1.Square roots are the ____ of perfect squares.

[tex](1+i)^2-3(2-i)^3=1+2i-1-3(8-12i-6+i)=2i-6+33i=\boxed{-6+35i}[/tex].

Hope this helps.

Answer:

see below

Step-by-step explanation:

a  R=k(L/A)

Substitute what we know into the equation

.08 = k (100/.05)

.08 = k 2000

Divide each side by 2000

.08/2000 = k

.00004 = k

R=.00004 (L/A)

b R=.00004 (L/A)

We know L = 4000 and A = .02

R=.00004 (4000/.02)

R = 8

Answer:

[tex] \frac{7}{3} [/tex]

Step-by-step explanation:

Given that,

p = -6,

q = 6

r = -19

Plug in the above values to evaluate the expression, [tex] \frac{\frac{q}{2} - \frac{r}{3}}{\frac{3p}{6} + \frac{q}{6}} [/tex]

[tex] \frac{\frac{6}{2} - \frac{(-19)}{3}}{\frac{3(-6)}{6} + \frac{6}{6}} [/tex]

[tex] \frac{\frac{3}{1} - \frac{(-19)}{3}}{\frac{-3}{1} + \frac{1}{1}} [/tex]

[tex] \frac{\frac{9 -(-19)}{3}}{3 + 1} [/tex]

[tex] \frac{\frac{28}{3}}{4} [/tex]

[tex] \frac{28}{3}*\frac{1}{4} [/tex]

[tex] \frac{28*1}{3*4} [/tex]

[tex] \frac{7*1}{3*1} [/tex]

[tex] \frac{7}{3} [/tex]

Answer:

0.36

Step-by-step explanation:

We need to solve the first bracket first and then the others,

    Value of  Cos^ - 1(1/3) =70.53°

        Then,  90 - the value of cosine

             =19.47°

Then, put the new in the calculator:

     Tan (19.47°)

and the answer comes 0.3535294237

 then I use the nearest formula and got the answer = 0.36

Answer:

[tex]\Large \boxed{\mathrm{\bold{B.} } \ x=7, \ y = 4\sqrt{2} }[/tex]

Step-by-step explanation:

We can split the shape into a right triangle and a rectangle.

tan θ = opp/adj

Let c be the missing base for the right triangle.

tan45 = 4/c

c = 4/tan45

c = 4

x = 3 + 4

x = 7

sin θ = opp/hyp

sin45 = 4/y

y = 4/sin45

y = [tex]4\sqrt{2}[/tex]

Answer:

add the expressions 832

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

From the question

y = - 4x + 3

Comparing with the general equation above

Slope / m = - 4

Since the lines are parallel their slope are also the same

Slope of parallel line = (-3 , 2) and slope

- 4 is

We have the final answer as

Hope this helps you

Answer:

y=-4x-14

Step-by-step explanation:

Answer:

Simple Linear Regression Correlation

Step-by-step explanation:

When it snows normally the schools continue .But constant snowing affects the schools continuity. As more and more snow falls more schools are closed.

There may be a situation where all the schools are closed at a certain temperature.

So it is a simple linear regression correlation because in it there are two variables and one variable is dependent on the other. In this example the schools are dependent on the average snowfall.

If there's a snow blizzard or extreme weather all the schools are definitely closed .

It can be represented by a graph.

Answer:

a - 1/2

Step-by-step explanation:

there are 3 even and 3 odd numbers so the probability is half of them

Answer:

Option 1, 3 and 5 are correct

Step-by-step explanation:

Given

Eggplants = $1.79 each

Apples = $0.59 each,

Bags of spinach = $2.55 each

Cartons of orange juice = $3.89 each

Required

Select three true statements

To do this, we'll check the options one after the other

1. 4 eggplants cost about $0.50 less than 3 bags  of spinach

First, we need to calculate the cost of 4 eggplants

4 Eggplants = 4 * 1 Eggplants

4 Eggplants = 4 * $1.79

4 Eggplants = $7.16

Next, we calculate the cost of 3 bags of Spinach

3 bags of Spinach = 3 * 1 bag of Spinach

3 bags of Spinach = 3 * $2.55

3 bags of Spinach = $7.65

Determine the difference

Difference = |Eggplants - Bags of Spinach|

Difference = |$7.16 - $7.65|

Difference = |-$0.49|

Difference = $0.49

This statement is true because $0.49 approximates to $0.50

2. Total cost of 4 apples and 2 eggplants $0.50 is more than $6.00

First, we need to calculate the cost of 4 apples

4 Apples = 4 * 1 Apples

4 Apples = 4 * $0.59

4 Apples = $2.36

Next, we calculate the cost of 2 Eggplants

2 Eggplants = 2 * 1 Eggplant

2 Eggplants = 2 * $1.79

2 Eggplants = $3.58

Add this two results together

Total = 4 Apples + 2 Eggplants

Total = $2.36 + $3.58

Total = $5.94

This statement is false because the sum is less than $6.00

3. Total cost of 4 eggplants, 4 apples and 1 carton of orange juice is $13.41

In (1) & (2) above

4 Eggplants = $7.16

4 Apples = $2.36

1 carton of orange juice = $3.89

Add the above together

Total = $7.16 + $2.36 + $3.89

Total = $13.41

This statement is true because the sum is $13.41

4. Total cost of 5 eggplants is greater than cost of 4 bags of spinach

First, we need to calculate the cost of 5 eggplants

5 Eggplants = 5 * 1 Eggplants

5 Eggplants = 5 * $1.79

5 Eggplants = $8.95

Next, we calculate the cost of 4 bags of Spinach

4 bags of Spinach = 4 * 1 bag of Spinach

4 bags of Spinach = 4 * $2.55

4 bags of Spinach = $10.20

This statement is false because 4 Eggplants costs less than $ bags of spinach

5. Total cost of 2 eggplants, 2 apples and 2 cartons of orange juice is $9.99 more than cost of 1 bag of spinach

From (2) above

2 Eggplants = $3.58

Next, we need to calculate the cost of 2 apples

2 Apples = 2 * 1 Apples

2 Apples = 2 * $0.59

2 Apples = $1.18

Next, we need to calculate the cost of 2 cartons of orange juice

2 Cartons = 2 * 1 Carton

2 Apples = 2 * $3.89

2 Apples = $7.78

Sum these up

Total = $3.58 + $1.18 + $7.78

Total = $12.54

1 Bag of spinach = $2.55 each

Subtract 1 Bag of spinach from the $12.54

Difference = $12.54 - $2.55

Difference = $9.99

This statement is true because the difference is $9.99

Answer:

Step-by-step explanation:

Since the square canvas was completely covered using 77.8 in.² of fabric without any overlap, to get the side length of the canvas, we will use the formula for calculating the area of a square.

Area of a square = Length * Length

A = L*L

A = L²

Given the Area of the area of the square canvas as 77.8 in², on substituting this values into the formula to get L we have;

77.8 = L²

Take the square root of both sides

√77.8 = √L²

L = √77.8

L = 8.82 in

L ≈ 9inches

The length 8.82in gotten was approximated to 9in because the first value after the decimal point is greater that 4 and once we have such case 1 will be added to the value before the decimal point i.e 8 to make it 9.

Hence measurement that is closest to the side length of this canvas in inches is 9inches.

Answer:

term=14x+19

cofficient=14+19

constant=19

Answer:

Terms :

14x , 19

Coefficients:

14

Constants:

19

Hope it helps.

Answer:

4 months

Step-by-step explanation:

Club A

registration fee: $0

monthly fee: $105

After every month, the total cost increases by $105.

month 0: $0

month 1: $105

month 2: $210

month 3: $315

month 4: $420

month 5: $525

month 6: $630

Club B

registration fee: $375

monthly fee: $80

Notice how Club B's total reaches Club A's total after 2 months.

month 0: $375

month 1: $455

month 2: $535

month 3: $615

month 4: $695

Complete question :

A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:

City - - - - - - - Price ($) -- - Sales

River City - - 1.30 - - - - - - 100

Hudson - - - 1.60 - - - - - 90

Ellsworth - - - 1.80 - - - - - 90

Prescott - - - - 2.00 - - - - 40

Rock Elm - - 2.40 - - 38

Stillwater - - 2.90 - - 32

Answer:

78.39%

Step-by-step explanation:

Given the data :

Price (X) :

1.30

1.60

1.80

2.00

2.40

2.90

Sales (y) :

100

90

90

40

38

32

The percentage of the total variation in candy bar sales explained by the regression model can be obtained from the value of the Coefficient of determination(R^2) of the regression model. The Coefficient of determination is a value which ranges between 0 - 1 and gives the proportion of variation in the dependent variable which can be explained by the dependent variable.

R^2 value is obtained by getting the squared value of R(correlation Coefficient).

The R value obtained using the online R value calculator on the data is : - 0.8854

Hence, R^2 = (-0.8854)^2 = 0.7839

Expressing 0.7839 as a percentage ;

0.7839 × 100 = 78.39%

Answer:

Pay for the day = $ 123.25

Step-by-step explanation:

From the question given:

Monday morning:

Time in: 8:15

Time out: 12:15 pm

Monday afternoon:

Time in: 13:00

Time out: 17:30

Pay = $ 14.5 /hr

Next, we shall determine the number of hours of work in the morning. This is illustrated below:

Time in: 8:15

Time out: 12:15 pm

Difference in time = 12:15 – 8:15 = 4 hrs

Next, we shall determine the pay for the work done in the morning. This can be obtained as follow:

Pay = $ 14.5 /hr

Pay for work done in the morning

= 4 × 14.5 = $ 58

Next, we shall determine the number of hours of work in the afternoon. This is illustrated below:

Time in: 13:00

Time out: 17:30 pm

Difference in time = 17:30 – 13:00 = 4 hrs 30 minutes

Next, we shall convert 4 hrs 30 minutes to hours. This is illustrated below:

60 minutes = 1 hr

30 minutes = 30/60 = 0.5 hrs.

Therefore,

4 hrs 30 minutes = 4 + 0.5 = 4.5 hrs

Next, we shall determine the pay for the work done in the afternoon. This can be obtained as follow:

Pay = $ 14.5 /hr

Pay for work done in the afternoon

= 4.5 × 14.5 = $ 65.25

Finally, we shall determine the pay for the day as follow:

Pay for work done in the morning

= $ 58

Pay for work done in the afternoon

= $ 65.25

Pay for the day = pay for morning + pay for afternoon

Pay for the day = $ 58 + $ 65.25

Pay for the day = $ 123.25

Therefore, the pay for the day is

$ 123.25

Answer:

15x3-25x

Step-by-step explanation:

5x(3x2 -5)

step1: distribute 5x to both sides

Step 2: 3x2 would change into 15x3 (because you're multiplying by 5x)

Step3: -5 would turn into -25x (because you are multiplying by 5x also)

Step4: put both answers together and your end product would be (15x3 - 25x)

Answer:

15x3-25x

Step-by-step explanation:

Answer:

3x+10+y

Step-by-step explanation:

5x-y-3x+10+x+2y

5x-3x+x+10-y+2y

3x+10+y

Answer:

3x+y+10

Step-by-step explanation:

Since we are trying to combine like terms, we must rearrange the terms, and  group the terms with an x, together, a y together, and the constants. Doing that, we get

(5x+x-3x)+(2y-y)+10

Now we start with the x terms, and we add 5x+x=6x and then 6x-3x= 3x, so you have 3x, and now for the y terms

we have 2y-y=y and lastly we have a ten, so adding them together, we get

3x+y+10

Answer:

0x²-7xy+10y²

Step-by-step explanation:

4x²-5xy+3y² + 8x²+7xy-6y²

4x²+8x²-5xy+7xy+3y²-6y²

=12x²+2xy-3y²

12x²-5xy+3y² + -2x²-9xy+13y²

12x²-5xy+3y² - 2x²-9xy+13y²

12x²-2x²-5xy-9xy+3y²+13y²

= 10x²-7xy+10y²

Hoped I helped

Answer:

First recipe needs = 3/8

Second recipe needs = 5/8

Step-by-step explanation:

Given:

Two recipes needs butter = 1 pound

One recipe needs 1/4 pound more

Find:

Each recipe needs butter

Computation:

Assume;

First recipe needs = x

Second recipe needs = x + (1/4)

Two recipes needs butter = First recipe needs + Second recipe needs

x + x + (1/4) = 1

2 x = 1 - (1/4)

2 x = 3/4

x = 3/8 pound

First recipe needs = 3/8

Second recipe needs = x + (1/4) = (3/8) + (1/4) = 5/8

Second recipe needs = 5/8

Answer:

A. 5 < AC < 10

Step-by-step explanation:

If ∆ABC is a right angled triangle, we use the Pythagoras formula:

c² = a² + b²

Where c = longest side

When given sides AB, AC and BC, the formula becomes:

AB² = AC² + BC²

Where AB = Longest side

In the question,

AB = 10 and BC = 5.

10² = AC² + 5²

AC² = 10² - 5²

AC² = 100 - 25

AC² = 75

AC = √75

AC = 8.6602540378

Therefore, the expression that is always true = A. 5 < AC < 10

Answer:

P ([tex]\hat p[/tex] ≤ 0.10)

Step-by-step explanation:

The probability in terms of statistics for this given problem can be written as follows.

Let consider X to the random variable that represents the number of 6's in 7 throws of a dice, then:

X [tex]\sim[/tex]Bin ( n = 72, p = 0.167)

E(X) = np

E(X) = 72× 0.167

E(X) = 12.024

E(X) [tex]\simeq[/tex]  12

p+q =1

q = 1 - p

q = 1 - 0.167

q = 0.833

V(X) = npq

V(X) = 72 × 0.167 × 0.833

V(X) = 10.02

V(X) [tex]\simeq[/tex] 10

∴ X [tex]\sim[/tex] N ([tex]\mu = 12, \sigma^2 =10[/tex])

⇒ [tex]\hat p = \dfrac{X}{n} \sim N ( p, \dfrac{pq}{n})[/tex]

where p = 0.167 and [tex]\dfrac{pq}{n}[/tex] = [tex]\dfrac{0.167 \times 0.833}{72}[/tex] = 0.00193

∴ P(at most 10% of rolls are 6's)

i.e

P ([tex]\hat p[/tex] ≤ 0.10)

Answers:

Distance = 14 km

Displacement = 4 km east

==============================================

Explanation:

The total distance is simply the sum of the values given. So he traveled a total of 5+4+5 = 9+5 = 14 km overall.

----------------------

The displacement is where a drawing may come in handy. Draw an xy axis. Place point A at the origin (0,0). This is where Michael starts his trip. Then move up to (0,5) to indicate he goes 5 km north. Call this point B.

Afterward, mark point C at (4,5) to show he has gone 4 km east. Finally, point D is at (4,0) because he went 5 km south

The displacement is only concerned with two points: The start and end point. Nothing else matters. We started at A(0,0) and ended at D(4,0). So we've gone 4 km east overall. The direction is important when it comes to displacement. Simply saying "4 km" isn't enough. So in a sense, we could take a shortcut from A directly to D, bypassing the other points B and C.

See the diagram below for a visual.

Answer: y=4/5x+12

Step-by-step explanation:

Slope-intercept form: y=ax+b, where a is the slope and b is the y-intercept

When a line is parallel to another line, they will have the same slope. So the slope of the new line is also 4/5.

y=4/5x+b

To find the y-intercept, we simply plug in the point it passes through.

y=4/5x+b

8=4/5(-5)+b

8=-4+b

b=12

y=4/5x+12

Hope this helps!! :)

Please let me know if you have any question

Answer:

The answer is below

Step-by-step explanation:

Velocity is the rate of change of displacement. Velocity is the ratio of distance to time.

The velocity v(t) = [tex]\frac{d}{dt}r(t)[/tex]

Where r(t) is the position function

Given that:

r(t)=⟨−8tsint,−8tcost,2t²⟩

[tex]v(t)=\frac{d}{dt}r(t)= <-8tcost-8sint,8tsint-8cost,4t>[/tex]

Acceleration is the rate of change of velocity, it is the ratio of velocity to time. Acceleration a(t) is given as:

[tex]a(t)=\frac{d}{dt}v(t)= \frac{d}{dt} <-8tcost-8sint,8tsint-8cost,4t>\\=<8tsint-16cost,8tcost+16cost,4>\\\\a(t)=<8tsint-16cost,8tcost+16cost,4>[/tex]

Speed = |v(t)| = [tex]\sqrt{(-8tcost-8sint)^2+(8tsint-8cost)^2+(4t)^2}\\\\ =\sqrt{64t^2cos^2t+128tcostsint+64sin^2t+64t^2sin^2t-128tsintcost+64cos^2t+16t^2}\\ \\=\sqrt{64t^2cos^2t+64t^2sin^2t+64sin^2t+64cos^2t+16t^2}\\\\=\sqrt{64t^2(cos^2t+sin^2t)+64(sin^2t+cos^2t)+16t^2}\\\\=\sqrt{64t^2+64+16t^2}=\sqrt{80t^2+64}[/tex]

Step-by-step explanation:

[tex] {( - 2x {y}^{4} })^{4} [/tex]

[tex] = {( - 2)}^{4} \times {x}^{4} \times { {y}^{4} }^{4} [/tex]

[tex] = 16 {x}^{4} {y}^{16} [/tex]

Answer:

What is the cost of a chicken shawarma wrap?

$10.99

What is the cost of one order of spiced potatoes?

$4.99

If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?

3x + 2y = $42.95..........Eq 1

5x + 4y = $74.91..........Eq 2

Step-by-step explanation:

Cost of a chicken sharwarma wrap = a

Cost of an order of spiced potatoes = b

Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.

3x + 2y = $42.95 .............Equation 1

Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.

5x + 4y = $74.91 ................Equation 2

So we have:

3x + 2y = $42.95..........Eq 1

5x + 4y = $74.91..........Eq 2

We use Elimination method

Multiply Equation 1 by coefficient of y in Equation 2

Equation 2 by coefficient of y in Equation 1

3x + 2t= $42.95 .............Equation 1 × 4

5x + 4y = $74.91 ................Equation 2 × 2

12x + 8y = 171.80..............Equation 3

10x + 8y = 149.82..............Equation 4

Subtract Equation 3 from Equation 4

2x = 21.98

x = 21.98/2

x = 10.99

Therefore, x = Cost of Chicken sharwarma wrap = $10.99

Subtitute 10.99 for 9in Equation 1

3x + 2y = $42.95 .............Equation 1

3(10.99) + 2y = 42.95

32.97 + 2y = 42.95

2y = 42.95 - 32.97

2y = 9.98

y = 9.98/2

y = 4.99

y = Cost of an order of spiced potatoes = $4.99

Hence,

The cost of a chicken sharwarma wrap = $10.99

The cost of an order of spiced potatoes = $4.99

Answer:

Well, there is a lot of answers to that. Check explanation, please!

Step-by-step explanation:

For example, some basic fractions that are less than 1/7 are:

You can also set up a number line, and compare the fractions.

Hopefully, this answer helps! :D

Answer:

-23

Step-by-step explanation:

Answer:

The slope would be 7/3

The y-intercept would be -11

Step-by-step explanation:

To find the answer rearrange your equation.

First subtract 14x from both sides, getting -6y= -14x + 66.

Then divide both sides by -6, getting y= 7/3x -11

This is now written in y=mx+b form. Your m is your slope and b is the y intercept!