The ways in which a kindergarten teacher distributes the books are (a) 20 ways (b) 100 ways (c) 3,628,800 ways.
(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.
(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.
(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.
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The complete question is:
A kindergarten teacher has five books to distribute to 20 children in her class.
(a) How many ways are there for her to distribute the books if they are all the same and no child gets more than one?
(b) How many ways are there for her to distribute the books if they are different and no child gets more than one? If Charlie gets Green Eggs and Ham and Amanda gets The Cat in the Hat, that is a different distribution from the one in which Amanda gets Green Eggs and Ham and Charlie gets The Cat in the Hat.
(c) How many ways are there for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child?
Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours). 1.6 1.4 2.7 2.3 2.5 2.3 2.6 3.0 1.3 2.3 With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours. (a) State the null and alternative hypotheses. H0: ???? = 2 Ha: ???? ≠ 2 H0: ???? < 2 Ha: ???? ≥ 2 H0: ???? ≤ 2 Ha: ???? > 2 H0: ???? ≥ 2 Ha: ???? < 2 H0: ???? > 2 Ha: ???? ≤ 2 (b) Compute the sample mean. (c) Compute the sample standard deviation. (Round your answer to three decimal places.) (d) What is the test statistic? (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (e) What is your conclusion? Reject H0. We cannot conclude that the mean tree-planting time differs from two hours. There is no reason to change from the two hours for cost estimating purposes.Do not reject H0. We cannot conclude that the mean tree-planting time differs from two hours. There is no reason to change from the two hours for cost estimating purposes. Do not reject H0. We can conclude that the mean tree-planting time differs from two hours. There is a reason to change from the two hours for cost estimating purposes.Reject H0. We can conclude that the mean tree-planting time differs from two hours. There is a reason to change from the two hours for cost estimating purposes.
The null hypothesis for the sample data set is given by H₀ : μ = 2 and the alternate hypothesis for the data is H₁ : μ > 2 .
a)H₀ : μ = 2
H₁ : μ > 2
We cannot reject the null hypothesis and conclude that no significant evidence exists to confirm that the mean tree-planting time differs from two hours.
Given :
X = 23.71,17.79, 29.87,18.78,28.76
b)Sample mean, x = Σx / n = 22/10 = 2.2
c) Standard deviation, s = 0.516
H0 : μ = 2
H1 : μ > 2
Test statistic :
(x - μ) ÷ (s/√(n))
n = 10
d) Test statistic :
=(2.2 - 2) ÷ (0.516/√(10))
=0.2 / 0.1631735
Test statistic = 1.23
Using the P-value from T-score we get the degrees of freedom:
df
= n - 1
= 10 - 1
= 9
P-value (1.23, 9) = 0.1249
e) Since, P-value > α ; We fail to reject the null and conclude that no significant evidence exists to support that mean tree-planting time differs from two.
A hypothesis is thetheory put up to explain a phenomenon. If a hypothesis cannot be tested by the scientific method, it cannot be referred to as a scientific hypothesis.
Scientific theories frequently start with historical observations that can't be adequately explained by the body of knowledge at this time. A hypothesis is a tested assertion regarding the relationship between two or more variables in the scientific area or a theory put out to explain an observed phenomena.
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Solve the inequality 5x > –15 for x.
Answer: x > -3
Steps:
5x > -15 Bring 5 to the other side (multiplication ---> division)
x > -15/5 Divide
x > -3
The solution of the inequality 5x > -15 after solving the inequality expression is x > -3.
Given an inequality expression:
5x > -15
It is required to find the value of x after solving the expression.
In order to solve this, it is required to isolate the value of the variable, in this case, x, on one side and the constant terms on the other side.
In order to isolate the variable:
Divide both sides by 5.
x > [tex]\frac{-15}{5}[/tex]
x > -3
Hence, the solution of the inequality expression is x > -3.
