The two points of intersection are (0, θ) and (0.247, θ).
The area enclosed in the intersection of the two graphs is 7π/2 square units.
To find the points of intersection of the curves:
We need to solve for θ when t = 6 cos(θ) = r/3.
We can substitute r = 2 sin(θ) into this equation to get:
6 cos(θ) = 2 sin(θ)/3
18 cos(θ) = 2 sin(θ)
9 cos(θ) = sin(θ)
Squaring both sides and using the identity sin^2(θ) + cos^2(θ) = 1, we get:
81 cos^2(θ) = 1 - cos^2(θ)
82 cos^2(θ) = 1
cos(θ) = ±sqrt(1/82)
Since we know that the curves intersect at the pole (r = 0), we only need to consider the positive root of cos(θ) to find the other point of intersection.
We can use the equation r = 2 sin(θ) to find the value of r:
r = 2 sin(θ) = 2 cos(θ) sqrt(1 - cos^2(θ)) = 2 sqrt(1/82) ≈ 0.247
So the two points of intersection are (0, θ) and (0.247, θ) where cos(θ) = sqrt(1/82) and θ is measured in radians.
To find the area enclosed in the intersection of the two graphs:
We can use the formula for the area of a polar region:
A = 1/2 ∫(r²) dθ
Since we know that the curves intersect at the pole and at (0.247, θ), we can split the integral into two parts:
A = 1/2 ∫(0 to π/2)(2 sin(θ))² dθ + 1/2 ∫(π/2 to π)(6 cos(θ))² dθ
A = π/4 + 27π/4
A = 7π/2
So the area enclosed in the intersection of the two graphs is 7π/2 square units.
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Averi walker paid off a 150-day note at 6% with a single payment, also known as a balloon payment, of $2,550. find the face value (p) and interest (i) for the simple interest note.
Answer:
To find the face value (p) of the note, we need to use the formula for simple interest:
I = P * r * t
where:
I = interest
P = principal or face value
r = interest rate per year
t = time in years
Since the note has a 6% interest rate and a 150-day term, we need to convert the time to years:
t = 150 / 365
t = 0.41096 years
Now we can solve for the face value:
I = P * r * t
2550 = P * 0.06 * 0.41096
2550 = 0.0246576P
P = 2550 / 0.0246576
P = 103364.99
So the face value (p) of the note is $103,364.99.
To find the interest (i), we can subtract the face value from the balloon payment:
i = 2550 - 103364.99
i = -100814.99
The negative interest result may seem strange, but it's because the balloon payment was higher than the face value of the note. In other words, Averi paid more than the note was worth in order to fully pay off the principal and interest.
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for each pair of numbers verify lcmm,n∙gcdm,n=mn. 60,90 220,1400 3273∙11, 23∙5∙7
lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers. We can verify lcmm,n∙gcdm,n=mn for each pair of numbers as follows:
For 60 and 90:
lcm(60,90) = 180
gcd(60,90) = 30
180 * 30 = 5400
60 * 90 = 5400
Since both sides of the equation are equal to 5400, the equation is verified.
For 220 and 1400:
lcm(220,1400) = 3080
gcd(220,1400) = 20
3080 * 20 = 61600
220 * 1400 = 61600
Since both sides of the equation are equal to 61600, the equation is verified.
For 3273∙11 and 23∙5∙7:
lcm(3273∙11, 23∙5∙7) = 15015
gcd(3273∙11, 23∙5∙7) = 161
15015 * 161 = 2418315
3273∙11 * 23∙5∙7 = 2418315
Since both sides of the equation are equal to 2418315, the equation is verified.
Therefore, lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers.
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Square root 2/3 + square root 6
Answer:
[tex] \sqrt{ \frac{2}{3} } + \sqrt{6} \\ = \frac{ \sqrt{2} }{ \sqrt{3} } + \sqrt{6} \\ = \frac{ \sqrt{2} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } + \sqrt{6} \\ = \frac{ \sqrt{6} }{3} + \sqrt{6} \\ = \frac{ \sqrt{6} }{3} + \frac{3 \sqrt{6} }{3} \\ = \frac{ 4\sqrt{6} }{3} [/tex]
Two parallel runways at an airport are intersected by another runway as shown. Find m∠5 and m∠8 if m∠3=118°
The value of angle 5 and angle 8 will be 118° and 62° respectively.
How to calculate the angleParallel lines are lines that are always the same distance apart and never intersect. In other words, they have the same slope and will never meet or cross each other. The symbol for parallel is ||.
For example, in the Cartesian coordinate system, the equation of a straight line is represented as y = mx + b, where m is the slope of the line and b is the y-intercept. If two lines have the same slope, they are parallel.
The value of angle 5 will be 118. Angle 8 will be:
= 180 - 118
= 62°
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A tool box has the dimensions of 9 in by 6 in by 7 in. If Mark plans to double one dimension to build a larger tool box, he believes he would double the volume of the tool box. Is he correct?
Yes, Mark is correct he believes that doubling one of the dimensions would double the volume of his toolbox.
Volume refers to the space occupied by a 3-Dimensional space. The volume of a cuboid is given by:
V = l * b * h
where l is the length
b is the breadth
h is the height
V = 9 * 6 * 7
= 378 cubic inches
If we double any of the dimensions, like
By doubling the 9 we get
V = 18 * 6 * 7
= 756 cubic inches
By doubling the 6 we get
V = 9 * 12 * 7
= 756 cubic inches
By doubling the 7 we get
V = 9 * 6 * 14
= 756 cubic inches
Then the volume of the toolbox is doubled as shown above.
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Four tangents are drawn from E to two concentric circles A, B, C, and D are the points of tangency. 1. Name as many pairs of congruent triangles as possible 2. Tell how you can show each pair is congruent
1. Congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD
2. Triangle EAB ≅ Triangle ECD and Triangle EAC ≅ Triangle EBD by ASA Congruence Postulate.
In this scenario, we have two concentric circles and four tangents drawn from point E to these circles, creating points of tangency A, B, C, and D.
1. Pairs of congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD
2. Showing congruence for each pair:
a) To show that Triangle EAB and Triangle ECD are congruent, we can use the following information:
- EA and EC are both radii of the larger circle, so EA = EC (congruent radii).
- AB and CD are tangents to the smaller circle, so the segments are parallel and form corresponding angles at points A and C. Thus, Angle EAB and Angle ECD are congruent (alternate interior angles).
- EB and ED are both radii of the smaller circle, so EB = ED (congruent radii).
With this information, we can prove Triangle EAB ≅ Triangle ECD using the Angle-Side-Angle (ASA) Congruence Postulate.
b) To show that Triangle EAC and Triangle EBD are congruent, we can use the following information:
- EA and EB are both radii of the larger circle, so EA = EB (congruent radii).
- AC and BD are tangents to the larger circle, so the segments are parallel and form corresponding angles at points A and B. Thus, Angle EAC and Angle EBD are congruent (alternate interior angles).
- EC and ED are both radii of the smaller circle, so EC = ED (congruent radii).
With this information, we can prove Triangle EAC ≅ Triangle EBD using the Angle-Side-Angle (ASA) Congruence Postulate.
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The square root of 7 more than a number is 12. Find the number.
Answer:
x=137
Step-by-step explanation:
sqrt(x+7)=12
x+7=144
x=137
3. [-/1 Points] DETAILS SCALCET9 4.7.005. What is the maximum vertical distance between the line y = x + 72 and the parabola y - x for - SxS9? Need Help? Watch
The maximum vertical distance between the line y = x + 72 and the parabola y = x^2 is 518.67 units.
To find the maximum vertical distance between the line and the parabola, we need to find the point(s) where the distance is maximum.
The line y = x + 72 is a straight line with slope 1, and it intersects the y-axis at 72.
The parabola y = x^2 is a symmetric curve with vertex at (0,0).
To find the point(s) where the distance is maximum, we can find the intersection point(s) of the line and the parabola.
Substituting y = x + 72 in the equation of the parabola, we get x^2 - x - 5184 = 0.
Solving for x using the quadratic formula, we get x = (1 ± sqrt(1 + 20736))/2.
The two intersection points are (108, 180) and (-107, 65).
The maximum vertical distance between the line and the parabola is the difference between the y-coordinates of these points, which is approximately 518.67 units.
Therefore, the maximum vertical distance between the line y = x + 72 and the parabola y = x^2 is 518.67 units.
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What is the simplified form of the following expression ? 25xy * sqrt(81/625 *x^2*y ^2) A. 9/25 * x * y B. 9/625 * x ^ 2 * y ^ 2 C. 9xy|xy| D. 9x ^ 2 * y ^ 2
Let's simplify the expression step by step:
25xy * sqrt(81/625 * x^2 * y^2)
= 25xy * (sqrt(81)/sqrt(625) * sqrt(x^2) / sqrt(y^2))
= 25xy * (9/25 * x/y)
= 9xy * 5/5
= 9xy
Therefore, the simplified form of the expression 25xy * sqrt(81/625 x^2y ^2) is option C, 9xy|xy|.
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Se the first five terms of the trigonometric series to approximate the value of cos 4pi/7 to four decimal places. Then compare the approximation to the actual value. A. –0. 9609, –0. 9659 c. –0. 9649, –0. 9659 b. –0. 2224, –0. 2225 d. –0. 9568, –0. 9659
The answer is (d) –0.9568, –0.9659.
How to approximate cos 4pi/7 using trigonometric series?To find the first five terms of the trigonometric series for cos(4π/7), we can use the formula:
cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...
Substituting x = 4π/7, we get:
cos(4π/7) = 1 - (4π/7)²/2! + (4π/7)⁴/4! - (4π/7)⁶/6! + (4π/7)⁸/8!
Using a calculator to evaluate each term and rounding to four decimal places, we get:
cos(4π/7) ≈ -0.9568
Comparing this approximation to the actual value of cos(4π/7), which is approximately -0.9659, we see that the approximation is fairly close but not exact. So, the answer is (d) –0.9568, –0.9659.
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Charlie collects dimes in a jar. The total mass of the dimes is 1. 265 x 10 grams. The mass of each dime is 2. 3 grams. How many dimes
are in the jar?
A 5. 5 x 103 dimes
B. 5. 5 x 102 dimes
C 2. 9 x 103 dimes
D2. 9 x 102 dimes
There are approximately 5500 dimes in the jar. A) 5.5 x 103 dimes.
How we find the dimes?To determine the number of dimes in the jar, we can divide the total mass of the dimes by the mass of each dime.
Total mass of dimes = 1.265 x 10 grams
Mass of each dime = 2.3 grams
Let "x" be the number of dimes in the jar. Then, we can set up the following equation:
x(2.3 grams) = 1.265 x 10 grams
Simplifying this equation, we get:
x = 1.265 x 10 / 2.3
x ≈ 5500
It is important to that this calculation assumes that all dimes have the same mass, and that there are no other objects in the jar.
the actual number of dimes may vary slightly due to measurement error or variability in the mass of each dime.
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David wants to buy a new bicycle that cost $295 before a 40% discount. He finds the cost
after the discount, in dollars, by evaluating 295 - 295(0. 40). His brother Michael finds the
same cost by evaluating 295(1 - 0. 40). What property can be used to justify that these two
expressions represent the same cost after the discount?
The expressions represent the same cost after the discount of 40%.
How to show that the two expressions 295 - 295(0.40) and 295(1 - 0.40) represent the same cost after the discount?
To show that the two expressions 295 - 295(0.40) and 295(1 - 0.40) represent the same cost after the discount, we can use the distributive property of multiplication over addition or subtraction.
The distributive property states that for any real numbers a, b, and c:
a(b + c) = ab + ac
a(b - c) = ab - ac
So, we can apply the distributive property as follows:
295 - 295(0.40)
= 295(1) - 295(0.40) [Multiplying 295 by 1]
= 295(1 - 0.40) [Using the distributive property]
Therefore, both expressions represent the same cost after the discount of 40%.
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The buying and selling rate of an American dollar in a bank are Rs 116. 85 and Rs 117. 30 respectively. How much American dollar should be bought and sold by the bank to get Rs 9000 profit?
The bank needs to buy and sell 20,000 dollars.
How to calculate exchange rate?To calculate the amount of American dollars that should be bought and sold by the bank to earn a profit of Rs 9000, we first need to determine the exchange rate difference between the buying and selling rates:
Exchange rate difference = selling rate - buying rate
Exchange rate difference = Rs 117.30 - Rs 116.85
Exchange rate difference = Rs 0.45
This means that for every dollar bought and sold by the bank, there is a difference of Rs 0.45. To earn a profit of Rs 9000, we need to find out how many dollars the bank needs to buy and sell to make this amount of profit.
Let X be the amount of American dollars the bank needs to buy and sell to earn a profit of Rs 9000.
Profit = Exchange rate difference × X
Rs 9000 = Rs 0.45 × X
To calculate the amount of American dollars that should be bought and sold by the bank to earn a profit of Rs 9000, we first need to determine the exchange rate difference between the buying and selling rates:
Exchange rate difference = selling rate - buying rate
Exchange rate difference = Rs 117.30 - Rs 116.85
Exchange rate difference = Rs 0.45
This means that for every dollar bought and sold by the bank, there is a difference of Rs 0.45. To earn a profit of Rs 9000, we need to find out how many dollars the bank needs to buy and sell to make this amount of profit.
Let X be the amount of American dollars the bank needs to buy and sell to earn a profit of Rs 9000.
Profit = Exchange rate difference × X
Rs 9000 = Rs 0.45 × X
To solve for X, we can divide both sides by 0.45:
X = Rs 9000 ÷ Rs 0.45
X = 20,000
Therefore, the bank needs to buy and sell 20,000 American dollars to earn a profit of Rs 9000.
To calculate the amount of American dollars the bank needs to buy and sell, we first need to determine the exchange rate difference between the buying and selling rates. This is done by subtracting the buying rate from the selling rate. The resulting exchange rate difference gives us the profit the bank earns for every dollar bought and sold.
Next, we use the exchange rate difference to calculate the amount of American dollars needed to earn a profit of Rs 9000. We set up an equation where the profit is equal to the exchange rate difference multiplied by the amount of American dollars bought and sold. We solve for X, which represents the amount of American dollars needed to earn the profit of Rs [tex]9000.[/tex]
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Can someone explain this to me I need to solve for "B" but I don't understand how
The value of b in the parallel line is 93 degrees.
How to find the angle in a parallel line?When parallel lines are crossed by a transversal line, angle relationships are formed such as alternate interior angles, alternate exterior angles, corresponding angles, same side interior angles, vertically opposite angles, adjacent angles etc.
Therefore, let's use the angle relationship to find the angle b as follows:
Alternate interior angles are the angles formed when a transversal intersects two parallel lines. Alternate interior angles are congruent.
Using the alternate interior angle theorem,
b = 180 - 65.5 - 21.5
b = 93 degrees.
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Scores at a local high school on the Algebra 1 Midterm are extremely skewed left with a mean of 65 and a standard deviation of 8. A guidance counselor takes a random sample of 10 students and calculates the mean score, x¯¯¯.
(a) Calculate the mean and standard deviation of the sampling distribution of x¯¯¯
(b) Would it be appropriate to use a normal distribution to model the sampling distribution? Justify your answer
The mean of the sampling distribution is 65 and the standard deviation is 2.53. Yes, it would be appropriate to use a normal distribution to model the sampling distribution of x¯¯¯ due to the central limit theorem.
(a) To calculate the mean of the sampling distribution of x¯ ¯ ¯, we can use the formula:
μx¯ ¯ ¯ = μ = 65
This means that the mean of the sampling distribution of x¯ ¯ ¯ is equal to the population mean of 65.
To calculate the standard deviation of the sampling distribution of x¯ ¯ ¯, we can use the formula:
σx¯ ¯ ¯ = σ/√n = 8/√10 ≈ 2.53
This means that the standard deviation of the sampling distribution of x¯ ¯ ¯ is approximately 2.53.
(b) Yes, it would be appropriate to use a normal distribution to model the sampling distribution because of the Central Limit Theorem.
The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.
In this case, we have a sample size of 10, which is relatively small, but it is still large enough for us to assume that the sampling distribution of x¯ ¯ ¯ is approximately normal. Additionally, the population distribution is not too skewed, so this further supports the use of a normal distribution to model the sampling distribution.
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5. Divide 6/13 by 6 /12 -
O A. 12/13
O B. 9/16
O C. 13/12
O D. 1/12
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.
lim x → 0
A.x2^x
B. 2^x - 1
The limit of A. x^(2^x) as x approaches 0 is 1, and the limit of B. 2^x - 1 as x approaches 0 is ln 2.
A. To find the limit of A. x^(2^x) as x approaches 0, we can take the natural logarithm of both sides and use the fact that ln(1 + a) is approximately equal to a for small values of a. This gives us:
ln(A. x^(2^x)) = 2^x ln x
ln(A. x^(2^x)) / ln x = 2^x
Taking the limit as x approaches 0, the right-hand side goes to 1, and using the continuity of the natural logarithm, we have:
ln(A) = 0
A = 1
Therefore, the limit of A. x^(2^x) as x approaches 0 is 1.
B. To find the limit of B. 2^x - 1 as x approaches 0, we can use L'Hopital's Rule:
lim x→0 (2^x - 1)
= lim x→0 (ln 2 * 2^x / ln 2)
= ln 2 * lim x→0 (2^x / ln 2)
= ln 2 * (lim x→0 e^(x ln 2) / ln 2)
= ln 2 * (lim x→0 e^(x ln 2 - ln 2) / (ln 2 - ln 2))
= ln 2 * (lim x→0 e^(ln 2 * (x - 1)) / 1)
= ln 2 * e^0
= ln 2
Therefore, the limit of B. 2^x - 1 as x approaches 0 is ln 2.
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an engineer for an electric company is interested in the mean length of wires being cut automatically by machine. the desired length of the wire is 12 feet. it is known that the standard deviation in the cutting length is .15 feet, suppose the engineer decided to estimate the mean length to within .025 with 99% confident. what sample size is needed?
According to the given standard deviation, the engineer would need a sample size of at least 75 wires to estimate the mean length to within 0.025 feet with 99% confidence.
To estimate the mean length of the wires being cut, the engineer needs to determine the sample size needed to achieve a certain level of confidence and level of precision. In this case, the engineer wants to estimate the mean length to within 0.025 feet with 99% confidence. This means that there is a 99% chance that the true population mean falls within the estimated range.
To determine the sample size needed, the engineer can use a formula that takes into account the desired level of confidence, level of precision, and the standard deviation of the population. The formula is:
n = (z² x s²) / E²
Where:
n = sample size needed
z = z-score for desired level of confidence (99% = 2.58)
s = standard deviation of the population (0.15 feet)
E = level of precision (0.025 feet)
Plugging in the values, we get:
n = (2.58² x 0.15²) / 0.025²
n = 74.83 ≈ 75
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prove the value of the expression
Step-by-step explanation:
Expressions are collection of algebric equetion and equal sighn and used for expresion of mankind problems like items, money and other mankind problem.
to know length by using degree but most of the time for the archtechture. soon
A ball of radius 11 has a round hole of radius 4 drilled through its center.
Find the volume of the resulting solid.
The volume of the resulting solid is estimated 4,128.38 cubic units.
How do we calculate?
The volume of the ball isgitten as:
V_ball = (4/3)πr^3
r is the radius of the ball. In this scenario
r = 11, so:
V_ball = (4/3)π(11)^3
V_ball = (4/3)π(1331)
V_ball = 4,396.46 cubic units
The volume of the hole is gotten as :
V_hole = (4/3)πr^3
r is the radius of the hole.
In thisscenario, r = 4, so:
V_hole = (4/3)π(4)^3
V_hole = (4/3)π(64)
V_hole = 268.08 cubic units
In conclusion, the volume of the resulting solid is:
V_resulting_solid = V_ball - V_hole
V_resulting_solid = 4,396.46 - 268.08
V_resulting_solid = 4,128.38 cubic units
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Mr. Phil asks his students to find the largest 2 -digit number that is divisible by both 6 and 8. One of his students, Dexter finds a number that is 5 less than the correct number. What is Dexter's number?
The largest two digit number that is divisible by both 6 and 8 that is Dexter's number is equals to the ninty-six.
Two digit numbers : 2-digit numbers are the numbers that have two digits and they start from the number 10 and end on the number 99. They cannot start from zero. We have specify that Mr. Phil asks his students to determine the largest 2 -digit number that is divisible by both 6 and 8. Let the dexter's two digit number be 'x'.
x is divisible by 8 so, here total 11 numbers in two digit numbers, 16, 24, 32,..., 96x is divisible by 6 implies it is divisible by 2 and 3.From the above list of 11 numbers the largest number that is multiple of 2 and 3 both. That is 96. So, the students answer is 91. The answer of one of his student is less than 5 the correct number. Hence, required value is 96.
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A delivery service charges $1. 25 for
each delivery, plus $0. 75 for each
mile the driver travels. The service
charged a customer $5. 75 for a
delivery. Which number line
represents the number of iniles the
driver could have traveled for the
delivery?
The driver could have traveled up to 5 miles for the delivery.
Let's denote the number of miles the driver traveled by "m".
According to the problem, the delivery service charged $1.25 for the delivery itself, and $0.75 for each mile traveled. This can be written as:
Total cost = $1.25 + $0.75 * m
We know that the service charged the customer $5.75, so we can set up an equation:
$5.75 = $1.25 + $0.75 * m
Solving for m, we get:
[tex]m = ($5.75 - $1.25) / $0.75 = 5[/tex]
To represent this on a number line, we can draw a line labeled from 0 to 5, with tick marks at each integer value.
We can label the tick mark at 0 as "0 miles" and the tick mark at 5 as "5 miles".
We can also indicate that the cost of the delivery increases as we move to the right by drawing an arrow pointing to the right, and labeling it "increasing cost".
Here's an example of what the number line might look like:
0 1 2 3 4 5
|---------|---------|---------|---------|---------|
0 miles 5 miles
increasing cost ⟶
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P(A)=0. 7P(A)=0. 7, P(B)=0. 86P(B)=0. 86 and P(A\text{ and }B)=0. 652P(A and B)=0. 652, find the value of P(A|B)P(A∣B), rounding to the nearest thousandth, if necessary
Using the conditional probability, the value of P(A|B)P(A∣B), rounding to the nearest thousandth, is 0.758
To find P(A|B), we use the formula:
P(A|B) = P(A and B) / P(B)
Substituting the given values, we get:
P(A|B) = 0.652 / 0.86
P(A|B) = 0.758
Rounding to the nearest thousandth, we get:
P(A|B) = 0.758
Alternatively, to find the value of P(A|B), we can use the conditional probability formula:
P(A|B) = P(A and B) / P(B)
Given the values in your question, we have:
P(A and B) = 0.652
P(B) = 0.86
Now we can plug these values into the formula:
P(A|B) = 0.652 / 0.86 = 0.7575
Rounding to the nearest thousandth, the value of P(A|B) is approximately 0.758.
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Find those values of x for which the given function is increasing and those values of x for which it is decreasing, y = 12x – x^3 • Increasing for x < 2, decreasing for x > 2 • Increasing for 4 4 • Increasing for X <-2.x > 2, decreasing for -2 2
The function y = 12x – x^3 is increasing for x < -2, -2 < x < 2, and x > 2, and is decreasing for -2 < x < 2.
The given function is y = 12x – x^3. To determine when the function is increasing or decreasing, we need to take the derivative of the function with respect to x:
y' = 12 - 3x^2
To find where the function is increasing, we need to look for values of x where y' is positive. To find where the function is decreasing, we need to look for values of x where y' is negative.
So, y' > 0 when:
12 - 3x^2 > 0
3x^2 < 12
x^2 < 4
-2 < x < 2
Therefore, the function is increasing for x values less than -2, between -2 and 2, and greater than 2. Specifically:
• Increasing for x < -2
• Increasing for -2 < x < 2
• Increasing for x > 2
On the other hand, y' < 0 when:
12 - 3x^2 < 0
3x^2 > 12
x^2 > 4
x < -2 or x > 2
Therefore, the function is decreasing for x values between -2 and 2. Specifically:
• Decreasing for -2 < x < 2
Overall, we can summarize that the function y = 12x – x^3 is increasing for x < -2, -2 < x < 2, and x > 2, and is decreasing for -2 < x < 2.
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Charlene sees a laptop being sold for $492. this is 18% less than the original price. what was the original price of the laptop?
The original price of the laptop was $600 because $492 is 82% of the original price (100% - 18% = 82%).
How to find the percentage of the laptop?The concept of percentage decrease. A percent decrease is the amount by which a quantity decreases, expressed as a percentage of its original value. In this case, the laptop is being sold for 18% less than its original price, so we can represent the percent decrease as 18%.
To find the original price of the laptop, we need to work backwards from the sale price. We can use the formula:
Sale price = Original price - Percent decrease of original price
where "Percent decrease of original price" is the percentage decrease of the original price, expressed as a decimal. In this case, the percent decrease is 18%, which we convert to a decimal by dividing by 100: 18/100 = 0.18.
Plugging in the values we know, we get:
$492 = Original price - 0.18 * Original price
Simplifying this equation, we get:
$492 = 0.82 * Original price
To isolate Original price, we can divide both sides by 0.82:
Original price = $492 / 0.82
Simplifying this expression, we get:
Original price = $600
the original price of the laptop was $600.
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Identify the fractions between 1/16 and 5/8
The fractions between 1/16 and 5/8 are 3/16 and 5/16
Identifying the fractions between 1/16 and 5/8The fraction expressions are given as
1/16 and 5/8
The above fractions are proper fractions because numerator < denominator
Express the fraction 5/8 as a denominator of 16
So, we have the following equivalent fractions
1/16 and 10/16
This means that the fractions between 1/16 and 5/8 can be represented as
a/16
Where
1 < a < 10
So, we have
Possible fraction = 3/16 and 5/16
Hence, the fractions between 1/16 and 5/8 are 3/16 and 5/16
Note that there are other possible fractions too
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Need help, i have the answer just need the steps
(8^2/7)(8^1/4)
Answer:
Step-by-step explanation:
we can use the laws of exponents, which state that when multiplying terms with the same base, we add their exponents. In this case,both terms have a base of 8, so we can add their exponents of 2/7 and 1/4.
First, let's write 8 as a power of 2: 8 = 2^3. Then we can rewrite the original expression as (2^3)^(2/7) * (2^3)^(1/4). Using the power of a power rule, we can simplify this to 2^(3 * 2/7) * 2^(3 * 1/4).
Next, we can simplify the exponents by finding a common denominator. The smallest common multiple of 7 and 4 is 28, so we can rewrite the exponents as 6/28 and 21/28, respectively. Thus, we have 2^(3 * 6/28) * 2^(3 * 21/28).
Now we can simplify the exponents by multiplying the bases and exponents separately: 2^(18/28) * 2^(63/28). We can simplify the fractions by dividing both the numerator and denominator by 2, giving us 2^(9/14) * 2^(63/28).
Finally, we can add the exponents since we are multiplying terms with the same base: 2^(9/14 + 63/28). We can simplify the exponent by finding a common denominator of 28,
giving us 2^(36/28 + 63/28) = 2^(99/28). This is our final answer, which is an irrational number that is approximately equal to 69.887.
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Joseph measures the ropes to tie boats to a dock. He records the lengths of the ropes in feet and then makes a line plot. Joseph concludes that the difference between the longest and shortest lengths is 2 1/2 feet. Martha disagrees and says that the difference is only 1 foot who is correct? no links please
Without the line plot or the actual measurements of the ropes, it is difficult to determine who is correct.
Joseph measures the lengths of ropes used to tie boats to a dock in feet and creates a line plot. He then concludes that the difference between the longest and shortest lengths is 2 1/2 feet. Martha disagrees with Joseph's conclusion and argues that the difference is only 1 foot.
To determine who is correct, we need to analyze the line plot and examine the data. If the line plot shows that the ropes vary greatly in length, with some being significantly longer than others, then Joseph's conclusion of a 2 1/2 foot difference could be accurate. However, if the line plot shows that the ropes are relatively similar in length, with only slight variations, then Martha's conclusion of a 1 foot difference could be correct.
Without the line plot or the actual measurements of the ropes, it is difficult to determine who is correct. Therefore, it is important to always examine the data before making conclusions.
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Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and then sell it to customers in their store. The function C(-) = 3x + 4287501 + 12250 models their total inventory costs (in dollars) as a function of the lot size for each of their orders from the supplier. The inventory costs include such things as purchasing, processing, shipping, and storing the equipment. What lot size should Glorious Gadgets order to minimize their total inventory costs? (NOTE: your answer must be the whole number that corresponds to the lowest cost.) What is their minimum total inventory cost?
Lot size of 1429167 minimizes Glorious Gadgets' total inventory costs, with a minimum cost of $9,276,002.
The given function C(x) = 3x + 4287501 + 12250 models Glorious Gadgets' total inventory costs (in dollars) as a function of the lot size x.
To minimize the total inventory cost, we need to find the value of x that minimizes C(x).
To do this, we can take the derivative of C(x) with respect to x and set it equal to zero:
C'(x) = 3
Setting C'(x) = 0, we get:
3 = 0
This is not possible, which means that C(x) has no local minimum or maximum.
Therefore, to find the minimum total inventory cost, we need to consider the endpoints of the possible lot sizes. Assuming that the lot size x must be a positive integer, we can consider lot sizes x = 1, 2, 3, ... , n, where n is the largest integer such that C(n) is less than or equal to Glorious Gadgets' budget.
We can calculate the total inventory cost for each of these lot sizes using the given function C(x).
For example, when x = 1,
we have:
C(1) = 3(1) + 4287501 + 12250 = 4299754
Similarly, we can calculate C(x) for each of the other lot sizes.
Once we have found the minimum cost, we can determine the corresponding lot size.
The minimum cost occurs when x = 1429167, and the corresponding minimum cost is:
C(1429167) = 3(1429167) + 4287501 + 12250 = 9,276,002
Therefore, Glorious Gadgets should order a lot size of 1429167 to minimize their total inventory costs, and the minimum total inventory cost is $9,276,002.
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04-13-2021 ne ) In his application for a job, Jamie must pass an oral interview and take a written test. Past records of job applicants show that that the probability of passing the oral test is 0. 56. The probability of passing the written test is 0. 68. The probability of passing the oral test, given that the candidate passes the written test is 0. 76. What is the probability that Jamie passes both the oral test and the written test?
The probability that Jamie passes both the oral test and the written test is 0.5168, or 51.68%.
To find the probability that Jamie passes both the oral test and the written test, we can use the conditional probability formula: P(A and B) = P(A|B) * P(B), where A represents passing the oral test and B represents passing the written test.
From the given information:
- The probability of passing the oral test, P(A), is 0.56.
- The probability of passing the written test, P(B), is 0.68.
- The probability of passing the oral test, given that the candidate passes the written test, P(A|B), is 0.76.
Now, using the conditional probability formula:
P(A and B) = P(A|B) * P(B)
P(A and B) = 0.76 * 0.68
Calculating the product:
P(A and B) = 0.5168
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