Answer: 3
Step-by-step explanation:
Answer:
2hrs 24 mins
Step-by-step explanation:
Ok so let's make this problem a bit simpler by splitting it up.
Tim paints a room in 6 hours.
So, we can also say that she paints 1/6 of that room in 1 hour
Bella paints it in 4 hours
So, we can also say that she paints 1/4 of that room in 1 hour
Now, lets see what we have:
Bella: 1/4 every hour
Tim: 1/6 every hour
The problem states that they are working together, so we need to add the values we have:
1/4 + 1/6
We cannot just add them, we must make them have the same common denominator.
LCD is 12, you can find that by just doing the times tables for 4 and 6 and seeing what number they match on first.
3/12 + 2/12 = 5/12
So, tim and bella working together paint 5/12 of a room in 1 hour.
They paint 5/12 of a room in 60 minutes
They paint 1/12 of the room in 12 minutes(divide both values by 5)
So if they paint 1/12 of the room in 12 minutes, we can multiply both values by 12 to get our answer.
They paint the full room in 144 minutes(12*12).
144 minutes is 2 hours and 24 minutes
A theater ticket costs £63 plus a booking fee of 3% what is the total price for the ticket
Answer:
The cost of Ticket = £63Booking Fee = 3% = 63*(3/100) = 1.89 = £ 1.89The total price of the ticket = £63 + £1.89 = £64.89. Therefore, the total price of the ticket is £64.89.
John is planning an end of the school year party for his friends he has $155 to spend on soda and pizza he knows he has to buy 10 2 L bottles of soda choose the any quality and calculate the greatest number of pizzas he can buy
If John has to buy 10 "2-Liter" bottles of soda, then the inequality representing this situation is "10(1.50) + 7.50p ≤ 150" and greatest number of pizzas he can buy is 18, Correct option is (d).
Let "p" denote the number of "large-pizzas" that John can buy.
One "2-liter" bottle of soda cost is = $1.50,
So, the cost of the 10 bottles of soda is : 10 × $1.50 = $15,
one "large-pizza's cost is = $7.50,
So, the cost of p large pizzas is : $p × $7.50 = $7.50p,
The "total-cost" of the soda and pizza must be less than or equal to $150, so we can write the inequality as :
10(1.50) + 7.50p ≤ 150
Simplifying the left-hand side of the inequality,
We get,
15 + 7.50p ≤ 150
7.50p ≤ 135
p ≤ 18
Therefore, John can buy at most 18 large pizzas with his remaining budget, the correct option is (d).
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The given question is incomplete, the complete question is
John is planning an end of the school year party for his friends he has $150 to spend on soda and pizza.
Soda (2-liter) costs $1.50;
large pizza cost $7.50;
He knows he has to buy 10 "2-Liter" bottles of soda.
Choose the inequality and calculate the greatest number of pizzas he can buy.
(a) 10(1.50) + 7.50p ≥ 150; 54 pizzas
(b) 10(7.50) + 1.50p ≤ 150; 53 pizzas
(c) 10(7.50) + 1.50p ≥ 150; 19 pizzas
(d) 10(1.50) + 7.50p ≤ 150; 18 pizzas
To solve 6÷1/4, james thinks about how the distance from his home to the store is 1/4 mile and he wonders how many times he would have to walk that distance to walk 6 miles. what is the quotient of 6 and 1/4? enter your answer in the box.
The quotient of 6 and 1/4 is 24.
We have applied division operation to this question. Firstly, we will understand the meaning of a proper fraction. A fraction in which the numerator is less than the denominator is called a proper fraction. This means that the denominators will always be bigger than the numerators for appropriate fractions.
We can represent this condition in either of the two ways.
Denominator < Numerator
(Or)
Numerator > Denominator
We are given a numerical expression which is 6÷ 1/4 and we have to solve this.
To convert this division sign into a multiplication sign, we will take the reciprocal of 1/4.
The reciprocal of 1/4 is 4.
Therefore,
6÷ 1/4
= 6 × 4
= 24
Therefore, the quotient of 6 and 1/4 is 24.
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A family camping in a national forest builds a temporary shelter with a
tarp and a 4-foot pole. the bottom of the pole is even with the ground, and one corner
is staked 5 feet from the bottom of the pole. what is the slope of the tarp from that
corner to the top of the pole?
A family camping in a national forest used a 4-foot pole and a tarp to build a temporary shelter. One corner of the tarp was staked 5 feet from the bottom of the pole. The slope of the tarp from that corner to the top of the pole is 0.8 or 4/5.
We can draw a right triangle with the pole being the height, the distance from the pole to the stake being the base, and the slope of the tarp being the hypotenuse. The hypotenuse is the longest side of the triangle and is opposite to the right angle.
Using the Pythagorean theorem, we can find the length of the hypotenuse
hypotenuse² = height² + base²
hypotenuse² = 4² + 5²
hypotenuse² = 41
hypotenuse = √(41)
Therefore, the slope of the tarp is the ratio of the height to the base, which is
slope = height / base = 4 / 5 = 0.8
So the slope of the tarp from that corner to the top of the pole is 0.8 or 4/5.
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If Tan=3 /5 fine the remaining trigonometric functions
The remaining trigonometric functions are:
sin (θ) = 3/√34
cos (θ) = 5/√34
csc(θ) = (√34)/3
sec (θ) = (√34)/5
cot(θ) = 5/3
How to find the remaining trigonometric functions?Trigonometry is a branch of mathematics that deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Since tan θ = 3 /5
Recall: tan = opposite/adjacent. Thus, opposite = 3, adjacent = 5
hypotenuse = √(3²+5²) = √34
Therefore, the remaining trigonometric functions are
sin (θ) = 3/√34
cos (θ) = 5/√34
csc(θ) = (√34)/3 (csc (θ) = 1/sin (θ))
sec (θ) = (√34)/5 (sec(θ) = 1/cos (θ))
cot(θ) = 5/3 (cot(θ) = 1/tan (θ))
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Carmen mixed 1/4 cup of strawberry frosting with 1/3 cup of lemon frosting Carmen needs 2 cups of her frosting mixture how many cups of strawberry frosting and how many cups of lemon frosting will Carmen need
Carmen needs (6/7) cups of strawberry frosting and (1 1/7) cups of lemon frosting to make 2 cups of the frosting mixture.
To determine the amount of strawberry frosting and lemon frosting that Carmen needs to make 2 cups of the frosting mixture, we need to use a proportion.
Let x be the amount of strawberry frosting needed in cups, and y be the amount of lemon frosting needed in cups.
From the given information, we know that Carmen mixed 1/4 cup of strawberry frosting with 1/3 cup of lemon frosting. Thus, the ratio of the amounts of strawberry frosting to lemon frosting is:
x/y = (1/4)/(1/3)
Simplifying this ratio, we get:
x/y = 3/4
We also know that the total amount of frosting needed is 2 cups, so:
x + y = 2
Using substitution, we can solve for x:
x + (4/3)x = 2
(7/3)x = 2
x = (6/7) cups
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Find dx/dy, if x=sin^3t,y=cos^3t.
dx/dy = -sin(t)/cos(t) when x = sin^3(t) and y = cos^3(t).
To find dx/dy, we first need to find dx/dt and dy/dt, and then we can use the chain rule.
Given x = sin^3(t) and y = cos^3(t),
dx/dt = d(sin^3(t))/dt = 3sin^2(t) * cos(t) (using the chain rule)
dy/dt = d(cos^3(t))/dt = -3cos^2(t) * sin(t) (using the chain rule)
Now, we can find dx/dy by dividing dx/dt by dy/dt:
dx/dy = (dx/dt) / (dy/dt) = (3sin^2(t) * cos(t)) / (-3cos^2(t) * sin(t))
Simplify the expression:
dx/dy = -sin(t)/cos(t)
So, dx/dy = -sin(t)/cos(t) when x = sin^3(t) and y = cos^3(t).
