You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 5 days later you determine that it has decayed down to 0.7 grams. What is its half-life? (Round your answer to three significant digits.)

y = cost = $25

25 = 0.75 +10

 subtract 10 from each side

15=0.75x

x = 15/0.75 = 20

 there were 20 words in the ad

Answer:

m=15

Step-by-step explanation:

cube root of 3375 =m

We need to solve the equation for m

[tex]\sqrt[3]{3375} = m[/tex]

In order to solve for m we need to find the cube root of 3375

3375 can be written as 3 times 3 times 3 times 5 times 5 times 5

[tex]\sqrt[3]{3375} = m[/tex]

[tex]\sqrt[3]{3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5} = m[/tex]

For same three factors inside the cube root we pull out one factor outside the cube root

[tex]\sqrt[3]{3 \cdot 3 \cdot 3} = 3[/tex]

[tex]\sqrt[3]{3 \cdot 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5} = m[/tex]

[tex]3 \cdot 5 = m[/tex]

m= 15

The value of the variable that makes the statement true is

m = 15

The given equation is:

[tex]\sqrt[3]{3375} = m[/tex]

We are looking for a number that we can multiply by itself 3 times to get 3375

Note that the given equation can be re-written as:

[tex]m =3375^{\frac{1}{3}[/tex]

This can be further simplified as:

[tex]m=15^{3(\frac{1}{3} )}\\\\m=15[/tex]

Therefore, the value of the variable that makes the statement true is m = 15

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The equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).

The slope of a line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Given that line passes through points (4, 7) and (0, 7)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 4, y₁ = 7

x₂ = 0, y₂ = 7

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 7 = (7 - 7)/(0- 4)[x -4]

⇒ y - 7 = (0)/(-10 )[x -4]

⇒ y - 7 = 0(x -4)

⇒ y - 7 = 0

⇒  y = 7

Therefore, the equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).

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-3w+2=-10w+30

add 3 w to each side

2=-7w+30

subtract 30 from each side

-28 = -7w

divide both sides by -7

w = 4

double check

-3(4) +2 = -10

-10(4) +30 = -10

 so w = 4

Subtraction of  8-4 1/2 is 3 1/2.

The correct option is D.

To subtract 8 - 4 1/2, we need to convert the mixed number 4 1/2 into an improper fraction.

To do this, we multiply the whole number (4) by the denominator (2), which gives us 8. Then we add the numerator (1) to get 9. So, 4 1/2 is equivalent to the improper fraction 9/2.

Now, we can subtract 8 from 9/2. To subtract fractions, the denominators must be the same. We can rewrite 8 as 8/1 to have a common denominator with 9/2.

Subtracting 8/1 from 9/2 gives us (8 - 9/2).

To subtract fractions, we need a common denominator, which is 2 in this case.

Converting 8/1 to have a denominator of 2, we get 16/2.

Now we can subtract the fractions: (16- 9)/2 = 7/2.

Therefore, the answer is 7/2, which can also be expressed as 3 1/2.

So the correct answer is D. 3 1/2.

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The present value of an ordinary annuity of $350 each year for five years with a 4 percent opportunity cost is $1,551.88, calculated using the present value formula for annuities.

To find the present value of an ordinary annuity, you can use the formula for the present value of an annuity:

[tex]\[ PV = Pmt \times \frac{{1 - (1 + r)^{-n}}}{{r}} \][/tex]

Where:

- PV is the present value of the annuity,

- Pmt is the annual payment (in this case, $350),

- r is the interest rate per period (in decimal form),

- n is the number of periods (in this case, 5 years).

Given that the opportunity cost (interest rate) is 4%, or 0.04 in decimal form, and there are 5 years of payments, we can plug these values into the formula:

[tex]\[ PV = 350 \times \frac{{1 - (1 + 0.04)^{-5}}}{{0.04}} \][/tex]

Let's calculate:

[tex]\[ PV = 350 \times \frac{{1 - (1.04)^{-5}}}{{0.04}} \][/tex]

[tex]\[ PV = 350 \times \frac{{1 - (0.8227)}}{{0.04}} \][/tex]

[tex]\[ PV = 350 \times \frac{{0.1773}}{{0.04}} \][/tex]

[tex]\[ PV \approx 350 \times 4.4325 \][/tex]

PV = $1551.88 (Approximately)

So, the present value of the annuity, assuming an opportunity cost of 4%, is approximately $1551.88.

Final answer:

Raul did better on the history test relative to his classmates, as indicated by a higher z-score of approximately 0.22, compared to 0.14 for the biology test.

Explanation:

To determine on which test Raul did better relative to the rest of the class, we need to calculate the z-scores for Raul's history and biology test results. A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, measured in terms of standard deviations from the mean. The formula for calculating a z-score is:

z = (X - μ) / σ

where X is the score, μ is the mean, and σ is the standard deviation. Let's apply this to Raul's scores:

For the history test:

z = (72 - 70) / 9 = 2 / 9 ≈ 0.22

For the biology test:

z = (71 - 70) / 7 = 1 / 7 ≈ 0.14

Comparing the two z-scores, we can see that Raul's z-score for history is higher than his z-score for biology. Hence, Raul did better on the history test relative to the rest of the class.

Final answer:

Peter invested $3,700 at a 3% loss and $7,800 at a 4% gain. By setting up a system of equations and solving them, we determined the amount invested in each.

Explanation:

To solve the problem of how much was invested by Peter in each investment, we need to set up a system of equations. Let's call the amount invested at 3% loss x, and the amount invested at 4% gain y. The total amount invested is $11,500, so we have x + y = $11,500.

Peter's net annual receipts were $201, which comes from a loss of 3% on investment x and a gain of 4% on investment y. The equation for this would be -0.03x + 0.04y = $201.

Now we have a system of two equations:

-0.03x + 0.04y = $201

Adding (1) and (2) gives us:

0.03y + 0.04y = $546

Combining like terms, we get:

0.07y = $546

Dividing both sides by 0.07, we find that:

y = $7,800

Substituting y back into the first equation, we get:

x = $11,500 - $7,800 = $3,700

So, Peter invested $3,700 in the investment with a 3% loss and $7,800 in the investment with a 4% gain.

Slope in math is the difference in y-values divided by x-values.

The slope helps determine the steepness of a line. Y-intercept is the y-value when x=0. The formula for slope, denoted as m, is (y2-y1)/(x2-x1).

Example: For the equation y = 2x - 1, if we have the point (-2, 2), we can calculate the slope by substituting the values into the formula: m = (2-(-1))/(-2-0) = 3/-2 = -1.5.

Y-intercept is the y-value when x=0, or where the graph crosses the y-axis.

Answer:  a. [tex]\dfrac{43}{87}[/tex]

Step-by-step explanation:

From the given table , it can be seen that the total number of flights are given : 43+33+6+5=87

Also, the the number of  Upstate Airlines flights on time = 43

Now if one of the 87 flights is randomly selected, the probability that the flight selected is an Upstate Airlines flight which was on time will be :-

[tex]\dfrac{\text{Number of Upstate Airlines flight on time}}{\text{Total flight}}\\\\=\dfrac{43}{87}[/tex]

Hence, the probability that the flight selected is an Upstate Airlines flight which was on time [tex]=\dfrac{43}{87}[/tex]

5/8 x 1/2 = 5/16 acre is lawn

5/16 x 2/3 = 10/48 reduces to 5/24 of the lawn was mowed

1200*0.15 = 180

1200-180 = $1020

$1020 after the rebate

The value of [tex]\( y \)[/tex] when x = 6 is 16.

Given that [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex], we can write the relationship as:

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

where [tex]\( k \)[/tex] is the constant of proportionality.

First, we need to determine the value of [tex]\( k \)[/tex]. We are given that [tex]\( y = 24 \)[/tex] when [tex]\( x = 4 \)[/tex].

[tex]\[ 24 = \frac{k}{4} \][/tex]

Solving for k:

[tex]\[ k = 24 \times 4 = 96 \][/tex]

Now that we have the value of [tex]\( k \)[/tex], we can find the value of [tex]\( y \)[/tex] when [tex]\( x = 6 \)[/tex]:

[tex]\[ y = \frac{96}{6} \][/tex]

[tex]\[ y = 16 \][/tex]

255-115 = 140 miles

140/70 = 2 hours

The standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.

As we know that,

So, it should be presented below.

Trillion   Billion     Million    Thousand     Hundred    Tens   Ones

 407   ,   000   ,     006   ,       105      ,       0                 2         8

Therefore we can conclude that the standard form of four hundred seven trillion six million one hundred five thousand twenty-eight is 407,000,006,105,028.

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The volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be 30 cubic inches.

Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (L × B × H) / 3

V = (Base area x H) / 3

The volume of a pyramid varies jointly with the base area of the pyramid and its height.

The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.

Then the volume of a pyramid with a base area of 10 square inches and a height of 9 inches will be

V = (10 x 9) / 3

V = 30 cubic inches

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The volume of a pyramid is obtained from the joint variation relationship with its base area and height. Given a certain pyramid's dimensions, we can determine the volume of another pyramid if we know its base area and height. The volume of the second pyramid is 30 cubic inches.

The student's question pertains to joint variation, a concept in mathematics, specifically applied here to understand how the volume of a pyramid relates to its base area and height. For a pyramid, this relationship can be expressed as V = k * A * H, where V is volume, A is base area, H is height, and k is the constant of variation.

First, we find the value of 'k' using the given pyramid's measurements; so 24 = k * 24 * 3 gives us k = 1/3.

Then, we use this constant to find the volume of the other pyramid whose base area is 10 square inches and height is 9 inches. Therefore, V = 1/3 * 10 * 9, which simplifies to V = 30 cubic inches.

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