Here we want to solve a question involving fractions, we will find that:
3/4 gallon fils the complete bin.
Ok, so we know that 1/2 gallon of water, fills 2/3 of the bin.
We want to find the total amount of water that would fill the entire bin.
So we could write an equation like:
amount of water = amount of the bin that it fills.
Then, using the above information, we have:
1/2 gal = 2/3 of a bin
Now we want to get at 1 on the right side, this would mean "1 bin"
Then we multiply both sides by (3/2)
(3/2)*(1/2) gal = (3/2)*(2/3) of a bin
3/4 gal = 1 bin
From this, we can conclude that (3/4) gallons of water would fill the complete bin.
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x = 0,75 gallons or x = 3/4 gallons The volume of the bin
The volume of the bin is: In terms of a fraction
1 = 3/3 or any unitary fraction 5/5 7/7 9/9
We will take 3/3 since we have the information that 2/3 of the volume of the bin was filled with 2/3 of a gallon
If 2/3 of the volume of the bin was filled with 1/2 gallon then we make a rule of three according to:
If 0,5 gal. fill 2/3 of the volume of the bin then
x gal fill 3/3 ( the volume of the bin)
solving
0,5 (gal) * 3/3 = (2/3)*x ( The equation)
0,5*3 = 2*x
x = (0,5*3)/2
x = 0,75 gallons or x = 3/4 gallons
If all possible random samples of size N are drawn from a population with a mean of mu and a standard deviation of sigma, then as N becomes larger, the sampling distribution of sample means becomes approximately normal with a mean of muy(bar) and a standard deviation of sigmay(bar). This statement is known as the:
Answer:
"Central limit theorem" is the right answer.
Step-by-step explanation:
A hypothesis essentially claims that whenever there seems to be a small variance throughout the big confidence intervals, the sampling is based on averages as well as the sampling distribution (mean) usually nearly the same as the public's median.
When,
Mean = [tex]\mu_y[/tex]Standard deviation = [tex]\sigma_y[/tex]Sample size = Nis sufficiently larger than [tex]\bar Y \sim N(\mu_y, \sigma_y)[/tex]
Thus, the above is the right answer.
Game consoles: A poll surveyed 341 video gamers, and 95 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that the proportion of gamers who prefer consoles differs from . Does the poll provide convincing evidence that the claim is true
Answer:
proportion of gamers who prefer console does not differ from 29%
Step-by-step explanation:
Given :
n = 341 ; x = 95 ; Phat = x / n = 95/341 = 0.279
H0 : p = 0.29
H1 : p ≠ 0.29
The test statistic :
T = (phat - p) ÷ √[(p(1 - p)) / n]
T = (0.279 - 0.29) ÷ √[(0.29(1 - 0.29)) / 341]
T = (-0.011) ÷ √[(0.29 * 0.71) / 341]
T = -0.011 ÷ 0.0245725
T = - 0.4476532
Using the Pvalue calculator from test statistic score :
df = 341 - 1 = 340
Pvalue(-0.447, 340) ; two tailed = 0.654
At α = 0.01
Pvalue > α ; We fail to reject the null and conclude that there is no significant evidence that proportion of gamers who prefer console differs from 29%
The following data represents the age of 30 lottery winners.
22 30 30 35 36 37 37
37 39 39 41 51 51 54
54 55 57 57 58 58 61
64 68 69 72 74 75 78 79 80
Complete the frequency distribution for the data.
Age Frequency
20-29
30-39
40-49
50-59
60-69
70-79
80-89
cho f(x)= sign x và g(x) = x(1-x^2). tìm f(g(x))
Answer:
[tex]f(g(x))= sign(x(1-x^{2})) = sign(x-x^{3})[/tex]
Step-by-step explanation:
cho A là ma trận vuông cấp 2 và detA=11, Khi đó det(3A)=
If the recipe takes 60 minutes to cook at a temperature of 350 degrees, how many minutes would it take at 200degrees
Answer:
The temperature has to be inversely proportional to the time therefore the solution will be:
60minutes/200degrees=x/350degrees
200x/200=21000/200
x=105minutes
I hope this helps
Answer:
105 minutes.
