A jar contains 20 yellow jellybeans, 20 orange jellybeans, 20 red jellybeans and 20 green jellybeans.
Required:
a. In how many ways can you put all the jellybeans in a row?
b. How many ways are there to select a handful of 20 jellybeans?
c. How many ways are there to select a handful of 20 jellybeans that contains at least 3 red?
d. How many ways are there to select a handful of 20 jellybeans that contains at least 3 red and at most 2 orange?
Answer:
A)
\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)
B)
\(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)
C)
= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)
D)
= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)
Step-by-step explanation:
A) How many ways can you put all Jellybeans in a row
Total number of Jellybeans = 80
The first jellybeans = 20 yellow , second is 20 orange jellybeans , third is 20 red jellybeans , fourth is 20 green jellybeans
Therefore the number of ways the Jellybeans can be put in a row is :
\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)
B) How many ways are there to select a handful of 20 jellybeans
lets assume:
yellow jellybeans = a , orange jellybeans = b , red jellybeans = c , green jellybeans = d
a + b + c + d = 20
This is the number Non-negative integer solutions
= \(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)
C) This is also the number of Non-negative integer solutions but in this case the value of C ≥ 3
hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red
= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)
D) In this case the value of C ≥ 3 and B ≤ 2
Hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red and at most 2 orange
= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)
It costs a car company $25,000,000 to develop and market the model of a new car. The company sells each car for $30,000 . Which of the following represents the number of cars, c , that the car company must sell to make over $5,000,000 in profit?
Answer:1,000
Step-by-step explanation:
So we add 25 million to 5 million which is 30 million. Then we divide 30 million to 30 thousand and get 1 thousand.
PLSS HELP ASAP
write the equation of a line with a slope of -1/3 that passes through (-4,8)
Answer:
y = -1/3 x + 6 2/3
Step-by-step explanation:
y = mx + b m = - 1/3
(-4,8) x = -4 y = 8
y intercept (b) = y - mx = 8 - (-1/3)*(-4) = 8 - 4/3 = 6 2/3
equation: y = -1/3 x + 6 2/3
(3.5x10^4)+(6.8x10^4)
Answer:
103000
Step-by-step explanation:
3.5 × \(10^{4}\) + 6.8 × \(10^{4}\)
Calculate 10 to the power of 4 and get 10000.
3.5 × 10000 + 6.8 × \(10^{4}\)
Multiply 3.5 and 10000 to get 35000.
35000 + 6.8 × \(10^{4}\)
Calculate 10 to the power of 4 and get 10000.
35000 + 68000
Add 35000 and 68000 to get 103000.
103000
Answer:
Couple of choice:
A. If those x's are the multiplication symbol then your answer is 103,000
B. If those x's are variables then you don't have a definite answer.
Step-by-step explanation:
Explanation for A:
We use PEMDAS and start inside the parentheses
We do exponents before multiplication and get 10,000 for 10^4
10,000*3.5= 35,000
10,000*6.8=68,000
35,000+68,000=103,000
Explanation for B:
If the x's are variables then your question is just and expression. Without it being equal to anything, I can't solve for x. Also if the question was asked as, "What is (3.5x10^4)+(6.8x10^4), when x = 5 (or any random number)" I could solve it because I know the value of x being asked. Maybe try posting the question again if this is what you meant
how to solve this separable differential equation?
The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,
\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).
What is a differential equation?Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.
The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).
Now, multiplying both sides by dx we,
\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).
Dividing both sides by \(2^{\sqrt{x}}\) we have,
\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).
\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).
\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).
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help meeeeeeeeee pleaseee !!!!!
The solution of the composition functions are represented as follows;
(fog)(x) = \(\sqrt{-2x+3}\)(g o f)(x) = -2√x + 3How to solve composite functions?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore, the composite function can be solved as follows:
f(x) = √x
g(x) = - 2x + 3
Hence,
(fog)(x) = f(g(x)) = \(\sqrt{-2x+3}\)
(g o f)(x) = g(f(x)) = - 2√x + 3 = -2√x + 3
Therefore, the composite function expression is as follows:
(fog)(x) = \(\sqrt{-2x+3}\)(g o f)(x) = -2√x + 3learn more on composite function here: https://brainly.com/question/24464747
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To find the end behavior
Answer:
hope this helps
Step-by-step explanation:
To determine its end behavior, look at the leading term of the polynomial function. Because the power of the leading term is the highest, that term will grow significantly faster than the other terms as x gets very large or very small, so its behavior will dominate the graph
Fine the missing length to the nearest 10th
The value of the missing length to the nearest tenth are;
a. x = 7.5
b. x = 7.8
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
Therefore ;
c² = a²+b²
a. x² = 9²-5²
x² = 81-25
x² = 56
x = √56
x = 7.5 ( nearest tenth)
b. using Pythagoras theorem also!
x² = 6²+5²
x² = 36+25
x² = 61
x = √61
x = 7.8( nearest tenth).
Therefore the value of the missing values are 7.5 and 7.8
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Write as the opposite of a square root. -3√5
The value of -3√5 as the opposite of the square root is -75.
What in mathematics is a square root?
The factor we can multiply by itself to obtain a given number is the number's square root.
Square root is represented by the symbol sqrt, which stands for square root of, end square root. Squaring an integer is the reverse of finding its square root.
-3√5
The opposite of the square root is the square, so,
-3√5 = -3 × 5²
-3√5 = - 3 × 25
-3√5 = - 75
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Twice the difference of a number and -3 is 4. Find the number.
Answer:
The number is 5
Step-by-step explanation:
Let us use an equation ( X is the unknown number)
2(x-3)=4
2x-6=4
2x-6+6=4+6
2x/2=10/2
x=5
I need Serious help here!
Answer:
4. 10mn - 35m
5. 8rs - 2r² + 16r
6. -4 (y +2)
7. -5p (p - 6q)
Step-by-step explanation:
For number four you basically times 5m to 2n and since it has different variables it would be 10mn ( keep the letters in alphabetical order) , then 5m times negative 7 would be '-35m'
For number five, it wants you to pass through the sign so negative times a negative always gives a positive so '-2r' times '-4s' would equal to '8rs', then -2r times r gives out -2r² since remember there are two same variables-in this case it is 'r' so to show there is two 'r' you put 'r squared' which is 'r²' and negative times a positive value gives negative.
For number 6, you take the Highest common factor out of the two values and in number 6 it would be -4 since there is a factor of -4 in both '-4' and '-8'. So if you take the -4 out of the bracket, there would be 'y' left and also '+2' since there is already a negative outside the bracket.
For number 7, similar to 6, take out the GCF/HCF which is -5 as it is factors in both of them. So -5 out of the bracket then 'p²' would be left and also if you divide 30 by -5 it would give -6 so the remainder would be -6pq. But if you see, you might notice there is both p in two of them so you can also take the p out with -5.
I know this is pretty long but if you don't understand have a read through them and if you still don't get please tell me what I did wrong. Thx
Pls help
SAS
SSS
AAS
HL
Answer:
Step-by-step explanation:
its none, if it was SAS then the 10 would be closer to the angle
Simply this algebraic expression y-3/3+12
Answer:
add 12 +9 because i had that same answer on my quiz last week
Answer:
(y - 3)/15
Step-by-step explanation:
Simplify the following:
(y - 3)/(3 + 12)
Hint: | Evaluate 3 + 12.
3 + 12 = 15:
Answer: (y - 3)/15
When Jerry makes concrete he uses cement, sand and gravel in the ratio 1 : 2 : 4. For one job he used 15kg of sand.
a) How much cement and gravel did he use?
b) What is the total mass of the concrete he made?
Answer:
a) 37.5
b) 52.5
Step by step explanation:
a). Cement : Sand : Gravel = 1 : 2 : 4
2x = 15kg
15/2 = 7.5
7.5 x 5 = 37.5
b). 37.5 + 15 = 52.5
A map has the scale 1/3inch = 8 miles. If city a and city b are 12 inches apart on my map then how far apart are the city’s in real life
find the missing side. round to the nearest tenth
The required angle is 24.5°.
Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,
To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.
The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.
In this case, the perpendicular side is 16 and the base is 35.
Let's denote the acute angle as θ.
Using the tangent function, we can set up the equation:
tan(θ) = perpendicular side / base
tan(θ) = 16 / 35
To find the value of θ, we can take the inverse tangent of both sides:
θ = tan⁻¹(16 / 35)
θ = 24.5°
Hence the required angle is 24.5°.
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Write an equation in slope-intercept form of the line that passes through ( 7,2 ) ( 2,12 )
Answer:
y = -2x + 16
Step-by-step explanation:
Slope-intercept form is:
y = mx + bWhere m = slope
b = y-intercept
To find the slope of the line containing (7,2) and (2,12), we have to find the slope, m.
m = (y2 - y1)/ (x2 - x1)= (12 - 2)/(2 - 7) = 10/-5 = -2Now, to find the y-intercept (b), insert m = -2 into the equation and one of the given points:
y = -2x + blet's use point (7,2) to find b:
2 = -2(7) + b2 = -14 + bb = 16Now, we can find the equation of this line:
y = -2x + 16Answer:
y=-2x+16
Step-by-step explanation:
First we should find the slope.
We can use the formula (y2-y1)/(x2-x1)
(12-2)/(2-7)=10/-5=-2
So, the slope is -2.
From there, we can plug in one of the points into the standard slope-intercept equation, y=mx+b, along with the slope we already found
y=-2x+b
12=-2(2)+b
12=-4+b
b=16
So, the slope-intercept equation is y=-2x+16
Write an equation for the line in slope-intercept form.
When the coordinate is (-3, -3) and the slope is -1, the y-intercept is -4.
What is slope?Slope is a measure of the stainless of a line what is surface and it represent by the letter m. It is calculated by dividing the vertical change in the line or surface by the horizontal change in the line or surface. Slope is used in mathematics engineering and other science to measure the rate of change between two point.
The y-intercept is the point at which a line crosses the y-axis when plotting coordinates on a graph. To find the y-intercept, you need to use the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = -1x - 4. This equation can be used to solve for the y-intercept when the coordinate is (-3, -3). By substituting -3 for x and -3 for y, the equation can be rearranged to -3 = -1(-3) - b, which simplifies to -4 = -b. Therefore, the y-intercept is -4.
