The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. The half-life of a substance is 4.9 years. How long will it take for 36 grams to decay to 10 grams? (Round your answer to one decimal place.)
M(x)=c(.5^x/h)

Answers

Answer 1

[tex]\bf M(x)=c(0.5)^{\frac{x}{h}}\implies 10=36(0.5)^{\frac{x}{4.9}}\implies \cfrac{10}{36}=0.5^{\frac{x}{4.9}} \\\\\\ \cfrac{5}{18}=0.5^{\frac{x}{4.9}}\implies log\left( \frac{5}{18} \right)=log\left( 0.5^{\frac{x}{4.9}} \right) \\\\\\ log\left( \frac{5}{18} \right)={\frac{x}{4.9}}\cdot log\left( 0.5 \right)\implies \cfrac{4.9\cdot log\left( \frac{5}{18} \right)}{log(0.5)}=x[/tex]

Related Questions

A right triangle has a hypotenuse of length 20 cm and another side of length 16 cm. what is the length of the third side of the triangle?

Answers

Apply the Pythagorean Theorem:

20^2 = 16^2 + x^2 => 400 = 256 + x^2 => 144 = x^2, or x = 12 cm (answer)

Joseph needs to find the quotient of 3.216 ÷8. In what place is the first digit in the quotient?

Answers

If you do long division you will see that 8 cannot go into 3 it will go into 3.2 so the first digit will be in the tenths place 0.4... no need to finish the division since all the question asks is the place of the first digit

Irving spent the day shopping and made the following purchases: Item Cost ($) Novel 8.75 Shirt 21.66 Lunch 9.13 Potted plant 16.89 When Irving was done, he checked his account balance and found he had a total of $95.06. How much money was in Irving’s account to begin with? a. $56.43 b. $151.49 c. $38.63 d. $142.36

Answers

Solution:

Amount spent by Irving:

Item cost($)

Novel 8.75

Shirt 21.66

Lunch 9.13

Potted plant 16.89

Total money spent = $56.43.

Amount of money In Irving account= $95.06.

Amount of money was in Irving’s account to begin with =$56.43+$95.06=$151.49.

Answer:$151.49.

When originally purchased, a vehicle costing $24,840 had an estimated useful life of 8 years and an estimated salvage value of $2,600. after 4 years of straight-line depreciation, the asset's total estimated useful life was revised from 8 years to 6 years and there was no change in the estimated salvage value. the depreciation expense in year 5 equals:?

Answers

Originally, the depreciation is the original price of $24,840 minus the salvage value of $2600 divided by the number of years of useful life which was 8 years. This means that (24840-2600)/8 = $2780 was being written off each year, so, at the end of year 4, (4*2780) = $11, 120 was written off. This leaves the value of the car at (24840 - 11120) = $13720 at the start of year 5. Since we are moving from 8 years to 6 years useful life, there are only 2 more years over which we can depreciate. The current value at the end of year 4 minus the salvage value, then divided by the 2 years useful life remaining gives us a depreciation expense of (13720 - 2600)/2 = $5560 in year 5

What is the 4th term of the sequence?
a1 = 8 and an = 6 + an – 1
a4 =

Answers

[tex]\bf \begin{array}{ll} term&value\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ a_1&8\\\\ a_2&6+a_{n-1}\\ &6+a_{2-1}\\ &6+a_1\\ &6+8\\ &14\\\\ a_3&6+a_{3-1}\\ &6+a_2\\ &6+14\\\\ a_4&6+a_{4-1}\\ &6+a_3 \end{array}[/tex]

notice, is an arithmetic sequence, simply adding 6 to get the next term's value.

Compare and contrast Euclidean geometry and spherical geometry. Be sure to include these points:

1. Describe the role of the Parallel Postulate in spherical geometry.
2. How are triangles different in spherical geometry as opposed to Euclidean geometry?
3. Geodesics
4. Applications of spherical geometry

Answers

Euclidean geometry is what describes the shortest path between and 2 points on a sphere is a along a circle. lines are a process in euclidean geometry however in spherical geometry they are not. in Euclidean geometry the sum of any triangles angle measures must equal a 180 degrees.

Final answer:

Euclidean geometry and spherical geometry have distinct characteristics. The Parallel Postulate, triangle properties, geodesics, and applications differ between the two. Euclidean geometry relies on parallel lines, triangles with interior angles summing to 180 degrees, and straight geodesics, while spherical geometry lacks parallel lines, features triangles with angles >180 degrees, and utilizes great circles as geodesics. Spherical geometry finds applications in astronomy, navigation, Earth sciences, and cartography.

Explanation:

Euclidean Geometry vs Spherical Geometry

Euclidean geometry and spherical geometry are two different branches of geometry that have distinct characteristics and applications. Let's compare and contrast them:

1. Role of the Parallel Postulate

In Euclidean geometry: The Parallel Postulate states that given a line and a point not on that line, there is exactly one line that passes through the point and is parallel to the given line.

In spherical geometry: The Parallel Postulate is not true. In fact, there are no parallel lines in spherical geometry. On a sphere, any two lines will eventually intersect.

2. Triangles in Euclidean Geometry vs Spherical Geometry

In Euclidean geometry: Triangles have interior angles that sum up to 180 degrees. The angles of a triangle are classified as acute, obtuse, or right.

In spherical geometry: Triangles have interior angles that add up to more than 180 degrees. In fact, the sum can be greater than 540 degrees. Spherical triangles on a sphere are classified as acute-angled, right-angled, or obtuse-angled based on their angles.

3. Geodesics

In Euclidean geometry: Geodesics are straight lines and shortest paths between two points.

In spherical geometry: Geodesics are great circles or the arcs of circles on the surface of the sphere. They represent the shortest path between two points on a sphere.

4. Applications of Spherical Geometry

Spherical geometry has practical applications in various fields, including:

Astronomy: Spherical coordinates are used to locate celestial objects.

Navigation: Spherical trigonometry helps navigate across the Earth's curved surface.

Earth sciences: Spherical harmonics are used to represent the Earth's gravitational field.

Cartography: Representing the Earth's surface on a map or globe.

Compute r6r6, l6l6, and m3m3 to estimate the distance traveled over [0, 3] if the velocity at half-second intervals is as follows:

Answers

For R6 and L6, t= (3- 0) / 6= 0.5. For M3, t= (3- 0)/ 3 = 1. Then

For R6 we will add all the velocity given from 12 to 20 and then multiply it by 0.5 seconds

R6 = 0.5 s ( 12 + 18 + 25 + 20 + 14 + 20 ) m/ sec = 0.5 (109) m = 54.5 m,

For L6 we will add all the velocity given from 0 to 14 and then multiply it by 00.5 as well.

L6 = 0.5 sec ( 0 + 12 + 18 + 25 + 20 + 14 ) m/ sec = 0.5 (89 ) m = 44.5 m.

For M3:

M3 = 1 sec (12 + 25 + 14) m/ sec = 51 m.

Final answer:

The question relates to integral calculus and the concept of Riemann sum approximation. The values r6r6, l6l6, and m3m3 need to be calculated given they represent velocities at half-second intervals. The estimated distance travelled would be the sum of these velocities multiplied by their respective time intervals.

Explanation:

The task here is to compute the expressions r6r6, l6l6, and m3m3, and use those to estimate the distance traveled over the interval [0,3], if the velocity changes at half-second intervals. From the details, it is indicative this is a problem involving the mathematical concept of integral calculus, specifically the area under velocity-time curve. The overall distance travelled is given by the area under the curve which is the integral of the velocity function over the given interval.

Let's suppose the values r6r6, l6l6, and m3m3 represent velocities at different half-second intervals of time. In order to estimate the total distance travelled, you would need to sum these velocities and multiply by the duration of each interval (0.5 seconds). This concept is also known as Riemann sum approximation in integral calculus.

For example, if r6r6 = 10 m/s, l6l6 = 12 m/s, and m3m3 = 8 m/s, the estimated total distance travelled would be calculated as (10*0.5 + 12*0.5 + 8*0.5) = 5 m + 6 m + 4 m = 15 m.

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PLZ ANSWER I BEG U
An airplane flies to San Francisco from Los Angeles in 4 hours. It flies back in 3 hours. If the wind is blowing from the north at a velocity of 20 mph during both flights, what was the airspeed of the plane (its speed in still air)?

Answers

the plane's airspeed is 140:)

Which set of ordered pairs contains only points that are on the graph of the function y = 12 − 3x?

Answers

(-18,10) (-6, 6) (18, -2)

find the area of the figure (sides meet at right angles)

Answers

4mm + 2mm + 12mm
18mm
18mm

write 18/24 as a percentage

Answers

divide 18 by 24 for a decimal number:

18 / 24 = 0.75

multiply 0.75 by 100 for the percent

0.75 * 100 = 75%

explain...................

Answers

First you change it into slope intercept and get y=3x+7. To make it perpendicular you flip the slope so 3/1 becomes 1/3. Then you make it the opposite so it becomes -1/3. The answer is y=-1/3x+7

The slopes of perpendicular lines are negative reciprocals. That means that when you multiply then together, you get -1.

The slopes of all the choices are easy to see because all the choices are in y = mx + b form, slope-intercept form.

If we write our equation in slope-intercept form also, then we can see its slope easily.

We solve -3x + y = 7 for y.
Add 3x to both sides to get
y = 3x + 7
The slope is 3.
We need a negative reciprocal slope to 3, so we need -1/3.

Only choice A has a slope of -1/3.

Answer: Choice A, y = -1/3x + 7

For problems 2-3: data were collected on the contents of 1-kilogram sugar packets of brands 1 and 2. assume contents are normally distributed. let and be the true average and standard deviation of contents for brand ( = 1, 2). data summaries are given below. data summary brand 1: = 16, ̅ = 1.053, = 0.058 brand 2: = 16, ̅ = 1.071, = 0.062 2. we would like to determine if there is evidence that brand 1 has a lower average content that brand 2. what hypothesis test will we conduct?
a. : − = 0 versus : − ≠ 0
b. : − = 0 versus : − > 0
c. : − < 0 versus : − = 0
d. : − = 0 versus : − < 0 3. what is the value of the test statistic for testing : = ?
a. 0.9355
b. 0.8751
c. −0.018
d. −0.848

Answers

the answer d right answer

4/25, 13%, 0.28, 7%, 21/100, 0.15 least to greatest

Answers

7%, 13%, 0.15, 4/25, 21/100, 0.28

Hello,

I think we should turn all of these numbers to decimals so that we can tell which one is least and greatest.

Let's start with 4/25. Let's get the divide 4 by 25 to get the decimal form. 4÷25=.16

Then 13%, move the decimal two places to the left to get it into percentage form. After you move the decimal, it is now .13

0.28 is already in decimal form, let's move to the next one.

7%, again let's move the decimal place two places to the left. After that, it i now .07

21/100, let's divide "21" from "100, 21÷100= 0.21

0.15 is already in decimal form, so now we are ready to order them from least to greatest.

Least to Greatest: 0.7 (7%), 0.13 (13%), 0.15, 0.16 (4/25), and lastly 0.21 (21/100).

Hope this helps!

May

A retangular box is 2 cm high, 4 cm wide and 6 cm deep. M packs the box with cubes, each 2 cm by 2 cm by 2 cm with no space left over . How many cubes fit in the box?

Answers

Sent a pic of the solution (s).

check the picture below.

how many times does 8 go into 48? well, that many cubes.

Can someone help me with this question?

State the Pythagorean Theorem and tell how you can use it to solve problems

Answers

The Pythagorean Theorem is [tex]a^{2} + b^{2} = c^{2} [/tex]

You can use the Pythagorean theorem to solve for the hypotenuse. For example lets say you have one side (a) equal to 3 and the other side (b) equal to 2. From there you can plug it in and find that the hypotenuse (c) is equal to 3.61

Hello, the Pythagorean Theorem states: the sum of the squares made on the sides is equivalent to the square made on the hypothenuse.

What does it mean? It may help you to draw a right triangle and to draw a square for each side. You can see that the sides of the triangle are the sides of the squares.

Then, if we sum the area of the squares on the sides (because they are equivalent = same area) we get the are of the square on the hypothenuse.

Call "a" and "b" the squares on the sides and "c" the squares on the hypothenuse.

a^2 + b^2 = c^2

Where can this Theorem be used? Of course, where you have to deal with geometry problems, in particular right triangles, rectangles and many more.

For example, we have to find the hypothenuse of a right triangle.

Let's follow the formula and we have that a = 4, b = 3...what's c?

4^2 + 3^2 = c^2

16+9 = c^2

25 = c^2

So, c^2 is 25.

We have c^2 but not c, so how do we solve it?

Simple, do the square root, c = square root of 25 = 5

Of course there are even inverse formulas:

a^2 = c^2 - b^2
b^2 = c^2 - a^2

[tex]r \frac{8}{11} r \frac{10}{11} [/tex] Simplify. Write your answer using a single, positive rational exponent

Answers

hmmmm I take it you meant those rationals to be exponents, so hmmm asumming that,

[tex]\bf r^{^\frac{8}{11}}\cdot r^{^\frac{10}{11}}\implies r^{^{\frac{8}{11}+\frac{10}{11}}}\implies r^{^\frac{18}{11}}[/tex]

Simone paid $12 for an initial years subscription to a magizine. The renewal rate is $8 per year. This situation can be represented by the equation y=8x+12, where x represents the number of years the subscription is renewed and y represents the total cost.

Answers

This is easy. Select different values for x to find y values.

For example, let x = 0.

y = 8x + 12

y = 8(0) + 12

y = 0 + 12

y = 12

On your table, you have x = 0 and y = 12.

Do the same using other values of x.

The table shows the solution for the linear equation.

What is linear equation?

"An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line".

For the given situation,

Cost for initial year subscription = $12

Cost for renewal = $8

The number of years the subscription is renewed be 'x' and

The total cost be 'y'.

This situation can be represented by the equation y = 8x+12.

For this linear equation, we need to make table by substituting different values of x to get y.

For [tex]x=1[/tex]

⇒[tex]y=8(1)+12[/tex]

⇒[tex]y=20[/tex]

For [tex]x=2[/tex]

⇒[tex]y=28[/tex]

For [tex]x=3[/tex]

⇒[tex]y=36[/tex]

For [tex]x=4[/tex]

⇒[tex]y=44[/tex]

For [tex]x=5[/tex]

⇒[tex]y=52[/tex]

The table below shows these interpretations.

Hence we can conclude that the table shows the solution for the linear equation.

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simplify the expression 2x - 4 + 3x

Answers

To simplify the equation. 2x - 4 + 3x, all you need to do is combine like terms, which are 2x and 3x. The resulting answer would be 5x - 4. Hope this helps and have a wonderful day!

5x - 4

I need to have atleast 20 characters so ill add this <3

At a local hospital, 35 babies were born. if 26 were boys, what percentage of the newborns were boys?

Answers

Remember to divide the numerator by the denominator and multiply it by 100.

So 26 divided by 35 is 0.7428..... Since the number doesn't end, you round it to the nearest tenth, which is 0.7. Now you multiply that number by 100. And the percentage would be... 70% of the babies would be boys.

G write the equation in spherical coordinates. (a) 7z2 = 8x2 + 8y2

Answers

Answer:

[tex]\displaystyle 7 \cos^2 \phi - 8 \sin^2 \phi = 0[/tex]

General Formulas and Concepts:
Multivariable Calculus

Spherical Coordinate Conversions:

[tex]\displaystyle r = \rho \sin \phi[/tex][tex]\displaystyle x = \rho \sin \phi \cos \theta[/tex][tex]\displaystyle z = \rho \cos \phi[/tex][tex]\displaystyle y = \rho \sin \phi \sin \theta[/tex][tex]\displaystyle \rho = \sqrt{x^2 + y^2 + z^2}[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle 7z^2 = 8x^2 + 8y^2[/tex]

Step 2: Convert

[Equation] Substitute in Spherical Coordinate Conversions:
[tex]\displaystyle 7( \rho \cos \phi )^2 = 8( \rho \sin \phi \cos \theta )^2 + 8( \rho \sin \phi \sin \theta )^2[/tex]Simplify:
[tex]\displaystyle 7 \rho^2 \cos^2 \phi = 8 \rho^2 \sin^2 \phi \cos^2 \theta + 8 \rho^2 \sin ^2 \phi \sin^2 \theta[/tex]Factor:
[tex]\displaystyle 7 \rho^2 \cos^2 \phi = 8 \rho^2 \sin^2 \phi \bigg( \sin^2 \theta + \cos ^2 \theta \bigg)[/tex]Simplify:
[tex]\displaystyle 7 \rho^2 \cos^2 \phi = 8 \rho^2 \sin^2 \phi[/tex]Simplify:
[tex]\displaystyle 7 \cos^2 \phi = 8 \sin^2 \phi[/tex]Rewrite:
[tex]\displaystyle 7 \cos^2 \phi - 8 \sin^2 \phi = 0[/tex]

∴ we have found the given equation in terms of spherical coordinates.

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Topic: Multivariable Calculus

Unit: Triple Integrals Applications

Which choice is the GCF and LCM of 24 and 48? A) GCF = 12, LCM = 12 B) GCF = 24, LCM = 48 C) GCF = 12, LCM = 24 D) GCF = 12, LCM = 48 PLZ HELP FAST

Answers

GCF = 24, and LCM = 48

, the GCF 36 and 48 is 12

In bowling you get a spare when you knock down the ten pins in two throws how many possible ways are there to get a spare

Answers

Sometimes, there's no replacement for just writing them all down. We have two throws, and we'll knock down a different number on our first throw. I'll write down the possibilities in coordinates like (first throw, second throw).

(0,10)
(1,9)
(2,8)
(3,7)
(4,6)
(5,5)
(6,4)
(7,3)
(8,2)
(9,1)
(10,0) <--- doesn't count since that would be a strike!

Counting only the ones that are spares, you'll see there are 10 ways to get a spare (count carefully!)

Answer:

Step-by-step explanation:

or more

Divide m2n2/p3 by mp/n2 .

Answers

8n^2 / 3p^2

Hope it helped!

Answer:

The answer is 'm'.

Step-by-step explanation:

Here, the given expression,

[tex]\frac{\frac{m^2n^2}{p^3}}{\frac{mp}{n^2}}[/tex]

[tex]=\frac{m^2n^2\times n^2}{p^3\times mp}[/tex]

[tex]=\frac{m^2n^{2+2}}{p^{3+1}m}[/tex] ( [tex]a^m.a^n=a^{m+n}[/tex] )

[tex]=\frac{m^2p^4}{p^4m}[/tex]

[tex]=m^2p^4p^{-4}m^{-1}[/tex] ( [tex]a^{m}=\frac{1}{a^{-m}}[/tex] )

[tex]=m^{2-1}p^{4-4}[/tex]

[tex]=m^1p^0[/tex]

[tex]=m[/tex]

Which measure of central location is meaningful when the data are categorical?

a. the range

b. the mean

c. the median

d. the mode?

Answers

The median is the measure of central location when data are categorical.

Find (3 × 104) − (5 × 102).

Answers

The answer is -198

(3*104) - (5*102)
312 - 510
-198

(3 × 10^4) − (5 × 10^2)
= 295 x 10^2
= 2.95 x 10^4

hope it helps

The average annual income I in dollars of a lawyer with an age of x years is modeled with the following function I=425x^2+45,500x-650,000

Answers

You did not include the questions, but I will give you two questions related with this same statement, and so you will learn how to work with it.

Also, you made a little (but important) typo.

The right equation for the annual income is: I = - 425x^2 + 45500 - 650000

1) Determine the youngest age for which the average income of a lawyer is $450,000

=> I = 450,000 = - 425x^2 + 45,500x - 650,000

=> 425x^2 - 45,000x + 650,000 + 450,000 = 0

=> 425x^2 - 45,000x + 1,100,000 = 0

You can use the quatratic equation to solve that equation:

x = [ 45,000 +/- √ { (45,000)^2 - 4(425)(1,100,000)} ] / (2*425)

x = 38.29 and x = 67.59

So, the youngest age is 38.29 years

2) Other question is what is the maximum average annual income a layer can earn.

That means you have to find the maximum for the function - 425x^2 + 45500x - 650000

As you are in college you can use derivatives to find maxima or minima.

+> - 425*2 x + 45500 = 0

=> x = 45500 / 900 = 50.55

=> I = - 425 (50.55)^2 + 45500(50.55) - 650000 = 564,021. <--- maximum average annual income

In the figure shown, what is the area of the rectangle, if the radius of each circle is 6 cm?

Answers

The diameter of each circle is 2(6 cm), or 12 cm.

Thus, the width of the rectangle is 12 cm. and the length is 24 cm.

The area of the rect. is (12 cm)(24 cm) = 288 cm^2

Final answer:

To find the area of the given rectangle with circles at its ends, we need to know the radius of the circles and the length of the rectangle in between. Length of the rectangle would be equal to the diameter of a circle plus the length between the two circles. Then, we multiply this length with the width equivalent to the diameter of the circle.

Explanation:

In this Mathematics question, the student is asked to find the area of a rectangle with two circles, each with a radius of 6cm, at its ends.

As we know, the area of a rectangle is found by the formula, Area = Length x Width.

The length of the rectangle can be determined from the radii of the circles, it's equal to the diameter of one of the circles (because the radius of the circle is 6, the diameter would be 2*6=12) plus the length of the rectangle that is between the two circles.

However, the width of the rectangle is smoothly equivalent to the diameter of one of the circles (which is 12cm as calculated).

Once we have both the length and width of the rectangle (assuming the length inside the rectangle is given or predetermined), we can easily determine the area of the rectangle by multiplying these two.

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Which equations have a greater unit rate than the rate represented in the table?
Choose more than one
x y
-----
3 2
6 4
9 6

A. y=5/7x
B. y=3/5x
C. y=1/3x
D. y=7/9x
E. y= 7/11x

Answers

Table slope = (4-2)/((6-3) = 2/3

A. 5/7 > 2/3
B. 3/5 < 2/3
C. 1/3 < 2/3
D. 7/9 > 2/3
E. 7/11< 2/3

(a) y=5/7x and (d) y=7/9x have a greater unit rate than the rate represented in the table.

What is slope intercept form?

y=mx+c is the slope intercept form where m is the slope and c is y intercept.

The given table is

x 3 6 9

y 2 4 6

The formula to calculate slope is m =y₂-y₁/x₂-x₁

(3,2 ) and (6, 4) are two points.

x₁=3, y₁=2 , x₂=6 and y₂=4

m=4-2/6-3

m=2/3.

Now let us check the equation with greatest slope

(a) y=5/7x

5/7 > 2/3

(b) y=3/5x

3/5 < 2/3

1/3 < 2/3

(d) y=7/9x

7/9 > 2/3

(e) y= 7/11x

7/11< 2/3

Hence (a) y=5/7x and (d) y=7/9x have a greater unit rate than the rate represented in the table.

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In how many ways can 3 boys and 3 girls sit in a row if the boys and girls are each to sit together?

Answers

the answer would be 36 because theres 6 people and 6 seats so 6*6 = 36

Final answer:

The boys and girls are each to sit together, and there are 3 boys and 3 girls. The total number of ways to arrange them is 36.

Explanation:

The boys and girls are each to sit together, meaning that the boys should sit together in one group and the girls should sit together in another group. We can consider these two groups as two separate entities.

The number of ways to arrange the boys within their group is 3! (3 factorial), because there are 3 boys. Similarly, the number of ways to arrange the girls within their group is also 3!. Since these two groups can be arranged independently of each other, the total number of ways to arrange the boys and girls is 3! * 3! = 6 * 6 = 36.

Other Questions

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