2 different expressions that involve only outs and powers of 2 which are equivalent 4 2/3 / 8 1/4
1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)
2) (2^5 * 3^1) / (2^6 * 4^-1)
1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)
This expression is equivalent to 4 2/3 / 8 1/4 because it is written in terms of powers of two. 4^2 is equal to 16, which is the numerator in 4 2/3. 2^-1 is the same as 1/2, which is the second fraction in 4 2/3. 3^1 is equal to 3, which is the numerator in 8 1/4. 8^1 is equal to 8, which is the denominator in 8 1/4. 2^-2 is the same as 1/4, which is the second fraction in 8 1/4. 4^-1 is equal to 1/4, which is the first fraction in 8 1/4. When all the terms are multiplied and divided, it is the same as 4 2/3 / 8 1/4.
2) (2^5 * 3^1) / (2^6 * 4^-1)
This expression is also equivalent to 4 2/3 / 8 1/4 because it is written similar to above equation.
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Can the measure of an exterior angle of a triangle ever equal the measure of its adjacent interior angle?
Group of answer choices
Yes, since the two angles must add to 180°, this can only happen when both angles are exactly 90°.
Yes, since the two angles must add to equal 180°, it can happen with any angle measures.
No, this is not possible since the angles have to add to equal 180° they can never be the same.
If the exterior angle is of 90º, it's adjacent interior angle will also be of 90º
What is exterior angle property of triangle?
According to the exterior angle theorem, the exterior angle that results from stretching a triangle's side is equal to the sum of the dimensions of the triangle's two opposed interior angles. The theorem can be used to determine a triangle's unknown angle's measurement. We must first determine the triangle's exterior angle and then its two remote inner angles in order to apply the theorem.
Using the concept of supplementary angles, it is found that the measure of an exterior angle of a triangle is equal to the measure of it's adjacent interior angle if both measure 90º.
Two angles are called supplementary if their measures add to 180º.
The exterior angle of a triangle is supplementary to it's adjacent interior angle.
Thus, if the exterior angle is of 90º, it's adjacent interior angle will also be of 90º.
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How do you use the binomial series to expand (1−x)^1/3?
The binomial series is used to expand a binomial expression of the form (a + b)^n, where 'a' and 'b' are constants and 'n' is a positive integer. In this case, we are expanding (1-x)^1/3.
Step 1: Rewrite the expression using the binomial theorem. We can rewrite (1-x)^1/3 as (1 + (-x))^1/3.
Step 2: Use the binomial theorem to expand the expression.
The binomial theorem states that (a + b)^n
= nC0*a^n + nC1*a^(n-1)*b + nC2*a^(n-2)*b^2 + ... + nCn*b^n.
Since 'n' is a 1/3 in this case, we can rewrite the expression as
(1 + (-x))^1/3
= 1C0*1^1/3 + 1C1*1^(1/3-1)*(-x) + 1C2*1^(1/3-2)*(-x)^2 + ...
Step 3: Substitute the values. We can substitute the values into the expression to get (1 + (-x))^1/3
= 1 + (-x) + (-x)^2 + ...
Step 4: Simplify the expression. The expression simplifies to
(1 - x + x^2 - x^3 + ...).
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Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles by SSS or SAS, write "not enough information." Explain your answer.
A. Triangle UTZ = Triangle -------------- (SAS)
B. Triangle UTZ = Triangle --------------( SSS)
c.The two triangles are not necessarily congruent. There is not enough information.
Answer:
B. [tex]\triangle UVZ \cong \triangle YVX[/tex] (SSS)
From the given image, we can say that the congruency postulate is that; Triangle UTZ ≅ Triangle YVX by SSS
How to identify congruent triangles?There are 6 main triangle congruency postulates namely;
1. SSS which means the three corresponding sides of both triangles are congruent.
2. SAS which means that 2 corresponding sides and the included corresponding angle are congruent.
3. ASA which means that 2 corresponding angles and the included corresponding side are congruent.
4. AAS which means that 2 corresponding angles and the non-included corresponding angle are congruent.
5. Hypotenuse-Leg Congruence Theorem which states that If the hypotenuse and leg in one right triangle are congruent to the hypotenuse and leg in another right triangle, then the two triangles are congruent.
From the given image of both triangles, we can see that all three corresponding sides are congruent to each other which indicates SSS Congruency postulate.
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How do I multiply a 1x2 matrix by a 2x3 matrix?
Matrix multiplication, also known as matrix product and the multiplication of two matrices, produces a single matrix. It is a type of binary operation. If A and B are the two matrices, then the product of the two matrices A and B are denoted by: X = AB.
The multiplication is done by adding the elements obtained by multiplying each element of the lines of the first matrix times the elements of the columns of the second matrix (Line× Column).
[tex]A=\left[\begin{array}{ccc}1&2\\\end{array}\right] _{1*2} \\B= \left[\begin{array}{ccc}4&5&6\\7&8&9\end{array}\right] _{2*3}[/tex]
2=2 yes it is possible to multiply
1*3= order of the resulting matrix
(line*column)
[tex]A*B=\left[\begin{array}{ccc}4+14&5+16&6+18\\\end{array}\right] _{1*3}[/tex]
[tex]A*B=\left[\begin{array}{ccc}18&21&24\\\end{array}\right] _{1*3}[/tex]
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if f(x) = , what is f(7.6)? 3 3.5 3.8 4
The solution of the given greatest integer function is found as 3.5.
Explain the term greatest integer function?The largest integer function is one that yields an integer that is closest to the specified real value. Additionally known as the step function. The closest integer is used to round off the input using the biggest integer function.We have to compute;
f(x) = 1/2[x]
Given what we have; f(7.6).
Enter x = 7.6 in the function provided;
f(7.6) = 1/2[7.6]
As ,the value (7.6) --> 7.0 (greatest integer function)
f(7.6) = 7/2
f(7.6) = 7/2
f(7.6) = 3.5
Thus, the solution of the given greatest integer function is found as 3.5.
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The correct question is-
If f(x) = 1/2[x], what is f(7.6)?
3
3.5
3.8
4
What is the value of n - 7 when n = 14
Answer: 7
Step-by-step explanation:
We substitute n for 14 to get the equation 14-7, which equals 7.
What happens when you have a double negative?
For a recipe, Val uses 4 cups of sugar for each cup of flour. How many cups of flour does Val need when he uses 1 cup of sugar?
Which one is correct
1/4
1/2
4
1
Answer:
1/4
Step-by-step explanation:
4 : 1 = 1 : x
x = 1 · 1 / 4
x = 1/4
Find the equation of the circle passing through the following points: (b) (-2,2), (2, 4) and (4,0)
The equation of the circle in general form is x² + y² - 2 · x - 2 · y - 8 = 0.
How to derive the equation of a circleIn this problem we need to derive the equation of a circle that contains three points: (x₁, y₁) = (- 2, 2), (x₂, y₂) = (2, 4), (x₃, y₃) = (4, 0). The general form of the equation of the circle is a second order polynomial of the form:
x² + y² + B · x + C · y + D = 0
Where B, C, D are real coefficients.
First, use the points to generate a system of linear equations:
- 2 · B + 2 · C + D = - 8
2 · B + 4 · C + D = - 20
4 · B + D = - 16
Second, resolve the system by means of numerical methods:
(B, C, D) = (- 2, - 2, - 8)
Third, write the general form of the equation is:
x² + y² - 2 · x - 2 · y - 8 = 0
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emma wants to know if long distance relationships in college have a greater likelihood of ending than relationships that are not long distance. she creates a questionnaire and recruits 100 students from her school to complete the questionnaire so she can test her hypothesis. emma is:
Emma is asking an empirical question so that she she can test her hypothesis
What is a Empirical hypothesis?
Something empirical is something based on real evidence .
Evidence that is verifiable by observation as opposed to something that is true in theory or by some kind of reckoning or logic
A hypothesis is a theory that is put forward for further examination to see if it is correct. It is not a call but it is an explanation that fits the available evidence so , An empirical hypothesis is a theory that is based on real evidence and experience but that has not been proven yet
So, According to the question
Emma wants to know if long distance relationship in college have a greater likelihood of ending than a relationship that are not long distance and for that she creates a questionnaire and the crowds 100 student from our school to complete the questionnaire so she can test her hypothesis
Here, Emma is asking an empirical questions ( question about experience) and will conclude the test based on these 100 students experience and thoughts.
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Which of the following is the axiom of congruence 2 points SSS SAS ASA SSA?
Two triangles are said to be congruent if their sides (S) and angles (A) are the same. SAS, ASA, SSS, and RHS serve as the triangle's congruence criteria. A triangle's congruency is not determined by SSA.
What does a math congruent mean?
Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.
Draw two circles with the same radius, for instance, then cut them out and stack them.
How are three congruent?
An equilateral triangle is one that has all three of its sides be in line with one another. We add a slash mark to the sides that are congruent. An equilateral triangle's angles are 60°.
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Create a fraction (and state the decimal number) that is exactly halfway between
15/24 and 1/8.
§. Show all of your thinking. Represent your answer as
fraction and decimal.
Answer:
Step-by-step explanation:
?
Avery had $25.27 in her wallet. If she bought lunch with 10.75% dollars from her wallet, how much money did she have in her wallet after lunch?
Answer:
$22.55
Step-by-step explanation:
Not 100% sure but you can double check...
A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area. To conduct the experiment, the biologist needs three treatment groups: a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2). The biologist chooses the first cloud-free night and catches the first 18 bats that fly out of a cave. The first six bats will be the control group, the second six will be treatment group 1, and the last six will be treatment group 2.
Which component is missing from the biologist’s process?
The biologist should have chosen a random night to catch the bats.
The biologist did not randomly assign the bats to the treatment groups.
The biologist did not allow each bat the same chance to be in each treatment group.
The biologist should have used random sampling when deciding which bats to catch.
answer is b
The component that is missing from the biologist's process is: c. The biologist did not randomly assign the each of the bats to the treatment groups.
How to interpret Randomization in statistics?When we carry out a research study that has created groups that you want to study, then the differences between and within groups can be thoroughly checked to make sure that they are not systematic when subjects are randomly assigned to groups.
Therefore this random assignment of subjects, gives the researcher the confidence that groups are the same in terms of variables, and any differences can be confidently allocated to experimental treatments.
Therefore, we can conclude that the component that is missing from the biologist's process is given in option C because the biologist did not randomly assign the each of the bats to the treatment groups.
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In an analysis of variance problem if SST = 120 and SSTR-80, then SSE is
a. 200
b. 40
c. 80
d. 120
The value of SSE (sum squared error) is 40 in the given analysis of the variance problem if SST = 120 and SSR = 80. Option b is correct.
How to find SSE in an analysis of variance problems with the SST and SSR values?Here the words SSE means Sum Squared Error, SST means Sum of Squares Total and SSR means Sum of Square Regression.
In the SSE accuracy measure, errors are squared and then added. It is used when the data points are similar in magnitude.
The formula is SST = SSR + SSE ⇒ SSE = SST - SSR
Calculation:The given values of the analysis of the variance problem are
SST = 120; SSR = 80
Then, the value of SSE = SST - SSR = 120 - 80 = 40
So, option b is correct.
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A 5-pound bag of potatoes cost $4.65. How many pounds, p, can you buy for $8.37
Answer: You can buy a 9-pound bag for $8.37.
Step-by-step explanation:
[tex]\frac{5lbs}{4.65} =\frac{p}{8.37}[/tex]
Then, we cross multiply, and we get:
5(8.37) = 4.65p
41.85 = 4.65p [We divided 4.65 by both sides]
9 = p
is there a regualr polygon with an interior angle sum of 9000 degrees? if so, what is it
Answer:
Yes, there is. It's called a regular 52-gon.
The function y = - 16t2 + 248 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff.
What is the original height of the stone before it is dropped?
How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.
The height of the stone before it is dropped is 4.64 feet, and the time taken to hit the ground is 3.94 seconds.
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The function y = - 16t² + 248
Calculate the value of t when f(t) = 0.
0 = -16t² + 248
t² = = 248 / 16 = 15.5
t = √15.5 ≈ 3.94 Seconds
Calculate the height at t = 3.94
y = -16 × 3.9² + 248
y = -243.36 + 248
y = 4.64 feet
Therefore, the height of the stone before it is dropped is 4.64 feet, and the time taken to hit the ground is 3.94 seconds.
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Solve for X and y PLEASE GIVE FULL EXPLANATION HOW YOU GOT IT
Answer:
(1, -1)
Step-by-step explanation:
we isolate y in the first equation
2x+y=1
-2x. -2x
y=1-2x
and now we fill y into second equation
4x-2(1-2x)=6
4x-2+4x=6
8x-2=6
+2 +2
8x=8
/8 /8
x=1
and now to find y we insert x
2(1)+y=1
2+y=1
-2. -2
y= -1
hopes this helps
the operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. he took a random sample of his remote controls and tested two brands of batteries. the number of minutes of continuous use before the batteries failed for each brand are given in battery.xlsx . if significance level is 10%, is there statistical evidence of a difference in longevity between the two batteries?
There is no sufficient evidence to support the claim that there is a difference in the longevity of the two brands of batteries , as the null hypothesis failed to be rejected.
So the mean and standard deviation for the sample of battery 1 is :
M(1)= 106+ 111+ 109+ 105/4 =107.75
standard deviation (1)=r√(x(i)-M/(n-1)=root(22.75/3)=2.754
Similarly, for the second battery, the mean and standard deviation is
M(2)= 125 +103+ 121+ 118/4=116.75
S(2)=√(276.75/3)=√(92.25)=9.605
Here the hypothesis test for the difference between populations means, here the claim is that the longevity of the two brands of batteries differs.So the alternative and null hypotheses are:
H(0)= μ1-μ2=0
H(1)=μ1-μ2 ≠0
Here the significance level is 0.05(α), The difference between sample means is M(d)=107.75- 116.75=-9 .Now the estimated standard error of the difference between the means is :
s(Md)=√(2.754²+9.605²/4)=4.996, Now the test static will be, t=-9-0/4.996=-1.8014 and the degree of freedom is 4+4-2=6 .Here the test is two-tailed with degrees of freedom of the test static is -1.8014, so the P-value for the test is : 2.P(t< -1.8014)=0.122
Here the P-value (0.122) is greater than the significance level so the effect is insignificant, and the null hypothesis failed to be rejected.
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the operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. he took a random sample of his remote controls and tested two brands of batteries. the number of minutes of continuous use before the batteries failed for each brand is given in battery.xlsx. if the significance level is 10%, is there statistical evidence of a difference in longevity between the two batteries?
The sample data for each battery is:
Battery 1: 106 111 109 105
Battery 2: 125 103 121 118
Steven uses a ladder to change the bulb in the floodlight on the front of the house because it is 15 feet above the ground. Stephen needs to place the end of the ladder 8 feet away from the house so that it does not crush the flowers in the flower bed.
How tall must the ladder be to reach the height of the floodlight?
(IGNORE MY ANSWER I DIDNT MEAN TO CLICK ON IT)
Answer:
17 feet
Step-by-step explanation:
We can use the Pythagorean therom, since the triangle has a 90 degree angle:
8^2 + 15^2 = x^2
64 + 225 = x^2
x^2 = 289
x = 17 feet
See the attached worksheet.
Kevin ate 2/5 of a pie. Su yung ate 3/10 of the pie. how much of the pie did Kevin and Su Yang eat together
The total amount of pie Kevin and Su Yung ate together is 7/10 of the pie
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount of pie Kevin and Su Yung ate be = A
Now , the equation will be
The amount of pie Kevin ate = 2/5 of the total pie
And ,
The amount of pie Su Yung ate = 3/10 of the total pie
So , the equation is
Total amount of pie Kevin and Su Yung ate = amount of pie Kevin ate + amount of pie Su Yung ate
Substituting the values in the equation , we get
Total amount of pie Kevin and Su Yung ate A = 2/5 + 3/10
Total amount of pie Kevin and Su Yung ate A = ( 4 + 3 ) / 10
Total amount of pie Kevin and Su Yung ate A = 7 / 10 of the total pie
Therefore , the value of A is 7/10
Hence ,
The total amount of pie Kevin and Su Yung ate together is 7/10 of the pie
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braulio has $15 less than adam. together they have $153. write the system of equations that could be used to determine the amount of money braulio, b, and the amount of money adam, a, has each. how much does braulio make?
The amount of money with Adam and Braulio as per given system of equations is equal to $84 and $69.
As given in the question,
Let 'a' be the amount of money with Adam
And 'b' be the amount of money with Braulio
System of equations as per given given data:
b = a - 15___(1)
a + b = 153 ___(2)
Substitute the value of 'b' in (2) we get,
a + a -15 = 153
⇒2a = 153 + 15
⇒2a = 168
⇒ a = $84
Amount of money with Adam is $84
Amount of money with Braulio is b = 84 - 15
= $69
Therefore, the amount of money with Adam and Braulio is equal to $84 and $69.
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y=px+q and y=rx+s are perpendicular and p=49|r| . Find the values of p and r
Answer:
[tex]r=-\frac{\sqrt{7}}{7} \implies p=\sqrt{7}[/tex]
Step-by-step explanation:
We know that [tex]pr=-1[/tex] and [tex]p=49|r|[/tex].
[tex]\frac{-1}{r}=49|r| \\ \\ \frac{1}{r^2}=49r^2 \\ \\ 1=49r^4 \\ \\ r^4=\frac{1}{49} \\ \\ r=-\frac{\sqrt{7}}{7} \implies p=\sqrt{7}[/tex]
convert this rational number to its decimal form and round to the nearest thousandth 1/4
The given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.
What is decimal form?We shall represent this as 1.5 pizzas in decimal form.
In this case, the dot stands in for the decimal point, the number before the dot, in this case, "1," represents one entire pizza, and the number after the decimal point, or the fractional component, represents the other half of the pizza.
So, we have the rational number:
1/4
Convert to decimal as follows:
1/4 = 0.25
Rounding off to the nearest thousandth: 0.2500 ⇒ 0.25
Therefore, the given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.
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a special window has the shape of a rectangle surmounted by an equilateral triangle. see the figure. if the perimeter of the window is 16 feet, what dimensions will admit the most light?
A triangle whose sides are all equal is called an equilateral triangle and its area is given by A=[tex]\frac{\sqrt{3} }{4}[/tex] [tex]x^{2}[/tex], where x is the side of the triangle.
The area of a rectangle is found by using the formula
A=lw, where l is the length and w is the width.
The given figure can be split into two shapes: a rectangle and an equilateral triangle as shown in the diagram. Let l be the length of the rectangle.
Add all of the sides of the window and equate their result to 16. Then solve for l.
x + x + l + x + l = 16
3x + 2l = 16
2l = 16 - 3x
l = [tex]\frac{16-3x}{2}[/tex]
The total area of the window will be the sum of the area of the equilateral triangle ABE and the area of rectangle BCDE.
A = [tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + lx
Subsitute [tex]\frac{16-3x}{2}[/tex] for l into the obtained equation and simplify.
A =[tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + ( [tex]\frac{16-3x}{2}[/tex])x
A = [tex]\frac{\sqrt{3} }{4} x^{2}[/tex] + 8x - [tex]\frac{3}{2} x^{2}[/tex]
Differentiate the obtained equation with respect to x and equate the first derivative to 0 to calculate the critical point x .
[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{4}[/tex] (2x) + 8 - [tex]\frac{3}{2}[/tex] (2x)
0 = [tex]\frac{\sqrt{3} }{2}[/tex] x - 3x + 8
x (3 - [tex]\frac{\sqrt{3} }{2}[/tex]) = 8
x = [tex]\frac{16}{6-\sqrt{3} }[/tex]≈3.74887
Again, differentiate the equation
[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]x - 3x + 8 with respect to x.
[tex]\frac{d^{2}A }{dx^{2} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] - 3
The value of the second derivative is [tex]\frac{\sqrt{3} }{2}[/tex]−3, which is negative. This implies that the area will be maximum at the critical point.
Subsitute x = 3.74887 into the equation
l = [tex]\frac{16-3x}{2}[/tex] and simplify
l = [tex]\frac{16-(3)(.74887)}{2}[/tex] ≈ 2.3767
The maximum light will enter through the window when the triangular portion will have the side length of 3.74887 feet and the dimensions of the rectangular portion will be 3.74887-ft-by-2.3767-ft.
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Albert has $1,000 in an account. The interest rate is 5% compounded annually.
To the nearest cent, how much interest will he earn in 4 years?
Answer:
$215.50
Step-by-step explanation:
To calculate the amount of interest that Albert will earn on his account over the course of 4 years, we can use the formula for compound interest:
Interest = principal * (1 + rate/n)^(n*t) - principal
Where:
principal is the initial amount of money in the account ($1,000 in this case)
rate is the annual interest rate (5% in this case)
n is the number of times that interest is compounded per year (annually in this case, so n=1)
t is the number of years the money is invested (4 years in this case)
Plugging these values into the formula, we get:
Interest = $1,000 * (1 + 0.05/1)^(1*4) - $1,000
= $1,000 * (1.05)^4 - $1,000
= $1,000 * 1.2155 - $1,000
= $215.50
To the nearest cent, the interest Albert will earn in 4 years is $215.50.
*URGENT* Sam has 2 part time jobs. At the grocery store, he earns $8/h and at the library, he earns $10/h. Before going on vacation, he would like to save $280. Determine the fewest number of hours he would need to work to reach his goal.
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Amount to earn = $280
Grocery store:
Earnings per hour = $8
1 hour = $8
Multiply 280/8 on both sides.
280/8 x 1 hour = $280
35 hours = $280
Library:
Earnings per hour = $10
1 hour = $10
Multiply 280/10 on both sides.
28 hours = $280
We see that,
Working in the Library would make $280 in fewer hours than working in the grocery store.
Thus,
The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.
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Can a triangle be formed with side lengths 4, 8, 11? Explain. No, because 11 − 8 < 4 Yes, because 11 − 4 < 8 No, because 4 + 8 > 11 Yes, because 4 + 8 > 11
A triangle can be formed with side lengths 4, 8, 11. Yes, because 4 + 8 > 11
How to illustrate the triangle?According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.
If the sum of any two sides is greater than the sum of the third, then the difference of any two sides is less than the sum of the third. The sum of any two sides must be greater than the sum of the third. The longest side in a triangle is the side opposite a larger angle.
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what is the probability that lamar and hareesh finish their jobs within 5 minutes of each other on a randomly selected day?
The probability that Lamar and Lawrence finish their jobs within 5 minutes of each other on a randomly selected day is 0.2892
Consider the time for the Lamar to finish the job as x and the time for the Lawrence to finish the job as x
Consider the random variable x-y
x-y normal with mean = 105 - 98
= 7
Similarly the variance of the random variable x-y
= 105 + 225
= 325
The standard deviation = [tex]\sqrt{325}[/tex]
= 18.03
Here we have to find the probability that Lamar and Lawrence finish their jobs within 5 minutes of each other on a randomly selected day
P(|x-y|<5) = P(-5<U<5)
Now we have to convert to standard normal variate Z
Then the it will be
(-5-7)/18.03 = -0.67
(5-7) / (18.03)= 0.11
The probability of the given condition will be
P(-0.67<Z<0.11) = 0.2454 + 0.0438
Add the terms
= 0.2892
Therefore, the probability is 0.2892
The complete question is:
Lamar and Lawrence run a two-person lawn-care service. they have been caring for Mr. Johnson's very large lawn for several years, and they have found that the time it takes Lamar to mow the lawn itself is approximately normally distributed with a mean of 105 minutes and a standard deviation of 10 minutes. meanwhile, the time it takes for Lawrence to use the edger and string trimmer to attend to details is also normally distributed with a mean of 98 minutes and a standard deviation of 15 minutes. they prefer to finish their jobs within 5 minutes of each other. what is the probability that this happens, assuming their finish times are independent?
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