Answer:
k(x) = 6x
Step-by-step explanation:
A function shows the relationship between two or more variables. It shows the relationship between an independent and a dependent variable.
Given that the amount of water being poured into the tube is given by f(x) = 12x, where x is in minutes and the amount of water draining out of the tub is given by the function g( x )=6x. The amount of water remaining in the tube after x minutes is gotten by finding the difference between the amount of water entering the tube and the amount leaving the tube after x minutes. If k is the function representing the amount of water in the tube after x minutes, it is given by:
k(x) = f(x) - g(x)
k(x) = 12x - 6x
k(x) = 6x
A recent survey asked 1200 randomly selected U.S. adults if they believe that the U.S. federal government is doing enough to keep U.S. elections safe from outside interference. After analyzing the results, the researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe. Which statement BEST describes how to interpret these results
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is D
Step-by-step explanation:
From the question the question we are told that
The researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe.
Generally a confidence interval states to what extent the chances of the true population is within the a given range
So the 95% confidence interval given in the question as 52.5% and 59.5% means that the chances of the true population mean being with this given range is 95%
So given that the the true population mean is within this range then it means that the population mean will be greater than 50%
So the statement that best describe and interprets this result is
The results show significant statistical support that most U.S. adults (over 50%) believe that the U. S. Federal government is not doing enough to keep U.S. election safe.
find the HCF of 72,108 and 180
Answer:
36 is the answer
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
72: 2×2×2×3×3
108: 2×2×3×3×3
180: 2×2×3×3×5
here, common factors are 2,2,3 and 3 ..
so.. HCF: 2×2×3×3
•°•HCF=36 ..
You flip two coins. What is the probability
that you flip at least one head?
Answer:
[tex]\boxed{Probability=\frac{1}{2} }[/tex]
Step-by-step explanation:
The probability of flipping at least 1 head from flipping 2 coins is:
=> Total sides of the coins = 4
=> Sides which are head = 2
=> Probability = 2/4 = 1/2
The difference between teenage female and male depression rates estimated from two samples is 0.07. The estimated standard error of the sampling distribution is 0.03. What is the 95% confidence interval
Answer:
The 95% confidence interval is [tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean difference is [tex]\= x_m - \= x_f = 0.07[/tex]
The standard error is SE = 0.03
Given that the confidence interval is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha =0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]
substituting values
[tex]E = 1.96 * 0.03[/tex]
[tex]E = 0.0588[/tex]
The 95% confidence interval is mathematically represented as
[tex](\= x_m - \= x_f ) - E < \mu_m - \mu_f <(\= x_m - \= x_f ) + E[/tex]
substituting values
[tex]0.07 - 0.0588 < \mu_m - \mu_f <0.07 + 0.0588[/tex]
[tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]
The difference between teenage female and male depression rates are given. The 95% percent confidence interval can be obtained using mean and standard error relation.
The confidence interval is (0.0016 , 0.1584).
Given:
The depression rates is [tex]0.07[/tex].
The standard error of sampling distribution is [tex]0.03[/tex].
The critical value [tex]z=1.96[/tex]
Write the relation for mean and standard error.
[tex]\mu\pm z_{\rm critical}+\rm standard\: error[/tex]
Substitute the value.
[tex]0.07\pm 1.96\times 0.03=(0.1288,\:0.0112)[/tex]
Therefore, the upper and lower boundary is [tex](0.1288,\:0.0112)[/tex]. Thus, The confidence interval is (0.0016 , 0.1584).
Learn more mean and standard error here:
https://brainly.com/question/20215215
Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?
Answer:
q = 0.105uC
Step-by-step explanation:
We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.
Considering the horizontal and vertical components.
