An unknown substance is decaying exponetially. You measure its initial mass to be q(0)=45 grams. One week later, its mass is measured to be q(7)=30 grams. This problem will guide you through the computation of this substance's half life.
First write down the half-life equation. The decay o this substance is modelled by the formula
q(t)=q0⋅2^−t/λ.
You are given the initial quality is q(0)=45 grams. Does this tell you what q0 is?
at t=7 (days) you have a quantity of 30 grams. Plug in t=7, q(7)=30 and solve for λ.
Finally, answer the question. What is the half-life? (include units). Give a decimal approximation that is within 1 hour of accurate.

Answer: A on Edge

Step-by-step explanation:

f(x) = (x –1)2 – 7

Answer:

A

Step-by-step explanation:

The annual rate of population growth in the US was about 1.2% in 2015, then the growth factor will be 1.012. The growth factor depends upon annual growth rate.

Growth factor typically refers to a constant multiplier that is used to calculate the growth or decay of a quantity over time. It is given as:

Growth factor = (1 + annual growth rate)

Therefore, the growth factor for the US in 2015 can be calculated as follows:

Growth factor (1+0.012) = 1.012

Therefore, the growth factor for the population of the US in the year 2015 was about 1.012.

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Answer:

24

Step-by-step explanation:

Perimeter of rectangle = 2 (4x + 2x)

288= 2* 6x

288 = 12x

x = 288/12

x = 24

2(2x+4x)=288

12x=288

x=24

Answer:

im mexican im not good at math

Answer:

1) 80 pencils for $32

2) 15 gallons for $52

3) 2  shirts for $60

Step-by-step explanation:

1)

At $42 for 100 pencils, each pencil = $42/100 = $0.42
At $32 for 80 pencils, each pencil = $32/80 = $0.40
So better buy is 80 pencils for $32

2)

15 gal of gas for $52 ==> $3.47 per gal

7 gal for 24.50 ==> $3.50
Better buy is 15 gal of gas for $52

3)

2 shirts for $60 ==> $30 per shirt
10 shirts for $320 ==> $32 per shirt

Better buy: 2 shirts for $60

Answer:

2^845 is greater than 5^362.

Step-by-step explanation:

To compare the two numbers, we can evaluate them using the logarithm function with base 2 and base 5 respectively.

2^845 = 2^(845 * log2(2)) = 2^(845 * 1) = 2^845

5^362 = 5^(362 * log5(5)) = 5^(362 * 1) = 5^362

The logarithm of a number is the exponent to which the base must be raised to give that number. Since logarithm function is a monotonically increasing function, if we compare log base a of x to log base a of y, logarithm of x is greater than y if x is greater than y.

So 2^845 > 5^362 if 845 > 362 * log5(2)

We can calculate log5(2) = log5(2)/log5(2) = 0.6309

so 845 > 362 * 0.6309

845 > 229.8198

so 845 is greater than 229.8198, therefore 2^845 is greater than 5^362.

Answer:

Step-by-step explanation:

2^845 = 2^5(2^7)^120 = 32(128)^120,

5^362 = 5^2(5^3)^120 = 25(125)^120,

2^845 is bigger.

Answer:

No, that would not be a straight angle.

Step-by-step explanation:

180 degrees is a horizontal line, so anything less or more than it would not be a straight angle.

Answer:

382.19cm²

Step-by-step explanation:

a / sin(A) = b / sin(B)

a / sin(68) = 53 / sin(95)

a = (53 x sin(68)) / sin(95)

a = 49.33

area = ½absin(C)

C = 180 - (95 + 68)

C = 180 - 163

C = 17°

area = ½(53)(49.33)sin(17)

area = 382.19cm²

Answer:

The fourth term is 11 and the tenth term is 29

Step-by-step explanation:

Let us use the given formula to solve the question

∵ A(n) = 2 + (n - 1)(3) is the formula of the nth term of an sequence

∵ n is the position of the term in the sequence

∴ For the fourth term n = 4

∴ For the tenth term n = 10

→ Substitute n by 4 in the formula above to find the fourth term

∵ A(4) = 2 + (4 - 1)(3)

∴ A(4) = 2 + (3)(3)

∴ A(4) = 2 + 9

∴ A(4) = 11

∴ The fourth term is 11

→ For the tenth term put n = 10

∵ n = 10

∵ A(10) = 2 + (10 - 1)(3)

∴ A(10) = 2 + (9)(3)

∴ A(10) = 2 + 27

∴ A(10) = 29

∴ The tenth term is 29

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = M(6, - 2) and (x₂, y₂ ) = N(8, 4)

m = \(\frac{4-(-2)}{8-6}\) = \(\frac{4+2}{2}\) = \(\frac{6}{2}\) = 3

Hi !

\(2x + 3 > 11\\\iff 2x > 8\\\iff x > \frac{8}{2}\\ \iff x > 4\)

Have a nice day ;)

Answer:

x > 4

Isolate the variable by dividing each side by the factors that don't contain the variable

The scatterplot of  the given data points are attached herewith.

A scatter plot uses dots to speak to values for two different numeric factors. The position of each dot on the level and vertical axis shows values for an individual information point. Scatter plots are utilized to watch connections between variables, Scatter plots’ essential uses are to observe and show connections between two numeric variables. The dots in a scatter plot do not as it were report the values of personal information points, but moreover designs when the information is taken as a whole.

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Answer: 7

Step-by-step explanation:

i did it a weird way

The perimeter of the room is approximately 49.272 feet.If the area of a rectangular room is 150 square feet, and one side of the room is 11 feet, we can find the length of the other side by dividing the area by the length of the known side:

Length × Width = Area

Width = Area ÷ Length

Width = 150 ÷ 11

Width ≈ 13.636 feet

Now that we know the length and width of the room, we can calculate the perimeter by adding up the length of all four sides:

Perimeter = 2 × Length + 2 × Width

Perimeter = 2 × 11 + 2 × 13.636

Perimeter ≈ 49.272 feet

Therefore, the perimeter of the room is approximately 49.272 feet.

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The cost of the jalapeno poppers is $8.87. Let's denote the cost of the jalapeno poppers as "x".

The total cost of the order, including nachos and jalapeno poppers, is $17.95 + x.

The friends each paid $8.94, which is one-third of the total cost. So, we can write the equation:

8.94 = (1/3) * (17.95 + x)

To find the cost of the jalapeno poppers, we can solve this equation for "x".

Multiplying both sides by 3 gives us:

26.82 = 17.95 + x

Subtracting 17.95 from both sides:

x = 26.82 - 17.95

x = 8.87

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Answer:

L=6x^2-4x+5

P=12x^2-4x-2

Step-by-step explanation:

A=WL

So, we know the area is 6x^2-8x-30 and the width is 2x-6

Substitute

(6x^2-8x-30)=(2x-6)(L)

L=(6x^2-8x-30)/(2x-6

Divide

L=6x^2-4x+5

P=2L+2W

Substitute

P=2(6x^2-4x+5)+2(2x-6)

P=12×^2-8x+10+4x-12

Simplify

P=12x^2-4x-2

The exponential growth equation is x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶ , where x ( t ) is the population in the year 2015 = 40,115,896

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units'

Given data ,

Let the exponential growth equation be represented as x ( t )

Now , the average percentage change from the year 2000 - 2009 is calculated by

The total percentage = ( 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93 )

The total number of years = 9 years

So , the average percentage change = total percentage / number of years

On simplifying , we get

The average percentage change = 12.21 / 9 = 1.35667 %

b)

The population in 2009 was 37,000,000

So , the population growth rate r = 1.35667 %

And , the population in the years 2015 is given by

The number of years n = 6 years

x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶

On simplifying , we get

x ( t ) = 37,000,000 ( 1.013567 )⁶

x ( t ) = 40,115,896

Hence , the population in the year 2015 is 40,115,896

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D = 24

D/3 - 10 = -2

d/3=8

d=24

I am from India,

please upvote if you want.

Answer:

Is 50

Step-by-step explanation:

I don’t know

Answer:

a = 21

Step-by-step explanation:

Given

\(\frac{a+19}{5}\) = 8 ( multiply both sides by 5 to clear the fraction )

a + 19 = 40 ( subtract 19 from both sides )

a = 21

The answer would be C!!!!!!!

\( - 4a - (8a + 1) = - 169 \\ \\ 4a + 8a + 1 = 169 \\ \\ 4a + 8a = 169 - 1 \\ \\ 12a = 169 - 1 \\ \\ 12a = 168 \\ \\ a = \frac{168}{12} \\ \\ a = 14 \\ \\ this \: was \: helping \: you\)

Step-by-step explanation:

Okay so remember the BODMAS rule where u start with brackets right; Since we're proving that RHS =LHS ,we look at the side which is more complicated and solve it first.

RHS: -4a-(8a+1) =-169

-4a-8a-1=-169

-4a-8a= -169+1 ( N:B like terms)

-12a= -168

-12a/-12= -168/-12

a= 14

Then go back to the original equation and subtitute .

where u see a u put the value u calculated.

-4a-(8a+1)=-169

-4(14)-(8(14)+1)= -169

-169= -169 and u DONE!!

In the scenario where she does the hypothesis test, the student should take into account the decision to reject H0 and the P-value.

A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis.

We can make probabilistic claims regarding population parameters through hypothesis testing.

The null hypothesis would be that 50% is true, and the alternative hypothesis would be that 50% is untrue, if someone wanted to test, for instance, whether a penny has an exact 50% chance of landing on heads.

There are 4 ways to test a hypothesis.

The student should incorporate the choice to reject H0 and the P-value in e the scenario in which she conducts the hypothesis test.

Therefore, in the scenario where she does the hypothesis test, the student should take into account the decision to reject H0 and the P-value.

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Answer:

lx-24l ≤ 8

Step-by-step explanation:

lx-24l ≤ 8

x ≤ 8 + 24

x ≤ 32

-----------------

-x + 24 ≤ 8

24 - 8 ≤ x

16 ≤ x

The absolute value equation that represents the minimum and maximum lengths is 8 = |x - 24|.

Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.  

For example, |5| is 5 because it is 5 units away from 0.  Also, |-5| is also 5 because -5 is 5 units from 0.

We have been given that for a poetry contest the minimum length of a poem is 16 lines. The maximum length is 32 lines.

To determine the absolute value equation that represents the minimum and maximum lengths.

First,  we need to find the difference between both solutions.

⇒ 32 - 16 = 16

Then, divide it by 2.

⇒ 16/2 = 8

⇒ 8 = |x - 32 + 8|

we could also write: 8 = |x - 32 + 8|

⇒ 8 = |x - 24|

Therefore, the absolute value equation that represents the minimum and maximum lengths is 8 = |x - 24|.

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The given pattern is an illustration of a linear equation. The students' equations are:

Given that:

\(n \to\) number of tiles

\(s\to\) step number

See attachment for the pattern, that is being analyzed by the students.

Dan

For each step, the number of tower is the same as the step number.

This means that:

\(n \to s\)

2 arms contain one less block means: 2 x (s - 1) blocks for both arms.

So, Dan's equation is::

\(n = s + 2 \times (s - 1)\)

\(n = s + 2(s - 1)\)

Sally

First, we calculate the slope (m) of the table

\(m = \frac{n_2 - n_1}{s_2 - s_1}\)

So, we have:

\(m = \frac{4-1}{2-1}\)

\(m = \frac{3}{1}\)

\(m =3\)

The equation is then calculated using:

\(n = m(s - s_1) + n_1\)

This gives:

\(n = 3(s - 1) + 1\)

Open bracket

\(n = 3s - 3 +1\)

\(n = 3s - 2\)

Hence;

Dan's equation is: \(n = s + 2(s - 1)\)

Sally's equation is: \(n = 3s - 2\)

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Answer:

400 m^2.

Step-by-step explanation:

The largest  area is obtained where the enclosure is a square.

I think that's the right answer because a square is a special form of a rectangle.

So the square would be 20 * 20  = 400 m^2.

Proof:

Let the  sides of the rectangle be x and y m long

The area A = xy.

Also the perimeter  2x + 2y = 80

x + y = 40

y = 40 - x.

So substituting for y in A = xy:-

A = x(40 - x)

A = 40x - x^2

For maximum value of A  we find the derivative and equate it to 0:

derivative A' =  40 - 2x = 0

2x = 40

x = 20.

So y = 40 - x

= 40 - 20

=20  

x and y are the same value so x = y.

Therefore for maximum area the rectangle is a square.

The largest area of rectangle will be 400 square meters.

Let us consider the length and breadth of rectangle is x and y respectively.

Perimeter of rectangle is given that 80 meters.

                                  \(2x+2y=80\\\\x+y=40\\\\y=40-x\)

 Area of rectangle is,

                                        \(=x*y\\\\=x*(40-x)\\\\A=40x-x^{2}\)

  For maximum area, differentiate Area with respect to x  and equate with zero.

                           \(\frac{dA}{dx} =\frac{d}{dx}(40x-x^{2} ) \\\\\frac{dA}{dx} =40-2x=0\\\\x=40/2=20m\)

       So,    \(y=40-20=20m\)

Area  = \(20*20=400m^{2}\)

Thus, The largest area of rectangle will be 400 square meters.

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Since the production of y must exceed the production of x by at least 100 units, we can write a second inequality:

Looking at the function P, we can see that the coefficient multiplying y is greater than the coefficient multiplying x, therefore increasing y instead of x will have a bigger increase in P.

But from the inequality x + 2y <= 1400, we can see that the "cost" of producing y is two times the "cost" of producing x, that is, for one y produced, we could have produced 2x instead.

The coefficient of y is greater, but it's not more than 2 times greater, therefore it's better to produce x than y.

Since y needs to be at least 100 more than x, let's choose the minimum amount of y to satisfy the inequalities:

Therefore the values of x and y that give the maximum profit are x = 400 and y = 500.

Graphing the two inequalities, we have:

The feasible region is the intersection region (between red and blue).

The vertices are:

(0, 100), (400, 500), (0, 700).

Calculating the maximum profit (with vertex (400, 500)), we have:

Therefore the production that yields the maximum profit is x = 400 and y = 500, and the maximum profit is P = 15700.

To calculate the standard error of estimate (SE), we can use the following formula:

SE = sqrt(SSE / (n-2))

where SSE is the sum of squared errors, and n is the number of observations.

Substituting the given values, we get:

SE = sqrt(2,540 / (30-2)) = 5.49

Therefore, the standard error of estimate is 5.49 (rounded to 2 decimal places).

b. The coefficient of determination (R-squared) is given by the ratio of the explained variation (SSR) to the total variation (SST):

R² = SSR / SST

where SSR is the sum of squared regression, and SST is the total sum of squares.

Since this is a simple linear regression, we have:

SST = SSR + SSE

where SSE is the sum of squared errors.

Substituting the given values, we get:

SST = 13,870

SSE = 2,540

Therefore, we can calculate SSR as:

SSR = SST - SSE = 13,870 - 2,540 = 11,330

Substituting these values into the formula for R-squared, we get:

R²= SSR / SST = 11,330 / 13,870 = 0.8188

Therefore, the coefficient of determination (R-squared) is 0.8188 (rounded to 4 decimal places). This means that 81.88% of the variation in the dependent variable (y) can be explained by the linear regression model with the independent variable (x).

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