Answer:
we will mix 55 liters of 20% solution and 20 Liters of 50% solutions.
Step-by-step explanation:
let the 20% solution = x liters
let the 50% solution = y liters
total solution of the mixture of the two solutions in % = 28%
total solution of the mixture of the two solutions in liters = 75 liters
considering the total solutions given, we will have the following equations if we mix the solutions in equal proportion;
20x + 50y = 28 (75)
0.2x + 0.5y = 0.28(75)
0.2x + 0.5y = 21 -------equation 1
Also,
x + y = 75 ------equation 2
y = 75 - x
(substitute this into equation 1)
0.2x + 0.5(75 - x) = 21
0.2x + 37.5 - 0.5x = 21
0.2x - 0.5x = 21 - 37.5
-0.3x = -16.5
x = -16.5 / -0.3
x = 55 liters
Recall, y = 75 - x
y = 75 -55
y = 20 Liters
Thus, we will mix 55 liters of 20% solution and 20 Liters of 50% solutions.
Find cos angle∠ C
A. 5/13
B. 12/13
C. 12/5
D. 13/5
Answer:
The answer is A.
Step-by-step explanation:
Recall SohCahToa, which tells us that cosine is the ratio of the adjacent side to the hypotenuse. In other words:
[tex]\displaystyle \cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side to ∠C is 10 and the hypotenuse is 26.
Therefore:
[tex]\displaystyle \cos(C)=\frac{10}{26}=\frac{5}{13}[/tex]
Our answer is A.
The domain of the function is all
The range of the function is all
The domain of a function is the set of all the x terms of the function and the range of a function is the set of all the y terms of a function.
For example, take a look below.
The domain is the set of all x terms in each ordered pair and the
range will be the set of all the y terms in each ordered pair.
What’s the correct answer for this question?
Answer:
D.
Step-by-step explanation:
For independent events
P(A and B) = P(A) × P(B)
FINDING P(B)
P(B) = P(A and B) /P(A)
P(B) = 0.6/0.8
P(B) = 0.75
Now, when you click ROLL, the simulator will keep track of the average of all rolls so far. For example, if you roll 2 and then 4, the average will be 3. ROLL sides What is the average after 10 rolls
Step-by-step explanation:
Suppose the results obtained are numbers from 1 to 10, then after 10 rolls, the average is
(1+2+3+4+5+6+7+8+9+10)/10
= 55/10
= 5.5
Answer:
5 , 3 , 3.5 C) The average would approach a set value.
Step-by-step explanation:
The first three numbers don't matter it could be anyone 1-6.
The last answer is C
The sum of a number and its reciprocal is 41/20. Find the number. smaller value larger value
Step-by-step explanation:
Let the number is x. Its reciprocal will be 1/x. According to given condition, we get :
[tex]x+\dfrac{1}{x}=\dfrac{41}{20}\\\\\dfrac{x^2+1}{x}=\dfrac{41}{20}\\\\20x^2+20=41x\\\\20x^2-41x+20=0[/tex]
It is a quadratic equation. The values of x are :
[tex]20x^2-25x - 16x+ 20 =0\\\\5x(4x - 5) -4( 4x - 5) = 0\\\\(5x-4)(4x-5)=0\\\\5x-4=0\ \text{and}\ (4x-5)=0\\\\x=\dfrac{4}{5}\ \text{and}\ x=\dfrac{5}{4}[/tex]
The smaller number is 4/5 and the larger number is 5/4.
In order to get promoted to the next grade, a student is required to score above 55 in the final test. Assume the scores to be normally distributed with a mean of 60 and a standard deviation of 5.5. Calculate the percentage of students who will be promoted to the next grade.
Answer:
[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]
And we can find this probability with the complement rule:
[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]
And we can use excel or the normal standard table and we got:
[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]
So then we expect about 81.8% of students that will be promoted
Step-by-step explanation:
Let X the random variable that represent the scores of promotion of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(60,5.5)[/tex]
Where [tex]\mu=60[/tex] and [tex]\sigma=5.5[/tex]
We want to find the following probability:
[tex]P(X>55)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the z score formula we got:
[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]
And we can find this probability with the complement rule:
[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]
And we can use excel or the normal standard table and we got:
[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]
So then we expect about 81.8% of students that will be promoted
At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time?
