James was painting the fence around his farm. He already painted 35% of the fence which was equal to 1,050 feet.

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the proba

Fittoniya [83]

Question:

A = {2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9?

A. 0.15

B. 0.20

C. 0.25

D. 0.30

E. 0.33

Answer:

Option B: 0.20 is the probability of the sum of the two integers.

Explanation:

The sample space for selecting 2 numbers is given by

$4\times 5 = 20$

We need to determine the probability that the sum of two integers will be equal to 9.

Hence, we need to add the two integers from the sets A and B such that their sum will be equal to 9.

Hence, the sets are $(2,7),(3,6),(4,5),(5,4)$

Thus, the total number of sets whose sum is equal to 9 = 4

The probability that the sum of the two integers will equal 9 is given by

$P=\frac{4}{20}$

$P=\frac{1}{5}$

$P=0.20$

Thus, the probability that the sum of the two integers will equal 9 is 0.20

Hence, Option B is the correct answer.

4 0

2 years ago

Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has

Whitepunk [10]

Answer:

Please find attached the required plot accomplished with an online tool

Part A:

1/4

Part B:

P''(-1, 0), Q''(0, -1), and R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent

Step-by-step explanation:

Part A:

Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)

Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)

The dimensions of the sides of the triangle are given by the relation;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment

For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);

By substitution into the length equation, we get;

The length of segment PQ = 4·√2

The length of segment PR = 4·√10

The length of segment RQ = 8

The length of segment P'Q' = √2

The length of segment P'R' = √10

The length of segment R'Q' = 2

Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4

Part B:

Reflection of (x, y) across the y-axis gives;

(x, y) image after reflection across the y-axis = (-x, y)

The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;

P'(1, 0) image after reflection across the y-axis = P''(-1, 0)

Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)

R'(-2, -1) image after reflection across the y-axis = R''(2, -1)

Part C:

Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.

6 0

2 years ago

PLEASE HELP ASAP WILL GIVE BRAINLIEST!!!!

max2010maxim [7]

Answer:

Step-by-step explanation:

y intercept is -6

the slope is already in it's fraction form but if you want it back to whole number it's y=1.33x-6

the slope is positive

Some plots you can put are (6, 2) and (12, 10)

Just start at (0, -6) and counts 4 up and 3 right

4 0

2 years ago

If f(x) = g(x+1) and g(x) = x^2, find the value of f(3).

Elena-2011 [213]

$\bf \begin{cases} f(x)=&g(x+1)\\ f(3)=&g(3+1)\\ &g(4)\\[-0.5em] \hrulefill& \hrulefill\\ g(x)=&x^2\\ g(4)=&4^2\\ &16 \end{cases}\qquad \qquad f(3)\implies g(4)\implies 16$

8 0

2 years ago

Which is not an equation of the line going through (3,-6) and (1, 2)?

Olegator [25]

Answer:

○ $\displaystyle y - 1 = -4(x - 2)$

Step-by-step explanation:

When you plug these coordinates into this equation, they will be confirmed as <em>false</em>.

I am joyous to assist you anytime.

3 0

2 years ago