A radioactive substance decays at a continuous rate of 14.4 % per day. After 15 days, what amount of the substance will be left if you started with 140 mg? (a) First write the rate of decay in decimal form. r = (b) Now calculate the remaining amount of the substance. Round your answer to two decimal places.

Answer:

Respuesta: 2,25 cm cuadrados

Explicación paso a paso:

PERIMETRO: 6

APOTEMA: 0,75

AREA DEL HEXAGONO REGULAR: 6 X 0,75 / 2 = 2,25 CM CUADRADOS

Step-by-step explanation:

Answer:

x = 23°

Step-by-step explanation:

We Know

The 67° angle + the x must be equal to 90°

Find the x.

Let's solve

67° + x = 90°

x = 23°

Answer:

P = $1341.53

Step-by-step explanation:

A(t) = amount in t years

P = Principal (original investment)

r = annual interest rate (in decimal form)

n = number of times that interest is compounded each year

A(t) = P(1 + r/n)nt

Substitute in the given values:  2000 = P(1 + 0.04/12)12(10)

2000 = P(1.490832682)

P = $1341.53

Answer:

Step-by-step explanation:

In a case whereby Michelle has 3 kg of strawberries that she divided equally into small bags with 1/5 kg in each bag  the number of bags of strawberries she make is 15bags of strawberries.

We should note that 1kg = 1000g

3kg = 1000g

Since each of the bag is  1/5 kg = 1000/5 g = 200g

The needed bag will now be =3000/200= 15

Therefore, we can see that she made 15bags of strawberries the conversion were made so that it can be calculated easily since ythe kg are very small.

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Answesar:

Step-by-step explanation:

SA = 10(5)² = 250cm²

Volume² = 2 (5)³ = 250cm³

They are not equal.

Surface area is in square cm and volume is in cm³.

Answer:

34

Step-by-step explanation:

This is sequnce has an easy pattern with adding 1 to the difference every time and goes +4, +5, +6 , so the next should be +7

Answer: think it’s a5=34

Step-by-step explanation:

The vocabulary for a is called the apothem

The area of the regular polygon is [tex]2419.68 cm^2.[/tex]

a = 7√3 cm

s = 14 cm

The perimeter of the polygon is:

P = ns

where n is the number of sides of the polygon. We can find n using the formula:

[tex]n = 360 / (180 - (360 / 2n))[/tex]

where n is the number of sides. Substituting the given value for s, we get:

[tex]n = 360 / (180 - (360 / 2*7)) = 14[/tex]

Therefore, the polygon has 14 sides.

a = [tex]\sqrt{31.820 cm)^2 - (14 cm/2)^2}[/tex])

= 24.615 cm

A = (1/2) * apothem * perimeter

[tex](\frac{1}{2} ) * 24.615 cm * 196 cm \\=\\ 2419.68 cm^2[/tex]

Therefore, the area of the regular polygon is [tex]2419.68 cm^2.[/tex][tex]2419.68 cm^2.[/tex]

In summary,

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Answer:

157,000

Step-by-step explanation:

π r² h

Therefore here, (5⁴)². 5⁶. (5⁸)².(5⁶)². (5⁸)² simplifies to 5⁸².

The integer's basic form is represented by its smallest equivalent fraction. How to determine the simplest form: Look for shared components in the denominator and numerator.

By applying the exponentiation laws, let's us gradually simplify this an expression is:

[tex](5^4)^2 = 5^(4*2) = 5^85^6 * 5^8 = 5^(6+8) = 5^1425^6 = (5^2)^6 = 5^(2*6) = 5^1225^8 = (5^2)^8 = 5^(2*8) = 5^16[/tex]

When all of these simplifications are put back into the original statement, we get the following:

[tex](5^4)^2. 5^6. 5^8. 25^6. 25^8 = 5^8 * 5^14 * 5^12 * 5^16 * 5^16[/tex]

Using the rule that is  [tex]a^b * a^c = a^(b+c)[/tex],

The first three terms can be combined to create:

[tex]5^8 * 5^14 * 5^12 * 5^16 * 5^16 = 5^(8+14+12) * 5^(16+16) = 5^50 * 5^32[/tex]

Using the same rule again, we can combine these two terms:

5⁵⁰* 5³²

= 5⁵⁰⁺³²

= 5⁸²

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After 5 years, there will be $4,528.73 in Charlie's account if no withdrawals are made.

Compound interest means addition of interest to the principal sum of a loan or deposit. To get the amount, we will use the formula [tex]A=P(1+r/n)^{nt}[/tex] to get sum of money in the account.

Data:

P = 4,200, r = 1.51%, m = 4, t = 5

Plugging the values, we get:

[tex]A = 4200(1+0.0151/4)^{4*5}\\A = 4200* {1.003775}^{20}\\A = 4200*(1.07826994224)\\A = $4528.73375741\\A = $4528.73.[/tex]

Complete question "A bank offers an investment account with an annual interest rate of 1.51% compounded quarterly. Charlie invests 4200 into the account for 5 years. Answer the questions below. Assuming no withdrawals are made, how much money is in Greg's account after 5 years?"

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Answer:

C

Step-by-step explanation:

0 is base like for example negatives are below and positives are above and zero is the thing right in between so sea level would be 0!

Correct answer is 0.

Sea level si always the parameter to use when indicating the elevation of any place on earth. If you happen to be located at the same altitude than the sea, then you are at level 0 altitude in any unit of measure.

the equation for the curve C as n approaches infinity     is           y = x This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).

what is diagonal line ?

A diagonal line is a straight line that runs obliquely (at an angle) between two opposite corners of a geometric shape, such as a rectangle or a square. It is called "diagonal" because it connects two non-adjacent vertices of the shape, forming a diagonal across the interior of the shape.

In the given question,

As n increases, the process described in the question creates a set of line segments that connect the equally spaced points on the x-axis to the equally spaced points on the y-axis. The resulting curve is a piecewise linear function that converges to a continuous curve as n approaches infinity.

To derive an equation for this curve, we can start by considering the line segment connecting the first mark on the x-axis to the last mark on the y-axis. Let's call this point (0, 1) and the nth mark on the x-axis (1, 0). The slope of the line connecting these two points is given by:

m = (0 - 1) / (1 - nth mark) = (1 - nth mark)^(-1)

where the nth mark on the x-axis is given by:

nth mark = 1 - (1/n)

Substituting this expression for nth mark into the equation for m, we get:

m = (n/(n-1))

The y-intercept of the line is given by:

b = 1 - m = 1 - (n/(n-1)) = 1/(n-1)

Therefore, the equation for the line segment connecting the first mark on the x-axis to the last mark on the y-axis is:

y = (n/(n-1))x + 1/(n-1)

Similarly, the equation for the line segment connecting the second mark on the x-axis to the second last on the y-axis is:

y = (n/(n-2))x + 1/(n-2)

Continuing this process for all n line segments, we get:

y = (n/(n-k))x + 1/(n-k)

where k = 1, 2, ..., n.

To get the equation for the curve C, we need to take the limit as n approaches infinity. As n goes to infinity, the value of k becomes insignificant compared to n, and we can approximate the equation for the curve as:

y = x

Therefore, the equation for the curve C as n approaches infinity is:

y = x

This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).

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1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.

In statistics, the unitary approach is a way towards resolving proportional problems. It entails first determining the value of a single unit of either a statistic, and then applying that knowledge to determine the value of any other required number of units. Consider the scenario where we are aware that 5 bananas cost $2.50. We can employ the unitary technique to calculate the price of seven apples as follows: Determine the price of a single apple: 2.50 ÷ 5 = 0.50 .Divide the price of one banana by the quantity you want of apples. 0.50 × 7 = 3.50 .It follows that 7 bananas would cost $3.50. Additionally, this technique can be applied to more challenging issues requiring numerous ratios and proportions.

given

Divide the total number of feet of coastline by the state's population to get the amount of coastline per person in Oregon:

Total shoreline / Population equals coastline per person.

coastline divided by population (3,800,000) equals 6,000,000 feet.

1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.

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There are 2000 milligrams in 2 grams of a substance, and it constitutes 40% of a 5-gram sample.

Convert grams to milligrams:

2 grams = 2 * 1000 milligrams

2 grams = 2000 milligrams

Calculate the percentage in a 5-gram sample:

Percentage = (2000 milligrams / 5000 milligrams) * 100

Percentage = (2 / 5) * 100

Percentage = 0.4 * 100

Percentage = 40%

Thus, there are 2000 milligrams in 2 grams of a substance, and it constitutes 40% of a 5-gram sample.

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​2 grams = ​ milligrams

How many milligrams are there in 2 grams of a substance, and what is the percentage of this amount in a 5-gram sample?

Observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.

A histogram is a graph that displays the values of a numeric variable's distribution as a collection of bars.

The height of a bar represents the frequency of data points with values falling within the relevant bin; each bar typically spans a range of numerical values known as a bin or class.

Similar to a bar chart, a histogram is produced with bars of varying widths.

In a histogram, the frequency is revealed by the bar's area rather than its height.

We plot the frequency density rather than frequency on the y-axis. To figure this out, divide a group's frequency by its width.

So, the x-axis of the given histogram represents the mass of the pumpkins.

The y-axis of the histogram represents the number of pumpkins.

Then, the pumpkins with greater mass than 6 kilograms:

= 8 + 6 + 2

= 16

Therefore, observing the given histogram we know that there are 16 pumpkins that have a mass greater than 6 kilograms.

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The expression "the cube root of the product of x and y, less twelve" can be mathematically represented as ³√(xy) - 12.

To understand this expression, let's break it down step by step:

Product of x and y:

We multiply the values of x and y together to find their product, denoted as xy.

Cube root of the product:

We take the cube root of the product obtained in the previous step.

The cube root of a number x is the value that, when raised to the power of 3, equals x. In this case, we take the cube root of xy, represented as ³√(xy).

Subtract twelve:  

Finally, we subtract twelve from the result obtained in the previous step, ³√(xy). This gives us the expression ³√(xy) - 12.

The expression ³√(xy) - 12 represents a mathematical operation involving the cube root of the product of x and y, followed by subtracting twelve from the result.

This can be useful in various mathematical contexts, such as solving equations or modeling real-world problems.

It's important to note that the expression is dependent on the values of x and y.

By substituting specific values for x and y, we can evaluate the expression to obtain a numerical result.

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The probability of choosing a red marble is 6/17.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.

To calculate this probability, we can use the formula:

P(red marble) = number of red marbles / total number of marbles

In this case, we substitute the numbers we know:

P(red marble) = 6 / 17

So the probability of choosing a red marble is 6/17 or approximately 0.35.

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The solution to the inputs of the given function are:

a) f(0) = 13

b) f(2) = -1

c) f(-2) = 27

d) f(1) + f(-1) = 26

The set of input values of a function is referred to as the domain of the function. Then, the set of output values of the function is referred to as the range of the function. Thus, if we possess a set of ordered pairs, we can find the domain by listing all of the input values, which are the x-coordinates.

We are given the function:

f(x) = (-x)³ - x² - x + 13

a) f(0) = (-0)³ - (0)² - 0 + 13

f(0) = 13

b) f(2) = (-2)³ - (2)² - 2 + 13

f(2) = -1

c) f(-2) = (2)³ - (-2)² + 2 + 13

f(-2) = 27

d) f(1) = (-1)³ - (1)² - 1 + 13

f(1) = 10

f(-1) = (1)³ - (-1)² + 1 + 13

f(-1) = 16

f(1) + f(-1) = 10 + 16 = 26

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Answer:

2 and 4

Step-by-step explanation:

1)

14x+6=2(5x+3)

14x+6=10x+6

No Solutions

2)

3(x-5)+6=x-(9-2x)

3x-9=3x-9

Infinitely Many

3)

2+5x-9=3x+2(x-7)

5x-7=5x-14

No Solutions

4)

3(4x-6)+2=-4(4-3x)

12x-16=12x-16

Infinitely Many

Answer:31.42

Step-by-step explanation:

C=2πr=2·π·5≈31.41593

Answer:

a) The population is the 1,500 employees, while the sample is the 60 female and 80 male employees selected using proportional allocation.

b) The scope of data collection is a sample survey, as only a subset of the population is being studied.

c) The variable of interest is the average monthly income of the employees.

d) The possible sources of data collection could include surveys or interviews of the selected employees, or obtaining salary data from the human resources department of the company.

e) The type of statistics used would be inferential statistics, specifically confidence interval estimation and hypothesis testing, to make inferences about the population based on the sample data.

The correct option is the last one, the mean will decrease.

For a set of N values {x₁, x₂, ..., xₙ} the mean is defined as the sum of the N values divided by N, this is:

mean = (x₁ + x₂ + ... + xₙ)/N

Now, here the mean is 3, and a family with 7 children (more than the mean) moves away.

That will cause a decrease in the mean, because we are removing one of the larger values.

The correct option is the last one.

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The missing part of the attached proof:

a) definition of angle congruence

b) ∠CPA ≅ ∠CPB

c) CP ≅ CP

The complete paragraph proof would be,

Because CP is perpendicular bisector of AB, CP is perpendicular to AB and point P is the midpoint of AB.

By definition of midpoint,

AP = BP

and by the definition of perpendicuar lines,

m∠CPA = m∠CPB = 90°

Then by definition of segment congruence,

AP ≅ BP

and by definition of angle congruence,

∠CPA ≅ ∠CPB

By the reflexive property of segment congruene,

CP ≅ CP

So, ΔCPA ≅ ΔCPB         ........by SAS congruence theorem

and CA ≅ CB because corresponding parts of congruent triangles are congruent.

So, CA = CB by the definition of segment congruence.

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4w+6.

The perimeter is just the summation of the length of all sides of a shape. In the case of a circle, the perimeters is its circumference length. So for this case, all we need to do is add up all the sides in a single expression that will represent the perimeter.

So perimeter for this triangle should be:

Side 1 + Side 2 + Side 3.

Where:

Side 1= w+4;

Side 2= 2w+2;

Side 3= w.

Then, perimeter is:

(w+4)+(2w+2)+(w)

Adding up all the like terms:

(w+2w+w)+(4+2)

(4w)+(6)

4w+6.

Answer:

To solve for z in terms of x and y using the given equations:

x + y = z ........(1)

y - z = x ........(2)

From equation (2), we get:

y - x = z (by adding z on both sides)

Substituting this value of z in equation (1), we get:

x + y = y - x

2x = 0

x = 0

Substituting x = 0 in equation (2), we get:

y - z = 0

y = z

Therefore, the solution is:

z = y

We cannot determine a specific value of z without knowing the values of x and y.

Answer:

they are correct

Step-by-step explanation:

Answer:

x = 7.9 (nearest tenth)

y = 24.6° (nearest tenth)

Step-by-step explanation:

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:

[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, x = 7.9.

[tex]\hrulefill[/tex]

The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:

[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, y = 24.6°.

The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

We have to given that;

The model shown below is a perfect cube with a volume of 27 cubic units.

Now, We can formulate;

⇒ V = 27 cubic units.

⇒ V = 3 × 9 cubic units.

⇒ V = 3 × 3² cubic units.

Thus, The correct statement which is true about all perfect cubes is,

⇒ A perfect cube represents 3 times the area of a face of the cube.

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