The number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55
A permutation is an act of putting things or numbers in a particular order. Combinations are a method of selecting objects or numbers from a group of objects or collections without regard for their order.
Given that soccer player = 11
We have to find in many ways we can choose a captain and one alternate captain from a team of eleven soccer players
Out of 11 player, we have to pick one captain and one alternate captain
nCr ways
nCr = n!/r!(n-r)!
Here n = 11 and r = 2
= 11C2
= 11!/2!(11-2)!
= 11! / 2!.9!
= ((11x 10 x 9!)/2!.9!)
= (11 x 10)/2
= 110/2
= 55
Therefore the number of ways we can select a captain and one alternate captain from a team of eleven soccer players is 55
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Help Please! Its a Math question. Need help asap.
The composite figure has a total area of 12 square centimeters.
How to determine the area of a composite figure
In this problem we find the area of a composite figure, which is the result of subtracting the areas of four triangles of same dimensions from the area of the entire square. Now we proceed to determine the area:
A = (6 cm)² - 4 · 0.5 · (2 cm) · (3 cm)
A = 36 cm² - 2 · (12 cm²)
A = 36 cm² - 24 cm²
A = 12 cm²
The area of the composite figure is 12 square centimeters.
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Greta sells advertising space for her school yearbook. Last year, a quarter-page ad cost $110.
This year, Greta's teacher asks her to mark down the price by 15% to attract more sponsors.
Greta wants to know the price after the markdown.
☐ Let q equal the price of a quarter-page ad after the markdown.
Which equation can you use to find q?
q=110-0.15(15)
q=110 +0.15(110)
q=110 - 0.15(110)
q=110 +0.15(15)
The equation that could be used to find q is q = 110-0.15(110) where q equal the price of a quarter-page ad after the markdown.
According to the question,
We have the following information:
Cost of a quarter-page ad cost = $110
Mark down in the price = 15%
Now, q represents the price of a quarter-page ad after the markdown.
(Note that when we remove the sign of % means that the number has to be divided by 100.)
So, the equation will be the difference of the markdown price from the original price:
q = 110-(15/100)110
q = 110-0.15*110
q = 110-0.15(110)
Hence, the correct option is the third one.
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0.1 times n equal's89.5
Find the distance from the point 4(2-1) to the liney=-x+4. Round your answer to the nearest fenth.
Answer:
2.12
Step-by-step explanation:
Discussion
The answer is given in the graph I've made for you. The distance you want is a contained in a line that is perpendicular to the given line and goes through (2,-1). If I have not interpreted this correctly please leave a comment under the question and I will edit it. I have ignored the 4.
The steps needed are
Find the slope of the line perpendicular to y = - x + 4Find the intersection point on y = - x + 4 and the new line.Use the distance formula to find the distance from (2,-1) to the intersection point found in the second stepGivens
line y = -x + 4
point (2,-1)
Solution
The slope of the second line is
m1 * m2 = - 1
m1= -1 From the given equation
m2 = ?
-1 * m2 = - 1
m2 = 1
Find the equation of the new line
x = 2
y = - 1 from the given point
-1 = 2 + b Subtract 2 from both sides
-1 - 2 = 2-2 + b Combine
-3 = b
Equation of the new line
y = x - 3
Intersection point of the two lines
y = -x + 4
y = x - 3 Add The xs cancel
2y = 1 Divide by 2
y = 1/2
1/2 = -x + 4 Subtract 4 from both sides
1/2 - 4 = -x + 4 -4 Combine
-3 1/2 = -x Multiply both sides by - 1
3 1/2 = x
So the intersection point is (3.5, 0.5)
Find the distance between (2,-1) and (3.5,0.5)
d = sqrt( (2 - 3.5)^2 + (-1 - 0.5)^2 )
d = sqrt( (-1.5)^2 + (-1.5)^2 )
d = ( 1..5 * sqrt(2) )
d = 2.12
if 269 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.03? round your answer to four decimal places.
The probability will be 0.9940.
The provided parameters are
p = 0.05 (the true proportion or the mean )
n = 269 ( sample size )
we can calculate standard deviation as follows
σ = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
σ = 0.0132
Now the values that 'x' can take are
x = [tex]x_{1}[/tex] ± [tex]x_{2}[/tex]
x = 0.05 + 0.03, 0.05 - 0.03
x = 0.08 , 0.02
Also the z-score is
z = (x - μ)/σ
z = [tex]\frac{0.08-0.05}{0.0132}[/tex] , [tex]\frac{0.02-0.05}{0.0132}[/tex]
z = 2.27 , -2.27
we now find the p-values for the z-scores
p values are = 0.9970 , 0.0030
The difference in these values will give the probability
∴ P = 0.9970 - 0.0030
P = 0.9940
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an experimenter would like to construct a 99% confidence interval with a width at most 0.5 for the average resistance of a segment of copper cable of a certain length. if the experimenter knows that the standard deviation of such resistances is 1.55. how big a sample should the experimenter take from the population? what happens if the standard deviation and the width of the confidence interval are both doubled?
64 is the standard deviation and the width of the confidence interval are both doubled .
What is standard deviation in math?
Your dataset's average level of variability is represented by the standard deviation. It reveals, on average, how far away from the mean each value is. A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.Margin of error(E)=0.5
Standard deviation(σ)=1.55
Significance level(α)=100%-99%=1% or 0.01
From Z distribution Critical value table
the Critical value(Zc)=2.58 at significance level=0.01
we know formula for the Margin of error
E = Zc * σ/√n
0.5 = 2.58 * 1.55/√n
√n = 2.58 * 1.55/0.5
√n = 3.999/0.5
√n = 7.998
n = ( 7.998)²
n = 63.968004
Aproximately
n = 64
the realtionship between the sample size and margin of error is inversly proportional.
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How do i graph this? 4x - 2y > 12
Step-by-step explanation:
X-intercept is where the line crosses the x-axis or where y = 0
So, put y = 0 in the given equation
4x + 2(0) = 12
4x = 12
x = 12/4
x = 3
A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 50 meters and a standard deviation 100 meters. What is the probability that the measured distance will be smaller than the true distance?.
The likelihood that the measured distance will be shorter than the actual distance is equal to 0.3085.
In this case, the chance that the measured distance will be less than the true distance will be determined using the z-score formula. The z score is a normal score that adheres to a normal distribution with a mean and standard deviation of 0 and 1, respectively.
Given that,
Mean, μ = 50
Standard deviation, σ = 100
Less than 0% of the time, the overestimation is likely.
Consequently, the necessary probability is P (X ≤ 0)
Now,
P (X ≤ 0) = P [(X − μ) / σ ≤ (0 − μ) / σ]
P (X ≤ 0) = P [Z ≤ (0 − 50) / 100]
P (X ≤ 0) = P [Z ≤ − 0.5]
Excel formula for the probability mentioned above:
=NORMDIST(-0.5,0,1,1)
P (X ≤ 0) = 0.3085
0.3085 is the likelihood that the measured distance will be shorter than the actual distance.
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A triangle has interior angles of 50°, 55°, and 75° with side lengths of 3.1 m, 3.2 m, and 4.0 m. A second
triangle has side lengths of 10.3 m, 10.5 m, and 12.0 m. What must the interior angles of the second triangle
be for the two shapes to be similar?
The interior angles of the second triangle will be 50°, 55°, and 75° respectively.
What are similar triangles?
If the corresponding angles and sides of two triangles are congruent, then the two triangles are said to be similar.
In other words, similar triangles have the same shape but may differ in size.
Given, a triangle has interior angles of 50°, 55°, and 75° with side lengths of 3.1 m, 3.2 m, and 4.0 m.
And, a second triangle has side lengths of 10.3 m, 10.5 m, and 12.0 m.
The corresponding sides of both triangles are 3.1 m, 3.2 m, and 4.0 m with 10.3 m, 10.5 m, and 12.0 m respectively.
Then, the angles of both triangles are also corresponding to each other.
So we get, the interior angles of the second triangle will be 50°, 55°, and 75° respectively.
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basic trig, need help please
Answer: θ≈18,553°
Step-by-step explanation:
[tex]\displaystyle\\sin\theta=\frac{7\ cm}{22\ cm} \\\\sin\theta=\frac{7}{22}\\\\\theta=arcsin\frac{7}{22} \\\\\theta\approx18.553^0[/tex]
Lines AB and CD are straight lines. Find x and y .
⇒ ∠AOC+∠AOE+∠EOD=180°(angles on a straight line are supplementary)
16°+90°+2y=180°
[tex]106+2y=180\\2y=180-106\\2y=74\\\frac{2y}{2} =\frac{74}{2} \\y=37[/tex]
∴y=37°
∠AOC+∠COF∠BOF=180°(angles on a straight line are supplementary)
16°+90°+4x=180
[tex]106+4x=180\\4x=180-106\\4x=74\\\frac{4x}{4} =\frac{74}{4} \\x=18.5[/tex]
∴x=18.5°
Which variable is most important to the following problem?
A company has 95,000 shares of stock to sell. A stockbroker decides to buy equal shares of the stock for each of her 250 clients. If the company has 75,000 shares of stock remaining after she makes her purchase, how many shares did each client receive?
The number of shares remaining after the stockbroker buys shares for her customers is 57500
Also, The number of the most important pretty definitely really variable for finding the number of shares the company particularly definitely for all intents and purposes has left in a generally really big way in a fairly big way. Also, The number of shares the company generally really definitely has left after stockbroker's purchase = 95000 - 150×250 = 5750 in a subtle way.
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Select all the equations that are equivalent to this equation. 14 (8x + 56) = 20 56 + 8x = 80 14 = 20 – 8x 2x + 14 = 5 2x = 6 x = 3
The equation that are equivalent to the equation 1/4 (8x + 56) = 20 are 56 + 8x = 80 and 2x = 6
The equation is
1/4 (8x + 56) = 20
Solve the equation
8x + 56 = 80
8x = 80 - 56
8x = 24
x = 24/8
x = 3
The first equation is
56 + 8x = 80
8x = 80 - 56
8x = 24
x = 24/8
x = 3
The second equation is
14 = 20 - 8x
8x = 20 - 14
8x = 6
x = 6/8
x = 3/4
The third equation is
2x + 14 = 5
2x = 5 - 14
2x = -9
x = -9/2
The fourth equation is
2x = 6
x = 6/2
x = 3
Hence, the equation that are equivalent to the equation 1/4 (8x + 56) = 20 are 56 + 8x = 80 and 2x = 6
The complete question is:
Which equations are equal to this equation? Select all that apply.
1/4 (8x + 56) = 20
a. 56 + 8x = 80
b. 14 = 20 - 8x
c. 2x + 14 = 5
d. 2x = 6
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What is the generator for the sequence: 1, 3, 9, 27, 81, ... *
O 2
O 4/3
O 8/3
O 3
Answer:
3
Step-by-step explanation:
what it means by generator is the continuance of the multiplication process so 1x3=3 and then 3x3=9 and so on.
Hudson goes to a store an buys an item that costs x dollars. He has a coupon for 20%
off, and then a 5% tax is added to the discounted price. Write an expression in terms
of a that represents the total amount that Hudson paid at the register.
If Hudson having a discount coupon of 20% off, wants to buy an item having a printed price of "x" dollars, and a 5% tax is added to the discounted price in the end, then the expression that can represent the final amount Hudson paid for the item will be [(4x/5) + (x/25)].
As per the question statement, Hudson goes to a store an buy an item that costs "x" dollars, with the intention of using his 20% flat discount coupon, and then, a 5% tax is added to the final discounted price.
We are required to determine an expression that can represent the final amount Hudson paid for the item as per the above case.
Since Hudson gets a discount of 20% over the cost price of his desired item, the discounted cost price of the item becomes, [x - {(20/100) * x}]
= [x - {(1/5) * x}]
= [x - (x/5)]
= (4x/5).
And then, a 5% tax is added to the final discounted price, which takes the final amount to [(4x/5) + {(5/100) * (4x/5)]
= [(4x/5) + {(1/20) * (4x/5)]
= [(4x/5) + (x/25)]
= (21x/25)
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Can anyone answer this question?
The equation of the graph in vertex form is: y = 1x – 3| + 5.
How to Write the Equation of a Graph?The graph in the diagram above is a graph of an absolute value equation. The equation can be expressed as y = a|x – h| + k (vertex form), where the vertex is represented as (h, k).
The vertex of the graph is the coordinate of the point where the two straight lines meet.
Given the graph above, the vertex is at point (3, 5). Therefore:
h = 3
k = 5
The graph opens up, so the value of a = 1.
Substitute h = 3 and k = 5 into y = a|x – h| + k:
y = 1|x – 3| + 5
y = 1x – 3| + 5
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Solve.
−46=21+3m
Enter your answer as a mixed number in simplest form in the box.
m =
Answer:
-22 1/3
Step-by-step explanation:
We should start by subtracting both sides of the equality by 21.
After doing this, we get that -67=3m.
Furthermore, we can divide both sides by 3 and get -67/3=m.
However, this is an improper fraction, not a mixed number.
If we divide -67 by 3, we get -22 1/3.
Therefore, m= -22 1/3
A class trip consists of 84 students and 6 teachers.
What is the student to teacher ratio?
What is 3/4-3/10for IXL “L.12
The difference of the given fractions is 9/20.
The given fractions are 3/4 and 3/10.
What is subtraction of fractions?Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.
The difference of the given fractions is
3/4 - 3/10
= 15/20 - 6/20
= 9/20
Therefore, the difference of the given fractions is 9/20.
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if m angle 1 =3x +15 and m angle 2 = 6x+3 find x
Answer:
x=27 I think
Step-by-step explanation:
1 = 3x + 15
2 = 6x + 3
We can solve by putting both equations together.
Let's multiple the top equation by -2
-2(1 = 3x + 15)
-2 = -6x - 30
2 = 6x + 3
0=x - 27
27=x
a company wants to study the effectiveness of a new pain relief medicine. they recruit 100100100 volunteers with chronic pain. each subject takes the new pain relief medicine for a 222-week period, and a placebo for another 222-week period. subjects don't know which pill is the actual medicine, and the order of the pills is randomly assigned for each subject. researchers will measure the difference in the overall pain level for each subject. what type of experiment design is this?
Completely random design is used in this experiment.
In the given question,
A business wants to investigate the efficacy of a novel painkiller.
100 participants who suffer from chronic discomfort are enlisted.
Each participant takes the brand-new painkiller for two weeks before switching to a placebo for an additional two weeks.
The order of the tablets is chosen at random for each participant, and the subjects are unaware of which pill contains the actual medication.
Each subject's variance in total pain will be measured by researchers.
We have to check what type of experiment design is this.
As we can see in the question that they recruit 100 volunteers with chronic pain and each subject they use new pain relief medicine for a 2-week period and a placebo for another 2-week period.
They assign each subject randomly.
As we know that in a completely random design, treatments are randomly assigned to sampling material. The usual method for doing this is to make a list of the treatments and give each one a random number.
So we can see that completely random design is used in this experiment.
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discuss three strengths of the linear regression. identify a peer-reviewed study that uses linear regression in its analysis. explain why linear regression was used and discuss one challenge in interpreting the results. include the permalink with your citation.
Linear Regression analysis has three key applications:
(1) evaluating predictor strength, (2) anticipating an effect, and as well (3) trend forecasting.
Define the term linear regression?Linear regression is a fundamental and widely used method of predictive analysis. The overall goal of regression is to investigate two things:
How well does a set of predictor factors predict an outcome (dependent) variable? Which variables, in particular, are significantly predictive of both the outcome variable, and how do they influence it?Regression analysis has three key applications:
evaluating predictor strength,anticipating an effect, trend forecasting.The formula y = c + b*x defines the simplest form of the regression equation with one dependent so one independent variable,
where,
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Waukee railroad is considering the purchase of a powerful, high-speed wheel grinder to replace a standard wheel grinder now in use. selected information on the two machines follows: standard wheel grinder high-speed wheel grinder original cost/new cost $ 45,000 $ 67,500 accumulated depreciation to date $ 18,000 $ 0 current salvage value $ 11,750 $ 0 estimated cost per year to operate $ 26,250 $ 16,250 remaining years of useful life 5 years 5 years required: compute the net advantage or disadvantage of purchasing the high-speed wheel grinder covering the five-year period. use only relevant costs in your analysis. ignore tax effects.
The net disadvantage of purchasing the high-speed wheel grinder is $ 5,750
What is net advantage or disadvantage?
Net advantage or disadvantage is the total of potentially monetary savings from action of a business choosing to purchasing or lease an asset.
First, we calculate the net advantage in year 0
= current salvage value of standard - Original cost of high-speed
= $ 11,750 - $ 67,500
= - $ 55,750
Next we calculate the net advantage in year 5
= net advantage in year 0 + cost saving in 5 years
= - $ 55,750 + ($ 26,750 - $ 11,750) * 5
= - $ 55,750 + $ 50,000
= - $ 5,750
Thus, the net disadvantage of purchasing the high-speed wheel grinder is $ 5,750
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Mia’s family drinks a total of 10 gallons of milk every 6 weeks. How many gallons of milk do they drink per week
Tyler uses 7.5 ounces of barbecue sauce from a full bottle.
He estimates that he used about 25% of the barbecue sauce in the bottle. About how much barbecue sauce was in the full bottle?
There was about
30
ounces of barbecue sauce in the full bottle.
b. Tyler uses 20% of the remaining barbecue sauce.
About how many ounces did he use the second time?
Tyler poured about
4.5
ounces the second time.
Barbecue sauce was in the full bottle is 30 ounces and he use the second time is 4.5 ounces.
Given:
Tyler uses 7.5 ounces of barbecue sauce from a full bottle ,he estimates that he used about 25% of the barbecue sauce in the bottle.
25% = 7.5
multiply by 4 on both sides
25%*4 = 7.5 * 4
100% = 75/10 * 4
= 300/10
Full bottle = 30 ounces.
b.
Tyler uses 20% of the remaining barbecue sauce.
Remaining sauce = 30 - 7.5
= 22.5
= 22.5*20/100
= 2.25*20/10
= 2.25*2
second time= 4.50 ounces
Therefore barbecue sauce was in the full bottle is 30 ounces and he use the second time is 4.5 ounces.
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Can anyone please help me with this question
The length of AD in the parallelogram is 143 cm.
How to find the side of a parallelogram?A parallelogram is a quadrilateral with opposite sides parallel to each other. The opposite angles of a parallelogram are equal. Two adjacent or consecutive angles of a parallelogram are supplementary.
Hence,
2x + 72 + 2x - 20 = 180
4x + 52 = 180
4x = 180 - 52
4x = 128
divide both sides by 4
4x / 4 = 128 / 4
x = 32
Therefore,
∠A = 2(32) + 72 = 64 + 72 = 136 degrees
z = 136°
Therefore,
AC = BC = BD = AD
AC = z + 7
AC = 136 + 7
AC = 143 cm
Hence,
AD = 143 cm
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EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the point slope form of the equation of the line through the given point with the given slope
(-2, -3) slope = 2
Answer:
y+3=2x+4
Step-by-step explanation:
Alvin's bill for dinner at a restaurant was $96. He left a 20% tip. What was the amount of
the tip?
Answer:$ 17.28
Step-by-step explanation:
Mark up and discount answers
A basketball backboard set that sold for $79 is discounted 15%. What is the sale price?
The sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.
We will use the method of percentage to solve the given question.
We are given:
A basketball backboard set that sold for $79 is discounted by 15%.
We need to find the sale price after the discount is given.
We will subtract the discount from the marked price.
Let us solve this;
Sale price = marked price - discount
Sale price = $79 - $79 * 15%
Sale price = $79 - $79 * 15 / 100
Sale price = $79 - $11.85
Sale price = $67.15
So, the sale price will be $67.15.
Thus, the sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.
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8.How do you know whether the graph of g(x) = a |x| is a vertical stretch or a vertical
shrink of the graph of f(x) = b |x|?
Answer
it’s because of the amplitude the value in the front controls the height
Step-by-step explanation:
A.