Step-by-step explanation:
1. Lower the confidence level.
2. Use a one-sided confidence interval. ...
3. Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. ...
4. Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter. ...
PLEASE MARK ME AS BRAINLIST
Answer:
Increase the sample size.
Usually, the more observations that you have, the narrower the interval around the sample statistic is.
Find the future value and interest earned if $8704.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuously.
intorntic compounded semiannually is approximately
a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is $11,949.50.
b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
How is the future value determined?The future value can be determined using an online finance calculator.
Data and Calculations:
a) Compounded Semiannually:Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Semi-Annually
Time (t in years): 8 years
Result:
A = $11,949.50
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,244.94
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 8,704.56(1 + 0.04/2)(2)(8)
A = 8,704.56(1 + 0.02)(16)
A = $11,949.50
b) Compounded Continuously:Using the formula A = Pert
Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Continuously
Time (t in years): 8 years
Result:
A = $11,987.29
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,282.73
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A, using the mathematical constant, e = 2.71828
A = Pert
A = 8,704.56(2.71828)(0.04)(8)
A = $11,987.29
Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is $11,949.50, the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
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If f(x) = -5^x - 4 and g(x) = -3x - 2, find (f - g) (x).
Answer:
-5^x + 3x - 2.
Step-by-step explanation:
(f - g) (x) = f(x) - g(x)
= -5^x - 4 - (-3x - 2)
= -5^x - 4 + 3x + 2
= -5^x + 3x - 2.
Questions are in the pictures
The revenue function in terms of q will be 200q - 3q².
How to calculate the revenue?The following can be deduced based on the information given:
P(q) = 200 - 3q
C(q) = 75 + 80q - q²
The revenue function in terms of q will be:
= Price × Quantity
= (200 - 3q) × q
= 200q - 3q²
The profit will be:
= Total revenue - Total cost
= (200q - 3q²) - (75 + 80q - q²)
= 200q - 3q² - 75 + 80q + q²
= -2q² + 280q - 75
= 2q² - 280q + 75
The average cost function will be:
= Total cost / Quantity
= (75 + 80q - q²) / q
= 75/q + 80 - q
The marginal cost will be 80 - 2q.
The marginal revenue will be 200 - 6q.
The marginal cost when q = 20 will be:
= 80 - 2q
= 80 - 2(20)
= 80 - 40
= 40
The marginal revenue when q = 20 will be:
= 200 - 6q
= 200 - 6(20)
= 200 - 120
= 80
The company should decrease production from 20 units in order to gain more profit.
The production level that gives the largest profit for the company will be gotten by finding the second derivative for the profit function as illustrated in the question. The profit function is 2q² - 280q. Then the production level will be 4.
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Which is a true statement about the function f(x)= 8x^3
Answer:
The function is odd because f(-x) = -f(x)
Step-by-step explanation:
[tex]f(x)=8x^3[/tex]
[tex]f(-x)=8(-x)^3[/tex]
[tex]f(-x)=-8x^3[/tex]
[tex]-f(x)=-(8x^3)[/tex]
[tex]-f(x)=-8x^3=f(-x)[/tex]
[tex]f(-x)=-f(x)[/tex], therefore the function is odd
The function is odd because f(-x)=-f(x).
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=8x³.
We need to find which statement would be true in the given options.
Let us find this by taking x as -x.
f(-x)=8(-x)³
We know that when a negative sign is multiplied three times we get negative sign.
f(-x)=-8x³
-f(x)=-(8x³)
-f(x)=-8x³=f(-x)
f(-x)=-f(x)
By the definition of odd function f(-x)=-f(x).
Hence, the function is odd because f(-x)=-f(x).
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"Solve the following first order differential equation for x(t):
x'=-9tx"
How do I do this?
I'm not sure if the last two apostrophes are part of the quote - "Solve ... " - or if you mean the second derivative [tex]x''[/tex]. I think you mean the first interpretation, but I'll include both cases since they are both solvable.
If the former is correct, separate variables to solve.
[tex]x' = -9tx \implies \dfrac{dx}{dt} = -9tx \implies \dfrac{dx}x = -9t\,dt[/tex]
Integrate both sides to get
[tex]\ln|x| = -\dfrac92 t^2 + C[/tex]
Solve for [tex]x[/tex].
