Using combination we get 20475 teams can made up of 3 girls and 2 boys and 37128 teams can be selected with at least 3 girls.
Why does combination mean?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.Since this is just a team of 5 children,
we have no of girls = 15
No of boys = 10
teams made up of 3 girls and 2 boys
girls out of 3 girls can be selected in ¹⁵C₃ ways and
2 boys out of 10 boys can be selected in ¹⁰C₂ ways.
[tex]\implies[/tex] ¹⁵C₃ X ¹⁰C₂
= 455*45 =20475 Ways
Teams can be selected with at least 3 girls
It is the probability of at least 3 girls which means P(3 girls,2 boys) or P(4 girls,1 boy) or P(5 girls, 0 boys)
[tex]\implies[/tex] ¹⁵C₃ X ¹⁰C₂ + ¹⁵C₄ X ¹⁰C₁ + ¹⁵C₅ X ¹⁰C₀
= 455 * 45 +1365*10+3003*1
=20475 +13650 +3003
=37128 ways
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I can't remember how to do this. I need help with this.
How many roots do the functions have in common?
f(x)=x^2-9
f and g share same roots?
f and g share one root in common but each have another root not shared?
f and g share no roots in common
Answer:
f and g share no roots in common
Step-by-step explanation:
The roots of [tex]f(x)=0[/tex] are [tex]x=\pm 3[/tex].
From the graph, the roots of [tex]g(x)=0[/tex] are where the graph of [tex]g(x)[/tex] intersects the [tex]x[/tex] axis, which are at [tex]x=2, 10[/tex].
nothing?????????????
Answer:
YES
Step-by-step explanation:
Julian's carpet has an area of 160 square feet. He hires the Carpet Pro carpet cleaning service, which is able to clean 9 square feet of his carpet every minute. Therefore, in the first minute, CarpetPro is able to clean 9 square feet of Julian's carpet (leaving 151 square feet remaining to be cleaned). In the second minute, the cleaner is again able to clean 9 square feet of carpet (leaving 142 square feet to be cleaned), etc. Which of the following functions expresses the number of square feet that still remain to be cleaned after t minutes from the time that the carpet cleaner began cleaning this carpet. O A(t) = 220 - 9t O A(t) = 220 - 0.1^t O A(t) = 220(0.1)^t O A(t) = 220(0.9t) O A(t) = 220 - 0.9t
The function that expresses the area of the 160 square feet carpet remaining after t minute is; A(t) = 160 - 9·t
What is a mathematical function?A function is a rule that maps the elements of a set known as the input of the function, to the elements of another set, known as the output of the function, such that each element of the input is mapped to exactly one element of the output set.
The area Julian's carpet covers = 160 square feet
The area the Carpet Pro cleaning service is able to clean every minute = 9 square feet.
A table of values showing the area of the carpet remaining after each minute of cleaning by Carpet Pro, can be presented as follows;
Time, t (minute) [tex]{}[/tex] Area remaining to be cleaned (square feet), A(t)
0 [tex]{}[/tex] 160
1 [tex]{}[/tex] 151
2 [tex]{}[/tex] 142
3 [tex]{}[/tex] 133
4 [tex]{}[/tex] 124
5 [tex]{}[/tex] 115
The change in the area of the carpet remaining is a constant and therefore, the first difference of the values in the above table is a constant which indicates that the relationship is a linear relationship, with an equation of the form y = m·x + c
Where;
m = The slope = (151 - 160)/(1 - 0) = -9
c = The y-intercept The value of the function when the input (time) is zero, which is 160
c = 160
x = The number of minutes that elapse, t
y = The number of square feet remaining after t minutes, A(t)
Plugging in the above value, we get;
A(t) = -9·yt + 160
The function that expresses the number of square feet remaining A(t) after t minutes from the time the carpet cleaner began cleaning the carpet is; A(t) = 160 - 9·t
The possible options based on a similar question posted online and the 160 square feet area of the carpet specified in the question are;
A(t) = 160 - 9·t
A(t) = 160 - 0.1^t
A(t) = 160·(0.1)^t
A(t) = 160·(0.9·t)
A(t) = 160 - 0.9·t
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In a right triangle the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg b, if:
c=5, a=3
Answer:
b=4
Step-by-step explanation:
[tex]a^{2}+b^{2}=c^{2}[/tex]
[tex]3^{2}+b^{2}=5^{2}[/tex]
[tex]9+b^{2}=25[/tex]
[tex]b^{2}=16[/tex]
[tex]\sqrt{b^{2}} = \sqrt{16}[/tex]
b=4
Find the surface area of the cylinder in terms of pi
Surface area of the cylinder is 211.5 [tex]cm^{2}[/tex]
What is Surface area of the cylinder?The entire area that is occupied by the flat surfaces of the cylinder's bases and its curving surface is known as the surface area of a cylinder.
