Determine which of the four postulates, if any, can be used to prove that the triangles are congruent.
50 points

Answer:

The expected number of people you will have to ask before you find someone with jumper cables is 6.25.

Step-by-step explanation:

        [tex]p_{X}(k)=(1-p)^{k-1}p;\ k={1, 2, 3...}[/tex]

        [tex]p_{X}(k)=(1-p)^{k}p;\ k={0, 1, 2, 3...}[/tex]

In this case the first scenario follows.

X = number of people you will have to ask before you find someone with jumper cables.

p = 0.16

Compute the expected number of people you will have to ask before you find someone with jumper cables as follows:

[tex]E(X)=\frac{1}{p}\\\\=\frac{1}{0.16}\\\\=6.25[/tex]

Thus, the expected number of people you will have to ask before you find someone with jumper cables is 6.25.

Answer:

40+2+0.1

Step-by-step explanation:

The ratio of the distance Jamal ran to the distance Lonnie ran is 4:1.

Note that 1 yard = 3 feet

Since Jamal ran a distance of 360 feet, this will be converted to yard and this will be: = 360/3 = 120 yards

Lonnie ran a distance of 30 yards.

Then the ratio of the distance that Jamal ran to the distance Lonnie ran all be: = 120/30 = 4/1 = 4:1

The ratio of the distance is 4:1

Read related link on:

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2 hours Step-by-step explanation:

Answer: 2 hours.

Step-by-step explanation:

2/5 hour = one load of laundry

2/5 x 5 = 10/5 = 2 hours.

It will take Shonda 2 hours to dry 5 loads of laundry.

Hope this helps!

Answer:

A) dS/dt = 2 - S/(100 + t) ; S(0) = 50

B) S(t) = (100 + t) - 5000/(100 + t)

C) 35%

Step-by-step explanation:

A) Let;

t = time in minutes

S = amount of syrup

dS/dt = rate at which syrup is flowing through tank

We are told that initially, the tank contains a mixture of 450 liters of cola and 50 liters of cherry syrup.

Thus,

At t = 0

Amount of cola = 450 litres

Amount of syrup = 50 litres

Total mixture = 450 + 50 = 500 litres

We are told that a well mixed solution of cherry cola is withdrawn at the rate of 5 liters per minute.

Thus, amount of liquid in the tank at a time "t" is; 500 + 5t

We are told that cherry syrup is added at the rate of 2 liters per minute.

Thus, rate at which syrup is flowing through tank is given as;

dS/dt = 2 - 5[S/(500 + 5t)]

Factorizing out, we have;

dS/dt = 2 - 5[S/5(100 + t)]

5 will cancel out to give;

dS/dt = 2 - S/(100 + t)

Since we have 50 liters of cherry syrup initially, the initial value problem is;

dS/dt = 2 - S/(100 + t) ; S(0) = 50

B) We have our initial value problem as;

dS/dt = 2 - S/(100 + t)

Rearranging, we have;

dS/dt + S/(100 + t) = 2

Multiplying through by 100 + t gives;

(dS/dt)•(100 + t) + S = 2(100 + t)

Integrating each term with respect to t gives;

(100 + t)S = (100 + t)² + c

Divide both sides by (100 + t) to get;

S = (100 + t) + c/(100 + t)

At t = 0;

S(0) = (100 + 0) + c/(100 + 0)

S(0) = 100 + c/100

Recall earlier in our initial value problem where we stated that S(0) = 50.

Thus;

100 + c/100 = 50

Subtract 100 from both sides to givw;

c/100 = 50 - 100

c/100 = -50

c = -50 × 100

c = -5000

Thus;

S(t) = (100 + t) - 5000/(100 + t)

C) The capacity of the tank is given as 1000 liters.

Earlier, we saw that amount of liquid in the tank at a time "t" is; 500 + 5t

Thus;

500 + 5t = 1000

5t = 1000 - 500

5t = 500

t = 500/5

t = 100 minutes

We want to find What percentage of the mixture is cherry syrup when the tank is full.

Thus we will plug in t = 100 minutes into S(t) = (100 + t) - 5000/(100 + t)

Thus;

S(100) = (100 + 100) - 5000/(100 + 100)

S(100) = 200 - 25

S(100) = 175 litres

We saw earlier that total mixture initially was 500 litres.

Thus, percentage of the mixture that is cherry syrup when the tank is full is;

175/500 × 100% = 35%

Answer:

Pretie sure answer is 0

Step-by-step explanation:

first you take the 1 and subtract it from -3

which is -2 then add the other 2 to the -2 which is 0

then you devide 5 with 5 and 5 with zero which leaves you with zero and 0=x

Answer:

125

Step-by-step explanation:

divide the Figure into 3 parts

1 st = 5 X 10 =50

2nd = 5×10 =50

3rd = 5×5 = 25

total = 50+50 + 25 = 125

Answer:

Depth of water is increasing at 0.143 ft/min.

Step-by-step explanation:

Answer:

the awnser is 8 as is it it the awnser

Step-by-step explanation:

It's C.

8x8 = 64,

64/8 = 8

Answer:

A

Step-by-step explanation:

9 items at $50 each would be 9 × $50 = $450, which is more money than he has.

Step-by-step explanation:

In an hour, there are 60 minutes.

100km * (12/60) = 20km.

Hence the train runs 20km in 12 minutes.

Answer:

d

Step-by-step explanation:

Answer:

the answer is D i think.

Answer:112

Step-by-step explanation:multiply and divide for your answer

Answer:

A, C, E

Step-by-step explanation:

I don't really know how to explain it but you can kinda substitute 9 for the variable to confirm if you want.

Answer:

8.75

Step-by-step explanation:

7/4 = 1.75 and ?/5 (5x1.75) = 8.75

Answer:

68°

Step-by-step explanation:

PRQ = SRQ gives:

3x-8 = 2x+6

x = 6+8 = 14

So PRQ = SRQ = 34

and

PRS = PRQ+SRQ = 68

Answer:

3) 146 degrees

4) 471 degrees

5) x = 100 and 3x = 300

Step-by-step explanation:

all three are polygons whose sum of all interior angles can be found by using the formula (n - 2)*180 where 'n' refers to the number of sides

In #3 and 5 there are 5 sides, so (5 - 2)*180 = 3(180) giving a total of 540 degrees. Add all known angles and deduct from 540.

#4 has 7 sides, so (7 - 2)*180 = 1260 degrees. Add all known angles and deduct sum from 1260.

#5 Add all integers plus 'x' + '2x' to get 240 + 3x = 540

Answer:

exact form:  -5/4

Decimal Form: -1.25

Step-by-step explanation:

The amount of money after five years will be $783.87. Then the correct option is B.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

[tex]\rm A = P \left (1 + \dfrac{r}{n} \right ) ^{nt}[/tex]

Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.

Samantha put $660 into a record that pays 3.5% interest accumulated every year. Samantha put aside no extra installments or withdrawals. And for yearly, the value of n will be one. Then the equation is given as,

[tex]\rm A = 660\times (1 + 0.035)^t[/tex]

The total amount of interest paid by this investment at the end of five years will be given as,

A = 660 x (1.035)⁵

A = $660 x 1.1876

A = $783.87

The amount of money after five years will be $783.87. Then the correct option is B.

More about the compound interest link is given below.

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Answer:

Step-by-step explanation:

Total number of integers from 300 through 780, inclusive:

Number of integers with at least one of digit 1:

The probability is:

Answer:

92°

Step-by-step explanation:

First, find the value of x.

3x + 23 = 4x (corresponding angles are congruent)

Subtract 3x from each side

23 = 4x - 3x

23 = x

x = 23

Angle ABC = 4x

Plug in the value of x

Angle ABC = 4(23)

Angle ABC = 92°

Answer:

Number of students = 441 Students

Step-by-step explanation:

Given:

Percent of women = 40%

Percent of women = 35.5%

Total number of people = 1,800

Find:

Number of students

Computation:

Percent of student = 100% - 35.5% - 40%

Percent of student = 24.5%

Number of students = 1,800 x Percent of student

Number of students = 1,800 x 24.5%

Number of students = 441 Students

Answer:

x=3, y=13. (3, 13).

Step-by-step explanation:

7x-8=5x-2

7x-5x-8=-2

2x-8=-2

2x=-2+8

2x=6

x=6/2=3

y=5(3)-2=15-2=13

Answer:

given y=7x-8 i

y=5x-2 ii

Step-by-step explanation:

equating equation i and ii which is i=ii

7x-8=5x-2

7x-5x= -2+8

2x=6

x=6÷2

x=3

now

putting the value of xbin equation i

y=7x-8

y=7×3-8

y=21-8

y=13

hence the value of x and y is 3 and 13 respectively