A soccer league is organizing teams. There are 60 boys to make up the boys' teams and 40 girls to make up the girls' teams. The teams should be the same size What is the largest number of people that can be on a team?The largest number of people that can be placed on a team is
There are 60 boys to make up the boys' teams and 40 girls to make up the girls' teams.
We are also told that the teams should be the same size.
This means that irrespective of the number of teams, each team should contain the same number of players.
Thus, the largest number of people that can be placed on a team is;
The highest common factor ;
The HCF is 10 x 2 = 20, therefore;
The largest number of people that can be placed on a team is 20.
if f(x)=2x^2+3x Find f(−5) step by step plese
The value of x for quadratic equation f(x) = 2x² + 3x when f(-5) is 35.
Given, f(x) = 2x² + 3x
To find: f(-5)
For the quadratic equation f(x) = 2x² + 3x substitute the value -5 in place of x as the f(-5) has been mentioned in the question.
So,
f(-5) = 2(-5)² + 3(-5)
A Square of -5 is 25 and 3 multiplied by -5 is 15,
f(-5) = 2(25) + (-15)
Multiple of 25 and 2 is 50 subtracted by 15,
f(-5) = 50 - 15
At last, subtract 50 by 15,
f(-5) = 35
∴ For equation f(x) = 2x² + 3x when f(-5), the value of x = 35.
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The volume of a cone with height
h
and radius
r
can be found using the formula
V
=
1
3
π
r
2
h
Find the volume of a cone with radius 8 feet and height 7 feet.
The volume of the cone has a value of 410.67 cubic meters
How to determine the volume of the cone?From the question. the height and the radius of the cone are given as
Height = 7 feet
Radius = 8 feet
The volume of the cone can be calculated using the following volume formula
Volume = 1/3πr^2h
Substitute the known values in the above equation
So, we have
Volume = 1/3 * 22/7 * 8 * 7^2
Evaluate the products
Volume = 410.67
Hence, the volume is 410.67 cubic meters
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what is the radius of the circle?
Answer:
The radius is from the middle to the edge, in this case it looks the radius is 4
6. Critical Thinking
Suppose point P divides the directed line segment XY so that the ratio of XP to PY is 3 to 5. Describe the
point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3.
Using proportions, the coordinates of the point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3 are given by:
[tex](x,y) = \left(\frac{3}{8}(x_y - x_x) + x_x, \frac{3}{8}(y_y - y_x) + y_x\right)[/tex]
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division from the given ratios.
Division of line segments is one application of proportions. The entire length of the line segment with endpoints XY is given by:
Y - X.
Now we have point P, dividing the line segment YX so that the ratio of YP to PX is 5 to 3, meaning that XP is 3/8 of XY, that is:
[tex]P - X = \frac{3}{8}(y - x)[/tex]
Then the x-coordinate of P is found as follows:
[tex]x - x_x = \frac{3}{8}(x_y - x_x)[/tex]
[tex]x = \frac{3}{8}(x_y - x_x) + x_x[/tex]
The y-coordinate is found applying the same rule with the y-coordinates of points X and Y, as follows:
[tex]y - y_x = \frac{3}{8}(y_y - y_x)[/tex]
[tex]y = \frac{3}{8}(y_y - y_x) + y_x[/tex]
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PLS HELPPPP
Is this right????
Answer:
yes that is the correct answers
The average flight time for the pilots is found to be 8.12 hours. The
standard deviation reported by the FAA is 0.72 hours, and there
were 81 pilots in the sample. What is the t-statistic for this
hypothesis test? Report to two decimal points
(Flights generally limit pilots to 8 hours of flight time during a 24-hour period)
The test statistic for this hypothesis test is; t = 1.5
What is the Test Statistic?
The formula for test statistic is;
t = (x' - μ)/(σ/√n)
where;
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
We are given;
Sample mean; x' = 8.12 hours
Population mean; μ = 8 hours
Standard deviation; σ = 0.72 hours
sample size ; n = 81 pilots
Thus;
t = (8.12 - 8)/(0.72/√81)
t = 0.12/0.08
t = 1.5
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is line k parallel to line /?
O a
Ob
122⁰
Yes
No
&
l
Answer:
Yes
Step-by-step explanation:
Parallel lines are 2 lines that go in the same direction that will never touch each other.
Hope that helps
A group of friends wants to go to the amusement park. They have no more than $325 to spend on parking and admission. Parking is $13, and tickets cost $39 per person, including tax. Write and solve an inequality which can be used to determine p, the number of people who can go to the amusement park.
Using inequality, we can conclude that maximum of 14 people can visit the amusement park.
What is inequality?A relation that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. On the number line, size comparisons between two numbers are typically made. Inequalities are relationships between two expressions that aren't equal to one another. The symbols, >, <, ≤, ≥ and ≠ are used to denote inequalities and mean "7 is greater than" (or "is less than 7," when read left to right).So, (p) a maximum number of people who can visit the park:
They can only spend a total of $325 on parking and admission.Parking costs $13 and tickets are $39 per person, tax included.Now, calculate as follows:
13+ $39p ≤ $325$39p ≤ $325 - $13p ≤ 14Therefore, using inequality, we can conclude that maximum of 14 people can visit the amusement park.
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Roy ate 2/3 of his personal pizza Roxy ate 3/5 of hers robbi ate 0.45 of hers and Russ ate 9/12 of his who ate the most of his or her pizza?
We will see that the largest number is 9/12, and Russ ate 9/12 of his pizza, so he is the one that ate most of his pizza.
Who ate the most of his/her pizza?Here we know that:
Roy ate 2/3 of his pizza.Roxy ate 3/5 of her pizza.Robby ate 0.45 of his pizza.Russ ate 9/12 of her pizza.So we just need to see which of the given numbers is the largest one.
We can rewrite the fractions as:
2/3 = 0.66
3/5 = 0.6
9/12 = 3/4 = 0.75
The largest number is 0.75, in this way we conclude that Russ is the one that ate more pizza.
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The mass of the Rock of Gibraltar is 1.78-102 kilograms. The mass of the Antarctic iceberg is 4.55-103 kilograms. Approximately how many more kilograms is the mass of the Antarctic iceberg than the mass of
the Rock of Gibraltar? Show your work and write your answer in scientific notation (10 points)
4.372 × [tex]10^{13}[/tex] more kilograms the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar.
Mass of the Antarctic iceberg = 4.55 × [tex]10^{13}[/tex]
Mass of the rock of Gibraltar = 1.78 × [tex]10^{12}[/tex]
Excessive mass of Antarctic Icebergs than the rock of Gibraltar,
4.55 × [tex]10^{13}[/tex] - 1.78 × [tex]10^{12}[/tex]
Subtract easily both should be in the same power of ten,
= 4.55 × [tex]10^{13}[/tex] - 1.78 × [tex]10^{12}[/tex]
= 43.72 × [tex]10^{12}[/tex]
= 4.372 × [tex]10^{13}[/tex]
Scientific notation is used to express quantities that are either too large or too little to be represented by decimals. Scientific format, standard index format, and standard format are other terms for the same thing.
