Answer:
Example of the distributive property: a(b + c) = ab + ac
Question #1:
a) 6(3a + 2) = 18a + 12
b) 2(7 - 5y) = 14 - 10y
c) 3(r + 1/3) = 3r + 1
d) 8(2m - 3/8) = 16m - 3
e) 5(x/5 + 4) = x + 20
Question #2:
a) 3y + 1/4 = 4
4 (3y + 1/4) = 4 (4)
12y + 1 = 16
b) x/6 + 7 = 10
6 (x/6 + 7) = 6 (10)
x + 42 = 60
c) 11/3 - 4c/3 = 2
3 (11/3 - 4c/3) = (3) 2
11 - 4c = 6
d) 2n - 1 = 1/2
2 (2n - 1) = 2 (1/2)
4n - 2 = 1
e) r/2 + 8 = 1/2
2 (r/2 + 8) = 2(1/2)
r + 16 = 1
Hope this helped!
please give a full explanation:)
Answer:
x = 5, y = 2.5
Step-by-step explanation:
Because the original image is scaling down 4, it means all of the values of the shape will be scaled down, or divided by 4.
20, which divided by 4, will make x equal 5.
10, which divided by 4, will make y equal 2.5
66x + 8= 20x -15
Solve
66x + 8 = 20x - 15
66x - 20x = -15 - 8
46x = -23
x = -23/46
x = -1/2
#CMIIWAt Midtown University, the average weight of freshman boys is 170 lbs with a standard deviation of 9 lbs. The average weight of freshman girls is 115 lbs with a standard deviation of 6 lbs. As new distribution is to be formed from the valued obtained when the weights of the girls and the boys are added together. What are the mean and standard deviation of this new distribution? Assume that the weights of boys and girls are independent
The standard deviation of the new distribution is 11.66 lbs
The mean of the new distribution is the sum of the means of the two distributions, which is 285 lbs. The standard deviation of the new distribution is the square root of the sum of the squares of the standard deviations of the two distributions, which is 11.66 lbs.
To calculate the mean of the new distribution, we add the means of the two distributions together. The mean of the freshman boys is 170 lbs and the mean of the freshman girls is 115 lbs. Therefore, the mean of the new distribution is 285 lbs (170 + 115 = 285).
To calculate the standard deviation of the new distribution, we take the square root of the sum of the squares of the standard deviations of the two distributions.
The standard deviation of the freshman boys is 9 lbs and the standard deviation of the freshman girls is 6 lbs. Therefore, the standard deviation of the new distribution is 11.66 lbs (√(9^2 + 6^2) = 11.66).
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Please help due ASAP
Show workings
Answer:
CD=66
Step-by-step explanation:
12x-30=6x+18
6x=48
x=8
12(8)-30=66
CD=66
a triangle has side lengths in the ratio is inscribed in a circle with radius . what is the circumference of the triangle?
Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.
To find the circumference of the triangle, we need to first find the lengths of its sides. Let the three sides be x, y, and z, such that x:y:z is the given ratio. Without loss of generality, we can assume that x is the shortest side.
Let k be a constant such that y = kx and z = lx, where k and l are constants. Then, we have:
x + kx + lx = 2r
Simplifying this equation, we get:
x(1 + k + l) = 2r
So, we have:
x = (2r)/(1 + k + l)
y = kx = k(2r)/(1 + k + l)
z = lx = l(2r)/(1 + k + l)
The circumference of the triangle is the sum of its three sides:
C = x + y + z
Substituting the expressions for x, y, and z, we get:
C = (2r)/(1 + k + l) + k(2r)/(1 + k + l) + l(2r)/(1 + k + l)
Simplifying this expression, we get:
C = (2r(1 + k + l))/(1 + k + l)
C = 2r
Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.
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The area of the triangle is equal to A) 8.64. The Correct option is A) 8.64.
Let the lengths of the triangle be, 3x,4x,5x
Square of largest side = \(25x^{2}\)
Sum of square of other sides = \(3x^{2} + 4x^{2} = 25x^{2}\)
It is a right-angled triangle because the square of the greatest side equals the sum of the squares of the other sides.
The circumference of a right-angled triangle has a diameter equal to its hypotenuse.
hence, 5x=6 or x= \(\frac{6}{5}\)
Now, two perpendicular sides are then, \(\frac{18 }{5} , \frac{24}{5}\)
\(Area = \frac{1}{2} \times \frac{18}{5} \times \frac{24}{5} = 8.64\)
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Question
A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to
A. 8.64
B. 12
C. 6
D. 10.5
Urgent Help! 100 points to whoever is willing ^-^
Noise-canceling headphones have microphones to detect the ambient, or background, noise. They interpret those noises as sinusoidal functions. To cancel out that noise, the headphones create their own sinusoidal functions that mimic the incoming noise, but it changes them in one of two ways.
1. The mimic function is the negative of the noise's function.
2. The mimic function is the noise function shifted one-half period.
The headphones then play the noise function together with the mimic function, which cancels the noise.
Instructions
• Find the frequency of any musical note in hertz (Hz).
• Use the frequency to write f(x), the sine function for the note. For example, \(A_4\) has a frequency of 440 Hz. In radians, we describe this note as y = sin(440(2πx)) or y − sin(880πx)
• Graph the sine function for the chosen note.
• Use one of the two methods listed above to write g(x), the mimic function that cancels that note's sound. Graph that function.
• Write a third function, h(x), that is the sum of f(x) and g(x). Graph it.
• Use your three graphs to explain why g(x) cancels out f(x).
Discuss the downsizing process in your own words and provide an
example.
Downsizing refers to the process of reducing the size and workforce of a company to cut costs, increase efficiency, or adapt to changing market conditions. It involves eliminating positions, reducing staff numbers, or even closing down certain business units or branches.
Downsizing can occur for various reasons, such as financial difficulties, mergers and acquisitions, technological advancements, or strategic reorganization. Companies often assess their operational costs and decide to downsize to improve their financial performance.
During the downsizing process, companies may calculate the potential cost savings by considering factors such as salaries, benefits, severance packages, and operational expenses. For example, if a company decides to eliminate 100 positions with an average salary of $50,000 per year, it could result in annual savings of $5 million.
While downsizing can help companies achieve short-term cost reductions, it often has significant implications for the affected employees, including layoffs, reduced morale, and increased workload for remaining staff. It is crucial for organizations to handle the downsizing process with sensitivity and transparency, providing support to affected employees and communicating the rationale behind the decisions.
It is important to note that downsizing should not be seen as a long-term solution, but rather as a strategic measure to address specific challenges. Companies should also explore alternatives to downsizing, such as retraining and redeploying employees, implementing productivity improvements, or seeking new business opportunities, to ensure sustainable growth and success in the long run.
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Laura used 12 square feet of cloth to make 3 dresses. How many square
feet of cloth are required to make 12 similar dresses?
Answer:
Its 150 square feet
Step-by-step explanation:
Hope this helps :3
0 0.1 1 0.05 2 0.3 3 0.55 find the mean of this probability distribution. round your answer to one decimal plac
The mean of the given probability distribution is 1.3 (rounded to one decimal place).
To find the mean of a probability distribution, we need to multiply each value by its corresponding probability, and then add up all the products. So, using the given values, we can calculate the mean as:
Mean = (0 x 0.1) + (0.1 x 0.05) + (1 x 0.3) + (2 x 0.55) = 1.25
Therefore, the mean of the given probability distribution is 1.3 (rounded to one decimal place).
To find the mean of a probability distribution, we need to multiply each value by its corresponding probability, and then add up all the products. In this case, the given values are 0, 0.1, 1, 0.05, 2, and 0.3, with their respective probabilities. We can calculate the mean by multiplying each value with its probability and then adding up the products. After the calculation, we get the mean as 1.25. Thus, the mean of the given probability distribution is 1.3 (rounded to one decimal place).
The mean of the probability distribution given as 0, 0.1, 1, 0.05, 2, and 0.3 is 1.3 (rounded to one decimal place). This means that on average, the value of the distribution is around 1.3. The mean is a useful measure of central tendency that helps us understand the characteristics of the probability distribution.
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I need help on this assignment
a) Probability of hitting the black circle is closer to zero than 1.
b) Probability of hitting the white portion is closer to 1 than 0
What is the probability of selection?To get the probability of getting any point in the given image, we have to first of all find the area of the square which is:
Area of Square = 9 * 9 = 81 sq. units
Area of Circle = π * 1.5² = 7.07 Sq.units
Area of white part = 81 - 7.07
Area of white part = 73.93 Sq.units
a) Probability of hitting the black circle = 7.07/81 = 0.095
This probability is closer to zero than 1.
b) Probability of hitting the white portion = 73.93/81 = 0.9127
This probability is closer to 1 than 0
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when a number, n, is increased by two and then the result is divided by five the quotient is equal to 14. write an equation and solve it to find the value of n.
NEED STEP BY STEP EXPLANATION
Step-by-step explanation:
We have (n + 2)/5 = 14.
=> (n + 2) = 14 * 5 = 70 (multiply 5 on both sides)
=> n = 70 - 2 = 68. (subtract 2 on both sides)
Hence the number n is 68.
the average of a list of 4 numbers is 92.0 . a new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40 , and the fourth number in the new list is 48 . what is the average of this new list of numbers?
The average of the new list of 4 numbers is 94.
If the average of the original list of 4 numbers is 90, then the sum of these 4 numbers is:
4 x 90 = 360
If the 4th number in the original list is 80, then the sum of the first 3 numbers in the original list is:
360 - 80 = 280
If the first 3 numbers in the new list are the same as in the original list then the sum of these new first 3 numbers is also:
280
If the 4th number in the new list is 96 then the sum of the 4 numbers in the new list is:
280 + 96 = 376
Therefore, the average of the new list of 4 numbers is:
376 / 4 = 94
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How do you use Pemdas ?
Answer:
So what you did was correct, 8/4 first which is equal to 2, and then add 3
Step-by-step explanation:
So pemdas stands for parenthesis, exponents, multiplication, division, addition, and subtraction (this is in order of what you have to do)
in the problem shown, you would do division and then subtraction
PEMDAS is the order that you solve a problem.
PEMDAS stands for:
Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction
If you have an equation or expression that you need to solve, you solve it in this order. You do the parenthesis first, then you solve the exponents, then you do the multiplication and division from left to right, and last you do addition and subtraction from left to right.
In the equation
2 + 3 * 5,
first you would do 3 * 5 because multiplication is before addition.
2 + 15
Then you would do the addition to get the answer:
17.
Please give brainliest
use the definition to find an expression for the area under the graph of f as a limit. do not evaluate the limit. f ( x ) = x 2 √ 1 2 x , 2 ≤ x ≤ 4
The expression for the area under the graph of f(x) over the interval [2, 4] is given by the limit as n approaches infinity of the Riemann sum: A = lim(n→∞) Σ[f(xi)Δx].
To express the area under the graph of f(x) as a limit, we divide the interval [2, 4] into n subintervals of equal width Δx = (4 - 2)/n = 2/n.
Let xi be the right endpoint of each subinterval, with i ranging from 1 to n. The area of each rectangle is given by f(xi)Δx.
By summing the areas of all the rectangles, we obtain the Riemann sum: A = Σ[f(xi)Δx], where the summation is taken from i = 1 to n.
To find the expression for the area under the graph of f(x) as a limit, we let n approach infinity, making the width of the rectangles infinitely small.
This leads to the definite integral: A = ∫[2, 4] f(x) dx.
In this case, the expression for the area under the graph of f(x) over the interval [2, 4] is given by the limit as n approaches infinity of the Riemann sum: A = lim(n→∞) Σ[f(xi)Δx].
Evaluating this limit would yield the actual value of the area under the curve.
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solve for x…..…………………
Answer:
x = 11
Step-by-step explanation:
From the diagram, we find,
(2x - 16) + (x - 8) = 9
=> 2x - 16 + x - 8 = 9
=> 2x + x - 16 - 8 = 9
=> 3x - 24 = 9
=> 3x = 9 + 24
=> 3x = 33
=> x = 33/3
=> x = 11
the probability distribution of all possible values of the sample proportion is the
Answer: The sampling distribution of p is the probability distribution of all possible values of the sample proportion p.
(52)3÷53 simplify please give correct answer
100 POINTS HELP WILL GIVE BRAINLIEST
Answer:
The correct ratio of strawberries to blueberries for the fruit salad is 8 strawberries : 30 blueberries, or C. To find this ratio, you can divide the number of strawberries by the number of blueberries to get the ratio of strawberries to blueberries. In this case, 8 strawberries / 30 blueberries = 8/30, or 8 strawberries : 30 blueberries.
Step-by-step explanation:
give me brailiest i give answer im indian living in parent basemen tpless they will cut pp
Answer:
C) 8 strawberries : 30 blueberries--------------------------
As per recipe:
the number of strawberries is 8 and the number blueberries is 30.Therefore the ratio of strawberries to blueberries is:
8 : 30Correct choice is C.
which of the following are equivalent to the expression below? sqrt -16
A. 4i
B. -4
C. -4i
D. 4
Answer:
A and C
Step-by-step explanation:
Using the fact that \(\sqrt{-1}\) = i , then
\(\sqrt{-16}\)
= \(\sqrt{16(-1)}\)
= \(\sqrt{16}\) × \(\sqrt{-1}\)
= ± 4 × i
= 4i → A
= - 4i → C
Find the value of x.
x = [?]
Answer: 8
Step-by-step explanation:
The triangles are congruent by SAS, so using CPCTC, the answer is 8
Select the correct answer from each drop-down menu. the probability of andy and anna having lunch together is 40%. the probability of them having lunch together at least 6 days a week is , and the probability of having lunch exactly 6 times in a week is .
The answer is the probability of having lunch at least 6 days per week is 0.019 or 1.9%. The probability of having lunch exactly 6 times is 0.017 or 1.7%.
The probability of having lunch together is \($p=40 \%=0.4$\)
The probability of not having lunch together is \($q=1-p=0.6$\)
Number of trials (days in a week) is \($\mathrm{n}=7$\)
Let \($r=$\) number of days in the week when Andy and Anna have lunch together.
\(P(r \text { of } n)={ }_{n} C_{r} p^{r} q^{n-r}\)
Use th graphing calculator to obtain
\($$\begin{aligned}&P(6 \text { of } 7)={ }_{7} C_{6}(0.4)^{6}(0.6)=0.017 \\&P(7 \text { of } 7)={ }_{7} C_{7}(0.4)^{7}(0.6)^{0}=0.002\end{aligned}$$\)
Therefore
\($\mathrm{P}($\) at least 6 of 7\($)=\mathrm{P}(1$\) of 7\($)+\mathrm{P}(2$\) of 7\($)+\ldots+\mathrm{P}(6$\) of 7)
\($$\begin{aligned}&=0.131+0.261+0.290+0.194+0.077+0.017 \\&=0.97 \text { or } 97 \% \\&P(\text { at least } 6 \text { of } 7)=0.017+0.002=0.019=1.9 \% \\&P(\text { exactly } 6 \text { of } 7)=0.017 \text { or } 1.7 \%\end{aligned}$$\)
What is probability ?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.To learn more about probability visit:
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Answer:
The probability of them having lunch together at least 6 days a week is
0.019,
and the probability of having lunch exactly 6 times in a week is
0.017.
Step-by-step explanation:
144 cubic meters in inches.
Answer:
I think is 8.787e+6 cubic inches.
You are planting a vegetable garden on a plot of land that is a sector of a circle, as shown below.
You want fencing along only the curved edge of the garden.
a. Use the figure to find the length of fencing you will need.
15 ft
75°
b. How much area will be available for planting?
Answer:
(a) 19.63 ft
(b) 147.26 ft^2
Step-by-step explanation:
(a) 75/360 degrees . 2 . pi . 15 = 19.63
(b) 75/360 degrees. pi . 15^2 = 147.26
Answer:
a) 19.63 ft (2 dp)
b) 147.26 ft² (2 dp)
Step-by-step explanation:
To find the length of the curved fence, use the formula for arc length of a circle.
To find the area of the vegetable garden, use the formula for area of a sector of a circle.
Formula
\(\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)\)
\(\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2\)
\(\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}\)
Calculation
Given:
\(\theta\) = 75°r = 15 ft\(\begin{aligned}\implies \textsf{Arc length} &=2 \pi (15)\left(\dfrac{75^{\circ}}{360^{\circ}}\right)\\ & = 30 \pi \left(\dfrac{5}{24}\right)\\ & = \dfrac{25}{4} \pi \\ & = 19.63\: \sf ft\:(2\:dp)\end{aligned}\)
\(\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{75^{\circ}}{360^{\circ}}\right) \pi (15)^2\\& = \left(\dfrac{5}{24}\right)\pi \cdot 225\\& = \dfrac{375}{8} \pi\\& = 147.26\: \sf ft^2 \:(2\:dp)\end{aligned}\)
List the next three numbers for the sequence:
34, 102, 408, 2040, ...
Answer:
12240
85680
685440
Step-by-step explanation:
We know that the sequence is growing rapidly
To see how rapidly divide the second term by the first term
102/34 =3
Check the third term divided by the second term
408/102 =4
Check the fourth term divided by the third term
2040/408=5
To get the second term, multiply by 3, to get the third term multiply by 4
to get the fourth term multiply by 5
to get the nth term multiply by (n+1)
The 5th term would be multiplied by 6
2040 *6 =12240
The 6th term by 7
12240*7=85680
The 7th term by 8
85680*8=685440
∫01xpln(x)dxa. a. Find the values of p for which the integral converges. The integral converges for all values ofpin the interval:
b. For the values ofpat which the integral converges, evaluate it.∫01xpln(x)dx=
a. The integral converges for all values of p in the interval p > -1.
b. For p > -1, \(\int\limits^1_0 {xp}ln(x) \, dx\) = (1/4) (1 - p²).
a. To determine the values of p for which the integral converges, we use the integral test for convergence. Specifically, we compare the given integral to the corresponding improper integral of the integrand from 0 to 1, which is:
∫0+xp ln(x) dx = limh→0+ ∫h1 xp ln(x) dx
Using integration by parts with u = ln(x) and dv = xp dx, we get:
∫xp ln(x) dx = (1/2) xp ln²(x) - (1/4) xp + (1/4) ∫x dx
= (1/2) xp ln²(x) - (1/4) xp² + (1/4) x² + C
where C is the constant of integration.
Now, applying the limit as h approaches 0 from the right, we get:
limh→0+ [(1/2) hpln²(h) - (1/4) hp² + (1/4) h² + C - (1/2) ln²(h) + (1/4) h]
Since ln(h) goes to negative infinity as h goes to 0 from the right, we have:
limh→0+ (1/2) hpln²(h) = 0
Therefore, the integral converges if and only if the improper integral of xp from 0 to 1 converges, which is the case if p > -1.
b. For p > -1, we can evaluate the integral using the formula we obtained earlier:
∫xp ln(x) dx = (1/2) xp ln²(x) - (1/4) xp² + (1/4) x² + C
Evaluating the definite integral from 0 to 1, we get:
∫01xpln(x)dx = (1/2) p ln²(1) - (1/4) p² + (1/4) - (1/2) ln²(0) + (1/4) (0)
= 0 - (1/4) p² + (1/4)
= (1/4) (1 - p²)
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PLS HURRY I ONLY HAVE 15mins LEFT WORTH 100 POINTS AND BRAINLEST
Which inequalities have the solution set graphed on the number line? Select two options. A number line going from negative 6 to positive 2. An open circle is at negative 4. Everything to the left of the line is shaded. x less-than negative 4 Negative 4 less-than x Negative 4 less-than-or-equal-to x Negative 4 greater-than x x greater-than negative 4
this is the correct answer
The surface area of a big ball is 4.5216m². Find the diameter of the ball.
The diameter of the sphere is 1.2 meters.
How to find the diameter of the ball?We know that for a sphere of radius R, the surface area is given by the formula:
S = 4πR²
Where π = 3.14
Here we know that the surface area is 4.5216m²
Then we can replace that and find the radius:
4.5216m² = 4*3.14*R²
Solving for R:
R = √(4.5216m²/(4*3.14))
R = 0.6m
Then the diameter, two times the radius, is:
D = 2*0.6m
D = 1.2 meters.
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what is the least common factor than thes two denominators 3/6, 2/12
The least common denominator for the fractions 3/6 and 2/12 is 12.
How to find the least common denominatorWe need to determine the smallest number that both 6 and 12 can evenly divide into.
The prime factorization of 6 is 2 * 3.
The prime factorization of 12 is 2 * 2 * 3.
To find the least common denominator, we take the highest power of each prime factor that appears in either denominator. In this case, the prime factors are 2 and 3.
From the prime factorizations, we can see that the least common denominator is 2 * 2 * 3 = 12.
Therefore, the least common denominator for the fractions 3/6 and 2/12 is 12.
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If A = (-1,-3) and B = (11,-8), what is the length of AB?
A. 14 units
B. 13 units
C. 11 units
D. 12 units
SUBMIT
A
Answer:
B
Step-by-step explanation:
Use the distance formula:
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Let (-1,-3) be \(x_1\) and \(y_1\), while (11,-8) be \(x_2\) and \(y_2\).
Thus:
\(d=\sqrt{((11)-(-1))^2+((-8)-(-3))^2\)
\(d=\sqrt{12^2+(-5)^2}\)
\(d=\sqrt{144+25} =\sqrt{169} =13\)
You build 7 model airplanes during the summer. At the end of the summer, you have 25 model airplanes. How many model airplanes did you have before the summer? Select the correct equation and solution. Check the solution.
Answer:
18
Step-by-step explanation:
You have 25 when you are done, but you made 7, so subtract that from 27.
25-7 equals 18.