The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545
No. of Blue balls in the urn = 6
No. of Orange balls in the urn = 6
Total no. of balls in the urn = No. of blue balls + No. of orange balls
= 6 + 6
= 12 balls
No. of blue balls to be selected = 2
No. of orange balls to be selected = 2
No. of balls to be selected = 4
The total. no of ways 4 balls can be selected =[tex]^{12}C_{4}[/tex]
The No. of ways 2 blue balls can be selected = [tex]^{6}C_{2}[/tex]
The No. of ways 2 orange balls can be selected = [tex]^{6}C_{2}[/tex]
Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn
= [tex]^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}[/tex]
Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls
P = (15×15)/495
= 225 / 495
P = 0.4545
Therefore, the no. of ways to select blue and orange balls is 0.4545
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a telemarketing company is conducting a study of new calling scripts. seventy-five employees will be randomly assigned to three new scripts using a table of random digits. the study leader will assign the subjects to the groups using a table of random digits. how many unique two-digit numbers within the range of 01 to 75 will the study designer need to select from the table? 3 25 50 75
Answer:
50
Step-by-step explanation:
this shows that the percentage in a normal distribution that is at most 1.65 sds above average is about 95%. explain why 1.65 is the right number of sds to use when constructing a 90% confidence interval. (6 points)
The correct number of Standard deviation to generate a confidence interval is therefore 1.65.
Given that;
This shows that the percentage in a normal distribution that is at most 1.65 standard deviation above average is about 95%.
Percentage above 1.65 SD equals 100 - 95 = 5.
Now, because of the symmetric distribution,
Percentage above 1.65 SD = % below 1.65 SD is what we can see:
Below 1.65 SD + between 1.65 SD below and 1.65 above + above 1.65 SD + % above 1.65 SD = 100%
=> 5% + between -1.65 SD below and 1.65 above + 5% = 100%
=> % between -1.65 SD and 1.65 SD above mean = (100 - 5 - 5)% = 90%
The correct number of SDs to generate a confidence interval is therefore 1.65.
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Write the equation of the line that is parallel to the line 14x - 2y = 51 and goes through the point(3, -11)
how many ways can 7 students be assigned a seat in a classroom if there are 10 seats in a row? a) 70 b) 604,800 c) 120 d) 3,628,800 e) 17 f) none of the above.
The correct option c) 120; for the assignment of 7 students to 10 seats in a row.
What is referred as the combination?Combinations are mathematical techniques that count the number of potential arrangements for a set of elements only when order of the selections is irrelevant. You can choose the constituents of combos in any order.The procedure for determining how many arrangements are feasible when only a few items are selected from a set of items that are unique is as follows:The formula for finding the combination is-
ⁿCₓ = n!/ x!(n - x)!
Where,
n = total value.x = selected valueFor the given question.
Total students to be assigned a seat = 7.
Total seats in a classroom = 10.
Thus, Applying combination;
¹⁰C₇ = 10!/7!(10 - 7)!
¹⁰C₇ = 120
Thus, if there are 10 seats in a row, there are 120 different ways that 7 students could be seated in a classroom.
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A famous piece of artwork was up for bid at a museum auction. The minimum bid was $25,000.
Determine which inequality represents the bid for the artwork.
b ≥ 25,000
b ≤ 25,000
b < 25,000
b > 25,000
The inequality that represents the bid for the artwork is A. b ≥ 25,000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the famous piece of artwork was up for bid at a museum auction and the minimum bid was $25,000.
Let the minimum bid be b. This will be b ≥ 25,000.
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Find the slope of the line passing through the points (4, -2) and (9, -2).
slope:
Find the slope of the line passing through the points (2, 9) and (2, - 7).
slope:
Answer:
x1 y1 x2 y2
1. 0 - explanation - (4, -2) (9, -2) -2 - -2
4 - 9 (put a fraction bar when you put the y2 and y1 together and put the x2 and y2 in the denominator spot) basically -2 subtract -2 equals 0
2. it would be defined or 0
7.69 to the nearest whole number.
Answer: 8
Step-by-step explanation:
7.69 to the nearest whole number is 8
Solve the equation for x. Show each step of the solution for full credit. (3 points - 2 points showing work, 1 point correct answer)
3.5(x +2) = 17
Answer:2.86
Step-by-step explanation:
3.5(x +2) = 17
3.5x + 7 = 17
3.5x =17 - 7
3.5x =10
x = 10/3.5
x = 2.86
What do you need to multiply the subtotal by in order to get the total?
Given: Subtotal: 42.00
Total: 45.99
Tax rate: 9.5%
Sales tax: $3.99
An investor invested a total of $2,900 in two mutual funds. One fund eamed a 7% profit while the other eamed a 3% profit. If the investor's total profit was $143, how much was invested in each mutual fund?
Answer:
one is 203
two is 87
Step-by-step explanation:
a box has a width of 15 inches and a length of 16 inches. the volume of the box is increasing at a rate of 569 cubic inches per second, with the width and length being held constant. what is the rate of change, in inches per second, of the height when the height is 6 inches?
The rate of change in height when height is 6 inches is 2.37 inches per second approximately.
We know that the volume of cube with length L, width W and height H is given by,
V = L*B*H
So given that the length is 15 inches
the width is 16 inches
Let the height be h inches.
So now the volume is given by,
V = 15*16*h
Differentiating the volume with respect to time 't' we get,
dV/dt = 15*16 dh/dt
Now given that the rate of change in volume per second is 569 cubic inches.
So, dV/dt = 569
So, 15*16 dh/dt = 569
dh/dt = 569/(15*16) = 569/240 = 2.37 (approx)
So the rate of change in height is 2.37 inches approximately.
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Equation 1: y = 2²
Equation 2: y=2x-5
Equation
3: y = x² +6
Equation 4: y=
Witch one is non linear
From the given three options the equation y = x^2 + 6 is non - linear.
What is linear equation?
A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.
Consider, the first equation
y = 2^2
⇒ y = 4
Since, the constant equations are linear.
So, first equation is linear.
Consider, second equation
y = 2x - 5
Here, the variable x and y both having degree 1.
So, second equation is also linear.
Consider, third equation
y = x^2 + 6
Here, the variable y having degree 1, but the variable x having degree 2.
Therefore, equation (3) is non - linear.
Hence, the equation y = x^2 - 5 is non - linear.
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Sofia is 38 years old. Write an equation that relates Sofia's age to Tony's age, t. How old is Tony?
(Sofia’s age is 2 times the combined ages of Carlos and Lily - Carlos’s age is 4 more years than Tony’s age - and Lily’s age is one more than 6 times Tony’s age)
Answer:
Let s, c, y and t represent the ages of Sofia, Carlos, Lily and Tony respectively.
c + y = 2s ------ equation (1)
t + 4 = c ------ equation (2)
6t + 1 = y ------ equation (3)
Since Sofia is 38 years old, substitute s = 38 into equation (1):
c + y = 2(38)
= 76 ------ equation (4)
Substitute equations (2) and (3) into equation (4):
t + 4 + 6t + 1 = 76
7t + 5 = 76
7t = 71
∴ t = 10 (to the nearest whole number)
∴Tony is 10 years old (to the nearest whole number).
a client who weighs 70 kg is receiving a solution of 0.9% sodium chloride (normal saline) 500 ml with dopamine 800 mg at 5 ml/hour. how many mcg/kg/minute is the client receiving? (enter the numeric value only. if rounding is required, round to the nearest tenth.)
1.904 mcg/kg/min is what the client receives.
The number of mcg/kg/minute = flow rate × concentration ÷ mass of client
Flow rate = 12 ml/ hour = 12 /60 = 1/5 = 0.2 ml/min
Formula:
Concentration = mass of dopamine/volume
mass of dopamine = 800mg
volume = 500ml
Concentration = 800/ 500
= 1.6 mg/ml
= 1.6 × 1000 mcg/mg
= 1600 mcg/mg
Here the mass of the client = 70kg
Now calculating mcg/kg/minute = flow rate× concentration÷ mass of client
= 0.08 ml/min × 1600mcg/ml ÷70 kg
= 320/70
= 1.904 mcg/kg/min
Therefore mcg/kg/min is 1.904.
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what 29,000 divided by 50,000
Answer:
.58
Step-by-step explanation:
Can anyone answer question 8?
What is the inverse of this function? f(x)=1/3x-2
The inverse of the function f(x) = 1/3x-2 is f^-1(x) = (1 + 2x)/3x.
Inverse of a functionA function f is has an inverse if it is both one-to-one and onto.
Given the function f(x) = 1/3x-2
we replace f(x) with y and make x the subject of the formula to derive the inverse function f^-1(x) as follows ;
y = 1/3x - 2
by cross multiplication
3x - 2 = 1/y
add 2 to both sides of the equation
3x = 1/y + 2
3x = (1 + 2y)/y
divide both sides of the equation by 3
x = (1 + 2y)/y ÷ 3
x = (1 + 2y)/3y
So, f^-1(x) = (1 + 2x)/3x
Therefore, the inverse of the function f is derived by interchanging the value of x for y and vice versa, that is f^-1(x) = (1 + 2x)/3x.
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What is an equation of the line that passes through the points (-4, -3) and (8, 6)?
Answer:
Y = 3/4x + 0
Step-by-step explanation:
Find the slope of the line = Rise/Run.
[tex]\frac{-3-6}{-4-8}[/tex] = [tex]\frac{-9}{-12}[/tex]
= 0.75 or 3/4.
Therefore, insert into point slope form using one of the corresponding points; (8, 6) for example;
Y-6 = 3/4(x-8)
= Y-6 = 3/4x-6
and simplify the equation;
Y = 3/4x + 0 also just Y = 3/4x.
7. What number multiplied by 2/3 has a product
of 1? (Example 2) it's saying 4/6 is wrong what do i do
Answer:
3/2
Step-by-step explanation:
To multiply fraction×fraction, you multiply top×top and bottom×bottom.
2/3 × 3/2
= 6/6
= 1
The 3/2 is called the reciprocal. Take the number in the problem and flip it over to find the reciprocal.
if the probability of pulling a four of hearts from a randomly shuffled deck is 1 / 52, and the probability of pulling a spade from a randomly shuffled deck are 1 / 4, then the probability of pulling a spade or a four of hearts from a randomly shuffled deck is:
The probability of pulling a spade or a four of hearts is 0.264 .
we have , from a deck of cards
probability of pulling a spade = 1/4 = 13/52
probability of not pulling a spade 3/4 = 39/52
probability of pulling a 4 of hearts = 1/52
probability of not pulling a spade = 51/52
we have to find the probability of pulling a spade or a four of hearts from a random shuffled deck
So we can get three cases :
case A :
getting a spade and not getting four of hearts
∴ P (A) = [tex](\frac{13}{52} ) (\frac{51}{52} )[/tex] = 663/2704
case B :
not getting a spade and getting four of hearts
P(B) = [tex](\frac{39}{52}) (\frac{1}{52} )[/tex] = 39/2704
case C :
getting a spade and getting four of hearts
P(C) = [tex](\frac{13}{52})(\frac{1}{52} )[/tex] = 13/2704
therefore , the required probability will become
P = P(A) +P(B) + P(C)
P = 715/ 2704
P = 0.264
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Which inequality has like variable terms on each side of the inequality symbol?
Inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
As given in the question,
Inequality which have like variables term on each side of the given inequality symbol is :
a. 15c + 25 ≤ 115
In the given inequality, on left hand side we have variable c and constant term while on the right hand side of the inequality only constant.
Not correct option.
b. 0.75r - 6.25 > 10
In the given inequality, on left hand side we have variable r and constant term while on the right hand side of the inequality only constant.
Not correct option.
c. 16 - 2x > x + 16
In the given inequality, on left hand side we have variable x and constant term while on the right hand side of the inequality also variable x and constant term.
Correct option.
d. 12.25h -175 < 5,000
In the given inequality, on left hand side we have variable h and constant term while on the right hand side of the inequality only constant.
Not correct option.
Therefore, inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
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Ahmad decided to increase his homework time of 8 hours per week by 15%,
Calculate his new homework time.
Give your answer in hours and minutes.
Answer:
it's a answer done bro
Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked how much is Nick share of the money. Nick and Pam are paid ?
Nick got a total of $33.25 for his part of work.
What is the general equation of a Straight line? How it represents a proportional relationship?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked.
Assume that Nick recieved $[x]. Then, Pam will get - (52.25 - x). For direct proportionality -
y₁/x₁ = y₂/x₂
We can write -
x/3.5 = (52.25 - x)/2
2x = 3.5(52.25 - x)
2x = 182.875 - 3.5x
x = 33.25
Therefore, Nick got a total of $33.25 for his part of work.
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Translate "eight more than the sum of y and x" into a variable expression.
Answer:
(y+x)+8
it is expressed like that i think
Answer:
(Y+x)+8
Step-by-step explanation:
Sutton takes 48 minutes to walk to work. after getting a new job, sutton takes 30.72 minutes to walk to work. what was the percent decrease in the travel time?
The percent decrease in the travel time after getting a new job is 36%.
Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".
First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.
decrease in time = 48 - 30.72
decrease in time = 17.28
Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.
percent decrease = (17.28 / 48) x 100
percent decrease = 36%
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Express 60 as the product of its prime factors.
60 = (Answer here)
Answer:
2x2x3x5= 60
I hope you like it
Answer:
2 X 2 X 3 X 5
Step-by-step explanation:
We divide 60 by 2 as many times as possible to get 60 = 15 x 2 x 2. 2 is a prime number so we don't need to break the 2's down any more. Instead we break 15 down. 15 doesn't divide by 2 so we try the next prime number: 3 Divide 15 by 3 to get 15 = 5 x 3, and so 60 = 5 x 3 x 2 x 2. Now we collect the factors, so our final answer is 60 = 5 x 3 x 22.
a car travels 75 miles in the same amount of time that it takes another car, moving 10 mph faster that has traveled 100 miles. what is the number of miles per hour in the speed of the faster car?
The speed of the faster car is 40 miles/hr.
both cars travel for same time , so let that time be 't'
car 1 :
distance travelled = 75 miles
let the speed of the car be = x miles/hr
∴ time (t) = distance / speed
t = 75 / x .............(1)
car 2 :
distance travelled = 100 miles
speed of the car is = x + 10 miles/hr ( already provided )
∴ time ( t) = distance / speed
t = 100/ (x+10) ..............(2)
now as the time for both the cases is same , so we equate eqn (1) and eqn (2) .
∴ 75/x = 100/ (x+10)
3x + 30 = 4x
x = 30
so the speed of the 1st car will be 30 miles / hr
and the speed of the 2nd car ( faster car ) will be x + 10 = 40 miles/hr
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Which ordered pair is NOT a solution to the equation y = 2x? Four points plotted on a coordinate plane. Point A has coordinates 1 comma 2. Point B has coordinates 2 comma 4. Point C has coordinates 3 comma 8. Point D has coordinates 5 comma 10. point A point B point C point D
Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.
Given that,
To determine which ordered pair is NOT a solution to the equation y = 2x.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given relation y = 2x
Now substitute every value of x from the ordered pair and match the output with the corresponding value of the ordered pair.
put x = 1, 2, 3, 5
Y = 2(1)
y = 2
Similarly the outcome of the values,
x = 2, 3, 5
y = 4, 6, 10
Thus, Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.
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Find two consecutive positive odd integers such that three times the sum of the largest number plus 22 is equal to the product of both numbers.
Answer:
Step-by-step explanation:
Let's say your consecutive numbers are A and B with A+2=B. Using the information we have been given, we can get the linear equation; AB=3B+22. A=B-2, so we can replace A with B-2 to get (B-2)(B)=3(B+22). Multiplying this out, we get B^2-2B=3B+66. Simplifying, we get B^2-5B-66=0. This is a quadratic equation. Using the quadratic formula, we get B=11,-6. B has to be positive, so B=11. A+2=11, so A=9
At the craft store, Tara bought 12 yards of fabric to make tote bags. Each bag requires 1.25 yards of fabric.
Write an equation that shows how the number of yards of fabric remaining, y, depends on the number of tote bags Tara sews, x.
The number of yards of fabric remaining, y, depends on the number of tote bags Tara sews, x is y = 12 - 1.25x.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, Tara bought 12 yards of fabric to make tote bags and each bag requires 1.25 yards of fabric.
The equation that describes the number of yards of fabric remaining, y, depends on the number of tote bags Tara sews, x is
y = 12 - 1.25x.
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