The function c(x) = 72 ⋅ (1.04)x models the cost in dollars, c, of 1 ounce of a certain chemical used in a laboratory. x represents the number of years since 2010.

How much does an ounce of the chemical cost in 2018?

$

The cone shaped pile can hold 235.5 feet sand.

What is volume of cone ?

  One-third the sum of the area of the cone's circular base and its height is the formula for a cone's volume. Cones are described as pyramids with circular cross sections in terms of geometric and mathematical ideas. A cone's volume can be quickly determined by measuring the cone's height and radius.

Here radius of cone = 5 feet

Height of cone h = 8 feet 10 inches = 8+1 = 9 feet

Now volume of cone is

=> V = \(\pi r^2\frac{h}{3}\) cubic unit

=> V= 3.14* 25 * 3 = 235.5 cubic feet.

Hence the cone shaped pile can hold 235.5 feet sand.

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Answer:

x=-14

Step-by-step explanation:

think the number is x

According to the question

x/7+12=10

=>x+84=70 (multiply both side by 7)

=>x=70-84

x=-14

No, the line passing through  (-4, 26) and (-2, 0) is  not parallel to line passing through (10, 18) and (5, 3) because slopes of both lines are different.

Line is possible in 2-d forms so, it has only x and y-co-ordinates. Z-co-ordinates is not possible.

We know very well that to prove any two lines are parallel to each other we need to prove only whether their slopes are equal or not.

Now, talking about the slopes we know that if any line is passing from point(x₁,y₁) and again passing from other point(x₂,y₂) then slope(m) of that line is given by the formula=(y₂-y₁) / (x₂-x₁)

So, for first line we have (x₁, y₁)=(-4,26)

and (x₂, y₂)=(-2,0)

So, slope(m₁) of first line is =(0-26)/(-2 - (-4))

                  =>m₁ = -26/2

                   =>m₁ = -13     ----(eq1)

Similarly, for second line, we have (x₁, y₁)=(10,18)

and (x₂, y₂)=(5,3)

So, slope(m₂) of second line is =(3-18) / (5-10)

                =>m₂ = -15/-5

                 =>m₂=     3   -------(eq2)

On comparing eq1 and eq2,we get

 =>m₁≠m₂.

Hence, the given lines are not parallel.

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(Complete question) is:

Is the line through (-4, 26) and (-2, 0) parallel to the line through (10, 18) and (5, 3)?

Answer:

4-(x-3)²

Step-by-step explanation:

5-6x-x²

=4-x²-6x+9

=4-(x-3)²

See the image uploaded for step by step explanation. thank you

Integral(upper=a, lower=0) Integral(upper=0, lower=a) r2sinθ dr dθ (1/3)a3sinθ

We can evaluate this iterated integral by converting it to polar coordinates.

The first integral has an upper bound of a and a lower bound of 0. This corresponds to the radial coordinate of r, which has a lower bound of 0 and an upper bound of a. The second integral has an upper bound of 0 and a lower bound of -√(a2-y2). This corresponds to the angular coordinate of θ, which has a lower bound of -π/2 and an upper bound of π/2.

Therefore, the integral in polar coordinates is:

Integral(upper=a, lower=0) Integral(upper=0, lower=a) r2sinθ dr dθ

We can then evaluate this integral by using the formula for the area of a sector:

Area = (1/2)r2θ

Substituting in the upper and lower bounds of the integrals, we get:

(1/2)(a2)(π/2) = (1/3)a3sinθ

Therefore, the answer is (1/3)a3sinθ.

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Say it is two o'clock, draw an imaginary line between the hour hand and twelve o'clock to create the north-south line. You know the sun rises in the east and sets in the west so this will tell you which way is north and which way south. If you are in the Southern Hemisphere then it will be the other way round.

and the answer should be 18 x 27. The answers were reversed.

Step-by-step explanation:

basically you can do (6x4) + 3 = 27

and (4x4) + 2 = 18.

A ratio shows us the number of times a number contains another number. The real size of the bedroom is 2536' by 1648'.

A ratio shows us the number of times a number contains another number.

Given that architectural drawing lists the scale as 1/4" = 1'. Therefore, we can write the scale ratio as,

1/4" = 1'

1" = 4'

Now, given that the bedroom measures 634" by 412" on the drawing. Therefore, the real dimensions of the bedroom are,

634" = 634 × 4' = 2536'

412" = 412× 4' = 1648'

Hence, the real size of the bedroom is 2536' by 1648'.

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Different types of integer models refer to different formulations and restrictions applied to the variables in mathematical optimization problems. Here are brief explanations of three commonly used types of integer models: total integer model, 0-1 integer model, and mixed integer model.

1. Total Integer Model: In a total integer model, all variables are required to take integer values. This means that the solution must consist of only whole numbers, without any fractional or decimal values. For example, if a variable represents the number of units to produce, a total integer model would ensure that only whole units can be produced.

2. 0-1 Integer Model: In a 0-1 integer model, the variables are binary and can only take two values: 0 or 1. This formulation is often used for decision variables that represent choices or binary decisions, such as selecting or not selecting a particular option. For example, in a facility location problem, a 0-1 integer variable can represent whether a facility is open (1) or closed (0).

3. Mixed Integer Model: A mixed integer model allows a combination of integer and continuous variables in the optimization problem. Some variables can take fractional or decimal values (continuous), while others must take integer values. This formulation is useful when there is a need to model both discrete decisions and continuous quantities in the same problem. For example, in a production planning problem, the number of machines (integer) and the amount of raw material used (continuous) can be decision variables in a mixed integer model.

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Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

a. x² + 6x + 9 = -22 + 9

Step-by-step explanation:

they moved the 22 to the right by subtracting it. this leaves a binomial on the left side, which if what you want to solve it.

then they completed the square by dividing b (6) by 2 = 3. then squaring 3 to get 9.

if you added 9 to the left, then you have to add 9 to the right, therefore resulting in -22 + 9.

Answer:

In TTM/Imagine Math it is top left or a.

Step-by-step explanation:

Answer:

It is 62 miles.

Step-by-step explanation:

Hope this helps! :)

Answer:

62miles in one hour

Step-by-step explanation:

First, you have to identify your miles and you hour.

496 miles in 8 hours.

This automatically implies division because we want to know how far the train goes in 1 hour

Divide 496 by 8

Answer is 62 miles in one hour.

Probability that selected chip is white: 1/2

Probability that the other chip in the bowl is red given if the selected chip is white: 1/3

Let A be the event that bowl A is randomly selected; let B be the event that bowl B is randomly selected; and let C be the event that bowl C is randomly selected. All these three bowls are equally likely to be selected:

P(A) = P(B) = P(C) = 1/3

The probability of selecting a white chip from a bowl depends on from which bowl the chip is selected.

Let W be the event that a white chip is randomly selected.

Attached is the picture solution.

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Answer:

648 floors.

Step-by-step explanation:

Since there are 4 large buildings and 1 would be unavailable, there would be three left. You multiply. 3 x 8 x 27 = 648 !

Given:

Step by step solution:

We need to comment on the number of solutions of the equation:

From here we can say that y will have only one solution, which is equal to y = 15.

Answer:

477,577 lb

Step-by-step explanation:

Volume of sphere:

V = (4/3)πr³

V = (1/2)(4/3)(3.14159)(14 ft)³ = 5,747.015 ft³

d = 83.1 lb/ft³

W = Vd

W = 5,747.105 ft³ × 83.1 lb/ft³

W = 477,577 lb

Answer:

the answer is c

Step-by-step explanation:

cause math

Answer:

Answer is C. y = 10x + 25

Step-by-step explanation:

This equation is in the form y = mx + b

we all know b is the y-intercept (where the line passes y axis)

When we look at the graph, we see that the line passes through y-axis at 25 which means our b is 25.

If we plug 25 in place of b in y = mx + b, C is the only option that makes sense

the probability of drawing 3 or more white marbles when 5 marbles are drawn from the bag without replacement.

To calculate this probability, we can use the formula for the hypergeometric distribution, which is:

P(X ≥ 3) = [C(10,3) * C(10,2)] / C(30,5) + [C(10,4) * C(10,1)] / C(30,5) + [C(10,5)] / C(30,5)

Where C(n,r) is the number of ways to choose r items from a set of n items.

formula is that we need to consider three different cases: drawing exactly 3 white marbles, drawing exactly 4 white marbles, and drawing all 5 white marbles. For each case, we calculate the probability of drawing the required number of white marbles and the probability of drawing the remaining marbles (non-white marbles), and then multiply them together. Finally, we add up the probabilities for all three cases to get the total probability of drawing 3 or more white marbles.

Using the formula, we get:

P(X ≥ 3) = [(C(10,3) * C(20,2)) + (C(10,4) * C(20,1)) + C(10,5)] / C(30,5)

= [(120 * 190) + (210 * 20) + 252] / 142506

= 0.209

Therefore, the probability of drawing 3 or more white marbles when 5 marbles are drawn from the bag without replacement is 0.209.

using the hypergeometric distribution formula, we can calculate the probability of drawing 3 or more white marbles from a bag containing 5 red marbles, 6 blue marbles, 10 white marbles, and 9 yellow marbles when 5 marbles are drawn without replacement. The probability is 0.209.

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Yes, women save more money than men. The value of the test statistic for this hypothesis test is 1.93.

The hypothesis test used in this case is a two-sample t-test. This test is used to compare two independent means from two different groups. The null hypothesis states that there is no difference between the means of the two groups, while the alternative hypothesis states that there is a difference.  

To begin, the value of the test statistic must be calculated. The test statistic is calculated by subtracting the two means and dividing by the standard error. The standard error is calculated by taking the standard deviation of each group and dividing it by the square root of the sample size. So, for this hypothesis test, the test statistic is calculated as follows: (54 - 50) / (10/√25 + 5/√30) = 4 / (2.06) = 1.93.

To determine if women save more money than men, the test statistic must be compared to the critical value associated with the significance level. As the significance level is 0.01, the corresponding critical value is -2.575 and 2.575. Since the test statistic (1.93) is greater than the critical value (2.575), the null hypothesis can be rejected. This indicates that there is sufficient evidence to suggest that women save more money than men.

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A correlation coefficient of 0.8 or higher indicates a strong association between two variables, while a coefficient between 0.5 and 0.7 indicates a moderate association and a coefficient of 0.4 or lower indicates a weak association.

0.8 - Strong Association

0.25 - Weak Association

0.9 - Strong Association

0.65 - Moderate Association

The strength of a correlation is determined by its correlation coefficient. A correlation coefficient of 0.8 or higher is considered strong, a correlation coefficient between 0.5 and 0.7 is considered moderate, and a correlation coefficient of 0.4 or lower is considered weak. A correlation coefficient of 0.8 indicates a strong association between two variables, a correlation coefficient of 0.25 indicates a weak association, a correlation coefficient of 0.9 indicates a strong association, and a correlation coefficient of 0.65 indicates a moderate association.

A correlation coefficient of 0.8 or higher indicates a strong association between two variables, while a coefficient between 0.5 and 0.7 indicates a moderate association and a coefficient of 0.4 or lower indicates a weak association. For the given correlation coefficients, 0.8 and 0.9 indicate strong associations, 0.25 indicates a weak association, and 0.65 indicates a moderate association.

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Answer:

49

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

sorry if i got it wrong!:(

Answer:

10

Step-by-step explanation:

50 times .2 is 10

Answer: -24x^2+28x

Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x

Yes, the statement "if x is rational and y is irrational, then x + y is irrational" is true.

To understand why, let's break it down step by step:

1. First, let's define what it means for a number to be rational or irrational:
  - A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.
  - An irrational number is a number that cannot be expressed as the ratio of two integers.

2. Given that x is rational and y is irrational, we can express x and y as follows:
  - x = a/b, where a and b are integers and b is not zero.
  - y = c, where c is an irrational number.

3. Now, let's consider the sum x + y:
  - x + y = (a/b) + c

4. To prove that x + y is irrational, we'll assume the contrary, that is, x + y is rational. This means we can express x + y as the ratio of two integers:
  - x + y = p/q, where p and q are integers and q is not zero.

5. We can rewrite this equation as follows:
  - (a/b) + c = p/q

6. Rearranging the equation, we get:
  - (a/b) = (p/q) - c

7. Since (p/q) is a rational number and c is an irrational number, the right side of the equation (p/q) - c would be the difference between a rational and an irrational number.

8. However, the difference between a rational number and an irrational number is always irrational. Therefore, the right side of the equation is irrational.

9. This contradicts our assumption that (a/b) is rational, leading us to conclude that x + y must be irrational.

In conclusion, if x is rational and y is irrational, then x + y is always irrational.

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Step-by-step explanation:

um I think it's the last one

because we cut both 7 and all its left is 2x/3

We can see that the points (1,0), (3,7), and (7,29.74) are on the graph of this equation. Therefore, the correct answers are (C.) (1,7), (G.) (56,2), (H.) (27,3).

An equation is a mathematical statement that shows the equality between two expressions. It is made up of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and roots. An equation is represented by an equal sign (=) which means "is equal to".

Equations are used in various fields of mathematics and science to represent relationships between variables and to solve problems. They can be linear or nonlinear, and may involve one or more variables.

Solving an equation involves finding the value(s) of the variable(s) that make the equation true. This may involve algebraic manipulation, substitution, or other techniques depending on the complexity of the equation.

First, let's simplify the given equation:

k = 3^(√(V/7))

We know that k is the scale factor by which the solid must be dilated, so let's solve the equation for V in terms of k:

k = 3^(√(V/7))

log3(k) = √(V/7)

(log3(k))^2 = V/7

V = 7*(log3(k))^2

Now, we can use this equation to find the values of V for different values of k:

For k = 1, V = 7*(log3(1))² = 0

For k = 2, V = 7*(log3(2))² ≈ 4.83

For k = 3, V = 7*(log3(3))² = 7

For k = 4, V = 7*(log3(4))² ≈ 12.11

For k = 5, V = 7*(log3(5))² ≈ 17.67

For k = 6, V = 7*(log3(6))² ≈ 23.57

For k = 7, V = 7*(log3(7))² ≈ 29.74

Based on these values, we can see that the points (1,0), (3,7), and (7,29.74) are on the graph of this equation. Therefore, the correct answers are:

(C.) (1,7)

(G.) (56,2)

(H.) (27,3)

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We can see that the points (1,0), (3,7), and (7,29.74) are on the graph of this equation. Therefore, the correct answers are (C.) (1,7), (G.) (56,2), (H.) (27,3).

An equation is a mathematical statement that shows the equality between two expressions. It is made up of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and roots. An equation is represented by an equal sign (=) which means "is equal to".

Equations are used in various fields of mathematics and science to represent relationships between variables and to solve problems. They can be linear or nonlinear, and may involve one or more variables.

Solving an equation involves finding the value(s) of the variable(s) that make the equation true. This may involve algebraic manipulation, substitution, or other techniques depending on the complexity of the equation.

First, let's simplify the given equation:

k = \(\sqrt[3]{}\)(V/7))

We know that k is the scale factor by which the solid must be dilated, so let's solve the equation for V in terms of k:

k = \(\sqrt[3]{}\)(V/7))

log3(k) = √(V/7)

(log3(k))² = V/7

V = 7*(log3(k))²

Now, we can use this equation to find the values of V for different values of k:

For k = 1, V = 7*(log3(1))² = 0

For k = 2, V = 7*(log3(2))² ≈ 4.83

For k = 3, V = 7*(log3(3))² = 7

For k = 4, V = 7*(log3(4))² ≈ 12.11

For k = 5, V = 7*(log3(5))² ≈ 17.67

For k = 6, V = 7*(log3(6))² ≈ 23.57

For k = 7, V = 7*(log3(7))² ≈ 29.74

Based on these values, we can see that the points (1,0), (3,7), and (7,29.74) are on the graph of this equation. Therefore, the correct answers are:

(C.) (1,7)

(G.) (56,2)

(H.) (27,3)

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