The fraction of students that play basketball is [tex]\mathbf{= \dfrac{1}{10}}[/tex].
What is the fraction of students that play basketball?The fraction of students that play basketball from the given information can be determined by assuming that the whole number of students in the middle school is whole i.e. (1)
Let us first determine the number of students that participate in sports, we have:
[tex]\mathbf{=1- \dfrac{3}{5}}[/tex]
[tex]\mathbf{= \dfrac{2}{5}}[/tex]
If 1/4 of these students play basketball, then we have:
[tex]\mathbf{= \dfrac{1}{4}\times (\dfrac{2}{5})}[/tex]
[tex]\mathbf{= \dfrac{1}{10}}[/tex] students play basketball.
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will give brainliest!!
Answer:
[tex]\huge\boxed{\sf n = 49}[/tex]
Step-by-step explanation:
Given expression:[tex]x^2-14x+n[/tex] ---------------(1)
We need to solve it using the following formula:
[tex]a^2-2ab+b^2=(a-b)^2[/tex]
Writing the middle term in the expression as 2ab
[tex](x)^2-2(x)(7)+n[/tex]
Form the expression, we come to now that
b = 7So, the we can write the expression as:
[tex](x)^2-2(x)(7)+(7)^2\\\\x^2-14n+49[/tex]
Comparing expression (1) with the above expression, we get:
n = 49[tex]\rule[225]{225}{2}[/tex]
What is the completely factored form of f(x) = x3 – 2x2 – 5x + 6?
f(x) = (x + 2)(x – 3)(x + 6)
f(x) = (x + 2)(x – 3)(x – 6)
f(x) = (x – 2)(x + 3)(x – 1)
f(x) = (x + 2)(x – 3)(x – 1)
Answer:
The last option, (x+2)(x-3)(x-1)
Step-by-step explanation:
The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,
⇒ f (x) = (x - 1) (x - 2) (x - 3)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
Function is,
⇒ f (x) = x³ - 2x² - 5x + 6
Now, We can factor the function as;
Since, 1 is a root of function as it satisfy the function.
So, One factor is,
⇒ (x - 1)
Find another roots as;
(x - 1) ) x³ - 2x² - 5x + 6 ( x² - x - 6
x³ - x²
----------
- x² - 5x
- x² + x
-------------
- 6x + 6
- 6x + 6
------------
0
Hence,
⇒ f (x) = x³ - 2x² - 5x + 6
⇒ f (x) = (x - 1) ( x² - x - 6 )
⇒ f (x) = (x - 1) ( x² - 3x - 2x - 6)
⇒ f (x) = (x - 1) ( x (x - 3) - 2 (x - 3))
⇒ f (x) = (x - 1) (x - 2) (x - 3)
Hence, The completely factored form of f (x) = x³ - 2x² - 5x + 6 is,
⇒ f (x) = (x - 1) (x - 2) (x - 3)
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Given the graph of g(x), describes the transformation of the parent function f(x)=2^x
Answer:
The transformation being described is from g(x)=x2 g ( x ) = x 2 to f(x)=x2 f ( x ) = x 2 . The horizontal shift depends on the value of h . The horizontal shift is described as: f(x)=f(x+h) f ( x ) = f ( x + h ) - The graph is shifted to the left h units
how do you find the area and perimeter
area is multiplication
perimiter is adding the numbers on each side, for example, if the right side is 7, the left side will be 7. Add them and it will givey ou 14
) Explain why the expression x2 + (p + q )x + pq leads to the need to determine integers that add to b and have a product c when factoring a trinomial of the form x2 + bx + c.
The reason why the expression x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c is because they follow the FOIL Technique
How to factorize Quadratic Equations?We want to explain why x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c.
Now, using the FOIL Technique we can say that the factors are;
(x + p)(x + q)
Expanding this gives;
x² + px + qx + pq
⇒ x² + (p + q)x + pq
Now, applying that to the trinomial; x² + 6x + 8, we can say that;
p + q = 6, and pq = 8
Thus, solving simultaneously gives;
p = 2 and q = 6.
Thus;
x² + 6x + 8 = (x + 2)(x + 6)
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Would the horizontal translations shift the square root right or left? Sort each into the appropriate category.
f(x)=√x+0.8
f(x)=√x-4.7
f(x)=√x-25
f(x)=√x+6
f(x)=√x-11
Answer:
Step-by-step explanation:
Shift right
f(x)=√x-4.7
f(x)=√x-25
f(x)=√x-11
Shift left
f(x)=√x+0.8
f(x)=√x+6
A rental car company charges $20 per day to rent a car and $0.10 for every mile driven. Addison wants to rent a car, knowing that:
She plans to drive 100 miles.
She has at most $80 to spend.
Considering the definition of an inequality, the inequality that can be used to determine x is 20x + 10≤ 80
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
This caseA rental car company charges $20 per day to rent a car and $0.10 for every mile driven.
