prove sin^6x+cos^6x+3 sin^2x cos^2x=1

Answer:

x = -3

Step-by-step explanation:

See steps of solution:

Answer is -3

Answer:

x = -3

Step-by-step explanation:

5(5x+3) - 4(2x-9) = 0     Multiply out.

5*5x + 5*3 - 4*2x + 36 = 0

25x + 15 - 8x + 36 = 0 Combine like terms.

25x - 8x + 15 + 36 = 0

17x + 51 = 0 Subtract 51 from both sides.

17x = - 51   Divide each side by 17.

17x/17 = -51/17

x = - 3

Answer:

.3

Step-by-step explanation:

P( defective) = number defective/ total

                     = 3/10

                      .3

Answer:

[tex]\huge\boxed{0.3}[/tex]

Step-by-step explanation:

Total CDs = 10

Defective CDs = 3

P(Defective) = 3/10

P(Defective) = 0.3

Terms = 9*6 is a term

            then, 23*3 isa term

then, 14x is also a term

Answer:

1) The average rte of change = 6

2) The average rate of change over an interval is the ratio of the total change in the determinate variable or function (values of the output of the function) to the change in the indeterminate variable (values of the input of the function)

Step-by-step explanation:

1) The average of change of the function is found as follows;

At x = 0.75, y = -0.5, at x = 1.125, y = 1.75

Therefore, the average rate of change = (1.75 - (-0.5))/(1.125 - 0.75) = 6

2) The average rate of change over an interval on a graph or of a curve is found by dividing the difference between the y-coordinate values of the two points on the graph by the difference of the x-coordinate values of the two points.

Answer:

63,565.

Step-by-step explanation:

The question is incomplete. Here is the complete question.

A company uses the formula below to determine the salary offered to a potential employee, where s is the salary and y is the number of years of experience the potential employee has. s = 1,856y + 45,005 What salary would be offered to a potential employee with 10 years of experience?

The modelled equation is expressed as

s = 1,856y + 45,005.

Since we are to get the salary that would be offered to a potential employee with 10 years of experience, we will substitute the variable y = 10 into the formula and calculate the value of s as shown:

s = 1,856y + 45,005

s = 1,856(10) + 45,005

s = 18,560 + 45,005

s = 63,565

Hence the salary that would be offered to a potential employee with 10 years of experience is 63,565.

Answer:

d. 4, 5, and 6  

Step-by-step explanation:

The sum of the lengths of the two shorter sides must be greater than that of the longest side.

4 + 5 > 6

a. is wrong. 10 + 12 ≯ 25.

b. is wrong. 5 + 6 ≯ 12.

c. is wrong. 2 + 2 ≯ 4

Answer:

167°

Step-by-step explanation:

<LMN = <LMT + <TMN

23° + 144° = 167°

<LMN = 167°

Answer:

7

Step-by-step explanation:

This is so because (+) × (-) is (-).

Just like (+) × (+) is (+) and (-) × (-) is (-).

So 10 + (-3) = 10 - 3 = 7.

Answer:

[tex]7[/tex]

Step-by-step explanation:

[tex]10 + ( - 3) \\ \\ (+) \: \times \: (- )= (- ) \\ so \: 10 - 3 \\ = 7[/tex]

Answer:

The probability is 0.25

Step-by-step explanation:

Here is a probability question.

We want to know the probability of picking a card which is in the spades suit.

Now, what we know is that there are a total of 52 cards and we have 4 suites.

Each suite have equal number of cards. So definitely the number of cards in the spades suit will be 52/4 = 13 cards

Thus, the probability of picking any card in the spades suit = number of cards in the spades suit/ Total number of cards in the deck

Mathematically that would be 13/52 = 1/4 = 0.25

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma[/tex] = 10 beats per minute  

     Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma\neq[/tex] 10 beats per minute  

(b) The value of chi-square test statistics is 35.704.

(c) P-value = 0.4360.

(d) We conclude that the pulse rates of men have a standard deviation equal to 10 beats per minute.

Step-by-step explanation:

We are given that a simple random sample of 36 men from a normally distributed population results in a standard deviation of 10.1 beats per minute.

If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute.

Let [tex]\sigma[/tex] = population standard deviation for the pulse rates of men.

(a) So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma[/tex] = 10 beats per minute      {means that the pulse rates of men have a standard deviation equal to 10 beats per minute}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma\neq[/tex] 10 beats per minute      {means that the pulse rates of men have a standard deviation different from 10 beats per minute}

The test statistics that will be used here is One-sample chi-square test for standard deviation;

                             T.S.  =  [tex]\frac{(n-1)\times s^{2} }{\sigma^{2} }[/tex]  ~  [tex]\chi^{2}__n_-_1[/tex]  

where, s = sample standard deviation = 10.1 beats per minute

            n = sample of men = 36

So, the test statistics =  [tex]\frac{(36-1)\times 10.1^{2} }{10^{2} }[/tex]  ~ [tex]\chi^{2}__3_5[/tex]

                                   =  35.70  4

(b) The value of chi-square test statistics is 35.704.

(c) Also, the P-value of the test statistics is given by;

                    P-value = P([tex]\chi^{2}__3_5[/tex] > 35.704) = 0.4360

(d) Since the P-value of our test statistics is more than the level of significance as 0.4360 > 0.10, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the pulse rates of men have a standard deviation equal to 10 beats per minute.

Answer:

[tex]Total\ Rent = 49 + 5m[/tex]

Step-by-step explanation:

Given

Rent per day = $49

Addition = 5 cents per mile

Required

Determine the rent for a day and m miles

First, we need to generate a formula from the given parameters;

Let d represent number of days and m represent additional miles;

[tex]Total\ Rent = 49 * d + 5 * m[/tex]

[tex]Total\ Rent = 49 d + 5 m[/tex]

Solving for the rent for a day and m miles

We have that: d = 1 and m = m

Substitute these in the formula above

[tex]Total\ Rent = 49 * 1 + 5 * m[/tex]

[tex]Total\ Rent = 49 + 5m[/tex]

Hence, the total rent is

[tex]Total\ Rent = 49 + 5m[/tex]

Answer:

[tex] \boxed{\sf D. \ x^2 + 2} [/tex]

Step-by-step explanation:

[tex] \sf Simplify \ the \ following: [/tex]

[tex] \sf \implies (2 {x}^{2} + 2x + 3) - ( {x}^{2} + 2x + 1)[/tex]

[tex] \sf - ( {x}^{2} + 2x + 1) = - {x}^{2} - 2x - 1 : [/tex]

[tex] \sf \implies (2 {x}^{2} + 2x + 3) - {x}^{2} - 2x - 1[/tex]

[tex] \sf Grouping \ like \ terms: [/tex]

[tex] \sf \implies (2 {x}^{2} - {x}^{2}) + (2x - 2x)+ (3 - 1)[/tex]

[tex] \sf 2 {x}^{2} - {x}^{2} = {x}^{2} : [/tex]

[tex] \sf \implies {x}^{2} + (2x - 2x)+ (3 - 1)[/tex]

[tex] \sf 2x - 2x = 0 : [/tex]

[tex] \sf \implies {x}^{2} + 0+ (3 - 1)[/tex]

[tex] \sf 3 - 1 = 2 : [/tex]

[tex] \sf \implies {x}^{2} +2[/tex]

Answer:

Step-by-step explanation:

1. m/-8 = -2.5

*-8 = *-8

m = -2.5*-8

m = 2.5*8

m = 20

2. 7/8a = 42

*8            *8

7a = 336

/7       /7

a = 336/7

a = 48

Hope this helped,

Kavitha

Answer: 0.137.

Step-by-step explanation:

Let p be the population proportion of musicians that are left-handed.

Given: Sample size : n= 2690   [subset of population]

Number of musicians that are left-handed: x= 368

Then the sample proportion: [tex]\hat{p}=\dfrac{368}{2690}\approx0.137[/tex]

Since sample proportion is the best point estimate of the population proportion.

Hence, a point estimate for p, the population proportion of musicians that are left-handed is 0.137.

Answer:

x = -16

Step-by-step explantion:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Hope this helps!

(・∀・(・∀・(・∀・*)

Answer:

sqrt 46

Step-by-step explanation:

irrational numbers are numbers cannot be define in a fraction. sqrt of 46 will give you infinite decimal which could not be express in a fraction form.

Answer - Blue; x > 2 and x ≤ -3

Ok so one most to the left shows an arrow going "lesser" and starting at -3. Since the dot covers -3, that means it is equal to or less than -3.

So the on most to the right starts at 2 and the arrow is point "greater"

The circle is hollow, meaning is does not include 2. So that means it's greater than 2.

♡  Hope this helped! ♡

❀ 0ranges ❀

Answer:

[tex]y=-5+4x[/tex]     and the slope intercept is [tex]y=4x-5[/tex]

Answer:

Use the slope intercept form, y=mx+b to find the slope m and the y intercept b

slope= -4

y intercept= (0,5)

#FreeMelvin

The coordinates of the point D of the rectangle after the translation is given by D' ( 1 , -12 )

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

Given data ,

Let the coordinates of the rectangle be ABCD

Now , the coordinate of the point D be D ( -5 , -2 )

And , the translation rule is ( x , y ) → ( x + 6 , y - 10 )

So , the point after translation be D'

where D' = D ( -5 + 6 , -2 - 10 )

The coordinates of D' = D' ( 1 , -12 )

Hence , the coordinates after translation is  D' ( 1 , -12 )

To learn more about translation click :

https://brainly.com/question/19007400

#SPJ7

Answer:

Step-by-step explanation:

We apply the properties of the power.

[tex]\left(r^3 \right)^{-2}=r^{3*(-2)}=r^{-6}=\dfrac{1}{r^6}[/tex]

Answer:

r^-6  OR  1 / (r^6)

Step-by-step explanation:

For this expression, we can use exponential power rules to simplify.

Power to a power, you multiply the exponents.

So, (r^3)^-2 == r^-6

We can use the fact that negative exponents will be the base to the power in the denominator.

r^-6 == 1/(r^6)

Cheers.

Answer:

Yes

Step-by-step explanation:

Let the numbers be p q r such that p>q>r

So p + q + r = 3q

2q = p+ r

And q< p but q> c,

So by Solving this would give

q= (p+ r)/2

so q is the mean of p & r.

Since the only other number that fits is q,

Then q is the mean of the numbers p,q,r

As so q is also the median of this set

Thus proving that the mean is the same as the median.

Answer:

Jordan lives 18 miles away from the store

Step-by-step explanation:

Distance=speed × time

Where,

d= distance

s= speed

t= time

Total driving time takes half an hour

Distance=speed × time

time=Distance/speed

t=1.5

Speed 1=30 mph

Speed 2:=20 mph

t=d/s1 + d/s2

1.5=d/30 + d/20

1.5=20d + 30d / 600

1.5=50d/600

Cross product

1.5×600=50d

900=50d

Divide both sides by 50

900/50=d

18=d

Therefore,

d=18 miles

Jordan lives 18 miles away from the store

Answer:

yearly salary = $54,708

Step-by-step explanation:

Let monthly salary be x

Let yearly salary be y

Let number of months be n

To estimate your average monthly salary, divide your yearly salary by the number of months in a year. This can be written as

x = y divided by n

[tex]x = \frac{y}{n}[/tex]

Therefore, writing an equation to determine yearly salary is the same as making the yearly salary 'y' the subject of the formula above:

[tex]x = \frac{y}{n}\\cross-multiplying\\n\ \times\ x= y\\y\ =\ nx[/tex]

where y = ???

x = $4,559

n = 12 months

[tex]y = 4,559\ \times\ 12 \\= \$\ 54,708[/tex]

Therefore yearly salary = $54,708

Answer:

Step-by-step explanation:

Zeros are x-axis intercepts therefore y=0, so it's always (x, 0)

{For given function:

(x - 3)² - 16 = 0

(x - 3)² = 16

x - 3 = 4    or    x - 3 = -4

x = 7        or       x = -1

Zeros:  (7, 0) and (-1, 0)}

Answer:

Given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down, which is also T₍₋₃, ₋₅₎, by transformation notation

Step-by-step explanation:

The coordinates of the point C is (1, -1)

The coordinates of the point C' is (-2, -6)

Therefore, the translation required to shift the point C from to point C' is found as follows;

The difference between the x, and y-coordinates of the points C and C' are given as follows;

Δx, C to C' = (-2 - 1) = -3

Δy, C to C' = (-6 - (-1)) = (-6 + 1) = -5

Therefore, the the transformation from C to C' it T₍₋₃, ₋₅₎

Which can be presented as, given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down.

Answer:

si

Step-by-step explanation:

no

freememeskids

Answer:

a. True.

Step-by-step explanation:

32k + 24 = 8(4k + 3)

32k + 24 = 32k + 24

32k - 32k = 24 - 24

0 = 0

Since 0 does equal 0, the statement is a. True.

Hope this helps!

Answer:

[tex]\Large \boxed{\mathrm{a. \ True}}[/tex]

Step-by-step explanation:

[tex]32k+24[/tex]

[tex]\sf Factor \ out \ 8 \ from \ the \ expression.[/tex]

[tex]8(4k)+8(3)[/tex]

[tex]8(4k+3)[/tex]

[tex]32k+24=8(4k+3)[/tex]

[tex]\sf The \ equation \ is \ true.[/tex]

Your question has been heard loud and clear.

Lhs = 2cos[5A+3A/2]cos[5A-3A/2]+2cos[15A+7A/2]cos[15A-7A/2]

=2cos4AcosA+2cos11Acos4A

=2cos4A[cosA+cos11A]

=2cos4A[2cos[11A+A/2]Cos[11A-A/2]

=2cos4A2cos5Acos6A

=4cos4Acos5Acos6A=Rhs

Thank you

Answer:

5x-1

Step-by-step explanation:

8x-3(x+1)-4

{open the brackets}3x-3

8x-3x-3-4

5x+(-7), which is 5x-7