ALGERA 2 Question: PLEASE HELP I WILL MARK BRANLYLIST

The cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value.

From the question , we are given that the laptop costs $350 more than the desktop, therefore,

let x represent the cost of the laptop thus, x-350 will be the cost of the desktop .

The total finance charge of $388 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as;

388 = 0.08(x) + 0.075(x - 350)

252 = 0.08x + 0.075x - 26.25

278.75 = 0.155x

x = 278.75/0.155

x = 1798

Recall that the cost of desktop = x -350

therefore:

1,798- 350 = 1448

The cost of laptop = $1798

The cost of desktop = $1448

Thus, the cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

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The inequality given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Let the number of gigabytes consumed be x,

The total cost per month will be 69.50 + 5x

accoding to the question the bill would not exceed $90.

So the inequality,

69.50 + 5x ≤ 90

Simplification for the maximum gigabyte he can buy,

5x ≤ 90 - 59.90

5x ≤ 20.5

x ≤ 4.1

Hence, the required inequality is given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

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A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations.

A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations. The use of sample data in hypothesis testing allows one to judge a hypothesis' veracity.

The null hypothesis states that the estimate is only based on chance. If the observed data (in the sample) do not differ from what would be predicted solely by chance, then the null hypothesis is true. The alternative hypothesis is what the null hypothesis has as its counterpart.

Two population parameters, such as an independent variable and a dependent variable, are said to be unrelated under the null hypothesis. It's possible that an experimental or sampling error caused the result if the hypothesis indicates a relationship between the two parameters.

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If the three sides of the triangle is (x + 5), (2x - 3), (21 - x), then the perimeter of the triangle is 23 + 2x

The perimeter of the triangle is the summation of all three sides of the triangle

Perimeter = a + b + c

= (x + 5) + (2x - 3) + (21 - x)

= 2x + 23

= 23 + 2x

Therefore, if the three sides of the triangle is (x + 5), (2x - 3), (21 - x) then the perimeter of the triangle  23 + 2x.

Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.

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Answer:

y = - [tex]\frac{3}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

6x + 4y = 16 ( subtract 6x from both sides )

4y = - 6x + 16 ( divide through by 4 )

y = [tex]\frac{-6}{4}[/tex] x + [tex]\frac{16}{4}[/tex] , that is

y = - [tex]\frac{3}{2}[/tex] x + 4 ← in slope- intercept form

Answer:

75÷50

Step-by-step explanation:

1.5 or 3÷2 is the correct answer

Answer:

[tex]7\sqrt{5}[/tex]

Step-by-step explanation:

Using the geometric mean theorem, [tex]n=\sqrt{28 \cdot 7}=14[/tex].

Using the Pythagorean theorem, [tex]m=\sqrt{7^2+14^2}=7\sqrt{5}[/tex]

The best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.

In the given question,

The best fitting line is one where the intercept of the regression equation:

As we know that;

The slope of the line of best fit is the coefficient in a simple regression with a single independent variable. The slope is a mixture of the two coefficients in this example and in any regression with two independent variables. The y-intercept of the line of best fit is constant C.

So, the best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.

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Using PEMDAS to solve the mathematical expression, the result is -637.947

The mathematical operation refers to calculating a value using operands and a math operator. The symbol of the math operator has predefined rules to be applied to the given operands or numbers.

In this kind of problem, we need to use the PEDMAS rule which is

Parenthesis, Exponents, Division, Multiplication, Addition and Subtraction.

The order in which this must be prioritized is from parenthesis and the least is subtraction.

Applying PEMDAS to this mathematical operation, we would have

19.42 - 34.89(19.3) + 10.23 + 5.78

Using a calculator which follows this rule, we would have;

19.42 - 34.89(19.3) + 10.23 + 5.78 = -637.947

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Answer:

Step-by-step explanation:

A line that is perpendicular to another will have the opposite slope.

y = [tex]-\frac{1}{3}[/tex]a + b

To find b, substitute y and a with the given values

6 =  [tex]-\frac{1}{3}[/tex](-6) + b

6 = 2 + b

-2  -2

4 = b

thus

y = [tex]-\frac{1}{3}[/tex]a + 4

Answer:

23

Step-by-step explanation:

Taking an algebraic approach

let the number be n, then (n - 17) is 17 subtracted from the number, and -2(n - 17) = - 12 ( divide both sides by - 2 )n - 17 = 6 ( add 17 to both sides ) which is n=23

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

760% can be written in fraction form as 38/5.

760% can be written in mixed form as 7(3/5).

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

760%

This can be written as a fraction.

760/100

= 76/10

= 38/5

or

= 7(3/5)

Thus,

760% can be written in fraction form as 38/5.

760% can be written in mixed form as 7(3/5).

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X=pi/2 only in the interval 0 to 4 . We have the maximum value of f(x) = sinx = 1

What is  function interval ?

If the value of the function f (x) grows with an increase in the value of x, the function interval is said to be positive.

                         The function interval, on the other hand, is said to be negative if the value of the function f (x) decreases as the value of x increases.

First of all to apply the extreme value theorem function must be countions at the interval 0 to 4.

F(x)=(x^2-16)/(x^2+x-20) is countinious int the given interval .

Now we find

F'(x)= d(F(x))/dx=1/(x+5)^2 so here we don't have in critical point therefore this choice is incorrect

Similarly if we take

F(x)= sinx

F'(x) = cosx

For critical point ,

Cosx =0

X=pi/2 only in the interval 0 to 4

And this point we have the maximum value of f(x) = sinx = 1

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The rational equation with the desired asymptotes and intercepts is given by: f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].

Vertical asymptotes are x values that are outside the domain and, in a fraction, are the denominator zeroes.

As long as this value differs from infinity, the horizontal asymptote is the value of f(x) as x approaches infinity.

The vertical asymptotes are related to the denominator roots, so:

f(x) = a / ( x + 5)( x + 2 )

f(x) = a / ( x² + 7x + 10 )

The x-intercepts are related to the function's numerator, so:

f(x) = [a( x + 1 )( x - 6) ] / [x² + 7x  + 10 ]

The y-intercept is to find a, hence, when x = 0, y = 5, thus:

4 = a(-6)/ 10

a = (-40/6)

a = -20 / 3

The equation will be written as,

f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].

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Answer:

Is that all

_______

_______

Answer:(2x+1)(3x-4)

Step-by-step explanation:Factor the expression out first by getting 6x^2+3x-8x-4. From there, factor again to 3x(2x+1)-4(2x+1) to get the answer (2x+1)(3x-4)

Answer:

(3x - 4)(2x - 1)

Step-by-step explanation:

6x^2 - 5x - 4

When factoring, we want to first find the GCF. In this case, the GCF is one so we leave it as that. Next, we want to try and find the sum and the product. Additionally, we have a leading coefficient. We will multiply the leading coefficient by the last term, which is -4. (You will need to remember this to continue on later.)

x^2 - 5x - 24

Now, we can find the sum and the product. To do this, we need to list the factors of 24. (Remember negatives as well!)

24: 1 and 24, 2 and 12, 3 and 8, 4 and 6.

As -24 is also a negative, that means it will have one positive and one negative factor. This must also add up to -5.

One pair that does this is -8 and 3. They multiply together to -24 and add up to -5.

Now, since we multiplied the leading coefficient in the beginning, we must bring it back down into the parenthesis.

(6x - 8)(6x - 3)

We must divide out and try to simplify this as much as we can to match the leading coefficient. The divisors must multiply up to 6.

(6x - 8)/2 and (6x - 3)/3.   3*2 = 6

(3x - 4)(2x - 1)

50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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Answer: Side of an empty cubicle carton = 9 cm.

Now as we know that volume of the cube is the cube of its side.

So the volume of an empty cubicle carton having side 9 cm, V = (9)3=729 cm3.

Now we have to find out can 1000 cubes of side 1cm fit in it.

So the volume of the cube of side 1 cm is, V’ = (1)3=1 cm3

So the volume of the 1000 such cubes = 1000 (1) = 1000 cubic centimeters.

Now if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 then we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not.

So the ratio of the volume of the empty cubicle carton to the volume of the 1000 cubes is,

⇒VV′=7291000=0.729 < 1

So as we see that the ratio is less than one so we cannot fit 1000 cubes of side 1 cm into an empty cubicle carton of side 9 cm.

Step-by-step explanation:

I really hope this works!

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hybrids research When she does, the camden depositor is actually higher than the reported percentage. Here, we have the report 126 percent, the winners on the portion computer. It indicates that the proportion of the underling hypothesis at noon will be equal to 26.

The abon 26 point notte will be greater than the b of the means 10. In this question, which is the right-hand exam, we will provide the sembiante 340, which will be equal to 31 percent, and we must contend with the statistical test. The test is therefore equal to the z moving forward. It will be calculated using the following formula: hat: minus b over square root, times: 1 minus p over the hot equal to 131 p equal to 261 square 261 minus 26. If we compare it to my 340 point, we get 126 times 74 divided by 340, then we take the square root of that number. The 131 minus 7.26 is then divided by the industry standard.I respond with a number equal to 2.10, rounding up to two decimal places before moving on to the step's following inquiry. 3. This is the 110 test since the test pair is on 1 here and then the next 1 in his right hand. The choice must be made hypotheses, though. Rule and we need to identify the critical value, and since that will be the right hand, we must make sure that the critical value is both equal to and far beyond that. 05. It will check the z table to see if the value equals 1.645, and if it does, we'll use the decision rule to reject the null hypothesis. If so, the test result will exceed the cutoff of 1.645 points, and we will observe Because the test we determined to be equivalent to 2.10 is higher than the 1.645 point, we can observe that. We will thus rule out the known hypothesis and come to the conclusion that there is sufficient evidence to back up the prediction that the proportion will be higher than 26%.

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The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.

We have,

i] f(x) = 8x  and
g(x) = (2x+8)

(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16

(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) =  8x.
(f ∘ g) (x) = 8(2x+8)  
= 16x + 64

ii]  f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2  
= 6x - 28

g [f(3)] = (6x + 2 ) - 5
= -30x - 10

Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10

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The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.

To find equivalent expression we can simplify the expression.

Therefore,

(6x² - 9x) - (2x -3)

open the brackets

6x² - 9x - 2x + 3

combine like terms

Therefore,

(6x² - 9x) - (2x -3) = 6x² - 11x + 3

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Reject H0 if the test statistic is less than  -1.321  or greater than  1.321  .

What is a hypothesis simple definition?

A tested assertion regarding the relationship between two or more variables .

                  a theory put out to explain an observed occurrence is referred to as a hypothesis (plural: hypotheses) in a scientific context.      

Reject H0 if the test statistic is less than  -1.321  or greater than  1.321  .

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The test statistic for the given test is t = 2.59.

What is a standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

Given data:

                    [tex]\bar D[/tex] = 4.1, Sd = 5, n = 10, μd = 0

Now the test statistic can be computed as

                [tex]t=\frac{\bar D-\mu_d}{S_d/\sqrt{n} }[/tex]

                [tex]t=\frac{4.10-0}{5/\sqrt{10}} \\\\t=2.59[/tex]

Hence, the test statistic for the given test would be t = 2.59.

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The initial value of the function obtained from the table of values for the linear function is; 7

A linear function is a function that when plotted, produces a straight line on the coordinate plane.

The initial value of a function is the value of the function, when the input value is 0.

The initial value indicates the point where the graph intersects the y-axis, which is the y-intercept. It the point the graph enters quadrant I, where the x and y-values are positive.

From the initial value, and to the right of the x-axis, the input variable (x) is positive, such that the values of the function for natural value input, such as time can be found, and the initial value then represents the start of the measurement of the output values of the function.

The data in the table indicates that when the input variable x = 0, the output variable, y = 7

Therefore:

Which indicates that at the initial point of the positive value inputs of the function, the output is 7

Question details are:

Please find the table of the linear function, which is to be examined, presented as follows:

[tex]\begin{array}{|c|c|}In put (x) & Out put (y)\\-3 &14 \\0 & 7 \\3 & 0 \\6 & -7 \\\end{vmatrix}[/tex]

The initial value of the function that the above table represents is required.

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the total force exerted on the new dam to that on the original dam f new is given by F = 624010000 lb.

What is Pascal's Principle.?

Consider a flat surface that is immersed vertically in a fluid whose weight density is p, according to Pascal's Principle.

A flat surface experiences fluid force (F) which is

F = ∫ph(x)w(x) dx

where h(x) is the height of the point x in the x-axis' vertical direction and w(x) is the surface's width.

to determine fluid force applied

Assume that x is equal to the height of the water. At height x on the dam, width of the dam is w(x) = 200 ft (given), and height is h(x) = x ft.

F = ∫ph(x)w(x) dx

F =0→100 ∫62.4 x  200 dx

F = 12480*  0 →100∫ x dx

F = 12480*  0 →100(x²/2)

F =

F = 6240((100)²- (0)²)

F= 6240(10000)

F = 624010000 lb

Hence the total force exerted on the new dam to that on the original dam f newf is given by F = 624010000 lb.

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Answer:

4 x^3 + 24 x^2 = 4 (x^3 + 6 x^2) = 4 x^2 (x + 6)

4 x^2 (x + 6)        seems to be the lowest factor

The number of sides in the polygon that has 1,260° as the sum of the interior angles, found using the formula for the sum of the interior angles in the polygon, S = 180·(n - 2) is 9 sides

A polygon is a figure consisting of a specified number of straight sides such that they form a closed loop. The number of sides in a polygon are three or more.

The formula for the sum of the interior angles of a polygon, S, can be be used to find the number of sides in the polygon as follows;

S = 180·(n - 2)

Where;

n = The number of sides the polygon has

The sum of the interior angles in the specified polygon = 1,260°

The number of sides in the polygon can be found by equating the formula for S to 1,260° as follows;

When S = 1.260°, we get;

1,260 = 180·(n - 2)

Which indicates;

n - 2 = 1,260 ÷ 180 = 7

Therefore; n - 2 + 2 = 7 + 2 = 9

n = 9

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Answer:

The 8th term of the AP= 113/5 or 22.6

Answer:

22.6

Step-by-step explanation:

Given:

Find the value of a₆:

[tex]\implies a+a_6=20[/tex]

[tex]\implies a_6=20-a[/tex]

[tex]\implies a_6=20-3[/tex]

[tex]\implies a_6=17[/tex]

Therefore:

General form of an arithmetic sequence:

[tex]\boxed{a_n=a+(n-1)d}[/tex]

Where:

Substitute a = 3 and a₆ = 17 into the formula and solve for d:

[tex]\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\implies a_n=3+(n-1)2.8[/tex]

[tex]\implies a_n=3+2.8n-2.8[/tex]

[tex]\implies a_n=2.8n+0.2[/tex]

To find the 8th term, substitute n = 8 into the equation for the nth term:

[tex]\implies a_8=2.8(8)+0.2=22.6[/tex]

Probability of people less than 19 year old = 0.5343

Probability of people greater than 10 year old = 0.8116

What is probability?

Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.

People under age 10 = 253

People between the age of 10-18 = 466

People between the age of 19-30 = 174

People above the age of 30 = 450

Total no. of people = 1343

a) people less than 19 years old = 253+466 = 719

probability of people<19 year old = P(age<19) = 719/1343 = 0.5354

b) people of age greater than 10 = 466+174+450 = 1090

probability of people >10 year old = P(age>10) = 1090/1343 = 0.8116

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