A quantity with an initial value of 870 decays continuously at a rate of 0.75% per day.
what is the value of the quantity after 10 weeks, to the nearest hundredth?

To solve this formula, we can simply use the formula of half-life of a radioactive substance to calculate the decay rate.

The disintegration constant or decay rate is calculated as 0.385min^-1

The half-life of a radioactive substance is defined as the time taken for the initial mass of the substance to reach half it's starting mass.

The formula is given as

[tex]T_\frac{1}{2} = \frac{\ln2}{\lambda}[/tex]

Let's substitute the value into the equation and solve through

[tex]T_\frac{1}{2} = \frac{\ln2}{\lambda} \\\lambda = \frac{\ln2}{T_\frac{1}{2} } \\\lambda = \frac{0.693}{1.8} \\\lambda = 0.385[/tex]

The disintegration constant or decay rate is calculated as 0.385min^-1

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Answer:

½ (a + b) h

Step-by-step explanation:

Answer:

114 feet

Step-by-step explanation:

To figure out the perimeter, we also need the width

The width can be found by dividing the area by the length

800/32 = 25

to find the perimeter, we use the equation 2L + 2W = P

L is the length

W is the width

2(32) + 2(25) = 64 + 50 = 114

114 feet is the perimeter

Give brainliest, please!

hope this helps :)

Answer: [tex]\frac{- 1}{11}[/tex]

Step-by-step explanation:

Note: the "." symbol stands for multiplication

Given,

[tex]\frac{2x+4}{3} \\[/tex]  - [tex]\frac{5x-7}{2}[/tex] = 5

First we the LCM = 6,

[tex]\frac{2(2x+4)}{2.3}[/tex] - [tex]\frac{3(5x-7)}{3.2}[/tex]= 5

Then, we join both sides, since they have same denominator

[tex]\frac{2(2x+4) - 3(5x-7)}{6}[/tex] = 5

Multiply again

[tex]\frac{4x+8 - 15x+21}{6}[/tex] = 5

Add the same numbers

[tex]\frac{-11x + 29}{6}[/tex] = 5

Transpose 6 to the other side

-11x + 29 = 5.6

-11x + 29 = 30

Transpose 29 to the other side

-11x = 30 -29

-11x = 1

Transpose 11 to the other side to get answer

x = [tex]\frac{-1}{11}[/tex]

Hope it helps! If you have any doubts, feel free to ask

A can is an example of a cylinder, and the volume of a cylinder is πr^2 x h. The diameter is 4, and the radius is half of a diameter so the radius is 2. The volume is π x 2^2 x 6 = 75.3982236862

Hope this helps :)

The inequality expression of the given word problem statement is;

t² - 3 ≤ 46

We are told that two numbers labelled t² and 3 have a difference that is at most 46.

Now, when we say at most, it means less than or equal to symbol.

Thus, the expression of the given statement is; t² - 3 ≤ 46

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Answer:

I don't know

Step-by-step explanation:

You didn't give a picture to see the rectangle.

Answer:

Graph B

Step-by-step explanation:

Rearrange in the form y > mx + c :

    2. x + y < 2

Graph which shows this inequality is : Graph B

B. is the correct graph.

Answer:

The Sum of supplementary angles is 180.

Therefore, <A + <B = 180

<A = 19<B

19<B + <B = 180

20<B = 180

<B = 9°

& <A = 19×9°

<A = 171°

Answer:

60

Step-by-step explanation:

AT = ½bh

AT = (6(20)) / 2

AT = 60

Answer:

The answer is 60

Step-by-step explanation:

^^

Happy to help :D

The volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16 is 24.74 cubic units.

Find the volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16

From the sphere and cylinder, the cylindrical coordinate will be

[tex]z = \pm \sqrt{16 - r^2}[/tex]

And the radius of the cylinder is |r| < 1 and the 0 ≤ θ ≤ 2π.

Then the volume will be given as

[tex]\rm V = \int _0^{2\pi} \int _0^1 \int _{- \sqrt{16 - r^2}}^{\sqrt{16-r^2}} \left ( r \ dz \ dr \ d\theta \right ) \\\\\\V = 2\pi \int_0^1 \left ( 2r\sqrt{16-r^2} \right ) \ dr\\\\\\V = 4\pi \left [ -\dfrac{1}{3} (16 - r^2)^{3/2} \right ]\\\\\\V = \dfrac{4\pi}{3} \left ( 16^{3/2} - 15^{3/2} \right )\\\\\\V = 24.74[/tex]

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Answer:

6

Step-by-step explanation:

8 * 3/4 = 24/4  = 6 WATER BOTTLES

Answer:

The baker needs 82 boxes.

Step-by-step explanation:

326/4=81 r 2.

But, you have to fit in all the cupcakes, so you round ir up to 82.

Answer:

−3k+6y

Step-by-step explanation:

Apply the distributive property.

5(2y)+5 (−3k)+4(3k−y)

Multiply 2 by 5.

10y+5(-3k)+4(3k−y)

Multiply −3 by 5.

10y−15k+4(3k−y)

Apply the distributive property.

10y−15k+4(3k)+4(−y)

Multiply :3 by 4

10y−15k+12k+4(−y)

Multiply: −1 by 4

10y−15k+12k−4y

Simplify by adding terms.

Subtract: 4y from 10y

−15k+12k+6y

Add: −15k and 12k

−3k+6y

Answer:

3

√

97.336

Decimal Form:

29.59770261

Step-by-step explanation:

Answer: $10.24

Step-by-step explanation: 12.95 * 0.15 = 1.94    12.95 - 1.94 = 11.01

11.01 * 0.07 = .77      11.01 - 0.77 = 10.24

Answer:

The student is incorrect and for parallelograms to be equal, included angles between them too should be equal.Explanation:When two quadrilaterals MNOP=TQRS, then not only all corresponding sides are equal, all corresponding angles too are equal.As MNOP and TQRS are parallelograms their diagonals bisect each other. And as MO=TR and NP=QS, it is apparent (see figure below) that MX=XO=TY=YR and NX=XP=SY=YQ. And hence two sides of all the four triangles (in each of the parallelogram) are equal.However, the angles included between the two diagonals can change (as is seen from the figure below),and hence MNOP≠TQRS

Step-by-step explanation:

Answer:

6.96

Step-by-step explanation:

2.9 x 1.5 = 4.35

3.3 - 1.5 = 1.8

1.8 x 2.9 = 5.22

5.22 divided by 2 = 2.61

4.35 + 2.61 = 6.96

Answer:

See below ~

Step-by-step explanation:

Things to Find

Volume of Toy

Volume of Circumscribing Cube

Difference in Volume

Slant height of cone

Surface Area of Toy

Answer:

  16 feet

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle. The Pythagorean theorem tells us the relationship between the various distances.

  EH² +HF² = EF²

  EH² + 12² = 20²

  EH² = 400 -144

  EH = √256 = 16

The hook is 16 feet below Edna.

Answer:

8 feet

Step-by-step explanation:

Answer:

Addition. Add 80 + 10 so

Step-by-step explanation:

a = amount invested at 7%

b = amount invested at 9%

we know the amount invested was ₹36000, thus we know that whatever "a" and "b" are, a + b = 36000.  We can also say that

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of a}}{\left( \cfrac{7}{100} \right)a}\implies 0.07a~\hfill \stackrel{\textit{9\% of b}}{\left( \cfrac{7}{100} \right)b}\implies 0.09b[/tex]

since we know the interest earned from the invested was ₹2920, then we say that 0.07a + 0.09b = 2920.

[tex]\begin{cases} a + b = 36000\\\\ 0.07a+0.09b=2920 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{a + b = 36000\implies \underline{b = 36000-a}}~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.07a~~ + ~~0.09(\underline{36000-a})~~ = ~~2920} \\\\\\ 0.07a+3240-0.09a=2920\implies 3240-0.02a=2920\implies -0.02a=-320 \\\\\\ a=\cfrac{-320}{-0.02}\implies \boxed{a=16000}~\hfill \boxed{\stackrel{36000~~ - ~~16000}{20000=b}}[/tex]

The difference of the two polynomials is 7x² + 11x. The correct option is the second option, 7x² + 11x

From the question, we are to determine the difference of the two polynomials

The given operation is

(9x²+8x) - (2x²+3x)

First, remove the brackets and collect like terms

That is,

9x²+ 8x - 2x² + 3x

9x² - 2x²+ 8x + 3x

Simplifying, we get

7x² + 11x

Hence, the difference of the two polynomials is 7x² + 11x. The correct option is the second option, 7x² + 11x

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Here is the complete and correct question:

What is the difference of the two polynomials? (9x2 + 8x) – (2x2 + 3x)
7x2 + 5x

7x2 + 11x

11x2 + 5x

11x2 + 11x

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Answer:

The mean hourly snowfall is 2.5 centimeters

Step-by-step explanation:

The mean hourly snowfall is the number of centimeters that fell during the period divided by the number of hours.

From 5 P.M. to 9 P.M., there are 4 hours

At 5 P.M., the total snowfall is 2 centimeters.

At 9 P.M., the total snowfall is 12 centimeters.

So in those four hours, the depth of snow increases 12-2 = 10 centimeters

10/4 = 2.5

The mean hourly snowfall is 2.5 centimeters

The total amount that Penny has budgeted for her trip to Egypt is £5351.62.

The exchange rate is the rate at which one currency is exchanged for another currency.  The total amount that was budgeted by Penny is the sum of the different compoments that she compiled for the trip.

Cost of international phone card in Egyptian pound = 41.38 x 5.3841 =£222.79

Cost of passport in Egyptian pound = 65 x 5.3841  = £349.97

Total cost =  3,241.77 + £222.79 + 494.25 +  £349.97+ 398.26 £ + 644.48 = £5351.62

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The highlighted part is known as the center of the circle. Then the correct option is C.

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Identify the highlighted part of circle O shown below.

The mid-point of the diameter is known as the center of the circle.

The highlighted part is known as the center of the circle.

Thus, the correct option is C.

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Answer:

The correct answer is A

Step-by-step explanation:

The books sold are 30,000, so that is our total sale for January. His sales are decreasing by an average of 500 books per month, which means he is losing sales so it is a negative value, and we multiply that by x (number of months) since the question has not stated the number of months. Therefore, the equation would be f(x) = 30,000 - 500x

Hope this is of help!