What are the 10 factors of 12?.

Example of  linear inequalities; y ≤ x – 1 and y < –2x + 1

A combination of linear inequality equations with the same variables is referred to as a system of linear inequalities.

There are five inequality symbols used to represent equations of inequality.

These are less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠). Inequalities are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable.

Example of  linear inequalities;

Graph the following system of linear inequalities:

y ≤ x – 1 and y < –2x + 1

Graph the first inequality y ≤ x − 1.

We will draw a solid border and shade below the line due to the "less than or equal to" mark.

On the same x-y axis, graph the second inequality, y -2x + 1.

In this instance, the less-than symbol will cause our boundaries to be dashed or dotted. Under the border, cast a shade.

As a result, the darker-colored zone extending indefinitely downward is the solution to this inequality problem, as seen below.

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The average speed of a car is 93.34 km/h

Average speed is the mean value of the speed of a body over a period of time. The formula for average speed is needed since the speed of a moving body is not constant and varies across a period of time.

Average speed formula is the average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as: Total distance travelled / total speed

According to the equation,

A car covers the road from city A to city B, 40 km, in 30 minutes, and the road from city B to C, 30 km, in 15 minutes

Total distance a car covers is 40 + 30

= 70km

Total time a car takes is 30 + 15

= 45minutes = 0.75 hours

Average speed = total distance / total time

Average speed = 70 / 0.75

= 93.34 km/h

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The quadrants that give the solution of the inequality y ≤ ²/₃x - 4 is; I, III, and IV

We are given the inequality as;

y ≤ ²/₃x - 4

Let us draft some coordinates before plotting the graph;

When x = 0;

y ≤ ²/₃(0) - 4

y ≤ -4

When x = 1;

y ≤ ²/₃(1) - 4

y ≤ -3¹/₃

When x = 2;

y ≤ ²/₃(2) - 4

y ≤ -2 ²/₃

when x = -1;

y ≤ ²/₃(-1) - 4

y ≤ -4²/₃

From the attached graph Inequality, it is clear that the shaded area which represents the quadrants that possess the solution to the inequality that;

Quadrants I, III, and IV

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(a) The mean is 32, and the standard error is 0.068 (b) The expected shape will be approximately normal (c) The probability of scoring less than 60% is 0.278

As the number of questions (n) is 50 and the probability of getting the correct answer (p) is 0.64, the mean can be calculated as follows;

E(x) = np

E(x) = 50 × 0.64

E(x) = 32

The standard error is calculated as follows;

SE = √p×(1-p) ÷ n

SE = √0.64 × (1-0.64) ÷ 50

SE = √0.004608

SE = 0.068

Therefore, the mean is calculated to be 32, and the standard error is 0.068

As the sample size is large therefore the expected shape will be approximately normal

To calculate the probability of scoring less than 60%, we first calculate the z-score using:

z = (x – μ) / σ

z = (0.60 - 0.64) / 0.068

z = -0.588

So we have;

P (x < 60%) = P (z < -0.588)

P (x < 60%) = 0.278

Therefore the probability of scoring less than 60% is 0.278

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Using compound interest formula [tex]A = p(1 +\frac{r}{n} )^{nt}[/tex] , the the amount after 5 years is  $15,095.39

The total amount a college student has in a saving account if 13000 dollars was invested and earned 3% compounded quarterly for 5 years can be calculated as follows:

Therefore, it is compounded quarterly which means  4 times.  

[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]

where

Therefore,

p = 13000 dollars

t = 5 years

n = 4

r = 3% = 0.03

Therefore,

[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]

[tex]A = 13000(1+ \frac{0.03}{4} )^{(4)(5)}[/tex]

A = 13,000.00(1 + 0.0075)²⁰

A = $15,095.39

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Answer:

1/6

Step-by-step explanation:

1/2 *1/3=1/6

The sum of and diffrence identities to find the exact values of sine cosine and tangent are calculated below :

Given that,

1. 75º = 30° + 45 2. 15º = 45° - 30° 3. 105° = 60° + 450 4. 165º = 135° + 30° 5. 195º = 225º – 30° 6. 255 – 300

To find them we need to know the respective formulas:

In relation to the illustration above, the key sin,cos,tan formulas are:

sin A = Opposite side/Hypotenuse = BC/AB

cos A = Adjacent side/Hypotenuse = AC/AB

tan A = Opposite side of triangle /Adjacent side of triangle = BC/AC

1) 75°

sin(75°)= 0.966

cos(75°)=0.259

tan(75°)=3.732

2) 105°

sin(105°)=0.966

cos(105°)= -0.259

tan(105°)= -3.732

3) 175°

sin(175°)=-0.259

cos(175°)= -0.966

tan(175 )=0.268

4) 11π/12

sin(11π/12)=0.050

cos(11π/12)=0.999

tan(11π/12)=0.050

5) 17π/12

sin(17π/12)=0.078

cos(17π/12)=0.997

tan(17π/12)=0.078

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By using the concept of integration, it can be proved that

The absolute value of the integral is less than or equal to the integral of the absolute value.

What is integration?

Integration is the process of adding of different individual parts into a whole.

Integration is the reverse of differentiation.

Integration is used to find the area under curve

Let [tex]f^+(x)[/tex] = max{f(x), 0} and [tex]f^-(x)[/tex] = -min{f(x) , 0}

[tex]f^+(x) + f^-(x) = \frac{1}{2}[f(x) + 0 + |f(x) - 0| - f(x) - 0+|f(x) -0|] = |f(x)|\\ f^+(x) - f^-(x) = \frac{1}{2}[f(x) + 0 + |f(x) - 0| + f(x) + 0-|f(x) -0|] = f(x)\\[/tex]

[tex]|\int^a_bf| = |\int^a_bf^+ -\int^a_b f^-| \leq \int^a_bf^+ + \int^a_bf^- = \int^a_b (f^+ + f^-) = \int^a_b|f|[/tex]

So [tex]|\int^a_bf|\leq\int^a_b|f|[/tex]

So, the absolute value of the integral is less than or equal to the integral of the absolute value.

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Answer:

[tex]\frac{1}{\sqrt{2}}[/tex]

Step-by-step explanation:

Hence, the property is based on addition property,

OG=NQ and GE=UY,

so OG +GE=NQ +UY.

When the same amount is added to both sides of an equation, the equation does not change, according to the addition property of equality. A = B remains valid even if a number x is added to both sides of the equation. It can be mathematically stated as A + x = B + x.

As demonstrated below

OG=NQ and GE=UY,

so OG +GE=NQ +UY

So this property leads to addition property.

So the correct option regarding this,

Addition property.

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The minimum sample size needed is 93.

Given:

A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%.

here

n = 101

p = 0.5

e = 5%=0.05

z score at 95% = 1.96

[tex]n'=\frac{n}{1+\frac{z^2*p(1-p)}{e^2} }[/tex]

On submitting and solving using calculator

n = 93

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The compound inequality describes the possible lengths for the third side, x is -4< c< 14.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as a trigon. Every triangle has three sides and three angles, with some of them being the same.

A triangle with A, B, and C vertices is symbolized by ΔABC

The Triangle Inequality Theorem states that given two triangle side lengths, the length of the third side must be greater than the difference and less than the sum of the two provided sides. The third side c of a triangle must be the same as the first two sides a and b:

(a - b) < c < (a + b)

As a result, let a = 5 and b = 9

(5-9) <c (5+9)

-4< c< 14

As a result, the third side of the triangle must follow the inequality, which is -4< c <14

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Answer: The answer is $6.00.

Step-by-step explanation: 25+5=30 then, 36-30=6.00

(I don't know if it makes sense to you, but the answer is $6.00)

(Also, can I get brainly for this?)

The inverse of the 4 × 4 matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] found using an online matrix tool  is presented as follows;

[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0\\ 0& 0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\begin{bmatrix}\dfrac{1}{a} & 0& 0 &0 \\\\ 0& \dfrac{1}{b} & 0 & 0\\\\0 &0 &\dfrac{1}{c} & \\\\0 &0 &0 &\dfrac{1}{d} \\\end{bmatrix}[/tex]

The inverse, A⁻¹ of a matrix, A, can be found using the formula;

[tex]A^{-1}=\dfrac{adj \, A}{det\, A}[/tex]

The adjugate of the specified matrix, [tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}[/tex] is found using an online tool as follows;

[tex]adj\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}=\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}[/tex]

The value of the determinant of the matrix found using an online calculator is presented as follows;

[tex]det\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix} = a\cdot b \cdot c\cdot d[/tex]

The inverse of the matrix in the question is therefore;

