the coefficient of 6x

Answer:

Standard Complex Form  : [tex]-\frac{25\sqrt{3}}{2}+\frac{25}{2}i[/tex]

Step-by-step explanation:

We want to rewrite this expression in standard complex form. Let's first evaluate cos(5π / 6). Remember that cos(x) = sin(π / 2 - x). Therefore,

cos(5π / 6) = sin(π / 2 - 5π / 6),

π / 2 - 5π / 6 = - π / 3,

sin(- π / 3) = - sin(π / 3)

And we also know that sin(π / 3) = √3 / 2. So - sin(π / 3) = - √3 / 2 = cos(5π / 6).

Now let's evaluate the sin(5π / 6). Similar to cos(x) = sin(π / 2 - x), sin(x) = cos(π / 2 - x). So, sin(5π / 6) = cos(- π / 3). Now let's further simplify from here,

cos(- π / 3) = cos(π / 3)

We know that cos(π / 3) = 1 / 2. So, sin(5π / 6) = 1 / 2

Through substitution we receive the expression 25( - √3 / 2 + i(1 / 2) ). Further simplification results in the following expression. As you can see your solution is option a.

[tex]-\frac{25\sqrt{3}}{2}+\frac{25}{2}i[/tex]

Answer:

T-test

Step-by-step explanation:

Significance of correlation between two variables x and y measures the strength and direction of their relationship. This is used to make future forecasts of the behaviour of a variable under study.

Correlation coefficient can be used to measure significance of correlation, but we can also use the t-test.

T-test is a statistics that is inferential. It measures the significance of difference between the means of two groups.

T-test is the statistic of choice when carrying out hypothesis testing.

T distribution values and degrees of freedom are used to determine statistical significance.

For example the means of two samples can be compared to determine of the come from the same population

Answer:

x = -6,3,15,-12; y = 11,5,-3,15

Step-by-step explanation:

Domain is the x value, so plugged in the x values into the equation and got the y values or range.

Answer:

 x:  y:

-6  11

3       5

15 -3

-12    15

Answer:

volume of  redwood tree is 6400 π ft^3(option 4)

Step-by-step explanation:

concept =

volume of cylinder = πr^2l

where r is the radius and l is the length of cylinder

circumference of cylinder = 2πr

_____________________________________

shape of  redwood tree can be taken as cylindrical

given

circumference of a redwood tree trunk is 16π ft

2πr = 16π

=> r = 16π/2π = 8

Thus, radius is 8 feet

Therefore volume of  redwood tree = πr^2l = π8^2*100 = π*64*100

volume of  redwood tree =6400 π ft^3

Answer:

6,400π ft3

Step-by-step explanation:

took test and got it right

Answer:

[tex]\boxed{-3(x+3)(x^2-6x+10)}[/tex]

Step-by-step explanation:

Hello,

As the polynomial has only real coefficients, it means that 3-i is a zero too, because we apply the Conjugate Zeros Theorem.

It means that we can write the expression as below, k being a real number that we will have to identify.

[tex]k(x+3)(x-3-i)(x-3+i)=k(x+3)((x-3)^2-i^2)\\\\=k(x+3)(x^2-6x+9+1)\\\\=k(x+3)(x^2-6x+10)[/tex]

And for x = 0, y = -90 so we can write

-90=k*3*10, meaning that k=-3

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Some texts are missing from the question, I found a possible match, and here it is:

A particular country has total of 45 states. If the areas of 35 states are added and the sum is divided by 35​, the result is 135,600 square kilometres. Determine whether this result is a statistic or a parameter.

Answer:

The result is a statistic because the data involved are samples.

Step-by-step explanation:

A Parameter is a numerical representation of an entire population. That is they are numbers summarizing data for an entire population. In this case, if all the 45 states were measured, the result would have been a parameter.

On the other hand, statistics are numbers that are subsets (representative portions) of an entire population. Since 35 states were chosen out of 45 states, the average area of the 35 states is a statistic and not a parameter.

