For each calculation choose the correct answer written in standard form.
a) (7 * 10°) ~ (3 x 10?)
A
B
21 x 100 21 x 10
С
2.1 x 10"
D
2.1 x 10
b) (2 x 10°) = (4 x 102)
A
2 x 10
B
5 x 10
с
0.5 x 10
D
2 x 10

Hello!

2√4³ =

2 × √4 ³ =

2 × 2³ =

2 × 8 = 16

Good luck! :)

Answer:

9. A. 2

Rectangle R:

Rectangle S:

Rectangle Area:

Rectangle R = L · W

Rectangle S = 2L · 2W = 2(L · W)

10.  A. (1, 3)

x + 2 = -2x + 5

x + 2x = 5 - 2

3x = 3

x = 1

y = x + 2 = 1 + 2 = 3

Given:

There are 35 times as many students at Wow University as teachers.

When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.

To find:

The total number of students.

Solution:

Let x be the number of teachers at Wow University. So, the number of student is :

[tex]35\times x=35x[/tex]

When all the students and teachers are seated in the 8544 seat auditorium, 12 seats are empty.

[tex]x+35x=8544-12[/tex]

[tex]36x=8532[/tex]

[tex]x=\dfrac{8532}{36}[/tex]

[tex]x=237[/tex]

The number of total students is:

[tex]35x=35(237)[/tex]

[tex]35x=8295[/tex]

Therefore, the total number of students is 8295.

Answer:

2402 people.

Step-by-step explanation:

Since a basketball court measures 998 inches on the sides while the baseline stretches 700 inches, and there is a circle in the middle of the court that has a diameter of 72 inches, and the team can fit 14 people in the circle at one time To determine how many people can fit on a court, the following calculation must be performed:

Area of a circle:

3.14 x (72/2) ^ 2 = X

3.14 x 36 ^ 2 = X

3.14 x 1.296 = X

4,069.44 = X

Area of a rectangle:

998 x 700 = X

698,600 = X

4,069.44 / 14 = 290.67

698,600 / 290.67 = 2,402

Answer:

A. x>11

Step-by-step explanation:

15 < 4 + x

take 4 to the LHS this becomes 15 - 4 < x

•°• 11 < x

< means less than

Therefore x is greater than 11

x > 11

Answer:

[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]

Step-by-step explanation:

Given

[tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]y(1) = 0[/tex]

[tex]y'(1) =e[/tex]

Required

The solution

Differentiate [tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]y' = c_1e^x - c_2e^{-x}[/tex]

Next, we solve for c1 and c2

[tex]y(1) = 0[/tex] implies that; x = 1 and y = 0

So, we have:

[tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]0 = c_1 * e^1 + c_2 * e^{-1}[/tex]

[tex]0 = c_1 e + \frac{1}{e}c_2[/tex] --- (1)

[tex]y'(1) =e[/tex] implies that: x = 1 and y' = e

So, we have:

[tex]y' = c_1e^x - c_2e^{-x}[/tex]

[tex]e = c_1 * e^1 - c_2 * e^{-1}[/tex]

[tex]e = c_1 e - \frac{1}{e}c_2[/tex] --- (2)

Add (1) and (2)

[tex]0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2[/tex]

[tex]e = 2c_1e[/tex]

Divide both sided by e

[tex]1 = 2c_1[/tex]

Divide both sides by 2

[tex]c_1 = \frac{1}{2}[/tex]

Substitute [tex]c_1 = \frac{1}{2}[/tex] in [tex]0 = c_1 e + \frac{1}{e}c_2[/tex]

[tex]0 = \frac{1}{2} e+ \frac{1}{e}c_2[/tex]

Rewrite as:

[tex]\frac{1}{e}c_2 = -\frac{1}{2} e[/tex]

Multiply both sides by e

[tex]c_2 = -\frac{1}{2} e^2[/tex]

So, we have:

[tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}[/tex]

[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]

Answer: 20%

Step-by-step explanation:

Human capital refers to the expertise that people gain as a result of working. This includes skills they gain from training and actually working. For instance, the skills a Brainly website designer gets from working on Brainly.

Research suggests that this human capital has led to about a 20% growth in U.S. productivity from the year 1950 to the year 2007 which means that it is a very significant factor in the growth of the country.

Answer:

red marbles

Step-by-step explanation:

Since the formula is;

Probability = number of required outcome

_______________________

number of possible outcome

3/8. = x/56

8x. = 168

x. 21 ( number of blue marbles)

Therefore if the total marbles = 56 and 21 of the marbles are blue then to get the red marbles

= 56 - 21

= 35

Answer:

124.4

Step-by-step explanation:

Perimeter of ∆HIJ = IJ + HJ + HI

IJ = 40

HJ = 37.6

HI = ?

Let's find HI

∆HIJ and ∆EFG are similar. Since they have equal corresponding angles. Therefore, the ratio of their corresponding sides would be equal.

Thus:

EF/HI = FG/IJ

EF = 117 (given)

HI = ?

FG = 100 (given)

IJ = 40 (given)

Plug in the values

117/HI = 100/40

117/HI = 2.5

117 = HI*2.5

117/2.5 = HI

HI = 46.8

✔️Perimeter of ∆HIJ = IJ + HJ + HI

= 40 + 37.6 + 46.8

= 124.4

Answer:

I think 84 but you may need to check just to be sure :)

Answer:

= 1728km2

Step-by-step explanation:

From the formula A = PRT/100%

Where; A is final

P is initial

T is time taken

R is the rate

Therefore A = 3600 × (6/100) × 8

= 1728km2

Answer:

x ≈ 60.6°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{IJ}{HI}[/tex] = [tex]\frac{3.9}{2.2}[/tex] , then

x = [tex]tan^{-1}[/tex] ([tex]\frac{3.9}{2.2}[/tex] ) ≈ 60.6° ( to the nearest tenth )

Answer:

1.)36

2.)54

Step-by-step explanation:

sana po makatulong gehehe

Answer:

A

Step-by-step explanation:

Start with the 3.

You know that there is a difference of 4 between (say) 2 and 5. The 3 is a sign that the sequence is increasing.  The members of the sequence are going up.

n - 1 means that the nth terms is calculated as an and uses the number of terms to be n-1. That means that the first term is a1 which is the starting point of the sequence.

The answer is an = a1 + (n-1)*d

d = 3

a1 = - 7

So let's try the formula out.

a4 = -7 + (4 - 1)*3

a4 = -7 + 3 * 3

a4 = -7 + 9

a4 = 2

Is 2 the 4th term in the series? Yes it is!

Answer:

x = 2

Step-by-step explanation:

note that 4096 = [tex]8^{4}[/tex] , then

[tex]8^{2x}[/tex] = [tex]8^{4}[/tex]

Since bases on both sides are equal, both 8 , then equate the exponents

2x = 4 ( divide both sides by 2 )

x = 2

Answer:

x = 2

Step-by-step explanation:

[tex]8^{2x} = 4096[/tex]

Step 1 :- Write 4096 in the exponential form with the base of 8.

[tex]8^{2x} = 8^4 [/tex]

Step 2 :- Since the base of both equation is same , set the exponents equal.

2x = 4

Step 3 :- Divide both side by 2

[tex]{2x}{2} = \frac{4 }{2}[/tex]

x = 2

Answer:

Population

Step-by-step explanation:

A population can be defined as the total number of living organisms living together in a particular place and sharing certain characteristics in common.

A sample survey is a statistical method used for the collection of data from a target population in order to draw an inference and reach a logical conclusion.

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

In this scenario, the entire group of registered voters in Florida is an example of a population.

Answer:

Uhh what??

Step-by-step explanation:

Do you mean like 1.75 in a decimal form??

Answer:

729/15625

Step-by-step explanation:

1. Evaluate the power

( (27/125) ÷ 1 )^2

2. divide

( 27/125 )^2

evaluate the power

( 27^2 / 125^2 )

729/15625

Answer: z=56

Step-by-step explanation:

Based on the figure, we can determine that 3y+8=68 and 4x=2z. With the knowledge that a trapezoid has 360°, we can first find the value of y to get the angle measures of the top angles. We can then subtract that from 360°.

3y+8=68        [subtract both sides by 8]

3y=60            [divide both sides by 3]

y=20

We now know the value of y is 20, but that is not relevant to solving this problem because we already know that the top angles are 68° each. So, we can subtract that from 360.

360-68-68=224

Now, we know that the bottom 2 angles have to add up to 224. Therefore, we can come up with 2 equations.

Equation 1: 4x=2z

Equation 2: 4x+2z=224

We can manipulate Equation 1 to be [tex]x=\frac{1}{2}z[/tex]. Once we plug that into Equation 2, we can find the value of z.

[tex]4(\frac{1}{2} z)+2z=224[/tex]         [multiply]

[tex]2z+2z=224[/tex]              [add]

[tex]4z=224[/tex]                      [divide both sides by 4]

[tex]z=56[/tex]

Now, we know that z=56.

Answer:

I'm assuming the chessboard is square so 49cm square.

Step-by-step explanation:

Area of a square= side × side

7×7=49

Have a nice day.

The area of the chessboard is 49 square inches, and which side length is 7 inches.

To find the area of the chessboard, we need to calculate the product of its length and width.

In this case, since the chessboard is a square, the length, and width are equal.

Given that the side length of the chessboard is 7 inches, we can calculate the area as follows:

Area of the chessboard = side length x side length

Area of the chessboard = 7 inches x 7 inches

Area of the chessboard = 49 square inches

Therefore, the area of the chessboard is 49 square inches.

Learn more about the area of the square here:

brainly.com/question/1561162

#SPJ2

Answer:

C. Shading should go below a dashed line

Step-by-step explanation:

y <

Y is less than. So, shade below where all the numbers are less than

And because it's NOT [tex]\leq[/tex] or [tex]\geq[/tex] , its dotted. Meaning the solutions are not on the line.

Answer:

V = 2

Step-by-step explanation:

P = 8/v

4 = 8/v

8/4 = 2

v = 2

Answer:

v=2

Step-by-step explanation:

p=8/v

When p = 4, 4=8/v

We multiply both sides by v, we get:

4v=8

Now we divide both sides by 4,

v=2

Answer:

Balance = 60x-1500

Step-by-step explanation:

Given data

total number of students= x student

amount paid by each student= Rs 60

Total amount= Rs 60*x

Advance paid for transport= Rs 1500

Hence the balance is = 60x-1500

Answer:

A) y = -5/8x + 6

Step-by-step explanation:

y2 - y`1 / x2 - x1

7/2 - 11 / 4 - (-8)

-15/2  / 12

= -5/8

y = -5/8x + b

11 = -5/8(-8) + b

11 = 5 + b

6 = b

Answer:

Option (A)

y = - 5 / 8 x + 6

Step-by-step explanation:

Two points are

(x', y') = ( - 8, 11 )

(x'', y'') = (4, 7/2)

The equation o line passing through two points is given by

[tex](y - y') = \frac{y'' - y'}{x''-x'}(x-x')\\\\(y - 11)= \frac{\frac{7}{2}-11}{4+8} (x + 8)\\\\y - 11 = \frac{-5}{8}(x + 8)\\\\y -11 = \frac{-5x}{8} - 5\\\\y = \frac{-5x}{8} + 6[/tex]

So, option (A) is correct.  

Answer: $268.75

Step-by-step explanation:

First, find the amount he earned from his sales:

1500(0.0125) = $18.75

Next, add that to his monthly salary:

$250 + $18.75 = $268.75

Answer:

The cost of an adult ticket is $12.50

Step-by-step explanation:

The given information are;

The cost of two adult tickets and three children tickets = $43.00

The cost of one adult ticket and one child ticket = $18.50

Whereby the cost of an adult ticket is represented by x and the cost of a child's ticket is represented by y, we get the following two simultaneous equations;

2·x + 3·y = 43.00...(1)

x + y = 18.5...(2)

(ii) Multiplying equation (2) by 2 and subtracting the result from equation (1) gives;

2·x + 3·y - 2×(x + y) = 43 - 2×18.5 = 6

2·x - 2·x + 3·y - 2·y = 0 + y = 6

∴ y = 6

The cost of each the children ticket = $6.00

From equation (2), where y = 6, we get;

x + y = 18.5

∴ x + 6 = 18.5

x = 18.5 - 6 = 12.5

The cost of an adult ticket, x = $12.50.