Solve the inequality below for z.
5z+2>3z-14

The rate of change of the volume of the sphere is 100,530.96 mm^3/s

How to calculate rate of change of the volume of the sphere?

Given,

radius = r = 80 / 2 = 40 mm

rate of change radius = \(\frac{dr}{dt}\) = 5 mm/s

Formula to calculate volume of the sphere is

\(V = \frac{4}{3}\pi r^{3}\)

Differentiating the volume formula and we get new formula to calculate rate of change of the volume.

\(\frac{dV}{dt} = \frac{4}{3}\pi 3r^{2}\frac{dr}{dt}\)

Simplify to

\(\frac{dV}{dt} = 4\pi r^{2}\frac{dr}{dt}\)

Now, we put the given value to formula and calculate it

\(\frac{dV}{dt} = 4\pi (40)^{2}(5)\)

\(\frac{dV}{dt} = 100,530.96\) mm^3/s

Thus, the rate of change of the volume of the sphere is 100,530.96 mm^3/s

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Answer:

ASA postulate

Step-by-step explanation:

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.

What is coefficient of determination?

The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.

R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.

R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.

You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:

Dots represent the observations.

The line of best fit, or predictions of the model, is displayed as a black line.

Purple lines represent the deviations (the residuals) between the data and their expected values.

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Given:

A synthetic division problem.

To find:

The missing number it in the given synthetic division problem.

Solution:

The given synthetic division problem is:

\(3|\overline{3\quad -2\quad 2\quad 4}\\\)

           \(\quad 6\quad 8\quad 20\\\)

     \(\overline{3\quad 4\quad ?\quad 24}\)

In synthetic division, we need to add first and second row to get the bottom row.

\(3+0=3\)

\(-2+6=4\)

\(4+20=24\)

Similarly,

\(2+8=10\)

Therefore, the missing value in the given synthetic problem is 10. Hence, the correct option is C.

Part A:

(26)x = 1

Solve for x by dividing both sides by 26:

X = 1/26

part B:

(50)x = 1

Solve for x by dividing both sides by 50:

X = 1/50

\(\\ \rm\Rrightarrow 26x=1\)

\(\\ \rm\Rrightarrow x=1/26\)

#B

\(\\ \rm\Rrightarrow 50x=1\)

\(\\ \rm\Rrightarrow x=1/50=0.02\)

By applying the number line concept, it can be concluded that option D (4 - 3 - 5 = -4) is not illustrated by the number line.

Number line is a line that is used to represent numbers. Each point on the number axis corresponds to a number. The number axis is also known as the number axis.

When analyzing a number line, we can use the points on the number axis to determine the number sentence that it illustrates.

For example, if there are two points on the number axis that are labeled 2 and 5, the number sentence that the number line illustrates could be 2 + 3 = 5.

Option D (4 - 3 - 5 = -4) describes number 4 moving 3 steps to the left (-3) and then moving 5 more steps to the left (-5). However, the number axis illustrated number 4 moving 5 steps to the left (-5) and then moving 3 more steps to the left (-3).

Therefore option D is not illustrated by the number line.

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Find the full question attached.

c). The entities on which data are collected are called elements.

Data collection is a process of gathering information from different sources which is later used for analysis and interpretation. Data is usually collected from elements, which are individual units like people, organizations, or any other physical or virtual entity.

Each element has a set of characteristics or attributes which are collected to form the data. For example, if data is being collected from people, the attributes would include age, gender, occupation, income, etc. This data is then collected and stored in some form that can be used for further analysis.

Data can also be collected from populations, which are a collection of elements or a group of elements with certain features in common. In this case, the data collected is the average of all the elements in the population, rather than data from individual elements.

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Answer:

72%

Hope this helps

Answer:

c. is the correct answer

Answer: 7 and 8

Step-by-step explanation:

Square root and squared cancel out

Answer:

a=7

b=32

Step-by-step explanation:

The first one (a) is 7 because if you square a square root, you get the number inside the root. Also, technically a square root has an exponent of (1/2) so when you have a power-to-a-power (power rule of exponents) you multiply the exponents. So (\(7^{1/2}\))^2 is 7.

For (b) you have to take it in two parts. Square the square root and you get 2. Square the 4 in front, you get 16. Multiply those two numbers (16 and 2) together and you get 32.

Edit: Check on your calculator, you get the same answers I got! :)

Answer:

ASA

Step-by-step explanation:

Because QR bisects ∠PQS, ∠PQR ≈ ∠SQR

QR = QR

It is given that ∠ PRQ ≈ ∠SRQ

One-half of the dogs in each shelter are between the weights represented by the first and third quartiles, which are approximately 20-55 pounds for the first shelter and 25-65 pounds for the second shelter, respectively.

A box plot is a visual representation of a set of data that shows the median, quartiles, and outliers of the data. The box represents the middle 50% of the data, with the bottom and top edges of the box representing the first and third quartiles, respectively. The line inside the box represents the median, or the middle value of the data set. The "whiskers" extend from the edges of the box to the minimum and maximum values of the data set, but outliers beyond the whiskers are represented as individual points.

Now, let's look at the two box plots showing the weights of dogs in two different animal shelters. One-half of the dogs in each shelter are between the first and third quartiles, which are represented by the edges of the box in each plot.

If we take the first box plot, we can see that the first quartile is approximately 20 pounds and the third quartile is approximately 55 pounds. Therefore, one-half of the dogs in this shelter weigh between 20 and 55 pounds.

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it is a scalene and a right angled triangle

The solution set of the quadratic inequality is (-1,5)

What is Quadratic inequality?

Inequalities can take many various forms, just like equations, one of which is the quadratic inequality.

A second-degree equation with a quadratic inequality substitutes an inequality sign for an equal sign.

The two roots are always provided in the answers to quadratic inequality. Different types of roots may exist, and discriminating between them is possible (b2 – 4ac).

The following are the quadratic inequalities' generic forms:

ax2 + bx + c < 0

ax2 + bx + c ≤ 0

ax2 + bx + c > 0

ax2 + bx + c >= 0

According to the given question

-a^2 + 4a + 7 > 2

-a^2 + 4a + 5 >0

multiplying with - 1

a^2 -4a -5 < 0

a^2 - 5a + a - 5 < 0

a(a-5) + 1(a-5) < 0

(a+1)(a-5) < 0

a<-1 & a< 5

a is in between -1 and 5

(-1,5)

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You did not post enough information.

Answer:

D) x=16 and x=-16

Step-by-step explanation:

D) x=16 and x=-16

If you replace x with either one of them and then take the absolute value, you would have 8.

Answer: There were 78 red apples at the party.

Step-by-step explanation:

This situation can be represented by the equation  

x + 3x + 2(3x) = 130    where x is the number of green apples, 3x is the number of  yellow apples and 2(3x) is the number  of red apples.

Now solve for x

x +3x +2(3x) =130

4x + 6x = 130

10x  = 130

x =  13  

Now we know that x is 13 so put it into the expression for red apples and solve for the actual number of red apples.

2 * (3*13)  = ?

2 * 39 = 78  

Answer:

A.) Angle CAD

Step-by-step explanation:

Hope this helps! :)

Answer:

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\huge\textbf{Equation:}\)

\(\mathbf{5(2x - 8) + 15 = 15}\)

\(\huge\textbf{Solving for the equation:}\)

\(\mathbf{5(2x - 8) + 15 = 15}\)

\(\huge\textbf{Distribute 5 within the parentheses: }\)

\(\mathbf{5(2x) + 5(-8) + 15 = 15}\)

\(\mathbf{10x - 40 + 15 = 15}\)

\(\huge\textbf{Combine the like terms:}\)

\(\mathbf{10x + (-40 + 15) = 15}\)

\(\mathbf{10x - 25 = 15}\)

\(\huge\textbf{Add 5 to both sides:}\)

\(\mathbf{10x - 25 + 25 = 15 + 25}\)

\(\huge\textbf{Simplify it:}\)

\(\mathbf{10x = 15 + 25}\)

\(\mathbf{10x = 40}\)

\(\huge\textbf{Divide 10 to both sides:}\)

\(\mathbf{\dfrac{10x}{10} = \dfrac{40}{10}}\)

\(\huge\textbf{Simplify it:}\)

\(\mathbf{x = \dfrac{40}{10}}\)

\(\mathbf{x = 40 \div 10}\)

\(\mathbf{x = 4}\)

\(\huge\textbf{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{x = 4}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

A. only 4

Step-by-step explanation:

Therefore, After 20 minutes, there are approximately 11.9 kg (rounded to one decimal place) of salt in the tank.

To solve this problem, we need to consider the rate of change of the amount of salt in the tank over time.

