Find all solutions to the equationin the interval [O, 27). Enter thesolutions in increasing order.cos 2x = cos X[?]Tx = 0,2Remember: cos 20 = cos20 – sin20

As per the concept of multiplication, the amount of molecules of water does a person drink in a year is 13.2 x ²⁷ or 1.32 x 10²⁸.

Molecules:

Molecules are referred as the smallest particle of a substance that has all of the physical and chemical properties of that substance. It is made up of one or more atoms.

Given,

There are about 6 x 10²⁴ molecules in a liter of water. it is estimated that a person drinks about 2.2 x 10³ liters of water a year.

Here we need to find the amount of molecules of water does a person drink in a year.

To calculate the total amount of molecules consumption for the year we have to use the following formula,

That is,

Total molecules per year = amount of water per year x molecules in water.

Here we know that,

the amount of water consumption per year = 2.2 x 10³ liters

And the amount of molecules of one liter water = 6 x 10²⁴

When we apply the values on the formula, then we get,

=> total amount of molecules consumption = (2.2 x 10³) x (6 x 10²⁴)

=> (2.2 x 6) x (10³ x 10²⁴)

=> 13.2 x 10³⁺²⁴

=> 13.2 x ²⁷

Therefore, the amount of molecules of water does a person drink in a year is 13.2 x ²⁷ or 1.32 x 10²⁸.

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Answer:

       2 0 8

×       2 6

+    1 2 4 8

+    4 1 6  

=  5  4 0 8

The Answer of 208 × 26 Is 5.408

= 208 × 26

= (208 × 6) + (208 × 20)

= 1.248 + 4.160

= 5.408

__________________

Class: Elementary School

Lesson: Multiplication

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We have the measure of angles 1 and angle 2, as we can see from the diagram in the image, angles 1 and 2 added form the right angle (90°) in the figure.

Thus, the sum of x-6 and 5x, must be equal to 90°.

(a) Write an equation:

(b) To find the degree measure of each angle, first we need to solve for the value of x in the equation.

Combining like terms:

Adding 6 from both sides:

Divide both sides by 6:

Now that we have x, we find angle 1:

And the measure of angle 2:

Given the set of data

sort

Commute data (x)

24,25,27,30, 35,35,46,50,52

Commute distance (y)

20,20,29,20,34,39,29,34,50

The line of best fit is given by

with

R= 0.75

with function

Correct answer

option D

Answer: r ≈ 0.75

              t ≈ 0.8d + 11.5

Step-by-step explanation:

You have to use a graphing calculator to solve this problem.

This is the correct answer (I just took the test).

The values of the variables x and y such that the conjugate of - 6 - j 24 is found are 3 and 3, respectively.

Let α + i β be a complex number, whose conjugate is the complex number α - i β. In this problem we find the values of the variables x and y such that:

(x + i y) · (3 + i 5) = - 6 + i 24

3 · x + i 3 · y + i 5 · x + i² 5 · y = - 6 + i 24

(3 · x - 5 · y) + i (5 · x + 3 · y) = - 6 + i 24

Then, we need to solve the following system of linear equations:

3 · x - 5 · y = - 6

5 · x + 3 · y = 24

Now we proceed to solve the system algebraically. Clear x in the first equation:

x = (- 6 + 5 · y) / 3

x = - 2 + (5 / 3) · y

Substitute x on the second equation and clear y:

5 · [- 2 + (5 / 3) · y] + 3 · y = 24

- 10 + (25 / 3) · y + 3 · y = 24

34 / 3 · y = 34

(1 / 3) · y = 1

y = 3

Finally, we substitute on y in the first equation:

x = - 2 + (5 / 3) · 3

x = - 2 + 5

x = 3

The values of the variables x and y are 3 and 3, respectively.

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You have the following expression:

"the sum of five squared and five"

the previous statement, in a mathematical form is:

5² + 5

It is important to point out that you have "the sum" of two numbers, which numbers? five squared and five.

The simplified form is:

5² + 5 = 25 + 5 = 30

8 dlls for silver

16 dlls for brass

5 dlls profit silver

7 dlls profit spheres

Then the price is

8+5= 13 dlls for silver

16+7=23 dlls for brass

Let S and B be the amount of magnetic silver and brass sphers that are sold, respectively.

Then, Ms. Ball estimation is that

Also, she doesn't want to invest more than 20000, so

The objective function is

Subjected to:

GRAPH

The interection is at

So, the extremes must be at (0,1250), (1500,500), (2000,0) , (0,0).

So, if we replace the points

So, the amount she will need to stock to maximize her profit is 1500 of silver and 500 of brass, and the maximum profit is going to be 11000 dlls.

so the answer is 2282

Division operation is operation helps calculate unit rates and unit prices.

Division operation -

What method do you employ to determine the unit rate?

Simple division of the numerator and denominator yields the unit rate. The outcome tells us how many of the units in the numerator to anticipate for each unit in the denominator.

What in mathematics are rate and unit rate?

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The coordinate of the image after the transformation is (4, 65536)

From the question, the coordinate of the point is given as

(4, 16)

From the question, the equation of the function is given as

f(x) = 2^x

When the function is transformed. we have the equation of the transformed function to be given as

f(x) = 2^4x65536

So, we substitute 4 for in the equation f(x) = 2^4x

So, we have

f(4) = 2^(4 x 4)

Evaluate the products

f(4) = 2^16

Evaluate the exponent

f(4) = 65536

So, we have (4, 65536)

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The statement that " There is a 45% chance that it will rain in neither place" is true.

In the question ;

it is given that

Probability of raining here = 50% = 0.5

Probability of raining on mars = 10% = 0.1

So, the probability of not raining here = 1-0.5 = 0.5

and probability of not raining on mars = 1-0.1 = 0.9

Hence the probability of rain in neither place = (probability of not raining here)×(probability of not raining on mars) .

Substituting the values , we get

probability of rain in neither place = 0.5×0.9

= 0.45

= 45%

Therefore , the statement " There is 45% chance that it will rain in neither place" is true.

The given question is incomplete , the complete question is

There is a 50% chance of rain here and a 10% chance of rain on Mars. Therefore, there is a 45% chance that it will rain in neither place.

Is the statement True or False ?

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Let the original price of sneakers be x.

Determine the original price of the sneakers.

Solution

Question A:

- The number of households in the sample that lost electricity is 5

Question B:

- The standard deviation is 2.121

Final answers

- The number of households in the sample that lost electricity is 5

- The standard deviation is 2.121

The division of 8 1/8 by 7 1/12 is 91/136.

Division simply has to do with reduction of a number into different parts. On the other hand, a mixed number is the number that's made up of whole number and fraction.

Dividing 8 1/8 by 7 1/12 will go thus:

8 1/8 ÷ 7 1/12

Change to improper fraction

65/8 ÷ 85/7

= 65/8 × 7/85

= 91/136

The division will give a value of 91/136.

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five and seventy-nine hundredths = 5.79

Answer:

D. 86°

Explanation:

Given:

• The center of the circle = P

• The measure of arc AB = 86°

We want to find the measure of the angle APB.

By Circle's theorem: The measure of an arc is equal to the measure of the central angle subtended by the same arc.

Applying this theorem, we have that:

The measure of the angle APB is 86 degrees.

Option D is correct.

We can solve that problem using a linear function, we know that

Where y0 is the initial population and m is the rate of decreasing, we know that for each "x" years we have -700 birds, therefore

Let's use t instead of x

That's the equation that represents the population at time t

Therefore after 7 years, the population will be 17100 birds.

occur

the answer is 12/13 or 0.932

Explanation

when you have an event A, the complement of A, denoted by.

consists of all the outcomes in wich the event A does NOT ocurr

it is given by:

Step 1

find the probability of event A :(P(A)

The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible

so

let

favorable outcome = 4 (there are four 7 in the deck)

total outcomes=52

hence,replacing

Step 2

now, to find the probability that the event does NOT ocurrs ( not drawing a 7)

let's apply the formula

replace

therefore, the answer is 12/13 or 0.932

I hope this helps you

Solution

For this case we can calculate the mean in the following way:

And the standard deviation would be:

Notice that the time for both trips is the SAME but not known (let's use the letter T to address this unknown).

We also assign St to the speed of the train, and Sp to the speed of the plane.

Then, the relationship between the speeds according to the information they provide, is given by the equation:

Sp = 5 * St - 30

we also know that the train covers 140 km in the time T, Then according to the formula for speed (distance divided by time) we can say:

St = 140 km / T, therefore T = 140 km / St

We do something similar with the information on the distance covered by the plane:

Sp = 630 km / T which solving for T gives:

T = 630 km / Sp

Now we equal the expressions for T (since that time is the SAME as we noticed before, and get:

630 km / Sp = 140 / St

we corss-multiply to get the speeds in the numerator:

630 St = 140 Sp

ANd we use the very first equation we wrote (Sp = 5 * St - 30)

to replace Sp in terms of St:

630 St = 140 (5 St - 30)

Now use distributive property on the right to eliminate the parenthesis:

630 St = 700 St - 4200

add 4200 to both sides, and subtract 630 St from both sides :

4200 = 700 St - 630 St

4200 = 70 St

divide both sides by 70 to isolate St completely:

St = 4200 / 70

St = 60 km/h (this is the speed of the train)

Now we can find the value of the speed of the plane, using the first equation again:

Sp = 5 * St - 30 = 5 (60) - 30 = 300 - 30 = 270 km/h

Then the speed of the plane is: 270 km/h

Answer:

P = 0.30

Explanation:

From the table, we see that:

When: x = -5, Probability = 0.15

When: x = 0, Probability = 0.05

When: x = 5, Probability = 0.1

Therefore, the probability of -5 ≤ x ≤ 5 is obtained by the sum of the probabilities from -5 to 5, we have:

Therefore, the probability is 0.30

Given:

The population was 100 after 10 mins.

The population was 1500 after 30 mins.

To fill the blanks:

Explanation:

According to the problem, we write,

Dividing equation (2) by equation (1), we get

So, the equation becomes,

a) To find: The initial population

When P = 100 and t = 10, then the initial population would be,

Therefore, the initial population is 25.82.

b) To find: The doubling time

Using the formula,

The doubling time is 5.12 mins.

c) To find: The population after 65 mins

Substituting t = 65 and the initial population is 25.82 in equation (3) we get,

Therefore, the population after 65 mins is 171467.56.

d) To find: The time taken for the population to reach 10000

Substituting P = 10000 and the initial population is25.82 in equation (3) we get,

Therefore, the time taken for the population to reach 10000 is 44.01 mins.

Final answer:

• The initial population is 25.82.

• The doubling time is 5.12 mins.

• The population after 65 mins is 171467.56.

• The time taken for the population to reach 10000 is 44.01 mins.

By applying the elimination method, the solutions to this system of three linear equations include the following:

In order to determine the solutions to a system of three linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

x – y - 3z = 4                .........equation 1.

2x + 3y – 3z = -2          .........equation 2.

x + 3y – 2z = -4            .........equation 3.

From equation 1 and equation 3, we would eliminate x as follows:

x – y - 3z = 4

x + 3y – 2z = -4

-4y - z = 8                  .........equation 4.

Next, we would pick a different pair of linear equations to eliminate x:

(x – y - 3z = 4) × 2   ⇒ 2x - 2y - 6z = 8

2x - 2y - 6z = 8

2x + 3y - 3z = -2

-5y - 3z = 10                ........equation 5.

From equation 4 and equation 5, we would eliminate z to get the value of y:

(-4y - z = 8) × 3 ⇒ -12y - 3z = 24

-12y - 3z = 24

-5y - 3z = 10

-7y = 14

y = 14/7

y = -2.

For the value of z, we have:

-4y - z = 8

z = -4y - 8

z = -4(-2) - 8

z = 8 - 8

z = 0

For the value of x, we have:

x – y - 3z = 4

x = 4 + y + 3z

x = 4 - 2 + 3(0)

x = 2

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Substitute x = - 12 in each of the given equation, if the equation satisfy then tha x = -1 2

F) 1/2x + 22 = 20

1/2 ( -12) + 22 = 20

(-6) + 22 = 20

16 is not equal to 22

G) 15 -1/2x = 21

Substitute x = -12 in the expression :

15 - 1/2( -12) = 21

15 + 1/2(12) =21

15 + ( 6) = 21

21 = 21

Thus, The equation 15 - 1/2x = 21 is true for x = -12

H) 11 - 2x = 17

Susbstitute x = ( -12) in the equation :

11 - 2x = 17

11 - 2( -12) = 17

11 + 24 = 17

35 = 17

Since, 35 is not equal to 17

D) 3x - 19 = -17

SUsbtitute x = ( -12)

3( -12) - 19 = -17

-36 - 19 = -17

-36 = -17 + 19

-36 = 2

Since - 36 is not equal 2

Answer : G) 15 - 1/2x = 21

ANSWER and EXPLANATION

We want to solve the problem by using dimensional analysis.

To do this, let us convert the speed of the Bluebirds baseball to miles per hour.

We have that:

1 feet per second = 0.6818 miles per hour

125.4 feet per second = 85.50 miles per hour

As we can see the baseball of the Bluebirds is slower than the Robins (90 miles per hour)

Now, to complete the explanation:

When I convert the Bluebirds pitcher's speed to the same units as the Robins pitcher's speed, the speed is _85.50_ mi/h.

Since the Bluebirds pitcher's speed is _less than_ the Robins pitcher's speed, the pitcher on the __Robins_ throws a faster ball.​

1) Considering that the Area of a rectangle is given as:

2) We can then write the following equation plugging into that the length= 5.

Say the area is "A", then we can find the width this way:

Note that we rewrote that to solve it for w (width).

All we need is to plug into the A the quantity of the area of this rectangle

Thus, the answer is w=A/5

Given a rectangle with sides "a" and "b":

The area of the rectangle is:

The perimeter of the rectangle is:

Given the sides of the rectangle:

a = 74 ft

b = 93 ft

(a)

The area of the rectangle is:

The perimeter of the rectangle is:

(b) The wood will cover all the area of the court, then the area must the used.

(c) The tape will be placed around the court, then the perimeter must be used.

Answer:

(a)

(b)

(c) Perimeter

The value of x that makes the equation true is - 3 / 8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Therefore, the value of x that makes the equation true is the value that makes the two sides of the equation equal.

Hence,

3x - 6 / 3 = 7x - 3 / 6

3x - 2 = 7x - 1 / 2

add 2 to both sides of the equation

3x - 2 = 7x - 1 / 2

3x - 2 + 2 = 7x - 1 / 2 + 2

3x = 7x - 1 / 2 + 2

3x = 7x + 3 / 2

subtract 7x from both side of the equation

3x  - 7x = 7x - 7x + 3 / 2

- 4x = 3 / 2

cross multiply

- 8x = 3

x = - 3 / 8

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The value of x which makes the equation true is - 3 / 8.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 3x-6/3= 7x-3/6

Three x minus six divided by three equal to seven times of x minus three divided by six

3x-6/3= 7x-3/6

(9x-6)/3=(42x-3)/6

Apply cross multiplication

6(9x-6)=3(42x-3)

Apply distributive property

54x-36=126x-9

add 36 on both sides

54x=126x-9+36

54x=126x+27

-27=126x-54x

-27=72x

x=-27/72

x=-9/24=-3/8

Hence value of x is -3/8 for equation 3x-6/3= 7x-3/6.

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2. 4+ (-10)

3. 3+(-15)

4.2+5

5. (-10)+(-5)