i will rate you brainliest
Answer:
D. Factoring trinomials
Step-by-step explanation:
The factoring trinomials method is the best way to factor the expression, since it is in the standard trinomial form ax² + bx + c
In this method, you can factor the expression by finding 2 factors of c that add up to b.
The expression is not in the simplest form, and difference of squares cannot be used because there are no perfect squares. Prime factorization is also not used for factoring expressions with variables.
So, D is the right answer.
In a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard. Compute the test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
Answer:
The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.
Step-by-step explanation:
We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.
In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.
Let [tex]p_1[/tex] = population proportion of cars driven at high altitudes who exceeded a standard of 10 grams.
[tex]p_2[/tex] = population proportion of cars driven at low altitudes who exceeded a standard of 10 grams.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1>p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}
The test statistics that will be used here is Two-sample z-test statistics for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of cars driven at high altitudes who exceeded a standard of 10 grams = [tex]\frac{24}{90}[/tex] = 0.27
[tex]\hat p_2[/tex] = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = [tex]\frac{42}{380}[/tex] = 0.11
[tex]n_1[/tex] = sample of cars driven at high altitudes = 90
[tex]n_2[/tex] = sample of cars driven at low altitudes = 380
So, the test statistics = [tex]\frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }[/tex]
= 3.234
The value of z-test statistics is 3.234.
Graph: y < 3x + 1 please help me
Answer:
Using a graphing calc.
Step-by-step explanation:
There are 4 roads leading from Bluffton to Hardeeville, 10 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon
Answer: 200 ways
Step-by-step explanation:
From the given information:
Total number of roads leading from Bluffton to Hardeeville = 4
Total number of roads leading from Hardeeville to Savannah = 10
Total number of roads leading from Savannah to Macon = 5
We need to find the total number of ways to get from Bluffton to Macon.
Total number of ways to get from Bluffton to Macon = 4 * 10 * 5
= 200
Therefore, there are 200 required number of ways to get from Bluffton to Macon.
For the regression equation, Ŷ = +20X + 200 what can be determined about the correlation between X and Y?
Answer:
There is a positive correlation between X and Y.
Step-by-step explanation:
The estimated regression equation is:
[tex]\hat Y=20X+200[/tex]
The general form of a regression equation is:
[tex]\hat Y=b_{yx}X+a[/tex]
Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.
The formula of slope is:
[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]
Here r (X, Y) is the correlation coefficient between X and Y.
The correlation coefficient is directly related to the slope.
And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.
Here the slope is positive.
This implies that the correlation coefficient must have been a positive values.
Thus, it can be concluded that there is a positive correlation between X and Y.
2 divided by ___=42 two divided by what equals 42?
i will rate you brainliest
Answer:
Option (2)
Step-by-step explanation:
In an arithmetic progression,
[tex]a_1,a_2,a_3.........a_{n-1},a_n[/tex]
First term of the progression,
a = [tex]a_1[/tex]
Common difference 'd' = [tex](a_2-a_1)[/tex]
Recursive formula for the sequence,
a = [tex]a_1[/tex]
[tex]a_n=a_{n-1}+d[/tex]
By applying these rules in the recursive formula,
[tex]a_1=\frac{4}{5}[/tex]
[tex]a_n=a_{n-1}+\frac{3}{2}[/tex]
Common difference 'd' = [tex]\frac{3}{2}[/tex]
Therefore, Option (2) will be the answer.
The numbers 1,2,3,4,5,6,7,8,9. How would you put them in each of a square block to create the sum on each line to make the number 15. The sum of each diagonals should also be 15.
Answer:
Here's one way:
4 9 2
3 5 7
8 1 6
Step-by-step explanation:
PLEASE ANSWER ASAP!!
Question is in the picture as well as the answer choices
any unrelated answers will be reported
Answer:
c
Step-by-step explanation
Please help with this
Choose the situation that represents a function.
A) The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie.
B) The inches of rainfall is a function of the day’s average temperature.
C) The time it takes to cook a turkey is a function of the turkey’s weight.
D) The number of sit-ups a student can do in a minute is a function of the student’s age.
Answer:c
Step-by-step explanation:
Answer: The answer is C.
Hope this helps you!
which graph shows a reflection across the line Y = X
Answer:
B
Step-by-step explanation:
"A" is not a reflection, it looks like a translation.
"C" is not a reflection, it is a rotation.
So, B is a reflection.
Answer:
[tex]\large \boxed{\mathrm{Graph \ C}}[/tex]
Step-by-step explanation:
The reflection is across the line y = x.
All options show reflection. Option C shows reflection across the line y = x.
In the reflection, the points on the triangle will also be reflected.
Point S is reflected across the line y=x, the reflected point is S’.
Point R is reflected across the line y=x, the reflected point is R’.
Point Q is reflected across the line y=x, the reflected point is Q’.
ab-0.5bab−0.5ba, b, minus, 0, point, 5, b when a=1a=1a, equals, 1 and b=5b=5
Answer:
2.5
Step-by-step explanation:
Put the values in place of the corresponding variables and do the arithmetic:
ab - 0.5b = (1)(5) -0.5(5) = 5 - 2.5 = 2.5
What is the following simplified product? Assume x greater-than-or-equal-to 0 (StartRoot 10 x Superscript 4 Baseline EndRoot minus x StarRoot 5 x squared EndRoot) (2 StartRoot 15 x Superscript 4 Baseline EndRoot + StartRoot 3 x cubed EndRoot) 10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot + x squared StartRoot 15 x EndRoot 11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus x Superscript 4 Baseline StartRoot 75 EndRoot + x squared StartRoot 15 EndRoot 10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x squared StartRoot 15 EndRoot 11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x cubed StartRoot 15 x EndRoot
Answer:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
Step-by-step explanation:
To find:
Simplified product of:
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})[/tex]
Solution:
First of all, let us have a look at some of the formula:
1. [tex](a+b) (c+d) = ac+bc+ad+bd[/tex]
2. [tex]a^b\times a^c =a^{b+c }[/tex]
3. [tex]\sqrt{a^{2b}} = \sqrt{a^b.a^b}=a^b[/tex]
4. [tex]\sqrt a \times \sqrt b = \sqrt{a\times b}[/tex]
Now, let us apply the above formula to solve the given expression.
[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\\Rightarrow(\sqrt{10x^4})(2\sqrt{15x^4})+(\sqrt{10x^4})(\sqrt{3x^3})-(x\sqrt{5x^2})(2\sqrt{15x^4})-(x\sqrt{5x^2})(\sqrt{3x^3})\\\\\Rightarrow2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\\Rightarrow\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
The answer is:
[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]
Answer:
Its D
Step-by-step explanation:
the number 73 can be written as the sum of 73 consecutive integers. What are the greatest and the smallest of those numbers?
Answer:
-35 and 37
Step-by-step explanation:
If you start with negative 35 and count up (including zero), you’ll cancel out when you get to positive 35 and have 71 numbers. Then you continue on with 36 and 37 which equals 73, and you have 73 consecutive integers.
Which methods could you use to calculate the y-coordinate of the midpoint of vertical line segment with endpoints at (0,0) and (0,15)? Check all that apply
Answer:
Midpoint formula.
The midpoint formula is (x_1+x_2)/2 , (y_1+y_2)/2
Step-by-step explanation:
This is one method. A list wasn't provided.
A local statistician is interested in the proportion of high school students that drink coffee. Suppose that 20% of all high school students drink coffee.
What is the probability that out of these 75 people, 14 or more drink coffee?
Answer:
the probability that out of these 75 people, 14 or more drink coffee is 0.6133
Step-by-step explanation:
Given that:
sample size n = 75
proportion of high school students that drink coffee p = 20% = 0.20
The proportion of the students that did not drink coffee = 1 - p
Let X be the random variable that follows a normal distribution
X [tex]\sim[/tex] N (n, p)
X [tex]\sim[/tex] N (75, 0.20)
[tex]\mu = np[/tex] = 75 × 0.20
[tex]\mu =[/tex] 15
[tex]\sigma = \sqrt{p (1-p) n}[/tex]
[tex]\sigma = \sqrt{0.20(1-0.20) 75}[/tex]
[tex]\sigma = \sqrt{0.20*0.80* 75}[/tex]
[tex]\sigma = \sqrt{12}[/tex]
[tex]\sigma = 3.464[/tex]
Now ; if 14 or more people drank coffee ; then
[tex]P(X \geq 14) = P(\dfrac{X-\mu }{\sigma} \leq \dfrac{X-\mu}{\sigma})[/tex]
[tex]P(X \geq 14) =P(\dfrac{14-\mu }{\sigma} \leq \dfrac{14-15}{3.464})[/tex]
[tex]P(X \geq 14) = P(Z \leq \dfrac{-1}{3.464})[/tex]
[tex]P(X \geq 14) = P(Z \leq -0.28868)[/tex]
From the standard normal z tables; (-0.288)
[tex]P(X \geq 14) = P(Z \leq 0.38667)[/tex]
[tex]P(X \geq 14) = 1 - 0.38667[/tex]
[tex]P(X \geq 14) = 0.61333[/tex]
the probability that out of these 75 people, 14 or more drink coffee is 0.6133
The distribution of baby weights at birth is left-skewed because of premies (premature babies) who have particularly low birth weights. However, within a close range of gestation times, birth weights are approximately Normally distributed. For babies born at full term (37 to 39 completed weeks of gestation), for instance, the distribution of birth weight (in grams) is approximately N(3350,440).N(3350, 440).10 Low-birth-weight babies (weighing less than 2500 grams, or about 5 pounds 8 ounces) are at an increased risk of serious health problems. Among those, very-low-birth-weight babies (weighing less than 1500 grams, or about 3 pounds 4 ounces) have the highest risk of experiencing health problems.
A. What proportion of babies born full term are low-birth-weight babies?
B. What proportion of babies born full term are very-low-birth-weight babies?
Answer:
a
[tex]P(X < 2500) = 0.02668[/tex]
b
[tex]P(X < 1500) = 0.00001[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 3350[/tex]
The standard deviation is [tex]\sigma = 440[/tex]
We also told in the question that the birth weight is approximately Normally distributed
i.e [tex]X \ \~ \ N(\mu , \sigma )[/tex]
Given that Low-birth-weight babies weighing less than 2500 grams,then the proportion of babies born full term are low-birth-weight babies is mathematically represented as
[tex]P(X < 2500) = P(\frac{ X - \mu }{\sigma } < \frac{2500 - \mu}{\sigma } )[/tex]
Generally
[tex]\frac{X - \mu}{ \sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X < 2500) = P(Z < \frac{2500 - \mu}{\sigma } )[/tex]
substituting values
[tex]P(X < 2500) = P(Z < \frac{2500 - 3350}{440 } )[/tex]
[tex]P(X < 2500) = P(Z <-1.932 )[/tex]
Now from the standardized normal distribution table(These value can also be obtained from Calculator dot com) the value of
[tex]P(Z <-1.932 ) = 0.02668[/tex]
=> [tex]P(X < 2500) = 0.02668[/tex]
Given that very-low-birth-weight babies (weighing less than 1500 grams,then the proportion of babies born full term are very-low-birth-weight babies is mathematically represented as
[tex]P(X < 1500) = P(\frac{ X - \mu }{\sigma } < \frac{1500 - \mu}{\sigma } )[/tex]
[tex]P(X < 1500) = P(Z < \frac{1500 - \mu}{\sigma } )[/tex]
substituting values
[tex]P(X < 1500) = P(Z < \frac{1500 - 3350}{440 } )[/tex]
[tex]P(X < 1500) = P(Z <-4.205 )[/tex]
Now from the standardized normal distribution table(These value can also be obtained from calculator dot com) the value of
[tex]P(Z <-1.932 ) = 0.00001[/tex]
[tex]P(X < 1500) = 0.00001[/tex]
Find the interquartile range of the data in the dot plot below. players blob:mo-extension://5f64da0e-f444-4fa8-b754-95
Answer:
[tex]IQR=Q_{3}-Q_{1}[/tex]
Step-by-step explanation:
The inter-quartile range is a measure of dispersion of a data set.
It is the difference between the third and the first quartile.
[tex]IQR=Q_{3}-Q_{1}[/tex]
The 1st quartile (Q₁) is well defined as the mid-value amid the minimum figure and the median of the data set. The 2nd quartile (Q₂) is the median of the data. The 3rd quartile (Q₃) is the mid-value amid the median and the maximum figure of the data set.
An animal population is increasing at a rate of 13 51t13 51t per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years.
Answer:
ΔP = 567
Step-by-step explanation:
The increasing rate of the population is 13,51*t.
That rate by definition is:
dP/dt where P is the population therefore
dP/dt = 13,51*t
dt = 13,51*t*dt
Integrating on both sides of the equation we get:
∫dp = ∫ 13,51*t*dt
P = 13,51*t²/2 + K ( K is population for t = 0 )
Now the population in 10 years P(₁₀)
P(₁₀) = 13,51* (10)² /2 + K
P(₁₀) = 675,5 + K (1)
And P(₄) is
P(₄) = 13,51*(4)²/2 * K
P(₄) = 108,08 + K (2)
Then substracting
P(₁₀) - P(₄) = ( 675,5 + K ) - ( 108,08 + K )
ΔP = 567,42
But we don´t have fraction of animal, then
ΔP = 567
PLEASE HELP 30 POINTS
How long will it take in hours for a car traveling from Tucson to Phoenix (120 km)
to reach Phoenix at a rate of 10km/hr.? How long would it take that car to circle the Earth
at the equator? (c= 2 nr) rof earth is 6,378 km.
Answer:
1. It would take the car to get from Tucson to Phoenix 12 hours.
2. for the car to go around the equator it would take 637 hours if it is still travelling at 10km/hr.
hope this helps
Step-by-step explanation:
1. 120 km divided by 10 = 12 hours
Please answer this correctly without making mistakes
Answer:
[tex]\large \boxed{\mathrm{4/5 \ cups}}[/tex]
Step-by-step explanation:
Subtract 1/10 from 9/10 to find out how much is left.
9/10 - 1/10
8/10 = 4/5
Answer:
4/5 cupsStep-by-step explanation:
[tex]Volume\:of \: syrup \:in \:cup\:from\:jug = \frac{9}{10}\\\\ She \:took\: \frac{1}{10} from \:the\:cup\:into\:the \:jug \\\\Volume \:of syrup\:in\:cup=?\\\\\frac{9}{10} -\frac{1}{10} \\\\= \frac{4}{5} cups[/tex]
How many numbers from 10 to 99 have a tens place exactly 3 times greater than their ones place? PLZZZ answer this question . I will be very happy whoever answers this I will give u brainliest too.
Answer:
45
Step-by-step explanation:
2 digit number starts from 10 ends at 99
between 10 and 19 there is only one number whose tens digit is more than ones digit.
that is 10
between 20 and 29 there are two numbers
20 and 21
like the same
between 30 and 39 there are 3 numbers
10–19. 1
20–29. 2
30–39. 3
40–49. 4
50–59. 5
60–69. 6
70–79. 7
80–89. 8
99–99. 9
sum of first n natural numbers is n(n+1)/2
9(9+1)/2=45
Three numbers between 10 and 99 have tens places that are precisely three times larger than their one's places.
What is Place value?The foundation of our whole number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number.
The tens digit must be three times larger than the units digit in order to meet the requirement. The units digit can have one of the following values: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
Since we are seeking two-digit integers, it is not possible if the unit digit is zero for the tens digit also be zero.
In the case when the unit digit is 1, the tens digit must be 3, resulting in the number 31. Similar to the previous example, if the unit digit is 2, the tens digit must be 6, resulting in the number 62.
As we proceed, we discover the following integers meet the condition:
31, 62, 93
Therefore, there are three numbers from 10 to 99 that have a tens place exactly 3 times greater than their one's place.
Learn more about place values here:
https://brainly.com/question/27734142
#SPJ3
Is the quotient of two rational numbers always a rational number? Explain.
Answer:
Yes,
Step-by-step explananation
The quotient of two rational numbers is always rational, and the reason for this lies in the fact that the product of two integers is always an rational number.
The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.
From Algebra, we know that a Rational Number is a Real Number of the form:
[tex]x = \frac{a}{b}[/tex], [tex]a, b\in \mathbb{N}[/tex], [tex]x \in \mathbb{R}[/tex] (1)
Where:
[tex]a[/tex] - Numerator.[tex]b[/tex] - Denominator.[tex]x[/tex] - Quotient.The Quotient can be an Integer or not. In the first case, all Quotients have their equivalent Rational Numbers.
Now, if we divide a Rational Number by another Rational Number, then we have the following expression:
[tex]x' = \frac{x_{1}}{x_{2}}[/tex]
If [tex]x'[/tex] is a Rational Number, then it must also an Integer and if [tex]x'[/tex] is an Integer, then [tex]x_{1}[/tex] and [tex]x_{2}[/tex] must be Multiples of each other.
The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.
Please see this question related to Rational Numbers: https://brainly.com/question/24398433
Using the digits 0-9, at most only one time each, fill in the boxes to
Answer:
2 * 3 + 4 * 5 = 26
5 * 7 + 1 * 8 = 43
Step-by-step explanation:
Given
_ * _ + _ * _ = _ _
Required
Fill in the boxes with digits 0 to 9
From the question we understand that the result must be two digits i.e. _ _
To solve this, we'll make use of trial by error method:
Fill the first two boxes wit 2 and 3: _ * _ becomes 2 * 3
Fill the next two boxes with 4 and 5: _ * _ becomes 4 * 5
So,we have
2 * 3 + 4 * 5
6 + 20
26
Hence, the first combination is 2 * 3 + 4 * 5 = 26
Another possible combination is:
Fill the first two boxes wit 5 and 7: _ * _ becomes 5 * 7
Fill the next two boxes with 1 and 8: _ * _ becomes 1 * 8
So,we have
5 * 7 + 1 * 8
35 + 8
43
Hence, another combination is 5 * 7 + 1 * 8 = 43
Note that; there are more possible combinations
Answer 9 and 11 with explanation on how you solved it.
Answer:
(9). Range; {8, 5, 2, -1, -4}
(10). Range; {-15, -7, 1, 9, 17}
Step-by-step explanation:
Domain of a function is (x-values) determined by the input values and Range of a function is determined by the (y-values) output values of the function.
(9). For the given function,
f(x) = -3x + 2
If the Domain of this function is a set of values,
{-2, -1, 0, 1, 2}
For Range,
x -2 -1 0 1 2
f(x) 8 5 2 -1 -4
Therefore, Range of the function 'f' will be; {8, 5, 2, -1, -4}
(11). f(x) = 4x + 1
Domain is {-4, -2, 0, 2, 4}
Table for input-output values will be,
x -4 -2 0 2 4
f(x) -15 -7 1 9 17
Therefore, Range of the function will be {-15, -7, 1, 9, 17}
help with math ASAP!
Answer:
1.) [tex]\frac{1}{9^4}*9^3[/tex]
2.) [tex]\frac{1}{w^7}[/tex]
3.)
Step-by-step explanation:
When you have a negative exponent, rewrite:
[tex]x^{-a}=\frac{1}{x^a}[/tex]
Rewrite using this to change all negative exponents.
Answer:
Multiple Answers
Step-by-step explanation:
Note: When multiplying numbers with exponents, you add the exponents. When dividing numbers with exponents, you subtract exponents.When you have a negative exponent, flip the fraction and write it as a positive exponent.
1) -4 + 3= -1
So we have (9^-4) + (9^3)= (1/(9^1)
2) (1/w)^7
3) cannot read problem, but just apply the rules I wrote under "Note"
4) 14/y
5) cannot read problem,but just apply the rules I wrote under "Note"
6) 20d^4 n^? --Cannot read n exponents--.
7) cannot read problem
8) Cannot read problem
9) 90/z^4---only if exponents are 5,-3,and-6
10) 1/(9^5)
11) 54b^4
12) Cannot read problem
13) 16d^8c^8 ---if exponents are 5,3,6,2--
14) s^8
Hope this helps! Plz give brainly, I kinda need it.
If f(x)=x/2-3and g(x)=4x^2+x-4, find (f+g)(x)
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
= x/2-3 + 4x²+x+4
= ..........
An urn contains two blue balls (denoted B1 and B2) and three white balls (denoted W1, W2, and W3). One ball is drawn, its color is recorded, and it is replaced in the urn. Then another ball is drawn and its color is recorded.
a. Let B1 W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. List all 25 possible outcomes of the experiment.
b. Consider the event that the first ball that is drawn is blue. List all outcomes in the event. What is the probability of the event?
c. Consider the event that only white balls are drawn. List all outcomes in the event. What is the probability of the event?
Answer:
(a) Shown below.
(b) The probability that the first ball drawn is blue is 0.40.
(c) The probability that only white balls are drawn is 0.36.
Step-by-step explanation:
The balls in the urn are as follows:
Blue balls: B₁ and B₂
White balls: W₁, W₂ and W₃
It is provided that two balls are drawn from the urn, with replacement, and their color is recorded.
(a)
The possible outcomes of selecting two balls are as follows:
B₁B₁ B₂B₁ W₁B₁ W₂B₁ W₃B₁
B₁B₂ B₂B₂ W₁B₂ W₂B₂ W₃B₂
B₁W₁ B₂W₁ W₁W₁ W₂W₁ W₃W₁
B₁W₂ B₂W₂ W₁W₂ W₂W₂ W₃W₂
B₁W₃ B₂W₃ W₁W₃ W₂W₃ W₃W₃
There are a total of N = 25 possible outcomes.
(b)
The sample space for selecting a blue ball first is:
S = {B₁B₁, B₁B₂, B₁W₁, B₁W₂, B₁W₃, B₂B₁, B₂B₂, B₂W₁, B₂W₂, B₂W₃}
n (S) = 10
Compute the probability that the first ball drawn is blue as follows:
[tex]P(\text{First ball is Blue})=\frac{n(S)}{N}=\frac{10}{25}=0.40[/tex]
Thus, the probability that the first ball drawn is blue is 0.40.
(c)
The sample space for selecting only white balls is:
X = {W₁W₁, W₂W₁, W₃W₁, W₁W₂, W₂W₂, W₃W₂, W₁W₃, W₂W₃, W₃W₃}
n (X) = 9
Compute the probability that only white balls are drawn as follows:
[tex]P(\text{Only White balls})=\frac{n(X)}{N}=\frac{9}{25}=0.36[/tex]
Thus, the probability that only white balls are drawn is 0.36.
Plzz help i cant figure this out..
Answer:
[tex]\large \boxed{\mathrm{B. \ \ \{-10, -6, 10\} }}[/tex]
Step-by-step explanation:
The domain is the x values.
D = {-1, 0, 4}
y = 4(-1) - 6 = -4 - 6 = -10
y = 4(0) - 6 = 0 - 6 = -6
y = 4(4) - 6 = 16 - 6 = 10
The range is the y values.
R = {-10, -6, 10}
