3) Use the situation to choose the correct answer.
A radioactive substance loses its mass at a rate of 12% every second. At the beginning
of an experiment, the substance has a mass of 6 centigrams.
After 5 seconds, how much mass is left of the radioactive substance? Round your
answer to the nearest hundredth centigram.
5.28 cg
03.17 cg
O 3.60 cg
O 0.72 cg

We can prove that if a, b, and c are in harmonic progression, then a(b+c), b(c+a), and c(a+b) are also in harmonic progression.

Let a, b, and c be in harmonic progression (HP) which means that:

1/a + 1/b = 2/c    or       b + a = 2ab/c     or      c = 2ab/(a+b)

Our goal is to show that  a(b+c), b(c+a), and c(a+b) are in HP.

Let x = a(b+c), y = b(c+a), and z = c(a+b).

We need to show that:

1/x + 1/y = 2/z

Rewriting x as:

x = a(b+c) = ab + ac

rewriting  y and z as:

y = b(c+a) = bc + ba

z = c(a+b) = ac + bc

substituting these mathematical expressions into the equation we want to prove:

1/x + 1/y = 1/(ab + ac) + 1/(bc + ba)

= (bc + ba + ab + ac)/(ab(bc + ba) + ac(bc + ba))

= (b+c)(a+c)/(abc(b+c))

= (a+c)/(ab+ac+bc)

= (a+c)/(2ab/c + ab + ac + bc)

= (a+c)/(2ab/(a+b) + ab + ac + bc)

= (a+c)/(2ab/(a+b) + (ab+ac+bc))

= (a+c)/[(2ab+ab+ac+bc)/(a+b)]

= (a+c)/[(a+b)(2a+2b+c)/(a+b)]

= (a+c)/(2a+2b+c)

In the same manner,  we can show that:

1/z = 1/(ac + bc) + 1/(ab + ba)

= (ac + bc + ab + ba)/(ac(ab + ba) + bc(ab + ba))

= (a+b)(a+c)/(abc(a+b))

= (a+c)/(ab+ac+bc)

= (a+c)/(2a+2b+c)

In conclusion, it has proved that if a, b, and c are in harmonic progression, then a(b+c), b(c+a), and c(a+b) are also in harmonic progression.

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Answer: The answer is 464

Step-by-step explanation:

Bc you do 98-7=91, Then you do 25+91*4, Next Do 25+91=116, Last you 116*4= 389 and If this is wrong use a Calaculator Ok

_ Mhart7109

Answer: The length of BC ≈ 12.4 cm

Step-by-step explanation:

The first thing we need to do is to find the length of BD which we can solve for with the tangent of 20° which is the opposite side over the adjacent side.

We get tan20° = BD/8.

Solve for BD and you get BD = 8tan20°.

Now we will need to solve for the length of CD which we can get from the tangent of 40°.

We get tan40° = 8/CD

Solve for CD and you get CD = 8/tan40°.

Now that we have the lengths of BD and DC, we can simply add them together to get the length of BC.

(8tan20°) + (8/tan40°) ≈ 12.4 cm

The perimeter of the equilateral triangle will be 27x - 48.

It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.

Therefore, the perimeter of the equilateral triangle will be:

= 3(9x - 16)

= 27x - 48

Therefore, the perimeter of the equilateral triangle will be 27x - 48.

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Find the perimeter of the equilateral triangle.

9x - 16

The equation of the area is 308 = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2) + 6 * (5 * 5) - 2 * (5 * 5)

From the question, we have the following parameters that can be used in our computation:

Area = 308

The formula used to calculate area

Area = S.A of the bottom + S.A of the top - 2 * Overlap

Using the given figure, we have

S.A of the top = 6 * (5 * 5)

S.A of the bottom = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2)

Overlap = 2 * (5 * 5)

So, we have

308 = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2) + 6 * (5 * 5) - 2 * (5 * 5)

Hence, the equation is (b)

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Answer:

$270

Step-by-step explanation:

Find her gross income....then subtract taxes:

       30 hr/week * $10/hr        - $ 30     = $270

Answer:

10:15

Step-by-step explanation:

Answer:

(c, b)

Step-by-step explanation:

Add the coordinates together and divide by 2

x coordinates: 2c + 0 = 2c, divided by 2 = c

y coordinates: 0 + 2b = 2b, divided by 2 = b

The distance between points R and S is  \(\sqrt{ (185)\). The correct answer is D. She made no errors.

Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:

RS = √(-4) (-3))² + (7 − 5)²

= √(-1)² + (2)²= √1 + 4

= √5

The error is with the order of subtraction in the formula for the distance between two points.

Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.

The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;

dAB = \(\sqrt{  ((x^2 - x1)^2 + (y2 - y1)^2)\)

Comparing the given question with the formula above, we have;

A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.

Therefore, we have;

RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)

On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS

= \(\sqrt{ (8^2 + 11^2)RS\)

= \(\sqrt{ (64 + 121)RS\)

= \(\sqrt{ (185)\)

Therefore, the distance between points R and S is  \(\sqrt{ (185)\).

From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.

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Answer:

\(3 \sqrt{2} \)

Step-by-step explanation:

Given

\( \frac{ \sin(60) \sec(60) \cot(30) }{ \cos( 45) ) } \)

Using the unit circle, we know that

\( \sin(60) = \frac{ \sqrt{3} }{2} \)

\( \cos(45) = \frac{ \sqrt{2} }{2} \)

We can find sec and cot by using reciprocal identies.

\( \sec(x) = \frac{1}{ \cos(x) } \)

\( \cos(60) = \frac{1}{2} \)

So

\( \sec(60) = 2\)

\( cot(x) = \frac{1}{ \tan(x) } \)

\( \tan(30) = \frac{1}{ \sqrt{3} } \)

so

\( \cot(30) = \sqrt{3} \)

Plug in the values.

\( \frac{ \frac{ \sqrt{3} }{2} \times 2 \times \sqrt{3} }{ \frac{ \sqrt{2} }{2} } \)

\( \frac{ \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{12} }{1} }{ \frac{ \sqrt{2} }{2} } \)

\( \frac{3}{ \frac{ \sqrt{2} }{2} } \)

\(3 \sqrt{2} \)

The provided translated function, f(x), shifts left by two units on the horizontal axis.

One type of transformation is translation. Both the scaling calculation and the compression calculation are performed using it. This approach wouldn't change the object's form or shape.

The given graph equation for the translation, as per the query, is g(x) = (x + 2)²

The translation of the given quadratic function is: y = g(x) = (x + 2)²

Consequently, the parent function is written as y = g(x) = x2.

Additionally, the vertex should be known when graphing the translated function:

a(x - h)2 + k = y = g(x);

where the parent function is (0, 0) and the vertex values are (h, k).

(h, k) = is the vertex for the function that is provided (-2, 0)

This information causes the translation function to move the graph two units to the left.

Horizontal translation is the name given to the translation.

As a result, the given function, f(x), shifts horizontally, or left, by 2 units.

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Answer:

30%

Step-by-step explanation:

Percentage discount

\( = \frac{discount}{original \: price} \times 100\% \\ = \frac{5 - 3.50}{5} \times 100\% \\ = 30\%\)

☆ Discount= original price -selling price

Answer:

14 + 2x I think

Step-by-step explanation:

Wait for more responses if needed

Answer:

\( {6x}^{2} + 4x\)

Step-by-step explanation:

1) Collect like terms.

\((7 {x}^{2} - {x}^{2} ) + 4x\)

2) Simplify.

\( {6x}^{2} + 4x\)

Therefor, the answer is 6x² + 4x.

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59\)

Answer:

1) Classroom 2

2) Classroom 3

3) Classroom 2

4) Classroom 4

The requreid,
(a) Approximate values of the given numbers are π ≈ 3.1, √6 ≈ 2.4, 2√6 ≈ 4.8, and √7 ≈ 2.6.
(b) √6  < √7 <  π  < 2√6

(a)

π ≈ 3.1 (since π is between 3 and 4, and is closer to 3.1 than to 3.2)

√6 ≈ 2.4 (since 6 is between 4 and 9, and the square root of 6 is closer to 2.4 than to 2.5)

2√6 ≈ 4.8 (since 2√6 is approximately twice the value of √6, which is 2.4)

√7 ≈ 2.6 (since 7 is between 4 and 9, and the square root of 7 is closer to 2.6 than to 2.7)

(b)

Order from least to greatest:

√6  < √7 <  π  < 2√6

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Considering the desired result of the hypothesis test, we the closest mean time to 1.5 hours, hence the correct option is:

C. 1.6 hrs

The closer the mean is to the sample mean, the less likely we are to reject the null hypothesis.

In this problem, the sample mean is of 1.5 hours, hence, the closest value, considering the absolute value of the difference, is of 1.6 hours, hence option C is correct.

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Derrick and Janis together plant a total of 30 + 90 = 120 strawberry plants on the first day.

To find out how many strawberry plants Derrick and Janis planted on the first day, we need to calculate the sum of the plants they individually planted.

Derrick planted 20% of the 150 strawberry plants:

20% of 150 = (20/100) * 150 = 30 strawberry plants.

Janis planted 60% of the 150 strawberry plants:

60% of 150 = (60/100) * 150 = 90 strawberry plants.

Therefore, on the first day, Derrick and Janis planted a total of 30 + 90 = 120 strawberry plants.

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The that will represent the exponential function is given in image

What are exponential functions, exactly?

A mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is referred to as the function's base and must be greater than zero. The most commonly used exponential function basis is the transcendental number e, which is approximately equivalent to 2.71828.

Exponentially increasing growth

In Exponential Growth, the amount expands incredibly slowly at first, then rapidly. With the passage of time, the rate of change quickens. The rate of growth quickens as time passes. The fast growth is supposed to indicate a "exponential ascent".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the proportion of increase.

Now,

As the function y=10x² represents the number of gummies after x months

the the graph will be  

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Applying the tangent ratio, the value of x in the image, rounded to the nearest thousandth is: 15.824.

The tangent ratio, commonly referred to as "tangent," is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. It is expressed as:

tan (∅) = opposite/adjacent

We have the following:

Reference angle (∅) = 53 degrees

Length of opposite side = 21

Length of adjacent side = x

Plug in the values:

tan 53 = 21/x

x * tan 53 = 21

x = 21 / tan 53

x = 15.824

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she could have scored the 10 points in 302400 ways.

The given parameters are

n= total points =10

r1 =one-point free throw = 1

r2 = two-point field goals = 2

r3 =  three-point field goals = 3

The number of ways (k) she could have scored the points is:

k=(n!)/(r1!×r2!×r3!)

The factorial function is a mathematical formula represented by an exclamation mark "!".

k= 10!/(1!×2!×3!)

k= 3628800/(1×2×6)

k= 302400

so.. she could have scored the 10 points in 302400 ways.

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Answer:

hundred thousands place

Step-by-step explanation:

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard as a function of x is (150/x - 10)(x - 4).

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides.

x = width of the billboard designer

Total Area including margin = 150 ft^2

Height of the billboard = Area/width

Height of the billboard = 150/x

Before the height of the billboard = (150/x - 5 × 2)

Before the height of the billboard = (150/x - 10) ft

The width of the printed region billboard = (x - 2 × 2)

The width of the printed region billboard = (x - 4) ft

The area of the printed region of the billboard = The width of the printed region billboard × The height of the printed region billboard

The area of the printed region of the billboard = (150/x - 10)(x - 4)

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The complete question is:

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 150 ft^2 (including the margins).

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard.

Area as a function of x =

Answer:

Step-by-step explanation:

3x5=15x3=45

Hello,

The answer is 3x² - x - 2

Step 1 : Apply distributive property by multiplying each term of " x - 1 " by each term of 3x + 2 :-

→ 3x² + 2x - 3x - 2

Step 2 : Combine 2x and -3x to get -x :-

→ 3x² - x - 2

✍️ By Benjemin ☺️

Answer:

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

There is a difference between the means

Step-by-step explanation:

Step(i):-

Given that mean of the Population = 5.9pounds/square inch

Given mean of the sample = 6.0pounds/square inch

Given that variance of the Population = 0.36

The standard deviation of the Population = √0.36 =0.6

critical value (Z₀.₀₅)= 1.96

Step(ii):-

Null Hypothesis:H₀: x⁻ = μ

Alternative Hypothesis:H₁:  x⁻ ≠ μ

Test statistic

              \(Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }\)

               \(Z = \frac{6.0-5.9 }{\frac{0.6}{\sqrt{160} } }\)

              Z  =  2.1097

Final answer:-

Calculated value Z = 2.1097 > 1.96 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means

Answer:

We want the ith row of the new matrix SijA to be the old jth row of A, so we need the ith row of Sij to extract the jth entry of column of A.

This mean the ith row of Sij must have a 1 in the jth entry and 0's everywhere else.

Similarly, the jth row of Sij must have a 1 in the ith entry and 0's everywhere else.

in the piecewise notation this is

(Sij)kl ={1 if k=i and l=j, 1 if k=k and l=i; 1 if k=l but k#i,j, 0 otherwise

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Expand to get    x^2 - 8x + 40 = 0

  a = 1      b = -8    c = 40

Answer: I’m pretty sure p represents 6 and the expression 4p represents 4x6

Step-by-step explanation:

Whenever a number has a letter next to it, that letter is just a variable and means that you have to multiply it. So if p equals 6, then 4x6=24. It fits into the equation. Sorry if my explanation is still confusing.