a trapezoids longer base is 4 times its shorter base. If the trapezoid has an area of 80 cm squared and a height of 8cm has what is the length of each base ​

Answers

Answer 1
Answer: Long One is 16
Short One is 4!!

A=base+base/2 * height

A=80

16+4/2 = 10

10 * 8 = 80!!

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A pet store has 32 dogs. The owner gives 2 treats to each dog until she has no treats left over. How many treats did she have?

Answers

Answer:

64

Step-by-step explanation:

because 32 x 2 = 64

Answer:

32*2=64  She had 64 treats

Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?

Answers

Answer:

Reese read 26 pages on Sunday.

Step-by-step explanation:

If she read twice the amount on Saturday than she read on Sunday, then you can replace the days with variables. 2x for Saturday and x for Sunday. That leaves you with 2x + x = 78. This can be simplified to 3x = 78. We can solve this by dividing both sides by 3. This leaves you with x = 26. If x represents the pages read on Sunday then Reese read 26 pages on Sunday.

Celine and Arlene shared $400. Celine received $50 more than Arlene. How much money did Arlene receive?

Answers

Answer:

Arlene had 175 and Celine had 225

Step-by-step explanation:

49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why?A) Convenience
B) Cluster
C) Random
D) Systematic
E) Stratified

Answers

Answer:

Stratified sampling

Step-by-step explanation:

In the question, students are selected from subgroups of Sophomore, Junior, and Senior classes.

We are told that 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.

This means that the sample numbers of 49, 34 and 48 students were selected in proportion to the subgroup sizes of 496, 348, and 481 students respectively.

Thus, due to the fact that subgroups were selected & that sample number of students were also selected in proportion to their respective subgroup sizes, this is therefore a stratified sampling.

Final answer:

The type of sampling used in this scenario is stratified sampling. The type of sampling in this case is E) Stratified sampling.

Explanation:

The type of sampling used in this scenario is stratified sampling. Stratified sampling is a method where the population is divided into different groups or strata, and then a sample is randomly selected from each stratum. In this case, the sophomore, junior, and senior classes are the different strata, and the sample sizes are proportional to the size of each stratum.

To further explain, let's consider the sophomore class with 496 students. If we are selecting a sample size of 49 from this class, it means that approximately 10% of the students (49/496 = 0.098) will be selected. Similarly, for the junior class with 348 students, approximately 10% (34/348 = 0.098) of the students will be selected. The same applies to the senior class with 481 students and a sample size of 48 students.

In stratified sampling, the goal is to ensure that the sample represents the characteristics of each stratum in proportion to their size in the population. By sampling from each of the classes, we can obtain a representation of the entire student population.

Learn more about Stratified Sampling here:

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Two cities are 3450 miles apart. A plane leaves one of​ them, traveling towards the other at an average speed of 310 miles per hour. At the same time a plane leaves the​ other, traveling towards the​ first, at an average speed of 380 miles per hour. How long will it take them to​ meet?

Answers

Answer:

5 hours.

Step-by-step explanation:

let they meet after t hours.

310t+380t=3450

690t=3450

69t=345

t=345/69=5

Complete the standard form of the equation of a hyperbola that has vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).

Answers

Answer:

((x-30)^(2))/(40^(2)) - ((y+15)^(2))/(3^(2)) = 1

Step-by-step explanation:

The equation of the horizontal hyperbola in standard form is:

((x-k)^(2))/(a^(2)) - ((y-k)^(2))/(b^(2)) = 1

The position of its center is:

C(x,y) = \left((-10 + 70)/(2), -15 \right)

C(x, y) = (30,-15)

The values for c and a are respectively:

a = 70 - 30

a = 40

c = 30 - (-11)

c = 41

The remaining variable is computed from the following Pythagorean identity:

c ^(2) = a^(2) + b^(2)

b = \sqrt{c^(2)-a^(2)}

b = \sqrt{41^(2)-40^(2)}

b = 3

Now, the equation of the hyperbola is:

((x-30)^(2))/(40^(2)) - ((y+15)^(2))/(3^(2)) = 1

Answer:

The above answer is correct but the 3 should be a 9

Step-by-step explanation:

Plato