Write equivalent fractions for
2/3
and
5/12
using the least common denominator.

−32i is the answer if you use DeMoivre's theorem to find (1−i)^10.

A formula for determining the powers of complex numbers is provided by De Moivre's theorem. It might be easier to comprehend de Moivre's theorem if we first look at what happens when we multiply a complex number by itself. This illustrates how the argument is multiplied by two and the absolute value is squared when squaring a complex number.

One of the most important and useful theorems in the study of complex numbers is DeMoivre's Theorem, which combines trigonometry with complex numbers. It's also helpful to find relationships between trigonometric functions at different angles. The name of the theorem pays homage to the well-known mathematician De Moivre, who made several contributions to mathematics, notably in the areas of probability theory and algebra. Attached below is the answer.

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Shana bought  5 bags of popcorn and 2 bottles of soda.

What is an equation?

An equation is consist of two expressions. At least one of the expression contain a variable.

Given that, the cost unit bottle of soda is $3.

The cost of unit bag popcorn is $4.

Assume that she bought s number of soda bottle and p number of bags of popcorn.

Then the cost of s number of soda bottle is $3s.

The cost of p number of bags of popcorn $4p.

She spent $26 in total.

Therefore

3s + 4p = 26.....(i)

She bought 7 things from the shop.

Therefore,

s + p =7 .....(ii)

Solve equation (i) and (ii) by using elimination method:

Multiply equation (ii) by 3 and subtract it from (i)

3s + 4p = 26.

3s + 3p =21

(-)   (-)      (-)

_________

        p = 5

Putting p = 5 in equation (ii)

s + 5 = 7

s = 2

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Answer:

(4) (-1,6)

Step-by-step explanation:

f(x) = x² - 3x + 4

1) (0,4) ==>x=0 and f(x)=4

4 = 0² - 3(0) + 4

4 = 0 + 4

4 = 4 ==> true X

2) (1.5,1.75)==> x=1.5 and f(x)=1.75

1.75 = (1.5)² - 3(1.5) + 4

1.75 = 2.25 - 4.5 + 4

1.75 = 2.25 - 0.5

1.75 = 1.75 ==> true  X

3) (5,14)

14 = (5)² - 3(5) + 4

14 = 25 - 15 + 4

14 = 10 + 4

14 = 14  ==> true X

4) (-1,6)

6 = (-1)² - 3(-1) + 4

6 = (|-1|)² - (-3) + 4  ==> the square of a negative number is equal to the square

                              of the absolute value of that number since the square of

                             a real number is always positive

6 = (1)²+ 3 + 4  ==> subtracting a negative number is equivalent to adding

                          the positive number

6 = 1 + 3 + 4

6 = 4 + 4

6 = 8  ==> false √√

Hence, the answer is (4) (-1,6).

Answer:

Domain:  (-∞, 1) ∪ (1, ∞)

Range:  (-∞, -2) ∪ (2, ∞)

Yes, it's a function.

Step-by-step explanation:

Information

The domain of a function is the set of all possible input values (x-values).

From inspection of the given graph:

Therefore, the domain is all values of x except x = 1:

The range of a function is the set of all possible output values (y-values).

From inspection of the given graph:

Therefore, the range is all values of y except between -2 and 2:

A function is a special type of relationship where each input (x-value) is related to exactly one output (y-value).

From inspection of the graph, as the two points where x = 1 are not included, each value in the range (y-values) corresponds to exactly one value in the domain, and so it is a one-to-one function.

The f(4) using is found using newton's interpolating polynomials of order 4.

function y=CL10_Exercise(part)

%% Input

% part: string for part a,b,c,d

%

%% Output

% y value of the underlying function at x=4

%

%% Write your code here

X=[1,2,3,5,6];

Y=[15,8,5.5,30,52];

x=4;

y=1;

switch part

case 'a'

%% Newton interpolation (Order 4)

a=X;

b=Y;

%x=input('Enter x: ');

[m,n]=size(a);

fx=0;

for i=1:n

%_____________Calculating Dividing Difference_____________________

s=0;

for j=1:i

p=1;

for k=1:i %Denominator part product

if(k~=j)

p=p*(a(j)-a(k));

end

end

s=s+b(j)/p; %summation f(x)/product

end

%_________________________________________________________________

p=1;

for j=1:i-1 %coefficient part of f[...]

p=p.*(x-a(j));

end

fx=fx+s.*p; %Polynomial!

end

y=fx;

case 'b'

%% not-a-knot spline

case 'c'

%% clamped spline

case 'd'

%% Hermite spline

end

end

Hence, the f(4) using is found using newton's interpolating polynomials of order 4.

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The variable y takes the value -7 when we have x = -3.

Here we have the linear equation:

y = x - 4

We want to find the value of x such that y = -7, to get that, we only need to replace the variable y by the number -7 in the linear equation above:

-7 = x - 4

Now we can solve the linear equation for x.

-7 = x - 4

-7 + 4 = x

-3 = x

That is the solution.

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Answer: D:22,

14,040-12,500=1540.  

1540/70 = 22

The number of miles that a signal sent from Station 1 to the satellite and then to Station 2 will have to travel is; 48135 miles

Let us first find the distance from Station 1 to the satellite:

Using trigonometric ratio, we have;

tan 8.7 = length of longest leg/length of shortest leg

Thus;

tan 8.7 =  3963/length of longest leg

Length of longest leg = 3963/tan8.7°

Length of longest leg = 3963/0.15302150298

Length of longest leg = 25,898 miles

Distance from Station 2 to satellite:

Using trigonometric ratio again, we have;

sin 8.7 = length of longest leg/ length of hypotenuse

sin  8.7 =  3963/length of hypotenuse

Length of hypotenuse =3963/ sin 8.7

Length of hypotenuse =3963/0.1526082024

Length of hypotenuse = 26, 200 miles

Thus, the difference is;

26200 - 3,963 = 22237 miles

Total distance will calculated as;

25898 miles  + 22237 miles = 48135 miles

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The complete question is:

A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles.

How many miles will a signal sent from Station 1 to the satellite and then to Station 2 have to travel?

Answer:

1/4 as a percent is 25%

25% as a decimal is .25

Step-by-step explanation:

1/4 is one quarter, .25

25%, move the decimal to the left twice

25----> 2.5------> .25

The no: of solutions that the equation -1/2(-8x+14) = 3x +9+x  has is 1

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

The no: of solutions that the equation is -1/2(-8x+14) = 3x +9+x is 1

as the equation is 1 degree polynomial.

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The time required = 4 hours

The time required by the car to move at a speed of 50 mph to reach a distance of 200 miles is 4 hours

What is Speed?

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the distance traveled by the car be = D

Now , the speed S of the car = 40 miles per hour

The time required by the car to travel D distance is T = 5 hours

So , the Distance D is calculated from the formula

Distance D = Speed S x Time T

So , substituting the values in the equation , we get

Distance D = 40 x 5

Distance D = 200 miles

Now , the distance traveled by the car remains the constant

The speed of the car is S = 50 miles per hour

And let the time taken by the car to cover 200 miles at 50 mph be = T

Now to calculate Time T ,

Time T = Distance D / Speed S

Substituting the values in the equation , we get

Time T = 200 / 50

Time T = 4 hours

Therefore , the value of T is 4 hours

Hence , The time required by the car to move at a speed of 50 mph to reach a distance of 200 miles is 4 hours

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a) With 98% confidence interval, the mean height of all college students is between 173.743 centimeters and 175.257 centimeters.

b) The possible size of our error if we estimate the mean height of all college students to be 174.5 centimeters is 0.976.

a) We want to construct a 98% confidence interval for the mean height of all college students.

Number of sample, n = 450

Mean, u = 174.5 centimeters

Standard deviation, s = 6.9 centimeters

For a confidence level of 98%, the corresponding z value is 2.33. This is determined from the normal distribution table.

We will apply the formula

Confidence interval = mean ± z × standard deviation/√n

It becomes

174.5 ± 2.33 × 6.9/√450

= 174.5 ± 2.33 × 0.325

= 174.5 ± 0.757

The lower end of the confidence interval is 174.5 - 0.757 =173.743

The upper end of the confidence interval is 174.5 + 0.757 =175.257

Therefore, with 98% confidence interval, the mean height of all college students is between 173.743 centimeters and 175.257 centimeters.

(b) The possible size of our error if we estimate the mean height of all college students to be 174.5 centimeters:

Thus, Error would be:

σ /√n

= 6.9/√50

= 0.976

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The equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].

What is perpendicular lines?

When two geometric objects intersect at a right angle, they are considered to be perpendicular in elementary geometry. By using the perpendicular symbol,, the condition of perpendicularity can be graphically represented. Between two lines, a line and a plane, or between two planes can be used to define it.

Consider the given equation of line

5x + 4y = 10

Convert it into the form y = mx + c

⇒ 4y = -5x + 10

y = -5/4x + 10/4

y = -5/4x + 5/2

Here the slope of line is, -5/4.

The slope of perpendicular line is negative reciprocal of the slope of given line.

So, the slope of perpendicular line is,

[tex]-\frac{1}{(-5/4)} = \frac{4}{5}[/tex]

Also the line passes through the point (5, -4).

By using the point slope form to find the equation of line

[tex]y-y_1 = m(x-x_1)\\y-(-4) = \frac{4}{5}(x-5)\\ y+4=\frac{4}{5}x - 4\\ y = \frac{4}{5}x - 4 - 4\\ y = \frac{4}{5}x - 8[/tex]

Hence, the equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].

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The minimum value, Q1, Median, Q3 and maximum value of the data are 2, 5, 12, 14 and 16 respectively

Given the data: 2, 4, 4, 5, 8, 10, 12, 12, 12, 13, 14, 14, 15, 16

The minimum value of the data is 2. Thus, Min = 2

The maximum value of the data is 16. Thus, Max = 16

The median is the data value in the middle.

2, 4, 4, 5, 8, 10, 12, 12, 12, 13, 14, 14, 15, 16

So the median (Q2) of the data is (12+12)/2 = 12. Thus, Med = 12

Consider the values to the left of the median with one of the median numbers included (since we have numbers in the middle):

2, 4, 4, 5, 8, 10, 12

Find the median of this set of numbers. The median is 5.  Q1 = 5

Also, consider the values to the right of the median with one of the median numbers included: 12, 12, 13, 14, 14, 15, 16. The median is 5. Q3 = 14

To create a box and whiskers plot use Min, Max, Q1, Median(Q2) and   Q3 (Check the attached image)

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Answer:

solve for N cause that is the only variable

Step-by-step explanation:

By using the concept of algebraic expression, it can be concluded that

The expression will be equal for all real numbers except -6

First option is correct.

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

The given rational expression in simplified form is

[tex]\frac{(x-2)(x+6)}{7(x+6)} = \frac{x-2}{7}[/tex]

For x = -6, the denominator of the left hand side is zero

So the expression on the left hand side is undefined for x = -6

So the expression will be equal for all real numbers except -6

First option is correct.

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Answer:

Answer Option A: AA Postulate

Answer: T  = 1

Step-by-step explanation:

As 6/9 is equivalent to 2/3, then 1/1.5 is similar to 10/15, which is also 2/3

Answer:

t = 1

Step-by-step explanation:

Given equation,

→ (6/9) = (t/1.5)

Now the value of t will be,

→ (6/9) = (t/1.5)

→ (t/1.5) = (6/9)

→ t = (6/9) × 1.5

→ t = (6 × 1.5)/9

→ t = 9/9

→ [ t = 1 ]

Hence, the value of t is 1.

Answer:

Step-by-step explanation:

Hello...

y=x-8

2x+y=-5 -> y=-2x-5

subsitution

-2x-5=x-8

3x=3

x=1

y=x-8

y=1-8

y=-7

(1,-7)

Answer:

d>9

Step-by-step explanation:

You need to do inverse operations to isolate the variable (d)

3d-6>21

get ride of the six by doing its inverse. The opposite of subtraction is addition so you'd add 6 to both sides. this moves the six to the other side of the inequality sign

3d>27

now that the variable is isolated the final step is to divide by the coefficient (3). 3/3 is 1, effectively giving you d, and 27/3=9

d>9

in this case you do not flip the sign as you did not divide by a negative

Answer:

Step-by-step explanation:

The fourth image because when looking for liner equations if you draw a line through them and it only touches once its linear equation!

sorry if im wrong...  

The probability that Lamar and Lawrence finish their jobs within 5 minutes of each other on a randomly selected day is 0.2892

Consider the time for the Lamar to finish the job as x and the time for the Lawrence to finish the job as x

Consider the random variable x-y

x-y normal with mean = 105 - 98

= 7

Similarly the variance of the random variable x-y

= 105 + 225

= 325

The standard deviation = [tex]\sqrt{325}[/tex]

= 18.03

Here we have to find the probability that Lamar and Lawrence  finish their jobs within 5 minutes of each other on a randomly selected day

P(|x-y|<5) = P(-5<U<5)

Now we have to convert to standard normal variate Z

Then the it will be

(-5-7)/18.03 = -0.67

(5-7) / (18.03)= 0.11

The probability of the given condition will be

P(-0.67<Z<0.11) = 0.2454 + 0.0438

Add the terms

= 0.2892

Therefore, the probability is 0.2892

The complete question is:

Lamar and Lawrence run a two-person lawn-care service. they have been caring for Mr. Johnson's very large lawn for several years, and they have found that the time it takes Lamar to mow the lawn itself is approximately normally distributed with a mean of 105 minutes and a standard deviation of 10 minutes. meanwhile, the time it takes for Lawrence to use the edger and string trimmer to attend to details is also normally distributed with a mean of 98 minutes and a standard deviation of 15 minutes. they prefer to finish their jobs within 5 minutes of each other. what is the probability that this happens, assuming their finish times are independent?

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The most appropriate test to use the given situation is option (B) two sample z test

Total number of alumni were surveyed = 1046

Number of alumni attempted at least one class reunion = 653

Similarly, in public university, 791 out of 1327 sampled alumni claimed they have attended at least one class reunion.

The two sample z test is used to compare the means of two samples to see if it is feasible that they come from the same population.

The difference in the sample proportion is statistically significant

Therefore, the correct test for the situation is option (B) two sample z test

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The length of the ramp Tyree will need to make from window to the sidewalk is 5√17 feet .

In the question ,

it is given that ,

height of the window is = 5 feet ,

distance of sidewalk from the Tyree's house is = 20 feet ,

We know that the angle between the wall and the floor is 90° ,

So , the system is making a right triangle  ,

let the length of the ramp be = "x" ,

So, According to Pythagoras Theorem ,

we get ,

x² = 5² + 20²

x² = 25 + 400

x² = 425

x = √425

x = 5√17 feet .

Therefore , the length of the ramp is 5√17 feet .

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The solution of the given equation  (w² x 12) ÷ 10⋅z is obtained as (-0.64).

The stated equation is-

= (w² x 12) ÷ 10⋅z

The values are-

w = −4, x = 2, and z = −5, put in the equation-

= [(-4)² × 2)]/ [10 × -5 ]

= [16 x 2]/)-50)

= 32 / -50

= -0.64

Thus, the solution of the given equation (w² x 12) ÷ 10⋅z is obtained as (-0.64).

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The total time ran by Katie on Tuesday and Wednesday together is given by the equation A = 16.23 minutes

where A is the total time

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total time ran by Katie on Tuesday and Wednesday be = A

Now , the equation will be

The time required by Katie to run a mile on Tuesday = 8.34 minutes

The time required by Katie to run a mile on Wednesday = 7.89 minutes

So ,

Total time ran by Katie on Tuesday and Wednesday A = time required by Katie to run a mile on Tuesday + time required by Katie to run a mile on Wednesday

Substituting the values in the equation , we get

Total time ran by Katie on Tuesday and Wednesday A = 8.34 minutes + 7.89 minutes

On simplifying the equation , we get

Total time ran by Katie on Tuesday and Wednesday A = 16.23 minutes

Therefore , the value of A is 16.23 minutes

Hence , The total time ran by Katie on Tuesday and Wednesday together is A = 16.23 minutes

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The range of the graph shown is

range { y | y < 0 }

When a figure is transported from one place to another without changing its size, shape, or orientation, a translation takes place.

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The graph's entire range, from lower to upper numbers vertically, represents the range.

The translation downwards, means that the graph moved down and considering the image of the attached graph, the effect of the translation means that the range to be numbers less than zero

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Based on the permutation concept, the allowed final result is 20

Permutation method

In statistics, permutation means a mathematical calculation of the number of ways a particular set can be arranged.

Given

Here we need to find how many bit strings of length 5 do have 3 consecutive zeros such that the remaining two bits are not not equal.

Let us consider T denote the number of bit strings of length  containing 3 consecutive 0's.

Total no. of bit strings of length = 5

And the no. of bit strings of length  not containing 3 consecutive 0's = 3

Then the possible combination of permutation is calculated as,

=> T = 5!/3!

=> T = 20

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x     f(x)
0       0
-2      -4
4       -2
You need to draw y = 2 f (x-1)
So you need to choose x so that  x-1 = 0, -2, 4 then you can use the above values.
New function
x-1 = 0,              x = 1,           y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0
x-1 = -2              x = -1           y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8
x-1 = 4               x = 5            y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4
So 3 points on the new graph are   (1, 0)   (-1, -8) and (5, -4)
Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move)  y = f(x)  a units to the right.
y = f(x) to y = 2 f(x),  you dilate f(x) with center (0,0) factor 2,  so  (a,b) > (2a, 2b)
So basically here you are doing both things.
So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b).

what is graph?

A diagram or pictorial depiction of facts or values that is arranged might be referred to as a graph. The relationships between two or more items are frequently represented by the points on a graph.

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The system that contains periodic function and an absolute value function has two solution

In the given system there are two function, those are periodic function and absolute value function

The function is defined as the statement that shows the relationship between one dependent variable and other independent variables. The function consist of different types of variables numbers and the mathematical operators

The periodic function is a function that repeats its value at a regular interval of time

The absolute value function is a function that contains the mathematical expression with absolute value symbols

The system contains periodic and absolute value function and it will contains two solution

Therefore, the system has two solution

I have solved the question in general, as the given question is incomplete

The complete question is:

The system below shows a periodic function and an absolute value function. how many solutions does the system have?

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