Garth was making lemonade for the school carnival. He bought 14 1/4 pounds of sugar to use for the lemonade. When he finished making lemonade, he had 4 3/4 pounds of sugar left over. How much sugar did he use for the lemonade?


A) 19


B) 18 1/2


C) 10 1/2


D) 9 1/2

A test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.

To find the test score that is 1.4 standard deviations above the mean, we need to use the formula:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.

In this case, we know that z = 1.4, μ = 100, and σ = 5. So we can rearrange the formula to solve for x:

x = z * σ + μ

Substituting the values we know, we get:

x = 1.4 * 5 + 100 = 107

Therefore, a test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.

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The snail moves a distance of 40 yards in one hour as it moves at a speed of 2 feet per minute.

We can start by converting the speed of the snail from feet per minute to yards per hour, since the distance moved is given in yards per hour.

There are 60 minutes in an hour, so the snail's speed in yards per hour is:

2 feet per minute * 60 minutes per hour * (1/3) yards per foot = 40 yards per hour

Hence,

The snail moves a distance of 40 yards in one hour.

Since we are given that the snail has moved a total of 3 yards, we can find the amount of time it took by dividing the distance by the rate:

time = distance / rate

time = 3 yards / 40 yards per hour

time = 0.075 hours or 4.5 minutes

Therefore, the snail will move a distance of 3 yards after 4.5 minutes and distance of 40 yards in one hour.

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The choice between using the standard deviation and standard error in the denominator of a z-score formula depends on the context of the problem and the type of data being analyzed.

To determine which z-score formula to use, consider the type of data and the context of the problem. If you have a sample with a known population standard deviation, use the first formula.  If the data represents a random sample of a larger population, the standard error is typically used to account for the variability in estimating the population mean. On the other hand, if the data represents the entire population, the standard deviation is used as the denominator. It's important to understand the distinction between a sample and a population and to choose the appropriate formula accordingly.

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The original price when 64% is applied to the item will be $200.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentile in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value × 100

Let 'x' be the Original Price. Then the equation is given as,

(1 - 0.64) x = $72

0.36 x = $72

x = $200

The original price when 64% is applied to the item will be $200.

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Online math courses can also offer some benefits, such as the flexibility to work at your own pace and the ability to review lectures and assignments as needed. Overall, taking an online math course requires self-discipline, motivation, and a willingness to seek help when needed.

Online classes are virtual classrooms that offer students the opportunity to learn from anywhere, at any time, with a reliable internet connection. The primary focus of online classes is to provide students with the same level of academic instruction as they would receive in a traditional classroom setting. Many educational institutions and organizations offer online classes, including colleges, universities, and K-12 schools.

One of the significant advantages of online classes is that they offer flexibility, which means students can manage their coursework according to their schedule. Students can also access course material, lectures, and assignments from anywhere, which eliminates the need to attend a physical classroom. Online classes also offer students the ability to work at their own pace and review course material as often as they need to.

Online classes provide students with access to a wide range of educational resources, including video lectures, interactive quizzes, discussion forums, and other learning tools. Many online classes also provide students with personalized support, including one-on-one virtual sessions with instructors or teaching assistants.

Taking an online math course can be different from taking other subjects online. Typically, online math courses involve watching pre-recorded video lectures, completing online assignments, and participating in online discussions or forums. Online math courses may also use virtual tools, such as interactive graphs or calculators, to enhance the learning experience.

Compared to other online courses, learning math online may require more self-discipline and motivation, as it can be challenging to stay engaged with the material without the structure of a traditional classroom. Additionally, math is a subject that often builds on previous concepts, so it is essential to stay on top of the material and seek help if needed.

However, online math courses can also offer some benefits, such as the flexibility to work at your own pace and the ability to review lectures and assignments as needed. Overall, taking an online math course requires self-discipline, motivation, and a willingness to seek help when needed.

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Answer:

$96

Step-by-step explanation:

We know

$22 if it has 11 attendees.

$22 divided 11 = $2 per attendee

So, we know per attendee costs $2

If there are 48 attendees, how much will the picnic cost?

2 x 48 = $96

So, the picnic cost $96.

Answer:

y = 2 and x = 6

Step-by-step explanation:

Let y = x - 4 be  equation a

Let 4x + y = 26 be equation b

Substitute a into b:

4x + (x-4) = 26

5x - 4 = 26

5x = 30

x = 6

Substitute the value of x into a:

y = x - 4

y = 6 - 4

y = 2

CHECK:

4x + y = 26

4*6 + 2 = 26

24 + 2 = 26

26 = 26

LHS = RHS

Therefore, y = 2 and x = 6

An objective tally of the results of a probability experiment is called a random variable. It gives a number to each potential result of the experiment, and its values are decided by chance.

How something is to Happen is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics defines series of events subject to probability.

Always between 0 and 1 are the possible outcomes. Probability = Number of favourable outcomes / Total number of outcomes is how the general probability formula is written. Alternatively, P(A) = f / N.

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For the given width length ratio and perimeter of rectangle, the length of rectangle is 80 cm.

The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Let the width of the rectangle be 3x, and the length be 4x (since the ratio of the width to the length is 3:4).

The perimeter of a rectangle is the sum of the lengths of all four sides, so we have:

Perimeter = 2(length + width)

Substituting the expressions for the length and width, we get:

280cm = 2(4x + 3x)

Simplifying the right-hand side, we get:

280cm = 14x

Dividing both sides by 14, we get:

x = 20

Therefore, the length of the rectangle is 4x = 4(20) = 80 cm

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The area of the field is 2.384 hectares and price of the field is $28,608

The area of a quadrilateral given its sides and the diagonal:

Area = 1/4 × √[4s^2d^2 - (b^2 + d^2 - a^2 - c^2)^2]

where s = (a + b + c + d)/2 is the semi perimeter,

a, b, c, d are the lengths of the sides

d is the length of the diagonal.

Substituting the given values,

s = (80 + 150 + 120 + 250)/2

= 300

a = 80, b = 150, c = 120,

d = √(250^2 + 80^2)

= 259.8076

Area = 1/4 × √[4(80+150+120+250)^2*(259.8076)^2 - (80^2 + 259.8076^2 - 150^2 - 120^2)^2]

≈ 23844.17 square meters

To convert square meters to hectares, we divide by 10,000:

Area = 23844.17 / 10,000 hectares

≈ 2.384 hectares

Therefore, the area of the field is approximately 2.384 hectares.

The price of the field = 12,000/hectare,

Total price = 2.384 hectares × $12,000/hectare

= $28,608

Therefore, the price of the field is $28,608.

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The equation of a line is y = -1/3x - 4

The general formula for the equation of a line is expressed as;

y = mx + c

Given that the parameters are;

From the information given, we have that;

Slope, m = -1/3

Substitute the values

-1 = -1/3(-9) + c

expand the bracket

-1 = 3 + c

collect like terms

= -4

Hence, the equation is y = -1/3x - 4

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The correct relationship of the three principles is: The well-ordering principle for the integers is equivalent to strong mathematical induction, and neither is equivalent to weak mathematical induction.

The well-ordering principle for the integers states that every non-empty set of non-negative integers has a least element. Strong mathematical induction is a proof technique that involves proving that a statement is true for a base case, and then assuming that it is true for all cases up to a certain value, and then proving that it must also be true for the next case.

This requires assuming the truth of all cases up to a certain value, which is where the well-ordering principle comes in. Weak mathematical induction is a proof technique that involves proving that a statement is true for a base case, and then assuming that it is true for a particular case, and then proving that it must also be true for the next case.

Weak mathematical induction does not require assuming the truth of all cases up to a certain value, and is therefore weaker than strong mathematical induction.

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The expression that can be used to calculate the rate per second at which the machine launches the balls is a) Fraction 12 over 2.

To calculate the rate per second at which the machine launches the balls is:

First, we need to know the meaning of rate is: it is the amount of something per unit of time. In this case, we want to find the rate at which the machine launches the balls per second.

The fraction 12 over 2 represents the number of balls launched by the machine in 12 seconds. If we want to find the rate per second, we need to divide this number by the number of seconds.

12/ 2 = 6, so the machine launches 6 balls in 1 second.

Therefore, the rate per second at which the machine launches the balls is 6.

So, the expression that can be used to calculate the rate per second at which the machine launches the balls is Fraction 12 over 2, which simplifies to 6.

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Answer:

Step-by-step explanation:

The slope of a line between two points (x1, y1) and (x2, y2) is given by:

m = (y2 - y1) / (x2 - x1)

In this case, we are given that m = -1/2, so substituting in the two points we have:

-1/2 = (9 - 12) / (x - 8)

Expanding and simplifying the equation:

-1/2 = -3 / (x - 8)

Multiplying both sides by -2:

1 = 3 / (x - 8)

Multiplying both sides by (x - 8):

x - 8 = 3

Adding 8 to both sides:

x = 11

So the x-coordinate of the second point is x = 11.

Answer:

Step-by-step explanation: umm hard the question doesn't sound like a question

Answer:

p = -1/2

q = 2

Step-by-step explanation:

Equations are:
3x - py = 4                         [1]

4x - 3y + q = 0                [2]

If x = 1 and y = 2, then substituting for these values in each equation will provide a solution for p and q

Plugging x = 1 in Equation [1]:
3(1) - p(2) = 4

→ 3 - 2p = 4

→ -2p = 4 - 3

-2p = 1

-2p/-2 = 1/-2

p = -1/2

For the second equation  4x - 3y + q = 0
x = 1, y = 2

→    4(1) -3(2) + q = 0

→    4 - 6 + q = 0

→    -2 + q =0

→    q = 2

The whole number whose sum is 72 cannot be in the ratio C. 3/4.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them

The whole number must   be divided by sum of two ratio particularly

A.5 + 7=12

72 can be divided by 12

B.3+5=8

72 can be divided by 8

C.4+3=7

72 can not be divided by 7

D.4+5=9

72 can be divided by 9

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The whole number whose sum is 72 cannot be in the ratio

A. 5/7

B. 3/5

C. 3/4

D. 4/5

Answer: 1) 29 (look at the image for the solution)

Step-by-step explanation:

The number of pages in the book is given as follows:

58 pages.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the graph, two points are given as follows:

(2,48) and (8, 18).

