Write the unit rate for the situation.

read 80 pages in 2 hours

20 pages/h

40 pages/h

8 pages/h

160 pages/h

Answer:

Clean price is $3,977.22

Dirty price = $4110.99

Step-by-step explanation:

We proceed as follows;

Semiannual coupon payments = $3000* 12%/2 = 6% * 3,000 = 6/100 * 3,000 = $180

Coupons are paid on 1st June and 1st December every year(semi-annually means twice a year, every 6 months)

No. of payments remaining = 11 (1 payment in 2020 on 1st December,2020 and 2 in each of the following 5 years)

Semiannual Yield = 6%/2 =3%

The clean price of the bond is given by

P = 180/1.03+ 180/1.03^2+.....+180/1.03^11+ 3200/1.03^11

=180/0.03*(1-1/1.03^11)+3200/1.03^11

=$3977.22

Dirty price = clean price +accrued interest

Accrued Interest = Interest from 1st June , 2020 to 1st December,2020

= no of days from 1st June to 15th October/no of days from 1st June to 1st December * $180

= 136/183*$180

=$133.77

So, Dirty price = $3977.22+$133.22 = $4110.99

Answer:

6.1 square units

Step-by-step explanation:

Since the triangle was translated from one position to another position, the dimensions of the triangle have not changed. The pre-image and image are congruent.

area = base * height/2

The two sides forming a right angle can be used as the base and the height in the area formula.

BC = base = 2

AB = A'B' = height = 6.1

area = 2 * 6.1/2

area = 6.1 square units

Answer:

Similarity:

In Both cosine and sine graphs, a positive and negative number vertically flips the graph and tells whether the graph starts at maximum (positive) or minimum (negative).

Difference:

The difference between the sine and the cosine graph is the point where they start.

The graph of positive cosine starts at the maximum while that of the negative cosine starts at the minimum.

The graph of a positive sine starts at the middle, goes up and then down while that of the negative sine starts at the middle goes down and then up.

Answer:

picture is attached

Step-by-step explanation:

there are many options but this is one

Answer:

solution,

<3+<4=180°( linear pair)----> equation (i)

<4+<5=180°( linear pair)------>equation (ii)

From equation (i) and (ii)

<3+<4=<4+<5

<3=<5 (vertically opposite angles)

hope this helps...

Good luck on your assignment

Hey there! :)

Answer:

arc AB = 2.5π in (in terms of pi) or ≈7.85 in. (pi = 3.14)

Step-by-step explanation:

Begin by finding the circumference of the circle. Use the formula:

C = 2rπ

C = 2(9)π

C = 18π.

Since ∠AQB equals 50°, set up a ratio to find the length of arc AB:

[tex]\frac{50}{360} = \frac{x}{18\pi }[/tex]

Cross multiply:

50 · 18π = 360x

900π = 360x

Divide both sides by 360:

x = 2.5π in, or ≈7.85 in.

I think the answer is D.

Answer:

Step-by-step explanation:

At maximum height, the velocity of the flare will be zero.

If the flare height above the ground is modeled by the equation

h = -16t²+64t+4

Velocity = dh/dt = 0

-32t + 64 = 0

-32t = -64

t = -64/-32

t = 2secs

This shows that the flare reaches its maximum height after 2secs.

To get the maximum height of the flare, we will substitute t = 2s into the equation h = -16t²+64t+4

h = -16(2)² + 64(2)+4

h = -64+128+4

h = 64+4

h = 68 feet

The maximum height of the flare is 64 feet.

Answer:

9/4

Step-by-step explanation:

Using the slope formula

m = (y2-y1)/(x2-x1)

    = (1--8)/( 4-0)

    = (1+8)/4

    = 9/4

Answer:

$2388.95

Step-by-step explanation:

The worth of a compound deposit after a period of n years is calculated using the formula:

[tex]A(n)=P(1+\frac{r}{k})^{nk}[/tex]

[tex]A(2)=2250(1+\frac{0.03}{12})^{12 \times 2}\\\\=2250(1+0.0025)^{24}\\=2250(1.0025)^{24}\\=\$2388.95[/tex]

At maturity, the deposit will be worth $2388.95.

Answer:

5 and 29

Step-by-step explanation:

If k= -2, l = 3, m = 4.

Then to solve

k + l + m and K^2 + l^2 + m^2 , we have to substitute the value of k, l and m with the respective values.

So for k + l + m :

k + l + m = -2 + 3 + 4 = -2 + 7 = 5

And for K^2 + l^2 + m^2:

K^2 + l^2 + m^2 = -2^2 + 3^2 + 4^2 = 4 + 9 + 16 = 29

Hope this helps

Answer:

yes, if AB ≅ DE

Step-by-step explanation:

Triangles are said to be congruent if they have the same sides and the same angles.

The following measures are used to determine if triangles are congruent:

1) Angle-side-angle: If two angles and a side of a triangle is equal to two angles and corresponding side of another triangle, then they are congruent.

2) Side-side-side: If all three sides of a triangle is equal to three sides of another triangle, then the two triangles are congruent.

3) Side angle side: If two sides and an included angle of a triangle is equal to the two sides and corresponding angle of another triangle, then they are congruent.

4) Hypotenuse - leg: If the hypotenuse and one leg of a triangle is equal to the hypotenuse and leg of another triangle then they are congruent.

From the triangles  DEF and ABC, already, they already have one equal triangle that is ∠F = ∠B and an equal side i.e DF = AC.

To satisfy congruence, two sides and an angle have to be equal, therefore if AB = DE then the two triangles would be congruent

Answer:

D). no, because the hypotenuses must have different lengths

Step-by-step explanation:

I just did the assignment on Edge and it's 100% correct.

Hope this helps!! Also heart and rate if you found this answer helpful!!  :)

Answer:

The probability that he doesn’t win is 6/(n + 6)

Step-by-step explanation:

Mathematically, the probability that an event occur is 1 minus the probability that the event doe not occur.

Thus, what we are saying here is that the sum of the probabilities that Paul wins the raffle draw and he doesn’t win the raffle draw is 1

This can be mathematically expressed as;

probability that he doesn’t win = 1 - probability that he wins

Thus we have;

1- n/(n+ 6)

= [(n+ 6) -(n)]/(n+6) = 6/n+ 6

We cannot simplify this further because 3 and 5 have no factors in common, other than 1. So we just leave it as is.

Answer:

Hey there!

Your answer would be 1/3 (12) hours.

Since it can fill 1/12 of the tank in 1/3 hour, then in 12 1/3 hr's, the tank would be filled.

Hope this helps :)

Answer:

1/3 * 12

4 hours

Step-by-step explanation:

We can use ratios to solve

1/12 tank          1 tank

---------------- = ----------------

1/3 hour          x hours

Using cross products

1/12 x = 1/3 *1

Multiply each side by 12

12 * 1/12 x = 1/3 * 12

x = 4

4 hours

Answer:

y = 3/2x + 3.

Step-by-step explanation:

With these two points, we can find the equation of line L.

y = mx + b

Slope: (5 --1) / (4 - 0) = 5 + 1 / 4 = 6 // 4 = 3/2

Intercept: [stated by the first pair of coordinates] (0, -1)

y = 3/2x - 1

Since the line is parallel to L, the slope is the same as line L.

y = 3/2x + b

The line passes through (-2, 0), so we can substitute the points into the equation and solve for b.

0 = 3/2 * -2 + b

b - 3 = 0

b = 3

So, the equation of the line which is parallel to L and passes through the point (-2, 0), is y = 3/2x + 3.

Hope this helps!

Answer:

by game 3(at 1:00 p.m.)

temperature increases to 5 degrees at 1:00 p.m

Answer:

-$0.67

Step-by-step explanation:

If you buy one ticket, the possible outcomes are:

100% chance of spending $1 (buying the ticket)

1 in 5,000 chance of winning $500

3 in 5,000 chance of winning $300

5 in 5,000 chance of winning $30

20 in 5,000 chance of winning $5.

The expected value of the raffle is determined by:

[tex]E(X)=-1+\frac{1}{5,000}*500+\frac{3}{5,000}*300+\frac{5}{5,000}*30+\frac{20}{5,000}*5\\E(X)=-\$0.67[/tex]

The expected value of this raffle if you buy 1 ticket is -$0.67.

Answer:

C

Step-by-step explanation:

A = [tex]\pi[/tex]r^2 h/3

A= 235.62

B = [tex]\pi[/tex]r^2 h

B = 235.62

They are equal

Answer:

[tex]\mathrm{D.} \: (\frac{5}{4} )^{\frac{7}{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{(\frac{5}{4})^7 }[/tex]

Apply rule : [tex]\sqrt{a} =a^{\frac{1}{2} }[/tex]

[tex]((\frac{5}{4})^7 )^{\frac{1}{2} }[/tex]

Apply rule : [tex](a^b)^c=a^{bc}[/tex]

[tex](\frac{5}{4} )^{7 \times \frac{1}{2} }[/tex]

[tex](\frac{5}{4} )^{\frac{7}{2}[/tex]

Answer:

(4x+1)(x²-2)

Step-by-step explanation:

one way to determine the factors of 4x^3 + x^2 - 8x - 2 by grouping:

x²(4x+1)-2(4x+1)

(4x+1)(x²-2)

Answer:

(x^2-2)(4x+1)

Step-by-step explanation:

4x^3 + x^2 - 8x - 2

Group:

(4x^3 + x^2)+( - 8x - 2)

Factor out as much as possible: (The GCF)

x^2(4x+1)-2(4x+1)

Regroup:

(x^2-2)(4x+1)

Answer:

3^x + 12x -4

Step-by-step explanation:

f(x) = 3^x + 10x

g(x) = 2x - 4,

(f + g)(x) = 3^x + 10x +  2x - 4

Combine like terms

             = 3^x + 12x -4

Answer:

(f + g)(x)= 3^x +12x -4

Step-by-step explanation:

To find (f+g)(x), we must add f(x) and g(x).

(f + g)(x)= f(x) + g(x)

We know that f(x)= 3^x + 10x and g(x)= 2x-4

Therefore, we can substitute these into the equation.

(f + g)(x)= (3^x+10x) + (2x-4)

Combine like terms. Add all the terms with an x.

(f + g)(x)= 3^x + (10x+2x) -4

(f + g)(x)= 3^x +12x -4

(f + g)(x) is 3^x +12x -4

Answer:

1) x = 71°, 2) x = 27°, 3) x= 32°

Step-by-step explanation:

1) Rectangle ABCD.

∠D = 90°

From ΔABE.

∠EAB +∠ABE + ∠BEA = 180°

45 + 90 +∠BEA = 180

∠BEA = 45

∠BEA + ∠AED +∠DEC = 180 °, because ∠BEC is a straight angle

45 + x + 64 = 180

x = 71°

2) Δ XYZ  is equilateral, all angles = 60°.

∠YZX = 60°.

∠YZW = 180°, because it is a straight angle.

∠YZX + ∠XZW= 180

60 +  ∠XZW= 180

∠XZW = 120.

From ΔXZW

∠ZXW + ∠XWZ + WZX = 180

x + 33 + 120 = 180

x = 27°

3) In ΔPQR,

PQ =  PR, so ∠PQR = ∠PRQ = 69°

∠PRQ + ∠PRS = 180, because ∠QRS = 180° as straight angle.

∠PRQ + ∠PRS = 180

69 + ∠PRS = 180

∠PRS  = 111°.

From ΔPRS

∠PRS  + ∠RSP + ∠SPR = 180

111 + 37 + ∠SPR = 180

111 + 37 + x= 180

x = 32

Answer:

  2x^2 -x +1 = 0

Step-by-step explanation:

For roots α and β, the original equation can be factored as ...

  f(x) = 2(x -α)(x -β)

If we add 1 to each of those roots, the factors become ...

  g(x) = 2(x -(α+1))(x -(β+1))

This can be rearranged to be ...

  g(x) = 2((x -1) -α)((x -1) -β)

That is, we can get the desired equation by replacing x with x-1, effectively shifting the function right one unit.

  2(x -1)² +3(x -1) +2 = 0

  2x^2 -x +1 = 0

Answer:

0.08

Step-by-step explanation:

The probability that the bus is late on any day is 0.2

The probability that it rains tomorrow is 0.4

The probability that it will rain tomorrow and the bus is late is the product of both individuals probabilities.

Therefore:

P(late & rains) = 0.2 * 0.4 = 0.08

Answer:

The probability that it rains and the bus is late is 1/7

Step-by-step explanation:

Practically, we can apply the Bayes’ theorem to solve this.

Mathematically, we use the Bayes’ problem as follows;

P( rain| late) = P(rain ^ late)/P(late) = P( late|rain) • P(rain)/[P(late|rain)P(rain) + P(not late|no rain)P(no rain)]

Where P(no rain) = 1-P(rain) = 1-0.4 = 0.6

P(on time) = 1-P(late) = 1-0.2 = 0.8

Kindly recall that P of raining = 0.4 and the probability that the bus is late is 0.2

Substituting these values into the Bayes’ equation above, we have;

P( rain| late) = (0.2)(0.4)/(0.2)(0.4) + (0.8)(0.6)

= 0.08/(0.08 + 0.48) = 0.08/0.56 = 1/7

Answer:

3x= 2x+18

3x-2×=2×-2×+18

×=18

Answer:

18

Step-by-step explanation:

3x = 2x + 18

3x - 2x = 18

x = 18

Answer:

T1=0

T2=2

T3=6

T4=12

T50=2450

59 is not a term in the sequence

Step-by-step explanation:

Tn=n(n-1)

182=n2 - n

0=n2 - n - 182

0=n2-14n+13n-182

0=n(n-14)+13(n-14)

0=(n-14) (n+13)

Since n cannot be negative n is not equal to -13

Therefore,

n=14

Answer:

The correct answer is A. [tex](-11, -9)[/tex].

Step-by-step explanation:

Given that the point is (8,6)

Let this point be A(8,6).

The composition is T3,30 RO,-180º

First translate the point by 3,3.

Let this point becomes A'.

A' is formed by translation of point A by 3,3

i.e.

x coordinate of A' = x coordinate of A + 3 and

y coordinate of A' = y coordinate of A + 3

So, A' (8+3, 6+3)

So, A'(11,9)

Now, a rotation of -180º is applied to point A'.

Let it becomes A''.

By a rotation of -180º,  the coordinate gets changed by 2 quadrants.

A is in 1st quadrant because both x and y coordinates are positive.

A'' will be in 3rd quadrant where both x and y coordinates are negative.

Please refer to the attached image for the graphical representation of A, A' and A''.

So, the answer will be option A. [tex](-11, -9)[/tex].