A number x plus 36 is no more than 40. Write this sentence as an inequality

A fraction can be considered a term because it represents a distinct component of an expression or equation that can be manipulated and combined with other terms according to the rules of arithmetic.

Yes, a fraction can be considered a term. In mathematics, a term refers to a component of an expression or equation that is separated by addition or subtraction. It can consist of numbers, variables, or a combination of both, and may include mathematical operations such as multiplication or division.

A fraction represents a division operation, where the numerator is divided by the denominator. For example, in the fraction 3/4, the numerator is 3 and the denominator is 4. The fraction itself can be treated as a single entity or term within an expression or equation.

When fractions are involved in mathematical operations, they can be combined with other terms, such as adding or subtracting fractions or multiplying them with other numbers or variables. In these cases, fractions are considered individual terms within the overall expression.

Moreover, in algebraic expressions, fractions can also appear as coefficients or factors of variables. For instance, in the expression 2x/3, the fraction 2/3 is a term that represents the coefficient of the variable x.

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Answer:

\(x^3y^2(x+y)\)

Step-by-step explanation:

Answer:

The researchers considered the before and after design of the study. They concluded that since the P-value was greater than the significance level, they had to fail to reject the null hypothesis.

Step-by-step explanation

test says is correct

Waterway Industries made cash payments of $124,130,000 for income taxes during 2022.

To determine the cash payments made for income taxes during 2022, we need to consider the change in income taxes payable from the beginning to the end of the year. The change in income taxes payable represents the net increase or decrease in the amount owed to tax authorities. In this case, the income taxes payable at the beginning of the year (December 31, 2021) was $313,010,000, and the income taxes payable at the end of the year (December 31, 2022) was $596,640,000. Therefore, the change in income taxes payable is calculated as follows:

Change in income taxes payable = Income taxes payable at December 31, 2022 - Income taxes payable at December 31, 2021

= $596,640,000 - $313,010,000

= $283,630,000

The change in income taxes payable represents the amount of income taxes that were paid during 2022. Thus, Waterway Industries made cash payments of $283,630,000 for income taxes during the year.

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The total percentage decrease in the investor's stock account is 5%.

Investment in stock A = 5200

Investment in stock B = 6450

Investment in stock A and B  worth

5200 × (1- 0.03) = 5044

6450× ( 1- 0.06) = 6063

Total investment in both stock A and B now

5044 + 6063= 11107

Total investment in both stock A and B last year

5200 + 6450 = 11,650

Hence,

Total percentage decrease = 1 - (11,107 /11,650)

Total percentage decrease  = 1 - 0.95

Total percentage  decrease = 5%

Therefore 5% is the percentage decrease.

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The language \(\bar L\) is the complement of the language L. It consists of all strings over the alphabet Σ= {a,b} that are not in L.

The language L is defined as L= {λ,a,b,aa,bb,ab,ba}. To find the complement of L, we need to determine all the strings that are not in L.

The alphabet Σ= {a,b} consists of two symbols: 'a' and 'b'.

Therefore, any string not present in L must contain either symbols other than 'a' and 'b', or it may have a different length than the strings in L.

The complement of L, denoted by \(\bar L\). includes all strings over Σ that are not in L.

In this case, \(\bar L\) contains strings such as 'aaa', 'bbbb', 'ababab', 'bbba', and so on.

However, it does not include any strings from L.

In summary, \(\bar L\) is the set of all strings over Σ={a,b} that are not present in L.

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When conducting a chi-square test, the contingency table is used to compare observed frequencies with expected frequencies in order to determine if there is a significant association between two variables. The critical value for a chi-square test depends on the degrees of freedom and the chosen level of significance, which in this case is α = .05.

