Answer:
39.16% probability of selecting three Democrats and three Republicans
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the people are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
3 Democrats, from a set of 8.
3 Republicans, from a set of 8.
[tex]D = C_{8,3}*C_{8,3} = (C_{8,3})^{2} = (\frac{8!}{3!5!})^{2} = 56^2 = 3136[/tex]
Total outcomes:
6 people from a set of 16.
[tex]T = \frac{16!}{6!10!} = 8008[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{3136}{8008} = 0.3916[/tex]
39.16% probability of selecting three Democrats and three Republicans
Which statement about √2x+3= √2x+3 is true? A.X=1/2 is an extraneous solution. B.X=1/2 is a true solution. C.X=2 is an extraneous solution. D.X=2 is a true solution
Answer:
B and DStep-by-step explanation:
This equation is true in either case, because the expression [tex]\sqrt{2x} +3[/tex] is equivalent to itself, that means the equation is true for all positive real numbers including the zero.
Therefore, the right answers are B and D, both numbers are true solutions of the expression.
Answer:
A: x=1/2 is an extraneous solution.
Step-by-step explanation:
The larger of two numbers is 33 more than the smaller. When added together, the sum of the larger number and five times the smaller number is 129. What are the two numbers? larger number = ___ smaller number = ____ Please Help!
Step-by-step explanation:
let the larger number be x and smaller number be y
according to this question
x=y+33----------(1)
y+33+5y=129----------(2)
6y+33=129
y=16
x=16+33(takimg equation (1)
x=49
Answer:
Larger number: 49.
Smaller number: 16.
Step-by-step explanation:
Let's say that the larger number is represented by y, and the smaller is represented by x.
y = 33 + x
y + 5 * x = 129
(33 + x) + 5x = 129
6x + 33 = 129
6x = 96
x = 16
y = 33 + 16
y = 49
Check our work...
49 + 5 * 16 = 49 + 80 = 129
49 = 33 + 16 = 49
Since it all works out, the larger number is 49 and the smaller number is 16.
Hope this helps!
Simplify the square root of 2 times the cube root of 2.
two to the one sixth power
two to the two thirds power
two to the five sixths power
two to the seven sixths power
Answer:
2 to the 1/6 th power
Step-by-step explanation:
square root = 1/2
Cube root = 1/3
so 1/3 x 1/2= 1/6
can i please have brainlest
Answer:
2 to the 1/6 th power
Step-by-step explanation:
square root = 1/2
Cube root = 1/3
so 1/3 x 1/2= 1/6
can i please have brainlest
The parabola x = y2 - 9 opens:
Answer:
To the RIGHT
Step-by-step explanation:
The parabola will open right if the y^2 is positive and will open left if the y^2 is negative.
5 ∑3i i=1 it was kinda hard to type but the five is on top plzzzzz helppppp
Answer:
45
Step-by-step explanation:
We are using sigma notation to solve for a sum of arithmetic sequences:
The 5 stands for stop at i = 5 (inclusive)
The i = 1 stands for start at i = 1
The 3i stands for expression of each term in the sum
oe has a cube shaped box that needs to be filled with package materials. if the length of one side is 2 feet, then what is the volume of the box
Step-by-step explanation:
use length x width x height
what is the value of x?
X = 30 degrees.
See the attached image
Triangle L M N is shown. Angle L M N is a right angle. Angles N L M and L M N are 45 degrees. The length of L N is x. Which statements are true regarding triangle LMN? Check all that apply. NM = x NM = LM = x StartRoot 2 EndRoot tan(45°) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction tan(45°) = 1
Answer:
A.) NM= x
C.) LM = x√2
E.) tan (45°) = 1
Step-by-step explanation:
If the legs are both x, then the hypotenuse is equal to [tex]x\sqrt{2[/tex]
Therefore, LM= [tex]x\sqrt{2[/tex] is correct and MN= x
Disclaimer: The sum is done according to the picture attached as the question given is wrong.
The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.What are isosceles right triangles?An isosceles triangle is a triangle where two sides and their corresponding angles are equal.
A right triangle is a triangle with one angle = 90°.
An isosceles right triangle is a right-angled triangle with two legs including the right angle are equal. Their corresponding angles are equal and each of them = 45°. So, the three angles of an isosceles right triangle are 45°, 45°, and 90°, always.