First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:
E=kq/r²
Where r = 20cm
= 20/100
= 0.2m
K = 9.0×10^9
9.0×10^9 × q /0.2²
9.0×10^9/0.04
2.25×10^11 q
These are vector fields of course
Sum the horizontal components
Ecos0 + Ecos300 = E+0.5E
= 1.5E
Sum the vertical components
Esin0 + Esin300 = -E√3/2
Resultant = √3E at -30° or 330°
So the force on q at the lower right corner is q√3×E
The balls have two forces, horizontal = √3×E×q
and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg
mg×tanθ = q√3E.
..1
Then θ will be...
Since the hypotenuse = 80cm
80cm/100
= 0.8m
The distance from the centroid to the lower right vertex is 0.1/cos30 =
0.1/0.866
= 0.1155m
Hence,
0.8×sinθ = 0.1155
Sinθ = 0.1155/0.8
Sin θ = 0.144375
θ = arch sin 0.144375
θ = 8.3°
From equation 1
mg×tanθ = q√3E
g = 9.8m/s^2
m = 3.0g = 0.003kg
0.003×9.8×tan(8.3)
0.00428 = q√3E
0.00428 = q×1.7320×E
Where E=kq/r²
Where r = 0.2m
0.0428 = kq^2/r² × 1.7320
K = 9.0×10^9
0.0428/1.7320 = 9.0×10^9 × q² / 0.2²
0.02471×0.04 = 9.0×10^9 × q²
0.0009884 = 9.0×10^9 × q²
0.0009884/9.0×10^9 = q²
q² = 109822.223
q = √109822.223
q = 0.105uC
Yuko added a 15 percent tip when she paid her cab driver. If the fare was $25.50, what was the total amount she paid? A. $28 B. $30 C. $31
Answer:
B. $30
Step-by-step explanation:
First, find the amount of the tip.
Multiply the tip rate and taxi fare.
tip rate * taxi fare
The tip rate is 15% and the taxi fare is $25.50
15% * 25.50
Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.
15/100=0.15
15.0 ---> 1.5 ---> 0.15
0.15 * 25.50
3.825
The tip amount is $3.825
Next, find the total amount she paid.
Add the taxi fare and the tip amount.
taxi fare + tip amount
The taxi fare is $25.50 and the tip amount is $3.825
$25.50 + $3.825
$29.325
Round to the nearest dollar. Typically, this would round down to $29, but that is not an answer choice. So, if we round up, the next best answer is $30.
Therefore, the best answer choice is B. $30
Please help me to find out the answer
9514 1404 393
Answer:
34.58 in
Step-by-step explanation:
Relative to the angle marked in this right triangle, the side given is the "adjacent" side, and the side length wanted is that of the hypotenuse. The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
Solving for the hypotenuse, we get ...
NP = (29 in)/cos(33°) ≈ 34.58 in
Please help asap, will mark Brainliest xoxo
Answer/Step-by-step explanation:
Given, [tex] b(x) = (\frac{6}{7})^{x} [/tex]
The table for the function are:
When x = -2
[tex] b(-2) = (\frac{6}{7})^{-2} [/tex]
[tex] b(-2) = \frac{1}{(\frac{6}{7})^{2}} [/tex]
[tex] b(-2) = \frac{1}{(\frac{36}{49})} [/tex]
[tex] b(-2) = 1*\frac{49}{36} [/tex]
[tex] b(-2) = \frac{49}{36} [/tex]
When x = -1
[tex] b(-1) = (\frac{6}{7})^{-1} [/tex]
[tex] b(-1) = \frac{1}{(\frac{6}{7})} [/tex]
[tex] b(-1) = 1*\frac{7}{6} [/tex]
[tex] b(-2) = \frac{7}{6} [/tex]
When x = 0
[tex] b(0) = (\frac{6}{7})^{0} [/tex]
[tex] b(0) = \frac{6^0}{7^0} [/tex]
[tex] b(0) = \frac{1}{1} [/tex]
[tex] b(0) = 1 [/tex]
When x = 1
[tex] b(1) = (\frac{6}{7})^{1} [/tex]
[tex] b(1) = \frac{6}{7} [/tex]
When x = 2
[tex] b(2) = (\frac{6}{7})^{2} [/tex]
[tex] b(2) = \frac{6^2}{7^2} [/tex]
[tex] b(2) = \frac{36}{49} [/tex]
Solve one and two tenths plus eight and one eighteenth
47
Is this it?
1 plus 2(10) plus 8 plus 1(18)
what is a 200% increase of 50
Answer:
150
Step-by-step explanation:
Increase = New Number - Original Number.
divide the increase by the original number and multiply the answer by 100.
I hope this helped! :)Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ = 7. Compute the probability
P(35 < X < 58)= ________
Answer:
Probability-Between .8574 = 85.74%
Step-by-step explanation:
Z1=-2.14 Z2=1.14
*x-1 35
*x-2 58
*µ 50
*σ 7
the bold answer is incorrect. what is the right answer?
Factor of
x2 – 14x + 24
A. (x - 6)(x - 4)
B. (x - 8)(x - 3)
C. (x - 12)(x - 2)
D. (x - 24)(x - 1)
Answer: The answer is C.
Step-by-step explanation:
Hi, there!!!
The answer is option C.
The solution is in picture.
I hope it helps....
the definition of parallel lines requires the undefined terms line and plane by the definition of perpendicular lines requires the undefined terms of line and point. what charcteristics of these geometric figures create the different requirements?
Answer:
Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.
Step-by-step explanation:
What is the value of x to the nearest tenth?
Answer:
x=9.6
Step-by-step explanation:
The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.
The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.
Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:
[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]
f (x) = x - 5. Find f'(x) and its domain.
Answer:
C
Step-by-step explanation:
f(x) = √x - 5
domain: [0. ∞)
range: [-5, ∞)
Let y = √x - 5
√x = y+5
x = (y+5)²
Switch x and y:
y = (x+5)²
f⁻¹(x) = (x+5)²
domain of f⁻¹(x) is the range of f(x): [-5,∞)
Find an equation of a plane containing the line r=⟨0,4,4⟩+t⟨−3,−2,1⟩ which is parallel to the plane 1x−1y+1z=−5 in which the coefficient of x is 1.
..?.. = 0.
The plane you want is parallel to another plane, x - y + z = -5, so they share a normal vector. In this case, it's ⟨1, -1, 1⟩.
The plane must also pass through the point (0, 4, 4) since it contains r(t). Then the equation of the plane is
⟨x, y - 4, z - 4⟩ • ⟨1, -1, 1⟩ = 0
x - (y - 4) + (z - 4) = 0
x - y + z = 0
9/10 - 4/10 = _
PLEASE ANSWER!! :)
Answer:
5/10
Step-by-step explanation:
Answer:0.5
Step-by-step explanatiolos divides ambos y después restarlos 0
Simplify 3m2 (−6m3 )
Answer:
3m2(-6m3)
since it's a term you have to multiply it by the number in bracket
6m(-6m3)
6m(-18m)
-108m²
What is 10,000,000 + 700,000,000 + 2,000,000 + 9,000 + 4 + 400,000 + 10,000 + 70 + 700 in standard form?
please mark this answer as brainlist
The highest attendance at this stadium was in 2007 when 91,547 people attended. The average cost of a ticket was $57. How much money was made on ticket sales for that game?
Answer:57*91547
Step-by-step explanation:
Need the help thanks guys
Answer:
1/4
Step-by-step explanation:
x^2 - x
Take the coefficient of x
-1
Divide by 2
-1/2
Square it
(-1/2)^2 = 1/4
Add it
x^2 -x +1/4
NEED ASAP I WILL GIVE BRAINLEYEST What is the value of the expression 22 + 82 ÷ 22? 8 10 17 20
Answer:
Exact Form:
283 /11
Decimal Form:
25. 72
Mixed Number Form:
25 8 /11
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
7 10/3 x 3 1/10= Can you explain step by step to me
Thanks
Answer:
710/3×31/10
[tex]reduce \: fraction \: to \: the \: lowest \\ term \: by \: canceling \: the \: greatest \\ common \: factor \: \\ = \frac{71 \times 31}{3} \\ calculate \: the \: first \: two \: terms \\ = \frac{2201}{3} \: is \: the \: answer[/tex]
2y-x=6 and y=2x+7 graphed equals how many solutions
Answer:
One solution
BRAINLIEST, PLEASE!
Step-by-step explanation:
2y - x = 6
2y = x + 6
y = x/2 + 3
y = 2x + 7
After graphing, they have one solution at (-2.667, 1.667).
How dose this input and output table work?
Aswer:I am sure of the answer it is 6 and 42
Step-by-step explanation:
5+30=3512+30=4230+30=6036+30=6640+30=60Find n for the arithmetic sequence for which sn=345, u1=12 and d = 5 .
Answer:
n = 10
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 5 and [tex]S_{n}[/tex] = 345, thus
[tex]\frac{n}{2}[/tex] [ (2 × 12) + 5(n - 1) ] = 345 ( multiply both sides by 2 )
n( 24 + 5n - 5) = 690 ← distribute and simplify left side
n(19 + 5n) = 690
19n + 5n² = 690 ( subtract 690 from both sides )
5n² + 19n - 690 = 0 ← in standard form
(5n + 69)(n - 10) = 0 ← in factored form
Equate each factor to zero and solve for n
5n + 69 = 0 ⇒ 5n = - 69 ⇒ n = - [tex]\frac{69}{5}[/tex]
n - 10 = 0 ⇒ n = 10
However, n > 0 , thus n = 10
Given g(x) = -x - 2, find g(3).
Answer:
g(3) = -5
Step-by-step explanation:
g(3) is basically the value of g(x) when x = 3. Therefore, g(3) = -3 - 2 = -5.
Answer:
[tex] \boxed{\sf g(3) = -5} [/tex]
Given:
g(x) = -x - 2
To Find:
g(3) i.e. g(x) where x = 3
Step-by-step explanation:
[tex]\sf Evaluate \ -x - 2 \ where \ x = 3:[/tex]
[tex] \sf \implies - x - 2 = - 3 - 2[/tex]
[tex] \sf - 3 - 2 = - (3 + 2) : [/tex]
[tex] \sf \implies - (3 + 2)[/tex]
[tex] \sf 3 + 2 = 5 : [/tex]
[tex] \sf \implies - 5[/tex]
a theater has (2x+1) rows of seats, with (x-3) seats in each row. how many seats are in the theater?
A. 2x^2- 5x- 3
B. 2x^2+ 5x- 3
C. 2x^2- 7x+ 3
D. 2x^2- 7x- 3
(2x+1)(x-3)
y(x-3) .... let y = 2x+1
y*x+y(-3) .... distribute
xy - 3y
x( y ) - 3( y )
x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1
2x^2 + x - 6x - 3 ..... distribute
2x^2 - 5x - 3
Answer is choice A
8.) It takes Fred 9 minutes to type and spell check 13 pages of a manuscript. Find how long it takes him to type and spell check 60 pages. Round to the nearest whole number. answer: minutes
It will take Fred 42 minutes to type and spell check 60 pages.
Let the first scenario be A.Let the second scenario be B.Let the unknown time be X.Given the following data;
Time taken A = 9 minutesNumber of pages A = 13 pagesNumber of pages B = 60 pagesTime taken B = X minutesTo find how long it takes him to type and spell check 60 pages;
We would use direct proportion to express the work described and solve for the unknown variable (time).
[tex]9 \;minutes : 13 \;pages\\\\X \;minutes : 60 \;pages[/tex]
Cross-multiplying, we have;
[tex]9[/tex] × [tex]60[/tex] [tex]= 13[/tex] × [tex]X[/tex]
[tex]540 = 13X\\\\X = \frac{540}{13}[/tex]
X = 41.54 ≈ 42 minutes
Therefore, it will take Fred 42 minutes to type and spell check 60 pages.
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