The total number of games would be 15 games.
What are the Permutation and Combination?
Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.
Consider each team playing with the other team once
Total number of games scheduled = Number of ways of selecting 2 from 6 teams
[tex]=^nC_r\\\\=^6C_2\\\\=\frac{6!}{2!*4!}\\\\=15[/tex]
Hence the total number of games would be 15 games.
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What is (-3 3/4) - (-2 1/4)?
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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Elsa is a software saleswoman. Her monthly salary is $1500 plus an additional $70 for every copy of History is Fun she sells.
Let S represent her total salary this month (in dollars), and let N represent the number of copies of History is Fun she sells. Write an equation relating S to N, and then graph your equation using the axes below.
Answer:
Step-by-step explanation:
rawr u fel me
The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations? (a) n 15 t 1.66 a 0.05 o Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
The null hypothesis must be rejected as there is enough evidence that the diameter differs from 0.5 inches.
Given values are
The population mean is 0.5 inches
The Null hypothesis is : H₀ : μ = 0.5 inches
The Alternative hypothesis is given by Hₐ : μ ≠ 0.5 inches
Now let us consider the parameter given:
sample size is n = 15
test statistics is t = 1.66
The level of significance : α = 0.05
The degree of freedom: df = n-1 = 15 -1 =14
Calculating the critical value : [tex]t_\frac{\alpha}{2} ,df[/tex] = 2.145
We are using the critical value of [tex]t_\frac{\alpha}{2}[/tex] as the test is one-tailed .
Comparing the value of t and [tex]t_\frac{\alpha}{2}[/tex] we can see that : [tex]t < t_\frac{\alpha}{2}[/tex]
Hence the null hypothesis can be rejected.
Given that the value of t does not fall within the range covered by (i.e., the range from -2.145 to the bottom of the normal distribution curve), we are unable to reject the null hypothesis.
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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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HELP!!! My question is "determine whether each ratio is equivalent to 1/2 3/9 or 5/7. Thee ratios are : 2/6,3/6,5/10,10/14,50/100,20/28,1/3,8/24. please show how to do the work with the answer!!
Answers:
Ratios equivalent to 1/2 are...
3/65/1050/100Ratios equivalent to 3/9 are...
2/61/38/24Ratios equivalent to 5/7 are...
10/1420/28===============================================
Explanation:
Let's see if 2/6 is equivalent to 1/2. For now, let's assume they are equal fractions. If so, then,
2/6 = 1/2
2*2 = 6*1 ... cross multiplying
4 = 6
The last equation is of course false, which then causes a domino effect to make the first equation false as well. This means 2/6 is not equivalent to 1/2.
You can use a calculator to find that
2/6 = 0.3333 approximately1/2 = 0.5 exactlyWhich is another way to see how the fractions aren't the same.
----------------
Let's check to see if 2/6 is equivalent to 3/9.
2/6 = 3/9
2*9 = 6*3 ... cross multiplying
18 = 18
We get the same thing on both sides, which means the third equation is true. By extension, the first equation is true as well. We have shown that 2/6 and 3/9 are equivalent.
Take note how both of those fractions reduce to 1/3, which is another way to see how they are equivalent.
Yet another way is to use a calculator to find that
2/6 = 0.3333...3/9 = 0.3333...Both approximate decimal values involve '3's going on forever.
Apply any of the methods discussed to check the other values, so you can properly sort each ratio mentioned. Let me know if you have any questions.
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
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:
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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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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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.
Select ALL the correct answers.
The graph shows a linear relationship.
Select all the true statements.
A right triangle with its hypotenuse along the line from (4,2) to (8,4) has legs measuring 4 units and 2 units.
A right triangle with its hypotenuse along the line from (2,1) to (4,2) has legs measuring 3 units and 1 unit.
A right triangle with its hypotenuse along the line from (2,1) to (4,2) has legs measuring 2 units and 1 unit.
A right triangle with its hypotenuse along the line from (2,1) to (6,3) has legs measuring 4 units and 1 unit.
A right triangle with its hypotenuse along the line from (4,2) to (8,4) has legs measuring 4 units and 3 units.
The true statements regarding the linear function are given as follows:
A right triangle with its hypotenuse along the line from (4,2) to (8,4) has legs measuring 4 units and 2 units.A right triangle with its hypotenuse along the line from (2,1) to (4,2) has legs measuring 2 units and 1 unit.What is correct regarding the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, representing the value of y when the function crosses the y-axis.In this problem, the function crosses the y-axis at the origin, hence the intercept is given as follows:
b = 0.
When x increases by one, y increases by 2, hence the slope is of:
m = 2.
Considering the slope, it means that the ratio of the legs of the right triangle with it's hypotenuse along the line is of 2.
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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
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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battery lifetime is normally distributed for large samples. the mean lifetime is 500 days and the standard deviation is 61 days. approximately what percent of batteries have lifetimes more than 561 days ?
15.87 % percent of batteries have lifetimes more than 561 days.
Given:
battery lifetime is normally distributed for large samples. the mean lifetime is 500 days and the standard deviation is 61 days.
μ = 500
σ = 61
we know that
z = X - μ / σ
z score :
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
Given X = 561 days
substitute
z = 561 - 500 / 61
= 61 / 61
z = 1
At z = 1 p value is 0.8413
1 - 0.8413 = 0.1587
= 0.1587 * 100 %
= 15.87 %
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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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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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consider 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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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
5/8 = 8/x
A.5
B.64
C.0.2
D.12.8
Answer: It's 64
Hope this helps!
Find the volume.
2ft 2ft 2ft
Answer:
Volume = 2×2×2 = 8 feet3
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:
y-x=2x-2/3x linear or nonlinear explain
Answer:
it is linear
Step-by-step explanation:
if you add x on both sides, you can get rid of the -x on the left side, and you are left with a linear equation in slope intercept form
y=7/3x
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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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]
a researcher studies language development by selecting a sample of two-year-old children and giving them a language skill test. each year for the next two years, the children are brought back and tested again. the researcher plans to compare the children's scores at age two, age three, and age four. this study is an example of a(n) .
The given study is an example of longitudinal developmental design.
Longitudinal developmental research design analyzes progress by observing or measuring a group of people over time. As a consequence, it assesses changes in behavior according to age over time by examining one group of participants of about the same age.
The same people's behavior is examined over time using longitudinal research designs. For instance, using our example of examining the relationship between intellect and aging, a scientist would carry out a longitudinal study to see whether 20-year-olds lose IQ as they get older.
Hence we get the required answer.
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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 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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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 helpppp!!! !!