The function S(t) = 4.5.3 models the growth of a tumor where t is the number of months since the tumor was discovered and Sis the size of the tumor in cubic millimeters. The size of the tumor when it was discovered was 4.5 cubic millimeters. Find the total change in the size of the tumor in the first 3 months and find the average rate of change in the size of the tumor in the first 3 months The total change in size of the tumor in the first 3 months was cubic millimeters. The average rate of change of the tumor in the first 3 months was cubic millimeters per month.

The ratio of the area of the smaller circle to the area of the larger circle is 1/2.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

From the information, the square is inscribed in a circle and then a smaller circle is inscribed in the square.

Let the radius of smaller circle be 2r, then length of side of larger square is ✓2r and the length of side of smaller square is  

The ratio of area of smaller square to larger square is:

= 4r² / 4(✓2r)²

= 1/2

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The simplified expression is (11/4)z + (15/2).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

3/4 (z + 2/5) + 2z

Multiplication over addition.

= (3/4)z + (3/4)x(2/5) + 2z

= (3/4)z + (15/2) + 2z

Combining the like terms.

= (3/4)z + 2x + (15/2)

= (11/4)z + (15/2)

Thus,

(11/4)z + (15/2) is the simplified expression.

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The quotient is 32 and the remainder is 6.

i.e,

32 R6

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

774 ÷ 24

24 ) 774 ( 32

      768

           6

The quotient is 32 and the remainder is 6.

Now,

We can write in this form,

(Quotient) R(remainder)

Thus,

The quotient is 32 and the remainder is 6.

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The required solution of the given graph is given as,
(a) Domain = [-2, 2]
(b) Range = [0, 2]
(C) Function, yes given graph is of absolute function.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

Here,
From the graph, Function is defined for x = -2 to x = 2
So the domain of the function is given as [-2, 2].

For the respective domain, the range of the function is given as[0, 2].

Also, yes the relation shown in the graph is a function,
F(x) = -|x| + 2

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Answer:

AA

Step-by-step explanation:

cus it can't be the other cus there is no side

The correct statement predicting the closest product is : 20

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given here : Two mixed fractions as 5⁵/₂₉ and 3¹²/₁₃

But 5⁵/₂₉=150/29 and 3¹²/₁₃=51/13

Thus the product of the two mixed fractions are as follows

150/29×51/13 =20.292

Clearly the most reasonable product is 20

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Answer:

$120

Step-by-step explanation:

Buying price

$80×6= $480

Selling price

$25×4×6= $600

Profit

$600-$480=$120

The profit on six dozen calculators is $120.

To calculate the profit on six dozen calculators, we need to find the cost of purchasing six dozen calculators and the revenue from selling six dozen calculators.

Since each dozen costs $80, the cost of purchasing six dozen calculators is:
$80 x 6 = $480

Since three calculators are sold for $25, the revenue from selling six dozen calculators is:
$25 x (6 x 12/3) = $25 x 24 = $600

The profit is the revenue minus the cost:
$600 - $480 = $120

The profit on six dozen calculators is $120.

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Answer:

-4+4i and -4-4i

Step-by-step explanation:

To start off, we can distribute the x into the x+8 to get x^2 + 8x = -20. From here we can create a polynomial by moving the -20 to the other side by adding 20 to both sides to get x^2 + 8x +20 =0. From here we can check if there is any real solutions by finding the discriminant (the sqrt part of the quadratic formula) so 8^2-4(1)(20). 16-80. Because this gets us a negative number in an actual square root, there answers we would get would be imaginary.

However to solve what the roots are, we would plug the entire equation into the quadratic equation. Getting -8+- sqrt(-64)/2 which simplified is -4+-4i. Therefore our two answers are -4+4i and -4-4i

The sample space of possible codes for the wireless garage door opener is 4096.

(a) The sample space for this batch of printed circuit boards would be 98 total boards, ordered such that the non-defective boards are first (90 boards), followed by minor defects (8 boards) and major defects (0 boards). The total number of ordered samples is given by the formula: nPr = n!/(n-r)! where n is the total number of boards in the batch and r is the number of boards selected from the batch. In this case, n = 98 and r = 2, making the total number of ordered samples 9703.

(b) The sample space for this batch of printed circuit boards would be 99 total boards, ordered such that the non-defective boards are first (90 boards), followed by minor defects (8 boards) and major defects (1 board). The total number of ordered samples is given by the formula: nPr = n!/(n-r)! where n is the total number of boards in the batch and r is the number of boards selected from the batch. In this case, n = 99 and r = 2, making the total number of ordered samples 9801.

For the wireless garage door opener, the code is determined by the up or down setting of 12 switches. This means that each switch can either be up or down for a total of 2 possible settings for each switch. The total number of possible codes is given by the formula [tex]2^12[/tex], which is equal to 4096. This is because each switch has 2 possible settings, and when multiplied by 12 switches, there are [tex]2^12[/tex] possible combinations. Therefore, the sample space of possible codes for the wireless garage door opener is 4096.

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The graph will have a slope of 15 and is attached with the answer below.

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

When y and x are two quantities that are directly proportional to one another, the proportionality constant k is defined as k=y/x.

Given that Nicole had a collection of 60 stuffed animals. She gave away 5 stuffed animals per month until all her stuffed animals were gone.

The equation can be written as:-

y = kx

The value of k will be calculated as :-

60 = k x 5

k = 60 / 5

k = 12

The equation will be:-

y = 12x

The graph of the linear relation is attached with the answer below.

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Answer:

Step-by-step explanation:

The hydrogen ion concentration of a solution can be calculated from the pH using the equation:

[H*] = 10^(-pH)

So for the apple juice with a pH of 3.1:

[H*(apple juice)] = 10^(-3.1) = 0.0005

And for the drinking water with a pH of 8.3:

[H*(drinking water)] = 10^(-8.3) = 1.7 x 10^(-9)

To find the ratio of the hydrogen ion concentration in apple juice to that in drinking water, we divide the concentration of the apple juice by the concentration of the drinking water:

[H*(apple juice)] / [H*(drinking water)] = 0.0005 / (1.7 x 10^(-9)) = 2.94 x 10^9

Therefore, the hydrogen ion concentration in apple juice is 2.94 x 10^9 times the concentration in drinking water.

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The expression can be used to show how much Jim spend on lunch each day is y = 7

Amount Jim uses to purchase school lunch = $7.00

Amount with Jim = y

If Jim has the same amount of money and spends the amount he has on school lunch each day;

y = 7

Therefore, Jim spent a total of $7 each day on lunch.

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An inequality that can be used to determine p, the number of people who can go to the amusement park, is,

28.75p + 17.25 ≤ 345.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A group of friends wants to go to the amusement park.

They have no more than $345 to spend on parking and admission.

Parking is $17.25, and tickets cost $28.75 per person, including tax.

An inequality that can be used to determine p, the number of people who can go to the amusement park, is,

28.75p + 17.25 ≤ 345.

Therefore, an inequality is 28.75p + 17.25 ≤ 345.

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To verify that the given function is an explicit solution of the given differential equation, we can plug it into the differential equation and see if it satisfies the equation.

Plugging in the given function, we get: dy/dt + 20y = 24; (6/5)e-20t - 6/5 = 24. Simplifying, we get 0 = 0, which is true. This means that the given function is an explicit solution of the differential equation, and it is valid on any interval I.

To find a function solution to a differential equation, you must first identify the type of equation you are dealing with. If it is a linear equation, you can use the method of integrating factors or the method of undetermined coefficients, depending on the equation.

If it is a nonlinear equation, you can use the method of separation of variables, the method of substitution, or the method of series solutions. Once you have identified the equation, you can use the appropriate method to find the solution.

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Answer:

Step-by-step explanation:

e.g. r = 2i – k + λ(4i – 7j + 5k).

Without more information about the specific situation (such as the height from which the bottle is dropped, the surface on which it is dropped, and so on), a value for p cannot be determined.

The probability of landing a bottle on the floor on any given try is a fixed value, typically represented by "p".

The probability that he will land the bottle on the floor on the tenth try is then given by:

P(tenth attempt landing) = (1 - p)9 * p

where (1 - p)9 represents the probability that he fails to land the bottle on the floor in the first nine attempts, and p represents the probability that he lands the bottle on the floor on the tenth attempt.

However, without more information about the specific situation (such as the height from which the bottle is dropped, the surface on which it is dropped, and so on), a value for p cannot be determined.

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Answer:

Answer for X

[tex]4x + y = 10[/tex]

[tex](4x + y) + ( - y) = 10 - y[/tex]

[tex]4x = 10 - y[/tex]

[tex] \frac{4x}{4} = \frac{10 - y}{4} [/tex]

[tex]x = \frac{10 - y}{4} [/tex]

Answer for y

[tex]4x + y = 10[/tex]

[tex](4x + y) + ( - 4x) = 10 - 4x[/tex]

[tex]y = 10 - 4x[/tex]

The slope of the linear relationship is -4/6

The general formula for the equation of a line is expressed as;

y = mx + c

Given that the parameters are;

The formula for determining the slope of a line is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

From the diagram shown, we have to substitute the values into the formula, we get;

Slope, m = -6 - (-2)/11 - 5

Expand the bracket

Slope,m  = -6 + 2/6

Subtract the values

Slope, m = -4/6

Hence, the value is -4/6

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the number of degrees in the smaller angle is 60 degrees.

The smaller angle is 60 degrees.

Let x = number of degrees in the smaller angle

Then the number of degrees in the larger angle = 3x

Given that the two angles are in the ratio of 2 to 3

2x = 3x

x = 60

Therefore, the number of degrees in the smaller angle is 60 degrees.

The two supplementary angles are supplementary angles because the sum of their angles is 180 degrees. This means that if we denote the number of degrees in the smaller angle as x, then the number of degrees in the larger angle must be 180-x. We know that their ratio is 2 to 3, which can be written as 2x = 3(180-x). Solving this equation gives us x = 60, so the number of degrees in the smaller angle is 60.

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A. The area under the curve of the probability density function must sum to 1.

Probability density functions of continuous random variables are used to represent the probability of a given outcome within a specific range. The area under the curve of the probability density function is equal to the probability of the outcome occurring. As the area represents the probability of any outcome occurring, the sum of the area under the curve must always equal 1. Therefore, it is always true that the area under the curve of the probability density function must sum to 1.

The complete question is :

Which of the following is always true for all probability density functions of continuous random variables?

A. The area under the curve of the probability density function must sum to 1.

B. The probability density function must be symmetric.

C. The probability density function must be positive.

D. The probability density function must be decreasing.

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The discount in the price of the headphones is of $17.67

If we apply a discount of D (D is the percentage in decimal form).

Then the new value (using A as the initial value) is:

A' = A*(1 - D)

If instead, we have an increase of I (also in decimal form) the new value is:

A' = A*(1 + D)

Here the original value is $57, and we have a discount of 0.4 and an increase of 0.15, then the new value will be:

A' = $57*(1 - 0.4)*(1 + 0.15) = $39.33

Then the discount is of:

$57 - $39.33 = $17.67

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The amount of radioactive kind of nitrogen will be left after 30 minutes

is 240 grams.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A radioactive kind of nitrogen has an initial mass of 1930 grams and it has a half-life of 10 minutes.

Therefore, The amount of radioactive kind of nitrogen that will be there after 30 minutes is,

= 1920/2³.    (As 30 = 10×3)

= 1920/8.

= 240 grams.

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Answer:

Step-by-step explanation:

r:4/3 cm/s or 1.33 cm/s

In Indiana become adults, and the number of children in Indiana increases by 2% as a result of births and immigration. If we let c0 = 6 million and a0 = 4 million.

Then the population of Indiana can be modeled by the following recursive equation:

ct = (1 + 0.02) * ct-1 + 0.05 * at-1

at = (1 - 0.05) * ct-1

This equation models the growth of the population of Indiana based on the number of children and adults in the previous year, taking into account the conversion of children into adults and the growth in the number of children.

The given information states that during any given year, 5% of all children become adults, while adults stay the same. Hence, the number of adults in year t can be determined as follows:

at = (1 + 0.05) * ct-1

Where ct-1 is the number of children in the previous year. This equation reflects that the number of adults in year t is the sum of the adults from the previous year plus 5% of the children in the previous year.

This model assumes that the growth in the number of adults is solely dependent on the children becoming adults, and no other factors, such as migration, birth, or death, are considered. This model is also based on the assumption that 5% of the children will become adults each year, which may not hold true in reality.

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Answer:

x=9

y=15

Step-by-step explanation:

Since it is a parallelogram, there is a property of a parallelogram that says that opposite sides are congruent/equal. So x would equal to 9 and y is equal to 15

Answer:

Step-by-step explanation:

X = 9

Y = 15

Answer:

Step-by-step explanation:

try 13 pairs of flippers

It’s in between 10 and 15