wrate 10 as a fraction of 30

The number of bacteria in 12 days is 143,555

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem,  

the starting = 63,740 bacteria

the base = 1 + rate = 1 + 0.07 = 1.07

the exponents = x = number of days

The number of bacteria will there be in 12 days

f(x) = a(b)^x

f(x) = 63740 * (1.07)^12

f(x) = 143,555

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The exponent property that justifies why ten to the one third power equals the cube root of ten is:

ten to the one third power all raised to the third power equals ten to the one third times three power equals ten.

The exponent property using in this problem is the power of power rule, which states that when a term is elevated to a power, and this power is elevated to another power, then the powers are multiplied.

Hence, considering the expression in this problem:

((10)^(1/3))^3

We have that:

Then the multiplication of the exponents is given as follows:

1/3 x 3 = 1.

And the result is:

10^1 = 10.

Since the number 10^(1/3) elevated to the cube has a result 10, the number is equivalent to the cube root of 10, giving the correct expression.

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II and III only

We split up the integration interval [1, 4] into 3 equally-spaced subintervals of length (4 - 1)/3 = 1 :

[1, 2], [2, 3], [3, 4]

The area over each subinterval [L, R] is either approximated by a trapezoid, whose area will be

1 • (f(L) + f(R))/2

or by a rectangle with height f((L + R)/2) and hence area

1 • f((L + R)/2)

For f(x) = x², the area under f(x) over [1, 4] is approximated by

• using trapezoids (T) :

\(\displaystyle \int_1^4 x^2 \, dx \approx \frac{4-1}{2\times3} (1^2 + 2\times2^2 + 2\times3^2 + 4^2) = \frac{43}2 = \frac{86}4\)

• using midpoints (M) :

\(\displaystyle \int_1^4 x^2 \, dx \approx \frac{4-1}3 \left(\left(\frac32\right)^2 + \left(\frac52\right)^2 + \left(\frac72\right)^2\right) = \frac{83}4\)

so T > M. (This eliminates "I only" and "all of the functions".)

For f(x) = √x, the area is approximated by

• T :

\(\displaystyle \int_1^4 \sqrt x \, dx \approx \frac{4-1}{2\times3} (\sqrt1 + 2\sqrt2 + 2\sqrt3 + \sqrt4) \approx 4.646\)

• M :

\(\displaystyle \int_1^4 \sqrt x\, dx \approx \frac{4-1}3 \left(\sqrt{\frac32} + \sqrt{\frac52} + \sqrt{\frac72}\right) \approx 4.677\)

so T < M. (This eliminates "none of the functions".)

Answer:

the percent increased in the dosage is 2%

The area of a parallelogram is 20 inches square

The area of a parallelogram is the base of the shape multiplied by the height

Area of parallelogram = b × h

Where h = height = 2 In

base = 10 in

Area = 2 × 10

Area = 20 Inches square

Thus, the area of a parallelogram is 20 inches square

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The transformation of f(x) to g(x) is :

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

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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Answer:

\(x_{1} + 3x_{2} + x_{3} = 0\\\)

X = \(\left[\begin{array}{ccc}x_{1}\\x_{2}\\x_{3}\end{array}\right]\) = \(\left[\begin{array}{ccc}5x_{3}\\-2x_{3}\\x_{3}\end{array}\right]\) = \(x_{3} \left[\begin{array}{ccc}5\\-2\\1\end{array}\right]\)

Step-by-step explanation:

Parametric vector form is the set of equation which form a line. The parametric equation is set and the vector matrix is formed based on the given equation. The solution set of x is found by equating the 0. It express a set of explicit independent variables.

Answer: C

she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.

-18/35 is the answer to (-3/5) divided by (7/6)

Notably, this response comes the nearest to choice A (83.3 wins). The right response is thus A.

A mathematical statement that shows the equivalence of two mathematical equations is what a solution in algebra means. For instance, the two numbers 3x + 5 and 14 make up the expression 3x + 5 = 14, which is separated by the sign "equal."

We can change x to 17 in the regression model y = 4.9x + 15.2 and calculate for y to get the number of victories for a squad with 17,000 spectators: y = 4.9(17) + 15.2 = 83.5

Consequently, 83.5 victories are expected for a squad with a 17,000-fan attendance.

To predict the number of wins for a team with an attendance of 17,000, we can substitute x = 17 into the regression equation y = 4.9x + 15.2 and solve for y:

y = 4.9(17) + 15.2 = 83.5

Therefore, the predicted number of wins for a team with an attendance of 17,000 is 83.5 wins.

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As a result, the following parametric equations describe the motion of the heat-seeking particle: x = a - 2t and y = b - 4t

As per the question given,

To find the path of a heat-seeking particle placed at point P on a metal plate with a temperature field T(x,y) = 100 - x^(2) - 2y^(2), we need to use the gradient vector of T(x,y).

The gradient of T(x,y) is given by:

∇T(x,y) = (-2x, -4y)

The heat-seeking particle moves in the direction of maximum increase of temperature, so it moves in the direction of the gradient vector, that is, (-2x, -4y).

To find the path of the particle, we need to integrate the gradient vector starting at point P = (a,b), where a and b are the coordinates of the point on the metal plate where the particle is placed.

So the path of the heat-seeking particle is given by the following parametric equations:

x = a - 2t

y = b - 4t

where t is the parameter that represents time.

These equations represent a straight line in the direction of the gradient vector of T(x,y). The particle moves from point P in the direction of the gradient vector, with a speed proportional to the magnitude of the gradient vector.

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Answer:

[-7, infinity)

Step-by-step explanation:

solid dot on -7 so [

arrow is to positive infinity

infinity always use )

Answer:

61

Step-by-step explanation:

f=98-37=61(exterior angle is equal to the sum of opposite Interior angles)

The number of people at the movie is 340

Let's represent the total number people at the movie as "x".

We know that the number of adults in the movie is 187 and the percentage of children is 45%

So we can write:

187 = (1 - 45%) * x

This gives

187 = 0.55x

To solve for x, we can divide both sides by 0.55:

x = 187/0,55

Evaluate

x = 340

Hence, the number of people is 340

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A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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Answer:

25

%

Step-by-step explanation:

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The probability that the two cards dealt to Patricia will both be yellow

is 1/4.

In mathematics, probability refers to the likelihood of an occurrence occurring. Simply put, how frequently the incidence occurs over a certain period of time.

Given, there are 12 cards left in the deck, and three are yellow.

To find the probability:

The probability= number of yellow cards in the deck / total number of cards in the deck.

= 3/12

= 1/4

Therefore, the probability is 1/4.

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Answer:

Area of shaded region:

12r^2 - (2(2r^2) + 2πr^2) =

12r^2 - 4r^2 - 2πr^2 =

(2r^2)(4 - π)

Probability of point chosen in shaded region:

(2r^2)(4 - π)/(12r^2) = (4 - π)/6 = .143 = 14.3%

The value of the expression a^2 - 2ac + 5b is, 175.

What is the value of expression?

When the variables and constants in the expression are given values, the calculation that this expression describes yields the value. In an algebraic expression, letters can substitute for numbers.

Consider, the given expression,

a^2 - 2ac + 5b

The values of a, b and c are

a = -8, b = 3, c = 6.

Plug these values in the above expression,

So, the expression becomes

(-8)^2 - 2(-8)(6) + 5(3) = 64 + 96 + 15 = 175

Hence, the value of the expression is, 175.

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1. We can see here that the modes of the given set of numbers will be: 12, 13, 14, 19.

2. The word in the sentence that is the mode is: the.

3. The mode of x is: 7

The mode of y is: - 2

In statistics, the mode is the value or values that occur most frequently in a given dataset. It is one of the most common measures of central tendency, along with the mean and the median.

To find the mode of a dataset, you need to look for the value that appears most often. If there is more than one value that occurs with the same highest frequency, the dataset is said to be bimodal or multimodal.

If no value appears more frequently than any other, the dataset is said to have no mode.

4. Modal class: 4-

Modal class: 12 - 20

5. Knowing the modal size of glass that its customers purchase can provide several benefits for the small company that sells glass. Here are some ways in which the company could benefit:

6. We can actually find the total frequency of the other three classes by subtracting the frequency of the first class from the total number of observations:

Total Frequency of the three classes = Total number of observations -Frequency of the first class

= 115 - 84 = 31

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Step-by-step explanation:

line A can be written as y1= 3/4.x -5/4

line B is a linear function : y2= ax +b

4a+b=7 and -a +b =3 so a=4/5 and b=19/5

so y2=4/5x +19/5

so they are not parallel

Line A goes through (0,-5/4) and (1,-1/2)

Gradient of line A = G1= (-1/2 - (-5/4))/(1-0) =3/4=0.75

Gradient of line B= G2= (7/3)/(4-(-1))=4/5=0.8

The Line A and Line B are not parallel to each other.

The equation of line A is,

                           \(3x-4y=5\)

Now write in slope intercept form,

                       \(3x-4y=5\\\\4y=3x-5\\\\y=\frac{3}{4} x-\frac{5}{4}\)

Slope of line A is \(\frac{3}{4}\).

Equation of line B is,

                    \(y-7=\frac{3-7}{-1-4}(x-4) \\\\y-7=\frac{4}{5} x-\frac{16}{5}\\ \\y=\frac{4}{5} x+\frac{19}{5}\)

Slope of line B is \(\frac{4}{5}\)

Since, the slope of both line A and B are different. therefore, Line A and Line B are not parallel to each other.

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If the volume of this pyramid is 234 units, the height of the pyramid is equal to 13 units.

Mathematically, the volume of a pyramid is given by the formula:

\(Volume = \frac{1}{3} \times base\;area \times height\)

For the base area:

The area of a right triangle is given by:

\(A=\frac{ab}{2} \\\\A=\frac{9 \times 12}{2} \\\\A=\frac{108}{2}\)

A = 54 square units.

Given the following data:

Volume of a pyramid = 234 units.

Side lengths of right triangle = 9 and 12 units.

Now, we can calculate the height of the pyramid:

\(234 = \frac{1}{3} \times 54 \times height\\\\234=18h\\\\h=\frac{234}{18}\)

h = 13 units.

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Answer:

Excuse me, I believe you forgot to put your questio! To get the desired answer, I highly recommend to oost another question!

Have a great day!

Yours Truely, TheAnimeCatUwU

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

i trieddddd, let me know if its right or not

She deposited $16,000 at 4% and $32,000 at 4.5%

She deposited $16,000 at 4% and $32,000 at 4.5%.

Let's assume Liza deposited an amount x at 4% interest. According to the given information, she deposited twice as much, which is 2x, at 4.5% interest.

To calculate the interest income from the deposits, we'll use the formula: Interest = Principal × Rate × Time.

At 4% interest, the interest earned is 0.04x (4% expressed as a decimal multiplied by x).

At 4.5% interest, the interest earned is 0.045(2x) (4.5% expressed as a decimal multiplied by 2x).

We know that the total annual interest income is $2080. Therefore, we can write the equation:

0.04x + 0.045(2x) = 2080

Simplifying the equation:

0.04x + 0.09x = 2080

0.13x = 2080

x = 2080 / 0.13

x ≈ 16,000

Liza deposited approximately $16,000 at 4% interest, and since she deposited twice as much at 4.5% interest, she deposited approximately $32,000 at 4.5% interest.

Therefore, she deposited $16,000 at 4% and $32,000 at 4.5%.

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Answer:

The standard deviation increases, it's mean, medium and mode, if you put them in order and then go through and get your middle number it'll be 81.

If a score of 50 is added to the data set,

The standard deviation increases.

The range increases.​

"It is the average of all elements of the data set."

"It is the middle number in a sorted list of numbers."

\(SD=\sqrt{\frac{\sum{(x-M)^{2}} }{N} }\)

where, SD is the population standard deviation

N : the size of the population

x : each value from the data

M : the mean of the data

range = maximum value - minimum value

For given situation,

Consider the original set of test scores: 71, 75, 80, 81, 81, 84, 89, 93

N = 8

range R = 93 - 71

⇒ R = 22

Mean M = (71 + 75 + 80 + 81 + 81 + 84 + 89 + 93)/8

⇒ M = 654/8

⇒ M = 81.75

Now, we find the median K

First we sort given data set: 71, 75, 80, 81, 81, 84, 89, 93

The middle numbers are 81 and 81

So, the median is the average of 81, 81

So, K = 81

Now, we calculate the standard deviation.

\(SD=\sqrt{\frac{[(71-81.75)^{2}+(75-81.75)^{2}+...+(89-81.75)^{2}+(93-81.75)^{2}] }{8} }\)

⇒ SD = 6.61

Consider, the set of test scores with 50 added to the data set.

N = 9

range R = 93 - 50

⇒ R = 43

Mean M =  (71 + 75 + 80 + 81 + 50 + 81 + 84 + 89 + 93)/9

⇒ M = 704/9

⇒ M = 78.22

Now, we find the median K

First we sort given data set: 50, 71, 75, 80, 81, 81, 84, 89, 93

The middle number is 81.

So, the median is K = 81

Now, we calculate the standard deviation.

\(SD=\sqrt{\frac{[(71-81.75)^{2}+(75-81.75)^{2}+...+(50-81.75)^{2}+(93-81.75)^{2}] }{9} }\)

⇒ SD = 11.76

So, we can observe that if a score of 50 is added to the data set, the correct statements are:

The standard deviation increases.

The range increases.​

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Step-by-step explanation:

The domain tells us the possible x values in a function.

Look at the function, it has a open circle at x=-4 and it has a closed circle at x=6. This means that we can any value of number that is between negative 4 and 6. It cannot be negative 4 since it has a open circle so our domain is

\( - 4 < x \leqslant 6\)

The range is possible y values. Looking at the function, the lowest y value is at y=-3 and it has a open circle,

the highest y value is 3 and it at a closed circle.

This means we can have any y value from -3 and 3 but not -3 since it at a open circle so our range is

\( - 3 < y \leqslant 3\)

Answer:

Step-by-step explanation: