EF is located at E (x,y) and F (7,-10) and was rotated around the origin. EF became E’F’ with coordinates E’ (4,5) and For (10,7

number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The n

Svet_ta [12734]

Answer:

The union of sets A and B is represented as A U B = {1,2,3,4,5,6,8}

Detailed explanation:

We begin by defining our sets.

Let ¢ signify the universal set (which includes every element in the given sets)

¢ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A= {2, 4, 6, 8}

B= {1,2,3,4,5,6}

Consequently: A U B (the union of A and B):

A U B = {1, 2, 3, 4, 5, 6, 8}

6 0

2 months ago

Beth drives 200 miles in 4 hours. She drives the first 18 miles at an average speed of 36 mph. Work out her average speed for th

Zina [12379]

Beth travelled the remaining distance with an average speed of 52 mph

Solution:

Given, Beth drives 200 miles in 4 hours.

The equation for distance speed is expressed as:

$\text { distance }=\text { speed } \times \text { time. }$ --- eqn 1

Calculating time spent for 18 miles:

She completes the initial 18 miles at an average speed of 36 mph.

Distance here equals 18 miles

speed equals 36 mph

Substituting values into eqn 1 yields,

$\begin{array}{l}{\rightarrow 18 \text { miles }=36 \mathrm{mph} \times \text { time }} \\\\ {\rightarrow \text { time }=\frac{1}{2} \text { hour }}\end{array}$

Determining average speed for the remaining journey:

The distance left to cover is = 200 miles – 18 miles = 182 miles

The time spent on the remaining trip equals the total time minus the duration for the first 18 miles

$4 \text { hours }-\frac{1}{2} \text { hours }=\frac{7}{2} \text { hours }$

Inserting values into eqn 1 gives us

$\begin{array}{l}{182 \text { miles }=\text { average speed } \times \frac{7}{2} \text { hours }} \\\\ {\text { Average speed }=\frac{182}{7} \times 2=52}\end{array}$