A road has a 10% grade. 1. What is the angle of elevation of the road? 2. If the road is 2km long, how much does it rise?

Answers

Answer 1

Answer: 1. m = rise/run
m = 10/100 = 0.1
tan α = 0.1
α = tan^(-1) 0.1
α = 5.71 °
2. 2 km = 2,000 m
x² + ( 0.1 x )² = 2,000²
x² + 0.01 x² = 4,000,000
1.01 x² = 4,000,000
x = 1,990 m
h = 1,990 m * 0.1
h = 199 m
The road rises 199 m.

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The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:High Low Q1 Q3 IQR Median Mean σ
College 20 6 8 18 10 14 13.3 5.2
High School 20 3 5.5 16 10.5 11 11 5.4

Which of the choices below best describes how to measure the spread of this data?
A. Both spreads are best described with the IQR.
B. Both spreads are best described with the standard deviation.
C. The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
D. The college spread is best described by the standard deviation. The high school spread is best described by the IQR.

Answers

Answer:

C. The college spread is best described by the IQR. The high school spread is best described by the standard deviation.

Step-by-step explanation:

If data is normally distributed we use Standard deviation otherwise we use Interquartile Range (IQR) for measuring the spread.

Further, data is said to be normally distributed if Mean = Median = Mode.

So, High School data is normally distributed but College data is not.

So, We measure the spread of College data by IQR and High School data by Standard Deviation.

Thus, Option C is the only correct option.

A study on how fast men can run the 100-meter race found that the athletes in the study were able to run it in an average of 10 seconds. Which of the following is a correct inference?On average, athletes run a 10-second 100-meter race

On average, male athletes run a 10-second 100-meter race

On average, males run a 10-second 100-meter race

On average, female athletes do not run a 10-second 100-meter race

Answers

A study on how fast men can run the 100-meter race found that the athletes in the study were able to run it in an average of 10 seconds. Thecorrect inference is On average, male athletes run a 10-second 100-meter race

2. A rectangular photograph measuring 8 in by 10 in is surrounded by a frame with a uniform width, xx.a. What type of function can best represent the area of the picture and the frame in terms of xx (the unknown frame’s width)? Explain mathematically how you know.
b. Write an equation in standard form representing the area of the picture and the frame. Explain how you arrive at your osition.

Answers

Answer: a) Quadratic equation b) $4x^2+36x+80$

Step-by-step explanation:

Since we have given that

Length of photograph = 8 inches

Width of photograph = 10 inches

It is surrounded by a frame with uniform width 'x'.

So, Length of picture and frame becomes

$x+8+x=2x+8$

Width of picture and frame becomes

$x+10+x=2x+10$

So, Area of picture and frame becomes

$Length* breadth\n\n=(2x+8)(2x+10)\n\n=2x(2x+10)+8(2x+10)\n\n=4x^2+20x+16x+80\n\n=4x^2+36x+80$

Hence, a) Quadratic equation b) $4x^2+36x+80$

How many unit tiles need to be added to the expressionx2 + 4x + 3 in order to form a perfect square trinomial

Answers

In the question "How many unit tiles need to be added to the expression x2 + 4x + 3 in order to form a perfect square trinomial" the correct answer is 1 unit tile. Because, to make the expression x^2 + 4x + 3 a perfecr square trinomial we have x^2 + 4x + 3 + 1 = x^2 + 4x + 4 = (x + 2)^2

Answer:

A) 1

Step-by-step explanation:

Which equals the product of (x – 3)(2x + 1)?A=2x2 – 7x – 3
B=2x2 – 5x – 3
C=3x – 2
D=6x2

Answers

The product of (x – 3)(2x + 1) will be 2x² - 5x -3. Thus, option B is correct.

What is a Quadratic equation?

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

Given

(x – 3)(2x + 1) is a expression.

How to find the quadratic equation?

The product of (x – 3)(2x + 1) will be.

(x – 3)(2x + 1)

2x² -6x + x - 3

2x² - 5x -3

The product of (x – 3)(2x + 1) will be 2x² - 5x -3.

Thus, option B is correct.

More about the quadratic equation link is given below.

brainly.com/question/2263981

All you have to do is to use the distributive property

(x)(2x)+(x)(1)+(-3)(2x)+(-3)(1)

= 2x² + x - 6x -3

= 2x² - 5x - 3

The answer is B

I hope that's help:0

Help i dont understand this.

Answers

1 * 1 = 1
11 * 11 = 121
111 * 111 = 12321
1111 * 1111 = 1234321
11111 * 11111 = 123454321
111111 * 111111 = 12345654321

the pattern is that with each '1' added, there is another consecutive number added. if there are 3 ones, it I'll go up to 3 and then back down to 1 (111*111=12321)
it is the same like that for every one.

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