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3 math questions multiple choice
1) the equation is:
[tex]2y+x=4[/tex]So we can rewrite the equation as a slope intercept so:
[tex]\begin{gathered} 2y=-x+4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]So the slope is -1/2
2) the equation is:
[tex]3x-2y=5[/tex]Now we evaluete the coordinates to see which one is not on the line so for (1,-1)
[tex]\begin{gathered} 3(1)-2(-1)=5 \\ 3+2=5 \\ 5=5 \end{gathered}[/tex]So is on the line
for (-1,-4)
[tex]\begin{gathered} 3(-1)-2(-4)=5 \\ -3+8=5 \\ 5=5 \end{gathered}[/tex]So it is on the line
for (3,2)
[tex]\begin{gathered} 3(3)-2(2)=5 \\ 9-4=5 \\ 5=5 \end{gathered}[/tex]So it is on the line
Finally for (1,2)
[tex]\begin{gathered} 3(1)-2(2)=5 \\ 3-4=5 \\ -1\ne5 \end{gathered}[/tex]So (1,2) is not on the line
3) if the slope is -2 and goes to the point (3,-1) we can use the equation of a line to find the intercept so:
[tex]\begin{gathered} y=-2x+b \\ -1=-2(3)+b \\ -1=-6+b \\ -1+6=b \\ 5=b \end{gathered}[/tex]So the intercept is 5 so the equation is:
[tex]y=-2x+5[/tex]Please help me
Thank you ;)
Answer:
they're similar
Step-by-step explanation:
hello again ;)
The distance between Dallas and Austin on a map is about 9 centimeters. The map uses a scale in which 1 centimeter represents 20 miles. What is the actual distance between Dallas and Austin in miles
please help due in an hour and i cannot fail!!!
Answer:
180
Step-by-step explanation:
9x20
in endurance horse racing, people over the age of 15 are called seniors and people 15 years or younger are called juniors. an endurance horse race consists of 30 seniors and 6 juniors. (give answer as a fraction or a decimal out to at least 4 places. if your answer is very small use scientific notation for example 3.3421e-6.)
a)P(all seniors) =(25C3)/(30C3) =0.5665
b)P(All Juniors)=(5C3)/(30C3) =0.0025
c)P(2 senior and 1 Junior) =(25C2)(5C1)/(30C3) =0.3695
d)P(1 senior and 2 Junior) =(25C1)(5C2)/(30C3) =0.0616
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In a class of 28 students, 6 are female and 7 have an A in the class. There are 17 students who are male and do not have an A in the class. What is the probability that a student is a male given that they have an A?
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
28 students in total.
6 are female.
so, we have 28-6 = 22 male students.
7 of the 28 students have an A.
17 male students do not have an A.
that means 22-17 = 5 male students have an A.
and that means 7-5 = 2 of the female students have an A.
"given that they have an A".
that reduces our totally possible cases to 7.
the probability that an A-student is male is therefore
5/7 = 0.714285714...
and FYI
the probability that an A student is female is
2/7 = 0.285714286...
The probability that a student is male given that they have an A is approximately 0.538.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
We can use Bayes' theorem.
P(male | A) = P(A | male) x P(male) / P(A)
We are given:
P(A | male) = 7/17
(7 students are male and have an A, out of 17 male students)
P(male) = 17/28
(17 students are male, out of 28 total students)
P(A) = (6+7) / 28
(13 students have an A, out of 28 total students)
Plugging in these values.
P(male | A) = (7/17) x (17/28) / (13/28) = 0.538
Therefore,
The probability that a student is male given that they have an A is approximately 0.538.
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Graph the image of the figure using the transformation given.
A graph of the image of triangle V'W'X' after a rotation of 90° counterclockwise about the origin is: graph A.
What is a rotation?A rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).
Note: Each interval on this graph represents 1 unit.
By applying a rotation of 90° counterclockwise to triangle VWX, the coordinates of the vertices of the image triangle V'W'X' include the following:
(x, y) → (-y, x)
Point V = (-2, -4) → Point V' = (-(-4), -2) = (4, -2)
Point W = (-2, -2) → Point W' = (-(-2), -2) = (2, -2)
Point X = (-5, -4) → Point X' = (-(-4), -5) = (4, -5)
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Rewrite the power as a product of powers (2ax)^3
The power as a product of powers can be rewritten (2ax)³ as (2ax )(2ax)(2ax )
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
The product can be defined as the multiplication operation of two or more terms so that another term can be gotten the same as the one that is been given that we were asked to rewrite.
Power is defined as the degree that is been found on the terms, the degree that can be on the term is 3, then it can be expressed in three terms
Therefore, the given expression is (2ax)³ can be rewritten as;
(2ax)³ = (2ax )(2ax)(2ax )
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Andrew writes the algebraic expression 2s+ 2.79 to represent the cost of his
lunch. He bought 2 sandwiches and a large drink. Identify any variables,
coefficients, and terms in the expression. Tell what each represents.
The sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant
What is Algebraic Expression?
An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x2 2xy + c
The cost of Andrew's lunch is written as the algebraic expression
2s + 2.79 as a given. He bought a huge drink and two sandwiches.
In the algebraic expression given;
2s + 2.79
Here, 2 stand in for the coefficients of s, which stands for the quantity of sandwiches he purchased.
The sandwich's price is represented by the variable s, which is a function of the coefficient.
And 2.97 represents both the cost of a big drink and a constant since no further letters have been added.
Hence, sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant
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Suppose that scores on a recent statistics exam were normally distributed, that students in the 80th percentile of scores earned 85 points, and that students in the 30th percentile of scores earned 65 points. What was the mean of all exam scores in the class?.
The mean of all exam scores in the class is found = 71
Normally distribution
A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
While data points are referred to as x in a normal distribution, they are called z or z-scores in the z-distribution. A z-score is a standard score that tells you how many standard deviations away from the mean an individual value (x) lies: A positive z-score means that your x-value is greater than the mean.
The z-score is found by;
z = (x - μ)/σ
x = sample mean
μ = mean score
σ = standard deviation
Now, from this,
x = zσ + μ
For p = 80th percentile= 0.8, see z value from z score table.
z = 0.85
x = 85 points
85 = 0.85σ + μ .....eq 1
For p = 30% = 0.3, see the z value from the z score table.
z = -0.3802
x = 65
65 = -0.3802σ + μ .....eq 2
Solving eq 1 and 2.
σ = 16.25
Put in eq 1
μ = 71.19
μ = 71
Thus, the mean of all exam scores in the class is found = 71
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grace and jack are playing a game with a gigantic bucket of markers. jack took a random sample of markers from the bucket and counted 121212 yellow markers, 373737 blue markers, and 111 red marker. use the observed frequencies to create a probability model for the color of the next randomly selected marker from the gigantic bucket of markers. input your answers as fractions or as decimals rounded to the nearest hundredth.
If grace and jack are playing a game with a gigantic bucket of markers. The probability are yellow 0.24, blue 0.74, red 0.02.
ProbabilityGiven data:
Yellow markers = 12
Blue markers =37
Red marker =1
Total number of markers = 12 + 37 + 1
Total number of markers = 50
Probability of an event occuring= Favorable number of outcomes / Total number of outcomes
Probability of getting an yellow marker = 12/50
Probability of getting an yellow marker = 0.24
Probability of getting an blue marker = 37/50
Probability of getting an blue marker = 0.74
Probability of getting an red marker = 1/50
Probability of getting an red marker = 0.02
Probability model
Type of maker Frequency Probability
Yellow 12 0.24
Blue 37 0.74
Red 1 0.02
Therefore the probability are 0.24, 0.74, 0.02.
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PLS HELPPOO!!!!!!!!!
Answer:
AC=8
Step-by-step explanation:
2x=2(8)
2x=16
x=16÷2
x=8
How many minutes are in two fifths of a day?
Answer:576 minutes
Step-by-step explanation:
For the bake sale, Lee baked 141 cookies. Esther baked 51 more cookies than Lee. How many cookies did Lee and Esther bake in all?
Answer: 333 Cookies
Step-by-step explanation:
Let E = Cookies by Esther
Let L = Cookies by Lee
The equation for amount of cookies: E+L
L=141
E=L+51
Substitute L
E=141+51=192
E+L=141+192=333
Answer:
[tex]10 \div x - 10 \div (x - 1) = 30[/tex]
Solve the system.
4x − 8y + 4z=5
- 6x + 6y - 8z = 1
3x + 3y + 6 = -9
Answer:
Point Form:
(
−
13
4
,
−
7
4
,
1
)
Equation Form:
x
=
−
13
4
,
y
=
−
7
4
,
z
=
1
Step-by-step explanation:
what is the probability that at least two of them have the same birthday (month and day)? (assume that each day is equally likely to be a student's birthday, that there are no sets of twins, and that there are 365 days in the year. do not include leap years).
Answer:
probability is 1.
Step-by-step explanation:
In a lot of probability problems when asking for “at least two” is usually easier to see the opposite case, that is, the “none of them” case…
P(“at least one … X”) = 1 - P(“none of them … X”)
I will we exclude 29th of February, that is, considering none of the people was born on the leap day of a leap year.
First, let’s see what happens for 2 people. We can name one of those 2 people as “first” and the other as “second”. Whatever the birthday of the “first” one is, the other has 364 out of 365 days in the year to have a different birthday.
p(2) = 1–364/365 = 1/365
For 3 people, the “first” has a birthday, the “second” has a probability of 364/365 to have a different birthday and the third has a probability of 363/365.
p(3) = 1 - 364/365 * 363/365= (365^2 - 364*363)/365^2
For 4 people:
p(4) = 1 - 364/365 * 363/365 * 362/365
…
For n people, if n is less than 366:
p(n) = 1 - (364! / [365 - n]! )/365^(n-1)
p(n)=1−364!(365−n)!⋅365n−1
Obviously, if n is 366 or more, since we excluded the leap day there must be always 2 people with the same birthday (pigeonhole principle), and then in this cases the probability is 1.
Help pls thx
King David was born in 1015 BC and died in 970 BC. The Roman Emperor Augusta was born in 63 BC and died in 14 AD. Which of these two men lived longer?
a triangle base is 6 inches long and it’s height is 5 inches. what the area of the triangle?
Answer:
Answer:The area of the triangle is 60 in.
explanation:
Because we have 6inches in the weigth and 5inches in the height .
A=1/2bhA=1/2x 5 x 6A=30A=1/2 ÷30A=60inLook at the steps and find the pattern.step 1step 2step 3How many dots are in the 4th step?dotsSubmit
40
Explanation
Step 1
a)initially we have 8 dots
after that
in step 2, we have a new row and , now there are 8 dots per row, so
[tex]\begin{gathered} \text{new row} \\ and\text{ number of dots= previous +1} \end{gathered}[/tex]in step 3, we should have
[tex]\begin{gathered} new\text{ row, it means now, there are 3 rows} \\ \end{gathered}[/tex]and
[tex]\begin{gathered} and\text{ number of circles = previous +1} \\ \text{ number of circles =}8+1=9 \\ \text{ number of circles =}9 \end{gathered}[/tex]as we can see, the rule works
Step 2
now, to find the patter in step 4, just apply
[tex]a\text{ new rounds, now, there are 4 row}[/tex]and
[tex]\begin{gathered} and\text{ number of dots = previous +1} \\ \text{ number of dots = 9}+1=10 \\ \text{ number of dots=}10 \end{gathered}[/tex]finally, to know the number of dots
Multiply the number of row, by the number of dots per row, so
[tex]\begin{gathered} \text{Number of dots=4}\cdot10 \\ \text{Number of dots=}40 \end{gathered}[/tex]therefore, the answer is 40
I hope this helps you
Solve: 5k = 100k =
A. 20
B. 10
C. 500
D. 50
Answer:
A,) 20
Step-by-step explanation:
First, I am assuming that the problem is 5k = 100, not "5k = 100k =" as it was written.
We need to end up with "k equals some number." This is called solving for k. In order to do this we need to have k by itself. We look at the problem and ask, "what is preventing k from being by itself?" In this case k has a "times 5" with it. How can we get rid of that? Well we can do the opposite of "times 5," and that is to divide the left side by 5. That leaves k by itself which is exactly what we need. But if do something to one side of an equation, we need to do it to the other side for the equation to still be true. So in this case we also have to divide the right side by 5 also, which gives us 20 on the right side. So in our original problem:
5k = 100
Divide both sides by 5 and we have the answer:
k = 20