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Bob is verifying the identity, Sine (StartFraction 3 pi Over 2 EndFraction + x) = negative cosine x. He took these steps: Step 1: Sine (StartFraction 3 pi Over 2 EndFraction + x) = sine StartFraction 3 pi Over 2 EndFraction. Cosine x minus cosine StartFraction 3 pi Over 2 EndFraction sine x Step 2: Equals sine StartFraction 3pi Over 2 EndFraction. Cosine x + 0 Step 3: Equals negative 1. cosine x + 0 He made a mistake at which step? Step .
Answer: 1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
just took test
Write the mixed number 9 3/5 as an improper fraction
===========================================
Explanation:
Use the formula
a & b/c = (a*c + b)/c
So,
9 & 3/5 = (9*5+3)/5 = (45+3)/5 = 48/5
there are 25 student in a class. five of then scored A and 10 of them score B while the other scored C for Biostatistics. if a student is selected at random, calculate the probability that the selected student scored A or B in biostastics.
There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.
To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.
Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):
Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.
Therefore, the probability that a randomly selected student scored A or B
in Biostatistics is:
Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.
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215 divided by 32 with remainder
quotient is 6 and the remainder is 23
select all that apply which of the following name an angle in the drawing
∠ECB and ∠ACB are the angles.
What is an angle?
An angle is formed when two lines or rays meet at the common vertex. The angle is represented by ∠ and it is measure in °.
In the given figure,
The line FA and BD intersects at the point C.
When two lines intersect at the same vertex it makes an angle.
So there is an angle at the point C.
From the given options, the angles are ∠ECB and ∠ACB.
Option (i) and (iv) is the correct option.
Hence, ∠ECB and ∠ACB are the angles.
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please help me with this question
Tony invested $9538 in an account at 8% compounded daily. Identify the compound
interest C after 1 years.
9514 1404 393
Answer:
$794.30
Step-by-step explanation:
The account balance for principal P invested at rate r compounded daily for t years is ...
A = P(1 +r/365)^(365t)
We have P=$9538, r=0.08, t=1, and we want the value of P-A, the interest earned.
P-A = P(1 +0.08/365)^365 -1) = $9538(1.08327757 -1) ≈ $794.30
The interest earned in one year is $794.30.
Jeremy Sullivan delivers newspapers for the Dispatch. He receive $0.127 per paper, 6 days a week (for the daily paper), and $0.65 for theSunday paper. He delivers 124 daily papers each day and 151 Sunday papers each week. What is his total pay for the week?
ANSWER
$192.64
EXPLANATION
Jeremy Sullivan delivers newspapers.
He receives $0.127 per paper 6 days a week.
He receives $0.65 for the Sunday paper.
He delivers 124 papers daily
He delivers 151 papers on Sundays.
To calculate his total pay, we multiply the number of papers for the week by the number of days and the respective pay and multiply the number of Sunday papers by the respective pay and then add them together.
For Monday to Saturday:
Pay = 0.127 * 6 * 124 = $94.49
For Sunday:
Pay = 0.65 * 151 = $98.15
His total pay will therefore be:
94.49 + 98.15 = $192.64
Moving sideways on the balls of the feet?
A. Striding
B. Skipping
C. Galloping
D. Sliding
I’m being timed i need to evaluate
2
3(5+1) ÷ 3² = 3(6) ÷ 3²
= 18 ÷ 3² = 18 ÷ 9 = 2
A rectangle is 4 times as long as it is wide. The perimeter is 30 feet. Find the dimensions.
Answer:
Express your length and width as algebraic expressions:
width = x
length = 4x
Use the formula for the perimeter of a rectangle to solve for x:
perimeter = 2(length) + 2(width)
50 = 2(4x) + 2(x)
50 = 8x + 2x
50 = 10x
5 = x
The width (x) is 5 feet and the length (4x) is 20 feet.
Step-by-step explanation:
Answer: 3 by 3 by 12 by 12
Step-by-step explanation: Two sides are x feet long. The two other sides are 4 times x feet long. 4x+4x+x+x =10x
Set that equal to 30 and solve. x=3
Plug back into the original 4x's and x's to get the lengths
4. A rancher noticed that, typically, the first day he has a new horse the horse eats 16 pounds of hay. The second
day on, the horse typically eats 24 pounds of hay per day.
Which equation could be used to determine the number of pounds, y, the horse will eat over x days?
OA.y=24x + 16 O C. y
24x - 16
B. y 24(x+16) O D. y
16x + 24
The equation (A) y = 24x + 16 can be used to find the y which is the pounds of hay the horse will eat in x days.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
So, we know that:
A new horse on day 1 eats 16 pounds of hay.
Usually, the horse the 2nd day eats 24 pounds of hay per day.
So, the equation that can be used to find y which is the pounds of hay the horse will eat in x days is:
y = 24x + 16
Therefore, the equation (A) y = 24x + 16 can be used to find the y which is the pounds of hay the horse will eat in x days.
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