Answer:
In 286 different ways 10 players can be selected.
Step-by-step explanation:
There are 6 girls and 7 boys in a class. So in total there are 6+7 = 13 number of students in the class.
A team of 10 players is to be selected from the class.
As there is no other conditions are given, we can pick any 10 students from 13 students.
The way we can select 10 players from 13 students is;
= (13 10)
= 13!/10!(13-10)!
= 13!/10! 3!
= (13 × 12 × 11 × 10!)/ 10! 3!
= ( 13 × 12 × 11)/6
= 286
what is the value of x to the nearest tenth?
Answer: 11.6
Step-by-step explanation:
We know that a radius that is perpendicular to a chord divides the chord into two equal parts .
Then by Pythagoras theorem of right triangle ,we have
[tex](6.5)^2=3^2+(\dfrac{x}{2})^2\\\\\Rightarrow\ 42.25=9+\dfrac{x^2}{4}\\\\\Rightarrow\ \dfrac{x^2}{4}=33.25\\\\\Rightarrow\ x^2=134\\\\\Rightarrow\ x=\sqrt{134}=11.5758369028\approx11.6[/tex]
Hence,the value of x = 11.6
Find the value of the angle x in the triangle below
Answer:
[tex]\large\boxed{x=53^o}[/tex]
Step-by-step explanation:
We know: the sum of the measures of the angles of the triangle is equal to 180 °.
Therefore e have the equation:
[tex]x+45^o+82^o=180^o[/tex]
[tex]x+127^o=180^o[/tex] subtract 127° from both sides
[tex]x=53°[/tex]
If Bradley has 4 times as many dimes as nickels and they have a combined value of 315 cents, how many of each coin does he have?
d=4n
315=5n+10d
315=5n+40n
315=45n
315/45=n
7=n
d=4n
d=4(7)
d=28
28 dimes and 7 nickels
PLEASE. HELP. ME I WILL GIVE BRAINLIEST I NEED TO ANSWER ALL OF THESE AND EXPLAIN THEM
What number divided by -3 gives 12 as the result?
A)-36
B)-4
C)4
D)36
Answer:
-36
Step-by-step explanation:
We don't need one, do we? It's just simple math.
An equation is formed of two equal expressions. The number which when divided by -3 gives 12 as the result is -36. The correct option is A.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number be represented by x.
Given that the number when divided by -3 gives 12 as the result. The given situation can be written in the form of an equation as,
x/-3 = 12
Solving the equation to get the value of x,
x/-3 = 12
x = 12 × -3
x = -36
Hence, the number which when divided by -3 gives 12 as the result is -36.
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Donna buys some fabrics to make place meta. She needs 1/5 yards of each fabrics. She has 9 different types of fabrics to make her design. Use the following equation. Write the number in the box to make the statement true.
Answer:
9/5 = 9 x 1/ 5
Answer:
9/5 = 9 * 1/5
Step-by-step explanation:
Make 2 equations for this geometric sequence:
36, 18, 9, 4.5, 2.25, 1.125, 0.5625, 0.28125...
what is the approximate area of a quarter circle with a radius of 22 m is using pi equals 3.14
Answer: The answer without estimation is 1,519.76 but with estimation it’s 1,520 m.
Step-by-step explanation:
The formula for this situation is A = pi(or in this case 3.14) times the radius squared. If you know the formula then the rest is just to plug in and estimate if you have too.
Morgan started the year with $615 in the bank and is saving $25 per week Kendall started with $975 and is spending $15 per week .when will they both have the same amount of money in the bank ?
Answer:
Step-by-step explanation:
You can represent Morgan's scenario with the expression, 25w + 615, and you can represent Kendall's scenario with the expression, 15w + 975. To find out when they both have the same amount of money in their accounts, you set them equal to each other and solve for w:
25w + 615 = 15w + 975
25w = 15w + 360
10w = 360
w = 36
Morgan and Kendall will have the same amount of money after 36 weeks.
To find the week when Morgan and Kendall will have the same amount of money in the bank, we set up the equation 615 + 25x = 975 - 15x and solve for x.
