Answer:
0.15
Step-by-step explanation:
What we can use to solve this problem is the Bernoulli approximation of the Binomial distribution.
When we say at most 3, it means 0 or 1 or 2 or 3 people out of the 13 made the purchase
Mathematically, the Bernoulli approximation is applied as follows
P(X = n) = nCr p^r q^n-r
let p = probability of making online purchase = 0.41
while q = 1-p = 1-0.41 = 0.59 which is the probability of not making an online purchase.
Mathematically for each of the approximations up to 3, we have ;
13C0 P^0 q^13 + 13C1 P^1 q^12 + 13C2 P^2 q^11 + 13C3 P^3 q^10
Making substitutions, we have
{1 * 0.41^0 * 0.59^13} + {13 * 0.41^1 * 0.59^12} + {78 * 0.41^2 * 0.59^11} + {286 * 0.41^3 * 0.59^10}
= 0.150820944904 which is 0.15 to 2 decimal places
Multiply -3i and it’s conjugate. Simplify.
Answer:
-3 + 9i
Step-by-step explanation:
The conjugate of -3i is - 3 - i.
(- 3 i) × (- 3 - i)
Multiply both terms.
-3 + 9i
The multiplication of the complex number -3i and it’s conjugate 3i is 9.
What is a complex number?A complex number is characterized by an ordered pair of numbers, the real and imaginary parts. It can be represented in multiple ways such as Standard form(rectangular form), Polar form, Exponential form.
For the given situation,
The complex number is -3i.
The conjugate of a complex number a+bi is a-bi.
So, the conjugate of a complex number [tex]-3i[/tex] is [tex]3i[/tex]
Now multiply -3i and 3i, we get
⇒ [tex](-3i)(3i)[/tex]
⇒ [tex]-9(i^{2} )[/tex]
⇒ [tex]-9(-1)[/tex] [∵ [tex]i^{2}=-1[/tex]]
⇒ [tex]9[/tex]
Hence we can conclude that the multiplication of the complex number -3i and it’s conjugate 3i is 9.
Learn more about complex numbers here
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A machine lifts up containers of coal from the mine and lowers empty containers down. The machine uses an electric motor connected to a 600 V d.c. supply.The maximum current in the motor is 4000 A. *Calculate the maximum power available from the motor. Give your answer in MW* power = voltage x current i believe
Answer:
The maximum power available to the motor is 2.4 MW
Step-by-step explanation:
The power of a circuit that has a current, I, and a voltage, V, is given by the relation
Electrical power, P = I²R = I× I×R = I × V
Therefore given that the parameters are;
Voltage in the d.c. power supply = 600 V d.c.
Maximum current in the motor = 4000 A
Therefore, we can find the power as follows;
Maximum motor power = Voltage × Current
The maximum motor power, P available = 600 V × 4000 A = 2400000 W which on converting to MW becomes;
The maximum power available to the motor , P = 2.4 MW.
In 9 minutes, Ivanna can type 36 words. What is her rate in words per minute?
Answer:
4
Step-by-step explanation:
9 divided by 36
Answer:
4 words/minute
Step-by-step explanation:
Since we need words per minute, we divide the number of words by the number of minutes.
words/minute = (36 words)/(9 minutes) = 4 words/minute
Write [tex]3x^{2} -x-3+x^{3}[/tex] in standard form. Identify the leading coefficient.
Answer:
Standard form: [tex]x^3+3x^2-x-3[/tex]
Leading coefficient: 1
Step-by-step explanation:
[tex]3x^2-x-3+x^3=\\x^3+3x^2-x-3[/tex]
The leading coefficient is 1 because the leading term is [tex]x^3[/tex].
What is the explicit formula of -1,-3,-9,-27
Answer:
(-1)* (3)^(n-1)
Step-by-step explanation:
common ratio is 3 and the first term is -1
the explicit formula is a * r^ ( n-1)
i.e., (-1) * 3^(n-1)
Which statements are true about the rules of multiplication for signed numbers? Check all that apply
The product of two negative integers is positive
The product of two integers with different signs is positive
huo numbers are the same sign then the product is positive
The product of a positive and a negative is negative
the signs of two integers are difierent, then the product is positive.
Answer:
see below
Step-by-step explanation:
The product of two negative integers is positive
True -*- = +
The product of two integers with different signs is positive
False - *+ = -
Two numbers are the same sign then the product is positive
True -*- = + and +*+ = +
The product of a positive and a negative is negative
True - * + = - and + * - = -
The signs of two integers are different, then the product is positive.
False - * + = - and + * - = -
Answer:
acd
Step-by-step explanation:
Find the angle of one interior angle in this regular polygon, round your answer to the nearest tenth if possible.
Answer:
144°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 10, thus
sum = 180° × 8 = 1440°
1 interior angle = 1440° ÷ 10 = 144°
factor: (a+3)^2-a(a+3)
Answer:
Factor (a+3)2−a(a+3)
3a+9
=3(a+3)
Answer:
3(a+3)
I hope this help :)
Answer:
(a+3)(3)
Step-by-step explanation:
(a+3)^2-a(a+3)
(a+3)(a+3)-a(a+3)
Factor (a+3)
(a+3)(a+3-a)
(a+3)(3)
The amount of money in Joe’s savings account is increased by 8% each year. Given that he has £500 in 2016. Work out how much Joe will have in 2021.
Answer:
£700
Step-by-step explanation:
First we find the interest on this money.
Interest = Principal * Rate * Time
=[tex]\frac{500 * 8 * 5}{100}[/tex]
=5 * 8 * 5
=£200
Interest = £200
Now you add his actual money to the interest you just found to give you the total amount.
Amount = £500 + £200
= £700
48/60 in its simplelest form
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{48}{60}[/tex]
To simplify find the highest common factor of 48 and 60, that is 12
Divide both values by 12
[tex]\frac{48}{60}[/tex] = [tex]\frac{4}{5}[/tex] ← in simplest form
The fraction is in simplest form when no other factor but 1 divides into the numerator and denominator
the probability of rolling a 6 on a biased dice is 1/5 1) complete the tree diagram. 2) Work out the probability of rolling two sixes.
Answer:
Step-by-step explanation:
Not 6 on all rolls in the diagram = 4/5
6 on all rolls in the diagram is 1/5
To find the probablity of rolling two sixes, 1/5 x 1/5 = 4/100 = 0.04 = 4%
1) The completed tree diagram is attached
2) The probability of rolling two sixes as worked out from the tree diagram is; P(6 | 6) = ¹/₂₅
Since the probability of rolling a six on the first roll is 1/5, then probability of not rolling a six on first roll is;
P(not 6) = 1 - 1/5
P(not 6) = 4/5
A) Please find attached the completed tree diagram
B) First Roll;
P(6) = ¹/₅
P(not 6) = ⁴/₅
Second Roll;
Let's begin with the P(6) Section;
P(6 | 6) = ¹/₅ × ¹/₅ = ¹/₂₅
P(6 | not 6) = ¹/₅ × ⁴/₅ = ⁴/₂₅
Let us now solve for the P(not 6) section;
P(not 6 | 6) = ⁴/₅ × ¹/₅ = ⁴/₂₅
P(not 6 | not 6) = ⁴/₅ × ⁴/₅ = ¹⁶/₂₅
Now, since we are looking for the probability of getting two sixes, it is gotten from the above; P(6 | 6) = ¹/₅ × ¹/₅ = ¹/₂₅
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Yoko flew on a plane from Tokyo to Sydney. The plane flew a distance of 7800 km. The flight time was 9 hours 45 minutes. Work out the average speed of the plane in kilometres per hour.
Answer:
The average speed is 800 km/h
Step-by-step explanation:
The first thing to do here is to completely write the speed in hours.
We have 9 hours 45 minutes
45 minutes in hours is 45/60 = 3/4 = 0.75
So 9 hours 45 minutes = 9.75 hours
The average speed mathematically = Total distance/ Total time
That would be;
7800/9.75 = 800 km/h
6.
(a) Pens cost 36 cents each.
Pencils cost 12 cents each.
(i) Write an expression for the cost of y pens.
Pens = 36y
Pencils 12y
This is because the cost of pens is 36 times however many pens you buy
The Sam Egeos for pencils except it’s 12 cents.
pls help me!!! I WILL GIVE BRAINLIEST!!!!!! probability question
Answer:
B
Step-by-step explanation:
0 to 9 has 10 numbers, and 7 numbers are 0, 1, 2, 3, 4, 5, 6, so the ans is B.
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Hope this helps you...
If the slope of the line joining the points (2k, -2) and (1, - k) be (-2), find k
Answer:
k=4/5
Step-by-step explanation:
(-k+2)/(1-2k) = -2 ( using the slope formula (y2-y1)/(x2-x1) )
-k+2 = -2 (1-2k)
-k+2 = -2 + 4k
2= -2 +5k
4 = 5k
k=4/5
Answer:
k = 4/5Step-by-step explanation:
To find k use the formula for finding the slope of a line and equate it to the slope which is - 2
So we have
(2k, -2) and (1, - k)
[tex] - 2 = \frac{ - k + 2}{1 - 2k} [/tex]
Cross multiply
That's
- 2( 1 - 2k ) = - k + 2
Expand and simplify
- 2 + 4k = - k + 2
Group like terms
4k + k = 2 + 2
5k = 4
Divide both sides by 5
k = 4/5
Hope this helps you
In a right-angled triangle, the hypotenuse is h cmlong aand the other two sides are f cm and g cm in height. Write down a formula which connects f g and h
Answer: f²+g²=h²
Step-by-step explanation:
In a right triangle, you use the Pythagorean Theorem: a²+b²=c² to find the hypotenuse of the triangle. I would believe that you could just substitute the variables in this equation with the ones that you have. This should show the relationship between the 3 unknown lengths of the sides.
Identify any outlier(s) in the data. {76, 78, 63, 70, 64, 90, 65, 28, 66, 83, 74}
Step-by-step explanation:
In my opinion 28
Is an outlier
I don’t understand what this question says, please help :(
Answer:
a(15) = 131
Step-by-step explanation:
Explicit Arithmetic Sequence Formula: an = a1 + d(n - 1)
We are given a1 and d, so plug them in:
an = 5 + 9(n - 1)
To find the 15th term, plug 15 in for n:
a(15) = 5 + 9(15 - 1)
a(15) = 5 + 9(14)
a(15) = 5 + 126
a(15) = 131
Answer:
Step-by-step explanation:
d = 9 ----> d is common difference
[tex]a_{1} = 5\\\\[/tex] ----> first term
In arithmetic sequence, the difference between two terms is constant.
to find nth term,
[tex]a_{n} = a_{1} + (n-1)d\\\\a_{15} = 5 + 14*9\\\\ = 5 + 126\\= 131[/tex]
Liam sits on a merry-go-round at the local fair. He completes 12 revolutions in 4
minutes. What is the period of the ride?
Answer:
1/3 min ( = 20 seconds)
Step-by-step explanation:
The period of the ride is the time he takes to complete 1 revolution
We are given:
12 revolutions -------> takes 4 min
1 revolution ------> takes 4/12 = 1/3 min (= 20 seconds)
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, favorite sports of respondents are identified as 100 for basketball, 200 for baseball, 300 for football and 400 for anything else. The average (mean) is calculated for 740 respondents and the result is 256.1. The data are at the______level of measurement.
Answer:
The data are at the nominal level of measurement
Step-by-step explanation:
Nominal Level of measurement is irrespective of orders or classes. In this survey we do not find out which game is ranked the most favorite.
Nominal; level is used just for counting. Its cannot be used as a measure or for quantitative analysis.
Such data cannot give the mean of the sample. And the two means cannot be compared.
In the given question it only gives the number of likes nothing more. The average cannot be calculated for such data.
Two cards are drawn in succession and without replacement from a standard deck of 52 cards. Find the probability that the second card is a face card if it’s known that the first card was a face card.
Answer:
The probability that the second card is a face card if it’s known that the first card was a face card is 0.0497
Step-by-step explanation:
Total number of face cards = 12
Total cards = 52
Probability of getting face card on first draw=[tex]\frac{12}{52}[/tex]
Remaining no. of face cards = 11
Remaining number of total cards = 51
Probability of getting face card on second draw=[tex]\frac{11}{51}[/tex]
The probability that the second card is a face card if it’s known that the first card was a face card =[tex]\frac{12}{52} \times \frac{11}{51}= \frac{12}{52} \times \frac{11}{51}=0.0497[/tex]
Hence The probability that the second card is a face card if it’s known that the first card was a face card is 0.0497
sin(2x)-tan(x)=cos(2x)tan(x) Please show steps, thank you!
Answer:
Step-by-step explanation:
We're going to leave the right side alone and work on the left side. In other words we are going to use a series of substitutions for these trig idenitites and get the left side manipulated to look like the right side.
Begin with the fact that sin(2x) = 2sin(x)cos(x) and make that first substitution:
2sin(x)cos(x) - tan(x) = right side
Now use the fact that the tangent is the same as the sin over the cos:
[tex]2sin(x)cos(x)-\frac{sin(x)}{cos(x)}[/tex] = right side
Now find a common denominator of cos(x) by multiplying the 2sin(x)cos(x) by cos(x) and writing the whole mess over that common denominator:
[tex]\frac{2sin(x)cos^2(x)-sin(x)}{cos(x)}[/tex] = right side
Now factor out a sin(x):
[tex]\frac{sin(x)(2cos^2(x)-1)}{cos(x)}[/tex] = right side
If we "split" that up and simplify at the same time, we'll see that sin(x) ovr cos(x) is the same as the tan(x), and that 2cos^2 - 1 is the same as cos(2x):
[tex]\frac{sin(x)}{cos(x)}(2cos^2(x)-1)=tan(x)cos(2x)[/tex] and that the left side now is the same as the right side. You MUST learn to recongize these identities. I'll attach a copy that I made and give to my pre-calculus and calculus classes every year, if I am able to.
What the answer question
Answer:
Step-by-step explanation:
UV & UT are the sides
A tree casts a 25 m shadow when the angle of elevation to the sun is
40°. Approximately how tall is the tree?
25 m
A 25 m
B 19 m
C 21 m
D 16 m
Answer:
C. 21 m
Step-by-step explanation:
As shown in the picture, we need to use tan∅ (opposite over adjacent) to solve for the height of the tree:
tan40° = h/25
25tan40° = h
h = 20.9775
h ≈ 21 m
Please answer this fast in 2 minutes
Answer: (4,10)
Step-by-step explanation:
This is the answer because you would have to plug in everything into the midpoint formula and then solve for x2 and y2. Hope this helps! :)
Answer:
(4,10)
Step-by-step explanation:
Drag each tile to the correct location on the table. Match each sentence to the term it’s describing.
Answer:
see below
Step-by-step explanation:
The premium is your cost for the insurance, paid to the insurance company.
The deductible is your cost for a claim, paid to settle your liability.
The limit is the maximum the insurance will pay for a given incident.
Evaluate the piecewise function at the given values of the independent variable. f left parenthesis x right parenthesis equals A left bracket. 5 x plus 4 if x less than 0 2 x plus 6 if x greater than or equals 0 (a) f left parenthesis negative 2 right parenthesis (b) f left parenthesis 0 right parenthesis (c) f left parenthesis 2 right parenthesis
Answer:
a. f(-2) = -6
b. f(0) = 6
c. f(2) = 10
Step-by-step explanation:
The function is given as:
f(x) = 5x + 4 if x < 0
f(x) = 2x + 6 if x ≥ 0
(a) f(-2)
x < 0:
=> f(-2) = 5(-2) + 4
f(-2) = -10 + 4
f(-2) = -6
(b) f(0)
x ≥ 0:
=> f(0) = 2(0) + 6
f(0) = 6
(c) f(2)
x ≥ 0:
=> f(2) = 2(2) + 6
f(2) = 4 + 6
f(2) = 10
An African elephant that weighs 16,500 pounds will need to drink 50 gallons of water every day right down the ratio of the amount of water consumed to the weight of the elephant a simplified ratio
Answer: 1:330
Step-by-step explanation:
Ratio is the the quantitative relation that exists between two amounts whihc shows the amount of times a particular value is contained in the other value.
From the question, we are told that the African elephant that weighs 16,500 pounds will need to drink 50 gallons of water every day. The ratio of the amount of water consumed to the weight of the elephant will be:
50:16500
We can simply further by finding the highest common factor for 50 and 16500 which is 50.
50 = 50 × 1
16500 = 50 × 330
Therefore, the simplified ratio will be:
1:330
Help im stuck on this question
Work out the area of the rectangle using a calculator and
giving your answer as a mixed number.
22 cm
5 cm
1
Note: To enter a mixed number in the answer boxes, please use the following method:
Type the fractional part of the mixed number first (e.g. for 6 first enter 5)
Then use the keyboard arrows to return to the front of the box and type the whole number (e.g. for 6
5 enter 6).
Answer:
11 17/21 cm²
Step-by-step explanation:
5 1/6 = (5*6 + 1)/6 = 31/6
2 2/7 = (2*7 + 2)/7 = 16/7
A = 31/6*16/7 = 496⁽²/42 = 248/21 = 11 17/21 cm²
The hypotenuse of a right triangle is 9[tex]\sqrt{2}[/tex] cm, and the shorter leg is 9 cm. Find the length of the other leg.
Answer:
9 cm
Step-by-step explanation:
If you were to imagine this right triangle, you would find it to be a 45 - 45 - 90 triangle. Perhaps the " shorter leg " piece of information was present to trick you, considering that the legs are congruent by converse to base angle theorem.
How is this triangle a 45 - 45 - 90? In such a triangle, the legs can be posed as x cm, as the base angles are congruent ( 45 and 45 ), thus the legs of the triangle are congruent as well. The hypotenuse would be x√2, and as we can see -
If legs = x, Hypotenuse = x√2 = 9√2
Thus, the length of the other leg is 9 centimeters ( 9 cm )
Hope that helps!