Complete Question:
In a jar there are 19 red jelly beans and 10 green jelly beans. In how many ways can you pick 4 red jelly beans and the same number of green jelly beans?
Answer:
[tex]Both = 813960[/tex]
Step-by-step explanation:
Given
Red Jelly Beans = 19
Green = 10
Required
Select 4 out of 19 red jelly beans and 4 out of 10 green jelly beans
The keyword in the question is pick and this implies combination;
4 from 19 red jelly beans is calculated as follows
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]
Where n = 19 and r = 4
[tex]^{19}C_4 = \frac{19!}{(19-4)!4!}[/tex]
[tex]^{19}C_4 = \frac{19!}{15!4!}[/tex]
[tex]^{19}C_4 = \frac{19 * 18 * 17 * 16 * 15!}{15! * 4 * 3 * 2 * 1}[/tex]
[tex]^{19}C_4 = \frac{19 * 18 * 17 * 16}{4 * 3 * 2 * 1}[/tex]
[tex]^{19}C_4 = \frac{93024}{24}[/tex]
[tex]^{19}C_4 = 3876[/tex]
Similarly;
4 from 10 green jelly beans is calculated as follows
[tex]^{10}C_4 = \frac{10!}{(10-4)!4!}[/tex]
[tex]^{10}C_4 = \frac{10!}{6!4!}[/tex]
[tex]^{10}C_4 = \frac{10 * 9 * 8 * 7 * 6!}{6! * 4 * 3 * 2 * 1}[/tex]
[tex]^{10}C_4 = \frac{10 * 9 * 8 * 7 }{4 * 3 * 2 * 1}[/tex]
[tex]^{10}C_4 = \frac{5040}{24}[/tex]
[tex]^{10}C_4 = 210[/tex]
Ways of selecting both is calculated as follows
[tex]Both = 3876 * 210[/tex]
[tex]Both = 813960[/tex]
Find the derivative of Y=2xcos2x
Answer:
Y' = -xsin(2x) + 2cos(2x)
Step-by-step explanation:
For this problem, we will need to use the product rule since you have two terms that contain the variable x.
The product rule is simply as follows:
The derivative of the function is the product of the first term times the derivative of the second term plus the derivative of the first term times the second term.
Note the derivative of 2x with respect to x, is 2.
Note the derivative of cos(2x) with respect to x is (-1/2) sin(2x).
With this in mind, let's find the derivative of our function with respect to x.
Y = 2xcos2x
Y = 2x * cos(2x)
Y' = 2x * (-1/2)sin(2x) + 2 * cos(2x)
Y' = (2x * -1 / 2) sin(2x) + 2 * cos(2x)
Y' = (-x)sin(2x) + 2cos(2x)
So the derivative of our function is Y' = -xsin(2x) + 2cos(2x) according to the application of the product rule.
Cheers.
three times the sum of d and 4 is 32
Answer:
d=6 2/3 or 6.6666
Step-by-step explanation:
3(d+4)=32
3d+12=32
3d=32-12
3d=20
d=6 2/3 or 6.6666
Use this information for problems 1 and 2. When full, one of the pools at Sapphire Island will hold 43,000 gallons of water. The pool currently holds 20,000 gallons of water and is being filled at a rate of 130 gallons per minute.
Write an equation that can be used to find h, the number of hours it will take to fill the pool from its current level.
a
\large 130+20000\left(60h\right)=43000
b
\large 60\left(130\right)+20000h=43000
c
\large 130\left(60h\right)-20000=43000
d
\large 130\left(60h\right)+20000=43000
Answer:
The correct option is;
d. 130·(60·h)+2000 = 43000
Step-by-step explanation:
The volume of water held by a pool at Sapphire island = 43,000 gallons
The volume of water the pool currently holds = 20,000 gallons
The rate at which the pool is being filled = 130 gallons/minute
The equation to find h, the number of hours it will take to fill the pool from its current level can be written as follows;
The rate at which the pool is being filled in gallons per hour = 130 × 60 gallons/hour = 7800 gallons/hour
We have;
The volume of water pumped in h hours = (130×60) gallon/hour × h hour = 130×60×h gallons
Whereby we want the total volume of water in the pool to be 43,000 gallons, we add the volume of water obtained from pumping for hours to the volume of water already in the pool, to get 43,000 gallons as follows;
130×60×h gallons + 20,000 gallons = 43,000 gallons
Therefore, the correct option is 130·(60·h)+2000 = 43000.
Determine three consecutive odd integers if the square of the largest integer is 33 less than the sum of the squares of the two smaller integers.
Identity the property shown in the example below.
-8+8= 0
Answer:
Commutative Property
Step-by-step explanation:
-8+8 = 0
0 = 0
how does brainstorm,decide,work,enjoy help with motivation?
Answer:
It helps because it gets you thinking. Personally, it would motivate me because that process itself is very helpful. Brainstorm will get you your idea, you can decide if you want to do it or not, then you work on it, and because you have the right attitude towards whatever you are working on, you'll enjoy it!
Johnathan makes $27 per hour and works 25 hours per week. Every week, he has to sell 20 items. If he sells more than 20 items in a week, he receives a commission of 14% on each set of additional 5 items he sells. This week he worked for 25 hours, he sold 25 items, and he made $1,000 in sales beyond the required 20 items. Which equation will help Johnathan to compute this weeks income?
Answer:
Total income = 27 [tex]\times[/tex] 25 + 14% of $1000= $815
Step-by-step explanation:
Number of hours for which Johnathan worked = 25
Salary for each hour = $27
So, income for 25 hours = 25 [tex]\times[/tex] 27 = $675
Now, it is given that he has sold 25 items.
Sales made beyond the 20 items = $1000
Additional income for additional sales = 14% on each set of 5 items
He has sold exactly 5 additional items that means 1 set of 5 additional items.
So, Additional income for additional sales = 14% [tex]\times[/tex] 1000 = $140
Therefore, total income of this week = Income for 25 hours + Income due to additional sales of 5 items
Therefore Total income = 27 [tex]\times[/tex] 25 + 14% of $1000= $815
when 5 times a number is added to twice the number the result is 10. what is the number?
Answer:
10/7
Step-by-step explanation:
5x+2x=10
7x=10
x=10/7
Which term best describes the
quadrilateral formed by A(2, 3),
B(4, 6), C(8, 9), and D(5,5)?
Answer:
A kite
Step-by-step explanation:
The coordinates of the vertices of the quadrilateral are;
A(2, 3), B(4, 6), C(8, 9), and D(5, 5), therefore, the length of the sides of the quadrilateral can be found using the following formula;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
(x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints on the side
For side AB, we have;
[tex]l_{AB} = \sqrt{\left (6 - 3 \right )^{2}+\left (4-2 \right )^{2}} = \sqrt{13}[/tex]
The slope = 1.5
For side BC, we have;
[tex]l_{BC} = \sqrt{\left (9 - 6 \right )^{2}+\left (8-4 \right )^{2}} = 5[/tex]
The slope = 3/4
For side CD, we have;
[tex]l_{CD} = \sqrt{\left (5 - 9 \right )^{2}+\left (5-8 \right )^{2}} = 5[/tex]
The slope = 4/3
For side DA, we have;
[tex]l_{DA} = \sqrt{\left (3 - 5 \right )^{2}+\left (2-5 \right )^{2}} = \sqrt{13}[/tex]
The slope = 2/3
Angle ADC = Actan (2/3 - 4/3)/(1 + 2/3*4/3) = -19.44 = 180-19.44 = 160.55°
Angle ABC = Actan (0.75 - 1.5)/(1 + 0.75*1.5) = -19.44 = 180-19.44 = 160.55°
Therefore, given that the quadrilateral has two pairs of equal adjacent sides and the angles are equal at the meeting point of the two squares, it is best described as a kite.
A park is a rectangle a fence runs along all four sides the area of the park is 5,400 yards squared the length is 1.5 times longer then the width what is the perimeter of the park
You are given an equation of a line and a point. Use substitution to determine whether the point is on the line. y = -x + 3; A(6,3)
Answer:
The point is NOT on the line.
Step-by-step explanation:
Step 1: Write out equation
y = -x + 3
Step 2: Define point
A(6, 3)
x = 6, y = 3
Step 3: Plug in coordinates
3 = -(6) + 3
3 = -6 + 3
3 ≠ -3
Answer:
(6, 3 ) is not on the line
Step-by-step explanation:
Substitute x = 6 into the right side of the equation and if the value is equal to the y- coordinate of the point, then it is on the line
y = - 6 + 3 = - 3 ≠ 3
Thus (6, 3 ) is not on the line
Nanette has 5 dimes and 5 pennies in her
pocket. What's the probability that Nanette
pulls out a dime and then a penny from
her pocket? (Assume that she doesn't put
the first dime back in her pocket.)
Answer:
2/9
Step-by-step explanation:
5 dimes and 5 pennies = 10 coins
P( dime) = number of dimes / total
=5/10 = 1/2
keep the dime
4 dimes and 5 pennies = 9 coins
P( penny) = number of penny / total
=4/9
P( dime, keep, penny) = 1/2 * 4/9 = 2/9
=================================================
Explanation:
There are 5+5 = 10 coins total, of which 5 are dimes. The probability of selecting a dime is 5/10 = 1/2.
The coin is not put back, so we have 10-1 = 9 coins overall. Of this, 5 are pennies. The probability of pulling a penny out is 5/9. Note how this is dependent on the first event above.
From here, multiply the two probabilities
(1/2)*(5/9) = 5/18
The rule used here is
P(A and B) = P(A)*P(B given A)
where A and B are the events "pulling out a dime on the first selection" and "pulling out a penny on the second selection"
If you were to plot the point (-2, -6) what would be the correct method? *
Solve the inequality. 15 < 4 + x
Answer:
x > 11
Step-by-step explanation:
15 < 4 + x
Subtracting 4 from both sides (to get rid of the 4 on the right side) gives us:
15 - 4 < 4 + x - 4
11 < x
Answer:
x>11
Step-by-step explanation:
15<4+x
Simplify both sides of the inequality.
15<x+4
Flip the equation.
x+4>15
Subtract 4 from both sides.
x+4−4>15−4
x>11
Four pounds of apples cost $5. Eight pounds of apples cost $10. If the total cost of apples, y, varies directly with the number of pounds of apples purchased, x, what is the cost of 6 pounds of apples? Round your answer to the nearest hundredth.
5 / 4 =1.25PER LB
1.25 x 6 =7.5
if i=√-1 , what is i^2 equal to ?
Answer:
-1
Step-by-step explanation:
If i = √-1, then i^2 = -1.
Convert 2 3/8 to a decimal
Answer:
[tex] \huge \boxed{ \bold{2.375}}[/tex]Step-by-step explanation:
[tex] \mathsf{2 \frac{3}{8} }[/tex]
Convert mixed fraction to improper fraction
⇒[tex] \mathsf{ \frac{2 \times 8 + 3}{8} }[/tex]
⇒[tex] \mathsf{ \frac{16 + 3}{8} }[/tex]
⇒[tex] \mathsf{ \frac{19}{8}} [/tex]
Calculate
⇒[tex] \mathsf{2.375}[/tex]
Learn more:
How to convert mixed fraction into improper fraction?
https://brainly.com/question/11500334
Hope I helped!
Best regards!
[10 points]
find the range of each of the following function. All the function are definied for all values of x.
f(x) = 3(x+5)² +2
Can you give the answer and explanation?
what does 'all the function are definied for all values of x'?
Heldpdlsoemss
Answer:
y ≥ 2
Step-by-step explanation:
The range is all of the values that f(x) can have. In order to find the range, let's first find the vertex. That's pretty easy to do since f(x) is already written in vertex notation (vertex notation is f(x) = a(x - c)² + d where (c, d) is the vertex). Since c = -5 and d = 2, the vertex is (-5, 2). Because the value of a is positive (a = 3 in this case, which is positive) we know that the parabola opens upward, therefore the vertex is the minimum. This means that the y-coordinate of the vertex is the smallest possible y-value of the function, therefore, since the y-coordinate of the vertex is 2, the range is y ≥ 2. Note that we use ≥ and not >, this is because y can be 2, therefore, it is included in the solution set.
Answer:
Hey there!
First, we must understand what range is. Range is just another word for all the possible y values of the equation.
This equation, f(x) = 3(x+5)² +2 is in vertex form. We see that this creates a parabola with a vertex at (-5, 2) and opens up.
Thus, the range of this graph would be: [2,∞) in interval notation. Note, the [ is used for greater than or equal to, or less than or equal to, and the ")" is used for less than or greater than.
We use ) for ∞, because ∞ is just a concept, not a real number.
Finally, all functions are defined for all values of x means that this is an f(x) function, and the f(x) is equal to something that can be written in terms of x.
Let me know if this helps :)
3. Compare the function y = tanx and its reciprocal. Identify two similarities and two
differences between the functions.
Answer:
The similarities are;
1) The tangent slope of the tangent graph and the cotangent graph are always the same sign through out
2) The period of each trigonometric ratio cot and tan is π/2
The differences are;
1) The sign of tangent function always positive while that of the cotangent function always negative
2) Where the value of cot x ranges from undefined to 0, the value of tan x ranges from 0 to undefined in the same domain
Step-by-step explanation:
F(x)=3x-5;given f^-1(x)=0
Answer:
Step-by-step explanation:
3x - 5 is f^(-1) (x) = (1 / 3) x + (5 / 3), which is a linear expression.
Factor the trinomial below.
x2 + 3x - 18
A. (x + 6)(x-3)
B. (x+9)(x-2)
C. (X-9)(x+2)
D. (x-6)(x+3)
Answer:
A
Step-by-step explanation:
Given
x² + 3x - 18
Consider the factors of the constant term (- 18) which sum to give the coefficient of the x- term (+ 3)
The factors are + 6 and - 3, since
6 × - 3 = - 18 and 6 - 3 = + 3, thus
x² + 3x - 18 = (x + 6)(x - 3) → A
Answer:
( x+6) ( x-3)
Step-by-step explanation:
x^2 + 3x - 18
What 2 numbers multiply to -18 and add to 3
6*-3 = -18
6+-3 = 3
( x+6) ( x-3)
11. Income: $500
Expenses: $120
find the profit
lesson 3.6 practice
WILL MARK THE BRAINLIEST!! PLEASE HELP If ∠1 = 3x, ∠2 = 5x + 18, and s ⊥ r, find m∠1. Question 5 options: A) 27° B) 63° C) 61° D) 9°
Answer:
A. 27°
Step-by-step explanation:
Given that s is perpendicular to r, and <1 = 3x, <2 = 5x + 18, therefore:
m<1 + m<2 = 90°
3x + (5x + 18) = 90°
Solve for x using this equation
3x + 5x + 18 = 90
8x + 18 = 90
Subtract 18 from both sides
8x + 18 - 18 = 90 - 18
8x = 72
Divide both sides by 8
x = 9
Find m<1
m<1 = 3x
Plug in the value of x
m<1 = 3(9) = 27°
HELP ME PLEASE ITS DUE TODAY AND EXPLAIN HOW U GOT IT AND ILL MARK U THE BRAINLIEST!!!!
Answer: p= 1/7
Step-by-step explanation:
5/7=p+4/7
-p=4/7-5/7
-p=-1/7
P=1/7
How many times greater is the value of 4 in 4735 than the value of the 4 in 6412
Answer:
10 times
Step-by-step explanation:
Since the leftmost value is called ones place.
the second leftmost value is called tens place.
the third leftmost value is called a hundred place.
the fourth leftmost value is called a thousand place and so on.
So, The value of 4 in 4,735 is 4 thousand = 4,000
and the value of 4 in 6,412 is 4 hundred = 400.
Hence, the value of the 4 in 4,735 is 10 times the value of the 4 in 6,412.
Answer:
10 times greater.
Step-by-step explanation:
4 in 4735 has a values of 4000.
In 6412 it has a values of 400.
Mr. Noel borrowed money from his cousin at a rate of 10% simple interest. After 1 year, $440
paid off the loan. How much did Mr. Noel originally borrow?
Answer:
$400Step-by-step explanation:
Using the formula for calculating the simple interest expressed as;
Simple Interest = Principal * rate * time/100
Note that the principal is the amount he originally borrowed
I = PRT/100 ............ 1
Amount paid off A = Principal+Interest
A = P+I ............ 2
From equation 2; I = A-P......... 3
Substitute equation 3 into 1;
A-P = PRT/100
Given A = $440, R = 10%, Time = 1year
Substitute the given parameters into the resulting equation;
440 - P = P*10*1/100
440-P = 10P/100
440-P = 0.1P
440 = 0.1P+P
440 = 1.1P
Divide through by 1.1;
1.1P/1.1 = 440/1.1
P = $400
Hence the amount Mr Noel originally borrow is $400
PLEASE HELP!! Find the length of UT¯¯¯¯¯¯¯+CV¯¯¯¯¯¯¯¯. A. 53 B. 4x + 35 C. 65 D. 59
Answer:
C. 65
Step-by-step explanation:
By the property of intersecting chords inside a circle.
[tex] TW\times WU = CW\times WV[/tex]
[tex] 14\times (2x + 2)= 12\times (2x + 5)[/tex]
[tex] 28x + 28= 24x + 60[/tex]
[tex] 28x - 24x =60-28[/tex]
[tex] 4x =32[/tex]
[tex] x =\frac{32}{4}[/tex]
[tex] x =8[/tex]
UT = 14+ 2x + 2
CV = 12+2x+5
UT + CV = 14 + 2x + 2 + 12 + 2x + 5
UT + CV = 4x + 33
UT + CV = 4*8+ 33 = 32 + 33 = 65
UT + CV = 65
25 precent of this square is shaded. What present of the square is not shaded
Answer:
75%
Step-by-step explanation:
Answer:
75%
Step-by-step explanation:
I'm sure you meant "percent," not "present."
If 25% of the square is shaded, then the percent that is not shaded is 75%.
Higher Order Thinking Describe the
transformation g of f(x) = |x| as a stretch and
as a compression. Then write two equations
to represent the function. What can you
conclude? Explain.
Answer:
Step-by-step explanation:
An absolute value function f when stretched or shrink vertically,
1). If a function f(x) = |x| is stretched vertically by a factor 'k',
g(x) = k[f(x)] = k|x| [where k > 1]
2). If the same function is vertically compressed by a factor 'k',
g(x) = k[f(x)] = k|x| [where 0 < k < 1]
Following these rules we can define a vertical stretch or compression of any function.
What’s an algebraic expression for 8 increased by three times a number
Answer:
3x + 8
Step-by-step explanation:
Number: x
Three times a number: 3x
Eight increased by three times a number: 3x + 8
Answer:
[tex]\huge\boxed{ 8 + 3x}[/tex]
Step-by-step explanation:
Let the number be x
So, three times x will be => 3x
Increases by 8 means adding 8 So, the final expression will be:
=> 8 + 3x