Match the Vocab Word to the definition.

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Question 3 options:

If a = b, and c ≠ 0, then a/c = b/c


If a = b, then a + c = b + c


If a > b, and c > 0, then a/c > b/c
If a > b, and c < 0, then a/c < b/c

If a > b, then a - c > b – c


If a = b, then c ∙ a = c ∙ b


If a > b, and c > 0, then c ∙ a > c ∙ b
If a > b, and c < 0, then c ∙ a < c ∙ b

If a = b, then a - c = b - c


If a > b, then a + c > b + c

1.
Addition Property of Equality

2.
Subtraction Property of Equality

3.
Multiplication Property of Equality

4.
Division Property of Equality

5.
Addition Property of Order

6.
Subtraction Property of Order

7.
Multiplication Property of Order

8.
Division Property of Order

The function f(x) = x³ - 7x + 1 for the given f''(x) = 6x, f'(-3) = 20 and f(-3) = -5. By using the antiderivative formula, the required function is evaluated.

The antiderivative formula for indefinite integrals is

\(\int f'(x)dx = f(x) + c\)

or we can also write this as

\(\int f^n(x)dx = f^{n-1} + c\)

It is given that,

f''(x) = 6x, f'(-3) = 20, f(-3) = -5

Then, by the antiderivative formula, we can write

\(\int f''(x)dx = f'(x) + c\) ...(1)

On substituting, we get

\(\int f''(x)dx = \int 6x dx = 6\int xdx\)

Since we have the formula for the indefinite integral, \(\int x^n dx = \frac{x^{n+1}}{n+1}+c\), we get

\(\int f''(x)dx = 6(\frac{x^{1+1}}{1+1})+c\)

⇒ \(\int f''(x)dx = 6(\frac{x^2}{2})+c=3x^2+c\)

So, from (1), we get f'(x) = 3x² + c

But we have f'(-3) = 20. So, on substituting x = -3 in the above function f'(x), we get

f'(x) = 3x² + c

⇒ f'(-3) = 3(-3)² + c

⇒ 20 = 3(9) + c

⇒ 20 - 27 = c

∴ c = -7

So, the second derivative function is f'(x) = 3x² - 7.

From the antiderivative expression, we can write

\(\int f'(x)dx = f(x) + c\) ...(2)

On substituting f'(x) in the above integral we get

\(\int f'(x) dx = \int (3x^2 +-7)dx\)

⇒ \(\int f'(x)dx = 3\int x^2dx -7\int dx + c\)

⇒ \(\int f'(x) dx = 3(\frac{x^3}{3})-7x+c\)

⇒ \(\int f'(x) dx = x^3 - 7x + c\)

From (2), we can write

f(x) = x³ - 7x + c

But we have f(-3) = -5;

Then,

f(-3) = (-3)^3 - 7(-3) + c

⇒ -5 = -27 + 21 + c

⇒ -5 = -6 + c

∴ c = -5 + 6 = 1

Thus, the function f(x) = x³ - 7x + 1.

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Answer:

S(-3,7)

Step-by-step explanation:

Rise/Run

M(1,4) R(5,1)

1+run=5        4+rise=1

run=4              rise= -3

1-4= -3       4+3=7

the coefficient of determination states that not much of the variability in the dependent variable is explained by the model: b. False.

The coefficient of determination, also known as R-squared, is a statistical measure that represents the proportion of the variance for a dependent variable that can be explained by an independent variable or variables in a regression model. A higher R-squared value (closer to 1) indicates that a greater proportion of the variability in the dependent variable is explained by the model, while a lower R-squared value (closer to 0) means that not much of the variability is explained by the model.

The statement is false because the coefficient of determination actually indicates the extent to which the variability in the dependent variable is explained by the model. A low R-squared value represents less variability explained, whereas a high R-squared value represents more variability explained by the model.

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The answer to the question is (b) false. The coefficient of determination, also known as R-squared, is a statistical measure that indicates how well the regression model fits the observed data.

Coefficient of determination represents the proportion of variability in the dependent variable that is explained by the independent variables in the model.

