Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
The Pythagorean theorem describes the relationship between the lengths of legs a and b and the hypotenuse c of any
right triangle.
a² + b² = c²
Complete the equation below by writing an expression equivalent to the length of a, the leg of a right triangle.

The following expressions rewritten below;

23 + 8b

No common terms or factors

= 23 + 8b

㎡ - 5g

No common terms or factors

= m² - 5g

1/8 q + 7a/3

= (3q + 56a) / 24

12k (g+h)

= 12kg + 12kh

(2x + 3)(2 - 5x)

= 4x - 10x² + 6 - 15x

combine like terms

= -10x² -11x + 6

Therefore, algebraic expressions are solved by multiplying and combining like terms.

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B=3b-b

C= 2b expressions are equivalent to 4 � 4b4, b .

b+2(b+2b)=b+2(3b)=b+6b=7b

3b+b=4b

2(2b)=4b Option B and C produce the outcome 4b. They are the expressions that are comparable to 4b as a result. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same nonzero value. If x4=2x+7, we can add 4 to both sides to get the following equation, which is equivalent: x4+4=2x+7+4. Of course, both sides of the equation can be made simpler. Constants x=2x+7+4 on the left side cancel each other out. If two systems of equations have the same solution, they are equivalent (s). In algebra, two equations are said to be equivalent if their roots or solutions are the same. The same number, symbol, or expression must be added to or subtracted from both sides of an equation to produce an equivalent equation.

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Answer:

TRIANGLE PROBLEM:

area : 6a^4

perimeter : 12a^2

SIMPLIFY problem:

-40c^2+26a^2+30ac

EVALUATE & FACTOR:

(q^2 - p) ( p^2 - q)

and the solved form is 240

hope it helps :)

Step-by-step explanation:

lol im an rsm kid too. but i hope these are right,

first i'm gonna start with 263 c.

AREA = 4a^2 * 3a^2 divided by 2.  

12a^4 divided by 2 = 6a^4.

AREA = 6a^4

Perimeter you can find with the pythag. th.

(4a^2) ^2 + (3a^2 ) ^2 = c^2

16a^4 + 9a^4 = c^2

, the missing side is 5a^2

therefore the perimeter is 4a^2 + 3a^2 + 5a^2 = 12a^2

ok next, im gonna do 266

the answer is -40c^2+26a^2+30ac

make sure to check this w/ symbo or mthway

ok last one!!

factored form is (q^2 - p) ( p^2 - q)

and the solved form is 240

There are 8.75 pounds of meat for 7 dogs

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another.

Since 2.5 pounds of meat for 2 dogs x pounds of meat for 7 dogs. We can write:

2.5/2 = x/7

2*x = 2.5*7

2x = 17.5

x = 17.5/2

x = 8.75

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Note that the body starts "with an initial velocity and moves with uniform acceleration."(Option C)

In mechanics, acceleration is defined as the rate of change of an object's velocity with respect to time. Vector quantities are accelerations. The orientation of an object's acceleration is determined by the orientation of its net force.

The distance covered by the particle in nth second

Sₙ = u + a/2(2n-1)

S₈ = 20m

S₈ = u + a/2(2x(8-1)

20 = u + 7.5a ...................()

S₉ = 22 = u + a/2(2*9-1)

22 = u + 8.5a ..................(2)

By solving equations 1 and 2 we have :

u=5m/s , a=2m/s²

Thus,

S₁₀ = u+ a/2(2*10-1)

S₁₀ = 5 + 1/2 * 2 (2 * 10-1)

S₁₀ = 5 + 19

S₁₀ = 24m

Thus, it is correct to state that the body starts with the initial velocity and moves with uniform acceleration, and the correct option is C.

