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2 years ago

Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution?

Mathematics

2 answers:

BlackZzzverrR [31]2 years ago

8 0

Answer: B. (2,1)

Step-by-step explanation:

The given system of equation :

$y=2x-3...........................(1)\\\\y=-2x+5.............................(2)$

Adding equation (1) and (2), we get

$2y=-3+5\\\\\Rightarrow\ 2y=2\\\\\Rightarrow\ y=1$

Substitute the value of y in the first equation , we get

$1=2x-3\\\\\Rightarrow\ 2x=1+3\\\\\Rightarrow\ 2x=4\\\\\Rightarrow\ x=2$

Therefore, the solution to the given system of equations = (2,1)

Nataly [62]2 years ago

7 0

Answer:

B (2,1)

Step-by-step explanation:

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According to a report for veterinarians in the United States, 36.5 percent of households in the United States own dogs and 30.4

aleksandrvk [35]

Answer :E) Not enough information is given to determine the probability.

Step-by-step explanation:

Le A denotes the event that households in the United States own dogs .

and B denotes the event that households in the United States own cats.

As per given , we have

P(A)=36.5%= 0.365

P(B)=30.4% = 0.304

To find the probability that the selected household will own a dog or a cat, we apply the following formula :

P(A or B)=P(A)+P(B)+P(A and B)

But P(A and B) is not given to us.

i..e the probability that a house hold own both a cat and adg is not given to us.

Therefore, The correct option is (E) Not enough information is given to determine the probability.

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2 years ago

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:

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

4 0

2 years ago

Which expression would be easier to simplify if you used the associative property to change the grouping

olga nikolaevna [1]

Answer:

A it is so simple just try it

6 0

2 years ago

Read 2 more answers

A square is made up of an L-shaped region and three transformations of the region. If the perimeter of the square is 40 units, w

Mila [183]

Answer:

20 units

Step-by-step explanation:

This implies that the square can be divided into four equal L-shaped regions. These regions with respect to transformation forms a square.

Perimeter of the square is 40 units. Since a square has equal length of sides, thus each side of the square is 10 units.

Thus, each L-shape region has dimensions; 8 units, 5 units, 5 units and 2 units.

Perimeter of each L-shape region = the addition of the length of each side of the shape

Perimeter of each L-shape region = 8 + 5 + 5 + 2

= 20 units

3 0

2 years ago

In order for a constitutional amendment to the Florida constitution to pass 60% of the popular vote must support the amendment.

max2010maxim [7]

Answer:

$H_{0}: p \leq 0.6\\H_A: p > 0.6$

Step-by-step explanation:

We are given the following in the question:

Percentage of vote required for constitutional amendment = 60%

p = 60% = 0.6

Hypothesis:

More than sixty percent of the voters would support a new amendment about higher education.

We design the null and the alternate hypothesis

$H_{0}: p \leq 0.6\\H_A: p > 0.6$

Interpretation:

The null hypothesis states that less than or equal to 60% of the voter support the new amendment and the alternative hypothesis states that gretaer than 60% supports the amendment about higher education.

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2 years ago