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wolverine [178]

3 years ago

7

suppose your grades on four science exams are 99, 86, 76, and 95. what grade do you need on your next exam to have a 91 average

on the five exams? A)99 B)89.4 C)93 D)90

1 answer:

ahrayia [7]3 years ago

6 0

99 because if you add 78+99+95+86 you get 356 and 356+99 is equal to 455 and 455 divided by 5 is 91.

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Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)

Luda [366]

Answer:

$a.b = (1*0) + (-4*2) +(1*-2)= -10$

And replacing we got:

$cos \theta = \frac{-10}{\sqrt{18} \sqrt{8}}= -\frac{10}{\sqrt{144}}= -\frac{10}{12}= -\frac{5}{6}$

And we can find the angle with the inverse cosine function and we got:

$\theta =cos^{-1} (-\frac{5}{6})= 146.44°$

Step-by-step explanation:

for this case we can use the following identity:

$cos \theta = \frac{a.b}{|a| |b|}$

We can begin finding the norm for each vector and we got:

$|a| =\sqrt{(1)^2 +(-4)^2 +(1)^2}= \sqrt{18}$

$|b| =\sqrt{(0)^2 +(2)^2 +(-2)^2}= \sqrt{8}$

Now we can find the dot product and we got:

$a.b = (1*0) + (-4*2) +(1*-2)= -10$

And replacing we got:

$cos \theta = \frac{-10}{\sqrt{18} \sqrt{8}}= -\frac{10}{\sqrt{144}}= -\frac{10}{12}= -\frac{5}{6}$

And we can find the angle with the inverse cosine function and we got:

$\theta =cos^{-1} (-\frac{5}{6})= 146.44°$

5 0

3 years ago

A company that sells yoga mats estimates its annual profit using the equation below, where x represents the wholesale price in d

Alborosie

Answer: (d)

Step-by-step explanation:

Given

Annual profit is given by

$P=10x^2-280x+1600$

When it is factored then,

$\Rightarrow 10x^2-280x+1600=0\\\Rightarrow 10\left( x^2-28x+160\right)=0\\\Rightarrow x^2-20x-8x+160=0\\\Rightarrow x(x-20)-8(x-20)=0\\\Rightarrow (x-8)(x-20)=0\\\Rightarrow x=8,20$

On factorization, we get that annual profit is zero at a whole prize of $8 and $20.

5 0

3 years ago

Jackie makes an $800 deposit into a bank account earning 4.5% interest.

Pepsi [2]

Answer:

a. $1251.5

b. $1254.64

c. 15.4 years

d. 30.56 years

Step-by-step explanation:

Given the information:

Principle (P) = $800
Interest = 4.5%

As we know, the formula to find the future value of Jackie deposit with interest is compounded monthly, quaterly, ..is

$A=P(1+\frac{r}{n} )^{nt}$ where:

P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time

Hence:

a. If the interest is compounded quarterly how much money will Jackie have in 10 years?

$A=P(1+\frac{r}{n} )^{nt}$

<=> $A=800(1+\frac{0.045}{4} )^{4*10}$

<=> A = $1251.5

d. If Jackie's money is compounded monthly, how long will it take her money to triple?

<=> $A=P(1+\frac{r}{n} )^{nt} = 3*800$

<=> $800(1+\frac{0.045}{12} )^{12*t} = 2400$

<=> $(1+\frac{0.045}{12} )^{12*t} = 3$

<=> t = 30.56 years

As we know, the formula to find the future value of Jackie deposit with interest is compounded continuously

A = P* $e^{rt}$ where e is the mathematical constant approximated as 2.7183.

b. If the interest is compounded continuously how much money will Jackie have in 10 years?

<=> A = 800* $2.7183^{0.045*10}$

<=> A = $1254.64

C. If Jackie's money is compounded continuously, how long will it take her money to double?

<=> P* $e^{rt}$ = 2*800

<=> 800* $2.7183^{0.045*t}$ = 1600

<=> $2.7183^{0.045*t}$ = 2

<=> t = 15.4 years

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3 years ago

What type of function is represented by the following graph:

MissTica

Answer:

b) quadratic

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Need some help with this please

saveliy_v [14]

-0.83 for it’s the lowest number

5 0

3 years ago