this I never got taught, need help bunch of points

The number of bacteria after 8 hours is approximately 2,713.

Let's apply the exponential growth formula:

N = N0 * e(rt),

N is the number of bacteria at a particular period. N0 is the initial bacterial population, e is the mathematical constant (about equal to 2.71828), r is the growth rate, and t is the amount of time that has passed.

The information provided in the problem can be used to determine the growth rate:

N1 = N0 * e(r*2)

N2 = N0 * e(r*4)

To get eliminate N0, divide the second equation by the first equation:

N2/N1 = e(r4) / e(r2)

385/135 = e(r4) / e(r2)

If we condense this expression, we get:

e(r*2) = 385/135

e(r*2) = 2.8519

When we take the natural logarithm of both sides, we get:

r*2 = ln(2.8519)

r = ln(2.8519)/2

r = 0.5457 (rounded to 4 decimal places)

The number of bacteria after 8 hours can now be determined using the exponential growth algorithm once more:

N = N0 * e(rt)

N = 135 * e(0.5457*8)

N = 2,713 (rounded to the nearest whole number)

Therefore, the number of bacteria after 8 hours is approximately 2,713.

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Answer:

  b1 = (28/h) -b2

Step-by-step explanation:

Filling in the given value for A, you have ...

  14 = (1/2)(b1 +b2)h

Multiply by 2/h:

  28/h = b1 +b2

Subtract b2:

  b1 = (28/h) -b2

Answer:

C

Step-by-step explanation:

Answer:

C. 40 and 50

Step-by-step explanation:

The median marks the mid-point of the data and is shown by the line that divides the box into two parts (sometimes known as the second quartile). Half the scores are greater than or equal to this value and half are less.

To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)

To simplify this expression, we can expand the square:

\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)

Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.

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Answer:

To find the z-score, we use the formula:

z = (x - mu) / (sigma / sqrt(n))

where:

x = sample mean = $5100

mu = population mean = $5000

sigma = population standard deviation = $250

n = sample size = 64

Substituting the values, we get:

z = (5100 - 5000) / (250 / sqrt(64))

z = 2.56

Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).

Step-by-step explanation:

I clicked on the black picture. thought is was the box to enter the answer.

The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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To determine whether the earlier measure of one variable is associated with the later measure of the other variable, we can calculate the cross-lag correlation between these two variables. This will give us a measure of the strength and direction of the relationship between the two variables.

If the cross-lag correlation between aggression in third grade and tv violence in 13th grade is positive and statistically significant, it would suggest that there is a positive relationship between the two variables, meaning that higher levels of aggression in third grade are associated with higher levels of tv violence in 13th grade.

On the other hand, if the cross-lag correlation is negative and statistically significant, it would suggest that there is a negative relationship between the two variables, meaning that higher levels of aggression in third grade are associated with lower levels of tv violence in 13th grade.

Similarly, we can also calculate the cross-lag correlation between tv violence in third grade and aggression in 13th grade to determine whether the earlier measure of one variable (tv violence in third grade) is associated with the later measure of the other variable (aggression in 13th grade).

By calculating both cross-lag correlations, we can address the directionality problem and establish temporal precedence between the two variables. This helps us understand the nature of the relationship between aggression and tv violence over time and how it may change as individuals age.

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The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

The area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The area of the triangle can be determined by using the midpoint formula, which states that the area of an isosceles triangle is equal to half the product of the two base lengths multiplied by the height.

In this case, the midpoint of the triangle is (3,0). This means that the triangle's base lengths are equal to 6 (the difference between the x coordinates of the midpoint and the two endpoints, 3-(-3)) and the height is equal to 6 (the difference between the y coordinates of the midpoint and the two endpoints, 3-(-3)).

Therefore, the area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.

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Answer:

\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Step-by-step explanation:

\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Answer:

0.8 gallons per second

Step-by-step explanation:

Given that :

Filling occurs at a constant rate ;

Change in gallon of water in pool within a 3 seconds time interval ;

Assume :

At t = 0 ; gallons = 5

At t = 3 ; gallons = 7.4

Chanhe in gallons with time.;

(7.4 - 5) / (3 - 0)

2.4 / 3

= 0.8 gallons per second

Answer: Aaron’s rate for mowing lawns is 0.5 acres per hour

Step-by-step explanation:

Hope this helps!!

The statement "The rate to mow a lawn is 0.5 acres per hour" correctly describes the slope of the line passing through the given points.

We have,

To determine the slope of the line passing through the points (3, 1.5) and (5, 2.5), we can use the slope formula:

Slope = (change in y) / (change in x)

Given the two points, we can calculate the change in y and the change in x:

Change in y = 2.5 - 1.5 = 1

Change in x = 5 - 3 = 2

Plugging these values into the slope formula:

Slope = 1 / 2 = 0.5

The slope represents the rate of change of the y-coordinate (area) with respect to the x-coordinate (time).

In this case, a slope of 0.5 means that for every hour it takes Aaron to mow a lawn (change in x), the area mowed (change in y) increases by 0.5 acres.

Therefore,

The statement "The rate to mow a lawn is 0.5 acres per hour" correctly describes the slope of the line passing through the given points.

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The concept Pythagoras theorem is used here to determine the length of the hypotenuse. It is an important theorem which explains the relation between the sides of a right angled triangle. The length of hypotenuse is

According to Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides. The sides of this triangle have been named perpendicular base and hypotenuse.

Hypotenuse² = Perpendicular² + Base²

9² + 4² = 97

√97 = 9.84 cm

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Your question is incomplete most probably your full question was:

What is the length of the hypotenuse of the triangle when x=9 now and other side y = 4.

Answer:

(-3,-76)

Step-by-step explanation:

(22x2 +  24x) -  40  = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  4x2 + 24x - 40  =   4 • (x2 + 6x - 10)

Trying to factor by splitting the middle term

3.2     Factoring  x2 + 6x - 10

The first term is,  x2  its coefficient is  1 .

The middle term is,  +6x  its coefficient is  6 .

The last term, "the constant", is  -10

Step-1 : Multiply the coefficient of the first term by the constant   1 • -10 = -10

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   6 .

     -10    +    1    =    -9

     -5    +    2    =    -3

     -2    +    5    =    3

     -1    +    10    =    9

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 3:

 4 • (x2 + 6x - 10)  = 0

STEP 4:

Equations which are never true:

4.1      Solve :    4   =  0

Answer:

Hope you can understand my handwriting though

The relationships between the figures is a dilation of 3.5 from the small triangle to the big triangle

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

The two triangles

From the figure, we can see that

These mean that the triangles are related by dilation

The constant of dilation is then calculated as

k = (7, 7)/(2, 2)

Evaluate

k = 3.5

Hence, the scale factor is 3.5

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The cost of 1 pound of trail mix is $3.25 and cost of 1 pound of jelly beans is $2.25

Pair of linear equation:

                                     Equation having two variables and degree one is called linear equation in two variables, while pair of these two equation is called pair of linear equation.

Let,

               The cost of 1 pound of trail mix is $x and cost of 1 pound of jelly beans is $y

5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $23

            so equation will be,

                                               \(5x + 3y =23\)    ............... (I)

2 pounds of trail mix and 6 pounds of jelly beans, the total cost is $20

             so equation will be,

                                               \(2x + 6y = 20\)   ................(II)

subtract  equation (II) from equation (I) x 2 (Elimination method for solving pair of linear equation)

                      \(10x + 6y = 46\)       .......... equation (II) x2

                       \(2x + 6y = 20\)  

                          \(8x = 26\)

                            \(x=\frac{26}{8}\)

                          \(x =\) $ 3.25

from equation (I)      

                               \(3y = 23 -5x\)

                                    = 23 - 5 x 3.25

                                   =  23 - 16.25

                             3y = 6.75

                              y = 6.75/3

                             y = $ 2.25

Hence,

           the cost of 1 pound of trail mix is $3.25 and cost of 1 pound of jelly beans is $2.25

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The disadvantages of the mode are: For many sets of data there is no mode.

The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.

However, one of the disadvantages of the mode is that for many sets of data, there may not be a distinct mode. In such cases, the data may have a uniform distribution where all values occur with equal frequency, or it may have multiple modes with similar frequencies.

The mode is not affected by extremely large or small values. It only considers the frequency of values and not their magnitude. Therefore, extreme values do not influence the mode.

The statement that the mode can only be computed for interval-level data or higher is incorrect. The mode can be computed for any type of data, including nominal, ordinal, interval, and ratio data. It is applicable to categorical as well as numerical data.

The main disadvantage of the mode is that for many datasets, there may not be a distinct mode.

The correct option is: For many sets of data there is no mode.

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Answer: 33.33%

Step-by-step explanation:

Answer:

33.3333...%

Step-by-step explanation:

33 x 3 = 99.9999...

The number of coffee shops per capita in the city is approximately 0.000124.

To calculate the number of coffee shops per capita in the given city, we divide the total number of coffee shops by the total population and round the result to six decimal places.

Number of coffee shops: 99

Population: 801,100

Coffee shops per capita = Number of coffee shops / Population

Coffee shops per capita = 99 / 801,100

Coffee shops per capita = 0.000123719

Rounding the result to six decimal places, the number of coffee shops per capita in the city is approximately 0.000124.

This means that for every person in the city, there are approximately 0.000124 coffee shops available. Another way to interpret this is that, on average, each person in the city can expect to have access to 0.000124 coffee shops.

Please note that this calculation assumes an equal distribution of coffee shops throughout the city and does not take into account factors such as location, density, or other variables that may affect coffee shop accessibility.

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Answer: sum of ZABC and ZCBD

Step-by-step explanation:

Factor the trinomial with the GCF.

The GCF of all of the terms is 3.

Using the GCF:

\(3(5n^2-9n-2)\)

Using 2 binomials to factor:

\(3(5n+1)(n-2)\)

When unfactorized, the expression will equal \(15n^2-27n-6\).

Answer:

use a calculator

Step-by-step explanation:

Answer:

positive and odd

Step-by-step explanation:

If a is a negative odd number, then a² can't be negative, because a number squared is always positive.

I'll illustrate this with an example.

Let's choose -7 as an example. Instead of a.

-7² = 49

So we see that the result is positive & odd.

So the words that describe a^2 are positive and odd.

Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

Answer:

$237

Step-by-step explanation:

4266 divided by 18

x is the number of bags of chips

1.05x means "1.05 times x". You could write 1.05*x or omit the multiplication symbol all together.

For example, if he bought x = 100 bags then he would spend 1.05*x = 1.05*100 = 105 dollars.