The option that best describes independent events is the results of all previous events do not affect the probability of future events.
What are independent events?Independents events are events whose occurrence do not depend on each other. They are random events.
For example, there is no relationship between the the colour of shoes you wear and the chances that it would rain. Thus, they are independent events.
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Answer:
D ✔️
Step-by-step explanation:
"The results of all previous events do not affect the probability of future events."
The distribution of the number of words in text messages between employees at a large company is skewed right
with a mean of 8.6 words and a standard deviation of 4.3 words. If a random sample of 39 messages is selected,
what is the probability the sample mean is more than 10 words?
0.0210
0.2454
0.3724
0.9790
The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The z score is given by:
z = (raw score - mean) / (standard deviation / √sample size)
Given mean of 8.6 words and a standard deviation of 4.3 words. If a random sample of 39 messages, hence, for x > 10:
z = (10 - 8.6) / (4.3 / √39) = 2.03
P(x > 10) = P(z > 2.03) = 1 - P(z < 2.03) = 1 - 0.9788 = 0.0212
The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%
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Answer:
A. .0210
Step-by-step explanation:
I'm taking the test... could be wrong though...
Answer with steps pls
Answer:
A) 2¹²
Step-by-step explanation:
Given :
3x - y = 12Equate the equation to y :
3x - y + y = 12 + y12 + y = 3x12 + y - 12 = 3x - 12y = 3x - 12Substituting in the expression :
[tex]\frac{8^{x} }{2^{y} }[/tex][tex]\frac{2^{3x} }{2^{3x-12} }[/tex][tex]{2^{3x-3x+12}}[/tex]2¹²The sum of terms of an A.P. is 136, the common difference 4, and the last term 31, find n
Step-by-step explanation:
[tex]\huge{\color{black}{\fbox{\color{pink}{\colorbox{pink}{\color{red}{Answer ✨☑️}}}}}}[/tex]
The number of terms are 8. Step-by-step explanation: Given : The sum n terms of an A.P is 136 the common difference is 4 and last term is 31.
Answer:
Sn=2n{2a+(n−1)d}
a+(n−1)d=31⇒a=31−4(n−1)
∴136=2n{2[31−4(n−1)]+(n−1)d}
n[70−8n+4n−4]=272
n(66−4n)=272
4n2−66n+272=0
2n2−33n+136=0
2n(n−8)−17(n−8)=0
(2n−17)(n−8)=0
∴n=8
Use three different values of n to demonstrate that 2 n + 3 n is equivalent to 5 n .
Answer:
2n + 3n equals to 5n in the end, so just set n equal to literally any number :)
Step-by-step explanation:
Example:
Let n = 1000
2(1000) + 3(1000) = 5(1000)
5000 = 500
Basically, plug in the number and solve on both sides each time. You will know you've demonstrated it if it's equal on both sides
Answer:
2n + 3n equals to 5n in the end, so just set n equal to literally any number
Step-by-step explanation:
Example:
Let n = 1000
2(1000) + 3(1000) = 5(1000)
5000 = 500
Basically, plug in the number and solve on both sides each time. You will know you've demonstrated it if it's equal on both sides
Does anybody know this? I keep getting the wrong answer. ABC~PRT AC=15 BC=12 and PT=6 find the ares of ABC if the area of PRT=24mm^2
Answer:
The area of triangle ABC is 60 mm^2
Step-by-step explanation:
x = the area of triangle ABC
15/6 * x/24
x=60
Answer:
(d) 150 mm²
Step-by-step explanation:
The scale factor between the triangles is the ratio of the lengths of corresponding sides. The area ratio is the square of the scale factor.
__
scale factorΔABC is larger than ΔPRT by the factor ...
AC/PT = 15/6 = 5/2
areaThe area of ΔABC is the square of this factor times the area of ΔPRT:
area ABC = (5/2)²×area PRT
area ABC = (25/4)×(24 mm²)
area ABC = 150 mm²
E
Describe the transformation that maps figure RSTU onto figure RSTU
611
6
4
S
U
S2
R
E
R
6-4-2 O
2
4
6
Drag the labels to explain your answer. Labels may be used once more than once, or not at all
Figure RSTU is the image of figure RSTU after a translation
units left and
units down, and a reflection across
the
#1
.: 2
14
+ X-axis
- y-axis
Answer:
8 then 2 and reflection on y axes
What is a simpler form of the expression?
(4k + 5)(3k^2 - 4k - 4)
Answer:
[tex]12k^3 -k^2-36k-20[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex](4k + 5)(3k^2 - 4k - 4)[/tex]
[tex](4k * 3k^2)+(4k*-4k)+(4k*-4)+(5*3k^2)+(5*-4k)+(5*-4)[/tex]
[tex]12k^3-16k^2-16k+15k^2-20k-20[/tex]
Step 2: Combine like terms
[tex]12k^3+(-16k^2+15k^2)+(-16k-20k)-20[/tex]
[tex]12k^3 -k^2-36k-20[/tex]
Answer: [tex]12k^3 -k^2-36k-20[/tex]
Which side is adjacent to Angle Q?
48
14
50
Answer: 48
Step-by-step explanation: 50 is the hypotenuse
14 is the opposite side - its opposite of angle Q
1. Jessica drove 345 miles on
Friday. To the nearest 100,
about how many miles did she
drive?
Answer:
To the nearest 100 miles, Jessica drove about 300 miles since we haven't reached 350 miles. If we have a number that is greater than 350 miles than we would've rounded it up to 400 but since ours is less than that we round down to the nearest hundred which is 300 miles.
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.
Enter the correlation coefficient. Round your answer to the nearest hundredth.
The correlation coefficient is 0.92
What is Correlation Coefficient ?
A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.
In other words, it reflects how similar the measurements of two or more variables are across a dataset.
When one variable changes, the other variables change in the same direction or opposite direction.
Perfect positive correlation :When one variable changes, the other variables change in the same direction.
Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.
[tex]\rm r = \dfrac{\sum (x_{i}-x')(y_{i}-y')}{\sqrt {\sum (x_{i}-x')^{2} \sum (y_{i}-y')^{2}}}[/tex]
After calculation we get
r = 0.92
Therefore it is a Perfect positive correlation
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What is 5log3+log4 as a single logarithm?
[tex]~~~5 \log 3 + \log4 \\\\=\log 3^5 + \log 4~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=\log(3^5 \cdot 4)~~~~~~~~~~~~~~~~~~~~~~;[\log_b(mn) = \log_b m + \log_b n]\\\\=\log(972)[/tex]
I'm having difficulties with this haha please help :(
If the function is h(t) = - 4.9t² + 39.2t + 5. Then the maximum height will be 83.4 meters.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The function is given as
h(t) = - 4.9t² + 39.2t + 5
Then the differentiation of the function will be
h'(t) = - 9.8t + 39.2
For the maximum height, put h'(t) equals zero. Then we have
h'(t) = 0
- 9.8t + 39.2 = 0
t = 4
Then the maximum height will be
h(t) = - 4.9(4)² + 39.2 x 4 + 5
h(t) = - 4.9 x 16 + 39.2 x 4 + 5
h(t) = - 78.4 + 156.8 + 5
h(t) = 83.4 meters
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need some help!
please be specific on how to do it
Answer:
Your first step in solving the system would be to substitute the value of a variable into one of the equations
Step-by-step explanation:
We know that x = 2y + 2 and y = -1/3x + 4, so we could insert one of these values as the variable in one of the equations
If we were to insert -1/3x + 4 for y, our new equation would be:
x = 2(-1/3x + 4) + 2 (as you can see, the value of y was inserted into the equation)
If a sprinkler rotated 90˚, paused and then rotated another 90˚, how many degrees
did it rotate altogether
Answer:180 or halfwayStep-by-step explanation:90 is 1/4 and 360 is a full rotation so it rotated halfway all together.
The triangles are similar. Find the missing measure.
Step-by-step explanation:
Triangle MŇO is congruent to Triangle UŤS
NO=4
MN=4
MO=5.6( Which is 140% bigger than 4)
UT=10
TS=10(Therefore this also should be 10)
US=14(Which is 140% bigger than 10)
I think this is the solution but I am not 100% sure
Answer:
x=14
Step-by-step explanation:
Lance paid 6% sales tax on a $30 game. What is the total amount did Lance pay?
Answer:
The answer is attached.
Perimeter and Area Geometry homework! {Jim Thompson}
Part A
The yard is a quadrilateral with the following corner points
(0,0)(0,40)(40,50)(50,0)I'll label those points A through D in the order presented above.
From A to B is 40 feet since 40-0 = 40. We can subtract the y coordinates because the x coordinates are the same.
In short: side AB is 40 feet long.
The length of side BC is not as simple. We'll need the distance formula.
[tex]B = (x_1,y_1) = (0,40) \text{ and } C = (x_2, y_2) = (40,50)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-40)^2 + (40-50)^2}\\\\d = \sqrt{(-40)^2 + (-10)^2}\\\\d = \sqrt{1600 + 100}\\\\d = \sqrt{1700}\\\\d = \sqrt{100*17}\\\\d = \sqrt{100}*\sqrt{17}\\\\d = 10\sqrt{17}\\\\d \approx 41.2311\\\\[/tex]
Segment BC is exactly [tex]10\sqrt{17}[/tex] feet long, which is about 41.2311 feet.
Use the distance formula again to find the distance from point C(40,50) to D(50,0)
[tex]C = (x_1,y_1) = (40,50) \text{ and } D = (x_2, y_2) = (50,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(40-50)^2 + (50-0)^2}\\\\d = \sqrt{(-10)^2 + (50)^2}\\\\d = \sqrt{100 + 2500}\\\\d = \sqrt{2600}\\\\d = \sqrt{100*26}\\\\d = \sqrt{100}*\sqrt{26}\\\\d = 10\sqrt{26}\\\\d \approx 50.9902\\\\[/tex]
Lastly, the side AD is exactly 50 feet because 50-0 = 50. We can subtract x coordinates because the y coordinates are the same. Use of the distance formula from A to D should show a result of 50 exactly.
We have these side lengths:
AB = 40
BC = 41.2311 (approximate)
CD = 50.9902 (approximate)
AD = 50
Add up those four sides and we'll get the perimeter of the quadrilateral.
AB+BC+CD+AD = 40+41.2311+50.9902+50 = 182.2213
Answer: About 182.2213 feet===================================================
Part B
The garden is a rectangle that is 15 feet across horizontally (since subtracting x coordinates gives us 25-10 = 15) and 20 feet vertically (since subtracting y coordinates gives us 35-15 = 20).
This 15 by 20 rectangle has an area of 15*20 = 300 square feet.
The deck is a trapezoid with the parallel bases of 20 feet up top and 35 feet down below. Like before, we subtract x coordinates to find the horizontal distance (since the y coordinates are the same). The height of this trapezoid is 15 feet. Subtract the y coordinates to find the height.
The area of the trapezoid is
A = h*(b1+b2)/2
A = 15*(20+35)/2
A = 412.5
That decimal value is exact.
Add it onto the area of the rectangle
412.5+300 = 712.5
Answer: 712.5 square feet exactlya student was asked to multiply a number by 3/2. instead he divided the number by 3/2 and obtained a number smaller by 2/3, the number is:
Answer:
[tex]\boxed{\bf \sf number : \ \frac{4}{5} }[/tex]
Explanation:
Let the number be n
According to students Condition:
[tex]\rightarrow \sf \dfrac{3}{2} \ x \ n \quad = \quad \dfrac{3n}{2}[/tex]
What He actually Did:
[tex]\rightarrow \sf n \div \dfrac{3}{2} \quad = \quad n \ x \ \dfrac{2}{3} \quad = \quad \dfrac{2n}{3}[/tex]
He got a smaller number by 2/3, so:
[tex]\rightarrow \sf \dfrac{3n}{2} - \dfrac{2n}{3} = \dfrac{2}{3}[/tex]
make the denominator's same
[tex]\rightarrow \sf \dfrac{3(3n)}{6} - \dfrac{2(2n)}{6} = \dfrac{2}{3}[/tex]
multiply the integers
[tex]\rightarrow \sf \dfrac{9n}{6} - \dfrac{4n}{6} = \dfrac{2}{3}[/tex]
Join the fractions
[tex]\rightarrow \sf \dfrac{9n-4n}{6} = \dfrac{2}{3}[/tex]
Subtract integers
[tex]\rightarrow \sf \dfrac{5n}{6} = \dfrac{2}{3}[/tex]
Cross multiply
[tex]\rightarrow \sf n = \dfrac{6 \ * \ 2}{5 \ * \ 3} \quad = \quad \dfrac{4}{5}[/tex]
Lets see
the number be x
The expression is
3x/2-2x/3=2/39x-4x)6=2/35x)6=2/315x=12x=12/15=4/5can you pleas help this is a math question
Answer:
10.5 baskets
Step-by-step explanation:
The median is the middle value, but for this one just add the two in the middle and divide by 2.
4+3 = 7
Each ball is 3 baskets
7×3 = 21
21/2 = 10.5
.The figure below includes a semicircle and
trapezoid. Find the area of the figure.
Answer:
244.93
Step-by-step explanation:
area formula for trapezoid:1/2*(b1+b2)*h
area formula for semi circles: (3.14*r^2)/2
so then we cut the figure to make a semi cirlce and trapazoid
semicircle- 14 is the full diameter, divide by 2 to make 7, 7×3.14×7)/2=76.93
trapezoid: base one is 18. base 2 is 14. 18+14=32 then times that by 10.5 which is 336 and divide that by 2 is 168
add both and you get 244.93
is 10 times as much as 20 1/10 of 2,000?
Answer:
IT IS 43./45455/.34 LIKE WHEN U ADD 10 TIMES 10 AND DIVIDED 2,000 FROM 20 U THAT ANSWER
Solids X and Y are similar. X has volume of 64cm^3, Y has a volume of 729cm^3, the surface area of X is 208cm^2, work out the surface area of Y
The surface area of solid Y given the ratio of volume to surface area of solid X is 2,369.25cm²
How to solve for surface area?Volume:
Solid X = 64cm³Solid Y = 729cm³Surface area:
Solid X = 208cm²Solid Y = xRatio of volume to surface area of solid X and Y respectively
64 : 208 = 729 : x
64/208 = 729/x
cross product64 × x = 208 × 729
64x = 151,632
x = 151,632 / 64
x = 2,369.25cm²
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A 5kg sample of plutonium-239 has a half-life of 21,400 years by emitting a 5.157 mev (million or mega electron volts) alpha particles. assume that the rate of decay is constant, how long will it take for the sample to degrade to 4.5kg?
Using an exponential function, it is found that it will take 3,252 years for the sample to degrade to 4.5kg.
What is the exponential function for the amount of a substance?It is given by:
[tex]A(t) = Pe^{-kt}[/tex]
In which:
P is the initial amount. k is the decay rate, as a decimal.The half-life is of 21,400 years, hence, A(21400) = 0.5P, and this is used to find k.
[tex]A(t) = Pe^{-kt}[/tex]
[tex]0.5P = Pe^{-21400k}[/tex]
[tex]e^{-21400k} = 0.5[/tex]
[tex]\ln{e^{-21400k}} = \ln{0.5}[/tex]
[tex]-21400k = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{21400}}[/tex]
k = -0.00003239005
Hence, considering the initial mass is of P = 5 kg, the amount after t years is given by:
[tex]A(t) = 5e^{-0.00003239005t}[/tex]
The amount will be of 4.5 kg at t for which A(t) = 4.5, hence:
[tex]4.5 = 5e^{-0.00003239005t}[/tex]
[tex]e^{-0.00003239005t} = 0.9[/tex]
[tex]\ln{e^{-0.00003239005t}} = \ln{0.9}[/tex]
[tex]-0.00003239005t = \ln{0.9}[/tex]
[tex]t = -\frac{\ln{0.9}}{0.00003239005}[/tex]
t = 3252.
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Solve for the exact values of x and y.
x =
y =
Answer:
Here is the solution...hope it helps:)
PLEASE HELP ILL GUVE EXTRA POINTS PLEASE!!!
Answer:
[tex]\boxed{\bf 7 \times 10 {}^{ - 3}} [/tex]
Step-by-step explanation:
[tex] \cfrac{6.3}{9} \times \dfrac {10 ^{ - 5} }{10 {}^{ - 3} }[/tex][tex]0.7 \times \cfrac{10 {}^{ - 5} }{10 {}^{ - 3} } [/tex][tex]0.7 \times 10 { }^{ - 5 - 3 \times - 1} [/tex][tex]0.7 \times 10 {}^{ - 5 + 3} [/tex][tex]0.7 \times 10 { }^{ - 2} [/tex]Write 0.7 *10^-2 into scientific notation:
[tex]7 \times 10 {}^{ - 3} [/tex]Hope this helps! ^^"
Answer:
[tex]7 \times 10^{-3}[/tex]
Step-by-step explanation:
[tex]\begin{aligned}\dfrac{6.3 \times 10^{-5}}{9 \times 10^{-3}} & =\dfrac{6.3}{9} \times \dfrac{10^{-5}}{10^{-3}}\\\\& = 0.7 \times \dfrac{10^{-5}}{10^{-3}}\end{aligned}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\begin{aligned}\implies 0.7 \times \dfrac{10^{-5}}{10^{-3}} &=0.7 \times 10^{-5-(-3)}\\& = 0.7 \times 10^{-2}\end{aligned}[/tex]
[tex]\textsf{Rewrite}\:0.7\:\textsf{as}\: 7 \times 10^{-1}:[/tex]
[tex]\implies 0.7 \times 10^{-2}=7 \times 10^{-1} \times 10^{-2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \times a^c=a^{bc}:[/tex]
[tex]\implies 7 \times 10^{-1} \times 10^{-2}=7 \times 10^{-3}[/tex]
Find the next two terms of the sequence 10, -11, -32, .
Answer:
B
Step-by-step explanation:
Answer: A
Step-by-step explanation:
Because.....
-11 - 10 = -21
-32 - (-11) = -21
This tells us that the sequence is adding by -21, which is why the next 2 terms will be -53 and - 74 since....
-32 + -21 = -53
-53 + -21 = - 74
Hence, the answer is A.
in veronica's neighborhood the ratio of cats to dogs is 3 to 4. if there are 28 dogs, how many cats are there
Answer:
21 cats!
Step-by-step explanation:
the ratio is 3:4
4 being dogs - 28/4 = 7 - 7 * 3 = 21
hope this helps!!! <3
Question is in the picture (I got it wrong)
Answer:
(B) 38.4 m³
Step-by-step explanation:
The volume of a prism is given by the formula ...
V = Bh
where B is the area of the base, and h is the height.
__
The picture tells you the area of the pool is 24 m² and its height is 1.6 m. The volume formula tells you its volume is ...
V = Bh = (24 m²)(1.6 m) = 38.4 m³
The volume of the prism is 38.4 cubic meters.
please help me I will give brainliest
Answer:
potential to kinetic energy
Can you help me plesae !?
Answer: Heyaa! ~
Your Answer is... 26.8
Step-by-step explanation:
The estimated answer is D. 27!
Hopefully this helps you! ^^
Answer:
27
Step-by-step explanation:
12.18 + 14.62= 26.80
if the number after the point is greater than 5 or equal to 5, we will add 1 to the number before the point, so now the number is 8 we will add 1 to the number before the point
26+1=27
therefore the sum of 12.18+14.62 = 27