A sample of 200 g of an isotope decays to another isotope according to the function
How much money does Dana Jones have after 7 years if she invests $ 1100 at 5% interest compounded continuously?
Dana Jones has $__-after 7 years.
(Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)

Answer:

c.7.4

Step-by-step explanation:

<BDE=90°

Now,in RT.angled triangle BDE,

BD=√(BE)²-(DE)²

or, BD=√64-9

or,BD=√55

:.BD=7.41

The first five terms in the sequence are 6, 4.5, 3.375, 2.53125 and 1.8984375

The first term of the sequence is given as

First term= 6

The constant multiple is given as

constant multiple = 3/4

These parameters can be represented as

a = 6

r = 3/4

The nth term of a geometric sequence is represented as

A(n) = a(r)ⁿ⁻¹

So, we have the following equation

A(n) = 6(3/4)ⁿ⁻¹

For the first term, we have

A(1) = 6

For other terms, we have

A(2) = 6(3/4) = 4.5

A(3) = 6(3/4)² = 3.375

A(4) = 6(3/4)³ = 2.53125

A(5) = 6(3/4)⁴ = 1.8984375

Hence, the other terms are 4.5, 3.375, 2.53125 and 1.8984375

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Answer:

400

Step-by-step explanation:

1 centimeter = 0.01 meter

400 centimeters = 4 meters

The number line which describes the the measure of third side of the triangle must be greater than 10 cm is the second figure.

Number line is a straight horizontal line on which numbers are written in a certain intervals.

We can use number line for basic mathematical operations like addition, subtraction, division and multiplication.

Here the situation described is that measure of the third side of the triangle must be greater than 10 cm.

The inequality sign is '> 10'.

Since the inequality sign does not contain the equal to (≥) sign, the point 10 does not belong to this set.

So we will mark an open circle at the point 10 and draw a line afterwards.

Hence the second number line describes the situation that the third side of the triangle must be greater than 10 cm.

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The required range of the given function is -4  < y < 6.

Range, it is the set of values that come out to an outcome for certain mathematical operations.

Here,
A graph of a function is shown,
From the graph, it has been determined that,
The function is defined for domain -11 < x < -3.
As every value on the y- axis for the respective domain represents the element of range so,
The respective domain range of the function on the graph is -4  < y < 6.

Thus, the required range of the given function is -4  < y < 6.

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Answer: C.5/12

Step-by-step explanation:

At 300 miles the rental costs for Company A and Company B are the same.

An assertion that two expressions containing variables or numerical values are equivalent is known as an equation. The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the unknown values that satisfy the equality are referred to as the equation's solutions.

Given :

Vehicle A: 150 + 0.5m = Cost A

Cost B = 60 + 0.8m for truck B.

Given that a one-day scenario was required by the challenge, the two equations are as follows:

Price B =60+0.8m Price A =150+0.5m

By combining the two equations, we get

150 + 0.5m = 60 + 0.8m.

150-60=0.8m-0.5m

90=0.3m

m=90/0.3

m=300 miles

Consequently, there are 300 miles in a day.

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Answer:

b

Step-by-step explanation:

Answer:

1,258,925,411.79cm

Step-by-step explanation:

earth quake is measured with the Richter Scale,

R (Magnitue) = log (I / I°)

where I° is the base intensity to the Richter Scale and will be taken as 1

9.1 = log I

10^9.1 = I

thus,

intensity I = 1,258,925,411.79 cm

The upper bounds on the probability that Adam sent at least five emails during the time interval is [0, 1].

in math upper bound refers a number that is greater than or equal to any number in a set

Here we have given that, Adam logs in to an email server at time zero. He then spends his time exclusively on writing emails. His friend Brianna also logs in to the server at time 1 (which means 1 hour later) and starts typing emails independently of Adam.

And we need to find the upper bounds on the probability that Adam sent at least five emails during the time interval.

While we looking into the given question, we have identified that Adam Poisson process with a rate λ A/hour and Brianna Poisson process with a rate λ B/hour.

Here let us consider that Y1 and Y2 be the times at which Adam's first and second emails were sent.

Here we know that the Brianna logs in to the server, you are told that Adam has sent exactly one email so far.

So, here the upper limit while logging is 1. So, the lower limit is 0.

Because these is the real life scenario so the negative value is not applicable.

Therefore, the resulting interval is [0, 1].

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The value of a is 71°, and the value of b is 109°.

A parallel lines is defined as those type of line that are equidistant to each other which are on the same plane and they doesn't meet each other till infinity.

When two parallel lines are being intersected by another line called the transverse line, the following relationship is bound to occur such as;

From model 4, the pair of alternate exterior angles are equal in measure. That is 71° = angle opposite b°.

That is 180 - 71 = 109°

Also in model 4, the pair of alternate interior angles are equal in measure. a = 71°.

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The true statement about J and K is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

The correct answer is option (c)

In this question, we have been given that a certain statistic will be used as an unbiased estimator of a parameter.

The sample size of J = 40.

and the sample size of K = 100.

We need to find the true statement about J and K.

By central limit theorem, both J and K will have same means.

An expression for standard deviation is:

s = σ/√n

From the above expression standard deviation is inversely proportional to the sample size n. This means, as the sample size increases, the standard deviation decreases.

Thus, the correct statement is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

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The complete question is:

A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.

Which of the following must be true about J and K ?

a. The expected values of J and K will be equal, and the variability of J will be less than the variability of K.

b. The expected values of J and K will be equal, and the variability of J will be equal to the variability of K.

c. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

d. The expected value of J will be greater than the expected value of K, and the variability of R will be greater than the variability of K.

e. The expected value of J will be greater than the expected value of K, and the variability of R will be less than the variability of K.

Use the multinomial rule, the possible number of paths from A to B is m! n1! ×n2!

How do you find the number of paths on a grid?

To generalize our formula for any NxN grid, we can write: Incidentally, there is an easier way to write this: the number D = N! / (K! * (N-K)!) is also called the binomial coefficient and we can write (N choose K).

You may create a table by combining several question kinds using the grid question type. This implies that you could, for instance, create a grid that included both a multiple-choice question and a free-text inquiry.

A map's grid is a pattern made up of both horizontal and vertical straight lines. They cross one another to create a group of squares. On a map, grids aid in location finding. At the top, there are numbered gaps between the horizontal (side-to-side) lines.

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After performing division on the given expression the quotient is x + 3 and the remainder is -16.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

x + 3) x² - 7 ( x + 3

         x² + 3x

       = 3x -7                

          3x + 9

        = -16 (Remainder)        

Hence, the quotient obtained after division is x+3.

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The probability of the Komets losing their race and the Galaxy winning theirs is

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

The probability of the Galaxy team winning is 22%.

And, The probability of the Komets team winning is 47%.

Now,

Since, The probability of the Galaxy team winning is 22%.

And, The probability of the Komets team winning is 47%.

Hence, The probability of the Komets team losing = 100% - 47%

                                                                              = 53%

                                                                              = 0.53

Then, The probability of the Komets losing their race and the Galaxy winning theirs is = 0.53 × 0.22

                         = 0.1166

Thus, probability of the Komets losing their race and the Galaxy winning theirs is 0.1166.

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Answer:

11.66%

Explanation:

I put 12% as my answer, but I got it wrong. So I talked to my teacher and she said the CORRECT ANSWER WAS 11.66%!!

Answer: 37.5

Step-by-step explanation: 9 students didn't fw math, divide 9 by the total (24) n u get 37.5%

Answer:

Below

Step-by-step explanation:

9 out of 24 did NOT

9/24 = .375    =     37.5 %

let's take from the basic of one dolla!!!  how long for a buck to turn into two bucks at 4.5%?

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years \end{cases} \\\\\\ 2=1e^{0.045\cdot t} \implies \log_e(2)=\log_e(e^{0.045t})\implies \log_e(2)=0.045t \\\\\\ \ln(2)=0.045t\implies \cfrac{\ln(2)}{0.045}=t\implies 15.4\approx t\qquad \textit{about 15 years and 146 days}[/tex]

Answer:

-9

Step-by-step explanation:

(y2-y1)/(x2-x1)

[tex]\frac{(-1--10)}{(-6--5)}[/tex]=-9

Answer:

slope m=-9

Step-by-step explanation:

m=−1−−10−6−−5

m=9−1

m = -9

Length of rectangle         Width of rectangle         Area of rectangle  

A. a + 5                                     3                                    3(a + 5) = 3a + 15

B. 6 + x                                     1/3                                  1/3(6 + x) = 2 + 1/3x

C. 3                                             r                                   r(1+1+1) = 3r

What is a rectangle?

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

A.

There are 2 rectangles with side a and 5.

Therefore the length of the rectangle is (a + 5).

The width the rectangle is 3.

The area of rectangle is product of length and width.

The area of the rectangle is 3(a + 5)

Applying distributive property:

= 3a + 15

B.

There are 2 rectangles with side 6 and x.

Therefore the length of the rectangle is (6 + x).

The width the rectangle is 1/3.

The area of rectangle is product of length and width.

The area of the rectangle is 1/3(6 + x)

Applying distributive property:

= 2 + 1/3 x

C.

There are 3 rectangles with side 1, 1, and 1.

Therefore the length of the rectangle is (1 + 1 + 1).

The width the rectangle is r.

The area of rectangle is product of length and width.

The area of the rectangle is r(1 + 1 + 1)

Applying distributive property:

= r + r + r

= 3r

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Answer: a = 180 - 63 - 90

Step-by-step explanation:

180 degrees in a triangle

90 degrees in a right triangle

180 = 63 + 90 + a

move 63 and 90 to the other side

a = 180 - 63 - 90

The value of the expression 3(4.1x - 3.9y) - 5 is 12.3x - 11.7y - 5.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, it should be noted that the expression is illustrated as:

3(4.1x - 3.9y) - 5

Open the parentheses

12.3x - 11.7y - 5

Therefore, the value of the expression is 12.3x - 11.7y - 5.

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Answer:

The absolute value of a is equal to 3 * √(2), which is the simplest form of the surd.

Step-by-step explanation:

The absolute value of a number is the distance of the number from zero on the number line. To find the absolute value of a complex number, we take the square root of the sum of the squares of the real and imaginary parts.

In this case, the absolute value of a is given by:

|a| = √((-9)^2 + 9^2) = √(81 + 81) = √(162) = √(9 * 18) = 3 * √(2)

Therefore, the absolute value of a is equal to 3 * √(2), which is the simplest form of the surd.

We have proved that ABCD is a rectangle.

What is the isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.

<EAD=<EDA  ------------------∆AED is isosceles triangle.

<EBC=<ECB    ------------------ ∆EBC is isosceles triangle.

AD= BC   -------------------------Given

<AED=<BEC       ------------------- Vertically opposite angle

<EAD=<ECB                              

2<EAD=180°- <AED

         = 180°-<BEC

            =2<ECB.

∆AED congruent to ∆BEC --------- By A-S-A Congruency.

AE=EC, DE=EB                   ----------Corresponding sides

ABCD is a parallelogram ----------- Diagonals bisect to each other.

AC=BD                                      

AE+EC=DE+EB.

ABCD is a rectangle.   ------------- Diagonals are equal.

Hence, we have proved that ABCD is a rectangle.

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Answer:

you could sell is for $10,000

Step-by-step explanation:

because it increased in value you could sell it for more

Answer: it's still $100 because the beginning of the year hasn't started yet so you need to wait for the year to end so the 1 percent can be added

Step-by-step explanation:

Answer:

she can buy 30

Step-by-step explanation:

8/0.26 = 30.7

round to 30 because you need a whole number.

The percent change in your salary is = 6%

Initial earning per hour =  $12.50

New earning per hour after the raise =  $13.25

The formula that we will be using to solve this question is -

= %change = [final value - initial value] ÷ [initial value] × 100

First, find the difference between the initial value and the final value

=  $13.25 - $12.50

=  $0.75

Divide the difference by the initial ( $12.50) value

=  $0.75 ÷ $12.50

=  0.06

Convert the quotient into a percentage

= 0.06 x 100

= 6%

Therefore, the percentage change in your salary is = 6%

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For the job paying $12.50 per hour, the percent change in your salary after the raise is 6%.

Given data:

Hourly increase:

= Hourly salary after the raise - Hourly salary before the raise

= $13.25 - $12.50

= $0.75

The percent increase is:

= (Hourly increase / Hourly salary before the raise) * 100

= ($0.75 / $12.50) * 100

≈ 6%.

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Answer:

3928.4087

Step-by-step explanation:

2441/0.6214

The width of Australia in kilometres will be equal to 3928.4087 km.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Australia is approximately 2441 miles in width. The width of Australia in kilometres will be calculated as,

1 km = 0.6214 miles

1 mile = 1 /0.624 kilometres

Width = 2441/0.6214

Width = 3928.4087 kilometres

Hence, the width of Australia in kilometres is 3928.4087.

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The shortest side of a triangle is just opposite of the angle 47°.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

All the angle of a triangle are,

⇒ 63°, 47°, 70°

Now,

Since, All the angle of a triangle are,

⇒ 63°, 47°, 70°

We know that;

The smallest side of a triangle is just opposite of the smallest angle.

Thus, The shortest side of a triangle is just opposite of the angle 47°.

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The exact value of the tan(75°), found using trigonometric identities for the tangent of the sum of two angles, indicates that the exact value of tan(75°) is (1+√3/3)/(1 - √3/3))

Trigonometric identities are equalities of expressions that includes trigonometric functions which are valid for all values of the argument, or the domain of the function.

The exact value of tan(75°) can be found from the formula for the tangent of the sum of two angles as follows;

tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)•tan(B))

tan(75°) = tan(45° + 30°)

tan(45° + 30°) = (tan(45°) + tan(30°))/(1 - tan(45°)•tan(30°))

tan(30°) = √3/3

tan(45°) = 1

tan(45° + 30°) = (1 + √3/3)/(1 - √3/3)

tan(75°) = (1 + √3/3)/(1 - √3/3)

The correct option is therefore option B

[tex]tan(75 ^{ \circ } ) = \dfrac{1 + \frac{ \sqrt{3} }{3} }{1 - \frac{ \sqrt{3} }{3} } [/tex]

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