Type I errors (also known as a "false positive") occur when a test erroneously rejects a true null hypothesis. In other words, the test incorrectly concludes that the observed effect is significant or real when, in fact, it is not.
A type I error is a statistical mistake where the null hypothesis is rejected, despite it being true. This is also known as a false positive. This means that the test concluded that the observed effect was significant when in reality, it was not. Type I errors are more likely to occur when the sample size is small or when too many tests are conducted at once. To avoid type I errors, it is important to use an appropriate sample size and to consider the power of the test before conducting it.
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The question: Define a variable, write an equation, and solve each problem. Then check your solution.
The problem: Three times the greatest of three consecutive even integers exceeds twice the least by 38. Find the integers.
Answer: 26, 28, 30
Explanation:
Let's define a variable x to represent the least of the three consecutive even integers. This means that the three integers are x, x + 2, and x + 4.
We can write the given information as an equation:
3 * (x + 4) = 2 * x + 38
We can solve for x by moving all the terms with x to one side of the equation and all the other terms to the other side:
3 * (x + 4) - 2 * x = 38
Then we can distribute the 3 and the -2 to get:
3 * x + 12 - 2 * x = 38
And then we can combine like terms on each side of the equation:
x + 12 = 38
Finally, we can subtract 12 from both sides to solve for x:
x = 26
Therefore, the three consecutive even integers are 26, 28, and 30.
We can check our solution by substituting these values back into the original equation and verifying that it holds true:
3 * (26 + 4) = 2 * 26 + 38
3 * 30 = 52 + 38
90 = 90
The equation holds true, so our solution is correct.
the steps derek used to solve an equation are shown below.
Solve: 0.4x + 5 + 0.2x = 17
Step 1 : 0.4x + 0.2x + 5 = 17
Step 2: 0.6x + 5 = 17
Step 3: 0.6x = 12
Step 4: x = 20
Which properties justify step 1 and step 3?
The commutative property of addition justifies step 1 and the substraction of the property of equality justifies step 3.
What is the Substitution Property of Equality?
The substitution property of equality is applied by replacing a variable with a number or quantity. For example, if we have:
5x + 3 = 18, if x = 3, we can substitute x = 3 into the equation by applying the substitution property of equality as shown below:
5(3) + 3 = 18
15 + 3 = 18
18 = 18.
We have,
0.4x + 5 + 0.2x = 17
Step 1 : 0.4x + 0.2x + 5 = 17
commutative property of addition
Step 2: 0.6x + 5 = 17
Step 3: 0.6x = 12
substraction of property of equality
so, step 1 : commutative property of addition
Step 3 : substraction of property of equality
Hence, the commutative property of addition justify for step 1 and the substraction of the property of equality justify for step 3.
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What i the quotient of 3. 12\time 10^83. 12×10
8
and 2. 6 \time 10^52. 6×10
5
expreed in cientific notation?
The quotient of 3.12 × 10⁸ and 2.6 × 10⁵ is 1.2 × 10².
What is quotient?
A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.
Given numbers are 3.12 × 10⁸ and 2.6 × 10⁵.
Now divides 3.12 × 10⁸ by 2.6 × 10⁵:
(3.12 × 10⁸)/(2.6 × 10⁵)
Break the number into two fractions:
= (3.12/2.6) × (10⁸/10⁵)
Applying formula a^m/a^n = a^(m-n):
= (3.12/2.6) × (10⁸⁻⁵)
= 1.2 × 10³
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cans of soda are samples to ensure proper weight. the overall average for the sample is 10 ounces. each sample contains 25 cans. the standard deviation is estimated to be 3 ounces. what are the 99.73% control limits? group of answer choices 0.000 to 7.824 5.200 to 14.800 8.602 to 11.398 none of the above 0.000 to 10.176
The 99.73% control limits are 8.602 to 11.398
The correct answer is an option (c)
In this question we have been given:
sample size = 25
mean = 10
Standard deviation = 3
We need to determine the 99.73% control limits.
We know that Confidence interval = sample mean ± margin of error
Margin of error = z* x population of standard deviation/√n
The value of z* for 99.73% confidence interval is 3.00
Margin of error = 3 × (3/√25)
Margin of error = 9/5
Margin of error = 1.8
So, the control limits would be,
upper limit = 10 + 1.8
= 11.8
And the lower limit = 10 - 1.8
= 8.2
Therefore, from given choices the control limits are 8.602 to 11.398
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Helpppp guys urgent!!!!
Answer:
C. Paying a cell phone bill
if it takes three concrete workers 1 hour to pour 5 yd3 of concrete, and each worker makes $15 an hour, how much will it cost to pour 25 yd3?
It will cost $225 to pour 25 yd3 of concrete with 3 workers working at a rate of $15 per hour.
To determine the cost to pour 25 yd3 of concrete, you can use the following formula:
cost = (number of workers * worker rate per hour * number of hours)
In this case, the number of workers is 3, the worker rate per hour is $15, and the number of hours can be calculated by dividing the volume of concrete to be poured (25 yd3) by the rate at which the workers can pour concrete (5 yd3 per hour). Therefore, the number of hours it will take to pour 25 yd3 of concrete is 25/5=5 hours.
Plugging these values into the formula gives:
cost = (3 workers * $15/hour * 5 hours) = $<<3155=225>>225
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Let h be a function defined for all x not equal to 0 such that h(4) = - 3 and the derivative of h is given by h'(x) = (x∧2 - 2)/x for all x not equal to 0.a. Find all values of x for which the graph of h has a horizontal tangent , and determine whether h has a local maximum, local minimum of neither at each of these values. Justify your answers.b. On what intervals, if any, is the graph of h concave up? Justify your answer.c. Write an equation for the line tangent to the graph of h at x = 4.d. Does the line tangent to the graph of h at x = 4 lie above or below the graph of h for x > 4? Why?
For a function h such that h(4) = -3 and h'(x) = (x² - 2)/ x for all x∈R-{0}, the function has two local minima at x = -2 and x = 2. The local maxima is not determined implying it would be at the critical value x = 0.
A graph has a horizontal tangent at a local minimum or local maximum and the slope is zero at that point. That is at points which has horizontal tangent. h'(x) = 0.
(x² - 2)/ x = 0
Thus x = 2 or x = -2
At the local minimum or local maximum, the slope is zero or tangent is horizontal as the graph change from decreasing to increasing or increasing to decreasing.
h''(x) = 1 + 2/x²
h"(2) = 1 + 2/ 4 > 0
h''(-2) = 1 + 2/ 4 > 0
Therefore at x = 2 and x = -2 we have local minimum.
The graph of h will be concave up between two local minimum. So graph is concave up in the interval -2<x<2.
Let us assume the tangent line is y = mx + c.
m = h'(4) = (4² - 2)/ 4
m = 3.5
we know h(4) = -3, that is
-3 = m×(4) + c
c = -3 - 4×3.5 = -17
Therefore the tangent line is y = 3.5x - 17.
The line tangent to the graph of h at x = 4 lie below the graph of h at x = 4 as x = 2 is a minimum and thus the slope is increasing for x>2.
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This system is a flexible tool for data analysis, since its reports do not have a fixed format.
A. Management information system
B. Decision support system
C. Transaction processing system
D. Executive support system
Option - B : Decision support system is a flexible tool for data analysis, since its reports do not have a fixed format.
Decision support systems, a subset of business intelligence, are created to help organisations make sensible business decisions based on vast volumes of analysed data. Huge volumes of data are analysed using an interactive information system called a decision support system (DSS) to aid in the direction of business choices. A DSS aids management, operations, and planning levels of an organisation in making better decisions by assessing the importance of uncertainties and the tradeoffs involved in selecting one option over another. A DSS uses a variety of raw data, papers, personal knowledge, and/or business models to aid users in making decisions. A DSS may make use of relational data sources, cubes, data warehouses, electronic health records (EHRs), income projections, sales projections, and other sources.
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Please help! Lots of love for the ones that do!! <3
Peter is mixing a small, test batch of paint to make a lavender color. He uses 3/5 qt of red, 1 qt of blue and 2/5 qt of white. He wants to make a larger batch with the same ratios using 15 qts of blue. How much red and white must he add so that the large batch is the same color as the test batch
To find the amount of red and white that Peter needs to add to the large batch, we can set up the following proportion:
(3/5 qt red) : (1 qt blue) : (2/5 qt white) = (x qt red) : (15 qt blue) : (y qt white)
The proportion states that the ratio of red to blue to white in the test batch is equal to the ratio of red to blue to white in the large batch.
Cross-multiplying and solving for x and y gives us:
(3/5)x = 15y
(2/5)y = 15x
Solving the first equation for y and substituting it into the second equation gives us:
(2/5)y = 15x
(2/5)(15x/3) = 15x
x = 9 qt
Substituting this value for x back into the first equation gives us:
(3/5)x = 15y
(3/5)(9 qt) = 15y
y = 6 qt
Therefore, Peter needs to add 9 qt of red and 6 qt of white to the large batch to make it the same color as the test batch.
The world’s largest freestanding escalator, which is located inside the CNN Center in Atlanta, Georgia, is 196 feet tall. Before visiting the escalator, Mary and Kenneth are discussing how fast they would like th escalator to rise.Mary wants the escalator to rise at 4 feet per second, and Kenneth wants the escalator to rise at 10 feet per second. Based on each persons desire, how long would it take the escalator to reach the top? Whose rate is safer? Explain
Answer:
Step-by-step explanation:
The world's largest freestanding escalator is 196 feet tall. If the escalator were to rise at 4 feet per second, it would take 49 seconds to reach the top. If it were to rise at 10 feet per second, it would take 19.6 seconds to reach the top.
Kevin conducted a poll using a random sample of students at his school in order to estimate how the upcoming vote would turn out. Of his random sample of students, 72 said they would vote yes, 90 said they would vote no, and 18 were undecided. Using these observed frequencies, develop a probability model for Kevin randomly choosing one more student for the poll. Enter the probabilities as decimals.
Answer:2.4
Step-by-step explanation:
what is the closest alloweable distance of the perpendicular distance between a point in face 2 and datum a
The closest allowable distance that a randomly chosen datum falls within the required 2 standard deviations of the mean is 0.95.
The likelihood that a data is within two standard deviations of the mean
By observation, the distribution depicted in the task content above is a normal distribution.
One can tell the difference between the following .
In the case of a standard normal distribution, 68% of the observations (datum) are within one standard deviation of the mean, 95% are within two standard deviations of the mean, and 99.9% are within three standard deviations of the mean.
On this note, when expressed as a percentage; the probability that the randomly selected datum falls with 2 standard deviations is; 95/100 = 0.95.
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Use the distributive property to factor the expression below.
54x²y - 12x²y²
Answer: The answer is 6x^2y(9 - 2y)
Step-by-step explanation: I am not completely sure sorry if its wrong
Find the zeros of the equation by factoring.
x2 + 4x - 32 = 0
( __, __) = 0
x = ___
factors should have two whole numbers separated by a: + or - . Do not type parenthese and no spaces. Examples: x+5 x-4
Answer:
x = - 8, 4
Step-by-step explanation:
x² + 4x - 32 = 0
to factorise , consider the factors of the constant term (- 32) which sum to give the coefficient of the x- term (+ 4)
the factors are + 8 and - 4 , since
+ 8 × - 4 = - 32 and + 8 - 4 = + 4 , then
(x + 8)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x - 4 = 0 ⇒ x = 4
zeros are x = - 8 , 4
Find the volume of a chest ( can someone please help me real quick and fast ) i will give u brain list
Answer:
15997.787145 cm³
Step-by-step explanation:
question 12 (essay worth 10 points) (05.04, 05.05 hc) let x equals negative 31 times pi over 6 period part a: determine the reference angle of x. (4 points) part b: find the exact values of sin x, tan x, and sec x in simplest form. (6 points)
Part A: The stated values is; x = 31π/6
A circle has 360 degrees. We must decrease the present angle to an angle between 0° and 360° in order to determine the reference angle.
As, 360° = 2π radians, subtract 2π = 12π/6 radians for each iteration.
Iteration 1 => 31π/6 - 12π/6 = 19π/6
Iteration 2 => 19π/6 - 12π/6 = 7π/6
0 ≤ 7π/6 ≤ 12π/6
Thus, reference angle is found as 7π/6 radians
Part B) The value for the sin x, tan x, and sec x.
sin (7π/6) = -1/2
tan (7π/6) = 1/√3
sec (7π/6) = 1/cos(7π/6) = -1/(√3)/2
sec (7π/6) = -2/√3
Thus, the simplest values of sin x, tan x, and sec x are found.
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Which sets are proper subsets of set A?
A= {1,3,5,7,9}
Select all that apply
A. {1,2,3,4}
B.{9}
C.{2,4,6,8}
D.{ }
E. {1,3,5,7,9}
F. {1,5,7}
Answer:
f.[157]
Step-by-step explanation:
set A consists of odd numbers and choise F also consists of odd numbers
we are not going for choise A because 2and4are even numbers choise E is a repetition
The options D. { } and F. {1, 5, 7} are the proper subsets of set A={1, 3, 5, 7, 9}.
To determine which sets are proper subsets of set A={1, 3, 5, 7, 9}, we need to understand the definition of a proper subset. A proper subset of a set A is a subset that contains fewer elements than A but is not equal to A.
Let's evaluate each option:
A. {1, 2, 3, 4}
This set is not a proper subset of A because it contains the element 2, which is not in A.
B. {9}
This set is not a proper subset of A because it is equal to A. A proper subset should have fewer elements than the original set.
C. {2, 4, 6, 8}
This set is not a proper subset of A because it does not have any elements in common with A.
D. { }
This set is a proper subset of A since it contains no elements, and it is always a subset of any set, including A.
E. {1, 3, 5, 7, 9}
This set is not a proper subset of A because it is equal to A, and we are looking for subsets with fewer elements.
F. {1, 5, 7}
This set is a proper subset of A since it contains fewer elements than A but is not equal to A.
Correct answers:
D. { }
F. {1, 5, 7}
So, options D and F are the proper subsets of set A={1, 3, 5, 7, 9}.
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if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then, p(b) =
The chance of the event B is 0.4 when using the probability for the two independent two event formula.
In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).
Events classified as independent do not depend on other events for their occurrence.
Event A's likelihood of happening is P(A)=0.65.
The likelihood of the two events A and B intersecting is P(A∩B)=0.26.
Given that the likelihood of the two independent events is:
P(A∩B) = P(A)⋅P(B)
Then the probability of the event B will be,
P(B) = P(A)/P(A∩B)
P(B) = 0.65/0.26
P(B) =0.4
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ILL MARK BRAINLIEST IF UR ANSWER IS ACTUALLY RIGHT
Question 13(Multiple Choice Worth 1 points)
(02.01 LC)
A linear function is shown on the graph.
A linear function beginning with closed circle at negative 4 comma 9 and ending with a closed circle at 3 comma negative 5.
What is the domain of the function?
{x | −4 ≤ x ≤ 3}
{x | −4 < x < 3}
{y | −5 ≤ y ≤ 9}
{y | −5 < y < 9}
Answer:
I believe the answer is the first one.
Step-by-step explanation:
The domain of a function is the lowest X value to the highest X value. The range of a function is the lowest Y value to the highest Y value. Since this question is asking about the domain, we can narrow down the answers to either 1, or 2 because 3 and 4 are for the range, with Y in them.
Next, we look at the points. The differences between them is that 1 has greater OR EQUAL and less than OR EQUAL, whereas 2 has just greater or less then. The circles are filled in on the graph, meaning they are closed. this means it could be equal. Since we know the equation must contain equals in it, we can eliminate 2 and 4 because they only have greater and less than signs.
This leaves the only correct answer for the domain of the graph to be 1.
The domain is the interval of x thus {x | −4 ≤ x ≤ 3} will be the domain so option (A) is correct.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given linear function,
The domain is the set of x that the function defines.
Since (-4,9) is a closed circle so -4 will be included and (3,-5) is also a closed circle thus 3 will also be included.
So the interval will be as {x | −4 ≤ x ≤ 3}.
Hence "The domain is the interval of x thus {x | −4 ≤ x ≤ 3} will be the domain".
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Last year at a certain high school, there were 80 boys on the honor roll and 88 girls on the honor roll. This year, the number of boys on the honor roll increased by 15% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
0.1% of honor roll students
Step-by-step explanation:
to get the total percentage, find the boy's and girl's percentage numbers first.
15% out of 80: 0.05
25% out of 88: 0.04
0.05+0.04=0.09
the total number of honor students increased: 0.09,
round to the nearest tenth: 0.1
and the total number of honor students are: 80+88=168
0.1 is=0.06% out of 168
0.1% of honor roll students increased this year.
a fruit fly population of 182 flies is in a closed container. the number of flies grows exponentially, reaching 340 in 18 days. find the doubling time (time for the population to double) to the nearest tenth of a day.
In this case, the amount of population of fruit flies doubled in 18 days, meaning the doubling time is 9.5 days.
The doubling time of a population is the amount of time it takes for a population to double in size. In this case, the population of fruit flies started at 182 individuals and grew to 340 in 18 days. To calculate the doubling time, we used the equation (182 x 2^(18/9.5)) = 340, where the 2^(18/9.5) is the exponentiation of the number of days divided by the doubling time. This equation can be rearranged to solve for the doubling time, yielding a result of 9.5 days. This means that the population of fruit flies doubled in size every 9.5 days, which is the doubling time of the population.
182 x 2^(18/9.5) = 340
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farmer has 200 feet of fencing to build rectangular chicken pen along side of barn, what is largest area possible
The largest area possible is when the length and width of the chicken pen are both 100 feet. In that case, the area of the chicken pen would be 10,000 square feet.
We are given that the farmer has 200 feet of fencing to build a rectangular chicken pen along the side of a barn. We need to find the largest possible area the chicken pen can have.
To do this, we need to find the length and width of the chicken pen such that the total amount of fencing used is 200 feet.
Since the total amount of fencing needed is 200 feet, the length and width of the chicken pen must both be 100 feet. In this case, the area of the chicken pen would be 10,000 square feet.
Therefore, the largest area possible is 10,000 square feet when the length and width of the chicken pen are both 100 feet.
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suppose that rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 222 different toppings. what is the probability that rosa's mom chooses sausage and onion?
The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to
(1/ ⁸C₂).
As given in the question,
Total number of different toppings = 8
Number of different toppings choose by Rosa's mom randomly = 2
Possibility of choosing sausage and onion (any one) = 1
Total number of outcomes = ⁸C₂
Number of favorable outcomes = 1
Probability of choosing sausage and onion ( exactly ) one topping
= ( Number of favorable outcomes ) / ( Total number of outcomes )
= ( 1/⁸C₂ )
Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).
The above question is incomplete, the complete question is:
A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings
below:
Pepperoni ,Sausage, Chicken , Green pepper , Mushroom ,Pineapple, Ham, Onion
Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.
What is the probability that Rosa's mom chooses sausage and onion?
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Answer:
1/8c^2
Step-by-step explanation:
Khan Acadmey
Carina and Rylee ran a mile in gym class. It took Carina 7.18 minutes and Rylee 7 4/25 minutes to complete. Who ran the quickest?
Answer:
Rylee
Step-by-step explanation:
Carina ran 7.18
and Rylee 7.16
7 4/25
4÷25= 0.16 7+0.16=7.16
of the 41 transgendered people polled 18 agreed and 4 were neutral. of the 50 non-binary people, 6 agreed and 12 were neutral. the rest disagreed with such a platform being allowed to exist in our society. the student wishes to test the hypothesis of independence using pearson's chi square test. how many degrees of freedom are there under the null hypothesis?
The observed chi square score rounded to the nearest hundredth is 31.32. So, the option D is correct.
In the given question;
Of the 47 men polled, 25 agreed and 10 were neutral.
Of the 50 women polled 14 agreed and 5 were neutral.
Of the 41 transgendered people polled 18 agreed and 4 were neutral.
Of the 50 non-binary people, 6 agreed and 12 were neutral.
The rest disagreed with such a platform being allowed to exist in our society.
We have to find how many transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis.
We can determine the anticipated frequencies for each cell in the contingency table using the following formula:
Expected Frequencies
Agree Disagree Neutral
Men 15.5 31.5 10
Women 8.5 41.5 5
Transgender 12.5 28.5 4
Non-binary 3.5 46.5 12
The formula for Pearson's chi square test to calculate the chi square score:
Χ² = ∑(Observed - Expected)² / Expected
Χ² = [(25 - 15.5)² / 15.5] + [(14 - 8.5)² / 8.5] + [(18 - 12.5)² / 12.5] + [(6 - 3.5)² / 3.5] + [(22 - 31.5)² / 31.5] + [(36 - 41.5)² / 41.5] + [(23 - 28.5)² / 28.5] + [(44 - 46.5)² / 46.5] + [(10 - 10)² / 10] + [(5 - 5)² / 5] + [(4 - 4)² / 4] + [(12 - 12)² / 12]
Χ² = 31.32
Hence, the option D is correct.
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The right question is:
A university student wishes to explore whether GENDER (man, woman, A university student wishes to explore whether GENDER (man, woman, trans, non-binary) is associated with AGREEMENT (agree, disagree, neutral) to the existence of a social media platform that allows almost all forms of non-violent free speech, with minimal content moderation to censure only the most egregious of posts, Of the 47 men polled, 25 agreed and 10 were neutral. Of the 50 women polled 14 agreed and 5 were neutral. Of the 41 transgendered people polled 18 agreed and 4 were neutral, Of the 50 nonbinary people, 6 agreed and 12 were neutral. The rest disagreed with such a platform being allowed to exist in our society. The student wishes to test the hypothesis of independence using Pearson's chi square test. Determine the observed chi square score rounded to the nearest hundredth.
A. 0.25
B. 0.53
C. 0.54
D. 31.32
E. None of the above
If triangle ABC, if m angle ABC and egment BF i an angle biector, find m angle BCE
In calculation, the precise bisector is a line section that separates a point into two equivalent points and parts.
The measure of P Q R is equal to the sum of ∠PQT and ∠TQR if line segment QT is the angular bisector of an angle ∠PQR.
∠PQR is equal to ∠PQT + ∠TQR.
There are three angular bisectors that can be made in a triangle, and all of them meet at the incenter of the triangle because line Q T is the angular bisector of P Q R. As a result, P Q T = T Q R.
BD divides ABC into two angles, ABD and DBC, given that line.
Additionally, given that DBC = 20 x + 16
ABD = 12 x + 24
Therefore, A B C = ABD + DBC (1) and ABD = DBC (2) respectively.
According to the second equation, 12 x + 24 = 20 x + 16 24 16 = 20 x 12 x 8 x = 8 x = 8 8 = 1
As a result, A B D = 12 (1) + 24; A B D = 36;
D B C = 20 (1) + 16; A B C = 36.
As a result of the equation (1), A B C = A B D + D B C;
A B C = 36; A B C = 72.
Therefore, ∠ABC measure 72.
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Full Question = Suppose line BD bisects ∠ABC. If m ∠ABD = 12 x + 24 and m ∠DBC = 20 x + 16, what is m ∠ABC?
During the summer, Kurt works on his uncle's goat farm. One of Kurt's many chores is to milk the goats. The proportional relationship between the number of hours milking, x, and the number of goats milked by Kurt, y, can be modeled by the equation y = 6x. If Kurt milked 21 goats, how many hours did it take?
A. 4.5
B 3.5
C 3
D 4
If Kurt milked 21 goats, then it will take 7/2 hours.
What is arithmetic?
Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.
Here, we have
Given
The proportional relationship between the number of hours milking, x, and the number of goats milked by Kurt, y, can be modeled by the equation y = 6x.
We have to find out if Kurt milked 21 goats, and how many hours did it take.
y = 6x
if Kurt milked 21 goats, then
21 = 6x
x = 21/6
x = 7/2
Hence, if Kurt milked 21 goats, then it will take 7/2 hours.
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There are 162 people waiting in line to ride a roller coaster when the line closes for the day. Each roller coaster car holds 12 people. After loading c cars on the roller coaster, there are 6 people still in line. Write an equation to represent the number of cars, c, that have been loaded on the roller coaster. Solve the equation to find the number of cars on the roller coaster
Answer: 13
Step-by-step explanation: First you have to subtract the remaining amount of people from the total. 162-6=156. Then you have to divide the remaking amount, (people who went on) by the amount of people that can fit in a car to get how many cars are left. 156/12=13.
Find the slope of the line:
Answer:
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Step-by-step explanation:
The slope of a vertical line is undefined since its calculation involves division by zero which is undefined.
Answer: undefined
One hundred people were surveyed about their breakfast preferences. They had between french toast and pancakes and between sausage and bacon. The results the table below.
Category french toast pancakes
sausage 25 21
bacon 23 31
1. What is the probability that a randomly selected person from the survey prefers bacon.
2. What is the probability that a randomly selected person from the survey prefers pancakes?
3. What is the probability that a randomly selected person from the survey prefers french toast given that they prefer bacon and pancakes?
4. What is the probability that a randomly selected person from the survey prefers french toast given that they prefer sausage?
The probabilities are 1. 27/50, 2. 3/4, 3. 31/100, 4. 25/46, 5. 25/48
What is probability ?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
A probability is the number of desired outcomes divided by the number of total outcomes.
Item 1:
54 out of 100 people prefer bacon, hence:
P = 54/100
= 27/50
Item 2:
Out of 100 people, 54 prefer bacon, 21 prefer sausage but pancakes, hence 54 + 21 = 75 desired outcomes, hence:
P = 75/100
= 3/4
Item 3:
31 out of 100 people prefer bacon and pancakes, hence:
P = 31/100
Item 4:
Out of 46 people that prefer sausage, 25 prefer french toast, hence:
P = 46 / 25
Item 5:
Out of 48 people that prefer french toast, 25 prefer sausage, hence:
P = 48 / 25
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