The 3rd term of an arithinetic progression is-9
and the 7th term is -29. Find the 10th term of the
progression.
Answer:
-64
Step-by-step explanation:
The computation of the 10th term of the progression is shown below:
The 3rd term is -9
A_n = a + (n - 1)d
-9 = a + (3 - 1)d
-9 = a + 2d
-9 - 2d = a
Now the 7th term is -29
A_n = a + (n - 1)d
-29 = a + (7 - 1)d
-29 = a + 6d
Put the a value to the above equation
-29 = -9 - 2d + 6d
-29 + 9 = 4d
-20 = 4d
d = -5
Now
-9 - 2d = a
-9 - 2(-5) = a
-9 - 10 = a
a = -19
Now finally the 10th term of the progression is
= a + (n - 1)d
= -19 + (10- 1)-5
= -19 -45
= -64
A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the disease. Also, if a person does not have the disease, the test will report that he or she does not have it with probability 0.9. Only 1% of the population has the disease in question. If a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the conditional probability that she does, in fact, have the disease
Answer:
8.33% probability that she does, in fact, have the disease
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[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.
In this question:
Event A: Positive test
Event B: Has the disease
Probability of a positive test:
10% of 100-1 = 99%
90% of 1%
So
[tex]P(A) = 0.1*0.99 + 0.9*0.01 = 0.108[/tex]
Positive test and having the disease:
90% of 1%
[tex]P(A \cap B) = 0.9*0.01 = 0.009[/tex]
What is the conditional probability that she does, in fact, have the disease
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.009}{0.108} = 0.0833[/tex]
8.33% probability that she does, in fact, have the disease
35. A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 6 workers has the same chance of being selected as does any other group (drawing 6 slips without replacement from among 45). a. How many selections result in all 6 workers coming from the day shift
Answer:
38760 selections result in all 6 workers coming from the day shift.
Step-by-step explanation:
The order in which the workers are chosen is not important, which means that we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
a. How many selections result in all 6 workers coming from the day shift:
20 workers are employed on the day shift, so this is a combination of 6 from a set of 20.
[tex]C_{20,6} = \frac{20!}{6!(20-6)!} = 38760[/tex]
38760 selections result in all 6 workers coming from the day shift.
Every day when commuting to and from work, Stefanie
drives her car a total of 143 miles for 2.5 hours. Her car
already has 45,300 miles on it.
a. Write a function that shows the total number of
miles, f(x), Stefanie's car will have been driven
after x more days. Explain how you know where
each number goes in the equation.
b. If Stefanie works 4 days a week, how many miles
will her car have been driven after 3 weeks? Show
and explain all your work.
Answer:
a) [tex]f(x) = 45300 + 143x[/tex]
In which 45300 is the current number of miles driven and 143 is the amount of miles she drives each day.
b) 47,016 miles.
Step-by-step explanation:
Question a:
Every day when commuting to and from work, Stefanie drives her car a total of 143 miles for 2.5 hours. Her car already has 45,300 miles on it.
So, after x days of work, the amount of miles driven will be given by
[tex]f(x) = 45300 + 143x[/tex]
In which 45300 is the current number of miles driven and 143 is the amount of miles she drives each day.
Question b:
After 4*3 = 12 days of work. So
[tex]f(12) = 45300 + 143*12 = 47016[/tex]
47,016 miles.
22:4 :: x : 16, what is the value of x, if all the four numbers are in proportion.
Answer:
= 22:4 :: x : 16
22*16 = 4x
352 = 4x
x = 352/4
x = 88
Hope this helps you. Do mark me as brainliest.
Color blindness is an inherited characteristic that is more common in males than females. Let F represent female, and C represent red-green color blindness.
P(C) = 0.039 P(F and C) = 0.004 P(F or C) = 0.548
2. Use the Addition Rule or the "OR" formula for probability, substitute the values given, and solve for the probability of a Female.
P(F or C) = P(F) + P(C) - P(F and C)
Answer:
0.513 = 51.3% probability of being a female.
Step-by-step explanation:
We are given the following formula:
[tex]P(F \cup C) = P(F) + P(C) - P(F \cap C)[/tex]
In which:
Event F: Female
Event C: Red-green color blindness.
Probability of a Female
We have to find P(F), which is given by:
[tex]P(F) = P(F \cup C) + P(F \cap C) - P(C)[/tex]
We are given by:
[tex]P(C) = 0.039, P(F \cap C) = 0.004, P(F \cup C) = 0.548[/tex]
So
[tex]P(F) = P(F \cup C) + P(F \cap C) - P(C) = 0.548 + 0.004 - 0.039 = 0.513[/tex]
0.513 = 51.3% probability of being a female.
Sue has four DVDs and Terry has six DVDs. They
put all their DVDs together and sold them for $10
for two DVDs. How much money will they earn if
they sell all of their DVDs?
Answer:
$50
Step-by-step explanation:
4+6=10/2=5*10=50
A pool has some initial amount of water in it. Then it starts being filled so the water level rises at a rate of 666 centimeters per minute. After 202020 minutes, the water level is 220220220 centimeters.
Answer:
y = mx + b
slope(m) = 6
(20,220)....x = 20 and y = 220
now sub and find b, the y int
220 = 6(20) + b
220 = 120 + b
220 - 120 = b
100 = b
so ur equation is : y = 6x + 100
to graph :
y = 6x + 100.....u have a slope of 6....u have a y int of 100 or (0,100)...
I would say plot (0,100) and since ur slope is 6, go up 6 and to the right 1...but that is not to helpful because ur graph is not in intervals of 1.
So we will find some points on ur line.
y = 6x + 100....when x = 5
y = 6(5) + 100
y = 30 + 100
y = 130....so another point on ur line is (5,130)
y = 6x + 100...subbing in 10 for x
y = 6(10) + 100
y = 60 + 100
y = 160....another point is (10,160)
keep finding points this way...here are some more...
(15,190) , (20,220), (25,250)
Step-by-step explanation:
Answer:
y = 6x + 100
Step-by-step explanation:
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. Choose the correct answer below. A. The matrix is not invertible because its determinant is zero. B. The matrix is invertible because its determinant is not zero. C. The matrix is not invertible because the matrix has 2 pivot positions. D. The matrix is invertible because its columns are multiples of each other. The columns of the matrix form a linearly dependent set.
Answer:
A. The matrix is not invertible because its determinant is zero.
Step-by-step explanation:
The matrix is invertible if the columns and rows are equal. The square matrix is invertible because it has equal rows and columns. The determinant of the matrix is zero then the matrix is no invertible.
Can someone please help me Ik it’s blurry but you have to zoom in it’s due tomorrow
Answer AND Step-by-step explanation:
1. x = 53° Supplementary Angles Theorem
2. x = 37° Complementary Angles Theorem
3. x = 45° Right angle = 90°, and 90 divided in half is 45, so 45 + 45 = 90
4. x = 180° Straight lines are 180 degrees.
5. x = 130° Vertical Angles Theorem
6. x = 90° Right Angle, and Vertical Angles Theorem
7. x = 15° Complementary Angles Theorem
8. x = 60° Supplementary Angles Theorem
9. x = 20° Complementary Angles Theorem
10. x = 140° Supplementary Angles Theorem
11. x = 47° Supplementary Angles Theorem
12. x = 18° Supplementary Angles Theorem
Supplementary Angles Theorem - two angles that are next to each other and add up to 180 degrees.
Complementary Angles Theorem - two angles that are next to each other and add up to 90 degrees.
Vertical Angles Theorem - Angles that are directly across from each other made by an intersection will have the same angle value.
#teamtrees #PAW (Plant And Water)
Maxine Frase plans to bake 12 dozen peanut butter cookies. She will use a recipe in
mperial más. The cookies are baked at 360 °F for 20 minutes.
Ingredients to make 3 DOZEN
1 cup peanut butter
cap chopped peanuts
2 eges
$ cuoces light brown sugar
pomd cake flour
1 teaspoon bicarbonate of soda
pinch of salt
Conversion Table
1 pound = 16 ounces = 480 g
1 teaspoon = 5 ml
250 ml
Convent cup to millilitres.
Answer:
What I don’t understand is this a question or a recipe
Step-by-step explanation:
In a random sample of 70 undergraduate students from a large university, it was found that 37 had used library books. Find the sample proportion
Answer:
The sample proportion of undergraduate students that used library books is 0.5286.
Step-by-step explanation:
The sample proportion is the number of desired outcomes divided by the size of the sample.
In this question:
Sample of 70 undergraduate students, 37 had used library books.
[tex]p = \frac{37}{70} = 0.5286[/tex]
The sample proportion of undergraduate students that used library books is 0.5286.
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
the answer is no. the solution is (1.333, 7.333)
Answer: No, it is not a solution
Step-by-step explanation:
Substitute the value of x as 1 and y as 6
y = x + 6
6 = 1 + 6
6 = 7 (no)
-----------------------------------------
y = 4x + 2
6 = 4(1) + 2
6 = 4 + 2
6 = 6 (Yes)
-----------------------------------------
Even though the solution works in the second equation, it does not work in the first
Therefore (1,6) is not a solution to the system of equations
Mickey’s Pizza charges $5 per Medium Pizza and a $4 delivery charge.
Make a table with the following information:
Pizzas: 1, 2, 3, 4, 5
Cost:
Equation:
WILL GIVE BRAINLIEST. NEED URGENTLY!
Use the FOIL method to find the product below.
(x + 3)(x2 - 6x)
A. x3 - 9x2 - 18
B. X8 - 9x2 - 18x
c. x3 - 3x2 - 18x
D. x2 – 3x2 - 18
Answer:
C) x³-3x²-18x
Step-by-step explanation:
x³-6x²+3x²-18x
x³-3x²-18x
Write 13 1/5 as a decimal.
Answer:
13.2
Step-by-step explanation:
The Fraction 13 1/5 as a decimal is 13.2.
To write 13 1/5 as a decimal, we can divide the fraction part by the denominator:
1 divided by 5 = 0.2
Then, we add the whole number part to the decimal part:
= 13 + 0.2
= 13.2
Therefore, 13 1/5 as a decimal is 13.2.
Learn more about Decimal here:
https://brainly.com/question/30958821
#SPJ6
2.
Chad drove 168 miles in 3 hours.
Part A
How many miles per hour did Chad drive?
Enter your answer in the box.
56
miles per hour
Part B
Chad will drive 672 more miles. He continues to drive at the same rate.
How many hours will it take Chad to drive the 672 miles?
Enter your answer in the box.
C
hours
Answer:
Part A) 56 mph
Part B) 12 hours
Step-by-step explanation:
Part A) 168/3 = 56 mph
Part B) 672/56 = 12 hours
Which names the figure correctly?
Group of answer choices
Lines DF and BE are parallel
Lines BD and CF are perpendicular
Lines DB and AC are intersectind
Lines FC and DB are parallel
Answer:
Step-by-step explanation:
I need a answer to 77.5% of 13.270
Answer:
10.28425
Step-by-step explanation:
I'll send a photo of the problem! :)
Answer:
ok
Step-by-step explanation:
Which conic section does the equation below describe? x+2^2=4y-3
Answer: Circle
Step-by-step explanation:
The owner of a local nightclub has recently surveyed a random sample of 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 35.5 years and population standard deviation was 5 years. What is the p-value associated with the test statistic
Answer:
0.0416
Step-by-step explanation:
Given :
Sample size, n = 300
Sample mean, x = 35.5
Population mean, m = 35
Standard deviation, s = 5
The test statistic :
Zstatistic = (x - m) / s/sqrt(n)
Zstatistic = (35.5 - 35) / 5/sqrt(300)
Zstatistic = 0.5 / 0.2886751
Zstatistic = 1.732
Using the p value calculator from Zstatistic :
One tailed P value at 95% confidence interval is : 0.0416
Triangle NOP is similar to triangle RST. Find the measure of side RS. Round your
answer to the nearest tenth if necessary. Figures are not drawn to scale
Answer:
Step-by-step explanation:
Remark
Try to make sure that when you set up your proportion, that the side you are trying to find is the numerator. Then all you have to do is multiply both sides by the numerator underneath the unknown side.
Equation
x / 11 = 27 / 7
Solution
Multiply both sides by 11
11 * x / 11 = 27 * 11 / 7
x = 297 / 7
x = 42.43
Does anyone know the real answer
Answer:
srry I'm dum need points
Lula has two dogs, one 35 pounds, the other 25 pounds. What is the average weight of Lula's dogs?
Answer:
30
Step-by-step explanation:
25+35= 60
60/2=30
Answer: 30
Step-by-step explanation:
The term average has a number of different meanings. Most generally, it is a single number that is used to represent a collection of numbers. In the context of mathematics, "average" refers to the mean, specifically, the arithmetic mean. It is a relatively simple statistical concept that is widely used in many areas.
The equation below is one of the more commonly understood definitions of the average: [tex]Average =[/tex] [tex]\frac{Sum}{Count}[/tex]
please help asap! It’s due today
I want to purchase a third of a cupcake for
myself, a third for my sister, and 4 thirds for our
cousin. Katara would be great. Please help! Quickly I’m waiting 5 mins :)
Answer:
Well it would be a total of 2 Cup Cakes
Step-by-step explanation:
1/3 + 1/3 + 4/3 =2
2/3 +4/3 = 6/3
ye
Answer:
Step-by-step explanation:
it would be 2
Help
Which product are greater than 2 and 5\6? Select all that apply
Answer:
B, C, & E
Step-by-step explanation:
The current i in ameperes at time t in a particular circuit is given by i=12 sin 5 cos t find the maximum current
Answer:
fart
Step-by-step explanation:
Charlie, Alexander, and Nate went to lunch. The bill, before sales tax and tip, was $37.50. A sales tax of 8% was added.
A) How much was the sales tax?
B)How much was the total bill including tax?
C) The group then tipped 18% on the amount after the sales tax was added. How much did they leave as a tip?
D)What was the total cost of lunch including tax and tip?
Answer:
A.$3.00
B.$40.50
C.$7.29
D.$47.79
BRAINLIEST PLEASE!!!!!!!!!!!!!!!!!!!!