[tex]\begin{bmatrix}a &0 &0 &0 \\ 0& b& 0& 0 \\ 0&0 &c &0 \\ 0& 0& 0& d\\\end{bmatrix}^{-1}=\dfrac{\begin{bmatrix}b\cdot c\cdot d &0 &0 &0 \\ 0& a\cdot c \cdot d& 0& 0 \\ 0&0 &a\cdot b\cdot d &0 \\ 0& 0& 0& a\cdot b\cdot c\\\end{bmatrix}}{a\cdot b\cdot c \cdot d} = \begin{bmatrix}\dfrac{1}{a} &0 &0 &0 \\ \\0& \dfrac{1}{b} & 0& 0 \\ \\0&0 &\dfrac{1}{c} &0 \\\\ 0& 0& 0& \dfrac{1}{b} \\\end{bmatrix}[/tex]

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Answer:

60

Step-by-step explanation:

the 6 is in the tens place so it is worth 60

Hopes this helps please mark brainliest

Answer: 60

Step-by-step explanation: the value of 263.7  is; 60 pls mark brainly i really need it pls i neeed it its important to me bc i have a gammy who just passed away last week

The 99% of a confidence interval for the average maximum HP for the experimental engine. (843.0906, 916.9094)

Given,

In the question:

Given that the mean of the Population = 830HP

Given that the size of the sample  'n' = 25

Given that the mean of the sample = 880HP

Given that the sample standard deviation = 55HP

To find the confidence interval for the average maximum HP for the experimental engine.

Use a significance level of α=0.01.

Now, According to the question:

Degrees of freedom = n-1 =25 - 1 = 24

t₀.₀₀₅ = 3.3554

The 99% of a confidence interval for the average maximum HP for the experimental engine.

[tex](x -\frac{t_0_._0_0_1}{2},24\frac{S.D.}{\sqrt{n} } , x^2 +\frac{t_0_._0_0_1}{2},24\frac{S.D.}{\sqrt{n} })[/tex]

(880 - 3.3554 [tex]\frac{55}{\sqrt{25} }[/tex] , 880 + 3.3554 [tex]\frac{55}{\sqrt{25} }[/tex])

(843.0906, 916.9094)

Hence, The 99% of a confidence interval for the average maximum HP for the experimental engine. (843.0906, 916.9094)

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24 hours takes all five machines to fill the same production order.

Given,

Four machines take 30 hours to fill a certain production order.

[tex]Rate = \frac{Work}{Time}[/tex]

Let, Total work = 1 unit

The rate of 4 machines = [tex]\frac{1}{30}[/tex]

We can let the rate of 5 machines be n and create the equation:

[tex]\frac{4}{\frac{1}{30} }=\frac{5}{n}[/tex]

[tex]120=\frac{5}{n}[/tex]

[tex]120n = 5[/tex]

[tex]n=\frac{5}{120}[/tex]

[tex]n=\frac{1}{24}[/tex]

Time taken by five machines = [tex]\frac{1}{\frac{1}{24} }[/tex]

Time is taken by five machines = 24 hours

Hence, 24 hours takes all five machines to fill the same production order.

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a) √2 t |1, -1>

b ) t√0 |0, 1>=0

c) 2t² |1, -1> are the eigenstates of S² with the appropriate eigen value.

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it. The associated eigenvalue, generally indicated by lambda, is the factor by which the eigenvector is scaled.

Eigenvalues and eigenvectors play an important role in the analysis of linear transformations. The prefix eigen- comes from the German word eigen, which means "property," "characteristic," or "own."

a) S- |1,0>= t√(1+0)(1-0+1) |1, 0-1>

=t√2 |1, -1>

=√2 t |1, -1>

∴S±(s, m>=t√(s±m)(s±m+1) |s, m±1>

b) S₊ |0, 0>= t√(0-0)(0+0+1) |0, +1>

=t√0 |0, 1>=0

S₋ |0, 0>=t√(0+0)(0-0+1_) |0. -1>

c) S² |1, 1>= 1(1+1)t² |1, 1>

=2t² |1, -1>

∴ S² |s, m>=s(s+1)t² |s, m>

Hence, |1, -1> and |1, -1> are eigen function of S² with eigen value 2t²s.

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The y-intercept of the given parabola is y = -12.

What is the y-intercept for the parabola?

A graph's y-intercept is the point at which the graph crosses the y -axis. (Because a function must pass the vertical line test, it can only have one y-intercept.) The y-intercept is frequently referred to simply as the y -value.

On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.

The given equation of the parabola is

                        y = x² - x - 12

To find the y-intercept of the given parabola we have to put x = 0 in the above equation, we get

                       y = (0)² - 0 - 12

                      y = -12

Hence, the y-intercept of the given parabola is y = -12.

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If your data contradict your hypothesis, it is by no means a failure.

Data that can be measured or gathered using some benchmark objectives, according to your experimental needs. According to the needs of your experiment, the data produced using this method should either be qualitative or quantitative.

Information not obtained through the random selection of study participants or as part of a controlled experiment. In social science research, non-experimental data are frequently employed, especially when collecting experimental data would be prohibitively expensive or immoral. Non-experimental data require more analysis and interpretation than experimental data since the researcher cannot control which people are placed in the treatment and control groups. Nonexperimental data examples include administrative files, test results, and survey data. As well, they are referred to as observational data.

If your data contradict your hypothesis, it is by no means a failure; in fact, it could be more intriguing since you might discover a fresh way to view the facts. In science, it's usual for theories to be wrong, and new investigations frequently begin as a result.

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The rate at which the distance between the runner and second base changes is 28.71 ft/s.

Given, a batter hits the ball and runs toward first base at a speed of 28 ft/s. we have to find the rate (in ft/s) at which the distance between the runner and second base change when the runner has run 20 ft.

As, distance = speed × time

d = st

On differentiating both the sides

d' = s't + s

d' = 20/28 + 28

d' = 0.71 + 28

d' = 28.71

Hence, the rate at which the distance between the runner and second base changes is 28.71 ft/s.

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The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(x-3)² + 9 = 0

(x-3)²= -9

(x-3)=√-9

(x-3)=√9×√-1

(x-3)=±3i

x=3±3i

Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

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The area of the shaded portion of the inscribed hexagon is; 3.395 ft²

We are given;

Diameter of circle = 5 ft

Thus;

radius; r = 5/2 = 2.5 ft

Now, the long diagonal of the hexagon is given as 5ft and we know that if the side of the hexagon is a, then;

a = d/2

where d is the length of the long diagonal

Formula for area of hexagon is;

A = (3/2) * √3 * a²

Thus;

A =  (3/2) * √3 * 2.5²

A = 16.24 ft²

Area of circle is gotten from the formula;

A = πr²

A = π * 2.5²

A = 19.635 ft²

Thus;

Area of shaded portion = 19.635 ft² - 16.24 ft² = 3.395 ft²

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The energy that an object has as a result of being in a gravitational field is known as gravitational potential energy. It may be expressed as,

U = mgh

Where, m is the object's mass, g is its gravitational field, and h is its height.

The body has a weight of 2 kg and a height of 60 cm. the gravitational potential energy is as follows:

U₁ = 60× 2×g

U₁ = 120kg

The body has a weight of 1 kg and a height of 60 cm. the gravitational potential energy is as follows:

U₂ = 60× 1×g

U₂ = 60g

A body that weighs 4 kg and measures 30 cm in height. the gravitational potential energy is as follows,

U₃ = 4 ×30× g

U₃ = 120g

A body that weighs 3 kg and measures 45 cm in height. the gravitational potential energy is as follows,

U₄ = 3×45×g

U₄ = 135g

The body  has a weight of 2 kg and a height of 30 cm. the gravitational potential energy is as follows,

U₅= 2×30× g

U₅ = 60g

A body that weighs 8 kg and measures 15 cm in height. the gravitational potential energy is as follows,

U₆ = 8 ×15×g

U₆ = 120g

Consequently, the initial gravitational potential energy of the specified pendulum has the following rank:

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The number of degrees of freedom we should use is 14 for makin95% confidence interval.

Degrees of freedom of an estimate is the number of independent pieces of information that went into calculating the estimate. It’s not quite the same as the number of items in the sample. In order to get the df for the estimate, you have to subtract 1 from the number of items.

Degree of freedom of sample size of n : n -1

When we don't have any idea about population standard deviation,

and also, the sample size is less than 30 .

We use t-distribution to calculated the statistics.

According to the question,

We are making a 95% confidence interval

The sample is 15 (<30) . So , we have to adjust and use a t-value instead of a Z score in order to account for the smaller sample size and using the sample SD.  

Note that the t-value depends on the degrees of freedom (df) as a reflection of sample size. When using the t-distribution to compute a confidence interval, df = n-1.

So , making 95% confidence interval for population mean from sample size 15 , we need degree of freedom of 14

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If p(x) and q(x) are arbitrary polynomials of degree at most 2 then

||p||||q|| = 26([tex]\sqrt{640}[/tex]) and angle between p(x) and q(x) is 0.233.

