Answer:
(a) 31101
(b) $5.65
(c) $113.38
Step-by-step explanation:
The complete question is:
A regional automobile dealership sent out fliers to prospective customers indicating that they had already won one of three different prizes: an automobile valued at $20,000, a $125 gas card, or a $5 shopping card. To claim his or her prize, a prospective print on the back of the flier listed the probabilities of winning. The chance of winning the car was 1 out of 31,101, the chance of winning the gas card was 1 out of 31,101, and the chance of winning the shopping card was 31, 099 out of 31,101.
Solution:
The information provided is as follows:
[tex]P(\text{Car})=\frac{1}{31101}\\\\P(\text{Gas Card})=\frac{1}{31101}\\\\P(\text{Shopping Card})=\frac{31099}{31101}[/tex]
(a)
The number of fliers the automobile dealership sent out is, n = 31,101.
This is because the probability of winning any of the three prize is out of 31,101.
(b)
Compute the expected value of the prize won by a prospective customer receiving a flier as follows:
[tex]E(X)=\sum x\times P(X=x)[/tex]
[tex]=[20000\times \frac{1}{31101}]+[125\times \frac{1}{31101}]+[5\times \frac{31099}{31101}]\\\\=0.6431+0.0040+4.9997\\\\=5.6468\\\\\approx 5.65[/tex]
Thus, the expected value of the prize won by a prospective customer receiving a flier is $5.65.
(c)
Compute the standard deviation of the prize won by a prospective customer receiving a flier as follows:
[tex]SD(X)=\sqrt{V(X)}=\sqrt{E(X^{2}-(E(X))^{2}}[/tex]
[tex]=\sqrt{[(20000)^{2}\times \frac{1}{31101}+(125)^{2}\times \frac{1}{31101}+(5)^{2}\times \frac{31099}{31101}]-(5.65)^{2}}\\\\=\sqrt{12854.9011}\\\\=113.37947\\\\\approx 113.38[/tex]
Thus, the standard deviation of the prize won by a prospective customer receiving a flier is $113.38.
3. The daily surface concentration of carbonyl sulfide on the Indian Ocean is normally distributed, with a mean of 9.1 picomoles per liter and a standard deviation of 3.5 picomoles per liter. Find the probability that on a randomly selected day, the surface concentration of carbonyl sulfide on the Indian Ocean is less than 13.5 picomoles per liter.
Answer: 0.8956
Step-by-step explanation:
Given: The daily surface concentration of carbonyl sulfide on the Indian Ocean is normally distributed, with a mean [tex]\mu=100[/tex] picomoles per liter and standard deviation of [tex]\sigma=3.5[/tex] picomoles per liter.
Let X be the daily surface concentration of carbonyl sulfide.
The probability that on a randomly selected day, the surface concentration of carbonyl sulfide on the Indian Ocean is less than 13.5 picomoles per liter [tex]= P(X<13.5)[/tex]
[tex]=P(\dfrac{X-\mu}{\sigma}>\dfrac{13.5-9.1}{3.5})\\\\=P(Z<1.257)\\\\= 0.8956\ \ \ [\text{By p-value table}][/tex]
Hence, the required probability = 0.8956
What fraction is equal to 5/7
The answer is
[tex]\frac{10}{14} \frac{15}{21} \frac{25}{35} \frac{30}{42} \frac{35}{49}[/tex]
To learn more, take a look at this chart please.
Answer:
Any of these
10/14
15/21
20/28
etc.
Step-by-step explanation:
Basically, if you multiply the fraction by the same number, it will be equal.
In 9.3 x 10-8 the exponent is a negative number. Which of these describes the value of a number in scientific notation that includes a negative exponent
Answer:
0.000000093
Step-by-step explanation:
Theres seven zeros after the decimal
SOMEONE PLS HELP ME W THIS QUESTION ASAP I’LL MARK BRAINLIEST
Answer:
i think it is A the first option
Step-by-step explanation:
a number increased by 15 is 114
Answer:
129
Step-by-step explanation:
all u have to do is add those two numbers
Answer:
114 - 15 = 99
Step-by-step explanation:
A "number" can be used as x since we don't know what it is at first- since it'd be x + 15 = 114 you can just do 114 - 15 to get the answer to x which is 99:)
In triangle QRS the measure of right angle S is SQ=90 degrees Sq=47 feet and Rs=70 feet. Find the measure of angle R to the nearest tenth of a degree
Answer:
x=33.9°
Step-by-step explanation:
Trigonometric Ratios
In a right triangle, i.e. the triangles that have an internal angle of 90°, the so-called trigonometric ratios are valid.
There are six trigonometric ratios that can be used in right triangles, depending on the data available for each problem.
The current question gives us two sides in a right triangle and requires us to calculate the angle x.
The angle x 'looks' at the sides of the triangle in this way: RS=70 is the adjacent leg, SQ=47 is the opposite leg, and RQ is the hypotenuse.
We should use the trigonometric ratio that relates both the adjacent and the opposite led. There are two possibilities: The tangent and the cotangent. We'll use the tangent for no particular reason.
The tangent of an angle is defined as:
[tex]\displaystyle \tan\x=\frac{\text{opposite leg}}{\text{adjacent leg}}\\[/tex]
Use the given values:
[tex]\displaystyle \tan x=\frac{47}{70}=0.6714[/tex]
Using a calculator (in degree mode), we calculate the angle:
[tex]x=\tan^{-1}(0.6714)=33.9^\circ[/tex]
x=33.9°
David is building a toy box. Its length will be 4 feet, its width will be 2.5 feet and its height will be 2 feet. What will the volume of the toy box be?
Answer:
the answer to this would be this 20 ft
Step-by-step explanation:
you would this by taking 4 times 2.5 times 2 and you would get the answer of 20 ft for the volume.
Three minus twice a number x is greater than fifty-five. Write an inequality to represent this statement.
Answer:
2x - 3 > 55
Step-by-step explanation:
the answer is above
What is 6 x 7 ones??
Answer:
42 it is the answer i think
Step-by-step explanation:
6 × 7 = 42
6×1 = 6
6×2 = 12
6×3 = 18
6×4 = 24
6×5 = 30
6×6 = 36
6×7 = 42
6×8 = 48
6×9 = 54
6×10 = 60
Which statement is true?(n+4)-7=18
Answer:
21
Step-by-step explanation:
(21 plus 4)=25
25 minus 7=18
~~~How I got 21~~~
I find the number that will be reasonable like 20 and work my way up
~~~Hope this helps~~~
Answer:
[tex](n+4)-7=18 \\ n = 18 + 7 - 4 \\ n = 21.[/tex]
7th grade help me pleasee
What is the value f(4) if f(x)=-4(x+3)-14
Answer:
f(4)=-42
Step-by-step explanation:
f(x)=-4(x+3)-14
(sub 4 for x in the equation f(x) to find f(4))
f(4)=-4×(4+3)-14
(simplify inside the bracket)
=-4×7-14
(multiply 7 and -4)
=-28-14
(simplify)
=-42
what is the mean (average) of 2,4,5,6,8
Answer:
5
Step-by-step explanation:
In order to figure out average, we need to add up all the numbers. So adding 2, 4, 5, 6, and 8 gives us 25. We now divide that total by the total number of terms we used to reach 25. So since we had 5 numbers, we divide 25 by 5 to get an average of 5.
Answer:
5.
Step-by-step explanation:
To find mean. you just add all the numbers up and divide by the number of numbers (5).
2+4+5+6+8=25
25/5=5
A new dining room is being built in Carol’s home. In a scale drawing of the room, 1 inch represents LaTeX: 2\frac{1}{2}212feet. A sketch of the drawing is shown
Answer/Step-by-step explanation:
Area of the dinning room table:
Given that scale of the sketch is 1 in = 2½ ft
Length of the dinning room table on the sketch = 2 in
Actual length of dinning room table = 2 × 2½ = 5 ft
Width of the dinning room table on the sketch = 1 in
Actual width of dinning room table = 1 × 2½ = 2.5 ft
Area of dinning room table = length × width = 5 × 2.5 = 12.5 ft²
Area of the dinning room:
Given that scale of the sketch is 1 in = 2½ ft
Length of the dinning room on the sketch = 7⅕ in
Actual length of dinning room = 7⅕ × 2½ = 18 ft
Width of the dinning room on the sketch = 4⅘ in
Actual width of dinning room = 4⅘ × 2½ = 12 ft
Area of dinning room = length × width = 18 × 12 = 216 ft²
Area of the dinning room not covered by the table = area of the dinning room - area of the dinning room table
= 216 - 12.5 = 203.5 ft²
What equation results from completing the square and then factoring?
x2 + 2x = 9
Answer: (x+1)^2=10
Step-by-step explanation:
Which decimal number is equal to 318 ? 0.167 0.16¯ 0.16¯¯¯¯ 0.167¯¯¯¯¯
The fraction 3/18 is equal to the decimal number [tex]\hat{0.167}[/tex]
What is an equation?An equation is an expression that is used to show the relationship between two or more numbers and variables.
Division is one of the four basic operations of arithmetic. Division is the act of dividing, or separating, a whole into pieces.
Given the expression:
3/18
Dividing gives:
= 0.16666666667
= [tex]\hat{0.167}[/tex]
3/18 is equal to [tex]\hat{0.167}[/tex]
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
A housing policy research group reported that the proportion of homeowners in the U.S. who struggle to make monthly mortgage payments is 0.29, or 29%. A real estate company is interested in examining this claim in a particular state that has experienced recent economic hardships Refer to the information above regarding the survey of homeowners with mortgages. The survey found that in a sample of 451 randomly selected homeowners, 183 reported having difficulty paying their mortgages each month. If a hypothesis test were to be conducted to determine if the problem is worse in this particular state, which of the following would be the correct value of the test statistic? Choose the closest value, taking all calculations to four decimal places.
a) 5.42
b) 0.45
c) 0.36
d) 18.99
e) 0.26
Answer:
The option is A
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.29[/tex]
The sample size is n = 451
The number that was having difficulty is k = 183
Generally the sample proportion is mathematically represented as
[tex]\^ {p} = \frac{k}{n}[/tex]
=> [tex]\^ {p} = \frac{183}{451}[/tex]
=> [tex]\^ {p} = 0.4058[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \^ {p} - p }{ \sqrt{\frac{p (1-p)}{n} } }[/tex]
=> [tex]t = \frac{0.4058 - 0.29 }{ \sqrt{\frac{0.29 (1-0.29)}{451} } }[/tex]
=> [tex]t = 5.42 [/tex]
In a certain community, 8% of all adults over 50 have diabetes. If a health service in this community correctly diagnoses 95% of all persons with diabetes as having the disease and incorrectly diagnoses 2% of all persons without diabetes as having the disease, find the probabilities that
a) the community health service will diagnose an adult over 50 as having diabetes.
b) a person over 50 diagnosed by the health service as having diabetes actually has the disease.
Answer and Step-by-step explanation:
Solution:
Given:
Let A is the event of a person over 50 diagnosed by health service.
B1 is the event that an adult over 50 actually has diabetes.
B2 is the event that an adult over 50 does not have diabetes.
P (B1) = 8% = 0.08
And P (B2) = 1 – P (B1)
= 1 – 0.08
= 0.92
Correctly diagnose of all persons with diabetes= 95%
P (A/B1) = 0.95
Incorrectly diagnose of all persons without diabetes= 2%
P (A/B2) = 0.02
(a) ) the community health service will diagnose an adult over 50 as having diabetes.
P (B1) P (A/B1) = (0.08) (0.95) = 0.076
P (B2) p (A/B2) = (0.92) (0.02) =0.0184
P (B1) P (A/B1) + P (B2) p (A/B2) = 0.076 + 0.0184
= 0.0944
(b) A person over 50 diagnosed by the health service as having diabetes actually has the disease.
By using formula:
P (B1/A) = P (B1) P (A/B1) / P (B1) P(A/B1) + P (B2) P (A/B2)
Put all the given values:
= (0.08) (0.95) / (0.08) (0.95) + (0.92) (0.02)
=0.076 / 0.076 + 0.0184
=0.076 / 0.0944
= 0.8050
Using conditional probability, it is found that there is a:
a) 0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.
b) 0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.Item a:
The percentages of a positive test is:
95% of 8%(have diabetes).2% of 92%(do not have diabetes).Hence:
[tex]P(A) = 0.95(0.08) + 0.02(0.92) = 0.0944[/tex]
0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.
Item b:
Event A: Positive test.Event B: Has the disease.From item a, [tex]P(A) = 0.0944[/tex].
The probability of both a positive test and having the disease is:
[tex]P(A \cap B) = 0.95(0.08)[/tex]
Hence, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.95(0.08)}{0.0944} = 0.8051[/tex]
0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.
A similar problem is given at https://brainly.com/question/14398287
There is a sidewalk of width x around a rectangular garden. If the garden measures twenty-feet by thirty-feet, then the combined area of the garden and sidewalk is
Answer:
Area = 200 + 50 + x
Step-by-step explanation:
Given
Length = 20
Width = 30
Side Walk = x
Required
Determine the area.
To do this we need to get the new worth and length by adding the length of the sidewalk.
This gives:
Length = 20 + x.
Width = 30 + x
So, area becomes.
Area = (20 + x)(30 + x)
Area = 600 + 20x + 30x + x²
Area = 200 + 50 + x²
Solve the system by substitution.
y=-x^2+2x+10
y=x+4
Answer:
x=3, y=7
x=-2, y=2
Step-by-step explanation:
System of Equations
We have the following equations:
[tex]y=-x^2+2x+10[/tex]
[tex]y=x+4[/tex]
We'll solve it by substitution. Since the second equation is already solved for y, we use that expression and substitute into the first equation:
[tex]x+4=-x^2+2x+10[/tex]
Since this is a quadratic equation, it's convenient to have all terms to one side:
[tex]x+4+x^2-2x-10=0[/tex]
Simplifying and reordering:
[tex]x^2-x-6=0[/tex]
Factoring:
[tex](x-3)(x+2)=0[/tex]
Solving:
x=3, x=-2
Those yield to two solutions for y:
y=x+4
y=7, y=2
The solutions of the system are:
x=3, y=7
x=-2, y=2
Rachel is driving her car at a constant 60 miles per hour. If she drives for four hours, what is the
total distance she drives?
Answer:
240
Step-by-step explanation:
60 x 4
Answer:
240 miles
Step-by-step explanation:
If she's going 60 miles per hour and she drives 4 hours then you multiply those two numbers together and get that she has drove 240 miles.
You pay $25 each month for satellite TV, plus $1.50 for every movie you purchase. Write and solve an equation to find the number of movies purchased during a month with a total bill of $38.50
Answer
9 movies
Step-by-step explanation:
$25 - 38.50 = $13.50
13.50/ $1.50 = 9
Let x be Bob's age. Heather is 5 years younger than Bob. Write an expression for Heather's age.
Answer:
x-5
Step-by-step explanation:
since we don't know bob's age, x will represent it. we know that heather is 5 years YOUNGER than bob.
x (bob's age) - 5 (because that's how many years heather is younger than bob is)
hope this helps :D
MY TEACHER TEXTED ME THIS IDK WHAT TO EVEN DO:( help i luv u
Answer:
yea
same
Step-by-step explanation:
Answer:
well i hope you can figure it out
Step-by-step explanation:
a cell phone company charged 49.95 per month plus 0.05 per call minute i used 200 call minutes last month proportional or not proportional
Answer:
Not sure what you are asking here but the answer is $59.95
Step-by-step explanation:
$49.95 + (10 * 0.05)
Can someone please help, ty!!
(Will mark brainliest)
Answer:
I believe it is four hours
Step-by-step explanation:
If an automobile slows from 26MS to 18 MS in a period of 4.0 S what was the average acceleration
6x-2x+11= -5
xs are unknown, not multiply.
Step-by-step explanation:
6x-2x+11=-5. 6x-2x=-5-11. 4x=16 4x/4=16/4. x=4
5x-25=-10
Please HELP
= 5x - 25 = -10
= 5x = -10 + 25 ( transposing-25 from LHS to RHS changes -25 to +25 )
= 5x = 15
= x = 15 ÷ 5 ( transposing ×5 from LHS to RHS changes ×5 to ÷5 l
= x = 3
Let us check whether or not we have found out the correct value by keeping 3 in the place of x :
= 5 × 3 - 25 = -10
= 15 - 25 = -10
= -10 = -10
LHS = RHS
We have found out the correct value of x .
Therefore x = 3 .
which expression is equivalent to -1/2(3- 2/5)
A. -3/2 - 1/5
B. -3/2 + 1/5
C. -3 1/2 - 1/5
D. -3 1/2 + 1/5
Answer: -3 1/2 - 1/5