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A researcher surveyed 220 residents of a city about the number of hours they
spend watching news on television each day. The mean of the sample was
1. 8 with a standard deviation of 0. 35.
The researcher can be 95% confident that the mean number of hours all the
residents of the city are watching news on television is 1. 8 with what margin
of error?
The researcher can be 95% confident that the mean number of hours all the residents of the city are watching news on television is between 1.7538 and 1.8462 hours, with a margin of error of 0.0462 hours.
Based on the information provided, the researcher surveyed 220 residents of the city and found that the mean number of hours they spend watching news on television each day is 1.8, with a standard deviation of 0.35.
The researcher wants to know the margin of error at a 95% confidence level for the mean number of hours all residents of the city are watching news on television.
To calculate the margin of error, we need to use the formula:
Margin of error = Critical value x Standard error
The critical value for a 95% confidence level is 1.96, and the standard error can be calculated as:
Standard error = Standard deviation /square root of sample space
Substituting the values given:
Standard error = 0.35 / sqrt(220) = 0.0236
Therefore, the margin of error can be calculated as:
Margin of error = 1.96 x 0.0236 = 0.0462
So, the researcher can be 95% confident that the mean number of hours all the residents of the city are watching news on television is between 1.7538 and 1.8462 hours, with a margin of error of 0.0462 hours.
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Ali needed new pencils for school today. He took 6 pencils from a new box of pencils. If there are 18 pencils left in the box, how many pencils were in the brand new box?
If Ali took 6 pencils from a new box of pencils and there are 18 pencils left in the box, then there were 24 pencils in the brand new box.
To see why, you can add the number of pencils Ali took to the number of pencils left in the box:
6 + 18 = 24
Therefore, there were 24 pencils in the brand new box before Ali took 6 of them.
Menlo Company distributes a single product. The company's sales and expenses for last month follow:
Per Unit
$ 40
28
$ 12
Sales
Variable expenses
Contribution margin
Fixed expenses
Net operating income
Total
$ 600,000
420,000
180,000
Required:
1. What is the monthly break-even point in unit sales and in dollar sales?
2. Without resorting to computations, what is the total contribution margin at the break-even point?
3-a. How many units would have to be sold each month to attain a target profit of $70,800?
3-b. Verify your answer by preparing a contribution format income statement at the target sales level.
146,400
$ 33,600
4. Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms.
5. What is the company's CM ratio? If the company can sell more units thereby increasing sales by $69,000 per month and there is no
change in fixed expenses, by how much would you expect monthly net operating income to increase?
Complete this question by entering your answers in the tabs below.
Req 1
Margin of safety
Req 3A
Req 3B
Req 2
Req 5
Refer to the original data. Compute the company's margin of safety in both dollar and percentage terms. (Round your
percentage answer to 2 decimal places (i.e. 0.1234 should be entered as 12.34).)
Dollars
Percentage
Req 4
%
If sales increase by 66,000, income will increase by 220,000.00
Net operating income 37,200.00
The margin of safety is 14.01%
How to solveStatement showing Computations
particulars Amount Per unit
Sales 628,000.00 40.00
Variable Expenses 439,600.00 28.00
Contribution Margin 188,400.00 $ 12.00
Fixed Expenses 151,200.00
Net operating income 37,200.00
'
1) BEP in unit sales = 151,200/12 12,600.00
.BEP in sales $ = 12,600 * 40 504,000.00
2) Total Contribution margin at BEP = Fixed costs 151,200.00
3)a Target Profit $ 64,800.00
Fixed Expenses 151,200.00
Desired Contribution 216,000.00
3b. No of units to be sold = 216,000/12 18,000.00
Sales 720,000.00
Variable Expenses 504,000.00
Contribution Margin 216,000.00
Fixed Expenses 151,200.00
Net operating income 64,800.00
4) Margin of safety = 628,000.00-540,000.00 88,000.00
MOS in % = 88,000/6280001 14.01%
5)CM Ratio = 188,400/628,000 0.3
If sales increase by 66,000, income will increase by 220,000.00
66,000/0.3
=220,000.
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write 1/r^2 in terms of spherical bessel functions
The function 1/[tex]r^2[/tex] can be expressed in terms of the spherical Bessel functions of the first kind, which are a family of solutions to the spherical Bessel differential equation.
The expansion involves a combination of the delta function and the first two spherical Bessel functions, j_0(r) and j_1(r). Specifically, the expansion can be written as (1/2)*[pi * delta(r) + (1/r)*d/d(r)(r * j_0(r)) + (1/[tex]r^2[/tex])*d/d(r)[[tex]r^2[/tex] * j_1(r)]]. This expansion is valid for all values of r except for r=0, where the first term dominates. The spherical Bessel functions are commonly used in physics, particularly in the context of scattering problems and wave propagation.
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(1 point) Use Lagrange multipliers to find the minimum value of the function f(x,y) = 2 + y subject to the constraint xy=5 Minimum:
function f(x,y) = 2 + y
The minimum value are f(√5, √5) = 2 + √5.
Lagrange multipliers:To find the minimum value of the function f(x,y) = 2 + y subject to the constraint xy=5 using Lagrange multipliers,
we first set up the Lagrangian function:
L(x,y,λ) = f(x,y) - λ(xy - 5)
Taking partial derivatives with respect to x, y, and λ, we get:
∂L/∂x = 0 = -λy
∂L/∂y = 1 - λx
∂L/∂λ = xy - 5
Solving for λ from the first equation and substituting into the second equation, we get:
x/y = 0/λ
1 - λx = 0
xy - 5 = 0
From the first equation, we see that either x = 0 or y = 0. But since xy = 5, neither x nor y can be zero.
Therefore, we have:
λ = 0
1 - λx = 0
xy - 5 = 0
Solving for x and y from the last two equations, we get:
x = 5/y
y = ±√5
We take the positive root for y since we are looking for a minimum value of the function.
Substituting y = √5 into x = 5/y, we get x = √5.
Therefore, the minimum value of f(x,y) = 2 + y subject to the constraint xy=5 is:
f(√5, √5) = 2 + √5.
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Water flows into an empty reservoir at a rate of 3200+ 5t gal/hour. What is the quantity of water in the reservoir after 11 hours? Answer:_____ gallons.
To find the quantity of water in the reservoir after 11 hours, we need to integrate the rate of flow with respect to time from 0 to 11. The quantity of water in the reservoir after 11 hours is 38,225 gallons.
∫(3200 + 5t) dt from 0 to 11
= [(3200 * 11) + (5/2 * 11^2)] - [(3200 * 0) + (5/2 * 0^2)]
= 35,200 + 302.5
= 35,502.5 gallons
Therefore, the quantity of water in the reservoir after 11 hours is 35,502.5 gallons.
To find the quantity of water in the reservoir after 11 hours with the rate of 3200 + 5t gal/hour, we need to first find the total amount of water that flows into the reservoir within that time.
Step 1: Identify the given rate of flow: 3200 + 5t gal/hour.
Step 2: Integrate the flow rate function with respect to time (t) to find the total quantity of water. The integral of the function will give us the quantity of water in gallons:
∫(3200 + 5t) dt = 3200t + (5/2)t^2 + C, where C is the constant of integration.
Since the reservoir is initially empty, the constant C will be 0.
Step 3: Substitute t=11 hours into the integrated function to find the total quantity of water:
Q(11) = 3200(11) + (5/2)(11)^2
Q(11) = 35200 + 3025
Step 4: Add the values to find the total quantity of water in gallons:
Q(11) = 38225 gallons
The quantity of water in the reservoir after 11 hours is 38,225 gallons.
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Select the equation that most accurately depicts the word problem. The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches. 68 = 9(L + 2) 68 = 2L + 2(9) 68 = 2(L - 9) 68 = 9L + 2 68 = 2/L + 2/9 68 = L/2 + 2(9)
The equation which most accurately represents the word problem, is (b) 68 = 2L + 2(9).
The word problem states that the perimeter of a rectangle is 68 inches, and the perimeter equals twice the length (L) plus twice the width (9). We can represent this relationship by using the equation as :
We know that, the perimeter of rectangle is : 2(length + width),
Substituting the value,
We get,
⇒ 68 = 2(L + 9);
⇒ 68 = 2L + 2(9); and this statement is represented by Option(b).
Therefore, the correct equation is (b) 68 = 2L + 2(9).
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The given question is incomplete, the complete question is
Select the equation that most accurately depicts the word problem.
"The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches".
(a) 68 = 9(L + 2)
(b) 68 = 2L + 2(9)
(c) 68 = 2(L - 9)
(d) 68 = 9L + 2
(e) 68 = 2/L + 2/9
(f) 68 = L/2 + 2(9)
Victor opened a savings account that earns 4.5% simple
interest. He deposited $5,725 into the account. What will be
Victor's account balance after five years? Round to the nearest
cent.
7.1
Answer:
(5,725)1.045^5
Step-by-step explanation:
(5,725)1.045^5
5,725 is the original amt of $
1.045 is the % of interest
5 is the # of years
Solve this and round the nearest
cent.
The original selling price of a jacket was
s
s dollars. The selling price was then changed on two occasions by the store owner. Its price is now represented by
0. 85
(
1. 4
s
)
0. 85(1. 4s). Which expression could explain what happened to the price of the jacket?
The expression that explains what happened to the price of the jacket is 0.85(1.4s), which represents a 40% increase in price followed by a 15% discount.
The expression 0.85(1.4s) represents the current selling price of the jacket, which includes two price changes.
To explain what happened to the price of the jacket, we can break down the expression into two steps:
1. The first change was an increase by 40%, which can be represented as multiplying the original price "s" by 1.4 (100% + 40% = 140% or 1.4). So, the price after the first change is 1.4s.
2. The second change was a discount of 15%, which can be represented as multiplying the price after the first change by 0.85 (100% - 15% = 85% or 0.85). So, the price after both changes is 0.85(1.4s).
So, the expression that explains what happened to the price of the jacket is 0.85(1.4s), which represents a 40% increase in price followed by a 15% discount.
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CI is tangent to circle O at point c. If arc CUH=244*, find m
The value of angle HCI is determined as 244⁰.
What is the value of angle HCI?The value of angle HCI is calculated by applying intersecting chord theorem as follows;
The intersecting chord theorem, also known as the secant-secant theorem, states that when two chords intersect inside a circle, the products of the segments of one chord are equal to the products of the segments of the other chord.
From the diagram, the value arc CUH is equal to the value of angle HCI.
Thus, angle HCI = 244⁰
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Consider the diagram shown. The sphere and cylinder have the same diameter. The height of the
cylinder is equal to the diameter of the sphere.
Find the approximate volume of the sphere by using 3.14 for 7. Round to the nearest tenth
of a cubic unit.
8.4
8.4
Answer:
310.2 cubic units
Step-by-step explanation:
since we know the diameter of the sphere (8.4), the radius is [tex]8.4/2 = 4.2[/tex]
The volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]
Plugging in 3.14 as [tex]\pi[/tex] and 4.2 as r, we get 310.2
Help I don't know what I did wrong.
[tex]4\sqrt{125} -2\sqrt{243} -3\sqrt{20}+5\sqrt{27}[/tex]
A triangle with area 28 square inches has a height that is six less than twice the width. Find the height and width of the triangle. [Hint: For a triangle with base b and height h , the area, A , is given by the formula
The height of the triangle is 8 inches and the width is 7 inches.
Find the height and width of a triangle with area 28 square inches, where the height is six less than twice the width.Let's start by using the formula for the area of a triangle:
A = (1/2)bh
where A is the area of the triangle, b is the base, and h is the height.
We are given that the area of the triangle is 28 square inches, so we can write:
28 = (1/2)bh
Next, we are given that the height h is six less than twice the width w. In other words:
h = 2w - 6
Now we can substitute this expression for h into the formula for the area:
28 = (1/2)bw(2w - 6)
Simplifying this equation, we get:
56 = bw(2w - 6)
28 = w(w - 3)
w^2 - 3w - 28 = 0
We can solve this quadratic equation using the quadratic formula:
w = [3 ± √ ([tex]3^2[/tex] - 4(1)(-28))] / 2
w = [3 ± √ (121)] / 2
w = (3 + 11) / 2 or w = (3 - 11) / 2
w = 7 or w = -4
Since a negative width doesn't make sense in this context, we can ignore the second solution and conclude that the width of the triangle is 7 inches.
Now we can use the expression for h in terms of w to find the height:
h = 2w - 6
h = 2(7) - 6
h = 8
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Admission Charge for Movies The average admission charge for a movie is $5. 81. If the distribution of movie admission charges is approximately normal with a standard deviation of $0. 81, what is the probability that a randomly selected admission charge is less than $3. 50
The probability that a randomly selected admission charge is less than $3. 50 is 0.23% or 0.0023.
To find the probability that a randomly selected admission charge is less than $3.50, we will use the z-score formula and a standard normal table. The z-score formula is:
Z = (X - μ) / σ
Where X is the value we are interested in ($3.50), μ is the average admission charge ($5.81), and σ is the standard deviation ($0.81).
Z = (3.50 - 5.81) / 0.81 ≈ -2.84
Now, look up the z-score (-2.84) in a standard normal table, which gives us the probability of 0.0023. Therefore, the probability that a randomly selected admission charge is less than $3.50 is approximately 0.23% or 0.0023.
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When finding the Quotient of 8,397 divided 12, Calida first divided 83 by 12
In a case whereby When finding the Quotient of 8,397 divided 12, Calida first divided 83 by 12, then she will be wrong, because the answer is 699.75.
What is division in maths?In maths, a division can be described as the process of splitting a specific amount which can be spread to equal parts instance of thisd is when we divide a group of 20 members into 4 groups and this can be done using the mathematical sign.
In the case of Calida above, the division can be made as
8,397 divided 12
=8,397 / 12
=699.75
Therefore we can say that the right answer to the querstion is 699.75
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How to show (sin 7x)/sin x = 64(cos x)^6 - 80(cos x)^4 +24(cos x)^2 - 1 ?
Following shows (sin 7x)/sin x = 64(cos x)^6 - 80(cos x)^4 +24(cos x)^2 - 1:
12sin^3 x - 8sin^
To show that (sin 7x)/sin x is equal to 64(cos x)^6 - 80(cos x)^4 + 24(cos x)^2 - 1, we can use trigonometric identities and algebraic manipulation.