How do we solve the given question?In the figure, we can see that we have a ΔLMN, with ∠L = 45°, ∠M = 45°, and ∠N = 90°. Also, we can see that LN = x.
The given angles of ΔLMN determine that it is an isosceles right triangle with a right angle at N.
Since, the two legs involving the right angle, that is N, are equal, we can say that, NM = LN = x.
The hypotenuse of the ΔLMN, that is the side opposite to ∠N, that is LM, can be found using the Pythagoras theorem, by which in a right-angled triangle,
Hypotenuse² = Base² + Perpendicular².
∴ LM² = LN² + NM² = x² + x² = 2x².
or, LM = √(2x²) = x√2.
The tangent of an angle ∅, that is, tan ∅ is computed using the formula,
tan ∅ = Perpendicular/Base.
To calculate tan 45°, that is, tangent to ∠L, we take Perpendicular = NM and Base = LN.
∴ tan 45° = NM/LN = x/x = 1.
Now, we check all the given options:
NM = x. TRUE (computed)NM = x√2. FALSE (∵ NM = x)LM = x√2. TRUE (computed)tan 45° = √2/2. FALSE (∵ tan 45° = 1)tan 45° = 1. TRUE (computed)∴ The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.Learn more about isosceles right triangle at
https://brainly.com/question/691225
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A line whose slope is 4 and passes through the point (0, -9) lies on the line whose equation is:
Answer:
y = 4x - 9
Step-by-step explanation:
Use the formula:
y = mx + b
Where m is the slope, b is the y-intercept.
The slope is 4.
y = 4x + b
The y-intercept is -9 because it passes through (0, -9).
y = 4x - 9
1. Meredith has 10 reports to file. If each report takes an average of 75 minutes to file, how long will it take her to file 70% of
them?
Answer:
70% of the reports will take 525 minutes (8 hours, 45 minutes) to file.
Step-by-step explanation:
Given;
total number of Meredith's report, N = 10
average time taken for each report to be filed is, t = 75 minutes per report
let the total time for the 10 reports = T
[tex]\frac{T}{N} = t\\\\T = N*t \\\\T = 10 *75\\\\T = 750 \ minutes[/tex]
The total time for the 10 reports is 750 minutes.
Time taken to file 70 % of 10 reports = (0.7 x 10) x (75 mins)
= 0.7 x 750
= 525 minutes (8 hours, 45 minutes)
Therefore, 70% of the reports will take 525 minutes (8 hours, 45 minutes) to file.
A population of protozoa develops with a constant relative growth rate of 0.7233 per member per day. On day zero the population consists of four members. Find the population size after six days.
Answer:
307 members
Step-by-step explanation:
Relative growth rate= Growth rate/population
Given: constant relative growth rate=0.7233
0.7233=[tex]\frac{dP/dt}{P}[/tex]
[tex]\frac{dP}{dt} =0.7233 P[/tex]
Theorem 2 states that solutions of the differential equation dy/dt = ky are in the form: y(t)=y(0)[tex]e^k^t[/tex]
Writing the soltuion of our dif. equation as:
P(t)=P(0)[tex]e^{0.7233t}[/tex]
since on day zero the population consists of four members.
P(t)=4[tex]e^{0.7233t}[/tex]
next is to find the population size after six days. i.e t=6
P(6)=4[tex]e^{0.7233\times 6}[/tex] ≈ 307 members
Delicious Candy markets a two-pound box of assorted chocolates. Because of imperfections in the candy making equipment, the actual weight of the chocolate has a uniform distribution ranging from 31 to 32.5 ounces. What is the probability that a box weighs more than 32.2 ounces?
Answer:
20% probability that a box weighs more than 32.2 ounces
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X higher than x is given by the following formula.
[tex]P(X > x) = \frac{b-x}{b-a}[/tex]
Uniform distribution ranging from 31 to 32.5 ounces.
This means that [tex]a = 31, b = 32.5[/tex]
What is the probability that a box weighs more than 32.2 ounces?
[tex]P(X > 32.2) = \frac{32.5 - 32.2}{32.5 - 31} = 0.2[/tex]
20% probability that a box weighs more than 32.2 ounces
An electrician earns $50 per hour, and expects to earn $5 additional per hour as each year passes. Find the electrician’s hourly wage after 8 years have elapsed.
50 POINTS PLEASE HELP will mark brainlest COMPRESSION BY A FACTOR OF 2 photos attached
Answer:
Point A'(-1,5) ........ corrected A' instead of A
Point B'(3,-3)
Step-by-step explanation:
The current function has vertex (2,-4), and passes through (6,0).
Using the standard formula
y = a(x-h)^2+k
we have
h = 2, k=-4
parabola passes through (6,0) =>
0 = a(6-2)^2 -4 = 16a -4
a = 1/4
so equation of given curve is
f(x) = (1/4)(x-2)^2-4
If the curve is compressed horizontally by a factor of 2, then the image is
g(x) = (1/4)(2(x-2))^2-4
=(x-2)^2 -4
Given A(-4,5), B(4,-3)
f(-4) = 5
f(4) = -4
With a compression factor of 2, coordinates of y do not change.
for point A'
5 = (x-2)^2 -4
5 = (x-2)^2 -4
(x-2)^2 = 9
(x-2) = +/- 3
x-2 = -3, x = -1 (to the left of vertex, ok)
x-2 = +3, x = 5 (to the right of vertex, alternate point x)
Point A'(-1,5) ........ corrected A' instead of A
For point B'
y = -3
-3 = (x-2)^2-4
(x-2)^2 =1
x-2 = +/- 1
x-2 = +1, x=3 (to the right of vertex, point required)
x-2 = -1, x= 1 (to the left of vertex, alternate point Y)
Point B'(3,-3)
Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $550 interest. The same amount invested in the other fund earns $770. Find the lower rate of interest. _________ %
Answer:
10% interest.
Step-by-step explanation:
Interest I = PRT/100
If the rate R = x% we have
550 = P*x *1 / 100
and
770 = P*(x + 4) * 1 / 100
so From first equation
Px = 55000 and from the second
Px + 4P = 77000
So Px = 77000 - 4P
Therefore 77000 - 4P = 55000
4P = 22000
P = 5,500
So x = 55000/5500 = 10%.
And the rate for the other fund is 10 + 4 = 14%.
Which choice is a solution to the system of equations?
To solve this system, I would use substitution.
Since our first equation tells us that y = 2x - 3, we can substitute a
2x - 3 in for the y in our second equation to get 2x - 3 - 9 = -x.
Simplifying on the left we get 2x - 12 = -x.
Moving the 2x to the right, we have -12 = -3x.
Now divide both sides by -3 and we have 4 = x.
To find y, plug 4 back into either one of the original equations.
I'll go with the first one.
So we have y = 2(4) - 3.
Solving from here, we find that y = 5.
So the solution to this system is (4,5).
Not sure about this.. please help!!
Answer:
Cube
Step-by-step explanation:
A cube is a 3-D shape that consists of 6 squares. A cube is the correct following shape that must have a square base or a square bottom since all of it's sides are the shape of a square.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Answer:
Step-by-step explanation:
The cube is the only one there that must have a square base.
The rectangular prism might have a square base, but most likely it does not. T
The pyramid can have a square base like the ones in Egypt but it can also have a triangular base.
A cone has a circular base.
Which of these equations, when solved, gives a different value of x than the other three? 1. 9.1 = -0.2x + 10 2. 10 = 9.1 + 0.2x 3. 10 – 0.2x = 9.1 4. 9.1 – 10 = 0.2x
Answer:
4. 9.1 – 10 = 0.2x
X= -4.5
Step-by-step explanation:
Let's solve for x in the equations given below
1. 9.1 = -0.2x + 10
9.1 - 10 = -0.2x
-0.9= -0.2x
-0.9/-0.2= x
4.5 = x
2. 10 = 9.1 + 0.2x
10-9.1 = 0.2x
0.9= 0.2x
0.9/0.2 = x
4.5 = x
3. 10 – 0.2x = 9.1
10-9.1= 0.2x
0.9= 0.2x
0.9/0.2= x
4.5 = x
4. 9.1 – 10 = 0.2x
-0.9 = 0.2x
-0.9/0.2= x
-4.5 = x
The different equation is equation 4
Reason because it's answer gave a negative value of x while others gave a positive value of x.
But in magnitude they all have same value of x
Answer:Its D
Step-by-step explanation:
I just did it on ed
mohsin is writing a 2400 words essay for his school project he writes 1/5 of the essay on the first day 2/3 of the remainder on the second day 220 words on third day now he has to write the conclusion how long was his conclusion
Answer: 420 words
Step-by-step explanation:
First find how much he did the first day by doing 1/5*2400=480.
Then find out how much he did the second day by doing 2400-480=1920, then doing 1920*(2/3)=1280.
Then, because he did 220 words the third day, simply do 2400-480-1280-220=420.
Hope it helps <3
Ans420 words per min
Step-by-step explanation:
the area of a right triangle is 77 m^2. the hypotenuse has a length of √317 m. what is the length of the legs?
Answer:
11 m and 14 m
Step-by-step explanation:
Legs: x and y
---
1/2xy= 77 ⇒ xy= 154
√x²+y²= √317 ⇒ x²+y²=317
x²+y²+2xy= (x+y)²= 2*154+317= 625 ⇒ x+y= √625= 25
x= 25-y
xy=154 ⇒ y(25-y)= 154 ⇒ 25y- y²=154 ⇒ y²- 25y +154=0 ⇒ y=11 and y=14
x= 25-y= 14 and 11
When plotting points on the coordinate plane below, which point would lie on the y-axis? A coordinate plane. (0, 1) (7, 0) (6, 8) (8, 2)
Answer:
Numbers 1,0,8,2 would lie on y-axis.
Step-by-step explanation:
This is because for example, (0,1)
we must prefer 0 as x-axis and 1 as y-axis. That's means left number or side will always be x-axis and right side will always be y-axis.
Answer: (0, 1)
Step-by-step explanation:
When the x is 0 is lies on the y axis.
What is the measure of ea
Answer:
u forgot picture
Step-by-step explanation:
if not then define ea
werido modz... up for a laugh? I can't answer a question that is measure ea with no picture nor any info
Which function represents a parabola that opens downward and has a vertex at (3,-4)
Answer:
y = -(x-3)² -4
Step-by-step explanation:
Select the correct answer for the blank: If everything else stays the same, the required sample size ____ as the confidence level decreases to reach the same margin of error. Answer:
Answer:
The required sample size increases.
Step-by-step explanation:
The margin of error of a confidence interval is given by:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level(the higher the confidence level the higher z), [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
The confidence level decreases, so z decreases.
For the margin of error to stay the same, the sample size also has to decrease.
The required sample size increases.
Divide and answer in simplest form: 1/5 ÷ 7
Answer: 1/35
Step-by-step explanation:
1/5 = 0.2
0.2/7= 1/35
Answer:
[tex] \frac{1}{35} [/tex]Step by step explanation
[tex] \frac{1}{5} \div 7[/tex]
Dividing is equivalent to multiplying with the reciprocal:
[tex] \frac{1}{5} \times \frac{1}{7} [/tex]
Multiply the fraction
[tex] \frac{1 \times 1}{5 \times 7} [/tex]
[tex] = \frac{1}{35} [/tex]
Hope this helps...
Good luck on your assignment.
69/8 as a mixed number
Answer:
Hey!
69/8 as a mixed number is...
8 5/8!
To get this answer, simply divide 69 by 8, then subtract the WHOLE NUMBER from 69 and then the left over number is the numerator over 8
Hope this helps!
Answer:
8 5/8
Step-by-step explanation:
Chris placed $7,400 in a savings account which compounds interest annually at a rate of 5.7%. How much will he have in the account after 4 years?
Answer:$9237.02
Step-by-step explanation:
A = p(1+r/n)^nt
A = 7400 (1 + 0.057)^4
A = 7400(1.057)^4
A = 9237.02
Do not add the .02 at the end of this answer
26.355 rounded to the nearest hundredth tell anser
Answer:
26.36
Step-by-step explanation:
Hundredths are the second decimal place from the decimal. You would round up to 26.36 because the number before that is up to 5. If it was below 5 you would round down to 26.35.
Convert 58% to a decimal
Answer: 0.58
Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100.
So we can think of 58% as the ratio 58 to 100 or 58/100.
Dividing by 100 moves the decimal point 2 places to the left so 58/100 would move the decimal point 2 places to the left which would give us .58 or 0.58. So 58% can be written as the decimal 0.58.
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The calculated value for the test statistic equals a. 20. b. 4. c. 2. d. -2.
Answer:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
Step-by-step explanation:
For this problem we have the following observed values:
Yes 40 No 60 No Opinion 50
And we want to test the following hypothesis:
Null hypothesis: All the opinions are uniformly distributed
Alternative hypothesis: Not All the opinions are uniformly distributed
And for this case the statistic would be given by:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4