The tottal number of ways to selct 15 cookies is 15504 and the ways are there to select 15 cookies if at least three is 6188.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
we have to select 15 Cookies from 6 varieties so we can think an n₁+n2+n3+n4 + N5 +N6=15 with each o≤ni ≤15
C([tex]\frac{20}{12}[/tex]) = 15504
NOW we have One category is fixed let K Chocolate chips are Selected in I way The A we have to (15-K) Cookies from the varieties
C([tex]\frac{19-k}{15-5}[/tex])
So for k=0, C1=3876
k=1, C2 =3060
k=2, C3=2380
So C =C1+C2+C3=9316.
So the number of ways 15504-9316= 6188.
Hence, The tottal number of ways to selct 15 cookies is 15504 and ways are there to select 15 cookies if at least three is 6188.
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A researcher wishes to see if there is a difference in the cholesterol levels of two groups of men. A random sample of 30 men between the ages of 25 and 40 is selected and tested, the average cholesterol level was 223 with standard deviation of 6.1. A second sample of 25 men between ages of 41 and 56 is selected and tested, the average cholesterol level for this group was 229 with standard deviation of 5.8. Assume the populations are normally distributed and the population standard deviation are unequal.
A. At [tex]\alpha = 0.01[/tex], is there a difference in the cholesterol levels between the two groups? Use traditional method.
B. Use confidence interval to verify your answers in (A).
a. There is a difference in the cholesterol levels between the two groups.
b. The confidence interval for the differences is of (1.7, 10.3), not containing 0 and thus verifying what was found in item a.
What are the hypothesis tested?At the null hypothesis, it is tested that there is no difference, that is, the mean of the subtraction is of zero, hence:
[tex]H_0: \mu_d = 0[/tex]
At the alternative hypothesis, it is tested if there is a difference, that is, the mean of the subtraction is different of zero, hence:
[tex]H_1: \mu_d \neq 0[/tex]
We have a two-tailed test, as we are testing if the mean is different of value, with 30 + 25 - 2 = 53 df, with a significance level of 0.01, hence the critical value is of:
t = 2.6718
Hence the decision rule, considering the test statistic t, is given as follows:
|t| < 2.6718: do not reject the null hypothesis -> not enough evidence to conclude that there is a difference.|t| > 2.6718: reject the null hypothesis -> enough evidence to conclude that there is a difference.What are the mean and the standard deviation of the distribution of differences?For each sample, the mean and the standard error are given as follows:
Sample 1: [tex]\mu_1 = 223, s_1 = \frac{6.1}{\sqrt{30}} = 1.1137[/tex].Sample 2: [tex]\mu_2 = 229, s_2 = \frac{5.8}{\sqrt{25}} = 1.16[/tex].Hence the mean and the standard error for the distribution of differences is given as follows:
Mean: [tex]\overline{x} = \mu_2 - \mu_1 = 229 - 223 = 6[/tex].Standard Error: [tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{1.1137^2 + 1.16^2} = 1.61[/tex]What is the test statistic?The test statistic is obtained as the division of the sample mean by the standard error, hence:
t = 6/1.61
t = 3.73.
t > 2.6718, hence the null hypothesis is rejected, and there is a difference in the cholesterol levels between the two groups.
What is the confidence interval?The confidence interval is obtained as the sample mean plus/minus the multiplication of the standard error and of the critical value.
Hence the lower bound of the confidence interval is of:
6 - 2.6718 x 1.61 = 1.7.
The upper bound is of:
6 + 2.6718 x 1.61 = 10.3.
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please help, i don't know what to do
Answer: x = 42
Step-by-step explanation:
true or false: with a well-designed sample survery, the sample percentage is very likely to equl the population percentage
This sentence is False, when the sample size is small, the sample percentage may not be equal to the population percentage.
In demographics, the sector population is the overall quantity of human beings presently residing. It turned into predicted by the United countries to have exceeded eight billion in November 2022. It took over 2 hundred,000 years of human prehistory and history for the human populace to attain one billion and only 219 years extra to attain 8 billion.