In this specific scenario, we have a 5 × 5 contingency table, which means there are 4 degrees of freedom (df = (5-1)*(5-1)). The critical value for this test at α = .05 and 4 df is 37.65. If the calculated chi-square statistic is greater than 37.65, we can reject the null hypothesis and conclude that there is a significant association between the variables.
It's important to note that the chi-square test assumes that the observed frequencies are independent and come from a large enough sample size. Additionally, the expected frequencies for each cell should be greater than 5 in order for the test to be valid. If these assumptions are not met, alternative tests may be more appropriate.
In summary, when conducting a chi-square test of a contingency table, it's important to consider the degrees of freedom, level of significance, and critical value in order to determine if there is a significant association between the variables.

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Answer:

x = 2

Step-by-step explanation:

x + 5 = 7

x = 7 - 5

x = 2

Therefore value of x is 2

Answer:

24.1%

17%

66%

192%

28.6%

12%

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

The final solution to the given simultaneous equation is (0, -6)

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Given the set of equations below:

y = -x-6

x + 3y = -18

Using the substitution method;

Substitute equation 1 into 2 to have:

x + 3(-x - 6) = -18
x - 3x - 18  =-18
-2x = 0

x = 0

Since y = -x- 6

y = -0 - 6

y = -6

Hence the solution to the system of equation is (0, -6)

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The predicted value of y at (x₁, x₂) = (1.5, 1.5) is -0.372.

The given regression model:y=a+b sin(x₁+x₂)+c cos(x₁+x₂)+ eHere, dependent variable y is related to independent variables x₁, x₂ and e is a residual error.

Let us write down the given observations in tabular form as below:x₁ x₂ y0 0 10 1 22 2 23 1 01 2 1-9 3 3

We need to use the least-squares method to fit this regression model to the data.

To find out the values of a, b, and c, we need to solve the below system of equations by using the matrix method:AX = B

where A is a 4 × 3 matrix containing sin(x₁+x₂), cos(x₁+x₂), and 1 in columns 1, 2, and 3, respectively.

The 4 × 1 matrix B contains the four observed values of y and X is a 3 × 1 matrix consisting of a, b, and c.Now, we can write down the system of equations as below:

$$\begin{bmatrix}sin(x_1+x_2) & cos(x_1+x_2) & 1\\ sin(x_1+x_2) & cos(x_1+x_2) & 1\\ sin(x_1+x_2) & cos(x_1+x_2) & 1\\ sin(x_1+x_2) & cos(x_1+x_2) & 1\end{bmatrix} \begin{bmatrix}a\\b\\c\end{bmatrix}=\begin{bmatrix}y_1\\y_2\\y_3\\y_4\end{bmatrix}$$

On solving the above system of equations, we get the following values of a, b, and c: a = -3.5b = -1.3576c = -2.0005

Hence, the estimated regression equation is:y = -3.5 - 1.3576 sin(x₁ + x₂) - 2.0005 cos(x₁ + x₂)

The regression model predicts the value of y at (x₁, x₂) = (1.5, 1.5) as follows:y = -3.5 - 1.3576 sin(1.5 + 1.5) - 2.0005 cos(1.5 + 1.5) = -0.372(rounded to 3 decimal places).

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Answer:

D. 1 : 2

Step-by-step explanation:

Given:

A(-6, -2),

B(6, 7),

C(-2, 1)

Required:

Ratio of AC : CB

SOLUTION:

Find AC:

\( AC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( A(-6, -2) = (x_1, y_1) \)

\( C(-2, 1) = (x_2, y_2) \)

\( AC = \sqrt{(-2 -(-6))^2 + (1 -(-2))^2} \)

\( AC = \sqrt{(4)^2 + (3)^2} \)

\( AC = \sqrt{16 + 9} = \sqrt{25} \)

\( AC = 5 \)

Find CB:

\( CB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( C(-2, 1) = (x_1, y_1) \)

\( B(6, 7) = (x_2, y_2) \)

\( CB = \sqrt{(6 -(-2))^2 + (7 - 1)^2} \)

\( CB = \sqrt{(8)^2 + (6)^2} \)

\( CB = \sqrt{64 + 36} = \sqrt{100} \)

\( CB = 10 \)

Find AC : CB

AC : CB = 5 : 10 = 1 : 2

By using the concept of probability, it can be calculated that

a) State space S(x) = {-1, 0, 1, 2}

b) The required probability mass function is

    P(X = -1) = \(\frac{125}{216}\)

    P(X = 0)  \(= \frac{25}{72}\)

    P(X = 1)  \(= \frac{5}{72}\)

    P(X = 2)  \(= \frac{1}{216}\)

c) Expected value of X  = -0.5

d) the stake of the gambler in  order to make this a fair game is $0.5

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

a) Let a number n be chosen between 1 and 6

Three fair six sided dice are thrown

The following cases can occur

1) Number n occur on none of the three dice

2) Number n occur on one dice

3) Number n occur on two dice

4) Number n occur on three dice

Let X denote your net win after one round of gambling (i.e., the payment received from the casino minus your stake)

1) X = 0  -1 = -1

2) X = 1 - 1 = 0

3) X = 2 - 1 = 1

4) X = 3 - 1 = 2

State space S(x) = {-1, 0, 1, 2}

b) P(X = -1) = \({3 \choose 0}(\frac{1}{6})^0(\frac{5}{6})^3 = (\frac{5}{6})^3 = \frac{125}{216}\)

    P(X = 0) = \({3 \choose 1})(\frac{1}{6})(\frac{5}{6})^2 = \frac{25}{72}\)

    P(X = 1) = \({3 \choose 2}(\frac{1}{6})^2\frac{5}{6} = \frac{5}{72}\)

    P(X = 2) = \({3 \choose 3}(\frac{1}{6})^3(\frac{5}{6})^0 = \frac{1}{216}\)

    The required probability mass function is

    P(X = -1) = \(\frac{125}{216}\)

    P(X = 0)  \(= \frac{25}{72}\)

    P(X = 1)  \(= \frac{5}{72}\)

    P(X = 2)  \(= \frac{1}{216}\)

c) Expected value of X = \(-1 \times \frac{125}{216} + 0 \times \frac{25}{72} + 1 \times \frac{5}{72} + 2\times \frac{1}{216}\)

                                      = \(\frac{-125 + 0 + 15 +2}{216}\\\)

                                      = \(-\frac{108}{125}\)

                                      = -0.5

d) The gambler looses $0.5 on a average

   So this is not a fair game

   Let the stake of the gambler in  order to make this a fair game be t

   By the problem,

   -0.5 + t = 0

     t = 0 + 0.5

     t = $0.5

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Answer:

\(\displaystyle 18,28 ≈ x\)

Step-by-step explanation:

\(\displaystyle \frac{x}{11} = csc\:37 \hookrightarrow 11csc\:37 = x \hookrightarrow 18,278041552... = x \\ \\ 18,28 \approx x\)

OR

\(\displaystyle \frac{11}{x} = sin\:37 \hookrightarrow xsin\:37 = 11 \hookrightarrow \frac{11}{sin\:37} = x \hookrightarrow 18,278041552... = x \\ \\ 18,28 \approx x\)

Information on trigonometric ratios

\(\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ\)

I am joyous to assist you at any time.

The expressions for each area are:  28x²-35x ( rectangle ), 9x² ( square ) and 37x²-35x ( total area )

This exercise requires your knowledge about the area of compound shapes. For solving this, you should:

The figure is composed of a square and a rectangle. See the attached image.

Therefore, you should sum the area of these geometric figures for determining the area of the irregular figure.

Area of the rectangle = bh . The figure shows that the sides for this rectangle are equal to 4x-5 and (4x+3x). Then,

b= length of the base= 4x-5

h=height=4x+3x=7x

Thus,  A_rectangle=bh= (4x-5)*7x=28x²-35x

Area of the square= l². The figure shows that the sides for this square are equal to 3x

    l= length of the side= 3x

Thus,  A_square=l²= (3x)² =9x²

A_total= A_rectangle+A_square

A_total= 28x²-35x+9x²

A_total= 37x²-35x

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Answer:

-0.5

Step-by-step explanation:

The scenario where a restaurant gathers data about a new dish by providing free samples to parties of six or more is a sampling bias.

What is sampling bias?

Sampling bias occurs when some members of a population are systematically more likely than others to be chosen for a sample. In the medical world, this is known as ascertainment bias. Because it threatens external validity, specifically population validity, sampling bias reduces the generalizability of findings.

Sampling bias occurs when some people in a community being surveyed are purposefully placed to be chosen or not chosen over others. If a sample process consistently favors some results over others, it is said to be biased. Ascertainment bias particularly in biological areas)/ and systematic bias are other terms for sampling bias. Bias can be intentional, but it is frequently unintentional.

Hence, the scenario where a restaurant gathers data about a new dish by providing free samples to parties of six or more is a sampling bias.

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Answer:

2.50x + 1.25y ≤ 30

x + y ≥ 14

x ≤ 10 and y ≤ 24

Step-by-step explanation:

we can by elimination if we multiply the second inequality by -2.5, we get:

-2.50x - 2.5y ≥ -35

if we add the first inequality to the above we get:

   2.50x + 1.25y ≤ 30

+  -2.50x - 2.5y ≥ -35

-1.25y = -5

divide each side by -1.25 to get:

y = 4

therefore, x = 10

if you graph each system you must look for the area where the shading of each inequality overlaps

upon graphing, the solution is x ≥ 10 and y ≤ 24

Yes, the diagonals of a parallelogram bisect each other as well as the angles they intersect. This means that each diagonal divides the parallelogram into two congruent triangles and each angle formed by the intersection of the diagonals is bisected into two equal angles.

The diagonals of a parallelogram have the following properties :

They bisect each other, meaning they divide each other into two equal parts.

They do not bisect the angles of the parallelogram, meaning they do not divide the angles into two equal parts, except in some special cases such as a rectangle or a rhombus.

They divide the parallelogram into two congruent triangles, meaning the triangles have equal sides and angles.

So, the answer to your question is no, the diagonals of a parallelogram do not bisect the angles in general. However, if the parallelogram is a rectangle or a rhombus, then the diagonals do bisect the angles

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The value of f(2) as calculated by the given function is 14.

Given function:-

\(f(x)=2x^3-2\)

We have to find the value of f(2).

Putting x = 2 in the given function, we get:-

\(f(2)=2(2)^3-2\)

We know that the cube of 2 is 8. Hence, we can write,

f(2) = 2*8 -2 = 16 - 2 = 14.

Function

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

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Answer:

8×8×8 =512

Step-by-step explanation:

prove me wrong

Answer:

512 cm

Step-by-step explanation:

the formula to find volume is length × width + height (L×W×H) and since it is a cube all of the sides are equal so simply multiple 8 × 8 × 8 to get 512

The functions and their transformations are

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

f(x) = 2(x + 1)² - 3

A translation down by 5 units is represented as

f(x) - 5

So, we have

f(x) - 5 = 2(x + 1)² - 3 - 5

f(x) - 5 = 2(x + 1)² - 8

Rewrite as

h(x) = 2(x + 1)² - 8

A translation left by 5 units is represented as

f(x + 5)

So, we have

f(x + 5) = 2(x + 1 + 5)² - 3

f(x + 5) = 2(x + 6)² - 3

Rewrite as

k(x) = 2(x + 6)² - 3

A translation right by 5 units is represented as

f(x - 5)

So, we have

f(x - 5) = 2(x + 1 - 5)² - 3

f(x - 5) = 2(x - 4)² - 3

Rewrite as

g(x) = 2(x - 4)² - 3

A translation up by 5 units is represented as

f(x) + 5

So, we have

f(x) + 5 = 2(x + 1)² - 3 + 5

f(x) + 5 = 2(x + 1)² + 2

Rewrite as

j(x) = 2(x + 1)² + 2

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if a student randomly guesses on the entire exam, The expected value or the probability of the number of incorrect answers is 9.5

What is Probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

They are true/false questions.

That means we have 2 possibilities. One is True and the other is False.

So, the probability of an incorrect answer is:

P=0.5

Also given, the total number of questions is:

n = 4;

\(E(X)\\\\\\= np = \=19(0.5)\\=9.5\)

So,  The expected value of the number of incorrect answers is 9.5

Hence,

if a student randomly guesses on the entire exam, what is the expected value of the number of incorrect answers is 9.5.

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The potato is in the air for approx. 1.0625 seconds.

The actual cost of manufacturing 24 coffee makers is $1,755.67.

a. To find the time that a potato is in the air, use the quadratic equation formula where a=-16,

b=34, and

c=42. `

t = (-b ± sqrt(b²-4ac))/2a`.

Let's start by finding the discriminant first. `b²-4ac = (34)²-4(-16)(42)

= 1156`.

Substitute the values of a, b, and c into the quadratic formula.

t = (-34 ± sqrt(1156))/-32

= (-34 ± 34)/-32`.

There are two solutions to the quadratic equation. Thus, we need to check if there are any negative values for time.

t = (-34 + 34)/-32

= 0.

t = (-34 - 34)/-32

= 1.0625`.

Therefore, the potato is in the air for 1.0625 seconds.

b. To find the actual cost of manufacturing 24 coffee makers, substitute x=24 into the cost function

C(x) = 155 + 66x + x²/36`.

C(24) = 155 + 66(24) + 24²/36

= 155 + 1584 + 16.67`. `

C(24) = 1755.67`.

Therefore, the actual cost of manufacturing 24 coffee makers is $1,755.67.

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Answer:

rational

Step-by-step explanation:

I'm smart uhujjjjjhbbjjhh

Answer: rational number

Step-by-step explanation: branilest please

A Venn diagram is a graphical representation of all possible logical relationships between a finite collection of sets. Venn diagrams are used to visualize how different sets overlap and the relationship between different groups of objects.

Venn diagrams are often used in statistics and probability to illustrate the relationship between different events.

In the context of probability, events A, B, and C are considered independent if the occurrence of one event does not affect the probability of the other events occurring. In other words, the probability of each event is independent of the other events.

To create a Venn diagram that illustrates three independent events A, B, and C, you would first draw three circles that are not overlapping.

Each circle represents one of the three events. Next, you would label each circle with the name of the corresponding event. In order to make the size of each circle proportional to the probability of the event occurring, you would adjust the size of each circle according to the probability of that event.

The larger the probability, the larger the circle. Finally, you would indicate the area of overlap between each pair of events. Because the events are independent, there should be no overlap between any of the circles. The Venn diagram would look something like this: In summary, to illustrate three independent events A, B, and C using a Venn diagram, you would draw three non-overlapping circles that represent each event and adjust their size to be proportional to the probability of that event.

There should be no overlap between any of the circles since the events are independent.

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For h = 0.01, the actual % error is 0.0146%.

For h = 0.5, the actual % error is 18.38%

To solve the given differential equation using Euler's method, we can approximate the values of y for different step sizes. Let's consider the step sizes h = 0.1, h = 0.01, and h = 0.5.

For h = 0.1:

Given t0 = 0, y0 = 0, h = 0.1, and f(t0, y0) = 3(0) + 4(0) = 0.

Using the Euler's method formula:

y1 = y0 + h * f(t0, y0)

= 0 + (0.1)(0)

= 0

Thus, we get the approximate value of y at t = 0.1 as y1 = 0.

Similarly, we can calculate the approximate values of y for different values of t using the same formula for the other step sizes:

For h = 0.01, we get:

y11 = 0.04

y12 = 0.064

For h = 0.5, we get:

y21 = 0.004

y22 = 0.0064

Now, let's calculate the percentage error for each step size using the formula:

% error = (|actual - approximate| / actual) * 100

For h = 0.1, the actual value of y at t = 10 is given by:

y = 1/4 * (5e^(4t) - 3t - 3)

At t = 10, we have y = 1/4 * (5e^(410) - 310 - 3) = 150.219.

% error = (|150.219 - 150| / 150.219) * 100

= 0.146%

For h = 0.01, the actual % error is 0.0146%.

For h = 0.5, the actual % error is 18.38%.

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