NEED HELP PLZ!! Use the definition, identities, and properties of imaginary numbers to simplify each of the following expressions. Match each item with its correct simplest form. 1. (i 3)5 2. -i 6 · i 3 · i -5 3. -(i 4) (i 0) (i 7) 4. (i 5 · i -2 · i 8)0 Choices: 1 -1 i -i

Answer:

In the form of

Y= mx+c

Y= 1/2x +2

m = 1/2

Step-by-step explanation:

A linear equation in it's standard form is in the format

Y= mx+c

Where m is the slope and c is the y intercept

Let's use these two points to determine both the slope and the equation

(2, 3), (4,4)

Slope= (y2-y1)/(x2-x1)

Slope= (4-3)/(4-2)

Slope= 1/2

Equation of the linear function

(Y-y1)/(x-x1)= m

(Y-3)/(x-2)= 1/2

2(y-3) = x-2

2y -6 = x-2

2y= x-2+6

2y= x+4

Y= 1/2x +2

Answer:

B) 47 units²

Step-by-step explanation:

It can be done by finding the area of the black, but it will be much easier to find the area of the white and subtract.

Total area of the grid equals 10x8=80

There are two rectangles at the bottom.  6+8=14

There are 4 triangles that each equal 4.5.  4.5*4=18

There is 1 small triangle at the top that equals 1.

80-14-18-1=47

Answer:

-70[tex]\frac{73}{100}[/tex]

Hope It Help

Answer:

-1 < x ≤ 2

Step-by-step explanation:

-2 < 2x ≤ 4

Divide by 2

-2/2 < 2x/2 ≤ 4/2

-1 < x ≤ 2

Open circle at -1  line going to the right to a closed circle at 2

Answer:

The best and most correct answer among the choices provided by the question is

The statement that points out his most serious omission is "What if the electric bill increases?".

Step-by-step explanation:

Answer:

[tex] \boxed{\sf Amount \ of \ food \ each \ elephant \ receive = 510 \ pounds} [/tex]

Given:

Total amount of food = 3,570 pounds

Total number of elephants = 7

To Find:

Amount of food each elephant receive

Step-by-step explanation:

7 elephants receive = 3,570 pounds

[tex] \sf 1 \: elephant \: receive = \frac{3570}{7} \: pounds[/tex]

= 510 pounds

So,

Amount of food each elephant receive = 510 pounds

Answer:

[tex]\frac{28x}{9}[/tex]

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

[tex]\frac{8x}{3} /\frac{6}{7}[/tex]

Step 2: KCF (Keep Change Flip)

[tex]\frac{8x}{3} (\frac{7}{6})[/tex]

Step 3: Multiply

[tex]\frac{56x}{18}[/tex]

Step 4: Simplify

[tex]\frac{28x}{9}[/tex]

Answer:

28x/9

Step-by-step explanation:

Dividing a fraction by fraction is the same as multiplying a fraction by the other fraction's reciprocal:

Here is the formula:

[tex]\frac{x}{y} / \frac{a}{b} = \frac{x}{y} * \frac{b}{a}[/tex]

Thus, [tex]\frac{8x}{3} / \frac{6}{7} = \frac{8x}{3} * \frac{7}{6}[/tex]

8x * 7 = 56x and 3* 6 is 18, so:

[tex]\frac{56x}{18}[/tex]

It can be further simplified by dividing both numerator and denominator by 2:

[tex]\frac{28x}{9}[/tex]

Answer: 0.08 yards

Step-by-step explanation: 1 centimeter equals to about  0.01 yards. You have to multiple 0.01 to 8 and it will give 0.08 yards.

Answer:

x = 0,087489064

Step-by-step explanation:

1 cm =  0.010936133 yards

8 cm = x

x = 8 cm x 0.010936133 yards/ 1 cm

x = 0,087489064

Answer:

C) 13

Step-by-step explanation:

A on the number line is about -5 and B is 8. Act as if there wasn't a negative sign in front of the 5. Add the two numbers together the get the distance.

I would have to say its AB<----

But im not 100% sure I wish you luck.

Answer:

See the attachment for formatted formulas

Step-by-step explanation:

Let X11, X12, ……,X1n  and X21 , X22……., X2n be two small independent random samples from two normal populations with means u1 and u2  and the standard deviations σ1 and σ2 respectively. If σ1= σ2 (=σ) but unknown then the unbiased pooled or combined estimate of the common variance σ2 (the term variance means that each population has the same variance) is given by

Sp2  = ((n_1-1)  s_(1^2 )+ (n_2-1) s_2^2)/(n_1+n_2-2)

Where

S12 = 1/(n_1- 1) ∑▒〖 (X_1i- X`_1)〗^2  and

S22 = 1/(n_2- 1) ∑▒〖 (X_2j- X`_2)〗^2

The test statistic

t = ((X_1`-X_2`)- (μ_1- μ_2))/(√(s_p&1/n_1 )+ 1/n_2 )

Has t distribution with v= n1 + n2 – 2 degrees of freedom.

It is used as a test statistic for testing hypotheses about the difference between two population means.

The procedure for testing hypothesis H0: μ_1- μ_2= ∆_0 in case of small independent samples when σ_1= σ_2 is as follows.

H0: μ_1- μ_2= ∆_0  against the appropriate alternative.

t = ((X_1`-X_2`)- ∆_0  )/(√(s_p&1/n_1 )+ 1/n_2 )

Which has t distribution with v= n1 + n2 – 2 degrees of freedom.

Answer:

(C.) d= sqrt (x2-x1)^2+(y2-y1)^2, where d is the distance between points (x1,y1) and (x2,y2).

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{\mathrm{C }}[/tex]

Step-by-step explanation:

[tex]\sf The \ distance \ formula \ is \ given \ as:[/tex]

[tex]d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2 }[/tex]

[tex]d \Rightarrow \sf distance[/tex]

[tex](x_1,y_1) \Rightarrow \sf Coordinates \ of \ the \ first \ point[/tex]

[tex](x_2,y_2) \Rightarrow \sf Coordinates \ of \ the \ second \ point[/tex]

Answer:

6214

Step-by-step explanation:

you round up 62 and 4 20 times and that is your answer but for give me if this answer wrong

Answer:

Length of square cut = 1.569 inches

Step-by-step explanation:

given data

Length of cardboard = 12 inches

Breadth of cardboard = 8 inches

solution

we will consider here side of the square = x

when we cutting out the square then there Length and breadth of candy box will be

Length of box = (12 - x - x)

Length of box = (12 - 2x) inches.

and

Breadth of box = (8 - x - x)

Breadth of box = (8 - 2x) inches.

and Height of candy box  wil be = x inches

so

Volume of a cuboid = L × b × h    .....................1

Volume of a cuboid = (12 - 2x) × (8 - 2x) × x

Volume of a cuboid = 96x - 40x² + 4x³

now we Differentiate with respect to x

V' = 96 - 80x + 12x²

and for maximum volume we put V' = 0

0 = 96 - 80x + 12x²

solve it we get

x = 5.097

x = 1.569

when x = 5.097 inches

Breadth of candy box = 8 - 10.194 = -2.194 inches

but we know breadth never be negative,

so we take

Length of square cut = 1.569 inches

Answer:

(0, 0) is a saddle point

(1, 1) is a local minimum

(-1, -1) is another point  of local minimum

Step-by-step explanation:

We first locate the critical points. In order to get the critical points we need to find the first derivatives and then set them to zero.

f(x, y) = x⁴ + y⁴ - 4 xy + 1  

Find the first derivatives wrt to x and y

[tex]f_{x}(x,y)[/tex] = 4x ³ - 4y  --> (1)

[tex]f_{y}(x,y)[/tex] = 4y³ - 4x  --> (2)

Solve (1) for y

4x ³ - 4y = 0

x ³ = y

y = x ³ ---> (3)

Solve (2) for x

4y³ - 4x = 0

4y³ = 4x

y³ = x

x = y³  ----> (4)

Plug  (3) into (2)

4y³ - 4x

4(x ³)³ - 4x = 0

4x⁹ - 4x = 0

4x (x ⁸ - 1) = 0

4x (x ⁴ - 1)(x⁴  + 1) = 0

4x (x ² - 1)(x ² + 1)(x ⁴ + 1) = 0

4x (x - 1)(x + 1)(x ² + 1)(x ⁴ + 1) = 0

So

x = 1 , -1 , 0

In order to find values of y, Plug each x value in (3)

For

x = 0

corresponding y value

y = x ³

y = 0 ³

y = 0

For

x = 1

y = x ³

y = 1 ³

y = 1

For

x = -1

y = x ³

y = (-1 )³

y = -1

Hence we get the critical points which are:

(0, 0)

(1, 1)  and

(-1, -1)

Now for each critical point, we have to compute D(x,y)

For a critical point (x,y), D computed as:

D(x, y) = [tex]f_{xx}[/tex] (x, y) - [tex]f_{yy}[/tex] (x, y) - ([tex]f_{xy}[/tex] (x, y))²

After computing D(x,y) check:

If D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) > 0:

f(x, y) is a local minimum.

If D(x, y) > 0 and  [tex]f_{xx}[/tex] (x, y) < 0:

f(x, y) is a local maximum.

If D(x, y) < 0:

then f(x, y) is a saddle point

Here first compute the second derivative in order to get  [tex]f_{xx}[/tex] ,  [tex]f_{yy}[/tex] and [tex]f_{xy}[/tex]

we have already computed:

[tex]f_{x}(x,y)[/tex] = 4x ³ - 4y  --> (1)

[tex]f_{y}(x,y)[/tex] = 4y³ - 4x  --> (2)

Now

[tex]f_{xx}(x,y)[/tex]  = 12x²

[tex]f_{yy}(x,y)[/tex]  = 12y²

[tex]f_{xy}(x,y)[/tex]  = -4

Compute D(x,y)

Critical Point (0, 0):

[tex]D(0, 0) = f_{xx} (0,0) f_{yy}(0,0)-(f_{xy}(0,0))^{2}[/tex]

Putting values of  [tex]f_{xx}(x,y)[/tex] , [tex]f_{yy}(x,y)[/tex] and [tex]f_{xy}(x,y)[/tex] in above equation:

D(0,0) = 12(0)² * 12(0)² - (-4)²

          = 0 * 0 -16

D(0,0) = -16

We know that if D < 0, the critical point f(x, y) is a saddle point.

D(0,0) < 0 because D(0,0) = -16

Hence (0, 0) is a saddle point

Compute D(x,y)

Critical Point (1, 1):

[tex]D(1, 1) = f_{xx} (1,1) f_{yy}(1,1)-(f_{xy}(1,1))^{2}[/tex]

Putting values of  [tex]f_{xx}(x,y)[/tex] , [tex]f_{yy}(x,y)[/tex] and [tex]f_{xy}(x,y)[/tex] in above equation:

D(1,1) = 12(1)² * 12(1)² - (-4)²

        = 12 * 12 - 16

D(1,1) = 128

We know that if D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) > 0 then f(x, y) is a local minimum.

D(1,1) > 0 because D(1,1) = 128

[tex]f_{xx}[/tex] (x, y) > 0 because  [tex]f_{xx}[/tex] (x, y) = 12

Hence (1,1) is the local minimum

Compute D(x,y)

Critical Point (-1, -1):

[tex]D(-1, -1) = f_{xx} (-1,-1) f_{yy}(-1,-1)-(f_{xy}(-1,-1))^{2}[/tex]

Putting values of  [tex]f_{xx}(x,y)[/tex] , [tex]f_{yy}(x,y)[/tex] and [tex]f_{xy}(x,y)[/tex] in above equation:

D(-1,-1) = 12(-1)² * 12(-1)² - (-4)²

          = 12 * 12 - 16

D(-1,-1) = 128

We know that if D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) > 0 then f(x, y) is a local minimum.

D(-1,-1) > 0 because D(-1,-1) = 128

[tex]f_{xx}[/tex] (x, y) > 0 because  [tex]f_{xx}[/tex] (x, y) = 12

Hence (-1,-1) is the local minimum

Answer:

The height and width are both 12 inches.

Step-by-step explanation:

2304/16=144

√144=12

Answer:

Step-by-step explanation:

Given that:

The mean μ = 310

The standard deviation σ =  40

Using the empirical rule to determine the following :

a. About 95 % of organs will be between what weights?

At 95% data values lies within 2 standard deviations of mean.

Thus, the  required range is :

= μ ± 2σ

= ( 310 - 2 (40) ,  310 + 2(40) )  

= (230, 390)

b. What percentage of organs weighs between 270 grams and 350 grams

Here:

μ ± σ = (310 - 40,  310 + 40)

μ ± σ = (270, 350)

Using empirical rule, 68% data values is in the range within 1 standard deviation of mean. This implies that 68% data values lie between (270, 350).

c. What percentage of organs weighs less than 270 grams or more than 350 grams?

The complement theorem can be use to estimate the  percentage of organs that weighs less than 270 grams or more than 350 grams,

This can be illustrated as :

= 100 % - 68 %

= 32 %

d. What percentage of organs weighs between 230 grams and 430 grams?

Using the empirical rule:

The percentage of organs weighs between 230 grams and 430 grams is:

u - 2σ  and  u + 3σ respectively.

Answer:

361-265＝96

96÷32＝3

3hours of labor was needed to complete the job

Answer:

the ratio will be 132 to 89

The ratio is 132 : 89.

A comparison of two quantities by division is called a ratio and the equality of two ratios is called proportion. A ratio can be written in different forms like x : y or x/y and is commonly read as, x is to y.

Ratio is the comparison of two quantities which is obtained by dividing the first quantity by the other. If a and b are two quantities of the same kind and with the same units, such that b is not equal to 0, then the quotient a/b is called the ratio between a and b. Ratios are expressed using the symbol of the colon (:). This means that ratio a/b has no unit and it can be written as a : b

Given:

Boys= 132

girls= 89

adults= 14

So,

the ratio of number of boys to number of girls is

= 132/89

=132 : 89

Learn more about ratio here:

https://brainly.com/question/13227971

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Answer:

5.36910

Step-by-step explanation

whatever you see like 95 can round up to 100.

5.369095... you just round up 95 to 100.

5 decimal is 5.36910

The number 5.36909546581 which is needed to be rounded off up to 5 decimal places is 5.36910.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. The method of representing numbers in the decimal system is commonly referred to as decimal.

Given the number 5.36909546581 which is needed to be rounded off up to 5 decimal places. Therefore, if we look at the sixth place after the decimal it is equal to 5.

Thus, fifth place is needed to be rounded off to the next number.

Hence, the number 5.36909546581 which is needed to be rounded off up to 5 decimal places is 5.36910.

Learn more about Decimal Numbers here:

https://brainly.com/question/4708407

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Replace x with each value and solve :

2 x 2^1 = 2 x 2 = 4

2 x 2^2 = 2 x 4 = 8

2x 2^3 = 2 x 8 = 16

2x 2^4 = 2 x 16 = 32

2 x 2^5 = 2 x 32 = 64

Now mark two points on the graph: (1,4) and (2,8) and draw a straight line though both points

The image is not rotated correctly...

Answer:

Q#2 y;; 4  8  16  32  64

Q#3 given below;

Step-by-step explanation:

Answer:

With 99 %  confidence, it can be said that the population mean driving distance to work ​ (in miles) is between the​ interval's endpoints [19.91 miles, 31.49 miles] .

Step-by-step explanation:

The complete question is: In a random sample of  six  ​people, the mean driving distance to work was  25.7 miles and the standard deviation was  6.7  miles. Assuming the population is normally distributed and using the​ t-distribution, a  99​%  confidence interval for the population mean  mu  is  left parenthesis 14.7 comma 36.7 right parenthesis  ​(and the margin of error is  11.0​).

Through​ research, it has been found that the population standard deviation of driving distances to work is  5.5 .  Using the standard normal distribution with the appropriate calculations for a standard deviation that is​ known, find the margin of error and construct a  99 ​%  confidence interval for the population mean  mu .

Interpret the results. Select the correct choice below and fill in the answer box to complete your choice.  ​(Type an integer or a decimal. Do not​ round.)  

A.  nothing ​%  of all random samples of  six  people from the population will have a mean driving distance to work​ (in miles) that is between the​ interval's endpoints.

B.  With  nothing ​%  ​confidence, it can be said that most driving distances to work​ (in miles) in the population are between the​ interval's endpoints.

C.  It can be said that  nothing ​%  of the population has a driving distance to work​ (in miles) that is between the​ interval's endpoints.  

D.  With  nothing %  confidence, it can be said that the population mean driving distance to work ​ (in miles) is between the​ interval's endpoints.

We are given that in a random sample of  six  ​people, the mean driving distance to work was  25.7 miles and the standard deviation was  6.7  miles.

Through​ research, it has been found that the population standard deviation of driving distances to work is  5.5 .

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~  N(0,1)  

where, [tex]\bar X[/tex] = sample mean driving distance to work = 25.7 miles

             [tex]\sigma[/tex] = population standard deviation = 5.5 miles

            n = sample of people = 6

             [tex]\mu[/tex] = population mean driving distance to work

Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation.

So, 99% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level

                                                      of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.99

P( [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.99

99% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                            = [ [tex]25.7-2.58 \times {\frac{5.5}{\sqrt{6} } }[/tex] , [tex]25.7+2.58 \times {\frac{5.5}{\sqrt{6} } }[/tex] ]

                                            = [19.91, 31.49]

Therefore, a 99% confidence for the population mean is [19.91, 31.49] .

The margin of error here is = [tex]2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex]

                                             = [tex]2.58 \times {\frac{5.5}{\sqrt{6} } }[/tex]  = 5.793

With 99 %  confidence, it can be said that the population mean driving distance to work ​ (in miles) is between the​ interval's endpoints [19.91, 31.49] .

Hi there! :)

Answer:

[tex]\huge\boxed{C.}[/tex]

We can examine each answer choice individually:

A. 569 × 10² = 569 × (10 · 10) = 569 · 100 = 56,900. Therefore, this choice is incorrect.

B. 569 · 10 = 5,690. This choice is incorrect.

C. 10³ · 569 = (10 · 10 · 10) ·569 = 1000 · 569 = 569,000. This choice is correct.

D. 10² · 569 = (10 · 10) · 569 = 56,900. This choice is incorrect.

Therefore, the correct option is C.

Answer:

 A. 569 × 10² = 569 × (10 · 10) = 569 · 100 = 56,900.

B. 569 · 10 = 5,690.

C. 10³ · 569 = (10 · 10 · 10) ·569 = 1000 · 569 = 569,000.

D. 10² · 569 = (10 · 10) · 569 = 56,900.

So your answer is C

Answer:

Each book costs $15 dollars

Step-by-step explanation

150-15=135

135/9=15

$15

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{28.28 \: }}}}}[/tex]

Step-by-step explanation:

Given, diameter of a circle = 6

pi ( π ) = 22 / 7

Finding the radius of the circle

We know that the radius of a circle is just half of the diameter. So, 6 / 2 = 3

Finding the area of circle having radius of 3

[tex] \boxed{ \sf{area \: of \: circle = \pi \: {r}^{2} }}[/tex]

plug the values

⇒[tex] \sf{area \: of \: circle = \frac{22}{7} \times {3}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{area \: of \: circle = \frac{22}{7} \times 9}[/tex]

Calculate

⇒[tex] \sf{area \:of \: circle = 28.28 \: }[/tex]

Hope I helped!

Best regards! :D

Answer:

Probability each player gets an ace, a $2 and a $3 = 0.0374

Step-by-step explanation:

The total number of ways to divide the card in triples among four players = 369600 ways

The total number of ways to share the cards such that no card is repeated in each triple = 13824 ways

Probability each player gets an ace, a $2 and a $3 = 13824/369600

Probability each player gets an ace a $2 and a $3 = 0.0374

Note: Further explanation is provided in the attachment.

Step-by-step explanation:

A proper noun is a specific name for a particular person, place, or thing.

The Internet is a communication network that gained popularity in the 1990s.