Bryan borrowed $2400 at 10% simple interest for 8 months to by a car. Find the simple interest he paid.

4-13 Students in a management science class have just re- ceived their grades on the first test. The instructor has provided inf

inessss [21]

Answer:

a) y = 0.74x + 18.99; b) 80; c) r = 0.92, r² = 0.85; r² tells us that 85% of the variance in the dependent variable, the final average, is predictable from the independent variable, the first test score.

Step-by-step explanation:

For part a,

We first plot the data using a graphing calculator. We then run a linear regression on the data.

In the form y = ax + b, we get an a value that rounds to 0.74 and a b value that rounds to 18.99. This gives us the equation

y = 0.74x + 18.99.

For part b,

To find the final average of a student who made an 83 on the first test, we substitute 83 in place of x in our regression equation:

y = 0.74(83) + 18.99

y = 61.42 + 18.99 = 80.41

Rounded to the nearest percent, this is 80.

For part c,

The value of r is 0.92. This tells us that the line is a 92% fit for the data.

The value of r² is 0.85. This is the coefficient of determination; it tells us how much of the dependent variable can be predicted from the independent variable.

3 0

3 years ago

Let H be the set of all polynomials having degree at most 4 and rational coefficients. Determine whether H is a vector space. If

Verizon [17]

Answer:

Yes. It is a vector space over the field of rational numbers $\mathbb{Q}$

Step-by-step explanation:

An element $p$ of the set $H$ has the form

$p(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}$

where $a_{0},a_{1},a_{2},a_{3},a_{4}$ are rational coefficients.

The operations of addition and scalar multiplication are defined as follows:

$p(x)+q(x)=(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+x_{4}x^4)+(b_{0}+b_{1}x+b_{2}x^{2}+b_{3}x^{3}+b_{4}x^{4})=(a_{0}+b_{0})+(a_{1}+b_{1})x+(a_{2}+b_{2})x^{2}+(a_{3}+b_{3})x^{3}+(a_{4}+b_{4})x^{4}$

$\lambda p(x)=\lambda (a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4})=\lambda a_{0}+\lambda a_{1}x+\lambda a_{2}x^{2}+\lambda a_{3}x^{3}+\lambda a_{4}x^{4}$

The properties that $H$ , together the operations of vector addition and scalar multiplication, must satisfy are:

Conmutativity
Associativity of addition and scalar multiplication
Additive Identity
Additive inverse
Multiplicative Identity
Distributive properties.

This is not difficult with the definitions given. The most important part is to show that $H$ has a additive identity, which is the zero polynomial, that is closed under vector addition and scalar multiplication. This last properties comes from the fact that $\mathbb{Q}$ is a field, then it is closed under sum and multiplication.

7 0

3 years ago

9 folders cost $2.50 9 notebooks cost $4 write equivalent expressions and then find the total cost

Leokris [45]

$2.50(f) + $4(n) = Total Cost

$2.50(9) + $4(9) = Total Cost

$22.50 + $36 = Total Cost

$58.50 = Total Cost

8 0

3 years ago

What is the measure of angle O in parallelogram LMNO? will give brainiest

Serhud [2]

Answer:

m∠O = 105°

Step-by-step explanation:

Step 1: Set up equation

x + 40 + 3x = 180

Step 2: Solve

4x + 40 = 180

4x = 140

x = 35

Step 3: Plug in

3(35) = 105°

And we have our answer!

3 0

4 years ago

Read 2 more answers

Multiplying fractions

mixas84 [53]

2/9 x -1/4

2x1=2 9x4=36

2/36

simplify

1/18

hope this helps

6 0

3 years ago

Read 2 more answers