Answer:
a. P(X>695)=0.026
b. P(X<485)=0.44
Step-by-step explanation:
The question is incomplete:
a. higher than 695 on the test.
b. at most 485 on the test.
We have a normal distribution with mean 500 and standard deviation of 100 for the test scores. We will use the z-scores to calculate the probabilties with the standard normal distribution table.
a. We want to calculate the probability that a randomly selected student scores higher than 695.
We calculate the z-score and then we calculate the probability:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{695-500}{100}=\dfrac{195}{100}=1.95\\\\\\P(X>695)=P(z>1.95)=0.026[/tex]
a. We want to calculate the probability that a randomly selected student scores at most 485.
We calculate the z-score and then we calculate the probability:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{485-500}{100}=\dfrac{-15}{100}=-0.15\\\\\\P(X<485)=P(z<-0.15)=0.44[/tex]
Find the area of the circles. Use 3.14 for . (Show work for full credit)
Answer:
Figure 1
The area of circle is 452.16 inches ².
Figure 2
The area of circle is 615.44km².
Figure 3
The area of circle is 132.665 km².
4) The radius of circle is 9 cm and diameter is 18cm.
14 fewer than 12 times the
number of people in my
family is 46.
Answer:
538
Step-by-step explanation:
12 times 46 is 552 then 552 minus 14 is 538
:D
Describe the steps you would use to solve the
following inequality
2x - 3
Answer: No answer
Step-by-step explanation:
Not an inequality, inequalities are of the form 2x - 3 > something.
If it's 2x - 3 > 0 for example, then add both sides by 3 to get 2x > 3, then div by 2 to get x > 3/2.
Hope that helped,
-sirswagger21
A circular plate has circumference of 37.7cm. Calculate the diameter of the plate
Anyone that answers I will mark as brilliant
Answer:
12.0
Step-by-step explanation:
d(pi)=37.7
d=12.0
Consider the following dice game, as played at a certain gambling casino: players 1 and 2 roll a pair of dice in turn. the bank then rolls the dice to determine the outcome according to the following rule: player i,i=1,2, wins if his roll is strictly
Ii={1 if i wins, 0 otherwise}
and show that I1 and I2 are positively correlated. Explain why this result was to be expected.
Answer:
they are positively correlated.
Step-by-step explanation:
We can calculate the individal expectations first. FIrst player will win if that player's roll is greater than the bank's roll. There are (6 possible rolls of player 1 * 6 possible rolls of bank =) 36 total possible rolls, out of which player 1 will win in 15 cases.
[tex]\therefore E(I_i) = 1\cdot \frac{15}{36} + 0 \cdot \frac{21}{36} = \frac{5}{12} \approx 0.4167[/tex]
For the joint expectation, there are (6 possible rolls of player 1 * 6 possible rolls of player 2 * 6 possible rolls of bank =) 216 total possible rolls.
Cases where both players win: Expectation = $2.
If bank rolls 1, both players will win in 5*5 = 25 cases. P1 is one of {2,3,4,5,6}, P2 is one of {2,3,4,5,6}
If bank rolls 2, both players will win in 4*4 = 16 cases.
If bank rolls 3, both players will win in 3*3 = 9 cases.
If bank rolls 4, both players will win in 2*2 = 4 cases.
If bank rolls 5, both players will win in 1*1 = 1 cases.
If bank rolls 6, both players will win in 0*0 = 0 cases.
Total cases = 25+16+9+4+1+0 = 55 cases.
Cases where player 1 wins $1 and player 2 loses: Expectation = $1.
If bank rolls 1, player 1 will win and player 2 will lose in 5*1 = 5 cases. P1 is one of {2,3,4,5,6}, P2 is {1}
If bank rolls 2, player 1 will win and player 2 will lose in 4*2 = 8 cases.
If bank rolls 3, player 1 will win and player 2 will lose in 3*3 = 9 cases.
If bank rolls 4, player 1 will win and player 2 will lose in 2*4 = 8 cases.
If bank rolls 5, player 1 will win and player 2 will lose in 1*5 = 5 cases.
If bank rolls 6, player 1 will win and player 2 will lose in 0*6 = 0 cases.
Total cases = 5+8+9+8+5+0 = 35
Cases where player 2 wins $1 and player 1 loses: Expectation = $1.
This is the same as above with player 1 and 2 exchanged.
Total cases = 35
Cases where both players lose: Expectation = $0.
If bank rolls 1, both players will lose in 1*1 = 1 cases. P1 is {1}, P2 is {1}
If bank rolls 2, both players will lose in 2*2 = 4 cases.
If bank rolls 3, both players will lose in 3*3 = 9 cases.
If bank rolls 4, both players will lose in 4*4 = 16 cases.
If bank rolls 5, both players will lose in 5*5 = 25 cases.
If bank rolls 6, both players will lose in 6*6 = 36 cases.
Total cases = 1+4+9+16+25+36 = 91 cases.
Total of all cases (we expect this to be 216 as mentioned above) = 55+35+35+91=216
So, joint expectation is:
[tex]E(I_1I_2) = \frac{2\cdot 55 +1\cdot 35+1\cdot 35+0\cdot 91}{216} = \frac{180}{216}= \frac{5}{6} \approx 0.8333[/tex]
So, the covariance is given by:
[tex]\texttt{Cov}(I_1I_2) =E(I_1I_2) -E(I_1)\cdot E(I_2)= \frac{5}{6}-\frac{5}{12}\cdot\frac{5}{12}=\frac{95}{144} \approx 0.6597[/tex]
As this is greater than 0 and closer to 1, they are positively correlated.
The reason why this result is expected is because the same bank roll is being used for both players. So, it is very likely that both players will win if the bank roll is 1 or even 2. Also, it is very likely that both players will lose if the bank roll is 6, 5, or even 4. This shows positive correlation between the events.
Jose makes custom bicycles. He sells each bicycle for $400.
A)How much revenue does he make if he sells 1 bicycle?
B)How much revenue does he make if he sells 2 bicycles?
C)How much revenue does he make if he sells X bicycles?
D)What is her revenue equation?
A) $400
B) $800
C) 400*X
D) revenue=400x
Please help me with this math problem
Answer:
[tex]7x^2-2x-2[/tex]
Step-by-step explanation:
[tex]-3x^2+9+10x^2-11-2x[/tex]
Combine like terms:
[tex]10x^2-3x^2-2x+9-11[/tex]
Simplify:
[tex]7x^2-2x-2[/tex]
Hope this helps!
Answer: 7x^2 - 2x - 2
Step-by-step explanation:
in this expression, all you have to do is combine like terms. those are -3x^2 and 10x^2, 9 and -11.
-3x^2 + 9 + 10x^2 - 11 - 2x rearrange to make easier
-3x^2 + 10x^2 - 2x + 9 - 11 combine like-terms
7x^2 - 2x - 2
Determine if two lines are parallel or perpendicular by comparing slopes
Question
Use slopes and y-intercepts to determine if the lines x = -1 and x = 0 are parallel.
Select the correct answer below:
Parallel
Not Parallel
Answer:
They are parallel because they are vertical lines, and all vertical lines are parallel.
Step-by-step explanation:
7. How much alcohol must be added to 480 grams of hand sanitizer that is 24% alcohol to
make it a hand sanitizer that is 40% alcohol? Correct your answer to the nearest whole
number
Answer:
the amount of alcohol to be added is 128 grams
Step-by-step explanation:
Given that:
The initial mass of the hand sanitizer = 480 grams
The initial strength of the hand sanitizer = 24 %
The new strength of the hand sanitizer = 40%
The objective here is to determine the final amount of alcohol that is to be added to get the new strength of the alcohol
First; let's find the mass of alcohol in the initial hand sanitizer;
SO;
= 24 % of 480
[tex]=\dfrac{24}{100}*480[/tex]
= 115.2 grams
If y should represent the mass of the alcohol added to have 40%; we have
The new amount of the alcohol to be[tex](115.2 + y) \ grams[/tex]
The new amount of the hand sanitizer will be[tex](480 + y) grams[/tex]
∴
For the new strength of sanitizer:
40 % of (480 + y) = (115.2 + y)
[tex]0.4 *(480 + y) = (115.2 + y) \\ \\ 192 + 0.4 y = 115.2 + y \\ \\ y (1 - 0.4) = 192 - 115.2 \\ \\ y= \dfrac{76.8}{0.6} \\ \\ y = 128 \ grams[/tex]
Thus ; we can conclude that the amount of alcohol to be added is 128 grams
The volume of this prism
[tex]answer = 66 \: {cm}^{3} \\ solution \\ volume = lwh \\ \: \: \: \: \: \: \: \: \: \: = \: 11 \times 3 \times 2 \\ \: \: \: \: \: \: \: \: \: = 66 \: {cm}^{3} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
[tex]= 66 {cm}^{3} \\ [/tex]
Step-by-step explanation:
[tex]volume = base \times length \times height \\ = 3cm \times 11cm \times 2cm \\ = 66 {cm}^{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
5. Lana pays a semiannual premium of $300 for automobile insurance, a monthly premium of $100 for health insurance, and an annual premium of $700 for life insurance.
Find her monthly expense.
Hey there! I'm happy to help!
We want to find out how much Lana pays per month. Let's dissect each payment we are given so we can find our monthly expense.
---------------------------------------------------------------------------
AUTOMOBILE INSURANCE
$300 for automobile insurance semiannually
The prefix semi- means half. Annual means year. So, she is paying $300 every half year, or six months. So, we can divide 300 by 6 to find how much she pays in one month!
300/6=50
Therefore, she pays $50 a month for automobile insurance.
---------------------------------------------------------------------------
HEALTH INSURANCE
We are told here that she pays $100 every month for health insurance. We don't need do anything else here!
---------------------------------------------------------------------------
LIFE INSURANCE
We see that Lana pays $700 per year on life insurance. We can divide this by 12 to find out how much there is in 1 month!
700/12≈58.33
Therefore, she pays $58.33 every month on life insurance.
---------------------------------------------------------------------------
SOLUTION
Now, we just add all of these monthly totals up to find Lana's monthly expense.
50+100+58.33=208.33
Therefore, Lana's monthly expense is $208.33.
I hope that this helps! Have a wonderful day!
What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
V=
Answer: V=4778.4 cm³
Step-by-step explanation:
[tex]V=\pi r^2\frac{h}{3}[/tex] is the formula for volume. Since we are given the height and radius, we can directly plug it into the equation
[tex]V=\pi (13)^2(\frac{27}{3})[/tex]
[tex]V=169\pi (9)[/tex]
[tex]V=1521\pi[/tex]
[tex]V=4778.4cm^3[/tex]
Please help . I’ll mark you as brainliest if correct! Only the one marked with an X is wrong . I don’t get it
Answer:
(x+7)² = 9
Step-by-step explanation:
x² + 14x + 40 = 0
(x² + 14x) + 40 = 0
(x² +14x +49) + 40 - 49 = 0
(x+7)² - 9 = 0
(x+7)² = 9
Hope this helps!
Answer:
(x+7)² = 9
Step-by-step explanation:
Define a function sinc(x) (pronounced "sink of x") by: text(sinc)(x)={(sin(x)/x text(if)\ x != 0, 1 text(if)\ x = 0.) (This function is used frequently in electrical engineering and signal processing.) Use this list of Basic Taylor Series to find the Taylor Series for f(x) = sinc(x) based at 0. Give your answer using summation notation and give the largest open interval on which the series converges. (If you need to enter [infinity] , use the [infinity] button in CalcPad or type "infinity" in all lower-case.)
Answer:
Step-by-step explanation:
To find the Taylor series of sinc(x) we will use the taylor series of sin(x). We have that
[tex]\sin(x) = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!}[/tex]
which is the taylor series expansion based at 0. Then for [tex]x\neq 0[/tex], by dividing both sidex by x, we have that
[tex]\text{sinc}(x) = \frac{\sin(x)}{x}= \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n+1)!}[/tex]
which is the taylor series expansion for the sinc function. Since the series of sine converges for every value of x. Then the taylor series of sinc converges for every value of x, but 0.
Help! Best Answer = brainiest!
Answer:
30 or younger
Step-by-step explanation:
A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100. Construct a 95% confidence interval for u1 -u2.
a) (-4081, 597)
b) (-2054, 238)
c) (-2871, 567)
d) (-3125, 325)
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean salary of city 1 librarians
x2 = sample mean salary of city 2 librarians
s1 = sample standard deviation for city 1
s2 = sample standard deviation for city 2
n1 = number of soles for city 1
n1 = number of soles for city 2
For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28
z = 2.048
x1 - x2 = 28,900 - 30,300 = - 1400
Margin of error = 2.048√(s1²/n1 + s2²/n2) = 2.036√(2300²/15 + 2100²/15)
= 1647
The upper boundary for the confidence interval is
- 1400 + 1647 = 247
The lower boundary for the confidence interval is
- 1400 - 1647 = - 3047
work out the length of the container. Giver your answer to the nearest whole centimetre.
Dennis is making a container for tomato plant. The container will be in the shape of a cuboid.
missing length ? 40cm by 55cm.
The capacity of the container will be 180 litres.
1 Litre =1000cm cuboid.
Answer:
Length of the container = 82 cm
Step-by-step explanation:
Given:
Breadth of the container is 40 cm and height of the container is 55 cm
Volume of the container is 180 litres
To find: length of the container
Solution:
A container is in the shape of the cuboid.
Volume of cuboid = length × breadth × height
Put breadth = 40 cm , height = 55 cm and volume = 180 litres = 180000 [tex]cm^3[/tex]
(as 1 litre = 1000 [tex]cm^3[/tex] )
Therefore,
[tex]180000=length\,\times \,40\times 55\\length = \frac{180000}{40\times 55}=81.82\approx 82\,\,cm[/tex]
What is X:Compute
|x|=−4
Answer:
The answer is No Solution
Answer:
No solution
Step-by-step explanation:
There is no solution to this question.
Since the x is an absolute number, the answer cannot be -4. It would have to equal 4
So if that x was a -4 it would equal 4 since it is in absolute value brackets
Which is the best estimate of 90/7 divided by 1 3/4
Answer:
90/4= 12.9
1*3/4= 0.75
Step-by-step explanation:
WHAT IS A VOLUME OF THE BOX WITH A HEIGHT OF 3\2 WIDTH OF 5\2 AND LENGHT OF 7\2
Answer:
13.125 or 105/8u^3
Step-by-step explanation:
To find the volume of the box, you can use the formula of length times width time height.
3 * 5 = 15
2*2=4
15/4*7/2=105/8 which can be divided to become 13.125
Assume that military aircraft use ejection seats designed for men weighing between 133.8 lb and 208.0 lb. If women’s weights are normally distributed with a mean of 172.6 lb and a standard deviation of 42.4 lb, what percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)? Enter your answer as a percent rounded to one decimal place (do not add a "%"); add a trailing zeros as needed. The percentage of women with weights between 133.8 and 208.0 lb is [EjectPct] percent.
Answer:
61.8
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 172.6, \sigma = 42.4[/tex]
What percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)?
We have to find the pvalue of Z when X = 208 subtracted by the pvalue of Z when X = 133.8 for the proportion. Then we multiply by 100 to find the percentage.
X = 208
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{208 - 172.6}{42.4}[/tex]
[tex]Z = 0.835[/tex]
[tex]Z = 0.835[/tex] has a pvalue of 0.798
X = 133.8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{133.8 - 172.6}{42.4}[/tex]
[tex]Z = -0.915[/tex]
[tex]Z = -0.915[/tex] has a pvalue of 0.180
0.798 - 0.18 = 0.618
0.618*100 = 61.8%
Without the %, the answer is 61.8.
Please answer this correctly
Answer:
Set the height up to 4
Step-by-step explanation:
Since there are 4 numbers between 1-5, set the height up to 4
Answer:
4 temperature recordings.
Step-by-step explanation:
2, 2, 4, 5
There are 4 recordings in the range of 1-5°C.
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2013?
Answer: The population will be 408,000 people.
Step-by-step explanation:
So in 2000 there were 200,000 people and it started to grow 8% every year so up to 2013.
so find 8% of 200,000 and then multiply it by the the number of years.
8% * 200,000 = 16,000
Find the difference between the years.
2013 - 2000 = 13 years
13 * 16000 = 208000 This is the amount of new people from 2000 to 2013 so add it to the original population.
208,000 + 200,000 = 408,000
A tree casts an 8-foot shadow on the ground. The length from the tip of the shadow to the top of the tree is 17 feet. What is the height of the tree?
Answer:
Height of tree = 15 ft
Step-by-step explanation:
Given:
Length of shadow (Base) = 8 ft
Length from the tip to top of the tree (Hypotenues) = 17 ft
Find:
Height of tree = ?
Computation:
Using Pythagoras theorem:
[tex]Height\ of\ tree = \sqrt{Hypotenues^2 - base^2} \\\\Height\ of\ tree = \sqrt{17^2 - 8^2} \\\\Height\ of\ tree = \sqrt{289-64}\\\\Height\ of\ tree = \sqrt{225}\\\\ Height\ of\ tree =15[/tex]
Height of tree = 15 ft
Answer:
The answer is 15 feet from the ground to the top of the tree.
Step-by-step explanation:
Find the equation of the line passing through the point (4,−1) that is parallel to the line 2x−3y=9 Find the slope of the line 2x−3y=9. Use a forward slash (i.e. "/") for all fractions (e.g. 1/2 for 12). m=____ What would the parallel slope be? m=______ Use the slope to find the y-intercept of the parallel line. b= _____
Answer:
Step-by-step explanation:
2x - 3y = 9
-3y = -2x + 9
[tex]y=\frac{-2}{-3}x + \frac{9}{-3}\\\\y=\frac{2}{3}x-3\\[/tex]
Parallel lines have same slope.So,
Slope m = 2/3
(4 , -1)
Equation: y - y1 = m(x - x1)
[tex]y-[-1]=\frac{2}{3}(x - 4)\\\\y+1=\frac{2}{3}*x - \frac{2}{3}*4\\\\y+1=\frac{2}{3}x-\frac{8}{3}\\\\y=\frac{2}{3}x-\frac{8}{3}-1\\\\y=\frac{2}{3}x-\frac{8}{3}-\frac{3}{3}\\\\y=\frac{2}{3}x-\frac{11}{3}[/tex]
b = -11/3
The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: "Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving." Possible responses were strongly agree, some what agree, some what disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, said that they some what agree, said they some what disagree, and said they strongly disagree with this statement.
Required:
a. Do the responses for this statement provide categorical or quantitative data?
b. Would it make more sense to use averages or percentages as a summary of the responses for this statement?
c. What percentage of respondents strongly agree with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
d. Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
Step-by-step explanation:
a. It would provide a quantitative data
b. Yes, it would make more sense to use percentages rather than averages as this is estimating a proportion.
c. 44% of the respondents strongly agree
d. the results do not indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving as the only respondents will be those that agree with the researchers claim and the study will be biased against those who do not agree.
3. (03.06)
Choose the point-slope form of the equation below that represents the line that passes through the points (-6, 4) and (2,0). (2 points)
Answer:
work is shown and pictured
Write a linear function f with f(−2)=6 and f(0)=−4 .
Answer:
y = -5(x) - 4
Step-by-step explanation:
Use the equation of a line and substitution.
Information given:
point 1: (-2,6)
x1 = -2 and y1 = 6
point 2: (0,4)
x2 = 0 and y2 = 4
Equation of a line: y = m(x) + b
m = slope
To find slope, you do the equation of a linear slope, which is:
m = [tex]\frac{rise}{run}[/tex] in other words m = [tex]\frac{Y2 - Y1}{X2-X1}[/tex]
plug in your values
[tex]\frac{6-(-4)}{-2-0}[/tex]
= -5
Great, we've found slope, now to find b
plug in the slope you found: y = -5(x) + b
Plug in and solve for each point given, aka (x,y) into the linear equation for both points.
FIRST POINT:
6 = -5(-2) + b
6 = 10 + b
6 - 10 = b
b = -4
SECOND POINT:
-4 = -5(0) + b
-4 = 0 + b
-4 - 0 = b
b = -4
We got -4 for both, meaning that this equation is correct, so if you add in b, your final equation will be y = -5(x) - 4.
Plug this into desmos.com/calculator, and you'll see this linear equation runs through both points given in the problem.
Answer:
f(x)=-5x-4
Step-by-step explanation:
You are given two points (-2, 6) and (0, -4)
Find the slope: m=(-4-6)/[(0-(-2)]=-5
So you have y=-5x+b
next, find the y intercept b.
the y intercept is when x=0. in this case, the y intercept is -4
so the linear function is f(x)=-5x-4
11. List and describe three factors that may affect body temperature.
it is age heart rate and weather
Bytecoin is a new cryptocurrency that is currently valued at $243 per coin. You want to make an investment and purchase 1 Bytecoin and cash out when its value reaches $1,000. Over the last 12 months, you ve seen the value of the Bytecoin grow exponentially at a rate of 15% per month! You want all of your friends and family to invest with you, but you need to make predictions about how long it will take for your $243 investment to earn $1,000. Write an exponential equation in the form y = a * b ^ x and explain what a and b represent
Answer:
Step-by-step explanation:
The growth rate of the coin is exponential. We would apply the formula for exponential growth which is expressed as
y = ab^x
y = b(1 + r)^ t
Where
y represents the value of the coin after x months.
x represents the number of months.
a represents the initial value of the coin.
b represents rate of growth.
From the information given,
a = 243
b = 1 + 15/100 = 1 + 0.15 = 1.15
Therefore, the exponential expression to determine the number of months, x it will take for the coin to attain a certain value, y is expressed as
y = 243(1.15)^x
If y = 1000, it means that
1000 = 243(1.15)^x
1000/243 = 1.15^x
4.115 = 1.15^x
Taking log of both sides, it becomes
log 4.115 = xlog1.15
0.614 = 0.061x
x = 0.614/0.061
x = 10 months
It will take 10 months