[tex]e^{\ln|x|} = e^{-9/2\,t^2 + C} \implies \boxed{x = Ce^{-9/2\,t^2}}[/tex]
If you meant the latter, then the ODE can be rewritten as
[tex]9t x'' + x' = 0[/tex]
Reduce the order of the equation by substituting [tex]y(t) = x'(t)[/tex] and [tex]y'(t) = x''(t)[/tex].
[tex]9t y' + y = 0[/tex]
Solve for [tex]y'[/tex] and separate variables.
[tex]y' = -\dfrac y{9t} \implies \dfrac{dy}{dt} = -\dfrac y{9t} \implies \dfrac{dy}y = -\dfrac{dt}{9t}[/tex]
Integrate.
[tex]\ln|y| = -\dfrac19 \ln|t| + C[/tex]
Solve for [tex]y[/tex].
[tex]e^{\ln|y|} = e^{-1/9 \,\ln|t| + C} \implies y = Ct^{-1/9}[/tex]
Solve for [tex]x[/tex] by integrating.
[tex]x' = Ct^{-1/9} \implies x = C_1 t^{8/9} + C_2[/tex]
Can someone please simplify this 9+4t=-3(1-2t)?
Answer:
simplification of the original equation is below/
Step-by-step explanation:
9+4t=-3(1-2t) can be simplified into
9+4t=-3+6t because of distributing the -3 to both the 1 and -2t.
however, this can simplified to
4t-6t=-3-9
and this can simplify to
-2t=-12
which can simplify to
t = 6
give brainliest please!
hope this helps :)
the cost of living is 230% of what it was 10 years ago. what mixed number is this?
Answer:
Step-by-step explanation:
23
Select the correct answer.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
OA.
y=3x+4
OB. y=3x-14
OC. y=3x-4
OD. y=3x + 12
Answer: [tex]\Large\boxed{A.~y=3x+4}[/tex]
Step-by-step explanation:
Given information
Slope = 3
Point = (-3, -5)
Given the format of the equation
Slope-intercept form: y = mx + b
m = Slopeb = y-interceptSubstitute values into the equation
y = (3)x + b
y = 3x + b
Substitute the given point into the equation to get the value of [ b ]
(-5) = 3(-3) + b
-5 = -9 + b
b = -5 + 9
b = 4
Therefore, the equation of the line is [tex]\Large\boxed{y=3x+4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
What must be true for line EF to not intersect plane L?
Answer:
If line EF is parallel to line CD, it will not intersect plane L.
Which answer choice shows that the set of irrational numbers is not closed under addition? π+(-π)=0
1/2+(-1/2)=0
π+π=2π
1/2+1/2=1
Answer:
(a) π + (-π) = 0
Step-by-step explanation:
You want a counterexample for the statement that irrationals are closed under addition.
Closed setA set is closed under addition if adding members of the set always results in a member of the set.
π + (-π) = 0This shows that adding members of the set can result in a rational number. This is the counterexample you're looking for.
(1/2) + (-1/2) = 0Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
π + π = 2πAn example of a sum that is an element of the set. This is not a counterexample.
(1/2) +(1/2) = 1Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
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Explain insurable interest and give an example
The examples of insurable interest is an employer under certain arrangements.
Insurable interest is a investment that protects anything subject to a financial loss. A person or entity has an insurable interest in an item, event, or action when the damage or loss of the object would cause a financial loss or other hardshapes. In order to have an insurable interest a person or entity would take out an insurance policy protecting the person,item, or event in question. The insurance policy is able to mitigate the risk of loss if something happens to the asset-like becoming damaged or lost.
Examples of insurable interest are:
YourselfYour spouse or former spouseYour children or grandchildrenA special needs adult childAn aging parentAn employer (under arrangements)Hence the examples of insurable interest is an employer under certain arrangements.
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Answer: Insurable interest means you must have a financial stake in the risk being insured. You can’t claim insurance for a risk that you don’t face directly.
If Rob’s dad’s car is stolen, his father will receive the insurance money, not Rob.
Step-by-step explanation: Edmentum
From the sample space S={1,2,3,4,...,15} a single number is to be selected at random. Given the following events, find the indicated probability.
A. the selected number is even
B. the selected number is a multiple of 4.
C. the selected number is a prime number.
P(BIA)
The probabilities of the given events are:
A. P(even) = P(A) = 7/15
B. P(multiple) = P(B) = 3/15
C. P(prime) = 6/15
D. P(B|A) = 3/7
What is probability?Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes.
P(E) = n(E)/n(S)
Calculation:The given sample space is S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
So, n(S) = 15
A. The selected number is even:
Consider the event as A.
The set of even numbers in the given sample is {2,4,6,8,10,12,14}
So, n(A) = 7
Then, the required probability is
P(A) = n(A)/n(S)
= 7/15
B. The selected number is a multiple of 4:
Consider the event as B.
The set of multiples of 4 in the given sample is {4,8,12}
So, n(B) = 3
Then, the required probability is
P(B) = n(B)/n(S)
= 3/15
C. The selected number is prime:
Consider the event as C.
The set of prime numbers in the given sample is {2,3,5,7,11,13}
So, n(C) = 6
Then, the required probability is
P(C) = n(C)/n(S)
= 6/15
D. calculate P(B|A):
Since events B and A are dependent events of the same sample,
n(A∩B) = 3 and the set is {4,8,12}. Then, P(B|A) is
P(B|A) = n(A∩B)/n(A)
⇒ P(B|A) = 3/7
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Una química tiene 3 soluciones acidas de varias concentraciones. La primera es 10% acida; la segunda 20% y la tercera 40%. ¿Cuántos mililitros de cada una debe ella usar para hacer 100ml de una solución al 18%, si tiene que usar cuatro veces mas de la solución al 10% que de la solución al 40%?
Based on the percentage of the first, second, and third acids, the milliliters of each acid that should be used to make 100 ml of 18% are:
10% acid = 40 ml20% acid = 50 ml40% acid = 10 mlWhat concentrations are needed to make the solution?Assuming the concentration of the 40% acid is denoted as x, the other acid concentrations would be:
10% acid = 4x
20% = 100 - 5x
The target solution is 100ml of 18%.
Solving gives:
(10% × 4x) + (20% × (100 - 5x)) + (40% × x) = 18% x 100
(80% × x) + 20 - x = 18
(80x - 100x) / 100 = 18 - 20
-20x / 100 = -2
20x = 200
x = 200 / 20
x = 10 ml
The 10% solution:
= 10 x 4
= 40 ml
20% acid:
= 100 - (5 x 10)
= 50 ml
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NO LINKS!! Please help me with this problem
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :
Length of transverse axis is :
[tex]\qquad \sf \dashrightarrow \: 2b = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: b = 6[/tex]
length of conjugate axis is :
[tex]\qquad \sf \dashrightarrow \: 2a = 8[/tex]
[tex]\qquad \sf \dashrightarrow \: a = 4[/tex]
Equation of hyperbola ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{ {x}^{2} }{ {a}^{2} } = 1[/tex]
plug in the values ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{ {x}^{2} }{ {4}^{2} } = 1[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{ {x}^{2} }{ {16}^{} } = 1[/tex]
Answer:
[tex]\dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]
Step-by-step explanation:
Standard form equation of a vertical hyperbola
[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]
where:
center = (h, k)vertices = (h, k±a)co-vertices = (h±b, k)foci = (h, k±c) where c² = a² + b²[tex]\textsf{asymptotes}: \quad y =k \pm \left(\dfrac{a}{b}\right)(x-h)[/tex]Transverse axis: x = hConjugate axis: y = kFrom inspection of the graph:
center = (0, 0) ⇒ h = 0, k = 0vertices = (0, 6) and (0, -6) ⇒ a = 6co-vertices = (4, 0) and (-4, 0) ⇒ b = 4Substitute the found values into the formula:
[tex]\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1[/tex]
[tex]\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]
Anthony travels from Newcastle to Manchester at an average speed of 65 miles per hour.
The journey takes him 2 hours and 15 minutes.
Declan makes the same journey in 2 hours and 35 minutes.
(a) Work out Declan's average speed for the journey.
Answer:
See below
Step-by-step explanation:
Distance = rate * time
= 65 m/hr * 2 1/4 hr = 146.25 miles
rate = distance / time
for Declan : rate = 146.25 miles / (2 hrs + 35/60 min) = 56.61 mph
mrs smith had 46$more than mrs wilson at first mrs wilson spent 4/7 of her money on some clothes and mrs smith spent 3/5 of her on household items after that they had an equal amount of money left find the total amount of money the two ladies spent.
please solve it as soon as posible
Using a system of equations, it is found that the total amount of money the two ladies spent was of $782.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Amount Mrs. Smith had initially.Variable y: Amount Mrs. Wilson had initially.Mrs smith had $46 more than Mr.s Wilson at first, hence:
x = y + 46.
Mrs Wilson spent 4/7 of her money on some clothes and, and Mrs. Smith spent 3/5 of her on household items, then they remained with an equal amount, so:
[tex]\frac{2}{5}x = \frac{3}{7}y[/tex]
Since x = y + 46, we have that:
[tex]\frac{2}{5}(y + 46) = \frac{3}{7}y[/tex]
14(y + 46) = 15y
y = 14 x 46
y = $644
x = 644 + 46 = $690
Hence the amount they spent is given as follows:
[tex]\frac{3}{5}x + \frac{4}{7}y = \frac{3}{5} \times 690 + \frac{4}{7} \times 644 = 782[/tex]
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Will mark brainliest
[tex]x^3[/tex] is strictly increasing on [0, 5], so
[tex]\max\{x^3 \mid 0\le x\le5\} = 5^3 = 125[/tex]
and
[tex]\min\{x^3 \mid 0 \le x\le5\} = 0^3 = 0[/tex]
so the integral is bounded between
[tex]\displaystyle \boxed{0} \le \int_0^5x^3\,dx \le \boxed{125}[/tex]
I NEED HELP ASAP PLS!!!
Answer:
C looks most correct
Step-by-step explanation:
elsa sold 24 drawings for $12 each at the art fair. She is going to use 1/3 of the money to buy books. The rest of the money is going into her savings account. How much money will she put into her savings account?
Given: LM ∥ KN
LP ⊥ KN , KL = MN
KN = 30, LM = 20
m∠KLM=126°
Find: LP
An angle is produced at the point where two or more lines meet. Thus the value of LP required in the question is approximately 14.
Two lines are said to be perpendicular when a measure of the angle between them is a right angle. While parallel lines are lines that do not meet even when extended to infinity.
From the question, let the length of LP be represented by x.
Thus, from the given question, it can be deduced that;
LM ≅ PN = 20
KP = KN - PN
= 30 - 20
KP = 10
LP = x
Also,
<MLP is a right angle, so that;
< KLP = < KLM - <PLM
= 126 - 90
<KLP = [tex]36^{o}[/tex]
So that applying the Pythagoras theorem to triangle KLP, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 36 = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{Tan 36}[/tex]
= [tex]\frac{10}{0.7265}[/tex]
x = 13.765
Therefore the side LP ≅ 14.
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Zoe is shopping for a new car and has to make some decisions. The model she’s chosen comes in two versions, hybrid and electric. For the exterior, she can choose red, blue, or green. For the interior, she can choose fabric, leather, or vinyl.
If Zoe randomly chooses from the options, the probability that Zoe picks a blue hybrid car with an interior that is not leather is
.
If Zoe randomly chooses from the options, the probability of Zoe picking an electric car in a color other than blue is
a) The probability is P = 1/9
b) The probability is P = 1/3.
How to get the probability?First, we need to count the total number of outcomes (different cars that can be made with the given options):
There are 2 versions (electric and hybrid).There are 3 exterior colors (red, blue, green).There are 3 interiors (fabric, leather, vinyl)Then there are 2*3*3 = 18 different cars.
a) Picking a blue hybrid car with an interior that is not leather.
There are 2 cars that meet that condition:
blue hybrid with fabric.blue hybrid with vinyl.2 out of the 18 cars meet the condition, then the probability is:
P = 2/18 = 1/9
b) picking an electric car in a color other than blue is
The cars that meet the condition are:
Green electric with any interior (3 options here)Red electric with any interior (3 options here)So 6 out of the 18 cars meet the condition, then the probability is:
P = 6/18 = 1/3
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can someone please help me
The formula that shows the relationship between the distance, rate and time is t = d/r and t = 5.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Given that:
d = rt
Hence:
t = d/r
For d = 40, r = 8:
t = 40 / 8
t = 5
The formula that shows the relationship between the distance, rate and time is t = d/r and t = 5.
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I neeeeed heeeelp please
Answer:
10b/y^2
Step-by-step explanation:
Hope this helps! :)
Evaluate The quantity of x cubed plus 3x squared minus 2x plus 7 divided by the quantity of x minus 2 end quantity period.
1. x squared minus 5x plus 2 plus 23 divided by the quantity of x minus 2
2.x cubed plus 5x plus 8 plus 11 divided by the quantity of x minus 2 end quantity
3.x squared minus 5x plus 6 plus 3 divided by the quantity of x minus 2 end quantity 4. x squared plus 5x plus 8 plus 23 divided by the quantity of x minus 2 end quantity
The value of x^3 + 3x^2 - 2x + 7 divided by x- 2 is (x^2 + 5x + 8) + 23/(x - 2)
What is a quotient?Quotients involve the result of dividing a dividend by a divisor.
In other words, quotient means division or the result of a division operation
How to solve the quotient?The quotient expression is given as:
(x^3 + 3x^2 - 2x + 7)/x- 2
Expand the numerator in the above expression
(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)
Rearrange the terms of the numerator in the above expression
(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)
Factorize the numerator in the above expression
[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)
Factor out x^2 + 5x + 8
[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)
Split the fractions
(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)
Divide the common factors
(x^2 + 5x + 8) + 23/(x - 2)
Hence, the value of x^3 + 3x^2 - 2x + 7 divided by x- 2 is (x^2 + 5x + 8) + 23/(x - 2)
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Complete question
Evaluate (x^3 + 3x^2 - 2x + 7)/x- 2
Answer:
4 / D | x^2 + 5x + 8 + 23/x - 2Step-by-step explanation:
The correct answer is D because when you divide & simplify the original question's equation, you get the results that are equivalent to answer D.
What value of b will cause the system to have an infinite number of solutions y=6x+b
-3x+1/2y=-3
A-(-6)
B(-3)
C(3)
D(6)
Answer: -6
Step-by-step explanation:
[tex]-3x+\frac{1}{2}y=-3\\\\\frac{1}{2}y=3x-3\\\\y=6x-6[/tex]
For there to be infinite solutions, b = -6.
please help urgently
Answer: no real solution
Thus, the function has no x- intercept
Step-by-step explanation:
Rebecca drew a graph with these key features:
The function is decreasing.
The left end is approaching a constant.
Which function could be represented by Rebecca’s graph?
Answer that was correct for me was: f(x) =-2(5/4)^x+3
The function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3
How to determine the function that could be represented by Rebecca’s graph?The properties are given as:
The function is decreasing.The left end is approaching a constant.For an exponential function to keep decreasing, one or more the following must be true:
The rate is less than 1The leading factor is negative and the rate is greater than 1For the left end of an exponential function to approach a constant, the following must be true:
The leading factor is negative and the rate is greater than 1The equation that has the above properties is f(x) =-2(5/4)^x+3
Hence, the function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3
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if 6m of a uniform iron rod weighs 21 kg what will be the weight of 16 m of the same rod?
Answer:
56kg
Step-by-step explanation:
If 6m of a rod is 21 kg, then 21/6 will give us the weight of 1m of the rod. 21/6 = 3.5 kg
16*3.5 = 56 kg
Use the normalcdf function on a calculator to find the probability that battery life is 20 ± 2 hours (between 18 and 22 hours) for each phone.
Prior values (If needed)
.159
.50
The probability that the battery life is 20 ± 2 hours (between 18 and 22 hours) for each of the phones is:
Phone C = 15.9%Phone T = 50%What is the probability of the battery life?Using the normalcdf function on a calculator, the probability that Phone C's battery would last between 18 and 22 hours can be found by inputing the function:
normalcdf (20, IE99, 18, 2)
The result is 0.158655 or 15.9%.
For Phone T, the function is:
normalcdf (20, IE99, 20, 3)
The result is 0.5 or 50%.
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Please put answer as a mixed number! :)
1 and 3/8* 1.5 + 5 and 5/8 ÷ 0.4 =
Answer: 7 1/16 and 1 9/16
Step-by-step explanation: 1 3/8 x 1.5 is 1 3/8 x 1 5/10 11/8 x 15/10 which is 165/80. We divide it by 5/5 to get 33/16. This as a mixed number is 2 1/16. We add 5 to get 7 1/16.
5/8 divided by 0.4 is 5/8 divided by 2/5. We divide this by first finding the reciprocal of 2/5 which is 5/2. 5/8 x 5/2 = 25/16. This as a mixed number is 1 9/16.
