In a certain fraction, the numerator is 4 less than a denominator. If 5 is added to both the numerator and denominator, the resulting fraction is equal to 6/10. Find the original fraction.

Answer:

I have not done this math in a while but I think it is -8

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

it's the slope because it's before x.

Answer: 3/2 is the answer

Answer:

7. Ans;

\( \frac{6 {a}^{5} {b}^{7} }{ - 2 {a}^{3} {b}^{7} } = \frac{2 {a}^{3} {b}^{7}(3 {a}^{2} ) }{ - 2 {a}^{3} {b}^{7} } = - 3 {a}^{2} \)

___o____o___

8. Ans;

\( \frac{ - 20 {x}^{3} {y}^{2} }{ - 5 {x}^{3}y } = \frac{ - 5 {x}^{3}y(4y) }{ - 5 {x}^{3}y } = 4y\)

___o___o___

9. Ans;

\( \frac{ - 16 a {b}^{4} }{4 {b}^{3} } = \frac{4 {b}^{3}( - 4ab) }{4 {b}^{3} } = - 4ab\)

____o____o____

10. Ans;

\( \frac{21 {m}^{8} {n}^{5} }{27 {m}^{5} {n}^{4} } = \frac{3 {m}^{5} {n}^{4}(7 {m}^{3} n) }{3 {m}^{5} {n}^{4}(9) } = \frac{7 {m}^{3}n }{9} \)

___o___o___

11. Ans;

\( \frac{ - 15 {x}^{5} {y}^{4} }{45x {y}^{3} } = \frac{ 15x {y}^{3} ( - {x}^{4} y)}{15x {y}^{3}(3) } = - \frac{ {x}^{4}y }{3} \)

___o___o___

12.Ans;

\( \frac{7 {p}^{2} {q}^{2} }{14 {p}^{2} {q}^{2} } = \frac{7 {p}^{2} {q}^{2} }{7 {p}^{2} {q}^{2} (2) } = \frac{1}{2} = 0.5\)

I hope I helped you^_^

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Answer:

3/5 x 5/8 is less 5/8

Step-by-step explanation:

3/5 x 5/8 = 15/40

Simply

15/40 = 3/8

•

5/8 > 3/8

No, some of the terms changed signs, the correct option is C.

Given

Maggie used the commutative property to write;

\(\rm \dfrac{4}{5} + 6.9y - 8\)

The commutative property of addition states that the sum of any two numbers remains the same even when the position of the numbers is interchanged.

Then,

She did not apply the commutative property correctly because she changed the signs of 4/5 and 8 and in consequence, the result will not be the same.

A, B and C, for a commutative property

(A+B)+C = C+(A+B)

4/5 + 6.9y - 8 as the equivalent expression of:

6.9y + 8 - 4/5

Hence, No, some of the terms changed signs.

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Therefore ,the solution to the given problem of proportion comes out to be karen got  £70.

The rule of three is used to link the measures because a proportion is a fraction of a total amount. It is possible to construct equation or relations between variables that are either direct (when both rise or decrease) or inverse proportional (when one increases and the other declines, or vice versa) in order to determine the necessary measures in the situation.

Here,

Given :

Siobhan and Ralph shared £700 in the

ratio 2:3.

Thus,

280 / 420 = 2/3

Thus,

Siobhan and Ralph has  £280 and £420  respectively.

and Siobhan gave a share of quarter to karen :

So,

280/4 =70

Therefore ,the solution to the given problem of proportion comes out to be karen got  £70.

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The area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10 is 174/3 units².

To find the area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10, we need to solve this problem in the following way:

Since the curves are already in the form of x = f(y), we need to use vertical strips to find the area.

So, the integral for the area of the region is given by:

A = ∫a b [x₂(y) - x₁(y)] dy

Here, x₂(y) = 10 - 2y² - 12y - 19/5 = - 2y² - 12y + 1/2 and x₁(y) = -4y - 10

So,

A = ∫(-3)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy + ∫(-2)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy

=> A = ∫(-3)⁻²[2y² + 8y - 19/2] dy + ∫(-2)⁻²[2y² + 8y - 19/2] dy

=> A = [(2/3)y³ + 4y² - (19/2)y]₋³ - [(2/3)y³ + 4y² - (19/2)y]₋² | from y = -3 to -2

=> A = [(2/3)(-2)³ + 4(-2)² - (19/2)(-2)] - [(2/3)(-3)³ + 4(-3)² - (19/2)(-3)]

=> A = 174/3

Hence, the area of the region enclosed by the curves is 174/3 units².

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The mean of the class is 147.5 and the standard deviation is 12.5.

Assuming that the scores in the class are normally distributed, we can use the formula for standard score:

z = (x - μ) / σ

where z is the standard score, x is the raw score, μ is the mean, and σ is the standard deviation.

For Anne, we have:

-2 = (120 - μ) / σ

For Medy, we have:

5 = (175 - μ) / σ

Solving for μ and σ in the two equations above, we get:

μ = 147.5 and σ = 12.5

Therefore, the mean of the class is 147.5 and the standard deviation is 12.5.

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The probability that at least one of them is a kindergartner; 0.643.

Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."

Probabilities are always expressed in mathematics as fractions, decimals, or percentages with values ranging from 0 to 1.

Calculation for the probability of the one of them is a kindergarden;

The total number of children is 8.

The total number of kindergarden are 3.

The total number of first graders are 5.

Let 'P' be the probability that at least one of them is kindergarden.

P(at least one kindergartner) = 1 - P(no kindergartner) = 1 - P(all first-graders)

The probability that all are first-graders = (5/8)×(4/7)

                                                                  = 5/14

Therefore, P(at least one kindergartner) = 1 - (5/14)

                                                                   = 9/14

                                                                   = 0.643

Therefore, if two children are ill then, the probability that at least one of them is a kindergartner is 0.643.

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The correct question is-

A carpool contains three kindergartners and five first-graders. if two children are ill, find the probability that at least one of them is a kindergartner.

Answer:

23

Step-by-step explanation:

The area is equal to 324π square units.

To find the area of a circle with radius 18 units, we can use the formula for the area of a circle, which is given by A = πr^(2), where r is the radius.

Given that the radius is 18 units, we can plug this value into the formula:

A = π(18)^2

Now, square the radius:

A = π(324)

Next, multiply 324 by π:

A = 324π

Therefore, the area of the circle with radius 18 units is 324π square units.

Now, let's compare the options with the given options:

a) 18π units^(2)- This is incorrect, as we calculated the area to be 324π square units.

b) 36π units^(2)- This is also incorrect, as our calculated area is 324π square units.

c) 9π units^(2)- This is incorrect, as our calculated area is 324π square units.

d) 324π units^(2)- This is the correct option , as we calculated the area to be 324π square units.

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Answer:

x = −1.714948, 3.346107

Using the hypergeometric distribution, it is found that the probability is 12/132

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The rolls are chosen from a sample without replacement, which means that the hypergeometric distribution is used to solve this question.

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Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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

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

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What is the probability of selecting two defective rolls?

This is P(X = 2). So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,12,2,4) = \frac{C_{4,2}*C_{8,0}}{C_{12,2}} = \frac{4 \times 3}{12 \times 11} = \frac{12}{132}\)

12/132 is the probability.

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Divide a row or column total by the grand total. The correct option is B.

In a two-way table, you must divide a row or column total by the total to find the marginal relative frequency. The sum of a row or column is divided by the overall sum.

The proportion or percentage of a certain category within a row or column in relation to the overall number of categories is represented by a marginal relative frequency.

You calculate it by dividing the overall count of a particular row or column by the sum of all the values in the table. This gives the proportion or relative frequency of that category in respect to the overall count.

To calculate the marginal relative frequency, the correct way is to divide a row or column total by the overall total.

Thus, the correct option is B.

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Step 1: Count the total number of students

The total number of students in the statistics class is 8.

Step 2: Count the number of women

There are 4 women in the statistics class.

Step 3: Calculate the frequency, proportion, and percentage of women

Frequency: The frequency of women in the statistics class is 4.

Proportion: The proportion of women in the statistics class is 4/8, or 0.5.

Percentage: The percentage of women in the statistics class is 50%.

The information in the question is not significant to calculate the frequency, proportion and percentage of women.

Statistical models for calculating gender through frequency involve counting the number of individuals in a population that identify as each gender. This can be done by collecting data on gender from surveys, census data, or other sources of information. The data collected is then used to calculate the frequency, proportion, and percentage of each gender in the population. This information can be used to better understand gender dynamics in a population and inform policies and practices that promote gender equity.

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Language tests or interviews are used to assess a person's required level of English proficiency during the naturalization process.

During the naturalization process, a person's required level of English proficiency is typically assessed through language tests or interviews.

These assessments are designed to evaluate the individual's ability to understand and communicate effectively in English, which is an essential requirement for citizenship in many countries.

The specific testing methods may vary depending on the country or jurisdiction, but they generally aim to assess the person's reading, writing, speaking, and listening skills in English.

The tests may be administered by government agencies or authorized language assessment providers.

Reading comprehension tests assess the individual's ability to understand written passages, instructions, or forms in English.

They may involve answering questions or completing tasks based on the given texts.

Writing tests evaluate the person's ability to express ideas, opinions, or personal experiences in written form. This could include writing essays, letters, or responses to specific prompts.

Speaking tests assess the person's ability to communicate orally in English. It may involve engaging in conversations, participating in interviews, or delivering short presentations.

The tests aim to evaluate the person's pronunciation, vocabulary, grammar, and fluency.

Listening tests measure the individual's ability to understand spoken English.

This could involve listening to recordings, dialogues, or conversations and answering questions or summarizing information based on what was heard.

In some cases, the language assessment may also include an interview component where the individual engages in a conversation with an examiner. This allows the examiner to assess the person's overall language proficiency, comprehension, and ability to interact in English.

The results of these language tests or interviews are used to determine whether the individual meets the required level of English proficiency for naturalization.

Achieving the required score or meeting the established language proficiency criteria is often a crucial step in the naturalization process, demonstrating the applicant's ability to integrate into the society and communicate effectively in the country's predominant language.

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Answer:

5:15 simplifies to 1:3.

Step-by-step explanation:

Answer:

1:3

Step-by-step explanation:

To solve this problem, we can use the binomial probability distribution. Let's define a "success" as scoring a goal and a "failure" as missing a goal.

Then, each attempt by Sky can be considered a Bernoulli trial with probability of success p = 1/2.

Let X be the number of goals that Sky scores in five attempts. Then, X follows a binomial distribution with parameters n = 5 and p = 1/2.

To find the probability that Sky scores at least two goals, we need to calculate the probability of the following events:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

We can use the binomial probability formula to calculate these probabilities:

P(X = k) = (n choose k) * \(p^k\) *\((1-p)^(n-k)\)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we get:

P(X = 2) = (5 choose 2) * \((1/2)^2\) * \((1/2)^3\) = 10/32

P(X = 3) = (5 choose 3) * \((1/2)^3\) * \((1/2)^2\) = 10/32

P(X = 4) = (5 choose 4) * \((1/2)^4\) *\((1/2)^1\) = 5/32

P(X = 5) = (5 choose 5) * \((1/2)^5\) * \((1/2)^0\) = 1/32

Therefore, the probability that Sky scores at least two goals is:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = (10 + 10 + 5 + 1)/32 = 26/32 = 13/16

So the probability that Sky scored at least two goals is 13/16.

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The total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. So the probability that Sky scored at least two goals is 13/16.

To find the probability that Sky scored at least two goals, we can use complementary probability, which means finding the probability that she scored fewer than two goals (either 0 or 1 goal) and subtracting that from 1.1.

Probability of scoring 0 goals: Since there are 5 attempts and she is equally likely to make a goal or miss (1/2 chance for each), the probability of missing all 5 is (1/2)^5 = 1/32.2.

Probability of scoring 1 goal: Sky could score in any of the 5 attempts, so we need to consider all possible ways of scoring one goal.

There are 5 ways (score in the 1st, 2nd, 3rd, 4th, or 5th attempt). The probability for each of these scenarios is (1/2)^5 = 1/32.

Therefore, the total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

To express this as a common fraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:26/32 = (26/2) / (32/2) = 13/16So the probability that Sky scored at least two goals is 13/16.

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Answer:

this type of sampling would be considered a multistage.

The slope of line from the given graph is 4/3.

The coordinates of line from the given graph are (4, 3) and (1, -1).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

Now, put (x1, y1) = (4, 3) and (x2, y2) = (1, -1) is slope formula, we get

Slope = (y2-y1)(x2-x1)

= (-1-3)/(1-4)

= 4/3

Therefore, the slope of line from the given graph is 4/3.

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Answer:

2:5

Step-by-step explanation:fraction sighn is equivilent to ratio sighn.

Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

Answer:

{x|x is a rational non-integer}

Step-by-step explanation:

the correct solution for the equation is 4.5

Answer:

21

Step-by-step explanation:

29 squared  then 20 squared

subtract them

then get the squared root

and then you have 21

\(5y = 6x + 21 \\ y = \frac{6}{5} x + \frac{21}{5} \)

y intercept:

\(y = \frac{21}{5} \)