Answer:
The steps to do :
\( - \frac{2}{5} \div \frac{6}{8} \)
\( = - \frac{2}{5} \times \frac{8}{6} \)
\( = - \frac{1}{5} \times \frac{8}{3} \)
\( = - \frac{1 \times 8}{5 \times 3} \)
\( = - \frac{8}{15} \)
What is the measure of JK?
A. 35
B. 55°
C. 145°
D. 125°
Answer:
125 degrees.
Step-by-step explanation:
L is the midpoint of NK so the arcs NM and Mk are equal.
So MK = 55 degrees and the arcs JN and JK are equal
Therefore
JK =
(360 - 2*55)/2
= (360 - 110) / 2
= 250 /2
= 125 degrees.
11. a box contain 20 items of which 20% are defective. a sample of 10 is selected. (a) if the sample is selected without replacement, find the probability that no more than 2 defectives will be obtained. (b) if the sample is selected with replacement, find the probability that no more than 2 defectives will be obtained.
The probability of selecting no more than 2 defectives in a sample of 10 a) without replacement is 0.36077 and b) with replacement is 0.14093
a)
Here it is given that the objects are selected without replacement one after the other and the box contains only 20 items
Here we can see that the no. of items i.e the population is finite and the items are selected one after another without replacement.
Hence, this is a case of Hyper-Geometric distribution.
For a Hyper-Geometric distribution
P(X = x) = \(\frac{^{k}C_x X ^{N-k}C_N-x }{^{N}C_n }\)
where,
N = The Population
n = no. of samples selected
k = no. of success.
Here
k = no. of defectives present
= 20% of 20
= 20/100 X 20
= 4
n = 10
N = 20
x = 2
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 0)
Therefore we get
⁴C₀ X ⁽²⁰ ⁻ ⁴⁾C₍₁₀ ₋ ₀₎ / ²⁰C₁₀ + ⁴C₁ X ⁽²⁰ ⁻ ⁴⁾C₍₁₀ ₋ ₁₎ / ²⁰C₁₀ +
⁴C₂ X ⁽²⁰ ⁻ ⁴⁾C₍₁₀ ₋ ₂₎ / ²⁰C₁₀
= ⁴C₀ X ¹⁶C₁₀ / ²⁰C₁₀ + ⁴C₁ X ¹⁶C₉ / ²⁰C₁₀ + ⁴C₂ X ¹⁶C₈ / ²⁰C₁₀
ᵇCₐ = b!/(b - a)! X a!
Therefore,
⁴C₀ X ¹⁶C₁₀ / ²⁰C₁₀ + ⁴C₁ X ¹⁶C₉ / ²⁰C₁₀ + ⁴C₂ X ¹⁶C₈ / ²⁰C₁₀
= 0.04334 + 0.24768 + 0.06975
= 0.36077
b)
Here the sample is selected with replacement
There are 4 defective and 16 non-defective items
Let A be the event of selecting not more than 2 defectives with replacement
According to the problem, 2 out of 4 defectives are selected while the rest are not defective.
Hence n(A) = n(getting 0 defective) + n(getting 1 defective) + n_getting 2 defectives)
= 16¹⁰ + 4 X 16⁹ + 4² X 16⁸
= 1443109011456
Similarly, the total no. of ways to choose an item is
n = 20¹⁰
Probability of any event
= no.of favorable outcomes/total no. of outcomes
Hence, P(A) = n(A) / n
= 4² X 16⁸ / 20¹⁰
= 0.14093
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HELPPP SOLVE THIS PLEASE ALL OF IT
Answer:
f = 3
g = -1
h = 6
r = 18
Step-by-step explanation:
Box 1
f(x) = \(2x^{4}\)-\(12x^{3}\)+\(16x^{2}\)+4x+15 with x = 3
f(3) = \(2(3^{4)}\) - \(12(3^{3} )\) + \(16(3^{2})\)+ 4(3) + 15
Reorder
Evaluate
Multiply
3f = 2 x 81 - 12 + 27 +16 x 9 + 12 +15
3f = 162 - 324 + 144 + 12 + 15
3f = 9
3 ÷ 3
f = 3
Box 1
g(x) = \(3x^{3}\) - \(16x^{2}\) - 7x - 36 with x = 6
g(6) = \(3(6^{3} )\) - \(16(6^{2})\) - 7(6) - 36
g6 = 3 x 216 - 576 - 42 - 36
g6 = -6
6 ÷ 6
g = -1
Box 2
h(x) = \(5x^{3}\) - \(2x^{2}\) - 3 with x = -1
h(-1) = \(5(-1^{3} )\) - \(2(-1^{2})\) -3
h-1 = -5 + 2 -3
h-1 = -6
-1 ÷ - 1
h = -6
Box 2
r(x) = \(4x^{4}\) - \(9x^{2}\) + 5x - 2 with x = 2
r(2) = \(4(2^{4} )\) - \(9(2^{2} )\) + 5(2) - 2
r2 = 64 - 36 + 10 - 2
r2 = 36
2 ÷ 2
r = 18
The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. Find the velocity and acceleration at t = pi/3 s. v(pi/3) = a(pi/3) =
The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.
Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s
Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s
Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².
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what is the unit rate price to the nearest cent of a 33-ounce bottle of juice that sells for $2.99?
Answer:
$0.09.
Step-by-step explanation:
2.99/33
= $0.0906
PLEASE PLEASE PLEASE HELP
The midpoint of CD is M(-3,-7). If the of C is (-2,-10), what is the of D??
x=
y=
Answer:
D is (-4, -4)
Step-by-step explanation:
M = (x1 + x2)/2
-3 = (-2 + x2)/2
-6 = -2 + x2
x2 = -4
M = (y1 + y2)/2
-7 = (-10 + y2)/2
-14 = -10 + y2
y = -4
A bag contains 150 marbles. Some are blue the rest is white. There are 21 blue marvles for every 4 white marbles. How many blue marbles are there.
There are 126 blue marbles.
Total marbles in the bag=150
There are 21 blue marbles for every 4 white marbles then the sequence will be⇒ 4+21+4+21+4+21+4+21+4+21+4+21=150
21 blue marbles appear 6 times for every 4 blue marbles
So 21×6=126 blue marbles and 4×6=24, then 126+24=150 total marbles
∴There will be a total of 126 blue marbles along with 24 white marbles among the 150 marbles.
Find the product. (3b-2)(3b+2) *
Answer:
9b²-4
Step-by-step explanation:
(3b-2)(3b+2)
9b²+6b-6b-4
9b²+0-4
9b²-4
first to answer, pls brainliest.
what is the probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles?
The probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles is 25.14.
To break this problem, we need to use the standard normal distribution, assuming that the distribution of tire continuances is roughly normal. We can regularize the value of 42,000 using the formula
z = ( x- μ)/ σ
where x is the value of interest( 42,000 long hauls), μ is the mean tire continuance( 40,000 long hauls), and σ is the standard deviation( 3,000 miles). Plugging in the values, we get
z = ( 42,000- 40,000)/ 3,000 = 0.67
Using a standard normal distribution table or calculator, we can find the probability that an aimlessly named tire will last further than 42,000 long miles by looking up the area to the right of z = 0.67 under the standard average wind. This probability is roughly 25.14.
thus, the probability that a tire named arbitrarily from this brand will last more than 42,000 miles is roughly 25.14.
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The correct question is given below-
A particular brand of tires lasts an average of 40,000 miles with a standard deviation of 3,000 miles. What is the probability a tire selected at random lasts more than 42,000 miles?
Find the sum of the first 15 terms: {12, 36, 108, . . . }.
Answer:
Step-by-step explanation:
hello : here is an solution
if h(t)=1248-160t+16t
Answer: 816
Step-by-step explanation:
h(3) = 1248 - 160(3) + 16(3)
h(3)= 1248 - 480 + 48
h(3)= 816
PLD HELP ME I WILL FAIL PLSx,
Answer:
1 /12
Step 1
eef
I need help with this
By applying Pythagoras' theorem, the length of x is equal to 10 units.
How to calculate the length of x?In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):
x² + y² = z²
Where:
x, y, and z represents the length of sides or side lengths of any right-angled triangle.
Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:
x² = y² + z²
x² = 8² + 6²
x² = 64 + 36
x = √100
x = 10 units.
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0.5 power of 2 + 0.3 power of 2?
Answer:
8.9
Step-by-step explanation:
Answer:
0.34
Step-by-step explanation:
\( {0.5 }^{2} + {0.3}^{2} \\ 0.25 + 0.09 \\ = 0.34\)
(I'm not sure if this is what you meant)
The results of a national survey showed that on average, adults sleep hours per night. Suppose that the standard deviation is hours. Round your answers to the nearest whole number. a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between and hours per day. At least
Answer:
Following are the solution to the given question:
Step-by-step explanation:
For point a:
\(6.5 - 4.9 = 2.4 \\\\\frac{2.4}{1.2} = 2 \\\\\sigma \ \ so \ k = 2\)
For point b:
\(\frac{3}{1.2}\ \ \sigma\ \ so \ k =\frac{3}{1.2} \ \ so\ \ 1- \frac{1}{k ^2} = 0.84\)
For point c:
Once again, we have k = 2 though with Chebyshev discrepancy of witness numbers in the same number of standard deviations off mean = at least 75 percent.
y square plus 5y equals to 0
Answer:
y^2 + 5y = 0
y(y + 5) = 0
y = 0, -5
The answer is y = 0 and y = -5.
The given question :
y² + 5y = 0y (y + 5) = 0y = 0, y = -5from the top of a 160-ft lighthouse, the angle of depression to a ship in the ocean is 26°. how far is the ship from the base of the lighthouse? (round your answer to the nearest foot.)
The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.
What is Angle Of Depression?The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item. When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects.Given:
Height of lighthouse = 160 feetAngle of depression = 26°To find: Distance of ship from the base of the lighthouse.
Finding:
Let 'x' be the distance of the ship from the base of the lighthouse and θ be the angle of depression.
Then, tanθ = \(\frac{160}{x}\)
=> x = \(\frac{160}{tan26}\)
=> x = \(\frac{160}{0.487}\)
=> x = 328.54m
Hence, The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.
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Yaritza is driving on a long road trip. she currently has 13 gallons of gas in her car. each hour that she drives, her car uses up 0.75 gallons of gas. how much gas would be in the tank after driving for 5 hours? how much gas would be left after t hours?
Answer:
9.25
13 - 0.75t
Step-by-step explanation:
0.75 * 5 = 3.75
13 - 3.75 = 9.25
hope this helps!
Identify the GCF of 6x2y2 − 8xy2 + 10xy3.
6x2y2
2x2y
2xy2
6xy2
Answer:
B is correct
Step-by-step explanation:
फरक परेछ? A person deposited Rs. 80,000 in bank 'P' for 2 years at the rate of 10% annual compound interest. But after one year bank has changed the policy and decided to pay semi-annual compound interest at the same rate. What is the percentage difference between compound interests of the first year and second year? Give reason with calculation,
Answer:
you nepali me nepali all are nepalese nepalese are only unintelligent
(I’ll give brainliset) Your friend makes a two dimensional model of a dividing cell as shown. The total area of the dividing cell is 350 square inches. What is the area of the shaded region to the nearest whole inch?
nearest whole inch?
Answer:
149.04 in^2
Step-by-step explanation:
The image of the question can be seen below.
In the image, we can see two circles that intersect at a given point.
We know that the total area of the image is 350 in^2
We want to find the area of the shaded part.
Ok, this seems to be hard, so instead, let's find the area of the two non-shaded parts (two semicircles) and just subtract that area from the total area of 350in^2
The two non-shaded parts are half a circle of diameter 16 inches.
We know that for a circle of diameter D, the area is:
A = pi*(D/2)^2
Where pi = 3.14
And because we want to find the area of two semicircles of diameter 16 inches, is exactly the same as finding the area for a single circle of diameter 16 inches.
This is:
A = 3.14*(16in/2)^2 = 3.14*(8in)^2 = 200.96 in^2
Now we can just subtract this from the total area:
shaded area = total area - A
shaded area = 350 in^2 - 200.96 in^2
shaded area = 149.04 in^2
Determine whether each system has a unique solution. If it has a unique solution, find it.
x+2 y+z=4 [ y=x-3 z=2 x]
The solution to the given system of equations is:x = 2
y = -1
z = 4.The given system of equations has a unique solution which is x = 2, y = -1, and z = 4.
To determine if the given system of equations has a unique solution, we need to substitute the given values of y, z, and x into the equation and check if it satisfies the equation.
Given:
x + 2y + z = 4
y = x - 3
z = 2x
Substituting the values of y, z, and x into the equation, we have:
x + 2(x - 3) + 2x = 4
x + 2x - 6 + 2x = 4
5x - 6 = 4
5x = 10
x = 2
Now, substitute the value of x back into the equations for y and z:
y = 2 - 3
y = -1
z = 2(2)
z = 4
Therefore, the solution to the given system of equations is:
x = 2
y = -1
z = 4
In conclusion, the given system of equations has a unique solution which is x = 2, y = -1, and z = 4.
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For 30 seconds of ad time during the 2021 Super Bowl, the cost is $5.1 million dollars.
This year the company, TurboTax will have one 45-second commercial. How much money will they
spend? Write your answer in scientific notation. Make sure to show your work.
Answer:
$7.65 million dollars / $7.55 * 10^6
Step-by-step explanation:
30*1.5=45 seconds
5.1*1.5=7.65
for scientific notation just take the number of zeros and use that for exponent, and make a dot so it is a number less than 10
if i payed for something for my brother which was $15 and we we're gonna split it that i pay only $5 for it and he pays $10, how much money does he have to give me back?
Answer:
$10
Explanation:
If you only have to pay $5 of the $15 you gave him, he has to pay you 15-5 or $10 back.
4. The area of a triangle measures 54 in? The height of the triangle is 18 inches. What is the base of the triangle? Base =
The area of a triangle is computed as follows:
\(A=\frac{b\cdot h}{2}\)where b is the base, and h is the height
Replacing with A = 54, h = 18, and solving for b, we get:
\(\begin{gathered} 54=\frac{b\cdot18}{2} \\ 54\cdot2=b\cdot18 \\ \frac{108}{18}=b \\ 6=b \end{gathered}\)The base of the triangle is 6 in
Find the value of x. Round to the nearest tenth.
Answer:
i believe it is
Step-by-step explanation:
a 10.7
Answer: c
Step-by-step explanation:
we can use process of elimination because the side that x is on is bigger than the opposite side so there fore it is c
The amount of money in a bank account doubles every 3 months, what would be the growth factor for 1 month? Explain how you got your answer.
Answer:
Explanation:
if you saved 25 thousand dollars an hour, 40 hours per week for 2020 years, how much money do u have saved up ?!
Answer:
i dunno
Step-by-step explanation:
Add
3/5+7/8+3/10
Enter your answer in the box as a mixed number in simplest form.
Please help with this problem thanks