A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².
Diameter is 9 cm, and height is 19 cm,
therefore r = 4.5 cm and height is 19 cm.
A = 2 r² π + 2 r π h
A = 2 * 4.5*4.5 π + 2 ·* 4.5* 19 π
A = 40.5 π + 171 π
A = 211.5 [tex]cm^{2}[/tex]
Surface area of the cylinder is 211.5 [tex]cm^{2}[/tex]
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Determine whether the following statement is Always, Sometimes, or Never true.
The smallest angle of a right triangle is across from the hypotenuse.
answer choices
Never. The hypotenuse is the longest side of a right triangle, so it will be across from the largest angle, which is a right angle.
Sometimes. The hypotenuse is across from the right angle of a right triangle, so it will only be across from the smallest angle when the right angle is the smallest angle of the triangle.
Always. The hypotenuse is the longest side and the longest side of any triangle is across from the smallest angle of the triangle.
The hypotenuse is always the longest side of a right triangle, hence it will always be across from the biggest angle, which is a right angle.
The hypotenuse of a right triangle is occasionally across from the right angle, therefore it will only be across from the smallest angle when the right angle is the smallest angle of the triangle.
The hypotenuse is never the longest side of any triangle, and the longest side of any triangle is always across from the smallest angle of the triangle.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.
Here,
It is always true that The hypotenuse is the longest side of a right triangle, so it will be across from the largest angle, which is a right angle.
It is sometimes true that The hypotenuse is across from the right angle of a right triangle, so it will only be across from the smallest angle when the right angle is the smallest angle of the triangle.
It is never true that The hypotenuse is the longest side and the longest side of any triangle is across from the smallest angle of the triangle.
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Hannah drove 450 miles to her brother's house at an average speed of 60 miles per hour. How long did she take?
Hannah drove 450 miles to her brother's house at an average speed of 60 miles per hour. How long did she take? (Time)
[tex]t=\dfrac{Distance}{Speed}[/tex]
[tex]t=\dfrac{450}{60}[/tex]
[tex]t=7.5hours[/tex]
Remember, time must be converted to seconds as it is the unit for time.
7.5 hours to seconds
1 hour = 3600 seconds
3600 seconds * 7.5 hours
[tex]=\fbox{27000 seconds}[/tex]
If you wanted to make $1071 by investing $4176 for 4 years in an account that pays simple interest, what interest rate you would need to achieve your goal?
The interest rate should be 6.4116% to achieve the required goal.
What is simple interest?
The daily interest rate, the principal, and the number of days between payments are multiplied to determine simple interest. Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest. Simple-interest loans are frequently used for auto loans and short-term personal loans.
Given data:
A = 4176 + 1071 = $5247
t = 4 years
P = $4176
r = ?
By using the formula,
A = P(1 + rt)
r = (1/4)((5247/4176) - 1)
= 0.06411638
r = 0.06411638
Converting r decimal to R a percentage
R = 0.06411638 * 100
= 6.4116% per year
Hence, the interest rate should be 6.4116% to achieve the required goal.
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pls help i will mark brainliest
Determine the value of y for the inequality 4 times the quantity y plus one fifth end quantity is less than or equal to four fifths.
y ≥ 0
y ≤ 0
y is greater than or equal to negative 1 over 40
y is less than or equal to negative 1 over 40
The value of y is less than or equal to 0 (y ≤ 0).
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Given:
4y + 1/5 ≤ 4/5
We have to find the value of y.
Subtract 1/5 from both sides,
4y + 1/5 - 1/5 ≤ 4/5 - 1/5
4y ≤ 3/5
Multiply both sides by 1/4
4y x 1/4 ≤ 3/5 x 1/4
y ≤ 3/20
y ≤ 0.15
Hence, the value of y is less than or equal to 0 (y ≤ 0).
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if a number is subtracted from its square the result is 30. find all possible values for the number
Answer:
It's 6 and -5.
Step-by-step explanation:
:D
If 0.05 = 2a + 5b and 0.2 = 8a + 2b are two normal equations, find the parameters a and b.
Step-by-step explanation:
0.05 = 2a + 5b
0.2 = 8a + 2b
the trick is to multiply the equations with contacts, so that an addition or subtraction of the equating can be made, and one variable is eliminated in that result, which allows us then to solve for the second variable.
and then we use one of the original equations to solve for the first variable.
in our case, multiplying the first one by 4 and then subtracting the second one sends to be the simplest approach :
0.2 = 8a + 20b
- 0.2 = 8a + 2b
-------------------------
0 = 0 + 18b
b = 0/18 = 0
0.05 = 2a + 5b = 2a + 5×0 = 2a
a = 0.05 / 2 = 0.025
a = 0.025
b = 0
6.20 Let the random variable Y possess a uniform distribution on the interval (0, 1). Derive the a distribution of the random variable W = Y. b distribution of the random variable W = VY.
Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.
What is Random Variable?
A continuous random variable is a random variable where the data or value can assume infinitely many values ( meaning it’s a continuous set of data. )
For example a random variable measuring the time taken for someone to cook rice is continuous since there are an infinite number of possible times that can be done.
a) If the random variable Y has a uniform distribution on the interval (0, 1), then the probability density function (PDF) of Y is given by:
[tex]f_Y(y) = 1 for 0 < y < 1[/tex]
= 0
If we let W = Y, then the PDF of W is simply the same as the PDF of Y, since W and Y are equal. Therefore, the PDF of W is given by:
[tex]f_W(w) = 1 for 0 < w < 1[/tex]
= 0
b) If we let W = VY, where V is a constant, then the PDF of W is given by:
[tex]f_W(w) = f_Y(w/V) / |V|[/tex]
Substituting in the expression for the PDF of Y, we get:
[tex]f_W(w) = 1/|V| for 0 < w/V < 1[/tex]
= 0
If V > 0, then this reduces to:
[tex]f_W(w) = 1/V for 0 < w < V[/tex]
= 0
If V < 0, then the range of w is reversed and the PDF becomes:
[tex]f_W(w) = -1/V for V < w < 0[/tex]
= 0
The normalization factor [tex]|V|[/tex] is necessary because the transformation
W = VY stretches or compresses the original uniform distribution on the interval (0, 1) by a factor of [tex]|V|[/tex].
Hence, Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.
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(3 pts total) Suppose local sales tax is 8.75% and the price of a car is $36,500.
a) How much tax would be paid when purchasing this car?
b) What is the total amount of money needed to buy the car (list price and tax)?
Answer:
a) 3193.75
b)39,693.75
PLEASE HELP ASAP The set of all numbers greater than -10 and less than -3
Answer
-15
Step-by-step explanation: your welcome
If a student is chosen at random, what is the probability that: Write your answers in percent form. Round to the nearest tenth of a percent. a) The student has competed in none of the categories? b) The student has competed in all three of these categories? c) The student has competed in Smooth or Standard, but not Rhythm? d) The student has competed in Rhythm and Standard, but not Smooth? e) The student has competed in Rhythm.
The student has completed in Rhythm will be 57.7%
What is probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.
To find,
a) The student has competed in none of the categories is 10.3%
b) The student has competed in all three of these categories is 14.1%
c) The student has competed in Smooth or Standard, but not Rhythm
d) The student has competed in Rhythm and Standard, but not Smooth is 17.9%
The student has completed in Rhythm will be 57.7%
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Someone help me with this please!
Answer:
y = x - 3
Step-by-step explanation:
1. slope-intercept form: y = mx + b
given: m = 1; (-4, -7)
2. plug in the values from the given point [(x, y) --> (-4, -7)] into the linear equation of the slope-intercept form.
y = mx + b
-7 = 1(-4) + b
-7 = -4 + b
b = -3
3. construct the final equation in slope-intercept form.
y = mx + b
y = x - 3
A small heater has a rectangular filter that has a width of 16.0 in. and a length of 20.0 in. Another larger heater requires a similar filter that has a 56 in. width. What is the length (in inches) of this larger filter? (Round your answer using the rules for working with measurements.)
The length of the larger filter is 6 inches.
What is area of rectangle ?
The area of a rectangle is the product of its length and width. That is, A = l x w where l is the length and w is the width
Given:
Small heater : Length = 20 inches , width = 16 inches
larger heater : Length = ?, width = 56 inches
Since, larger heater requires a similar filter
∴Area of small heater = Area of larger heater
(length * width) of smaller heater = (length * width) of larger heater
20 * 16 = length * 56
length = 20*16/56 = 320/56
length = 5.714
0r , length = 6 inches
Hence , the length of the larger filter is 6 inches.
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Which of the following describes a situation in which the total distance a baseball player travels is 0 meter from his starting point? (5 points)
The player runs 3 meters forward and then runs 3 meters in the opposite direction.
The player runs 4 meters forward and then runs 3 meters in the opposite direction.
