Maci is paid biweekly and earns $1500 each paycheck. What is his yearly salary?

Answer:

[tex]\theta = 108.29[/tex]

Step-by-step explanation:

Given

[tex]u = <2,6>[/tex]

[tex]v = <4,-7>[/tex]

Required:

Calculate the angle between u and v

The angle [tex]\theta[/tex] is calculated as thus:

[tex]cos\theta = \frac{u.v}{|u|.|v|}[/tex]

For a vector

[tex]A = <a,b>[/tex]

[tex]A = a * b[/tex]

[tex]cos\theta = \frac{u.v}{|u|.|v|}[/tex] becomes

[tex]cos\theta = \frac{<2,6>.<4,-7>}{|u|.|v|}[/tex]

[tex]cos\theta = \frac{2*6+4*-7}{|u|.|v|}[/tex]

[tex]cos\theta = \frac{12-28}{|u|.|v|}[/tex]

[tex]cos\theta = \frac{-16}{|u|.|v|}[/tex]

For a vector

[tex]A = <a,b>[/tex]

[tex]|A| = \sqrt{a^2 + b^2}[/tex]

So;

[tex]|u| = \sqrt{2^2 + 6^2}[/tex]

[tex]|u| = \sqrt{4 + 36}[/tex]

[tex]|u| = \sqrt{40}[/tex]

[tex]|v| = \sqrt{4^2+(-7)^2}[/tex]

[tex]|v| = \sqrt{16+49}[/tex]

[tex]|v| = \sqrt{65}[/tex]

So:

[tex]cos\theta = \frac{-16}{|u|.|v|}[/tex]

[tex]cos\theta = \frac{-16}{\sqrt{40}*\sqrt{65}}[/tex]

[tex]cos\theta = \frac{-16}{\sqrt{2600}}[/tex]

[tex]cos\theta = \frac{-16}{\sqrt{100*26}}[/tex]

[tex]cos\theta = \frac{-16}{10\sqrt{26}}[/tex]

[tex]cos\theta = \frac{-8}{5\sqrt{26}}[/tex]

Take arccos of both sides

[tex]\theta = cos^{-1}(\frac{-8}{5\sqrt{26}})[/tex]

[tex]\theta = cos^{-1}(\frac{-8}{5 * 5.0990})[/tex]

[tex]\theta = cos^{-1}(\frac{-8}{25.495})[/tex]

[tex]\theta = cos^{-1}(-0.31378701706)[/tex]

[tex]\theta = 108.288386087[/tex]

[tex]\theta = 108.29[/tex] (approximated)

Answer:

60 seconds make 1 minute,60 minute make 1 hours.

The amount of money that Matt and Chris have after 5 years will be $362.66 and $415.69, respectively.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

[tex]\rm A = P \left (1 + \dfrac{r}{n} \right ) ^{nt}[/tex]

Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.

Matt put $300 into a five-year account with a 3.8% annual interest rate compounded on a monthly basis. Then the amount after 5 years will be

[tex]\rm A = 300\left (1 + \dfrac{0.038}{12} \right ) ^{12 \times 5}[/tex]

Simplify the equation, then we have

A = 300 x 1.2089

A = $362.66

Chris put $350 into a savings account with a 5-year compounded yearly return rate of 3.5 percent.

A = 350 (1 + 0.035)⁵

Simplify the equation, then we have

A = 350 x 1.1877

A = $415.69

The amount of money that Matt and Chris have after 5 years will be $362.66 and $415.69, respectively.

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Given:

The function is

[tex]f(x)=2x^4-4x^3+20x-100[/tex]

To find:

The remainder if f(x) is divided by (x+11).

Solution:

According to the remainder theorem, if a function f(x) is divided by (x-c), then the remainder is f(c).

On comparing (x+11) and (x-c), we get c=-11.

Using remainder theorem, if a function f(x) is divided by (x+11), then the remainder is f(-11).

Putting x=-11 in the given function.

[tex]f(-11)=2(-11)^4-4(-11)^3+20(-11)-100[/tex]

[tex]f(-11)=29282+5324-220-100[/tex]

[tex]f(-11)=34606-320[/tex]

[tex]f(-11)=34286[/tex]

Therefore, the remainder is 34286 when f(x) is divided by (x+11).

Answer:

BC = [tex] 1.8 [/tex]

Step-by-step explanation:

∆ABC is an equilateral ∆ because all three angles are equal. Therefore, all its sides would be equal also. This means AB = BC = AC

Thus, let's find the value of x.

[tex] \frac{7}{4}x - 1 = \frac{9}{3}x - 3 [/tex]

Collect like terms

[tex] \frac{7}{4}x - \frac{9}{3}x = 1 - 3 [/tex]

[tex] \frac{7x}{4} - 3x = -2 [/tex]

[tex] \frac{7x - 12x}{4} = -2 [/tex]

[tex] \frac{-5x}{4} = -2 [/tex]

Multiply both sides by 4

[tex] \frac{-5x}{4}*4 = -2*4 [/tex]

[tex] -5x = -8 [/tex]

Divide both sides by -5

[tex] x = \frac{8}{5} [/tex]

AB = BC = AC

Therefore,

BC = [tex] \frac{7}{4}x - 1 [/tex]

Plug in the value of x

BC = [tex] \frac{7}{4}*\frac{8}{5} - 1 [/tex]

BC = [tex] \frac{56}{20} - 1 [/tex]

BC = [tex] 2.8 - 1 [/tex]

BC = [tex] 1.8 [/tex]

Answer:

This is a very vague question. We can't find out the width if it doesn't tell us the area. Comment on my answer the area and I can help.

Answer:

Also a negative number

Step-by-step explanation:

negative times negative is equal to positive, positive times negative is equal to negative

First calculate the cube of the number as if it is a positive number and then just put minus (-) sign before the resultant.

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, b are real numbers and i is an imaginary number.

If x is a real number,

-x is a negative real number,

(-x)³=-(x³)

e.g.(-3)³=-(3³)= -27

(-½)³=-(½)³= -(1/8)

The cube of a negative number can be calculated in the same way as you calculate for the positive number.

First calculate the cube of the number as if it is a positive number and then just put minus (-) sign before the resultant.

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Answer:

satingin ko po at B I not sure

Step-by-step explanation:

i hope it help

Answer:

8/12

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

A. 1/12

Step-by-step explanation:

Answer:

What are "the following equations" supposed to be?

Step-by-step explanation:

:)

Answer:

A

Step-by-step explanation:

A is probably the best one!

Answer:

x=10

Step-by-step explanation:

1/2x+4=9

subtract 4 from both sides

1/2x=5

multiply both sides by 2 to get x by itself

x=10

Answer:

1/2x+4=9 is x=1/10

Step-by-step explanation:

theres no explanation

Answer: 9 and 21

Step-by-step explanation:

board=30m

divide by 2 pieces

one piece, we call it a

b, the other piece is b= 2a+3

a+b=30

a+2a+3=30

3a=30-3

3a=27

a=9

b=21

Answer:

57

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

This function is y=-2 which is a line that doesn't overlap.

Answer: Yes

Step-by-step explanation:

When you have these problems, you can know the answer by seeing if any of the x values are the same. If there are, it will only be a function if the y value is the same.

For example:

{(1,-2),(2,3),(1,-2),(3,4) would be a function because the x values of "1" have the same y value.

Another example:

{(1,-2),(1,3),(3,4),(4,5) would not be a function because the x values of "1" does not have the same y value

Hope this helps!

Answer:

From a starting location of 75 feet below sea level, the submarine is descending 50 feet per hour. Answer is.D

Step-by-step explanation:

Used an Calculator  

I hope this helps

Answer:

D

Step-by-step explanation:

the reason why it's D, is because i did the test bro and it had a green check which means it's right.

your welcome.

Answer:

22^6

Step-by-step explanation:

Answer:22^6

Step-by-step explanation:

because you have 22*22 6 times take the 6 twenty twos and make that an exponent of 6 you have the base of 22 you have the exponent of 6 so you have to power of 22 to the sixth

Only 80% students passed the second exam and also passed the first exam .

Conditional probability is used to find the probability of an event A given that event B has already occurred.

It is denoted by P(A/B)=P(A∩B)/P(B)  .

In the given question

Let A be the event for students passed in first exam.

Let B be the event for students passed in second exam.

Given

Only 48% passed in both the exam that means

P(A∩B)=48%=0.48   ...(i)

and

60% students passed the second exam , that is

P(B)=60%=0.60       ...(ii)

To find the probability of students passed in second exam given that they passed in first exam , conditional probability is used that is P(A/B), denoted by

P(A/B)=P(A∩B)/P(B)

Substituting the values from equation (i) and (ii) we get

P(A/B) = 0.48/0.60

=48/60

Converting 48/60 to percent

=48/60*100

=80%

Therefore , Only 80% students passed the second exam and also passed the first exam , the correct option is 80%.

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Answer:

36m 40s

Step-by-step explanation:

To find out how much time was spent on playing soccer, we need to find out the total number of hours spent on exercising.

Total amount of time for exercise = 3h + [tex]\frac{2}{3}[/tex]h

                                                        = [tex]\frac{11}{3}[/tex]h

Total amount of time for soccer = [tex]\frac{1}{6}[/tex] × [tex]\frac{11}{3}[/tex]h

                                                     = [tex]\frac{11}{18}[/tex]h

                                                     = 36m 40s

√ 3 can be classified as a non negative square root of the number 3 which is also a real and irrational number.

We are given a number √ 3.

We need to classify the number.

First we can see that, this is the non negative square root of the number 3.

That is when we multiply √ 3 two times, we get the number 3.

Also, we can see that, it will be an irrational number as it will be non terminating and non repeating number.

That is it will be a real irrational number.

Therefore, we get that, √ 3 can be classified as a non negative square root of the number 3 which is also a real and irrational number.

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Answer:

A. $3

Step-by-step explanation:

20 × 15% =

20 × 15/100 =

20 × 3/20 = 60/20 = 3

Answer:

$23

Step-by-step explanation:

I hope this helps!

Answer:

theres no situations or answers.

Step-by-step explanation:

Answer:

x ≤ 12.83

(Any number under or equal to 12.8333...)

Step-by-step explanation:

154 ≥ 12x

12.833.... ≥ x

x ≤ 12.83

If an input of -9 is given to machine having Function A, then output will be 84 and if it is given to machine having Function B, then the output will be 3i-2.

The machine having Function A is given by y = x² + 3 and the machine having Function B is given by y = (√x) - 2.

Here, input will be the value of x and output will be the value of y as x id the independent variable and y is the dependent variable. If we put x = -9 in both the machines, then;

The output by machine A will be given by

y = (-9)² + 3

y = 81 + 3

=> y = 84

The output by machine B will be given by

y = (√-9) - 2

y = 3(√-1) - 2

=> y = 3i - 2.

Now, if Eric wants to get an output zero, he can get it by using machine B as Function A has square and addition both so any negative number will also give a positive result and the result will never be zero. But in Function B the result zero can be obtained by giving the input as 4 that is x = 4. The output will be given by:

y = (√4) - 2

y = 2 - 2

=>y = 0.

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2,infinity

Hope this helps

Answer:[2,♾)

Step-by-step explanation:

Answer:

Y=300

X= 4

M= 49x9=4

3x4=3

Step-by-step explanation: