The four matches can be sequenced in 1350 different ways, ensuring that each player gets to play at least once.
What is a sequence?A sequence is an enumerated collection of things in mathematics where repetitions are allowed and order is important. It includes members, much like a set (also called elements, or terms). A sequence can be formalized as a function from natural numbers (the positions of sequence elements) to the elements at each place. An indexed family, which is a function from any index set, can be thought of as a generalization of the concept of a sequence.
The final matches can be between any two players after we have made sure that every player has played at least one match (except those three matches played)
We can select any two players from a pool of six for the first game =[tex]6_{c_{2} }[/tex]
We can select either of the two players from a total of four for the second match is [tex]4_{c_{2} }[/tex]
We have a choice of two players for the third game.=[tex]2_{c_{2} }[/tex]
Any of the two players from the pool of six can be selected for the fourth match= [tex]6_{c_{2} }[/tex]
P(x) =[tex]6_{c_{2} }[/tex]×[tex]4_{c_{2} }[/tex] ×[tex]2_{c_{2} }[/tex] × [tex]6_{c_{2} }[/tex]
P(x) = 15 × 6 × 1 × 15
P(x) = 1350
Therefore, the four matches can be arranged in 1350 different ways, ensuring that each player gets to play at least once.
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for a standard normal distribution, what is the probability that z is greater than 1.75? a) 0.0401 b) 0.0459 c) 0.4599 d) 0.9599
For the standard normal distribution , the probability will be 0.0401 which means option a is the correct choice.
A standard deviation (or σ) is a degree of ways dispersed the records is when it comes to the mean. Low general deviation approach records are clustered across the mean, and excessive general deviation suggests records are extra unfold out.
Using a standard normal table the area to the right of z = 1.75 is given by
P(z > 1.75) = .0401
Therefore, the correct option is a.
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A mixture of monatomic and diatomic gases has specific-heat ratio gamma = 1.52. What fraction of its molecules are monatomic?
Its molecules' monatomic fraction is 0.444.
Define fractionAn element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
The fact that
The formula gamma monatomic
Determines the specific heat ratio of monoatomic gas.
5/3=1.67
Calculates the specific heat ratio of a diatomic gas.
Gamma monatomic =7/5=1.4
We have a monoatomic and diatomic gas mixer with a gamma mixer specific heat ratio of 1.52.
Calculating the monoatomic gas fraction is as follows:
Let's assume that "x" is the percentage of monoatomic
1.67* x+1.4* (1-x)=1.52
1.67* x+1.4-1.4* x=1.52
0.27* x=0.12
x = 0.12/0.27
x= 0.444
Its molecules' monatomic fraction is 0.444.
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an experiment involves selecting a random sample of 256 middle managers for study. one item of interest is their annual incomes. the sample mean is computed to be $35,420.00. if the population standard deviation is $2,050.00, what is the standard error of the mean? a) $128.13 b) $138.36 c) $2,050.00 d) $8.01
An experiment involves selecting a random sample of 256 middle managers for study. one item of interest is their annual incomes. the sample mean is computed to be $35,420.00. if the population standard deviation is $2,050.00, the standard error of the mean is $128.125
What is standard error?The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error. It reveals how much the sample mean would change if a study were to be repeated with fresh samples drawn from a single population.
How do you calculate standard error?By dividing the standard deviation by the square root of the sample size, the standard error is determined. By taking into account the sample-to-sample variability of the sample means, it provides the precision of a sample mean.
Standard error of the mean = 2050/sqrt {256} = $128.125
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25. A bakery made 350 cupcakes. They sold 280 of those cupcakes.
What percentage of the cupcakes did they sell?
A. 20%
B. 70%
C. 80%
D. 125%
Answer:
C. 80%
Step-by-step explanation:
To find the percentage of cupcakes that were sold, you can divide the number of cupcakes sold by the total number of cupcakes and multiply the result by 100%. In this case, the percentage of cupcakes sold is:
280 cupcakes / 350 cupcakes * 100% = 80%
Therefore, the correct answer is C: 80%.
In the figure shown, what is the value of x
The value of x is 1
Given that,
AB=DE
AC=DF
∠CAB=∠FDE
So by the triangle property of SAS, ΔABC and the ΔDEF are equal means ΔABC≅ΔDEF.
And we know that if two triangles are equal then by their properties their respective sides and angles will also be equal to each other.
So we can write that,
⇒13x-12=7x-6
⇒13x-7x=12-6
⇒6x=6
⇒x=1
Therefore the value of x is 1.
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In triangle ACE points B, D and F are midpoints of the sides. If AC=48 and FB=23 Find EC.
Answer: In ΔABF & ΔACE
AB/FB = AC/EC (As both the triangles are similar)
as B is the midpoint of AC = 48
AB = 24
So,
24/23 = 48 / EC
EC = 46
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The value of EC is equal to 69 units
What is the triangle midpoint theorem?Triangle Midpoint Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
Given here, AX=24 And FB=23
Now applying the triangle midpoint theorem we get the value of
AC =3×23
= 69 units
Hence, The value of EC is equal to 69 units
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Vladmir sketches the graph of the function f(x)=12(x+6)2−3
as shown below
He then translates this function 11 units to the right and 4 units down to obtain the new function g(x)=12(x−h)2+k
. Which function correctly shows integer values for h and k?
The function that correctly shows the value of k and h is g(x) = 12(x - 5)² - 7
How to determine the function correctly?From the question, we have the following parameters that can be used in our computation:
f(x) = 12(x + 6)² - 3
The transformation is given as
11 units to the right and 4 units down
This is represented as
(x - 11, y - 4)
So, we have the following representation
g(x) = 12(x + 6 - 11)² - 3 - 4
Evaluate
g(x) = 12(x - 5)² - 7
Hence, the function is g(x) = 12(x - 5)² - 7
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Solve pls brainliest
Answer:
The correct answers are D and E
Step-by-step explanation:
D is correct because according to exponent rules, you add them when you multiply.
E is correct because the expression will equal 64 when calculated.
what is the probability that in a random sample of size 10, a total of more than 90 pizzas are consumed? (hint: what is the mean number of pizzas consumed by the sample of 10 students?)
The probability that more than 90 pizzas will be devoured in a random sample of 10 people is 85.31%.
Large Population Z-test:A hypothesis test called the Z-test uses the z-statistic, which has means and variance and follows the normal distribution. Whenever the variance is known, the Z-test reveals whether 2 population means are distinct. The Z-test is presented asFor the stated question-
mean μ of 10standard deviation σ of 3random sample of size 's' is 10pizzas are consumed n = 90Estimate the probability for the consumed pizzas.
P(x > 90/10) = P(x = 9)
P(x = 9) = P[x - μ/ σ/√n > z > (9 - 10) / (3/√10)]
P(x = 9) = P(z > -1.05)
P(x = 9) = 1 - P(z > -1.05)
P(x = 9) = 1 - 0.1469
P(x = 9) = 0.8531
Thus, the probability that more than 90 pizzas will be devoured in a random sample of 10 people is 85.31%.
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The complete question is-
The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3.
what is the probability that in a random sample of size 10, a total of more than 90 pizzas are consumed? (hint: what is the mean number of pizzas consumed by the sample of 10 students?)
How do you convert 22/55 into a percent and decimal?
Answer:
22/55 = 40% = 0.4
Step-by-step explanation:
22/55
Reduce the fraction by dividing the numerator and denominator by 11.
22/55 = 2/5
Now use a calculator, or long division, to divide 2 by 5.
22/55 = 2/5 = 0.4
To change a decimal to a percent, multiply the decimal by 100%.
0.4 × 100% = 40%
Answer: 22/55 = 40% = 0.4
From an angle of depression of 50 degrees, John watches his friend approach his building while standing on his rooftop. The rooftop is 16 m from the ground and John's eyelevel is about 1.8m above the rooftop. What is the distance between John's friend and the building?
The distance between John's friend and the building is 14.9 metres.
How to find the distance between the building and John's friend?From an angle of depression of 50 degrees, John watches his friend approach his building while standing on his rooftop. The rooftop is 16 m from the ground and John's eyelevel is about 1.8m above the rooftop.
Therefore, the distance of John's friend from the building can be calculated as follows:
This situation forms a right angle triangle.
Hence, using trigonometric ratios,
tan 50 = opposite / adjacent
tan 50 = 16 + 1.8 / x
tan 50° = 17.8 / x
cross multiply
x tan 50° = 17.8
x = 17.8 / tan 50
x = 17.8 / 1.19175359259
x = 14.9359734675
x = 14.9 metres
Therefore,
distance of John's friend to the building = 14.9m
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In triangle LMN, m∠L = (6c + 35)°. If the exterior angle to ∠L measures 79°, determine the value of c. c = 24 c = 7 c = 44 c = 11
The value of c, if In triangle LMN, m ∠ L = (6c + 35)°. If the exterior angle to ∠ L measures 79° is 11, so option D is correct.
