The polygon circumscribes the circle. Which of the following is the perimeter of the polygon?
A. 39 cm
B. 56 cm
C. 61 cm
D. 78 cm
Answers
The perimeter of the polygon is 78 cm. (Option D)
The perimeter of a geometric shape refers to the length that encompasses the figure. Hence, the perimeter of any irregular pentagon can be determined by the adding up the lengths of all sides. As the given polygon circumscribes a circle, the sides of the polygon are tangent to the circle. The two tangent theorem states that if two lines are drawn from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same. Hence, if two lines that are tangent to a circle meet at a point, then the distance from that point to the points of intersection between the tangents and the circle are equal. Hence, the perimeter of the pentagon is:
P = 8 + 8 + 16 + 16 + 6 + 6 + 9 + 9 = 78 cm
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Related Questions
Can someone please help me answer the second part of this question
Answers
The compositions of the two given functions are:
g(f(x)) = √(2*x + 29) - 2
f(g(x)) = √(2*x + 25)
How to find the composition of functions?Here we have the two functions:
f(x) = √(2x + 29)
g(x) = x - 2
We want to find the compositions:
f(g(x))
So we just need to evaluate f(x) on g(x), we will get:
f(g(x)) = √(2*g(x) + 29)
Now we can replace g(x) there:
f(g(x)) = √(2*(x - 2) + 29)
f(g(x)) = √(2*x - 2*2 + 29)
f(g(x)) = √(2*x + 25)
The other composition is:
g(f(x)) = f(x) - 2
g(f(x)) = √(2*x + 29) - 2
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Which of the following expressions represent the difference of 3 times a number and 10?
A. 3n-10 B. 3n+10 c. 3(n-10) D. 3n-2(10)
Answers
Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.
a) {(a, b) | a and b are the same age}
b) {(a, b) | a and b have the same parents}
c) {(a, b) | a and b share a common parent}
d) {(a, b) | a and b have met} e) {(a, b) | a and b speak a common language}
Answers
Relations in the options (a), (b) and (e) are the Equivalence relations as, the relations are reflexive, symmetric and transitive all.
Given, five relations as,
a) {(a, b) | a and b are the same age}
b) {(a, b) | a and b have the same parents}
c) {(a, b) | a and b share a common parent}
d) {(a, b) | a and b have met}
e) {(a, b) | a and b speak a common language}
we have to find which of them are equivalence relations
a) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.
So, R = {(a, b) | a and b are the same age} is an equivalence relation.
b) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.
So, R = {(a, b) | a and b have the same parents} is an equivalence relation.
c) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) need not to be in R for some a, b, c. Hence, Non - Transitive.
So, R = {(a, b) | a and b share a common parent} is not an equivalence relation.
d) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) need not to be in R for some a, b, c. Hence, Non - Transitive.
So, R = {(a, b) | a and b have met} is not an equivalence relation.
e) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.
So, R = {(a, b) | a and b speak a common language} is an equivalence relation.
Hence, the relations in options (a) , (b) and (e) are the equivalence relations.
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Triangle CAT is transformed by a sequence of rigid motions that maps onto triangle DOG. Which three congruency statements would show ASA congruency for these triangles? (select all that apply)
A.∠ A ≅ ∠ T
B.CA ≅ DO
C.AT ≅ OG
D.CT ≅ DG
E.∠ A ≅ ∠ O
F.∠ C ≅ ∠ D
Answers
Answer:
B, E and F.-----------------------------
Since the triangles CAT and DOG overlap, their corresponding parts are congruent.
As we are looking for ASA congruency, we need to select two angles and the included side.
Let's review the given options, considering names of triangles and the order of vertices in those names.
A. ∠ A ≅ ∠ T
Incorrect as angles T and A are not corresponding.B. CA ≅ DO
Yes, possible side.C. AT ≅ OG
Yes, possible side.D. CT ≅ DG
Yes, possible side.E. ∠ A ≅ ∠ O
Yes, possible angle.F. ∠ C ≅ ∠ D
Yes, possible angle.So we have corresponding angles A and C and the included side must be AC.
Looking, at the options, we can get ASA with combination of options B, E and F.
take the van der pol equation . (a) set and . convert the above second order differential equation to a two dimensional system of differential equations:
Answers
The van der Pol equation which is a second-order differential equation is given by
d²x/dt² - μ(1 - x²)dx/dt + x = 0
Here we are asked to convert it to a two-dimensional system.
Here we need to set y = dx/dt, where y represents the system's velocity.
Hence we will rewrite it as
d²x/dt² = μ(1 - x²)y + x
Now if we set the derivatives of x and y with respect to time to be equal to different variables we get
dx/dt = y
dy/dt = μ(1 - x²)y + x
Hence we get the above systems of equations as the 2-dimensional representation of the Van der Pol equation where x and y represent the system's position and velocity respectively.
If we set μ = 1 and x = 0, then we get
dx/dt = y
dy/dt = y
Hence we get the system of differential equations representing the behavior of the van der Pol equation with μ = 1 and x = 0 in two dimensions.
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Most insurance companies will replace a vehicle any time an estimated repair exceeds 80% of the "blue-book" value of the vehicle. Michelle's insurance company paid 9100$ for repairs on her car after an accident. What can be concluded about the blue-book value of the car?
Answers
We can find this out by creating and solving the inequality 9100 < .8x, which represents that 9100 is less than 80% of the blue book value (x). To solve it we divide both sides by .8 to get 11375 > x.
I don’t understand number 2
Answers
Answer:
x=-6.-3.0.3.6
y=6.3.0.-3.-6
Step-by-step explanation:
So in this problem you're given the table at the top for your values of X is going across their corresponding P of X values and their corresponding Q of X values. So in part A we want to find P fq of X. So first off we're gonna start when X is equal to zero. So that would mean we want to find p. of Q. of zero. So remember you start with your inside function. Well Q of zero is equal to zero. So now we need to find P. Of zero which is equal to three. Alright so next we want to find when X is one. So we have P of Q of one. Well Q of one is equal to one and I'm sorry that would leave us with PS one and PS one happens to also be one. So that'll be value for one. Next for one. X. is to so api of Q of two. Well Q two is equal to four and then P. Of four. That would leave us a pr four and pr four is equal to five. So that will be our answer for the next one. It will be five. Alright, next for three. So we have p. of Q. of three. So we have two of three which is equal to two. So now sorry that should be a P. Then we find P. F two which is also to So that'll be the answer to the 3rd 1 Next we need it for four. So we're looking for p of Q of four. Well looking according to our thing. Q4 is equal to five and then we have to find P. Of five which is zero. And lastly for five. So first we'll start with p. of Q. of five. So Q. A. Five we're told is three. So then we have to find pf three which is equal to four. So that's how you would find your first values. Okay, So now part B. We want to find sfx but no, this is the opposite way this time it's Q. A. P. Of X. So when X zero, we're going to be looking for Q. Of P. Of zero. Well no this P. Of zero is equal to three. So then we have to find Q. of three which is equal to two. It'll be our first answer. Next we'll do one. So we're gonna have Q. Of P. Of one. Well p. of one is equal to one. So then we find Q. Of one which is also one. So bring that down. All right, so now for two. First we're gonna start with Q. A. P. F. Two. Well P. F two is two. So that means we're essentially just finding Q. Of two which is four. Alright, next for three. So you're gonna have cute Of p. of 3? Well p of three is equal to four And Q four is equal to five. So I'll be your answer there. I'll do a new color because I think we're running out of room here. So next we're doing for, so I'm gonna go right here. So we're gonna have Q. A. P. Of four. Well if you four is equal to five, so that means we have to find Q. Of five which is three. And lastly for five. So we're gonna have Q. A. P. Of five. So first we'll find PFE which is zero. So that means now we need Q. Of zero which is zero. And now we filled out both of your tables.
given sales for the year of $218,000, cash expenses of $92,000 and depreciation expense of $23,000, net cash flow for the year is blank . multiple choice question. $195,000 $126,000 $103,000 $218,000
Answers
Answer:
$126,000
Step-by-step explanation:
The net cash flow for the year is $103, 000.
What is Net cash flow?After all debts have been settled, net cash flow can represent either a gain or a loss in money over a time period. A company is said to have positive cash flow if, after paying all of its operational expenses, it still has cash left over.
We have,
Sales for the year = $ 218, 000
Cash expenses = $92, 000
Depreciation Expenses = $23, 000
So, the Net cash flow is
= 218,000 - (92, 000 + 23, 000)
= $ 103, 000.
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Over 18 days, Sophia rode her bike an average of 12 miles each day.
What is the total number of miles she biked?
Enter your answer as a number like this: 42
Answers
The total Number of miles she biked, was 216.
In the given question, over 18 days, Sophia rode her bike an average of 12 miles each day.
We have to find the total number of miles she biked.
As we know that average is the sum of all numbers divide by total numbers.
As from the question, there is a total average of 18 days.
So the total number of days is 18.
The average distance of her bike for one day is 12 miles.
So we have to find the total number of miles that she biked.
We can find the total number of miles by multiplying the total number of days with the average speed of one day. So;
Total Number of Distance = Total Days × Average Speed of One Day
Total Number of Distance = 18 × 12
Total Number of Distance = 216 miles.
So, the total Number of Distance she biked, was 216 miles.
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courtney borrows $38,100 to make improvements to her new house. the loan is a 6-year loan with an apr of 4%. find her monthly payment to the nearest dollar.
Answers
Ashu's mother is three times as old as Ashu. After 5 years if Ashu's age would be 25. How old is Ashu's mother today?
Answers
Answer:
60 years old
Step-by-step explanation:
A=Ashu's age. M=Ashu's Mother's Age
M=A*3
M/3 = (A*3)/3 ==> divide 3 on each side to solve for A
A = M/3
A+5 = M/3 + 5 ==> A+5=25 since that'll be Ashu's age 5 years from now
25 = M/3 + 5 => plug in 25 for A+5
25-5 = M/3 + 5 - 5 ==> solve for M
20 = M/3
M = 20 * 3
M = 60 years old
Graph: y ≤ 3x + 4
A. Is (1,7) a solution? yes or no
B. Is ( 0,0) a solution? yes or no
Answers
A.
[tex]7 \leqslant 3(1) + 4 \\ 7 \leqslant 3 + 4 \\ 7 \leqslant 7[/tex]
B.
[tex]0 \leqslant 3(0) + 4 \\ 0 \leqslant 0 + 4 \\ 0 \leqslant 4[/tex]
BOTH ARE TRUE
Answer:
A. yes
B. yes
Step-by-step explanation:
You want a graph of y ≤ 3x +4 and an indication whether (1, 7) and (0, 0) are solutions.
GraphThe graph is attached. The boundary line is solid because points on that line are in the solution set. Points in the shaded area are also in the solution set.
A. (1, 7)This point is on the boundary line. It is a solution.
B. (0, 0)This point is in the shaded area of the graph. It is a solution.
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The LA Lakers had a PCT of 583 in the 2020-21 season. What does this mean in practical terms?
Answers
The meaning when LA Lakers had a PCT of 58.3 in the 2020-21 season is that the percentage of winning is 58.3%.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
From the information given, the LA Lakers had a PCT of 58.3 in the 2020-21 season. It should be noted that PCT simply means percentage. Therefore, it denotes 58.3 percent.
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Complete question
The LA Lakers had a PCT of 58.3 in the 2020-21 season. What does this mean in practical terms
Jill is going to make weekly deposits of $100 into an account for 3 years. The account earns 5.2%/a compounded weekly. How much money will she have in her account at the end of 3 years? How much money did she make on this investment?
Answers
Answer:
every week jill is going to make 5.20 dollars then you do 5.20 x 1095 days in 3 years = $5694 a year
Step-by-step explanation:
solve the problem. in terms of effective interest rate, order the following nominal rate investments from lowest to highest: i 4.87% compounded quarterly ii 4.85% compounded monthly iii 4.81% compounded daily (365 days) iv 4.79% compounded continuously ii, iii, iv, i iv, iii, ii, i iii, iv, i, ii i, ii, iii, iv
Answers
The nominal rate investment ranges from 4.90%, 4.92%, 4.95%, and 4.96%.
Part (c), or IV, III, II, and I, is therefore the right response to the question.
We must now determine the effective interest rate [tex]R_{e}[/tex] , we'll use the formula:-
[tex]R_{e} = (1 + i)^{k} - 1[/tex]
where, i = r / k
Here,
r = interest rate,
I = the nominal interest rate,
k = is the number of times that interest is compounded annually.
(i) 4.87% compounded quarterly
Then i = (4.87 / 100) * 4 =
i = 0.0487 * 4 = 0.012
So, [tex]R_{e}[/tex] = (1 + 0.012)⁴ - 1
[tex]R_{e}[/tex] = 0.0496 = 4.96 %
Therefore, the effective Interest Rate = 4.96%
(ii) 4.85% compounded monthly
Then i = (4.85 / 100) * 12
i = 0.0485 * 12 = 0.0040
So, [tex]R_{e}[/tex] = (1 + 0.0040)⁴ - 1
[tex]R_{e}[/tex] =0.04959 = 4.95 %
(iii) 4.81% compounded daily (365 days)
Then i = (4.81 / 100) * 365
i = 0.0481 * 365 = 0.00013
So, [tex]R_{e}[/tex] = (1 + 0.00013)⁴ - 1
[tex]R_{e}[/tex] = 0.0492 = 4.92 %
(iv) 4.79% compounded continuously
Then i = (4.79 / 100)
i = 0.0479
So, [tex]R_{e}[/tex] = (1 + 0.0479)⁴ - 1
[tex]R_{e}[/tex] = 0.0490 = 4.90 %
Therefore, the nominal rate investment is as follows: 4.90%, 4.92%, 4.95%, and 4.96%.
The right response to the question is section (c), which is IV, III, II, and I.
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The length of a rectangle is three times its width. If the perimeter of the rectangle is 40 m, find its length and width.
Answers
Answer:
The width would be 5, and the length would be 15.
Step-by-step explanation:
To solve this problem, first look at the perimeter. If the perimeter of the rectangle is 40m, then we can now solve the problem.
Since we don't know the width or the length, first, say that the width is w.
Width=w
Now, since the length is three times the width, we can write 3w for the length.
Length=3w.
Now, combine like terms.
w+3w+w+3w=40
8w=40
Divide by 8 on both sides.
40/8=5
w=5.
Since now we know that the width is 5, plug in 5 for w.
3(5)=15
w=5
The width would be 5, and the length would be 15.
Hope this helps! Have a great day! :D
Answer:
Length = 15 m Width = 5 mStep-by-step explanation:
Let us assume that,
→ Perimeter = 40 m
→ Width = x
→ Length = 3x
Perimeter of rectangle formula,
→ P = 2(l + w)
Forming the equation,
→ 2(3x + x) = 40
Now the value of x will be,
→ 2(3x + x) = 40
→ 2(4x) = 40
→ 8x = 40
→ x = 40/8
→ [ x = 5 ]
Then the length and width is,
→ Width = x = 5 m
→ Length = 3x = 3(5) = 15 m
Hence, these are the answers.
Please help me with this question
Answers
Answer:
y = -1/2 x - 1
Step-by-step explanation:
A (-2,0)
B (0,-1)
slope = (-1-0)/(0-(-2)
-1/2
y intercept = -1
y = -1/2 x - 1
Answer:
y = e^(-1/2x -1)
Step-by-step explanation:
You want the equation for y(x), which is graphed as a straight line on a semi-log scale.
GraphLet z = ln(x). The graph shows a straight line with a z-intercept of -1 and a slope of "rise"/"run" = -1/2. That means the slope-intercept equation for this line can be written as ...
z = -1/2x -1
EquationUsing z = ln(y), we can find the equation for y by taking antilogs:
ln(y) = -1/2x -1
y = e^(-1/2x -1)
__
Additional comment
The attached graph shows y = f(x) and the line ln(y).
suppose that y1 and y2 are independent and that both are uniformly distributed on the interval (0,1), and Let U1 and U2 be independent uniform random variables, both on (0,1). Let Y1 = U1U2 and let Y2=U2. (a) Find the joint density of Y1 and Y2.
(b) What is the marginal density for Y1?
Answers
a) The joint density of Y1 and Y2 is f(y1, y2) = 1, for 0 ≤ y1, y2 ≤ 1.
b) The marginal density for Y1 is f(y1) = 1, for 0 ≤ y1 ≤ 1.
Explanation:
(a) The joint density of Y1 and Y2 is found by multiplying the two individual densities together. Since Y1 and Y2 are independent, this is simply the product of the two densities.
The density for U1 is the same for all values of U1 on the interval (0,1), which is 1. The density for U2 is also the same for all values of U2 on the interval (0,1), which is also 1.
Therefore, the joint density of Y1 and Y2 is:
f(Y1,Y2) = f(U1U2,U2)
= f(U1) x f(U2)
= 1 x 1
= 1
(b) The marginal density for Y1 is the density of Y1 without regard to Y2. Since Y2 is uniform on (0,1), we can integrate the joint density over the interval (0,1) to obtain the marginal density of Y1:
f(Y1) = ∫f(Y1,Y2)dY2
= ∫1dY2
Y2 = 1
Therefore, the marginal density of Y1 is 1
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consider the following data for two independent random samples taken from two normal populations. sample 1 10 7 14 7 9 7 sample 2 9 7 8 4 5 9
a. Compute the two sample means.
Sample 1: Answer 9
Sample 2: Answer 7
b. Compute the two sample standard deviation (to 2 decimals).
Sample 1: Answer 2.28
Sample 2: Answer 1.79
c. What is the point estimate of the difference between the two population means? Answer
d. What is the 90% confidence interval estimate of the difference between the two population means (to 2 decimals - - use 9 degrees of freedom)? Answer
Answers
C. The point estimate of the difference between the two population means is 2.
D. The 90% confidence interval estimate of the difference between the two population means is (1.748, 0.867)
Given that:
Sample 1 mean (x1) = 9
Sample 2 mean (x2) = 7
Sample 1 standard deviation (σ1^2) = 2.28
Sample 2 standard deviation (σ2^2) = 1.79
C. To find point estimate of the difference between the two population means.
sample mean(x1) - sample mean(x 2)
= 9 - 7
= 2
Therefore, point estimate = 2
D. To find 90% confidence interval estimate of the difference between the two population means
90% confidence for 't'
df = (n1 + n2) - 2
= 12-2
= 10
90% confidence with df = 10 is t
t = 1.812
point estimate + 1 - t * [tex]\sqrt{\frac{s^2_{1} }{n_{1} } + \frac{s^2_{2} }{n_{2} } }[/tex]
2 + 1 - 1.812*[tex]\sqrt{\frac{2.28^2}{6} + \frac{1.79^2}{6} }[/tex]
3 - 1.812 *[tex]\sqrt{0.866 + 0.534}[/tex]
1.188 * 0.9305 + 0.7307
(1.748, 0.867)
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What are some possible solutions for the following inequality? 2f - 8 ≤ 6f + 4
-4.5
-8
-1
4
0
Answers
Answer:
Solutions: -1, 4, and 0
Step-by-step explanation:
f= -4.5
2f - 8 ≤ 6f + 4
2 (-4.5) -8 ≤ 6 (-4.5) + 4
-9 - 8 ≤ -27 + 4
-17 ≤ -23
Not True
f= -8
2f - 8 ≤ 6f + 4
2 (-8) - 8 ≤ 6 (-8) + 4
-16 - 8 ≤ -48 + 4
-24 ≤ -44
Not true
f= -1
2f - 8 ≤ 6f + 4
2 (-1) - 8 ≤ 6 (-1) + 4
-2 - 8 ≤ -6 + 4
-10 ≤ -2
True
f= 4
2f - 8 ≤ 6f + 4
2 (4) - 8 ≤ 6 (4) + 4
8-8 ≤ 24 + 4
0 ≤ 28
True
f= 0
2f - 8 ≤ 6f + 4
2 (0) - 8 ≤ 6 (0) + 4
0 - 8 ≤ 0 + 4
-8 ≤ 4
True
Graph the solution to this inequality on the number line. 2/3z > 4/5
Answers
The solution to the inequality, 2/3z > 4/5, is calculated as z > 1.2. See attachment for the graph of the solution.
How to Solve and Graph the Solution to an Inequality?The solution to an inequality is determined by finding he value of the variable in the inequality that will make it true.
Given the inequality, 2/3z > 4/5, isolate the variable z to one side to determine its value:
2/3z > 4/5 [given]
Multiply both sides by 3/2:
2/3z × 3/2 > 4/5 × 3/2
z > (4 × 3) / (5 × 2)
z > 12 / 10
Simplify further:
z > 6/5
z > 1.2
The solution is z > 1.2. The graph of the solution is shown in the image that is given in the attachment below.
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A four-wheel-drive vehicle is transporting an injured hiker to the
hospital from a point that is 30 km from the nearest point on a straight
road. The hospital is 50 km down that road from that nearest point. If
the vehicle can drive at 30 kph over the terrain and at 120 kph on the
road, how far down the road should the vehicle aim to reach the road
to minimize the time it takes to reach the hospital?
Answers
The final distance is 31 km.
Time, t = Distance, d/Velocity, v
Let's assume the ambulance drives a distance of x along the road, which leaves us 50-x on the road, after which it has reached the road.
It forms a triangle, after which we can use Pythagoras Theorem.
Using it, we get distance down the hill, d1, and we can calculate distance on the road remaining till the hospital, d2.
t = d1/v1 + d2/v2
= [tex]\frac{\sqrt{x^{2} + 30^{2} } }{30} + \frac{50 - x}{120}[/tex]
We need to minimise t. Therefore, we have to differentiate.
On differentiating and equating it to 0, we get the value of x as [tex]\sqrt{60} = 7.75[/tex]
How far down the road should the vehicle aim to reach the road to reach the hospital at the minimum time?
[tex]= \sqrt{900 + 7.75^{2} } = 31 km[/tex]
Thus, the final distance is 31 km.
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for how many integers $n$ between 1 and 1990 is the improper fraction \[\frac{n^2 7}{n 4}\] not in lowest terms? (a) 0 (b) 86 (c) 90 (d) 104 (e) 105
Answers
86
Step-by-step explanation:
(Graphing Proportional Relationships LC)
The table shows a proportional relationship.
x 15 9 21
y 5 3 7
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (15, 5).
A line passes through the point (0, 0) and continues through the point (7, 21).
A line passes through the point (0, 0) and continues through the point (5, 15).
A line passes through the point (0, 0) and continues through the point (3, 9).
Answers
The graph of the given proportional relation shows that the line passes through the point (0, 0) and continues through the point (15, 5). The relation is represented by the equation y = -0.33x. So, option A is correct.
What is the proportional relationship of the given table of proportions?The given table shows the x and y coordinates of a line.
So, we can find the relationship among them by writing an equation from the given points as
y - y₁ = {(y₂ - y₁)/(x₂ - x₁)} × (x - x₁)
Here we have (x₁, y₁) = (15, 5); (x₂, y₂) = (9, 3)
⇒ y - 5 = (3 - 5)/(9 - 15) × (x - 15)
⇒ y - 5 = (-2)/(-6) × (x - 15)
⇒ y - 5 = 1/3 × (x - 15)
⇒ 3y - 15 = x - 15
⇒ 3y = x + 0
∴ y = 0.33x
Thus, the equation for the given proportions is y = 0.33x.
Since the line is in the form of y = mx, it passes through th point (0, 0) and continues through the point (15, 5).
So, option A is correct.
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Drag each tile to the correct box. Arrange the steps in the expansion of the binomial (3x + 2y)³ in the correct sequence. 27x³ + (3x)³ + x 9x²2y + 3x2 × 3x × 4y² + 8y³ 2x1 (3x)²2y + 3(3-1) (3x) (2y)² + (2y)³ 21 27x³ +54x²y +36y² + 8y³ ↓
Answers
The solution of the algebraic expression (3x + 2y)³ is
[tex]\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]
What is algebraic expression?
Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.
Now, algebraic expressions are of different types. They are-
Monomial, Binomial and trinomial.
Algebraic expression with only one term is called monomial
Algebraic expression with two terms are called binomial
Algebraic expressions with three terms are called trinomial.
Algebraic expressions with more than three terms are called polynomial.
Based on degree, algebraic expression may be called as linear, quadratic, cubic and so on
Algebraic expression of degree one is called linear
Algebraic expression of degree two is called quadratic
Algebraic expression of degree one is called cubic
The given algebraic expression is (3x + 2y)³
Now,
[tex](3x +2y)^3\\(3x)^3 + 3 \times (3x)^2 \times (2y) + 3 \times 3x \times (2y)^2 + (2y)^3\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]
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2. A bond quote of 75.65 is equal to ___ in dollars
A. $765.50
B. $75.65
C. $756.50
D. $760.00
Answers
A bond quote of 75.65 is equal to $75.65 in dollars. The correct option is B.
What is a bond quote?A bond quote is the most recent price at which a bond traded, converted to a point scale and expressed as a percentage of par value. Par value is typically set at 100, or 100% of a bond's $1,000 face value. If a corporate bond is quoted at 99, for instance, it is currently trading at 99% of its face value. In this instance, each bond costs $990 to purchase.
The most recent price at which a bond traded is referred to as a bond quote.
Bond quotes are converted to a point scale and expressed as a percentage of par (face value). The standard par value is 100, which equals 100% of a bond's $1,000 face value. Bond quotes can include fractional values.
Therefore, based on the information given, the correct option is B.
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A 20 cm nail ,just fit inside cylindrical can.Three identical spherical balls need to fit entirely within the can.What is the maximum radius os each ball?
Answers
A radius is a part of a circle that doubles to form its diameter. The radius of each sphere is 3.34 cm.
A circle is a shape bounded by curved line known as circumference. some of its parts of a circle are; diameter, radius, arc, chord etc.
A radius is that part of the circle that is half of its diameter. This implies that;
radius = [tex]\frac{diameter}{2}[/tex]
Such that;
diameter = 2*radius
A sphere is an object that can be derived from the volume of a circle.
Given that the height of the cylindrical can is 20 cm, and three identical spherical balls would fit entirely within the can.
Then;
diameter of each spherical balls = [tex]\frac{20}{3}[/tex]
= 6.67 cm
Thus;
the radius of each of the spherical balls = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{6.67}{2}[/tex]
radius of each of the spherical balls = 3.335 cm
Therefore, the maximum radius of each ball is 3.34 cm.
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Emma has $140 cash to spend at a music store. How much can she spend on items if there is %7 sales tax?
Answers
Answer:
$130.84
Step-by-step explanation:
If a 7% sales tax is applied, the cost of the item (including tax) will be 107% of the original price.
To calculate how much Emma can spend if she has $140 cash to spend, divide $140 by 107%:
[tex]\implies \dfrac{140}{107\%}[/tex]
[tex]\implies \dfrac{140}{\frac{107}{100}}[/tex]
[tex]\implies 140 \times \dfrac{100}{107}[/tex]
[tex]\implies \dfrac{14000}{107}[/tex]
[tex]\implies 130.84[/tex]
Therefore, Emma can spend $130.84 on items if there is a 7% sales tax.
Please help I've done it but I want to check my answer!
There are several marbles of different colours in a bag in front of you. Your job is to select three marbles and record the colour of each marble you chose. In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles and 3 purple marbles. What are the chances of selecting one red marble, one yellow marble and a blue marble?
Assume that once each marble is chosen, it is not returned to the bag.
Answers
Answer:
the probability of selecting one red marble, one yellow marble, and a blue marble is 1/52. This can also be expressed as a percentage by dividing the probability by 1 and multiplying by 100%, which gives a probability of approximately 1.9%.
Step-by-step explanation:
2. The box and whisker plot below shows the starting salaries for 120 graduates of a small college.
a) What is the range of the starting salaries?
b) About 30 graduates make below what amount?
c) How many graduates have a salary above $33,000 ?
d) $25 of the graduates make above what amount?
Answers
The range of the starting salaries is 53,000
Given,
The box and whisker plot below shows the starting salaries
The number of graduates in a small college = 120
We have to find the range of the starting salaries;
Range of a data;
The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.
Here,
Lowest value = 19,000
Highest value = 72,000
Then,
Range of the set = 72,000 - 19,000 = 53,000
That is,
The range of the given data set is 53,000
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