Step-by-step explanation:
As 200 degrees is less than 350 it will take longer at 200.
By proportion that would be (350/200) * 60
= 60 * 7/4
= 105 minutes.
what 30 + 30+60+(56)-82=?
94 is the correct answer for that question
Step-by-step explanation:
30+30+60+56-82=94
Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height 5h. Use cylindrical shells to compute the volume V of a napkin ring of height 5 h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h .
Answer:
V = 1/6 π ( 5h)^3
Step-by-step explanation:
Height of napkin rings = 5h
Compute the volume V of a napkin ring
let a = 5
radius = r
express answer in terms of h
attached below is the detailed solution
Find the missing length indicated
Answer:
x = 175
Step-by-step explanation:
A problem is given to three students A,B and C whose chances of solving 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
Answer:
because
1/2+1/3+1/4
1/2x6+1/3x4+1/4x3
1/12+1/12+1/12
1+1+1/12
3/12
1/4
1:4 so,their is a proability that the problem will be solved.
A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.
Answer:
48, 6
Step-by-step explanation:
The ratio of the pieces is 6 to 1
Add them together to get the total
6+1 = 7
Divide the total length by 7
56/7 = 8
Multiply the ratios by 8
6*8 = 48
1*8 = 6
The peices are 48 and 6
If 800g of a radioactive substance are present initially and 8 years later only 450g remain, how much of the substance will be present after 16 years? (Round answer to a whole number)
A=Pe^(rt)
P = 800g
t = 8 years
A = 450g
r = This is what we will try and find to start with
450=800e^(r*8)
After running the math through a calculator, we end with r = -0.07192
Now we just re-input this information into our equation: A=800e^(-0.07192*16)
A=800e^(1.15072)
Now we will re-write the equation using the negative exponent rule:
A = 800 1/e^1.15072
Combine right side:
A = 800/e^1.15072
Then do the math:
A = 253.12709836......
That will give us A = 253 (rounded to the whole number)
I hope this helps! :)
The substance that should be presented after 16 years is 253.
Given that,
If 800g of a radioactive substance are present initially and 8 years later only 450g remain.Based on the above information, the calculation is as follows:
We know that
[tex]A=Pe^{rt}[/tex]
Here
P = 800g
t = 8 years
A = 450g
[tex]450=800e^{r\times 8}\\\\A=800e^{-0.07192\times 16}\\\\A=800e^{1.15072}\\\\A = 800 \ 1 \div e^{1.15072}\\\\A = 800\div e^{1.15072}[/tex]
A = 253
Therefore we can conclude that the substance that should be presented after 16 years is 253.
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Help please!! Based on Pythagorean identities, which equation is true ??
Answer:
Last answer: [tex]cot^{2} \alpha - csc^{2} \alpha = -1[/tex]
sorry couldn't find theata so I just used alpha.
Rate of change or rate of change
A farmer has 80 feet of wire mesh to surround a rectangular pen.
A) Express the area A of the pen as a function of x, also draw the figure of A indicating the admissible values of x for this problem.
B) What are the dimensions of the maximum area pen?
Answer:
Step-by-step explanation:
A). Let the dimensions of the rectangular pen are,
Length = l
Width = x
Since, farmer has the wire measuring 80 feet to surround the the pen.
Perimeter of the pen = 80 feet
2(l + x) = 80
l + x = 40
l = 40 - x ------(1)
Area of the rectangular pen = Length × width
= lx
By substituting the value of l from equation (1),
Area (A) of the pen will be modeled by the expression,
A = (40 - x)
A = 40x - x²
B). For maximum area of the pen,
Derivative of the area = 0
[tex]\frac{d}{dx}(A)=0[/tex]
[tex]\frac{d}{dx}(A)=\frac{d}{dx}(40x-x^2)[/tex]
= 40 - 2x
And (40 - 2x) = 0
x = 20
Therefore, width of the pen = 20 feet
And length of the pen = 40 - 20
= 20 feet
Dimensions of the pen should be 20 feet by 20 feet.
Jean threw a disc in the air. The height of the disc can be modelled by the function
h = -5t^2 + 31.5t + 2, where h is the height in metres after t seconds.
Patrick fired a paintball at the disc. The path of the paintball is modelled by the function h = 30t + 1, with the same units. How long will it take the paint ball to hit the disc?
Answer:
It will take 0.62 seconds for the paint ball to hit the disc.
Step-by-step explanation:
Height of the disk:
[tex]H_d = -5t^2 + 31.5t + 2[/tex]
Height of the paintball:
[tex]H_p = 30t + 1[/tex]
When the paintball will hit the disk?
When they are at the same height, so:
[tex]H_d = H_p[/tex]
[tex]-5t^2 + 31.5t + 2 = 30t + 1[/tex]
[tex]5t^2 - 1.5t - 1 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
Quadratic equation with [tex]a = 5, b = -1.5, c = -1[/tex]
So
[tex]\Delta = (-1.5)^2 - 4(5)(-1) = 22.25[/tex]
[tex]t_{1} = \frac{-(-1.5) + \sqrt{22.25}}{2(5)} = 0.62[/tex]
[tex]t_{2} = \frac{-(-1.5) - \sqrt{22.25}}{2(5)} = -0.32[/tex]
Time is a positive measure, so 0.62.
It will take 0.62 seconds for the paint ball to hit the disc.
Please help on this initial amount problem
What is the degree of the monomial 4x7y3
Answer:
degree 10
Step-by-step explanation:
The degree of the monomial is the sum of the exponents of the variables, so
4[tex]x^{7}[/tex]y³ ← is of degree 10 ( 7 + 3)
When a fridge is imported, a customs value of 10% must be paid for its value. If the value of the fridge after paying the customs value is rs. 55,000/-. What is the value before paying customs duty?
Answer:
55000×100/90
61,111.111
find the value of g-¹(-2) if g (x) =4-2x
Answer:
Solution given:
g-¹(-2)=?
we have
g(x)=4-2x
let
g(x)=y
y=4-2x
Interchanging role of x and y
x=4-2y
2y=4-x
dividing both side by 2
2y/2=(4-x)/2
y=(4-x)/2
f-¹(x)=(4-x)/2
now
Substitute value -2 in place of x
f-¹(-2)=(4-(-2))/2=(4+2)/2=6/2=3
the value of g-¹(-2) is 3.
How do you do this I’ve been stuck on this
9514 1404 393
Answer:
x^(1/6)
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
__
Here, we have a=X, b=1/2, c=1/3, so the quotient is ...
(X^(1/2))/(X^(1/3)) = X^(1/2 -1/3) = X^(1/6)
_____
Expressed as a radical, this is ...
[tex]\displaystyle X^{\frac{1}{6}}=\sqrt[6]{X}[/tex]
Answer:
Step-by-step explanation:
x^1/2÷x^1/3=(x)^1/2-1/3= x^1/6--->⁶√x...it's positive answer.
Help solve problem please
Answer:
1 / 13
Step-by-step explanation:
The total number of cards in a deck = 52
The total number of aces in a deck = 4
Since selection is drawn with replacement, then probability of drawing a certiaj number of card from the deck will be the same each time a selection is made :
Probability = required outcome / Total possible outcomes
The required outcome = number of aces = 4
Total possible outcomes = total number of cards = 52
P(drawing an ace) = 4 / 52 = 1 /13
How would yo expand ln (1/49k)?
Answer:
Step-by-step explanation:
It depends on whether you mean ln(1/49k) or ln(1/(49k)).
Which expression is equivalent to 9+y+y+3
Answer:
b
Step-by-step explanation:
You only need to add the real numbers and the ys.
Answer:
12 + 2y
Step-by-step explanation:
9+y+y+3
Combine like terms
9+3 + y+y
12 + 2y
If a right circular cone is intersected by a plane only at its vertex, as in the
picture below, what shape is produced?
A. A parabola
B. An ellipse
C. A point
D. A line
E. A circle
F. A hyperbola
Answer:
A point
Step-by-step explanation:
Hopefully this helps :)
If a right circular cone is intersected by a plane passing through its vertex and perpendicular to its base, the resulting shape is a point.
What is mean by cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
Now, If a right circular cone is intersected by a plane passing through its vertex and perpendicular to its base, the resulting shape is a point.
Since, This is because a plane passing through the vertex of a cone and perpendicular to its base intersects the cone at only one point, which is the vertex of the cone.
Alternatively, if the plane intersects the base of the cone at any other point than the center, the resulting shape would be a triangle.
Therefore, the required form is a point.
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4. In SI, motor output is rated in
A. horsepower.
B. newtons.
C.foot-pounds per second.
D. kilowatts.
Answer:
in so in Newton motor out put is rate
Which of the following statements are true?
A. Both graphs are exponential functions.
B. Both graphs are logarithmic functions.
C. Both graphs have exactly one asymptote.
D. Both graphs have been shifted and flipped.
Answer:
A, C, and D are the answers to this question
The true statements about the graphs are; A. Both graphs are exponential functions. C. Both graphs have exactly one asymptote. D. Both graphs have been shifted and flipped.
How to Interpret Function Graphs?The graphs are exponential functions because as x increases, the value of y approaches infinity.
Likewise the graphs have exactly one asymptote.
Lastly, we can see that both graphs appear to have been shifted and flipped especially when we look at their respective coordinates.
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Quit smoking: In a survey of 444 HIV-positive smokers, 202 reported that they had used a nicotine patch to try to quit smoking. Can you conclude that less than half of HIV-positive smokers have used a nicotine patch
Answer:
The p-value of the test is of 0.0287 < 0.05(standard significance level), which means that it can be concluded that less than half of HIV-positive smokers have used a nicotine patch.
Step-by-step explanation:
Test if less than half of HIV-positive smokers have used a nicotine patch:
At the null hypothesis, we test if the proportion is of at least half, that is:
[tex]H_0: p \geq 0.5[/tex]
At the alternative hypothesis, we test if the proportion is below 0.5, that is:
[tex]H_1: p < 0.5[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.5 is tested at the null hypothesis:
This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*(1-0.5)} = 0.5[/tex]
In a survey of 444 HIV-positive smokers, 202 reported that they had used a nicotine patch to try to quit smoking.
This means that [tex]n = 444, X = \frac{202}{444} = 0.455[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.455 - 0.5}{\frac{0.5}{\sqrt{444}}}[/tex]
[tex]z = -1.9[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.455, which is the p-value of z = -1.9.
Looking at the z-table, z = -1.9 has a p-value of 0.0287.
The p-value is of 0.0287 < 0.05(standard significance level), which means that it can be concluded that less than half of HIV-positive smokers have used a nicotine patch.
help help me please!!!!!!!
9514 1404 393
Answer:
a) 3092.5 (rounded to tenths)
b) 39,600
c) ₹28,755
Step-by-step explanation:
These are all simple calculator problems. The arithmetic involved is something you learned in 2nd or 3rd grade.
__
a) Since we divide using the division algorithm, it isn't clear what "check your answer by division algorithm" is intended to mean. The result of the division (stopping at 1 decimal place) is 3092.5.
The usual method of checking a division problem is to multiply the quotient by the divisor to see if the dividend value is the result. Here, we have ...
13×3092.5 = 40202.5
This differs by from the dividend of 40203 by 0.5, which is the remainder showing in our long division. In short, the answer checks OK.
__
b) The value of each 4 is found by setting other digits to 0.
Most significant 4: 40,000
Least significant 4: 400
Difference in place value: 40,000 -400 = 39,600
__
c) The balance in the account is found by subtracting withdrawals from deposits:
₹35000 -6245 = ₹28,755
Find the slope of the line
A)-1/4
B)1/4
C)-4
D)4
Answer:
b) 1/4
The slope of the line is 1/4
The beginning balance in a person's checking account was 45 dollars. After writing three checks for $6, $17
and $18 and making a deposit of $80, what was the new balance in the account?
Initial balance = $45
Withdrawal amount
= $6 + $17 + $18
= $41
So, new balance
= $45 - $41
= $4
Deposited amount = $80
So, final balance
= $4 + $80
= $84
So, the final balance is $84.