Let's start with the left-hand side of the equation:
(sin 7x)/sin x
Using the trigonometric identity for sin(A + B):
sin(A + B) = sin A cos B + cos A sin B
We can rewrite sin 7x as sin (6x + x):
sin (6x + x) = sin 6x cos x + cos 6x sin x
Now we can substitute sin 7x with sin 6x cos x + cos 6x sin x:
(sin 6x cos x + cos 6x sin x)/sin x
Next, we can simplify this expression by dividing both terms by sin x:
(sin 6x cos x)/sin x + (cos 6x sin x)/sin x
The sin x term cancels out, leaving us with:
sin 6x cos x + cos 6x
Now, we can use the double-angle identity for sin 2A:
sin 2A = 2sin A cos A
To rewrite sin 6x cos x, we can treat it as sin 2A with A = 3x:
sin 6x cos x = 2sin 3x cos 3x
Next, we can use the triple-angle identity for sin 3A:
sin 3A = 3sin A - 4sin^3 A
To rewrite sin 3x, we can treat it as sin A with A = x:
sin 3x = 3sin x - 4sin^3 x
Substituting this into our expression:
2sin 3x cos 3x = 2(3sin x - 4sin^3 x) cos 3x
Expanding further:
= 6sin x cos 3x - 8sin^3 x cos 3x
Now, we can use the double-angle identity for cos 2A:
cos 2A = cos^2 A - sin^2 A
To rewrite cos 3x, we can treat it as cos A with A = x:
cos 3x = cos^2 x - sin^2 x
Substituting this into our expression:
6sin x cos 3x - 8sin^3 x cos 3x = 6sin x (cos^2 x - sin^2 x) - 8sin^3 x (cos^2 x - sin^2 x)
Expanding further:
= 6sin x cos^2 x - 6sin x sin^2 x - 8sin^3 x cos^2 x + 8sin^3 x sin^2 x
Now, we can use the Pythagorean identity for sin^2 x + cos^2 x:
sin^2 x + cos^2 x = 1
To rewrite sin^2 x, we can subtract cos^2 x from both sides:
sin^2 x = 1 - cos^2 x
Substituting this back into our expression:
= 6sin x (cos^2 x - (1 - sin^2 x)) - 8sin^3 x cos^2 x + 8sin^3 x sin^2 x
= 6sin x (2sin^2 x) - 8sin^3 x cos^2 x + 8sin^3 x sin^2 x
= 12sin^3 x - 8sin^
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Need this really fast !
consider the function whose criterion is f(x) = = ax + b si x 3 The required values for a and t for the function to be continuous at X=3
The function will be continuous at x = 3 for any values of a and b.
How to determine the values for the function?f(x) = ax + b to be continuous at x = 3
A function is continuous at a point x = c if:
1. f(c) is defined
2. The limit of f(x) as x approaches c exists
3. The limit of f(x) as x approaches c is equal to f(c)
For f(x) = ax + b to be continuous at x = 3:
1. f(3) is defined:
f(3) = a(3) + b
2. The limit of f(x) as x approaches 3 exists.
3. The limit of f(x):
lim (x->3) (ax + b) = a(3) + b
There are no specific values for a and b that must be satisfied. The function will be continuous at x = 3 for any values of a and b.
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the operation manager at a tire manufacturing company believes that the mean mileage of a tire is 37,014 miles, with a standard deviation of 4617 miles. what is the probability that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires if the manager is correct? round your answer to four decimal places.
Probability or p-vale that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires is equals to zero if the manager is correct.
We have data of an operation manager at a tire manufacturing company.
Mean mileage of a tire, [tex] \mu[/tex]
= 37,014 miles
standard deviation, [tex] \sigma[/tex]
= 4617 miles.
Sample size, n = 56
We have to determine the probability that the sample mean would differ from the population mean by less than 221 miles. Using Z-score formula in normal distribution, [tex]\small z= \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}},[/tex]
Plugging all known values in above formula, [tex]z = \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}[/tex]
= 59.634
[tex]P( \bar x < 221) = P ( \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}} < \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}) \\ [/tex]
=> P ( z < 59.63) = P( \bar x < 221)
Using the Z-distribution table, probability value is equals to 0. Hence, required probability is zero.
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Find the derivative y = cos(sin(14x-13))
To find the derivative of y = cos(sin(14x-13)), we will use the chain rule.
