Find the hypotenuse, find x and round to the nearest tenth.

Kyle received the following course grades for 10 (three-credit) courses during his freshman year:

timofeeve [1]

Answer:

(a) The average grade point is 2.5.

(b) The relative frequency table is show below.

(c) The mean of the relative frequency distribution is 0.3333.

Step-by-step explanation:

The given data set is

4, 4, 4, 3, 3, 3, 1, 1, 1, 1

(a)

The average grade point is

$Average=\frac{\sum x}{n}$

$Average=\frac{4+4+4+3+3+3+1+1+1+1}{10}$

$Average=2.5$

Therefore the average grade point is 2.5.

(b)

$\text{Relative frequency}=\frac{\text{Frequency of number}}{\text{Total frequency}}$

The relative frequency table is show below:

x f Relative frequency

4 3 $\frac{3}{10}=0.3$

3 3 $\frac{3}{10}=0.3$

1 4 $\frac{4}{10}=0.4$

(c)

Mean of the relative frequency distribution is

$Average=\frac{0.3+0.3+0.4}{3}$

$Average=0.3333$

Therefore the mean of the relative frequency distribution is 0.3333.

4 0

3 years ago

Topic: The Quadratic Formula

Finger [1]

Answer:

Step-by-step explanation:

The quadratic formula for a equation of form

ax²+bx + c = 0 is

$x= \frac{-b +- \sqrt{b^2-4ac} }{2a}$

For the first equation,

x²+3x-4=0,

we can match that up with the form

ax²+bx + c = 0

to get that

ax² = x²

divide both sides by x²

a=1

3x = bx

divide both sides by x

3 = b

-4 = c

. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.

Plugging our values into the equation, we get

$x= \frac{-3 +- \sqrt{3^2-4(1)(-4)} }{2(1)} \\= \frac{-3+-\sqrt{25} }{2} \\ = \frac{-3+-5}{2} \\= -8/2 or 2/2\\= -4 or 1$

as our possible solutions

Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.

Next, we have

x²+3x+4=0

Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus

$x= \frac{-3 +- \sqrt{3^2-4(1)(4)} }{2(1)}\\= \frac{-3 +- \sqrt{9-16} }{2}\\= \frac{-3 +- \sqrt{-7} }{2}\\$

Because √-7 is not a real number, this has no real solutions. However,

(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions

Finally, for

4x² + 1= 4x,

we can start by subtracting 4x from both sides to maintain the desired form, resulting in

4x²-4x+1=0

Then, a=4, b=-4, and c=1, making our equation

$x=\frac{-(-4) +- \sqrt{(-4)^2-4(4)(1)} }{2(4)} \\= \frac{4+-\sqrt{16-16} }{8} \\= \frac{4+-0}{8} \\= 1/2$

Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution

7 0

3 years ago

Is 14 200 000 in scientific notation 1.42 10x,5

Elan Coil [88]

Yes, the rules of scientific notation are:

1. All non-zero digits are significant

2. Zeros in between non-zeros are significant.

3. Zeros to the left of the first non-zero number are NOT significant.

4. Zeros to the right of non-zero numbers are significant IF a decimal point is present.

P.S: if you need help with sig fig rounding, let me know.

6 0

3 years ago

Jason has 5 shirts for every 2 pairs of pants. His brother John has 7 shirts for every 3 pairs of pants. Compare the ratio by co

postnew [5]

Answer:

john has a greater ratio of shirts to pants

Step-by-step explanation:

jason- 5:2

table:

shirt :5 10 15 20 25 30 35 40 45

pants:2 4 6 8 10 12 14 16 18 20

john-7:3

table:

shirts:7 14 21 28 35 42 49 56 63

pants:3 6 9 1 2 15 18 21 24 27

4 0

3 years ago

Find the area of the following figure:

RoseWind [281]

The area of the figure is 11. 27 cm²

The figure given is a parallelogram

Note that the formula for area of a parallelogram is given as;

Area = base × height

Base = 2. 3cm

height = 4. 9cm

Area = 2. 3 × 4. 9

Area = 11. 27 cm²

Thus, the area of the figure is 11. 27 cm²

Learn more about a parallelogram here:

brainly.com/question/970600

#SPJ1

6 0

2 years ago