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1.  The average rate of range for 3 to 4 days is -3.9.

2. Approximate rate of range for 3 days is 34.8.

Adding a very small increment, for example, can help us approximate the instantaneous rate of change at x = a.

The instantaneous rate of change is equal to the slope of the tangent line at a given location. The slope of secant lines can be used to calculate the slope at a point as each secant line's "run" gets closer to zero (the slope of the tangent line).

You can find the instantaneous rate of change of a function by computing the derivative at a specific point and then entering the point's x-value.

The speed at which that function changes right now.

IROC = f(a + 0.001) - f(a) / 0.001 f(a) = 0.1

1.

[tex]$$\begin{aligned}& \text { A.R.C }=\frac{\mathrm{A}(4)-\mathrm{A}(3)}{4-3} \\& \mathrm{~A}(4)=100(0.5)^{\frac{4}{15}} \\& \mathrm{~A}(4)=83.12378 \\& \mathrm{~A}(3)=100(0.5)^{\frac{3}{16}} \\& \mathbf{A}(3)=87.05505\end{aligned}$$A. R. C $=\frac{83.12378-87.05505}{1}$$$=-3.93127$$A. R. $\mathrm{C}=-3.9$[/tex]

2. it can be obtained by takibg derivative with respect 't';

[tex]$\mathrm{A}^{\prime}(\mathrm{t})=100\left(\frac{\mathrm{t}}{15}\right)(0.5)^{\left(\frac{t}{15}\right)-1}$\\rate of change in 3 days:$$\begin{aligned}& \mathrm{A}^{\prime}(3)=100\left(\frac{3}{15}\right)(0.5)^{\left(\frac{3}{15}\right)-1} \\& \mathrm{~A}^{\prime}(3)=34.82202\end{aligned}$$Approximate rate of change;$$\mathrm{A}^{\prime}(3) \approx 34.8$$[/tex]

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5x - 3y = 7 is in slope intercept form is y = 5/3x - 7/3

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

You can utilize two different versions of a line's general form to figure out its equation.

These are the formulas:

1) (y - y1) = m (x – x1), the Point-Slope Formula

2) The formula for slope-intercept, y = mx + b

The form you use depends on the information you are provided at the beginning, as the names suggest.

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Answer:

Step-by-step explanation: i can't see the lab top

The derivative of f at (a, b) is the gradient vector [4a - b, -a].

From the question, we have the following parameters that can be used in our computation:

f(x, y) = 2x^2 − xy

The two-variable function f(x, y) = 2x^2 - xy is differentiable at any point (a, b) if its partial derivatives exist and are continuous at that point.

This is represented as

∂f/∂x = 4x - y

∂f/∂y = -x

The derivative of f at (a, b) can be calculated by evaluating the partial derivatives of f at (a, b):

∂f/∂x(a, b) = 4a - b

∂f/∂y(a, b) = -a

Hence, the derivative of f is [4a - b, -a].

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Answer:  -1/10

Step-by-step explanation:

The linear function f with the given values is f(x) = 2x + 2

From the question, we have the following parameters that can be used in our computation:

f(0) = 2 , f(-2) = -2

A linear equation can be represented as

f(x) = mx + c

Substitute the known values in the above equation, so, we have the following representation

m * 0 + c = 2

m * -2  + c = -2

Solving 0 * x + c = 2, we have

c = 2

So, we have

m * -2 + c = -2

This gives

-2 * m + 2 = -2

Evaluate

-2m = -4

Evaluate

m = 2

So, we have

f(x) = 2x + 2

Hence, the function is f(x) = 2x + 2

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Answer:

One can use the formula for a compound annuity

A = (1 - (1 + i)^-n) / i

n = payments = 360 (12/yr * 30 yr)

i - interest rate = .075 / 12 = .00625

The formula tells you what $1 / mo will be worth after 360 mos

A = (1 - 1.00625^-360) / .00625 = (1 - .10362) / .00625

A = 143.02

To have 150,000 after 30 yrs the monthly payment needs to be

150000 / 143.02 = 1048.82

Answer: 5.75pi(yards)

Step-by-step explanation: We know the radius is 3 so the area is 9pi. The shaded area has an angle of 230 and the total angle of a circle is 360. We multiply the area by the fraction of the angle which is 230/360(9pi).

Answer:

I have graphed it and attached an image in the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation: Multiply 20 by 12 and divied 8 that should give u your answer

Answer: 21x + 21

Step-by-step explanation:

Simply multiply 7 to 3x and 3 respectively.

In this problem the statement that the mean is greater than the median is true. So, the correct answer is option(a).

We have a histogram which shows the distribution of the annual hours of commuting delay per traveler for 46 small, medium and urban areas, fewer than one million in population. See the diagram carefully and try to draw the conclusion. The shape of the histogram showing that positive skewed or right skewed distribution since Curve increases fastly and decreases slowly. A positive skewed distribution is a type of distribution where most of the values are concentrated in the left tail of the distribution and the right tail of the distribution is longer. In positive skewed distribution,

i) Mean > Median

ii) (Q₃ - Q₂) > (Q₂ - Q₁)

iii) Sqrt(β₁) >0

Hence, The mean is greater than the median is true.

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Answer:

2/6 +2/6= 4/6 and 4/6 reduced down is 2/3

Step-by-step explanation:

hope this helps

The statements about the functions are true A. f(x) = 1/2ˣ

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

We are given that On a coordinate plane, 2 exponential functions are shown. f (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1.

When evaluated in zero we have:

f(0) = 2(1/2)^0 = 2

So it crosses through the point (0, 2).

And when evaluated in x = 1, then

f(1) = 2(1/2)^1 = 1

Then it also passes through (1, 1).  It goes crosses the y-axis at (0, 14) and goes through (1, 5) and (2, 2).

The answers are A, D, and E

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Answer:a,d,e

Step-by-step explanation:

i took the test

The solution to the radical equation is 2/5

From the question, we have the following radical equation

6y2−22y+16⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√+4=4y

Complete the equation

So, we have the following representation

6√y² − 22y + √16 + 4 = 4y

Evaluate the radicals

The equation becomes

6y - 22y + 4 + 4 = 4y

So, we have

6y - 22y + 8 = 4y

Evaluate the like terms

So, we have the following

20y = 8

Divide both sides by 20

y = 2/5

Hence, the solution is 2/5

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The team loses 20 people/audience with each loss.

The slope formula defines to the formula used to calculate the steepness of a line and determines how much it's inclined. To calculate the slope of the lines, the x and y coordinates of the points lying on the line can be used.

The formula to calculate slope is:

m = (y2 - y1)/(x2 - x1) = Δy/Δx

When the team lost eight games, 295 people attended the next game.

When the team lost 13 games, 199 people attended the next game.

Slope = 295-199/8-13

slope=100/-5

slope=-20

Therefore, the team loses 20 people/audience with each loss.

And the attendance loss is 20 times as great as the number of games lost/losses

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We need to assume the sample was randomly selected because we are making inferences about parameters.

In mathematics, the parameter is a variable for which the range of possible values identifies a collection of distinct cases in a problem. Any equation expressed in terms of parameters is a parametric equation. The general equation of a straight line in slope-intercept form, y = mx+b, in which m and b are parameters, is an example of a parametric equation.

In statistics, the parameter in a function is a variable whose value is sought by means of evidence from samples. The resulting assigned value is the estimate or statistic.

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The required percentage of teachers who teach math but not English is 21%. Option B is correct.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Total teachers = 104
A number of teachers teach math but not English = 22

Percentage = 22 / 104 × 100%
Percentage = 21%

Thus, the required percentage of teachers who teach math but not English is 21%. Option B is correct.

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Answer:

Answer: x > -11

Step-by-step explanation:

3x + 7 > 2x - 4

First, we can simplify the right side of the equation by combining like terms:

3x + 7 > 2x - 4

then we can subtract 2x from both sides of the equation:

3x + 7 - 2x > -4

This gives us:

x+7 > -4

then we can add 4 to both sides of the equation:

x + 7 + 4 > 0

This gives us:

x + 11 > 0

then we can subtract 11 from both sides of the equation:

x + 11 - 11 > 0 - 11

This gives us:

x > -11

so the number is greater than -11.

The given series consists of prime numbers starting from 2. So, the missing term is the prime number after 11, which is 13.

So, None of the above will be the correct answer.

A×(B∩C)=(A×B)∩(A×C)

We have B∩C={1,2,3,4}∩{5,6}=ϕ

∴ L.H.S = A×(B∩C)=A×ϕ=ϕ

A×B={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4)}

A×C={(1,5),(1,6),(2,5),(2,6)}

∴R.H.S.=(A×B)∩(A×C)=ϕ

∴L.H.S=R.H.S

Hence A×(B∩C)=(A×B)∩(A×C)

To verify: A×C is a subset of B×D

A×C={(1,5),(1,6),(2,5),(2,6)}

B×D={(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),

(3,8),(4,5),(4,6),(4,7),(4,8)}

which is 13.

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a) The 95​% confidence interval about μ with n = 26 is given as follows: (109, 117).

b) The 95​% confidence interval about μ with n = 15 is given as follows: (107.5, 118.5).

c) The 90​% confidence interval about μ with n = 26 is given as follows: (109.7, 116.3).

d) The intervals could not have been computed if the population was not normally distributed, as the sample size is less than 30.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The sample mean and standard deviation for this problem are given as follows:

[tex]\overline{x} = 113, s = 10[/tex]

The critical values are given as follows:

The bounds of the interval for item a are given as follows:

The bounds of the interval for item b are given as follows:

The bounds of the interval for item c are given as follows:

The Central Limit Theorem states that the intervals can only be calculated for non-normal populations if the sample size is greater than 30.

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Answer: The distributive property is a property where there is a coefficient/number, that is being multiplied to a group of numbers enclosed in parentheses. The coefficient can be distributed/multiplied to the numbers in the parentheses individually or after solving the expression in it.

Step-by-step explanation:

You can spot when the distributive property is used when you see a number in front of a group of numbers, such as these examples (in bold):

1. 4(5 + 6) = 46 , in this problem you can solve 5+6 before multiplying it by 4, or multiply 4*5 and 4*6 and then add it.

2. 2(x-3) = 12 , in this situation x is the unknown variable so you must distribute the 2 individually, so the result would look like: (2*x) + (2*-3) -> 2x - 6 = 12

Answer: To help you with this problem, I need to know the discount percentage.

Step-by-step explanation:

Solving given algebra problem, value of x is equal to -1. It is the area of mathematics that uses arithmetic to manipulate or operate abstract symbols rather than actual numbers.

Isolate the squared term and the constant term on the opposite sides of the equation to solve quadratic equations using the square root method. After that, take the square root of both sides, plus or minus the side with the constant term.

Given equation,

[tex]12+\sqrt{1-5x} =18\\\sqrt{1-5x}=18-12\\ \sqrt{1-5x}=6\\\\square\\ case1\\1-5x=64x=-1\\case2\\1-5x=-6\\x=7/5[/tex]

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The equation to represented the situation of drop the price of each item $5 at the end of each week until the item sells as used by the manager of the clothing store is

Information given in the problem include

the managers drop the price of each item $5 at the end of each week

until the item sells

let c represent the cost of the item at the beginning

;et x represent the number of weeks

let y represent the cost at the end of each week

The equation is modeled as follows

the present cost c will drop by $5 each week

c - $5x

The cost after the drop that is at the end of the week

y = c - $5x

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Answer:

2x4 is 8

Step-by-step explanation:

4 to times so 4+4 =8 thx

Match the word to its definition or symbol.

1. ∈                                            element

2. { }                                           braces representing a set with no elements

3. C                                            subset

4. {whole numbers]                  finite set

5. ∅                                           symbol for the empty set or null set

6. A set limited by definition - infinite set

7. ∉                                            not an element

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form.

Curly brackets are typically used to represent sets.

Sets with a finite/countable number of members are referred to as finite sets. Due to their ability to count, finite sets are often referred to as countable sets.

A set with an infinite number of elements is one that cannot be numbered. Any set that has no last element is said to be infinite Set

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