Answer:
0.1835
Step-by-step explanation:
This question can be solved by way of binomial distribution.
Let’s have the probability of success as p which is the probability that they stay with the company for more than five years;
p = 8/100 = 0.08
probability of failure, meaning not staying is q = 1-p = 1-0.08 = 0.92
Now let’s write the expression for the binomial distribution. That would be;
probability = 12C2 * 0.08^2 * 0.92^10
= 0.1835
Probabilities are used to determine the chances of an event.
The probability that exactly two stays more than 5 years is 0.1835
The given parameters are:
[tex]\mathbf{n = 12}[/tex] ---- sample
[tex]\mathbf{x = 2}[/tex] --- selected
[tex]\mathbf{p = 80\%}[/tex] --- sample proportion
So, the probability that exactly two stays more than 5 years is calculated using the following binomial probability:
[tex]\mathbf{P(x) = ^nC_x p^x (1 - p)^{n -x}}[/tex]
So, we have:
[tex]\mathbf{P(x) = ^{12}C_2 (8\%)^2 (1 - 8\%)^{12 -2}}[/tex]
[tex]\mathbf{P(x) = ^{12}C_2 (8\%)^2 (92\%)^{10}}[/tex]
Solve 12C2 using a calculator
[tex]\mathbf{P(x = 2) = 66 \times (8\%)^2 \times (92\%)^{10}}[/tex]
[tex]\mathbf{P(x = 2) = 0.1835}[/tex]
Hence, the probability that exactly two stays more than 5 years is 0.1835
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What is the difference between the measure of an arc and the arc length? Explain.
The measure of an arc is the degree/radian measure. You measure the central angle to find the measure of an arc.
The arc length is the actual length (like 2pi inches or 7 cm, etc.). You find the length of the curved part (the arc), not the straight distance between the 2 points given.
Khan academy plz help me
Answer:
B is filling the tank most quickly
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
A, (7,2), the time goes slow, so it cannot be correct.
C, you can see is more lower than the other two. That means it is the slowest.
B, is going at a average rate, but faster than A and C. If you find a coordinate on B, for an example (2,2). 2 gallons in 2 minutes.
What's the circumference
of a bicycle wheel with
a 27-inch diameter?
| Solution:
Given:
The diameter of the bicycle wheel is 27 inches.
We need to determine the circumference of the bicycle wheel.
Circumference of the bicycle wheel:
The circumference of the bicycle wheel can be determined using the formula,
[tex]C=\pi d[/tex]
where d is the diameter of the bicycle wheel.
Substituting d = 27 and π = 3.14, we have;
[tex]C=(3.14)(27)[/tex]
Multiplying, we get;
[tex]C=84.78 \ in[/tex]
Thus, the circumference of the bicycle wheel is 84.78 inches.
ABC is a triangle.
work out angle x. give your answer to 3 significant figures.
Answer:
x = 50.5°
Step-by-step explanation:
∠ BDC and ∠ BDA are adjacent and supplementary, thus
∠ BDC = 180° - 78° = 102°
Calculate ∠ BCD using the Sine rule in Δ ABC, that is
[tex]\frac{5.6}{sinC}[/tex] = [tex]\frac{9.3}{sin50}[/tex] ( cross- multiply )
9.3 × sinC = 5.6 × sin50° ( divide both sides by 9.3 )
sinC = [tex]\frac{5.6sin50}{9.3}[/tex] ≈ 0.4613, thus
C = [tex]sin^{-1}[/tex] (0.4613 ) ≈ 27.5°
The sum of the 3 angles in Δ BCD = 180°, thus
x = 180° - (102 + 27.5)° = 180° - 129.5° = 50.5°
The angle x is also 52 degrees.
To find the measure of angle x in triangle ABC, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Given that angle A is 78 degrees and angle B is 50 degrees, we can find angle C using the following equation:
Angle C + Angle B + Angle A = 180 degrees
Angle C + 50 degrees + 78 degrees = 180 degrees
Now, subtract the known angles from 180 degrees to find the measure of angle C:
Angle C = 180 degrees - (50 degrees + 78 degrees)
Angle C = 180 degrees - 128 degrees
Angle C = 52 degrees
Now that we know angle C is 52 degrees, we can use the fact that the angles in a triangle add up to 180 degrees to find angle x:
Angle A + Angle B + Angle x = 180 degrees
78 degrees + 50 degrees + Angle x = 180 degrees
Now, subtract the known angles from 180 degrees to find angle x:
Angle x = 180 degrees - (78 degrees + 50 degrees)
Angle x = 180 degrees - 128 degrees
Angle x = 52 degrees
So, angle x is also 52 degrees.
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India joining figured PNP be intelligent trumpet with circle with Center see if angle APB is going to 40 degree then find angle ACB
Step-by-step explanation:
40° + 90° + 90° + angle ACB = 360°
220° + angle ACB = 360°
angle ACB = 360° - 220°
Therefore angle ACB = 140°
Hope it will help :))
Leah is measuring the weight of adult rhinos at the zoo. Which unit of measurement should she use to eliminate the need to write the values in scientific notation
Answer:
TONS!!!!!!!!!!!!Step-by-step explanation:
The tons should be used to measure the weight of the rhino to eliminate the scientific notation option fourth is correct.
It is given that Leah is measuring the weight of adult rhinos at the zoo.
It is required to find the unit of measurement she should use to eliminate the need to write the values in scientific notation.
Given options:
1) grams
2) feet
3) gallons
4) tons
What is measurement?It is defined as the numerical quantity that gives an idea about an object's weight, length, width, and many more. It can be used to compare two objects.
We know the feet are the unit of measuring the length and gallons are the unit of measuring the volume.
The grams and tons are the units of measuring the weight.
Grams would use to measure a small amount of weight whereas we would use the tons to measure a large amount of weight. Ton is a metric unit that equals 1000 kilograms.
Thus, the tons should be used to measure the weight of the rhino to eliminate the scientific notation option fourth is correct.
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What is an expression to represent the equation
Answer:
8 + [tex]\frac{x}{4}[/tex]
Step-by-step explanation:
I'm assuming you want an answer to the top section of the question.
We can start with 8.
8
When a problem asks for the sum, it's looking for addition, so we use the + sign.
8 +
The problem says "a number," so let's represent that with x. Basically, x just means a number we don't know.
8 + x
The "number" is divided by 4, so we'll just put x/4 as our second term.
8 + [tex]\frac{x}{4}[/tex]
Suppose that 17 inches of wire costs 85 cents.
At the same rate, how much (in cents) will 39 inches of wire cost?
Answer:
195¢
Step-by-step explanation:
1 inch of the wire costs
[tex]\frac{85}{17}[/tex] cents
So we just multiply by 39 to get the total cost.
[tex]\frac{85}{17} * 39 = 195[/tex]
Answer: 195 cents
Explanation:
17 inches cost 85 cent
Means 1-inch will cost 85/17 = 5 cents
At the same rate 39 inches will cost 39×5= 195 cents
A cube has side length of 1 meter. Determine the volume of the cube. Include all of your calculations in your final answer.
Answer:
1
Step-by-step explanation:
Volume of Cube = a³
a is the length of one side of cube
Volume = a³ = 1³ =1x1x1 = 1
Need help I’m stuck on this one. I should ask my teacher but I get help from here faster. Need the answer ASAP. Thank you guys so much
Answer:
(0, 15/6) (15/7,0)
Step-by-step explanation:
Just set the other value to 0 and you can very quickly solve these.
what is the measure of JKL?
Answer:
97
Step-by-step explanation:
83 and JKL form a straight line so they add to 180 degrees
83+ JKL = 180
Subtract 180 from each side
83-83+ JKL = 180-83
JKL = 97
Answer:
97°
Step-by-step explanation:
Interior + exterior angle = 180
Interior angle (JKL) = 180 - 83
97
c=1 when a randomly chosen card out of a standard deck of 52 playing cards is a heart and c=2 otherwise. draw a histogram showing probibility distribution for the random variable
Answer:
The possible values of c are 1 or 2. There are 13 hearts in a deck of cards and 52-13 = 39 cards that are not. There are a total of 52 cards to choose from, so the possibilities for each value of c are found by dividing the number of results for that value by 52. (Image 1)
Histogram is attached for your reference.
find perimeter and area pleasee
Answer:
Perimeter: 36 m
Area: 60 m squared
Step-by-step explanation:
The perimeter is the sum of the exterior side lengths of the shape. Here, we see that there are two side lengths given, but we need to find the third one.
Notice that the triangle is split up into two right triangles, which means that we can use the Pythagorean Theorem to solve for half of the remaining side. The right triangles have hypotenuses of 13 and one leg of 12. That means the second leg will be [tex]\sqrt{13^2-12^2} =\sqrt{169-144} =\sqrt{25} =5[/tex].
So, the third side is made up of the two legs with length 5. This makes the length of the remaining side: 5 + 5 = 10.
Now, we can calculate the perimeter: P = 10 + 13 + 13 = 36 meters.
The area is calculated by the formula: [tex]A=\frac{1}{2} bh[/tex] , where b is the base and h is the height. Here, the base is what we found above, 10, and the height is the length that makes a perpendicular with the base, which is 12. So, the area is: [tex]A=(1/2)*10*12=(1/2)*120=60[/tex]. So, the area is 60 square meters.
Hope this helps!
Answer:
36m
60m²
Step-by-step explanation:
Base of 1 right angle triangle:
sqrt(13² - 12²)
5
Base of the bigger triangle:
5 + 5 = 10
Perimeter = 13 + 13 + 10
36 m
Area = ½ × 10 × 12
60 m²
can absolute value equations be equal to zero? my textbook says no but there are multiple equations equaling 0 or a negative numbers once I simplify.
Absolute value equations can equal zero but cannot equal a negative number. This is because the absolute value of a number is its distance from zero on the number line, which is always zero or positive.
Explanation:In the field of mathematics, absolute value equations can indeed be equal to zero. The absolute value of a number is its distance from zero on the number line, irrespective of direction. Therefore, the only number whose absolute value (distance from zero) is zero, is zero itself.
One can encounter such a situation in an equation like |x|=0, where the solution is x=0, simply because 0 is the only number that is at zero distance from zero. However, for an absolute value equation to be equal to a negative number, this is impossible, because absolute value is a measurement of distance and cannot be negative. So, if your simplified equations are resulting in negative values, you might want to double-check your work.
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The combined volume of all the things and aquarium is 1.25×10 to the six power gallons the aquarium plants to install a new dolphin take with a volume of 250,000 gallons what was the total volume of all the tanks at the aquarium after the new dolphin tank is installed
Answer:
1,500,000 gallons
Step-by-step explanation:
In this question, we are to calculate the total volume of the aquarium after installing a new dolphin tank.
Mathematically, to calculate this, we simply need to add the the volume of the new dolphin tank to the volume of the things in the aquarium before bringing the dolphin tank.
The volume of all the things in the aquarium before installing the dolphin tank is 1.25 * 10^6 = 1,250,000 gallons
now let’s add the volume of the dolphin tank which is 250,000 gallons
that would be 1,250,000 + 250,000 = 1,500,000 gallons or 1.5 * 10^6 gallons
Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?
Step-by-step explanation:
x3 - 9x2 + 5x - 45
x2 (x - 9) + 5(x - 9)
(x - 9) and (x2 + 5) are the factors
Answer:
C
Step-by-step explanation:
EDGE 20-21
Alec can buy bottles of water in packages of 6 for $12.12 or in packages of 4 for $9.72. How much money does he save by buying 48 bottles of water at the better price?
48/6 = 8
He needs to buy 8 of the six pack size for a total of :
8 x 12.12 = $96.96
Or
48/ 4 = 12 Of the 4 packs for a total of
12 x 9.72 = $116.64
He would save
116.64 - 96.96 = $19.68 by buying 8 of the six packs.
Answer:
—————————————-
He saves $19.68
—————————————-
Hope this helps!!!!
—————————————-
Step-by-step explanation:
—————————————-
6 bottles for $12.12
Find the unit rate:
12.12/6
=2.02
This tells us that using this price, each bottle costs $2.02
—————————————-
4 bottles for $9.72
Find the unit rate:
9.72/4
=2.43
This tells us that using this price, each bottle costs $2.43
—————————————-
The first deal is better because you are paying less for each bottle.
—————————————-
So now you know which “deal to use,”
—the first one— (6 bottles for $12.12)
Since each bottle costs $2.02 here, you can multiply:
48 x $2.02 = $96.96
—————————————-
In the second deal, where 4 bottles cost 9.72 bucks,
Each bottle is for $2.43
48 x $2.43 = $116.64
—————————————-
How much does he save by going with the first deal?
$116.64 - $96.96 = $19.68
Solve for x
-14 - 5 = -10x - 45
Answer:
x = -13/5 OR -2.6
Step-by-step explanation:
Take steps to isolate x:
-14 - 5 = -10x - 45
-19 = -10x -45
26 = -10x
x = 26/-10
x = -13/5 OR -2.6
Answer:X=-13/5 is the simplified answer
Step-by-step explanation:
-14-5=-10x-45
-19=-10x-45
-19+45=-10x-45(+45)
26=-10x
26/-10=x
x=-13/5
If Bill has 5 apples and eats 3 of them, how much is left.
Answer:
2 apples Follow me if u have any more request next time
Step-by-step explanation:
5-3=2
For this question please tell me if I'm right or wrong. If I'm wrong please correct me.
Please use the following image below in order to answer the question correctly:
Tell whether PK is best described as a radius, chord, diameter, secant, or tangent of ⊙P.
What can PK be best described as?
Please show all the work on how you got your answer.(Note: I am not asking for an explanation if you're unable to give me one. All that I am asking for is for the work to be shown so I can see how you got your answer)
Answer:
PK represents a radius. Radius only goes half way of the circle.
Answer:
B) chord
Step-by-step explanation:
N and M are two points on the circumference and the segment MN doesn't pass through the centre, so it's a chord
to display The number of female members in band class over the past five years use a
Answer:
For the 1st row its Line Graph and Changes over time.
For the 2nd Row its Bar Graph and Categorical.
Step-by-step explanation:
) Jennifer and Krystal have to stuff and mail 1000 envelopes for a new marketing campaign. Jennifer can do the job alone in 6 hours. If Krystal helps, they can get the job done in 4 hours. How long would it take Krystal to do the job by herself?
Answer:
12 hours
Step-by-step explanation:
Let's call the Jennifer's speed J, and the Krystal's speed K.
If Jennifer works alone, she can do the job in 6 hours, so:
J*6 = 1000
J = 1000/6 = 500/3
If Jennifer and Krystal work together, they can do the job in 4 hours, so:
(J+K)*4 = 1000
J+K = 250
Using the value of J, we can find K:
500/3 + K = 250
K = 250 - 500/3 = 250/3
Now, to find the time that Krystal would take if she works alone:
K * time = 1000
250/3 * time = 1000
time = 1000/ (250/3) = 1000*3/250 = 12 hours
Answer:
12 hours
Step-by-step explanation:
please check the attached files for explanation
Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1.5 m/s, how fast is the area of the spill increasing when the radius is 30 m?
Answer:
The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.
Step-by-step explanation:
Derivative Rule:
[tex]\frac{d}{dx}x^n=nx^{n-1}[/tex] [tex]\frac{d}{dx}(y^n)=ny^{n-1}\frac{dy}{dx}[/tex]Given that
The radius of the oil spill increases at a rate 1.5 m/s.
i.e [tex]\frac{dr}{dt}= 1.5\ m/s[/tex]
We need to find the rate of area increase i.e [tex]\frac{dA}{dt}[/tex] .
We know,
The area of the oil spills A = [tex]\pi r^2[/tex] ( since it spreads in circular pattern)
[tex]\therefore A=\pi r^2[/tex]
Differentiating with respect to t
[tex]\frac{dA}{dt}=\pi. 2r\frac{dr}{dt}[/tex]
Plug the value of [tex]\frac{dr}{dt} =1.5 \ m/s[/tex]
[tex]\frac{dA}{dt}=\pi. 2r(3\ m/s)[/tex]
[tex]\Rightarrow \frac{dA}{dt}=6\pi r \ m/s[/tex]
Plug r= 30 m
[tex]\Rightarrow \frac{dA}{dt}=6\pi (30\ m) \ m/s[/tex]
=180 π m²/s
The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.
What is the surface area of a cylinder with base radius 4 and height 7?Either enter an exact answer in terms of \pi or use 3.14 for \piπpi and enter your answer as a decimal
Answer:
The surface area is 88*pi square units.
Step-by-step explanation:
The surface area of a cylinder is given by two times the area of the base plus the area of the sides. This is given bellow:
surface area = 2*(base area) + (side area)
base area = pi*r²
base area = pi*(4)²
base area = pi*16 = 16*pi
side area = 2*pi*r*h
side area = 2*pi*4*7
side area = 8*7*pi
side area = 56*pi
surface area = 2*(16*pi) + 56*pi
surface area = 32*pi + 56*pi
surface area = 88*pi
The surface area is 88*pi square units.
Answer:
112π cubic units
Step-by-step explanation:
The volume of a cylinder is the area of the base × height.
The area of a circle is πr to the 2nd power
So the area of the base is π × 4 to the second power = 16π
The height of the cylinder is 7, so the volume is 16π × 7 = 112π cubic units
7 t-shirts cost £67.55. How much do 11 t-shirts cost?
Answer:
11 tshirts would cost £106.15
Step-by-step explanation:
67.55 divided by 7 = 9.65
9.65 x 11 = 106.15
Therefore the total would be £106.15.
Answer: 106.15
Step-by-step explanation:
The Drama Club is showing a video of their recent play. The first showing begins at 3:45 p.M. The second showing is scheduled at 6:25 p.M. With a 1 2 −hour break between the showings. How long is the video in hours and minutes? Pt. 2 The second showing started 20 minutes late. Will the second showing be over by 8:45 p.M.?
Answer:
the movie is 2 hours and 10 min long
no it will not be over by 8:45pm
Step-by-step explanation:
if the movie begins at 3:45 pm and the next begins at 6:25pm with a half hour break you need to take 30 min from 6:25 to see what time the movie ended which is 5:55pm then you figure the time between 3:45pm and 5:55pm which is 2hours and 10 min.
since thw movie is starting 20 min late from 6:25pm that is now a start time of 6:45pm if the movie is 2hours and 10 min it will not be over by 8:45pm since that is only 2 hours
What is the range of possible sizes for side x? it is a triangle with one side having 4.0, and the other having 5.6. picture attached below, thanks in advance :)
Given:
Given that the two sides of the triangle are x, 4.0 and 5.6
We need to determine the range of possible sizes for the side x.
Range of x:
The range of x can be determined using the triangle inequality theorem.
The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".
Thus, applying the theorem, we have;
[tex]x=4.0+5.6[/tex]
[tex]x=9.6[/tex]
Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".
Thus, we have;
[tex]x=5.6-4.0[/tex]
[tex]x=1.6[/tex]
Thus, the range of possible values for x are [tex]1.6<x<9.6[/tex]
In accordance with the triangle inequality theorem, the range for the length of the third side (x) in a triangle with sides of 4.0 and 5.6 is greater than 1.6 but less than 9.6.
Explanation:In the field of Mathematics, specifically geometry, to find the range of possible lengths of a side of a triangle, you need to understand the triangle inequality theorem. The triangle inequality theorem states that the length of a side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference.
Given you have two sides, 4.0 and 5.6, the possible length for side x should be less than (4.0 + 5.6 = 9.6) and greater than the absolute difference (5.6 - 4.0 = 1.6). So, the range for side x should be 1.6 < x < 9.6.
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What is the value of d?
Answer:
57
Step-by-step explanation:
the angles of a triangle together make 180 degrees.
using this, we can find the unknown angle is 115 degrees.
from here, we subtract 1 from both sides of 2d+1=115, then divide by 2, to get the d alone.
114/2=57
d=57
Answer:
d=57
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees
38 +27 +2d+1=180
Combine like terms
(38+27+1) +2d= 180
66+2d=180
Now, solve for d by isolating it
Subtract 66 from both sides
66-66 +2d=180-66
2d=114
Divide both sides by 2
d=57
It would take 150 minutes to fill a swimming pool using 5 taps.
a) How many minutes will it take to fill the pool if only 3 of the taps are used?
Complete the following.
b) An assumption being made in my working is that all the taps are flowing at the same time.
Answer:
250 minutes
Step-by-step explanation:
a) Assuming all taps flow at the same rate, the time is inversely proportional to the number of taps. Using 3/5 of the total taps will take 5/3 of the time required when all taps are used.
For 3 taps, the time is ...
(5/3)(150 minutes) = 250 minutes
__
b) An assumption being made in my working is that all the taps are flowing at the same rate.
a) It will take 250 minutes to fill the pool using 3 taps. B) The assumption being made here is that all the taps are flowing at the same rate r and that they are all turned on at the same time, working in parallel to fill the pool.
Let's denote the rate at which each tap fills the pool as r liters per minute.
With 5 taps working together, it takes 150 minutes to fill the pool. Therefore, the combined rate of 5 taps is [tex]\( \frac{1}{150} \)[/tex] of the pool per minute. We can express this as:
[tex]\[ 5r = \frac{1}{150} \][/tex]
Now, we want to find out how long it will take to fill the pool using only 3 taps.
The combined rate of 3 taps will be 3r.
To find the time t it takes for 3 taps to fill the pool, we set up the equation:
[tex]\[ 3r = \frac{1}{t} \][/tex]
We can solve for r using the first equation:
[tex]\[ r = \frac{1}{5 \times 150} \][/tex]
Substituting this value into the second equation gives us:
[tex]\[ 3 \times \frac{1}{5 \times 150} = \frac{1}{t} \][/tex]
Solving for t
[tex]\[ t = \frac{1}{3 \times \frac{1}{5 \times 150}} \][/tex]
t = 250
So, it will take 250 minutes to fill the pool using 3 taps.
b) The assumption being made here is that all the taps are flowing at the same rate r and that they are all turned on at the same time, working in parallel to fill the pool.
This implies that the flow rate of each tap does not change regardless of how many taps are being used simultaneously, and that there are no other factors (like water pressure changes) affecting the flow rate when fewer taps are used.
Total amount of rain each county received for five days. Palm Beach 2.3., Broward 3.5,and Dade 3.0. On average,how many inches of rain did each county received each day.
Answer: On average, each country receives 2.93 inches of rain each day.
Step-by-step explanation:
Since we have given that
Palm Beach = 2.3
Broward = 3.5
Dade = 3.0
So,the average inches of rain each country would receive each day would be :
[tex]\dfrac{2.3+3.5+3.0}{3}=\dfrac{8.8}{3}=2.93\ inches[/tex]
Hence, on average, each country receives 2.93 inches of rain each day.