The mass of a radioactive substance follows a continuous exponential decay model with a decay rate parameter of 7% per day. A sample of this radioactive substance was taken two days ago. If the sample has a mass of 3 kg today, find the initial mass of the sample. Round your answer to two decimal places.

Answer:

(3, 4)

Step-by-step explanation:

Answer:

y = mx + 3

m = Δy/Δx = -3/3 = -1

y = -1x+3

Step-by-step explanation:

Answer:

6 < x

Step-by-step explanation:

4(3x + 2) <5(3x - 2)

Distribute

12x +8 < 15x -10

Subtract 12 x from each side

12x +8-12x < 15x-12x -10

8 < 3x - 10

Add 10 to each side

8+10 < 3x-10+10

18 < 3x

Divide by 3

18/3 < 3x/3

6 < x

Answer: 4.3

Step-by-step explanation:

The chance of randomly selecting an orange marble from the bag is 25%.

Given, A bag contains 7 green marbles, 8 purple marbles, and 5 orange marbles.

Here we want to find the probability of selecting an orange marble from the bag.

So,

we are dividing the number of orange marbles by the total number of marbles in the bag.

So,

The total number of marbles in the bag is 7 + 8 + 5 = 20

According to question, the number of orange marbles is 5.

Therefore, the probability of selecting an orange marble is 5/20 or 1/4, which can be expressed as a decimal fraction of 0.25 or a percentage of 25%.

In conclusion, the chance of randomly selecting an orange marble from the bag is 25%.

Learn more about probability here,

https://brainly.com/question/31895831

#SPJ4

Answer:

48

Step-by-step explanation:

55+65=120 and 2/5 of 120 is 48

Answer:

1.25

Step-by-step explanation:

DIVIDE 4 with 5

I hope it helps pls mark me a brainliest

Answer:

0.8

Step-by-step explanation:

Each of the five guests will receive 0.8 of a burrito.

4 ÷ 5 = 0.8

The maximum sum of the products taken two at a time is 180, and this can be achieved by choosing 60, 60, and 60 as the three numbers.

In order to write the number 180 as a sum of three numbers so that the sum of the products taken two at a time is a maximum, one way to do it is to use the formula:

\((x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + xz + yz)\)

Let the three numbers be x, y, and z.

Then the product of the numbers taken two at a time is: \(xy + xz + yz\)

If we want to maximize the sum of the products taken two at a time, we need to maximize \(xy + xz + yz\).

In the formula: \((x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + xz + yz)\)

We can see that the first three terms on the right-hand side are fixed since they depend on x, y, and z. Therefore, to maximize the sum of the products taken two at a time, we need to maximize 2(xy + xz + yz). Since we have the number 180, we can let: \(x + y + z = 180\)

Then, we need to maximize: 2(xy + xz + yz) Using calculus, we can find that the maximum value of 2(xy + xz + yz) is attained when: \(x = y = z = 60\)

Therefore, the three numbers that can be used to write the number 180 as a sum of three numbers so that the sum of the products taken two at a time is a maximum are: 60, 60, 60.

Learn more about sum of the products here:

https://brainly.com/question/25520277

#SPJ11

The z-score corresponding to a sample mean of 84 for a sample size of 9 scores, with a population mean of 80 and a population standard deviation of 12, is 1.

To find the z-score corresponding to a sample mean of m = 84 with a population mean (μ) of 80 and a population standard deviation (σ) of 12, the z-score can be calculated using the formula z = (x - μ) / (σ / √n).

In this case, the population mean (μ) is 80 and the population standard deviation (σ) is 12. The sample mean (m) is given as 84, and the sample size (n) is 9.

To calculate the z-score, we use the formula:

z = (x - μ) / (σ / √n)

Substituting the given values, we have:

z = (84 - 80) / (12 / √9)

Simplifying the expression, we get:

z = 4 / (12 / 3)

z = 4 / 4

z = 1

Therefore, the z-score corresponding to a sample mean of 84 for a sample size of 9 scores, with a population mean of 80 and a population standard deviation of 12, is 1. This indicates that the sample mean is one standard deviation above the population mean. The z-score allows us to compare the sample mean to the population distribution and assess how unusual or typical the sample mean is relative to the population.

Learn more about standard deviation here;

https://brainly.com/question/29115611

#SPJ11

Answer:

Step-by-step explanation:

2x4=8

4+4=8

Or

2+2+2+2=8

Answer:

Option (B) is the correct answer.

Step-by-step explanation:

Let 'x' the starting point be

She walks down 2 flights to visit a friend.

so walking down means we need to add 2 units to the starting point x

\(x+2\)

Then he walks up 3 flights to deliver a message to a neighbor.

now subtracting 3 units from (x+2)

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

x = -1 means now he is UP to 1 point where he started his flight.

Thus, he needs to walk down 1 more flight to reach her starting point

Thus, -1 is the number of flights Brandie must walk to get back to her starting point.

Therefore, option (B) is the correct answer.

To estimate the proportion of all new cell phone batteries that fail to last through a claimed number of charges, a consumer group will use a random sample and construct a percent confidence interval based on the proportion of batteries that fail to last through the charges in the sample.

To construct a confidence interval to estimate the proportion of all such batteries that fail to last through charges, the following steps can be followed:

Determine the sample size:

The consumer group should select a random sample of cell phones with the new battery and use the phones through charges of the battery.

The sample size should be determined based on the desired level of precision and confidence level.

A larger sample size will provide a more precise estimate.

Calculate the sample proportion:

The consumer group should record the proportion of batteries that fail to last through charges in the sample.

Calculate the standard error:

The standard error can be calculated using the formula:

\(SE = \sqrt{(p_hat * (1 - p_hat) / n) }\)

where \(p_hat\) is the sample proportion and n is the sample size.

Calculate the margin of error:

The margin of error can be calculated using the formula:

ME = z * SE

where z is the critical value from the standard normal distribution corresponding to the desired confidence level.

For example, if the desired confidence level is 95%, then z = 1.96.

Calculate the confidence interval: The confidence interval can be calculated using the formula:

\(CI = (p_hat - ME, p_hat + ME)\)

This interval represents the range of values within which the true proportion of batteries that fail to last through charges is expected to fall with the desired level of confidence.

For example, suppose a random sample of 100 cell phones with the new battery is selected, and the proportion of batteries that fail to last through charges is found to be 0.10. If a 95% confidence level is desired, the standard error can be calculated as:

SE = \(\sqrt{(0.10 * 0.90 / 100)}\) = 0.03

The margin of error can be calculated as:

ME = 1.96 * 0.03 = 0.06

The 95% confidence interval can be calculated as:

CI = (0.10 - 0.06, 0.10 + 0.06) = (0.04, 0.16)

Therefore, we can say with 95% confidence that the proportion of all such batteries that fail to last through charges is expected to be between 0.04 and 0.16.

For similar question on proportion.

https://brainly.com/question/19994681

#SPJ11

Answer:

0.000096m2

Step-by-step explanation:

Incase you don't understand feel free to ask!!!

A rhombus is a quadrilateral whose all sides are of equal length, and the opposite are parallel to each other. The area of the rhombus is equal to 9.6 × 10⁻⁵ hectares.

A rhombus is a quadrilateral whose all sides are of equal length, and the opposite are parallel to each other. It can also be said that a rhombus is a parallelogram with all the sides being equal.

4a² = d₁² + d₂²

4(100)² = d₁² + (120)²

4 × 10000 = d₁² + 14400

d₁² = 25600

d₁ = 160

Area of rhombus = ( d₁ × d₂) ÷ 2

                            = (120 × 160)/2

                            = 9600 cm²

Since 1 sq. cm is equal to 10⁻⁸ hectares. Therefore, the area of the rhombus will be,

Area = 9600 cm²

        = 9600 ×  10⁻⁸ hectares

        = 9.6 × 10⁻⁵ hectares

        = 0.000096 hectares

Hence, the area of the rhombus is equal to 9.6 × 10⁻⁵ hectares.

Learn more about Rhombus here:

https://brainly.com/question/14462098

#SPJ2

The square root of one hundred forty > the square root of one hundred three ninths

In this question, we need to compare the square root of one hundred forty and the square root of one hundred three ninths.

We write the square root of one hundred forty as,

√(140)

The value of  the square root of one hundred forty is,

√(140) = 11.8                        ..............(1)

We write the square root of one hundred three ninths as,

√(11.44)

The value of the square root of one hundred three ninths is,

√(11.44) = 3.4                      ...................(2)

From (1) and (2),

11.8 > 3.4

i.e., the square root of one hundred forty is greater than the square root of one hundred three ninths

Therefore, the square root of one hundred forty > the square root of one hundred three ninths

Learn more about the square root here:

https://brainly.com/question/3120622

#SPJ1

the expression to a single logarithm using the properties of logarithms log(x) + log(z^3) - log(y^(1/2))
We can use the properties of logarithms to condense the expression. Firstly, we can use the rule that says log(a) - log(b) = log(a/b). Applying this rule to the first two terms gives us log(x/y^(1/2)). Next, we can use the rule that says nlog(a) = log(a^n).

Applying this rule to the last term gives us log(z^3). Finally, we can use the rule that says log(a) + log(b) = log(ab) to combine the first and last terms, giving us log(xz^3/y^(1/2)).
Therefore, the condensed expression using the properties of logarithms is log(xz^3/y^(1/2)).
 The condensed expression is log(x * z^3 / y^(1/2)).

To condense the given expression using properties of logarithms, we need to apply the following rules:

1. log(a) - log(b) = log(a/b)
2. log(a^n) = n * log(a)

So, let's apply these rules to the given expression:

log(x) - (1/2)log(y) + 3log(z)

First, apply rule 2:

log(x) - log(y^(1/2)) + log(z^3)

Next, apply rule 1:

log(x * z^3 / y^(1/2))

The expression log(x) - (1/2)log(y) + 3log(z) can be condensed to a single logarithm as log(x * z^3 / y^(1/2)).

To know more about single visit:

https://brainly.com/question/19227029

#SPJ11

Answer:

20×4=80

4×2×10=80

Step-by-step explanation:

To estimate the result of multiplication (product), round the numbers to some close numbers that you can easily multiply mentally.

One method of estimation is to round all factors to the biggest digit (place value) they have.

you need to round 24 to the nearest ten which is 20 and leave 4 as it is

The closest answer choice is A. Domain: All real numbers; Range: All real numbers.

What are the domain and range?

The domain of a function is the set of all possible input values (often represented by x) for which the function is defined. The range of a function is the set of all possible output values (often represented by y) that the function can produce, based on its input values. In other words, the domain is the set of all valid inputs, and the range is the set of all possible outputs.

The domain and range of an exponential growth function depend on the specific equation of the function.

However, in general, an exponential growth function has a domain of all real numbers and a range of y > 0.

This is because an exponential growth function always has a positive output, and it can take any positive input value.

Therefore, the closest answer choice is A. Domain: All real numbers; Range: All real numbers.

To learn more about the domain and range visit:

https://brainly.com/question/2264373

#SPJ1

Solution :

Volume of ball = Volume of outer ball - Volume of inner ball

\(V = \dfrac{4\pi R^3}{3} - \dfrac{4 \pi r^3}{3}\\\\V = \dfrac{4\pi}{3}( R^3 - r^3 )\\\\V = \dfrac{4\pi}{3}( 200^3 - 100^3 )\\\\V = \dfrac{4\pi}{3}(2^3 - 1^3) \times 10^6\\\\V = 2.93 \times 10^7 \ m^3\)

Now, density of iron is, d = 7300 kg/m³.

So, mass of iron ball is :

\(m = d\times V\\\\m = 7300\times 2.93 \times 10^7 \ kg\\\\m = 2.14 \times 10^{11}\ kg\)

Hence, this is the required solution.

Given:

Number of samples n =58

Mean

Standard deviation

Required:

Find the confidence interval.

Explanation:

The confidence interval formula is

Substitute the given values in the formula.

Given,D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item.

S(x) is the price, in dollars per unit, that produces are willing to accept for x units.

D(x) = -3x+7, S(x) = 2x+2

To find the equilibrium point we need to equate the two equations and solve for x.

D(x) = S(x)-3x+7 = 2x+2-3x+7 = 2x7 = 5xx = 7/5

Thus, the equilibrium point is x = 7/5.

Now, let's move on to the next step.The consumer surplus is the difference between the amount the consumer is willing to pay and the market price.

We know that D(x) represents the amount a consumer is willing to pay for x units of an item at any given price. Therefore, the consumer surplus at the equilibrium point is calculated as follows:

Consumer surplus = D(7/5) - Equilibrium price Consumer surplus = (-3 x 7/5 + 7) - (2 x 7/5 + 2) Consumer surplus = (1/5) - (14/5) Consumer surplus = -13/5

At the equilibrium point, the producer surplus is the difference between the market price and the minimum price that producers are willing to accept.

S(x) represents the minimum price that producers are willing to accept for x units of an item at any given price. Therefore, the producer surplus at the equilibrium point is calculated as follows:

Producer surplus = Equilibrium price - S(7/5)Producer surplus = (2 x 7/5 + 2) - (2 x 7/5 - 2)Producer surplus = 14/5 + 2Producer surplus = 24/5

Therefore,a. The equilibrium point is x = 7/5.

b. The consumer surplus at the equilibrium point is -13/5.

c. The producer surplus at the equilibrium point is 24/5.

To know more about equilibrium point visit:

https://brainly.com/question/30843966

#SPJ11

Answer:

Step-by-step explanation:

The function g(t) = 7t² - 6t + 4 is a quadratic function. To find the value of g(t), we can substitute a specific value for t into the function and evaluate it.

For example, if we want to find g(2), we substitute t = 2 into the function:

g(2) = 7(2)² - 6(2) + 4

     = 7(4) - 12 + 4

     = 28 - 12 + 4

     = 20

Therefore, g(2) = 20.

In general, you can find the value of g(t) by substituting the desired value of t into the function and simplifying the expression.

Keep in mind that quadratic function can have different values for different inputs, so the value of g(t) will vary depending on the chosen value of t.

Learn more about quadratic function here: https://brainly.com/question/27958964

#SPJ11

Answer:

25ft per second

Answer:

A

Step-by-step explanation:

4x + 3 (2x - 1) - 4x

4x + 6x - 3 -4x

4x + 6x - 3 - 4x

6x - 3

Hope I helped!

The area and the perimeter of the compound figure are 95 square units and 43 units, respectively.

In this question we must compute the area of a compound figure formed by four squares of different size. The area formula of a square are listed below:

A = l²

Where l is the side length of the square.

Now we proceed to determine the area of the compound figure by addition of areas:

A = 1² + 2² + 3² + 9²

A = 1 + 4 + 9 + 81

A = 14 + 81

A = 95

And the perimeter of the figure is equal to:

p = 3 · 3 + 4 · 1 + 6 + 3 · 9

p = 9 + 4 + 6 + 27

p = 16 + 27

p = 43

To learn more on areas of composite figures: https://brainly.com/question/31040187

#SPJ1

Answer:

It is possible.

Step-by-step explanation:

Since the shorter two sides (16 and 17 feet) added together are greater than the longest side(20 feet) it meets the triangle inequality theorem

26.5  base  10 to binary, octal, and hexadecimal:

a. Binary: 11010.1

b. Octal: 32.4

c. Hexadecimal: 1A.8

To convert 26.5  base  10  to binary, we split the number into its integer and fractional parts. The integer part 26 can be represented as 11010 in binary. The fractional part 0.5 can be represented as 0.1 in binary. Combining the integer and fractional parts, we have

26.5  base  10 = 11010.1 in binary.

To convert 26.5  base  10 to octal, we group the binary digits into sets of three from left to right. In this case, we have 11010.1, which can be grouped as 011 and 010. Converting each group to octal, we get 3 and 2, respectively. Combining these results, we have 26.5  base  10 = 32.4 in octal.

To convert 26.5  base  10  to hexadecimal, we group the binary digits into sets of four from left to right. In this case, we have 11010.1, which can be grouped as 0001 and 1010. Converting each group 26.5  base  10= 1A.8

Learn more about   binary digits here:

brainly.com/question/32801139

#SPJ11

Ms. murphy has to create a relay team in 3024 ways.

What is combination?

A combination is a collection of components produced under a certain set of constraints and conditions.

Selections are another name for combinations. The choice of items from a predetermined group of items corresponds to combinations. We don't want to organize anything here. We are going to choose them. We use the symbols n C r to represent the number of distinct r-selections or combinations among a set of n items.

As given, Ms murphy has to select 4 swimmers out of 9  swimmers to create a relay team.

By using the combination formula we can find the number of ways to create a relay team.

\(C^{n}_r = \frac{n!}{(n-r)!}\)

Where,

n is the number of all objects and r is a number of selected objects.

Here, n = 9 and r = 4.

So,

\(C^{9}_4 = \frac{9!}{(9-4)!} = \frac{9!}{5!} = \frac{x}{y} = 3024\)

Therefore, she create a relay team in 3024 ways.

To know more about the combination, click on the link

https://brainly.com/question/1941169

#SPJ4