The probability that at least five wear sunglasses is 0.9464
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
In a random sample of 10 adults, the probability that at least five wear sunglasses
P(X ≥ 5) = P(X = 5) + P(X = 6 ) + P(X=7) + P(X=8) + P(X=9) + P(X=10)
P(X ≥ 5) = 10[tex]C_{5}[/tex] × [tex](0.7)^{5}[/tex]×[tex](0.3)^{5}[/tex] + 10[tex]C_{6}[/tex]×[tex](0.7)^{6}[/tex]× [tex](0.3)^{4}[/tex]+ 10[tex]C_{7}[/tex]×[tex](0.7)^{7}[/tex]×[tex](0.3)^{3}[/tex] + 10[tex]C_{8}[/tex]× [tex](0.7)^{8}[/tex]×[tex](0.3)^{2}[/tex] +10[tex]C_{9}[/tex] ×[tex](0.7)^{9}[/tex]×[tex](0.3)^{1}[/tex]+10[tex]C_{10}[/tex]×[tex](0.7)^{10}[/tex]×[tex](0.3)^{0}[/tex]
P(X ≥ 5) = 0.9464
The probability that at least five wear sunglasses is 0.9464
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in government data, a household consists of all occupants of a dwelling unit. choose an american household at random and count the number of people it contains. here is the assignment of probabilities for the outcome. the probability of finding 3 people in a household is the same as the probability of finding 4 people.
The probability that the household contains 3 people must be 0.16
The probability of finding 3 people in a household is the same as the probability of finding 4 people.
The probability = Number of favorable outcomes / Total number of outcomes
The probability is the occurrence of the random event. The value of the probability varies from 0 to 1
Therefore if we add all the probability together, the result will be one
Also The probability of finding 3 people in a household is the same as the probability of finding 4 people.
Consider the probability of finding 3 people = Probability of finding 4 people = x
Then the equation will be
0.25 + 0.32 + x + x + 0.07 + 0.03 + 0.01 = 1
Add the terms
0.68 + 2x = 1
2x = 1 - 0.68
2x = 0.32
x = 0.32 / 2
x = 0.16
Hence, the probability that the household contains 3 people must be 0.16
The complete question is:
In government data, a household consists of all occupants of a dwelling unit. choose an American household at random and count the number of people it contains. here is the assignment of probabilities for the outcome. the probability of finding 3 people in a household is the same as the probability of finding 4 people. what is the probability of finding 3 people in the household ?
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Fill in the equation for the missing components of the line through (3, 5) and (8, 10)
"ENTER ANSWER AS A DECIMAL
y-5=__(x-3)
The equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)
The first point = (3, 5)
The second point = (8, 10)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (10-5) / (8-3)
= 5 /5
= 1
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope of the line
Consider the point (3, 5)
Substitute the values in the equation
y-5 = 1(x-3)
Hence, the equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)
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If the sale of jacket is 160 what is the original price before the 80 percent
Marc has $256 to spend on coins for his collection. He buys the first coin for $8.
If he pays twice as much for each coin as he paid for the previous coin, how many coins can he buy in all?
OA. 7
OB. 6
O C. 5
OD. 4
Answer:
Option C: 5
Step-by-step explanation:
1st coin = $8
2nd coin = $16
3rd coin = $32
4th coin = $64
5th coin = $128
Total spent = $248
Julie made 7 out every 10 baskets she attempted during a basketball game. If she attempted to make 30 baskets, how many did she make?
Answer: 21
Step-by-step explanation:
If she makes 7 out of 10 shots she makes 70% of her shots (7/10 x 100 = 70%)
So if she makes 30 shots, 21 will go in the basket
(30)(0.70) = 21
1. What number is 1.23 x 10^6 without scientific notation?
The number 1.23 x 10⁶ without scientific notation is 12,30,000.
Scientific Notations:Scientific notation is a way to display extremely big or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper.
We use positive exponents for base 10 when expressing any huge integers in scientific notation. For example:
500000 = 5 x 10⁵, where 5 is the positive exponent.
We use negative exponents for base 10 when expressing any small integers in scientific notation. For example:
0.00005 = 2 x 10⁻⁵, where -5 is the negative exponent.
Here we have
The number 1.23 x 10⁶
We need to write the given number without scientific notation
In the given number the exponent of 10 = 6 and positive
Then we need to move the decimal place 7 places to the right or multiply the given decimal number with 1000000
Therefore,
1.23 x 10⁶ = 1.23 × 1000000 = 12,30,000.
Hence,
The number 1.23 x 10⁶ without scientific notation is 12,30,000.
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1. 6:N=2:5
2. 5:3=N:6
3. N:20=5:10
4. 1:4=2:N
expand and simplify (x+5)(x-3)
The simplified expression is x² + 2x - 15.
We are given a mathematical expression. The expression has two terms. The first term is (x + 5) and the second term is (x - 3). The terms are multiplied by each other to obtain the final expression. Let the resulting expression be represented by the variable "E". The expression has been solved below.
E = (x + 5)(x - 3)
We will use the distributive property.
E = x*(x - 3) + 5*(x - 3)
E = x*x - x*3 + 5*x - 5*3
E = x² - 3x + 5x - 15
E = x² + 2x - 15
Hence, the expanded and simplified form of the given expression is x² + 2x - 15.
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A, B & C lie on a straight line. G, B & F lie on a different straight line. D, E & F lie on a straight line parallel to AC. DEB = 104°. GBA = 24°. Work out EBF.
The measure of angle EBF is 80° .
In the question ,
it is given that ,
point A, B and C lie on a straight line .
and G , B and F lie on a different straight line .
angle GBA = 24° so ,
GBA + GBC = 180° ...because linear pair
So , GBC = 180 - 24 = 156°
angle CBF = 24° ......because vertically opposite angles are equal .
from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,
156° = ABE + EBF .....(1)
Since the line AC and DF are parallel and BE is the transversal
So , angle DEB + angle ABE = 180°
104° + ABE = 180°
ABE = 180-104
ABE = 76°
Substituting ABE = 76° in the equation (1) ,
we get ,
156 = 76+ EBF
EBF = 156 - 76
EBF = 80°
Therefore , The measure of angle EBF is 80° .
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How do i write the equation
Answer:
[tex]y=-\frac{1}{5}x[/tex]
Step-by-step explanation:
Start by finding the slope of the line. Slope is defined as the RISE over the RUN. Find two points on the line with clear coordinate pairs. The line clearly passes through the origin, and the point (5,-1). To get from one point to the other, I have to go DOWN 1 unit. This is the RISE. The rise is -1 because I am going down. I also have to go RIGHT 5 units. This is the RUN. Slope is rise divided by run. Since a positive number divided by a negative number is a negative number, I move the negative sign outside the fraction: [tex]-\frac{1}{5}[/tex]. This is the slope!
The line crosses the y-axis at 0, so the y-intercept is 0.
Point-slope form is a way to write linear equations. It looks like this:
[tex]y=mx+b[/tex]
The letter m represents the slope, and the letter b represents the y-intercept. Let's plug in the values we found for those respectively:
[tex]y=-\frac{1}{5}x+0[/tex]
This simplifies to the equation below! This is the equation of the line!
[tex]y=-\frac{1}{5}x[/tex]
Local stores have donated 30 packets of flower seeds and 105 packets
of vegetable seeds. Carter wants to know what portion of the seeds are
flower seeds. Write a fraction to represent the ratio of flower seeds to the
total amount of seeds. Then, write the fraction as a decimal number.
The ratio of flower seeds to the total amount of seeds is 2/7 = 0.2857.
What is meant by GCF?The greatest common divisor of two or more numbers that are not all equal to zero is the largest positive integer that divides each of the integers. This term is used in mathematics. The symbol represents the two integers x and y's greatest common factor. The GCF of two or more numbers is the greatest number among all the common factors of the given numbers.
Given that,
The local stores have donated 30 packets of flower seeds and 105 packets of vegetable seeds.
30/105
We have to find the GCF of 30 and 105=15
30/15=2
105/15=7
So, the answer is 2/7
The ratio of flower seeds to the total amount of seeds is 2/7.
By converting fractions as a decimal number we get,
2/7=0.2857
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9) Give the following expression in index form
a) √3
For the given expression √3, its index form is written as ( 3 )¹/² .
As given in the question,
Given expression is equal to :
√3
Standard form of writing expression in index form is given by:
√ ( square root ) will express the value in index form as 1 / 2 in the exponent.
√x = ( x ) ¹/²
Here x = 3 substitute the value of x in the standard way of index form we have:
Index form of the given expression is written as :
√3
= ( 3 )¹/²
Therefore, for the given expression √3, its index form is written as ( 3 )¹/² .
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Write a function for the tranformations described below:
"The cubic function shifts 7 units right and 5 units up."
The function for the transformation "The cubic function shifts 7 units right and 5 units up. is written as f(x) = (x - 7)^3 + 5.
How to write the function for the given transformationLet the cubic function be = f(x) = x^3
The transformation required include shifts 7 units right and 5 units up
shifting 7 units to the right is achieved by subtracting 7 units from x in the function hence f(x) = (x - 7)^3
moving 5 units up is achieved by adding 5 units to the function hence
f(x) = (x - 7)^3 + 5
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Which i the inequality in factored form that repreent the region greater than or equal to the quadratic function with zero –3. 5 and 11. 5 and include the point (8. 5, –54) on the boundary?
y greater-than-or-equal-to three-halve (x minu 3. 5)(x 11. 5)
y greater-than-or-equal-to negative three-halve (x 3. 5)(x minu 11. 5)
y greater-than-or-equal-to negative three-halve (x minu 3. 5)(x 11. 5)
y greater-than-or-equal-to three-halve (x 3. 5) (x minu 11. 5)
The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).
What is the expression of the quadratic inequality?
Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic function by solving this system of linear equations:
(x₁, y₁) = (- 3.5, 0)
12.25 · a - 3.5 · b + c = 0 (1)
(x₂, y₂) = (11.5, 0)
132.25 · a + 11.5 · b + c = 0 (2)
(x₃, y₃) = (8.5, - 54)
72.25 · a + 8.5 · b + c = - 54 (3)
The solution of the system is a = 3.6, b = - 54, c = 144.9.
Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:
y ≥ 3.6 · (x² - 15 · x + 40.25)
y ≥ 3.6 · (x - 11.5) · (x + 3.5)
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Find the slope (3,-20),(5,8)
Answer: 14
Explanation:
(3, -20) (5, 8)
x1 y1 x2 y2
[tex]\frac{y2 - y1}{x2 -x1}[/tex]
[tex]\frac{8 - -20}{5-3}[/tex] = [tex]\frac{8+20}{5-3} = \frac{28}{2} = 14[/tex]
A spinner has 8 evenly spaced different colored sections. You spun the spinner 10 times and landed on yellow 2 times. How many times can you expect to land on yellow if you spin the spinner 100 times?
20 times can you expect to land on yellow if you spin the spinner 100 times.
Given:
A spinner has 8 evenly spaced different colored sections. You spun the spinner 10 times and landed on yellow 2 times.
10 times spinning = landed on yellow 2 times.
divide by 10 on both sides
1 time spinning = landed on yellow 2/10 times
1 time = 1/5 times
multiply by 100 on both sides
1 time * 100 = 1/5*100 landed on yellow
100 times spinning = 20 times landed on yellow.
Therefore 20 times can you expect to land on yellow if you spin the spinner 100 times.
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Daniel has saved $2,000 in a savings account that earns 0. 5% interest annually. What will most likely happen to the purchasing power of his savings over time?.
Daniel's purchasing power will decrease because the interest rate is lower than the historical rate of inflation.
Purchasing power can be portrayed as the quantity of labor and products that a unit of cash or an amount of cash can buy. The connection between financing cost and inflation rate influences the buying force of a saving record.
At the point when the loan cost is higher than the inflation rate, purchasing power increments. Yet, when the interest rate is lower than the expansion rate, buying power falls. For example, In the United States for the 12 months ending April 2022, the annual inflation rate was 8.3%. Since the 0.5% annual interest rate being earned by Daniel is lower than the 8.3% annual inflation rate, the most likely thing to happen to the purchasing power of his savings over time is to fall.
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Complete the equation describing how
and y are related.
XOL2345
911 13 15
1
y
7
17
y = [? ]x + [ ]
Enter the answer that
belongs in [?].
The equation that describing how x and y are related is y = 2x + 7
From the given table we have to choose two points
The first point = (1, 9)
The second point = (2, 11)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (11-9) / 2 - 1
= 2 / 1
= 2
From the table
At x = 0 the value of y = 7
Therefore the y intercept = 7
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Then,
y = 2x + 7
Hence, the equation that describing how x and y are related is y = 2x + 7
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(b) Let m be the number of minutes it takes for the two
towers to contain the same number of gallons. Set
up and solve an equation for m.
Answer:
y = mx + b
PLEASE GIVE BRAINLIEST THANK YOU!!!
What are the solutions to the following system?
StartLayout Enlarged left-brace 1st row negative 2 x squared + y = negative 5 2nd row y = negative 3 x squared + 5 EndLayout
The given system of equations has solutions (-2, -1) and (-2, -1) respectively.
Solving system of equationsCalculating the unknown variables while keeping the equations balanced on both sides is the process of solving a system of equations.
Finding the value of the variable that makes the condition of all the given equations true is how we solve an equation system.
Given the system of equation below:
-2x² + y = -5
y = -3x² +5
Substitute equation 2 into 1 to have:
-2x² + (-3x+5) = -5
-2x²-3x² +5 = -5
-2x²-3x² +10=0
-5x² = -10
x² = 10/5
x² = 2
x = ±√2
If x = -√2
y = -3x² +5
y = -3(2) + 5
y = -1
If x = √2
y = -3x² +5
y = -3(2) + 5
y = -1
Hence the solutions to the given system of equations are (-√2, -1) and (√2, -1).
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Finn wants to buy a sweater for $29.50 and jeans for $42.50 if the sales tax rate is 8.25% what will be the amount of cell taxes on finn’s purchase
The amount of cell taxes on finn’s purchase is $5.94.
How to calculate the value of the tax?Since Finn wants to buy a sweater for $29.50 and jeans for $42.50, the total cost will be:
= $29.50 + $42.50
= $72
If the sales tax rate is 8.25%, the amount on tax will be:
= Tax rate × Total cost
= 8.25% × $72
= $5.94
The tax is $5.94.
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Find the area of the circle pictured above.
Round your answer to the nearest tenth
Answer:
153.9 units squared
Step-by-step explanation:
A = pi*r^2
A = pi* 7^2
A = pi* 49
A = 153.9
Write an equation of the line passing through the point $A\left(-6,\ 5\right)$ that is parallel to the line $y\ =\ \frac{1}{2\ }x-7$
.
The equation of the line through the point (-6,5) and parallel to the line is y=[tex]\frac{1}{2}[/tex]x-7 is y=[tex]\frac{1}{2}[/tex]x+8.
What is equation of line ?
Any location with an x and y axis can have a line equation constructed using the slope of the line. To build a line with a certain point, one uses the equation for a straight line. Any two points can be used to find the slope. Slope is the part of a straight line that is steep.
Here the given equation is y=[tex]\frac{1}{2}[/tex]x-7
We know that equation of line is y=mx+c , where m = slope.
Then slope of given line is m= 1/2 . Now the line is parallel to given line so slope of the equation is also equal.
=> slope m=1/2.
Now the given point [tex](x_1,y_1)=(-6,5)[/tex] .
Using equation of the line is ,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-5 = 1/2(x+6)
=> 2y-10=x+6
=>2y=x+16
=>y=[tex]\frac{1}{2}[/tex]x+8
Hence the equation of the line is y=[tex]\frac{1}{2}[/tex]x+8.
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I really need help on this question to so here’s a
A total of 123 fifth grade students are going to Fort Verde State historic Park. Each bus host 38 students all of the bus harmful except one. How many students will be in the bus that is not full.
Whoever is going to be answering this question, please give me a valid answer and show your work
Answer: 9 students will be on a bus that is not full
Step-by-step explanation:
123/38 = 3.23684210526 = 3 bus that is full.
38 x 3 = 114, 123 - 114 = 9
So, 9 students will be on a bus that is not full while the other 3 bus will be full of students.
Answer:
there will be nine students in the bus that is not full.
Step-by-step explanation:
if each bus holds 38 in your first bus you have 38 and then there are 85 students left so in the second bus there are also 38 and you should have 47 students left that need to go in a bus so then again in bus 3 there are also 38 which means in the fourth/last bus there are only 9 students left
1. Giuseppe is 74 inches tall, and Raymond is 6 feet 1 inch tall. Who is
taller? Explain.
Answer: Giuseppe is taller.
Step-by-step explanation:
Giuseppe is 74 inches tall, and we know that 12 inches is one foot, so 74/12 is ~6.1677777... versus 6.1.
Another way you can check this is by converting feet to inches. So 6 feet 1 inch would be (6 x 12) + 1 which is ~73.
For what values of x and y are the triangles congruent by HL?
Answer:
Step-by-step explanation:
4x maybe
please help me find the zero of y=-5x+5
Answer:
1
Step-by-step explanation:
To find the zero of an equation you set the equation equal to 0
That means you do this:
-5x+5=0
Then you solve for x
-5x=-5
x = -5/-5
x= 1
Solve :
22r^2+1144r-7656=0
a bag contains 10 red marbles, 5 white marbles, and 6 blue marbles. you draw 5 marbles out at random, without replacement. what is the probability that exactly two marbles are red?
The probability that exactly two marbles are red, is 0.365.
In the given question we have to find the probability that exactly two marbles are red.
A bag contains 10 red marbles, 5 white marbles, and 6 blue marbles.
Total marbles is
10+5+6=21
We draw 5 marbles out at random, without replacement.
Marbles taken out =5
Total possibility of taking 5 marbles out of 21 marbles is [tex]^{21}C_{5}[/tex].
Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
So [tex]^{21}C_{5}=\frac{21!}{5!(21-5)!}[/tex]
[tex]^{21}C_{5}=\frac{21!}{5!16!}[/tex]
[tex]^{21}C_{5}=\frac{21\times20\times19\times18\times17\times16!}{5\times4\times3\times2\times1\times16!}[/tex]
Simplifying
[tex]^{21}C_{5}[/tex] =7×19×9×17
[tex]^{21}C_{5}[/tex] = 20,349
Probability of exactly two marbles are red is
Possible out comes of exactly two red marbles equal to 2 red and other color marble 3.
Total red marbles are 10. So [tex]^{10}C_{2}[/tex]
The remaining marble except red marble is 11. So [tex]^{11}C_{3}[/tex]
[tex]=^{10}C_{2}\times^{11}C_{3}[/tex]
Simplifying
[tex]=\frac{10!}{2!(10-2)!}\times\frac{11!}{3!(11-3)!}[/tex]
[tex]=\frac{10!}{2!8!}\times\frac{11!}{3!8!}[/tex]
[tex]=\frac{10\times9\times8!}{2\times1\times8!}\times\frac{11\times10\times9\times8!}{3\times2\times1\times8!}[/tex]
=5×9×11×5×3
=7,425
So the probability that exactly two marbles are red
P(R)=7,425/20,349
P(R)=0.365
Hence, the probability that exactly two marbles are red, is 0.365.
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Write down the factors of 28 Then,write down the prme factors of 28
the factors of 28 are : 1, 2, 4, 7, 14, and 28.
the prime factors of 28 are : 2, 2, and 7.