Explanation:To find the week when Morgan and Kendall will have the same amount of money in the bank, we need to set up an equation. Let x represent the number of weeks. The equation for Morgan's savings is 615 + 25x, and the equation for Kendall's savings is 975 - 15x. To find the week when they have the same amount of money, we set up the equation 615 + 25x = 975 - 15x. Solving this equation will give us the value of x, which represents the number of weeks.
615 + 25x = 975 - 15x
Combine like terms:
40x = 360
Divide both sides by 40:
x = 9
Therefore, Morgan and Kendall will have the same amount of money in the bank after 9 weeks.
Find the sum.
Homework: 9.4 arithmetic series
Answer:
Step-by-step explanation:
a1 = 3(1) - 7 = - 4
a2 = 3(2) - 7 = -1
d = a2 - a1
d = -1 - (-4)
d = -1 + 4
d = 3
a60 = 3(60) - 7
a60 = 180 - 7
a60 = 173
n = 60
Sum = (a1 + a60) * n / 2
Sum = (-4 + 173) * 60/2
Sum = (169)*30
Sum = 5070
==================
Just to check, we'll use the second summation formula
d = 3
n = 60
a1 = -4
Sum = (2*a1 + (n - 1)*d )*n / 2
Sum = (2*(-4) + (60 -1)*3)* 60/2
Sum = (-8 + 59*3) * 30
Sum = (177 - 8)*30
Sum = 169 * 30
Sum = 5070
Same answer.
Solve for r.
r16≥8
r≥2
r≤2
r≥128
r≤128
The equation doesn't provide enough context to definitively solve for 'r'. Given the original equation r16 ≥ 8, r shouldn't be less than 1 if only integer values are accepted.
Explanation:In Mathematics, the original equation provided here, 'r16 ≥ 8', seems to indicate that a value 'r' is being multiplied by 16 and the product should be greater than or equal to 8. To solve for 'r', you would normally divide both sides of the equation by 16. However, each sub-question provided 'r ≥ 2', 'r ≤ 2', 'r ≥ 128', and 'r ≤ 128', indicates different potential solutions for 'r'. Without the proper context or further information it is difficult to properly solve for 'r'. Given the original equation, if only integer values are allowed, 'r' should not be less than 1 to maintain the inequality. Further clarification on the nature of 'r' and the context of the question is highly recommended.
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find the equation to a circle with a radius of 10 and a center at (-1, 7)
Answer:
[tex]\large\boxed{(x+1)^2+(y-7)^2=100}[/tex]
Step-by-step explanation:
The equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (-1, 7) and the radius r = 10. Substitute:
[tex](x-(-1))^2+(y-7)^2=10^2\\\\(x+1)^2+(y-7)^2=100[/tex]
Evaluate C(8, 2). 56
28
40,320
20,160
Answer:
option B
28
Step-by-step explanation:
Given in the question,
C(8,2)
Formula to use
nCr = n! / r! * (n - r)!here n = 8
r = 2
We have to calculate combinations of 8 object taken 2 at a time, then
C(8,2)
8C2
8! / 2! * (8 - 2)!
[tex]\frac{8*7*6*5*4*3*2*1}{2*1(6!)}[/tex]
[tex]\frac{8*7*6*5*4*3*2*1}{2*1(6*5*4*3*2*1)}[/tex]
[tex]\frac{8*7}2[/tex]
56/2
28
So, 8C2 = 28
The combination C(8, 2) in the given problem equals 28.
Mathematically, a combination refers to a selection of items from a larger set without regard to the order of selection. It is a way to count the number of different subsets or groups that can be formed from a given set.
In other words, a combination is a selection of r objects from a set of n distinct objects, where the order of selection is not considered. The number of combinations represented as C(n, r), represents the count of possible combinations.
It is known that C(n, r) = [tex]\frac{n!}{r!(n - r)!}[/tex],
So,
C(8, 2) = [tex]\frac{8!}{2!(8- 2)!}[/tex],
= [tex]\frac{8!}{2!6!}[/tex]
= [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{(2\times 1) (6\times 5\times 4\times 3\times 2\times 1)}[/tex]
= 28.
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i NEEEED HELP PLEASE COMMENT IF U WILL HELP ME. ITS AN ALGEBRA QUESTION Enter your answer and show all the steps that you use to solve this problem in the space provided.
f(x)=9x3+2x2−5x+4and g(x)=5x3−7x+4.what is f(x)−g(x)?
Show all of your steps and write your final answer in factored form.
PLEASE HELP FAST 20 PTS
f(x)= 9x^3+ 2x^2 -5x+ 4
g(x)= 5x^3 -7x+ 4
f(x) - g(x)
= (9x^3+ 2x^2 -5x+ 4) - (5x^3 -7x+ 4)
= 9x^3+ 2x^2 -5x+ 4 -5x^3+ 7x -4
= (9x^3 -5x^3)+ 2x^2+ (7x -5x)+ (4-4) (combine like terms)
= 4x^3+ 2x^2+ 2x
= 2x* (2x^2+ x+ 1)
The final answer is 2x* (2x^2+ x+ 1).
The final answer in factored form is 2x(x² + x + 1).
f(x) = 9x³ + 2x² - 5x + 4
g(x) = 5x³ - 7x + 4
To find f(x) - g(x) ,, we subtract g(x) from f(x) term by term.
Subtract the like terms from f(x) and g(x):f(x) - g(x) = (9x³ + 2x² - 5x + 4) - (5x³ - 7x + 4) = 4x³ + 2x² + 2x
The final answer in factored form is 2x(x² + x + 1).
Layla wants to build a wooden box with a volume of 454545 cubic centimeters. She started with a width of 3\text{ cm}3 cm3, space, c, m and a height of 3\text{ cm}3 cm3, space, c, m.
How long should Layla make the box?
Answer:
91,125
Step-by-step explanation:
V=Bh
V=l*w*h
V=45*45*45
V=2,025 *45
V=91,125
Answer:
50,505 cm
Step-by-step explanation:
In order to calculate this you just have to calculate the length necessary to create a wooden box with the volume of 454545 cubic centimeters, and now you just have to calculate since you have the base of the area, measuring 3 cm by 3 cm, that would be 9 square centimeters, so you just have to divide the desired volume by 9 square centimeters:
454545/9=50,505 cm
So the length of the wooden box should be 50,505 cm in order to have a 454545 cubic centimeters wooden box.
The “p hat” is calculated as
Formula of [tex]p hat = \frac{X}{n}[/tex] help us to calculate p hat , where X represents the number of occurrence of desired event and n represents the specified of sample space.
What is p hat?" p hat is defined as the probability of the occurrence of random event to the specified sample space."
According to the definition,
p hat can be calculated using formula
[tex]p hat = \frac{X}{n}[/tex]
'X' represents the number of occurrence of the desired event
'n' represents the specified sample space.
p hat is nothing but the probability of finding specified sample size.
Hence, formula of [tex]p hat = \frac{X}{n}[/tex] help us to calculate p hat.
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Help plz show work plz
Answer: c) 286.5 in²
Step-by-step explanation:
S.A.= 2π r · h
= 2π (7.3/2) · 12.5
= 2π (3.65) (12.5)
= 286.5
Paula needs to sod square feet of land. Assuming that Paula can cut the sod into pieces, the number of 3 square foot pieces of sod she needs how many?
Step-by-step explanation:
You would need how many square feet. Divide the amount of square feet of land by 3. That should be the answer if it divides evenly, if there is a decimal or a fraction after it then round up to the next whole number
Answer:
Paula needs to sod
3,855
square feet of land. Assuming that Paula can cut the sod into pieces, the number of 3-square-foot pieces of sod she needs is
1,285
.
Step-by-step explanation:
The diagram shows one way to decompose this shape into two rectangles. One rectangle is 75 feet × 50 feet, and the other is 7 feet × 15 feet.
50 POINTS PLEASE HELP ME IM RUNNING OUT OF TIME!!!!!!!!!
Given the vertices of ∆ABC are A (2,-5), B (-4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
Rx = 3 T<3,-6> r(90◦, o)
Answer:
Step-by-step explanation:
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how do you solve for the indicated variable. 8x+4y=12;y
Answer:
x=1
Step-by-step explanation:
8x+4y=12y
-4y -4y
8x=8y
x=1
PLEASE HELP QUICK
Celia uses the steps below to solve the equation -3/8(-8-16d)+2d=24
Step 1 Distribute -3/8 over the expression in parentheses.
3-16d+2d=24
Step 2 Simplify like terms.
3-14d=24
Step 3 Subtract 3 from both sides of the equation.
-14d=21
Step 4 Divide both sides of the equation by –14.
d=21/-14=-3/2=-1 1/2
Which corrects the error in the step in which Celia made the first error?
In step 1, she should have also distributed -3/8 over 2d, to get 3-16d+(-3/4d)=24.
In step 1, she should have also distributed -3/8 over –16d, to get 3+6d+2d=24. In step 3, she should have added 3 to both sides of the equation to get -14d=27.
In step 3, she should have first divided both sides by –14 to get 3+d=24 .
Answer:
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over –16d, to get 3 + 6 d + 2 d = 24.
Step-by-step explanation:
(B)
The error in the step 1, she should have also distributed -3/8 over –16d, to get 3 + 6d + 2d = 24
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
Given the equation:
(-3/8)(-8-16d) + 2d = 24
Step 1: Distribute -3/8 over the expression in parentheses:
3 + 6d + 2d = 24
Step 2 Simplify like terms:
3 + 8d = 24
Step 3 Subtract 3 from both sides of the equation:
8d = 21
Step 4 Divide both sides of the equation by 8:
d = 21/8
The error in the step 1, she should have also distributed -3/8 over –16d, to get 3 + 6d + 2d = 24
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!!!!!!!!!!!!!!!!!!!!!
ANSWER
A. (x+4)
EXPLANATION
The given binomial is
[tex] {x}^{2} + 12x + 32[/tex]
Split the middle term:
[tex] {x}^{2} + 8x + 4x + 32[/tex]
Factor;
[tex]x(x + 8) + 4( x + 8)[/tex]
Factor further;
[tex](x + 8)(x + 4)[/tex]
Therefore
[tex](x + 4)[/tex]
is a factor.
What is the simplified expression for 4 to the power of negative 3 multiplied by 3 to the power of 4 multiplied by 4 to the power of 2 whole over 3 to the power of 5 multiplied by 4 to the power of negative 2
To simplify the expression, combine the exponents and evaluate the values to get the simplified expression 1/12.
Explanation:To simplify the expression, we can combine the exponents of the same base. Let's break it down step-by-step:
Combine the exponents of 4: (-3+2) = -1Combine the exponents of 3: (4-5) = -1Combine the exponents of 4: (2-2) = 0So, the simplified expression is 4-1 * 3-1 * 40. Any number raised to the power of 0 is equivalent to 1, so the expression can be further simplified to 4-1 * 3-1 * 1. Finally, we can evaluate the values: 4-1 = 1/4, and 3-1 = 1/3.
Therefore, the simplified expression is (1/4) * (1/3) = 1/12.
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The expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex] simplifies to [tex]\(\frac{4}{3}\).[/tex]
To simplify the expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex], follow these steps:
Combine the exponents for the similar bases using the exponent rules.For the base 4: [tex]\(4^{-3 + 2} \times 4^{2} \times 4^{2}\)[/tex]Combine into: [tex]\(4^{-3 + 2 + (-(-2))} = 4^1\)[/tex]For the base 3: [tex]\(3^4 / 3^5 = 3^{4-5} = 3^{-1}\)[/tex]Simplify the expression: [tex]\(\frac{4}{3}\)[/tex]So the simplified expression is [tex]\(\frac{4}{3}\)[/tex] .
Corrected question:
What is the simplified expression for [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex]
Find the value of x if A,B,and C are collinear points and B is between A and C. AB=3x, BC=2x-7, AC=2x+35
Answer:
x = 14
Step-by-step explanation:
3x+2x-7=2x+35
then solve for x
Answer:
x = 14
Step-by-step explanation:
We are given that A, B and C are collinear points and B is in between A and C.
The length from A to B is [tex] 3 x [/tex], length from B to C is [tex] 2x - 7 [/tex] and AC is [tex] 2 x + 35 [/tex].
We are to find the value of x.
[tex] A B + B C = A C [/tex]
[tex] 3 x + 2 x - 7 = 2 x + 3 5 [/tex]
[tex] 3 x + 2 x - 2 x = 3 5 + 7 [/tex]
[tex] 3 x = 4 2 [/tex]
[tex] x = \frac { 4 2 } { 3 } [/tex]
x = 14
How to solve a Solve 4(3x-1) = 20
Answer:
x = 2
Step-by-step explanation:
expand the brackets firstly,
so 12x-4 = 20
then add the -4 onto the other side
so 12x = 24
then divide 24 by 12 to get x
so x = 2
the student council at Madison Middle School has five sixth graders 5 7 grade and 5 eight graders. 1 student council member will be selected at random to represent the school at a conference what is the probability that the selected student council member will be in the 7th grade
5/15 or 1/3 would be the correct answer
HELP!!!!
Write an explanation for both Part A and B using 3-4 complete sentences.
Part A:
Explain how you can determine if a system of equations will have no solution when comparing the graph of the equations.
Part B:
Explain how you can determine if a system of equations has no solution by comparing each algebraic equation.
Be sure that your explanation includes 3 of the 4 words below:
-parallel
-slope
-y-intercept
-slope intercept form
Answer:
See below.
Step-by-step explanation:
Part A: A system will have no solution when the graphs are parallel and do not intersect.
Part B: A system will have no solution when the equations have the exact same slope. The same slope means they are parallel and do not intersect. This is done easiest in slope-intercept form.
If 30% of the students in Mrs.Rutherfords class like chocolate ice cream, then how many students are in Mrs. Rutherford’s class if six like chocolate ice cream
Answer: 20
Step-by-step explanation:
6/30 = 0.2
0.2 times 100 = 20
Final answer:
After setting up a proportion and solving the equation 0.30x = 6, we find that there are 20 students in Mrs. Rutherford's class.
Explanation:
To determine how many students are in Mrs. Rutherford's class when 30% like chocolate ice cream and we know that 6 students like chocolate ice cream, we can set up a proportion where 30% (or 0.30) of the total number of students (which we will call x) is equal to 6. Therefore, the equation to find x is 0.30x = 6.
To solve for x, we divide both sides of the equation by 0.30:
0.30x = 6
x = 6 / 0.30
x = 20
So, there are 20 students in Mrs. Rutherford's class.
Your yard is in a shape of a trapezoid
Answer:
1725
Step-by-step explanation:
50+65=115 divided by 2 =57.5 57.5*30H= 1725
An animal shelter has a total of 275 animals composed of dogs and cats. The number of cats is 5 more than one half of the number of dogs. How many dogs are in the shelter?
Answer: There are 180 dogs in the shelter.
Step-by-step explanation:
Let be "c" the number of cats in the shelter and "d" the number of dogs in the shelter.
You know that the total number of dogs and cats in the animal shelter is 275. Then you can express this with:
[tex]d+c=275[/tex]
If the number of cats is 5 more than one half of the number of dogs, you can express it with:
[tex]c=\frac{d}{2}+5[/tex]
Then, substitute [tex]c=\frac{d}{2}+5[/tex] into [tex]d+c=275[/tex] and solve for "d" to calculate the number of dogs that are in the shelter. Then:
[tex]d+c=275\\\\d+\frac{d}{2}+5=275\\\\d+\frac{d}{2}=275-5\\\\\frac{2d+d}{2}=270\\\\\frac{3d}{2}=270\\\\3d=270*2\\\\d=\frac{540}{3}\\\\d=180[/tex]