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a farmer collected some eggs from his farm and found b eggs broken. he packed the remaining eggs in c egg cartons. each egg carton can hold a dozen eggs and no eggs were leftover. write an algebraic expression for the number of eggs he collected initially in terms of b and c.
The algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.
What is an algebraic expression?
In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.).
The total number of eggs he collected = 12c + b.
Because 12 eggs are a dozen multiplied by unknown, you get a multiple of twelve then you add your broken eggs for the total.
Hence, the algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.
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Find the Average Rate of Change between each pair of points.
1) (-10, 7), (6, 20)
Answer:
13/16
Step-by-step explanation:
Given g(x) = -5x + 1, find g(1).
Answer:
-4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
g(x) tells us what the variable is and what variable should be replaced with a value.
g(1) tells us the value that will replace x.
Plug in 1 to the equation:
-5(1) + 1 = g(1) (multiply)
-5 + 1 = g(1) (combine like terms)
-4 = g(1)
Therefore, g(1) is equal to -4
In a school, 105 students are sixth graders. If 35% of the students in the school are sixth graders, how many students are there in the school?
The total number of schools such that 35% of it is 105 will be 300.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
Suppose the total number of students is x.
35% of x = 105
(35/100)x = 105
x = 105(100/35)
x = 300 students
Hence "The total number of schools such that 35% of it is 105 will be 300".
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Monica deposits $100 into a savings account that pays a simple interest rate of 3.3%. Paul deposits $200 into a savings account that pays a simple interest rate of 2.1%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
[tex]~~~~~~ \stackrel{\textit{\LARGE Monica}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$100\\ r=rate\to 3.3\%\to \frac{3.3}{100}\dotfill &0.033\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (100)(0.033)(1) \implies I = 3.3 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \stackrel{\textit{\LARGE Paul}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$200\\ r=rate\to 2.1\%\to \frac{2.1}{100}\dotfill &0.021\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (200)(0.021)(1) \implies I = 4.2[/tex]
well, Monica needs to check more closely what was in that last cup of coffee she drank, she's hallucinating.
JUST WANT THE ANSWER NO EXPLINATION NEED HELP ASAP!
Answer:
Step-by-step explanation:
11. First option
12. 5p+4 > 14
> symbol is greater than and has an open circle, going right
Answer:
Option A for both questions--------------------------
The first questionThe graph indicates the inequality n ≤ 1, since highlighted part is to the left from the 1 and there is a closed circle.
Double both sides to get 2n:
n ≤ 1 ⇒ 2n ≤ 2And add 5 to both sides to get 7:
2n + 5 ≤ 2 + 5 ⇒ 2n + 5 ≤ 7This is matching the option A.
Question 12The graph indicates the inequality p > 2, since highlighted part is to the right from the 2 and there is a open circle.
Multiply both sides by 5 to get 5p:
p > 2 ⇒5p > 10Add 4 to both sides to get 14:
5p > 10 ⇒5p + 4 > 14This is matching the option A.
Consider how the following scenario could be modeled with a binomial distribution, and answer the question that follows. 54.4% of tickets sold to a movie are sold with a popcorn coupon, and 45.6% are not. You want to calculate the probability of selling exactly 6 tickets with popcorn coupons out of 10 total tickets (or 6 successes in 10 trials).
The value used for the parameter p is 0.544.
The number of successes in a sample of size n drawn with replacement from a population of size N is typically modeled using the binomial distribution. The mean for this type of distribution is computed by multiplying the number of trials (n) by the probability that they will succeed (p). Then, mean = n×p. The variance is n×p×q, where q is the probability that the event fails. The standard deviation is √(n×p×q).
Here, given that the percentage of tickets sold with popcorn is 54.4% and those not sold is 45.6%, the parameter (p) we used to calculate when the event occurs is 0.544. Because it is the probability that the sale of movie tickets with popcorn occurs.
The answer is 0.544.
The complete question is -
Consider how the following scenario could be modeled with a binomial distribution, and answer the question that follows.
54.4% of tickets sold to a movie are sold with a popcorn coupon, and 45.6% are not.
You want to calculate the probability of selling exactly 6 tickets with popcorn coupons out of 10 total tickets (or 6 successes in 10 trials).
What value should you use for the parameter p?
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Donald reads 1000 words in five minutes what is the unit rate of words per minute
on a standardized test with a normal distribution, the mean was 64.3 and the standard deviation was 5.4. what is the best approximation of the percent of scores that fell between 58.9 and 75.1?
the best approximation of the percent of scores that fell between 58.9 and 75.1 is 4.
The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.
Find the difference between these two figures and the mean, divide it by the standard deviation of 5.4, and you will know how many standard deviations 75.1 and 61.5 are above and below the mean:
(75.1−64.3)/5.4
=2sd
According to the empirical rule, 95% of data are within two standard deviations of the mean.
So, the answer is 4.
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in a periodic review system, yyou place and order every 14 days. the lead time is 8 days. what is the uncertainty period? state your answer as a whole number, for example 44
In a periodic review system when an order is placed every 14 days, the uncertainty period is 22 days.
Lead time is the time that passes from the start to the conclusion. It helps in measuring the time taken to complete a project. It varies from industry to industry.
It is normally calculated as:
Lead time = processing time + post-processing time.
Given,
lead time = 8 days
Order place date = 14 days
uncertainty period = order date + lead time
uncertainty period = 14 + 8 = 22 days
So, we can say that in a periodic review system when an order is placed every 14 days, the uncertainty period will be 22 days.
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(3x +33)"
(4x+8)
Find B
Answer: B=90 degrees maybe
Step-by-step explanation:
When 2/9is rewritten using long division the result is best described as an?
Answer:
a mixed fraction or decimal
what determined whether college freshmen who had been randomly paired for a welcome week dance liked each other?
Physical attractiveness determined whether college freshmen who had been randomly paired for a welcome week dance liked each other.
What is random pair?Samples with natural or matched couplings are known as paired samples (sometimes referred to as dependent samples). This results in the creation of a data set where each data point from one sample is uniquely linked with a data point from the other sample. In statistics, paired data, also known as ordered pairs, refers to two variables in a population's individuals that are linked together to ascertain their association. We refer to two datasets that are identical in length and in which each observation can be "paired" with an observation from the other dataset as having "paired data." Each observation in one dataset must only be paired with one observation in the other dataset in order for the two datasets to be paired.
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y=(x+5)²-4
Vertex:
Axis of Symmetry:
x-intercepts:
y-intercept:
Is the vertex a maximum or minimum?
A boat is heading towards a l, whose beacon-light is 113 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 11 ∘ ∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)?
113 % = 1893per capacity
Step-by-step explanation:
first you have to calculate the 113 feet with its equation then calculate the quation with the number 69 divisible by it then divide it and your answer is there
Casey’s bedroom is shaped like a square. The distance between opposite corners is 12√2 feet. How long is each side of the bedroom?
Answer:
12 feet
Step-by-step explanation:
You want the length of the side of a square with a diagonal length of 12√2.
Diagonal of a squareThe diagonal of a square is the hypotenuse of a right triangle with equal-length sides. Such an isosceles right triangle has side lengths in the ratio ...
1 : 1 : √2
That is, the hypotenuse is √2 times the side length.
The given hypotenuse is 12√2, so the side length is 12.
Each side of the bedroom is 12 feet.
best answer gets brainliest
Answer:g(-8)=-62
Step-by-step explanation:
8x+2=-62. minus 2 to both sides
8x=-64. divide both sides by 8 to isolate x of the left
x=-8. final answer
g(-8)=-62
What estimate can i do for 3.5x0.4
Answer:
The answer is 1.4
The dimensions of the base of box 2 are: width: x; length: 3 width: x; length: 4x â€"" 1 width: x; length: x â€"" 4 width: x; length: 4x 1
Answer: 4x - 1
Step-by-step explanation:
Answer:
4x-2
Step-by-step explanation:
i did it
Angle d is a circumscribed angle of circle o. What is the perimeter of kite obde? 17 units 23 units 27 units 60 units.
