Simplify to one trigonometric expression.
4 sin
()2 cos()

1/2 - 5i/4 is the simplified form of the expression ( 5 + 2i ) / 4i.

Given the expression in the question;

( 5 + 2i ) / 4i

To simplify, multiply the numerator and denominator by the conjugate of 4i

( 5 + 2i ) / 4i

( 5 + 2i ) × i / 4i × i

( 5 + 2i )i / 4ii

Apply distributive property

( 5i + 2ii ) / 4ii

Not that i × i = i² = -1

( 5i + 2i² ) / 4i²

( 5i + 2( -1 ) ) / 4( -1 )

( 5i - 2 ) / -4

( -2 + 5i ) / -4

Split the fraction

-2/-4 + 5i/-4

1/2 - 5i/4

Therefore, the simplified form is 1/2 - 5i/4.

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The value of the test statistic when the engineer has designed a valve is -2.83.

From the information, the following can be deduced:

Sample mean = 5.8

Population mean = 6.0

Population standard deviation = 1

Significance level = 0.02

(Sample mean - Population mean) /(Standard Deviation / ✓200)

= (5.8 - 6.0) / (1 / ✓200)

= -0.2 ✓200

= -2.83

The value is -2.83.

It's important to note that the test statistic is the z value. This will be:

=

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The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5).

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

The given point K(-2,-5)

If we reflect a point(x,y) along the y-axis then the coordinate after reflection converts as K'(-x,y)

The reflection of K(-2,-5) along the y-axis will be  K'(2,5).

Hence "The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5)".

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The year for which the population of the small town is 11,511 is; Choice B; 1958.

It follows from the task content that the year for which the population of the small town in discuss becomes 11,511 be determined.

Given the function: P = 2,511 + 500t

11,511 = 2511 + 500t

9,000 = 500t

t = 9,000 / 500

t = 18 years.

Hence, the year in which case the population of the small town is; 11,511 is; 1940 + 18 = 1958.

Therefore, the year in which the population of the small town in discuss becomes 11,511 as required in the task content is Choice B; 1958 is correct.

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⇒ let us first write the given equation in the form

[tex]ax^{2} +bx+c=0[/tex]

⇒[tex]49x^{2} -64=0[/tex]

⇒ Note in this case bx=0

Let us factorize the equation...49 is a square number and 64 is also a square number ..This equation is a difference of two squares which can be written as:

[tex](7x-8)(7x+8)=0[/tex]

⇒The answer is (7x-8)(7x+8)=0

Answer:

1) find the point on the function where it crosses the x-axis

2) find the set of values where x = 0

3) set x = 0 and solve for y; then put the two values into a coordinate pair

Answer:

your question is cutoff, cant read it

Answer:

I believe there is supposed to be something in the the corner box (Top left).

Step-by-step explanation:

Answer:

$66

Explanation:

Sam earns a 5.5% commission on everything he sells. He sells a television for $1200. What is 5.5% of $1200?

Convert 5.5% to decimal form: 0.055. Now, multiply 1200 by 0.055.

Sam will earn $66 because 5.5% of 1200 is 66.

Step-by-step explanation:

sqrt(7) is larger than 2 (2² = 4) but smaller than 3 (as 3² is 9).

sqrt(220) is larger than 14 (14² = 196) but smaller than 15 (15² = 225).

so, the integers between them are

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

these are 12 integer values.

Point A will represent the input-output values of the function.

What is number line ?

Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.

In the graph of y = f(x),

For every x-value (input value), value of the function is the y-value (output value).

For the input value x = 2,

Output value of the function will be,

y = f(2)

Therefore, point A will represent the input-output values of the function.

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Answer:

Domain: {0 \leq x} Range {0 \leq y}

Step-by-step explanation:

btw \leq means less than or equal to

DT is congruent to TD.

A line segment is always equal to itself.

Given,

The figure;

We have to find the segments which are congruent because of the reflexive property of congruence.

Reflexive property of congruence;-

An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry. If angle A is an angle, then angle A is a congruent angle of angle A

Here,

DT = TD,

A line segment is always equal to itself.

So, DT is congruent to TD.

Congruence;-

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence.

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Step-by-step explanation:

the exponential growth function is

f(t) = v0 × (1 + k)^t

1977 to 1989 is 12 years (t).

a)

so, we have

467 = 209 × (1 + k)¹²

467/209 = (1 + k)¹²

12th root(467/209) = 1 + k = 1.069295033...

k = 0.069295033...

b)

f(t) = 209 × 1.069295033...^t

c)

2009 = 32 years after 1977

f(32) = 209 × 1.069295033...³² = $1,783.478472... ≈

≈ $1,783.48

d)

double the value of 209 is 418.

418 = 209 × 1.069295033...^t

2 = 1.069295033...^t

t = log1.069295033...(2) =

= log(2)/log(1.069295033...) = 10.34554457... ≈

≈ 10.3 years

e)

2221 = 209 × 1.069295033...^t

2221/209 = 1.069295033...^t

t = log1.069295033...(2221/209) =

= log(2221/209)/log(1.069295033...) =

= 35.27452616... years ≈

≈ 35.3 years

35 years would mean end of 2012. so, 35.3 years would be early 2013.

Answer:

The answer for number 7 is A

Step-by-step explanation:

I hope this helps

Answer:

7.25 %

Step-by-step explanation:

58 out of 800g  is    58 / 800 = .0725    which is  7.25 %

Answer:

  $920

Step-by-step explanation:

You want to know the original price of a suit on sale for $331.20, if that price represents a 64% discount.

The discounted price is found by subtracting the amount of the discount from the original price. That amount is the product of the original price and the rate of the discount.

  discounted price = price - (discount)·(price)

  discounted price = price · (1 - discount)

The the original price is ...

  price = (discounted price)/(1 - discount) = $331.20/(1 -0.64)

  price = $920

The original price of the suit was $920.00.

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Answer:

second option

Step-by-step explanation:

the solution to the system of equations is at the points of intersection of the two graphs.

the graphs intersect at (- 2, - 3 ) and (1, 0 ) , then

the solutions are (- 2, - 3 ) and (1, 0 )

The expected value of x is 10.8

Expected value is defined as the predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

Given :

x|  0       4       8       12     16

p| 0.15 0.05 0.25  0.05  0.5

The expected value of x, E(x) =Σ xp

E(x) = (0×0.15) + (4×0.05) + (8×0.25) + (12×0.05) + (16×0.5)

E(x) = 0 + 0.2 + 2 + 0.6 + 8

E(x) = 10.8

Therefore, the expected value of x is 10.8

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Periods are the rows that span the periodic table. Families or groups are the columns that go from Page 2 up.

The maximal energy level of the electrons serves as a marker for the period (or row) in the periodic table that an atom belongs to (1 through 7). The table has 7 periods, hence there are 7 energy levels. The first period's atoms have electrons in the first energy level. The second period's atoms have electrons in two different energy states. The third period's atoms have electrons in three different energy levels. The fourth period's atoms have electrons in four different energy levels. Typically, the number of the period itself is the same as the number of energy levels in each period. The first period's atoms have electrons in the first energy level.

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The missing values of the ordered pairs using the given equation are:

x = -1; y = 8

The table is:

x  | y  

-3   8

-1,   2

To find the missing values of an ordered pair that satisfies a given equation, plug n the given value of one of the variables into the equation and solve to find the value of the other variable.

The equation given is y = -3x - 1

Find the missing value of the ordered pair (-3, y) by plugging in x = -3 into the equation given:

y = -3(-3) - 1

y = 8

Find the missing value of the ordered pair (x, 2) by plugging in y = 2 into the equation given:

2 = -3x - 1

2 + 1 = -3x - 1 + 1

3 = -3x

x = 3/-3

x = -1

The ordered pairs are: (-3, 8) and (-1, 2).

Therefore, we would have:

x  | y  

-3   8

-1,   2

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Answer:      List all of the solutions.

3.75

=

1.89

=

dollar

=

3

=

Step-by-step explanation:

The 98% confidence interval limits are given by 1.6 < μ < 33.7.

What is the confidence interval in statistics?

A confidence interval is the mean of your estimate plus and minus its variation. Within a certain confidence level, this is the range of values you expect your estimate to fall between if you redo your test. In statistics, confidence is another word for probability.

Given data: 10, 32, 24, 0, 5, 27, 5, 50, 6.

Sample mean = ∑x/n = 159/9 = 17.66

Sample variance = s² = ∑(x - sample mean)²/n-1

                                   = 2206/8

                                   =  275.75

Sample standard deviation = s = [tex]\sqrt{s^2}[/tex]

                                                    = [tex]\sqrt{275.75}[/tex]

                                                    = 16.60

Significance level = α = 1 - 0.98 = 0.02

Degree of freedom (d.f.) = n - 1 = 9 - 1 = 8

Critical value = [tex]t_{{\frac{\alpha}{2}},d.f}[/tex]

                      = 2.896

Margin of error = E = critical value * [tex]\frac{s}{\sqrt{n} }[/tex]

                                = 16.03

Limits of 98% confidence level are given by:

Lower limit = sample mean - E = 17.66 - 16.03 ≈ 1.6

Upper limit = sample mean + E = 17.66 + 16.03 ≈ 33.7.

Hence, the 98% confidence interval limits are given by 1.6 < μ < 33.7.

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Answer:

Step-by-step explanation:

a. 1 hectare = 2.471 acres 

6 hectares x (2.471 acres / 1 hectare)

=14.826 acres

b. prices per acre: 150,000/14.826

=10,117.36 per acre

If an American is selected at random, the probability that he or she will disapprove or have no opinion on the issue is 33%.

Given data:

Approved human embryonic stem cell research = 67% or 0.67

Now let find the probability that the human embryonic stem cell research will be disapprove using this formula

P(disapprove or no opinion) = 1 - Approved

Let plug in the formula

P(disapprove or no opinion)  = 1 - 0.67

P(disapprove or no opinion) = 0.33 or 33%

Therefore 33% is the probability of disapprove or no opinion.

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Step-by-step explanation:

x = the original number

2x + 16 = 2/5 x

multiply both sides by 5 to get rid of the fraction :

10x + 80 = 2x

divide both sides by 2 :

5x + 40 = x

subtract x from both sides :

4x + 40 = 0

divide everything by 4 :

x + 10 = 0

subtract 10 from both sides :

x = -10

Answer : x = -10

Step-by-step explanation :

x = original number

2x + 16 = 2/5x

Change 2/5 to decimal

2x + 16 = 0,4x

Change the position of 16 and 0,4x

2x - 0,4x = -1

Subtract 2 by 0,4

1,6x = -16

Divide -16 by 1,6

x = -10

You can use this way or the other one but this way is faster than the others

Hope it helps !

The equation of the red graph is (d) y - 3 = f(x)

Graph

Graph means the pictorial representation of statistical data or of a functional relationship between variables.

Given,

Here we have the graph with black and red lines in it.

Now, we need to find the equation for the red line.

While we looking through the potions we have identified that the first two options are not in the proper equation form.

So, we have to check only the (c) and (d) equation, to identify which one is the suitable one.

In order to find the correct function, we have to identify the points in it.

Here we have the points in the red line are (-6,1), (-2,4) and (-1,-4)

Now, we have to apply these values on the equation to find which one will produce the correct x value for the given y value,

First, we have to take the option (c) y + 3 = f(x)

-6 + 3 = 1

-3 ≠ 1

So, this one is not applicable.

Next, we have to take the function (d) y - 3 = f(x)

When we apply the value on it,

-1 -3 = -4

-4 = -4

Therefore, this is the function for the given graph.

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Answer:

3/12 or 40%

not 10000% sure on this tho

Answer:

y = 0.4x

Step-by-step explanation:

given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 4 when x = 10 , then

4 = 10k ( divide both sides by 10 )

[tex]\frac{4}{10}[/tex] = k , that is

k = 0.4

y = 0.4x ← equation of variation

By using concept of ratio, it can be calculated that

100 boys attended the camp

What is ratio?

Ratio between two numbers determines how much one number is greater than the other.

The first part of the ratio is called antecedent and the second part of the ratio is called consequent.

Here, concept of ratio will be used

Let the number of boys be 4x and the number of girls be 6x

There were 50 more girls than boys

By the problem,

6x - 4x = 50

2x = 50

[tex]x = \frac{50}{2}[/tex]

x = 25

Number of boys who attended the camp = 4 [tex]\times[/tex] 25 = 100

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