Use the exponential decay equation
A = A0(0.5)t/k,
where A is the amount of a radioactive material present after time t, k is the half-life of the radioactive substance, and A0 is the original amount of the radioactive substance. Round to the nearest tenth.
An isotope of technetium is used to prepare images of internal body organs. The isotope has a half-life of approximately 6 h. A patient is injected with 30 mg of the isotope.
(a) What is the technetium level in the patient after 5 h?
A = mg
(b) How long (in hours) will it take for the technetium level to reach 23 mg?
t = h

The amount of pounds of sweet potatoes that she uses to buy paper is 35/8.

To model the problem with a tape diagram, we can draw 5 boxes representing the 5 pounds of white potatoes, and then draw 7/8 of that number of boxes to represent the number of sweet potatoes.

[5 white potatoes]

[4 sweet potatoes (7/8 * 5 = 7/8)]

Hence, since Maribella bought 5 pounds of white potatoes

This becomes 5x7/8= 35/8

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The relatively prime positive integers of m+n is 409.

Since ABCD is an isosceles trapezoid

An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure.

=>∠BAD = ∠ CDA Angles formed by the non parallel sides of an isosceles trapezoid are equal.

Given, AB = BC

Join AC

In ΔABC

∠BCA = ∠BAC Angle formed by the equal sides of and isosceles triangle

with its base are equal.

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length

AB = BC-CD Arcs formed by same side chords on the circle are equal.

Measure of complete angle is 360 degrees.

=2θ+2θ+2θ+2Φ+2Φ+2Φ

=6θ+6Φ=360

[tex]$$& \widehat{A B}+\widehat{A F}=\widehat{B F}=120 \\[/tex]

∠CDE=120

Join FB

In ΔFAB,

By Law of Cosine:

[tex]$$\begin{aligned}& c^2=a^2+b^2-2 a b \cos C \\& \Rightarrow B F^2=3^2+5^2-2.3 \cdot 5 \cos 120 \\& \Rightarrow B F^2=3^2+5^2-30 \cos 120 \\& \Rightarrow B F^2=9+25-30 \cdot(-0.5) \\& =B F^2=34-30.5 \\& \Rightarrow B F^2=34+15 \\& \Rightarrow B F^2=49 \\& \Rightarrow B F=7\end{aligned}$$[/tex]

Laws of Sine:

⇒[tex]$ & \sin A / a=\sin B / b={Sin} C / c[/tex]

⇒[tex]& \sin \Theta=5 \sqrt{3} / 14 \ \& \sin \Phi=3 \sqrt{3} / 14 \\[/tex]

In ΔAFD,

⇒[tex]& \angle A F D=3 \Phi \ \& \angle A D F=\Theta \\[/tex]

[tex]& \Rightarrow {Sin} \Theta / 5=\sin 3 \Phi / A D \\& \Rightarrow {Sin} \Theta=5 \sqrt{3 /} / 14 \\& \Rightarrow{Sin} 3 \Phi={Sin}(\Phi+2 \Phi) \\& \Rightarrow {Sin} 3 \Phi={Sin} \Phi . {Cos} 2 \Phi+{Cos} \Phi . {Sin} 2 \Phi[/tex]

[tex]& \Rightarrow {Sin} 3 \Phi= {Sin} \Phi \cdot {Cos} 2 \Phi+{Cos} \Phi \cdot {Sin} 2 \Phi \\& \Rightarrow {Sin} 3 \Phi={Sin} \Phi \cdot\left(1-2 \sin ^2 \Phi+2 {Sin} \Phi \cdot \cos ^2 \Phi\right) \\& \left.\Rightarrow {Sin} 3 \Phi={Sin} \Phi \cdot\left(1-2 \sin ^2 \Phi\right)+2\left(1-\sin ^2 \Phi\right)\right) \\& \Rightarrow {Sin} 3 \Phi={Sin} \Phi \cdot\left(3-4 \sin ^2 \Phi\right) \\[/tex]

[tex]& \Rightarrow {Sin} 3 \Phi=3 \sqrt{3} / 14 \cdot(3-27 / 49) \\& \Rightarrow {Sin} 3 \Phi=3 \sqrt{3} / 14 \cdot(120 / 49) \\& \Rightarrow {Sin} 3 \Phi=180 \sqrt{3} / 343[/tex]

Now,

[tex]$$&{Sin} \Theta / 5={Sin} 3 \Phi / A D \\& \Rightarrow A D=5 {Sin} 3 \Phi / {Sin} \Theta \\& \Rightarrow A D=180 \sqrt{3} / 343 / 5 \sqrt{3} / 14 \\& \Rightarrow A D=180 \sqrt{3} / 343 X 14 / 5 \sqrt{3} \\& \Rightarrow A D=360 / 49 \\& m+n=360+49 \\& \Rightarrow m+n=409[/tex]

Therefore, the value of m + n is 409.

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Answer: 42258

Step-by-step explanation:

multiply by 2 because if 1 hour is 21,189 feet 2 hours is 2 times more!

Hope this helps!

Riemann Sum: A mathematical operation that involves splitting a region into rectangles and calculating the sum of the areas of the rectangles in order to estimate the area under a curve.

R: (3^3)(3) + (6^3)(3) + (11^3)(3) + (14^3)(3)

= 4,845 \sM: (3.5^3)(3) + (7.5^3)(3) + (11.5^3)(3) + (14.5^3)(3)

= 5,827.5

Riemann Sum is a numerical method for approximating the curve's area under the curve. To do this, the area is divided into rectangles, and the total of those areas is used. The product of the rectangle widths and the function evaluated at the sample locations is multiplied to determine the sum. The sample points may be taken at the rectangles' midpoints, right endpoints, or left endpoints.

In this instance, the partition points are at 3, 6, and 11 and we are computing the Riemann sum for f(x) = x3, 3 x 14. The Riemann total is 4,845, if the sample points are at 4, 9, and 12. The Riemann sum is 5,827.5 if the sample points are located at the midpoints of the rectangles. Because of this, the midpoint and endpoint Riemann sums are larger

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If line L passes through point (1, 2, 3) and is perpendicular to the xy-plane,  the coordinates of the points on the line which are at a distance 7 from the point P(3,-1, 5) are (1, 2, 11) or (1, 2, -1).

Equation of the xy - plane is z = 0. So, direction ratio perpendicular to xy - plane is (0,0,1)

So, the equation of line passing point (1, 2, 3) and is perpendicular to the xy-plane is:

          x-1/0 = y-2/0 = z-3/1 = t (say)

x = 1, y = 2 and z = t + 3

Let, (1, 2, t+3) be any point on the line that is at a distance 7 units from the point (3, -1, 5)

Then, ( (1 - 3)² + (2 + 1)² + (t + 3 - 5)²)^1/2 = 7

                                          4 + 9 + (t - 2)² = 49

                                                      (t - 2)² = 36

                                                         t - 2 = ± 6

                                                              t = 8, -4

Hence, the coordinates of the points on the line which are at a distance 7 from the point P(3,-1, 5) are (1, 2, 11) or (1, 2, -1).

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In linear equation, $ 1300 is the cost for 80 employees.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.      

                             The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Given that cost of a company picnic varies directly as the number of employees attending the picnic

Let "c" be the company picnic cost

Let "n" be the number of employees attending the picnic

Therefore,

 cost ∝ number of employee attending picnic

       c ∝ n

   c = kn

Where "k" is the constant of proportionality

c = kn ---------- eqn 1

Given that company picnic costs $487.50 for 30 employees

Therefore substitute c = 487.50 and n = 30

   487.50 = k(30)

  k =   487.50/30

   k = 16.25

Substitute n = 80 and k = 16.25 in eqn 1

    c = 16.25(80)

    c = 1300

Thus $ 1300 is the cost for 80 employees.

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[tex]5(2x+7)=4x-3[/tex]

Distribute numbers outside of parentheses:

[tex](5)(2x)+(5)(7)=4x-3[/tex]

[tex]10x+35=4x-3[/tex]

Subtract 4x from both sides:

[tex]10x+35-4x=4x-3-4x[/tex]

[tex]6x+35=-3[/tex]

Subtract 35 from both sides:

[tex]6x+35-35=-3-35[/tex]

[tex]6x=-38[/tex]

Divide both sides by 6:

[tex]\dfrac{6x}{6} =\dfrac{-38}{6}[/tex]

[tex]\boxed{x = -\frac{19}{3} }\texttt{ or }\boxed{x =-6.33}[/tex]

Answer:

x = -19/3

Step-by-step explanation:

Given equation,

→ 5(2x + 7) = 4x - 3

Now the value of x will be,

→ 5(2x + 7) = 4x - 3

→ 10x + 35 = 4x - 3

→ 10x - 4x = -3 - 35

→ 6x = -38

→ x = -38/6

→ [ x = -19/3 ]

Hence, value of x is -19/3.

Answer:

the answer is 9.6

Step-by-step explanation:

Answer:

Area = (1/2) x (12)(15)sin(92)

The number of inches will it grow in 4 days is 11.2 inches if If an elephant grows 2 4/5 inches a day

What is a mixed fraction ?

A fraction represented with its quotient and the rest is a mixed fraction. for instance, 2 1/3 is a blended fraction, where 2 is the quotient, 1 is the remainder. So, a combined fraction is a mixture of a whole quantity and a right fraction.

Given ,

If an elephant grows 2 4/5 inches a day,

We have to find how many inches will it grow in 4 days

So, the expression for calculating could be,

let n be number of days.

As it grows  2  4 / 5 = 10+4 / 5  = 14 /5

for n number of days = n * 14 /5

so, put n= 4

that is 4*14/ 5 = 56 / 5 = 11 . 2

Therefore, The number of inches will it grow in 4 days is 11.2 inches if If an elephant grows 2 4/5 inches a day

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Answer: 16 meters

Step-by-step explanation:

1 cm         4cm

--------    =  ---------

4m             16m

In the given case-Equivalent ratios are created by multiplying or dividing the two terms of a ratio by the same number.

What are ratios used for?

The ratio is written as a/b when the ordered pair's second number, b, is not equal to 0. A ratio can be used to compare similar quantities or show relationships between them. We use ratios to contrast comparable items.

The ratio between two numbers when they are measured in different units is expressed using a rate. A ratio in mathematics depicts the quantity of smaller numbers that make up a larger number.

The equivalent ratios are linked to one another through the multiplication of a number. To create equivalent ratios, a ratio's two terms must be multiplied or divided by the same number.

8 : x = 2 : 1

x = 4 (hours)

8 : x = 1 : 4

x = 32 (hours)

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If the length, width, and height of a right rectangular prism are halved, the surface area will be reduced by a factor of four.

The surface area of a right rectangular prism can be calculated by adding up the areas of all six of its faces.

To see why, consider that each of the original face's area was given by the product of two of the original dimensions. If each of those dimensions is halved, the area of each face is reduced to one-fourth of its original size. Because there are six faces, the total surface area is reduced by a factor of four.

In other words, if the original surface area was 2 * (44 cm * 22 cm + 44 cm * 77 cm + 22 cm * 77 cm) = 6176 square cm, the surface area of the halved rectangular prism would be 6176 square cm / 4 = 1544 square cm.

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For the inequality expression 4x < 34, x = 8 is a solution.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given is a linear inequality 4x < 34.

We have to solve the inequality to find the solutions.

Dividing both sides of the inequality by 4,

4x / 4 < 34 / 4

x < 8.5

That is, values of x are below 8.5.

So x = 8 is a solution and x = 10 is not a solution.

Hence x = 8 is a solution for the given inequality.

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The bought amount of banana is less than 3 pounds, found from the conversion and this, it will not be enough.

As per the known information, 1 ounce is equivalent to 0.0625 pound. Based on this information, the amount of bought banana will be calculated.

So, the amount of banana = bought amount of bananas in ounces × value of one ounce

The amount of bought banana = 42 × 0.0625

Performing multiplication on the Right Hand Side of the equation

The amount of bought banana = 2.625 pounds

The bought amount of banana is less than the required amount. Therefore, the bought amount will not be enough.

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Answer:

Um, answer my recently asked question l ol It's called"Their eyes were watching god" and im on ch 5.

Step-by-step explanation:

Answer:

answer my recently asked question please.

x=55, if Scura produces and sell 55000 bottles of sunblock.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Scura makes sun block and their annula revenues depends on how much they sell.

Let x be the quantity of 5 oz. bottles of sun block that they make and sell each year measured in 1000's of bottles.

Thus if x=10 then theu make and sell 10000 bottles of sun block each year. If x=25 then they make and sell 25000 bottles of sun block each year.

a) When x=50

Number of bottles = 50×1000

= 50000

b) Number of bottles are 55000

So, x= Number of bottles/1000

x= 55000/1000

x=55

Therefore, x=55, if Scura produces and sell 55000 bottles of sunblock.

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The probability that we have picked exactly n cards by multiplying the probability of picking each card, which is [tex]$\frac{13}{52}[/tex]

Verified that, after taking summation over n = 1, 2, . . ., the sum of the probabilities above equals to 1.

(1) The probability of picking exactly n cards to cover all 4 shades can be calculated as follows:

For n = 1, the probability of picking exactly 1 card is 0, as it is not possible to pick only one card and cover all 4 shades.

For n = 2, the probability of picking exactly 2 cards is:

[tex]$=(\frac{13}{52})\times (\frac{12}{52} )\\\\= \frac{13\times12}{52\times 52}[/tex]

For n = 3, the probability of picking exactly 3 cards is:

[tex]$=(\frac{13}{52})\times (\frac{12}{52} )\times(\frac{11}{52}) \\\\= \frac{13\times12\times11}{52\times 52\times52}[/tex]

And so on, we can calculate the probability of picking exactly n cards by multiplying the probability of picking each card, which is [tex]$\frac{13}{52}[/tex].

(2) To verify that the sum of the probabilities is equal to 1 , we can add up the probabilities for all values of n from 1 to 52 :

[tex]$& \mathrm{P}=\left(\frac{13}{52}\right) \times\left(\frac{12}{52}\right)+\left(\frac{13}{52}\right) \times\left(\frac{12}{52}\right) \times\left(\frac{11}{52}\right)+\ldots+\left(\frac{13}{52}\right) \times\left(\frac{12}{52}\right) \times \ldots \times \frac{52-(\mathrm{n}-1)}{52} \\[/tex]

P = 1

This verifies that the sum of the probabilities is equal to 1.

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From a set of 52 poker cards (without 2 jokers), we keep taking cards randomly one by one with replacement, until all the cards taken by us can cover all 4 shades.

(1) Compute the probability that we have picked exactly n cards.

(2) Verify that, after taking summation over n = 1, 2, . . ., the sum of the probabilities above equals to 1.

On solving the provided question, we can say that the function is y = f(x) and (7.-6) and (7,3); nm = 3+6//-/7 => m = not defined

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the function is

y = f(x)

and (7.-6) and (7,3)

m = 3+6//-/7

m = not defined

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This question can be solved using 2 variables x and y.

Putting the variables in the equation according to the conditions given would give the value of the variable.

In 6 years time the age of Mark will be 18+6=24 years and his mother will be 42+6=48 years which will be twice of 24.

Let the present age of Mark be x and his mother be y.

Then according to the given conditions.

x+y= 60 ---- equation 1

y+6= 2(x+6)

y+6= 2x+12

y-6= 2x------equation2

From equation 1 the value of y is found to be

Given the problem:

–19k − –16k + 13k + –8k = –20

(I'm going to assume that is a minus sign between -19k and -16k)

(Subtracting a negative = add)

Combine all like terms:

2k=-20

Divide both sides by 2:

k=-10

If we take a ride that goes around 5 times, we will travel for 502.86 feet. The result is obtained by using the formula for circumference.

Circumference is the perimeter of a circle. It can be calculated by the following formula.

C = 2πr

Where

A Ferri wheel has a radius of 16 feet. If you take a ride that goes around 5 times, determine the distance you traveled!

(Round answer to the nearest hundredth and for pi use π = 22/7)

The shape of the wheel is round (a circle). The distance traveled is the circumference multiplied by the number of rounds.

We have

Distance traveled

= C × n

= 2πr × 5

= 2(22/7)(16) × 5

= 502.86 feet

Hence, the distance traveled by the wheel is 502.86 feet.

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Answer:578

Step-by-step explanation:

219+359=578

Answer:

The fourth term in the series 5+9+13+__ is 85. The series follows an arithmetic pattern, where each subsequent term is 4 greater than the previous one. Therefore, the fourth term in the series is 5+9+13+17 = 85.

The value of i/s is 0.02.

Now, According to the question:

"Information available from the question"

s/a = 4; l/a = 0.20; i/e = 0.10; a = l e and a = 100.

We have to find the i/s

We can first find the value of e, using the equation a = l + e, where l/a = 0.20 and a = 100:

e = a - (l/a) * a = 100 - (0.20 * 100) = 100 - 20 = 80

Next, we can find the value of i using the given information i/e = 0.10:

i = i/e * e = 0.10 * 80 = 8

Finally, we can find the value of i/S using the equation i/S = i / (S/a) * a = 8 / (4 * 100) = 8 / 400 = 0.02.

So, the value of i/S is 0.02.

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The polygons that are congruent are as attached.

Congruent polygons are two or more polyggon shapes that have the same size and shape. In other words, they have the same number of sides, the same length of sides, and the same interior angles. If you were to superimpose one congruent polygon over the other, they would perfectly fit and cover each other.

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Because we have two lines non-parallel, the system has only one solution, then the correct option is the fourth one.

Remember that a system of linear equations:

y = f(x)

y = g(x)

Can have:

In this case we know that the lines intercept at (4, 5), so the two lines are not parallel, then the system has only one solution.

Then the correct option is the fourth one, because there aren't other points that can be the solution of the system.

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In order to solve for the missing sides of a right triangle, you need to use the Pythagorean Theorem.

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This equation depicts all x values such that -3 x 2 is true. These values encompass every real figures within -3 and 2, but not the actual integers -3 and 2.

The concept of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A range of variables for x are represented by the inequality -9 4x + 3 11 in which they meet the inequality. We must first isolate x solely on a single side of the discrepancy before determining the variable x that cause the inequality to hold true.

First, subtract 3 from both sides:

-12 < 4x < 8

Next, divide both sides by 4:

-3 < x < 2

This solution represents all values of x such that -3 < x < 2. These values include all real numbers between -3 and 2, but do not include -3 and 2 themselves.

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The slope for the trend line for the scatter plot shown is option B: 3.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The first two data points obtained form the graph is -

(1,8) and (2,11)

The slope of a line can be found using the formula -

m = (y2 - y1) / (x2 - x1)

Substitute the values into the equation -

m = (11 - 8) / (2 - 1)

Apply the arithmetic operation of subtraction -

m = 3 / 1

Apply the arithmetic operation of division -

m = 3

Therefore, the slope value is 3.

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