Let's start by defining two functions:
u = sin(14x-13)
v = cos(u)
We can now apply the chain rule:
dy/dx = dv/du * du/dx
First, let's find dv/du:
dv/du = -sin(u)
Next, let's find du/dx:
du/dx = 14*cos(14x-13)
Now we can put it all together:
dy/dx = dv/du * du/dx
dy/dx = -sin(u) * 14*cos(14x-13)
But we still need to substitute u = sin(14x-13) back in:
dy/dx = -sin(sin(14x-13)) * 14*cos(14x-13)
So the derivative of y = cos(sin(14x-13)) is:
dy/dx = -14*sin(sin(14x-13)) * cos(14x-13)
To find the derivative of the function y = cos(sin(14x - 13)), we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
Let u = sin(14x - 13), so y = cos(u). Now we find the derivatives:
1. dy/du = -sin(u)
2. du/dx = 14cos(14x - 13)
Now, using the chain rule, we get:
dy/dx = dy/du × du/dx
dy/dx = -sin(u) × 14cos(14x - 13)
Since u = sin(14x - 13), we can substitute back in:
dy/dx = -sin(sin(14x - 13)) × 14cos(14x - 13)
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If we roll a regular, 6-sided die 5 times. What is the probability that at least one value is observed more than once
The probability that at least one value is observed more than once when rolling a regular 6-sided die 5 times is approximately 0.598.
The total number of possible outcomes when rolling a die 5 times is 6⁵ = 7776 (since there are 6 possible outcomes for each roll and there are 5 rolls). To calculate the number of outcomes where no value is repeated, we can use the permutation formula: P(6,5) = 6! / (6-5)! = 6! / 1! = 720, since there are 6 possible outcomes for the first roll, 5 for the second roll (since one outcome has been used), and so on.
So, the probability of not observing any repeated values is P(no repeats) = 720 / 7776 ≈ 0.0926. Therefore, the probability of observing at least one repeated value is P(at least one repeat) = 1 - P(no repeats) ≈ 0.9074.
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This table shows dogs’ weights at a competition.
Dogs' Weights (pounds)
35, 22, 31, 23, 35, 22, 30, 35, 40
One 42-pound dog could not make it to the competition. ++++Select all++++ the ways the measures of center of the data set change if she had entered the competition.
A. The median increases
B. The mode increases
C. The mean increases
D. The median decreases
E. The mode decreases
F. The mean decreases
The measures of central tendencies changed as mode remained the same, the median increased and the mean increased.
How will the data set change if she had entered the competition?To determine how the data set would've changed if she entered the competition, we simply need to work on the mean, median and mode of the data.
Given data;
35, 22, 31, 23, 35, 22, 30, 35, 40
Rearranging this data;
22, 22, 23, 30, 31, 35, 35, 35, 40
The mean of this data will be
mean = 30.3
The mode = 35
The median = 31
When her weight is added, the measures of central tendencies change to;
mean = 31.5
median = 33
mode = 35
The median decreases, the mode remains the same and the mean increases
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How is the product of a complex number and a real number represented on the complex plane?
Consider the product of 2−4i and 3.
Drag a value or phrase into each box to correctly complete the statements
The product of 2-4i and 3 is represented on the complex plane as a vector with magnitude 6√5 and angle -63.43 degrees, starting from the origin.
To represent the product of a complex number and a real number on the complex plane:
We multiply the real part and the imaginary part of the complex number by the real number.
The magnitude (or length) of the resulting complex number is multiplied by the absolute value of the real number.
The angle (or argument) of the resulting complex number is the same as the angle of the original complex number.
For the product of 2−4i and 3:
We multiply the real part (2) and the imaginary part (-4i) of the complex number by the real number (3), to get:
3(2) + 3(-4i) = 6 - 12i
The magnitude of the resulting complex number is:
|6 - 12i| = √(6² + (-12)²) = √180 = 6√5
The angle of the resulting complex number is the same as the angle of the original complex number (2-4i), which can be found using the inverse tangent function:
tanθ = (imaginary part) / (real part) = (-4) / 2 = -2
θ = atan(-2) ≈ -1.107 radians or ≈ -63.43 degrees
Therefore, the product of 2-4i and 3 is represented on the complex plane as a vector with magnitude 6√5 and angle -63.43 degrees, starting from the origin.
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How much money did Susan earn per hour
Answer:
$9.50
Step-by-step explanation:
Divide the total earnings by total hours.
