To find the probability that there won't be enough parking spaces for all the cars, we can use the binomial distribution formula and calculate the probability of having more than 30 cars in a sample of 50. The probability is approximately 0.9999999999.
Explanation:To find the probability that there won't be enough parking spaces for all the cars, we need to find the probability that the number of cars exceeds the capacity of the parking lot. The number of cars follows a binomial distribution with a probability of success of p = 0.12 and a sample size of n = 50. We can use the binomial probability formula to calculate this probability:
P(X > 30) = 1 - P(X ≤ 30)
where P(X ≤ 30) is the probability that the number of cars is less than or equal to 30. We can use a binomial calculator or software to find this probability:
P(X > 30) ≈ 0.9999999999
What are the coordinates of the vertex of the table? Is it a minimum or a maximum? X Y 0 1 -1 -2 -2 -3
Need Help! I don't get it
If two chords are the same distance from the center of a circle, then they are _____________.
a. parallel
b. congruent
c. perpendicular
Answer: Congruent
Step-by-step explanation:
If two chords are the same distance from the center of a circle, then they are congruent, the correct option is B.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
We are given that;
The distance between the chords is same
Now,
According to 1 and 2, if two chords are the same distance from the center of a circle, then they are congruent. This means they have the same length and subtend equal angles at the center.
Therefore, the answer will be congruent.
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Each statement describes a transformation of the graph of y = log2x.
Which statement correctly describes the graph of y = log2(x + 3) - 9?
It is the graph of y = log2x translated 3 units down and 9 units to the left.
It is the graph of y = log2x translated 9 units down and 3 units to the right.
It is the graph of y = log2x translated 9 units down and 3 units to the left.
It is the graph of y = log2x translated 3 units up and 9 units to the left.
it's C: It is the graph of y = log2x translated 9 units down and 3 units to the left.
2 cards are drawn from a standard deck of 52 playing cards. how many different 2-card hands are possible if the drawing is done without replacement?
Final answer:
There are 1326 different 2-card hands possible when drawing without replacement from a standard deck of 52 playing cards, using combinations to calculate it.
Explanation:
To determine how many different 2-card hands are possible from a standard deck of 52 playing cards when drawing without replacement, we need to consider combinations since the order of the cards does not matter. Using the combination formula C(n, r) = n! / (r!(n - r)!), where n is the total number of items and r is the number of items to choose, we calculate C(52, 2).
We have:
n = 52 (total number of cards)
r = 2 (number of cards to choose)
Therefore, the calculation is as follows:
C(52, 2) = 52! / (2!(52 - 2)!) = 52! / (2! * 50!) = (52 * 51) / (2 * 1) = 1326.
So, there are 1326 different 2-card hands possible when drawing without replacement from a standard deck of cards.
a cookie recipe calls for 2/3 cup of sugar if you have three cups of sugar in your pantry how many batches of cookies can you make
The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas?
(I will give Brainliest/5 stars to correct answer)
Find a ⋅ b.
a = 7i - 4j, b = 4i + 3j
A) <28, -12>
B) 16
C) -40
D) <11, -1>
There are 3 grams of sodium in 1/2 of a liter of soda.how much is in 2/3 of a liter
What are the lower, middle, and upper quartiles of this data? 122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77
Answer:
The lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.
Step-by-step explanation:
The given data set is
122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77
Arrange the data set in ascending order.
71, 71, 77, 84, 85, 98, 98, 104, 111, 114, 122, 147, 164
Divide the data set in equal parts.
(71, 71, 77, 84, 85, 98), 98, (104, 111, 114, 122, 147, 164)
Now divide each parenthesis in two equal parts.
(71, 71, 77), (84, 85, 98), 98, (104, 111, 114), (122, 147, 164)
Lower quartile is
[tex]Q_1=\frac{77+84}{2}=80.5[/tex]
Middle quartile is
[tex]Median=Q_2=98[/tex]
Upper quartile is
[tex]Q_3=\frac{114+122}{2}=118[/tex]
Therefore, the lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.
The semicircle shown at left has center X XX and diameter W Z ‾ WZ start overline, W, Z, end overline. The radius X Y ‾ XY start overline, X, Y, end overline of the semicircle has length 2 22. The chord Y Z ‾ YZ start overline, Y, Z, end overline has length 2 22. What is the area of the shaded sector formed by obtuse angle W X Y WXYW, X, Y?
The area of the shaded region is 4π/3 square units.
We have given that x= center diameter =wz w and z end over line radius=2
Triangle XYZ is equilateral,
What is the central angle of equilateral ?
120 degrees
so the central angle of the sector is 120°,
In radian
=120×[tex]\pi[/tex]/180
=2π/3 radians.
The area of a sector of central angle β is given by,
[tex]A = (1/2)r^2(\beta )[/tex] . . . . . . β in radians
[tex]A = (1/2)*2^2*(2\pi /3)[/tex]
= 4π/3 . . . . square units
Therefore the area of the shaded region is 4π/3 square units.
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The length of a rectangle is 5 times the width. If the perimeter is to be greater than or equal to 108 meters. What are the possible values of the width?
The smallest possible value for the width of the rectangle is 9 meters, given that the perimeter must be greater than or equal to 108 meters and the length is 5 times the width.
The question asks for the possible values of the width of a rectangle where the length is 5 times the width and the perimeter is greater than or equal to 108 meters.
Step-by-step explanation:
Let's call the width of the rectangle w. The length is then 5w. The perimeter P of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.
In this case, P = 2(5w) + 2w = 10w + 2w = 12w. Now, we know that P >= 108, so 12w >= 108.
To find the smallest value for w, we divide both sides by 12: w >= 9. Thus, the width of the rectangle must be at least 9 meters.
Can someone please help me with this assignment
Evaluate the expression when y=-5
Y^2-8Y+4
A total of 60% of the customers of a fast food chain order a hamburger, french fries, and a drink. if a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?
The probability that 10 or more will show that the above three food items were ordered is 0.403.
What is Binomial Distribution?The binomial distribution summarises the number of trials or observations where each trial has the same chance of achieving a specific value. The binomial distribution indicates the likelihood of observing a given number of successful outcomes in a given number of trials.
Given:
n= 15
p= 0.6
q= 1-0.6= 0.4
r= 10
Now, P(10<=x<=15) = 1 - binomcdf (15,0.6,9) = 0.4032
Then, P (x≥0) = [tex]\sum_{x=0}^n[/tex][tex]^{15}C_{10}(0.6)^{10}(0.4)^{10}[/tex]
= [tex]\sum_{x=0}^{15[/tex] 3003 x (0.0060466176) (x 0.0001048576)
= 0.403
Hence, the probability is 0.403.
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PLEASE HELP!!!!
Which equation matches the graph of the greatest integer function given below?
A. y=[x]-3
B. y=[x]-2
C. y=[x]+2
D. y=[x]+3
the correct answere is B
Three consecutive even integers add to −6. What are these integers?
The tennis ball has a radius of 10 cm. Calculate the approximate volume of the tennis ball. Round to the nearest tenth
A. 4,186.7 cubic centimeters
B. 523.3 cubic centimeters
C. 2,356.2 cubic centimeters
D. 658.9 cubic centimeters
Find the two numbers that have a
difference of 3 and a sum of 27.
In triangle NOP, Np is extended through Point P to Point Q, m < NOP =(x+17) degrees, m< PNO =(2x-4) degrees, and m< OPQ=(5x-17) degrees. Find m< OPQ
To find the measure of angle OPQ, set up an equation using the given angles in triangle NOP. Simplify the equation and solve for x. Substitute the value of x back into the expression for angle OPQ to find the measure of the angle.
Explanation:To find the measure of angle OPQ, we can set up an equation using the given angles in triangle NOP:
(x+17) + (2x-4) + (5x-17) = 180
Simplifying the equation, we get: 8x - 4 = 180
From this, we can solve for x: 8x = 184, x = 23.
Now that we have the value of x, we can substitute it back into the expression for angle OPQ: 5(23) - 17 = 108 degrees.
Thus, the measure of angle OPQ is 108 degrees.
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The base of a triangle is 12 in. The height is 7 in. What is the area of the triangle? A) 19 in2 B) 28 in2 C) 42 in2 D) 84 in2
Answer:
C. 42
Step-by-step explanation:
One side of a square flower bed is 22 feet long. How many plants are needed if they are to be spaced 22 inches apart around the outside of the bed?
To find out how many plants are needed, we calculate the perimeter of the square flower bed, convert that to inches, and then divide by the spacing of the plants. In this case, about 48 plants would be needed.
Explanation:This problem can be solved using the properties of a square and unit conversion. Since a square has four equal sides and each side of the square flower bed is 22 feet long, the total perimeter of the flower bed would be calculated as 22 feet * 4, which is 88 feet. Next we need to convert these feet to inches since the plants are spaced 22 inches apart. There are 12 inches within a foot, so 88 feet equals 1,056 inches (88*12).
Once you have the total length in inches, you can determine the number of plants by dividing the total length in inches by the distance each plant is to be spaced. Thus, 1,056 inches divided by 22 inches gives us approximately 48 plants.
So, if you want to space your plants 22 inches apart around a square flower bed where each side is 22 feet, you will need 48 plants.
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Solve the equation using square roots. x2 -9=0
Answer: x = 3, x= - 3
Step-by-step explanation:
x^2 - 9 = 0
=> x^2 = 9
=> x = 3, x= - 3
caros ran 5.25 miles each day for d days. h ran a total of 157.5 miles. which eqution represents the number of days carlos ran?
The table below shows the distance d(t) in feet that an object travels in t seconds:
t
(seconds)
d(t)
(feet)
3
126
4
224
5
350
6
504
What is the average rate of change of d(t) between 3 seconds and 5 seconds, and what does it represent?
A square with one side length represented by an expression is shown below. 6(3x+8)+32+12x. Use the properties of operations to write three different equivalent expressions to represent the lengths of the other three sides of the square. One of your expressions should contain only two terms
The length of each side of the square can be represented by the equivalent expressions 30x + 80, 10(3x + 8), and 2(15x) + 2(40), with the first expression being in the simplest form and containing only two terms.
The student is provided with an expression for the side length of a square and is asked to write equivalent expressions representing the lengths of the other three sides. Since all four sides of a square are equal, we simply need to simplify the given expression and use it to represent each side. The given expression is 6(3x+8)+32+12x.
First, we can simplify this by distributing and combining like terms:
6(3x+8) becomes 18x + 48
Adding the 32 gives us 18x + 48 + 32
Finally, add the 12x to get 18x + 12x + 48 + 32
Combining like terms results in 30x + 80.
Now we have our simplified expression, which is 30x + 80, to represent the length of each side of the square. For different but equivalent forms:
As two terms: 30x + 80 (this meets the requirement of containing only two terms)
Factored form: 10(3x + 8)
Expanded form by distributing a common factor: 2(15x) + 2(40)
These are three different equivalent expressions we can use to represent the lengths of each side of the square.
Juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x) = 10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container. Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?
Answer: There is approximately 8.2 amount of radioactive material that will remain after 10 hours.
Step-by-step explanation:
Since we have given that
[tex]f(x)=10(0.98)^x[/tex]
where, f(x) represents the amount of radioactive material that will remain after x hours in the container.
Since we have given that x = 10 hours.
So, our equation becomes,
[tex]f(10)=10\times (0.98)^{10}\\\\f(10)\approx 8.17\\\\f(10)\approx 8.2[/tex]
Hence, there is approximately 8.2 amount of radioactive material that will remain after 10 hours.
A polygon that has all sides the same measure and all angles the same measure is called what? A. Convex polygon B. Concave polygon C. Irregular polygon D. Regular polygon
Write a number with one decimal place,that is bigger than 6 4/5 but smaller than 7 how can I solve this
Mora ate 8.5 Containers of Yogurt one week. Each Container Held 5.4 Ounces Of Yogurt . HOW Many Ounces Of Yogurt Did she eat in all
Final answer:
Mora ate a total of 45.9 ounces of yogurt after consuming 8.5 containers, with each container holding 5.4 ounces.
Explanation:
The student asked how many ounces of yogurt Mora ate after consuming 8.5 containers, with each container holding 5.4 ounces. Mora ate 8.5 containers of yogurt, with each container holding 5.4 ounces of yogurt. To calculate the total amount of yogurt consumed, we multiply the number of containers by the amount of yogurt each container holds.
To solve this, simply calculate 8.5 containers × 5.4 ounces/container = 45.9 ounces of yogurt in total. This is the total amount of yogurt Mora ate during that week.