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The average rate of change for 3.5 ≤ x ≤ 4 is 2[f(4) - f(3.5)]

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

given:

Interval: 3.5 ≤ x ≤ 4

Now, For average rate

= [f(4) - f(3.5)]/(4 - 3.5)

= 2[f(4) - f(3.5)]

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Answer:

x=102/25 y=9/5

Step-by-step explanation:

Answer: 360 plants

Step-by-step explanation:

90% is equivalent to 0.90.
You multiply 0.90 and get your answer of 360.

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Answer:

A

Step-by-step explanation:

If Monica has $50 dollars to spend on the video arcade, and each game costs $0.25 then we can use an equation that looks something like this:

total = amount of money × cost of one game

50 × 0.25 = 200

Now look at the graphs.

The graph that best matches this equation is A.

The ordered pair that describes the location of Q' is (-3, -1)

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

Point Q = (3, -1)

This point can be represented as

(x, y) = (3, -1)

Also, from the question, we have the transformation to be:

Point Q is reflected over the y-axis

Mathematically, this can be expressed as

(x, y) = (-x, y)

So, we have the following representation

Point Q' = (-3, -1)

Hence, the image is (-3, -1)

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Answer:

[tex]117.8cm ^{2} [/tex]

Step-by-step explanation:

[tex]a = {r}^{2} \theta \: \div 2 \\ = 100 \times 135 \div 2 \\ = 117.8 \: {cm}^{2} [/tex]

The amount that Josephine will be paid is $644.30.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.

In this situation, Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales and she sold $843 worth of goods.

The amount she'll be paid will be:

= $560 + (10% × $843)

= $560 + $84.3

= $644.30

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The time t = 3.4209 will it take for the concentration to reach 350,000 material per millimeter.

In an hour, there are 60 minutes. Divide the number of minutes by 60 to convert it to hours. For instance, 120/60=2 means that 2 hours are equal to 120 minutes.

The millimeter, abbreviated mm in the International System of Units (SI), or millimeter, abbreviated mm in the American spelling, is a unit of length that is one thousandth of a metre long, the SI base unit of length. As a result, a metre is made up of 1000 millimeters.

We are going to use formula

y = a * e ^ (b * t)

a and b are constants and t is for time.

Initially there are 100,000 bacteria, so;

100000 = a * e ^ (b * 0)

100000 = a * 1

a = 100000

given condition is that the concentration doubles every 3 hours so

300000 = a * e ^ (b * 3)

As a equals to 100,000

e ^ (b * 3) = 3

b * 3 = ln 3

b = (ln 3) / 3

b = 0.3662

now we have to find value of the time when concentration of bacteria reaches to 350,000:

350000 = 100000 * (e ^ 0.3662 * t)

3.5 = e ^ 0.3662* t

ln 3.5 = 0.3662* t

t = 1.2527 / 0.3662

t = 3.4209

That is the required value of time

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The linear equation on the graph shown is:

y = (2/3)*x + 4

We can see that we have a linear equation on the graph, remember that a general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

On the graph, we can see that the line intercepts the y-axis at y = 4, then the y-intercept is b = 4

y = a*x + 4

To find the slope we can use another point on the line, for example, we can see that (-6, 0) is also on the line, replacing these values in the linear equation above we will get:

0 = a*-6 + 4

6a = 4

a = 4/6 = 2/3

Thus, the line is:

y = (2/3)*x + 4

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Part a: The significance of the piece-wise function is define.

Part b: r(t) be the total amount of snow in cubic ft. is calulated.

Part c: Total volume of the ice is not removed.

For the given question, the rate function is given as;

f(t) = { 0, 0 ≤ t < 6 ,

       125, 6 ≤ t < 7

       108, 7 ≤ 9  }

Part a: The significance of the piece-wise function is-

Part b: r(t) be the total amount of snow in cubic ft.

Part c: total ice accumulated is;

62.5 ft + 54 ft. = 116.5 cubic ft.

Total volume of the ice accumulated = 367.5 cubic ft.

Thus, no total volume of the ice is not removed.

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Answer: Two dice

Step-by-step explanation:

For the two dice, there are 5 possible: (6, 2);(5, 3);(4, 4);(3, 5);(2, 6)

So two dice, the probability is 5/36 = 30/216

For three dice, the number of favorable cases is 21

The probability is 21/216

So the two dice are more likely

Using an exponential function to represent the exponential decay, it will take approximately 4 weeks to reach 320 gallons

An exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

To solve this problem, we have to write an exponential equation to calculate the exponential decay.

Data;

A = P(1 + r)⁻ˣ

320 = 625(1 + 0.2)⁻ˣ

x = 3.67

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Answer:

I'm pretty sure it would be 3:00

Step-by-step explanation:

I could be wrong tho-

Answer:

Step-by-step explanation: One denominator in the question is 4/5 and another is 1/2. A common denominator would be /10 because it applies to /5 and /2.

The measure of the interior angles of a polygon is determined by the formula ((n - 2)180)/n = interior angle

measure

It needs to be shown that <W = <H by the SAS congruent theorem

The question is added as an attachment

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

The SSS congruent theorem implies that the corresponding sides of the triangles in question and the angles between them are congruent

From the question, we can see that the following corresponding sides on the triangles have the same mark

W O and H O

AO and AO

This implies that these sides are congruent sides

For the triangle to be congruent by SAS, the following sides must also be congruent

Angle W must be congruent to Angle H

Hence, the additional info is <W = <H

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Complete question

To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that____

The probability that the student takes technology given that he is taking Math 8 is 0.075.

What is conditional probability?

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Here, we have

Given:

The probability that a student takes Technology and Math 8 is 0.012.

P(Technology and Math 8) = 0.012

The probability that a student takes Math 8 is 0.16.

P(Math 8) = 0.16

We have to find the probability that a student takes Technology given that the student is taking Math 8

we use conditional probability

P(Technology|Math 8) = P(Technology and Math 8)/P(Math 8)

P = 0.012/0.16

P = 0.075

Hence, the probability that the student takes technology given that he is taking Math 8 is 0.075.

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The equation of the lines is,

1. (4, -1); m = 3 : - y = 3x - 13

2. (-8, 0); m = -4 :- y = -4x - 24

3. (-6, -10); m = 1/6 :- y = -1/6x - 9

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The equation of the lines will be,

y = mx + c

y = 3x + c

-1 = 4 x 3 + c

c = -13

y = 3x - 13

y = mx + c

y = -4x + c

0 = -4 x -8 + c

c = -24

y = -x -24

y = mx + c

y = 1/6x + c

-10 = -1 + c

c = -9

y = -1/6x - 9

Therefore, the equation of the lines is,y = 3x - 13 y = -4x - 24 and y = -1/6x - 9.

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Answer:

It is y = 3/5x - 19/5

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes. Thus, the slope is 3/5x. Plug in -2 as x and solve for the intercept. It ii -19/5.

If each survey has a sample size of 70, a value which falls within the interval where 95% of the sample means occur is: C) 14.96.

In this scenario, the confidence interval at 95% can be represented by this mathematical expression p - E < p < p + E

Based on the parameters provided, we would determine both the lower limit and upper limit for the interval where 95% of the sample means occur as follows;

Lower limit = 15 - 1.88/√70

Lower limit = 15 - 0.23

Lower limit = 14.77

For the upper limit, we have:

Upper limit = 15 + 1.88/√70

Upper limit = 15 + 0.23

Upper limit = 15.23

For 95% of the sample means to occur, the confidence interval is given by;

Confidence interval = (14.77, 15.23)

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Answer:

y = -8x + 23

Step-by-step explanation:

8y=x-16

we need to turn this into slope-intercept form by dividing 8 on both sides

y = x/8 - 2

to make a line perpendicular from another, we must make sure the slope is the negative reciprocal of the original line.

Right now, it's the same as the original. To make it a negative reciprocal, switch the places of the denominator and numerator and flip the signs

-8x is the negative reciprocal of x/8

Does it go through (4,-9)? No.

To make sure it goes through 4,-9, we change it's y-intercept.

Plug in the coordinate given (4,-9) in the y = -8x + b ( we removed -2 since it's not the right answer.

y = -8x + b

(-9) = -8(4) + b

-9 = -32 + b

-9 +32= -32 + b +32

23 = b

plug in b and we get our answer

y = -8x + 23

Answer:

106

Step-by-step explanation:

A linear pair adds to 180

180 - 74 = 106

After solving the given equation for c, we know that the value of c is (A) -56.

Equivalent systems refer to sets of equations with the same solution.

We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.

So, we have the equation:

-5 = 9+(c/4)

Now, solve for the subject c as follows:

-5 = 9+(c/4)

-5 -9 = (c/4)

-14 = c/4

c = -14*4

c = -56

Therefore, after solving the given equation for c, we know that the value of c is (A) -56.

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Using elimination method, the solution to the system of equation is as follows:

x = 2 and y = -5

System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's use elimination method to solve the system of equation as follows:

7x + 3y = - 1

4x + y = 3

multiply equation(ii) by 3

Hence,

7x + 3y = - 1

12x + 3y = 9

subtract equation(i) from equation(ii)

5x  = 10

x = 10 / 5

x = 2

Let's find y

7x + 3y = - 1

7(2) + 3y = -1

14 + 3y = -1

3y = -15

y = -15 / 3

y = -5

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Answer:

Step-by-step explanation:

(0, 2) (4, 0)

(0 - 2)/(4 - 0) = -2/4 = -1/2

y - 2 = -1/2(x - 0)

y - 2 = -1/2x + 0

y = -1/2x + 2

Answer:

Step-by-step explanation:

y = -2x + 8

perp.: 1/2

y + 5 = 1/2(x - 8)

y + 5 = 1/2x - 4

y = 1/2x - 9

Min needs to gain 80 marks to raise her average to 75.

Average number is got from sum of all numbers divided by the number of values.

Average value is used to compare among different quantities of same terms.

given, Min receives an average score 70 from 5 math test.

let she needs to gain X in her 6th test to obtain an average of 75 from the total six test.

she gained average 70 from 5 test

if average is 75 then

75 = (X+ 70)/2

X=80

hence, in the 6th test she needs to gain 80 marks.

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