Answer:
28 l of 80%
42 l of 30%
Step-by-step explanation:
Target is 70 l of 50% solution
It will contain 70*0.5= 35 l of alcohol
x l of 80% solution and y l of 30% solution mixed to get the target solution
x+y=70 is the equation for total volume, and
0.8x+0.3y= 35 is the equation for the alcohol content. Solving this:
y= 70-x0.8x+0.3*(70-x) = 350.8x+21- 0.3x= 350.5x= 35-210.5 x= 14x= 14/0.5x=28 l of 80% solutionthen
y= 70-x= 70 -28 l= 42 l of 30% solutionWill give brainliest answer
Answer:
A=50.26548246units^2
Step-by-step explanation:
Radius is 4 because half the diameter (8) is the radius (4)
A=πr^2
A=π(4)^2
A=50.26548246units^2
Answer:
16 pi unit^2
Step-by-step explanation:
The diameter is 8 so we can find the radius
r = d/2 =8/2 = 4
The area is given by
A = pi r^2
A = pi ( 4)^2
A = pi *16
Round 113.04 to the nearest foot
Answer:
113 nearest tenth
Step-by-step explanation:
what do you mean by foot?
Answer:
are u sure it’s not nearest tenth?
Step-by-step explanation:
if so it’s 113
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1 to catch rainwater off his roof.he has a full 2 liters tin of paint in his store and decides to paint the tank (not the base) If he uses 25ml to cover 1m^2 will he have enough paint to cover the tank with one layer of paint
Answer:
yes
Step-by-step explanation:
The lateral area of a cylinder is ...
LA = πdh
Putting in the given numbers, we find the area to be ...
LA = π(1.1 m)(1.4 m) ≈ 4.838 m²
At 25 mL per m², the amount of paint Tublu needs is ...
(4.838 m²)(25 mL/m²) = 120.95 mL
2 liters is 2000 mL, so Tublu easily has enough paint for one layer.
___
The amount he has is enough for more than 16 coats of paint, so he could paint inside and out with the paint he has.
Answer:
he should.
Step-by-step explanation:
Plz help me plzzzzzz!!!!
Answer: D, 6
Step-by-step explanation:
Match each side from XYZ to ABC (you are trying to find the scale factor of triangle 1 to triangle 2) into a fraction then simplify
Ex 30/5= 6 or 24/6= 6 or 18/3
7
Find the sum of
and
11
26
13
Answer:
50
Step-by-step explanation:
If you mean find the sum of 11, 26, and 13, all you have to do is add those three together.
11 + 26 + 13 = 50
Answer:
11+26+13=50
Step-by-step explanation:
PLZ MARK BRAINLIEST
Use the function below to find f(4).
f(x)=1/3x4^x
A. 8/3
B.256/3
C.64/3
D.16/3
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
Simply replace X with 4
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
PLEASE HELP SOLVE THIS!!!!!
Answer:
20) -43
21) 25
22)-9
Step-by-step explanation:
20) -6 (-6 + 49)/6 = -43
21) 10 - (-10 - (-1 + 6)) = 25
22) 1 - 10/2 - 5 = -9
Step-by-step explanation:
22Let's calculate the expression khowing that m= 1 and n = 5
m-[tex]\frac{m+m}{2}[/tex] -nm- [tex]\frac{2m}{2}[/tex]-n m-m-n0-n0-5-520Let's calculate the expression khowing that n= -7 and p= - 6
[tex]\frac{p(p+n^{2}) }{6}[/tex] [tex]\frac{-6(-6+(-7)^{2}) }{6}[/tex][tex]\frac{-6(-6+49)}{2}[/tex] [tex]\frac{-6*43}{6}[/tex] -1*43-4321Let's calculate the expression khowing that n = -6 and m = -1 and p = -10
mp-(p-(m-n))mp-(p-m+n)mp-p+m-n(-1)*(-10)-(-10)+(-1)-(-6)10+10-1+620-1+619+625PLEASE HELP ME!!!!! A quadrilateral with vertices (0,0), (4,0), (3,2), (1,1) is mapped to a quadrilateral with vertices (6,3).(-2,3),(0,-1),(4,1). What is the center of the dilation and what is the scale factor.
Answer:
( 2,1) is the center of dilation and -2 is the scale factor
Step-by-step explanation:
We can use the formula
A' = k( x-a) +a, k( y-b)+b where ( a,b) is the center of dilation and k is the scale factor
(0,0) becomes (6,3)
( 6,3) = k( 0-a) +a, k( 0-b)+b
6 = -ka+a
3 = -kb+b
We also have
(4,0) becomes (-2,3)
( -2,3) = k( 4-a) +a, k( 0-b)+b
-2 =4k -ka+a
3 = -kb+b
Using these two equations
6 = -ka+a
-2 =4k -ka+a
Subtracting the top from the bottom
-2 =4k -ka+a
-6 = ka -a
-------------------
-8 = 4k
Divide by 4
-8/4 = 4k/4
-2 = k
Now solving for a
6 = -ka +a
6 = - (-2)a +a
6 = 2a+a
6 = 3a
Divide by 3
6/3 =3a/3
2=a
Now finding b
3 = -kb+b
3 = -(-2)b+b
3 = 2b+b
3 = 3b
b=1
Answer:
hope this helps uh.....
11- In
how many ways 3 mathematics books, 4 history books ,3
chemisidy books and a biology books can be arranged
on an Shelf so thet all books of the same subjects are
together!
Answer: 20,736
Step-by-step explanation:
Math and History and Chemistry and Biology and Subjects
3! x 4! x 3! x 1! x 4! = 20,736
What is the radius of a circle what circumference is 44cm
A. 42cm
D. 24cm
B. 48cm
C. 12cm
Hello!!
Circumference of a circle = 2πr
and
Given, 2πr = 44cm
So,
πr = 44/2 = 22
r = 22 × 7/22
r = 7cm is the answer.
Stay safe and God bless!
- eli <3
Answer:
7 cm
Step-by-step explanation:
Circumference of a circle is 2 π r
2πr = 44
Solve for radius.
r = 44/(2π)
r = 7.002817
The monthly starting salaries of students who receive an MBA degree have a standard deviation of $110. What size sample should be selected to obtain a 0.95 probability of estimating the mean monthly income within $20 or less
Answer:
116.21Step-by-step explanation:
Using the formula for calculating margin error to tackle the question.
Margin error = [tex]\frac{Z \sigma}{\sqrt{n} }[/tex]
Z is the value at 95% confidence
[tex]\sigma[/tex] is the standard deviation
n is the sample size to be estimated
Since the mean monthly income is within $20 or less, our margin error will be $20
Given [tex]\sigma[/tex] = $110, Z value at 95% confidence = 1.96 we can calculate the sample side n.
Making n the subject of the formula from the equation above;
[tex]M.E = \frac{Z \sigma}{\sqrt{n} }\\\\\sqrt{n} = \frac{Z \sigma}{M.E } \\\\[/tex]
[tex]n = (\frac{Z \sigma}{M.E })^{2}[/tex]
Substituting the give value into the resulting expression;
[tex]n = (\frac{1.96 * 110}{20})^{2}\\\\n = (\frac{215.6}{20}) ^2\\\\n = 10.78^2\\\\n = 116.21[/tex]
This shows that the sample size that should be selected to obtain a 0.95 probability of estimating the mean monthly income within $20 or less is approximately 116.21
2 + 4x - 4 = 0 which gives x =
Answer:
[tex]x = \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]2 + 4x - 4 = 0 \\ 2 + 4x = 0 + 4 \\ 2 + 4x = 4 \\ 4x = 4 - 2 \\ 4x = 2 \\ \frac{4x}{4} = \frac{2}{4} \\ x = \frac{1}{2} [/tex]
Answer:
x = 1/2
Step-by-step explanation:
2 + 4x - 4 = 0
4x = 0 + 4 - 2
4x = 2
x = 2⁽²/4
x = 1/2
As an example, 15,000 Men 18-34 watched program X at 7-8 pm on Monday night. 32,000 Men 18-34 had their TV on during the same time period. There are 200,000 Men 18-34 in the television households in the market. What would be the rating for Men 18-34 for program X? Group of answer choices 47 rating points 7.5 rating points 16 rating points 23.5 rating points
Answer:
7.5 rating points
Step-by-step explanation:
The computation of the rating for Men 18-34 for program X is shown below:
Given that
Number of men 18 -34 watched a program X = 15,000 = X
Number of men 18 - 34 watched in a same time = 32,000
And, the total households in the market = 200,000 = Y
So, the rating for men 18-34 for program x is
[tex]= \frac{X}{Y}[/tex]
[tex]= \frac{15,000}{200,000}[/tex]
= 7.5 rating points
We simply applied the above formula
I NEED HELP ASAP! THANKS :)
Answer:
Option B
Step-by-step explanation:
Answer:
[tex]35\sqrt[5]{49}[/tex]
Step-by-step explanation:
I simply plugged it into my calc and solved it.
QUESTION 8
Find Future Value Using Compound Interest Formula:
You deposit $6,000 in an account earning 4% interest compounded monthly. How much will you have in the account in 5 years?
A $9,677.95
B. $6,100.67
C. $7,325.98
D. $7,200
QUESTION 9
Find Future Value Using Compound Interest Formula:
You deposit $5,000 in an account earning 5% interest compounded quarterly. How much will you have in the account in 10 years?
A $5,661.35
B. $7,500
C. $8,235.05
D. $8,218.10
Answer:
8.) $7325.98
9.) $8218.10
Step-by-step explanation:
Compounded Interest Rate Formula: A = P(1 + r/n)^nt
Simply plug in our known variables into the formula:
A = 6000(1 + 0.04/12)^60 = 7325.98
A = 5000(1 + 0.05/4)^40 = 8218.10
In an aquarium, there are 7 large fish and 6 small fish. Half of the small fish are red.
One fish is selected at random. Find the probability that it is a small, red fish.
Write your answer as a fraction in simplest form.
Answer:
3/13
Step-by-step explanation:
There are a total of 13 fish (6+ 7 = 13). There are 3 small, red fish. (1/2 · 6 = 3). Put the number of small, red fish over the total number of fish because the small, red fish is being selected from the entire tank of fish. 3/13 cannot be simplified any further.
Pls help see the picture posted
Use a proportion to solve the problem. Round to the nearest tenth as needed.
Triangle in a triangle Find the height of the building. Assume that the height of the person is 5 ft.
104 ft
building
13 ft
5 ft
Answer:
Height of the building is 40 feet
Step-by-step explanation:
From the figure attached,
Height of the person DE = 5 feet
Let height of the building BC = h feet
Since, ΔABC ~ ΔADE,
Their corresponding sides will be proportional,
[tex]\frac{DE}{BC}=\frac{AD}{AB}[/tex]
[tex]\frac{5}{h}=\frac{13}{104}[/tex]
h = [tex]\frac{104\times 5}{13}[/tex]
h = 40 feet
Therefore, height of the building is 40 feet.
What is the circumference of the circle below? (Round your answer to the nearest tenth.)
Answer:
Its 69.1 cm
Step-by-step explanation:
To find circumstance of any circle main formula is 2*pie*r .
Here pie is equal to 3.14 approx and r =11 cm
so
2*3.14*11 = 69.08 cm
This little difference is just because of pie's approximately value used
Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y= 5 with the sphere
x^2+y^2+z^2=125
The parametrization shown below,
[tex]x(t),y(t),z(t)=10cost,5,10sint[/tex]
Given equation of sphere,
[tex]x^{2} +y^{2} +z^{2} =125[/tex]
Substitute y = 5 in above relation.
[tex]x^{2} +z^{2}=125-25=100\\ \\x^{2} +z^{2}=10^{2}[/tex]
For parametrization,
Substitute [tex]x=rcos(t),z=rsin(t)[/tex] and [tex]r=10[/tex]
So that, [tex]x(t),y(t),z(t)=10cost,5,10sint[/tex]
Learn more:
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Binomial factor of 25x2 + 40xy + 16y2 ?
Answer:
(5x +4y)^2
Step-by-step explanation:
The first and last terms are both perfect squares, and the middle term is twice the product of their roots. That means the trinomial is the perfect square trinomial ...
25x^2 +40xy +16y^2 = (5x +4y)^2
_____
It matches the pattern ...
a^2 +2ab +b^2 = (a +b)^2
Answer:
(5x +4y)^2
Step-by-step explanation:
A piece of wire 27 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.(a) How much wire should be used for the square in order to maximize the total area?(b) How much wire should be used for the square in order to minimize the total area?
Answer:
a).length of wire for square = 15.25 m
b). length of wire for triangle = 11.75 m
Step-by-step explanation:
Length of a piece of wire = 27 m
This wire was cut into 2 pieces of length 'x' m and (27 - x) m
One was bent into an equilateral triangle and other into a square.
Area of the square shape = Side²
A = [tex](\frac{27-x}{4})^2[/tex]
Similarly, Area of the equilateral triangle = [tex]\frac{\sqrt{3}}{4}(\text{Side})^2[/tex]
A' =[tex]\frac{\sqrt{3}}{4}(\frac{x}{3})^{2}[/tex]
Total area of both the figures = A + A'
F = [tex]\frac{(27-x)^2}{16}+\frac{\sqrt{3}}{4}(\frac{x}{3} )^2[/tex]
Now we find the derivative of 'F' with respect to x and equate it to zero.
F' = [tex]\frac{1}{16}(-1)[2(27-x)]+\frac{\sqrt{3}}{36}(2x)[/tex] = 0
[tex]\frac{\sqrt{3}}{18}(x)=\frac{1}{8}(27-x)[/tex]
x = 15.25 m
a). Length of wire required for a square = 15.25 m
b). Length of wire required for an equilateral triangle = 11.75 m
A) The amount of wire that should be used for the square in order to maximize the area is; 0 m
B) The amount of wire that should be used for the square in order to minimize the area is; 11.74 m
A) We are told that length of wire is 27 m.
Now, let the length cut for the square be x. Thus, length cut for the triangle will be; (27 - x) m.
Since the length for the square is x, then a side of the square is;
Length of side of square = x/4
Length of side of equilateral triangle = (27 - x)/3
Thus;
Area of square; A_s = (x/4)²
Area of equilateral triangle; A_t = ((27 - x)/3)²(¹/₄√3)
Thus, total area is;
A(x) = (x/4)² + ((27 - x)/3)²(¹/₄)√3)
⇒ A(x) = ¹/₁₆x² + ¹/₃₆((27 - x)²√3)
B) Total area is; A(x) = ¹/₁₆x + ¹/₃₆((27 - x)²√3)
To minimize the total area, we will differentiate and equate to zero.
A'(x) = ¹/₈x - ¹/₁₈((27 - x)√3)
At A'(x) = 0, we have;
¹/₈x - ¹/₁₈((27 - x)√3) = 0
¹/₈x = ¹/₁₈((27 - x)√3)
¹/₈x = ³/₂√3 - ˣ/₁₈√3
¹/₈x + ˣ/₁₈√3 = ³/₂√3
x(¹/₈ + ¹/₁₈√3) = ³/₂√3
x = (³/₂√3)/(¹/₈ + ¹/₁₈√3)
x = 11.74 m
Now, A''(x) = ¹/₈ + ¹/₁₈√3
This is greater than zero and so x = 11.74 m is a minimum
Thus, length cut for triangle = 27 - 11.74
length cut for triangle = 15.26 m
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Alonzo and Cheryl are both members of a population, and a simple random sample is being conducted. If the chance of Alonzo being selected is 1/2900, what is the chance of Cheryl being selected?
Answer:
¿Consideras que la gente que discrimina por aspectos como el color de la piel, clase social, por el género, etc., no saben lo que las personas valen y por eso no las valoran?
¿Consideras que la gente que discrimina por aspectos como el color de la piel, clase social, por el género, etc., no saben lo que las personas valen y por eso no las valoran?
Answer: 1/2900
Step-by-step explanation: if they are both in the same population and they are both being randomly selected then they both have the same possibility of being picked
Please answer this correctly
Answer:
Question 2 is the right answer.
Step-by-step explanation:
Answer:
Question 2
Step-by-step explanation:
Temperature in the morning = 2°F above normal temperature = + 2
Temperature at dinner time = 2° F lower than the morning = -2
+2 - 2 = 0° F
PLZZZ I NEED HELP I’ll give 20 POINTS
What is the median of the following data set?
