Express the following expression in the form of a + bi: (39 + 34i) + (76 + 89i) - (47 +26i).

the answer is -67 because you use the given function to set up and simplify  f(7).

Answer:

x = 1

Step-by-step explanation:

Given

30 = 5(x + 5) ← divide both sides by 5

6 = x + 5 ( subtract 5 from both sides )

1 = x

Answer:

Step-by-step explanation:

30 = 5(x + 5) ← divide both sides by 5

6 = x + 5 ( subtract 5 from both sides )

x=1

Answer:

120

Step-by-step explanation:

you would do length times width equals area. First you would multiply 8 by 15 which would give you 120 square feet. So Maragaret would be covering 120 square feet with paint

Answer:

Step-by-step explanation:

True

Answer: 32

Step-by-step explanation:

Answer:

the sum of the this series is Sn = [n(n+1)] / 2

Answer:

to two decimal places

= 6.04 mega joules

Step-by-step explanation:

The volume of the half tank

= πr²h

r= 2 m

h= 14/2= 7 m

Volume= 22/7 *2² *7

Volume= 88 m³

work (in mega-joules) needed to pump all of the water to the top of the tank

= Volume*mass density *acceleration*distance

= 88*1000*9.8*7

= 6036800 joules

In mega joules

= 6.036800 mega Joules

to two decimal places

= 6.04 mega joules

The work needed to pump all of the water to the top of the tank is 6.03 MJ

Work is said to be done whenever a force move a body through a certain distance.

To calculate the work needed to pump the water to the tank, first we need to find the volume of the water in the tank half full.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Finally, to get the work needed to pump all the water to the top of the tank, we use the formula below.

Where:

From the question.

Given:

Substitute these values into equation 2

Hence, The work needed to pump all of the water to the top of the tank is 6.03 MJ.

Learn more about work here: https://brainly.com/question/8119756

Answer:

If radius = 8 cm and we needed perimeter of complete circle then

circumference (or perimeter) = 2*PI * 8 = 50.2654824574  cm

or 50.27 cm (rounded)

Step-by-step explanation:

Answer:

la distancia del punto de observación A al incendio = 5.5 millas

la distancia del punto de observación B al incendio = 3.8 millas

Step-by-step explanation:

La expresión esquemática de la pregunta se puede ver en la imagen adjunta a continuación :

Del siguiente diagrama;

Usando la sine regla:

[tex]\dfrac{sin \ F}{f} = \dfrac{sin \ A }{a}[/tex]

[tex]\dfrac{sIn \ 79}{6} = \dfrac{sin \ 63}{a}[/tex]

a sin 79 = 6 sin 63

[tex]a =\dfrac{6 \times sin \ 63}{sin \ 79}[/tex]

[tex]a =\dfrac{6 \times 0.8910}{0.9816}[/tex]

a = 5.446 millas

la distancia del punto de observación A al incendio = 5.5 millas (a la décima más cercana)

[tex]\dfrac{sin \ F}{f} = \dfrac{sin \ B}{b}[/tex]

[tex]\dfrac{sin \ 79}{6} = \dfrac{sin \ 38}{b}[/tex]

b sin 79 = 6 sin 38

[tex]b = \dfrac{6 \times sin \ 38}{sin \ 79}[/tex]

[tex]b = \dfrac{6 \times0.6157 }{0.9816}[/tex]

b = 3.7635 millas

la distancia del punto de observación B al incendio = 3.8 millas (a la décima más cercana)

Answer:C

Step-by-step explanation:

9+7=16

16 times 4 = 64

36+28=64

Answer:How many miles can a car be driven in 3 hours at 50 miles per hour? Under normal circumstances and the generally assumed conditions, the answer is of course (3 hours) * (50 miles / hour) = 150 miles.

3.5 hours

It will take you 3.5 hours to go 280 miles at 80 miles an hour.It travels at constant speed for the remaining time. Let x be the time traveled at the unknown constant speed. The total itme for the trip was 6 hours so: 6 = time traveled at 50 mph + time traveled at 60 mph + time traveled at x mph.

Step-by-step explanation:So you drive 25 miles / hour. then 25 miles/ 1 hour = 225 miles / nb of hours.2 minutes

However, traveling at 30 MPH for 1 mile (1 lap) takes 2 minutes, which means that your average will never be 60MPH.approximately 0.6818 miles per hour.

Answer:

The null hypothesis is  [tex]H_o: \mu_1 = \mu_2[/tex]

The  alternative hypothesis is  [tex]H_1 : \mu_1 \ne \mu_2[/tex]

The test statistics is  [tex]t = -1.667[/tex]

Step-by-step explanation:

From the question we are told that

  The first sample size is  [tex]n_1 = 12[/tex]

   The  first sample  mean is  [tex]\= x_1 = 79.8[/tex]

    The first standard deviation is  [tex]\sigma _1 = 8.8[/tex]

   The second sample  size is  [tex]n_2 = 17[/tex]

    The  second  sample  mean is  [tex]\= x_2 = 85.2[/tex]

    The second  standard deviation is  [tex]\sigma _2 = 8.3[/tex]

The null hypothesis is  [tex]H_o: \mu_1 = \mu_2[/tex]

The  alternative hypothesis is  [tex]H_1 : \mu_1 \ne \mu_2[/tex]

Generally the test statistics is  mathematically represented as  

                 [tex]t = \frac{\= x_ 1 - \= x_2 }{ \sqrt{ \frac{\sigma_1^2 }{n_1 } +\frac{\sigma_2^2 }{n_2} } }[/tex]

   =>          [tex]t = \frac{ 79.8 - 85.2 }{ \sqrt{ \frac{8.8^2 }{12} +\frac{ 8.3^2 }{17} } }[/tex]

=>                [tex]t = -1.667[/tex]

Answer:

x ≤ 3

Step-by-step explanation:

In the graph given, values of variable x is represented.

From the plot, we note that a small circle is at point 3 on the numberline. This small "o" is shaded, which indicates that the values of x includes 3.

The arrow which starts at 3 on the numberline, points towards our left. This means that the values of x are less than or equal to 3. No value of x is greater than 3.

Therefore, the following inequality can be written for the graph:

x ≤ 3

Answer:

[tex]Sum=4*[\frac{n^2-1}{n^2}][/tex]

For n=10:

Sum=3.96

For n=100:

Sum=3.9996

For n=1000:

Sum=3.999996

For n= 10000:

Sum=3.99999996

Step-by-step explanation:

Formula:

[tex]\sum_{k=1}^n \frac{12k(k-1)}{n^3}[/tex]

Rearranging the above formula:

[tex]\sum_{k=1}^n \frac{12}{n^3}*k(k-1)\\\sum_{k=1}^n \frac{12}{n^3}*(k^2-k)[/tex]            Eq (1)

According to summation formula:

[tex]\sum_{k=1}^n\ k= \frac{n(n+1)}{2}\\ \sum_{k=1}^n\ k^2= \frac{n(n+1)(2n+1)}{6}\\[/tex]

Putt these in Eq (1), and we will get:

[tex]=\frac{12}{n^3}[\frac{n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}]\\Taking\ n\ as\ common\\=n*\frac{12}{n^3}[\frac{(n+1)(2n+1)}{6}-\frac{(n+1)}{2}] \\=\frac{12}{n^2}*[\frac{(n+1)(2n+1)}{6}]-\frac{12}{n^2}*[\frac{(n+1)}{2}] \\=\frac{2*(n+1)(2n+1)}{n^2}-\frac{6(n+1)}{n^2}\\[/tex]

Taking [tex]2(n+1)[/tex] as common:

[tex]=2(n+1)*\frac{2n+1-3}{n^2} \\=(2n+2)*\frac{2n-2}{n^2}\\=\frac{4n^2-4}{n^2}[/tex]

After more simplifying,

[tex]Sum=4*[\frac{n^2-1}{n^2}][/tex]

Now ,for n=10:

[tex]Sum=4[\frac{(10^{2})-1}{10^{2}}]\\Sum=3.96[/tex]

For n=100:

[tex]Sum=4[\frac{(100^{2})-1}{100^{2}}]\\Sum=3.9996[/tex]

For n=1000

[tex]Sum=4[\frac{(1000^{2})-1}{1000^{2}}]\\Sum=3.999996[/tex]

For n=10000:

[tex]Sum=4[\frac{(10000^{2})-1}{10000^{2}}]\\Sum=3.99999996[/tex]

Answer:

-2

Step-by-step explanation:

We can find the slope for two points

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

    = ( 12 - 4)/(-6- -2)

   = 8/( -6+2)

   = 8/-4

   = -2

Question:

Carl throws a single die twice in a row. For the first throw, Carl rolled a 2; for the second throw he rolled a 4. What is the probability of rolling a 2 and then a 4? Answer choices are in the form of a percentage, rounded to the nearest whole number. O 22% 36% O 3% O 33%

Answer:

The probability of rolling a 2 then 4 is 3%

Step-by-step explanation:

Given

A die rolled twice

Required

Probability of rolling a 2 then 4; i.e. P(2 n 4)

First, we need to list out the sample space

[tex]S = \{1,2,3,4,5,6\}[/tex]

[tex]n(S) = 6[/tex]

Next, is to calculate P(2)

[tex]P(2) = \frac{n(2)}{n(S)}[/tex]

[tex]P(2) = \frac{1}{6}[/tex]

Next, is to calculate P(4)

[tex]P(4) = \frac{n(4)}{n(S)}[/tex]

[tex]P(4) = \frac{1}{6}[/tex]

Next,is to calculate the required probability using the following formula

[tex]P(2\ n\ 4) = P(2) * P(4)[/tex]

[tex]P(2\ n\ 4) = \frac{1}{6} * \frac{1}{6}[/tex]

[tex]P(2\ n\ 4) = \frac{1}{36}[/tex]

[tex]P(2\ n\ 4) = 0.02777777777[/tex]

Convert to Percentage

[tex]P(2\ n\ 4) = 2.777777777\%[/tex]

Approximate

[tex]P(2\ n\ 4) = 3\%[/tex]

Hence, the probability of rolling a 2 then 4 is 3%

Answer:

3%

Step-by-step explanation:

Answer:

n = 5

Step-by-step explanation:

All of the other choices are true except for n = 5, which is a counterexample. [tex]4^{5}[/tex] = 1024, which is greater than the other side as the other side is:

and [tex]4^{2}[/tex] = 16, 16 + 250 = 266

1024 < 266 is definitely false.

Therefore, the counterexample is n = 5.

Answer:

A rectangle has_four_sides that are straight lines, _parallel_ and _equal_ opposite sides, and angles of [tex]90^o[/tex]_.

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

First find the inverse function.  Rewrite the given function as

y = 5(x + 4) - 6  =  5x + 20 - 6  =  5x + 14

Second, interchange x and y:

x = 5y + 14

Third, solve this result for y:

5y = 14 - x, or y = (1/5)(14 - x)

This last result is the inverse function of the given f(x).

The value of this inverse at x = 19 is (1/5)(14 - 19) = (1/5)(-5) = -1

Julio's hourly rate is going to be $14.4 per hour

Answer:

Step-by-step explanation:

Since angles R and S are supplementary angles it means that the sum of their angles add up to 180°

To find R we must first find x

To find x , add angles R and S and equate them to 180

That's

R + S = 180

80 - x + 3x - 30 = 180

2x + 50 = 180

2x = 180 - 50

2x = 130

Divide both sides by 2

x = 65°

From the question

R = 80 - x

But x = 65°

Substitute the value of x into the expression

That's

R = 80 - 65

We have the final answer as

Hope this helps you

Answer:

2009 data set is most homogeneous

Step-by-step explanation:

As per coefficient of variation, which is around 5% for the year 2009 and around 20% for the year 2010 we can state that the data set for the year 2009 is most homogeneous

Homogeneous means similar, it can be observed on the graph as well that the data for the year 2009 is less variant

Hope it answers your question.

Answer:

x = 0.6

Step-by-step explanation:

3x - 1.1 = 0.7

3x = 1.8

x = 0.6

Answer:

x = .6

Step-by-step explanation:

3x – 1.1 = 0.7

Add 1.1 to each side

3x – 1.1+1.1 = 0.7+1.1

3x = 1.8

Divide each side by 3

3x/3 = 1.8/3

x = .6

Answer:

A.

Step-by-step explanation:

All you have to do is convert all those fractions to 20.

So 3/4 will be 15/20, 3/10 would be 6/20, 4/5 would be 16/20 and 1/2 would be 10/20. It could be a or b. Does it say select all possible answers?

Answer: False

Step-by-step explanation:

Primary technology skills are simply the skills which are vital in order to attain success in online education. It should be noted that technical skills are knowledge and abilities that are related to information technology which are needed to do certain tasks.

It should be noted that online education is the form of education that is delivered and being administered through the internet.

For one to learn online, it should be noted that being able to open and close windows is a primary technology skill.

Therefore, the statement in the question is false.

Answer: F

I already did the test

Answer:

10 and 11

Step-by-step explanation:

Let the first integer be x.

Then the next one, since it's consecutive, must be (x+1).

The two equals 21. Thus:

[tex](x)+(x+1)=21[/tex]

Combine like terms:

[tex]2x+1=21[/tex]

Subtract 1 from both sides:

[tex]2x=20[/tex]

Divide both sides by 2:

[tex]x=10[/tex]

So, the first integer is 10.

And the second integer is 10+1=11.

Answer:

10 , 11

Step-by-step explanation:

The sum of two consecutive integers is 21.

Let the least of the integer be signified by the variable x.

Consecutive means "directly after", which means the other integer would be: x + 1

Set the equation:

(x) + (x + 1) = 21

Simplify. Combine like terms:

x + x + 1 = 21

(x + x) + 1 = 21

2x + 1 = 21

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 1 from both sides:

2x + 1 (-1) = 21 (-1)

2x = 21 - 1

2x = 20

Next, divide 2 from both sides:

(2x)/2 = (20)/2

x = 20/2

x = 10

Plug in 10 for x in the equation:

(x) + (x + 1) = 21

10 + (10 + 1) = 21

10 + 11 = 21

21 = 21 (True)

The two numbers are 10, 11.

~

Answer:

15 years.

Step-by-step explanation:

We have the equation:

20000 = 10000(1 + 0.048)^t     where t is the number of years.

1.048 t = 20000/10000 = 2

Taking logs:

t ln 1.048 = ln 2

t = ln 2 / ln 1.048

t = 14.78

Answer:

The round off values are- 3.14, 6.12, and 4.57 respectively.

Step-by-step explanation:

The given value to which we have to round off is a. 3.14159 b. 6.12356 c. 4.56787

In order to round off the number we must keep in mind that there should be three digits in total and we will increase the value by one if the right-hand side value is more than 5.  

Thus round off figure of 3.14159 is 3.14.

The round off figure of 6.12356 is 6.12.

The round off figure of 4.56787 is 4.57.