What is the triangle?Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.
Given:
In triangle LMN, m ∠ L = (6c + 35)°
∠ L = 79°
Calculate the angle as shown below,
m ∠ L = 180 - 79
m ∠ L = 101
101 = 6c + 35
6c = 101 - 35
c = 66 / 6
c = 11
Therefore, the value of c, if In triangle LMN, m ∠ L = (6c + 35)°. If the exterior angle to ∠ L measures 79° is 11.
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A new bank customer with $3500 wants to open a money market account. The bank is offering a simple interest rate of %1.1
How much interest will the customer earn in 10 years?
The interest that will the customer earn in 10 years is $385.
What is simple interest?
Simple interest is a method for figuring out how much interest was paid on a sum of money during a specific time period at a specific rate.
Simple interest has a constant principal amount. Simple interest is a straightforward and easy technique for calculating interest in money. Interest is always applied to the initial principal amount under the simple interest method, and the rate of interest is the same for each time cycle. When we deposit money in a bank, the bank pays us interest on our investment. Banks charge various sorts of interest, one of which is simple interest.
The customer deposit $3500 when he opens the account.
The interest rate of the bank is 1.1% = 0.011.
He deposits the amount for 10 years.
The formula of simple interest is I = PRT.
I = 3500 × 0.011 × 10
I = 385
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solve each of these equations. explain or show your reasoning.
2(x+5)=3x+1
3y-4=6-2y
3(n+2)=9(6-n)
Answer: n = 4
9 = x
y = 2
Step-by-step explanation:
2 ( x + 5 ) = 3x + 1
2x +10 = 3x + 1
10 = 1x + 1
- 1 -1
9 = 1x
9 = x
3y - 4 = 6 - 2y
5y -4 =6
5y = 10
y = 2
3 (n + 2) = 9 ( 6-n)
3n + 6 = 54 -9n
3n +9n = 54 - 6
12n =54 -6
12n =48
n = 4
Total aid
(9
10)
In a library, the ratio of students with younger siblings to those without younger
siblings was 4:3, There were 42 students without younger siblings. Let y be the
number of students with younger siblings. Set up a proportion to solve for y. Then,
find the total number of students.
Total number of students is 70.
What do you mean by ratio?
A ratio is a comparison of two quantities. The ratio of a to b can also be expressed as: a:b
A ratio is the equality of two ratios. Write ratios to help you find equivalent ratios and solve for unknown quantities.
Two common types of relationships are part-to-part and part-to-whole.
In a library, the ratio of students with younger siblings to those without younger siblings was 4:3
There were 42 students without younger siblings.
As the given ratio is 4:3
So, let the number of students with younger siblings = 4x
let the number of students without younger siblings = 3x
There were 42 students without younger siblings.
3x = 42
x = 42/3
x = 14
Let y be the number of students with younger siblings
y = 4x = 4(14) = 56
Total students = students with younger siblings + students without younger siblings
= 14 + 56
= 70
Therefore, total number of students is 70.
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Complete. If m∠6=x,m∠7=x−20, and m∠11=80, then x=______?
The value of x = 50
Exterior angle:
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex.
If every internal angle of a simple polygon is less than π radians (180°), then the polygon is called convex.
In contrast, an exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.
given that
m∠6 = x
m∠7 = x-20
m∠11 = 80
we solve this by using exterior angles
sum of 2 interior angles is equal to one exterior angle
m∠6 + m ∠7 = m∠11
x + x - 20 = 80
2x = 80 + 20
2x = 100
x = 100/2
the value of x = 50
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PLS ANSWER ASAP
40 POINTS
The function g(x) = √x + 4 is the result of a vertical translation 4 units up of the function f(x) = √x. (Right choice: B)
What kind of transformation should be used to obtain the image of a function?
In this problem we find the definition of a function f(x) and its image g(x). Both f(x) and g(x) are radical functions and we need to determine the transformation rule to obtain the latter function. By direct inspection, g(x) is the result of applying a vertical translation, whose definition is shown below:
g(x) = f(x) + k
Where:
f(x) - Original function.g(x) - Resulting function.k - Translation step.Please notice that k indicates a translation in the +y direction. k > 0 indicantes a vertical shift k units up.
Then, g(x) is the result of a vertical translation (4 units up) on f(x).
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Find the value of x in the triangle shown below: 2.5 6.5 Choose 1 answer: I =6 3 = V48.5 x = 9 x = V9
Answer:
x = 6 units
Step-by-step explanation:
We know that, By pythagoras theorem,
Hypotenuse2 = base2 + perpendicular2
Given, Hypotenuse = 6.5
perpendicular = 2.5
base = x
So, by putting the values,
6.52 = 2.52 + x2
42.25 = 6.25 + x2
36 = x2
Hence, x = 6 units
Does the limit of 1/n diverge? I know that the Series of 1/n, diverges because of harmonic series. But if the LIMIT of 1/n converges, please explain why the two are different.
The limit of 1/n does not diverge.The difference of limit of 1/n is explained below.
It converges to 0 as n approaches infinity. The difference between a series and a limit is that a series is the sum of the terms in a sequence, while a limit is a value that a sequence approaches as its terms become increasingly large. In other words, the limit of a sequence is the "endpoint" of the sequence, while the series is the sum of all the terms in the sequence. In the case of 1/n, the series does not converge because the terms gradually increase with no endpoint. However, the limit of 1/n does converge because the terms become progressively smaller and approach 0 as n approaches infinity. Therefore, the limit of 1/n does converge, while the series of 1/n does not.
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solve each proportion. if necessary, round to the nearest hundredth
1-12
The proportions in this problem are given as follows:
1. a = 40.
2. t = 1.
3. q = 29.25.
4. g = 3.
5. m = 9.8.
6. v = 12.9.
7. w = 1.3.
8. n = 2.28.
9. n = 0.84.
10. k = 1.2.
11. t = 0.57.
12. z = 63.4.
How to solve the proportions?The proportions are solved using these two steps presented as follows:
Cross multiplication with the equal sign.Isolating the unknown variable.Then, for item a, the proportion is given as follows:
3/8 = 15/a
Applying cross multiplication, we have that:
3a = 15 x 8
Then, the variable a is isolating applying the division operation, as follows:
a = 15 x 8/3
a = 5 x 8 (as 15/3 = 5)
a = 40.
Then the second proportion is solved as follows:
t/2 = 6/12
12t = 12
t = 1.
And the same procedure is then applied to obtain any of the remaining 10 proportions. Some include operations with decimals, hence calculator used is recommended.
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How do you translate "2 more than a number" into a mathematical expression?
"2 more than a number" is equivalent to the mathematical expression X+2.
"2 more than a number" denotes addition because of the word "more." Since we aren't given a definite number, we use a variable in its place (such as x). So, x+2 can be used to represent "2 greater than a number."
An arithmetic value used to indicate an amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. You can think of a number as a count, like when we yell, "3, 2, 1, GO!" during a race, or as a measurement, like John Cena's weight of 275 lbs. There are also decimals like 3.14 and fractions like 22/7.
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Find the sum of ten terms of the G. P 1,1.3,1.69
Answer:
Sum of G.P. series is given by,
Sum=
r−1
a(r
n
−1)
when r>1
Where a= first term, n=n
th
term and r is common ratio.
Here, a=1,n=10,r=
3
S
10
=
(
3
−1)
1×{(
3
)
10
−1}
=
(
3
−1)
(3
5
−1)
×
(
3
+1)
(
3
+1)
=
(3−1)
242(
3
+1)
=121(
3
+1).
60 POINTS ANSWER FOR BRAINLIST AND PROVIDE THE GRATH!! Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day. Draw a graph to represent
this situation.
Answer: He needs 9 days to complete all his overdue assignments and if this is happening to you sry I feel your pain. Just vibing to k-pop while having a mental breakdown doesn't sound bad until you feel it :(
Step-by-step explanation:
Well, he has 36 overdue assignments, and if he completes 4 overdue assignments each day you need 9 days to complete all his overdue assignments.
36 divide 4 = 9 days
four feet of wire is used to form a square and a circle. how much wire should be used for the square and how much should be used for the circle to enclose the maximum total area
The total maximum area enclosed by both the shapes square and a circle using given wire is equal to 2.27 square feet.
As given in the question,
Let 'x' be the side length of the square
And 'r' be the radius of the circle.
