Q4 Two consecutive numbers are such that the larger number when
added twice the smaller number gives a sum of 70. Find the two numbers.

a) The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2

b) The value of g'(x) = 2 The value of g''(x) =1

c) g has neither a relative maximum nor a relative minimum at x= 1

d) the graph of g has a point of inflection at each of x=-2 ,  x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

There are several types of functions in maths. Some important types are:

Injective function or One-to-one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

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The quotient will be = 2m^2 + 6m - 9m

The remainder will be = 0

Long division algorithm is below:

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The function type is Linear function.

What is Linear function?

The terms "linear function" in mathematics refer to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

From the given figure it is easily noticed that the function is increasing in nature for [tex]$x < 0$[/tex] and the function is constant in nature for [tex]$x > 0$[/tex] because the value of [tex]$\mathrm{y}$[/tex] remains unchanged for any value of [tex]$\mathrm{x}$[/tex], where [tex]$x \geq 0$[/tex].

The value of function is 3 at x=0.

The value of the function is always 3 for all [tex]$x \geq 0$[/tex]. So, f(x)=3 for [tex]x \geq 0$.[/tex]

The function is a straight line with intercepts (-3,0) and (0,3).

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Answer:

Step-by-step explanation:

the ability to hold, receive, store, or accommodate. : a measure of content : the measured ability to contain : volume. a beaker with a capacity of one liter.

Answer:

Capacity is the maximum amount that something can contain; Volume, or the amount that something can produce.

Capacity is a noun

Hope this helps

Answer:

A potential energy function is given by U(x) = (3.6)x + (1.2)x3. What is the force function F(x) that is associated with this potential energy function

Step-by-step explanation:

After using the quadratic equation the answer is [tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]

What is quadratic equation ?

Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).

[tex]\frac{2}{x-2} (x-3) = \frac{2(x-3)}{x-2} \\\\ \frac{2}{x-1} (3-x) = \frac{2(3-x)}{x-1} \\\\\frac{1}{1-x} (2-x) = \frac{2-x}{1-x} \\\\[/tex]

[tex]\frac{2\left(x-3\right)}{x-2}+\frac{2\left(3-x\right)}{x-1}+\frac{2-x}{1-x}[/tex]

[tex]\frac{2(3-x)}{x-1} + \frac{2-x}{1-x}[/tex]

[tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]

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The value of the chi squared test statistic is 3.27

Chi square test means  a statistical test used to compare observed results with expected results.

Here we have given that Rachel recorded the number of calls she made at work during the week:

Monday: 18

Tuesday: 14

Wednesday: 24

Thursday: 16

And we need to find the chi squared test statistic

While looking into the given question, we have identified that, She expected to make 18 calls each day

Here when a test statistic is smaller than in a left tailed test we would reject H₀.

And if we go to the standard normal chart and use 1% or 0.01, we will search for the closest value to 1% as closely as possible.0.0099 corresponds with a z-score of 3.27

Therefore, option (c) is correct.

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Answer: hope it helps

Step-by-step explanation:

2 1/2 + x = 5 1/3

(2 + 1/2) + x = (5 + 1/3)

6x = 17

x = 17/

6

= 2.83333333

x = 17/

6

≈ 2.833333

[tex] \huge \underline{ \boxed{ \tt Solution: }}[/tex]

[tex] \tt \pink{\large\dagger} \: \: \: \: \: \: 2\dfrac{1}{2} + x = 5\dfrac{1}{3} \\ \tt : \implies \dfrac{5}{2} + x = \dfrac{16}{3} \\ \tt : \implies x = \dfrac{16}{3} - \dfrac{5}{2} \\ \tt : \implies x = \dfrac{16 \times 2}{3 \times 2} - \dfrac{5 \times 3}{2 \times 3} \\ \tt : \implies x = \dfrac{32}{6} - \dfrac{15}{6} \\ \tt : \implies x = \dfrac{32 - 15}{6} \\ \tt : \implies x = \dfrac{17}{6} [/tex]

[tex] \tt \pink{ \star \: Hence \: the \: answer \: is \: \dfrac{17}{6}.}[/tex]

Answer:

the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.

Step-by-step explanation:

The amplitude of a sinusoidal function is half the difference between the maximum and minimum values of the function. In this case, the shortest day in Miami is 10 hours and 52 minutes long, and the longest day is 13 hours and 45 minutes long, so the difference between the maximum and minimum values is 2 hours and 53 minutes, which is equal to 173 minutes. Half of this is 86.5 minutes, which is the amplitude of the function.

To express this in hours, divide the amplitude in minutes by 60. This gives an amplitude of 86.5 / 60 = 1.44 hours.

So, the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.

Answer:

x <> -3, 8

Step-by-step explanation:

x² - 5x - 24 (the denominator of the fraction) must not be 0, because n/0 is not defined for any n.

since this is a quadratic equation, it must have 2 solutions.

therefore, the second answer must be right.

let's check.

a quadratic equation

ax² + bx + c = 0

has the solutions

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (5 ± sqrt((-5)² - 4×1×-24))/(2×1) =

= (5 ± sqrt(25 + 96))/2 = (5 ± sqrt(121))/2 =

= (5 ± 11)/2

x1 = (5 + 11)/2 = 16/2 = 8

x2 = (5 - 11)/2 = -6/2 = -3

correct.

There are 37 students in drama club and 27 students in yearbook club.

And the system of equations will be 1.x + 1.y = 64.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

Total number of students in drama club and yearbook club = 64,

Also, there is a yearbook club. Students in drama club has 10 more than yearbook club,

If x represents the number of students in the drama club and y represents the number of students in yearbook club.

According to given condition,

x+ y = 64        (1)

and x = y + 10

Substitute the value of x in equation (1),

y + 10 + y = 64

2y = 54

y = 27

And x = 27 + 10 = 37

The required system of equations,

1.x + 1.y = 64

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From the given matrices, the values w,x,x and z are 5,-8,4 and -3 respectively.

Matrices is the rectangular arrangement of numbers and letters in rows and columns  

An equation is defined as a mathematical expression showing the equality of two sides of the statement

The given matrices are;

[tex]2\left[\begin{array}{ccc}w&2&\\5&z&\/\end{array}\right] -3\left[\begin{array}{ccc}2&x&\\-2&-6&\\\end{array}\right] =4\left[\begin{array}{ccc}4&7\\y&3\\\end{array}\right][/tex]

Opening the brackets in the matrices

[tex]\left[\begin{array}{ccc}2w&4\\10&2z\\\end{array}\right] -\left[\begin{array}{ccc}6&3x\\-6&-18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y&12\\\end{array}\right][/tex]

Adding the Left hand side

[tex]\left[\begin{array}{ccc}2w-6&4-3x\\16&2x+18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y12&6\\\end{array}\right][/tex]

Equate Left hand side with Right hand side to form linear equations

2w-6=16

2w=10

w=5

4-3x=28

-3x=28-4

-3x=24

x=-8

16=4x

4=x

2z+18=12

2x=12-18

2x=-6

x=-3

These are how the various values are gotten

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Null hypothesis: H₀: population mean, μ ≥ 36hours

Alternate hypothesis: H₁: population mean, μ < 36hours

Given that,

A maker of cell phones promises that the average battery life of its most recent cell phone model is at least 36 hours. To refute this assertion, you are required to create a hypothesis test.

We have to find

a. Describe the null and alternative hypotheses, then choose the one that best supports the claim.

b. Explain type I and type II mistakes for the claim's hypothesis test.

c. Describe if the hypothesis test has left-, right-, or two-tailed distributions.

d. Describe how to read a conclusion that rejects the null hypothesis. a. Describe how you should evaluate a choice that does not rule out the null hypothesis.

We know that,

a. Null hypothesis: H₀: population mean, μ ≥36hours

Alternate hypothesis: H₁: population mean, μ < 36hours

b. Type 1 error: is an error made when we reject the null hypothesis, when the null hypothesis is true. This happens the significance level % of time. In our example, a type 1 error would be made when the population mean is actually greater than 36 hours, but we conclude that the population mean is less than 36 hours.