The solution to this question is 27 units the perimeter of kite OBDE.
The definition of perimeterThe perimeter of a shape is the entire length of the shape's boundary as used in geometry. A form's perimeter can be calculated by adding the lengths of all of its sides and edges. In order to calculate it, linear distances such as centimeters, meters, inches, or feet are used.
Here
This is because 15x15 =225
8x8 = 64
225+64=289 and
the square root of 289 is 17 and that is the diameter of the circle and the hypotenuse of the triangle and since the kite has two congruent sides which are both radii or can be written as half of a diameter times two would be the same as the length of the diameter which is17+the two bottom sides (which are both 5 and 5 )
So 5+ 5 = 10 and
10 + 17 =27 or the perimeter of the kite.
Therefore ,the perimeter of kite OBDE is 27 units.
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a multiple choice exam has a mean of 100 and a standard deviation of 13. about what percent of people would be expected to score 115 or more on the exam?
1.15 percentile of people would be expected to score 115 or more
What is Standard Deviation?
A standard deviation (or σ) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.
Solution:
Mean = 100
Standard Deviation = 13
To solve the given problem we need to calculate the Z - Score
Z = X - Mean / Standard Deviation
P(X > 115)
Z = 115 - 100 / 13
Z = 15 / 13
Z = 1.15 Percentile
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59 tanya prepared 4 different letters to be sent to 4 different addresses. for each letter, she prepared an envelope with its correct address. if the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address? a) 24 1 b) 8 1 c) 4 1 d) 3 1 e) 8
There is a 1 in 4 probability, or 25%, that the envelope will contain just one letter with the proper address.
Tanya wrote four distinct letters that she was going to send to four different addresses. She prepared an envelope with the correct address for each letter. The probability that only 1 letter will be placed into the envelope with the correct address if the 4 letters are randomly placed into the 4 envelopes is
1 in 4, or 25%
(4c4/4c1).
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37. What type of interval training consists of overhead squats, front squats, and romanian deadlifts?
LSD training is type of interval training consists of overhead squats, front squats, and romanian deadlifts
Whats the definition for intervals?
in·ter·val ˈin-tər-vəl. plural intervals. : a space of time between events or states. a two-month interval between medical treatments. There were long intervals during the game in which nothing exciting happened
The area of focus of the Single Leg Romanian Deadlift is the back of the individuals legs and hips. By engaging in this activity, a person is getting a great workout for his or her glutes, hamstrings, lats. It requires the person to lift one leg directly beside the balance leg and then bend from waist to slowly reach hand toward the toes of the balance leg.
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If Amy is tardy, then she will get a detention
Write the CONVERSE of this statement
Answer:
Amy will get detention if she is tardy
Step-by-step explanation:
Calculate the ditance between the point H= (−9, 0) and J= (−1,−8) in the coordinate plane
The distance between the point H= (−9, 0) and J= (−1,−8) in the coordinate plane is 8√2 units.
Define the term distance formula?The Pythagorean theorem is used to calculate the distance using the distance formula. If we are aware of the coordinates of both the 2 points as in XY plane, we may calculate the distance between them. The distance formula can be used to calculate the distance between both P and Q if P(x1, y1) with Q(x2, y2) are the two main points in a plane.For the stated question-
Distance formula;
d = √(x2 -x1)² + (y2 - y1)²
H(x1, y1) = (−9, 0)
and J(x2, y2) = (−1,−8)
Put the values;
HJ = √(-1 + 9)² + (-8 - 0)²
HJ = √(64 + 64)
HJ = 8√2
Thus, the distance between the point H= (−9, 0) and J= (−1,−8) in the coordinate plane is 8√2 units.
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Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence increases the margin of error will and the confidence interval will be A larger sample size will improve the accuracy of the confidence interval, therefore margin of error will and the confidence interval will be A) Decrease, wider. Increase, narrower B) Decrease, narrower. Increase, wider C) Increase, wider. Decrease, narrower. D) Increase, narrower. Decrease, wider.
For the given statement option C increase, wider and decrease , narrower is correct.
What is confidence interval?
A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used.
When constructing a confidence interval, if the level of confidence increases, the margin of error must Increase and the confidence interval will be Wider.
Hence Increase; wider is the correct answer.
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o of the four expressions x y, x 5y, x – y, and 5x – y are chosen at random, what is the probability that their product will be of the form of x 2 – (by) 2 , where b is an integer?
The probability of the product of the given expressions is in the form of x² - (by)² is equal to 1/6.
As given in the question,
Given four expressions are:
( x + y ) , ( x + 5y ) , ( x - y ) and ( 5x - y )
Product of any two expression to have two degree expressions :
( x + y )( x + 5y ) = x² + 6xy + 5y²
( x + y )( x - y ) = x ² - y²
( x + y )( 5x - y ) = 5x² + 4xy -y²
( x + 5y )( x - y ) = x² + 4xy -5y²
( x + 5y )( 5x - y ) = 5x² + 24xy -5y²
(x - y) ( 5x - y) = 5x² - 6xy + y²
Total number of possible outcome of the product with degree 2 = 6
Favourable outcomes in the form of x² - ( by )² is x² - y² = x² -(1y)²
Here b = 1 is an integer.
Number of favourable outcomes = 1
Required probability = 1/6
Therefore, the probability of the product in the form of x² - ( by )² is equal to 1/6.
The complete question is:
If two of the four expressions x + y, x + 5y, x – y, and 5x – y are chosen at random, what is the probability that their product will be of the form of x2 – (by)2, where b is an integer?
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Data was collected for sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below . Which statement best describes the meaning of onle of the bars in the histogram? 210 snacks have mg of sugar 1 snacks have about 210 mg of sugar. The largest number of snacks have 12 mg of sugar 210 snacks have betwcen 200 and 220 mg of sugar
The histogram's best summary is option (D), "there are a total of 12 snacks with the same amount of sugar."
What is a histogram?While bar charts show categorical variables, histograms show quantitative or numerical data.
The majority of the time, a histogram's numerical data will be continuous (having infinite values).
It would be ridiculous to try and show all possible values of a continuous variable along an axis.
So, the y-axis displays the number of snacks.
The x-axis displays how much sugar is in each snack.
The histogram's first column reveals that 2 snacks each contain between 220 and 224 mg of sugar.
The second column reveals that around 3 snacks have 224–228 mg of sugar.
The third column reveals that 8 snacks range in sugar content from 228 to 232 mg.
Twelve snacks are identified in the fourth column as having between 232 and 236 mg of sugar.
Twelve snacks are identified in the fourth column as having between 232 and 236 mg of sugar.
The fifth column reveals that 11 snacks range in sugar content from 236 to 240 mg.
Three snacks are shown to contain between 240 and 244 mg of sugar in the sixth column.
According to the seventh column, 2 snacks contain 244–248 mg of sugar.
The total number of observations is 41 nibbles, or 2+3+8+12+11+3+2.
So, the best statement that describes the histogram is "The most snacks with the same quantity of sugar are 12 in total."
Therefore, the histogram's best summary is option (D), "there are a total of 12 snacks with the same amount of sugar."
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Complete question:
Data were collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. Which statement best describes the meaning of one of the bars in the histogram?
2
4
6
8
10
12
amount of sugar (mg)
220
224
228
232
236
240
244
248
Frequency
a. 2 snacks have about 226 mg of sugar.
b. 226 snacks have 2 mg of sugar.
c. 226 snacks have between 224 and 228 mg of sugar.
d. The largest number of snacks have 12 mg of sugar