Solve the following in-equations and graph the solution on the number line

The given figure is :

According to the given figure

Area of ABCDEF = Area of rectangle ABCDG and Area of square GDEF

In rectangle ABCG

Length = 10, Width = 4 unit

Area of recatngle ABCG = 10 x 4

Area of rectangle = 40 unit²

In the square GDEF

Side length = 4 unit

Area of GDEF =4 x 4

Area of GDEF = 16 unit²

Area of the figure = 40 + 16

Area of the figure = 56 unit²

Answer : 56unit²

To make a 360mL mixture that contains 9% vinegar, use 240mL of the first brand and 120mL of the second brand.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

You want to set up an equation that will match the word problem. Let's call the amount of the first brand, F, and the amount of the second brand, S.

We want the total mixture to be 360mL so: F + S = 360

Also, you want the total mixture to contain 9% vinegar so:

.08F + .11S = .09(360)

Now, we can solve the system of equations using substitution.

F + S = 360

.08F + .11S = .09(360)

F = 360 - S      [solve 1st equation for F]

.08(360 - S) + .11S = .09(360)     [substitute into 2nd equation]

28.8 -.08S +.11S = 32.4

.03S = 3.6

S = 120

F + 120 = 360     [substitute answer for S back into original equation]

F = 240

Answer: To make a 360mL mixture that contains 9% vinegar, use 240mL of the first brand and 120mL of the second brand.

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Answer:

1/4

Step-by-step explanation:

use 2 points from the graph (-4,5) and (0,6) and  put them in the distance equation.

(y2-y1)

----------

(x2-x1)

6-5

-------

0-(-4)

1/4

American adults believes in alien for the  given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).

As given in the question,

Sample of American adults surveyed 'n' = 200

Percent of people believes in aliens are success  'p'= 72%

                                                                                      = 0.72

Percent of people who don't believes (failure) in aliens ' 1 - p'  = 1 - 0.72

                                                                                          = 0.28                                                                                    

95% Confidence interval that represents Americans adults who believes in aliens

value of z - score for 95% confidence interval = ± 1.96

Margin of error 'MOE'= (z-score)√p ( 1- p) /n

                                   = ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200

                                   = 1.96 ( √0.2016 / 200)

                                   = 1.96 ×√0.001008

                                   = 0.063

Lower limit = p - MOE

                 = 0.72 - 0.063

                 = 0.66

Upper limit =  p + Margin of error

                 = 0.72 + 0.063

                 = 0.78

Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).

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Answer:

B. y=1/2x-5

Step-by-step explanation:

From the graph, we read the slope of line JK.

slope = rise/run = -3/-6 = 1/2

The equation we need has the same slope.

y = mx + b

y = (1/2)x + b

It passes through point P(6, -2). Now we find b.

-2 = (1/2)(6) + b

-2 = 3 + b

b = -5

The equation is

y = (1/2)x - 5

To solve the equation -2.5(e + 17.4) = -50, we can use algebraic techniques to isolate the variable e on one side of the equation.

First, we can simplify the left-hand side of the equation by distributing the -2.5 to the expression inside the parentheses:

-2.5e - 2.5(17.4) = -50

Next, we can simplify the expression on the left-hand side by multiplying:

-2.5e - 43.5 = -50

To isolate the variable e, we can add 43.5 to both sides of the equation:

-2.5e = -6.5

Finally, we can solve for e by dividing both sides of the equation by -2.5:

e = 2.6

Therefore, the solution to the equation -2.5(e + 17.4) = -50 is e = 2.6.

Answer:

C. Neither

Step-by-step explanation:

Answer:

2x^2+5x-1=0

ax^-bx+c=0

b^2-4ac = 5^2-4(2)(-1) =33

Answer:

Hi! The answer to your question is \(29\)

Step-by-step explanation:

\(3(7)+8\)

\(3(7) = 21\)

\(21 + 8\)

\(= 29\)

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Answer:

2/25

Step-by-step explanation:^2 = 1/25

Cubic Root 8 = cubic root = 2^3 = 2

(1/25)*(2) = 2/25

The product of the numbers is B. thirteen and one eighth.

From the information, we are negative four and one-sixth times negative three and fifteen hundredths.

The product will be:

= (-4 1/6) × (-3 15/)

= - 4 1/6 × 3 3/20

= - 25/6 × -63/20

= 13 1/8

The correct option is thirteen and one eighth.

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Answer:

To find the slope of the line, you can use the formula for slope: slope = (y2 - y1)/(x2 - x1). In this case, you can rewrite the equation 2-y = 8x as y = 2 - 8x. This is the standard form of a line: y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

Since the equation of the line is already in standard form, you can find the slope by looking at the coefficient of the x term. In this case, the coefficient of the x term is -8, so the slope of the line is -8.