Answer:

4.5cm

Step-by-step explanation:

Circumference = 2[tex]\pi[/tex]r

28.3=2[tex]\pi[/tex]r

28.3/2[tex]\pi[/tex]=r

4.456

The radius of the circle O is 4.5 cm.

A radius is a measure of distance from the center of any circular object to its outermost edge or boundary.

Given that, a circle having a circumference of approximately 28.3 cm, we need to find its radius,

So, Circumference = 2 π × radius

2 π × radius = 28.3

Radius = 28.3 / 2π

Radius = 28.3 / 6.28

Radius = 4.5

Hence, the radius of the circle O is 4.5 cm.

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Answer:

800= about 1.76 lbs

700= about 1.54 lbs

(there are about 453.5 grams in a pound

Step-by-step explanation:

Answer:

800 grams = 1.76  pounds

700 grams =  1.54  pounds

Step-by-step explanation:

i googled it

Answer:

|b|= 4b+15

-b=4b+15

-b-4b= 15

-5b= 15

b= 15/-5

b= -3

the ans -3

If [tex]a<0[/tex] the [tex]|a|=-a[/tex]

So

[tex]|b|=4b+15\\-b=4b+15\\5b=-15\\b=-3[/tex]

Answer:

( x +4)^2 + ( y-7)^2 = 36

Step-by-step explanation:

We can write the equation of a circle as

( x-h)^2 + ( y-k)^2 = r^2

where ( h,k) is the center and r is the radius

( x- -4)^2 + ( y-7)^2 = 6^2

( x +4)^2 + ( y-7)^2 = 36

Answer:

(x+4)[superscript]2 + (y-7)[superscript]2 = 36

Answer:

Below

Step-by-step explanation:

The quadratic equations form is:

● ax^2+bx+c

Using the zeroes, we can write a factored form.

● a (x-x') (x-x")

x and x' are the zeroes

■■■■■■■■■■■■■■■■■■■■■■■■■■

●y = a (x-x') (x-x")

x' and x" are khown but a is not.

We are given a point so replace x and y with its coordinates to find a.

So the steps are:

● 1) Write the factored form of the quadratic equation

● 2) replace x' and x" with their values.

● 3) replace x and y with the coordinates of a khwon point.

● 4) solve the equation for a.

The steps are write the factored form of the quadratic equation then, replace x' and x" with their values. To replace x and y with the coordinates of a known point. To solve the equation for a.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Using the zeroes, we can write a factored form;

a (x-x') (x-x")

x and x' are the zeroes

y = a (x-x') (x-x")

x' and x" are known but a is not.

We are given a point so replace x and y with their coordinates to find a.

So the steps are:

1) Write the factored form of the quadratic equation

2) To replace x' and x" with their values.

3) To replace x and y with the coordinates of a known point.

4) To solve the equation for a.

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Answer:

15.2 inches

Step-by-step explanation:

a^2 + b ^2= c^2

5^2 + b ^2=16^2

b ^2=256 - 25

√b ^2=√231

b= 15.2 inches

Answer:

15.2

Step-by-step explanation:

Answer:

3.5 yards of fabric

Step-by-step explanation:

Find 2/3 of 5 1/4:

5 1/4(2/3)

= 3.5 yards of fabric

Answer:

Option D - Because the Z* was only a little bigger than the Zc, the test supports the null hypothesis and we conclude μ = 10

Step-by-step explanation:

In z-value problems, the normal practice is that If the calculated z-value is less than the critical z-value, we will reject the null hypothesis and accept the alternative hypothesis but if it's greater than the critical z-value, we will fail to reject the null hypothesis and say that the test was not statistically significant.

In this problem, the calculated z-value of -1.49 is greater than -1.645, so we will fail to reject the null hypothesis and say that the test was not statistically significant.

Thus, in this question, we fail to reject the null hypothesis because the calculated value of z was bigger the value of z_c.

Complete Question:

Mike took clothes to the cleaners three times last month.​ First, brought 4 shirts and 1 pair of slacks and paid ​$11.45. Then brought ​7 shirts, 2 pairs of​ slacks, and 2 sports and paid ​$35.39. ​Finally, brought 5 shirts and 2 sports and paid ​$21.43 . How much was charged for each​ shirt, each pair of​ slacks, and each sports​ coat?

Answer:

The charges

For each Shirt = $1.49

For each pair of slacks = $5.49

For each sports coat = $6.99

Step-by-step explanation:

Let Shirt = a

Let pair of slacks = b

Let sports coat = c

First, brought 4 shirts and 1 pair of slacks and paid ​$11.45

= 4a + b = 11.45 ..........Equation 1

b = 11.45 - 4a

Then brought ​7 shirts, 2 pairs of​ slacks, and 2 sports and paid ​$35.39

= 7a + 2b + 2c = 35.39.........Equation 2

5 shirts and 2 sports and paid ​$21.43

5a + 2c = 21.43............Equation 3

Hence:

4a + b = 11.45 ..........Equation 1

7a + 2b + 2c = 35.39.........Equation 2

Using elimination method

Multiply Equation 2 by the coefficient of b = 1 in Equation 1

Multiply Equation 1 by the coefficient of b = 2 in Equation 2

8a + 2b = 22.9 .......Equation 4

7a + 2b + 2c = 35.39.........Equation 2

Subtracting Equation 2 from Equation 4

= a - 2c = -12.49 ........Equation 5

a = -12.49 + 2c

Subtituting -12.49 + 2c for a in Equation 3

5a + 2c = 21.43............Equation 3

5(-12.49 + 2c) + 2c = 21.43

= -62.45 + 10c + 2c = 21.43

Collecting like terms

10c + 2c = 21.43 + 62.45

12c = 83.88

c = 83.88/12

c = 6.99

5a + 2c = 21.43............Equation 3

Substituting 6.99 for c in Equation 3

5a + 2(6.99) = 21.43

5a + 13.98 = 21.43

5a = 21.43 - 13.98

5a = 7.45

a = 7.45/5

a = 1.49

4a + b = 11.45 ..........Equation 1

Substituting 1.49 for a in Equation 1

4(1.49) + b = 11.45

b = 11.45 - 4(1.49)

b = 11.45 - 5.96

b = 5.49

Therefore, since the charges

For each shirt = a

The charges for each Shirt = $1.49

For each pair of slacks = b

The charges for each pair of slacks = $5.49

For each sports coat = c

The charges for each sports coat = $6.99

Answer:

around 16 minutes. you partition an hour and a half (all out) by what number of sections he read (5.5

Step-by-step explanation:

Answer:

  C.  70°

Step-by-step explanation:

The inscribed angle marked 15° intercepts an arc that is double that measure, so the intercepted arc on the right is 2×15° = 30°.

The external angle marked 20° is half the difference of the intercepted arcs, so is ...

  20° = (1/2)(x - 30°)

  40° = x - 30° . . . . . . multiply by 2

  70° = x . . . . . . . . . . . add 30°

The value of x is 70°.

Answer:

The score is  [tex]x = 1884[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 1500[/tex]

     The standard deviation is  [tex]\sigma = 300[/tex]

From the question we are told that the score follow a normal distribution

i.e     [tex]X \~ \ N( 1500 , 300)[/tex]

The proportion of score in the top 10% is mathematically

           [tex]P(X > x ) = P( \frac{X - \mu}{\sigma } > \frac{x - \mu}{\sigma } ) = 0.10[/tex]

Where x is the minimum score required to be in the top 10%

Now the [tex]\frac{X - \mu}{\sigma } = Z (The \ Standardized \ value \ of \ X)[/tex]

  So

            [tex]P(X > x ) = P( Z > \frac{x - \mu}{\sigma } ) = 0.10[/tex]

So

            [tex]P(X > x ) = P( Z > \frac{x - 1500}{300} ) = 0.10[/tex]

So the critical value of  0.10  from the normal distribution table is  [tex]Z_{0.10} = 1.28[/tex]

So

               [tex]\frac{x - 1500}{300} = 1.28[/tex]

              [tex]x = 1884[/tex]

Answer:

3800 meters

Step-by-step explanation:

Answer:

2.8 < x < 5.4

Step-by-step explanation:

Given the triangle with two known sides, 4.1 and 1.3, the range of possible values of the third side, x, can be ascertained by considering the triangle inequality theorem.

According to the theorem, when you add any two of the angles in a triangle, it should give you a value greater than the third side.

If a, b, and c are 3 sides of a triangle, the theorem implies that:

a + b > c.

Therefore, a - b < c < a + b

We can use this logic to find the possibly values of x in the given triangle above.

Thus,

4.1 - 1.3 < x < 4.1 + 1.3

2.8 < x < 5.4

Range of possible sizes of x is 2.8 < x < 5.4

Greetings from Brasil...

The TV format is 4:3.

4 ÷ 3 = 1.33...

Let's assign the smallest side of the TV screen as X. Since the ratio between the sides is 4:3 = 1.33, then the other side (the largest) will be 1.33 times larger than the smaller side X, that is

smaller side  = X

bigger side = 1.33X

The diagonal expression of the rectangle is:

D = √(base² + height²)

35" = √[(1.33X)² + X²]

35" = √(1.7689X² + X²)       squaring both members

(35")² = 1.7689X² + X²

1225" = 2.7689X²

X² = 1225/2.7689

X² = 442.414

X = √442.414

X ≅ 21"

Tthe bigger side:

1.33X

1.33 · 21 ≅ 28"

Rectangle Area = base × height

Rectangle Area = 28 × 21

Answer:

x = 17/5

y = -2/5

Step-by-step explanation:

2x + 2y = 6

3x - 2y = 11

sum both equations results

5x + 0 = 17

x = 17/5

2x + 2y = 6

2*17/5 + 2y = 6

34/5 + 2y = 6

2y = 6 - 34/5

2y = 30/5 - 34/5

2y = -4/5

y = (-4/5)/2

y = -2/5

verify:

3x - 2y = 11

3*17/5 - 2*-2/5 = 11

51/5 + 4/5 = 55/5

51 + 4 = 55

Answer:

The standard deviation is  [tex]\sigma = 24.10[/tex]

Step-by-step explanation:

From the question we are told that

     The proportion of those that suffer from insomnia is  p  =  6%  =  0.06

      The  sample size is  n =  10300

Generally the proportion of those that do not suffer from  insomnia is mathematically represented as

               [tex]q = 1-p[/tex]

substituting values

               [tex]q = 1 -0.06[/tex]

               [tex]q = 0.94[/tex]

Generally the standard deviation is mathematically evaluated as

         [tex]\sigma = \sqrt{n * p * q }[/tex]

substituting values

         [tex]\sigma = \sqrt{ 10300 * 0.06 * 0.94 }[/tex]

        [tex]\sigma = 24.10[/tex]

Using the binomial probability concept, the standard deviation of the number of people who suffer from insomnia is 24.10

Recall :

Substituting the values into the equation :

[tex] standard \: deviation, σ = \sqrt{10300 \times \: 0.06 \: (1 - 0.06)} [/tex]

[tex] standard \: deviation, σ = \sqrt{10300 \times \: 0.06 \: 0.94} [/tex]

[tex] standard \: deviation, σ = \sqrt{580.92} = 24.10[/tex]

Hence, the standard deviation is 24.10.

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Answer:

8×8×8×8×8

= 8^5

because there are five 8 number

I hope this helps

if u have question let me know in comments ^_^

[tex]8\cdot8\cdot8\cdot8\cdot8=8^5[/tex]

Answer:

B. y = –2.9x + 13.5

Step-by-step explanation:

You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is

y = a + bx, where a is the y intercept and b is the slope.

To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.

x    y    xy    x²  

1  .  11 = 11 → x² = 1² = 1

2 .  8 = 16 → x² = 2² = 4

3 .  4 = 12 → x² = 3² = 9

4 .  1 = 4 → x² = 4² = 16

5 .  0 = 0 → x² = 5² = 25

Total x = 1 + 2 + 3 + 4 + 5 = 15

Total y = 11 + 8 + 4+ 1 + 0 = 24

Sum of xy = 11 + 16 + 12 + 4 + 0 = 43

Sum of x² =  1 + 4 + 9 + 16 + 25 = 55

n = 5

So b =  5 (43) - (15) . (24) / 5 (55) - 15² = -2.9

a =  y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5

Answer:

x=9/2

Step-by-step explanation:

Let's solve your equation step-by-step.

5x+4(−x−2)=−5x+2(x−1)+12

Step 1: Simplify both sides of the equation.

5x+4(−x−2)=−5x+2(x−1)+12

5x+(4)(−x)+(4)(−2)=−5x+(2)(x)+(2)(−1)+12 (Distribute)

5x+−4x+−8=−5x+2x+−2+12

(5x+−4x)+(−8)=(−5x+2x)+(−2+12) (Combine Like Terms)

x+−8=−3x+10

x−8=−3x+10

Step 2: Add 3x to both sides.

x−8+3x=−3x+10+3x

4x−8=10

Step 3: Add 8 to both sides.

4x−8+8=10+8

4x=18

Step 4: Divide both sides by 4.

4x/4=18/4

x=9/2

Answer:

[tex]\boxed{\sqrt{65}}[/tex]

Step-by-step explanation:

Magnitude is solved with the following equation: [tex]\sqrt{x^{2}+y^{2}}[/tex]

Therefore, just plug in your x and y-values and solve.

[tex]\sqrt{4^{2}+7{^{2}}[/tex]

[tex]\sqrt{16 + 49}[/tex]

[tex]\sqrt{65}[/tex]

Because [tex]\bold{\sqrt{65}}[/tex] cannot be simplified further, this is the magnitude of the vector.

Answer:

The equation is [tex]x(t) = -13 cos (8 \pi t )[/tex]

Step-by-step explanation:

From the question we are told that

      The  amplitude is  [tex]A = 13 \ in[/tex]

       The period is  [tex]T = 0.25[/tex]

Generally the displacement function for a simple harmonic motion is mathematically represented as

        [tex]x(t) = A cos (wt )[/tex]

Here  [tex]w[/tex] is the angular frequency which is mathematically represented as

          [tex]w = \frac{2 \pi }{T}[/tex]

substituting values

          [tex]w = \frac{2 \pi }{ 0.25}[/tex]

          [tex]w = 8\pi[/tex]

Given that at t =  0  the displacement is equal to 0 it means that there is no phase shift and also  we are told that it is initially moving downward which implies that its Amplitude is  [tex]A = -13\ in[/tex]

So the equation modeling the displacement d as a function of time t is mathematically represented as

          [tex]x(t) = -13 cos (8 \pi t )[/tex]

Answer:

0.572

Step-by-step explanation:

From the question,

We have

n = 1090 of US adults

x = 623 selected from this population at random who consider the occupation to be one of great prestige

So we have that

The probability of X = x/n

= 623/1090

= 0.572

We conclude that 0.572 is the probability that a US adult selected at random thinks the occupation has great prestige.

Answer:

The circumference is 50.24 in. and the area is 200.96 in².

Step-by-step explanation:

The circumference formula is C = 2πr where C = Circumference, π = pi and r = radius. We know that r = 8 and π = 3.14 and that we're solving for C, so we can substitute those values into the equation to get C = 2 * 3.14 * 8 = 50.24 in.

The area formula is A = πr² where A = Area, π = pi and r = radius. Again, we're solving for A and we know that r = 8 and π = 3.14 so A = 3.14 * 8² = 3.14 * 64 = 200.96 in².

Answer:

The circumference is 50.24 in. and the area is 200.96 in².

Step-by-step explanation:

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