Answer:
(a)0.0005
(b)0.2720
Step-by-step explanation:
Total Number of Transistors = 16
To find the probability that 4 selected at random are defective (or non-defective), we find the probability of the 1st, 2nd, 3rd, and 4th defective (or non-defective) items in that order, Note that the selection is without replacement.
(a)Probability that all are defective
Number of Defective Transistors =4
P(all are defective) [tex]=\dfrac{4}{16} \times \dfrac{3}{15} \times \dfrac{2}{14} \times \dfrac{1}{13}[/tex]
=0.0005
(b)Probability that none are defective
Number of Non-Defective Transistors =16-4=12
P(none are defective) [tex]=\dfrac{12}{16} \times \dfrac{11}{15} \times \dfrac{10}{14} \times \dfrac{9}{13}[/tex]
=0.2720
The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 9,000 after 3 years. What was the initial population P0? (Round your answer to one decimal place.)
Answer:
Step-by-step explanation:
Let P be the population of the community
So the population of a community increase at a rate proportional to the number of people present at a time
That is
[tex]\frac{dp}{dt} \propto p\\\\\frac{dp}{dt} =kp\\\\ [k \texttt {is constant}]\\\\\frac{dp}{dt} -kp =0[/tex]
Solve this equation we get
[tex]p(t)=p_0e^{kt}---(1)[/tex]
where p is the present population
p₀ is the initial population
If the initial population as doubled in 5 years
that is time t = 5 years
We get
[tex]2p_o=p_oe^{5k}\\\\e^{5k}=2[/tex]
Apply In on both side to get
[tex]Ine^{5k}=In2\\\\5k=In2\\\\k=\frac{In2}{5} \\\\\therefore k=\frac{In2}{5}[/tex]
Substitute [tex]k=\frac{In2}{5}[/tex] in [tex]p(t)=p_oe^{kt}[/tex] to get
[tex]\large \boxed {p(t)=p_oe^{\frac{In2}{5}t }}[/tex]
Given that population of a community is 9000 at 3 years
substitute t = 3 in [tex]{p(t)=p_oe^{\frac{In2}{5}t }}[/tex]
[tex]p(3)=p_oe^{3 (\frac{In2}{5}) }\\\\9000=p_oe^{3 (\frac{In2}{5}) }\\\\p_o=\frac{9000}{e^{3(\frac{In2}{5} )}} \\\\=5937.8[/tex]
Therefore, the initial population is 5937.8Find the mean, median, and mode of the following data set:
2, 2, 4, 3, 4, 8,5
A box is filled with 6 red cards, 8 green cards and 4 blue cards what is the probability that the card is not green that is chosen
Answer:
10/18
=5/9
pls mark as brainliest
Answer:
5/9
Step-by-step explanation:
6 red cards, 8 green cards and 4 blue cards = 18 total cards
not green cards = 6 red+ 4 blue = 10 cards
P( not green) = number not green / total
= 10/18
=5/9
A researcher studying the effect of price promotions on consumers' expectations makes up two different histories of the store price of a hypothetical brand of laundry detergent for the past year. Students in a marketing course are randomly assigned to view one or the other price history on a computer. Some students see a steady price, while others see regular promotions that temporarily cut the price. Then the students are asked what price they would expect to pay for the detergent.
Is this study an experiment? Why?A. Yes. Each subject is randomly assigned to a treatment.B. No. Each subject is randomly assigned to a treatment. C. Yes. Each subject is not randomly assigned to a treatment.D. No. Each subject is not randomly assigned to a treatment.
Answer:
A. Yes. Each subject is randomly assigned to a treatment
Step-by-step explanation:
In an experimental study design, subjects are usually grouped into one or more groups in a random manner or by chance, in order to study and ascertain the effect of a treatment.
In the study cited in the question above, students were grouped by chance it randomly into a treatment group or the other. This is typical of an experimental study where subjects are usually categorised and placed randomly in control and treatment groups.
clara is building a triangular garden. sh wants the length of the longest side to be be three or more than twice as long as the length of the shortest side , and the third side would be twelve feet long.
what expression could she write to determine the perimeter of the triangle iof s represents the length of the shortest side?
Answer:
s+(2s+3)+12
Step-by-step explanation:
What is 80,000,000,000,000 in standard form (80 billion)
Answer:
8x10^13
Step-by-step explanation:
Please answer this correctly without making mistakes
Answer:
The perimeter is 26 yards
Step-by-step explanation:
Area of rectangle = A= l x w
1st rectangle = 6 x 5 = 30 yards squared
2nd rectangle= 10 x 3 = 30 yards squared
perimeter of rectangle = 2l+2w= 10 + 10 + 3 + 3= 26
Write 0.00000306 in scientific notation.
Answer:
3.06×10^-6
Step-by-step explanation:
0.00000306 = 3.06×0.000001 = 3.06×10^-6
__
Your calculator or spreadsheet can display numbers in scientific notation.
image 30 points) math
Answer:
[tex]\pi =\frac{C}{d}[/tex]
Step-by-step explanation:
[tex]C=\pi d[/tex]
[tex]\pi =\frac{C}{d}[/tex]
Answer:
I'm not 100%sure but i'm think that it is c
Step-by-step explanation:
Hope this helps! May have gotten it wrong really sorry if I did
a number when added to its one third gives 96.find the number?
Answer: 72.
Step-by-step explanation:
You can solve this by representing the number in an equation that models the problem given. I will use the variable x to represent the number:
[tex]x + \frac{1}{3}x = 96[/tex]
In the equation, I listed the number and added one-third of the same number to it to equal 96.
Now, solve:
[tex]\frac{4}{3}x = 96\\ \\x = 96 / \frac{3}{4} \\\\x = 96 * \frac{3}{4} \\\\x = 72[/tex]
The number is 72.
Students are given a spinner with 5 equal sectors numbered 1-5. They are instructed to spin 50 times and record the number the arrow lands on. If there are 5 groups of students spinning, which of the following is most likely the total number of times the spinner lands in the 3 sector?
Answer: Around 50 times.
Step-by-step explanation:
If the spinner is fair, then each number should have the same probability, that is P = 1/5 = 0.20 for each of the numbers.
Now, we know that we have 5 groups, and each group spins 50 times (so we have a total of 5*50 = 250 spins)
Then we can expect to see the number 3 around:
0.20*150 = 50
Please answer this question !! Thank u tons !! Will give brainliest !!
Answer: D
Step-by-step explanation:
The key to finding the line perpendicular to the one given is teh slope. The slope is the opposite reciprocal of the original line.
m=3
perpendicular m=-1/3
Now that we know the slope, we can see which of our answer choices have -1/3 as the slope. We can see D is the only option that has -1/3 for slope.
Answer:
D) y = -1/3x - 4
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes. This means that since the slope of this line is 3, the slope of a line perpendicular to it would be -1/3 because:
Original slope: 3 (3/1)
Reciprocal (flipped): 1/3
Negative reciprocal (opposite sign): -1/3
The only equation with a slope of -1/3 is D. Therefore, that is the correct answer.
Hope this helps!
Use the triangle shown on the right to complete the statement:
_____ (75*)=14.1/x
Answer: cos
2nd part: Use the equation shown to solve for the value of x. Round to the nearest tenth.
cos(75*)=14.1/x x=14.1/cos(75*)
Answer: 54.5 in
Answer:
Step-by-step explanation:
The answer is 54.5 on edg
For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
What is right angle triangle property?In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.
[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]
Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.
The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.
Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,
[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]
Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.
For the second part, we need to find the value of x. Thus solve the above equation further as,
[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]
Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
Learn more about the right angle triangle property here;
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match each object with vocabulary word that best matches it LJM KM LMK LKM
Answer:
9 + 10 = 21 higkjiitbughu
Answer:
LMK Let me know. KM Kilometer's
Step-by-step explanation:
Evaluate 16x^0 if x= -3
Answer:
16
Step-by-step explanation:
[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]
Hope this helps!
x = -3
[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]
Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]
A sample of size =n48 has sample mean x=54.6 and sample standard deviation =s9.2. Part: 0 / 20 of 2 Parts Complete Part 1 of 2 Construct a 99.9% confidence interval for the population mean μ. Round the answers to one decimal place. A 99.9% confidence interval for the population mean is:____________ .
Answer:
[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]
[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]
The confidence interval is given by (49.94, 59.26)
Step-by-step explanation:
Info given
[tex]\bar X=54.6[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=9.2 represent the sample standard deviation
n=48 represent the sample size
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
The Confidence is 0.999 or 99.9%, and the significance is [tex]\alpha=0.001[/tex] and [tex]\alpha/2 =0.0005[/tex], and the critical value would be [tex]t_{\alpha/2}=3.51[/tex]
And replacing we got:
[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]
[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]
The confidence interval is given by (49.94, 59.26)
4(x-2+y)=
?????????????
[tex]\text{Solve:}\\\\4(x-2+y)\\\\\text{Use the distributive property:}\\\\4x-8+4y\\\\\text{Since you can't simplify it any further, that'll be your answer}\\\\\boxed{4x-8+4y}[/tex]
Answer:
4x-8+4y
Explanation:
///
Which of the following describe an angle with a vertex at Y?
Check all that apply.
Answer:
X
Step-by-step explanation:
X and Y make up a graph
The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. You are visiting the island and have the following encounters with natives. (a) Two natives A and B address you as follows. A says: Both of us are knights. B says: A is a knave.
Answer:
A is a knave
B is a knight
Step-by-step explanation:
If A is telling the truth, then both are knights and B cannot be lying. However, since B claims that A is a knave, they can't be both knights, and there is no possible way that A is a knight.
If A is knave and thus is lying, they aren't both knights. Since B claims A is a knave, his statement can be true and thus B can be knight and A will be knave.
There different kinds of puzzle. The option that is correct about the puzzle is option A which states that A is a knave and B is a knight.
This is known to be a type of progressively hard puzzle that is titled "knights and knaves" puzzles.It is known as a logic puzzles that took place on an island with two kinds of people. It is a puzzle by American mathematician and musician called Raymond Smullyan in his book written in 1978.
Note that knave often lie and thus A may be lying when He said he was a knight Since B claims A is a knave, his statement can be said to be true and thus B can be regarded as knight.
See full question below
The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. You are visiting the island and have the following encounters with natives. (a) Two natives A and B address you as follows. A says: Both of us are knights. B says: A is a knave.
What are A and B?
A. A is a knave and B is a knight.
B. A is a knave and A is a knight.
C. Both A and B are knights.
D. Both A and B are knaves.
Learn more about knight from
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MTH 154 - DOBM
Homework: Homework 4B
Score: 0 of 1 pt
22 of 27 (21 complete)
V Score: 777
4.B.63
* Question H
Use the appropriate compound interest formula to compute the balance in the account afte
stated period of time
$14,000 is invested for 6 years with an APR of 5% and quarterly compounding.
Answer:
$18,862.91
Step-by-step explanation:
The appropriate formula is ...
A = P(1 +r/n)^(nt)
where P is the amount invested (14,000), r is the APR (.05), n is the number of times per year interest is compounded (4), and t is the number of years (6).
Filling in the numbers and doing the arithmetic, we get ...
A = 14,000(1 +.05/4)^(4·6) = 14,000·1.0125^24 ≈ 18,862.91
The balance after 6 years will be $18,862.91.
A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers, familiar with both languages, are asked to code a standard function in both languages, and the time (in minutes) is recorded. The data follow:
Programmer Design Language 1 Design Language 2
1 17 18
2 15 14
3 21 20
4 13 11
5 18 22
6 24 21
7 15 10
8 14 13
9 21 19
10 23 24
11 13 15
12 18 20
(a) Is the assumption that the difference in coding time is normally distributed reasonable?
(b) Find a 95% confidence interval on the difference in mean coding times. Is there any indication that one design language is preferable?
(a) The assumption that the difference in coding time is normally distributed
isis not
reasonable.
(b) The 95% confidence interval is (
,
) Round your answers to 3 decimal places (e.g. 98.765).
There is no / is significant indication that one design language is preferable at a 5% significance level.
Answer:
Step-by-step explanation:
The histogram shown in the attached file show that the distribution of differences is approximately normal.
So, we can assume that the distribution is normal.
.
b)
The 95% confidence level for [tex]\mu _D=\mu_1-\mu_2[/tex] is found
[tex]\bar d \pm t_{0.025,11}\frac{S_D}{\sqrt{n} }[/tex]
[tex]=0.666667 \pm 2.201\frac{(2.964436)}{\sqrt{12} } \\\\0.666667 \pm 2.201(0.85576)\\\\=0.666667+ 1.883525474=2.5502\\\\=0.666667- 1.883525474=-1.2169\\\\=(-1.2169,2.5502)[/tex]
since 0 is in the confidence interval. we do not reject the null hypothesis.
No, there is no indication of one design language is available.
What is the numerator for the simplified sum?
Answer:
The numerator would be [tex]4x+6[/tex]
Step-by-step explanation:
[tex]\frac{x}{x^{2}+3x+2 } +\frac{3}{x+1}[/tex]
= [tex]\frac{4x^{2}+10x+6 }{x^3+4x+5x+2}[/tex]
= [tex]\frac{2(2x+3)(x+1)}{(x+1)(x+1)(x+2)}[/tex]
= [tex]\frac{4x+6}{x^2+3x+2}[/tex]
the numerator is always the top number/value of a fraction thus it being [tex]4x+6[/tex]
brainliest pls
A line contains the points (3,1) and (-6,4). What is the equation for this line in slope-intercept form?
Answer:
y = (-1/3)x + 2
Step-by-step explanation:
Equation of line in slope-intercept form is given by
y = mx +c
where m is the slope of line
c is y intercept
Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)
_________________________________________________
let the equation of required line be y = mx +c
Since points given are (3,1) and (-6,4)
Then, its slope is
m = 4-1/-6-3 = 3/-9 = -1/3
Thus, slope of line is m = -1/3
lets use m = -1/3 in place of m in equation y = mx +c
y = (-1/3)x + c
Since points (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation.
hence lets plug 3 in place of x and 1 in place of y
1 = (-1/3)3 + c
=> 1 = -1 + c
=> c = 1 +1 = 2
Thus, intercept is 2.
Thus, Equation of line in slope-intercept form is y = (-1/3)x + 2.
StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction Solve the proportion for x. After using cross products, the proportion becomes the equation . Isolate the variable by dividing both sides of the equation by . x = .
Answer:
StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction
Solve the proportion for x.
After using cross products, the proportion becomes the equation
✔ 4x = 10
.
Isolate the variable by dividing both sides of the equation by
✔ 4
.
x = ✔ 2.5
.
The value of x is 2.5 for the given proportion.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
The proportion is given in the question, as follows:
4/2 = 5/x
Using cross-product, the proportion becomes the equation as:
4x = 2 × 5
4x = 10
Divide by 4 into both sides of the above equation,
x = 10/4
x = 2.5
Thus, the value of x is 2.5 for the given proportion.
Learn more about the proportion here:
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2. How much time do the students in my school spend on the Internet each
night?
3. What is the height of the tallest waterslide at Wild Rides Water Park?
4. What are the cabin rental prices for each of the state parks in Kentucky?
State whether each question is a statistical question. Explain your reasoning
Answer:
Only the question 2 is a statistical question.
Step-by-step explanation:
Questions
2. How much time do the students in my school spend on the Internet each night?
3. What is the height of the tallest waterslide at Wild Rides Water Park?
4. What are the cabin rental prices for each of the state parks in Kentucky?
The question 2 is a statistical question.
Is the only question that can be answered with a parameter of a population (mean number of hours spent on the internet by the students).
The other two ask for individual values: the height of the tallest waterslide at Wild Rides Water Park, and the cabin rental prices for each of the state parks in Kentucky. This need specific values that are not statistical, but deterministic.
A motorboat moves across the lake at a constant speed when it begins it is which function describes the motor boats distance from the shore a Y equals 4X +50 PY equals 9X +50 CY equals negative 9X +50 DY equals negative 4X +50
What’s the correct answer for this question?
Answer:
what's the question?
it's not showing
Answer:
C.
Step-by-step explanation:
To find the perimeter, we'll use the distance formula
Distance Formula = √(x₂-x₁)²+(y₂-y₁)²
Finding Distance of AB
|AB| = √(-2+5)²+(3+1)²
|AB| = √25
|AB| = 5
Now For BC
|BC| = √(6+2)²+(-3-3)²
|BC| = √(8)²+(-6)²
|BC| = √100
|BC| = 10
FOR CA:
|CA| = √(-5-6)²+(-3+1)²
|CA| = √125
Perimeter of Triangle = 10 + 5 + √125
= 15 + √125
multiply (5 4/7) times (- 2 2/5)
Answer: -13.37
Explanation: I did it in decimals because I didn’t know if your assignment required fraction or decimal. 5 4/7= 5x7=35+4=39/7 so this means 5 4/7 is equal to 39/7. -2 2/5= -2x5=-10+2=-8/5. So it comes out to 39/7x-8/5.
Find the required annual interest rate to the nearest tenth of a percent for $1100 to grow to $1900 if interest is compounded quarterly for 10yr. The required annual interest rate is _%?
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 1100
A = 1900
n = 4 because it was compounded 3 times in a year and n = 12/3 = 4
t = 10 years
Therefore,.
1900 = 1100(1 + r/4)^4 × 10
1900/1100 = (1+ r/4)^40
1.73 = (1+ r/4)^40
Taking log to base 10 of both sides, it becomes
Log 1.73 = 40log(1 + 0.25r)
0.238 = 40log(1 + 0.25r)
Log(1 + 0.25r) = 0.238/40 = 0.00595
Take exponent of both sides, it becomes
10^log(1 + 0.25r) = 10^0.00595
1 + 0.25r = 1.0138
0.25r = 1.0138 - 1 = 0.0138
r = 0.0138/0.25
r = 0.0552
The The required annual interest rate is
0.0552 × 100 = 5.5%
 any help would be great
Answer:
k = P - m - n
Step-by-step explanation:
The question is asking you to rearrange the equation so that k is alone on one side.
P = k + m + n
P - k = (k + m + n) - k
P - k = m + n
(P - k) - P = m + n - P
-k = m + n - P
-1(-k) = -1 (m + n - P)
k = -m - n + P
The equation is completely simplified so this is your answer.