Half-Life N(t)=No(12)th N= final amount No= initial amount t= time h= half-life Iodine-123 is sometimes used in thyroid scans and has a half-life of 15 hours. a) How much of a 250 mg sample would remain after 40 hours (round to hundredths)? b) How much time does it take for 250 mg to decay to 100 mg (round to the nearest hour)? Use logarithms to solve it algebraically. You must show your work for each step to get credit.

Answer:

3 grams are in one chicken wing

Step-by-step explanation:

Set up an equation:

Variable x = grams per 1 chicken wing

1000/3000 = 1/x

Cross multiply

1000 × x = 3000 × 1

1000x = 3000

Divide both sides by 1000 to isolate the variable x

x = 3

Answer:

3

Step-by-step explanation:

3000/1000=3

Answer:

A, (10⁵) (10⁻²) > 8⁹/8⁶

Explanation:

A, (10⁵) (10⁻²) > 8⁹/8⁶ = 10³ > 8³ True

B, (10⁵) (10⁻²) < 8⁹/8⁶ = 10³ < 8³ False

C, (10⁵) (10⁻²) = 8⁹/8⁶ = 10³ = 8³ False

Answer:

20cm^3

Step-by-step explanation:

The volume of a rectangular prism is just the 3 values multiplied by each other. So that would be 6x5x2/3 = 20cm^3

Answer:

166°

Step-by-step explanation:

Supplementary angles have a sum of 180 degrees

That being said, we can find the measure of the missing angle by subtracting the measure of the given angle by 180

(the giving angle having a measure of 14°)

so missing angle = 180 - 14

180 - 14 = 166

Hence, the measure of the second angle 166°

Answer:

34 Units ^2

Step-by-step explanation:

Answer:

[tex] \frac{dh}{dt} = - 32t + 64 = 0 \\a) \: t = \frac{ - 64}{ - 32} = 2 \\ \\ b = - 16 \times 4 + 64 \times 2 + 6 = - 64 + 2 \times 64 + 6 = 64 + 6 = 70[/tex]

Answer:

a) t = 2 seconds

b) 70 feet

Step-by-step explanation:

First of all, we are going to take the derivative of the function (which is a displacement function) to make find its velocity function.

[tex]h(t) = -16t^{2} +64t+6[/tex]

To find the derivative of the equation, we must multiply the coefficient by the exponent and then minus one from the exponent for each term.

[tex]v(t)=(-16)(2)t^{2-1} +64(1)t^{1-1}+6(0)t^{0-1} \\v(t) = -32t +64[/tex]

Now we can substitute in v=0

This is because the ball is at the top of its parabola path, it is the turning point and the slope is 0. The velocity physically speaking would also be 0 at the very top of its path.

[tex]0=-32t+64[/tex]

Rearrange and we get:

[tex]32t = 64\\t=2[/tex]

Ball attains maximum height at 2 seconds.

To find the maximum height, we now just have to substitute back in the time into the original equation to find the height.

[tex]h(t) = -16t^{2} +64t+6[/tex]

[tex]h(2) = -16(2)^{2} +64(2)+6\\h(2)=-64+128+6\\h(2) = 70[/tex]

The maximum height attained is 70 feet.

Hope this helped!

Answer:

1. Yes

2. No

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

by the Pythagorean theorem;

8x8 + 15x15 = 289

and the root of 289 is 17

Answer:

10.8

Step-by-step explanation:

The value of x is 5.26.

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles. The ratios used to study this relationship are called trigonometric ratios, namely, sine, cosine, tangent, cotangent, secant, cosecant.

There are basic six ratios in trigonometry that help in establishing a relationship between the ratio of sides of a right triangle with the angle. If θ is the angle in a right-angled triangle, formed between the base and hypotenuse, then

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

The value of the other three functions: cot, sec, and cosec depend on tan, cos, and sin respectively as given below.

cot θ = 1/tan θ = Base/Perpendicualr

sec θ = 1/cos θ = Hypotenuse/Base

cosec θ = 1/sin θ = Hypotenuse/Perpendicular

Given:

H= 12

angle= 26°

Using Trigonometry

sin 26 = B/ H

0.4383= x/ 12

x= 5.26

Hence, the value of x is 5.26

Learn more about Trigonometry here:

https://brainly.com/question/26719838

#SPJ2

Answer:

B

Step-by-step explanation:

cause f ones have 5 lb and t ones have 2.5 lb

Answer:

B

Step-by-step explanation:

The correct answer is B!

Answer:

2.9

Step-by-step explanation:

5% of 58

58 × 5 ÷ 100 = 2.9

Step-by-step explanation:

Convert 5% to a fraction first.

[tex]5\% = \frac{5}{100} \\ = \frac{1}{20} [/tex]

5% of 58

=

[tex] \frac{1}{20} \times 58 \\ = \frac{58}{20} \\ = \frac{29}{10} \\ = 2.9[/tex]

Answer:

120

Step-by-step explanation:

180(6-2)/6

Answer:

1. F

2. (2,2)

3.  points P and E

Step-by-step explanation:

Answer:

It's 35 months old and weighs 82 kilograms

The data is given in x, y, so the answer will also go in the order x, y.

Hope this helps! :)

Answer:

Option A

Step-by-step explanation:

Degree of the polynomial function = 4

That means highest degree term of the given polynomial has power = 4

If the roots of a quadratic polynomial are a, b, c, d then the polynomial function will be,

f(x) = (x - a)(x - b)(x - c)(x - d)

It's given in the question that roots are x = -2, -1, 1 and 3

Therefore, polynomial function will be,

f(x) = (x + 2)(x + 1)(x - 1)(x - 3)

From the given options, graph A shows that the graph intersects the x-axis at x = -2, -1, 1 and 3

Therefore, Option A will be the answer.

Answer:

11. Classification on basis of angles - Acute angled triangle

Classification on basis of sides - Isosceles triangle

12. Classification on basis of angles - Right angled triangle.

Classification on basis of sides - Scalene triangle

13. Classification on basis of angles - Obtuse angled triangle.

Classification on basis of sides - Isosceles triangle.

Answer:

[tex]\text{log}_a(1.5^{-1})=\frac{-9}{5}[/tex]

Step-by-step explanation:

Given;

[tex]\text{log}_a(2)=\frac{1}{2}[/tex]

[tex]\text{log}_a(3)=5[/tex]

By using logarithmic properties,

[tex]\text{log}_a(2)-\text{log}_a(3)=\frac{1}{2}-5[/tex]

[tex]\text{log}_a(\frac{2}{3})=\frac{1}{2}-5[/tex]

[tex]\text{log}_a(\frac{1}{\frac{3}{2}})=\frac{1}{2}-5[/tex]

[tex]\text{log}_a(\frac{1}{1.5})=\frac{1}{2}-5[/tex]

[tex]\text{log}_a(1.5^{-1})=\frac{1-10}{5}[/tex]

[tex]\text{log}_a(1.5^{-1})=\frac{-9}{5}[/tex]

Answer:

The largest angle needed is [tex]95.1^{o}[/tex].

Step-by-step explanation:

To determine the larges angle as required, let us apply the cosine rule.

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C

Since in triangles, the longest side is opposite to the largest angle, then;

[tex]15^{2}[/tex] = [tex]8^{2}[/tex] + [tex]12^{2}[/tex] - 2(8 x 12) Cos θ

225 = 64 + 144 - 192 Cos θ

225 = 208 - 192 Cos θ

192 Cos θ = 208 -225

192 Cos θ = -17

Cos θ = [tex]\frac{-17}{192}[/tex]

Cos θ = -0.08854

θ = [tex]Cos^{-1}[/tex] -0.08854

  = 95.07962

θ = [tex]95.1^{o}[/tex]

The largest angle needed is [tex]95.1^{o}[/tex].

Answer:

60

Step-by-step explanation:

5*3=15

3*3=9

4*3=12

4*3=12

4*3=12

(12*3)+9+15= 60

Answer:

i think the voulme would be 60 cm

Step-by-step explanation:

im sorry if its wrong

Answer:

Point L

Step-by-step explanation:

L

Answer: B. L

Hope this helps

Answer:

36

Step-by-step explanation:

the volume of the prism is, the area of the base x height

.

b x 16 = 576

b = 36

so the answer is 36

Answer:

C) 36

Step-by-step explanation:

Answer:

uhhh- sorry I cant see the picture :>

Step-by-step explanation:

But this guy knows the answer >:3

Cory1288 avatar

A) is 76 and B) is 180

why? bc-

cory1288 avatar

104+76=180 and a circle is 360

- Thx for the points have a nice day! ^ω^

Answer:

A. 76

B. 256

Step-by-step explanation:

DF is a diameter so that means the right side of the

circle measure 180 degrees. Angle DGE measures 104, since that the central angle that means Arc DE measures 104 also.

Using arc addition, part of the right side measure 104 so that means the remaining arc must add up to 180.

[tex]104 + x = 180[/tex]

[tex]x = 76[/tex]

Arc EF measure 76.

2. A circle has 360 degrees in it. We are asked to find the measure of the circle expect the Arc ED.

Arc ED measures 104 so

[tex]360 - 104 = 256[/tex]

Answer:

I think 113.04

Step-by-step explanation:

The formula for the area of the circle is:

A=

[tex]\pi \times r { }^{2} [/tex]

Resolving:

[tex]\pi \times 6 {}^{2} = 113.097[/tex]

Answer:

answer is ABCD

Step-by-step explanation:

I took the quiz

Answer:

[tex]\frac{0.2}{20}[/tex]

Step-by-step explanation:

ez

Answer:

36.5625

Step-by-step explanation:

so, if it decays at a rate of 7.5% every 2 days, and we have 234 hours, we do the following, 234/24, since there are 24 hours in a day, that gives us 9.75, "7.5% every 2 days" so we do this, 9.75/2 = 4.875

4.875 * 7.5 = 36.5625

i migt be wrong, but i'm pretty sure this is the answer, i'm not saying this is the answer like some people do, please let me know if i'm wrong.

Answer:

3897.77

Step-by-step explanation:

Decays 7.5%→r=0.075 (divide by 100)

Decays every 2 days: exponent of  t/2

(where t is in days)

function- f(t)=5700(1−0.075) ^t/2

234 hours→234/24→9.75 days

Plug in t=9.75

f(9.75)=5700(1−0.075)  ^9.75/2

3897.76635734  

≈3897.77

Answer:

$37.26

Explanation:

firstly, we find the total original price: $34 + $12 = $46.

next, we can multiply this by 100% - 25% = 75% to find the discounted price:

$46 × 75%

= $46 ÷ 100 × 75

= $34.50

finally, add on the sales tax which is 100% + 8% = 108%:

$34.50 × 108%

= $34.50 ÷ 100 × 108

= $37.26

i hope this helps! :D