Alternatively, you can plug in the coordinates of two points on the line into the formula for slope to find the slope. For example, if you know that the line passes through the points (1, -14) and (2, -10), you can use these points to find the slope:

slope = (y2 - y1)/(x2 - x1) = (-10 - (-14))/(2 - 1) = (-10 + 14)/1 = 4/1 = 4

This method gives the same result as using the standard form of the equation.

Step-by-step explanation:

Refer to the attachment for figure:

The height of the rectangle = 11 inches

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x= height

Width becomes x+49

Diagonal BD=61 inches

By pythagoras theorem,

BD²=BC²+CD²

61²= (x+49)²+x²

3721=x²+98x+2401+x²

On simplification,

x²+49x-660=0

Find the factors

(x+60)(x-11)=0

x=-60, x=11

Consider positive value for height

height = 11 inches

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The value of the technological equipment when it was new according to an exponential decay model is approximately $37,633.52.

It is given to us that the value of a new technological equipment depreciates (decreases) after it is purchased, the value of the technological equipment depreciates according to an exponential decay model.

We know that the value of the equipment is $20000 at the end of 6 years, and its value has been decreasing at the rate of 10% per year.

Let the purchase price of machine be $P

Rate of depreciation = 10% p.a.

Period years.

∴ Present value = $20,000

Depreciated value can be calculated by t(6) ---> [∵ Depriciated value = A]

⇒ $20,000 = P(1−10/100)⁶

⇒ $20,000 = P(9/10)⁶

⇒ P = $20,000 (9/10)⁶ A = P(1-100)t

⇒ P = $20,000 × 10/9 × 10/9 × 10/9 × 10/9 × 10/9 × 10/9

⇒ P = $37,633.528463178 ≈ 37,633.52

The value of the technological equipment when it was new was approximately $37,633.52.

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Answer:

11

Step-by-step explanation:

i just need 11 more than ill be fine

The value of  \(125x^3 + 27y^6z^9\) factors to \((5x + 3y^2z^3)(25x^2 - 15xy^2z^3 + 9y^4z^6).\) and option D is the correct answer.

In algebra, there are two opposing operations: factoring and expanding. In order to create a longer and more complex expression, expanding entails multiplying out expressions. On the other hand, factoring entails dissecting a complicated expression into smaller factors.

In conclusion, factoring entails division whereas expanding involves multiplication.

To factor \(125x^3 + 27y^6z^9\), we can use the sum of cubes formula:

\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)

In this case, a = 5x and \(b = 3y^2z^3\):

Simplify the expression by using the identity and rearranging the expression to get the desired output:

\(125x^3 + 27y^6z^9 = (5x)^3 + (3y^2z^3)^3\\= (5x + 3y^2z^3)((5x)^2 - (5x)(3y^2z^3) + (3y^2z^3)^2)\\= (5x + 3y^2z^3)(25x^2 - 15xy^2z^3 + 9y^4z^6)\)

Therefore, \(125x^3 + 27y^6z^9\) factors to \((5x + 3y^2z^3)(25x^2 - 15xy^2z^3 + 9y^4z^6).\) Hence, option D is the correct answer.

2. The difference of cubes is given by the equation

8x¹⁵ - 125y³

The expression can be written as:

(2x⁵)³ - (5y)³

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The number of students who knows all the 3 languages is 12

Total number of students = 80

Number of students who knows English = 50

Number of students who knows French = 55

Number of students who knows German = 46

Number of students who knows English and French = 37

Number of students who knows French and German = 28

Number of students who knows English and German = 25

Number of students who knows none of the languages = 7

Here we have to use the equation of the union of set

n(E∪F∪G) = n(E) + n(F) + n(G) - n(E∪F) - n(F∪G) - n(E∪G) + n(E∩F∩G)

80 - 7 = 50 + 55 +46 - 37 - 28 -25 + n(E∩F∩G)

n(E∩F∩G) = 73 - 50 -55 -46 +37 +28 +25

n(E∩F∩G) = 12

Hence, the number of students who knows all the 3 languages is 12

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Answer:

The shortest side of the fence can have a maximum length of 80 feet

Step-by-step explanation:

Inequalities

To solve the problem, we use the following variables:

x=length of the longer side

y=length of the sorter side

The perimeter of a rectangle is calculated as:

P = 2x + 2y

The perimeter of the fence must be no larger than 500 feet. This condition can be written as:

\(2x + 2y \le 500\)

The second condition states the longer side of the fence must be 10 feet more than twice the length of the shorter side.

This can be expressed as:

x = 10 + 2y

Substituting into the inequality:

\(2(10 + 2y) + 2y \le 500\)

This is the inequality needed to determine the maximum length of the shorter side of the fence.

Operating:

\(20 + 4y + 2y \le 500\)

Simplifying:

\(20 + 6y \le 500\)

Subtracting 20:

\(6y \le 500 - 20\)

\(6y \le 480\)

Solving:

\(y \le 480 / 6\)

\(y \le 80\)

The shortest side of the fence can have a maximum length of 80 feet

Answer:

25 ft

Step-by-step explanation:

based on the graph on the width of the porch with the greatest area is 25

Answer: 8 more dogs.

Step-by-step explanation:

All you have to do is subtract 10 by 2 and you’ll get your answer.

Answer:

2

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

7x-3=18

7x=18+3

7x=21

x=3

Answer:

2x+5

Step-by-step explanation:

if you look at the x and the y coordinates, you'll see that if you multiply the 'x' coordinate by 2 and then add 5, you get the y coordinate

The coating thickness distribution is normal and has a mean value of 1.245.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode.

To calculate the data's coating thickness, sample mean is employed.

The following formula is used to determine the mean value's point estimate:

\(\bar x = \frac{1}{n} \sum x_i\)

The typical probability plot shown there has a rather straight pattern. Assume right now that the coating thickness distribution is normal and has a mean value:

\(\bar x = \frac{19.92}{16}\\\\\bar x = 1.245\)

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Answer:

The probability that the industry will locate in both cities is 0.4. The probability that it will locate in either Shanghai or Beijing or both is 0.8.

Step-by-step explanation:

The probability that the industry will locate in both cities is 0.41. The probability that it will locate in either Shanghai or Beijing or both is 0.81. We can use the formula P(A and B) = P(A) * P(B|A) to calculate the probability of an event occurring in both cities. Let A be the event that the industry locates in Beijing and B be the event that it locates in Shanghai. Then, P(A or B) = P(A) + P(B) - P(A and B) = 0.8. Therefore, P(A and B) = P(A) * P(B|A) = (0.4 * 0.4)/0.8 = 0.2. The probability that the industry will not locate in either city is given by P(neither A nor B) = 1 - (P(A) + P(B) - P(A and B)) = 1 - (0.4 + 0.4 - 0.2) = 0.2.

yw;)

Answer:The solution is in the attached file

Step-by-step explanation:

Point estimate from the sample is 0.985, margin error is 0.003.

Confidence interval is defined as the interval which is the estimate for the parameter of the sample or population to be contained.

(a) To calculate point estimate or sample mean :

Point estimate is the mid point of the confidence interval.

Given that true mean weight of candy bars is 0.982 ounces to 0.988 ounces.

Point estimate = (0.982 + 0.988) / 2 = 1.97 / 2 = 0.985

(b) Margin error is the one half of the total width of the interval.

Margin error = (0.988 - 0.982) / 2 = 0.003

(c) The confidence level of 90% in this problem can be interpreted as , if we do the interval construction for many times, about 90% of the total constructed intervals has the true population mean of weight of fun size candy bars.

Hence the point estimate and margin error are 0.985 and 0.003 respectively.

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Answer:

Step-by-step explanation:

P=2x+2y+4

y=p/2-x-2

The equation can represent as y = P/2 - x - 2 after solving for y if the equation is P = 2x + 2y + 4.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Solve for y P=2x+2y+4

From the data given in the question:

The linear equation is:

P=2x+2y+4

To solve for make the subject as y:

2y = P - 2x - 4

y = (1/2)[P - 2x - 4]

Or

y = P/2 - x - 2

Thus, the equation can represent as y = P/2 - x - 2 after solving for y if the equation is P = 2x + 2y + 4.

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To estimate the integral ∫ sin(t)/t using a Taylor polynomial for sin t about t = 0 of degree 5, we can first write out the Taylor series for sin t:

sin t = t - (t^3)/3! + (t^5)/5! - (t^7)/7! + ...

If we truncate this series at the fifth degree, we get:

sin t ≈ t - (t^3)/3! + (t^5)/5!

Now, we can substitute this approximation into the integral:

∫ sin(t)/t dt ≈ ∫ (t - (t^3)/3! + (t^5)/5!)/t dt

= ∫ (1 - (t^2)/3! + (t^4)/5!)/dt

= t - (t^3)/(3*3!) + (t^5)/(5*5!) + C

where C is the constant of integration. We can evaluate this expression between limits, say from 0 to 1, to get an estimate for the integral:

∫ sin(t)/t dt ≈ 1 - (1^3)/(3*3!) + (1^5)/(5*5!) - (0^3)/(3*3!) + (0^5)/(5*5!) + C

= 0.946

So, the estimate for the integral ∫ sin(t)/t using a Taylor polynomial for sin t about t = 0 of degree 5 is approximately 0.946.
To estimate the integral ∫sin(t) using a Taylor polynomial for sin(t) about t=0 of degree 5, we first need to write the Taylor polynomial of sin(t). The Taylor polynomial of degree 5 for sin(t) about t=0 is:

P_5(t) = t - (t^3)/6 + (t^5)/120

Now, to estimate the integral, we integrate P_5(t) with respect to t:

∫sin(t) ≈ ∫(t - (t^3)/6 + (t^5)/120) dt

The integral of this polynomial is:

∫P_5(t) dt = (t^2)/2 - (t^4)/24 + (t^6)/720 + C

Here, C is the constant of integration.

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