In the town of Rockville, 3/5 of the students in middle school participate in organized sports after school. If 1/4 of them play basketball, what fraction of the students play basketball?
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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Find the value of 2a + 3b
Answer: 19
Step-by-step explanation:
Using the sum of an arithmetic series formula,
[tex]\sum^{30}_{n=2} (an+b)=2407 \implies 29(16a+b)=2407 \implies 16a+b=83\\\\\sum^{40}_{n=1} (an+b)=4220 \implies 20(41a+2b)=4220 \implies 41a+2b=211[/tex]
Multiplying the second equation by 2 gives us [tex]32a+2b=166[/tex].
Subtracting this from the second equation, we get that [tex]9a=45 \implies a=5[/tex].
Substituting this back into the first equation, we get that [tex]b=3[/tex].
Therefore, [tex]2a+3b=2(5)+3(3)=19[/tex]
2x-3/x divided 7/x^2
Answer:
2x-3/7x
Step-by-step explanation:
scientist released 8 rabbits into a new habitat in year 0. Each year, there were twice as many rabbits as the year before. How many rabbits were there after X years? Write a function to represent this scenario.
Answer:
Step-by-step explanation:
his function will be an exponential function, because the number of rabbits double each year
the basic form for exponential functions is
where s is the starting number, c i s the constant (rate of change like double, triple, etc.) and x is the number repeats (in this case, years)
so in this case, the starting number (year 0) is 8, and the rate of change is 2
therefore, the equation is:
f(X) =8 times 2
hope this helps!
p.s. can i have brainliest?
The graph of a line passes through the two points below
(2,-4);(-3,1)
Which of these can be used to determine the slope of the line
The expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)
What are slopes?The slope of a line is the gradient or the average rate of change of the line or a line equation
Note that linear equations are equations that have constant average rates of change, slope or gradient
How to determine the slopes?The two points are given as
(2,-4);(-3,1)
The slope of a line is calculated using
m = (y2 - y1)/(x2 - x1)
Substitute the coordinates of the points in the above equation
m = (1 + 4)/(-3 - 2)
Evaluate the numerator
m = 5/(-3 - 2)
Evaluate the denominator
m = 5/-5
Rewrite the quotient as
m = -5/5
Evaluate the quotient
m = -1
Hence, the expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)
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someone please help me with this
Answer:
x = 60 degrees
Step-by-step explanation:
1. We know that a triangle has a total angle of 180. If we look at the image closely, triangle GEH can be found, and since we know two angles, which are 40 and 80, we can find the other angle. 180 - (40+80) = 60. Angle GEH is 60 degrees.
2. If angle GEH is 60 degrees, angle EFD will also be 60 degrees, since they have the same angle side. To prove this, we can use alternate interior angles. This means that if a line crosses two parallel lines, the inner angles made have the same size.
3. Since angle EFD is x, we can find that x is equal to 60 degrees.
• If a doctor orders 60mg of Benadryl, and each tablet contains 7 mg, how many tablets should
be given to the patient?
• Also, if the patient is only to take 1 tablet per day, how many days should the patient stay on the
medication?
A patient should be given 8 and a half tablets and Approx. 8 days should the patient stay on the medication.
How many tablets should be given to the patient and how many days should the patient stay on the medication?Given:
A doctor orders 60mg of Benadryl.Each tablet contains 7 mg.To find:
How many tablets should be given to the patient?If the patient is only to take 1 tablet per day, how many days should the patient stay on the medication?Solution:
If each tablet contains 7 mg and the doctor orders 60 mg of Benadryl.
Then the patient should be given 60/7 tablets i.e., 8 and a half tablets.
If the patient is only to take 1 tablet per day, then approx 8 days the patient we stay on the medication.
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3 p2 9 p = 6 Add 6 to both sides to set the right side to o 3 p2 9 p 6=04 Divide everything by 3 p2 3 p 2 =0 ( P 1)(p 2) = 0 P 1 = 0 OR P 2 = 0 P=-1 P= -2
The solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2
Finding the solution of a quadratic equation
The given equation is:
[tex]3p^2-9p=6[/tex]
This can be re-written as:
[tex]3p^2-9p-6=0[/tex]
Solve for p by factorization
[tex]3p^2-3p-6p+6=0\\\\3p(p-1)-6(p-1)=0\\\\(3p-6)(p-1)=0[/tex]
Equate each of the factors to zero
3p - 6 = 0
3p = 6
p = 6/3
p = 2
p - 1 = 0
p = 1
Therefore, the solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2
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Choose the correct product of (6x - 2)(6 x + 2).
The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4
How to determine the product?The expression is given as:
(6x - 2)(6 x + 2).
