What is the value of f-1(4)

Answer:

13

Step-by-step explanation:

I counted the X's of 1-3 and got 13 in total.

(Let me know if that was correct) :)

Answer:

13 students

Step-by-step explanation:

To solve this you count the x's above 1, 2, and three.

I hope this helps!!

Answer:

7

Step-by-step explanation:

42/6=7

if the bacterial is doubling, that means the growth rate is 100%, or 100% plus whatever it was before, so

\(\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &1500\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=minutes\\ c=period\dotfill &30 \end{cases} \\\\\\ A=1500(1 + 1)^{\frac{t}{30}}\implies A=1500(2)^{\frac{t}{30}} \\\\\\ \stackrel{\textit{after two hours, or 120 minutes, t = 120}~\hfill }{A=1500(2)^{\frac{120}{30}}\implies A=1500(2)^4\implies A=24000}\)

\(~\dotfill\\\\ \stackrel{\textit{current amount being 12000}}{12000=1500(2)^{\frac{t}{30}}}\implies \cfrac{12000}{1500}=(2)^{\frac{t}{30}}\implies 8=(2)^{\frac{t}{30}}\implies 8=\sqrt[30]{2^t} \\\\\\ 8^{30}=2^t\implies (2^3)^{30}=2^t\implies 2^{90}=2^t\implies 90=t\)

The given values, we have Vx = 24.8 * cos(23.4°). Similarly, to calculate Vy, we use the formula Vy = V * sin(θ), which gives us Vy = 24.8 * sin(23.4°).

To find Vx and Vy, we need to break down the vector into its x and y components. Vx represents the horizontal component of V, while Vy represents the vertical component.

In detail, to calculate Vx, we can use the formula Vx = V * cos(θ), where V is the magnitude of the vector and θ is the angle it makes with the x-axis. Substituting the given values, we have Vx = 24.8 * cos(23.4°). Similarly, to calculate Vy, we use the formula Vy = V * sin(θ), which gives us Vy = 24.8 * sin(23.4°).

By calculating Vx and Vy using the given formulas, we can obtain the horizontal and vertical components of the vector. The values obtained will be expressed using three significant figures. To check if our calculations are correct, we can use Vx and Vy to calculate the magnitude of V using the Pythagorean theorem. The magnitude of V is given by |V| = sqrt(Vx^2 + Vy^2). Additionally, we can find the direction of V by using the inverse tangent function: θ = tan^(-1)(Vy/Vx).

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When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the classical method.

This method is based on the idea that all possible outcomes of an experiment are equally likely to occur, and therefore the probability of any one outcome occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes.

For example, if there are 6 possible outcomes and 2 of them are favorable, the probability of a favorable outcome occurring is 2/6, or 1/3. The classical method is often used in situations where there is no prior information or data available to help determine the probabilities of different outcomes.

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The dropdown numbers is an illustration of combination

The smallest dropdown number is 1025

From the question, we have the following parameters:

We start counting from 1023, 1024, 1025, 1026...........

The number 1025 satisfies the given conditions

Hence, the smallest dropdown number is 1025

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Answer:

In both cases, we have similar figures.

This means that the shape of the figures is the same, but the size is different:

PQST is similar to STNR and to NRPQ

VUYZ is similar to YZWX and to VUWX

this means that, for example, in problem 18, the ratio between ST and NR must be the same as the ratio between PQ and ST. This happens because the measure increases by the same scale factor.

With this in mind, we can solve the problem:

18)

ST = 7.5

NR = 5.5

Then the quotient ST/NR is:

ST/NR = 7.5/5.5

And, as we said above:

PQ/ST = ST/NR

PQ/7.5 = 7.5/5.5

PQ = (7.5/5.5)*7.5 = 10.23

19) Here we should have:

YZ/VU = WX/YZ

Then:

22.9/35 = WX/22.9

(22.9/35)*22.9 = WX = 14.98

Answer:

4k + 13

Step-by-step explanation:

Base Expression: 8(2 - k) - 3(1 - 4k)

Step 1 - Distribution:

The values in the parenthesis must be simplified -

This is done simply by distributing the value in front of the parenthesis (8) into each of the values in the parenthesis (2 and -k).

The 8 is multiplied into the 2 giving us 16

The 8 is multiplied into the -k giving us -8k

Now we are left with 16 - 8k - 3(1 - 4k).

