Answer:
0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.
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 = 200, \sigma = 50[/tex]
Find the probability that he weighs between 170 and 220 pounds.
This is the pvalue of Z when X = 220 subtracted by the pvalue of Z when X = 170.
X = 220
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{220 - 200}{50}[/tex]
[tex]Z = 0.4[/tex]
[tex]Z = 0.4[/tex] has a pvalue of 0.6554
X = 170
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{170 - 200}{50}[/tex]
[tex]Z = -0.6[/tex]
[tex]Z = -0.6[/tex] has a pvalue of 0.2743
0.6554 - 0.2743 = 0.3811
0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.
Does the point (3.28) lie on the line y = 19+ 3x
Answer:
yes
Step-by-step explanation:
y = 19+ 3x
Let x = 3 and y = 28
28 = 19 + 3*3
28 =19+9
28 = 28
This is true so the point is one the line
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is: Temperature = 110 ‑ 2(Latitude). How does the estimated temperature change when latitude is increased by one?
Answer:
Decreases by 2 degrees
Step-by-step explanation:
The expression that describes temperature as a function of latitude is:
[tex]T=110-2(Latitude)[/tex]
This equation represents a linear relationship between latitude and temperature in a way that an increase in latitude causes a decrease in temperature. The magnitude of this decrease is quantified by the slope of the linear equation, which is -2. Therefore, the estimated temperature decreases by 2 degrees when latitude is increased by one.
Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustain-ability perspective, PHB offers many attractive proper-ties though it is more expensive to produce than standard plastics. The accompanying data on melting point (°C) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in the article "The Melting Behaviour of Poly(3-1-1ydroxybutyrate) by DSC. Reproducibility Study" (Polymer Testing, 2013: 215-220).
180.5 181.7 180.9 181.6 182.6 181.6
181.3 182.1 182.1 180.3 181.7 180.5
Compute the following:
a. The sample range
b. The sample variance S2 from the definition (Hint: First subtract 180 from each observation.]
c. The sample standard deviation
d. S2 using the shortcut method
Answer:
(a) 2.3
(b) 0.5245
(c) 0.7242
(d) 0.5245
Step-by-step explanation:
The data provided is:
S = {180.5, 181.7, 180.9, 181.6, 182.6, 181.6, 181.3, 182.1, 182.1, 180.3, 181.7, 180.5}
(a)
The formula to compute the sample range is:
[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]
The data set arranged in ascending order is:
S' = {180.3 , 180.5 , 180.5 , 180.9 , 181.3 , 181.6 , 181.6 , 181.7 , 181.7 ,, 182.1 , 182.1 , 182.6}
The minimum value is, 180.3 and the maximum value is, 182.6.
Compute the sample range as follows:
[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]
[tex]=182.6-180.3\\=2.3[/tex]
Thus, the sample range is 2.3.
(b)
Compute the sample variance as follows:
[tex]S^{2}=\frac{1}{n-1}\sum(x_{i}-\bar x)^{2}[/tex]
[tex]=\frac{1}{12-1}\times [(180.5-181.41)^{2}+(181.7-181.41)^{2}+...+(180.5-181.41)^{2}]\\\\=\frac{1}{11}\times 5.7692\\\\=0.524473\\\\\approx 0.5245[/tex]
Thus, the sample variance is 0.5245.
(c)
Compute the sample standard deviation as follows:
[tex]s=\sqrt{S^{2}}[/tex]
[tex]=\sqrt{0.5245}\\\\=0.7242[/tex]
Thus, the sample standard deviation is 0.7242.
(d)
Compute the sample variance using the shortcut method as follows:
[tex]S^{2}=\frac{1}{n-1}\cdot [\sum x_{i}^{2}-n(\bar x)^{2}][/tex]
[tex]=\frac{1}{12-1}\cdot [394913.57-(12\times (181.41)^{2}]\\\\=\frac{1}{11}\times [394913.57-394907.80]\\\\=\frac{5.77}{11}\\\\=0.5245[/tex]
Thus, the sample variance is 0.5245.
Define f(0,0) in a way that extends f(x,y)=x^2 - y^2/x^2 + y^2 to be continuous at the origin.
Answer:
It cannot be extended.
Step-by-step explanation:
Consider the function [tex]f(x,y) = \frac{x^2-y^2}{x^2+y^2}[/tex]. To extend this functions so it is continous at (0,0) we must define [tex] f(0,0) = \lim_{(x,y)\to(0,0)\frac{x^2-y^2}{x^2+y^2}[/tex]. However, this implies that the limit exists. So, we should find if the limit exists or not.
In this case, consider the case in which y =0. When y=0 then
[tex]\lim_{(x,y)\to(0,0) \frac{x^2-0^2}{x^2+0^2} = \lim_{x\to 0}\frac{x^2}{x^2}= 1[/tex]
But, when x=0, we get
[tex]\lim_{(x,y)\to(0,0) \frac{0^2-y^2}{0^2+y^2} = \lim_{y\to 0}\frac{-y^2}{y^2}=-1[/tex].
So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.
Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?
Answer:
A lies along the positive x-axis and B lies along negative x - axis .
Step-by-step explanation:
They tell us that we have two vectors, A and B. And they give us a series of conditions for this, now, what would be the correct possibility.
A lies along the positive x-axis and B lies along negative x - axis .
This is because when both vectors will be in x axis but opposite to each other, then the angle between them will be 180 ° and cos180 ° is -1.
Please answer this correctly
Answer:
25%
Step-by-step explanation:
Total cards = 4
The number 4 = 1
p(4) = 1/4
In %age:
=> 25%
Answer:
25%
Step-by-step explanation:
There is only 1 four card from the 4 cards.
1 card out of 4 cards.
1/4 = 0.25
P(4) = 25%
Which best compares the volumes of the two cylinders? Geometry
Answer:
The correct answer would be C
Step-by-step explanation:
please mark brainliest
The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.
Which best compares the volumes of the two cylinders?From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.
Read more on cylinders;
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A shipment of 60 inexpensive digital watches, including 9 that are defective,is sent to a department store.The receiving department select's 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective.What is the probability that the shipment will be rejected?
Answer: 0.627 or 62.7 %
Step-by-step explanation:
The probability that shipment will be rejected P(rejected) = 1- probability that shipment will be accepted.
P(rejected)= 1-P(accepted)
P(accepted) is equal to probability when all 10 watches are not defective.
The probability that 1st one randomly selected watches are not defective is 51/60 (51 watches are not defective and 9 are defective)
The probability that 2-nd one randomly selected watches are not defective is 50/59 ( because the total number of the watches now is 1 unit less 60-1=59, and the total number of not defective watches is 1 unit less 51-1=50 units)
The probability that 3rd one randomly selected watches are not defective is 49/58 (49 watches are not defective total number of watches is 58)
Similarly P(4th)= 48/57 P(5th)=47/56 P(6th)=46/55 P(7th)=45/54
P(8th)=44/53 P(9th)=43/52 P(10th)=42/51
So P(accepted)= P(1st)*P(2nd)*P(3rd)*P(4th)*P(5th)*P(6th)*P(7th)*P(8th)*P(9th)*P(10th)=
=51*50*49*48*47*46*45*44*43*42/(60*59*58*57*56*55*54*53*52*51)=
= approx= 0.373
So P(rejected)=1-0.373=0.627
Let $x$ be the smallest multiple of $11$ that is greater than $1000$ and $y$ be the greatest multiple of $11$ less than $11^2$. Compute $x - y$.
Answer:
891
Step-by-step explanation:
x has to be 1001 and y has to be 11 * 10 = 110 so x - y = 1001 - 110 = 891.
Answer:
891
Step-by-step explanation:
[tex]$1001$ is the smallest integer greater than $1000$. It also happens to be a multiple of $11$, since $1001 = 11 \cdot 91$. So $1001$ is the smallest multiple of $11$ greater than $1000$ and thus $x = 1001$.The greatest multiple of $11$ that is less than $11^2 = 11 \cdot 11$ is$$11 \cdot (11 - 1) = 11 \cdot 10 = 110$$Thus $y = 110$, and we compute$$x - y = 1001 - 110 = \boxed{891}$$[/tex]
Hope this helped! :)
Given O below, if WX and YZ are congruent, what is the measure of YOZ? A. 103 B. 257 C.77 D.206
Answer: your answer should be 103
Answer:
Step-by-step explanation:
103
A large mixing tank initially contains 1000 gallons of water in which 30 pounds of salt have been dissolved. Another brine solution is pumped into the tank at the rate of 4 gallons per minute, and the resulting mixture is pumped out at the same rate. The concentration of the incoming brine solution is 2 pounds of salt per gallon. If represents the amount of salt in the tank at time t, the correct differential equation for A is:__________.A.) dA/dt = 4 - .08AB.) dA/dt = 8 -.04AC.) dA/dt = 4-.04AD.) dA/dt = 2-.04AE.) dA/dt = 8-.02A
Answer:
(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]
Step-by-step explanation:
Volume of fluid in the tank =1000 gallons
Initial Amount of Salt in the tank, A(0)= 30 pounds
Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.
Rate In=(concentration of salt in inflow)(input rate of brine)
[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]
The resulting mixture is pumped out at the same rate, therefore:
Rate Out =(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]
Therefore:
The rate of change of amount of salt in the tank,
[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]
The graphed line shown below is y = 5 x minus 10. On a coordinate plane, a line goes through (2, 0) and (3, 5). Which equation, when graphed with the given equation, will form a system that has no solution? y = negative 5 x + 10 y = 5 (x + 2) y = 5 (x minus 2) y = negative 5 x minus 10
Answer:
y = 5 (x + 2)
Step-by-step explanation:
Equations with a different x-coefficient will graph as lines that intersect the given one, so will form a system with one solution.
The equation with the same slope and y-intercept (y = 5(x -2)) will graph as the same line, so will form a system with infinite solutions.
The line with the same slope and a different y-intercept will form a system with no solutions:
y = 5 (x + 2)
Answer:
B
Step-by-step explanation:
got it on edge
the flagpole casts an 8 foot shadow and is 20 feet high, At the same time the oak tree casts a 12 foot shadow how tall is the tree
Answer:
30 feet
Step-by-step explanation:
We can use ratios to answer this question:
8 foot shadow: 20 feet high
Therefore if we multiply both sides by 1.5
12 foot shadow: 30 feet high
Find measure of arc or angle indicated
A population of monkeys' tail lengths is normally distributed with a mean of 25 cm with a standard deviation of 8 cm. I am preparing to take a sample of size 256 from this population, and record the tail length of each monkey in my sample. What is the probability that the mean of my sample will be between 24 and 25 cm?
Answer:
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
Step-by-step explanation:
Step(i):-
Given mean of the Population 'μ'= 25c.m
Given standard deviation of the Population 'σ' = 8c.m
Given sample size 'n' = 256
Let X₁ = 24
[tex]Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2[/tex]
Let X₂ = 25
[tex]Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0[/tex]
Step(ii):-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)
= P( Z≤0) - P(Z≤-2)
= 0.5 + A(0) - (0.5- A(-2))
= A(0) + A(2) ( ∵A(-2) =A(2)
= 0.000+ 0.4772
= 0.4772
Final answer:-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
to prove triangleABC is isosceles, which of the following statements can be used in the proof?
(idk the answer)
Answer:
Step-by-step explanation:
An isosceles triangle is a triangle in which two of its sides are equal. This also means that in the triangle, two angles are equal. The angles are usually the base angles. Looking at the given triangle ABC, the base angles are angle Angle A and Angle B, thus angle A = ang B
Therefore, the statement that can be used in the proof is
Angle CAB = angle CBA
what is the solution of the inequality shown below
Answer:
there is no inequality..
Step-by-step explanation:
Answer:
???
Step-by-step explanation:
13. [-/1 Points]
DETAILS
AUFEXC4 9.2.039.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
A management consulting firm recommends that the ratio of middle-management salaries to management trainee salaries be 9:4. Using this recommendation, what is the annual middle
management salary if the annual management trainee salary is $24,000? (Round your answer to the nearest dollar.)
Enter a number
Answer:
67500
Step-by-step explanation:
you would set up the equation:x/y=5/4
A = P(1 + nr) for r
Answer:
r = (An−nP)/P
Step-by-step explanation:
A = P(1 + nr)
Divide P on both sides.
A/P = 1 + nr
Subtract 1 on both sides.
A/P - 1 = nr
Divide n on both sides.
A/P/n - 1/n = r
(An−nP)/P = r
The answer is, r = (An−nP)/P
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here, we have,
given that,
A = P(1 + nr)
Divide P on both sides.
A/P = 1 + nr
Subtract 1 on both sides.
A/P - 1 = nr
Divide n on both sides.
A/P/n - 1/n = r
(An−nP)/P = r
hence, answer is (An−nP)/P = r.
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two lines, 3y-2x=21 and 4y+5x=5, intersect at the point Q. find the coordinates of Q.
Answer:
Q = (- 3, 5 )
Step-by-step explanation:
Given the 2 equations
3y - 2x = 21 → (1)
4y + 5x = 5 → (2)
Multiplying (1) by 5 and (2) by 2 and adding will eliminate the x- term.
15y - 10x = 105 → (3)
8y + 10x = 10 → (4)
Add (3) and (4) term by term to eliminate x
23y = 115 ( divide both sides by 23 )
y = 5
Substitute y = 5 into either of the 2 equations and solve for x
Substituting into (2)
4(5) + 5x = 5
20 + 5x = 5 ( subtract 20 from both sides )
5x = - 15 ( divide both sides by 5 )
x = - 3
Solution is (- 3, 5 )
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer: m=0.5 or m=1/2
Step-by-step explanation:
To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Since we are given the coordinate points, we can directly plug them in.
[tex]m=\frac{0.25-0}{0.5-0} =\frac{0.25}{0.5} =0.5[/tex]
Yolonda wanted to see if there was a connection between red hair and green eyes. She observed people walking past her on the street
Answer:
I saw one person that way
Step-by-step explanation:
she had red hair and green eyes with pale skin
A study was conducted on 64 female college athletes. The researcher collected data on a number of variables including percent body fat, total body weight, lean body mass, and age of athlete. The researcher wondered if total body weight (TBW), lean body mass (LBM), and/or age are significant predictors of % body fat. All conditions have been checked and are met and no transformations were needed. The partial technology output from the multiple regression analysis is given below. How many degrees of freedom does the F-statistic have in this problem?
Answer:
Hello please your question is in-complete attached is the complete question
degree of freedom = -62.90 ( e )
Step-by-step explanation:
The formula for calculating the F-statistic/test statistic is
test - statistic = Coef ( LBW) / SE Coef ( LBW )
= -0.72399 / 0.01151
= - 62.90
the degree of freedom the F-statistic has = -62.90
F-statistic test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. the value of the test can be gotten from running an ANOVA test or regression analysis on the statistical models
Using the definition of degrees of freedom, it is found that the F-statistic has 63 df.
When a hypothesis is tested, the number of degrees of freedom is one less than the sample size.
In this problem, the sample size is of n = 64.
Hence:
df = n - 1 = 64 - 1 = 63
The F-statistic has 63 df.
A similar problem is given at https://brainly.com/question/16194574
the line through (5, 7) and (1, - 5)
Answer:
Hey there!
Slope of the line: [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope of the line: [tex]\frac{12}{4}[/tex], which is equal to 3.
Point slope form: y2-y1=m(x2-x1)
Point slope form: y-7=3(x-5)
Y intercept form: y-7=3x-15
Y intercept form: y=3x-8
Let me know if this helps :)
Please answer this correctly
Answer:
5/12
Step-by-step explanation:
The probability of rolling a number greater than 1 is 5/6, because 5 numbers on a 6-sided dice are greater than 1.
The probability of rolling an even number is 3/6, because 3 numbers on a 6-sided dice are even numbers.
[tex]5/6 \times 3/6[/tex]
[tex]=15/36[/tex]
[tex]=5/12[/tex]
an experiment consists of rolling two fair dice and adding the dots on the two sides facing u. Find the probability of the sum of the dots indicate. A sum less than or equal to 6
Answer:
41.67% probability of the sum of the dots indicate a sum less than or equal to 6
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes:
In this problem, we have these possible outcomes:
Format(Dice A, Dice B)
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
There are 36 possible outcomes.
Desired outcomes:
Sum of 6 or less. They are:
(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)
15 desired outcomes
15/36 = 0.4167
41.67% probability of the sum of the dots indicate a sum less than or equal to 6
The mean and standard deviation of a random sample of n measurements are equal to 34.5 and 3.4, respectively.A. Find a 95 % confidence interval for μ if n=49.B. Find a 95% confidence interval for μ if n=196.C. Find the widths of the confidence intervals found in parts a and b.D. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?1. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4.2. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2.3. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the on confidence interval by a factor of 4.4. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval.5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Answer:
a. The 95% confidence interval for the mean is (33.52, 35.48).
b. The 95% confidence interval for the mean is (34.02, 34.98).
c. n=49 ⇒ Width = 1.95
n=196 ⇒ Width = 0.96
Note: it should be a factor of 2 between the widths, but the different degrees of freedom affects the critical value for each interval, as the sample size is different. It the population standard deviation had been used, the factor would have been exactly 2.
d. 5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Step-by-step explanation:
a. We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=34.5.
The sample size is N=49.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{49}}=\dfrac{3.4}{7}=0.486[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=49-1=48[/tex]
The t-value for a 95% confidence interval and 48 degrees of freedom is t=2.011.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.011 \cdot 0.486=0.98[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 34.5-0.98=33.52\\\\UL=M+t \cdot s_M = 34.5+0.98=35.48[/tex]
The 95% confidence interval for the mean is (33.52, 35.48).
b. We have to calculate a 95% confidence interval for the mean.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{196}}=\dfrac{3.4}{14}=0.243[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=196-1=195[/tex]
The t-value for a 95% confidence interval and 195 degrees of freedom is t=1.972.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.972 \cdot 0.243=0.48[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 34.5-0.48=34.02\\\\UL=M+t \cdot s_M = 34.5+0.48=34.98[/tex]
The 95% confidence interval for the mean is (34.02, 34.98).
c. The width of the intervals is:
[tex]n=49\rightarrow UL-LL=33.52-35.48=1.95\\\\n=196\rightarrow UL-LL=34.02-34.98=0.96[/tex]
d. The width of the intervals is decreased by a factor of √4=2 when the sample size is quadrupled, while the others factors are fixed.
Please answer this correctly
Answer:
1/9
Step-by-step explanation:
The probability of picking a even number is 1/3
The probability of picking another even number is 1/3(if u put the first one back)
So u multiply 1/3 times 1/3 which gives u 1/9 which is ur answer hope this helps
Answer:
1/9
Step-by-step explanation:
3 cards total
1 even number
P(even) = even/total
1/3
Put the card back
3 cards total
1 even number
P(even) = even/total
1/3
P(even, replace, even) = P(even) * P(even) =1/3*1/3 = 1/9
The volume of a gas in a container varies inversely with the pressure on the gas. A container of helium has a volume of 370in3 under a pressure of 15psi (pounds per square inch). Write the equation that relates the volume, V, to the pressure, P. What would be the volume of this gas if the pressure was increased to 25psi?
Answer:
Step-by-step explanation:
When two variables vary inversely, it means that an increase in one would lead to a decrease in the other and vice versa. Since the volume of a gas, V in a container varies inversely with the pressure on the gas, P, if we introduce a constant of proportionality, k, the expression would be
V = k/P
If V = 370 in³ and P = 15psi, then
370 = k/15
k = 370 × 15 = 5550
The equation that relates the volume, V, to the pressure, P would be
V = 5550/P
if the pressure was increased to 25psi, the volume would be
V = 5550/25 = 222 in³
Answer:
v=5550/p
222
Step-by-step explanation:
pls answer quickly!!!
Answer:
x = 90
y = 100
z = -10
Step-by-step explanation:
To find x and y in the above parallelogram ABCD as shown above, recall that one of the properties of a parallelogram is: the consecutive angles in a parallelogram are supplementary.
This means that the sum of angle A and angle B in the parallelogram ABCD = 180°.
Thus,
(x + 30)° + (x - 30)° = 180°
Solve for x
x + 30 + x - 30 = 180
x + x + 30 - 30 = 180
2x = 180
Divide both sides by 2
2x/2 = 180/2
x = 90
=>Find y:
Also, recall that opposite angles in a parallelogram are congruent.
This means, angle A and angle C in parallelogram ABCD above are equal.
Thus,
(x + 30)° = (y + 20)°
Plug in the value of x to solve for y
90 + 30 = y + 20
120 = y + 20
Subtract 20 from both sides
120 - 20 = y
100 = y
y = 100
=>Find z, if z = x - y
z = 90 - 100
z = -10