The probabilities we found in this exercise are.
0.2268 = 22.68% probability that a country is in Asia.0.2423 = 24.23% probability that a country is in Europe.0.2784 = 27.84% probability that a country is in Africa.0.1186 = 11.86% probability that a country is in North America.0.0722 = 7.22% probability that a country is in Oceania.0.0619 = 6.19% probability that a country is in South America.0.5 = 50% probability of drawing a red card in a standard deck of 52 cards.0.25 = 25% probability of drawing a club in a standard deck of 52 cards.In this exercise, probability concepts are used.
A probability is the number of desired outcomes divided by the number of total outcomes.
Total number of countries:
23 + 12 + 47 + 44 + 54 + 14 = 194
Let A = the event that a country is in Asia.
44 of the 194 countries are in Asia, thus:
[tex]P(A) = \frac{44}{194} = 0.2268[/tex]
0.2268 = 22.68% probability that a country is in Asia.
Let E = the event that a country is in Europe.
47 out of 194 countries are in Europe, thus:
[tex]P(E) = \frac{47}{194} = 0.2423[/tex]
0.2423 = 24.23% probability that a country is in Europe.
Let F = the event that a country is in Africa.
54 out of 194 countries are in Africa, thus:
[tex]P(F) = \frac{54}{194} = 0.2784[/tex]
0.2784 = 27.84% probability that a country is in Africa.
Let N = the event that a country is in North America.
23 out of 194 countries are in North America, thus:
[tex]P(N) = \frac{23}{194} = 0.1186[/tex]
0.1186 = 11.86% probability that a country is in North America.
Let O = the event that a country is in Oceania.
14 out of 194 countries are in Oceania, thus:
[tex]P(O) = \frac{14}{194} = 0.0722[/tex]
0.0722 = 7.22% probability that a country is in Oceania.
Let S = the event that a country is in South America.
12 out of 194 countries are in South America, thus:
[tex]P(S) = \frac{12}{194} = 0.0619[/tex]
0.0619 = 6.19% probability that a country is in South America.
18. What is the probability of drawing a red card in a standard deck of 52 cards?
In a standard deck of 52 cards, 26 are red, and thus:
[tex]p = \frac{26}{52} = 0.5[/tex]
0.5 = 50% probability of drawing a red card in a standard deck of 52 cards.
19. What is the probability of drawing a club in a standard deck of 52 cards?
In a standard deck of 52 cards, 13 are clubs, and thus:
[tex]p = \frac{13}{52} = 0.25[/tex]
0.25 = 25% probability of drawing a club in a standard deck of 52 cards.
For more about probabilities, you can check https://brainly.com/question/24104122
the ages of two students are in the ratio of 3:5,if the older is 40yrs. How old is the younger student
Answer:
24 years
Step-by-step explanation:
total ratio =8
older student=40 years
3/8*40 ÷ 5/8=24
Find the missing side round your answer to the nearest tenth
Answer: 15
Step-by-step explanation:
Which equation results from isolating a radical term and squaring both sides of the equation for the equation
Vc-2-vc=5
Answer:
[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{c-2} - \sqrt c = 5[/tex]
Required
Isolate radical, then square both sides
We have:
[tex]\sqrt{c-2} - \sqrt c = 5[/tex]
Isolate radical
[tex]\sqrt{c - 2} = 5 + \sqrt c[/tex]
Square both sides
[tex](\sqrt{c - 2})^2 = (5 + \sqrt c)^2[/tex]
[tex]c - 2 = 25 + 2 * 5 * \sqrt c + c[/tex]
[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]
One book is 4cm thick, find out how many such books can be placed in a space of 53cm.
An urn contains 12 balls, five of which are red. Selection of a red ball is desired and is therefore considered to be a success. If three balls are selected, what is the expected value of the distribution of the number of selected red balls
The expected value of the distribution of the number of selected red balls is 0.795.
What is the expected value?The expected value of the distribution is the mean or average of the possible outcomes.
There are 12 balls in an urn, five of which are crimson. The selection of a red ball is desired and hence considered a success.
In this case, the possible outcomes are 0, 1, 2, or 3 red balls.
To calculate the expected value, we need to find the probability of each outcome and multiply it by the value of the outcome.
The probability of selecting 0 red balls is :
[tex]$\frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$[/tex].
The probability of selecting 1 red ball is :
[tex]$3 \cdot \frac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{315}{660}$[/tex].
The probability of selecting 2 red balls is
[tex]:$\dfrac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$.[/tex]
The probability of selecting 3 red balls is
[tex]$\dfrac{5}{12} \cdot \frac{4}{11} \cdot \frac{3}{10} = \frac{15}{660}$[/tex]
The expected value is then :
[tex]$0 \cdot \frac{105}{660} + 1 \cdot \frac{315}{660} + 2 \cdot \frac{105}{660} + 3 \cdot \frac{15}{660} = \frac{525}{660} = \frac{175}{220} \approx \boxed{0.795}$[/tex]
To learn more about the expected value of the distribution click here:
https://brainly.com/question/29068283
#SPJ5
Which equation describe the line through the points (2,-4) and (5,8)
Answer:
Your equation would be
y=4x-12
Step-by-step explanation:
So an easy way to figure this out is graph the points and look at the distance the points are away from each other. In this case it was 12 up and 3 right. This is your slope. Simplify the fraction to 4/1. Then from (2,-4) use the given slope to work back to a point that is on the y axis, which is (0,12). Plug all of the given information you found into y=mx+b and you get the given formula.
find the mid-point of the line segment joining the points (10, 13) and (-7, 7)?
Answer:
(3/2,10)
Step-by-step explanation:
Mid point is ((10-7)/2,(13+7)/2)=(1.5,10)
A particle is moving such that its height h at time t is given by h(t) = 2 + 8t - 3t^2 + 1/5t^3. The average velocity of the particle on the period [0,3] is
[tex]\\ \Large\sf\longmapsto h(t)[/tex]
[tex]\\ \Large\sf\longmapsto 2+8t-3t^2+\dfrac{1}{5}t^3[/tex]
[tex]\\ \Large\sf\longmapsto 2+8(3)-3(3)^2+\dfrac{1}{5}(3)^3[/tex]
[tex]\\ \Large\sf\longmapsto 2+24-3(9)+\dfrac{27}{5}[/tex]
[tex]\\ \Large\sf\longmapsto 26-27+5.4[/tex]
[tex]\\ \Large\sf\longmapsto -2+5.4[/tex]
[tex]\\ \Large\sf\longmapsto h(t)=3.4m[/tex]
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use absolute values where appropriate.)
f(x) = 45−5x, x>0 .
Answer:
F(x) = 45*x - (5/2)*x^2 + C
Step-by-step explanation:
Here we want to find the antiderivative of the function:
f(x) = 45 - 5*x
Remember the general rule that, for a given function:
g(x) = a*x^n
the antiderivative is:
G(x) = (a/(n + 1))*a*x^(n + 1) + C
where C is a constant.
Then for the case of f(x) we have:
F(x) = (45/1)*x^1 - (5/2)*x^2 + C
F(x) = 45*x - (5/2)*x^2 + C
Now if we derivate this, we get:
dF(x)/dx = 1*45*x^0 - 2*(5/2)*x
dF(x)/dx = 45 - 5*x
QUESTION 9
Each person drinks half a litre carton of orange juice. How many cartons of orange juice do Joe's guests drink in total?
A rectangle is 19 inches long and 6 inches wide find it’s area
Step-by-step explanation:
how to find the area
multiply the length times the width
19 × 6 = 114 inches squared
The area of the rectangle is 114 square inches if the length and breadth of the rectangle are 19 inches and 6 inches.
A rectangle is one of the elementary geometric figures. It is a quadrilateral with a pair of equal and parallel sides. All angles of a rectangle are right angles.
The length of the rectangle is given as 19 inches.
The breadth of the rectangle is given as 6 inches.
The area of the given rectangle is given as:
Area = length × breadth
Area = 19 × 6
Area = 114 square inches
Thus, the area of the given rectangle is 114 square inches.
Learn more about Rectangles here:
https://brainly.com/question/29123947
#SPJ3
Which inequality represents all values of x which the product below is defined Square root 4x Square root x+2
Answer:
Option (D) x≥ 0 is absolutely correct
Step-by-step explanation:
The reason is that the square root function is defined for only non negative numbers.
Answer: x is greater than or equal to 0
Step-by-step explanation:
Prove: Quadrilateral ABCD is a parallelogram.
m∠AEB = m∠CED
Answer:
m∠ AEB = m∠ CED ......... By Vertical Angles Theorem.
Step-by-step explanation:
Vertical Angles Theorem: Vertical angle theorem states that vertical angles, angles that are opposite each other and formed by two intersecting lines, are congruent. If two lines intersect each other, we have the two pair of vertical opposite angles. As shown in the figure. Here, ∠ 1 and ∠ 2 are vertical opposite angles, and also they are equal. ∠ 3 and ∠ 4 are also vertical opposite angles, and also they are equal. For, step 3. m∠ AEB = m∠ CED Therefore, the reason for this proof is Vertical Angles Theorem.
The weight of potato chip bags filled by a machine at a packaging plant is normally distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. What is the probability that a randomly chosen bag will weigh more than 15.6 ounces
Answer:
0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 15.0 ounces and a standard deviation of 0.2 ounces.
This means that [tex]\mu = 15, \sigma = 0.2[/tex]
What is the probability that a randomly chosen bag will weigh more than 15.6 ounces?
This is 1 subtracted by the p-value of Z when X = 15.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.6 - 15}{0.2}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a p-value of 0.9987.
1 - 0.9987 = 0.0013
0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.
please help me with geometry
Answer:
x = 8
Step-by-step explanation:
Set 2x + 3 = 3x - 5
Solve for x
x = 8
help me with this please
Find the length of BC
Answer:
53.68
Step-by-step explanation:
tan54 = bc/39
bc = 39tan54
Step-by-step explanation:
Hey there!
From the given figure;
Angle CAB = 54°
Side AC = 39
To find: side BC
Taking Angle CAB as reference angle;
Perpendicular (p) = BC = ?
Base (b) = AC = 39
Hypotenuse (h) = AB
Taking the ratio of tan;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep value;
[tex] \tan(54) = \frac{bc}{39} [/tex]
Simplify it;
1.376381*39 = BC
Therefore, BC = 53.678.
Hope it helps!
A product is introduced into the market. Suppose a product's sales quantity per month q ( t ) is a function of time t in months is given by q ( t ) = 1000 t − 150 t 2 And suppose the price in dollars of that product, p ( t ) , is also a function of time t in months and is given by p ( t ) = 150 − t 2 A. Find, R ' ( t ) , the rate of change of revenue as a function of time t
Answer:
[tex]r'(t) = 298t -850[/tex]
Step-by-step explanation:
Given
[tex]q(t) = 1000t - 150t^2[/tex]
[tex]p(t) = 150t - t^2[/tex]
Required
[tex]r'(t)[/tex]
First, we calculate the revenue
[tex]r(t) = p(t) - q(t)[/tex]
So, we have:
[tex]r(t) = 150t - t^2 - (1000t - 150t^2)[/tex]
Open bracket
[tex]r(t) = 150t - t^2 - 1000t + 150t^2[/tex]
Collect like terms
[tex]r(t) = 150t^2 - t^2 + 150t - 1000t[/tex]
[tex]r(t) = 149t^2 -850t[/tex]
Differentiate to get the revenue change with time
[tex]r'(t) = 2 * 149t -850[/tex]
[tex]r'(t) = 298t -850[/tex]
Quentin is one third the age of his aunt. And 20% older than his sister. If Quentin's sister is 15 years old, how old is his aunt?
Answer:
54
Step-by-step explanation:
20% of 15 is 3 so Quentin is 18 years old
If Quentin is one thrid his Aunt's age that means his aunt is three times older.
18 * 3 = 54
So his Aunt is 54 years old
The age of Quentin's aunt is 54 years if the Quentin is one third the age of his aunt if we solve by making the Quentin's Aunt age as variable x.
What is a equation?
An equation is a formula that expresses the equality of variables.
How to determine age of aunt?
let the age of the aunt is x years.
According to the question the age of Quentin is x/3 years.
The age of Quentin's sister is x/3*100/120
=5x/18
We have been given the age of Quentin's sister is 15 years.
So, 5x/18=15
=x=54 years
Hence the age of aunt is 54 years old.
Learn more about equations at https://brainly.com/question/2972832
#SPJ2
Player Productions theatre finds that their ticket sales for Friday night performances (number of tickets sold) is given by the function h , where h ( t ) measures the number of tickets sold, and where t is the play length (measured in hours). Regal Theatre found that their ticket sales for Friday nights performances can be modeled by the function, g , where g (t)= 1.6h(t + 0.25).
Required:
How do the ticket sales for Friday night perfomances at Player Productions compare to the ticket sales for a Friday night perfomance at Regal Theatre?
Answer:
Regal Theatre makes 1.6 times more than Player Productions when they have 0.25 hours longer productions
Step-by-step explanation:
Given
[tex]h(t) \to[/tex] player production theatre
[tex]g(t) \to[/tex] regal theatre
Where:
[tex]g(t) = 1.6h(t + 0.25)[/tex]
Required
Compare both functions
We start from the bracket
[tex]t + 0.25[/tex]
The + in [tex]t + 0.25[/tex] means longer hours of production
So:
[tex]t + 0.25[/tex] means 0.25 hours longer that player productions
[tex]g(t) = 1.6h(t + 0.25)[/tex] can be rewritten as:
[tex]g(t) = 1.6 * h(t + 0.25)[/tex]
The above means 1.6 times player production when they have 0.25 longer hours.
Instructions: Find the missing length indicated.
Answer:
x = 65
Step-by-step explanation:
x = √(25×(25+144))
x = √(25×169)
x = 5×13
x = 65
Answered by GAUTHMATH
I need help answering this ASAP
can you zoom in on my pic more or no does it say 1/z
Answer:
Option A. Reciprocal
Answered by GAUTHMATH
A normal distribution has a mean of 20 and a standard deviation of 4. Determine the z-score for the data value of 42.
Answer:
Z = (42-20)/4 = 5.5
Z = X-μ / σ
Step-by-step explanation:
The z-score for the data value of 42 is 5.5.
What is a z-score?A z-score is defined as the fractional representation of data point to the mean using standard deviations.
Formula of z-score = (X - μ) / σ
Given,
μ = 20
σ = 4
X = 42
z-score = (X - μ) / σ
Substitute the values,
z-score = (42-20)/4
z-score = 22/4
z-score = 5.5
Hence, the z-score for the data value of 42 is 5.5.
Learn more about z-score here:
brainly.com/question/13793746
#SPJ5
Infues Gentamicin 100 mg in 100ml in 15 minutes. What will you set the infusion pump at ml/hr
9514 1404 393
Answer:
400 mL/h
Step-by-step explanation:
The required rate is ...
(100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h
the quotient of (x^4 - 3x^2 + 4x - 3) and a polynomial is (x^2 + x - 3) what is the polynormial
Answer:
Hello,
polynomial is x²-x+1
Step-by-step explanation:
if a=b*c+r then a=c*b+r
Using a long division, see the picture.
plzzzzz helppp i will give brainlyist
Answer:
C. (2)
Step-by-step explanation:
an integer is a WHOLE NUMBER
have an amazing day :)
Answer:
2 is an integer
Step-by-step explanation:
An integer is a whole number, it does not have a fractional part
A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 50 cells.
Required:
a. Find the relative growth rate.
b. Find an expression for the number of cells after t hours.
c. Find the rate of growth after 6 hours. (Round your answer to the nearest integer.)
d. Find the number of cells after 6 hours.
Answer:
a. Relative Growth rate = 10% (6/60 * 100)
b. Number of cells after t hours = 50 * 1.1^t
c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)
d. The number of cells after 6 hours is
= 89 cells
Step-by-step explanation:
A cell divides into two cells every 20 minutes
In one hour, the cell will divide into 60/20 * 2 = 6 cells
Each cell growth 6 cells per hour
Initial population of a culture = 50 cells
t = time in hours
a. Relative Growth rate = 10% (6/60 * 100)
b. Number of cells after t hours = 50 * 1.1^t
c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)
d. The number of cells after 6 hours = initial population * growth factor
= 50 * 1.772
= 88.6
= 89 cells
A ball is thrown from an initial height of
1 meter with an initial upward velocity of
1 m/s. The ball's height h
(in meters) after t
seconds is given by the following. h=1+30t-5t^2
Find all values of t
for which the ball's height is 11
meters.
Round your answer(s) to the nearest hundredth.
Answer:
Step-by-step explanation:
If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:
[tex]11=-5t^2+30t+1[/tex] and
[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get
t = .35 seconds and t = 5.6 seconds
Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.
Find m
a 24.7
b 79.2
c 68.3
d 57.4
e 46.5
f 80.1
g 35.6
Answer:
68.3 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan I = opp side / adj side
tan I = sqrt(82) / sqrt(13)
tan I = sqrt(82/13)
Taking the inverse tan of each side
tan ^-1 ( tan I) = tan ^-1( sqrt(82/13))
I = 68.2892
Rounding to the nearest tenth
I = 68.3 degrees
12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?
Answer:
3.2 hours
Step-by-step explanation:
12 workers * 4 hours = 48 worker hours
15 workers * x hours = 48 worker hours
48 /15 =3.2 hours
Answer:
3 hours and 12 minutes.
Step-by-step explanation:
12 Workers complete a job in 4 hours
1 worker complete a job 12 × 4 = 48
15 workers complete a job = 48/15 = 3³/¹⁵ = 3¹/⁵
= 3 hours + 1/5 × 60 minutes = 3 hours 12 minutes.
