two grains of salt have a mass of approximatley one microgram or 0.000001g which expression represents this number in scientific notation

Answer:

The amount invested at 3–yr CD was $3,600 and the amount invested at 6–month CD was $2,600

Step-by-step explanation:

Let

x -----> the amount invested at 3–yr CD

x-$1,000 ----> the amount invested at 6–month CD

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

3–yr CD

[tex]t=3\ years\\P=x\\r=0.038[/tex]

substitute in the formula above

[tex]I1=x(0.038*3)[/tex]

[tex]I1=0.114x[/tex]

6–month CD

[tex]t=6/12=0.5\ years\\P=x-1,000\\r=0.02[/tex]

substitute in the formula above

[tex]I2=(1,000-x)(0.02*0.5)[/tex]

[tex]I2=10-0.01x[/tex]

Remember that

the total amount of interest from these investments was $424.00

so

[tex]I1+I2=424[/tex]

substitute and solve for x

[tex]0.114x+10+0.01x=424[/tex]

[tex]0.115x=414[/tex]

[tex]x=\$3,600[/tex]

[tex]x-\$1,000=\$2,600[/tex]

therefore

The amount invested at 3–yr CD was $3,600 and the amount invested at 6–month CD was $2,600

Answer:

24

Step-by-step explanation:

- (5*5) +6*5 +19

-25 + 30 + 19 = 24

The solution to the equation a+5=-5a+5 is a=0.

We are given that;

The expression a+5=-5a+5

Now,

To solve the equation a+5=-5a+5, we need to isolate the variable a on one side of the equation.

We can do this by adding 5a to both sides of the equation:

a + 5 + 5a = -5a + 5 + 5a

Combining like terms gives:

6a + 5 = 5

Subtracting 5 from both sides of the equation gives:

6a = 0

Dividing both sides of the equation by 6 gives:

a = 0

Therefore, by algebra the answer will be a=0.

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Answer:

all work is shown and pictured

Answer:

C

Step-by-step explanation:

This curve will only have one maximum point at (-3, 2)

The nature of the graph from point A to B : The graph increases, then decreases.

Given,

Graph is x -y coordinates.

Now,

Graph is concave downwards.

Coordinates of point A : (0,0)

Coordinates of point B : (6,0)

So,

The graph firstly increases from x = 0 to x = 3.

Then,

The graph decreases from x = 3 to x = 6 .

Therefore the graph increases and then decreases.

Thus option D is correct.

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Answer:

[tex]\frac{\sqrt[5]{810x^3}}{3x}[/tex]

Step-by-step explanation:

We are given that an expression

[tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex]

We have to simplify the given expression.

[tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex]

Multiply numerator and denominator by  [tex]81x^2[/tex]

[tex]\sqrt[5]{\frac{10\cdot 81x^3}{243x^5}}[/tex]

After multiplying ,then we get

[tex]\sqrt[5]{\frac{810x^3}{243x^5}}[/tex]

[tex]\frac{\sqrt[5]{810x^3}}{3x}[/tex]

Hence, option d is true.

Answer:[tex]\frac{\sqrt[5]{810x^3}}{3x}[/tex]

Answer:it’s D. On edge

Step-by-step explanation:

Answer:The standard deviation is about 3.6.

Step-by-step explanation:

According to the Range Rule of Thumb  : The range is about four times the standard deviation.

i.e.  [tex]R\approx4\sigma\Rightarrow\ \sigma\approx\dfrac{R}{4}[/tex]   (i)

Given , The race speeds for the top eight cars in a 200-mile race are :

185.9 179.5 189.2 176.7 175.8 188.7. 188.3 177.9

Here , minimum speed =  175.8 and maximum speed = 189.2

Range = maximum speed - minimum speed

i.e. R = 189.2-175.8 =13.4

from (i),

[tex]\sigma\approx\dfrac{13.4}{4}\\\\\Rightarrow\sigma\approx3.6[/tex]

Hence, the standard deviation is about 3.6.

Answer:

g= - 4/11 in 3+g=1/4

Step-by-step explanation:

Use the site that I will comment . But it won't show you the step to the answer if you each month. I can't submit the answer with the site's name.

Answer:

20

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = 3x² - 2 + 4x + 2 = 3x² + 4x

Substitute x = 2 into f(x) + g(x)

(f + g)(2) = 3(2)² + 4(2) = (3 × 4) + 8 = 12 + 8 = 20

Answer:

The missing portion is + 16x + 16.

Step-by-step explanation:

In order to get [tex]f(g(x))[/tex], we put

[tex]g(x)= \dfrac{1}{2x+4}[/tex]  

into

[tex]f(x)= \dfrac{1}{x^2}[/tex],

which gives us

[tex]f(g(x))= \dfrac{1}{(g(x) )^2}[/tex]

[tex]f(g(x))= \dfrac{1}{(\dfrac{1}{2x+4} )^2}[/tex]

[tex]f(g(x))= (2x+4)^2[/tex]

we expand and get:

[tex]f(g(x))= 4x^2+16x+16[/tex].

Thus, we see that the missing portion is [tex]16x+16.[/tex]

Answer:

42 that's ur answer u just multiply all the numbers

The multiplication of 3, 7, and 2 (which are all prime numbers) equals to 42. Therefore, 42 is the number which has a prime factorization of 2, 3, and 7.

The product of 3 x 7 x 2 gives us the number for which this is the prime factorization. The prime factorization of a number is the breaking down of that number into its simplest factors that are prime numbers, in this case, it would be 2, 3, and 7. By multiplying these number together: 3 x 7 x 2, we get the number 42, hence, 42 is a number we are looking for.

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Answer:

r=-16

Step-by-step explanation:

21=6r+5-7r

1) Combine alike terms on the right side (6r and -7r):

21=-r+5

2) Subtract a 5 from both sides:

16=-r

3) Divide both sides by -1:

r=-16

Step-by-step explanation:

first combine like terms : 6r and -7r = -1r

21=5 -1r

cancellation cancel the same terms on both sides of the equation by inverse operations:

subtract 5 from both sides 21-5= 16 5-5=0

16=-1r

divide both ends of the equation by -1

16÷1 = 16 1÷ -1= 1

16=r

Answer:

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

1

2

(8x+20)=18

Simplify: (Show steps)

4x+10=18

Step 2: Subtract 10 from both sides.

4x+10−10=18−10

4x=8

Step 3: Divide both sides by 4.

4x

4

=

8

4

x=2

Answer:

x=2

Mari has 42 coins consisting of nickels, dimes, and quarters. The total value of the coins is $9.35. The number of dimes is one less than three times the number of nickels. Mari has 17 nickels, 8 dimes, and 17 quarters.

Let's use algebraic equations to solve this problem.

Let "n" be the number of nickels, "d" be the number of dimes, and "q" be the number of quarters.

We have three pieces of information from the problem:

1. The total number of coins: n + d + q = 42

2. The total value of the coins: 0.05n + 0.10d + 0.25q = 9.35

3. The number of dimes is one less than three times the number of nickels: d = 3n - 1

Now, let's substitute the third equation into the first equation to express "d" in terms of "n":

(3n - 1) + n + q = 42

4n + q = 43

q = 43 - 4n

Next, we'll substitute the values of "q" and "d" into the second equation:

0.05n + 0.10(3n - 1) + 0.25(43 - 4n) = 9.35

0.05n + 0.30n - 0.10 + 10.75 - n = 9.35

0.35n + 10.65 = 9.35

0.35n = 9.35 - 10.65

0.35n = -1.30

n = -1.30 / 0.35

n ≈ 3.71

Since the number of coins can't be a fraction, we'll round down to the nearest whole number. Therefore, Mari has 3 nickels.

Now, let's find the number of dimes:

d = 3n - 1

d = 3(3) - 1

d = 9 - 1

d = 8

Finally, we can find the number of quarters using the equation for "q":

q = 43 - 4n

q = 43 - 4(3)

q = 43 - 12

q = 31

In conclusion, Mari has 3 nickels, 8 dimes, and 31 quarters.

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Answer:

12.700

or 12.7

or 12.70

Answer: the answer is 48 with a remander of 0 my friend

Step-by-step explanation:

Answer:

In year 2030 the population is predicted to be 71.75 million

Step-by-step explanation:

* Lets explain how to solve the problem

- Using data from 2010 and projected to 2020, the population of

 the United Kingdom (y, in millions) can be approximated by the

 equation  10.0 y − 4.55 x = 581

- x is the number of years after 2000

- We need to know in what year the population is predicted to be

  71.75 million

* Lets substitute the value of y in the equation by 71,75

∵ The equation of the population is 10.0 y - 4.55 x = 581

∵ y = 71.75

∴ 10.0(71.75) - 4.55 x = 581

∴ 717.5 - 4.55 x = 581

- Subtract 717.5 from both sides

∴ - 4.55 x = - 136.5

- Divide both sides by - 4.55

∴ x = 30

∵ x represents the number of years after 2000

∵ 2000 + 30 = 2030

∴ In year 2030 the population is predicted to be 71.75 million

Final answer:

The population of the United Kingdom is predicted to be 71.75 million in the year 2030, calculated by substituting the given population value into the equation and solving for the year.

Explanation:

To find the year in which the population of the United Kingdom is predicted to be 71.75 million, you can use the given equation 10.0y - 4.55x = 581. Here, x is the number of years after 2000, and y is the population in millions.

First, substitute y with 71.75:

Now, add the number of years, x, to the base year, 2000:

Therefore, the population of the United Kingdom is predicted to be 71.75 million in the year 2030.

Answer:

Step-by-step explanation:

Find the prime factorization of 10

10 = 2 × 5

Find the prime factorization of 24

24 = 2 × 2 × 2 × 3

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2 × 2 × 2 × 3 × 5

LCM = 120

Answer:

f = -15

Step-by-step explanation:

f/5 - 22 = -25 -------- add -22 to both sides to isolate 'f'

f/5 = -3 ------- multiply 5 to both sides to further isolate 'f'

f = -15

Answer:$1340

Step-by-step explanation:

Answer:

2x-3 = -11

Step-by-step explanation:

|2x-3| = 11

by definition of absolute numbers,

2x-3 = 11 (given)

or

2x-3 = -11 (answer)

Answer:

○ B) 624π mm.²

Step-by-step explanation:

[tex]\pi r(r + \sqrt{ {r}^{2} + {h}^{2}}) = S. A. \\ \\ \pi (12)(12 + \sqrt{{12}^{2} + {40}^{2}}) \\ \\ 12\pi(12 + \sqrt{1744}) = 12\pi(12 + 38) = 12\pi(50) = 600\pi \\ \\ 600\pi ≈ 624\pi[/tex]

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Answer:

The correct answer is 2 1/36.

To find out how many books Molly read over four weeks during the summer, multiply the number of books she read in one week by four.

Molly read a few books each week during the summer. To calculate how many books she read over four weeks, we can multiply the number of books she read in one week by four.

If she read 'x' books per week, then over four weeks she would have read 4x books.

Therefore, if she read 5 books per week, Molly would have read a total of 20 books over four weeks.

Answer:

[tex]\frac{175}{2x}[/tex]

Step-by-step explanation:

Jon works the same number of hours on Friday and Saturday, therefore x represents the number of hours worked on Friday and also the number of hours worked on Saturday.

So the total hours worked between Friday and Saturday is 2X

If the total for the 2X hours worked is equal to 175 $  

To know how much you earn per hour, we must divide the profit by the total hours worked.

Then we have the following expression

To know how much you earn per hour, we must divide the profit by the total hours worked.

[tex]\frac{175}{2x}[/tex]

Answer:

1

Step-by-step explanation:

1 to any power is 1, so you are basically just saying 1*1, and that equals 1

Answer:

D. A'(2, -5)

Step-by-step explanation:

Since point A is at (2, 5), and you are reflecting it across the x-axis, you take a look at the y-coordinate. Since it is five above the x-axis, you go five below the x-axis, or just give the OPPOSITE of 5, which is -5.

So, A' is at (2, -5).

I am delighted to assist you anytime.

When point A(2, 5) is reflected over the x-axis, its y-coordinate becomes -5 while the x-coordinate remains the same, resulting in the image point A'(2, -5).

The correct answer is option B.

When a point is reflected over the x-axis, its y-coordinate changes sign while the x-coordinate remains the same.

Let's apply this reflection to point A(2, 5):

Original point A(2, 5) has an x-coordinate of 2 and a y-coordinate of 5. When reflected over the x-axis, the x-coordinate remains 2, but the y-coordinate changes sign to -5. Therefore, the image of point A after the reflection is A'(2, -5).

So, the correct answer is:

D. A’(2, -5)

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