The question is down below

The percentage of the original sample that is left after 115 days is; 23.4733%

Formula for radioactive decay is;

A = A₀ * (1/2)^(t/t_¹/₂)

where;

A = quantity of the substance remaining

A₀ = initial quantity of the substance

t = time elapsed

t_¹/₂ = half life of the substance

Thus;

A/A₀ =  (1/2)^(115/55)

A/A₀ =  0.234733 or 23.4733%

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Answer:

46.67 %

Step-by-step explanation:

Total thickness = 30  

  14 of this is concrete      14/30 x 100% = 46.67 %

Considering the given graph, it is found that f(-3) = 1.

First we identity x on the horizontal axis, then we look at the value of y on the vertical axis for which the function is marked at this point.

At this graph, when the horizontal axis is of -3, the vertical axis is of 1, hence f(-3) = 1.

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Step-by-step explanation:

ATTACHED IS THE SOLUTION.

Answer:

m<2=115

m=180-115

=75

your answer is 75 because house is hanged in 180

Answer:

look below

Step-by-step explanation:

first way ,10 x 22 = 220

second way , 20 x 11 = 220

There are many ways other than this but I cant tell all of them.  for example, the person can just give Rs. 1000 to the shopkeeper and receive a change of Rs. 780

There are 12 ways he can pay this amount using the notes he has the answer is 12.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

Let x be the number of Rs10 notes and y be the Rs20 note

10x + 20y = 220

The whole number of x and y which satisfy the above equation:

x = 0, y =11

x = 2, y =10

x = 4, y =9

x = 6, y =8

x = 8, y =7

x = 10, y =6

x = 12, y =5

x = 14, y =4

x = 16, y =3

x = 18, y =2

x = 20, y =1

x = 22, y =0

Total number of ways = 12

Thus, there are 12 ways he can pay this amount using the notes he has the answer is 12.

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Answer:

3 2/3

Step-by-step explanation:

10 rpms - 6 1/3 rpms = 3 2/3

Applying partial fractions, the system of equations that can be used to find the values of A and B is given as follows:

The partial fraction is given as follows:

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A}{5x - 2} + \frac{B}{(5x - 2)^2}[/tex]

Applying the least common multiple at the right side, we have that:

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A(5x - 2) + B}{(5x - 2)^2}[/tex]

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{5Ax - 2A + B}{(5x - 2)^2}[/tex]

Hence, comparing both sides of the equality:

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Answer:

The answer is Be

Step-by-step explanation:

5A=-15

-2A+B=10

Answer:

1/25

Step-by-step explanation:

The bag has:

The probability of picking a yellow marble is 2/10=1/5.

So, the answer is (1/5)² = 1/25

f(x) is a linear function that increases with x. represents the number of free nights earned as a function of x, the number of nights that you stay.

We know that f(x) represents the number of free nights earned as a function of x, the number of nights that you stay.

Such that:

f(x) = x/10.

Notice that, if x = 10, then:

[tex]f(10) = 10/10 = 1[/tex]

This means that if you stay for 10 nights, then you get a free night.

If you stay for 20 nights, then you win two free nights, and so on.

f(x) is a linear function that increases with x.

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Answer:

Step-by-step explanation:

The true statement is (A) A customer earns 1 free night per 10 nights stayed.

The function is given as:

From the above function, we can see that the number of nights (x) is divided by 10.

This means that, for every 10 nights stayed, the visitor gets one free night.

Hence, the true statement is (A) A customer earns 1 free night per 10 nights stayed.

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Answer:

A) Yes, because the sum of any two side lengths is greater than the third side length.

Step-by-step explanation:

All triangles have a property that the sum of two side lengths is greater than the remaining side length.

4 + 8 = 12 > 10, making it a triangle

The number which could be added to both sides of the equation to complete the square is; -2.25.

The quadratic equations give in the task content is; 1=x²-3x. Hence, to express the equation by completing the square method; we have;

1 - 2.25 = (x -3/2)² - 2.25

Hence, the number which should be added to both sides of the equation is; -2.25.

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Answer:

$9450

Step-by-step explanation:

Answer:

A = $9,450.00

A = P + I where

P (principal) = $9,000.00

I (interest) = $450.00

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 9,000.00(1 + 0.05/1)(1)(1)

A = 9,000.00(1 + 0.05)(1)

A = $9,450.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $9,000.00 at a rate of 5% per year compounded 1 times per year over 1 years is $9,450.00.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Given

ab = [tex]\frac{1}{4}[/tex]

bc = [tex]\frac{1}{3}[/tex]

ac = [tex]\frac{1}{3}[/tex]

We will use the first equation to find b in terms of a.

b = [tex]\frac{1}{4a}[/tex]

Now we will substitute b into 2nd equation to find c in terms of a.

[tex](\frac{1}{4a} )(c)=\frac{1}{3} \\\frac{c}{4a} =\frac{1}{3} \\3c = 4a\\c = \frac{4a}{3}[/tex]

Now we will substitute c into 3rd equation to find value a.

[tex]a(\frac{4a}{3} )=\frac{1}{3} \\\frac{4a^{2} }{3} =\frac{1}{3} \\4a^{2} =1\\a^{2} =\frac{1}{4} \\a=\sqrt{\frac{1}{4} } \\=\frac{1}{2}[/tex]

Now we will substitute a into first equation to find b.

b = [tex]\frac{1}{4(\frac{1}{2}) } \\=\frac{1}{2}[/tex]

Next we will substitute a into the 3rd equation to find c.

c = [tex]\frac{4(\frac{1}{2}) }{3} \\=\frac{2}{3}[/tex]

Now we got all 3 values, when we multiply them together,

a x b x c = [tex]\frac{1}{2} *\frac{1}{2} *\frac{2}{3} \\=\frac{2}{12} \\=\frac{1}{6}[/tex]

Answer:

(2) / ((x + 5)(x - 1))

           &

(3x) / ((x - 6)(x - 1))

Step-by-step explanation:

The question is asking you to factor the denominator. In this case, you cannot simplify either of the numerators. You can factor the denominator by asking yourself the question: which two numbers multiply to equal the final number in the quadratic and add to equal the middle number in the quadratic?

1.) 2 / (x² + 4x - 5)

-----> Which two numbers multiply to -5 and add to 4? These numbers are 5 and -1. This makes the factors (x + 5) and (x - 1). The fully simplified answer: (2) / ((x + 5)(x - 1))

2.) 3x / (x² - 7x + 6)

------> Which two numbers multiply to 6 and add to -7? These numbers are -6 and -1. This makes the factors (x - 6) and (x - 1). The fully simplified answer: (3x) / ((x - 6)(x - 1))

*Please let me know if I misinterpreted the question or you need further clarification <3

Answer:

D. c/6 - x

Step-by-step explanation:

Rearranging with subject '6y':

6y = c - 6x

Dividing the above equation by 6 to get subject 'y':

y = c/6 - x

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Extract the common factor 6.

[tex]\bf{6(x+y)=c }[/tex]

Divide both sides by 6.

[tex]\bf{x+y=\dfrac{c}{6} }[/tex]

Subtract x from both sides.

[tex]\bf{y=\dfrac{c}{6}-x \ \ \to \ \ \ Answer }[/tex]

Therefore, the correct option is "D".

3x² + 6x - 24

Simplify 3.

3(x² + 6x - 8)

Think of x² +2x−8. Factor the expression by grouping. First, we need to rewrite the expression as x² + ax + bx - 8. To find a and b, set up a system to be solved.

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −8.

Calculate the sum of each pair.

The solution is the pair that gives sum 2

Rewrite x² + 2x − 8 as (x² − 2x ) + (4x − 8).

Simplify x in the first group and 4 in the second.

Simplify the common term x−2 with the distributive property.

The entire factored expression is rewritten.

3 ( x − 2 )( x + 4 ) ===> Answer

We conclude that the correct option is "B".

Using proportions, it is found that the meaning of 1 + x is the percent of original price being paid.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the total cost of the toy is given by:

15.85(1 + x).

In which x is the sales tax.

We have that:

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The required value of mean and variance is 203 and 3942 respectively.
Hence option B is correct.

The sample includes the following claims: 192, 113, 200, 287, and 225.

The statistic is the study of mathematics which deal with relations between comprehensive data.

Mean(x) = 192+113+200+287+225/5
x = 203

variance =[tex]\frac{\sum(x-x_i)^2}{n^2-1}[/tex]

=summation of squared value/n^2−1

=15769/25−1

=15769/24

=3942

Thus, the required value of mean and variance is 203 and 3942 respectively.

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Answer: y=7.5

Step-by-step explanation:

Given

y∝(1/√x)

this implies that

y=k/√x    eq(*)

when y=5 and x=36 then

5=k/√36

5=k/6

30=k        eq(1)

to find y when x is 16

put values in eq(*)

y=30/√16

y=30/4

y=7.5

The expression can be simplified to a polynomial of degree 2.

[tex]x^2 - 10x + 2[/tex]

Here we have the expression:

[tex](3x^2 -11x - 4) - (2x^2 - x - 6)[/tex]

We can directly simplify this by taking the variable as common factor:

[tex](3 - 2)*x^2 + (-11 + 1)*x + (-4 + 6)\\\\x^2 - 10x + 2[/tex]

This is a polynomial, as you can see, the maximum exponent is 2, so the degree of the polynomial is 2.

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Step-by-step explanation:

1) the difference betwee the terms given is 3-8=-2-3= -5, then

2) for n-th term: aₙ=8-5(n-1);

3) for the 9-th term: a₉=8-5*8=-32.

Answer:

x < 1 or x > 1

Step-by-step explanation:

The domain of a function is the range of values of the input is real and defined

In this particular function, x = 1 is the only value at which the function is not defined since the denominator x -1 becomes 0 and the function is undefined since division by zero is undefined

The solution of the given inequality is:

x ≤ 15.24

We know that the maximum that she can spend on gasoline is the 12% of $400.

That is:

(12%/100%)*$400 = 0.12*$400 = $48

Now, we know that each gallon of gas costs $3.15, then if x is the number of gallons of gas that she buys, we have the inequality:

x*$3.15 ≤ $48

To solve the inequality, we need to divide both sides by $3.15

x ≤ $48/$3.15

x ≤ 15.24

So the maximum number of gallons of gasoline that she can buy is 15 gallons (actually a little more).

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By performing two experiments a lot of times, your brother will see that catching the coin mid-air does not affect the probability.

We assume that the probability of each outcome of the coin is equal, so the probability of getting tails is 0.5 and the probability of getting heads is 0.5

Then, you can say to your brother to perform his experiment a lot of times. In two ways.

First, he lets the coin came down to his hand around 100 times.

Then, he catches the coin in mid-air another 100 times.

He will see that the probability of getting heads (or tails) is (almost) the same in both cases, this will mean that his theory is false.

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Answer:

13/40

Step-by-step explanation:

Rewrite a percentage as a decimal: [tex]\frac{32.5}{100}[/tex]

Convert decimals to integers: [tex]\frac{325}{100}[/tex]

Reduce the fraction: [tex]\frac{13}{40}[/tex]

Answer: [tex]\frac{13}{40}[/tex]

32.5% as a fraction in simplest form is 13/40.

Here we have to find fractional form of 35 percent

Since we knw that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

To convert a percentage to a fraction,

we can simply write it as a fraction with a denominator of 100.

Then,

we simplify the resulting fraction to its simplest form.

For 32.5%,

we can write this as,

⇒ 32.5/100

Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

The GCF of 32.5 and 100 is 12.5,

so we can divide both by 12.5,

⇒ 32.5/100 = (32.5 ÷ 12.5) / (100 ÷ 12.5)

                   = 13/40

Therefore, 32.5% as a fraction in simplest form is 13/40.

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The polygon formed was convex polygon.

A polygon that has at least one interior angle greater than 180 degree is called concave polygon . It usually has an irregular shape.

A convex polygon has all angles less than 180 degree.

It is given to follow some steps

1. A rectangular sheet of paper is taken .

2. It if folded and unfolded in random directions

3. Lines are drawn on the creases

4. The intersection points are marked A,B,C,D,E,F,G

5. The figure formed is a convex polygon as all the angles measure were less than 180 degree.

Therefore the polygon formed was convex polygon.

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Answer:

$4020.52

Step-by-step explanation:

The future value is the principal multiplied by the amount $1.00 is worth in the future.

$4,000 × 1.00513 = $4020.52

Answer:

0.98 miles

Step-by-step explanation:

Answer:

Shown in the attachment.

Step-by-step explanation:

Shown in the attachment.

Answer:

x = 1

Step-by-step explanation:

Simplifying

7(x + 1) + -2 = 5(x + 1) + 2

Reorder the terms:

7(1 + x) + -2 = 5(x + 1) + 2

(1 * 7 + x * 7) + -2 = 5(x + 1) + 2

(7 + 7x) + -2 = 5(x + 1) + 2

Reorder the terms:

7 + -2 + 7x = 5(x + 1) + 2

Combine like terms: 7 + -2 = 5

5 + 7x = 5(x + 1) + 2

Reorder the terms:

5 + 7x = 5(1 + x) + 2

5 + 7x = (1 * 5 + x * 5) + 2

5 + 7x = (5 + 5x) + 2

Reorder the terms:

5 + 7x = 5 + 2 + 5x

Combine like terms: 5 + 2 = 7

5 + 7x = 7 + 5x

Solving

5 + 7x = 7 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

5 + 7x + -5x = 7 + 5x + -5x

Combine like terms: 7x + -5x = 2x

5 + 2x = 7 + 5x + -5x

Combine like terms: 5x + -5x = 0

5 + 2x = 7 + 0

5 + 2x = 7

Add '-5' to each side of the equation.

5 + -5 + 2x = 7 + -5

Combine like terms: 5 + -5 = 0

0 + 2x = 7 + -5

2x = 7 + -5

Combine like terms: 7 + -5 = 2

2x = 2

Divide each side by '2'.

x = 1

Simplifying

x = 1

Answer:

Hello! The answer is x = 1.

Step-by-step explanation:

To solve this equation, we need to find x.

The first step in approaching this problem would be to use the distributive property:

7(x + 1) - 2 = 5(x + 1) + 2 will turn into:

7x + 7 - 2 = 5x + 5 + 2

Now, you can combine like terms on each side of the equation:

7x + 5 = 5x + 7

Now, you want to get the x's on one side and the whole numbers on the other side. In order to do this, we will subtract 5 from both sides and subtract 5x from both sides:

7x + 5 = 5x + 7

-5x -5   -5x  -5

This will leave us with:

2x = 2

We will have to now divide both sides by 2 to get x by itself:

2x = 2

--     --

2     2

This leaves us with the result: x = 1