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Full Question:

A body covers 20 m, 22 m, 24 m, in 8th, 9th, and 10th seconds respectively. The body starts:

from rest and moves with uniform velocity.

from rest and moves with uniform acceleration.

with an initial velocity and moves with uniform acceleration.

with an initial velocity and moves with uniform velocity.

a) Probability that all four are the same suit = 0.0106 b) Probability that all four are red =0.055 c) Probability each has a different suit = 0.105

Total number of cards =52

No. of cards for each suit =13

Total types of four suit =4 (heart, spades, diamonds, clubs)

Total numbers of ways = [tex]^{52}C_4[/tex] =270,725 ways

a) number of ways choosing four cards of the same suit

= [tex]^{13}C_4+^{13}C_4+^{13}C_4+^{13}C_4[/tex]

= [tex]4 \times ^{13}C_4\\[/tex]

= [tex]4 \times \frac{13!}{4!(13-4)!}[/tex]

=2860 ways

Probability that all four are the same suit is 2860/270,725 = 0.0106

b) Number of ways all four cards are red

=[tex]^{26}C_4[/tex]

= 4,950 ways

Probability that all four are red = 4950/270,725 =0.055

c)  Number of ways each card has a different suit

=[tex]^{13}C_1\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex]

= 28,561 ways

Probability each has a different suit is 28561/270725 = 0.105

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Answer:

B. More money was given than expected in 1994

Step-by-step explanation:

Nowhere is it mentioned what amount was expected as donations. Only actual amounts received are shown on the graph

Hence this is an assumption and not necessarily fact

Answer:

3x² + 9x + 1

Step-by-step explanation:

5x - 2 + 3x² + 4x + 3

= 9x - 2 + 3x² + 3

= 9x + 1 + 3x²

= 3x² + 9x + 1

The question that can be answered using the expression 3 ÷ 1 is "How many 1-pound pieces of fudge are in a 3-pound fudge?". The correct option is B.

The expression "3 ÷ 1" is a mathematical expression that represents a division operation. In this case, the operation is "3 divided by 1".

To understand what this expression means, we can think of it in terms of a real-world scenario. For example, we can think of it as dividing 3 pounds of fudge into 1-pound pieces.

If we divide 3 pounds of fudge into 1-pound pieces, we can ask the question "How many 1-pound pieces of fudge are in 3 pounds of fudge?" This is the question that can be answered using the expression "3 ÷ 1".

To solve this division problem, we simply divide 3 by 1. The result is 3. This means that there are 3 one-pound pieces of fudge in 3 pounds of fudge.

So, to summarize, the expression "3 ÷ 1" means "3 divided by 1" and can be interpreted as dividing 3 pounds of fudge into 1-pound pieces. The answer to the question "How many 1-pound pieces of fudge are in 3 pounds of fudge?" is 3.

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Answer:

To convert 6 feet into meters, first create a conversion factor to convert from feet to meters. Make sure the original unit is in the denominator, then cancel feet. Next, multiply the original measure by the conversion factor to get 1.8288 meters, or 1.83 meters if you simplified it.

Step-by-step explanation:

The simple interest on Rs 7560 will be Rs 1102.50 at a rate of 25/4% per annum after approximately 1 month (0.09 years).

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, and not on any accumulated interest. It is usually calculated as a percentage of the principal amount, multiplied by the time period for which the interest is being calculated.

We can use the formula for simple interest to solve this problem:

Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)

We know that the principal is Rs 7560, the rate is 25/4% per annum, and the interest is Rs 1102.50. Substituting these values into the formula, we get:

1102.50 = 7560 x (25/4) x T

Simplifying:

1102.50 = 47250T/4

Multiplying both sides by 4 to eliminate the fraction:

1102.50 x 4 = 47250T

4410 = 47250T

Dividing both sides by 47250:

T = 4410/47250

T = 0.093 or approximately 0.09 years.

To convert this to months or days, we can multiply by 12 or 365, respectively.

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Answer:

0.75y + 0.5x = 8.00

Step-by-step explanation:

The slope formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line and m is the slope of the line. To use the formula, you need to know the coordinates of two points on the line. If you have the coordinates of two points, you can substitute them into the formula to find the slope.

We have drawn the graph for the given inequality.

What is inequality?

