Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
We know that there's a probability of [tex]p=\frac{40}{50}=\frac{4}{5}=0.8[/tex] of choosing an electronic component that is not defective and a probability of [tex]q=\frac{10}{50}=\frac{1}{5}=0.2[/tex] of choosing an electronic component that is defective:
[tex]\displaystyle P(X\geq4)=P(X=4)+P(X=5)+P(X=6)\\\\P(X\geq4)=\binom{6}{4}(0.8)^4(1-0.8)^{6-4}+\binom{6}{5}(0.8)^5(1-0.8)^{6-5}+\binom{6}{6}(0.8)^6(1-0.8)^{6-6}\\\\P(X\geq4)=\frac{6!}{4!(6-4)!}(0.8)^4(0.2)^2+\frac{6!}{5!(6-5)!}(0.8)^5(0.2)^1+\frac{6!}{6!(6-6)!}(0.8)^6(0.2)^0\\ \\P(X\geq4)=0.90112[/tex]
So, if 6 components are drawn at random from the container, the probability that at least 4 are not defective is 0.90112
Problem 2
[tex]\displaystyle P(X=3)=\binom{8}{3}(0.2)^3(1-0.2)^{8-3}\\\\P(X=3)=\frac{8!}{3!(8-3)!}(0.2)^3(0.8)^5\\ \\P(X=3)\approx0.1468[/tex]
So, if 8 components are drawn at random from the container, the probability that exactly 3 are defective is 0.1468
The probability of exactly 3 of the containers being defective is given as 0.1468
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
to solve for the probability
We have to set p as the probability of container being non- defective
We have p as the probability of container being defective 50 - 10 = 40
p = 40/50
= 0.8
q = 10/50
= 0.2
P(3) = 8c3 * 0.2² * 0.8⁵
= 0.1468
Hence the probability that the container has exactly 3 defective containers is 0.1468
Read more on probability here:
brainly.com/question/24756209
#SPJ7
What is the axis of symmetry of h(x) = 5x2 40x 64?
The axis of symmetry of h(x) = 5x2 + 40x + 64 = -4
The formula for calculating the axis of symmetry is expressed as:
Axis of symmetry x = -b/2a
h(x) = 5x^2 + 40x + 64
a = 5 and b = 40
find the slope of a line perpendicular to the line containing (-5,-3) and (10,2)
Answer:
slope = 1/3
Step-by-step explanation:
slope,m = vertical change/ horizotal change
that means (-3)-2/(-5)-10 or 2-(-3)/10-(-5)
and we got -5/-15 or 5/15.
So the answer is 1/3.
Find the equation
of the line
that goes through (-3,4) and
(6,7) in the form of y=mx+b.
Answer:
y = (1/3)*x + 5
Step-by-step explanation:
Step 1: determine slope or m
m = change in y-coordinates ÷ change in x-coordinates
m = (4-7)/(-3-6) = -3/-9 = 1/3
Step 2: determine y-intercept or b
y = m*x + b
y = (1/3)*x + b
4 = (1/3)*(-3) + b
4 = -1 + b
b = 5
Step 3: substitute values for m and b into the slope intercept equation
y = (1/3)*x + 5
solve/answer the question and help me understand this question please
thank you to all user that will help me!
Answer:
5.25 m
Step-by-step explanation:
A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.
__
understanding the directionIn navigation problems, direction angles are specified a couple of different ways. A bearing is usually an angle in the range [0°, 360°), measured clockwise from north. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...
N 35° E . . . . . . . 35° east of north
Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.
the two vectorsA vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;
magnitude∠directionmagnitude cis directionIn the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.
Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.
__
The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.
The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.
vector sumThe final position is the sum of these two changes in position:
3∠0° +2.5∠35°
Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:
= 5.24760∠15.8582°
This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)
__
You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...
a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°
Using the values we know, this becomes ...
a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373
a = √27.5373 = 5.24760 . . . . meters
The distance from the original position is about 5.25 meters.
_____
Additional comment
The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...
(0, 3) +(1.434, 2.048) = (1.434, 5.048)
The distance can be found using the Pythagorean theorem:
OB = √(1.434² +5.048²) ≈ 5.248
Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case. ( pls answer fast )
Answer:
95
Step-by-step explanation:
The smallest number that divided by 6, 15, and 18 leavses 5 in each case is 95
(THIS IS IMPORTANT!!! I NEED RIGHT NOW)
The table below shows the linear relationship between the number of weeks since birth and the weight of Samuel’s pet rabbit. Based on the table, what is the rate of change of the weight of the rabbit in pounds per week? Write your answer as a whole number or a decimal.
Based on the table, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.
How do explain the linear relationship?In the first week, there's 9.5 pounds. This can be illustrated using the arithmetic progression. The formula will be:
= a + (n - 1)d
where,
a = first term
d = common difference
3rd term = a + 2d
13 = 9.5 + 2d
2d = 13 - 9.5
2d = 3.5
d = 3.5/2
d = 1.75
Therefore, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.
Learn more about rate on:
https://brainly.com/question/25537936
#SPJ1
An airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). What is the total number of miles it flies? Each unit represents 1 mile.
Answer:
The airplane flies 95 miles.
Step-by-step explanation:
First we need to find the distance for the first segment using the formula for distance [tex]D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}[/tex]. Let's say [tex](x_{1},y_{1})[/tex] is (0, 0) and [tex](x_{2},y_{2})[/tex] is (33, 56). This gets us that the length of this segment is 65 miles.Next, we need to find the distance for the second segment. Using the same formula for distance [tex]D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}[/tex], we can say [tex](x_{1},y_{1})[/tex] is now (33, 56) and [tex](x_{2},y_{2})[/tex] is now (23, 32). This gets us that the length of this segment is 26 miles.To get the total distance traveled, add the length of these two segments together (65 miles + 26 miles) to get 91 total miles traveled.Question:
An airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). What is the total number of miles it flies? Each unit represents 1 mile.
Answer:
The plane flew 91 miles.
Step-by-step explanation:
City 1 - City 2
---------------------------------------------------------------------------------------------------------
[tex]d_{1}[/tex] = [tex]\sqrt{(33 - 0)^{2} + (56 - 0)^{2}[/tex]
[tex]d_{1}[/tex] = [tex]\sqrt{33^{2} + 56^{2}[/tex]
[tex]d_{1[/tex] = [tex]\sqrt{1089 + 3136[/tex]
[tex]d_{1}[/tex] = [tex]\sqrt{4225}[/tex]
[tex]d_1[/tex] = [tex]65[/tex]
---------------------------------------------------------------------------------------------------------
City 2 - City 3
[tex]d_2[/tex] = [tex]\sqrt{(33 - 23)^2 + (56 - 32)^2[/tex]
[tex]d_2[/tex] = [tex]\sqrt {10^2 + 24^2}[/tex]
[tex]d_2[/tex] = [tex]\sqrt{676}[/tex]
[tex]d_2[/tex] = 26
---------------------------------------------------------------------------------------------------------
[tex]d_1 + d_2 = 65 + 26[/tex]
[tex]d_1 + d_2 = 91[/tex]
---------------------------------------------------------------------------------------------------------
Therefore, the airplane flew a total of 91 miles through every city
---------------------------------------------------------------------------------------------------------
Key words: the airplane, 91 miles, through, every, city, flies, City 1, City 2, City 3, total, number, unit, represent, mile.
<3 Lots of love!
-The Book Worm.
hi can someone help me
Step-by-step explanation:
mean value is always the sum of all data divided by the number of data points.
we can see just by looking at the numbers that team B is way below team A.
mean team A : 1529/8 = 191.125
mean team B : 1141/8 = 142.625
so, clearly, team B had to make dinner.
the median is the value of all the data points, where half of the others are smaller, and the other half are bigger.
in case of an even number of data points (like here with 8), we find the 2 middle values and calculate the mean value of these 2 :
median team A : (180+189)/2 = 184.5
median team B : (143+134)/2 = 138.5
the mode is the number in the set of data that occurred must often. if they are all unique, then they ALL are the mode. it is NOT 0 or empty. it is then really all the data points.
mode team A : 212
mode team B : 99, 102, 105, 134, 143, 145, 202, 211
PLS I NEED 100% TO GET A GOOD MATH GRADE THIS YEAR
The following box plot shows the number of years during which 24 schools have participated in an interschool swimming meet:
At least how many schools have participated for 1 year or less? (5 points)
6 schools
8 schools
12 schools
14 schools
1 year or less is at the first quartile mark in the box plot, therefore, the number of schools that participated for a year and less is: A. 6 schools.
What is the First Quartile of a Data Represented in a Box Plot?The data point at the beginning of the edge of the rectangular box in a box plot is the first quartile mark of the data, which is 1/4 or 25% of the data.
1 year or less is at the first quartile mark in the box plot. That is 1/4 of the total number of schools.
Therefore, schools that participated for a year and less = 1/4(24) = 6 schools.
Learn more about the first quartile on:
https://brainly.com/question/10005803
#SPJ1
a man drove 180 km in 2 hours what was his speed
speed = distance/time
speed = 180/2
speed = 60km/hr
hope it helps...!!!
If f(x)=5x-4, what is the value of f(3)?
Answer:
11 hope this helps you and write
Find two numbers such that their product is four and the sum of their squares is seventeen.
The system of equations of two unknowns is formulated and solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ x\times y = 4 \\ x^2+y^2 = 17 \end{matrix}\right. \ \Longrightarrow \ y=\dfrac{4}{x}} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+\left (\dfrac{4}{x} \right )^2=17\ \Longrightarrow\ x^4+16=17x^2 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{align*} 0&=(x^2)^2-17(x^2)+16\\ =(x^2-16)(x^2-1) \\ \ \ \ \ \ \ \ \ \ \ =(x+4)(x-4)(x+1)(x-1) \end{gathered}$}[/tex]
Possible number pairs are 4, 1 and -4, -1 .
write an equation of the line that passes through (-6, 6) and is parallel to the line y = -2x + 2.
Answer:
y = -2x - 6
Step-by-step explanation:
We know that the slopes of the lines are equal when the lines are parallel to each other.
So, the equation of the given line is y = -2x + 2.
Here,
y = mx + c
y = -2x + 2
slope ⇒ m ⇒ -2
Therefore, the slope of the new line will be ( - 2 ).
And now we have to find the y-intercept ( c ).
For that let us use the given coordinate.
( -6 , 6 ) ⇒ ( x , y )
To find the y-intercept we have to make c the subject of the equation y mx + c.
Also, we have to replace m with ( - 2 ) as the slope of the new line is -2.
Let us solve it now.
y = m x + c
6 = -2 × -6 + c
6 = 12 + c
6 - 12 = c
-6 = c
Now we have found that,
m ⇒ - 2
c ⇒ -6
And now let us write the equation of the line.
y = m x + c
y = -2x - 6
How do I solve this?
a) Recall the integration by parts formula:
[tex]\displaystyle \int u \, dw = uw - \int w \, du[/tex]
Then with [tex]u = x[/tex] and [tex]dw = e^x\,dx[/tex] we have
[tex]\displaystyle v = \int e^x x \, dx = xe^x - \int e^x \, dx[/tex]
[tex]\implies \boxed{v = xe^x - e^x + C}[/tex]
since [tex]w=\int e^x\,dx=e^x[/tex] and [tex]du=dx[/tex]. (C is of course an arbitrary constant that can be determined exactly if you know the velocity at some given value of x.)
b) No?
[tex]\displaystyle \int e^xx\,dx = \int xe^x\,dx[/tex]
because multiplication is commutative. I get the feeling I'm missing something here...
You are invited to a family gathering to celebrate the "Happiness day" and you are in charge
of bringing the sweets. And since "you can't buy happiness, you can buy a Polar Pizza from
Baskin Robbins and that's kind of the same thing". You contact Baskin Robbins to provide
you with the cost of Polar Pizza per in² so you can decide which Polar Pizza size is the
best deal.
Baskin Robbins Polar Pizzas come in two different sizes as listed below.
Size
Price
Diameter
Large
$12
Medium
$10
12 inches
14 inches
1. In the table below, find the area of each pizza and the cost per in². Show your work.
Answer:
first one
Step-by-step explanation:
because its cheap as for 1 NM it would be 10$ which is 2.5 AED so yehh
Help asap!!!! WILL MARK BRAINLIEST
Step-by-step explanation:
un is the balance of the loan after n years.
so,
u12 is the balance of the loan after 12 years.
A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees. At some later time, Luis takes another measurement and finds the angle of depression to the boat (now at point B) to be 39 degrees. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Help pls serious answers only!!! HW DUE TODAY! pls show steps ;-;
Using the slope concept, it is found that the distance from point A to point B is of 465 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
To find the horizontal position at point A, we have that:
tan(10º) = 107/dA
dA = 107/tan(10º)
dA = 607.
For the horizontal position at point B, we have that:
tan(37º) = 107/dB
dB = 107/tan(37º)
dB = 142.
Hence the distance is given by:
D = dA - dB = 607 - 142 = 465.
More can be learned about the slope concept at https://brainly.com/question/18090623
#SPJ1
10) Eve has a fall job to pick pumpkins at the farm.
She earns $4.00 every 12 minutes that she picks pumpkins.
• She earns $4.40 every 12 minutes that he picks apples.
• She picked pumpkins for an hour and apples for 48 minutes.
How much money did Eve earn?
For pumpkins
Total 12mins sets
1hr/12min60min/12min5earnings
4(5)$20.00For apples
Total 12 mins
48/124Earnings
4(4.40)$17.60Total earnings
20.00+17.60$37.60Answer:
$37.60
Step-by-step explanation:
Eve earns:
$4.00 per 12 minutes spent picking pumpkins$4.40 per 12 minutes spent picking applesMoney earned from picking pumpkins:
1 hour = 60 minutes
[tex]\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 60\:minutes\\\\& = \sf \$4.00\:per\:12\:minutes \times 60\:minutes\\\\& =\sf \dfrac{\$4.00}{12\:minutes} \times 60\:minutes\\\\ & = \sf \$4.00 \times \dfrac{60\:minutes}{12\:minutes}\\\\ & = \sf \$4.00 \times 5\\\\ & = \sf\$20.00\end{aligned}[/tex]
Money earned from picking apples:
[tex]\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 48\:minutes\\\\& = \sf \$4.40\:per\:12\:minutes \times 48\:minutes\\\\& =\sf \dfrac{\$4.40}{12\:minutes} \times 48\:minutes\\\\ & = \sf \$4.40 \times \dfrac{48\:minutes}{12\:minutes}\\\\ & = \sf \$4.40 \times 4\\\\ & = \sf\$17.60\end{aligned}[/tex]
Total earned:
= money earned from picking pumpkins + money earned from picking apples
= $20.00 + $17.60
= $37.60
n music, a quaver is one-eighth of a semibreve (whole note). What fraction of a semibreve is a hemidemisemiquaver? (Hint: hemi-, demi-, and semi- are prefixes each of which represents a multiplication by one-half).
Answer:
[tex]\dfrac{1}{64}[/tex]
Step-by-step explanation:
Hemi-, demi- and semi- are prefixes which mean half.
When applied to musical notation, each time a prefix is added it means the note's value is halved.
Therefore, if a quaver is one-eighth of a semibreve, then a semiquaver is half of a quaver, which means it's one-sixteenth of a semibreve.
[tex]\large \begin{aligned}\sf quaver & = \sf\dfrac{1}{8}\:of\:a\:semibreve\\\\\implies \sf hemisemidemiquaver & = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times quaver\\\\& = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{8}\\\\& = \sf \dfrac{1}{64}\:of\:a\:semibreve\end{aligned}[/tex]
Therefore, a hemisemidemiquaver is one-sixty-fourth of a semibreve.
when factoring the following trinomial,you need two numbers that multiply to equal "-24" and add to "-10" choose the two correct numbers
6
-8
-3
4
-6
-4
12
3
8
-2
-12
2
Answer:
-12 and 2
Step-by-step explanation:
-12 × 2 is -24
and
-12 + 2 is -10
Solve for X. Round to the nearest tenth.
IMAGE ABOVE
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER
Answer:
x ≈ 95.6
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides of a right triangle. Here, the hypotenuse of the triangle and the side adjacent to the given angle are marked, so the relationship of choice is ...
Cos = Adjacent/Hypotenuse
__
Using the values shown, we have ...
cos(15°) = x/99
Solving for x gives ...
x = 99·cos(15°) ≈ 95.6
The length of the side marked x is about 95.6 units.
the situation.
Sheryl makes $7 per pair of
earrings, e, and $13 per necklace,
n, she sells. What expression
represents her total income?
The expression which represents Sherly's total income is 7e + 13n.
What is Cost Price?The cost price represents the specific value that represents unit price purchased.
Here,
total pair of earrings = e
total pair of necklaces = n
Cost of 1 pair of earring = $ 7
Cost of 1 necklace = $ 13
earning from earring = 7e
earning from necklace = 13n
Total earning = earning from earring + earning from necklace
Total earning = 7e + 13n
Thus, the expression which represents Sherly's total income is 7e + 13n.
Learn more about Cost Price from:
https://brainly.com/question/17716968
#SPJ1
I need help asap please? and this is for the math question? what is the missing side and exterior angle of the triangle?
Answer:
the missing angle is 30 and the missing exterior angle is 150
Step-by-step explanation:
180-90=90-60=30
180-30=150
Answer: Exterior angle = 150 degrees
Step-by-step explanation:
Hope that helps!
:)
what is the center of the circle given by the equation (x-2)2+(y+4)2=6
Answer:
(2,-4)
Step-by-step explanation:
Here, h=2 and k=-4, so the center is (2,-4)
Gabby is a makeup artist and carries a lot of makeup around with her. she has 20 cosmetics in her bag, including 4 eye shadows. what is the probability that a randomly selected makeup item from her bag will be an eye shadow? write your answer as a fraction or whole number.
The probability that a randomly selected makeup item from her bag will be an eye shadow is 1/5 or 20%.
The probability of selecting an eye shadow from Gabby's bag can be calculated by dividing the number of eye shadows in the bag by the total number of cosmetics in the bag.
There are 4 eye shadows in Gabby's bag, and a total of 20 cosmetics. Therefore, the probability of selecting an eye shadow is:
P(eye shadow) = 4/20 = 1/5
This means that there is a 1 in 5 chance, or a 20% chance, that a randomly selected makeup item from Gabby's bag will be an eye shadow.
The probability can be expressed as a fraction or a whole number, depending on the context of the problem. In this case, we can express the probability as the fraction 1/5, which means that out of 20 possible cosmetics, only 4 are eye shadows.
We can also express the probability as the whole number 0.2 or 20%, which represents the proportion of eye shadows in Gabby's bag.
To learn more about probability click on,
https://brainly.com/question/16245115
#SPJ1
solve y=mx+b for x
please help me
Answer:
x = (y - b)/m.
Step-by-step explanation:
y=mx+b
Subtract b from both sides :-
y - b = mx
Divide both sides by m:-
(y - b) /m = x.
A pool is being filled with water. First, 14 liters are poured into the pool. Then, another 7 liters are poured into the pool.
How many liters of water are poured into the pool in all?
Enter your answer in the box.
Answer:
21 liters
Step-by-step explanation:
14 liters + 7 liters = 21 liters
Hope this helped :)
Triangle ABC has perimeter 22 cm.
AB = 8 CM
BC = 5cm
By calculation, deduce whether triangle ABC is a right-angled triangle.
Answer:
Triangle ABC is not a Right Triangle
Step-by-step explanation:
The perimeter of a triangle is all of the sides added together so we can model our equation like so:
AB + BC + CA = P
or
8 + 5 + CA = 22
We first combine like terms
13 + CA = 22
Then make the variable have no numbers on its side
13 + CA = 22
-13 -13
CA = 9
So now that we know what CA is, we can determine whether or not its a right triangle
We can use the Pythagorean Theorem for this:
a^2 + b^2 = c^2 (the '^' symbol means 'to the power of')
or
5^2 + 8^2 = 9^2
Now we Solve
5^2 = 25
8^2 = 64
9^2 = 81
25 + 64 =? 81
89 does not equal 81
So Triangle ABC is not a Right Triangle
El 62% de las personas de una fiesta son mujeres y hay 95 hombres, ¿cuantas mujeres hay en la fiesta?
find the missing length??
Answer:
? = x = 12
Step-by-step explanation:
Remark
This is a proportion question. A proportion is 2 equal ratios. The two triangles are similar, which means that a proportion can be set up.
Givens
? = x
x + 8
9
9 + 6
Equation
x/(x + 8) = 9 / (9 + 6) Combine
Solution
x/(x + 8) = 9/15 Cross multiply
15x = 9(x + 8) Remove the brackets
15x = 9x + 72 Subtract 9x from both sides
15x - 9x = 72 Combine
6x = 72 Divide both sides by 6
6x/6 = 72/6
x = 12
Answer x = 12