The isotope thulium-167 is used in laser scans for medical treatments. Its rate of decay is −0.075. How many days does it take 500 grams of the isotope to decay to 250 g?

Thank you!

Answer:

[tex]\huge\boxed{\dfrac{34}{51}=\dfrac{2}{3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{34}{51}\\\\34=17\cdot2\\51=17\cdot3\\\\LCM(34,\ 51)=17\qquad/\text{Largest Common Multiple}/\\\\\dfrac{34}{51}=\dfrac{34:17}{51:17}=\dfrac{2}{3}[/tex]

Answer:

Step-by-step explanation:

2

—

3

Answer:

Answer C.12

Step-by-step explanation:

v/V=(h/H)^3

1/8=(h/24)^3

1/8=h^3/24^3

1/8=h^3/13824

8h^3=13824

H=1728√3

h= \sqrt[3]{1728}

h=12 cm

the height of the smaller pyramid is 12 inches.

A triangular pyramid is a 3D geometric shape in which all the three lateral faces are triangles with a common vertex. If all the three triangular faces are equilateral, then such a pyramid is called a tetrahedron.

For the given situation,

The ratio of the volumes of two geometrically similar pyramids = 1:8

The height of the larger pyramid = 24 inches.

Let the volume of smaller pyramid be v1 and larger pyramid be v2.

Let the height of smaller pyramid be h1 and larger pyramid be h2.

The relation between the volume of pyramid and height is given as

[tex]v=\frac{1}{3} (base area)(height)[/tex]

Let us consider the triangle to be equilateral triangle. So all the sides are equal.

We know that, Base area = [tex]a^{2}[/tex] and [tex]a=h[/tex]

The volume becomes [tex]v=\frac{1}{3} h^{3}[/tex]

The ratio becomes,

⇒ [tex]\frac{v1}{v2} =\frac{h1^{3} }{h2^{3}}[/tex]

⇒ [tex]\frac{1}{8} =\frac{h1^{3} }{24^{3}}[/tex]

⇒ [tex]h1^{3}=\frac{24^{3} }{8}[/tex]

⇒ [tex]h1^{3}=\frac{13824 }{8}[/tex]

⇒ [tex]h1^{3}=1728[/tex]

⇒ [tex]h1=\sqrt[3]{1728}[/tex]

⇒ [tex]h1=12[/tex]

Hence we can conclude that the height of the smaller pyramid is           12 inches.

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Answer:

what is the question

Step-by-step explanation:

Answer:

OK UMMMM CAN YOU PUT THEE QUESTION

Step-by-step explanation:

Answer:

9 cm tall

Step-by-step explanation:

The formula to find the volume of a cylinder is

V = pi r^2 (h)

pi r^2 is the base

Plug in the volume and the base

198 = 22 (h)

divide by 22

9 = h

I think c

Step-by-step explanation:

Answer: C. answering the last two questions correctly

Step-by-step explanation: If each question were worth 3 points if he got it correctly then he would have to get 2 questions right since he has -6

Answer:

A) no solution

Step-by-step explanation:

Parallel lines never intersect

Answer:

11 1/4 or 11.25.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

you have to minus the 7 by 6 which you get from adding all the other numbers up together

Answer:

3,006.0578‬ is your answer.

Step-by-step explanation:

3   ×   1000   +   6   ×   100   +   3   ×   10   +   7   ×   0.1   +   2   ×   100   +   8   ×   0.0001 =‬ 3,006.0578‬

Answer:3630.728

Step-by-step explanation:

Answer:

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited or borrowed.

Answer:

100 pi (314.16)

Step-by-step explanation:

Because the diameter is 20 in, that makes the radius = 20/2 inches = 10 inches.

10^2 * pi = area

100 pi =  area

314.16 is approx. area.

Answer:

It should be 1,256.6 in square inches

Step-by-step explanation:

Answer: 4.50

Step-by-step explanation:

Pay attention in math class

Answer:x+7.50 is less than or equal to 12

Step-by-step explanation: x is less than or equal to 4.5

Step-by-step explanation:

log 47.2 in four decimal places

= 1.6739

Final answer:

To find log 47.2 to four decimal places, use the logarithmic function. The result is approximately 1.6739

Explanation:

To find log 47.2 to four decimal places, we need to use the logarithmic function. The logarithm function is the inverse of exponentiation. In this case, we are looking for the logarithm of 47.2.

Using a scientific calculator or logarithmic tables, we can find that log 47.2 ≈ 1.6739 to four decimal places.

The four decimal places are determined by the precision of the logarithm function and the number of significant figures in the input value (47.2 has four significant figures).

Answer:

-1500

Step-by-step explanation:

"descends," means to go down (ascend means to go up), so the number would be negative. The number given is 1500, so we use that, and get -1500.

Answer:

-1500

Step-by-step explanation: Descending means "going down" negative numbers are below normal. They had descended  from the normal numbers.

Answer:

3x^3

Step-by-step explanation:

57/19=3

x^5 - x^2 = x^3

Answer:

3x^3

Step-by-step explanation:

You have to divide 15 over nineteen, which is 3x with the exponent of 5 over x with the exponent of 2. Then you have to apply the exponent rule and subtract the exponents:5-2, which would give you 3x with the exponent of 3

Answer:

14 -2i

Step-by-step explanation:

9 + sqrt(-4) - ( -5 + sqrt(-16))

We know the sqrt of a negative number is i * sqrt(number)

9 + isqrt(4) - ( -5 + isqrt(16))

9 + 2i - (-5 + 4i)

Distribute the negative sign

9+2i +5 -4i

Combine like terms

14 -2i

Answer:

The answer is 43 minutes I'm pretty sure.

Answer:

43 mins

Step-by-step explanation: All you have to do is subtract 57 from 14 then you will get your amount of time. And that is all you have to do

The remainder when the 100th term of the Fibonacci sequence is divided by 8 is 3.

The Fibonacci sequence is a sequence where each term is the sum of the previous two terms. The sequence starts with 1, 1, and then continues with 2, 3, 5, and so on. To find the remainder when the 100th term of the sequence is divided by 8, we can calculate the terms of the sequence modulo 8 until we reach the 100th term.

We can see from the pattern that the terms modulo 8 repeat every 6 terms. Therefore, to find the remainder when the 100th term is divided by 8, we can calculate the remainder when 100 is divided by 6. 100 mod 6 = 4. So, the remainder when the 100th term of the Fibonacci sequence is divided by 8 is the same as the remainder when the 4th term is divided by 8, which is 3.

Final answer:

Both vendors cost about the same for 20 pairs of soccer shoes.

Explanation:

For Sports Shoe Warehouse, the cost for 11 pairs is $1100, and each additional pair costs $66. So, the total cost for x additional pairs would be $1100 + $66x.

For Winning Team Shoes, the cost for 11 pairs is $825, and each additional pair costs 6% more than the previous pair. So, the total cost for x additional pairs would be $825 + 0.06(825)x.

To find when both vendors cost the same, we set their expressions equal: $1100 + $66x = $825 + 0.06(825)x. Solving for x gives x = 20. Therefore, both vendors cost about the same for 20 pairs of soccer shoes.

Given:

[tex]\cos 15^{\circ}[/tex]

To find:

The exact value of cos 15°.

Solution:

[tex]$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}[/tex]

Using half-angle identity:

[tex]$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}[/tex]

[tex]$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}[/tex]

Using the trigonometric identity: [tex]\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}[/tex]

            [tex]$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}[/tex]

Let us first solve the fraction in the numerator.

            [tex]$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}[/tex]

Using fraction rule: [tex]\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}[/tex]

            [tex]$=\sqrt{\frac {2+\sqrt{3}}{4}}[/tex]

Apply radical rule: [tex]\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]

           [tex]$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}[/tex]

Using [tex]\sqrt{4} =2[/tex]:

           [tex]$=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

[tex]$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

The dimensions of playing card is L = 10 centimeter and W=5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.

Step-by-step explanation:

The given is,

                  Playing card has an area of 50 square centimeters

                  A perimeter of 30 centimeters

Step:1

                 A playing card is in the shape of rectangle,

                 Formula for perimeter of rectangle is,

                                      [tex]Perimeter, P = 2(l+w)[/tex] .........................(1)

                 Formula for area of rectangle is,

                                             [tex]Area, A= lw[/tex]......................................(2)

                  Where, l - Length of rectangle

                             w - Width of rectangle

Step:2

                From the given values equation (1) becomes,

                                                       [tex]30 = 2(l+w)[/tex]              

                                                       [tex]\frac{30}{2}=(l+w)[/tex]      

                                                       [tex]15 =(l+w)[/tex]

                                                       [tex]w=15-l[/tex]  .............................(3)

                Width value in terms of length is calculated.

Step:2

                Equation (2) becomes,

                                                      [tex]50 = (15-l)(l)[/tex]

                                                      [tex]50= 15l -l^{2}[/tex]

                                      [tex]l^{2}-15l+50=0[/tex]

              Solving the above equation,

                                                          [tex]=10[/tex]

                                                       [tex]l=10 cm[/tex]

Step:3

                 Equation (3) becomes,

                                                       [tex]w=15-l[/tex]

                                                           [tex]=15-10[/tex]

                                                           [tex]=5[/tex]

                                                     w = 5 cm

Result:

           The dimensions of playing card is L = 10 centimeter and W = 5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.

Final answer:

By creating an equation system using the area and perimeter formulas for a rectangle, the dimensions of the playing card are found to be either 5 cm by 10 cm or 10 cm by 5 cm.

Explanation:

To determine the dimensions of a playing card given its area and perimeter, we need to set up an equation system based on the properties of a rectangle. Let's call the length L and the width W. The area (A) of a rectangle is A = L × W, which in this case is 50 sq cm. The perimeter (P) is P = 2(L + W) and is given as 30 cm.

From the perimeter, we can rearrange this to find L in terms of W:
30 cm = 2(L + W)
15 cm = L + W
L = 15 cm - W

Now, substituting L in the area equation gives us:
50 cm² = (15 cm - W) × W
This can be rearranged to form a quadratic equation:

0 = W² - 15W + 50

Factoring, we find:
0 = (W - 5)(W - 10)
So we have two solutions, W = 5 cm or W = 10 cm.

If we take W as the width, then L (the length) would be the other dimension, which would be 15 cm - W. So, we have two possible dimension pairs based on the standard card size: (5 cm by 10 cm) or (10 cm by 5 cm).

Answer:

6.25? is that even possible?

Step-by-step explanation:

Answer:

[tex]12[/tex]

Step-by-step explanation:

Step 1:  Set x to 3 and solve

[tex]4x[/tex]

[tex]4(3)[/tex]

[tex]4 * 3[/tex]

[tex]12[/tex]

Answer:  [tex]12[/tex]

Answer:

[tex]v = {210cm}^{3} [/tex]

Step-by-step explanation:

Formula for finding the volume of a triangular prism is given as:

[tex]v = \frac{1}{2} \times b \times h \times l[/tex]

where,

b = breadth = 7cm

h = height = 6cm

l = length = 10cm

Thus,

[tex]v = \frac{1}{2} \times 7cm \times 6cm \times 10cm[/tex]

[tex]v = \frac{1}{2} \times 420 {cm}^{3} [/tex]

[tex]v = \frac{ {420cm}^{3} }{2} [/tex]

[tex]v = {210cm}^{3} [/tex]

The answer to your question would be:

B-  f(x) has the greatest maximum.  

C-  All three functions have a y-intercept.

(I know this question is old but I hope it helps someone else.)

:)

Answer:

72, 90, 110, 132, 156

Step-by-step explanation:

The pattern goes, (56+16), (72+18), (90+20), (110+22), (132+24), (156+26), etc.

With the beginning pattern of +6, add +2 to each +6 for the following numbers.

Answer:

[tex]a_n=(n+1)(n+2)[/tex]

Step-by-step explanation:

Notice that the terms given in the sequence are the products of two consecutive numbers as follows:

[tex]a_1=6=2*3\\a_2=12=3*4\\a_3=20=4*5\\a_4=30=5*6\\a_5=42=6*7\\a_6=56=7*8\\a_7=72=8*9[/tex]

Therefore, we can write the nth term of the sequence as the product of a number and its consecutive, starting with the factor "2" for the first term instead of "1", thus making:

[tex]a_n=(n+1)(n+2)[/tex]

Answer:

7.30

Step-by-step explanation:

T = 2π √(L/32)

3 = 2π √(L/32)

3/(2π) = √(L/32)

(3/(2π))² = L/32

L = 32 (3/(2π))²

L ≈ 7.30

The length of the pendulum in feet nearest to hundredth is 7.29 feet.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given that the equation for the time of one swing of a pendulum is

T = 2π √(L/32).

And pendulum makes one swing in 3 seconds.

Now T is 3 second.

So , substituting the value of T in given expression;

3 = 2π √(L / 32)

3 / (2π) = √(L / 32)

Taking square on both sides,

{ (3/(2π) }² = L / 32

L = 32 × { 3 / (2π) }²

L = 7.295

L ≈ 7.29

Therefore, the length of the pendulum in feet nearest to hundredth is 7.29 feet.

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Answer:

we need the question

Step-by-step explanation: