Answer:
8
Step-by-step explanation:
Answer:
8 and 6.
Step-by-step explanation:
2.86 has tenths and hundredths place.
After the decimal point is the tenths place and after the tenths place is hundredths place.
The number 8 is the tenths place and the number 6 is in the hundredths place.
what is 21+23.3+323.45
Answer:
367.75
Step-by-step explanation:
21+23.3+323.45
Add the three terms.
= 367.75
The sum of theses numbers is 367.75.
Answer:
[tex]= 367.75 \\ [/tex]
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: \: \: 21 \\ + \: \: \: \: 23.3 \\ = \: \: 44.3 \\ + 323.45 \\ = 367.75[/tex]
Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
See the answers below.
Step-by-step explanation:
[tex]a.\:\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2x^2-x-5-\left(2a^2-a-5\right)}{x-a}\\\\=\frac{2x^2-x+a-2a^2}{x-a}\\\\=\frac{2\left(x+a\right)\left(x-a\right)-1\left(x-a\right)}{x-a}\\\\=\frac{\left(x-a\right)\left[2\left(x+a\right)-1\right]}{x-a}\\\\=2x+2a-1\\\\\\b.\:\frac{f\left(x+h\right)-f\left(x\right)}{h}=\frac{2\left(x+h\right)^2-\left(x+h\right)-5-\left(2x^2-x-5\right)}{h}\\\\=\frac{2\left(x^2+2xh+h^2\right)-\left(x+h\right)-5-\left(2x^2-x-5\right)}{h}\\[/tex]
Expand and simplify to get:
[tex]=\frac{2h^2+4xh-h}{h}\\\\=\frac{h\left(2h+4x-1\right)}{h}\\\\=2h+4x-1[/tex]
Best Regards!
A company makes wax candles shaped like rectangular prisms. Each candle is 7cm long, 2cm wide, and 10cm tall. If they used 5740cm^3 of wax, how many candles did they make?
Answer: 41 candles
Step-by-step explanation:
Multiply the dimensions of the candle first.
V = l*w*h
7 * 2 = 14
14 * 10 = 140
Now, divide the total amount of wax used by the amount of wax used for one candle.
5,740 / 140 = 41
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class, and 16 in the German class. There are 12 students who are in both Spanish and French, 4 who are in both Spanish and German, and 6 who are in both French and German. In addition, there are 2 students taking all 3 classes. If two students are randomly chosen, what is the probability that at exactly one of them does exactly two language classes.
Answer:
The probability that at exactly one of them does exactly two language classes is 0.32.
Step-by-step explanation:
We can model this variable as a binomial random variable with sample size n=2.
The probability of success, meaning the probability that a student is in exactly two language classes can be calculated as the division between the number of students that are taking exactly two classes and the total number of students.
The number of students that are taking exactly two classes is equal to the sum of the number of students that are taking two classes, minus the number of students that are taking the three classes:
[tex]N_2=F\&S+S\&G+F\&G-F\&S\&G=12+4+6-2=20[/tex]
Then, the probabilty of success p is:
[tex]p=20/100=0.2[/tex]
The probability that k students are in exactly two classes can be calcualted as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{2}{k} 0.2^{k} 0.8^{2-k}\\\\\\[/tex]
Then, the probability that at exactly one of them does exactly two language classes is:
[tex]P(x=1) = \dbinom{2}{1} p^{1}(1-p)^{1}=2*0.2*0.8=0.32\\\\\\[/tex]
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. In a talent competition, half of the contestants are eliminated in each round. At the end of the nth round, 32 contestants remain. If there were 1,024 contestants at the start of the competition, what is the value of n? The value of n is .
Answer:
n =32
Step-by-step explanation:
If 1 contestant is eliminated each round
then of 1024contestants
32 left
1024/32=32
Answer:
n=32
Step-by-step explanation:
Given: m∠AOB=50°, m∠FOE=70°. Find: m∠AOC, m∠BOD, m∠COE and m∠COD.
Answer:
m∠AOC= 120°
, m∠BOD = 130°
m∠COE = 110°
m∠COD.= 60°
Step-by-step explanation:
Let's note that
AOF = COD= 60°
BOC = FOE= 70°
AOB = DOE= 50°
Given: m∠AOB=50°, m∠FOE=70°. m∠AOC
, m∠BOD,
m∠COE
m∠COD. = AOF = (360-(2(70)+2(50)))/2
AOF = (360-240)/2
AOF = 120/2
AOF = 60°= COD
COE = COD+DOE= 60+50= 110°
BOD = BOC + COD = 70+60= 130°
AOC = AOB + BOC = 50+70 = 120°
Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. Suppose that we select 3 random samples of 500 adults from this population. Which of the following is most likely to occur with the three samples?
A. The number that had never been married will equal 20% in each of the three samples.B. The number that had never been married will vary in each sample due to the random selection of adults.C. The average for the three samples of the number of adults that had never been married will equal 20%.D. The number of adults that had never been married will increase for each sample because the number is generally increasing over time.
Answer:
Option B
Step-by-step explanation:
The number that had never been married will vary in each sample due to the random selection of adults.
This number will vary in each sample to the random selection process but they might or might not be as close as possible to one another after sampling.
Find the possible ones place digit in the square root of the following (apply the properties) a) 2039184
b) 10,004,569
How many natural numbers lie between the squares of 41 and 42?
What will be the value of ‘ x’ in Pythagorean triplet (41, 9, x)?
Check whether 15028 is a perfect square? If not find the smallest number by which 15028 be divided to make it a perfect square. Also find the square root of the new number formed.
A gardener has 5190 plants. He wants to plant in such a way that the number of rows and columns remains the same. Find the minimum number of plants left in this arrangement.
Answer:
The answer is given below
Step-by-step explanation:
1) Find the possible ones place digit in the square root of the following
a) 2039184
The number 2039184 ends with 4, therefore the square root of the number can either end in 2 or 8
2² = 4, √4 = 2
8² = 64, √64 = 8
b) 10,004,569
The number 10,004,569 ends with 9, therefore the square root is the number will end in 3
3² = 9, √9 = 3
2) How many natural numbers lie between the squares of 41 and 42
42² = 1764 and 41² = 1681
Therefore the numbers that lie between 1764 and 1681 = (1764 - 1681) - 1 = 83 - 1 = 82
3) What will be the value of ‘ x’ in Pythagorean triplet (41, 9, x)
Pythagorean consist of three positive numbers a, b, c such that a² + b² = c². Therefore: x² + 9² = 41²
x² = 41² - 9² = 1681 - 81
x² = 1600
x = √1600 = 40
4) Check whether 15028 is a perfect square
15028 = 2 × 2 × 13 × 17 × 17
15028 = 2² × 13 × 17²
It is not a perfect square. If it is divided by 13 it becomes a perfect square, that is:
15028/13 = 2² × 17²
15028/13 = (2 × 17)² = 34²
34² = 15028/13
34² = 1156
The square root of the new number formed is 34 (i.e √1156)
5) A gardener has 5190 plants. He wants to plant in such a way that the number of rows and columns remains the same.
let the number if rows be x. Since the rows and columns are the same, the number of columns = x.
x² = 5190
x = √5190 = 72² + 6.
Therefore at least six plant would be left out
Given that 9 x − 4 y = 20 Find y when x = − 2 Give your answer as an improper fraction in its simplest form
Answer:
[tex]\boxed{\df\ \dfrac{-19}{2}}[/tex]
Step-by-step explanation:
Hi,
x=-2
it gives
9*(-2)-4y=20
<=> -18-4y=20
<=> 18-18-4y=20+18=38
<=> -4y=38
<=> y = -38/4=-19/2
hope this helps
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cmys. Find the rate at which the area within the circle is increasing after (a) 1 s, (b) 3 s, and (c) 5 s. What can you conclude?
Answer:
a) [tex]t = 1\,s[/tex], [tex]\dot A \approx 22619.467\,\frac{cm^{2}}{s}[/tex], b) [tex]t = 3\,s[/tex], [tex]\dot A \approx 67858.401\,\frac{cm^{2}}{s}[/tex], c) [tex]t = 5\,s[/tex], [tex]\dot A \approx 113097.336\,\frac{cm^{2}}{s}[/tex]. The rate at which the area within the circle is increasing linearly inasmuch as time passes by.
Step-by-step explanation:
The area of a circle is described by the following formula:
[tex]A = \pi \cdot r^{2}[/tex]
Where:
[tex]A[/tex] - Area, measured in square centimeters.
[tex]r[/tex] - Radius, measured in centimeters.
Since circular ripple is travelling outward at constant speed, radius can be described by the following equation of motion:
[tex]r (t) = \dot r \cdot t[/tex]
Where:
[tex]\dot r[/tex] - Speed of the circular ripple, measured in centimeters per second.
[tex]t[/tex] - Time, measured in seconds.
The rate of change of the circle is determined by deriving the equation of area and replacing radius with the function in terms of the speed of the circular ripple and time. That is to say:
[tex]\dot A = 2\cdot \pi \cdot r \cdot \dot r[/tex]
[tex]\dot A = 2 \cdot \pi \cdot \dot r^{2}\cdot t[/tex]
Where:
[tex]\dot A[/tex] - Rate of change of the circular area, measured in square centimeters per second.
[tex]\dot r[/tex] - Speed of the circular ripple, measured in centimeters per second.
[tex]t[/tex] - Time, measured in seconds.
If [tex]\dot r = 60\,\frac{cm}{s}[/tex], then:
a) [tex]t = 1\,s[/tex]
[tex]\dot A = 2\cdot \pi \cdot \left(60\,\frac{cm}{s} \right)^{2}\cdot (1\,s)[/tex]
[tex]\dot A \approx 22619.467\,\frac{cm^{2}}{s}[/tex]
b) [tex]t = 3\,s[/tex]
[tex]\dot A = 2\cdot \pi \cdot \left(60\,\frac{cm}{s} \right)^{2}\cdot (3\,s)[/tex]
[tex]\dot A \approx 67858.401\,\frac{cm^{2}}{s}[/tex]
c) [tex]t = 5\,s[/tex]
[tex]\dot A = 2\cdot \pi \cdot \left(60\,\frac{cm}{s} \right)^{2}\cdot (5\,s)[/tex]
[tex]\dot A \approx 113097.336\,\frac{cm^{2}}{s}[/tex]
The rate at which the area within the circle is increasing linearly inasmuch as time passes by.
What is the formula for area of a trapezuim??
Answer:
The formula is 1/2h(a+b)
h stands for the perpendicular height
a and b stand for the two horizontal lengths which are parallel to each other
Among coffee drinkers, men drink a mean of 3.2 cups per day with a standard deviation of 0.8 cups. Assume the number of cups per day follows a normal distribution.
a. What proportion drink 2 cups per day or more?
b. What proportion drink no more than 4 cups per day?
c. If the top 5% of coffee drinkers are considered "heavy" coffee drinkers, what is the minimum number of cups consumed by a heavy coffee drinker?
d. If a sample of 20 men is selected, what is the probability that the mean number of cups per day is greater than 3?
Answer:
a) 0.9332 = 93.32% drink 2 cups per day or more.
b) 0.8413 = 84.13% drink no more than 4 cups per day
c) The minimum number of cups consumed by a heavy coffee drinker is 4.52.
d) 86.86% probability that the mean number of cups per day is greater than 3
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 3.2, \sigma = 0.8[/tex]
a. What proportion drink 2 cups per day or more?
This is 1 subtracted by the pvalue of Z when X = 2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2 - 3.2}{0.8}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
1 - 0.0668 = 0.9332
0.9332 = 93.32% drink 2 cups per day or more.
b. What proportion drink no more than 4 cups per day?
This is the pvalue of Z when X = 4.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4 - 3.2}{0.8}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.8413 = 84.13% drink no more than 4 cups per day
c. If the top 5% of coffee drinkers are considered "heavy" coffee drinkers, what is the minimum number of cups consumed by a heavy coffee drinker?
This is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 3.2}{0.8}[/tex]
[tex]X - 3.2 = 1.645*0.8[/tex]
[tex]X = 4.52[/tex]
The minimum number of cups consumed by a heavy coffee drinker is 4.52.
d. If a sample of 20 men is selected, what is the probability that the mean number of cups per day is greater than 3?
Sample of 20, so applying the central limit theore with n = 20, [tex]s = \frac{0.8}{\sqrt{20}} = 0.1789[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 3.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3 - 3.2}{0.1789}[/tex]
[tex]Z = -1.12[/tex]
[tex]Z = -1.12[/tex] has a pvalue of 0.1314
1 - 0.1314 = 0.8686
86.86% probability that the mean number of cups per day is greater than 3
100 pts You have a bag of 15 marbles: 5 blue, 3 red, 4 green, and 3 yellow. You draw 3 marbles without replacement. Which action, performed before the draws, increases the probability of drawing 3 green marbles in a row?
Answer:
see below
Step-by-step explanation:
You can remove one or more of the other color marbles to increase the probability of drawing a green marble
or
You can add one or more green marbles to have more green marbles in the bag
Solve for x: −3x + 3 < 6
Answer:x>-1
Step-by-step explanation:
Step 1: Subtract 3 from both sides.
-3x+3-3<6-3
-3x<3
Step 2: Divide both sides by -3.
-3x/-3<3/3
X>-1
The temperature is −18.2 Celsius in South Dakota and -9.7 Celsius Minnesota. Which one of the following inequalities correctly compares the temperatures? Choose 1 answer: Which one of the following descriptions is correct?
Answer:
The answer is A) -9.7 > -18.2
Step-by-step explanation:
This is because, when you are thinking about negative numbers, the closer they are to 0, the greater they are. So, it is warmer in Minnesota.
Answer:
A and A
Step-by-step explanation:
Please help !! Correct and first answer I’ll give you brainesttttt ! What is the equation of the line?
Step-by-step explanation:
can u give image PlZzzzz ....
Answer:
Hey!
Your answer should be Y=2x+4
Step-by-step explanation:
Hope this helps!
y= -3/2x-6 x=15 plssssssssssssssssssssssss help
Answer:
-45/2 - 12/2 = -57/2
Step-by-step explanation:
Substitute 15 for x in the given equation: y = (-3/2)x - 6 becomes
y = (-3/2)(15) - 6 = -45/2 - 6 when x = 15. This is equivalent to -57/2
What is the inverse of the function f(x) =1/4 x – 12?
Step-by-step explanation:
solve f(x) by supposing it has y and and then interchange it with x .
hope this is helpful
The answer to – 7x + y = -10
Step-by-step explanation:
y=7x-10
Answer:
[tex]\huge \boxed{y=7x-10}[/tex]
Step-by-step explanation:
[tex]-7x+y=-10[/tex]
[tex]\sf Add \ 7x \ on \ both \ sides.[/tex]
[tex]-7x+y+7x=-10+7x[/tex]
[tex]y=7x-10[/tex]
Please any help with this math problem
Answer:
y = 1/4X + 1/2
Step-by-step explanation:
the formula of a line is y = aX + b
a = the slope, so a = 1/4. you get the following:
y = 1/4X + b
to find b we need to fill in the coordinates:
1/2 = 1/4 • 0 + b
b = 1/2
so the answer is:
y = 1/4X + 1/2
PROBLEM 6. 10 A histogram has mean 70 and standard deviation 5 If the histogram is not bell shaped but it is symmetric. Find the least proportion of data falls between 70 and 80 If the histogram is bell shaped. Find the proportion of data between 65 and 77
Answer:
a. 0.4772 = 47.72 %
b. 0.7605 = 76.05 %
Step-by-step explanation:
What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.
We have that z is equal to:
z = (x - m) / (sd)
x is the value to evaluate, m the mean, sd the standard deviation
a. ind the least proportion of data falls between 70 and 80 If the histogram is bell shaped:
So for 70 copies we have:
z = (70 - 70) / (5)
z = 0
and this value represents 0.5
So for 80 copies we have:
z = (80 - 70) / (5)
z = 2
and this value represents 0.9772
p (70 > x > 80) = 0.9772 - 0.5
p (70 > x > 80) = 0.4772 = 47.72 %
b. Find the proportion of data between 65 and 77
So for 65 copies we have:
z = (65 - 70) / (5)
z = -1
and this value represents 0.1587
So for 77 copies we have:
z = (77 - 70) / (5)
z = 1.4
and this value represents 0.9192
p (65 > x > 77) = 0.9192 - 0.1587
p (65 > x > 77) = 0.7605 = 76.05 %
If a tank holds 4500 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as V = 4500 (1 − 1 /50 t )^2. 0≤ t ≤ 50. At what time is the water flowing out the fastest?
Answer:
t = 0
Before it starts rushing that's when it will be fastest
Step-by-step explanation:
For the water ib the tank to flow very fast it means that there is a big volume of water present.
And for volume of water to be present that much it means that the water must
have not leaked much or at all.
And for that it signifies large volume of water.
If we do the calculation we'd see that time will be actually equal to zero for the pressure and the volume of the water to be biggest.
V = 4500 (1 − 1 /50 t )^2
V = 4500
4500 = 4500(1- 1/50t)²
1 = 1- 1/50t
0 = -1/50t
t = 0
Imagine you have a rectangular wooden block with dimensions of 10 cm x 3 cm x 8 cm (L x W x H). Required:a. What is the volume of your wooden block?b. What is the density of this wooden block if it has a mass of 168 g?
Answer:
a) The volume of the wooden block is 240 cm^3.
b) The density of the wooden block is 0.7 g/cm^3.
Step-by-step explanation:
The volume of the rectangular wooden block can be calculated as the multiplication of the length in each dimension: length, wide and height.
With dimensions 10 cm x 3 cm x 8 cm, the volume is:
[tex]V=L\cdot W\cdot H = 10\cdot 3\cdot 8=240[/tex]
The volume of the wooden block is 240 cm^3.
If we know that the mass of the wooden block is 168 g, we can calculate the density as:
[tex]\rho = \dfrac{M}{V}=\dfrac{168}{240}=0.7[/tex]
The density of the wooden block is 0.7 g/cm^3.
Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. Then, from the gas station, she travels 5 miles to return home. The entire trip forms a triangle. What was the smallest angle made at her trip? A. At the gas station B. At Lucy's home C. At the post office D. It depends on the direction she is traveling
Answer:
the correct choice is A. At the gas station
Step-by-step explanation:
Lucy starts at home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at the post office.
Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.
From the given data:
HP=3;
PG=4;
GH=5;
∠P=90°.
The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.
Answer:
a
Step-by-step explanation:
Please answer this correctly
Answer:
30
Step-by-step explanation:
Answer:
It would decrease by 9.
Step-by-step explanation:
52 is the original mean or the initial mean.
43 is the final mean.
52-43 = 9
So 9 is the difference.
Hope this helped!
State the size of angle 'n' in the triangle illustrated below.
Answer:
Option B
Step-by-step explanation:
<r = 32 degrees (alternate angles )
<r = <n = 32 degrees (vertical angles)
Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience, she knows that 60% of her students do homework regularly. Moreover, 95% of the students who do their homework regularly generally pass the course. She also knows that 85% of her students pass the course.
a. What is the probability that a student will do homework regularly and also pass the course?
b. What is the probability that a student will neither do homework regularly nor will pass the course?
c. Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.
d. Are the events "pass the course" and "do homework regularly" independent? Explain.
Answer:
a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57
b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12
c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.
d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.
Step-by-step explanation:
Let the event that a student does homework regularly be H.
The event that a student passes the course be P.
- 60% of her students do homework regularly
P(H) = 60% = 0.60
- 95% of the students who do their homework regularly generally pass the course
P(P|H) = 95% = 0.95
- She also knows that 85% of her students pass the course.
P(P) = 85% = 0.85
a) The probability that a student will do homework regularly and also pass the course = P(H n P)
The conditional probability of A occurring given that B has occurred, P(A|B), is given as
P(A|B) = P(A n B) ÷ P(B)
And we can write that
P(A n B) = P(A|B) × P(B)
Hence,
P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57
b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')
From Sets Theory,
P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1
P(H n P) = 0.57 (from (a))
Note also that
P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)
0.60 = P(H n P') + 0.57
P(H n P') = 0.60 - 0.57
Also
P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)
0.85 = P(H' n P) + 0.57
P(H' n P) = 0.85 - 0.57 = 0.28
So,
P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1
Becomes
0.03 + 0.28 + 0.57 + P(H' n P') = 1
P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12
c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.
Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,
P(A n B) = 0.
But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.
Hence, the two events aren't mutually exclusive.
d. Are the events "pass the course" and "do homework regularly" independent? Explain
Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when
P(A|B) = P(A)
P(B|A) = P(B)
P(A n B) = P(A) × P(B)
To check if the events pass the course and do homework regularly are mutually exclusive now.
P(P|H) = 0.95
P(P) = 0.85
P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671
P(H) = 0.60
P(H n P) = P(P n H)
P(P|H) = 0.95 ≠ 0.85 = P(P)
P(H|P) = 0.671 ≠ 0.60 = P(H)
P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)
None of the conditions is satisfied, hence, we can conclude that the two events are not independent.
Hope this Helps!!!
Please help with this problem
Answer:
The length of the short side is 14.5 units, the length of the other short side is 18.5 units, and the length of the longest side is 23.5 units.
Step-by-step explanation:
The Pythagorean Theorem
If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
This relationship is represented by the formula:
[tex]a^2+b^2=c^2[/tex]
Applying the Pythagorean Theorem to find the lengths of the three sides we get:
[tex](x)^2+(x+4)^2=(x+9)^2\\\\2x^2+8x+16=x^2+18x+81\\\\2x^2+8x-65=x^2+18x\\\\2x^2-10x-65=x^2\\\\x^2-10x-65=0[/tex]
Solve with the quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=-10,\:c=-65:\quad x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}\\\\x_{1}=\frac{-\left(-10\right)+ \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5+3\sqrt{10}\\\\x_{2}=\frac{-\left(-10\right)- \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5-3\sqrt{10}[/tex]
Because a length can only be positive, the only solution is
[tex]x=5+3\sqrt{10}\approx 14.5[/tex]
The length of the short side is 14.5, the length of the other short side is [tex]14.5+4=18.5[/tex], and the length of the longest side is [tex]14.5+9=23.5[/tex].
Make a the subject of the formula: T= a + 4
Answer:
a = T - 4
Step-by-step explanation:
Simply just subtract 4 on both sides to get the answer!
Answer:
a=T-4
Step-by-step explanation:
subtract 4
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n equals 1036 and x equals 583 who said "yes." Use a 90 % confidence level.
Required:
a. Find the best point estimate of the population proportion p.
b. Identify the value of the margin of error E =_______
c. Construct the confidence interval.
d. Write a statement that correctly interprets the confidence interval.
1. One has 99% confidence that the sample proportion is equal to the population proportion.
2. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
3. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
Answer:
a. p=0.562
b. E = 0.0253
c. The 90% confidence interval for the population proportion is (0.537, 0.587).
d. We have 90% confidence that the interval (0.537, 0.587) contains the true value of the population proportion.
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.562.
[tex]p=X/n=583/1038=0.562[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.562*0.438}{1038}}\\\\\\ \sigma_p=\sqrt{0.000237}=0.0154[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.0154=0.0253[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.562-0.0253=0.537\\\\UL=p+z \cdot \sigma_p = 0.562+0.0253=0.587[/tex]
The 90% confidence interval for the population proportion is (0.537, 0.587).
We have 90% confidence that the interval contains the true value of the population proportion.