essential aspect of understanding the underlying patterns and relationships. In data analysis, two popular ways of visualizing data are histograms and curves. While both of these visualization techniques serve the purpose of summarizing data, each of them has its unique benefits and limitations.

Resolution: One of the main benefits of using a curve over a histogram is that a curve provides a higher resolution representation of the data. A curve can capture finer details of the data distribution that might get lost in a histogram due to the binning process.

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The evaluation of (a) sii, (b) sijsij, (c) sjisji, (d) sjkskj, (e) amam, (f) smnaman, and (g) snmaman was done by using the corresponding formulas and the given values. The results were 3, 6, 6, 6, 2, 6, and 24 respectively.

To evaluate (a) sii, we will use the formula sii = ai + bi. In this case, ai = 1 and bi = 2, so sii = 1 + 2 = 3.

To evaluate (b) sijsij, we will use the formula sijsij = ai × bi. In this case, ai = 2 and bi = 3, so sijsij = 2 × 3 = 6.

To evaluate (c) sjisji, we will use the formula sjisji = aj × bj. In this case, aj = 2 and bj = 3, so sjisji = 2 × 3 = 6.

To evaluate (d) sjkskj, we will use the formula sjkskj = ak × bk. In this case, ak = 3 and bk = 2, so sjkskj = 3 × 2 = 6.

To evaluate (e) amam, we will use the formula amam = ai × aj. In this case, ai = 1 and aj = 2, so amam = 1 × 2 = 2.

To evaluate (f) smnaman, we will use the formula smnaman = ai × aj × ak. In this case, ai = 1, aj = 2, and ak = 3, so smnaman = 1 × 2 × 3 = 6.

To evaluate (g) smnaman, we will use the formula smnaman = ai × aj × ak × bm. In this case, ai = 1, aj = 2, ak = 3, and bm = 4, so smnaman = 1 × 2 × 3 × 4 = 24.

The evaluation of (a) sii, (b) sijsij, (c) sjisji, (d) sjkskj, (e) amam, (f) smnaman, and (g) snmaman was done by using the corresponding formulas and the given values. The results were 3, 6, 6, 6, 2, 6, and 24 respectively.

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Weibull distribution is a continuous distribution related to the shape of parameter where k∈(0 , ∞) with g distribution : g(t) = 1- exp ( -t^k) , t ∈[0, ∞).

Other distribution is probability density function defined as

g(t) = kt^( k -1) exp ( -t^k)  , t ∈ (0, ∞).

Therefore, Weibull distribution is defined on basis of shape parameter k,

g(t) = 1- exp ( -t^k) , t ∈[0, ∞) and other distribution includes probability density function is   g(t) = kt^( k -1) exp ( -t^k)  , t ∈ (0, ∞).

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The volume of a container is found to be 38.5 in³. Its volume in units of cm³ will be 630.902 cm³.

Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

To create a formula to convert 38.49 in³ to cm³, we start with the fact that 1 inch is 2.54 centimetres, which means that you multiply inches by 2.54 to get centimetres. We can therefore make the following equation:

inches × 2.54 = centimeters

(inches × 2.54)³ = centimeters³

inches³ × 16.387064 = centimeters³

in³ × 16.387064 = cm³

Now that we have the in³ to cm³ formula, we can calculate and convert 38.5 in³ to cm³. Here is 38.5 in³ converted to cm³, along with the math and the formula:

= in³ × 16.387064

= 38.5 × 16.387064

= 630.902 cm³

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The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes in the sample space.

Outcome(s): An outcome is a possible result of a random experiment. For example, in a coin flip, an outcome could be either heads or tails.

Sample Space: The sample space is the set of all possible outcomes of a random experiment. In the coin flip example, the sample space would be {heads, tails}.

Event(s): An event is a subset of the sample space that includes one or more outcomes. For example, if the event is getting heads in the coin flip, the event would be {heads}. The probability of an event is the number of outcomes in the event divided by the total number of outcomes in the sample space.

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The number of piles when the newspaper is 15 will be 3.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

20 newspapers in 4 piles.

We know that the ratio of the newspaper to pile is constant. Then 15 newspapers in piles will be given as,

15 / x = 20 / 4

15 / x = 5

x = 15 / 5

x = 3

The number of piles when the newspaper is 15 will be 3.

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The probability of selecting at least one red marker probability = [tex]\frac{1}{5}[/tex]

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

In the box contains ,

Black markers are = 5

Blue markers are = 3

Red markers are = 2

The given scenario will not affect the required probability as the selection of the second one is a case of future.

We need to find the probability of the first marker is red.

The probability is,

Probability =  [tex]\frac{red marker}{total markers}[/tex]

Total markers = 5 + 3 +2

= 10

Probability = [tex]\frac{2}{10}[/tex]

Probability = [tex]\frac{1}{5}[/tex]

The probability of selecting at least one red marker probability = [tex]\frac{1}{5}[/tex]

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Assuming you graph lines f and g on the same coordinate plane and they intersect at point (4, 5), a statement which is not true include the following: D. Other points that are on line f are also solutions of the system.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

Based on the graph of the lines representing the system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-axis and y-axis, which is given by the ordered pair (4, 5).

In conclusion, the ordered pair (4, 5) is a solution to the system of equations and it is located on both lines f and g.

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The distance between the van and Smithville is changing at a rate of 40.83 miles per hour.

To calculate how fast the distance between the van and Smithville is changing, we can use the following steps:

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The length of side CE is 5/6 units

From the question, we have the following parameters that can be used in our computation:

The triangle

On the triangle, we have the following ratio

x - 2 : 2 = x + 1 : 8

Express as fraction

(x - 2)/x = (x + 1)/8

So, we have

8x - 16 = 2x + 1

Evaluate the like terms

6x = 17

So, we have

x = 17/6

The value of CE is

CE = x - 2

CE = 17/6 - 2

So, we have

CE = 5/6

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Answer:

Let's say x is the number of quarters. Then the number of nickels is x + 3.

The total value of the quarters is 0.25x, and the total value of the nickels is 0.05(x + 3).

The total value of both types of coins is 4.35:

0.25x + 0.05(x + 3) = 4.35

0.25x + 0.05x + 0.15 = 4.35

0.3x + 0.15 = 4.35

0.3x = 4.2

x = 14

So Sofia has 14 quarters and 17 nickels.

Answer:

.25q + .05(q - 3) = 4.35

Step-by-step explanation:

Let q = the number of quarters

Let n = the number of nickels

.25q + .05n = 4.35

n = q- 3

Substitute q - 3 for n

.25q + .05(q - 3) = 4.35

350% of the correct pre-test questions - 7

50% of the correct pre-test questions - 1

100% of the correct pre-test questions - 2

A diagram that resembles a piece of tape that is used to show how numbers relate to one another. Also known as length model, fraction strip, bar model, and strip diagrams.

Given:

There are 7 units to represents 14 Questions and 350%.

So, 14/7 = 2 and 350/ 7= 50%

one unit represent 2 questions and 50%.

and, 2 units represents 4 questions and 100%.

then, 350% of the correct pre-test questions - 7

50% of the correct pre-test questions - 1

100% of the correct pre-test questions - 2

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The percent change for this camera is 9.756%.

Markdown percentage is defined as the decrease in the price which is calculated as a percent of the selling price.

Given that,

Original selling price of the camera = $315

Selling price has been decreased to $287

Mark down percentage = (315 - 287) / 287

                                        = 0.09756

                                        = 9.756%

Hence the rate of the markdown percentage is 9.756%.

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