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Answer:

10x^2y

Step-by-step explanation:

If I'm correct im sure I'd be 41

If you drove a bus with 43 people on board from Chicago and stopped at Pittsburgh. the bus driver is 41 old.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

If you drove a bus with 43 people on board from Chicago and stopped at Pittsburgh.

To pick up 7 more people and drop off 5,

So, 43 + 7

= 50 -5

= 45

then at Cleveland to pick up 4 more people and drop off 8, and arrive at Philadelphia 20 hours later.

= 45 + 4

= 49 - 8

= 41

Therefore, the bus driver is 41 old.

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Answer:

Below

Step-by-step explanation:

Radians =  degrees * pi /180

Radians * 180/pi   =  degrees

While a large number of bins can generate noise and obscure the underlying pattern, a limited number of bins can oversimplify the distribution and conceal significant characteristics equation  

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.

Depending on the data and the goal of the presentation, a histogram's ideal number of bins will vary. Nonetheless, as a rule of thumb, the square root of the total number of data points may be used to approximate the number of bins.

In this instance, we have 56 bits of data, and 56 squared is around 7.5. In order to give the histogram a solid foundation, we can start with a range of 7-8 bins.

It's crucial to keep in mind, though, that changing the number of bins might have an effect on how the data are interpreted. While a large number of bins can generate noise and obscure the underlying pattern, a limited number of bins can oversimplify the distribution and conceal significant characteristics.

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Answer:

I have no idea because I can not see angle BCA

Step-by-step explanation:

Answer:

Um, there wasnt a picture added, you can post the question again with an imagine so we can see the angle :)

I'd love to help so let me know if you post it again and I'll take a look

Step-by-step explanation:

Answer: This should be your answer D. 1

The limit of the sequence (1) {2}, (2) {(-1)^n}, and (3) {n sin(n)}, converges to DNE (does not exist) or the sequence diverges. The limit of the sequence (4) {sin(nπ)} is undefined, as it oscillates between -1 and 1.

In the case of sequence (1) {2}, the limit is a constant value, and the sequence converges to that value. However, in the case of sequence (2) {(-1)^n}, the sequence oscillates between -1 and 1, and there is no single value that it approaches as n tends to infinity. Therefore, the limit does not exist, and the sequence diverges.

Sequence (3) {n sin(n)} also does not have a limit as n tends to infinity. The term n sin(n) oscillates between positive and negative values without approaching a specific value. Hence, the limit of this sequence is DNE, and it diverges.

In the case of sequence (4) {sin(nπ)}, the term sin(nπ) oscillates between -1 and 1 as n varies. Since there is no convergence to a specific value, the limit of this sequence is undefined.

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Answer & step-by-step explanation:

Convex: Triangle, Square, Pentagon. (Has to be equal sided and angled)

Non-Convex: Draw a weird shape, such as a deformed star, a 5 sided shape with no equal sides, such as these listed below:

Answer:

i think das a pineapple

Step-by-step explanation:

Answer:

22.5552m to 22.86m

this is the answer of ur question

Answer:

4^-10

Step-by-step explanation:

(4^-2)^5

4^-2 x 5

= 4^-10

hope this helped have fun doing school haha

Answer:

\(\frac{1}{32768}\)

Step-by-step explanation:

\((4^{-2})^{5}\)

\((\frac{1}{4^{2} }) ^{5}\)

\((\frac{1}{8})^{5}\)

\(\frac{1}{32768}\)

Let A(t) be the number of grams of salt in the tank at time t. At any time t, let x(t) be the number of liters of brine in the tank.

Initially, there are 20 grams of salt in 120 liters of fluid, so the concentration of salt is 20/120 = 1/6 g/L.

When x liters of brine are added, the amount of salt in the tank increases by x/6 grams, since the concentration of the brine is 1 g/L.

Therefore, we have the differential equation:

dA/dt = (1/6) * 4 - (1/6) * (A / (x + 120)) * 4

The first term on the right-hand side represents the increase in the amount of salt due to the addition of brine, and the second term represents the decrease in concentration due to the removal of fluid.

A(t) = (40/3) * (1 - e^(-t/30)) for t >= 0

Therefore, the number of grams of salt in the tank at time t is A(t) = (40/3) * (1 - e^(-t/30)) g.

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The probability of drawing a green or red marble from the bag is 0.4 or 40%.

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

To find the probability of drawing a green or red marble from the bag,

we need to calculate the number of favorable outcomes (marbles that are either green or red) and divide it by the total number of possible outcomes (all the marbles in the bag).

Given the information provided, we can determine the number of green or red marbles as follows:

Small marbles: There are 3 green and 2 red marbles.

Big marbles: There are 2 green and 1 red marble.

Therefore, the total number of green or red marbles is: 3 + 2 + 2 + 1 = 8.

The bag contains a total of 20 marbles, so the probability can be calculated as:

P(green or red) = (Number of green or red marbles) / (Total number of marbles)

P(green or red) = 8 / 20

P(green or red) = 0.4

Hence, the probability of drawing a green or red marble from the bag is 0.4 or 40%.

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Answer:

1:1

Step-by-step explanation:

The ratio from the initial figure PQ: QR is 1:1 because the figure is a square.

The ratio of P'Q': Q'R' is still 1:1 because even if we dilated the figure we actually compare the sides P'Q' to Q'R' that had the proportions preserve.

Answer:

a - 8

Step-by-step explanation:

1/2 a - 4

if we scale both numbers by the same factor, we will be creating an equivalent expression.

So, let's say we multiply the equation by 2.

1/2 a (2) = 1 a = a

-4 (2) = -8

One equivalent expression would be

a - 8

[If you want to test this out, try plugging in any number for a. For example, if you plug in 10...

1/2 of 10 = 5, 5 - 4 = 1

1 times 10 = 10, 10 - 8 = 2

These answers are the same scaled as the original equation, the answer for the first expression is multiplied by 2 to get the second expression]

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer: X= -10, and X=2

Step-by-step explanation:

Answer:

X=-10 and x=2

Step-by-step explanation: so the answers would be A. And D.

The given finite sequence is: -5, -15, -25.

This sequence is related to arithmetic sequence. An arithmetic sequence is a sequence where the difference between any two consecutive terms is constant. To find the related arithmetic sequence we need to determine the common difference d for the sequence.

Here the common difference d = a2 - a1, where a1 is the first term and a2 is the second term.

So d = -15 - (-5)

= -15 + 5

= -10.

The arithmetic sequence for the given sequence is:

a1 = -5,

a2 = -15,

a3 = -25

.

.

.

.

an = -5 - (n - 1) × 10

So, the n-th term for the sequence -5, -15, -25 is -5 - (n - 1) × 10.

The given finite sequence is -5, -15, -25. This is related to arithmetic sequence. In an arithmetic sequence, the difference between any two consecutive terms is constant. The common difference d for this sequence is found by subtracting the second term from the first term. Here the common difference d = a2 - a1, where a1 is the first term and a2 is the second term.

Thus d = -15 - (-5)

= -15 + 5

= -10.

Now, to find the arithmetic sequence, we can use the following formula: an = a1 + (n - 1)d, where a1 is the first term and d is the common difference. Here the first term is -5 and the common difference is -10, we can write the nth term of the sequence as

an = -5 - (n - 1) × 10

Therefore, the arithmetic sequence for the given sequence is: -5, -15, -25, -35, -45,.... etc

Thus, we have found the related arithmetic sequence for the finite sequence -5, -15, -25.

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Data set (ii) because it has two entries that are far from the mean. the deviations from the mean are smaller,

The sample standard deviation measures the dispersion or spread of data points in a data set. To determine which data set has the greatest sample standard deviation, we need to consider the distribution of values relative to the mean.

In data set (ii), which has two entries that are far from the mean, the presence of these outliers can significantly increase the sample standard deviation. Outliers are data points that deviate significantly from the majority of the data, and their inclusion in a data set can inflate the standard deviation.

This is because the standard deviation calculates the average distance between each data point and the mean, and outliers contribute to larger distances.

Data set (i), on the other hand, having more entries that are close to the mean, suggests a more concentrated or clustered distribution of values.

When data points are closer to the mean, the deviations from the mean are smaller, resulting in a smaller standard deviation compared to a data set with outliers.

Data set (iii), with more entries that are farther away from the mean, may also have a higher sample standard deviation. However, without specific information about the magnitude of these deviations and the overall distribution of values,

we cannot definitively conclude that data set (iii) has the greatest standard deviation. Therefore, based on the information provided, the data set (ii) with two entries that are far from the mean is likely to have the greatest sample standard deviation.

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a. the equilibrium price is $52 per bushel and the equilibrium quantity is 20 bushels.

b. the new equilibrium price is $42 per bushel and the new equilibrium quantity is 15 bushels.

Equilibrium price and quantity:

The equilibrium is the point where the supply and demand curve intersect each other. The point where the demand and supply curve intersect each other, P and Q determine the equilibrium price and quantity respectively.

The given equations for demand and supply of the bananas in Binghamton are:

P = 92 - 2QP = 12 + 2QThe equilibrium price and quantity can be obtained by equating the demand and supply equations,92 - 2Q = 12 + 2Q⇒ Q = 20P = 92 - 2(20)⇒ P = 52

Therefore, the equilibrium price is $52 per bushel and the equilibrium quantity is 20 bushels.

The given equations for demand and supply of the bananas in Binghamton are:

P = 92 - 2QP = 12 + 2QThe demand for bananas increases due to the National Institutes of Health’s study, which shows that bananas reduce the risk of cancer.

The new demand equation is given by:

P = 132 - 2QAt the original equilibrium price ($52), the quantity demanded exceeds the quantity supplied.

Therefore, there is a shortage.

The shortage can be calculated as follows:

Quantity demanded at equilibrium price (P = $52) = Quantity supplied at equilibrium price (P = $52)Qd = 92 - 2(20) = 52 bushels Qs = 12 + 2(20) = 52 bushels Shortage = Qd - Qs= 52 - 52 = 0

Therefore, the shortage is 0 bushels.

c.  Show graphically.

The new demand equation is given by:

P = 132 - 2QTo find the new equilibrium price and quantity, we need to equate the new demand equation with the original supply equation,P = 12 + 2Q (original supply equation)P = 132 - 2Q (new demand equation)⇒ 12 + 2Q = 132 - 2Q⇒ 4Q = 60⇒ Q = 15P = 12 + 2(15)⇒ P = 42

Therefore, the new equilibrium price is $42 per bushel and the new equilibrium quantity is 15 bushels.

The graphical representation is given below:

Graphical representation of new equilibrium price and quantity.

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If Jason paid $88.50 in tax on a table that cost $1,180, the tax rate (sales tax) is 7.5%.

The tax rate is the percentage that is paid in tax.

For sales tax (consumption tax), the tax rate is fixed, making it a proportional tax rate system.

For income tax, the tax rate follows a progressive tax rate system.  The percentage of tax increases as the taxable income increases.

Some tax rates are said to be retrogressive as the rates reduce with increased taxable income.

The amount of sales tax on the table = $88.50

The cost of the table = $1,180

Tax rate = 7.5% ($88.50/$1,180 x 100)

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Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

Answer:

There are 1084 pupils in that school.

Step-by-step explanation:

If there are 542 girls and boys then you would have to double 542 to get the total number of people. So, there are 1084 people in that school.

Hope this helps!

Answer:

1084

Step-by-step explanation:

542+542

Circumference = pi x diameter

Given circumference: 8pi

Diameter = 8

Correct answer: D) 8 cm

Hope this helps!

Answer:

a). 3a² + 17a - 1

b). 4y (7y-6)

Step-by-step explanation:

in the second question, we find a number that can divide 28 and 24 without a remainder, which is 4

Answer:

x = 124°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , then

x = 180° - (32 + 24)° = 180° - 56° = 124°

Step-by-step explanation:

well if it's 10 meters and 10 you would divide 10 by 10 and get 1 meter letting every girl have 1 meter of ribbon

Answer:

Hi how are you doing Jasmine

The length of segment RS is given as follows:

RS = 24.

The angle addition postulate states that if two or more angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the measures of each of the angles.

The segment RT is the combination of segments RS and ST, hence:

RT = RS + ST.

Hence the length of segment RS is given as follows:

41 = RS + 17

RS = 24.

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