what's the rate of change of -7≤x≤-2

[tex]\cfrac{\sqrt[3]{27xy^3}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{\sqrt[3]{3^3 xy^3}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{(3^3 xy^3)^{\frac{1}{3}}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{3^{3\cdot \frac{1}{3}}x^{\frac{1}{3}}y^{3\cdot \frac{1}{3}}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{3x^{\frac{1}{3}}y}{5x^{\frac{4}{3}}y^2}[/tex]

[tex]\cfrac{3}{5}\cdot \cfrac{x^{\frac{1}{3}}y}{x^{\frac{4}{3}}y^2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}}yx^{-\frac{4}{3}}y^{-2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}}x^{-\frac{4}{3}}yy^{-2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}-\frac{4}{3}} y^{1-2} \\\\\\ ~\hfill {\Large \begin{array}{llll} \stackrel{a ~~~~ b ~~ ~~ c}{0.6 x^{-1}y^{-1}} \end{array}}~\hfill[/tex]

The upper bound for the difference between the number of people at the football match and at the cricket match  is 29750<=p<=29849 .

p = number of people

The true value of p is unknown, but we know that it rounds to 29800 when rounding to the nearest hundred people.

The smallest p could be is 29750 since that rounds to 29800.

The largest is 29849; note that 29850 rounds to 29900.

We have this interval 29750<=p<=29849

r = the rate in which the people leave

This rate is in "people per minute".

Like p, the true value of r is unknown.

The midpoint of 350 and 400 is (350+400)/2 = 375, which represents the smallest value r could be if we round to the nearest 50.

The value 374 would round to 350.

On the other side of the spectrum, (400+450)/2-1 = 425-1 = 424 rounds to 400 as well when rounding to the nearest 50.

The value 425 rounds to 450.

To wrap this section up, you have this interval 375<=r<=424

Summary so far:

29750<=p<=29849

375<=r<=424

where p is the number of people and r is the rate in which they leave (in people per minute).

If we have the smallest number of people (29750) and the highest rate in which they leave (424), then we'll get the lower bound of how long it takes everyone to leave.

This can be thought of as the floor value.

time = (number of people)/(rate)

time = (29750)/(424)

time = 70.1650943396227

time = 70.165

Hence, the upper bound for the difference between the number of people at the football match and at the cricket match  is 29750<=p<=29849 .

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Answer:La masse d'un atome de cuivre est de 1,05 x 10^-25 kg. Un atome de cuivre comporte 29 électrons. Ces electrons constituent le nuage electronique de l'atome. chaque electron a une masse de 9,11 x 10^-311.

Step-by-step explanation:

Equation represents the amount of money lydia spent of apples and bananas is 5x + 3y = 8.50. Equation represents the amount of money ari spent on apples and bananas is 3x + 2y = 5.25.

Let x be the cost per pound of apples, and let y be the cost per pound of bananas. Then, the system of equations representing the given situation is:

5x + 3y = 8.50 (Equation 1)

3x + 2y = 5.25 (Equation 2)

Equation 1 represents the amount of money Lydia spent on 5 pounds of apples and 3 pounds of bananas. It shows that the total cost of the apples and bananas that Lydia bought is $8.50. To find the cost per pound of each fruit, we need to solve for x and y.

Equation 2 represents the amount of money Ari spent on 3 pounds of apples and 2 pounds of bananas. It shows that the total cost of the apples and bananas that Ari bought is $5.25. To find the cost per pound of each fruit, we need to solve for x and y.

To solve for x and y, we can use the method of substitution or elimination. Once we find the values of x and y, we can substitute them back into Equation 1 or Equation 2 to find the cost of each fruit for Lydia and Ari.

In summary, the given situation can be represented by a system of two equations. Equation 1 represents the amount of money Lydia spent on apples and bananas, and Equation 2 represents the amount of money Ari spent on apples and bananas. To find the cost per pound of each fruit, we need to solve for x and y using substitution or elimination.

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Complete question is:

Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. Determine a system of equations that represents the given the situation. Let x be cost per pound of apples and let y be the cost per pound of bananas. Which equation represents the amount of money Lydia spent of apples and bananas? Which equation represents the amount of money Ari spent on apples and bananas?

The value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.

What do you mean by Expression?

In mathematics, an expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions can be combined and simplified to solve problems, find relationships, and evaluate the truth of statements. For example, the expression "3 + 4" is a simple expression that represents the value 7 when evaluated.

Expressions can also be more complex, involving multiple operations, variables, and functions. For example, the expression "2x + 3y - z" is a more complex expression that involves three variables and three different operations.

Given the expression (3x + 5)(8x + 10), to find the value of x and y, we have to multiply the two expressions inside the parentheses and simplify the result.

Multiplication of the expressions:

(3x + 5)(8x + 10) = 24x^2 + 76x + 50

So, the value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.

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Answer:

70

Step-by-step explanation:

Let x be the number of kangaroos adopted last year.

Twice the number adopted last year is 2x.

So, the number adopted this year is 2x - 24.

Equating this to the given number of kangaroos adopted this year, we have:

2x - 24 = 116

Adding 24 to both sides, we get:

2x = 140

Dividing both sides by 2, we get:

x = 70

So, the number of kangaroos adopted last year was 70.

Answer:

112.13 square mm

Step-by-step explanation:

Decompose the composite figure into familiar shapes. One such decomposition is shown in the attached figure

There are four familiar shapes

A semicircle and 3 rectangles

The diameter of the semicircle = 6 mm and therefore its radius is 3mm

Area of the semicircle = 1/2 x area of circle = 1/2 x π x 3²
= 1/2 x 3.14 x 9
= 14.13 square mm

The rectangle below the semi circle has height 5 mm and width 10 mm
Area of this rectangle= 5 x 10 = 50 square mm

The rectangle at the bottom left has width = 6 mm and height = 7mm
Area of this rectangle = 6 x 7 = 42 square mm

The bottom right rectangle has width 2 mm and height 3 mm
Area of this rectangle = 2 x 3 = 6 square mm

Area of the three rectangles = 50 + 42 + 6 = 98 square mm

Total area of composite figure

= Area of 3 rectangles + Area of semicircle

= 98 + 14.13

= 112.13 square mm

Step-by-step explanation:

Since y is on a straight line, it'll be easy

The degree of a straightine is 180

You have one angle of 57, so all we do is subtract 57 from 180

180-57 = 123

3

Step-by-step explanation:

35 times 3.sub

Answer:

Step-by-step explanation:

If you are implying that the equation is "6x = 60"

Divide both sides by 6 to get just x by itself, then you'd have your answer.

X  = 10

The posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.

With your positive test result from Test 2, we must apply Bayes' theorem to get Doctor B's posterior probability that you have cogscitis, which is:

P(A|B) = P(B|A) * P(A) / P(B)

The following probabilities are known:

P(A) = 0.001 (the population prevalence and previous likelihood of getting cogscitis)

P(B|A) = 0.95 (the possibility of receiving a positive Test 2 result while having cogscitis)

P(B|not A) = 0.10 (the possibility of receiving a positive test result from Test 2 even if you do not have  cogscitis)

The law of total probability, which asserts the following, can be used to determine the marginal probability of a positive test result (P(B)):

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where:

P(not A) = 1 - P(A) = 0.999 (the multiplier of the previous probability of contracting cogscitis)

Substituting the values, we get:

P(B) = 0.95 * 0.001 + 0.10 * 0.999 = 0.1008

The posterior probability of developing cogscitis can now be determined, given a positive test result from Test 2:

P(A|B) = P(B|A) * P(A) / P(B)

= 0.95 * 0.001 / 0.1008

= 0.0094

Therefore, the posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.

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One serving of Christian's lemonade has 0.125 cups more water than one serving of Hayden's lemonade.

Lemonade is a sweetened beverage made from lemon juice, water, and sugar. It is typically served cold, and may also include other ingredients such as fruit, herbs, or carbonated water. Lemonade is a popular summer drink that is enjoyed in many parts of the world.

First, we can find the amount of water per serving in Hayden's lemonade by dividing the total amount of water (2.25 cups) by the number of servings (9 people):

Water per serving in Hayden's lemonade = 2.25 cups / 9 = 0.25 cups per serving

Next, we can find the amount of water per serving in Christian's lemonade by dividing the total amount of water (3.75 cups) by the number of servings (10 people):

Water per serving in Christian's lemonade = 3.75 cups / 10 = 0.375 cups per serving

To find how much more water is in one serving of Christian's lemonade compared to one serving of Hayden's lemonade, we can subtract the water per serving in Hayden's lemonade from the water per serving in Christian's lemonade:

Water per serving difference = 0.375 cups per serving - 0.25 cups per serving = 0.125 cups per serving

Therefore, one serving of Christian's lemonade has 0.125 cups more water than one serving of Hayden's lemonade.

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For small particles such as atoms and subatomic particles, quantum mechanics produces more accurate results than classical mechanics. As the particle size decreases, the differences between classical and quantum mechanical results become more pronounced.

The particle in an infinite square well potential is treated as a point particle with well-defined position and momentum in classical mechanics. The classical solution to the infinite square well problem involves a particle bouncing back and forth between the well's walls, its energy being provided by the kinetic energy associated with its motion inside the well.

In quantum mechanics, on the other hand, the particle in an infinite square well potential is treated as a wave function that solves the Schrödinger equation. The probability distribution of the particle's position and momentum inside the well is described by the wave function. The allowed energy levels of the particle are quantized and can be calculated using the problem's boundary conditions.

The following formula gives the classical result for a particle's energy in an infinite square well potential:

[tex]n2*h2/(8ma2) = E n[/tex]

where n is an integer, h is Planck's constant, and m is the particle's mass. According to this formula, energy levels are continuous and can take any value.

The quantum mechanical result for a particle's energy in an infinite square well potential, on the other hand, is given by the formula:

[tex]E n = (n2 * pi2 * h2) / (2ma2).[/tex]

n must be a positive integer. According to this formula, energy levels are quantized and can only take on discrete values.

As a result, the classical result for the energy of a particle in an infinite square well potential differs greatly from the quantum mechanical result. The classical result predicts continuous energy levels, whereas the quantum mechanical result predicts quantized energy levels.

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The shape of the graph b will be linear with an immediate decrease in speed.

In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled by an object from its starting position with respect to the time when it is started moving.

Generally speaking, the position or distance traveled by a physical object in a position vs time graph is always plotted on the y-coordinate while time is always plotted on the x-coordinate (x-axis).

In this scenario, the rate of change of the shape's position can be calculated as follows:

Rate of change = (30 - 50)/(40 - 30)

Rate of change = -20/10

Rate of change = -2.

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If a certain pregnancy had a z-score of -2.5 with mean 266 days and standard deviation 16 days , the pregnancy lasted 230 days.

We know that the length of human pregnancies can be modeled by a normal distribution with a mean of 266 days and a standard deviation of 16 days.

We are also given that a certain pregnancy had a z-score of -2.5. The z-score is a measure of how many standard deviations a data point is away from the mean. A negative z-score means that the data point is below the mean.

We can use the formula for converting a z-score to an actual value in a normal distribution:

z = (x - mu) / sigma

where z is the z-score, x is the actual value we want to find, mu is the mean, and sigma is the standard deviation.

Plugging in the given values, we get:

-2.5 = (x - 266) / 16

Solving for x, we get:

x = (-2.5 * 16) + 266 = 230

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Answer:

Your already got it.

Step-by-step explanation:

I have no explanation for this.

The two points that a line of fit will go through to best fit the data are;

B: ( 3, 7) and (9, 1)

Scatter plots are defined as the graphs that present the relationship between two variables in a data-set. It is used to represent data points on a two-dimensional plane or on a Cartesian system. The independent variable or attribute is plotted on the X-axis, while the dependent variable is plotted on the Y-axis.

A line of best fit is a straight line drawn through the maximum number of points on a scatter plot. It should have an equal number of points above and below that line. This is best represented on the blue line on the attached graph. It touched 4 points and is between the green and red line.

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Answer:

The amount that will be in Heidi’s account after 15 years is option A. $164,146.52.What is  Future Value?It can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:FV = M  (((1 + r)^n - 1) / r)Where;FV = Future value of the amount need to findM = total monthly contribution which is Heidi’s monthly contribution of 11% of her monthly salary + Employer monthly contribution of 6% of Heidi’s monthly salary can be calculated as;= (11% of Heidi’s monthly salary + 6.25% of Heidi’s monthly salary) = (11% of $3,250) + (6.25% x $3,250) = $552.50r = Monthly interest rate= Annual interest rate of 401(k) / 12 = 6.25% / 12 = 0.0625 / 12 r = 0.00520833333333333n = number of months = Number of years x 12 = 15 x 12 n= 180Substituting all the values into equation (1), we have;FV = $552.50  (((1 + 0.00520833333333333)^180 - 1) / 0.00520833333333333)FV = $552.50 x 297.097770863934FV = $164,146.518402324Rounding to the nearest cent, we get;FV = $164,146.52Therefore, the amount that will be in Heidi’s account after 15 years is option A. $164,146.52.

Step-by-step explanation:

.

Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex]  => AC = [tex]\sqrt{115}[/tex]

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.

Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.

Here, in this triangle by Pythagorean theorem

[tex]A^2 = B ^2 + c^2[/tex]

AC = [tex]\sqrt{14^2- 9^2}[/tex]

AC = [tex]\sqrt{196- 81}[/tex]

Ac = [tex]\sqrt{115}[/tex]

Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.

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The number that, when raised to the power of three, equals 500000 is approximately 100.

To find this number, we can use the cube root function:

x^3 = 500000

x = cube root of (500000)

x = approximately 100

So, the number that, when raised to the power of three, equals 500000 is approximately 100.

a. The flagpole is 5 feet away from the building.

b. The height of the flagpole is 8 feet.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

The distance from the building to the flagpole is,

tan35° = 3.5/x.

x = 3.5/0.7.

x = 5 feet.

Now, tan48° = x/5.

x = 5/1.11.

x = 4.5 feet.

Therefore, The height of the flagpole is 4.5 + 3.5 = 8 feet.

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We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added.

Let's assume that there are initially "x" red balls in the box. This means that there are (12 - x) non-red balls in the box.

When 6 more red balls are added, the total number of red balls becomes (x + 6), and the total number of balls in the box becomes (12 + 6) = 18.

We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added. This means that the probability of drawing a red ball before the extra balls were added was:

P(red) = x / 12

And the probability of drawing a red ball after the extra balls were added is:

P(red) = (x + 6) / 18

We are also told that the second probability is twice the first:

(x + 6) / 18 = 2 * (x / 12)

Simplifying this equation, we get:

(x + 6) / 9 = x / 6

Multiplying both sides by 18, we get:

2(x + 6) = 3x

Expanding the left-hand side, we get:

2x + 12 = 3x

Subtracting 2x from both sides, we get:

12 = x

Therefore, there are initially 12 red balls in the box.

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Based on your knowledge of the two data sets described below, would you expect a scatter plot describing the two data sets to have a no correlation.

Based on my knowledge, I would not expect there to be a strong correlation between hourly pay and total number of sick days allowed. These two variables are not directly related to each other and there is no clear reason to expect a positive or negative correlation between them. Therefore, I would expect the scatter plot to show no correlation between the two variables. However, it's worth noting that without actually seeing the data, it's difficult to definitively determine whether there is any correlation present.

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After a period of 32 minutes 128 gallons of oil is moved from a large tank to a small one.

What is the flow rate?

The quantification of bulk fluid movement is called flow measurement. The mass of a material that moves per unit of time is known as the mass flow rate. The amount of fluid moving per unit of time is known as the volumetric flow rate.

Here, we have

Given that the flow rate is recorded at -4 gallons per minute, which is negative.

It means that the oil is flowing in the small tank.

The rate of flow, r is 4 gallons per minute, here work is oil flowing into a tank

Rate of flow, r  = oil flown in a tank/time taken

Given that time, t = 32 minutes

∴ rate of flow × time taken = Oil flown in small tank

⇒ r× t = oil flown in small tank = 4 × 32 = 128 gallons

Hence, after a period of 32 minutes 128 gallons of oil is moved from a large tank to a small one.

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Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note for this question, we will have to make x the subject and solve for x.

The solution of the expression for the value of k is [tex]\dfrac{8}{3^{15}}[/tex].

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

The given expression is,

[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]

The given expression will be solved as below,

[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]

Apply the properties of exponents which say that the number with the same base its exponents will be added.

[tex]\dfrac{3^{16}}{8}\times k = 3[/tex]

Now cross-multiply the number 3 by the ratio of 8 and the 3¹⁶ and solve for the value of k,

[tex]k = \dfrac{8}{3^{15}}[/tex]

Therefore, the value of k will be calculated as the ratio  [tex]\dfrac{8}{3^{15}}[/tex].

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The simplified ratios are shown below:

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

We have ratios

1. 30: 45

= 30/45

= 2 /3

2. 350 : 400

= 350/400

= 7/8

3. 600g : 4 Kg

= 600 / 4000

= 6/ 40

= 3/20

4. 65:91

= 5 / 7

5. 12 cm  : 1 m

= 12 / 100

= 3 /25

6. 3 Km: 50 m

= 3000 / 50

= 60

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The combinations that are more affected by extreme observations are mean and standard deviation, while the combinations that are less affected are median and IQR.

The mean is more affected by extreme observations, because it takes into account the value of every observation in the data set, whereas the median only considers the middle value(s) and is therefore less sensitive to extreme values.

The standard deviation is more affected by extreme observations, because it takes into account the difference between each observation and the mean of the data set. A single extreme value can have a large impact on the mean, and therefore on the standard deviation.

On the other hand, the interquartile range (IQR) is less affected by extreme observations, because it only considers the range of the middle 50% of the data. The median and IQR are often used together to describe a data set that has extreme values or is not normally distributed.

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The population and the sample is option a population: all of the students in the high school sample: the 10 students selected from the front row

In this scenario, the population refers to the entire group of students that the teacher is interested in studying. The population could be all students in the high school, all high school students within the country, all students in the class, or high school students in New York, depending on the research question.

A sample, on the other hand, is a smaller subset of the population that is actually observed or measured. The teacher selected 10 students from the front row as the sample for her study.

It's important to note that the accuracy of the conclusions drawn from a sample depends on how well the sample represents the population. In this case, the teacher may have concluded that the class did extremely well based on the scores reported by the 10 students in the front row. However, it's possible that the front row students are not representative of the entire class or the entire population, which could lead to inaccurate conclusions.

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For the given inequality, the values of u are:

We want to see which ones of the values are solutions of the inequality:

u ≤ 10

So u can be smaller than 10, or equal to 10.

For example, for the irst case u = 8.

8  ≤ 10

This is true, because 8 is smaller than 10.

Then:

u = 8 is a solution.

u = 4 is a solution.

u = 10 is a solution.

u = 13 is not a solution.

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