The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 9.8% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 9.8% of his customers buy a magazine is correct, what is the probability that exactly 5 out of the first 10 customers buy a magazine? a) 0.00136008 b) 0.000796803 c) 0.002090 d) 0.00142299 e) 0.000882963 f) 0.000404963
Answer:
a) 0.00136008
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of any other customer. Thus, the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
9.8% of his customers buy a magazine
This means that [tex]p = 0.098[/tex]
What is the probability that exactly 5 out of the first 10 customers buy a magazine?
This is [tex]P(X = 5)[/tex] when [tex]n = 10[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{10,5}.(0.098)^{5}.(0.902)^{5} = 0.00136008[/tex]
Thus, the correct answer is given by option A.
why mathematical induction is used ?(write a 100 words paragraph)
Answer:
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers ( non-negitive integers). The simplest and most common form of mathematical induction proves that a statement involving a natural number that holds for all values.
WILL GIVE BRAINLIEST IF CORRECT (Right angle) Trigonometry please help! Explain what you did to get the answer aswell
Hello please help me solve this inequality shown in the graph, thank you so much!
Using the equation y=kx and the table below, find the constant of proportionality (k).
Answer:
k = 9/4
Step-by-step explanation:
To find k, use the equation
y = kx
Pick a point
72 = k *32
Divide each side by 32
72/32 = k
9/4 = k
Answer:
k = 9/4
Step-by-step explanation:
Here , we have given equation and we need to find k.
To find k, we have given equation which is y = kx
pick any point from the table and substitute in the equation.
y = kx
We choose :- x = 8 and y = 18
18 = 8 × k
Divide each side by 8
18/8 = k
9 / 4 = k
The price of admission to a World War I history museum is $8.29 for adults and $6.47 for children. A family of 2 adults and 4 children visits the museum. What is the total cost, in dollars, of admission?
Answer:
cost for adults=$8.29
cost for children=$6.47
cost for 2 adults and 4 children are =$(2×8.29)+(4×6.47)=$16.58+25.88=$42.46
A chain weighs 10 pounds per foot. How many ounces will 3 inches weigh?
Answer:
40 ounces
Step-by-step explanation:
One foot = 12 inches
3 inches is 1/4 of a foot
Divide 10 pounds by 4 to get 2.5 pounds
Convert to ounces
Austin was budgeted $ 825 to spend on chairs for his upcoming event. If each chair costs $ 15 , how many chairs can he purchase?
Answer:
55 chairs
Step-by-step explanation:
825/15=55
Use the graph below to determine the equation of the circle in a center radius form and a general form
Don’t save the answer and I really need help
9514 1404 393
Answer:
zero solutions
Step-by-step explanation:
The first inequality has a boundary line with a slope of 3 and a y-intercept of 9. Shading is above the boundary line.
The second inequality has a parallel boundary line with a slope of 3 and a y-intercept somewhat lower, at -1. Shading is below this boundary line.
There is a gap between the shaded areas, so no points will be solutions to both inequalities.
A machine cuts dry wall screws with specifications such that the length of each screw is 1.25 inches with an allowable margin of error of 0.02 inches. Use this information to complete each statement.
Answer:
[tex](a)\ x = 1.25 \± 0.02[/tex]
[tex](b)[/tex]
[tex]Minimum = 1.23in[/tex]
[tex]Maximum = 1.27in[/tex]
Step-by-step explanation:
Given
[tex]L = 1.25in[/tex] --- Length
[tex]E=0.02in[/tex] -- Margin of error
Solving (a): The equation of the length
This is calculated as:
[tex]x = L \± E[/tex]
So, we have:
[tex]x = 1.25 \± 0.02[/tex]
Solving (b): The range of value of x
In (a), we have:
[tex]x = 1.25 \± 0.02[/tex]
Split:
[tex]x = 1.25 - 0.02[/tex] [tex]x = 1.25 + 0.02[/tex]
Solve for x
[tex]x = 1.23[/tex] [tex]x = 1.27[/tex]
So, we have:
[tex]Minimum = 1.23in[/tex]
[tex]Maximum = 1.27in[/tex]
Evaluate the function.
f(x) = -x2 - 4x - 19
Find f(-9)
Help plsss
Given the quadratic function below:
[tex] \large{f(x)= - {x}^{2} - 4x - 19}[/tex]
To find f(-9), simply substitute x = -9 in the function.