The same distribution must now be done on the other values in the parenthesis as well -

Again, the value in front of the parenthesis (-3) must be multiplied with the values inside the parenthesis (1 - 4k)

The -3 is multiplied into the 1 giving us -3

The -3 is multiplied into the -4k giving us 12k

Now our expression is 16 - 8k - 3 + 12k

For no reason other than simplicity, let's move the values around so they are easier to add and subtract:

16 - 8k - 3 + 12k  --->  16 - 3 + 12k - 8k

(no arithmatic is done here, but it is important to preserve the signs of all the values when moving them around)

From here we simply subtract the values to fully simplify the expression:

16 - 3 = 13

12k - 8k = 4k

4k + 13 is the final and most simplified expression of the original expression (without knowing the value for k)

P.S.: 13 + 4k is also technically correct, but, it's most often proper ettiquite (and often the simplest) to put more complex monomials (numbers) first in the expression.

Ex: 2x² + 6x + 8 rather than 8 + 2x² + 6x.

Hope this was comprehensive and helpful, good luck!

Answer: 10

Step-by-step explanation: Volume = length*width*depth. 180 = 6*3*depth. 6*3 = 18. We divide 180 by 18, to get 10. Depth = 10

Answer:

20 feet

Step-by-step explanation:

Let's start by using the formula for the volume of a rectangular box:

\(\sf\qquad\dashrightarrow V = lwh\)

where:

We know that the box is half filled with grain, so the volume of the grain is:

\(\sf:\implies V_{grain} = 0.5V = 0.5lwh\)

We also know that the volume of the grain is 180 cubic feet, so we can set up an equation:

\(\sf\qquad\dashrightarrow 0.5lwh = 180\)

We are given that the box is 6 feet wide and 3 feet long, so we can substitute those values in:

\(\sf:\implies 0.5(3)(6)h = 180\)

Simplifying:

\(\sf:\implies 9h = 180\)

\(\sf:\implies \boxed{\bold{\:\:h = 20\:\:}}\:\:\:\green{\checkmark}\)

Therefore, the depth of the box is 20 feet.

Answer:

1

Step-by-step explanation:

Answer: Add 7 to n to make it a positive number and easier to work with

Step-by-step explanation:

first all 7 then divide by divide by 3

Answer:

where is model A

Step-by-step explanation:

Thus, the obtained area of sector for the given circle is found as 43.96 in².

Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle assessment and radius measurement are both crucial for solving circle-related difficulties.

The curved portion that runs along the circle's perimeter and joins the ends of a two radii that make up a sector is known as the sector arc.

given data:

Formula for the area of sector:

area of sector = Ф /360 * (πr²)

area of sector = 140/360 * (3.14 *6²)

area of sector = 7/18 * 3.14 *36

area of sector = 43.96 in²

Thus, the obtained area of sector for the given circle is found as 43.96 in².

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To determine the explicit rule for the nth term of the given geometric sequence 5, 20, 80, 320, 1,280, ..., use the formula:`an = a1 * r^(n - 1)`, where an represents the nth term of the sequence.`a1`represents the first term of the sequence.`r` represents the common ratio between terms of the sequence.

The given sequence is 5, 20, 80, 320, 1,280, ...Let's now apply the formula to find the explicit rule for the nth term of the given sequence.`an = a1 * r^(n - 1)`Where a1 = 5 (first term of the sequence)`r` can be found by dividing any term by the preceding term, as `r = (second term) / (first term)`In this case,`r = (20) / (5) = 4`

Substituting the values in the formula:`an = a1 * r^(n - 1)``an = 5 * 4^(n - 1)` Therefore, the explicit rule for the nth term of the given geometric sequence is `an = 5 * 4^(n - 1)`.You can use this formula to find the value of any term in the sequence, given its position (n) in the sequence.For example, to find the 150th term of the sequence, substitute n = 150 in the formula: `a150 = 5 * 4^(150 - 1)`. This simplifies to `a150 = 1.442 x 10^90`.

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The expression that can find the number that comes next in the pattern is: x ≈ 4.71 * 215 ≈ 1011.65

To identify a pattern in the multiplication table, we can look for common factors or multiples among the numbers in the table. In this case, we can observe that the shaded numbers are all odd and are arranged in a diagonal pattern from the upper left to the lower right of the multiplication table.

If we write out the sequence of shaded numbers, we get:

9, 35, 99, 215, …

To find the next number in the sequence, we can try to identify the pattern of how the numbers increase. One possible way to do this is to look at the difference between consecutive terms in the sequence. If there is a constant difference, then the sequence may be arithmetic. If there is a constant ratio between consecutive terms, then the sequence may be geometric.

To calculate the differences between consecutive terms, we can subtract each term from the next:

35 - 9 = 26

99 - 35 = 64

215 - 99 = 116

The differences between consecutive terms are not the same, so the sequence is not arithmetic. However, if we calculate the ratios between consecutive terms, we get:

35 / 9 = 3.89

99 / 35 = 2.83

215 / 99 = 2.17

The ratios between consecutive terms are not the same, but they are approximately equal to 3.89 / 2.83 ≈ 1.37 and 2.83 / 2.17 ≈ 1.30, respectively. If we assume that this trend continues, we can use a geometric sequence to find the next term in the sequence.

If we let x be the next number in the sequence, then we have:

215 / 99 ≈ 2.17 ≈ x / 215

Solving for x, we get:

x ≈ 215 * 2.17 / 99 ≈ 4.71 * 215

Rounding to the nearest whole number, the next number in the pattern should be 1012.

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The inequality which models the given situation will be;

⇒ x < - $10

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The condition is;

''A bank sends an e-mail to its customers when their accounts fall below -10$.

Now,

Let the total balance in his account = x

Then, we can formulate;

The inequality for the given situation is;

⇒ x < - $10

Therefore,

The inequality which models the given situation will be;

⇒ x < - $10

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Answer:

The number 10/7 is a rational number, which means it can be expressed as a fraction. Also, if we divide it would give a decimal infinite periodical number, which means it has a pattern on its decimal numbers.

On the other hand, the square root of 2 is irrational number, that means it can't be expressed as a fraction, because its decimal numbers don't have any pattern at all.

So, Mai's brother can see these type of numbers as crazy (irrational numbers) and sane (rational numbers).

At last, another important characteristic to shows that they aren't equal is that they don't have the exactly decimal numbers.

8×11/4+12

2×11+12

22+12

33

Answer:

the answer is 9

Step-by-step explanation:

When scores are measured on a nominal scale, the appropriate frequency distribution graph is a bar graph. Therefore, the correct answer is option D: Only a bar graph.

A nominal scale is the lowest level of measurement, where data is categorized into distinct categories or groups without any inherent order or magnitude. In this type of measurement, the data points are labeled or named rather than assigned numerical values. Examples of variables measured on a nominal scale include gender (male/female), marital status (single/married/divorced), or eye color (blue/brown/green).

A bar graph is a visual representation of categorical data that uses rectangular bars of equal width to depict the frequency or count of each category. The height of the bars represents the frequency or count of observations in each category. The bars in a bar graph are usually separated by equal spaces, and there is no continuity between the bars. The categories are displayed on the x-axis, while the frequency or count is displayed on the y-axis.

A bar graph is particularly useful for displaying and comparing the frequencies or counts of different categories. It allows for easy visualization of the distribution of categorical data and helps to identify the most common or least common categories. The distinct separation of the bars in a bar graph is suitable for representing data measured on a nominal scale, where the categories are discrete and do not have a natural order or magnitude.

Histograms, polygons, and other types of frequency distribution graphs are more appropriate for variables measured on ordinal, interval, or ratio scales, where the data points have numerical values and a specific order or magnitude.

In summary, when scores are measured on a nominal scale, the most appropriate frequency distribution graph is a bar graph. It effectively represents the frequencies or counts of different categories and allows for easy visualization and comparison of categorical data.

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If derivative of \(f(x)=ln(x+4+e^{(-3x)})\), then f '(0) = -2/5.

What is derivative?

In calculus, the derivative of a function is a measure of how the function changes as its input changes. More specifically, the derivative of a function at a certain point is the instantaneous rate of change of the function at that point.

To find f'(0), we first need to find the derivative of f(x) with respect to x. Using the chain rule, we get:

\(f'(x) = 1 / (x+4+e^{(-3x)}) * (1 - 3e^{(-3x)})\)

Now we can find f'(0) by substituting the value x=0:

\(f'(0) = 1 / (0+4+e^{(-3(0))}) * (1 - 3e^{(-3(0))})\)

f'(0) = 1 / (4+1) * (1 - 3)

f'(0) = -2/5

Therefore, f'(0) = -2/5.

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Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

Part A

Given

Solution

We ask to double the time i.e

Part B

Given

Solution

The half-life would be 5

Answer:

Length is 35 width is 25

Step-by-step explanation:

Answer:

y = 6

Step-by-step explanation:

Perform the indicated multiplication:  6y + 12 = 8y

Consolidate y terms on the right:                12 = 8y - 6y = 2y, or y = 6

The separable differential equations among the given options are A. xy/(1+x²) and E. (x+x²y)dx = xdy. These equations can be separated into variables and solved using integration.

A separable differential equation is one that can be written in the form dy/dx = f(x)g(y), where f(x) and g(y) are functions of x and y, respectively. By rearranging the equation, we can separate the variables and integrate both sides to find the solution.

Among the given options, equation A can be written as (1+x²)dy = xydx. Dividing both sides by (1+x²), we get dy/dx = (xy)/(1+x²). This equation is separable since it can be written as dy/(xy) = dx/(1+x²), where f(x) = 1/(1+x²) and g(y) = y/x. Integrating both sides gives ln(|y|) = arctan(x) + C, where C is the constant of integration.

Similarly, equation E can be written as (x+x²y)dx - xdy = 0. Dividing both sides by x(1+xy), we get (1/x)dx - (1/(1+xy))dy = 0. This equation is also separable and can be written as (1/x)dx = (1/(1+xy))dy. Integrating both sides gives ln(|x|) = ln(|1+xy|) + C, where C is the constant of integration.

The other equations (B, C, D, F, and G) are not separable differential equations since they cannot be written in the form dy/dx = f(x)g(y).

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The wind tunnel should be operated at a pressure that results in an air density of 0.068 kg/m³ to achieve dynamically similar test conditions. The expected drag force on the full-scale torpedo is 7535 N.

To achieve dynamically similar test conditions, the Reynolds number of the model in the wind tunnel should be the same as the Reynolds number of the prototype in water. The Reynolds number is given by:

Re = (ρvL)/μ

where ρ is the density of the fluid (air or water), v is the velocity, L is a characteristic length (diameter for the torpedo), and μ is the dynamic viscosity of the fluid.

For the prototype in water:

ρ = 1000 kg/m³

v = 28 m/s

L = 6.7 m

μ = 0.001 Pa·s (for water at 20°C)

Re = (1000 kg/m³ × 28 m/s × 6.7 m) / 0.001 Pa·s

Re = 1.876 × 10^8

For the model in the wind tunnel:

v = 110 m/s (maximum speed in wind tunnel)

L = 1/3 × 6.7 m = 2.233 m (scaled length)

μ = 0.0000183 Pa·s (for air at 20°C)

We can solve for the density of air required to achieve the same Reynolds number as the prototype:

ρ = (μRe)/(vL)

ρ = (0.0000183 Pa·s × 1.876 × 10^8) / (110 m/s × 2.233 m)

ρ = 0.068 kg/m³

Therefore, the wind tunnel should be operated at a pressure that results in an air density of 0.068 kg/m³ to achieve dynamically similar test conditions.

To find the drag force on the full-scale torpedo, we can use the drag coefficient of the model in the wind tunnel, assuming it is the same as the full-scale prototype. The drag force is given by:

Fd = 1/2 ρ v² Cd A

where Cd is the drag coefficient and A is the cross-sectional area of the torpedo.

For the model in the wind tunnel:

ρ = 0.068 kg/m³

v = 28 m/s (prototype operating speed)

Cd = (measured drag force on model) / (1/2 ρ v² A)

Cd = 618 N / (1/2 × 0.068 kg/m³ × 28 m/s² × π(533/2 mm)²)

Cd = 0.00744

For the full-scale prototype:

ρ = 1000 kg/m³

v = 28 m/s

A = π(533 mm/2)²

Fd = 1/2 × 1000 kg/m³ × 28 m/s² × 0.00744 × π(533/2 mm)²

Fd = 7535 N

Therefore, the expected drag force on the full-scale torpedo is 7535 N.

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The cost of the souvenir is approximately $15.92.

Let's assume the cost of the souvenir is S.

According to the given information, the cost of the burger is 1/4 of the cost of the souvenir, which means the cost of the burger is (1/4)S.

The cost of the pass is 2/3 of the cost of the souvenir, which means the cost of the pass is (2/3)S.

Hannah had $2.00 left over after buying these items, so we can write the equation:

$40.50 - (1/4)S - S - (2/3)S = $2.00

To solve for S, we'll combine like terms:

$40.50 - (9/12)S - (12/12)S - (8/12)S = $2.00

$40.50 - (29/12)S = $2.00

Next, we'll isolate the variable by subtracting $40.50 from both sides:

-(29/12)S = $2.00 - $40.50

-(29/12)S = -$38.50

To solve for S, we'll divide both sides by -(29/12):

S = (-$38.50) / -(29/12)

S ≈ $15.92

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