Which expression is equivalent to 8a + 20? (5 points)

Select one:
a. 4(2a + 20)
b. 4(2a + 5)
c. 4(4a + 16)
d. 4(4a + 5)

The initial number of carbon-14 atoms in the organism at the time of death was 200 atoms.

The initial number of carbon-14 atoms in the organism at death can be calculated using the formula for exponential decay:

[tex]\[ N(t) = N_0 e^{-\lambda t} \][/tex]

where:

- [tex]\( N(t) \)[/tex] is the number of undecayed carbon-14 atoms at time [tex]\( t \),[/tex]

- [tex]\( N_0 \)[/tex] is the initial number of carbon-14 atoms at time \[tex]( t = 0 \[/tex]) (the time of death),

- [tex]\( \lambda \)[/tex] is the decay constant for carbon-14,

- [tex]\( t \)[/tex] is the time that has passed since the time of death.

 Given that after 5730 years (the half-life of carbon-14), the number of undecayed carbon-14 atoms is half the initial amount, we can write:

[tex]\[ \frac{N_0}{2} = N_0 e^{-\lambda \times 5730} \][/tex]

To find the decay constant [tex]\( \lambda \)[/tex], we use the half-life formula:

[tex]\[ \lambda = \frac{\ln(2)}{t_{1/2}} \][/tex]

 where [tex]\( t_{1/2} \)[/tex] is the half-life of carbon-14, which is 5730 years. Plugging in the values:

[tex]\[ \lambda = \frac{\ln(2)}{5730} \][/tex]

Now, we can solve for [tex]\( N_0 \)[/tex]using the information provided:

[tex]\[ 100 = N_0 e^{-\frac{\ln(2)}{5730} \times 573[/tex]

 Since [tex]\( e^{-\ln(2)} = \frac{1}{2} \)[/tex], the equation simplifies to:

[tex]\[ 100 = N_0 \times \frac{1}{2} \][/tex]

Solving for [tex]\( N_0 \):[/tex]

[tex]\[ N_0 = 100 \times 2 \][/tex]

[tex]\[ N_0 = 200 \][/tex]

 Therefore, the initial number of carbon-14 atoms in the organism at the time of death was 200 atoms.

Answer:

Step-by-step explanation:

2nd one

Answer:

What is your question?

Is " n " to the left or the right?

How many units are on the number line?

It may be the number 3.

The values of n is a distance of 3 units from 1 1/2 on a number line are 4.5 units and -1.5units

The number line consists of positive values to the right of zero and negative values to the left.

Given the value 1 1/2 units, it is 1.5 units to the right of zero.

If the value of n is a distance of 3 units from 1 1/2 on a number line, the value of n can be 3 units to the right or to the left.

Valuee to the right  = 3 + 1.5 = 4.5units

Value to the left = 1.5 - 3 = -1.5 units

Hence the values of n is a distance of 3 units from 1 1/2 on a number line are 4.5 units and -1.5units

Learn more here: https://brainly.com/question/23379455

Answer:

m∠8 = 124°

Step-by-step explanation:

1. Find m∠1

m∠1 and m∠2 are supplementary, since they are on the same line.

That means m∠1 + m∠2 = 180.

Plug in: 4x + 2x - 6 = 180

Simplify + subtract: 6x = 186

Divide: x = 31

Plug in: m∠1 = 4(31) --> m∠1 = 124°

2. Since ∠1 and ∠4 are vertical, they are congruent. Since ∠4 and ∠8 are corresponding on parallel lines, they are also congruent. Therefore, ∠1 and ∠8 are congruent, which means m∠1 = m∠8

Plug in: m∠8 = 124°

X is 4 and Y is 4 Square Root of 2 (or 5.656854)

Answer:

2=9

4=17

Step-by-step explanation:

4(2)+1

8+1=9

4(4)+1

16+1=17

37.5% as a fraction is 3/8.

Answer:

3/8

Step-by-step explanation:

To write a percent as a fraction, divide the percent by 100.

37.5% = 37.5/100

Now we reduce the fraction. First, multiply the numerator and denominator by 2 to get rid of the decimal in the numerator.

37.5% = 37.5/100 = 75/200

Both the numerator and denominator are divisible by 5, so we divide them by 5.

37.5% = 37.5/100 = 75/200 = 15/40

Both the numerator and denominator are divisible by 5 again, so we divide them by 5 again.

37.5% = 37.5/100 = 75/200 = 15/40 = 3/8

Answer: 37.5% = 3/8

Answer:

a rectangle with two triangles.

Step-by-step explanation:

this way you will  be able to find the area of the rectangle then add it to the area of the two triangles.

Answer:

the correct answer is b

Step-by-step explanation:

Answer:

x = - 1

Step-by-step explanation:

Given

3x + 2 = y and y = - 1

Substitute y = - 1 into the equation and solve for x, that is

3x + 2 = - 1 ( subtract 2 from both sides )

3x = - 3 ( divide both sides by 3 )

x = - 1

This is verified by the point on the graph with coordinates (- 1, - 1)

Method 1: By substitution

Step 1: In the equation 3x + 2 = y when you see a y replace it with -1

3x + 2 = -1

Step 2: Combine like terms by subtracting 2 to both sides

3x + (2-2) = -1 - 2

3x = -3

Step 3: Isolate x by dividing 3 to both sides

[tex]\frac{3x}{3} = \frac{-3}{3}[/tex]

x = -1

Method 2: By looking at the graph

To solve this way you see where the line on the graph has y = -1 and look for its complimentary x

If you look at the graph attached below you can see that at y = -1 the x also equals -1

x = -1

Hope this helped!

The answer is:

The area of this figure is 946 square inches.

We can see that the figure is composed by two rectangles with diferrent dimensions, so, to calculate the area of the entire figure.

So,

For the first rectangle, we have:

[tex]Base=7in\\Height=28in[/tex]

The area will be:

[tex]Area=Base*Height=7in*28in=196in^{2}[/tex]

For the second rectangle, we have:

[tex]Base=25in\\Height=30in[/tex]

The area will be:

[tex]Area=Base*Height=30in*25in=750in^{2}[/tex]

Now, calculating the area of the entire figure, we have:

[tex]TotalArea=FirstRectangleArea+SecondRectangleArea\\\\TotalArea=196in^{2}+750in^{2}=946in^{2}[/tex]

Have a nice day!

Answer:

3x+5

Step-by-step explanation:

i took test

ANSWER

[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]

EXPLANATION

The given functions are

[tex]f(x) = {x}^{3} - 27[/tex]

and

[tex]g(x) = 3x - 9[/tex]

[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]

[tex]( \frac{f}{g} )(x) = \frac{ {x}^{3} - 27}{3x - 9} [/tex]

[tex]( \frac{f}{g} )(x) = \frac{ (x - 3)( {x}^{2} + 3x + 9) }{3(x -3 )} [/tex]

Cancel the common factors,

[tex]( \frac{f}{g} )(x) = \frac{ {x}^{2} + 3x + 9 }{3} [/tex]

OR

[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]

Hello There!

The first one seems alright.

The second one it would be 1/2.

This is because half of the options have “R” on them.

Answer: 1. is 5/6

2. is 1/2

Step-by-step explanation:

Durain beans cost $9 per pound and they sold 11 pounds.

Multiply the cost by the amount sold: 9 x 11 = $99

Subtract that from the total sold:

196 - 99 = $97

Now divide the amount left by the cost per pound for Ice cream beans:

97 / 10 = 9.7 pounds.

Round the answer as needed to match one of your choices.

This is just a ONE STEP equation.

It is, because all you must do to solve for "x" is subtract 2

Answer:

one-step equation

x+2=14

x+2-2=14-2

x=12

Answer:

Days, Hours

Step-by-step explanation:

1 day  = 24 hours

2 days = 48 hours

3 days = 72 hours  

4 days = 96 hours

(its increasing by 24)

Answer:

a) The sold games of Jezebel had the greatest spread.

b) The middle 50% of the games sold by Colin has the least spread.

c) Jezebel sold more games than colin.

Step-by-step explanation:

Range is sued to calculate the spread of the given data.

Range is given by:

Range=Max Value-Min Value

So,

Part a)

For Collin:

Range=21-3=18

For Jezebel:

Range=26-5=21

Part b)

Middle 50% of the values will be the values between 1st quartile and 3rd quartile

So, to find quartiles:

For Colin:

=3,9,9,14,15,16,17,20,21

The median is 15.

The lower half is 3,9,9,14

Q1 = (9+9)/2= 18/2 = 9

The upper half is 16,17,20,21

Q3 = (17+20)/2= 37/2= 18.5

The middle 50% is first quartile subtracted from third quartile

So, the spread is:

18.5-9=9.5

For Jezebel:

4,5,8,10,11,14,20,20,26

The median is 11.

The lower half is 4,5,8,10

Q1 = (5+8)/2=13/2=6.5

The upper half is 14,20,20,26

Q3 = (20+20)/2=40/2=20

The middle 50% values' spread is:

20-6.5=13.5

Part c) The answer to part a tells us that Jezebels sold games have more spread than Colin's sold games. Similarly the answer of part b tells us that the spread of middle 50% values of Jezebel's sold games was more than the spread of middle 50% values of Colin's sold games ..

[tex]

(2x^2+2x+3)-(x^2+2x+1) \\

2x^2+2x+3-x^2-2x-1 \\

\boxed{x^2+2}

[/tex]

The answer is your mom. Nah it’s B)10

For this case we have that the perimeter of the figure is given by the sum of its sides, they tell us that the perimeter is 62 feet.

So:

Let "x" be the variable that represents the length of the unlabeled wall, so the perimeter is:

[tex]x + 8 + 5 + 13 + 18 + 8 = 62[/tex]

We find the value of "x":

[tex]x = 62-8-5-13-18-8\\x = 10[/tex]

Thus, the length of the unlabeled wall is 10 feet.

Answer:

Option B

Answer:

Option d) [tex]P=\frac{4}{17}[/tex]

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]

In this problem we have

[tex]x=13-1=12[/tex]

[tex]y=52-1=51[/tex]

substitute

[tex]P=\frac{12}{51}[/tex]

Simplify

[tex]P=\frac{4}{17}[/tex]

Answer:

B

Step-by-step explanation:

rsu is equal to vst, so you can solve 5x+17=9x-11, which yields x=7.

So vst=52 and wsv=90-52=38.

For this case we have to define trigonometric relations of rectangular triangles that:

Then, according to the figure we have:

[tex]Sin (M) = \frac {3} {5}\\M = ArcSine (\frac {3} {5})[/tex]

[tex]M = 36.87[/tex] degrees

Answer:

36.87 degrees

Answer:

60 out of 250 children will prefer organized sports.

Step-by-step explanation:

We are given the results of a random survey of children between the ages of 13 and 18 about their favorite activity.

Based on these results, we are to find the number of children who will prefer organized sports if 250 children were asked about their favorite activity.

Children who will prefer organized sports = [tex]\frac{37}{155} \times 250[/tex] = 60

There are 16 oz in a pound, so 2 lbs is 32 oz.

Answer: two pounds is equivalent to 32 ounces.

Step-by-step explanation: 1 pound is equal to 16 ounces, and since 2 is 1 two times, just multiply 16 by 2, 16x2=32 ounces

ANSWER

[tex](1-7x)(1+9x) =- 63 {x}^{2} + 2x + 1[/tex]

EXPLANATION

The given product is (1-7x)(1+9x).

Expand using the distributive property.

[tex](1-7x)(1+9x) = 1(1 + 9x) - 7x(1 + 9x)[/tex]

[tex](1-7x)(1+9x) = 1 + 9x - 7x - 63 {x}^{2}[/tex]

Simplify to obtain:

[tex](1-7x)(1+9x) = 1 + 2x - 63 {x}^{2}[/tex]

You can rewrite in standard form to get,

[tex](1-7x)(1+9x) =- 63 {x}^{2} + 2x + 1[/tex]

Answer:

1+2x-63x^2

Step-by-step explanation:

factor 1(1+9x)=1+9X

-7x(1+9x)=-7x-63x^2

add 1+9x-7x-63x2

Answer:

y = 0.10x + 8, $12

Step-by-step explanation:

y = monthly bill

x = number of message units

Each message unit costs $0.10, so the cost of x message units is 0.10x.  The phone adds $8 to the monthly bill.  Therefore:

y = 0.10x + 8

If x = 40, then:

y = 0.10 (40) + 8

y = 4 + 8

y = 12

The monthly bill is $12.

Answer:

  27

Step-by-step explanation:

The central angle of 120° is 1/3 of the entire circle of 360°, so the sector area is 1/3 of the circle area:

  1/3×81 = 27

The sector area is 27.

Answer:

Multiply the length and the width of the shape together to get the area of the square or rectangle in square feet.

10 multiplied by 8 equals 80 square feet

Step-by-step explanation:

Got a 100 on it.

Final answer:

To cover a rectangular garden measuring 10 feet by 8 feet, multiply the length by the width to get an area of 80 square feet, which is the amount of material needed.

Explanation:

Calculating the Area of a Rectangular Garden

To determine the number of square feet required to cover your rectangular garden, you need to calculate the area of the garden. The area of a rectangle is found by multiplying the length by the width. In this case, the garden has a length of 10 feet and a width of 8 feet.

Steps to Calculate the Area

Measure the length and width of the garden using a measuring tape.

Multiply the length by the width to get the area in square feet: 10 feet (length) × 8 feet (width) = 80 square feet.

Therefore, you would need 80 square feet of material to cover the entire garden.

Answer:

The answer is 75

Step-by-step explanation:

The answer is .22222..., 3/10, .53, and 3/5.

Hope this helps!

Hello there!

The numbers in order from least to greatest are:

0.2222, 3/10, 0.53, 3/5

Start by turning all the numbers into either decimals. To do this, take the two fractions, 3/5 and 3/10 and divide them out.

3 divided by 5 = 0.6

3 divided by 10 = 0.3

Now let's look at our numbers again.

0.3, 0.222, 0.6, 0.53.

We know that 2 is less than 3, and 3 is less than 5, and 5 is less than 6, so lets rearrange the numbers into that order.

0.2222, 0.3, 0.53, 0.6

Now, convert any fractions that were converted into decimals back into their original forms.

0.2222, 3/10, 0.53, 3/5

This is your final answer. I hope this helps and have a great day!