which word best describes f(x)=sin x?


a) cyclic


b) hyperbolic


c) idyllic


d) linear


e) quadratic

9514 1404 393

Answer:

  900 grams

Step-by-step explanation:

The equation tells you the initial amount of A is 700 grams.

The table tells you B is being cut in half each hour, so the amount when h=0 is 2×800 = 1600 grams.

The difference in the initial amounts is ...

  1600 -700 = 900 . . . grams

Answer:

70 inches

Step-by-step explanation:

Larry forms a right triangle with the ground (this is one leg of a right triangle) and he is 24 inches from his shadow (this is the second leg).

74 inches is the hypotenuse of the right triangle

use pythagorean theorem:  a^2 + b^2 = c^2

let h = Larry's height

h^2 + 24^2 = 74^2

h^2 + 576 = 5476

h^2 = 4900

h = sq rt 4900

h = 70

The solutions to the system of equations are given as follows: (1, -3) and (-4,2).

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The equations are given as follows:

From the second equation:

y = -2 - x.

Replacing in the first:

(x + 3)² + (y + 2)² = 17.

(x + 3)² + (-2 - x + 2)² = 17

x² + 6x + 9 + x² = 17

2x² + 6x - 8 = 0

2(x² + 3x - 4) = 0

2(x + 4)(x - 1) = 0.

Then the solutions for x are:

The solutions for y are:

Hence the solutions are:

(1, -3) and (-4,2).

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Answer:

x = 8

Step-by-step explanation:

6x/4 = 12

Multiply 4 on both sides to get rid of it:

6x = 4(12) = 48

Divide 6 on both sides:

x = 48/6 = 8

Answer:

(100x² + 6) / (5x)

Step-by-step explanation:

20x + 6 ÷ 5x

Order of operations says to multiply or divide before adding/subtracting.

So we simplify the above statement to:

\(20x+\frac{6}{5x}\)

To simplify even further, we need to find a common denominator for the two terms and then add them together.

\(\frac{100x^{2} }{5x} + \frac{6}{5x}\)

Notice that I've multiplied the first term by 5x/5x, to get a common denominator without changing the value of 20x.

So now we add the two terms and our answer is:

\(\frac{100x^{2}+6 }{5x}\)

Answer:

Step-by-step explanation:

The required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system. which is the correct answer would be an option (A).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The video game system will cost at least $450.

He earns $6 per hour babysitting and $10 per hour tutoring.

Let x be the number of hours babysitting and y be the number of hours of tutoring.

According to the given situation, we can write the inequality would be as:

⇒ 6x + 10y ≥ 450

Rearrange the terms of variables in the above inequality,

⇒ 10y ≥ 450 - 6x

Divided by 10 into both sides of the above inequality,

⇒ 10y/10 ≥ 450/10 - 6x/10

⇒ y ≥ 45 - 0.6x or

⇒ y ≥ - 0.6x + 45

Thus, the required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system.

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71% subtracted from 100% is 29%

Add or subtract the given percent from 100%.

71%

The percentage (p) is given as:

p = 71%

When subtracted from 100%, we have:

100% - p

Substitute p = 71%

100% - 71%

71 subtracted from 100 is 29.

So, we have:

100% - 71% = 29%

Hence, 71% subtracted from 100% is 29%

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There will be approx four teaspoons of US measurement system in 20 ml. That is the unit conversion of 20 mililitre is equals to four teaspoons.

A milliliter is a unit of volume equal to 1/1000 of a liter. It is the same as a cubic centimeter. A US teaspoon is a unit of volume in the cooking system that is equal to 1/3 of a tablespoon or 1/48 of a US cup. To calculate the value in milliliters to the corresponding value in teaspoons [US], multiply the amount in milliliters by 0.2028841362 (conversion factor). Here is the formula: Value in teaspoons [US]

= value in milliliters × 0.2028841362

Now we need to convert 20 ml to teaspoons. So using the above formula we can write the number of teaspoons in 20 ml is Value in teaspoons [US]

= value in milliliters × 0.2028841362

= 20 ml × 0.2028841362

= 4.057682724 ~ 4

Hence required value is 4 teaspoons.

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Answer:

No, since they fail the Triangle Inequality Theorem as 16 + 21 is less than 39.

Step-by-step explanation:

Thus, the three side lengths fail the Triangle Inequality Theorem so they can't form a triangle.

The can contains 15.7 g of sugar per 100 mL. So if the can holds 330 mL of soft drink, then overall it contains

(15.7 g) / (100 mL) × (330 mL) = 51.81 g

of sugar, and this is

(51.81 g) / (90 g) ≈ 0.575667 ≈ 57.6%

so Tom's friend is correct.

Answer:

18-22 0.169

23-27 0,324

28-32 0,265

33-37 0,243

Answer:

b only

Step-by-step explanation:

The type of function that fits the given description is D. Exponential decay.

In an arithmetic sequence, the difference between consecutive terms remains constant. If the y-values of a function form an arithmetic sequence that decreases in value, it means that the difference between consecutive terms is negative.
Exponential decay functions exhibit a constant ratio between consecutive terms, resulting in a decreasing sequence. As the x-values increase, the y-values decrease at a consistent rate. This is represented by the formula y = ab^x, where b is a constant between 0 and 1.
In contrast, linear functions have a constant difference between consecutive terms, resulting in an arithmetic sequence. However, since the y-values are decreasing, the function cannot be linear.
Exponential growth functions, on the other hand, have a constant ratio between consecutive terms, but they result in an increasing sequence. The y-values of an exponential growth function increase as the x-values increase.

Therefore, based on the given information, the most appropriate type of function is D. Exponential decay.

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Answer:

yes

Step-by-step explanation:

6 is half of 12. 15 is half of 30. The ratios are equal, so the fractions are proportional.

Answer: yes

Also, you can reduce both fractions.

Divide the numerator and denominator of 6/12 by 6 to get 1/2.

Divide the numerator and denominator of 15/30 by 15 to get 1/2.

Since both fractions reduce to 1/2, 6/12 and 15/30 are equivalent fractions and are proportional.

Answer:

\(\frac{1}{5}\)

Step-by-step explanation:

There are a total of 30 number between 1 and 30, so the total events is 30.
Now for the favorable events (A: even and multiple of 3) there's a total of 5 numbers (6,12,18,24,30)

Using classic probability law the probability is given by the favorable events between the total events

\(P(A)=\frac{6}{30}=\frac{1}{5}\)

The difference of the fractions 8/2 and 3/5 is given as follows:

17/5.

The difference operation for this problem is defined as follows:

8/2 - 3/5.

8 is divisible by 2, with a quotient of 4, hence the subtraction can be simplified as follows:

4 - 3/5.

With a common denominator of 5, we have that 4 x 5 = 20, hence:

20/5 - 3/5.

As the fractions now have a common denominator, we can subtract the numerators while keeping the denominator constant, thus the subtraction is given as follows:

(20 - 3)/5 = 17/5.

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Answer:

50/b if I may say I think my answer is wrong

Answer:

It's 10 inches

Step-by-step explanation

1/2bh=A

1/2x5xh=25

5/2xh=25

2x5/2xh=25x2

5h=50

5/5h=50/5

h=10

Answer:

\(y=c_1\cos(x)+c_2\+\sin(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}}}\)

Step-by-step explanation:

Given the second-order differential equation, \(y'' + y = cos2(x)\), solve it using variation of parameters.

(1) - Solve the DE as if it were homogenous and find the homogeneous solution\(y'' + y = cos2(x) \Longrightarrow y'' + y =0\\\\\text{The characteristic equation} \Rightarrow m^2+1=0\\\\m^2+1=0\\\\ \Longrightarrow m^2=-1\\\\\ \Longrightarrow m=\sqrt{-1} \\\\\Longrightarrow \boxed{m=\pm i} \\ \\\text{Solution is complex will be in the form} \ \boxed{y=c_1e^{\alpha t}\cos(\beta t)+c_2e^{\alpha t}\sin(\beta t)} \ \text{where} \ m=\alpha \pm \beta i\)

\(\therefore \text{homogeneous solution} \rightarrow \boxed{y_h=c_1\cos(x)+c_2\sin(x)}\)

(2) - Find the Wronskian determinant

\(|W|=\left|\begin{array}{ccc}y_1&y_2\\y'_1&y'_2\end{array}\right| \\\\\Longrightarrow |W|=\left|\begin{array}{ccc}\cos(x)&\sin(x)\\-sin(t)&cos(x)\end{array}\right|\\\\\Longrightarrow \cos^2(x)+\sin^2(x)\\\\\Longrightarrow \boxed{|W|=1}\)