The human population experienced a non-stop boom following the Great Famine of 1315–1317 and the end of the Black dying in 1350 when it became nearly 370,000,000. the very best worldwide populace growth quotes, with increases of over 1.8% in line with 12 months, took place between 1955 and 1975, peaking at 2.1% between 1965 and 1970. The increased charge declined to one.1% between 2015 and 2020 and is projected to say no further within the twenty-first century. the worldwide population continues to increase, however, there's sizable uncertainty approximately its long-term trajectory due to converting fertility and mortality fees. The UN Department of Economics and Social Affairs tasks between 9 and 10 billion people by 2050 and offers an 80% self-assurance c language of 10–12 billion by using the cease of the twenty-first century, with a growth charge by using then of zero. other demographers are expecting that the human populace will start to decline in the 2d half of the 21st century.
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What multiplication facts can be found by using the arrays for 5x6 and 2x6
The multiplication of the two arrays will be 360.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.
The given arrays of the numbers are 5x6 and 2x6. The multiplication of the two numbers will be done as,
M = ( 5 x 6 ) x ( 2 x 6 )
Multiply both the numbers and solve,
M = 30 x 12
M = 360
Therefore, the multiplication of the two arrays will be 360.
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a new surgical procedure is said to be successful 90% of the time. suppose the procedure is performed five times. assume that the results of each procedure are independent of one another. in this binomial distribution application, which excel statement will find the probability of between 2 and 4, inclusively, successful surgical procedures?
The required probability is p(xS 2) =F(2).
Given that,
90% of the time, a novel surgical technique is deemed to be successful. Imagine that the technique is carried out five times. Count on the outcomes of each procedure being distinct from one another. in this application of the binomial distribution
BINOMDIST (2,5,90%, TRUE) is used to find the probability of 2 or fewer
to get 0.00856 because x =2 and n= 5 and TRUE indicates the cumulative
and the required probability is p(xS 2) =F(2)
Therefore, the required probability is p(xS 2) =F(2).
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Can someone help me? (again and it wont be the last)
Answer: sure I just need to know what you need help with to help you
Step-by-step explanation:
please helpppp!!! !!
Priya and Han each wrote an equation of a line with slope 1/2 that passes through the point (1,2) Priya's equation is y-2=1/3(x-1) and Han's equation is 3y - x = 5. Do you agree with either of them?
Explain or show your reasoning
Both Priya's equation and Han's equation are wrong . So , I don't agree with either of them
Slope-intercept form of equation of line is y =mx + b
where m is a slope of line
b is y-intercept
According to the question,
Slope of line is given as 1/2
m = 1/2
Putting the value of m in equation of line
y = 1/2 x + b --------(1)
It is given that line(1) passes through (1,2)
so, x = 1 and y = 2
Substituing the value of x and y in equation (1)
2 = 1/2 +b
Multiplying by 2 both sides
4 = 1 + 2b
=> 2b = 3
=> b = 3/2
substituting the value of b
Equation of line is y = 1/2 x + 3/2
=> 2y = x + 3
Therefore, Both Priya's equation and Han's equation are wrong
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A casino only has red playing chips for $10 each and blue playing chips for $5 each. Jack paid $400 to purchase 50 playing chips at the cashier's window. How many red playing chips were given to him?
The number of red playing chips that were given to him is 30.
How to calculate the number of red chips?Let the red chips be illustrated as r.
Let the blue chips be illustrated as b
The appropriate equation to solve the question will be:
r + b = 50.......... i
10r + 5b = 400 ......... ii
From equation i, r = 50 - b.
Put the value of r into equation ii
10r + 5b = 400
10(50 - b) + 5b = 400
500 - 10b + 5b = 400
500 - 5b = 400
Collect like terms
5b = 500 - 400
5b = 100
Divide
b = 100/5
b = 20
Therefore, red chips will be:
r = 50 - b
r = 50 - 20
r = 30
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Please help with this!
Answer:
∠KIH ≅ ∠IKJ---------------------------------
We can see three marked angles in the diagram.
One of them marked with the small square, it means this is a right angle.
The other two are marked with 3 small parallel curves, it means they are congruent:
∠KIH ≅ ∠IKJ,You can name them differently but it doesn't change angles:
∠HIK ≅ ∠JKI.What is (-3 3/4) - (-2 1/4)?
when 40 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution.
Answer:
5
Step-by-step explanation:
Let x be that number.
(x^2) - 40 = 3x
x^2 - 40 = 3x
x*2-3x-40=0
(x-5)(x+8)=0
x=5
5/8 = 8/x
A.5
B.64
C.0.2
D.12.8
Answer: It's 64
Hope this helps!
Solve for b.
5/b = 45/36
b = ?
Answer:
b = 4
Step-by-step explanation:
Step 1: Divide 45 by 36 on the right side
1. 5/b = 1.25
Step 2: Multiply both sides by b and flip the equation
2. 1.25b = 5
Step 3: Divide both sides by 1.25
3. b = 4
[tex]\fbox{b=4}[/tex]
Cross multiply:
[tex]\dfrac{5}{b} =\dfrac{45}{36}[/tex]
[tex](5)\times(36)=45\times(b)[/tex]
[tex]180=45b[/tex]
Flip the equation:
[tex]45b=180[/tex]
Divide both sides by 45:
[tex]\dfrac{45b}{45} =\dfrac{180}{45}[/tex]
[tex]b=4[/tex]
chegg suppose 60% of all college professors like tennis, 65% like bridge, and 50% like chess; 45% like any given pair of recreations. (a) should you be suspicious if told 20% like all three recreations?
If you are told 20% of people prefer all three forms of recreation is 60 when 60% of all college professors enjoy tennis, 65% enjoy bridge.
Given that,
Assume that 60% of all college professors enjoy tennis, 65% enjoy bridge, 50% enjoy chess, and 45% enjoy any certain pair of recreational activities.
We have to find if you are told 20% of people prefer all three forms of recreation, should you be suspicious.
We know that,
Let the total professors be =100
n(tennis) = 60
n( bridege) = 65
n( chess)= 50
n( T U B) = 45, n(BU C) = 45, n(T UC)=45
n( T UBUC)= n(T) + n(B) + n(C) - n( T U B) - n( BU C) - n(TUC) + n(T∩B∩C)
100 = 60 + 65 + 50 - 45-45-45 +n(T∩B∩C)
n(T∩B∩C)=60
Therefore, If you are told 20% of people prefer all three forms of recreation is 60 when 60% of all college professors enjoy tennis, 65% enjoy bridge.
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The graph shows a scatter plot for a set of data. Scatter plot with x-axis labeled year and y-axis labeled megawatts. The 18 points plotted are 1982 and 76.2, 1983 and 50.6, 1984 and 46.4, 1985 and 35.5, 1986 and 31.1, 1987 and 26.1, 1988 and 21, 1989 and 15.6, 1990 and 14.9, 1991 and 13.8, 1992 and 13, 1993 and 13, 1994 and 10, 1995 and 10, 1996 and 7, 1997 and 6.9, 1998 and 6.6, and 1999 and 6.
What type of correlation exists? Is the model linear or non-linear?
The graph shows a negative correlation, and it is a linear model.
The graph shows a positive correlation, and it is a linear model.
The graph shows a negative correlation, and it is a non-linear model.
The graph shows a positive correlation, and it is a non-linear model.
The graph shows a negative correlation, and it is a non-linear model.
What is positive and negative correlation?
When two variables behave in unison, rising or falling in lockstep with one another, there is a positive correlation. When two variables move in opposition to one another—that is, when one rises, the other falls—this is known as a negative correlation.
As given data from the graph, y values goes decrease with increasing x values.
So, we can conclude that the graph shows a negative correlation.
And, the given data in the graph are not linear.
Hence, the graph shows a negative correlation, and it is a non-linear model.
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Answer:
The graph shows a negative correlation, and it is a non-linear model.
Step-by-step explanation:
a) How many prime numbers are multiples of 5?
b) How many prime numbers are multiples of 8?
Answer:
afternoon and
a) =1
Step-by-step explanation:
because there is only one prime number in multiples of 5 that is 5
d) 1consider carrying out m tests of hypotheses based on independent samples, each at significance level (exactly) 0.01. (a) what is the probability of committing at least one type i error when m
The probability of committing when at least one type I error at a significance level (exactly) 0.01 at m = 11 is equivalent to 0.1047.
Given that:
The hypotheses are based on independent samples with each at a 0.01 level of significance.