(a) Let's denote the amount of salt in the tank after t minutes as y (in kg). We can set up a differential equation to represent the rate of change of salt:

dy/dt = (rate of salt in) - (rate of salt out)

The rate of salt in is given by the concentration of salt in the incoming water (0 kg/L) multiplied by the rate at which water enters the tank (90 L/min). Therefore, the rate of salt in is 0 kg/L * 90 L/min = 0 kg/min.

The rate of salt out is given by the concentration of salt in the tank (y kg/9000 L) multiplied by the rate at which water leaves the tank (90 L/min). Therefore, the rate of salt out is (y/9000) kg/min.

Setting up the differential equation:

dy/dt = 0 - (y/9000)

dy/dt + (1/9000)y = 0

This is a first-order linear homogeneous differential equation. We can solve it by separation of variables:

dy/y = -(1/9000)dt

Integrating both sides:

ln|y| = -(1/9000)t + C

Solving for y:

y = Ce^(-t/9000)

To find the particular solution, we need an initial condition. We know that at t = 0, y = 12 kg (the initial amount of salt in the tank). Substituting these values into the equation:

12 = Ce^(0/9000)

12 = Ce^0

12 = C

Therefore, the particular solution is:

y = 12e^(-t/9000)

(b) To find the amount of salt in the tank after 20 minutes, we substitute t = 20 into the particular solution:

y = 12e^(-20/9000)

y ≈ 11.8767 kg (rounded to one decimal place)

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Answer:

The points P, Q, R and S all lie on the same line segment, in that order, such that the ratio of PQ : QR: RS is equal to 4:2:1.

Step-by-step explanation:

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Answer:The value of the digit in the hundredths place is 10 times as great as the value of the digit in the tenths place.

Explained: The model shows that your number is 0.11

We have to find what we can multiply to become the 1 in the tenths place. Since they are the same number but in different places, we just multiply it by 10 to change the value.

So, if you multiply 10 by the 1 in the hundredths place, it will get you to the 1 in the tenths place.

♡Hope it helps♡

The standard matrix of a linear transformation T can be found by using the formula A = [T(e1) T(e2) ... T(en)], where A is the standard matrix, e1, e2, ..., en are the columns of the identity matrix, and T(e1), T(e2), ..., T(en) are the images of the identity matrix columns under the transformation T.

1. For the first transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(3,1,3,1) (-5,2,0,0)] = [[3 -5] [1 2] [3 0] [1 0]]. Therefore, the standard matrix of T is [[3 -5] [1 2] [3 0] [1 0]].

2. For the second transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2) T(e3)] = [(1,3) (4,-7) (-5,4)] = [[1 4 -5] [3 -7 4]]. Therefore, the standard matrix of T is [[1 4 -5] [3 -7 4]].

3. For the third transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [cos(31/2) -sin(31/2) sin(31/2) cos(31/2)], where cos(31/2) and sin(31/2) are the cosine and sine of 31/2 radians, respectively. Therefore, the standard matrix of T is [cos(31/2) -sin(31/2) sin(31/2) cos(31/2)].

4. For the fourth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [cos(-1/4) -sin(-1/4) sin(-1/4) cos(-1/4)], where cos(-1/4) and sin(-1/4) are the cosine and sine of -1/4 radians, respectively. Therefore, the standard matrix of T is [cos(-1/4) -sin(-1/4) sin(-1/4) cos(-1/4)].

5. For the fifth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(1,0) (2,1)] = [[1 2] [0 1]]. Therefore, the standard matrix of T is [[1 2] [0 1]].

6. For the sixth transformation, the standard matrix of T can be found by using the formula A = [T(e1) T(e2)] = [(1,0) (3,1)] = [[1 3] [0 1]]. Therefore, the standard matrix of T is [[1 3] [0 1]].

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Answer:

36km/h

hope this helps!

Answer:

h(g(f(x))) = (-8)x^2+(-40)x+(-50).

Step-by-step explanation:

We have:

h(x) = -2x

g(x) = x^2

f(x) = 2x + 5

So, we can replace the respective value:

h(g(f(x)))

first substituting the value of f(x) in x of g(x).

h(g(2x + 5))

second, substituting the value of g(x) in x of h(x).

h((2x + 5)^2)

expanding value using the formula (a+b)^2=a^2+2ab+b^2

h(4x^2+20x+25)

Thirdly, substituting the value of h(x) in x of h(x).

-2(4x^2+20x+25)

opening bracket

-8x^2-40x-50

Therefore, h(g(f(x))) = -8x^2-40x-50.