Addison wants to rent a car, knowing that:
She plans to drive 100 miles.She has at most $80 to spend.On the other hand, x represents the maximum number of days Alyssa can afford to rent for while staying within her budget.
Then, the inequality that can be used to determine x is:
20x + 0.1×100≤ 80
So:
20x + 10≤ 80
In summary, the inequality that can be used to determine x is 20x + 10≤ 80
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A bag contains 3 red balls, 4 green balls, and 2 yellow balls. Deborah reaches into the bag and pulls out the following 4 balls: red, red, green, yellow Deborah reaches into the bag to pick out another ball. What's the probability that the ball she picks is green?
The probability that the ball Deborah picks is green is; 3/5.
What is the probability that the ball picked last is green?Since the bag initially contains; 3 red balls, 4 green balls, and 2 yellow balls, after Deborah pulls out the 4 balls: red, red, green, yellow.
The balls remaining are; 1 red ball, 3 green and 1 yellow.
Hence, the probability that the final ball she picks is green is; 3/(3+1+1) = 3/5.
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R = 15 when m = 6 s= 4 inversely when m=24 s =4
The value of r If r varies directly with the square of m and inversely with s is 240
Variation
Suppose r varies directly with the square of m and inversely with s.
If r varies directly with the square of m and inversely with s, then;
r = km²/s
Given that R = 15 when m = 6 s= 4
15 = k(6)²/4
60 = 36k
k = 60/36
k = 5/3
If the value of m = 24 and s = 4, hence;
r = 5/3*24²/4
r = 240
Hence the value of r If r varies directly with the square of m and inversely with s is 240
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3⁵.2⁴.2¹.3⁶.(3²)⁴ and down (2³)².3⁶
Answer:
[tex]\dfrac{3^{13}}{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot (3^2)^4}{(2^3)^2 \cdot 3^6}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \dfrac{3^5 \cdot 2^4 \cdot 2^1 \cdot 3^6 \cdot 3^8}{2^6 \cdot 3^6}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \dfrac{3^{(5+6+8)} \cdot 2^{(4+1)}}{2^6 \cdot 3^6}[/tex]
[tex]\implies \dfrac{3^{19} \cdot 2^{5}}{2^6 \cdot 3^6}[/tex]
[tex]\implies \dfrac{3^{19} \cdot 2^{5}}{3^6 \cdot 2^6}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 3^{(19-6)} \cdot 2^{(5-6)}[/tex]
[tex]\implies 3^{13} \cdot 2^{-1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{3^{13}}{2^1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]
[tex]\implies \dfrac{3^{13}}{2}[/tex]
Answer:
The result is 3¹³ /2
Step-by-step explanation:
Greetings
What are the values of a₁ and r of the geometric series?
2-2+2-2+2
O
a₁ = 2 and r=-2
O a₁ = -2 and r = 2
O
a₁ = -1 and r = 2
a₁ = 2 and r=-1
Answer:
Step-by-step explanation:
Therefore, the values of
a
1
and r are 2 and -1, respectively.
The values of a₁ and r of the geometric series are 2 and -1 respectively.
What is Geometric Sequence?Any term divided by the preceding term is a constant in a geometric series. The common ratio of the sequence is the name given to this constant. Any term in the sequence can be divided by the prior term to determine the common ratio.
We have the series 2, -2, 2, -2, ......
Here, The first term is 2.
and, the Common Ratio = -2 / 2
= 2/(-2)
= -1
So, the first term is 2 and r is -1.
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Tim wants to build a rectangular fence around his yard. He has 42 feet of fencing. If he wants the length to be twice the width. What is the largest possible length
Answer: The largest he can possibly build is x = 14
Step-by-step explanation:
A board is 59.69cm long. How long is the board in inches ? Use the following conversion 1in is 2.54cm
Answer:
Given,
1in= 2.54cm
59.69cm=
[tex] \frac{59.69}{2.45} in[/tex]
=23.5 in
A cellular network transmits its signals in a circular pattern. The tower is considered the origin, (0,0), of the signal and there is a house located on the edge of the circle at (2, 4). Which of the following coordinates could represent the location of another house that is also on the edge of the circle?
A.(1.3)
B.(-2,-4)
C.(3,3)
D.(4,4)
Answer:
B
Step-by-step explanation:
because at origin they are both positive and when it rotates about 270 both will change to negative
Determine whether AB and CD are parallel, perpendicular, or neither. A(-3, 2), B(5, 1), C(2, 7), D(1, -1)
Answer:
perpendicular
Step-by-step explanation:
We'll find the slope of both lines and see what it tells us.
If the slopes are the same, the lines are parallel. If the slopes are opposite sign and flipped (negative reciprocals) then they are perpendicular.
The slope is y-Y on top of a fraction and x-X on the bottom.
Slope of AB:
m = 2-1 / -3 -5
= 1/-8 = -1/8
Slope of CD:
m = 7- -1 / 2-1
= 8/1 = 8
Since the slopes are -1/8 and 8, the lines are perpendicular, because they are opposite sign and flipped (negative reciprocals)
Find the shortest distance from A to B in the diagram below. A. 505‾‾‾‾√ m B. 17 m C. 329‾‾‾√ m D. 10 m
The shortest distance from A to B in the diagram is 17 m.
How to find the shortest distance?The shortest distance from D to B can be found as follows:
using Pythagoras theorem,
c² = a² + b²
where
c is the hypotenusea and b are the other legsTherefore,
DB² = 15² + 8²
DB² = 225 + 64
DB² = 289
DB = √289
DB = 17 m
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Answer:
B, 17 m
Step-by-step explanation:
Founders 23
Find the value of t; log3y=2 and log3ty=6
Answer: [tex]10^4[/tex]
Step-by-step explanation:
Assuming we are using the common log (base 10),
[tex]\log 3ty=6\\\\\log 3y +\log t=6\\\\2+\log t =6\\\\\log t=4\\\\t=10^4[/tex]
13)
Medical officials want to determine if birth weights are lower than usual in Southeast Asia. They randomly weigh 100 babies, and they determine that the average birth weight is 6 pounds 8 ounces.
State the variable.
What are the units for the variable?
State the population.
State the sample.
POINTS Out OF
7
What is the individual.
What is the Parameter.
What is the statistic.
See below for the response to each question
The variableThis is the item that is being surveyed.
The surveyed item is birth weights
Hence, the variable is birth weights
The units of the variableFrom the question, we have:
Average birth weight is 6 pounds 8 ounces.
Hence, the units of the variable are pounds and ounces
The populationThis is the total number of babies in Southeast Asia
Hence, the population of interest is the babies in Southeast Asia
The individualThis is the people in the survey
Hence, the individual in the study is the 100 babies that were randomly surveyed
The parameter of interestThis is the value that gives the required information.
Hence, the parameter of interest is the average birth weight
What is the statistic involvedThe statistic is the average
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Multiply.
x²+3x+2
x 2x²+3x-1
OA. 2x¹ +9x² + 12x² + 3x-2
OB. 2x¹ +9x2 - 2
OC. 3x2 + 6x +1
OD. 2x¹ +21x² + 3x-2
The multiplication of the expression (x² + 3x + 2) (2x² + 3x + 1) is 2x⁴ + 9x³ + 14x² + 9x + 2
Multiplication(x² + 3x + 2) (2x² + 3x + 1)
= 2x⁴ + 3x³ + x² + 6x³ + 9x² + 3x + 4x² + 6x + 2
collect like terms= 2x⁴ + 3x³ + 6x³ + x² + 9x² + 4x² + 3x + 6x + 2
= 2x⁴ + 9x³ + 14x² + 9x + 2
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The difference of four times a number and seven is 21
Answer: 4n - 7 = 21, n = 7
Step-by-step explanation:
A difference indicates subtraction of two terms. Four times a number indicates that a number of any value has to be multiplied by 4.
Hence, the equation that is represented by the question is
[tex]4x - 7 = 21[/tex]
We can also solve this equation (i.e., find the value of x that makes this equation true).
Adding 7 to both sides, we get
[tex]4x - 7 + 7 = 21 + 7[/tex]
Since the -7 and 7 add to 0, the equation becomes
[tex]4x = 28[/tex]
To get x by itself, we can divide both sides by 4, making the equation
[tex]x=7[/tex]
Hence, x must be 7 to make the equation true, or 7 is a solution to the equation.
For what values of x is the expression below defined?
√x+3 ➗√1-x
A. 3≤x≤1
B. 3>x>1
C. -3
D. 3> x≤-1
Answer: [tex]-3 \leq x < 1[/tex]
Step-by-step explanation:
[tex]\sqrt{x+3} \geq 0 \longrightarrow x \geq -3\\\\\sqrt{1-x} > 0 \longrightarrow 1-x > 0 \longrightarrow x < 1\\\\\therefore -3 \leq x < 1[/tex]
Please help ASAP!
What is the measure of arcXY shown in the diagram below?
Applying the angles of intersecting secants theorem, the measure of arc XY is: 32°.
How to Apply the Angles of Intersecting Secants Theorem?According to the angles of intersecting secants theorem, m∠XZY = 1/2(arc VW - arc XY).
Plug in the values:
39 = 1/2(110 - arc XY)
2(39) = 110 - arc XY
78 = 110 - arc XY
78 - 110 = - arc XY
-32 = - arc XY
Arc XY = 32°
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mangleR = 120° and mangleS = 100°. Find mangleT. The diagram is not drawn to scale.
What are the steps you would need to take to find slope from data?
A cash deposit box has five-dollar and ten-dollar bills in it totaling $450. There are eight times as many five-dollar bills as ten-dollar bills. How many bills are in the box?
Answer:
81
Step-by-step explanation:
60 POINTS IF CORRECT AND BRAINLIEST ANSWER FOR COMPLETE ANSWER
1. The solution to the first percent puzzle is as follows:
75% 66²/₃ 11¹/₉
33¹/₃% 25% 22¹/₅% 3⁷/₁₀%
50% 37¹/₂% 33¹/₃% 5¹/₂%
50% 37¹/₂% 33¹/₃% 5¹/₂%
2. The solution to the second percent puzzle is as follows:
10% 90%
50% 5% 45%
50% 5% 45%
What is a percent puzzle?A percent puzzle is a puzzle that engages students to practice working with percentages.
The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.
The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.
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You have nine line segments with the lengths of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.
How many ways are there to form a square by connecting the ends of some of these
line segments? No overlapping of the line segments is allowed.
The number of ways to forma a square by connecting the ends of some of the line segments is 3, 024 ways
What is permutation?From the given information, we should use the formula for permutation without repetition.
The formula is given as;
Permutation = [tex]\frac{n!}{n -r !}[/tex]
Where n = number of set = 9
r = 4, this is so because, the sides of a square a four
Permutation = [tex]\frac{9!}{9 - 4!}[/tex]
Permutation = [tex]\frac{9!}{5!}[/tex]
Permutation = [tex]\frac{362, 880}{120}[/tex]
Permutation = 3, 024 ways
Thus, the number of ways to forma a square by connecting the ends of some of the line segments is 3, 024 ways
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9
What is the price of a two year bond with a 9% annual coupon and a yield to maturity of 8%?
97.51
102.53
101.78
105.25
The price of a two-year bond is 101.78 and the correct option is C.
Given that a 9% annual coupon and a yield to maturity of 8%.
Simple yield is the amount of interest received by a bond issuer divided by the current market price of the associated bond.
Implicit Face value, FV=$100
Time, N=2 years
Coupon, C=(9/100)×$100=9
The yield of maturity, r=8%=0.08
Now, we will find the bond price using the formula
Price of bond = C× [1-{1/ (1+r)ⁿ}/r] +M/ (1+r)ⁿ
Substitute the values in this formula, we get
Price of bond=9×[1-{1/(1+0.08)²}/0.08]+100/(1+0.08)²
Price of bond=9×[1-{1/(1.08)²}/0.08]+100/(1.08)²
Price of bond=9×[1-{1/1.1664}/0.08]+100/1.1664
Price of bond=9×[(1-0.857)/0.08]+85.73
Price of bond=9×[0.143/0.08]+85.73
Price of bond=9×1.7875+85.73
Price of bond=16.0875+85.73
Price of bond=101.78
Hence, the price of a two-year bond with a 9% annual coupon and a yield to maturity of 8% is 101.78.
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The roots of the quadratic function describing the relationship between number of products produced and
overall profit margin are x = 0 and 26. The vertex is (13, -50).
The vertex is a minimum at (13, -50). The company actually loses money on their first few products as it
costs them more to make them, but once they hit 26 items they break even again.
The worst case scenario is that they produce
first root tells us that the profit will be 0 when
Check
items, as they will have a profit of
products are sold.
dollars.
In Economics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.
This ultimately implies that, all producers of any product generally work to maximize their profits and make them as large as possible, in order to enable them break even and successful.
Based on the information provided, we can logically deduce that this function has its roots at x = 0 and x = 26 and its vertex is a minimum. Thus, this quadratic function which describes the relationship between the number of products produced and the overall profit margin is an increasing function:
0 < x < 26, f(x) < 0, which implies a negative profit is generated when between 0 and 26 items are produced.x > 26, f(x) > 0, which implies a positive profit is generated when more than 26 items are produced.x is equal to 26 is the break even point.Therefore, once they hit 26 items they break even again. The worst case scenario is that they produce 13 items, as they will have a profit of -50 dollars because the minimum point is at (18, -35). Also, the first root tells us that the profit will be 0 when 0 products are sold.
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Which of the following rational functions is graphed below?
Answer:
D
Step-by-step explanation:
As the function approaches a certain x-value, it makes a very sharp turn and doesn't touch the axis as you can see in the graph. It does that because if the x-value is applied to the function, it would make it undefined. In this case, the graph is approaching x = -3 and x = +7 since at those points, the lines for the graph change suddenly. You would look for a function that if x is -3 or 7, it makes the y-value undefined.
Another way to easily do this would be to substitute values that are in front of the value that the graph is avoiding like 6 or 8 for 7 and -2 and -4 for -3. You can see if the y-values that would output from substituting those numbers are correct.