Z = -3a + 1 Solve for a Thanks

Cadie is going to toss three coins simultaneously. What is the probability that exactly two of the coins will land on heads?

Contact [7]

For each coin, there are 2 outcomes, heads (H) or tails (T), so for the 3 coins, the number of outcomes are:

2 x 2 x 2 = 8 outcomes:

HHH / HHT / HTH / THH / TTT / TTH / THT / HTT

Out of all these outcomes, there are 3 ways, we get exactly 2 Heads:

HHT / HTH / THH

So, the probability of exactly 2 coins landing on Heads is 3/8, or 0.375

4 0

2 years ago

All the info is in the pictures

Hunter-Best [27]

Bearing in mind that an absolute value expression is in effect a piece-wise function with two cases, thus

$\bf |-n|=
\begin{cases}
+(-n)\\
-(-n)
\end{cases}\implies 
\begin{cases}
-n\\
n
\end{cases}
\\\\\\
n|-n|=2n\implies 
\begin{cases}
n-n=2n\implies 0=2n\implies &0=n\\
n+n=2n\implies 2n=2n\impliedby &inconsistent
\end{cases}$

6 0

3 years ago

Am i right? i just want to make sure

marysya [2.9K]

Answer:

yes

Step-by-step explanation:

can i have brainliest

4 0

2 years ago

If triangle CAT is similar to triangle DOG, which of the following statements is incorrect?

jeyben [28]

Answer:

1. triangle TCA ~ triangle GOD

4. If TC/GD=3/2, then m<T/m<G=3/2.

Step-by-step explanation:

The statements of the question are

1. triangle TCA ~ triangle GOD

2. AT: OG= AC:OD

3. If TC/GD=3/2, then AC/OD=3/2.

4. If TC/GD=3/2, then m<T/m<G=3/2.

5. If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3.

6. If AC is twice as long as AT, then OD is twice as long as OG

Verify each statement

1) triangle TCA ~ triangle GOD

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

triangle CAT ~ triangle DOG -----> is given

so

Reorder

Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement

triangle TCA ~ triangle GDO

therefore

The statement is not correct

2). AT: OG= AC:OD

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

triangle CAT ~ triangle DOG -----> is given

so

Applying proportion

$\frac{AT}{OG}=\frac{AC}{OD}=\frac{TC}{GD}$

The statement is true

3). If TC/GD=3/2, then AC/OD=3/2.

we have that

$\frac{AT}{OG}=\frac{AC}{OD}=\frac{TC}{GD}$ ---> see part 2)

so

$\frac{TC}{GD}=\frac{AC}{OD}$

therefore

The statement is true

4). If TC/GD=3/2, then m<T/m<G=3/2

Remember that

In two similar triangles, corresponding angles are congruent

so

$m\angle T=m\angle G$

$m\angle T/m\angle G=1$

therefore

The statement is false

5). If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3

we know that

If the scale factor of triangle CAT to triangle DOG is a/b. then the scale factor of triangle DOG to triangle CAT is b/a

The scale factor will be the reciprocal

therefore

The statement is true

6). If AC is twice as long as AT, then OD is twice as long as OG

we know that

$\frac{AT}{OG}=\frac{AC}{OD}$

Reorder

$\frac{AT}{AC}=\frac{OG}{OD}$

If AC is twice as long as AT ----> AC=2AT

If OD is twice as long as OG ----> OD=2OG

substitute

$\frac{AT}{2AT}=\frac{OG}{2OG}$

simplify

$\frac{1}{2}=\frac{1}{2}$ ----> is true

therefore

The statement is true

5 0

2 years ago

Extra Example 3: Hazel has $23.28 in her purse. She has $5.60 more than Nixon.

sveticcg [70]

Answer:

Yolanda is correct.

Step-by-step explanation:

If Hazel has $23.28 and $5.60 more than Nixon, then Nixon will have $17.68 because 23.28-5.60 is 17.68.

The only way Paul would be right is if Nixon has $5.60 more than Hazel because 23.28+5.60 is 28.88.

4 0

2 years ago