Answer:
27 children.
Step-by-step explanation:
Let's call the number of children who chose apples x. Then, the number of children who chose bananas is 0.25x. The number of children who chose watermelon is 60 - x - 0.25x = 60 - 1.25x.
Since 30% of the children chose apples, we know that:
0.30 * 60 = x
So, x = 18, which means 18 children chose apples.
And since 25% of the children chose bananas, we know that:
0.25 * 60 = 0.25x = 15
So, 15 children chose bananas.
Finally, the number of children who chose watermelon is:
60 - 18 - 15 = 27 children.
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
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. TheP-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
we now are using two z score formulas. the denominator is the standard deviation on the first one we learned. the denominator is the standard error on the second one we learned. how do you know which z score formula to use? g
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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Transcribed image text: T8.7 A marketing assistant for a technology firm plans to randomly select 1000 customers to estimate the pro- portion who are satisfied with the firm's performance. Based on the results of the survey, the assistant will construct a 95% confidence interval for the propor- tion of all customers who are satisfied. The market- ing manager, however, says that the firm can afford to survey only 250 customers. How will this decrease in sample size affect the margin of error? (a) The margin of error will be about 4 times larger. (b) The margin of error will be about 2 times larger. (c) The margin of error will be about the same size. (d) The margin of error will be about half as large. (e) The margin of error will be about one-fourth as large. T8.8 Thirty-five people from a random sample of 125 work- ers from Company A admitted to using sick leave when they weren't really ill. Seventeen employees
The answer is (b) The margin of error will be about 2 times larger.
The margin of error in a confidence interval is affected by the sample size, so decreasing the sample size will generally increase the margin of error. Specifically, the margin of error is inversely proportional to the square root of the sample size.
That is, if we reduce the sample size by a factor of k, then the margin of error will increase by a factor of sqrt(k).
In this case, the original sample size was 1000, and the proposed sample size is 250, which is 1/4 of the original size. Therefore, the margin of error for the smaller sample will be:
sqrt(1000/250) times the original margin of error.
Simplifying this expression, we get:
sqrt(4) times the original margin of error.
So the margin of error for the smaller sample will be about 2 times the original margin of error.
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the scores on a standardized test are normally distributed with a mean of 100 and standard deviation of 5. what test score is 1.4 standard deviations
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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Determine the period.
10
Check the picture below.
Two simultaneous equations are given below, where p and q are constants.
3x-py = 4
4x - 3y + q = 0
The solution to these equations is x = 1, y = 2.
Find the value of p and q.
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
PLEASE HELP!!!
Write a linear equation given slop is -1/3 and the point (-9,-1)
The equation of a line is y = -1/3x - 4
How to determine the equation of the lineThe general formula for the equation of a line is expressed as;
y = mx + c
Given that the parameters are;
y is a point on the y-axis of the linem is the slope of the linex is a point on the x-axis of the linec is the intercept of the line on the y -axisFrom 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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In a quadrilateral field ABCD angle b is equal to 90 degree ab is equal to 80 metre BC is equal to 150 m c d is equal to 120 m and DA is equal to 250 m find the area of the field in the actor find the price of the field if it goes to 12000 rupees per hector
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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Original Price Percent of Discount Sale Price
$
64% $72
The original price when 64% is applied to the item will be $200.
What is the percentage?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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A snail moves at a speed of 2 feet per minute. How many yards will the snail have moved in one hour? The snail has moved a total of
3
yards
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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QUESTION FOR FOR LIH04
Explain why the comparison is either reasonable are unreasonable
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.
what is the cost of fencing a circular garden of radius 28 with five rounds of wire if the wire cost Rupees 50 per metre.
Answer:
7,000 Rupees
Step-by-step explanation:
Pls show your work thank you will mark the Brainliest
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.
Sam wants to make five banana pancakes. He has a recipe for 20 pancakes,
and the recipe requires two-thirds of a cup of milk. How much milk is needed
for 5 pancakes?
The recipe requires two-thirds of a cup of milk, and Sam needs 1/3 cup of milk to make 5 banana pancakes.
What is the proportion?
A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.
The recipe for 20 banana pancakes requires 2/3 cup of milk.
To find out how much milk is needed for 5 pancakes, we can use proportion. We can set up a proportion that relates the amount of milk needed to the number of pancakes:
(milk needed) / 2/3 cup = 5 pancakes / 20 pancakes
Simplifying the right side of the equation, we get:
(milk needed) / 2/3 cup = 1/4
To solve for the milk needed, we can cross-multiply:
milk needed = (2/3 cup) * (1/4) = 1/3 cup
Therefore, Sam needs 1/3 cup of milk to make 5 banana pancakes.
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xwhat is the correct relationship of the three principles: weak mathematical induction, strong mathematical induction, and the well ordering principle for the integers? [only one answer is correct.] group of answer choices they are none of them equivalent to each other. any one of the three is equivalent to each of the other two of the three. the well-ordering principle for the integers is not equivalent to either mathematical induction, which are equivalent to each other. the well-ordering principle for the integers is equivalent to strong mathematical induction and neither is equivalent to weak mathematical induction.
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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At 7:00 A.M. Joe starts jogging at
6 mi/h. At 7:10 A.M. Ken starts off
after him. How fast must Ken run in
order to overtake him at 7:30 A.M.?
Provide steps please
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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which three values are smaller than 1/2:
A. 1/4
B. 0.26
C. 3/5
D. 67%
E. 0.74
F. 40%
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%
which expression can be used to calculate the rate per second at which the machine launches the balls? (5 points) a fraction 12 over 2 b fraction 2 over 12 c fraction 48 over 2 d fraction 2 over 48
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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A___is a numerical measure of the outcome of a probability experiment
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.
What exactly is probability?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.
The probability equation is what?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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5. Ella checks out a book from the library. She does not read any pages that day. Starting the next day, she reads the same number of pages each day. The graph shows the number of pages Ella has left to read to finish the book. Determine the number of pages in the book. Assume that the relationship between the two quantities is linear. Library Book Number of Pages Unread 60 54 48 42 36 30 24 18 12 6 0 1 2 3 4 5 6 7 8 9 10 x Number of Days a. b. C. d. 5 5 8 48 58
The number of pages in the book is given as follows:
58 pages.
How to obtain a linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.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.
Missing InformationThe graph is given by the image presented at the end of the answer.
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There is a total of
wholes in 72
.
The remaining fractional part is .
2
The whole number whose sum is 72 cannot be in the ratio C. 3/4.
How to explain the ratioRatio 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
Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.
The simplified form of the expression √x × ⁴√x in rational exponent form is x^3/4.
What is the simplified form of the expression?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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(8,12) and (x,9) where m = -1/2
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.
Solve the inequality for x and identify the graph of its solution.
2|x+3|< 4
Choose the answer that gives both the correct solution and the correct graph.
$22 if it has 11 attendees. If there are 48 attendees, how much will picnic cost? Assume the relationship is directly proportional.
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.
Use the substitution method to solve the system of linear equations.
y = x - 4
4x + y = 26
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
Discount % is always calculated on the:
a) CP ( cost price).
b) SP ( selling price).
c) MP ( marked price).
d) None of these.
the perimeter of a ractangle is 280cm the ratio of the width to the length is 3:4. what is the length of the rectangle?
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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4x^-3 y^-2 for x = 2 and y = 1? Pls Show work
Answer:
To substitute x = 2 and y = 1 into the expression 4x^-3 y^-2, we simply replace x with 2 and y with 1:
4 * (2)^-3 * (1)^-2 = 4 * (1/8) * (1) = 4/8 = 0.5
So the expression 4x^-3 y^-2 evaluated at x = 2 and y = 1 is equal to 0.5.
Step-by-step explanation:
