[tex]\text{Find the distance from one corner to the other}\\\\\text{In this question, we would use the Pythagorean theorem to find the length}\\\text{between corners}\\\\\text{Pythagorean theorem:}\\\\a^2+b^2=c^2\\\\\text{We are trying to find c}\\\\\text{Plug in and solve:}\\\\7^2+6^2=c^2\\\\49+36=c^2\\\\85=c^2\\\\\text{Square root}\\\\\sqrt{85}=\sqrt{c^2}\\\\\sqrt{85}=c\\\\\text{In decimal form, it's: 9.219544}\\\\\text{Round to the nearest tenths place}\\\\\boxed{9.2\,\, feet}[/tex]
Galina had two boxes with pieces of paper in each. In the first box, each piece of paper had one possible outcome from flipping a coin 4 times (e.g. HHTH). There was one piece of paper for every possible outcome.
How many pieces of paper were in the first box?
Answer:
B
Step-by-step explanation:
Please help me ASAP I need this done D,: and it’s confusing me
Answer:
D.
Step-by-step explanation:
A) ∠V and ∠Y is not the alternate interior angles.
B)∠W and ∠Z is not the alternate interior angles.
C) Not this one because the reflexive property of congruence means that an angle, line segment, or shape is always congruent to itself.
D)∠VXW ≅∠ZXY because they are vertical. ∠W≅∠Y because they are right angles. So, triangles are similar by AA.
Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 fewer than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−5)=9.45 for s to find the number of 49-cent stamps Travis bought.
Answer:
15 49-cent stamps
Step-by-step explanation:
We can solve this problem with the equations 0.49(x) + 0.21(y) = 9.45 and x - 5 = y. Well, 0.49(15) + 0.21(10) = 9.45, so we know that there are 15 49-cent stamps and 10 21-cent stamps. The question is asking for the number of 49-cent stamps, so we can tell Travis bought 15 49-cent stamps.
Hope this helps! Plz give me brainliest, it will help me achieve my next rank.
The number of 49-cent stamps that Travis bought given the equation is 15.
What he number of 49-cent stamps Travis bought?Given this equation: 0.49s+0.21(s−5)=9.45 take the following steps to determine the value of s
Expand the bracket: 0.49s + 0.21s - 1.05 = 9.45Combine similar terms : 0.49s + 0.21s = 9.45 + 1.05Add similar terms: 10.50 = 0.70sDivide both sides of the equation by 0.70: s = 15To learn more about mathematical equations, please check: https://brainly.com/question/26427570
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which one doesn't belong? anything helps thx!!
Answer:
in 1,2 options they r in exponential form
in 4,option also, we can write it as xpower1/2 so this also in exponential form
but in third option y=x there is no exponential form
The number 128 is divided into two parts in the ratio 7:9. Find the absolute difference between the two parts.
Express it in slope-intercept form.
Hey there! :)
Answer:
y = 1/4x - 3.
Step-by-step explanation:
Use the slope-formula to find the slope of the line:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in two points from the line. Use the points (-4, -4) and (0, 3):
[tex]m = \frac{-3 - (-4)}{0 - (-4)}[/tex]
Simplify:
m = 1/4.
Slope-intercept form is y = mx + b.
Find the 'b' value by finding the y-value at which the graph intersects the y-axis. This is at y = -3. Therefore, the equation is:
y = 1/4x - 3.
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 147 adult males, the mean pulse rate is 69.5 bpm and the standard deviation is 11.2 bpm. Find the value of the test statistic.
Answer:
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{69.5-69}{\frac{11.2}{\sqrt{147}}}=0.541[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=69.5[/tex] represent the sample mean
[tex]s=11.2[/tex] represent the sample standard deviation
[tex]n=69[/tex] sample size
[tex]\mu_o =69[/tex] represent the value that we want to test
t would represent the statistic (variable of interest)
Hypothesis to test
We want to check if the true mean is 69, the system of hypothesis would be:
Null hypothesis:[tex]\mu =69[/tex]
Alternative hypothesis:[tex]\mu \neq 69[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{69.5-69}{\frac{11.2}{\sqrt{147}}}=0.541[/tex]
An object of height 2.50cm is placed 20.0cm from a converging mirror of focal length 10.0cm. What are the height and the magnification of the image formed?
First find the distance it is reflected:
D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.
Now calculate the magnification: -20/ 20 = -1
Now calculate the height:
-1 x 2.50 = -2.50
The negative sign means the image is inverted.
The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.
5x +3y=210 x+y=60 Witch can represent a linear equation
Answer:
both
Step-by-step explanation:
Both of the equations shown here are linear equations in standard form.
5x + 3y = 210
x + y = 60
Create a unique equation using the graphic above with the solution (answer) of 36.
Find a solution to the linear equation y=12x−24
Answer:
I didn't know which one you wanted...
Step-by-step explanation:
1. Finding the x an y-intercepts
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (2,0)
y-intercept(s): (0,−24)
2. Finding the slope and y-intercept
Use the slope-intercept form to find the slope and y-intercept.
Slope: 12
y-intercept: −24
The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let mu denote the true average reflectometer reading for a new type of paint under consideration. A test of
H0:μ=20 versus Ha:μ is greater than 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.)
a. n = 17, t = 3.1, α=0.05
State the conclusion in the problem context.
A. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
B. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
C. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
b. n = 10, t = 1.8, α=0.01
State the conclusion in the problem context.
A. Do not reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
B. Reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
C. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
c. n = 24, t = -0.4, p-value =
Answer:
a) D. Reject the null hypothesis. There is sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
b) C. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the new paint has a reflectometer reading higher than 20.
Step-by-step explanation:
a) We have a hypothesis test with the following hypothesis:
[tex]H_0: \mu=20\\\\H_a:\mu> 20[/tex]
The significance level is 0.05 for this right-tailed test.
The sample size is n=17.
This means we have 16 degrees of freedom.
[tex]df=n-1=17-1=16[/tex]
The test statistic has already been calculated and has a value of t=3.1.
This test is a right-tailed test, with 16 degrees of freedom and t=3.1, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.1)=0.0034[/tex]
As the P-value (0.0034) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the new paint has a reflectometer reading higher than 20.
b. The hypothesis are the same as point a:
[tex]H_0: \mu=20\\\\H_a:\mu> 20[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
The significance level is 0.01.
The test statistic has already been calculated and has a value of t=1.8.
This test is a right-tailed test, with 9 degrees of freedom and t=1.8, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>1.8)=0.0527[/tex]
As the P-value (0.0527) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is not enough evidence to support the claim that the new paint has a reflectometer reading higher than 20.
Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use
α = 0.05
and test to see whether the consultant with more experience has the higher population mean service rating.
Consultant A Consultant B
n1 = 16
n2 = 10
x1 = 6.82
x2 = 6.28
s1 = 0.65
s2 = 0.75
(a)
State the null and alternative hypotheses.
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 > 0
Ha:
μ1 − μ2 ≤ 0
H0:
μ1 − μ2 ≠ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 > 0
H0:
μ1 − μ2 = 0
Ha:
μ1 − μ2 ≠ 0
(b)
Compute the value of the test statistic. (Round your answer to three decimal places.)
(c)
What is the p-value? (Round your answer to four decimal places.)
p-value =
(d)
What is your conclusion?
Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Do not reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating. Do not Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Answer:
A) Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Test statistic = t = 1.878
C) p-value is 0.038823.
D) Reject the Null hypothesis H0
Step-by-step explanation:
We are given;
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
A) The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
B) Formula yo determine the test statistic is;
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
Plugging in the relevant values, we have;
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
C) The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Plugging in the relevant values, we have;
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value;
From online p-value calculator from t-score and DF which i attached, we have the p-value as;
The p-value is 0.038823.
D) The p-value result is significant at p < 0.05
Thus, we reject the Null hypothesis H0
A) Null hypothesis: μ1 − μ2 ≤ 0
B) Test statistic = t = 1.878
C) The p-value is 0.038823.
D) Reject the Null hypothesis H0.
HypothesisWhat all information we have ?
α = 0.05
n1 = 16
n2 = 10
bar x1 = 6.82
bar x2 = 6.28
s1 = 0.65
s2 = 0.75
Part A)
The hypothesis is as follows;
Null hypothesis; H0: μ1 − μ2 ≤ 0
Alternative hypothesis; Ha: μ1 − μ2 > 0
Part B)
The formula to determine the test statistic is :
t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))
t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))
t = 0.54/√(0.02640625 + 0.05625)
t = 0.54/0.2875
t = 1.878
The formula to determine the test statistic is t = 1.878.
Part C)
The formula for the degree of freedom is;
Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))
Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))
Δ = 0.00683205566/(0.000046486 + 0.0003515625)
Δ ≈ 17
Thus, the P-value is 0.038823.
Part D)
The p-value result is significant at p < 0.05 is :
Thus, we reject the Null hypothesis H0.
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A man is twice the age of his son,in 20 years time, the son's age will be 2/3 of that his father. what is the son's present age?
Answer:
20 years old.
Step-by-step explanation:
Let us say that the man's age is represented by x and the son's age is represented by y.
As of now, x = 2y.
In 20 years, both ages will increase by 20. We can have an equation where the son's age increased by 20 equals 2/3 of the man's age plus 20.
(y + 20) = 2/3(x + 20)
Since x = 2y...
y + 20 = 2/3(2y + 20)
3/2y + 30 = 2y + 20
2y + 20 = 3/2y + 30
1/2y = 10
y = 20
To check our work, the man's age is currently double his son's, so the man is 40 and the son is 20. In 20 years, the man will be 60 and the son will be 40. 40 / 60 = 2/3, so the son's age is 2/3 of his father's.
So, the son's present age is 20 years old.
Hope this helps!
Suppose a random sample of 80 measurements is selected from a population with a mean of 25 and a variance of 200. Select the pair that is the mean and standard error of x.
a) [25, 2.081]
b) [25, 1.981
c) [25, 1.681]
d) [25, 1.581]
e) [80. 1.681]
f) None of the above
Answer:
d) [25, 1.581]
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [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, which is also standard error, [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:
[tex]\sigma = \sqrt{200}, n = 80[/tex]
So the standard error is:
[tex]s = \frac{\sqrt{200}}{\sqrt{80}} = 1.581[/tex]
By the Central Limit Theorem, the mean is the same, so 25.
The correct answer is:
d) [25, 1.581]
Not sure how to solve
Answer:
(x, y, z) = (13/7, 19/7, 25/7)
Step-by-step explanation:
You know that the vector whose components are the coefficients of the equation of the plane is perpendicular to the plane. That is (1, 2, 3) is a vector perpendicular to the plane.
The parametric equation for a line through (1, 1, 1) with this direction vector is ...
(x, y, z) = (1, 2, 3)t +(1, 1, 1) = (t+1, 2t+1, 3t+1)
The point of intersection of this line and the plane will be the point in the plane closest to (1, 1, 1). That point has a t-value of ...
(t +1) +2(2t +1) +3(3t +1) = 18
14t +6 = 18
t = 12/14 = 6/7
The point in the plane closest to (1, 1, 1) is ...
(x, y, z) = (6/7+1, 2(6/7)+1, 3(6/7)+1)
(x, y, z) = (13/7, 19/7, 25/7)
George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(3) mean about George's new store?
This is a great question!
When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -
[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]
____
Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,
[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]
Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,
( 1. The new store will have a profit of $3400 after its third month in business.
( 2. The new store will have a profit of $2400 after its third month in business.
( 3. The new store will sell 2400 items in its third month in business.
( 4. The new store will sell 3400 items in its third month in business.
The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
Substitution:The substitution method is the algebraic method to solve simultaneous linear equations.
Given function is,
[tex]r(x) = x^2+5x+14[/tex]...(1)
And [tex]c(x) = x^2-4x+5[/tex]...(2)
Now, substituting the value into the equation (1) and (2).
[tex]r(5) = (5)^2+5(5)+14=64[/tex]
[tex]c(5) = (5)^2-4(5)+5=10[/tex]
Therefore,
[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]
Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
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Which of the following are congruent? ΔSTV and ΔTVU ST and TV ∠STV and ∠SVT UV and SV ∠U and ∠S ∠TVU and ∠SVT
Answer:
ΔSTV and ΔUTV
UV and SV
∠U and ∠S
∠TVU and ∠SVT
Step-by-step explanation:
A D E F
ΔSTV And Δ UTV , UV and SV , ∠ U and ∠ S , ∠ TVU and ∠ SVT are congruent .
What is congruency?Two figures are said to be congruent if we can superimpose them on each other. For congruency there are three criteria:
three corresponding sides are equaltwo pair of corresponding sides and corresponding angles are equalTwo corresponding pairs of angles and the corresponding sides are equal.How to check congruency?For congruency firstly check first part of question which is STV and TVU triangles because two corresponding sides TS and TU and SV and UV and angle TSV and angle TUV are equal so these two triangles are congruent.
ST and TV are not congruent
angle STV AND SVT are also non congruent
UV and SV are congruent because these are shown in the figure that these are equal.
Angle U and S are congruent as these are the alternate angles of the two triangles.
Angle TVU and SVT are also congruent because these are also alternate angles.
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A trough of water is 8 meters deep and its ends are in the shape of isosceles triangles whose width is 5 meters and height is 2 meters. If water is being pumped in at a constant rate of 6 m3Isec. At what rate is the height of the water changing when the water has a height of 120 cm?
Answer:
0.3 m/s
Step-by-step explanation:
The first thing is to attach the allusive graphic to the question. Now yes, let's move on to the solution that would be:
If the through is completely filtered the its volume will:
V = l * [1/2 w * h] = 1/2 l * w * h
Now we derive with respect to time and we are left with:
dV / dt = 1/2 * l * w * dh / dt
We solve by dh / dt and we have:
dh / dt = (2 / (l * w)) * (dV / dt)
We know that l = 8 and w = 5, in addition to dV / dt = 6, we replace:
dh / dt = (2 / (8 * 5)) * (6)
dh / dt = 0.3
Therefore the rate at which the height of the water changes is 0.3 m / s
a coin will be tossed 10 times. Find the chance that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses
Answer:
The chance that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses is P=0.0488.
Step-by-step explanation:
To solve this problem we divide the tossing in two: the first 5 tosses and the last 5 tosses.
Both heads and tails have an individual probability p=0.5.
Then, both group of five tosses have the same binomial distribution: n=5, p=0.5.
The probability that k heads are in the sample is:
[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{5}{k}\cdot0.5^k\cdot0.5^{5-k}[/tex]
Then, the probability that exactly 2 heads are among the first five tosses can be calculated as:
[tex]P(x=2)=\dbinom{5}{2}\cdot0.5^{2}\cdot0.5^{3}=10\cdot0.25\cdot0.125=0.3125\\\\\\[/tex]
For the last five tosses, the probability that are exactly 4 heads is:
[tex]P(x=4)=\dbinom{5}{4}\cdot0.5^{4}\cdot0.5^{1}=5\cdot0.0625\cdot0.5=0.1563\\\\\\[/tex]
Then, the probability that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses can be calculated multypling the probabilities of these two independent events:
[tex]P(H_1=2;H_2=4)=P(H_1=2)\cdot P(H_2=4)=0.3125\cdot0.1563=0.0488[/tex]
According to the Stack Overflow Developers Survey of 20184 , 25.8% of developers are students. The probability that a developer is a woman given that the developer is a student is 7.4%, and the probability that a developer is a woman given that the developer is not a student is 76.4%. If we encounter a woman developer, what is the probability that she is a student
Answer:
3.26%
Step-by-step explanation:
The computation of the probability that she is a student is shown below:
Percentage of student developers = 25.8% = SD
The Percentage of the developer is student = 7.4% = DS
The percentage of the developer is not student = 76.4% = ND
Based on this, the probability is
[tex]= \frac{SD \times DS}{SD \times DS + DS \times ND}[/tex]
[tex]= \frac{25.8\% \times 7.4\%}{25.8\% \times 7.4\% + 7.4\% \times 76.4\%}[/tex]
=3.26%
we simply considered all the elements
of the boxes of cruncho cereal on a supermarket shelf 25 percent contain a prize and the other 75 percent contain no prize.if Gerry buys two boxes of cruncho cereal which of the following is closest to the probability that neither box contain a prize??
Answer:
The probability that neither box contains a prize is 0.5625 or 56.25%
Step-by-step explanation:
It's referred as to the case when the probability of success (or failure) of the event A doesn't interfere with the probability of B. In this question we'll assume there are enough boxes of cereal of each type to make the choosing of one of them affect very little the choosing of the other one.
Let's call p=0.25 to the probability of getting a cereal box with a prize, and q=0.75 to the negation of p, i.e. the probability of getting a ceral box without a prize. There are four possible combinations: {pp,pq,qp,qq}. We need to find the probability of the combination qq. We compute it as the product of the individual probabilities
In other words, the probability that neither box contains a prize is 0.5625 or 56.25%
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If A and B are independent events, P(A) = 0.25, and P(B) = 0.3, what is P(AB)?
O A. 0.25
B. 0.3
C. 0.15
O D. 0.075
Answer:
[tex] P(A) = 0.25, P(B= 0.3[/tex]
And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :
[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]
And the best option would be:
[tex] P(A \cap B) =0.075[/tex]
Step-by-step explanation:
For this case we have the following events A and B and we also have the probabilities for each one given:
[tex] P(A) = 0.25, P(B= 0.3[/tex]
And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :
[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]
And the best option would be:
[tex] P(A \cap B) =0.075[/tex]
Write the equation in the form Ax + By = C. Find an equation of a line passing through the pair of points (4,7) and (3,4).
Answer:
[tex] 3x - y = 5 [/tex]
Step-by-step explanation:
The two pint equation of a line:
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
We have
[tex] x_1 = 4 [/tex]
[tex] x_2 = 3 [/tex]
[tex] y_1 = 7 [/tex]
[tex] y_2 = 4 [/tex]
[tex] y - 7 = \dfrac{4 - 7}{3 - 4}(x - 4) [/tex]
[tex] y - 7 = \dfrac{-3}{-1}(x - 4) [/tex]
[tex] y - 7 = 3(x - 4) [/tex]
[tex] y - 7 = 3x - 12 [/tex]
[tex] 5 = 3x - y [/tex]
[tex] 3x - y = 5 [/tex]
if the line〈3 + 2t,1 +t,2−t〉intersects the unit sphere inR3given byx2+y2+z2= 1,and if so, at what points.
Answer:
[tex]( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\[/tex]
Step-by-step explanation:
Solution:-
- We are given a parametric form for the vector equation of line defined by ( t ).
- The line vector equation is:
L: < 3 + 2t , t + 1 , 2 -t >
- The same 3-dimensional space is occupied by a unit sphere defined by the following equation:
[tex]S: x^2 + y^2 + z^2 = 1[/tex]
- We are to determine the points of intersection of the line ( L ) and the unit sphere ( S ).
- We will substitute the parametric equation of line ( L ) into the equation defining the unit sphere ( S ) and solve for the values of the parameter ( t ):
[tex]( 3 + 2t )^2 + ( 1 + t )^2 + ( 2 - t)^2 = 1\\\\( 9 + 12t + 4t^2 ) + ( t^2 + 2t + 1 ) + ( 4 + t^2 -4t ) = 1\\\\t^2 + 10t + 13 = 0\\\\[/tex]
- Solve the quadratic equation for the parameter ( t ):
[tex]t = -5 + 2\sqrt{3} , -5 - 2\sqrt{3}[/tex]
- Plug in each of the parameter value in the given vector equation of line and determine a pair of intersecting coordinates:
[tex]( x_1 , y_1 , z_1 ) = < -7 + 4\sqrt{3} , -4 + 2\sqrt{3} , 7 - 2\sqrt{3} >\\\\( x_2 , y_2 , z_2 ) = < -7 - 4\sqrt{3} , -4 - 2\sqrt{3} , 7 + 2\sqrt{3} >\\[/tex]
The sum of 9 distinct positive integers is 2009. Find the maximum possible value of the greatest common divisor of these 9 numbers.
Answer:
49
Step-by-step explanation:
The greatest common divisor of the addends must also be a divisor of 2009. That number can be factored as ...
2009 = 1×2009 = 7×287 = 41×49
The largest possible factor such that the other factor can be a sum of 9 positive integers is 49.
The maximum value of the GCD is 49.
IZ OT 50
Mathematics is the science of patterns and is the foundation for
algebra.
a. True
b. False
Answer:True
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Because it can but does not
Forty one people were riding bus number 527. At 8:45 am,it arrived at the 109th street stop. There,19 people got off and then 20 people boarded. How many riders were on the bus when it traveled to the next stop?
Answer:
1 because jahahdhekskdbsks
A sample of size 42 college students produced a 95% confidence interval of (3.1, 5.2) for the mean number of coats owned. Then there is a 95% chance that these 42 students own on average between 3.1 and 5.2 coats.
a. True
b. False
Answer:
b. False.
Step-by-step explanation:
According to the presented information, at the 95% confidence level, the mean number of coats owned will be between 3.1 and 5.2. That does not mean that there is a 95% chance that they will own that many coats; just that you are 95% confident that they will own the coats.
Hope this helps!
Figure ABCDE was reflected across the line y=x to create figure A’B’C’D’E’. What are the coordinates of the pre image of E?
Answer
so I need to know the coordinates for me to tell you the answer but I think I can still help you by explaining.
In order for E to become E' the rule for reflection over y=x is (y, x) so you basically switch the x and the Y to have E'. so for you to be able find out E, you need to witch the x and the y.
for example:
if E' was (-2, 3)
E in the pre image would be (3, -2)
hope this helps :)
Answer:
(-2,6)
Step-by-step explanation:
Just did it edge 2021