The above expression is a difference of two squares.
And this is represented as
(a - b)(a + b)= a^2 - b^2
So, we have
(6x - 2)(6 x + 2) = (6x)^2 - 2^2
Evaluate
(6x - 2)(6 x + 2) = 36x^2 - 4
Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4
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For a population with a mean of μ = 72 and a standard deviation of σ = 8, find the z-score corresponding to the sample mean M= 80 and sample size n = 22 scores.
The z score corresponding to the sample is -6.25
z-score of a populationThe formula for calculating the z-score is expressed as
z = x- μ/σ
Given the following parameters
x = 22 (sample size)
Mean μ = 72
standard deviation σ = 8
Substitute
z = 22-72/8
z = -50/8
z = -6.25
Hence the z score corresponding to the sample is -6.25
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What is the distance between point (3, 2) and line
1
y=-x-9
4
Select the best answer from the cholces provided.
OA.
OB. 41
√5
O C.
41
√17
O D.
13
2
2
√17
The distance between the coordinate point (3, 2) and line y = ¹/₄x - 9 is; 10.25 units
How to find the distance between a line coordinate?
We want to find the distance between the coordinate point (3, 2) and line y = ¹/₄x - 9.
Thus, we will plug in 3 for x in the line equation given to get;
y = ¹/₄(3) - 9
y = 0.75 - 9
y = -8.25
Thus, we can say that point on the line is (3, -8.25)
The difference in y-values would give us the required distance;
Required distance = -8.25 - 2
Required distance = -10.25
However distance cannot be negative and so we will take the absolute value as 10.25 units.
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Which statement correctly describes the diagram?
On a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C.
1. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A..
2. Triangle B is a reflection of triangle A across the y-axis. Triangle C is a reflection of triangle A across the line y = x + 3.
3. Triangle B is a reflection of triangle A across the y-axis. Triangle C is not a reflection of triangle A.
4. Triangle B is a reflection of triangle A across the x-axis. Triangle C is a reflection of triangle A across the line y = x + 3.
The correct statement is Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A.
Given that in a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C.
From the given figure , it says that Triangle B is a reflection of triangle An across the x-pivot. Triangle C isn't a reflection of triangle A" in light of the fact that Triangle A is in the main quadrant and its appearance with x-axis makes the triangle-B in the fourth quadrant and the triangle C which is in second quadrant can not be a reflection and annot be a rotation of triangle-A. Triangle C is drawn by taking firstly the reflection of triangle A and then rotate on the same place and increased x+3 units in above direction.
Hence, the statement correctly describes the diagram is "Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A".
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Answer:
A. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A..
Step-by-step explanation:
goodluck
The average heart rate of an adult human is 72 beats per minute. For an adult elephant, the average heart rate is 35 beats per minute.
A. Whose heart beats more times in one hour
B. Whose heart makes 1,000,000 beats in less time
Answer:
A. the adult human
B. the adult human
Step-by-step explanation:
A. There are 60 minutes in an hour, and the human's heart beats 72 bpm (beats per minute). If you multiply 60 by 72, you get 4,320 bpm. If you multiply 60 by 35, you only get 2,100 bpm.
B. If you use the same logic that 72 is greater than 35, than you can assume that the human hear makes 1,000,000 beats in less time. However, if you want to do the math, then simply divide 1,000,000 by 72. Then, divide 1,000,000 by 35. Whichever has the smaller number is the one that can make more heart beats in a faster time.
Which is the equation of the given line?
x = 4
y = 3
y=−2x
y = x
Number graph that ranges from negative five to five on the x and y axes. A line passes through the labeled points (four, three) and (four, negative two).
Since the x-coordinates are equal, hence the equation of the line will be x =4
Equation of a lineThe equation of a line in slope-intercept form is expressed as:
y = mx + b
where
m is the slope
b is the intercept
From the given coordinate points (four, three) and (four, negative two), we can see that the x-coordinates are equal, hence the equation of the line will be x =4
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Between permanent life insurance and term life insurance, which typically has the lower premium and why?
a.
Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life.
b.
Term life insurance has the lower premium because you cannot renew the insurance after your term has ended.
c.
Permanent life insurance has the lower premium because you are making more premium payments (your whole life versus a set period of time), so the amount per premium payment is less.
d.
Permanent life insurance has the lower premium because the amount you contribute is then invested and makes interest for the life insurance company.
Please select the best answer from the choices provided
A
B
C
D
Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life. (Option A)
What is insurance?Insurance is when a third-party (the insurer) promises to indemnify another party (the insured) for losses they might suffer in the future in exchange for agreed upon payments.
Permanent life insurance is a type of insurance that provides a coverage that never expires. The person with a permanent life insurance is covered until he or she passes on. Whole life insurance is a type of permanent life insurance that has a fixed and guaranteed premium and a fixed death benefit.
Term life insurance is a type of insurance that provides coverage to a person only for a scheduled period of time. For example, a person who buys a 10 year term life insurance, the person's insurance only lasts for 10 years. If the person passes on within the 10 years, his beneficiary receives payments. If the person passes on after 10 years, his beneficiary does not receive any payments.
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The cost price was $10000 she made a down payment of 2500 and agreed to pay the balance in 24 monthly installments of $350 how much did Jen pay for microwave?
Answer:
in total she spent 10900
Step-by-step explanation:
We know she made a down payment of 2500 dollars and she agreed to pay the balance in 24 monthly installments of 350 dollars. Thus we can do simple multiplying of 24 x 350 which gives us 8400. We also need to add in her down payment which is 2500 so in total we got 10900
Polygon ABCD is rotated 90º counterclockwise about the origin to create polygon A′B′C′D′. Match each set of coordinates to the vertices of polygon A′B′C′D′. (-1, 3)
B′
(-2, 2)
C′
(-2, 1)
D′
(-1, 1)
Answer:Rules for rotating points about the origin
1. The point (a,b) rotated 90° counterclockwise about the origin
becomes (-b,a).
A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)
A (a,b)-----------------A′ (-b,a)=(-1, 3)----------->A( 3,1)
B (a,b)-----------------B′ (-b,a)=(-2, 2)----------->B( 2,2)
C (a,b)-----------------C′ (-b,a)=(-2, 1)----------->C( 1,2)
D (a,b)-----------------D′ (-b,a)=(-1, 1)----------->D( 1,1)
Step-by-step explanation:
A group of neighbors is holding an end of summer block party. They buy p packs of hot
dogs, with 8 hot dogs in each pack. All together, they have 56 hot dogs for the party.
Write an equation to describe this situation.
How many packs of hot dogs did the neighbors buy?
Answer:
7 packs of hots dogs if they had 56 for the party 8 divided by 56 is 7
The equation is 8p=56. Hence p=7 and they bought 7 packs of hot dogs. Hope it helps : )
find an angle measure of angle A and B
A (5y-3)
C (3y+27)
The measure of angle A and C will be 94.5° and 85.5°.
How to calculate the angle?(5y - 3) + (3y + 27) = 180
Collect like terms
5y + 3y - 3 + 27 = 180
8y = 180 - 27 + 3
8y = 156
y = 156/8 = 19.5
(5y - 3) = (5 × 19.5) - 3 = 94.5
(3y + 27) = (3 × 19.5) + 27 = 85.5
Therefore, the measure of angle A and C will be 94.5° and 85.5°.
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43 POINTS!!,!,!!,!,!!
Alex went to a furniture shop to buy chairs and tables for his cafe. Find the maximum numbers of chairs he can buy if, he spent $300 for 3 tables cost of 1 chair is $30 and, he cannot spend more than $800 on the furniture.
Answer:
16 chairs
Step-by-step explanation:
800 - 300 = 500
500/30 = 16.6 since it's money you can only afford 16
PLS HELP OR I WILL FAIL I BEG U HELP
Answer:
The first one, you cannot factor because the two values do not share any common factors. Hence, the answer would just be:
a. 51x-25
The other one, we can factorise to:
b. 3x(4-x)
Step-by-step explanation:
For the second option:
Common factor between 12x and 3x^2 is 3x.
Take this out to the front, we are left with:
3x(4-x)
A website I recommend you use (math calculator with some instructions) is Symbolab.
https://www.symbolab.com/solver/factor-calculator/factor%2012x-3x%5E%7B2%7D?or=input
The function P=48∙e^((.045t)) gives the number of bacteria in a population as a function of time in hours.
a) How many bacteria are there in t = 8 hours? *Accurate to four decimal.
b) How fast is this population growing in t = 8 hours? *Accurate to four decimals.
The number of bacteria when t = 8 is approximately 66 bacterias
Exponential functionsGiven the function that gives the number of bacteria in a population as a function of time in hour expressed as:
P=48∙e^((0.045t))
If the value of t is 8, hence;
P=48∙e^((0.045(8))
P = 48e^0.36
P = 65.933
Hence the number of bacteria when t = 8 is approximately 66 bacterias
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Factor the greatest common binomial factor from each polynomial
6x^2(5x-1) +5x-1
The factored polynomial is given as follows:
(5x - 1)(6x² + 1)
How are polynomials factored?Polynomials are factored placing the common factor in evidence, then dividing all terms by the common factor.
The polynomial is:
6x²(5x - 1) + (5x - 1).
The common factor is (5x - 1), hence:
[tex](5x - 1)\left(\frac{6x^2(5x - 1)}{5x - 1} + \frac{5x - 1}{5x - 1}\right) = (5x - 1)(6x^2 + 1)[/tex]
Hence the factored polynomial is given as follows:
(5x - 1)(6x² + 1)
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Find the slope of a line parallel to a line that contains the points (8, -3) and (2, 5).
Select the best answer from the choices provided.
OA
413
OB. 4
O D.
413
3
OC 3
3|4
314
Answer:
[tex]-\frac{4}{3}[/tex](Your answer choices were really confusing, so I just put the plain answer)
Step-by-step explanation:
To find the slope of a line with just two points, we can use the formula [tex]\frac{y2-y1}{x2-x1}[/tex]. In this case, [tex]\frac{5-(-3)}{2-8}[/tex]. This is [tex]\frac{8}{-6}[/tex]. This reduces to [tex]-\frac{4}{3}[/tex]
What is the equation,in point-slope from ,of the line that is perpendicular to given line and passes through the point (-4,-3)?
The equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is y + 3 = 1/4(x + 4)
How to determine the equation of the line?The complete question is added as an attachment
The points on the line are given as:
(-1, 1) and (0, -3)
Start by calculating the slope of the line using
m = (y2 - y1)/(x2 - x1)
The slope of the perpendicular line is
m2 = -(x2 - x1)/(y2 - y1)
So, we have:
m2 = -(0 + 1)/(-3 - 1)
This gives:
m2 = 1/4
The equation of the line is then calculated as
y - y1 = m(x - x1)
This gives
y + 3 = 1/4(x + 4)
Hence, the equation, in point-slope from, of the line that is perpendicular to the given line and passes through the point (-4,-3) is y + 3 = 1/4(x + 4)
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Solve the proportion
12
8
=
7.5
x
Answer:
9.8 is the final anwser
Step-by-step explanation so easy
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs \$8 dollar sign, 8.
Let R represent the number of additional rolls that Sofia orders.
Sofia will order 7 more rolls of sushi (84 pieces) and pay $56St
Step-by-step explanation: im right
Joy wants to invest $3000 in a savings account. Determine the interest rate (simple interest) required for Joy 's investment to double in value in 18 years. Round your answer to the nearest tenth of a percent.
The interest rate needed to double the investment in 18 years is 6%.
What is the interest rate?Interest earned is a function of the amount invested, interest rate and time. The future value of the investment is to be $6000 (3000 x 2). Interest earned would be $3000 (6000 - 3000)
Interest rate = interest earned / (amount invested x time )
$3000 / ($3000 x 18) = 6%
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Find the value of t for which (4,6,3, t) is a linear combination of (1,3,-4,1), (2,8,-5,-1) and (-1,-5,0,2)
The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.
How to find a vector as a linear combination of other vectors
In this question we must solve for t such that (4, 6, 3, t) is a linear combination of vectors (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2), which means that non-zero coefficients have to be found by algebraic handling:
(4, 6, 3, t) = α₁ · (1, 3, - 4, 1) + α₂ · (2, 8, - 5, - 1) + α₃ · (- 1, - 5, 0, 2)
Which is equivalent to this system of linear equations:
α₁ + 2 · α₂ - α₃ = 4
3 · α₁ + 8 · α₂ - 5 · α₃ = 6
- 4 · α₁ - 5 · α₂ = 3
α₁ - α₂ + 2 · α₃ - t = 0
Whose solution is (α₁, α₂, α₃, t) = (38, - 31, - 28, 13). The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.
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Question 4 (Essay Worth 10 points)
(07.03, 07.05 HC)
Use the function f(x) = 2x²-5x+3 to answer the questions.
Part A: Completely factor f(x). (2 points).
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points) HELP ASAP
Part A
[tex]f(x)=(x-1)(2x-3)[/tex]
Part B
[tex](x-1)(2x-3)=0\\\\x=1, \frac{3}{2}[/tex]
So, the x-intercepts are [tex](1,0)[/tex] and [tex]\left(\frac{3}{2}, 0 \right)[/tex]
Part C
As [tex]x \to \infty[/tex], [tex]f(x) \to \infty[/tex] because the leading coefficient is positive.
As [tex]x \to -\infty[/tex], [tex]f(x) \to \infty[/tex] because the degree is even and the leading coefficient is positive.
Part D
Plot the x-intercepts on the graph, and then find the value of [tex]f(x)[/tex] at [tex]x=\frac{5}{4}[/tex] (the midpoint of the two roots) to plot the vertex. Then, draw a curve through these three points that approaches infinity as [tex]x \to \pm \infty[/tex]