To compare % and ¾, we can convert them both to decimals or both to fractions.
Method 1: Converting to decimals
% = 0.01 x % value
So, % = 0.01 x 100 = 1
¾ = 0.75
Now, we can compare the decimals: 1 > 0.75
Therefore, % is greater than ¾.
Method 2: Converting to fractions
% = 100%
So, % = 100/100 = 1
¾ = 6/8 (we can simplify by dividing both numerator and denominator by 2)
Now we can compare the fractions:
100/100 > 6/8
By cross multiplying, we get:
100 x 8 > 6 x 100
800 > 600
Therefore, % is greater than ¾.
Answer: Using both methods, we have shown that % is greater than ¾.
Find the divergence of F(x,y)
Hence,the divergence of F is 1 / (x² + y²).
what is the divergence of function?The limit of the surface integral of F out of the closed surface of the volume V enclosing x tends to 0 to the volume of V so, V shrinks to zero is the definition of the divergence of a vector field F(x) at a point x tends to 0.
How do be calculate divergence of function?we are multiply the vector by the f. Now, dot product and cross product may be used to define the divergence function and curl function in terms of the same odd vector. A vector field F=f,g,h divergence is defined as the F=x,y,z,f,g,h=f,x+g,y,h,z.
we first need to find the partial derivatives of each component with respect to x and y:
∂F₁/∂x = (x² + y² - 2x²)/ (x² + y²)² = (-x² + y²) / (x² + y²)²
∂F₂/∂y = (x² + y² - 2y²)/ (x² + y²)² = (x² - y²) / (x² + y²)²
Then, we can use the definition of divergence:
div(F) = ∂F₁/∂x + ∂F₂/∂y
Substituting in the partial derivatives we found above, we get:
div(F) = (-x² + y²) / (x² + y²)² + (x² - y²) / (x² + y²)²
Simplifying the numerator, we get:
div(F) = (x² + y² - x² + y²) / (x² + y²)²
And finally, simplifying the fraction, we get:
div(F) = 1 / (x² + y²)
So the divergence of F is 1 / (x² + y²).
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please help,
Identifying a Discontinuous Piecewise Defined Function from Rule.
A, B, or C?
The graph of the piecewise function is the one at B.
Which is the graph of the piecewise function?Here we want to identify which one of the given graphs is the one of the given picewise function.
If you look at the domains, you can see that these are:
x ≤ -2
-2 < x < 0
0 < x
So, we need to have:
A closed circle at x = -2An open circle at x = -2 and at x = 0An open circle at x = 0The only option that has these is the middleone, so the correct option is B.
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The CEO of a large company claims that 85% of customers are repeat customers. They define a repeat customer as someone who makes more than one purchase per month. A random sample of 200 customers shows that 162 are repeat customers. Do these data provide convincing evidence at the 5% significance level that less than 85% of customers of this company are repeat customers?
Are the conditions for inference met?
Random: We have a random sample of .
10%: 200 customers < 10% of .
Large Counts: There are expected successes and expected failures, which are both at least .
A company CEO says that 85% of their customers are repeat customers. A sample of 200 customers was taken, and it was found that 162 of them were repeat customers. We want to know if this sample supports the CEO's claim, or if it suggests that less than 85% of the company's customers are repeat customers. We performed a statistical test and found that the sample provides evidence at a significance level of 5% that less than 85% of customers are repeat customers. The conditions for this test are met because the sample was taken randomly, and the sample size is small enough compared to the overall population size.
First, second, and third prizes are to be awarded to three different people. If there are
8 eligible candidates, how many outcomes are possible?
Answer: So there is only 1 possible outcome when choosing 8 candidates out of a pool of 8, which is simply selecting all 8 candidates.
Step-by-step explanation: Assuming that the order of the candidates does not matter, the number of possible outcomes can be calculated by finding the number of ways to choose a group of 8 candidates out of a total of 8.
This can be represented by the combination formula:
nCr = n! / (r! * (n-r)!)
where n is the total number of candidates and r is the number of candidates to be chosen.
In this case, we have:
n = 8 (total number of candidates)
r = 8 (number of candidates to be chosen)
Therefore, the number of possible outcomes is:
8C8 = 8! / (8! * (8-8)!) = 1
So there is only 1 possible outcome when choosing 8 candidates out of a pool of 8, which is simply selecting all 8 candidates.
3. Probabilities for two events, event A and event B, are given.
P(A and B) = 0.14
P(B) = 0.4
What is the probability of event A given B?
Hint: Probability of A given B = P(A and B) divided by P(B)
*100 points*
The probability of event A given the event B is 0.35 or 7/20.
It is given that A and B are two events.
Given probabilities are as follows:
Probability of A and B is = P(A and B) = 0.14
Probability of B = P(B) = 0.4
We know that the conditional probability of event A given B is given by,
P(A | B)
= P(A and B)/P(B)
= 0.14/0.4 [Substituting the value which are given]
= 14/40
= 7/20 [Eliminating the similar values from numerator and denominator]
= 0.35
Hence the probability of event A given the event B is 0.35 or 7/20.
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Find an equation of the line passing through the given points: (-4,21) and (0,1)
Step-by-step explanation:
You want to find the equation for a line that passes through the point (4,21) and has a slope of 01.
First of all, remember what the equation of a line is:
y = mx+b
Where: m is the slope, and b is the y-intercept
To start, you know what m is; it's just the slope, which you said was 01. So you can right away fill in the equation for a line somewhat to read:
y=01x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(4,21). When x of the line is 4, y of the line must be 21.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: . b is what we want, the 1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (4,21).
please help. I don’t get this one
Answer:
I guess it's (-3,-2)?(-3,a)
10.
9.
1. The rectangular prism below has a
volume of 288 cubic centimeters. If the
area of the base is 12 square
centimeters, what is the height of the
prism?
6. A rectangular pyramid has a volume
of 2,050 cubic centimeters. If the base
area of the rectangular pyramid 300
square centimeters, what is the height of
the pyramid?
Step-by-step explanation:
the volume of a regular shape is always
ground area × height
9.
so, the ground area is 12 cm².
the whole volume is 288 cm³.
therefore,
288 = 12 × height
height = 288/12 = 24 cm.
10.
we do this almost exactly the same way.
but here we have no regular shape (uniform from the bottom to the top). we have a pyramid.
the volume for a pyramid is
ground area × height / 3.
the ground area is 300 cm².
the volume is 2,050 cm³.
2,050 = 300 × height / 3.
6,150 = 300 × height.
height = 6150/300 = 20.5 cm
The area of a trapezoid is 48 square centimeters. The height is 6 centimeters and one base is 3 times the length of the other base. What are the lengths of the bases?
The requried shorter base is 4 centimeters and the longer base is 3 times that, or 12 centimeters.
Let's call the shorter base of the trapezoid "b" and the longer base "3b" (since one base is 3 times the length of the other). We know the height is 6 centimeters, and the area is 48 square centimeters. The formula for the area of a trapezoid is:
Area = (b₁ + b₂) * h / 2
where b₁ and b₂ are the lengths of the two parallel bases and h is the height.
Plugging in the values given in the problem, we get:
48 = (b + 3b) * 6 / 2
48 = 2b * 6
4 = b
Therefore, the shorter base is 4 centimeters and the longer base is 3 times that, or 12 centimeters.
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Michelle can swim 4 laps in 6 minutes and 12 seconds. If michelle swims at the same pace, how long would it take her to swim 10 laps?
Answer:
9 laps takes 5 minutes 25 seconds.
Step-by-step explanation:
Here is given:
4 laps takes 6 minutes 12 seconds.
We have to find how long 1 lap takes.
4/4 6/4 12/4 --> 1 lap takes 2 minutes 33 seconds.
Now, multiply each by 9 because you want to find 9 laps, so:
1x9 2x9 33x9 --> 9 laps takes 5 minutes 25 seconds.
Hope this helps :)
Please help fast! Determine which set of side measurements could be used to form a right triangle. 4, 8, 11 or 6, 8, 13 or square root of 3, square root of 5, 8 or square root of 3, square root of 13, 4.
The following sets of side dimensions could be combined to create a right triangle 6, 8, 13 is √3, √13, 4.
What is a right-angle triangle?In the triangle, there are three angles: two acute angles and one 90-degree angle. The hypotenuse, perpendicular, and base are the terms used to describe the sides of a right-angled triangle.
The next choice shows the triangle's side length:
The point is,
The hypotenuse square of a right-angled triangle is equal to the sum of its squares on its other two sides, according to Pythagoras' Theorem.
Using Pythagoras' Theorem.
Use the formula:
a² + b² = c²
For 4, 8, 11
4, 8, 11
4² + 8² = 16 + 64 = 80
11² = 121
80 is not equal to 121 it cann ot form a right triangle
For 6, 8, 13
6² + 8² = 36 + 64 = 100
13² = 169
100 is equal to 169 - 69 can form a right triangle
For √3, √5, 8
(√3)² + (√5)² = 3 + 5 = 8
8² = 64
8 is equal to 64 cannot form a right triangle
For √3, √13, 4
(√3)² + (√13)² = 3 + 13 = 16
4² = 16
16 is equal to 16 can form a right triangle
In order to create a right triangle, one may utilise the following set of side measurements √3, √13 and 4 form a triangle.
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please help ASAP!!!!
a) The complete form of the table is given below
b) The mean estimate of the mean waiting time is 2.56
Calculating an estimate for the meanFrom the question, we are to complete the table and calculate the estimate of the mean
The complete form of the given table is
Waiting Time Midpoint (x) Number of customers(f) fx
0- 0.5 5 2.5
1- 1.5 28 42
2- 2.5 32 80
3- 3.5 26 91
4 - 5 4.5 9 40.5
100 256
b)
Mean is given by the formula,
Mean = ∑(fx) / ∑f
Thus,
Mean = 256 / 100
Mean = 2.56
Hence, the mean estimate is 2.56
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One of your company's salesmen estimates he will drive 20,000 miles this year and each of the next two years. As the service manager for the company's fleet of six-cylinder compact automobiles, you are asked to determine the total costs for each of the three years.
Year 1 Total Cost: $
Year 2 Total Cost: $
Year 3 Total Cost: $
The solution is, the total costs for year 1 will be $2,240, for year 2 they will be $2,040, and for year 3 they will be $2,120.
Here, we have,
Given that one of your company's salesmen estimates he will drive 20,000 miles this year and each of the next two years, and as the service manager for the company's fleet of six-cylinder compact automobiles, you are asked to determine the total costs for each of the three years, to determine said cost, the following calculation must be made:
Year 1:
20000 x 0.112 = X
2,240 = X
Year 2:
20000 x 0.102 = X
2,040 = X
Year 3:
20000 x 0.106 = X
2,120 = X
Therefore, the total costs for year 1 will be $2,240, for year 2 they will be $2,040, and for year 3 they will be $2,120.
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Segments AB and BC are tangent to circle P.
What is the value of x? Show your work and explain your reasoning. (CER)
Answer:
x = 82°
Step-by-step explanation:
From inspection of the given diagram:
Point P is the center of circle P.Line segments PA and PC are the radii of circle PLine segments AB and BC are tangent to circle P.The tangent of a circle is always perpendicular to the radius.
Therefore, m∠BAP = m∠BCP = 90°.
Since the sum of the interior angles in a quadrilateral is 360°, then:
⇒ m∠BAP + m∠APC + m∠BCP + m∠ABC = 360°
⇒ 90° + 98° + 90° + x = 360°
⇒ 278° + x = 360°
⇒ 278° + x - 278° = 360° - 278°
⇒ x = 82°
Therefore, the value of x is 82°.
Construct a free commutative monoid on an arbitrary (not necessarily finite) set?
Find the arc length, s when r=4 and 0=7pi/8 radians
Step-by-step explanation:
Entire circle (2 pi) circumference is pi d = 8 pi
you want 7pi/8 ths of this entire 2 pi circumference
7pi / 8 / (2 pi) * 8pi = 7/2 pi = ~ 11 units
Answer:
Length of arc is 7pi/2
Step-by-step explanation:
s=r0
s=4×7pi/8
S=7pi/2
Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n
Answer:
24 = 31.4n + (-8.4) is the correct equation.
Not sure if I’m 100% correct about this question need some help on it!
Answer:
1 4 2
hope that helps.
Step-by-step explanation:
_7x2
-6x
Diamond problem 6x is bottom and 7xsquared
The factorization of 7x^2 -6x is x(7x - 6).
How to factorize the valueIt should be noted that to factorize 7x^2 -6x, we need to find two numbers that can multiply to give 7 times the coefficient of x^2 (which is 7), and add to give the coefficient of x (which is -6).
The first step is to factor out the greatest common factor (GCF) of the two terms, which is x:
7x^2 - 6x = x(7x - 6)
Now we can see that the two numbers we need are 7 and -6, since 7 times -6 is -42 and 7 + (-6) is 1. So we can rewrite the expression as:
7x^2 - 6x = x(7x - 6) = x(7x + (-6)) = x(7x - 6)
Therefore, the factorization of 7x^2 -6x is x(7x - 6).
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Factorize 7x^2 -6x
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 13 m/s. The ball's height / (in meters) after t seconds is given by the
following.
h=2+13t-5t^2
Find all values of t for which the ball's height is 9 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button)
so we'd want to find all "t" when the ball was 9 meters up in the air, or namely what's "t" when h(t) = 9, well, let's simply set h(t) = 9
[tex]\stackrel{h(t)}{9}=2+13t-5t^2\implies 0=-5t^2+13t-7 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-5}t^2\stackrel{\stackrel{b}{\downarrow }}{+13}t\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]
[tex]t= \cfrac{ - (13) \pm \sqrt { (13)^2 -4(-5)(-7)}}{2(-5)} \implies t = \cfrac{ -13 \pm \sqrt { 169 -140}}{ -10 } \\\\\\ t= \cfrac{ -13 \pm \sqrt { 29 }}{ -10 }\implies t= \begin{cases} \frac{ -13 + \sqrt { 29 }}{ -10 }\\\\ \frac{ -13 - \sqrt { 29 }}{ -10 } \end{cases}\implies t\approx \begin{cases} 0.76\\\\ 1.84 \end{cases} ~~ \textit{\LARGE seconds}[/tex]
there are two values, Check the picture below, that's about the parabolic path for the object, and it hits 9 meters high twice, once on the way up, and again on the way down.
Your basketball team scored 4 fewer than twice as many points, x
, as the other team.
a. Write an expression for the number of points your team scored.
expression:
b. The other team scored 24 points. How many points did your team score?
Your team scored
points.
a. The expression for the number of points scored by your team is 2x - 4.
b. Your team scored 24 points.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
a. As per the given situation,
The expression for the number of points your team scored can be written as 2x - 4.
b. If the other team scored 24 points, we can substitute that value into the expression we found in part (a) and solve for x:
2x - 4 = 24
2x = 28
x = 14
Therefore, your team scored 2x - 4 = 2(14) - 4 = 24 points.
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how to prove that √2 isn't real number
√2 is an irrational number
What are Irrational numbers?Irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers. For example, there isn't number among integers and fractions that equals Square root of 5.
Also √2 doesn't have numbers among integers and fraction that can be equal to it. Other examples of irrational numbers are √3, √11 e.t.c.
Therefore since we don't have any integer or fractions that equals square root of 2 or √2, then √2 is an irrational number not a real number.
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Amy received a S 70 gift card for a coffee store. She used it in buying some coffee that cost $8.24 per pound. After buying the coffee, she had $20.56 left on her card. How many pounds of coffee did she buy?
Answer: 6 pounds of coffee
Step-by-step explanation: 70.00 - 20.56 = 49.44(how much the person spent). then take 49.44 and divide that by the price per pound 8.24. you will get an even answer of 6 pounds.
Answer:
We first need to calculate how much money Amy spent on coffee. Since she had a $70 gift card and had $20.56 remaining after purchasing coffee, she spent $70 - $20.56 = $49.44 on coffee.
Next, we can determine how many pounds of coffee she bought. Since the cost of the coffee was $8.24 per pound, we can set up an equation:
$8.24/pound × pounds of coffee = $49.44
Solving for pounds, we can divide both sides of the equation by $8.24 to get:
pounds of coffee = $49.44 ÷ $8.24 = 6
Therefore, Amy bought 6 pounds of coffee with her gift card
help identify numbers of solutions
Answer:
There are two solutions: x = 2 and x = 4.
Q.3. A pressure vessel is to be fabricated from steel plate which may be either (i) Maraging (18% Ni) steel with oy = 1900 MN/m², Kic= 82 MNm-3/2 (ii) Medium strength steel with oy = 1000 MN/m², Kic= 50 MNm-3/2 Which of these two steels has a better tolerances to defects and compare their fracture toughness if they are to have same defect to tolerance, A factor of safety of 2 to be used as design stress.
Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.
How to determine the steel with better tolerance to defects and fracture toughnessThe tolerance to defects and fracture toughness of a material can be evaluated using its fracture toughness parameter, Kic. The higher the Kic value, the better the material's tolerance to defects and fracture toughness.
To compare the two materials, we can use the concept of critical stress intensity factor (Kic) and factor of safety (FoS). The critical stress intensity factor is the maximum value of stress intensity factor (K) that a material can withstand without fracturing. The factor of safety is the ratio of the maximum allowable stress to the design stress, and it is used to ensure a safety margin in the design.
Assuming that the two materials have the same defect to tolerance ratio, we can calculate the maximum allowable stress for each material using the following formula:
σmax = FoS * Kic / (π * a)
where σmax is the maximum allowable stress, FoS is the factor of safety (assumed to be 2), Kic is the fracture toughness parameter, and a is the size of the defect.
Let's assume a defect size of 1 mm for both materials. Using the values given in the question, we get:
For Maraging (18% Ni) steel:
σmax = 2 * 82 * 10^6 / (π * 1 * 10^-3) = 52.1 GPa
For Medium strength steel:
σmax = 2 * 50 * 10^6 / (π * 1 * 10^-3) = 31.8 GPa
Therefore, Maraging steel has a higher maximum allowable stress, which indicates that it has a better tolerance to defects compared to medium strength steel.
To compare the fracture toughness of the two materials, we can use their respective Kic values. The higher Kic value indicates a better tolerance to defects and fracture toughness.
Comparing the given values, we can see that Maraging (18% Ni) steel has a higher fracture toughness parameter (Kic= 82 MNm-3/2) compared to Medium strength steel (Kic= 50 MNm-3/2).
Therefore, Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.
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Which relation represent functions?
Answer:
A
Step-by-step explanation:
each input has it’s own output value
What is the least possible degree of the polynomial graphed above?
Using it's critical points, it is found that the least possible degree of the polynomial graphed above is 4.
What are the critical points of a function?The critical points of a function are the values of x for which:
f'(x) = 0
At these critical points, the behavior of the function changes from increasing to decreasing or vice versa.
If a function has n critical points, the least possible degree is of n + 1.
From the changes in behavior of the graph, the function has critical points at:
x ≈ -3.5
x ≈ -1.5
x ≈ 0.25
The function has 3 critical points, hence the least possible degree of the polynomial graphed above is 4.
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How many inches are in 4 1/3 feet? Enter only a number. Do not enter units.
Step-by-step explanation:
4 ⅓ feet = 51.95999 inch ~ 52 inches.
hope this helps.
What shape was used as a designation for the prisoners unless they were Jewish?
A. circles
B. squares
C. hexagons
D. triangles
You have a bag of M&Ms. The bag contains 10 brown, 5 green, 6 red, 8 yellow, and 7
blue M&Ms. You choose and eat a green, then a blue.
O 35/1225-1/35
O 35/1190-1/34
O 35/245-1/7
O 12/35
Answer:The answer is
A
Step-by-step explanation:
