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1 day ago

How do you write 37,015.08 in expanded form

Mathematics

1 answer:

AnnZ [3.8K]1 day ago

3 0

Answer:

Thirty-seven thousand fifteen point zero eight

Step-by-step explanation:

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Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC

Svet_ta [4321]

We are given the triangle

△ABC, with m∠A=60° and m∠C=45°, and AB=8.

To start, we will calculate all angles and sides.

Finding angle B:

The total of all angles in a triangle equals 180.

m∠A + m∠B + m∠C = 180.

Substituting the known values,

60° + m∠B + 45° = 180.

This gives us m∠B = 75°.

Calculating BC:

Using the law of sines,

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

We can substitute in the values.

$\frac{8}{sin(45)}=\frac{BC}{sin(60)}$

$BC=\frac{8}{sin(45)} \times sin(60)$

$BC=9.798$

Finding AC:

$\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

Now we'll input the values.

$\frac{8}{sin(45)}=\frac{AC}{sin(75)}$

$AC=\frac{8}{sin(45)} \times sin(75)$

$AC=10.928$

Calculating Perimeter:

$p=AB+BC+AC$

We substitute values here as well.

$p=10.928+8+9.798$

$p=28.726$

Calculating Area:

Using the area formula,

$A=\frac{1}{2}AB \times AC \times sin(A)$

we can then insert values.

$A=\frac{1}{2}8 \times 10.928 \times sin(60)$

$A=37.85570$ ...............Answer

6 0

12 days ago

Read 2 more answers

Imagine that after washing 5 distinct pairs of socks, you discover that two socks are missing! of course, you would like to have

Zina [3914]

Part A:

Considering the best possible outcome

The ideal case occurs if the two missing socks are from the same pair.
Consequently, there are 4 complete pairs remaining.

To choose 2 from the total of 10 socks (5 pairs), the number of combinations is given by 10C2 = 45.

Choosing 2 that are from the same pair means selecting one from 5 pairs, so the count is 5C1 = 5.

Thus, the probability for this best case is 5 / 45 = 1 / 9.

Part B:

Considering the worst-case outcome

This scenario occurs when the two missing socks are from different pairs.
As a result, we have 3 complete pairs left.

The total ways to select 2 socks from 10, again, is 10C2 = 45.

To select 2 that do not belong to the same pair, we calculate as follows: 10C2 - 5C1 = 45 - 5 = 40.

Therefore, the probability for the worst-case scenario is 40 / 45 = 8 / 9.

5 0

2 days ago

A laundry basket contains 18 blue socks and 24 black socks. What is the probability of randomly picking 2 black socks, without r

Svet_ta [4321]

<span>P(black socks): 24/42 or 12/21
P(black socks without replacement): 23/41. Consequently, the chance of randomly selecting 2 black socks, without replacement, from the basket is 12/21×23/41=276/861, equivalent to 32%. Hope this helps!</span>

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2 days ago

Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more than 590 calories riding her bike at the same

Svet_ta [4321]

Response:

354

Detailed explanation:

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4 days ago

the number of years that brad has been on the soccer team is 2 less than 5 times the number of years that scott has in total the

PIT_PIT [3919]

Let the number of years Brad has been on the soccer team be represented by x, and let y represent the number of years Scott has been on the same team.

From the information given, we formulate the equations:
5y - 2 = x -----(1)

x + y = 10 -----(2)

Now, substituting equation (1) into equation (2):
5y - 2 + y = 10
6y - 2 = 10
6y = 12
y = 2
Next, substituting this value back to find x:
x = 5×2 - 2
x = 8

So, Brad has spent a total of 8 years in the team.

8 0

6 days ago