Step-by-step explanation:
The probability of success = 8/(8 + 17) = 8/25 = 0.32.
Let X be the random variable denoting the number of successes (number of times the individual won a prize) in four picks.
Hence, X ~ Bin(4, 0.32).
Thus, P(X = 1) = [tex]4C_1=(0.32)(1-0.68)^{4-1}=4C_1(0.32)(0.68)^3[/tex]
The probability the individual will win a prize exactly one time is
C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
There are a total of eight ducks with “Win” written on the underside of the duck, and there are 17 ducks with “Lose” written on the underside of the duck.
The probability of success
P = 8/(8 + 17)
P = 8/25
P = 0.32
Let's suppose the X is the random variable denoting the number of the individual won a prize in four picks.
So,
X ~ Bin(4, 0.32).
Thus, P(X = 1) = C(4, 1)(0.32)(1 0.32)⁴⁻¹
= C(4, 1)(0.32)¹ (0.68)³
Thus, the probability the individual will win a prize exactly one time is
C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.
Learn more about the probability here:
brainly.com/question/11234923
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A password for a website must have 4 different digits. What is the probability a password chosen at random is 7654?
Please show work thanks
The 1st digit is 1 out of 10 numbers
The 2nd digit is 1 out of 9 numbers
The 3rd digit is 1 out of 8 numbers
The 4th digit is 1 out of 1 numbers.
Total combinations are 10 x 9 x 8 x 7 = 5040
Since the combination 7654 is one out of the total the probability would be 1/5040
I am just confused can someone help please...
Answer true or false to each statement concerning a confidence interval for a population mean.a) The length of a confidence interval can be determined if you know only the margin of error.b) The margin of error can be determined if you know only the length of the confidence interval.c) The confidence interval can be obtained if you know only the margin of error.d) The confidence interval can be obtained if you know only the margin of error and the sample mean.e) The margin of error can be determined if you know only the confidence level.f) The confidence level can be determined if you know only the margin of error.g) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.h) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
Answer:
The true statements Include
A) The length of a confidence interval can be determined if you know only the margin of error.
B) The margin of error can be determined if you know only the length of the confidence interval.
D) The confidence interval can be obtained if you know only the margin of error and the sample mean.
G) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
F) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
The false statements include
C) The confidence interval can be obtained if you know only the margin of error.
E) The margin of error can be determined if you know only the confidence level.
F) The confidence level can be determined if you know only the margin of error.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
The critical value is obtained using the confidence level (and sample size for t-distributions).
Standard Error of the mean = (Standard deviation)/[√(sample size)]
Standard error of the mean = σₓ = (σ/√n)
Taking each of the statements one at a time
a) The length of a confidence interval can be determined if you know only the margin of error.
According to the mathematical expression of the confidence interval, the length of the confidence interval is 2 × Margin of error. Hence, the length of the confidence interval can be truly obtained from only the margin of error.
This statement is true.
b) The margin of error can be determined if you know only the length of the confidence interval.
This is another way of phrasing statement A. The margin of error is half of the length of the confidence interval.
Hence, this statement is also true.
c) The confidence interval can be obtained if you know only the margin of error.
The confidence interval can be obtained from an expression that involves the sample mean and margin of error.
Confidence Interval = (Sample mean) ± (Margin of error)
The confidence interval cannot be obtained from just the margin of error. Hence, this statement is false.
d) The confidence interval can be obtained if you know only the margin of error and the sample mean.
Like o stated in (c) above, the confidence interval can be obtained from an expression that involves the sample mean and margin of error.
Confidence Interval = (Sample mean) ± (Margin of error)
Hence, this statement is true.
e) The margin of error can be determined if you know only the confidence level.
To obtain the margin of error, if the confidence interval isn't used, an expression involving the critical value and the standard error of the mean is used.
Margin of Error = (Critical value) × (standard Error of the mean)
The critical value is obtained using the confidence level, but the margin of error cannot be obtained from just that, we still need the standard error of the mean.
Hence, this statement is false.
f) The confidence level can be determined if you know only the margin of error.
This is another way of phrasing statement E. Hence, this statement too is false.
g) The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.
This is true as these is all that is required to obtain the margin of error.
h) The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.
This can be a bit stressful to obtain, but it is true. It is easy to see this from all the explanation from the beginning to this point.
Hope this Helps!!!
A standard card deck has 52 cards consisting of 26 black and 26 red cards. Three cards are dealt from a shuffled deck, without replacement. Complete parts a through c below. a. Determine whether the following statement is true or false. The probability of being dealt three black cards is one half times one half times one half equals one eighth . If true, explain why. If false, show how to get the correct probability.
Answer:
6 / 51
Step-by-step explanation:
It is false.
Reason:
The probability of picking a black card at first is:
26 / 52 = 1/2
There are now 25 black cards and 51 cards in total.
The probability of picking another black card, if there's no replacement is now:
25 / 51
Now, there are 24 black cards and 50 cards left in total.
The probability of picking a black card without replacement now becomes:
24 / 50 = 12 / 25
Hence, the probability of picking three black cards without replacement is:
1/2 * 25/51 * 12 / 25 = 300 / 2550
In simplest form, it is 6 / 51
factorise fully 24x+16
Answer:
8(3x + 2)
Step-by-step explanation:
→To factorize this expression, you must take out the GCF (Greatest Common Factor). The GCF is the biggest number that you can take out of all the terms in the expression, meaning the number has to be able to be divide by 24x and 16.
→The GCF is 8:
8(3x + 2)
Answer:
8(3x+2)
Step-by-step explanation:
24x+16
8*3*x + 8*2
Factor out an 8
8(3x+2)
If (x + 5) - 2(4x - 1) = 0, what is the value of x?
Answer:
x=1
Step-by-step explanation:
(x + 5) - 2(4x - 1) = 0
Distribute
x+5 - 8x +2 =0
Combine like terms
-7x +7 = 0
Add 7x to each side
-7x+7 +7x = 7x
7 = 7x
divide by 7
7/7 = 7x/7
1 =x
3. Barbara was asked to create a set of numbers that contained only integers. Which of the sets does
NOT contain only integers?
А
12
B
-3, -4,600,
9, 100, - 4, 12, -6, 5
5. 3, -6, -14, 3.5, 7
с
24
12
D 22, -12.0, 9, -14, 28, 4
Answer:
C (5.3, -6, -14, 3.5, 7)
Step-by-step explanation:
Integers are the sets of positive and negative whole numbers including zero.
In set notation, we denote the set of integers using the letter [tex]\mattbb{Z}[/tex].
From the given options:
In Option C (5. 3, -6, -14, 3.5, 7), we have the number 3.5 and 5.3 which are not whole numbers. Therefore 3.5 and 5.3 are not integers.
Option C is the set which does not contain only integers.
What is the value of X?
Answer:
the answer to the problem is 35.
Answer:
he horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa"
Step-by-step explanation:
When vector is added to vector , the resultant is vector such that . This resultant vector has components Rx=Ax+BxRx=Ax+Bx and Ry=Ay+ByRy=Ay+By. How do you determine the direction of , the angle the vector makes with the positive x-axis?
Answer:
a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.
b. ∅ = [tex]tan^{-1}[/tex](Rx/Ry)
Step-by-step explanation:
Vectors are used to express physical quantities with magnitude and direction. Vectors can be added by the parallelogram method or the triangular method of addition. the magnitude and direction of the resultant vector is usually proportional to the magnitude and direction of the component vectors.
The direction of the angle is found as
tan∅ = Rx/Ry
∅ = [tex]tan^{-1}[/tex](Rx/Ry)
What is the surface area of the figure shown?
Answer:
90 square feet.
Step-by-step explanation:
Let's set up an equation!
SA= 2(xy)+2(xz)+2(yz).
Lets say that x=3 y=6 and z=3
We plug it in.
2(18)+2(9)+2(18)= SA
36+18+36=SA
72+18=SA
90=SA
90 square feet = Surface area.
rewrite the following without an exponent (-7)-1
Answer:
Step-by-step explanation:
-7-1=-8
The required return on equity is:
A) It has nothing to do with market risk premium
B) generally less than post-tax debt costs.
C) A debt/capital ratio of 0.5 is smaller than WACC.
D) is directly related to the risk of the company's assets.
E) It is generally the reciprocal of inflation.
Answer:
D) is directly related to the risk of the company's assets.
Step-by-step explanation:
Equity which may be defined as what the difference between what your business worth minus what you owe in it.
It can also be put in a way as the remaining value of an owners interest in a particular company after all debt might have been cleared.
Equity= assets - liability
So equity has a lot to do in the risk management of a business or a particular company.
Which symbol should go into the box to make the statement true?
|17| ? 17.
A.< B.> C.equal sign with a line through it D. =
Answer:
the 3rd option is the right one
Directions:
Write and solve a proportion to answer the question.
1/5 is 40% of what number?
Answer:
20/40
Step-by-step explanation:
1/5=40/100*x
x=1/5*100/40
x=20/40 or 10/20 or 0.5
At 5:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 38520 ft and is descending at the rate of 750 ft/min. Airplane #2 has an elevation of 9400 ft and is climbing at the rate of 550 ft/min. (1) Let t represent the time in minutes since 5:00 am, and let E represent the elevation in feet. Write an equation for the elevation of each plane in terms of t . plane #1: E ( t ) = plane #2: E ( t ) =
Answer:
Plane 1
[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]
Plane 2
[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]
Step-by-step explanation:
As each plane is travelling at constant speed, each equation can be modelled after this expression:
[tex]y = y_{o} + \dot y \cdot t[/tex]
Where:
[tex]y_{o}[/tex] - Intial elevation of the airplane, measured in feet.
[tex]\dot y[/tex] - Climbing/Descending rate of the airplane, measured in feet per minute. (Positive - Climbing, Negative - Descending)
[tex]t[/tex] - Time, measured in minutes.
Equations are described below:
Plane 1
[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]
Plane 2
[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
- 8b³+5ab²+7a²b
Step-by-step explanation:
(32ab³ - 20a²b² - 28a³b)/(-4a)= - 8b³+5ab²+7a²b
What is the completely factored form of polynomial 5X cubed +20 X squared plus 2X +8
Step-by-step explanation:
5x3 + 20x2 + 2x + 8
5x2 (x + 4) + 2(x + 4)
(5x2 + 2) (x + 4)
Amy's car holds at most 19 gallons of gas. Now it has 9 gallons. Use pencil and paper. Explain how to find the amount of gas she needs, in liters, to fill the gas tank.
Answer:
37.8541 litres.
Step-by-step explanation:
To find the amount of gas that she needs to fill her gas tank is 19 -9. She needs 10 gallons to fill her tank.
It says to state in litres, so convert.
1 gallon is about 3.78541 liters, so 10 gallons is 37.8541 litres
Hope that helped : )
Terry, Edin and Gordon are hygiene inspectors. Three takeaways, kebab, fish and chips and pizza. It is decided to share the work so that all inspectors will visit one takeaway each, chosen at random. List all the possible different ways they could share the work. (TK-EF-GP,
Answer: There are 6 different ways in which they can share the work.
Step-by-step explanation:
Suppose that Terry selects first the place where he goes, in the selection he has 3 options at random to chose.
Then Edin selects, Edin has two options (because one is already taken)
Then Gordon selects, he has only one options.
The number of combinations is equal to the product of the number of options for each selection, this is:
Combinations = 3*2*1 = 6
There are 6 different ways in which they can share the work.
A DVD is on sale for $1.05 off. This is a 15% discount from the original price. Use an equation to find the origina
price
O $16.05
$15.75
$10.50
O $7.00
Answer:
D. $7.00
Step-by-step explanation:
I just did it.
Ravi is 1 1/4 (mixed fraction).dinesh is 1 1/15 times as tall as Ravi .what is Dinesh's height
Keep getting this wrong please help!!!
Answer:
14.13 in³
Step-by-step explanation:
Volume of a ball (sphere) is:
V = ⁴/₃ π r³
Circumference of a ball (circle) is:
C = 2π r
Use the circumference to find the radius.
9.42 in = 2π r
r = 1.50 in
Use the radius to find the volume:
V = ⁴/₃ π (1.50 in)³
V = 14.13 in³
Find the angle of least positive measure that is coterminal with 541 degrees
Answer: 181 degrees.
Step-by-step explanation:
If we have an angle A, between, then the angle B is coterminal to A if:
B = A + n*360°
where n can be any whole number (if n = 0, we have B = A)
Then, if we take our angle as A = 541°
we can take n = -1 and get:
B = 541° - 1*360° = 181°
Now, if we subtract again 360°, we will end with an angle of negative measure, so 181° is the least positive measure angle that is coterminal with 541°
