Pleaseeee help me. I'm stuck on a math question.

a) The decay formula for the mass of Strontium-90 is m(t) = 75 · [tex]e^{-t /40.395}[/tex].

b) The sample of Strontium-90 has a mass of approximately 13.258 miligrams after 70 days.

c) The sample of Strontium-90 takes a time of approximately 146.405 days.

The mass of Strontium-90 decays exponentially in time, whose model is described below:

m(t) = m' · [tex]e^{- t /\tau}[/tex]

Where:

And the time constant can be estimated by the following formula:

τ = t' / ㏑ 2

Where t' is the half-life of the isotope.

a) If we know that m' = 75 mg and t' = 28 d, then the expression for the mass of the sample is:

τ = 28 / ㏑ 2

τ ≈ 40.395 d

m(t) = 75 · [tex]e^{-t /40.395}[/tex]

b) And the mass of the isotope after 70 days is:

m(70) = 75 · [tex]e^{- 70 / 40.395}[/tex]

m(70) ≈ 13.258 mg

The current mass is approximately 13.258 miligrams.

c) If we know that m(t) = 75 · [tex]e^{-t /40.395}[/tex] and m(t) = 2 mg, then the time needed for the decay is:

75 · [tex]e^{-t /40.395}[/tex] = 2

[tex]e^{-t /40.395}[/tex] = 2 / 75

- t / 40.395 = ㏑ (2 / 75)

t = - 40.395 · ㏑ (2 / 75)

t ≈ 146.405 d

The needed time is approximately 146.405 days.

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Answer:

Let the girls be x

then, 5:4 = 5x and 4x

,

total stud.=36 so,

5x+4x=36

9x=36

x=36÷9

hence

x=4

now, boys = 5x=5×4=20

girls= 4x=4×4=16

so there are 16 girls

Answer: Yes

Step-by-step explanation:

Yes, it is because if you multiply 2 and 5, you get 10. 2 and 5 LCM is also 10. If you check 2 and five multiples you see this is also proved true.

2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ...

5 - 5, 10, 15, 20 ...

Functions that are symmetric with respect to the x-axis are those with even degree of y, i.e y², y⁴ etc.

Correct choices are:

Answer:

[tex]x=\dfrac{1}{8}y^2[/tex]

[tex]x=-y^2+9[/tex]

Step-by-step explanation:

Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

Therefore, any function that includes the term y² will be symmetric with respect to the x-axis since (-y)² = y².

[tex]\begin{aligned}&\textsf{Given}: \quad& x&=\dfrac{1}{8}y^2\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=\dfrac{1}{8}(-y)^2\\&\textsf{Simplify}: \quad &x&=\dfrac{1}{8}y^2\\\end{aligned}[/tex]

Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.

[tex]\begin{aligned}&\textsf{Given}: \quad& x&=-y^2+9\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=-(-y)^2+9\\&\textsf{Simplify}: \quad &x&=-y^2+9\\\end{aligned}[/tex]

Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.

The equation of the line d that is parallel to line c is y = -5x + 4.

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, c has an equation y = -5x + 3. Line d is parallel to line c. Therefore, they have the same slopes. Parallel lines have the same slope.

Hence, let's find the equation of line d passing through (2, -6)

Let's find the y-intercept

-6 = -5(2) + b

-6  = -10 + b

b = -6 + 10

b = 4

Therefore, the equation of the line d is y = -5x + 4

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Answer: All Are correct

Step-by-step explanation:

Look at graph, the vertex hits the origin, the parent function is on the top half of the graph (quads 1 and 2), both the left and right side have a slope of 1, and it is v shaped!

Answer:

30%

Step-by-step explanation:

130980-91686=39294

39294/130908=0.3

Answer: 168,609 ton

Hi, to answer this question, first we have to calculate the amount of the weight decrease by multiplying the original weight of the goods (240,870) by the percentage decrease in decimal form ( divided by 100)

Mathematically speaking:

240,870 (30/100) =72,261 ton

Finally we have to subtract that value to the original weight:

240,870-72,261 = 168,609 ton

Feel free to ask for more if needed or if you did not understand something.  

Step-by-step explanation:

The amount of money that must be deposited today is $749   .

In the question ,

it is given that ,

the amount that is need to be made (A) = $2250

time (t) = 20 years

rate percent (r) = 5.5%  = 0.055

let the amount that must be deposited today be P .

The amount that is needed to be deposited today at 5.5% compounded continuously can be calculated using the formula .

A = P×[tex]e^{r\times t}[/tex]

Substituting the values , we get
2250 = P × [tex]e^{0.055\times 20}[/tex]

2250 = P × [tex]e^{1.1}[/tex]

P = 2250/ [tex]e^{1.1}[/tex]

P = 748.9599

P ≈ 749

Therefore , The amount of money that must be deposited today is $749   .

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Answer: The answer is 5.

Step-by-step explanation:

4.5  ÷  0.9 = 450/90.
Convert decimal 4.5 to fraction 45/10

Convert decimal 0.9 to fraction 9/10

Divide 450/90

Simply 450/90 = 5

Answer:

5

Step-by-step explanation:

The equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.

According to the question,

We have the following information:

Initially the plant was 2 inches tall and it grew at an average rate of change of 0.125 inches per day.

2, 2.125, ...

Now, this series will become an arithmetic progression.

Formula to find the nth term:

an = a+(n-1)d

H = 2+(d-1)0.125

H = 1.875+0.125d

Now, the height after 15 days will be:

H = 1.875+0.125*15

H = 1.875+1.875

H = 3.75 inches

Hence, the equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.

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Step-by-step explanation:

x + y = 42

5x + 9y = 190

x = 42 - y

5(42 - y) + 9y = 190

210 - 5y + 9y = 190

210 + 4y = 190

4y = -20

y = -5

x = 42 - y = 42 - -5 = 42 + 5 = 47

The annual rainfall in 2016 is 336 mm.

Let the annual rainfall in 2016 be 100x mm.

Now it is given that rainfall in 2017 is 25% more than rainfall in 2016.

So. rainfall in 2017 is = 100x + 100x*(25/100) = 100x+25x = 125x mm

Also given that the amount of rainfall in 2017 = 420 mm.

According to question the suitable equation is,

125x = 420

x = 420/125

x = 3.36

Hence the rainfall in 2016 is = 100x = 100*3.36 = 336 mm.

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Answer:

Step-by-step explanation:

f(0) = 4

f(x)=0   when x = 0.75

f(x) =5  when x =3

A{ x ∈ R ║ 3≤x}

The value of derivative of d/dx[5f(x)-4x] at x=2 = 16.

From the table:

At x=2,

f'(x) = 4

f(x) = 4x

= d/dx(5*4x - 4x)

= d/dx(20x - 4x)

= d/dx(16x)

= 16

Therefore the value of derivative of d/dx[5f(x)-4x] at x=2 = 16.

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A real world situation that could be modeled by the expression, 300+7x is that Bob bought goods for $300 and then bought 6 pens that cost x dollar each.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both

In this case, Bob bought goods for $300 and then bought 6 pens that cost x dollar each. The total cost will be:

= 300 + (7 × x)

= 300 + 7x

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Answer:

[tex] \binom{?}{?} [/tex]

Step-by-step explanation:

$40 Pam use type diagram

$45. bro

Answer: 35

Step-by-step explanation:

[tex]f(4)=7(4+2)-7\\\\f(4)=7(6)-7\\\\f(4)=7(5)\\\\f(4)=35[/tex]

Let the present age of student be x

Present of teacher will be 4x

After 20 years,

Age of student = x + 20

Age of teacher = 4x + 20

According to the given condition after 20 years,

x + 20 = (4x + 20)/2

x + 20 = 2x + 10

2x - x = 20 - 10

x = 10

So student's present age is 10 years while teacher's is 4 x 10 i.e 40 years.

Hope This Helps You!

Answer:

315

Step-by-step explanation:

2/180=3.5/x

2x=630

x=315

The ratio of cranberry juice to apple juice to orange juice in the fruit punch is  = 1 : 2 : 3

Let the total quantity of juice is 60 ml .

Now the apple juice is 1/3 of 60 = 20 ml

The orange juice is 1/2 of 60 = 30 ml

Therefore cranberry juice = 60 -(20+30) ml = 10 ml

Now the ratio of cranberry juice to apple juice to orange juice

= 10 : 20 : 30

= 1 : 2 : 3

We can exactly find out how much of one simple quantity is included in the other by simply comparing two amounts of the same units. Ratios can be divided into two smaller groups.

One is the part to the whole ratio; the other is the part to the part ratio. The exact relationship that is between the two distinct entities or groupings is only exactly depicted by the part-to-part ratio.

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Answer: (-12,-1)

Step-by-step explanation: Point A=-1 and Point B=-12

:)

Answer:r

Step-by-step explanation:r

The number of ways to split the integers, given the condition and using the Fundamental Counting Theorem, is of:

144.

It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes considering all trials is calculated by the multiplication of the factorials as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Given the condition that the greater number is at least 2 times the lesser number we have that the pairs are composed by one number between 1 and 7 and another number between 8 and 14.

Hence the pairs of each number are built as follows:

Hence the number of ways to split the numbers is:

2 x 3 x 4 x 3 x 2 = 144.

(the numbers were multiplied because of the Fundamental Counting Theorem).

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Answer:

x=10

y=5

Step-by-step explanation:

you have to find the length

The time that would be taken for the money to double is 9 years.

Given that a compound interest has to do with the type of interest that is charged both on the principal and on the interest. We know that the principal is the money that was invested.

Let the principal be P and let the time taken be t. Let us now apply the formula;

A = P(1 + r)^n

Where A = 2P and r = 0.08

2P = P(1 + 0.08)^n

2P/P = (1.08)^n

2 = (1.08)^n

ln2 = nln1.08

n = ln2/ln1.08

n = 0.693/0.077

n = 9

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The value for the side of rectangle XZ is equal 14, using the trigonometric ratios of cosine and sine of angles.

The trigonometric ratios concerns the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the triangle WYZ, the cosine of angle Y;

cos(Y) = 21/YZ {adjacent/hypotenuse}

YZ = [21/cos(Y)] {cross multiply}

Considering the triangle XYZ, the cosine of angle Y;

cos(Y) = YZ/28

YZ = 28 × cos(Y)

Therefore,

28cos(Y) = [21/cos(Y)]

cos²(Y) = 21/28 {cross multiply}

cos(Y) = √(21/28) {take the square root of both sides}

cos(Y) = 0.8660

Y = cos^(-1)(0.8660) {cross multiply}

Y = 30°

To get the side XZ, considering the triangle XYZ the sine of 30°;

sin30° = XZ/28 {opposite/hypotenuse}

by cross multiplication

XZ = 28 × sin30°

XZ = 14

Therefore, by proper application of the trigonometric ratios of cosine and sine of the angle for the given triangle, the side XZ = 14.

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Answer: you prob fininshed 5,3

Step-by-step explanation:

also this is easy im srry for doing this

Answer:40%

Step-by-step explanation:

Answer:

if what I think you want is the number of bachelor degrees from from 1970 to 2014 for both men and women is then:

men: 617.6

women: 940.8

Step-by-step explanation:

from 1970 to 2014 it is 44 years so we plug 44 into x for both equations

Men:

y = 3.9(44) + 446

y = 171.6 + 446

y = 617.6

Women:

y = 14.2(44) + 316

y = 624.8 + 316

y = 940.8