Which of the following is a rational number?
√√12
√47

√22

√9

We will need 14 lb of raisins for a mixture worth of $2.75/lb

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

Lets call (x) = number of pounds of raisins we have:

$3.00(x)+$2.40(10) = $2.75(10+x)

3x + 24 = 27.5 + 2.75x

3x - 2.75x = 27.5 - 24

Clearing the variable we have:

0.25x = 3.5

x = 3.5/0.25

x = 14

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Therefore , the solution of the given problem of fraction comes out to be   0.25 inches per hour average rainfall per hour.

To represent a whole, any number of equal sums or decimals can be utilized. The quantity of a particular size is expression as a fraction in standard English. 8, 3/4. Fractions are included in wholes. In mathematics, the fraction to numerator ratio is used to represent numbers. All of these fractions of integers are simple fractions. A challenging fraction has a percent in the denominator. because actual fractions have different calculations, numerators, and numerators.

Here,

Given :

=> 6 1/2 hours or 13/2 hours

=> 6.5 hours

7/8 pf an inches.

So,

the average rainfall per hour is :

=> 7/8 / 3.5

=> 0.25 inches per hour

Therefore , the solution of the given problem of fraction comes out to be   0.25 inches per hour average rainfall per hour.

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D) On a coordinate plane, a graph titled Total Pages Jacqueline Has Read has days on the x-axis and Pages on the y-axis. A line goes through points (1, 25) and (2, 50).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, Jacqueline reads 25 pages every night. Here y is the total number of pages that Jacqueline has read after x days.

Since she reads 25 pages every day and she starts with 0 pages.

Thus, the Total number of pages she reads and a number of days have a proportional relation.

she reads 25 pages a night Meaning that the total number of pages Jacqueline has read (Variable Y) = 25 pages a night (x)

therefore, The correct answer is) D.  Because on the graph you can see that it increases by 25 each day which follows the equation Y=25x.

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The cubic expression of (1 + i) is given as follows:

(1 + i)³ = 0.

The cubic expression is obtained elevating the binomial (1 + i) to the third power, as follows:

(1 + i)³.

Then we expand the expression, applying the rule for the cube of a binomial, hence:

(1 + i)³ = i³ + i² + i + 1.

The basic complex number relation is:

i² = -1.

Hence:

i³ = i² x i = -1 x i = -1.

Then the expression is given as follows:

i³ + i² + i + 1 = -i - 1 + i + 1 = 0.

The problem asks for the cubic expression for (1 + i).

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Sherina should have added 56 to both sides of the equation.

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Sherina wrote and solved the equation, x minus 56 = 230 and obtained x = 174:

Sherina’s error is that she should have added 56 to both sides of the equation.

To solve for x in the equation, you need to add 56 to both sides of the equation. That is:

x - 56 = 230

x -56 + 56 = 230 + 56

x = 230 + 56

x = 286

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Answer:

The answer is D (Sherina Should of have added 56 to both sides of the equation.)

Step-by-step explanation:

In this type of math, subtraction and addition are switched. I know that may be confusing.

Example:

x minus 42 - 88

You can do this:    42 + 88 = 130  

Your answer = x  

x = 130

The area of the given Trapezoid is calculated as; 42.5 m².

A trapezoid is defined as a quadrilateral with four sides where two sides are parallel to each other.

The parameters of the trapezoid are;

Short base length = 3 m

Height = 5 m

Large base length = 4 + 3 + 7 = 14 m

Thus;

Area of a trapezoid = 1/2 * (Short base + Large base) * h

Area = 1/2 * (3 + 14) * 5

= 1/2 * 17 * 5

= 42.5 m²

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Answer:

it 56 cm your welcome'

Step-by-step explanation:

The direct variation equation that relate the amount of concrete needed and the number of posts is y = 5/4x

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

To solve this problem, we have to state the equation using the information of the problem:

Information about the problem:

Calculating the number of concrete according to the number of posts we have:

6 1/4

= [(4*6)+1] / 4

= (24 + 1) / 4

= 25/4

Number of concrete per post = 25/4 bags / 5 post

Number of concrete per post = 5/4 bags / post

Writing the equation according to the information gave, we have:

y = 5/4x

Lets called (y) the amount of concrete needed and (x) the number of posts

The "y" variable is the dependent variable, it will change according to the number of posts x (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the the number of posts.

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Answer:

x<11

Step-by-step explanation:

4x>54-10

4x>44

x<11 [sign change]

Answer:

x > 11

Step-by-step explanation:

4x + 10 > 54

Step 1: Subtract 10 from both sides.

4x + 10 - 10 > 54 - 10

4x > 44

Step 2: Divide both sides by 4.

4x/4 > 44/4

x > 11

If it takes 10 workers 2.5 years to build a 20 story building, it will take 2.5 sec 20 workers to build a 40 story building.

Given that a skyscraper's height and the number of workers needed to build it determine how long the project takes, We must make the time.

Allow the time t, height h, and number of workers to be ω.

Then, based on the relationship,

t = kh/ω

where k is constant.

The formula in the term of k is:

k = tω/h

Additionally, it takes 10 employees t0 2.5 years to construct a 20-story skyscraper.

Now putting the value

k = (2.5 × 10)/20

k = 25/20

k = 5/4

If a 40-story skyscraper requires 20 workers to construct, we have

t = kh/ω

t = (5/4) × (40/20)

t = 5/2

t = 2.5 sec

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The complete question is:

The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers. If it takes 10 workers 2.5 years to build a 20 story building, how long will it take 20 workers to build a 40 story building?

The rate of the given situation will be 2 inches per minute.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

The distance is a one-seventh inch and the time is one-fourteenth minutes. Then the rate as a unit rate is given as,

Rate = (1/7) / (1/14)

Rate = (1/7) x (14/1)

Rate = 14/7

Rate = 2 inches per minute

The rate of the given situation will be 2 inches per minute.

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There are 45 possible choices for the five members.

There are ten people on the debate team, but only two of them can be in position 5. Positions 1 through 4 can be filled by any 10 members. Using the combination formula nCr, where n is the total number of items and r is the number of items chosen from that set, we can determine the number of ways to select these five members.

In this instance, we have 10C2, which simplifies to 10!/(2!(10-2)!)) or 10 items chosen from a set of 10. This can be reduced to 45, or 109/2. As a result, there are 45 ways to select the five debate team members.

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There are $15 received in change after buy 10 vegetarian pizzas.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

You buy 10 vegetarian pizzas and pay with $100.

Here, The cost of the three vegetarian pizzas is 25 dollars and 50 cents.

Hence, The cost of the three vegetarian pizzas = $25.5

Thus, The cost of the 10 vegetarian pizzas = $25.5 × 10 / 3

                                                                 = $255/3

                                                                  = $85

Since, You buy 10 vegetarian pizzas and pay with $100.

Hence, The change to receive = $100 - $85

                                                = $15

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Answer:

288

Step-by-step explanation:

1. 176 = 55% × N

2. 176 = [tex]\frac{55}{100}[/tex] × N

3. N= 176×[tex]\frac{100}{55}[/tex]

4. N=320

5. [tex]\frac{90}{100}[/tex] × 320

=288

The required probability is P(G|F) = 0.5.

Renate's chance of winning a Green Card, given that she was a finalist, can be calculated as follows:

P(G|F) = P(G and F) / P(F)

Where P(G and F) is the probability of both Renate winning a Green Card and Renate being a finalist, and P(F) is the probability of Renate being a finalist.

Since Renate was one of 110,000 finalists, P(F) = 110,000 / 6.5 million = 0.016923076923076924

Out of the 110,000 finalists, 55,000 won a Green Card, so P(G and F) = 55,000 / 6.5 million = 0.008461538461538462

Therefore, Renate's chance of winning a Green Card, given that she was a finalist, can be calculated as follows:

P(G|F) = P(G and F) / P(F) = 0.008461538461538462 / 0.016923076923076924 = 0.5

Thus, Renate had a 5% chance of winning a Green Card, given that she was a finalist.

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--The given question is incomplete; the complete question is

"In 1994, the U.S. government held a lottery to issue 55,000 Green Cards (permits for non-citizens to work legally in the U.S.). Renate Deutsch, from Germany, was one of approximately 6.5 million people who entered this lottery. Let G = won Green Card.

In the summer of 1994, Renate received a letter stating she was one of 110,000 finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to win, what was Renate's chance of winning a Green Card? Let F = was a finalist. Write your answer as a conditional probability statement. (Round your answer to four decimal places.)"--

The percentage of people should be seen by doctor between 11 and 23 min is =  99.7%

The wait time at a doctor office is 17 minutes with a deviation of 2 min

we want to find the percentage of people seen by the doctor between 1 to 23 min

to find this we will find z score

the mean is 17 min and deviation is 2

the people should be seen by the doctor =

x = 11 and 23

z = 11-17/2 = -3

z= 23-17/2 = 6

lets use the standard normal distribution and you will find the answer.

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The confidence interval provides evidence that the true mean volume is likely to fall within a certain range, but it does not provide conclusive evidence that the true mean volume is equal to 12 ounces.

A confidence interval is a range of values that is likely to contain the true population mean with a certain level of confidence, usually 95%.

When it comes to the question of whether the confidence interval provides convincing evidence that the true mean volume is 12 ounces, the answer is no, it does not provide conclusive evidence.

The confidence interval provides a range of values that the true mean is likely to fall within, and just because the true mean is within the confidence interval, it does not mean that the true mean is exactly equal to 12 ounces.

Let's say the confidence interval for the mean volume is 11.5 to 12.5 ounces. This means that if we repeated our sample many times, 95% of those samples would have a mean that falls within this range.

However, it is still possible that the true mean volume is outside of this range, and the only way to know for sure is to collect more data or conduct a more comprehensive study.

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The value of the function f(x) = -16x³ + 68x + 2 for 2f(x) is - 452.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -16x³ + 68x + 2

Now,

Multiply 2 on both sides.

2f(x) = -32x³ + 136x + 4

Substitute x = 3.

2f(3) = -32 x 3³ + 136 x 3 + 4

2f(3) = -32 x 27 + 136 x 3 + 4

2f(3) = -864 + 408 + 4

2f(3) = -452

Thus,

The value is -452.

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Based on the table, the number of widgets that the company should produce will be B. 4

Gain is the best definition of profit, particularly when it is attained by raising the price of goods so that consumer spending exceeds producer expenses and a sizable return on investment is left. Profit is the amount of money that remains after expenditures and expenses have been paid.

This table shows how much it costs for a company to produce x number of widgets, and how much revenue the company makes for each additional widget produced. The widget should be based on where the most profit will be made. This is at 4 unit as the profit will be:

= $49 - $16

= $33

This is the highest profit that can be gotten.

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60 engineering students are divided into 24 who take math and 29 who take physics. 10 students take statistics and physics together, 13 students take math and physics together. a) There are 26 students take statistics. b) P(A/B)=4/13.

The science of statistics is concerned with the research and advancement of methods for collecting, analyzing, interpreting, and presenting empirical data. The science of learning from data is called statistics, which is also possibly an art. The discipline's focus is on the gathering, analyzing, and interpretation of data as well as the efficient dissemination and presentation of findings that rely on data.

We can assume the following:

1). There are 13-8=5 pupils who study physics and math together but not statistics (green colour)

2). There are 10-8=2 pupils who study physics and statistics together but not math (grey colour)

3). Students who take algebra and statistics but not physics total 11-8=3. (yellow colour)

4). There are 14 pupils (29-5-8-2) who only take physics (pink colour)

We can now determine how many students solely take statistics by doing the following: The number of students enrolled in at least one course (60–7) less the number taking only math or just physics or just statistics but not math.

53-24-14-2=13 students take only statistics

There are 26 students who take statistics, or 13 + 2 + 3 + 8

b) Let's say A takes all three, and B takes statistics. Finding conditional probability is the goal.

P(A/B)= P(A⋂B)/P(B)

P(A⋂B)= 8/60, P(B)=26/60

So,

P(A/B)=P(A⋂B)/P(B)=8/26=4/13

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Answer:

Step-by-step explanation:

the rise is 100

Answer:

3%=0.03 3%1÷2 =0.015. ..........,...

[tex]3 \frac{1}{4} - 4 \frac{1}{2} \\ \\ \longrightarrow \: \frac{13}{4} - \frac{9}{2} \\ \\ taking \: LCM \\ \\ \longrightarrow \: \frac{13 - 18}{4} \\ \\ \longrightarrow \: \boxed{ \frac{ - 5}{4} }[/tex]

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There were 27 commercials during the shows. The unit rate of commercials per hour must be determined. As a result, the hourly unit rate is 18 commercials. And it is determined by Division.

A division is the process of dividing a given amount into equal parts.

Wendy spent one and a half hours on Saturday morning watching her favourite shows on television.

There were 27 commercials during the shows.

The unit rate of commercials per hour must be determined.

To find this we have to devide 27 by number of hours I.ei.e [tex]\frac{27}{1\frac{1}{2} }[/tex]

Convert [tex]1\frac{1}{2}[/tex] to improper fraction= [tex]\frac{27}{\frac{3}{2} }[/tex].

When a whole number is devided by fraction, the denominator is multiplied with the whole number= [tex]27*\frac{2}{3} =\frac{54}{3} =18.[/tex]

Hence, the unit rate is 18 commercials per hour.

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The constant of variation is 62.5 and this means that the bus travel 62.5 miles per hour.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

The given relation is,

⇒ y = 62.5x

Where, y represent distance in mile and x represent the time in hour.

We know that;

The proportional relation is defined as;

⇒ y = kx

Where, k is constant of variation.

Hence, By comparing,

The constant of variation is 62.5 and this means that the bus travel 62.5 miles per hour.

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The values of each variable in the parallelogram are given as follows:

For a parallelogram, the two sides that are divided by the intersection point of the diagonal have the same length, hence the relations are given as follows:

The second bullet point already gives the value of m, which is of m = 8.

For the first bullet point, we must solve it to obtain the value of variable k, as follows:

k + 4 = 11

k = 11 - 4

k = 7.

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The mass of the chemicals at the end of the experiment is between 54.7 g and 54.71 g.

The lower bound for the mass of the chemicals at the end of the experiment is

            = 62 - 7.3

            =54.7 g.

The upper bound for the mass of the chemicals at the end of the experiment is 62 - 7.3 + 0.01 = 54.71 g.

Therefore, the mass of the chemicals at the end of the experiment is between 54.7 g and 54.71 g.

Note: The rounding to 2 significant figures means that the mass of the chemicals could be slightly different from the values given, but the difference would be less than 0.01 g.

What is lower bound?

The lowest number that can be rounded to obtain an estimated value is referred to as the lower bound (LB).

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The total miles Jim walked in 3 weeks is 36.3 miles

A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a 'real-life' scenario.

Word problems are interpreted into mathematics equations

Jim walks 3 times In a week,

Monday he walked 3.6 miles

Wednesday he walked 5.8 miles

Friday he walked 2.7 miles

The total miles he walked in a week is 3.6+ 5.8+2.7= 12.1 miles

The distance he will walk in three weeks will be

3 × 12.1 = 36.3 miles

therefore in three weeks Jim will walk 36.3 miles

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Step-by-step explanation:

So it's...

[tex] \frac{5\pi}{4} - \frac{\pi}{4} [/tex]

Since the denominators are the same (both of the fractions have 4 on the bottom), you can do simple subtraction to the top while keeping the bottom 4

[tex]5\pi - \pi = 4\pi[/tex]

Which means the answer is

[tex] \frac{4\pi}{4} [/tex]

The measure of side e is, 16.3 inches.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In ΔDEF, m ∠E = 54°, d = 14 in., and f = 20 in.

Now, We know that;

⇒ cos E = (d² + f² - e²) / 2df

Substitute all the values, we get;

⇒ cos 54° = (14² + 20² - e²) / 2×14×20

⇒ 0.59 = (196 + 400 - e²) / 560

⇒ 0.59 × 560 = 596 - e²

⇒ 330.4 = 596 - e²

⇒ e² = 596 - 330.4

⇒ e² = 265.6

⇒ e = √265.6

⇒ e = 16.3 inches

Thus, The measure of side e is, 16.3 inches.

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If x and y are complementary angles, then x and y are supplementary vertical.

Complementary angles are two angles whose sum is equal to 90 degrees. Supplementary vertical angles are two angles that are vertically opposite each other and add up to 180 degrees.

Therefore, the correct answer is as given above. It could then be concluded that the correct answer in the case of x and y being complementary angles, then x and y are supplementary vertical.

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