Inequality is a mathematical statement that compares two values or expressions and shows their relative size. It is represented by the symbols >, <, ≥, or ≤, which respectively mean "greater than", "less than", "greater than or equal to", and "less than or equal to". Inequalities can also include variables and can be used to describe a range of possible values for that variable.

For the given inequality y ≤ 3/5x-5

we can draw the graph as shown below:

Hence, we have drawn the graph for the given inequality.

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The equation of the line are;

a. y = 5/2x + 2

b. y = -1/5x - 1

c. y = -5/2x - 3

d. y = -x - 7

a.

The line passes through point (-2, -3) and it is perpendicular to y = -2/5x

The equation of the line is y = 5/2x + 2

b.

The line passes through the point (5, -2) and it is perpendicular to y = 5x + 4

The equation of the line is y = -1/5x - 1

c.

The line passes through (-2, 2) and it is perpendicular to y = 2/5x - 4

Th equation of the line is y = -5/2x - 3

d.

The line passes through (-4, -3) and it is perpendicular to y = -x + 2

The equation of line is y = -x - 7

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Among the following statements, The true statements are:

Option (1) a 95% confidence interval is a random interval that contains the true parameter 95% of the time, (2)the true parameter is a random value that has 95% chance of falling in the 95% confidence interval, (3) i perform a linear regression and get a 95% confidence interval from 0.4 to 0.5. there is a 95% probability that the true parameter is between 0.4 and 0.5, (4) the true parameter (unknown to me) is 0.

A 95% confidence interval is a random interval that contains the true parameter 95% of the time.

The true parameter is NOT a random value, and it is not correct to say that it has a 95% chance of falling in the 95% confidence interval.

If you perform a linear regression and get a 95% confidence interval from 0.4 to 0.5,

it means that if you repeated the same experiment many times, 95% of the resulting confidence intervals would contain the true parameter.

It is not correct to say that there is a 95% probability that the true parameter is between 0.4 and 0.5 because the true parameter is either in the interval or not.

If the true parameter is 0.5 and you sample data and construct a 95% confidence interval, the interval may or may not contain 0.5.

The 95% confidence interval is a statement about the probability of the interval containing the true parameter, not about the probability of the true parameter being any specific value.

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By using the concept of combinations, we have determined that there are 210 three-digit numbers that can be formed using the digits 0-6 without repeating any of them. Among them, there are 90 odd numbers and 120 numbers greater than 330.

Combinations are a fundamental concept in mathematics, particularly in the field of combinatorics, which deals with counting and arranging objects.

To solve this problem, we can use the concept of combinations, which is a way of counting the number of ways we can choose k items from a set of n items. In this case, we want to find the number of three-digit numbers we can form from the set {0, 1, 2, 3, 4, 5, 6}, without repeating any of the digits.

First, we can determine the number of ways we can choose the first digit. Since there are seven digits to choose from, we have 7 options for the first digit.

Next, we can determine the number of ways we can choose the second digit. Since we have already used one of the digits, we only have 6 options left for the second digit.

Finally, we can determine the number of ways we can choose the third digit. Since we have used two of the digits, we only have 5 options left for the third digit.

Therefore, the total number of three-digit numbers we can form is given by the product of the number of choices for each digit:

7 x 6 x 5 = 210

So there are 210 different three-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, and 6, without repeating any of the digits.

To find the number of odd numbers, we need to consider that the last digit must be either 1, 3, or 5, since these are the only odd digits in the set. We can choose the first two digits in the same way as before, and then choose one of the three odd digits for the last digit. Therefore, the number of odd three-digit numbers is:

6 x 5 x 3 = 90

To find the number of three-digit numbers greater than 330, we need to consider that the first digit must be either 3, 4, 5, or 6. We can choose the first digit in 4 ways, and then choose the remaining two digits as before. Therefore, the number of three-digit numbers greater than 330 is:

4 x 6 x 5 = 120

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Answer:
11i√√3

Step-by-step explanation:

The frequency distribution table of the data is illustrated below.

The data we have been given represents the percentage of people who have completed 4 or more years of college education in different states. To create a frequency distribution, we need to first decide on the number of classes we want to use. In this case, we will use 7 classes.

Next, we need to determine the range of values for each class. To do this, we first find the minimum and maximum values in the data set, which are 18.9 and 37.9, respectively.

The range of values for each class will be (max value - min value) / number of classes, which in this case is (37.9 - 18.9) / 7 = 2.86.

We will start with the first class, which will include all values from 18.9 to 21.76 (the lower limit of the first class plus the range of values for each class). The next class will include values from 21.76 to 24.62, and so on, until we reach the final class which will include all values from 33.18 to 36.04 (the upper limit of the final class plus the range of values for each class).

To create the frequency distribution, we count the number of values in the data set that fall into each class. For example, the first class includes values between 18.9 and 21.76, and there are 2 values in the data set that fall into this range (21.4 and 20.0). We continue this process for each class until we have a table that shows the frequency of values in each class.

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Complete Question:

Percentage of People Who Completed 4 or More Years of College Listed by state are the percentages of the population who have completed 4 or more years of a college education. Construct a frequency distribution with 7 classes.

21.4,26.0,25.3,19.3,29.5,35.0,34.7,26.1,25.8,23.4,27.1,29.2,24.5,29.5,22.1,24,3,28.8,20,0,20.4,26.7,35.2,37.9,24.7,31.0,18.9,24.5,27.0

Answer:

Step-by-step explanation:

The simplest form of the fraction equivalent to 0.7 is 7/10

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, to show the denominator of the fraction in the simplest form that is equal to 0.7

To convert 0.7 into a fraction, we have to write it in p/q form, where p and q are positive integers.

we can write .7 as 0.7/1

now to remove the decimal point we will multiply and divide by 10

therefore,

0.7/1 ×  10/10  = 7/10

Hence, the simplest form of the fraction equivalent to 0.7 is 7/10

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There are 10 cars in a race, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.

An arrangement of particulars in a specific order is appertained to as a permutation. Then, the factors of sets are arranged in a direct or successional order. For case, the set A = ,6 has a permutation of 2, which is. There's no other way to organise the factors of set A, as you can see.

There are 10 cars in the race,

Three cars finish the race in the 1st ,2nd and 3rd order

1st finish the race have 10 chances

P(A) = 10

2nd finish the race have 9 chances

P(B) = 9

3rd finish the race have 8 chances

P(C) = 8

The number in which this can be put,

= P(A) x P(B) x P(C)

= 10*9*8

=720 ways

Therefore, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.

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The length of earthworm will be 4 cm after 4 hours. And the length is 14 cm after 49 hours.

Proportions are defined when two or more ratios are made to be equal to each other.

Two quantities are said to be directly proportional if a positive change in one quantity also lead to a positive change in the other quantity.

If a is proportional to b, we denote it as a ∝ b.

Given,

Length of an earthworm, l ∝ square root of the number of hours, n, which have elapsed since it's birth.

l ∝ √n

l = k √n, for some constant k.

If a worm is 2 cm long after 1 hour, we can write it as,

2 = k × √1

⇒ k = 2

So the proportionality constant is 2.

After 4 hours,

l = k √4

l = 2 × 2 = 4 cm

If the length is 14 cm,

14 = 2 √n

√n = 14 / 2

√n = 7

n = 7² = 49 hours

Hence the length of worm is 4 cm after 4 hours. It will take 49 hours to grow to a length of 14 cm.

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the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.

Given the probabilities, you can use Bayes' theorem to calculate the probability that it will rain on the following day, given that it rained tomorrow. Bayes' theorem states that: P(A|B) = P(B|A) * P(A) / P(B)

Where: P(A|B) is the likelihood that event A will occur assuming event B has already happened. P(B|A) is the probability of event B given that event A has occurred. The prior probability of event A is P(A). The prior probability of event B is P(B).

In this case, let A be the event that it rains on the following day and B be the event that it rains tomorrow.

So, P(A|B) = P(B|A) * P(A) / P(B) = 0.9 * 0.3 / P(B)

To calculate P(B), you can use the total probability theorem:

P(B) = P(B|A) * P(A) + P(B|~A) * P(~A) = 0.9 * 0.3 + 0.08 * 0.7 = 0.327

Now, you can substitute the values into the formula for P(A|B) to get:

P(A|B) = 0.9 * 0.3 / 0.327 = 0.75

So, the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.

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a. The best data type for the number of siblings would be an integer.

An example of a typical value for this variable would be 3, as someone might have 3 siblings. An integer is the best data type because the number of siblings is a whole number and can never be a fraction or a negative number.

b. The best data type for the final grade in this class would be a floating-point number. An example of a typical value for this variable would be 85.5, as a final grade may include decimal points. A floating-point number is the best data type because a final grade can have a decimal point and may include fractions.

c. The best data type for the population of Earth would be a long integer. An example of a typical value for this variable would be 7,794,798,739, as of the year 2020. A long integer is the best data type because the population of Earth is a large number and cannot be expressed using a regular integer.

d. The best data type for the population of a U.S. county would be an integer. An example of a typical value for this variable would be 100,000, as the population of a county can vary greatly. An integer is the best data type because the population of a county is a whole number and can never be a fraction or a negative number.

e. The best data type for the number of passengers on a bus would be an integer. An example of a typical value for this variable would be 20, as a bus can carry a varying number of passengers. An integer is the best data type because the number of passengers on a bus is a whole number and can never be a fraction or a negative number.

f. The best data type for one player's score in a Scrabble game would be an integer. An example of a typical value for this variable would be 45, as a score in Scrabble is calculated in whole numbers. An integer is the best data type because a score in Scrabble is a whole number and can never be a fraction or a negative number.

g. The best data type for one team's score in a Major League Baseball game would be an integer. An example of a typical value for this variable would be 7, as a team's score is calculated in whole numbers. An integer is the best data type because a team's score is a whole number and can never be a fraction or a negative number.

h. The best data type for the year a historical event occurred would be an integer. An example of a typical value for this variable would be 1776, as the year the United States declared independence. An integer is the best data type because a year is a whole number and can never be a fraction or a negative number.

i. The best data type for the number of legs on an animal would be an integer. An example of a typical value for this variable would be 4, as many animals have four legs. An integer is the best data type because the number of legs an animal has is a whole number and can never be a fraction or a negative number.

j. The best data type for the price of an automobile would be a floating-point number. An example of a typical value for this variable would be $25,000.50, as a price for a car can include decimal points. A floating-point number is the best data type because the price of a car can have a decimal point and may include fractions.

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The graph which is most likely to represent the residuals from the best fit line is Option C.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that from the graphs of residuals is  the same set of data using different lines to fit the data.

The best fit line is the line that minimizes the sum of the squared residuals.

In other words, it is the line that has the smallest sum of the squared differences between the actual data points and the predicted values from the line.

The residuals represent the differences between the actual data points and the predicted values, and any systematic pattern in the residuals would suggest that the line is not a good fit for the data.

Hence, Option C is correct, the graph which is most likely to represent the residuals from the best fit line.

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The values of the t statistic that are statistically significant at the α=0.005 level are t < -2.977 or t > 2.977.

To determine the values of the t statistic that are statistically significant at the α=0.005 level, we need to find the critical values of the t-distribution with 14 degrees of freedom (df = n - 1 = 15 - 1 = 14).

Using a t-table or a calculator, we can find that the critical values for a two-tailed test with α=0.005 are -2.977 and 2.977. This means that any t statistic less than -2.977 or greater than 2.977 would be considered statistically significant at the α=0.005 level.

In other words, if the calculated t statistic falls within the range of -2.977 to 2.977, we would fail to reject the null hypothesis (H0: μ=10) and conclude that there is not enough evidence to suggest that the population mean is different from 10. However, if the calculated t statistic falls outside of this range, we would reject the null hypothesis and conclude that there is evidence to suggest that the population mean is different from 10.

So, the values of the t statistic that are statistically significant at the α=0.005 level are t < -2.977 or t > 2.977.

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