The player runs 3 meters forward and then runs 0 meter in the opposite direction.
The player runs 3 meters forward and then runs 4 meters in the opposite direction.
The total distance a baseball player travels is 0 meter from his starting point in the first case when he runs 3 meters forward and then runs 3 meters in the opposite direction.
What is distance ?
A measurement of how far away two things or points are might be quantitative or occasionally qualitative.
If an object covers the same distance in the forward and opposite direction, it will cover 0 meter from his starting point.
It happens because when it covers a distance say 5 Km in forward direction and then, when it goes in the opposite direction with equal distance, it reaches to its starting point from where it was started.
Hence, If the player runs 3 meters forward and then runs 3 meters in the opposite direction, h will be at his starting point or we can say, he will cover 0 meter from his starting point.
However, in all other cases, the distance is not equal in both forward and opposite direction.
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write I. decimal the one hundred forty nand sixty-nine hundredth
Answer:
140.69
Step-by-step explanation:
I hope this helps
NO LINKS!!
The supply and demand curves for a business dealing with wheat are:
Supply: p = 1.55 + 0.00014x^2
Demand: p = (2.358 - 0.007x)^2
where p is the price in dollars per bushel and x is the quantity in bushels per day. Use a graphing utility to graph the supply and demand equations and find the market equilibrium. (The market equilibrium is the point of intersection of the graphs for x > 0. Round your answers to 2 decimal places.)
x= ________ bushels
p = $_________
Given curves:
p = 1.55 + 0.00014x²p = (2.358 - 0.007x)²See the attached, where both curves and their intersection is shown.
According to this we have:
x = 96.05p = $2.84Answer:
x = 96.05 bushels
p = $2.84
Step-by-step explanation:
Graph the two equations (see attachment).
The market equilibrium is the point of intersection of the graphs for x > 0.
From inspection of the graph, the point of intersection is (96.05, 2.84).
Therefore:
x = 96.05 bushelsp = $2.84How much would you need to deposit in an account now in order to have $5,000.00 in the account in 697 days?
Assume the account earns 5% simple interest.
You would need to deposit _____ in your account now.
Step-by-step explanation:
To find out how much you need to deposit in an account now to have a certain amount after a certain number of days, you can use the formula:
P = F / (1 + r * t)
where:
P is the present value or the amount you need to deposit now.
F is the future value or the amount you want to have in the account after a certain number of days.
r is the annual interest rate, expressed as a decimal.
t is the number of years for which the money will be invested.
In this case, you want to have $5,000 in the account in 697 days, which is equivalent to 697 / 365 = 1.91 years. The annual interest rate is 0.0375. Plugging these values into the formula, we get:
P = 5000 / (1 + 0.0375 * 1.91)
Solving this equation, we find that you would need to deposit $4,921.15 in your account now to have $5,000 in the account in 697 days.
Which of the following are irrational? Explain how you know?
a. √27
b. 5.0287
c. √49
d. _³√125
c. √49 and d. _³√125 are irrational numbers .
RATIONAL NUMBERS
A rational number is a number that can be written in the form p/q , where p and q are integers and q ≠ o.
IRRATIONAL NUMBER
An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.
a. √27 = 5.196152.
Do you think the decimal part stops after 5.196152? No, it is never-ending. Therefore, it is a non-terminating decimal with non-repeating numbers.
The number 5.1961524227... can't be written in p/q form. So √27 is an irrational number.
b . The number 5.1961524227... can't be written in p/q form. So it is an irrational number.
c. The number √49 can be written in p/q form as 7/1 . So √49 is an irrational number.
d. The number 3√125 can be written in p/q form as 5/1 . So it is an irrational number.
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In the diagram below, TU is parallel to QR. If TU is 6 more than Q T, T S=12, and Q R=18, find the length of QT. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The value of the missing side QT using the similar triangles concept is;
QT = 6
How to solve similar triangles?We are given;
TU is parallel to QR.
TS = 12
QR = 18
Now, TU is 6 more than QT, Thus;
TU = QT + 6
From the concept of similar triangles, we can say that;
QS/TS = QR/TU
Plugging in the relevant values gives us;
(12 + QT)/12 = 18/(QT + 6)
(12 + QT)(QT + 6) = 18*12
QT² + 18QT + 72 - 216 = 0
QT² + 18QT - 144 = 0
Solving this using online quadratic equation calculator gives;
QT = 6
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Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x+4=7
X=
Answer:
x=3
Step-by-step explanation:
7-3=4 or 4+3=7
find the equation of the line passing through the point (4,-2) and parallel to the line 6y=7x-5
Answer: 6y = 7x - 40
Step-by-step explanation:
the wieght of ram and sam are in the ratio 4:7 and weight of aari and ram are in the ratio 3:2 .what is the maximum wieght if the maximum difference in the wieght of any two is 15 kg
Answer:
Step-by-step explanation:
If the weight of Ram and Sam are in the ratio 4:7, and the weight of Aari and Ram are in the ratio 3:2, you can use this information to set up a system of equations to represent the weights of the three people. Let's say that Ram weighs x kilograms. Then, the weight of Sam is 7x/4 kilograms, and the weight of Aari is 3x/2 kilograms.
The maximum difference in weight between any two people is 15 kilograms, so we can set up the following equation to represent this constraint:
|x - (7x/4)| <= 15
|x - 3.5x| <= 15
|-2.5x| <= 15
|x| <= 6
This equation tells us that the weight of Ram (x) must be less than or equal to 6 kilograms or greater than or equal to -6 kilograms.
Since the weight of a person cannot be negative, the maximum weight for Ram is 6 kilograms. Therefore, the maximum weight for Sam is 7x/4 = 76/4 = 10.5 kilograms, and the maximum weight for Aari is 3x/2 = 36/2 = 9 kilograms.
Thus, the maximum weight of the three people is 6 + 10.5 + 9 = 25.5 kilograms.
Solve the following for x
(2x-5)°
Based on the definition of isosceles triangle, the value of x is: 25.
What is an Isosceles Triangle?An isosceles triangle has two base angles that are equal and are opposite two equal sides.
The image shows an isosceles triangle that is inscribed in the circle. Therefore, the two base angles will each equal (2x - 5).
To find the value of x, create the equation below:
2(2x - 5) + 90 = 180
4x - 10 + 90 = 180
4x + 80 = 180
Subtract 80 from both sides:
4x + 80 - 80 = 180 - 80
4x = 100
Divide both sides by 4:
4x/4 = 100/4
x = 25
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Solve the following fractions
2 3/8+2 1/8
Answer:
[tex] \sf \: 4 \frac{4}{8} [/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: 2 \frac{3}{8} + 2 \frac{1}{8} [/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: 2 \frac{3}{8} + 2\frac{1}{8} [/tex]
[tex] \sf \rightarrow \: \frac{19}{8} + \frac{17}{8} [/tex]
[tex] \sf \rightarrow \: \frac{(19 + 17)}{8} [/tex]
[tex] \sf \rightarrow \: \frac{36}{8} [/tex]
[tex] \sf \rightarrow \: 4 \frac{4}{8} [/tex]
Hence, the answer is 4 4/8.
A child has the magnet numbers 1 through 50 on their fridge. What is the probability that the child will choose a number that is not a multiple of 9?
The probability that the child will choose a number that is not a multiple of 9 is 90%.
What is probability?Probability refers to the chance or likelihood that an expected outcome occurs when multiple developments or events could have happened.
Probability describes the ratio between expected favorable outcomes and possible outcomes.
Probability as a ratio is described as a fractional value when it is not 100% certain or uncertain.
In such cases, probability hovers between zero and 1.
The multiples of 9 from 1 through 50 are five (9, 18, 27, 36, and 45).
The other numbers from 1 to 50 are 45 (50 - 5).
The probability of choosing a multiple of 9 is 10% (5/50 x 100).
The probability of choosing a number that is not a multiple of 9 is 90% (45/50 x 100) or (1 - 0.05).
Thus, the probability that the child chooses a non-multiple of 9 between 1 and 50 is 90%.
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Complete the following table.
For country A , the doubling time = 26
For country B , the growth rate = 1.5
Define growth rate?
The growth rate is the fractional change per unit time, ∆x. x. ∆t , the fractional change divided by the length of the time period.
For Country A :
Formula for doubling time,
T = [tex]\frac{log 2}{log (1 + \frac{k}{100} )}[/tex]
The given growth rate , k% = 2.7%
T = [tex]\frac{log 2}{lod (1 + \frac{2.7}{100} )}[/tex]
= [tex]\frac{log 2}{log (1 + 0.027)}[/tex]
= [tex]\frac{log 2}{log (1.027)}[/tex]
= 26.017
≅ 26
Therefore, the doubling time (T) = 26 years
For Country B :
Formula for growth rate
k = 100 [tex][2^{1/T} - 1][/tex]
k = 100 [tex][2^{1/46} - 1 ][/tex] (Since T = 46 years)
k = 100 [1.01518 - 1]
k = 100 [0.01518]
k = 1.518
k ≅ 1.5
Therefore, the growth rate is 1.5 % per year.
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