Length of the wire = 4 feet
Maximum side length of the square is:
4x = 4
⇒ x = 1feet
Maximum area of the square = x²
= 1²
= 1
Maximum radius of the circle is:
2πr = 4
⇒ r = 2 / π
Maximum area of the circle = πr²
= π × (2/π)²
= 4 / π
Total maximum area enclosed by square and a circle
= 1 + (4/π)
= 1 + 1.27
= 2.27 square feet.
Therefore, the total maximum area enclosed by square and a circle from the given wire is equal to 2.27 square feet.
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Which of the following describes the nature of the solutions of the quadratic
equation-2x^2-x-1=0?
A. One real, rational solution
B. Two real, rational solutions
C. Two real, irrational solutions
D. Two complex conjugate solutions
Answer:
D
Step-by-step explanation:
To find the solutions, let's calculate the determinant:
Δ = (-1)²-4(-2)(-1) = 1-8 = -7
the solution is: (1 ±√-7)/(-4)
√-7 indicates there are two complex solutions
20x - 4y=11
10x - 2y=6
The given pair of equations has no solution.
Two equations can be solved through three different methods:
Substitution MethodElimination MethodGraphing the equationsLet's use the elimination method in this question
20x - 4y = 11 .....(I)
10x - 2y = 6 .....(II)
Multiply (II) by 2
20x - 4y = 11 .....(I)
20x - 4y = 6 .....(II)
Now, subtracting equations (I) and (II) we will get no solution.
It is possible for the two lines to be parallel and not intersect. In this situation, we cannot identify a shared point between the two, and as a result, the system of the two equations representing the two lines cannot provide a solution!
This question is incomplete. The correct question is
Consider the two equations and solve for x and y.
20x - 4y = 11
10x - 2y = 6
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The length of each side of a square is with the area of 1600 square inches is increased by 20 inches what is the resulting area
The area of the resulting square is 3600 in²
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a square has area 1600 in² whose length has been increased by 20 in each side.
Area of the square = side²
Let the original side length be x, then,
x² = 1600
x = 40 (neglecting -40, because length of anything can not be negative)
After 20 in increase, the side is (40+20) = 60 in
Area of new square = 60x60 = 3600 in²
Hence, The area of the resulting square is 3600 in²
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please help me :( If you traveled 6,000,000,000 miles into outer space, you would be about one-fourth of the way to Venus. Write this measurement in scientific notation.
A. 6 x 106 miles
B. 60 x 106 miles
C. 6 x 109 miles
D. 60 x 109 miles
The given measurement in scientific notation as [tex]6\times10^9[/tex]. Therefore, option D is the correct answer.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.56\times10^7[/tex].
The given distance is 6,000,000,000 miles.
There are 9 zeros in the given number
So, scientific notation is [tex]6\times10^9[/tex]
Therefore, the number in scientific notation is [tex]6\times10^9[/tex].
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Round 45,621 to each place given below. a. to the nearest ten ___ b. to the nearest hundred ___ c. to the nearest thousand ___ d. to the nearest ten thousand ___
The number on round off to each place will be 45,621.
The decimal number is rounded to any place by the following concept -
We look at the number to the right of concerned digit. If that number is more than five or exactly five, then we add 1 to our number. However, if it is less than five, then the number remains same.
For instance, if we round 45.621 to nearest tenth, we will get 45.6. This is because on right to it, the number 2 is less than 5. Now, in the mentioned digit which is 45,621, we see there is no decimal and number after that. So, as the digits are 0 which is less than 5, the number will remain as it is.
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The graph of y=h(x)y=h(x)y, equals, h, left parenthesis, x, right parenthesis is a line segment joining the points (-7,-5)(−7,−5)left parenthesis, minus, 7, comma, minus, 5, right parenthesis and (-1,-2)(−1,−2)left parenthesis, minus, 1, comma, minus, 2, right parenthesis.
Drag the endpoints of the segment below to graph y=h^{-1}(x)y=h
−1
(x)y, equals, h, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis.
Answer:
(-5, -7) and (-2, -1)
Step-by-step explanation:
The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2). (Blue line on the attached graph).
The graph of the inverse function is a reflection in the line y = x.
Therefore, the endpoints of the inverse function are:
(-5, -7) and (-2, -1)The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.
Answer:
(-5, -7) and (-2, -1)
Step-by-step explanation:The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2). (Blue line on the attached graph).The graph of the inverse function is a reflection in the line y = x.Therefore, the endpoints of the inverse function are:(-5, -7) and (-2, -1)The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.
Step-by-step explanation:
