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4 years ago

If angle B=35 degrees , then angle B’=_____

Mathematics

1 answer:

Rufina [12.5K]4 years ago

8 0

Answer:

35 degrees

Step-by-step explanation:

because the size and shape doesn't change, the only that changes is where it is located in the graph.

Hope it helps!

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A boat’s sail is a right triangle. The length of one side of the sail is 7 feet more than the other side. The hypotenuse is 13 f

Svetach [21]

Answer: the other two sides are 5 feet and 12 feet

Step-by-step explanation:

Length of one side be x , that means the other side is x + 7

by Pythagoras theorem:

$x^{2}$ + $(x+7)^{2}$ = $13^{2}$

expanding , we have:

$x^{2}$ + $x^{2}$ + 14x + 49 = 169

$2x^{2}$ + 14x + 49 - 169 = 0

$2x^{2}$ + 14x - 120 = 0

divide through by 2 , we have

$x^{2}$ + 7x - 60 = 0

By factorizing , we have

(x - 5)(x+12) = 0

Therefore:

x = 5 or x = -12

Since , the side can not be negative , so

x = 5

That means the other side will be 5+ 7 = 12

8 0

4 years ago

Which number is equivalent to the fraction 18/5? A.5/18 B.3 C.3 3/5 D.2 8/5

alisha [4.7K]

Answer:

C 3 3/5

Step-by-step explanation:

18/5 = 3.6

3 3/5 = 3.6

7 0

3 years ago

Read 2 more answers

Two professors are applying for grants. Professor Jane has a probability of 0.61 of being funded. Professor Joe has probability

Anna11 [10]

Answer:

a. 0.1647;
b. 0.7153;
c. 0.4453.

Step-by-step explanation:

By definition, if two event $A$ and $B$ are independent, then

$P(A\cap B) = P(A) \cdot P(B)$ . ( $P(A\cap B)$ is the probability that the outcome of both event $A$ and event $B$ are true.)

Since the outcome of these two events are independent,

$\begin{aligned}P(\texttt{Jane} \cap \texttt{Joe}) &= P(\texttt{Jane}) \cdot P(\texttt{Joe})\\ &= 0.61 \times 0.27 \\&= 0.1647\end{aligned}$ .

The logic not operator $\lnot$ or the prime superscript $^{\prime}$ denotes that an event does not happen.

$P(\texttt{Jane}^{\prime}) = 1 - P(\texttt{Jane}) = 1- 0.61 = 0.39$ .

$P(\texttt{Joe}^{\prime}) = 1 - P(\texttt{Joe}) = 1- 0.27 = 0.73$ .

Since the two events $\texttt{Jane}$ and $\texttt{Joe}$ , $\texttt{Jane}^{\prime}$ and $\texttt{Joe}^{\prime}$ are also independent. Probability that neither professor got funded:

$P(\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime}) = P(\texttt{Jane}^{\prime}) \cdot P(\texttt{Joe}^{\prime}) = 0.39 \times 0.73 = 0.2847$ .

Probability that at least one professor got funded- in other words, it is not true that neither professor got funded:

$P((\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime})^{\prime}) = 1- P(\texttt{Jane}^{\prime} \cap \texttt{Joe}^{\prime}) = 0.7153$ .

Similarly, since the two events $\texttt{Jane}$ and $\texttt{Joe}$ , $\texttt{Jane}$ and $\texttt{Joe}^{\prime}$ are also independent. Probability that Jane but not Joe got funded:

$P(\texttt{Jane} \cap (\texttt{Joe}^{\prime})) = P(\texttt{Jane}) \cdot P(\texttt{Joe}^{\prime}) = 0.61 \times 0.73 = 0.4453$ .