(3) - Find W_1 and W_2

\(\boxed{W_1=\left|\begin{array}{ccc}0&y_2\\g(x)&y'_2\end{array}\right| and \ W_2=\left|\begin{array}{ccc}y_2&0\\y'_2&g(x)\end{array}\right|}\)

\(W_1=\left|\begin{array}{ccc}0&\sin(x)\\\cos^2(x)&\cos(x)\end{array}\right|\\\\\Longrightarrow \boxed{W_1= -\sin(x)\cos^2(x)}\\\\W_2=\left|\begin{array}{ccc}\cos(x)&0\\ -\sin(x)&\cos^2(x)\end{array}\right|\\\\\Longrightarrow \boxed{W_2= \cos^3(x)}\)

(4) - Find u_1 and u_2

\(\boxed{u_1=\int\frac{W_1}{|W|} \ and \ u_2=\int\frac{W_2}{|W|} }\)\

u_1:

\(\int(\frac{-\sin(x)\cos^2(x)}{1}) dx\\\\\Longrightarrow-\int(\sin(x)\cos^2(x)) dx\\\\\text{Let} \ u=\cos(x) \rightarrow du=-sin(x)dx\\\\\Longrightarrow\int u^2 du\\\\\Longrightarrow \frac{1}{3}u^3\\ \\\Longrightarrow \boxed{u_1=\frac{1}{3}\cos^3(x)}\)

u_2:

\(\int\frac{\cos^3(x)}{1}dx\\ \\\Longrightarrow \int \cos^3(x)dx\\\\ \Longrightarrow \int (\cos^2(x)\cos(x))dx \ \ \boxed{\text{Trig identity:} \cos^2(x)=1-\sin^2(x)}\\\\\Longrightarrow \int[(1-\sin^2(x)})\cos(x)]dx\\\\\Longrightarrow \int \cos(x)dx-\int (\sin^2(x)\cos(x))dx\\\\\Longrightarrow \sin(x)-\int (\sin^2(x)\cos(x))dx\\\\\text{Let} \ u=\sin(x) \rightarrow du=cos(x)dx\\\\\Longrightarrow \sin(x)-\int u^2du\\\\\Longrightarrow \sin(x)-\frac{1}{3} u^3\)\

\(\Longrightarrow \boxed{u_2=\sin(x)-\frac{1}{3} \sin^3(x)}\)

(5) - Generate the particular solution

\(\text{Particular solution} \rightarrow y_p=u_1y_1+u_2y_2\)

\(\Longrightarrow y_p=(\frac{1}{3}\cos(x))(\cos(x))+(\sin(x)-\frac{1}{3} \sin^3(x))(\sin(x))\\\\ \Longrightarrow y_p=\frac{1}{3}\cos^4(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)\\\\\Longrightarrow \boxed{y_p=\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}\)

(6) - Form the general solution

\(\text{General solution} \rightarrow y_{gen.}=y_h+y_p\)

\(\boxed{\boxed{y=c_1\cos(x)+c_2\+\sin(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}}}\)

Thus, the solution to the given DE is found where c_1 and c_2 are arbitrary constants that can be solved for given an initial condition. You can simplify the solution more if need be.

Answer:

It should be about 11

3 2/3 + 4 1/8 + 3 1/4 = 264/24= 11 1/24

A fraction is a part of a whole. If Mr. Garcia's class ate 3 2/3 = pizzas. Mrs. Rizzoli's class ate 4 1/8 - pizzas, and Mrs. Tindal's class 3 1/4 ate 3 - pizzas. About 9 pizzas eaten by all three 4 classes.

A fraction is a part of a whole.

Given,

Mr. Garcia's class ate 3 2/3 = pizzas.

Mrs. Rizzoli's class ate 4 1/8 - pizzas, and

Mrs. Tindal's class 3 1/4 ate - pizzas.

We need to find total number of pizzas eaten by all three 4 classes.

3 2/3+4 1/8+ 3 1/4

11/3+33/8+13/4

We need to find LCM of 3, 8 and 4

The LCM of 3,8 and 4 is 24

(11(3)+3(33)+13(6))/2

210/24

8.75

About 9.

Therefore total pizzas eaten by all is about 9 pizzas.

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"The mean will be higher than the median in any distribution that" ;

has a positively skewed distribution

A positively skewed distribution is one in which the majority of data values are clustered towards the lower end of the range, while the rest of the values are spread out towards the higher end of the range. As a result, the mean (the average of all the data values) will be higher than the median (the middle value of the data set).

This is because the mean is affected by the higher values in the distribution, while the median is not.

Positively skewed distributions are common in real-world data sets and are often seen in income distributions, stock market returns, and other economic data.

For example, a distribution of incomes may have a few very high earners pushing up the mean, while the majority of people make much lower amounts, resulting in a median that is lower than the mean.

Similarly, stock market returns may have a few very large returns that pull the mean up, while the majority of returns are much lower, resulting in a median that is lower than the mean.

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Answer: 35 square units.

Step-by-step explanation:

- In this question you need to substitute in the given values to the triangle to fulfill the equation for the area of triangle.

Area of a triangle = \(\frac{1}{2}\) x base x height.

The base was 'x', which was 14 units.

The height was 'h', which was given as 5 units.

Substitute these into the equation.

Answer: __________________________________________

3x + 9

Answer: 3x + 9

Step-by-step explanation:

Answer:

6.5 * 10 ^5

Step-by-step explanation:

650,000

Scientific notation is of the form

a * 10 ^b where a is between 1 and less than 10

Move the decimal 5 places to the left

6.50000

5 becomes the exponent b,  since we moved it to the left, the exponent is positive

6.5 * 10 ^5

Answer:

the answer is:6.5times 10to the power of 5

When 6 fewer than s is no less than −78, the solution in interval notation is (84,∞)

Interval notation is a way of writing subsets of the real number line

Given,

6 fewer than s is no less than -78

6-s < -78

Move 6 to right hand side

-s < -78-6

-s < -84

s > 84

Then the interval notation is (84,∞)

Hence, when 6 fewer than s is no less than −78, the solution in interval notation is (84,∞)

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Answer:

220 divided by it self (220) will get you 1

Step-by-step explanation:

220/220=1

Answer:

220

Step-by-step explanation:

Answer:

3 > n - 1 =  n < 4

t − 3 > −2 = t > 1

4 < p - 2 = p > 6

2 ≥ h − 5 = h ≤ 7

v − 5 > −9 = v > 4

p + 3 ≤ 4 = p ≤ 1

- 7 < 7 + t = t > 14

6 + k > 5 = k > 1

12 ≤ r + 5 = r  ≥  7

w − (−4) < 8 = w < 4

Step-by-step explanation:

Hope this helps

Answer:

the one that looks like a v

Step-by-step explanation:

bc for every y-input, there is only one output-x

The correct logarithm form is: a. log5 125 = 3

Question is about finding the logarithm form of 5³ = 125 using the given options.

The correct logarithm form is:

a. log5 125 = 3

Here's the step-by-step explanation:

1. The exponential form is given as 5³= 125.
2. To convert it to logarithm form, you have to express it as log(base) (argument) = exponent.
3. In this case, the base is 5, the argument is 125, and the exponent is 3.
4. Therefore, the logarithm form is log5 125 = 3.

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The determinant of the linear transformation t(f)=2f 3f' from p2 to p2 is 36.

To find the determinant of the linear transformation t(f)=2f 3f' from p2 to p2, we first need to represent the transformation as a matrix.

Let's start by choosing a basis for p2, say {1,x,x²}. Then, the linear transformation t can be represented by the matrix

[2 0 0]
[0 3 0]
[0 0 6]

To find the determinant of this matrix (and hence the determinant of the linear transformation), we can use the formula for the determinant of a 3x3 matrix:

det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)

Plugging in the entries of our matrix, we get:

det(t) = 2(3×6 - 0×0) - 0(2×6 - 0×0) + 0(2×0 - 3×0)
      = 36

Therefore, the determinant of the linear transformation t(f)=2f 3f' from p2 to p2 is 36.

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Answer:

1,500 points per minute

Step-by-step explanation:

You can tell it's 1500 points per minute because the lines meet up at (2,3) meaning that 3/2 = 1500, to double check you could do 9/6 where the points also meet up at the exit of the graph which is ALSO 1.5 meaning 1,500 points per minute