[tex] \large{f( - 9) = - {( - 9)}^{2} - 4( - 9) - 19} \\ \large{f( - 9) = - 81 + 36 - 19} \\ \large{f( - 9) = - 100 + 36 \longrightarrow \large \boxed { \purple{f( - 9) = - 64}}}[/tex]
Answer
f(-9) = -64Let me know if you have any doubts regarding the function.
Please help me with this math problem. Only answer if your sure it’s correct. Pls answer ASAP!
Answer:
Step-by-step explanation:
Using distance formula (search it up, it's BIG) we start by plugging in the coordinates. the second x coordinate minus the first x coordinate is equal to -2 - - 4. You can't subtract a negative from an negative, so you add them. We change it to -2 + + 4 which equals 2. According to the distance formula (look it up), we square that (meaning it's equal to 4) and add it to the y value. The y value is equal to the second y coordinate minus the first y coordinate. This is represented by -3 - 0. This equals -3, but according to the distance formula, we square it which makes it equal to 6. Now, what do we do with the numbers 6 and 4? Following the distance formula, we add them which is equal to 10. Now we are left with the square root of 10 according to the distance formula. Your answer is the square root of 10 or in decimal form, 3.162277......... I hope this helped!
Step-by-step explanation:
hear Is your answer check
Find the surface area of the regular pyramid.
determine the value of a x1-3x3=-3 and 2x1+ax2-x3=-2 has no solution
Answer:
Step-by-step explanation:has no solution
RDTQ is a trapezoid. Find measure of angle R
Answer: 170°
Step-by-step explanation: 8x +34 - (6x-22) =90 ==> 2x +56 =90 ==> x = 17 ==> góc R = 8*17 +34 = 170°
What is the length of the segment XY?
Answer:
xy = 12
Step-by-step explanation:
The Trapezoid Midsegment Theorem states that a line segment connecting the midpoints of the legs of the trapezoid is parallel to the bases, and equal to half their sum.
xy = (8 + 16)/2
xy = 24/2
xy = 12
Solve the system useing elimination 4x+8y=16 6x-8y=4
Answer:
x=2 and y=1
Step-by-step explanation:
Add the two equations to remove "y" and solve for x:
4x+8y=16
6x-8y=4
________
10x=20
x=2
Plug x=2 into one of the original equations to get the value of "y":
4x+8y=16
4(2)+8y=16
8+8y=16
8y=8
y=1
Therefore, x=2 and y=1
3. Pedro used of a 33 ounce bottle of
soap to wash his mother's car. How
many ounces of soap did Pedro use?
A 22 ounces
C 28 ounces
B 20 ounces
D 30 ounces
Answer:
question unclear
Step-by-step explanation:
this is unclear I have no idea what this
Answer:
I would say D
Step-by-step explanation:
if there was a 33 oz. bottle and Pedro uses it all for the car, maybe the other 3 oz is from the actual container and not the liquid inside.
Which of the following represents the factorization of the polynomial below? 2x^2+5x+3
Answer:
(2x + 3)(x + 1)
Step-by-step explanation:
you didn't show them, the factors are
(2x + 3)(x + 1)
Answer:
[tex](x+1)(2x+3)[/tex]
Step-by-step explanation:
[tex]2x^{2} +5x+3[/tex]
[tex]2x^{2} +3x+2x+3[/tex]
[tex]x(2x+3)+2x+3[/tex]
[tex](x+1)(2x+3)[/tex]
During a football game, a team lost 9 yards on the first play, then gained 3 yards on each of the next 3 plays. Which
integer represents the total number of yards at the end of the first four plays?
оооо
9
18
Simplify the radical completely.
Answer:
D
Step-by-step explanation:
But basically, one by one you try moving the terms out of the radical.
75 is also 25 * 3 and since 25 has a perfect square root of 5 that goes out and 3 stays inside the radical.
x^3 is also x^2 * x and since x^2 has a perfect square root which is just x that goes outside while the remaining x stays inside.
y^9 is also y^8 * y and since we move variables out the radical in twos y^ goes outside the radical and y stays inside alone.
Finally, z is just z it can't be taken out so it stays inside the radical.
Hope that helps!
What is the range and domain of the set? :R: {(−11, 16), (17, 23), (2, -13), (7, 4), (-7, −21)}
Step-by-step explanation:
the range is the biggest number subtracted by the smallest 23-(-11)= 34
if a =(2/3)and m is any scalar find ma
Answer:
[tex]ma = \frac{2m}{3}[/tex]
Step-by-step explanation:
Multiplication of an scalar by a fraction:
We consider the multiplication of a fraction by a symbolic scalar the same as the multiplication of a fraction by any other numbers, that is, multiplication of the numerators divided by the multiplication of the denominators.
In this question:
Fraction 2/3
Scalar m
[tex]\frac{2}{3} \times m = \frac{2m}{3}[/tex]
So
[tex]ma = \frac{2m}{3}[/tex]
The sum of two numbers is zero. When 10 times the smaller number is added to 6 times the larger, the result is 3. Find the two numbers.
Answer:
3/4 and -3/4
or
0.75 and -0.75
but there is no solution for
10 times the smaller number added to 6 times the larger number to get 3 as result.
the absolute values of x and y must be equal and with opposite signs (due to their sum being 0).
therefore, 10 times the negative value can never be compensated by 6 times the same but positive value. the sum will always be negative and not positive (and therefore not +3).
it only works with 10 times the larger (positive) number plus 6 times the smaller (negative) value.
Step-by-step explanation:
x + y = 0
10×x + 6×y = 3
=>
x = -y
10×(-y) + 6×y = 3
-10y + 6y = 3
-4y = 3
y = -3/4
=>
x = -y = -(-3/4) = 3/4
control :
10×(3/4) + 6×(-3/4) = 30/4 - 18/4 = 3
12/4 = 3
3 = 3
correct
what is 300+45-9x2+22-1+2
Answer:
350
Step-by-step explanation:
Use PEMDAS.
[tex]300+45-9*2+22-1+2[/tex]
300+45-18+22-1+2
345-18+22-1+2
327+22-1+2
349-1+2
348+2
350
Express it in slope-intercept form.
Answer:
y = 1/4x - 4
Step-by-step explanation:
The slope is four points behind the origin, so we subtract -4 from the equation:
y = 1/4x - 4
use two points on the line to find the slope:
(0,-4) (4,2)
Slope = change in y over change in x
Slope = (2 - -4) / (4-0) = 6/4 = 3/2
Y-intercept is the y value when x is 0, the line goes through y=2 at x = 0, so the t intercept is 2
The equation is:
Y = 3/2x + 2
I’ll mark brainliest
Answer:
D
Step-by-step explanation:
Hi there!
We're given the equation y=-75x-50, which represents a submarine DESCENDING towards the ocean floor, where y is the depth in feet, and x is the number of minutes the submarine is descending
Since the submarine is DESCENDING, we can immediately eliminate A and C, which talk about the submarine ASCENDING
That leaves B and D
Looking at the given equation, y=-75x-50, -75 is the slope, or rate of change, and -50 is the y intercept, or the "beginning" (where the equation will "start")
Therefore, the submarine will start at -50 feet, or 50 feet below sea level
As x is the number of minutes the submarine is descending, that means that if the submarine travels 1 minute, it will descend 75 feet (-75*1=-75), at 2 minutes, it'll descend 150 feet (-75*2=-150), and so on
So that means the submarine must be descending at a rate of 75 feet per minute
Therefore D is the correct answer
Hope this helps! Good luck on your assignment :)
[50 POINT QUESTION]
FInd the area of the trapezoids.
Answer:
7.5
Step-by-step explanation:
Take the figure apart to make one rectangle and 2 triangles.
the rectangle with the endpoint T has a width of 3 and a height of 1.
The Area for the rectangle is A = wl = 3 * 1 = 3
The first, smaller triangle with points R and A has a height of 3 and a base of 1.
The Area for the triangle is A = h b/2 = 3 * 1/2 = 1.5
The large triangle with points T and P has a height of 3 and a base of 2.
Using the same formula for the Area of a triangle you get 3
Now add all areas together
3+1.5+3 = 7.5
Mary plants roseas in 1/4 of her garden. She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. What fraction of Mary's garden has tulips?
Let x represent the full area if Mary's garden.
Mary plants roses in 1/4 of her garden. This means that the portion of the garden on which she planted roses would be 1/4 × x = x/4
She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. This means that the portion if the garden that she has left to plant more flowers would be 1/12 × x = x/12
The portion of the garden on which she planted tulips would be
x - (x/4 + x/12) = x - (3x + x)/12 = x - 4x/12
x - x/3 = (3x - x)/3 = 2x/3
Therefore, the fraction of Mary's garden that has tulips would be
(2x/3) /x = 2/3