Given that

<p,q> = p(-1)q(-1) + p(0) q(0) + p(3)q(3)

and p(x) = 2x²+ 6 , q(x)= 4x²-4x

then the values of p and q at x = -1,0,3 are given as;

x = -1,

p(-1) = 2(-1)² + 6 = 8   ,    q(-1) = 4(-1)² - 4(-1) = 8

x = 0,

p(0) = 2(0)² + 6 = 6   ,    q(0) = 4(0)² - 4(0) = 0

x = 3,

p(3) = 2(3)² + 6 = 24  ,  q(3) = 4(3)²- 4(3) = 24.

<p,q> = p(-1)q(-1) + p(0)q(0) + p(3)q(3)

         = (8)(8) + (6)(0) + 24(24)

         = 64 + 0 + 576

<p,q> = 640

Now we have to find ||p|| ||q||, for this we'll find ||p|| and ||q||

||p|| = [tex]\sqrt{ < p,p > }[/tex]

     = [tex]\sqrt{8(8) + 6(6) + 24(24)}[/tex]

     = [tex]\sqrt{676}[/tex]

||p|| = 26

and

||q|| = [tex]\sqrt{ < q,q > }[/tex]

      =[tex]\sqrt{8(8) + 0(0) + 24(24)}[/tex]

||q||  =[tex]\sqrt{640}[/tex]

∴||p||||q|| = 26([tex]\sqrt{640\\[/tex])

Now we have to find angle between p(x) and q(x),

∴ α = cos⁻¹[tex]\frac{ < p,q > }{||p||||q||}[/tex]

      = cos ⁻¹ [tex]\frac{640}{26(\sqrt{640}) }[/tex]

      = cos ⁻¹ [tex]\frac{4\sqrt{10} }{13}[/tex]

  α  = 13.34°

In radian

α = 0.233.

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The dollar interval would be ± 6.70 to present in order to obtain a probability of 0.500.

What is probability?

Probability is a branch of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of error in research by using probability.

z value for the probability of 0.5  is 0.67

standard error = sd/√n = 80/√64 =10

dollar interval = z*se

                      = 0.67*10

                       =6.70

Hence, the dollar interval would be ±6.70.

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By Changing the order of integral we can find five iterated integral that are equal to [tex]\int\limits^2_0 \int\limits^2_y \int\limits^y_0 {f(x,y,z)}\, dz dx dy[/tex]

Changing the order of integral means switching the dx dy order of integration into dy dx .

According to the question ,

The given integral is

=> [tex]\int\limits^2_0 \int\limits^2_y \int\limits^y_0 {f(x,y,z)}\, dz dx dy[/tex]

where;

the region is bounded by 0 ≤ z ≤ y, y≤ x ≤ 2, 0 ≤ y ≤ 2

(a) Changing the order of integral from dzdxdy to dzdydx

When y= 0 => x = y

and y = 2 => x = 2

[tex]\int\limits^2_0\int\limits^x_0 \int\limits^y_0 {f(x, y ,z )} \, dz dy dx[/tex]

(b) Now , changing the order of integral from dzdxdy to dxdzdy

When x = 0 => z = 0

x = 2 => z =  y

[tex]\int\limits^2_0\int\limits^y_0 \int\limits^2_y {f(x, y ,z )} \, dx dz dy[/tex]

(c) Now ,Changing the order of integral from dzdxdy to dxdydz

[tex]\int\limits^2_0\int\limits^2_z \int\limits^2_y {f(x, y ,z )} \, dxdydz[/tex]

(d) Now ,Changing the order of integral from dzdxdy to dydzdx

[tex]\int\limits^2_0\int\limits^x_0 \int\limits^x_z {f(x, y ,z )} \, dydzdx[/tex]

(e) Now ,Changing the order of integral from dzdxdy to dydxdxz

[tex]\int\limits^2_0\int\limits^2_0 \int\limits^x_0 {f(x, y ,z )} \, dydxdz[/tex]

Are the five iterated integral that are equal to the    integral         [tex]\int\limits^2_0 \int\limits^2_y \int\limits^y_0 {f(x,y,z)}\, dz dx dy[/tex].

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Answer: A googolplexian

Step-by-step explanation: A googolplexian is a number with a googol of zeros after it.

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The total percentage of athletes who enjoy cycling is given by:

74.5%.

A percentage is the division of an amount by a total amount, which is then multiplied by 100%.

In this problem, the percentages are already given for the entire population.

The percentage of athletes who enjoy cycling is divided into two nodes, as follows:

The percentages associated from each node are given on the text as follows:

Hence the proportion of athletes who enjoy cycling is given as follows:

0.45 x 0.80 + 0.55 x 0.70 = 0.745.

Then the percentage is of:

0.745 x 100% = 74.5%.

Which means that the last option is correct.

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