We know that:
P (at least one type I error is committed) = 1 - [P (No error - type I error is committed)]^m
P (at least one type I error is committed) = 1 - [(1 - 0.01)]^11
P (at least one type I error is committed) = 1 - [0.99]^11
P (at least one type I error is committed) = 1 - 0.8953
P (at least one type I error is committed) = 0.1047
So, the probability of committing when at least one type I error is equivalent to 0.1047.
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Benjamin invested $20,000 in an account paying an interest rate of 7&5/8 % compounded monthly. Kehlani invested $20,000 in an account paying an interest rate of 7&3/4 compounded quarterly. After 10 years, how much more money would Kehlani have in her account than Benjamin, to the nearest dollar?
If Benjamin invested $20,000 in an account paying an interest rate of 7&5/8 % compounded monthly. The amount of money that Kehlani have in her account than Benjamin is: $322.83.
How to find the compounded amount?Using this formula to find the compounded amount
A = P(1+r/n)^nt
Where
A = Amount
r =Interest rate.
n =Number of years
P =Principal
Benjamin
P = $20,000
r = 7 5/8% = 7.625% = 0.07625
n = 12 months
t = 10 years
Hence,
A = 20,000 (1+0.07625/12)^12× 10
A = 20,000 (1+0.006354)^120
A = 20,000 (1.006354)^120
A = $42,768.42
Kehlani
P = $20,000
r = 7 3/4% = 7.75= 0.0775
n = 4 months
t = 10 years
Hence,
A = 20,000 (1+0.0775/4)^4× 10
A = 20,000 (1+0.019375)^40
A = 20,000 (1.019375)^40
A = $43,091.25
Difference:
Difference = $43,091.25 - $42,768.42
Difference = $322.83
Therefore the amount of money is $322.83.
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Answer:322
Step-by-step explanation:
Please help me with this question. I need it immediately, and it is Grade 7 math.
To meet the goal, the tree must be at least 250 centimeters tall. This will take at least 10 years. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Scott has a tree in his lawn. The tree grows 25 centimeters every year. Since the tree began developing, Scott has managed 16 centimeters off its level. The objective for the tree's level is given by 25x - 16 ≥ 234, where x is the quantity of years the tree develops.
Simplify the inequality, then we have
25x - 16 ≥ 234
25x ≥ 234 + 16
25x ≥ 250
x ≥ 10
To meet the goal, the tree must be at least 250 centimeters tall. This will take at least 10 years. Then the correct option is B.
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1/4 t + 4 = 3/4 (t + 8)
Answer: T= -4
Step-by-step explanation: Well i guess it would be that ? If it's not sorry but it should be that
nebraska, the home of the amc, changed its license plate scheme. each old license plate consisted of a letter followed by four digits. each new license plate consists of three letters followed by three digits. if $a$ is the number of possible license plates in the old scheme and $b$ is the number of possible license plates in the new scheme, what is the value of $b/a$? express your answer as a decimal to the nearest tenth.
The value of b/a of the number plates is 0.0
What is decimal?Decimals with the same number of decimal places are referred to as like decimals (after the decimal point). For instance, because both 2.33 and 4.52 include up to two decimal places, they are similar to decimals. Likely decimals are those that do not have the same number of decimal places (after the decimal point).
What are the 3 types of decimals?Decimal fractions and recurring (repeating or non-terminating, like) decimals are the three different types of decimals.
According to the above question
26 x 10000 = 260,000
If letter and digit repeats are allowed, the number of license plates that can be created under the new system is (26)3 * 1000 = 17,576, 000.
In other words, 260,000 / 17,576,000 = 0.0148, which, when rounded to the nearest tenth, equals 0!
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Find the volume.
2ft 2ft 2ft
Answer:
Volume = 2×2×2 = 8 feet3
the mean score of 888 players in a basketball game was 14.514.514, point, 5 points. if the highest individual score is removed, the mean score of the remaining 777 players becomes 121212 points. what was the highest score?
The highest score is 12794706708
What is mean ?
The average of a set of data is referred to as the mean in statistics and arithmetic. The simple arithmetic mean, geometric mean, and harmonic mean are some of the methods that can be used to calculate the mean. The basic arithmetic mean involves adding the numbers together and dividing the result by the number of observations.
At first (remaining + top player) /888 = 14514514
So remaining + top = 12888888432
Now after removing top
Remaining/777 = 121212
Remaining = 94181724
So top = 12888888432 - 94181724
= 12794706708
12794706708 is the score of the top player
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A pterodactyl could fly 75 miles in 3 hours. At this rate, how far could a pterodactyl travel in 5 hours?
A pterodactyl could fly 75 miles in 3 hours. At this rate, how far could a pterodactyl travel in 5 hours?
Answer:
125 miles
Step-by-step explanation:
75/3 to find the distance in 1 hour=25
25x5=125
Answer:
125 miles
Step-by-step explanation:
75/3 to find the distance in 1 hour=25
25x5=125
i dont know what im doing please help
Answer:
x = 62°
Step-by-step explanation:
You want the base angle in an isosceles triangle with a vertex angle of 56°.
Isosceles triangle
The sides of any triangle are proportional to the sine of the opposite angle. When two sides have the same measure, their opposite angles will have the same measure. Since the sum of angles in a triangle is always 180*, this means ...
56° +x° +x° = 180°
2x = 124° . . . . . . . . . . subtract 56°
x = 62° . . . . . . . . . . divide by 2
The measure of the angle marked x is 62°.
__
Additional comment
The sides are all specified. This means you can find the angles of the triangle by solving it based on the side lengths. If you do that, you find that x ≈ 61.641°, as shown in the first attachment. This rounds to 62°.
As you can see in the second attachment, a better length for the side opposite the 56° angle would be 5.6 units instead of 5.7.
In short, the answer you get depends on how you use the given information.
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PLEASE HELP!!
GIVE A LOT OF POINTS IF HELP!!!!!
CAULATE IT PLEASEEEEEEEEEEEEEEEEEEE!!!!!!!!! GIVE BRAINLISTT!!
HELP CUALATE THE SQUARE ROOT
Answer: There are no values that make the equation true . No solution
A rectangular box has a square base. Its height is half the width of the base. Find a function that models its volume v in terms of its width w.
The function that models the volume of a rectangular box in terms of width is (lw²)/2.
What is the volume of rectangle-based solids?The basic formula for volume is length×width, whereas the basic formula for area of a rectangular shape is length×width×height.
Given: The base of a rectangular box is square. Half of the base's width is its height.
Let,
length = w (since it has a square base)
width = w
height = w/2
Volume of a rectangular box = length×width×height
V = w×w×(w/2)
V = (lw²)/2
Therefore, the function that models the volume of a rectangular box in terms of width is (lw²)/2.
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Directions: Graph and label each figure and its image under the rotation about the given point. Give the
coordinates of the image.
Parallelogram ABCD with vertices A(6, 8), B(10, 9), C(9. 3).
and D(5, 2): 90° counterclockwise rotation about P(4, 1)
Answer:
See below
Step-by-step explanation:
This is a hard to explain without showing you, if it does not make sense it is not you, it is just hard to explain without showing you.
use green's theorem to evaluate the line integral along the given positively oriented curve. c cos(y) dx x2 sin(y) dy c is the rectangle with vertices (0, 0), (3, 0), (3, 1), (0, 1)
30(1-cos2) is the evaluated line integral along the given positively oriented curve.
What is Green's Theorem?Green's theorem is mostly utilized to evaluate the line integral of a single direction and a curved plane. The link between a line integral and a surface integral is demonstrated by this theorem. It is connected to several theorems, including the Gauss theorem and the Stokes theorem.
To integrate the derivatives in a certain plane, one uses Green's theorem. This thesis can be employed to transform a given line integral into a surface integral, double integral, or conversely.
One of the four calculus foundational theorems, all 4 of whom are intimately connected to one another, is the Green's theorem.
How to solve?
By Green's theorem, we have
∫c (cist dx + x² siny dy ) = ∫∫r [μ(x²siny)/μx - μcosy/μy dxdy
where C is the *boundary* of the rectangle .
The integral is then
=(cos0 -cos2)∫(5,5)(2x +1)dx
=(1-cos2)(5²+5)
=30(1-cos2)
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