When x increases by 6, y decays by 30, hence the slope m is given as follows:

m = -30/6

m = -5.

Hence:

y = -5x + b.

When x = 2, y = 48, hence the intercept b, representing the number of pages in the book, is given as follows:

48 = -10 + b

b = 58.

The graph is given by the image presented at the end of the answer.

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Answer:

Reasonable

Step-by-step explanation:

The comparison 3.84 > 3.8 is reasonable.

In this comparison, 3.84 is a larger number than 3.8, so it makes sense to say that 3.84 is greater than 3.8. When comparing decimal numbers, we can simply compare the values to the right of the decimal point. In this case, both 3.84 and 3.8 have two digits to the right of the decimal point, so we can compare those digits directly. Since 4 is greater than 8, it follows that 3.84 is greater than 3.8.

The comparison is reasonable because it is based on a correct understanding of the relative sizes of the numbers involved.

a. If H0 is true then the test is designed for probability of type I error of 0.025 .b. Here the p Value is 0.10 . So this indicates that the H0 is true in this test . But there is a decision error if we Reject the Null hypothesis H0.

A hypothesis is an educated guess or statement that attempts to explain a particular phenomenon or answer a specific research question. It is an essential element of the scientific method, which involves testing a proposed explanation through experimentation or observation. The purpose of a hypothesis is to guide researchers in designing an experiment that can be used to either support or refute the proposed explanation.

A hypothesis is typically based on prior knowledge, observations, or theories related to the research question. It is important for a hypothesis to be testable, measurable, and specific to allow researchers to evaluate the results objectively. A hypothesis can be developed in various fields of study, including natural sciences, social sciences, and humanities.

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Complete Question: -

A significance test about a proportion is conducted using a significance level of 0.025. The test statistic equals 1.33. The​P-value is 0.10. a. If Upper H 0 were​ true, for what probability of a Type I error was the test​ designed? b. If this test resulted in a decision​ error, what type of error was​ it?

a. If Upper H 0 were​ true, for what probability of a Type I error was the test​ designed?

b. If this test resulted in a decision​ error, what type of error was​ it? Type II Type Upper I

Answer: A, B, F

Step-by-step explanation:

For convenience sake, let's establish early on that 1/2 is equal to 0.5 or 50% in their decimal and percentage forms respectively.

- A as a decimal is 0.25, which is not only smaller than 1/2, but it is exactly half of the value, so A works.

- B is also smaller than the decimal of 0.5, therefore it counts.

- 3/5 as a decimal is 0.5, which is greater, so doesn't count.

- 67% is bigger than 50%, so doesn't count.

- 0.74 is bigger than 0.5, so doesn't count.

- 40% is smaller than 50%, so it counts.

Answer:

A, B, and F

Step-by-step explanation:

A. 1/4 = 25%

B. .26 = 26%

F. 40%

The speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.

What is meant by the speed of an object?

The size of a change in an object's position over time is measured by its speed. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. It is a scalar value.

Given,

Time at which Joe starts jogging  = 7 am

Time at which Ken starts jogging = 7.10 am

Speed of Joe = 6mi/h

Let Speed of Ken required to overtake Joe = x mi/h

Since Ken has to overtake Joe by 7.30, both will have travelled the same distance by 7.30.

Time taken by Ken to cover the distance = 7.30 - 7.10  20 minutes = 20/60=1/3 h

Time taken by Joe to cover the distance = 7.30 - 7 = 30 minutes = 1/2 h

Distance = speed * time

Both cover the same distance.

6 * 1/2 = x * 1/3

x = 9 mi/h

Therefore the speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.

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The simplified form of the expression √x × ⁴√x in rational exponent form is x^3/4.

Given that, square root of x times the fourth root of x.

√x × ⁴√x

To simplify the expression, rewrite using the least common index of 4.

Since ⁿ√xᵃ = x^(x/n)

√x = x^(1/2)

and

⁴√x = x^(1/4)

Hence, we have;

x^(1/2) ×  x^(1/4)

Using exponent rule

x^( 1/2 + 2/4 )

Add 1/2 and 1/4

x^( 1/2 + 1/4 )

x^3/4

Therefore, the simplified form is x^3/4.

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Answer: A

Step-by-step explanation: There isn't much work to be shown here, however you can look at graphical patterns to get your answer. It says the initial value is $200000 so you can eliminate B and D because they start at $100000. That leaves A and C. C is increasing at a higher rate and is greater than 100% per year. That leaves option A.

Check the picture below.

Answer:

7,000 Rupees

Step-by-step explanation: