I was wondering if you could help me with this problem. I am not sure where to start solving it. Thank you.

Given -

Substance present initially = 340 grams

Substance present 50 years later = 170 grams

To Find -

How much of the substance will be present after 120 years =?

Step-by-Step Explanation -

Since the substance was reduced to half of what it is initially in 50 years.

So,

The half-life time of the substance = 50 Years.

It means that every 50 years, the substance will reduce to half of its quantity.

And, we know the formula:

Where,

A = the remaining amount of Substance =?

S = the amount of Substance you start with = 340grams

t = the amount of time in years = 120 years

h = the half-life time = 50 years

Simply putting the values, we get:

Final Answer -

The substance that will remain after 120 years = 3.22 gram

1 + c + 1.4 = c + 2.4

c + 2.4 = c + 2.4

c = c + 2.4 - 24

c = c

The surface area of the right cone is:

The surface area of a right cone is:

Here, r = 9 in, and h = 12 in

so

aWe can factorize by a common factor

ANSWER

8(2m+3n)

The Quadratic format is

The answer to the question is that the factors must multiply to form c

we know that

The equation is of the form

y=ax+b

The given values are

a=0.872

b=25.263

substitute

therefore

The equation is

Let x and y be the two numbers

x + y = 72 ------------------------------(1)

x - y = 4 ----------------------------------(2)

Add equation (1) and equation (2)

2x = 76

Divide both-side of the equation by 2

x = 38

substitute x = 38 into equation (1) and then solve for y

38 + y = 72

subtract 38 from both-side of the equation

y = 72 - 38

y = 34

The two numbers are 34 and 38

Answer:

32.2 feet

Explanation:

The diagram given is a right angled triangle

Using the SOH CAH TOA identity

Given the following

Hypotenuse = 38

Opposite = x

Sin theta = opposite/hypotenuse

Sin 58 = x/38

x = 38sin58

x = 38(0.8480)

x = 32.23

Hence the length of VT to the nearest tenth of a foot. is 32.2feet

Number line

Let's

[tex]15 + 0.10x = 0.15(60) + 0.15(x) \\ 15 + 0.10x = 9 + 0.15x \\ \\ 0.10x - 0.15x = 9 - 15 \\ - 0.05x = - 6 \\ \frac{ - 0.05x}{ - 0.05} = \frac{ - 6}{ - 0.05} \\ x = 120[/tex]

ATTACHED IS THE SOLUTION

The function 2x + 3x^2 represents the result of adding the two provided functions, f(x) and g(x).

An operation known as "function composition" takes two functions, f and g, and produces a new function, h, that is equal to both g and f and has the property that h(x) = g.

Given the f(x) = 2x and g(x) = 3x^2 functions

The sum of the two functions must be calculated as illustrated;

f(x) + g = (f+g)(x)

Put the provided functions in place of (f+g)(x) to have:

(f+g)(x) = 2x + 3x^2

Standard version of the expression is (f+g)(x) = 2x + 3x^2

Consequently, the sum of the functions f(x) and g(x) is2x + 3x^2

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a) In this election voted: 7+9+2+5+3+6=32

b) For a majority you can follow the next rule:

The 50% of 32 is: 32*0.5=16, then, are needed at least 17 votes

c) Candidate A had 3 last-place votes, candidate B had 0 last-place votes, candidate C had 15 last-place votes, candidate D had 5 last-place votes and candidate E had 9 last-place votes.

Thus, the candidate with the fewest last-place votes is candidate B

Step 1 : To determine the matrices as shown below

The domain restrictions on the rational equation

[tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex]  are  Options A and C. x = 5 and x = - 5 .

The numbers that makes the denominators zero and the entire expression infinite or undefined are the domain restrictions.

Consider the denominators,

       [tex]x^{2}[/tex] - 25 ≠ 0 --(1)

       [tex]x^{2}[/tex] ≠ 25

       x ≠ 5 and x ≠ -5

       2x - 10 ≠ 0  ---(2)

       2x ≠ 10

        x ≠ 10/2

        x ≠ 5

The domain restrictions on the rational equation  [tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex]  are

x ≠ 5 and x ≠ -5 .

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Given data:

The given expression is x^2 -6x-7=0.

The given expression can be written as,

Thus, the number 9 is added on both sides to complete square.

The amount of extra money a month that Mrs. Laurence pays in her car payment is $72.

We can get the amount of extra amount that Mrs. Laurence pays each month when compared to Mr. Gannon by dividing the amount that they pay by the number of months they need to make these payments.

This can be done as follows:

26304 ÷ 24 = 1096

20480 ÷ 20 = 1024

1096 - 1024 - 72

So, the amount of extra money that Mrs. Laurence has to pay each month when compared to that of Mr. Gannon is $72.

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Answer:

the y intercept is -1.

Step-by-step explanation:

the y intercept is -1 because it goes through the point (0,-1)

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

We are given the diameter is 5

r = d/2 = 5/2 = 2.5 in

V = pi ( 2.5)^2 (7)

V =pi ( 6.25)*7

V = 43.75 pi

Assuming a value for pi of 3.14

V =137.375 in ^3

Rounding to the nearest hundredth

V = 137.38 in ^3

Assuming a value for pi by using the pi button

V = 137.44468

Rounding to the nearest hundredth

V = 137.44 in ^3

Answer:

answer of the given question

The Euler's polyhedron formula states that, for a polyhedron with F faces, E edges and V vertices, we have:

F + V - E = 2

For E = 12 and V = 6, then we have:

F + 6 - 12 = 2

F = 2 + 12 - 6

F = 8

Given the equation:

Let y = distance

Let x = time

- The distance from Denver when she began is given by x = 0, therefore:

Answer 1. 475 miles

- The change for each four hours, this is x = 4, so:

Answer 2. 235 miles

Part A.

Given:

P = (5, 4), Q = (7, 3), R = (8, 6), S = (4, 1)

Let's find the component of the vector PQ + 5RS.

To find the component of the vector, we have:

For vector RS, we have:

Hence, to find the vector PQ+5RS, we have:

Solving further:

Therefoee, the component of the vector PQ+5RS is:

<-18, -26>

• Part B.

Let's find the magnitude of the vector PQ+5RS.

To find the magnitude, apply the formula:

Thus, we have:

Therefore, the magnitude of the vector is:

ANSWER:

Part A. <-18, -26>

Part B. 10√10

Original price = x

Price with 15% off = x - 0.15x

Price with 15% off and 7.5% tax = (x - 0.15x)(1.075)

Answer:

Option B: (x - 0.15x)(1.075)

step 1

Find the measure of the third interior angle of triangle

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

x+109+13=180

solve for x

x=180-122

x=58 degrees

step 2

Applying the law of sines

?/sin(13)=6/sin(58)

solve for ?

?=(6/sin(58))*sin(13)

Given:

As the first matrix has 2 rows and 1 column. And the second matrix has 3 rows and 1 column.

The dimension of both the matrix is not the same.

For the subtraction of two matrices must have the same size.

So, we can not determine the values of variables.

Answer: not possible.

A)140 adults and 72 children

Explanation

Step 1

Let x represents the number of childrend attending

Let y represents the number of adults attending

then

total cost for the children=4x

total cost for the adults=6y

if you raise 1128,

Now, 212 people attend,Hence

Step 2

solve for x and y

a)isolate x in equation (2), then replace in equation (1)

it means 140 adults are attending

b)replace y=140 in equatin (2) to find x

so, the number of children is 72 and 72 children

The regular price of an item is $65

Lena bought it on sale for 60% off the regular price.

Then it means that she paid only (100% - 60% = 40%) of the price.

Let us find the 40% of $65

Therefore, Lena paid only $26 for the item.

Answer:

• m∠1 =168 degrees

• m∠2 =12 degrees

Explanation:

From the diagram, Angles 1 and 2 are on a straight line.

We know that the sum of angles on a straight line is 180 degrees.

Therefore:

Substituting the given values, we have:

The measures of angles 1 and 2 are:

The measures of angles 1 and 2 are 168 degrees and 12 degrees respectively.

an = ar^ (n- 1)

for n = 3 (3rd term)

r = common ratio = 4/ 2 = 2

a3 = 2 (2) ^ (3-1)

a3 = 2 (2)^2

a3 = 2 (4)

a3 = 8

n= 4 (4th term)

a4 = 2 (2)^(4-1)

a4 = 2 (2)^3

a4 = 2 (8)

a4 = 16

2, 4 , 8 , 16

The probability that the subject tested negative or did not use marijuana is 145/293.

What is probability?

Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.

As given in the question,

Total positive results are 143 out of which 24 are false, and

total negative results are 150 out of which 5 are false.

We know that,

probability = favorable outcome/ Total outcome

so,

Total outcome = total tests

total tests = 143 + 150

total outcome = 293

and favorable outcome = true negative outcome

true negative outcome = total negative outcome - false negative outcome

true negative outcome = 150 - 5

favorable outcome = 145

Therefore, the probability is equal to 143/293

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