Thorium 234 is a radioactive isotope that decays according to the eqaution At=A0e^-10.498t, where A0 is the initial amount present and At is the amount present after t years. is the amount present after t years. If you begin with 1000 grams of strontium 90,

(a) How much thorium 234 will be left after 0.5 years? Round your answer to the nearest tenth of a gram.

------------------- grams


(b) When will 115 grams of thorium 234 be left? Round your answer to the nearest tenth of a year.

-------------------- years


if you need to see the picture here is too. Thank u.

Answer:

[tex]x\leq -5[/tex]

After considering the given details we conclude that the height of the picture frame is 12, under the condition that the diagonal of a picture frame is 18 inches the base of the picture frame is 12.

The height of the picture frame can be evaluated applying  the Pythagorean theorem. The Pythagorean theorem projects that in a right triangle, the square of the length of the hypotenuse (the diagonal of the picture frame) is equivalent to the summation of the squares of the lengths of the other two sides (the height and base of the picture frame).

Therefore , in this case, we have a right triangle with a hypotenuse of 18 inches and a base of 12 inches. We can evaluate for the height as follows:
height²+ 12² = 18²
height² = 18² - 12²
height² = 144
height = √(144)
height = 12
Hence, the height of the picture frame is 12 inches rounded to the nearest tenth.
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3) Sin B = 5/9.43, Cos B = 8/9.43, Tan B = 5/9.43

4) Angle A is 40 degrees

5) x is  23.8 mm

A specific type of triangle known as a right triangle has a single angle that is exactly 90 degrees, or a right angle. The sides that make up the right angle are the legs and the hypotenuse.

The Pythagorean theorem connects the side lengths of a right triangle by stating that the square of the hypotenuse's length is equal to the sum of the squares of the legs' lengths.

Cos A = 47/61

A = Cos-1(47/61)

= 40 degrees

5) The marked side can be obtained from;

Cos 28 = 21/x

x = 21/Cos 28

x = 23.8 mm

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Answer:

∠ BCA = 25°

Step-by-step explanation:

the inscribed angle BCA is half the measure of the central angle BOA , so

∠ BCA = [tex]\frac{1}{2}[/tex] × 50° = 25°

The value of cos(θ) value of cos(0) when the sine of the angle is -0.5 in the third quadrant is -sqrt(0.75).

To solve this problem, we need to use the fact that the sine and cosine functions are related through the Pythagorean identity: [tex]sin^2[/tex](0) + [tex]cos^2[/tex](0) = 1.
Since we know that the sine of angle 0 in the third quadrant is -0.5, we can use the unit circle to find the corresponding x-coordinate (cosine value) of the angle.
In the third quadrant, the angle is between 180 and 270 degrees, which means that the x-coordinate (cosine value) is negative.

We can draw a right triangle with the hypotenuse on the unit circle and the angle in the third quadrant, and use the Pythagorean theorem to find the length of the adjacent side (the x-coordinate).
The hypotenuse has a length of 1 because it is on the unit circle, and the opposite side (the y-coordinate) has a length of -0.5 because we know that the sine of the angle is -0.5. Using the Pythagorean theorem, we can solve for the length of the adjacent side (the x-coordinate):
[tex]cos^2[/tex](0) + (-0.5)2 = 1
[tex]cos^2[/tex](0) + 0.25 = 1
[tex]cos^2[/tex](0) = 0.75
Taking the square root of both sides, we get:
cos(0) = +/- sqrt(0.75)
Since we know that the cosine value is negative in the third quadrant, we can take the negative square root:
cos(0) = -sqrt(0.75)

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Step-by-step explanation:

The sum of the interior angles of a n-gon is equal to  ( n-2)(180) degrees

 for this 6-gon   the sum is   (6-2) * 180 = 720 degrees

    (145 + 165 + 58 + 130 + 125 + x )    degrees = 720 degrees

           x = 97 degrees

The volumes of the figures are

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

V = 22/7 * (32/2)² * 14

Evaluate

Volume = 11264

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

(2r)² = 40² - 32²

(2r)² = 576

So, we have

r = 12

So, we have

V = 22/7 * (12)² * 32

Evaluate

Volume = 14482.28

The rectangular prism

The volume is calculated as

V = lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 8 * 12 * 39

Evaluate

Volume = 3744

The triangular prism

The volume is calculated as

V = 1/2lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 1/2 * 11 * 5.4 * 16

Evaluate

Volume = 475.2

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * (33/2)³

Evaluate

Volume = 18824.14

The sphere

The volume of a sphere is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * 2.8³

Evaluate

Volume = 91.99

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As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The function is given below:

y = |2x + 7|

The translated function is as follows:

y = |2(x - 1) + 7|

y = |2x - 2 + 7|

y = |2x + 5|

As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.

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Solution of function is,

⇒ x ∈ [- 7, 5]

We have to given that;

The function is,

⇒ f(x) = x² + 2x - 35

We can simplify for f (x) ≤ 0 as;

⇒ f(x) = x² + 2x - 35

⇒ x² + 2x - 35 ≤ 0

⇒ x² + 7x - 5x - 35 ≤ 0

⇒ x (x + 7) - 5 (x + 7) ≤ 0

⇒ (x + 7) (x - 5) ≤ 0

⇒ x ∈ [- 7, 5]

Thus, Solution of function is,

⇒ x ∈ [- 7, 5]

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

Here, we have,

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Here is the descriptive statistics table for the four variables, including skew and kurtosis for each variable:

Variable Mean Median Standard Deviation Skewness Kurtosis

Height 68.2 68.0 3.0 0.2 -0.6

Weight 170.0 168.0 30.0 0.4 -0.6

Age 25.0 25.0 2.0 0.0 -1.0

IQ 100.0 100.0 15.0 0.0 -1.0

The skewness and kurtosis values for all four variables are close to 0, which suggests that the data is approximately normally distributed.

In addition to the descriptive statistics table, we can also assess normality by creating a histogram of the data.

The histograms for height, weight, and age are all approximately bell-shaped, which suggests that the data for these variables is approximately normally distributed. However, the histogram for IQ is slightly skewed to the right, which suggests that the data for IQ may not be truly normally distributed.

Overall, the descriptive statistics and histograms suggest that the data for height, weight, and age is approximately normally distributed.

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Hello!

1 book => [tex]1^{\frac{3}{8} }[/tex]

14 books => [tex]14*1^{\frac{3}{8} }[/tex]

[tex]14*1^{\frac{3}{8} }\\\\= 14 * 1\\\\ \boxed{=14}[/tex]

The answer is 14 inches thick.

The equivalent monthly interest rate is 1.91%

To determine the value, we need to know the formula for simple interest, we have that;

I = PRT/100

Such that the parameters of the formula are;

From the information given , we have that;

The annual interest rate R = 23%

Then, to determine its equivalent monthly, we get;

If 12 months = 23%

Then 1 month = x%

cross multiply the values, we have;

12x = 23

Divide by the coefficient

x = 23/12 = 1. 91%

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Answer:

dört yarım saat 2 saattir

Step-by-step explanation:

The student would spend $18 on books and lab manuals.

An expenditure refers to the spending of money on something or the money that is spent on something.

Total Expenditure = Lab fee + Materials fee + Tuition + Books and lab manuals + Tools

Total Expenditure = 8% + 10% + 38% + 18% + 26%

Total Expenditure = 100%

We will calculate the amount spent on books and lab manuals. The amount spent on books and lab manuals is:

= (Books and lab manuals percentage / Total Expenditure percentage) * $100

= (18% / 100%) * $100

= 0.18 * $100

= $18.

Missing details:

On pie chart  for School Expenditures; Lab fee = 8% Materials fee =10% Tuition = 38% Books and lab manuals = 18% Tools = 26%

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After considering the given data we conclude that the system of equations are x=-3 and y=2², under the condition that the given system of equations are x+2y=1 -3x-2y=5

considering the system of equations x+2y=1 and -3x-2y=5. The coefficient matrix is

| 1  2 |
| -3 -2 |

and its determinant is 1×(-2)-(-3)×2 = 4. The matrix obtained by replacing the first column by the right-hand sides of the equations is

| 1  2 |
| 5 -2 |

and its determinant is 1×(-2)-5×2 = -12. The matrix obtained by replacing the second column by the right-hand sides of the equations is

| 1  1 |
| -3 5 |

and its determinant is 1×5-(-3)×1 = 8. Therefore, x=-3 and y=2².
Cramer's rule consist of a  formula which is required for  solving a system of linear equations with as many equations as unknown variables, applying determinants. It expands the solution in terms of the determinant of the coefficient matrix and the matrices taken from it by replacing one column by the right-hand sides of the equations.
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The probability of spinning a quadrilateral is 1/3 and probability of spinning a polygon with at least 5 sides is 0.5

Probability is a measure of the likelihood of an event to occur.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

In the given problem, we can determine the probability of each event by following this simple formula.

a. The probability of spinning a quadrilateral.

P(quadrilateral) = 2 / 6 = 1/3

NB: A quadrilateral is any figure or shape with four sides.

b. The probability of a polygon with at least 5 sides.

P(polygon > 5 sides) = 3/6 = 1/2

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The volume of the composite solids that consists of rectangular prisms is: A. 190 m³.

Note that the formula for finding the volume of a rectangular prism is given as:

Volume of rectangular prism = length * width * height.

Find the volume of each rectangular prism and add them together:

Volume of prism 1:

length = 10 m

width = 4 m

height = 3 m

Volume = 10 * 4 * 3 = 120 m³

Volume of prism 2:

length = 10 m

width = 1 m

height = 7 m

Volume = 10 * 1 * 7 = 70 m³

Total Volume = 120 + 70 = 190 m³.

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Answer: 3 1/3

Step-by-step explanation:

if the width of the rectangle is equal to “x” then the length is equal to 3x+2

The area is 40ft^2

so: 40=(3x+2)(x)

Then we simplify and subtract 40 in both sides:

0=3x^2+2x-40

Then we will use the quadratic formula to solve for x

X=(-2-sqr(2^2-4(3)(-40)))/2*3

And

X=(-2+sqr(2^2-4(3)(-40)))/2*3

then x is either equal to 3 1/3 or -4, since the answer cannot be negative, the answer is 3 1/3

The statements that justify why the table does not represent a probability distribution are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Considering that the number of outcomes cannot be negative, negative probabilities do not exist.

For a distribution, the sum of all the probabilities must be of one, hence:

-1/3 + 2/5 + 1/5 + 2/5 = 1 - 1/3 = 2/3 -> Different of one.

The table is given by the image presented at the end of the answer.

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The critical value for a confidence level of 98% with a sample size of 32 is given as follows:

t = 2.4528.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.

(df is one less than the sample size).

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The number of unique preferences represented in the table is given as follows:

B. Five.

Unique outcomes are the outcomes that appear in a data-set, however we only count them twice.

For example, if João and Elisa are Buffalo Bills fans, while Chanel and Laura are Atlanta Falcons fans, we have two unique outcomes(Bills and Falcons fans).

Hence the outcomes for this problem is given as follows:

Hence the number of unique outcomes is given as follows:

5.

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Hello!

it's a multiplication

The mass of the milk with a density of 1.03 g/cm³ is 417.15 g.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

To determine the mass of the milk, plug the given values into the above formula and simplify.

p = m / v

m = p × v

m = 405 × 1.03

m = 417.15 g

Therefore, the mass is 417.15 grams.

Option D) 417.15 g is the correct answer.

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The 3 consecutive odd numbers are 5, 7, and 9

3 consecutive odd numbers can be written as:

x

x + 2

x + 4

Such that x is an odd number.

Here we want that 4 times the middel number is equal to 14 more than the sum of the first and the third, then we can write the linear equation:

4*(x + 2) = x + x + 4 + 14

Solving this for x, we will get:

4x + 8 = 2x + 18

4x - 2x = -8 + 18

2x = 10

x = 10/2 = 5

The 3 numbers are 5, 7, and 9

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a) Approximately 778.7 grams of thorium 234 will be left after 0.5 years.

b) Approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

(a) To find the amount of thorium 234 left after 0.5 years, we can use the equation:

[tex]A_t = A_0 e^{(-10.498t)}[/tex]

where A₀ is the initial amount, which is 1000 grams, t is the time in years, and At is the amount after t years.

Substituting t = 0.5, we get:

[tex]At = 1000 e^{(-10.498\times0.5)} = 778.7 \ grams[/tex]

Therefore, approximately 778.7 grams of thorium 234 will be left after 0.5 years.

(b) To find the time at which 115 grams of thorium 234 will be left, we can use the same equation and solve for t:

[tex]A_t = A_0 e^{(-10.498t)[/tex]

Dividing both sides by A₀ and taking the natural logarithm of both sides, we get:

ln(At/A₀) = -10.498t

Substituting At = 115 grams and A₀ = 1000 grams, we get:

ln(115/1000) = -10.498t

Solving for t, we get:

t = (ln(115/1000)) / (-10.498) ≈ 2.1 years

Therefore, approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

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Step-by-step explanation:

Sometimes it is hard to 'see' the factorization....so you can take the HCF out of the three terms to perhaps see it better:

Factor out a '4'

4* ( 2n^2 + 17n + 21  )

4 ( 2n +3 )(n +7 )                    DONE.

The annual deposit for John for total amount of annuity is A = $ 29,060.29

Given data ,

To determine the annual deposit amount needed for John to have a total of $500,000 by the time he retires, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where FV is the future value, P is the annual deposit, r is the annual yield (interest rate), and n is the number of years.

In this case, we are given:

FV = $500,000

r = 5% = 0.05

n = 25 years

Substituting these values into the formula, we have:

$500,000 = P * [(1 + 0.05)^25 - 1] / 0.05

And , the value of P is

P = ($500,000 x 0.05) / [(1.05^25) - 1]

P ≈ ($25,000) / (1.858734... - 1)

P ≈ ($25,000) / 0.858734...

P ≈ $29,060.29

Hence , John must deposit approximately $29,060.29 into the retirement account each year to accumulate a total of $500,000 by the time he retires in 25 years

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