Find all solutions to the equation.

sin x = square root of three divided by two.

Answer:

The correct answer is -

monthly payment = 521.99

total pain intrest = 4319.14

Step-by-step explanation:

Given:

a or the borrowed amount = 27000

r or the interest rate = 6%

n = 5 years or 60 months

Monthly payment = ?

total intreset = ?

Formula:

The formula for the monthly payment is -

[tex]\frac{a}{\frac{{[(1+r)^n]-1}}{[r(1+r)^n]}} = P[/tex]

or, [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex] = P

Where, the amount of the loan = a

r = 0.005 (6% annual rate—expressed as 0.06—divided by 12 monthly payments per year)

n = 60 months

Solution:

Putting all the values in the either of the following formula will give monthly payments:

[tex]\frac{27000}{\frac{{[(1+0.005)^{60}]-1}}{[0.005(1+0.005)^{60}]}} = P[/tex] or  [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex]

= 521.9856 or to the nearest cent 521.99.

The total intrest would be -

= (monthly payment*number of month) - amount borrowed

= 521.99*12-27000

= 31319.14-27000

= 4319.14

Answer:

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

Step-by-step explanation:

Tem.Before    Tem.After       diff.      

103.7                   102.6            1.1

103.7                   102.7             1

100.7                     98.8             1.9

102.7                    103.5            -0.8

100.7                      99.4             1.3

102.4                      101.41           (Mean)

1.4                             1.9              0.9       Std. Dev.

n =  6

df  =  6  -  1  =  5

CI we propose to be 95 %

Then  α  = 5 %  α = 0.05    

The test is a one-tail test ( we want to know if taking aspirin will reduce a child´s fever

Hypothesis test

Null Hypothesis                      H₀         μd  = 0

Alternative Hypothesis          Hₐ         μd > 0

(NOTE:)   μd (average) = Temp Before  -  Temp. after

Therefore if   μd >  0   means that there is a statistical difference between values before ( bigger ) and after  or that the aspirin will reduce a child´s fever

To find t(c)  from t-student table  df = 5  and α = 0.05

t(c)  =  2.015

To compute  t(s)

t(s)  =  μd/ sd/√n      t(s)  =  0.98/ 0.9/√6

t(s)  =  2.66

Comparing  t(s) and  t(c)

t(s) > t(c)    

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

Answer:

[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]

Step-by-step explanation:

Given

See attachment for parallelogram

Required

Proof that ABCD is a parallelogram

We know that opposite sides are equal and parallel.

First, we calculate the slope of BC

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{q - r}{m- n}[/tex]

Next, the slope of AD using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{p - s}{m - n}[/tex]

For ABCD to be a parallelogram; then:

[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]

Answer:

i velo you

Step-by-step explanation:

Answer:

x = 52.0

Step-by-step explanation:

Reference angle = 68°

Length of side Opposite to reference angle = x

Adjacent length = 21

Apply the trigonometric function, TOA, which is given as:

Tan 68° = Opp/Adj

Substitute

Tan 68° = x/21

21 × Tan 68° = x

51.9768238 = x

x = 51.9768238 ≈ 52.0 (approximated to nearest tenth)

Answer:

(x-3) * (x-2

Step-by-step explanation:

Answer:

[tex]m =-4[/tex]

Step-by-step explanation:

Given

[tex]p(m-3 , -6) = p(-7 , -6)[/tex]

Required

Find m

[tex]p(m-3 , -6) = p(-7 , -6)[/tex]

By comparison:

[tex]m-3 = -7[/tex]

Add 3 to both sides

[tex]m = -7+3[/tex]

[tex]m =-4[/tex]

Answer:

B) The function has a maximum value of (1)

Step-by-step explanation:

The given function has a maximum value, as its curve is inverted. The maximum value is the largest (y) value that a function can attain. As one can see, this value is (1), because the (y-coordinate) of the highest point on its curve is (1). This function has no minimum value, its endpoints go on infinitely in a negative direction.

9514 1404 393

Answer:

  3/(√(3(x+h)) +√(3x))

Step-by-step explanation:

The conjugate of a binomial is the same sum, but with the sign changed. That is (a +b) and (a -b) are a conjugate pair: each is the conjugate of the other.

The purpose of multiplying expressions involving roots or complex numbers by their conjugate is to take advantage of the relation ...

  (a +b)(a -b) = a² -b²

Here. you want to eliminate the h from under the radical, so squaring the radical containing h is useful for the purpose. Hence the conjugate gets involved.

"Multiply by the conjugate" means multiply both the numerator and the denominator by the conjugate. (Effectively, multiply by 1.)

__

  [tex]\displaystyle\frac{f(x+h)-f(x)}{h}=\frac{\sqrt{3(x+h)}-\sqrt{3x}}{h}\\\\=\frac{(\sqrt{3(x+h)}-\sqrt{3x})(\sqrt{3(x+h)}+\sqrt{3x})}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\frac{3(x+h)-3x}{h(\sqrt{3(x+h)}+\sqrt{3x})}\\\\=\frac{3h}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\boxed{\frac{3}{\sqrt{3(x+h)}+\sqrt{3x}}}[/tex]

_____

Additional comment

In the end, you will want the limit as h → 0, which will be 3/(2√(3x)). You will notice that h=0 no longer makes the denominator zero, so the limit is found by simple evaluation.

When the "binomial" is a complex number of the form a+bi, its conjugate is a-bi, regardless of the sign of b. That is, the conjugate of a complex number is found by negating its imaginary part. The sign of the real part is left alone.

C. a translation and a dilation

Step-by-step explanation:

the other person isn't wrong they just put it in the wrong order

Answer:c

Step-by-step explanation:took the test

Answer:

17

Step-by-step explanation:

_____________ Hair color

Eye color ___ Brown ___ Black ___ total

Green _____ 22 ________ 15 ____ 37

Blue _______ 18 ________ 19 ____ 37

Total _______40 ________34 ____ 74

Calculate the expected frequency of Blue Eyes and Black Hair?

The expected frequency Count ;

(row total * column total) / total number of observations

Expected frequency ;

Blue eye n black hair = (37 * 34) / 74

Expected frequency count = 1258 / 74 = 17

Expected count = 17

Answer:

The row total of blue eyes is 18 + 19 = 37.

The column total of black hair is 15 + 19 = 34.

The total of the whole table is 22 + 15 + 18 +19 = 74.

Step-by-step explanation:

E=(37)(34)/74=1258/74=17

Answer:

9notebooks

Step-by-step explanation:

5×y≤45( where y is number of notebooks)

$5=1notebook

$45=$45/$5x1

=9

therefore, you'll be able to buy nine notebooks with$45

Answer:

$5n = $45

n = 9

Step-by-step explanation:

Let n represent the amount of notebooks

$5n = $45

Divide each side by 5

$5n/5 = $45/5

n = 9

so the maximum number of notebooks you can buy is 9

Answer:

The average rate of change is 22

Step-by-step explanation:

Given

[tex]f(x) = x^4 - 5x[/tex]

Required

Average rate of change over [0,3]

This is calculated as:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

So, we have:

[tex]Rate = \frac{f(3) - f(0)}{3 - 0}[/tex]

[tex]Rate = \frac{f(3) - f(0)}{3}[/tex]

Calculate f(3) and f(0)

[tex]f(x) = x^4 - 5x[/tex]

[tex]f(3) = 3^4 - 5 * 3 =66[/tex]

[tex]f(0) = 0^4 - 5 * 0 = 0[/tex]

So, we have:

[tex]Rate = \frac{f(3) - f(0)}{3}[/tex]

[tex]Rate = \frac{66-0}{3}[/tex]

[tex]Rate = \frac{66}{3}[/tex]

[tex]Rate = 22[/tex]

Answer:

Step-by-step explanation:

7*(4) - 2(-3) - (-3)^2

28 +  6 - 9

34 - 9 = 25

ko  iê ế t???????????????    t

Answer:

Law of Sines, two angles and an opposite side are known

Step-by-step explanation:

Law of Sines, two angles and an opposite side are known

q/sinQ = p/sinP

q = p/sinP * sinQ

Answer:

x=1; y=2; z=3

Step-by-step explanation:

Rearrange for convince:

2y-4z+6x = -2

-4y+2z-3x=-5

-6y+3z+4x=1

Now we take to pairs and eliminate the same var.:

2y-4z+6x = -2 *2

-4y+2z-3x=-5

and

-4y+2z-3x=-5 *-3

-6y+3z+4x=1. *2

We get:

4y-8z+12y=-4

-4y+2z-3x=-5

= -6z+9x=-9

and

12y-6x+9x=15

-12y+6x+8x=2

= 17x=17

We now know x = 1, so z is:

-6z+9=-9

-6z=-18

z=3

Let’s grab the first formula and find y:

6+2y-12=-2

6+2y=10

2y=4

y = 2

Answer:

x = 5

Step-by-step explanation:

a) The third interior angle of this triangle is 180 - 20 x.  

The three interior angles must sum up to 180 degrees.

Therefore,  60 + 7x + 5 + 180 - 20x = 180, or

                       65  + 180 - 13x = 180, or

                               65 -  13x     = 0

Finally, 13x = 65, and so x = 5

Answer:

Step-by-step explanation:

Have a good grades and study well sweetie

Answer:

The efficiency of this line is 0.85 = 85%.

Step-by-step explanation:

Efficiency:

The efficiency is given by the following formula:

[tex]E = \frac{T_t}{tn}[/tex]

In which [tex]T_t[/tex] is the total task time, [tex]t[/tex] is the largest assigned cycle time and n is the number of workstations.

5 workstations

This means that [tex]n = 5[/tex]

The sum of the 21 task times is 85 minutes.

This means that [tex]T_t = 85[/tex]

The largest assigned cycle time is 20 minutes.

This means that [tex]n = 20[/tex]

What is the efficiency of this line?

[tex]E = \frac{T_t}{tn} = \frac{85}{20*5} = \frac{85}{100} = 0.85[/tex]

The efficiency of this line is 0.85 = 85%.

Answer:

NQ : Summary

CodeNQOne-letter codeXMolecule name2-HYDROXYNAPHTHOQUINONESynonyms2-HYDROXY-1,4-NAPHTHOQUINONESystematic namesProgram Version Name ACDLabs 10.04 2-hydroxynaphthalene-1,4-dione OpenEye OEToolkits 1.5.0 2-hydroxynaphthalene-1,4-dione

27 is the answer

gbu...

Answer:

- 9 × - 3 = 27

Step-by-step explanation:

when we multiply two negative numbers then the sign of the product convert to positive sign

I.e( - )×( - )= (+) product

Answer:

C. 90√3

Step-by-step explanation:

5√2 . 9√6 = 45√12 = 45×2√3

= 90√3

The simplified form is 90√3.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Given expression is, 5√2×9√6

                               =5×9×√(2×6)

                               =45×√12

                               =45×2√3

                               =90√3

Hence, the simplified form is 90√3 .

To learn more on multiplication click:

https://brainly.com/question/5992872

#SPJ2

Answer:

[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]

Step-by-step explanation:

Given

[tex]\cos(x - y)[/tex]

Required

State the formula

From trigonometry identity, the formula of [tex]\cos(x - y)[/tex] is:

[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]

Answer:

0.6328 = 63.28% probability that he obtains at most one correct answer

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he obtains the correct answer, or he does not. The probability of obtaining the correct answer on a question is independent of any other questions, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Five-question

This means that [tex]n = 5[/tex]

Each question has exact four choices for the answer, but only one of which is correct.

This means that [tex]p = \frac{1}{4} = 0.25[/tex]

Find the probability that he obtains at most one correct answer

This is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]

[tex]P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955[/tex]

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2373 + 0.3955 = 0.6328[/tex]

0.6328 = 63.28% probability that he obtains at most one correct answer

Answer:

(a) The slope of f(x) is greater than the slope of g(x)

(b) f(x) has a greater y intercept

Step-by-step explanation:

Given

[tex]\begin{array}{cc}x & {f(x)} & -1&-9&0&-1&1&7 \ \end{array}[/tex]

[tex]g(x) = 3x - 2[/tex]

Solving (a): Compare the slopes

The slope (m) of f(x) is calculated as;

[tex]m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]

This gives:

[tex]m = \frac{f(0) - f(1)}{0 - 1}[/tex]

[tex]m = \frac{f(0) - f(1)}{- 1}[/tex]

Substitute values for f(0) and f(1)

[tex]m = \frac{-1 - 7}{- 1}[/tex]

[tex]m = \frac{-8}{- 1}[/tex]

[tex]m = 8[/tex]

The slope of g(x) can be gotten using the following comparison

[tex]g(x) = mx + b[/tex]

[tex]m \to slope[/tex]

So:

[tex]g(x) = 3x -2[/tex]

[tex]m = 3[/tex]

[tex]m_{f(x)} > m_{g(x)}[/tex]

Solving (b): Compare the y intercept

y intercept is when [tex]x = 0[/tex]

From the table of f(x)

[tex]f(0) = -1[/tex]

From the equation of g(x)

[tex]g(x) = 3x -2[/tex]

[tex]g(0) = 3*0-2[/tex]

[tex]g(0) =-2[/tex]

[tex]f(0) > g(0)[/tex]

Answer:

15 days

+

Step-by-step explanation:

A

200 pages / (8 pages / day) =

= 200 pages days / 8 pages =

= 200 days / 8 = 25 days

B

200 pages / (5 pages / day) =

= 200 pages days / 5 pages =

= 200 days / 5 = 40 days

40-25 = 15 days

A will finish 15 days sooner than B.

A will finish her report 15 days sooner than B.

The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Writer A averages 8 pages a day,

Number of pages per day written by writer A = 8 per day

Writer A will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (8 pages / day)

⇒ 200 pages days / 8 pages

⇒ 200 days / 8

⇒ 25 days

Writer B averages 5 pages a day

Number of pages per day written by writer B = 5 per day

Writer B will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (5 pages / day)

⇒  200 pages days / 5 pages

⇒  200 days / 5

⇒  40 days

Difference between both of time when they finished their report = 40-25 = 15 days

Hence, A will finish her report 15 days sooner than B.

Learn more about Ratio here:

brainly.com/question/1504221

#SPJ5

Answer:

0.28 = 28% probability that a randomly selected driver will come to complete stop

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

Recording of 75 drivers.

Of those, 21 came to a complete stop.

Then

21/75 = 0.28

0.28 = 28% probability that a randomly selected driver will come to complete stop