The function that can be used to find the total area is: (x^2 + 25) sq. ft.
What is a square?A square is a type of quadrilateral which has an equal length of sides. So then its area can be calculated as;
area of a square = length x length
We have from the question that; a square surface that has a side length of x feet. So that;
area of the square surface = length * length
= x * x
= x^2 square feet
But since the contractor always adds 25 square feet to the area, he buys extra paint, then the function required is:
total area = (x^2 + 25) sq. ft.
The function is (x^2 + 25) sq. ft.
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Answer:
A(x) = x² + 25----------------------
In order to find the total area, we need to consider both the area of the square surface and the extra paint he always adds.
Find the area of the square surface:
A = x² (since the side length is x feet)Add the extra 25 square feet of paint:
A(x) = A + 25Combining these steps, the function is:
A(x) = x² + 25Square 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]
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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Riya has pens and pencils, which together are 40 in number. If she had 5 more pencils and 5 less pens, then the number of pencils would become four times the number of pens. Find the original number of pens and pencils.
Answer:
Pens=13
Pencils=27
Step-by-step explanation:
1. Pens = x, Pencils = y
x+y=40
2. y+5 & x-5 --> y=4x
3. Rearrange the x+y=40 to y=40-x. Then substitute y=4x and y=40-x to 4x=40-x.
4. Solve. 4x=40-x, 5x=40, x=8
5. Plug in x=8 to y=4x -> y=32.
6. Reverse the y+5 & x-5. y=27, x=13.
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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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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A $750 gift was shared equally by 5 people. After spending $90 of her share, Clarissa divided the amount remaining into 2 equal parts. What amount of money is now in each part of Clarissa's money?
Answer:
$30 for each part
Step-by-step explanation:
$750 ÷ 5 = $150 each people
Clarissa's money is $150
$150 - $90 = $60
Clarissa's money after she spent is $60
$60 ÷ 2 = $30
Clarissa's money for each part out of 2 parts is $30
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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Which expression is equivalent to the given expression? ( 10 c 6 d - 5 ) ( 2 c - 5 d 4 ) A. 20 c d B. 20 c d C. 20 c 30 d 20 D.
So the equivalent expression that matches one of the answer choices is option C, 100c/3d.
What is expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a value. An expression can represent a single number or a more complex calculation, and it can be written using symbols, variables, and/or numbers.
Here,
To simplify the given expression, we need to multiply the two binomials using the distributive property:
(10c6d - 5)(2c - 5d/4)
= 10c * 2c + 10c * (-5d/4) - 5 * 2c - 5 * (-5d/4)
= 20c² - 25cd + 10c + 25/4 d
None of the answer choices match this expression exactly, but we can simplify it further. Factoring out a common factor of 5 from the last two terms, we get:
20c² - 25cd + 10c + 25/4 d
= 5(4c² - 5cd + 2c + 5/4
20c/3 * 5d/4
= 100c/3d
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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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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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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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A spring with a 9-kg mass and a damping constant 7 can be held stretched 0.5 meters beyond its natural length by a force of 1.5 newtons. Suppose the spring is stretched 1 meters beyond its natural length and then released with zero velocity, In the notation of the text, what is the value c2 – 4mk? m²kg / sec? Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t with the general form Great cos(Bt) + czert sin(8t)
The value of [tex]c2 – 4mk[/tex] in scenario is[tex]c2 – 0.748[/tex]m and the position of the mass after t seconds is x(t) = [tex]e^(-7t/36) cos(0.433t) + 0.5e^(-7t/36) sin(0.433t)[/tex],which can be written in the general form Great [tex]cos(Bt) + czert sin(8t).[/tex]
The value of c2 – 4mk in this scenario can be found using the equation [tex]c2 – 4mk = c2 – 4mω02[/tex], where ω0 is the natural frequency of the spring. To calculate ω0, we can use the equation[tex]ω0 = sqrt(k/m)[/tex], where k is the spring constant and m is the mass.
Plugging in the given values, we get [tex]ω0 = sqrt(1.5/9) = 0.433[/tex]. Substituting this into the first equation, we get [tex]c2 – 4mk = c2 – 4m(0.433)2 = c2 – 0.748m.[/tex]
Using the given initial condition of the spring being stretched 1 meter beyond its natural length and then released with zero velocity, we can determine that A = 1 and B = 0.5. Plugging in all the values, we get [tex]x(t) = e^(-7t/36) cos(0.433t) + 0.5e^(-7t/36) sin(0.433t).[/tex].
This equation represents the motion of the spring-mass system as it oscillates back and forth around its equilibrium position. The exponential term represents the damping of the system, while the sinusoidal terms represent the oscillation.
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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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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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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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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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A maker of homemade candles makes a scatter plot to show data of the diameter of a candle and the total burn time of the candle. A line of best fit of this data is T = 6. 5d + 11. 8, where T is the total burn time, in hours, and d is the diameter of the candle, in inches. Approximately how long is the total burn time of a candle with a diameter of 0. 5 inch?
answers: A. 2 hours B. 5 hours
C. 10 hours D. 15 hours
Answer:
The given line of best fit is: T = 6.5d + 11.8
We can use this equation to estimate the total burn time for a candle with a diameter of 0.5 inches:
T = 6.5(0.5) + 11.8
T = 3.25 + 11.8
T = 15.05
So, according to the line of best fit, the total burn time of a candle with a diameter of 0.5 inch would be approximately 15.05 hours.
Therefore, the answer is D. 15 hours.
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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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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
what are complementary angles and supplementary angles difference between them?
Answer:
Supplementary angles are angles that have a sum of 180°. When two angles are supplementary, we say that one angle is the supplement of the other.
Complementary angles are angles that add up to 90°. When two angles are complementary, we can say that one angle is the complement of the other
Step-by-step explanation:
Median & IQR Question: The data shows the number of hours a part-time waiter works each week. Tell whether each statement about the data is True or False. Statements and numbers are listed in the picture.
The statements regarding the median and the quartiles are given as follows:
a. True.
b. True.
c. False.
What are the median and the quartiles of a data-set?The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The ordered data-set in this problem is given as follows:
7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 13.
Hence:
The first quartile is of 8. -> option b is true.The median is of 9. -> option a is true.The third quartile is of 11.More can be learned about median and quartiles at https://brainly.com/question/3514929
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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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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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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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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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5. Divide 6/13 by 6 /12 -
O A. 12/13
O B. 9/16
O C. 13/12
O D. 1/12
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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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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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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