Considering the given probabilities, it is found that the correct option about whether the events are independent is given as follows:
p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).
What are independent events?Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Researching this problem on the internet, the probabilities are given as follows:
[tex]P(X) = \frac{4}{5}, P(Y) = \frac{1}{4}, P(X \cap Y) = \frac{1}{5}[/tex]
Hence:
[tex]P(X)P(Y) = \frac{4}{5} \times \frac{1}{4} = \frac{1}{5} = P(X \cap Y)[/tex]
Hence the events are independent and the correct option is given by:
p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).
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Which statements about the design are true? select three options. each sprinkler head is placed more than 3 feet from the walkway. if two additional sprinkler heads are placed on the lawn, every square foot of the yard would be watered. the total area watered by each sprinkler is approximately 63.6 square feet. the total area watered by all the sprinklers is approximately 254 square feet. if the sprinklers were placed in two straight lines on the yard, they would water a greater amount of the lawn.
The statements about the design that are true are:
each sprinkler head is placed more than 3 feet from the walkwaythe total area watered by each sprinkler is approximately 63.6 square feet. the total area watered by all the sprinklers is approximately 254 square feet.How to explain the design?As we can see the distance from the sprinklers head to the walkway is more than one grid and length of one grid is 3 feet, so each sprinkler is placed more than 3 feet from the walkaway.
The radius of the area watered by each sprinkler = 1.5 grid = 1.5×3 = 4.5 feet. So area watered by each sprinkler = π×r² = (3.14)(4.5)² = 63.58 ≈ 63.6 feet². Area watered by one sprinkler = 63.6 feet², therefore total area covered by four sprinklers = 4×63.6 = 254 feet²
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Answer:
A&C&D
Step-by-step explanation:
Trust
Simplify the expression. Write your answer as a power.
The simplified expression is
Answer:
(-4)^5
Step-by-step explanation:
(-4)^(8 + 3)/(-4)^(4 + 2) = (-4)^11/(-4)^(6) = (-4)^(11-6) = (-4)^5
Troy wants to join Universal Gym. The gym charges a one-time membership fee of $50 and $24.50 per month. Write a function that represents this situation.
a. f(m) = 50m + 24.50
b. f(m) = 50 + 24.50m
c. f(m) = 50m + 24.50m
d. (m) = 50 + 24.50
Answer: B
Step-by-step explanation:
B is the correct one because the $50 is one time payment and the $24.50 gets charged every month
I think my answer is correct? Not so sure though haha
Find the slope of every line that is perpendicular to this one
Answer:6-
Step-by-step explanation:
The shape is composed of squares and quarter circles. What is the perimeter?
Find the perimeter of the parallelogram whose vertices are A (-1,1), B (-9,6), C(-12,11) and D(-4,6) Give your answer correct to one decimal place
Answer: 30.5
Step-by-step explanation:
A building that is used for storage has the dimensions shown. What is the volume of the building?
The total volume of this building based on the volume of its two sections is 3808 cubic feet.
How to calculate the volume of the building?In this case, it is necessary to calculate the volume of the base that has a rectangular prism shape and the volume of the top part that has a right triangular prism shape.
What is the volume of the base?length x widht x height28 x 8 x 14 = 3136 cubic feetWhat is the volume of the top part?0.5 x base x height x length0.5 x 14 x 8 x 12 = 672 cubic feetWhat is the total volume?3136 + 672 = 3808 cubic feetNote: This question is incomplete because the image is missing; here is the missing section.
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solve inequality
-3m > 75
Step-by-step explanation:
-3m > 75
3m < -75
m < -25
that's it.
Answer:
m< - 25
Step-by-step explanation:
-3m > 75
(-3m)/(-3) <75/(-3) (divide both members by (-3) (which is a negative number so ">" becames "<")
m<-25
When 2(x+2y-x-1-2y+3) is simplified, what is the resulting expression?
X+
0 17 x + 2 y +6 plssss help
Answer:
4
Step-by-step explanation:
2x+ 4y -2x-2-4y+6
2x-2x+4y-4y-2+6
0+0+4
Rewrite the equation by completing the square x^2-14x+49=0
Answer:
Here is the ans ...hope it helps:)
A bag contains 8 red marbles, 4 blue marbles and 7 green marbles. If two marbles are
drawn out of the bag, what is the exact probability that both marbles drawn will be
red?
Answer:
28/171
Step-by-step explanation:
The probability initially of drawing a red would be 8/19 since there were 19 marbles in the bag in the beginning. However, without replacement, the probability of drawing another red would be 7/18 as there would be one less red and one less marble in the bag so to find the combined probability of getting 2 red marbles, multiply 8/19 by 7/18 to get: 56/342 = 28/171
The diameter of a pipe is 6 cm. If the pipe is 35 cm long, what is its volume?
Use the value 3.14 for 7, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
I can't solve it.
Step-by-step explanation:
Please help me please help me
If the total profit per month is 200000 and the revenue per month can be obtained as twice the cost per month minus 50000. what is the revenue and cost?
Answer:
300,000
Step-by-step explanation:
[tex]2000000 - 50000 = 150000[/tex]
[tex]150000 \times 2 = 300000[/tex]
I need help for this one.
Answer:
5
Step-by-step explanation:
When you are looking for a pattern, look at one of the examples, makeup the pattern, then check it on the other examples.
Wrong answers may work on one, but not all the completed examples.
The right answer will work on all of the examples, then use that rule on the incomplete one.
So, I looked at the second one in the top row. The two bottom numbers, 5 + 13 makes 18. And 18÷3 (the top number, gives the center number) Check on other examples.
bottom + bottom=_
_÷top=center.
8+4=12, 12÷3 =4.
9+5=14, 14÷2=7
Both of these work.
So use the rule for the last one.
Add the bottom numbers, divide by the top number, fill it in the middle.
14+6=20
20÷4=5
Fill in 5.
A plane flies from Dubbo on a bearing of 139° for 852 km, then turns and flies on a bearing of 285° until it is due west of Dubbo. How far from Dubbo is the plane, to the nearest km?
Answer:
Step-by-step explanation:
So first you add them together which gives you infinity and then you divide infinity by (139+285) then keep doing it until you realise this is a scam
which graph best describes the solution of 3m > 21
Answer:
See below
Step-by-step explanation:
I don't see any graphs, but if you solve the inequality by dividing 3 on both sides, you get [tex]m > 7[/tex]. This means that all [tex]m[/tex] greater than 7, except 7 itself, are included in the solution set.
Ideally, I assume the answer would be a number line with an open circle at m=7 to show it is not included, and then a shaded arrow pointing to the right to show all possible solutions greater than 7.
find the value of 6.4⋅(8+15)
Answer:
The Answer is 147.2
Step-by-step explanation:
Hope this helps Have a great day and Sry if i'm wrong :)
Solve y=x+5 and 2x-3y=4
Answer:
x= -19
y= -14
Step-by-step explanation:
Substitution.
It tells you what y is already. You substitute that into the second equation and then solve. Then you use that answer and substitute it back into the first equation's x, and then you'll get your full answer.
Hope this helps <3
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
To solve such problem there are two method by elimination method or substitution methodI have solved with substitution method juz' refer to attachment for understanding the ans ![tex]{ \boxed{ \: ✟\underline{ \boxed{ \sf{ \: x = - 19 ✓}}}✟ \:}} \\ { \boxed{ \: ✟\underline{ \boxed{ \sf{ \: y = - 14✓ }}}✟ \:}} \\\\ [/tex]
Hope it helps !
i cant find the height to the area!!! THE SHAPE IS A TRIANGLE
area is 21.9
the base is 6
and the height is x
Answer:
x = 7.3
Step-by-step explanation:
area = base × height / 2
21.9 = 6 × x / 2
43.8 = 6x
x = 7.3
Answer:
7.3
Step-by-step explanation:
The formula to find the area of a triangle is (1/2)(a)h = A.
Replace the variable h (height) with x.
Isolate the x variable (height) in order to find the height value.
(1/2)(6)x = 21.9
3x = 21.9
x = 21.9/3
x = 7.3
PLEASE HELP!
Six guinea pigs are released in an area with no natural predators. The guinea pig population quadruples every year. Write a function P that represents the guinea pig population at a given time T measured in years. Choose the function below that represents the inverse function P-1
Use the inverse function to find how long it will take the guinea pig population to reach 1,000 and choose the response that correctly states this information.
The time taken for the population of the pig to reach 1000 will be almost four years.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
Six guinea pigs are released in an area with no natural predators.
The guinea pig population quadruples every year.
Write a function P that represents the guinea pig population at a given time T measured in years.
Then the function will be
[tex]\rm P = 6 (4)^T[/tex]
Then the inverse function of P will be
[tex]\rm T = 6 (4)^P\\\\\\P \ln 4 = \ln \left (\dfrac{T}{6} \right )\\\\\\P = \dfrac{\ln (T/6)}{\ln 4}[/tex]
Then the time taken for the population of the pig to reach 1000 will be
[tex]\rm 1000 = 6 (4)^T\\\\\\166.667 = 4^T\\\\\\T = 3.69 \\\\\\T \approx 4 \ years[/tex]
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A
12
13
14
TIME REMAINING
01:48:01
What will be the result of substituting 2 for x in both expressions below?
3x+4
x+6–3x-2
O Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
O Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
o One expression equals 5 when substituting 2 for x, and the other equal2 because the expressions are not
equivalent
o One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent
Mark this and return
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None of the given options are matching. For the expression after putting the value 2 on the place of x. We will get 10 for expression 1 and 0 for the expression 2.
How can we find the solution to an equation?
We do same operations on both the sides so that equality of both expressions doesn't get disturbed.
Solving equations generally means finding the values of the variables used in it for which the considered equation is true.
The given equation is;
Equation 1;
[tex]\rm 3x+4[/tex]
Equation 2;
[tex]x+6-3x-2[/tex]
After putting the value 2 on the place of x we get;
Equation 1;
[tex]\rm = 3x+4[/tex]
[tex]=3 \times 2+4 \\ =10[/tex]
Equation 2;
[tex]= x+6-3x-2\\\\\ =2+6-3\times 2-2 \\\\ =2+6-6-2\\\\ =8-6-2 \\\\ = 0[/tex]
Hence, the none of the given options are matching.
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b) What is the measure of ZE? Explain how you know. (1 point)
i cant give you a answer because there is no other problems
Use the summation notation to write the series
10+5+0+(-5)+(-10)+(-15)
Hey there!
10 + 5 + 0 + (-5) + (-10) + (-15)
= 10 + 5 - 5 - 10 - 15
= 15 - 5 - 10 - 15
= 10 - 10 - 15
= 0 - 15
= -15
Therefore, the answer should be: -15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
what is the area, in square centimeters, of the isosceles trapezoid below?
Answer:
65.28
Step-by-step explanation:
1/2 × (15.2+5.2) × 6.4 = 65.28
hope this helps ;)
What is 3.9047 rounded to the nearest thousandth?
Answer: 3.905 rounded
Step-by-step explanation: The thousandth in this number is 4.
Round it up since when its 5 or more you add 1 more/raise the score
The answer is 3.905
nth term of -4 ,1, 12 ,29, 52
Answer:
[tex]3n^2-4n-3[/tex]
Step-by-step explanation:
The difference between each number is 5,11,17,23 and the difference between these numbers is 6. So by dividing 6 by 2, you get the n^2 co-efficient which in this case is [tex]3n^2[/tex].
Then compare the [tex]3n^2\\[/tex] pattern to the original pattern so:
-4, 1, 12, 29, 52
3, 12, 27, 48, 75
Subtract the original nth term sequence by the new [tex]3n^2\\[/tex] pattern and you will get:
-7, -11, -15, -19, -23
The nth term of this new sequence is -4n-3.
By combining the 2 nth terms together, you get [tex]3n^2-4n-3[/tex].
Hope this helps!
Using f(x) = 4x + 6 with a domain of {-1, 0, 2), find the range.
A. {10, 6, 15)
B. {2, 14)
C. {-4, 0, 8}
D. {2, 6, 14}
Answer:
D
Step-by-step explanation:
Start by plugging in all the domain values (domain means input) into the function.
f(-1) = 4(-1) + 6 =-4+6=2
f(0) = 4(0) +6=0+6= 6
f(2) = 4(2) +6 = 8+6=14
A company produces 3000 memory cards each day. Every
day 25 are randomly selected for testing. One day, 1 of those
tested failed. About how many of the memory cards
produced that day are likely to fail?
Answer:
120 failures
Step-by-step explanation:
1 out of 25 or 1/25 th of 3000
1/25 * 3000 = 120
The proportion of all US adults who eat popcorn when they go to the movie theater is p = 0.87. A random sample of 20 US adults was selected and asked if they eat popcorn when they go to the movie theater. Which of the following is the shape of the sampling distribution of p hat ?
The sampling distribution of p hat is approximately Normal because n p = 17.4 greater-than 10.
Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10, the sampling distribution of p hat is not approximately Normal. The sampling distribution of p hat is skewed right and centered at 0.87.
Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.
Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10, the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the right.
The option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution [tex]\rm \hat{p}[/tex] is not approximate normal because p=0.87 is closer to 1 than zero.
Sampling distribution [tex]\rm \hat{p}[/tex] is skewed to the left.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
Because the requirement for normal is greater than 10, n×p is greater than 10 and nx(1-p) is also greater than 10.
This situation is abnormal because it is not valid. If p is close to 1 in a normal graph, then p is left skewed.
Thus, the option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution [tex]\rm \hat{p}[/tex] is not approximate normal because p=0.87 is closer to 1 than zero. Sampling distribution [tex]\rm \hat{p}[/tex] is skewed to the left.
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