What is the expression in scientific notation? (7 x 10^−12)(4 x 10^5)?

The decay factor of the exponential function represented by the table is \[tex]( \frac{1}{3} \).[/tex]

The decay factor of an exponential function in the form[tex]\( y = ab^x \)[/tex]is represented by the base, denoted as 'b.' In this scenario, we're given data in a table format. When observing the relationship between the input and output values, notice that as the input increases by 1 unit, the output decreases by a factor of [tex]\( \frac{1}{3} \) ([/tex]e.g., going from 2 to 6, a change in input by 1 unit results in the output decreasing from 6 to 2, a factor of \( \frac{1}{3} \) of the previous output).

The pattern here illustrates a consistent reduction by a factor of [tex]\( \frac{1}{3} \)[/tex]as the input increases. This characteristic aligns with the decay factor in an exponential function, indicating that the base 'b' in the function[tex]\( y = ab^x \) is \( \frac{1}{3} \).[/tex]This base value of[tex]\( \frac{1}{3} \)[/tex] signifies that the function is an exponential decay, where the output diminishes rapidly as the input increases.

Understanding the relationship between the input and output values is crucial in determining the behavior of an exponential function. In this case, recognizing the consistent factor by which the output decreases as the input increases helps identify the decay factor as [tex]\( \frac{1}{3} \),[/tex]indicating the rate of decrease in the exponential decay function.

The consistent reduction by a factor of[tex]\( \frac{1}{3} \)[/tex] establishes the decay pattern in the given exponential function, leading to the conclusion that the decay factor of the function is [tex]\( \frac{1}{3} \).[/tex]

The decay factor of the exponential function is 1/3

How to determine the decay factor of the exponential function

From the question, we have the following parameters that can be used in our computation:

The table of values

Where, we have

f(0) = 6

f(1) = 2

The decay factor (k) of the exponential function is calculated as

k = f(1)/f(0)

Substitute the known values into the equation

k = 2/6

Evaluate

k = 1/3

Hence, the decay factor of the exponential function is 1/3

Answer and Step-by-step explanation:

A system of equations is a group of equations that need to be manipulated in some way that will figure out the values of the variables.

The most common system of equations seen is a system of linear equations, which means that the degree of the variables is no more than 1. These can be solved using elimination, substitution, or even graphing, if applicable.

Hope this helps!

Answer:

A system of equations is 2 or more equations that need to be solved. When you solve a system of equations, the answer is where the equations intersect on a graph. Sometimes there is 2 solutions (equations intersect twice), 1 solution (equations intersect once), no solution (equations don't intersect), or infinite solutions ( equations are the same).

They are usually solved using substitution, elimination, or simply looking at a graph to see where the lines intersect.

Some examples:

2x+3y=15

x-3y=3

y=x^2+1

2x-y= -4

Answer:

-294

Step-by-step explanation:

-273 ÷ -21 = 13

hope this helps

Answer:

Sometimes

Step-by-step explanation:

If the volumes of two triangular prisms are the same, that means that:

[tex]\frac{1}{3} B_1h_1=\frac{1}{3} B_2h_2[/tex] , where B_1 and h_1 belong to one prism and B_2 and h_2 belong to the second.

It is possible that if the volumes are the same, the prisms are congruent. That means that B_1 = B_2 and h_1 = h_2. However, this isn't always the case. Here's a counterexample:

PRISM 1: B = 4, h = 3  ⇒  V = (1/3) * 4 * 3 = 4

PRISM 2: B = 2, h = 6  ⇒  V = (1/3) * 2 * 6 = 4

Their volumes are the same, but their dimensions certainly aren't. So this statement is true only sometimes.

Hope this helps!

Answer:

Sometimes true

Step-by-step explanation:

Volume = ⅓(base area × height)

The product 'base area × height' can be equal if the base and height are congruent, but there are other possibilities too

Example:

Base area of the second one is double but the height is half.

The answer should be:

x=0, 10/3

Answer:

Soda- 156

Hot Dogs- 52

Step-by-step explanation:

Final answer:

The vendor sold 156 sodas and 52 hot dogs at the basketball game. This was determined by setting up a system of equations using the total number of items sold and the ratio of sodas to hot dogs, then solving for each.

Explanation:

To find the number of sodas and hot dogs sold at the basketball game, we can set up a system of equations based on the information provided:

Let S represent the number of sodas sold.

Let H represent the number of hot dogs sold.

The problem states two key pieces of information:

The total number of sodas and hot dogs sold is 208: S + H = 208.

The number of sodas sold was three times the number of hot dogs sold: S = 3H.

We can substitute the second equation into the first to solve for H:

3H + H = 208

4H = 208

H = 208 / 4

H = 52

Now that we have the number of hot dogs sold (52), we can find the number of sodas sold:

S = 3H

S = 3 \\( 52 \)

S = 156

The vendor sold 156 sodas and 52 hot dogs.

Answer:

A. Reflection over the y-axis and rotation 90° counterclockwise

Answer:

The answer is A (:

Step-by-step explanation:

Answer:

21.25 feet or 255 inches.

Step-by-step explanation:

The first step in this problem is to covert each measurement to the same system of measurement (feet, inches, meters, etc.).

Let's convert 4 inches to feet.

As there are 12 inches in a foot, and 4/12 = 1/3, 4 inches = 1/3 foot.

Now, multiply 1/3 foot by 63 3/4 (the amount of feet in mixed number form).

63 3/4 * 1/3 = 21 1/4, or 21.25.

Therefore, the final answer is 21.25 feet.

If you want the answer in inches, all you have to do is multiply 21.25 by 12, as there are 12 inches in a foot.

21.25*12 = 255.

So, the alternative answer is 255 inches.

Answer:

10 inches

Step-by-step explanation:

take the cube root of the volume to find the lenght of each side.

Answer:

10 inches

Step-by-step explanation:

The volume of a cube is of the form: [tex]V=s^3[/tex] , where s is the side length.

Here, we know the volume V, but not the side length. So, we can plug in the value 1000 in for V and solve for s:

1000 = [tex]s^3[/tex]

Cube root both sides:

s = [tex]\sqrt[3]{1000} =10[/tex]

Thus, each side is 10 inches.

Hope this helps!

Answer:

1. It

2. We

3. They

Step-by-step explanation:

1. "The book" is talking about a singular object. So, we need to use either he, she, or it. Obviously, books are not referred to by female or male, so we use the pronoun "it".

2. "Sanjay and I" is a plural form that includes oneself. So, we use "we".

3. "Frogs and elephants" are multiple objects. However, we don't refer to them by any gender, so they are simply "they".

Hope this helps!

Answer:

1) It

2) We

3) They

Step-by-step explanation:

The book was a gift from my sister.

It was a gift from my sister.

Sanjay and I plan to go to the parade on Saturday.

We plan to go to the parade on Saturday.

Frogs and elephants are my favorite animals.

They are my favorite animals.

Answer:

18 1/2 is the greatest snake length. 12 1/2 is the least.

Step-by-step explanation:

To calculate the cost of filling a planter in the shape of a square pyramid, first, find the volume of the planter using the volume formula of a pyramid (1/3*Base Area*Height) then multiply the volume with the cost of the soil per cubic foot.

To calculate the cost of filling the planter with soil, we first need to know the volume of the square pyramid. The formula to calculate the volume of any pyramid is 1/3*Base Area*Height. Once we know the volume, we can multiply it by the cost of the soil per cubic foot, which in this case is $0.78.

For instance, if the volume of your pyramid planter was 10 cubic feet, you would calculate 10 * $0.78 = $7.80. Therefore, in our example, it would cost you $7.80 to fill your square pyramid planter with soil.

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Answer:

363

Step-by-step explanation:

The formula is distance time n-1 plus term one.

-92, -85

Every time it adds 7.

7*65+-92=363

Answer:

8.1

Step-by-step explanation:

1) There are 360 degrees in a circle.  Therefore, the arc measure of PQ would be 360-(73+150+65)= 72.  

2) The intercepted arc is the same measure as the central, making it 72.  Therefore it takes up 72/360 of a circle or 1/5.  

3) To find the measure of it, you would find 1/5 of the circumference.  C=2πr . C=2(3.14)(6.48)≈ 40.7 .

4) 1/5 of the circumference would be (40.7)/(5)≈8.1

8.1 in.

Final answer:

The upper bound for 96.3 cm, measured to the nearest tenth of a cm, is 96.4 cm. This represents the highest possible value that would round down to 96.3 cm.

Explanation:

The student is asking to find the upper bound for the measurement of 96.3 cm, given that it is measured to the nearest tenth of a cm (centimeter). When measurements are taken to the nearest tenth, this indicates that the actual length could be anywhere from the stated length up to, but not including, 0.1 cm greater. To find the upper bound, you would add 0.1 cm to the stated measurement without including it, meaning the maximum possible actual length just before it would round up to the next tenth of a cm.

To calculate the upper bound for 96.3 cm, you simply add 0.1 cm to it:
96.3 cm + 0.1 cm = 96.4 cm
So, the upper bound is 96.4 cm, as that is the largest value that would still round down to 96.3 cm when measured to the nearest tenth of a cm.

Answer:

answer is c.(16 , 15)

Step-by-step explanation:

Answer:

a. 31

Step-by-step explanation:

It's 31 on edge :)

Answer:

(2,6)

Step-by-step explanation:

To determine the best deal, divide the total cost by the total quantity for each option to find the cost per unit. Option 4, 25000 ball bearings for $275.00, offers the best deal with the lowest cost per unit.

The best deal can be determined by comparing the cost per unit of each item. To do this, divide the total cost by the total quantity for each option.

Based on these calculations, option 4, 25000 ball bearings for $275.00 offers the best deal with the lowest cost per unit.

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Answer:

x>_6.8

Step-by-step explanation:

.

Answer:

1. 2

Step-by-step explanation:

1. cross multiply then simplify

Answer to problem 1:

x=2

Reasoning:

1) Simplify 10/20 to 1/2

2) Multiply the numerator and denominator by 2 to get 2/4

Answer to problem 4:

1 in: 18 in

Reasoning:

1) Convert 15 feet to inches

15*12=180

2) Use a ratio of 10 inches to 180 in and simplify it to 1:18

Answer to problem 5:

m = 38.44

1) Use the technique "Cross multiplication" and make the following equation

8.45*7.5=3.6m

2) 8.45*7.5=138.375

3) 138.375=3.6m and divide 3.6 from both sides of the equation,

4) You get 38.4375, and round up to the nearest hundredth of 38.44

Answer to problem 6:

92°

When 2 triangles are similar, their lengths are needed to multiplied by a scale factor but, the angles remain the same.

Sorry, I didn't have enough time to answer the other question...

Hope this helped...

Answer:

92%

The average of 82%, 72%, 74%, and 92% is 80%

She need 92% on her fourth test in order to have an average of 80% on the first four tests.

Here,

Carmen had scores of 82%, 72% and 74% on her first three tests of the term.

We have to find the score of fourth test.

What is Average?

The average (mean) is equal to the sum of all the data values divided by the number of values in the data set.

Now,

Carmen had scores of 82%, 72% and 74% on her first three tests of the term.

To find the score of fourth test  in order to have an average of 80% on the first four tests we use the formula of average,

Let the score of fourth test is x.

Then, Average = [tex]\frac{82+72+74+x}{4}[/tex]

           [tex]80 = \frac{82+72+74+x}{4}\\\\320 = 228 + x\\\\x = 92[/tex]

Hence, She need 92% on her fourth test in order to have an average of 80% on the first four tests.

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The complete question says: "Cheyenne holds a $7,500 portfolio that consists of four stocks. Her investment in each stock, as well as each stock’s beta, is listed in the following table:"  The complete table for the question can be seen in the image attached below.

Cheyenne’s portfolio’s beta is 0.965 and the required return is 9.31%

A portfolio's beta is the model that measures the stock's return while estimating the market risk.

The required rate of return is the minimal return an investment will take for holding a company's shares in exchange for taking on a certain amount of risk.

The formula for calculating Portfolio's Beta is:

= Sum of (Beta × Weights)

[tex]\mathbf{= (1 \times (\dfrac{2625}{7500})) + (1.50 \times (\dfrac{1500 }{ 7500})) + (1.10 \times (\dfrac{1125 }{ 7500})) + (0.50 \times (\dfrac{2250 }{ 7500}))}[/tex]

= 0.35 + 0.30 + 0.165 + 0.15

= 0.965

Required Return = Risk Free Rate + (Beta × Premium Market Risk)

= 4% + (0.965 × 5.5%)

= 0.04 + (0.965 × 0.055)

= 9.31%

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I believe the answer is 3 minutes

At the 3 minute mark, Maxine will be half way done and Sammie will still have 6 minutes left to mow the grass

Answer: [tex]\frac{4^{0.5 a}}{2^{b}}=4[/tex]

Step-by-step explanation:

We are told [tex]a-b=2[/tex] being [tex]a[/tex] and [tex]b[/tex] positive integers, hence:

[tex]a=2+b[/tex] (1)

Now we have the following expression:

[tex]\frac{4^{0.5 a}}{2^{b}}[/tex] (2)

Which can be also written as:

[tex]\frac{2^{2(0.5 a)}}{2^{b}}[/tex] (3)

Since [tex]4=2^{2}[/tex]

Then, substituting (1) in (3):

[tex]\frac{2^{2(0.5(2+b))}}{2^{b}}[/tex] (4)

Since we have exponents with the same base, we can do the following:

[tex]\frac{2^{2+b}}{2^{b}}=2^{2+b} 2^{-b}[/tex] (5)

Finally:

[tex]2^{2+b} 2^{-b}=2^{2+b-b}=2^{2}=4[/tex] (6)

Hence:

[tex]\frac{4^{0.5 a}}{2^{b}}=4[/tex]

Answer:

4

Step-by-step explanation:

Answer:

620

Step-by-step explanation:

20% = 124

20%*5 = 124*5

100% = 620

Answer:

i need more details of the question

Step-by-step explanation:

Answer:

Let speed be S

Then hypothetical speed = S + 12

Solve for S to get a speed of 60 mph  

Step-by-step explanation:

Answer:

x=(3,1/4)

Step-by-step explanation:

Be sure to use the formula...

[tex]-b + or - sqrt{b^{2} - 4ac } / 2a[/tex]

- First, move all variables to one side (left) of the equation. You want one side to be equivalent to zero.

-Next, you need to find a, b, and c. This should be...

a=4

b=-13

c=3

- Knowing this, fill in these variable to go along with the formula. I cannot do this for you, as you should try it on your own. But, you should end up with the solution x= (3,1/4).

- Hope this helps! If you need a further explanation or help on any more problems please let me know, as I would be glad to help anytime.

Answer:

7.2 feet

Step-by-step explanation:

1.2 x 6 = 7.2

hope this helps <3

The total length of the ribbon Samantha would need is given by the equation A = 7.2 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total length of the ribbon be represented as A

Now , the equation will be

The number of pieces of ribbon required = 6 pieces

The length of each piece of ribbon = 1.2 feet

So , the total length of the ribbon A = number of pieces of ribbon required x length of each piece of ribbon

Substituting the values in the equation , we get

The total length of the ribbon A = 6 x 1.2

On simplifying the equation , we get

The total length of the ribbon A = 7.2 feet

Therefore , the value of A is 7.2 feet

Hence , the total length of the ribbon is 7.2 feet

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Answer:

42

Step-by-step explanation:

9 × 6 = 54

So 7 × 6 = 42 successful throws