(6,3, 9, 1,7)
03
06
08
09
Answer:
6
Step-by-step explanation:
Arrange the data from smallest to largest
1,3,6,7,9
The median is the middle number
1,3 ,6, 7, 9
The middle number is 6
Hurry!! Determine the intervals for which the function shown below is decreasing.
Answer:
everywhere except between 2 and 5
(between -inf and 2 and between 5 and inf)
Step-by-step explanation:
Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all x.
(a) Use a linear approximation to estimate g(2.95) and g(3.05).
g(2.95) =
g(3.05) =
(b) Are your estimates in part (a) too large or too small? Explain.
A) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie below the curve. Thus, the estimates are too small.
B) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie below the curve. Thus, the estimates are too small.
C) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie above the curve. Thus, the estimates are too large.
D) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie above the curve. Thus, the estimates are too large.
Answer:
g(2.95) ≈ -1.8; g(3.05) ≈ -0.2A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.Step-by-step explanation:
(a) The linear approximation of g(x) at x=b will be ...
g(x) ≈ g'(b)(x -b) +g(b)
Using the given relations, this is ...
g'(3) = 3² +7 = 16
g(x) ≈ 16(x -3) -1
Then the points of interest are ...
g(2.95) ≈ 16(2.95 -3) -1 = -1.8
g(3.05) ≈ 16(3.05 -3) -1 = -0.2
__
(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)
Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years.
a. Calculate a 95% two-sided confidence interval on the death rate from lung cancer.
b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03?
c. How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.03, regardless of the true value of p?
Answer:
a) [tex]0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799[/tex]
[tex]0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847[/tex]
The 95% confidence interval would be given by (0.799;0.847)
b) [tex]n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79[/tex]
And rounded up we have that n=622
c) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Step-by-step explanation:
Part a
[tex]\hat p=\frac{823}{1000}=0.823[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values obtained we got:
[tex]0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799[/tex]
[tex]0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847[/tex]
The 95% confidence interval would be given by (0.799;0.847)
Part b
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79[/tex]
And rounded up we have that n=622
Part c
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Select the expression that is equivalent to (x - 1)2.
O A. x2 - 2x + 2
O B. x2 - x + 2
O C. x2 - x + 1
O D. x2 – 2x + 1
Answer:
x^2 -2x+1
Step-by-step explanation:
(x - 1)^2
(x-1) * (x-1)
FOIL
first: x^2
outer: -1x
inner: -1x
last: 1
Add together
x^2 -1x-1x+1
Combine like terms
x^2 -2x+1
Answer:
[tex] \boxed{\sf D. \ {x}^{2} - 2x + 1} [/tex]
Step-by-step explanation:
[tex] \sf Expand \: the \: following: \\ \sf \implies {(x - 1)}^{2} \\ \\ \sf \implies (x - 1)(x - 1) \\ \\ \sf \implies x(x - 1) - 1(x - 1) \\ \\ \sf \implies (x)(x) - (1)(x) - (1)(x) - (1)( - 1) \\ \\ \sf \implies {x}^{2} - x - x - ( - 1) \\ \\ \sf \implies {x}^{2} - 2x - ( - 1) \\ \\ \sf \implies {x}^{2} - 2x + 1[/tex]
The manufacturer of a certain brand of hot dogs claims that the mean fat content per hot dog is 20 grams. Suppose the standard deviation of the population of these hot dogs is 1.9 grams. A sample of these hot dogs is tested, and the mean fat content per hot dog of this sample is found to be 20.5 grams. Find the probability that the sample mean is at least 20.5 when the sample size is 35.
Answer:
[tex]z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557[/tex]
And using the normal standard distribution and the complement rule we got:
[tex]P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06[/tex]
Step-by-step explanation:
For this case we define our random variable X as "fat content per hot dog" and we know the following parameters:
[tex]\mu = 20, \sigma =1.9[/tex]
We select a sample of n=35 and we want to find the following probability:
[tex] P(\bar X>20.5)[/tex]
For this case since the sample size is >30 we can use the central limit theorem and we use the z score formula given by:
[tex]z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Replacing we got:
[tex]z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557[/tex]
And using the normal standard distribution and the complement rule we got:
[tex]P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06[/tex]