Type 2 error: is an error made when we fail to reject the null hypothesis, when the null hypothesis is false. This is represented by beta. In our example, a type 2 error would be made when the population mean is actually less than 36 hours, but we conclude that the population mean is not less than 36 hours.

c. The test is left tailed since the area of rejection is on the left side (less than side).

d. We would interpret that at x% confidence level (generally 95%), we reject the claim that the population mean is greater than 36 hours. We would conclude that we have enough evidence from the sample that the population mean is significantly less than 36, and hasn't happened as a matter of chance.

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Answer: A

Step-by-step explanation:

A y-intercept is a point where a function (i.e a line) intercepts the y-axis.

Every point on the y-axis has a x value of 0.

The ordered pair will look like this (0,y)

In answer a, you have an x value of 0 with a corresponding y value of 3.

This point is (0,3).

You could also graph the points and look for where the function crosses the y-axis.

Answer:

16R = T or T = 16R

Step-by-step explanation:

R represents the unknown amount of rows and we know there are 16 boxes in each row.

This means to find the total number of boxes on display, you will have to times the number of rows by 16 as the clerk puts 16 boxes of cereal in each row

e.g, if there are 3 rows, then to find the total amount of cereal boxes, you would do 3 × 16 = 48

Since it's an expression, you need something to represent the total number so that can be represented by any letter ( I chose T ) — in most cases you can probably represent the total as x

Hence the expression should be 16R = T or T = 16R

...at least I think so

Answer:

1. Given

2. Vertical Angles Theorem (1st Occurrence)

3. Vertical Angles Theorem (1st Occurrence)

4. Transitive Property of Congruence

5. Converse of the Alternate Interior Angles Theorem

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Transitive Property of Congruence

If one pair of angles is congruent to a third angle, then the first angle is congruent to the third angle.

Converse of the Alternate Interior Angles Theorem

If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.

[tex]\begin{array}{l|l}\vphantom{\dfrac12} \sf Statements & \sf Reasons \\\cline{1-2}\\1. \; \angle 2 \cong \angle 7 & 1.\; \sf Given\\\\2. \; \angle 2 \cong \angle 3 & 2.\; \sf Vertical\;Angles\;Theorem\;(1st\;Occurrence)\\\\3. \; \angle 6 \cong \angle 7 & 3.\;\sf Vertical\;Angles\;Theorem\;(2nd\;Occurrence)\\\\4. \; \angle 3 \cong \angle 6 & 4.\;\sf Transitive\;Property\;of\;Congruence\\\\5. \; a \parallel b & 5.\;\sf Converse\;of\;the\;Alternate\;Interior\;Angles\;Theorem\\\\ \end{array}[/tex]

From inspection of the given diagram, we can see that angles 2 and 3 are vertical angles, similarly angles 6 and 7 are vertical angles.  Therefore, the Vertical Angles Theorem applies.

According to the Transitive Property of Congruence,  if ∠2 ≅ ∠7 and ∠2 ≅ ∠3 and ∠6 ≅ ∠7 then ∠3 ≅ ∠6.

The two lines a and b are intersected by transversal [tex]\ell[/tex] so that the alternative interior angles 3 and 6 area congruent, then the lines a and b are parallel.  This is the Converse of the Alternate Interior Angles Theorem.

Answer:

1.33333 , it just keeps going

Step-by-step explanation:

divide 4/3 you can use a long division or a calculator.

Hope this helps!!

Answer:

The number 11.661903 rounded to the nearest hundredth is 11.66.

Step-by-step explanation:

We have the following number:

And we need to round this number to the nearest hundredth.

To determine that, we can proceed as follows:

1. Round a number to the nearest hundred is equivalent to rounding the number to two decimal places.

2. Now, we can see that the number in the third decimal position or thousandth place is 1:

3. If this number were 5 or greater than 5, we would need to round up that number to the next following number, that is, 7. However, this is not the case.

4. Therefore, if we have to round that number to the nearest hundredth, then the number is 11.66.

Hence, in summary, the number 11.661903 rounded to the nearest hundredth is 11.66.

(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)

Stay positive and Take care,

A fellow mate,

Cheers !

The following given table with input and output is a function.

A relation between a domain and range is called a function when each value in the domain only has one value in the range. This notion is violated by relations that are not functions. They have at least one domain value that corresponds to two or more range values.

Into, onto, bijective and surjective are the types of function.

As every input has only one output so the given table is function.

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The following given table with input and output is a function.

What is function?

A function is a self-contained block of code that performs a specific task. It is a logical grouping of instructions and operations that can be used multiple times throughout a program. Functions help to keep code organized and modular, making it easier to debug and maintain. They also allow for code reuse, which can result in faster development times and greater efficiency. Furthermore, functions can be used to pass data between different parts of a program, making it easier to share information and reduce the need for redundant code.

Write names of type of functions.
Into, onto, bijective and surjective are the types of function.
As every input has only one output so the given table is function.

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The confidence level is 60600<μ<3,524.786, assuming a standard deviation of $13,553 and the confidence level for estimating the population mean is 90%.

What do you mean by confidence level?

A confidence interval is a range of values that can contain the true value of the parameter being studied in statistics. It is created using observed data and calculated at a desired level of confidence.

The confidence level—for instance, a 95% confidence level—relates to the accuracy of the estimation process, not to the degree to which it is certain that the computed confidence interval contains the actual value of the parameter under investigation.

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Answer:

8.44 minutes

Step-by-step explanation:

The tank initially contained 105 liters so the amount of water needed is 181 - 105 = 76 litters

if the rate is 9 L/min then the number of minutes is

76/9 = 8.44 minutes

Answer:

y=7

Step-by-step explanation:

y is always the same and it is 7

The following steps are used to set up a regression

Regression analysis is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables. It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them.

Here , first we identify which variable is independent and which is affect by this independent variable

Then , we plot the data to analyze the pattern between them

Then we find correlation between them after we will able to draw our conclusion about regression.

Therefore, the regression analyses are performed a couple of times to produce the best analysis results, including the test statistics and the predicted fitted regression.

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Answer:

x > –1/2

or x > –0.5

Step-by-step explanation:

2x + 8 > – 4x + 5

2x + 4x > 5 – 8

6x > –3

x > –3/6

x > –1/2

or x > –0.5

Answer:

30

Step-by-step explanation:

200 x .15   (1-.85 = .15)

30

The confidence interval for the given equation will be: 0.504.

What is confidence interval?

In frequency statistics, the confidence interval (CI) is the range of estimated values ​​for an unknown parameter. Confidence intervals are computed at the specified confidence level. A 95% confidence level is the most common, but other levels such as 90% and 99% are sometimes used. The confidence level represents the proportion of corresponding CIs over time that contain the true value of the parameter. For example, 95% of all intervals computed at the 95% level must contain the true value of the parameter.

Factors that affect the width of the CI include sample size, sample variability, and confidence level. All else being equal, a larger sample results in a narrower confidence interval, a more varied sample results in a wider confidence interval, and a higher confidence level results in a wider confidence interval.

Therefore, The confidence interval for the given equation will be: 0.504.

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When 2x-4 = 6, the value of 3x + 2 is 17.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

When 2x - 4 = 6, the value of x will be:

2x - 4 = 6

2x = 6 + 4

2x = 10

Divide

x = 5

Therefore, 3x + 2 will be:

3x + 2 = 3(5) + 2

= 15 + 2

= 17

The value is 17.

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Answer:

(-3,6)

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{4}[/tex] y = 1  Divide all the way through by 12 to clear the fraction

4x + 3y = 12  Add this to the second equation

2x -3y = -30

6x = -18   Divide both sides by 6

x = -3

Substitute -3 into either of the original equations to solve for y

4x + 3y = 12

4(-3) + 4y = 12

-12 + 4y = 12  Add 12 to both sides

4y = 24  Divide both sides by 4

y = 6

8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.

An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable. By deleting parentheses and merging like terms, you can simplify either side of an equation and find its solution.

Identify the variable term on one side of the equation by adding or subtracting. You can find the variable's value by multiplying or dividing. When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. Depending on the language, the definition of the word equation and its cognates may alter slightly. For instance, an equation is what is meant in French.

8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.

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