To calculate the probability that at least one dog will be adopted out of nine visits to an animal shelter, given a single visit adoption probability of 0.20, you use the complementary probability principle: 1 minus the probability of no adoptions in nine visits (0.80^9).
Explanation:The question asks to calculate the probability that at least one dog will be adopted out of nine visits to an animal shelter, given that the probability of adopting a dog on any visit is 0.20. To find this, we need to use the concept of complementary probability, which states that the probability of at least one event occurring is equal to 1 minus the probability of the event not occurring at all. Here, the event not occurring at all means no dogs are adopted in nine visits.
First, let's find the probability of not adopting a dog on a single visit, which is 1 - 0.20 = 0.80. Next, to find the probability of not adopting a dog in nine visits, we raise this number to the ninth power: 0.80^9. Lastly, to find the probability of at least one adoption in nine visits, we subtract this value from 1.
So, the calculation goes as follows:
Probability of not adopting a dog in one visit = 1 - 0.20 = 0.80Probability of not adopting a dog in nine visits = 0.80^9Probability of at least one adoption in nine visits = 1 - (0.80^9)Performing the arithmetic gives us the answer.
Consider the exponential function f(x) = 3 and its graph. Which statements are true for this function and graph? Check all that apply. The initial value of the function is . The growth value of the function is . The function shows exponential decay. The function is a stretch of the function f(x) = . The function is a shrink of the function f(x) = 3x. One point on the graph is (3, 0).
The function shows exponential growth a stretch of the function f(x) = (1/3)^x .
What are exponential functions?When the expression of a function is such that it involves the input to be present as the exponent (power) of some constant, then such a function is called an exponential function. Their usual form is specified below. They are written in several equivalent forms.
Given that the exponential function f(x) = 3
The initial value of the function is 2.
The base of the function is 3.
When the intial value is where x=0
where x=0, the value of f(0)=3
The growth is 1/3 but it is decay, that might be correct, or not because it is decay.
It is a stretch of the function f(x)=(1/3) power of x
when x=3, then f(3)=1/9
The function shows exponential growth a stretch of the function f(x) = [tex](1/3)^x[/tex].
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A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 4 miles per hour faster than the southbound train. After 2.5 hours, they are 330 miles apart. At what speeds are the two trains traveling?
Fifteen more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by 15. She worked the same number of hours each week. How many hours did she work?
To find the number of hours Carla worked, we'll set up and solve equations based on the information given.
Explanation:To solve this problem, we'll set up an equation based on the information given.
Let x be the number of hours Carla worked last week and y be the number of hours she worked this week.
According to the problem, 15 more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by 15:
2x + 15 = 3y - 15
Next, we'll set up another equation based on the fact that Carla worked the same number of hours each week:
x = y
We can now solve this system of equations to find the value of y, which represents the number of hours Carla worked this week:
Substituting y for x in the first equation: 2y + 15 = 3y - 15
Combining like terms: 15 = y - 15
Adding 15 to both sides: 30 = y
So, Carla worked 30 hours this week.
What is the solution to the system of equations?
Answer:
C. [tex](0,-5)[/tex]
Step-by-step explanation:
We have been given a graph of system of equation on coordinate plane. We are asked to find the solution for the system of equations.
We know that we can find solution of a system of linear equations by graphing. The solution of the system is the point, where both lines intersect.
Upon looking at our given graph, we can see that both lines intersect at point [tex](0,-5)[/tex] that is at y-axis.
Therefore, the solution to the system of equations is [tex](0,-5)[/tex] and option C is the correct choice.
Find the volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane.
The volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane is 6 cubic unit.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
It is given that
The solid between the planes z = 3x + 2y + 1 and z = x + y, and above the
triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane.
r(u) = (1, 2)
r(v) = (-2, -1)
|r(u)xr(v)| = 3
The volume of the solid:
∬S(3x + 2y + 1 − x − y)ds = ∫₀¹ ∫(u, 0)(2x + y +1)3 dv du
After solving:
= 3(4/3 - 5 /6 + 3/2)
= 6
Thus, the volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane is 6 cubic unit.
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Final answer:
The volume of the solid region between the planes z = 3x + 2y + 1 and z = x + y, above the triangular region in the xy-plane, can be found using a double integral over the triangular area defined by vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0).
Explanation:
To find the volume of the solid region between the planes z = 3x + 2y + 1 and z = x + y, and above the triangular region in the xy-plane, we can use a double integral over the triangular region. The volume is given by the difference between the two planes integrated over the area of the triangle formed by the vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0).
First, define the vertices of the triangle in the xy-plane: A(1, 0), B(2, 2), and C(0, 1).
Second, find the equations of the lines forming the sides of the triangle, which helps in defining the limits of the integral.
Lastly, set up the double integral:
∫∫ (3x + 2y + 1) - (x + y) dA,
after solving, we get volume = 6
where dA is the differential area element in the xy-plane, and the limits of integration are determined by the triangular region.
The integration can be simplified by determining a suitable ordering for dx and dy, often choosing to integrate in x first and then y, or vice versa, based on the geometry of the triangle. The exact bounds for x and y need to be worked out from the equations of the lines defining the triangle's edges.
The result of this integral will give the volume of the solid region bounded by the two planes and above the triangle.
which function is an even function?
This graph shows a portion of an even function. Use the graph to complete the table of values.
1, 1, 3, 3 - I just did it on e2020 and got it correct
Evaluate the series 50 + 10 + 2 + . . .
Which triangle has 0 reflections of symmetry
Answer:
The answer would be option A the scalene triangle
Answer:
The first triangle, or, A !!
Step-by-step explanation:
Why does multiply numbers by 10 move the decimal point to the right but multiplying by 0.10 move the decimal point to the left
A finite population consists of four elements: 6, 1, 5, 3. (a) how many different samples of size n = 2 can be selected from this population if you sample without replacement? (sampling is said to be without replacement if an element cannot be selected twice for the same sample.)
Which equation represents a direct variation?
Answer:
a y=.5x
Step-by-step explanation:
please dont look at my name
Is y=7x+2 x+7y=8 parallel, perpendicular, or neither?
5x + 2y = 6 3x + y = 4 Which of the following is part of the solution to the system of equations?
1)x = -2
2)y = -2
3)x = 1
The solution is Option B.
The value of x = 2
The value of y = -2
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
The value of A is
5x + 2y = 6 be equation (1)
Let the second equation be B
The value of B is
3x + y = 4 be equation (2)
Now , on simplifying the equations , we get
Multiply equation (2) by 2 , we get
6x + 2y = 8 be equation (3)
Subtracting equation (1) from equation (3) , we get
x = 8 - 6
x = 2
So , the value of x = 2
Substituting the value of x in equation (2) , we get
3x + y = 4
3 ( 2 ) + y = 4
6 + y = 4
Subtracting 6 on both sides of the equation , we get
y = -2
So , the value of y = -2
Hence , the solution to the system of equations is x = 2 and y = -2
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On a trip to the beach, you travel 200miles in 300 minutes. How fast did you travel?
The current (I) in an electrical conductor varies inversely as the resistance (r) of the conductor. The current is 2 amperes when the resistance is 960 ohms. What is the current when the resistance is 480 ohms?
Suppose you are taking the bus home, and can take either the 51 or the 82. you know that the 82 will arrive in exactly 10 minutes, but because the 51 is unreliable, you suspect that the amount of time until it arrives is uniformly distributed between 0 and 30 minutes. you take the first bus that arrives. let t be the number of minutes you wait until you board a bus. find e[t].
Final answer:
The expected waiting time for a bus, E[t], is 8.33 minutes, which is calculated considering the possibility of either bus 51, which has a uniform arrival time between 0 to 30 minutes, or bus 82, which arrives in exactly 10 minutes.
Explanation:
The problem you are dealing with involves finding the expected waiting time, E[t], for either bus 51 or bus 82 to arrive. The expected value of a uniformly distributed random variable on an interval [a, b] is given by the formula (a + b)/2. However, we need to account for the fact that if bus 82 arrives in exactly 10 minutes, then if the 51 bus hasn't arrived by then, you will take the 82 bus.
To compute E[t], if the 51 bus arrives within the first 10 minutes, the expected waiting time is the average of 0 and 10 minutes, which is 5 minutes. If the 51 bus does not arrive within 10 minutes, you will take the 82 bus at exactly 10 minutes. Therefore, the expectation must only account for the time if the 51 bus arrives before the 82. This gives us:
The probability that the 51 bus arrives in the first 10 minutes is 10/30 = 1/3.
The expected waiting time if 51 arrives in the first 10 minutes is 5 minutes.
If the 51 bus does not arrive within 10 minutes, you'll wait exactly 10 minutes for the 82 bus.
So, E[t] = (1/3) * 5 minutes + (2/3) * 10 minutes = (5 + 20)/3 = 25/3 minutes.
Therefore, the expected waiting time E[t] is 8.33 minutes (rounded to two decimal places).
The table represents a linear function.
Answer:
The slope of the function is 5.
Step-by-step explanation:
Remember that to calculate the slope of any function you just need the equation of the function on slope form: y=mx+c or any two points in the graph that are result of the function, in this case we have a table, and we will use the first two points:
(-4,-16)
(-2.-6)
So the formula for slope is:
[tex]\frac{y2-y1}{x2-x1}[/tex]
We insert the values of our two points:
[tex]\frac{y2-y1}{x2-x1} \\\frac{-6-(-16)}{-2-(-4)}\\\frac{10}{2}\\ Slope=5[/tex]
So the slope of the function is 5.
Consider the linear function that is represented by the equation y=-10x+6 and the linear function that is represented by the equation y-36=8(x-4). Which statement is correct regarding their slopes and y-intercepts?
a. The function that is represented by the equation y=-10x+6 has a steeper slope and a greater y-intercept.
b. The function that is represented by the equation y=-10x+6 has a steeper slope, and the function that is represented by the equation y-36=8(x-4) has a greater y-intercept.
c. The function that is represented by the equation y-36=8(x-4) has a steeper slope, and the function that is represented by the equation y=-10x+6 has a greater y-intercept.
d. The function that is represented by the equation y-36=8(x-4) has a steeper slope and a greater y-intercept.
This is about understanding slopes.
Option A is correct.
We are given two linear functions which are;y = -10x + 6 - - - (eq 1)
y - 36 = 8(x - 4) - - - (eq 2)
Formula for straight line equation is;y = mx + c
Where m is slope and c is the y intercept.
Let's expand eq 2 to be in the form of y = mx + c
Thus;
>>y - 36 = 8(x - 4)
>> y - 36 = 8x - 32
>> y = 8x - 32 + 36
>> y = 8x + 4 - - - (eq 3)
Thus, slope of eq 1 is -10 and y-intercept is 6.
Similarly, slope of eq 3 is 8 and y-intercept is 4.
This means y = -10x + 6 has a greater y-intercept than y - 36 = 8(x - 4).
Also, the slope in y - 36 = 8(x - 4) which is 8 will slope to the right while the slope of y = -10x + 6 which is -10 will slope to the left. This means that line represented by y = -10x + 6 has a steeper slope.
This is because the higher the slope, the steeper the line.
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After rewriting both equations in slope-intercept form, we find that the function y = -10x + 6 has a steeper slope and the function y - 36 = 8(x - 4) has a greater y-intercept, making option (b) the correct answer.
The question involves comparing the slopes and y-intercepts of two linear functions, represented by the equations y = -10x + 6 and y - 36 = 8(x - 4). To compare them, we need to write both equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
The first equation, y = -10x + 6, is already in slope-intercept form, with a slope of -10 and a y-intercept of 6. For the second equation, y - 36 = 8(x - 4), we first distribute the 8 to get y - 36 = 8x - 32 and then add 36 to both sides to get the slope-intercept form, y = 8x + 4, which has a slope of 8 and a y-intercept of 4.
Comparing the slopes, -10 for the first equation and 8 for the second, we see that the first equation has a steeper slope because -10 has a greater magnitude than 8. Comparing the y-intercepts, 6 for the first equation and 4 for the second, the first equation has a greater y-intercept. Therefore, the correct statement regarding their slopes and y-intercepts is (b) The function that is represented by the equation y = -10x + 6 has a steeper slope and the function that is represented by the equation y - 36 = 8(x - 4) has a greater y-intercept.
How to solve -5 3/14 to the thousandths place?? Please help
How many different 4-digit personal identification numbers are possible if no digit can be used twice? a. 1,000 b. 5,040 c. 9,000 d. 10,000
Answer:
5040
Step-by-step explanation:
To Find : How many different 4-digit personal identification numbers are possible if no digit can be used twice?
Solution :
Since we are given that no digit can be used twice
SO, when one digit is used so next digit will be chosen from the remaining digit an so on .
the digits can be 0,1,2,3,4,5,6,7,8,9
Since these are 10 in number
out of these 10 we need to choose 4 but no digit can be used twice
⇒[tex]_{10}\textrm{C}_1 *_{9}\textrm{C}_1 *_{8}\textrm{C}_1*_{7}\textrm{C}_1 [/tex]
Formula : [tex]_{n}\textrm{C}_r=\frac{n!}{r!(n-r)!}[/tex]
thus using this formula
⇒[tex]\frac{10!}{1!(10-1)!} *\frac{9!}{1!(9-1)!}*\frac{8!}{1!(8-1)!}*\frac{7!}{1!(7-1)!}[/tex]
⇒[tex]\frac{10!}{9!} *\frac{9!}{8!}*\frac{8!}{7!}*\frac{7!}{6!}[/tex]
⇒[tex]10*9*8*7[/tex]
⇒[tex]5040[/tex]
Thus different 5040 number of 4-digit personal identification numbers are possible if no digit can be used twice
from january to june a company spent 60.00 per month on office supplies. in july the price increased by 15% and remained the same for the rest of the year. how much did the company spend on supplies for the year?
Someone please help me!
If twice a number decreased by 5 and the result is multiplied by 4, the result is 36. find the number
Mohammad would like to graph the line that represents the total number of baseball cards he will have collected, T, after m months, given that he buys 5 cards each month and he started with no cards. He would like the graph to show the number of cards after 6 and 12 months. Select from the drop-down menus to correctly complete each statement. To best show this information, the scale for the T-axis of his graph should go from 0 to at least , and the m-axis of his graph should go from 0 to at least .
Solution:
Number of Baseball cards bought by Mohammad each month = 5
As number of baseball cards is represented by T , which are
T = 0,5,10,15,20,25,30,35,40,45,50,55,60 →→ Y axis
Number of months(m) from which Mohammad started buying cards is given as
m = 0,1,2,3,4,5,6,7,8,9,10,11,12 →→ X axis
The given information represented in equation form
T = 5 m
This is a equation of line in two variable passing through origin.
Slope of line = 5 =Amount of baseball card bought each month
Number of cards bought after 6 months = 5 × 6=30
Number of cards bought after 12 months = 5 ×12 =60
Graph is depicted below.
The scale for the T-axis of his graph should go from 0 to at least 60 , and the m-axis of his graph should go from 0 to at least 12 .
what is the basic ratio for 30:42
The basic ratio of 30:42 is 5:7. This was found by simplifying the ratio to its lowest terms, which is done by dividing both sides of the ratio by the largest number that can evenly divide both numbers, the greatest common factor (GCF).
Explanation:The basic ratio of 30:42 is found by simplifying the ratio to its lowest terms. To do this, find the greatest common factor (GCF) of the two terms, which is the largest number that can evenly divide both numbers. In this case, the GCF of 30 and 42 is 6. Therefore, by dividing both sides of the ratio by 6, we get the simplified ratio: 5:7. So, the basic ratio for 30:42 is 5:7.
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Holland added three decimals that made a sum of 2. One of the decimals was 0.34. What are two other decimals Holland could have used to make a sum of 2
Answer:
In general the two other decimals are x and y that satisfy x + y = 1.66 where x ≤ .99 and y ≤ .99
One particular pair would be x = 0.99 and y = 0.67
Step-by-step explanation:
If Holland added three decimals that made a sum of 2 and one of them was 0.34, we are going to name x and y to the other 2 decimals.
We are going to write the equation:
[tex]0.34 + x +y= 2\\x+y=2-0.34\\x+y = 1.66[/tex]
So we have that both the other numbers have to sum 1.66, however, we know both numbers are decimals so neither one of them can be greater than 1.
So this problem has many answers and the answers would be all the numbers that satisfy x + y = 1.66 where x ≤ .99 and y ≤ .99
For example, if x = 0.99, y would be:
y = 1.66 -0.99 = 0.67.
And our pair of numbers would be 0.99 and 0.67.
If x = .80, y would bey = 1.66 - 0.80 = 0.86
And our pair of numbers would be 0.80 and 0.86
This way, we can find more than 1 answer for the other two decimals.
convert y=2x-7 to slope intercept form
baby sister took nap for 2 hours and 22 minutes and 1 hour and 35 minutes yesterday. how many more minutes did she sleep yesterday than today
There are 45 new house bulky in the neighborhood. Last month 1/3 of the were sold . This month 1/5 of the remaining houses were sold . How many houses are left to be sold