Finding slope given the graph of a line on a grid
Find the slope of the line graphed below.

5 x 3²⁴  bacteria will there be after one day.

What is exponents?

Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".

Consider what is actually happening in the question.

You begin with 5 bacteria, and after 1 hour it has tripled so you now have

5x 3=15.

Next hour, it triples again so you now have 5 x 3 x 3=45

You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 3⁴  means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).

Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:

n x 324 where n is the number of bacteria you begin with.

Since you begin with 1 bacteria, the solution is 5 x 3²⁴.

Hence 5 x 3²⁴  bacteria will there be after one day.

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Average rate of change for given function from x=4 to x=10 is -0.66

Average rate of change can be defined as slope of function between two fixed values of x. It can also be defined as change in function per unit or we can say as an average.

At x = 4 we have y = 8

At x = 10 we have y = 4

As y is nothing but value of function f(x) at x.

So, we can write them as f(4) = 8 and f(10) = 4

Average rate of change (from x = a to x=b) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Using above formula of average rate of change and substituting for x=4 to x=10, we get

Average rate of change = [tex]\frac{4-8}{10-4} = \frac{-2}{3}[/tex]

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Answer:

y=2/3x-2

Step-by-step explanation:

The equation is y = mx + b and m is the slope. You were already given the slope and you were even given a point. All you have to do is graph the point and use the slope until it intercepts the y-axis.

1. Plot the point (9,-8)

2. Go up 2, left 3 spots until the line hits the y-axis (the vertical one)

3. That point is what b will be equal to in y = mx + b

OR you can convert a point-slope equation into slope intercept

1. The formula for point slope is y – y1 = m(x – x1)

2. Plug in the given numbers and it will look like this: y+8=2/3(x+8)

3. Do the math and get a solution of y=2/3x-2

Answer:

see explanation

Step-by-step explanation:

the mistake is that a zero should be inserted to indicate the x - term

the standard form of a polynomial of degree 3 is

ax³ + bx² + cx + d

given

[tex]\frac{3m^3-2m^2-150}{m-4}[/tex]

there is no m- term in the numerator so a zero has to be inserted in its place, that is

4 | 3   - 2   0  - 150

     ↓    12   40  160

   ---------------------------

     3   10  40    10

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6500\\ P=\textit{original amount deposited}\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ t=years\dotfill &16 \end{cases} \\\\\\ 6500=Pe^{0.0475\cdot 16} \implies \cfrac{6500}{e^{0.0475\cdot 16}}=P\implies 3039.83\approx P[/tex]

Answer:

A. No

B. Yes

C. No

Step-by-step explanation: To determine if each pair is a solution to the equation, substitute the x and y variables in the pairs for the corresponding variables in the equation. If the left and right sides are equal once you solve, you will know that the pair is a solution,

(9,1)   2(9)+7(1)=16    18+7=16    25=16    No

(8,0)    2(8)+7(0)=16    16+0=16    16=16    Yes

(0,0)    2(0)+7(0)=16    0+0=16    0=16    No

Answer:  D. A'(-5,10)   B'(-1,10)   C'(-1,7)   D'(-5,6)

Step-by-step explanation:

A(-5,5)  B(-1,5)  C(-1,2)  D(-5,1)

A'(-5,5+5)   B'(-1,5+5)   C'(-1,2+5)   D'(-5,1+5)

A'(-5,10)   B'(-1,10)   C'(-1,7)   D'(-5,6)

The value of y when x = 2 is 16/25 and when z = 6 is 200/36

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

Given that, Y varies directly as x and inversely as the square of z and y=8 when x=25

That means, y ∝ x and y ∝ 1/z²

Let  constant of proportionality be k, then,

y = kx and y = k/z²

Now, finding k, when x = 25

8 = k25

k = 8/25

For x = 2,

y = 8/25X2

y = 16/25

Finding k when y = 5

8 = y/25

y = 200

Now, when z = 6

y = 200/36

Hence,  The value of y when x = 2 is 16/25 and when z = 6 is 200/36

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Step-by-step explanation:

The expression 5x + 6y - 3x is equivalent to:

2x + 6y

This is because 5x and -3x can be combined by adding them together, which gives 2x.

The expression 5x + 6y - 3x is also equivalent to:

x + 6y - 3x

This is because 5x and -3x can be combined by adding them together, which gives x.

However, the expression 5x + 6y - 3x is not equivalent to:

2x - 3y

This is because the coefficient of the y term is 6, not -3.

The expression 5x + 6y - 3x is also not equivalent to:

x + y

This is because the coefficient of the y term is 6, not 1.

The three decimal places are :28.288< μ < 43.712

degree of freedom = 17-1 = 16

critical t value = 2.1199

lower limit = 36-2.1199*15/sqrt(17) = 28.288

Upper limit = 36+2.1199*15/sqrt(17) = 43.712

Answer:28.288< μ < 43.712

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The ball will rise 15 cm height on the right-hand incline when friction is discounted.

The force preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction.

Given that,

The height of the ball  = 15 cm

Since, the friction force is not counted here, this implies that there will be no friction force to stop the object.

The rise of the height on the right-hand incline will be same to the initial height.

Therefore, the ball will rise 15 cm height on the right-hand incline.

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Using the distance formula, [tex]JP=\sqrt{(0-4)^2+(1-(-2))^2}=\boxed{5}[/tex]

The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.

Hence, The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.

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Answer:

Not possible with given

Step-by-step explanation:

on dividing the given term we get

12.2105.

The graph that could be used to determine the possible variance levels that would result in an acceptable height is the third graph.

Fron the information, the required model height for the designed clothes should be less than or equal to 5 feet 10 inches. In this case, the equation for the variance in height is of the straight line form;

y = m·x + c

Where x is the height  in inches

Given that the maximum height allowable is 70 inches, when x = 0 we have;

y = m·0 + c = 70

Therefore, c = 70

Also when the variance = 0 the maximum height should be 70 which gives the x and y-intercepts as 70 and 70 respectively such that m = 1

The equation becomes;

y ≤ x + 70

Also when x > 70, we have y ≤ -x + 70   with a slope of -1

In this case, to graph an inequality, we will need to shade the area of interest which in this case of ≤ is on the lower side of the solid line.

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When Bobby takes out a mortgage for $30 years at 4% interest with $835.48 in monthly payments, the total principal loan amount is $255644.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Here,

The interest paid per month=$835.48

Interest paid in 30 years=835.48*12*30

Rate of interest=4%=0.04

Time=30 years

Principal=I/RT

=(835.48*30*12)/(0.04*30)

=$250644

The principal loan amount is $250644 when Bobby takes out a mortgage for 30 years at an interest rate of 4% and his monthly repayments are $835.48.

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Choices B, C and D are required answer choices.

What is an isosceles triangle?

Any triangle with two equal sides and angles with equal measures on opposite sides is said to be an isosceles.

Based on the given diagram,

BD is perpendicular to AC because the given angle D is 90 degrees.

And, AD = DC (Given)

or, 4x = x + 9

or, 4x -x = 9

or, 3x = 9

or, x = 3

Then, AD = 4x = 4*3 = 12

And, AB = BC

So, the two sides of a given triangle are equal to each other.

Then, triangle ABC is an isosceles triangle.

Based on the above calculation and data, we can conclude that

Hence, Choices B, C and D are required answer choices.

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Complete Question,

Answer:

5.5

Step-by-step explanation:

earthquake is measured with the Ritcher Scale:

R (Magnitude) = ㏒base 10 (I)

where I = Intensity

thus,

R = ㏒ base 10 (316227.77)

R ≅ 5.5

Answer:

if the base is on the x-axis, the width of the rectangle is = xif the height is based on the parabola, the length = 7-x^2

the area of a rectangle = length * width

thus, area = x*(7-x^2)= 7x-x^3

in order to maximize the area, you would need to take the derivative of the area and set it equal to 0

Area = 7x-x^3Area' = 7 - 3x^2

7-3x^2 = 0thus, x = 1.5275

this x represents the x needed to create the largest possible area with the given parameters.

Thus:Width (x-axis) = 1.5275Length (y-axis) = 7 - (1.5275)^2 = 4.6667

Answer:

as a result you get approximately 2.8949 which in thousands of units is 2894 (rounded down since you can't have a fraction of a unit).

For an average intake of 2200 calories per day, the number of acres of land owned will be 2.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that, The function that models the number of calories consumed daily by a person owning x acres of land in a developing country is,

C(x)=270 ln (x+1)+1900

If an average intake of 2200 calories per day,

C(x)= 2200

2200=270 ln (x+1)+1900

2200-1900=270 ln (x+1)

270 ln (x+1)=2200-1900

270 ln (x+1)=300

ln (x+1)=300/270

ln (x+1)=1.11

(x+1)=ln⁻¹(1.11)

x+1=e¹¹¹

x=e¹¹¹-1

x=3.034-1

x=2.034≈2

Thus, for an average intake of 2200 calories per day, the number of acres of land owned will be 2.

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Answer:

he paid 20.20 for the patch

Answer:

The equation could you use to find the price of one tire patch select all that apply 4x + 1.9 = 22.2 and 22.2-4x= 1.9

Answer:

You need to multiple

Step-by-step explanation:

0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.

Given that,

Standard deviation (σ) = 5.2 oz

mean (μ) = 10 oz

Number of students (n) = 120

As we know,

P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ[tex]\sqrt{n}[/tex]}/σ])

                        = P (z > [{12.7 - 10[tex]\sqrt{120}[/tex]}/5.2])

                        = P (z > 1.86)

                        = 1 - P ( z < 1.86)

                        = 1 - 0.862394

                        = 0.137606

Thus, P( z > 12.7 oz.) = 0.137606

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The required value of the given function f(-1) is 2.

What is a function?

Exactly one value from the set of second components of the ordered pair is connected with each value from the set of first components of the ordered pairs in a relation known as a function.

For the given graph,

For x = -1, the exact y value will be 2.

So, f(-1) = 2

Hence, the required value of the given function f(-1) is 2.

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