What is the inequality 2/3k-6<24 expressed in its simplest form? (2mks)
CO
JK COPIER

The required forms of the equation are;

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

Completing the square is a method used to rewrite a quadratic expression in standard form by adding and subtracting a constant to make it a perfect square trinomial. Completing the square is a useful method to solve quadratic equations and to rewrite quadratic expressions in standard form.

The standard form of a quadratic equation  is ax² + bx + c = 0

We have that;

x²-8x+5=0

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

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Answer:

midsegment = 23

Step-by-step explanation:

the midsegment is half the sum of the bases, that is

midsegment = [tex]\frac{18+28}{2}[/tex] = [tex]\frac{46}{2}[/tex] = 23

The mean absolute deviation for the data-set in the table is given as follows:

1.52 million.

The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.

Hence the mean for the data-set in this problem is given as follows:

(1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10 = 2.54.

The deviations are given as follows:

Hence the mean absolute deviation is given as the sum of the deviations divided by the number of observations, hence:

(1.04 + 1.26 + 1.24 + 1.06 + 0.46 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24)/10 = 1.52 million.

The table is given by the image presented at the end of the answer.

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The estimated proportion of adults in the country who have donated blood in the past two years is approximately 0.1803 or 18.03%. the 95% confidence interval for the proportion of adults in the country who have donated blood in the past two years is approximately 0.1589 to 0.2017.

(a) Estimate the proportion of adults in the country who have donated blood in the past two years.

To estimate the proportion of adults who have donated blood, we divide the number of adults who have donated blood by the total number of adults surveyed.

Number of adults who have donated blood = 414

Total number of adults surveyed = 2290

Proportion of adults who have donated blood = Number of adults who have donated blood / Total number of adults surveyed

Proportion of adults who have donated blood = 414 / 2290

Proportion of adults who have donated blood ≈ 0.1803 (rounded to four decimal places)

Therefore, the estimated proportion of adults in the country who have donated blood in the past two years is approximately 0.1803 or 18.03% (rounded to two decimal places).

(b) Construct a 95% confidence interval for the proportion of adults in the country who have donated blood in the past two years.

To construct a confidence interval, we can use the formula for a proportion with a confidence level of 95%:

Confidence interval = Sample proportion ± Margin of error

Sample proportion = Proportion of adults who have donated blood = 0.1803 (from part a)

Margin of error = Z * √[(Sample proportion * (1 - Sample proportion)) / Sample size]

Z represents the critical value for a 95% confidence level. Since the sample size is large (n > 30), we can use the standard normal distribution and take Z = 1.96.

Sample size = Total number of adults surveyed = 2290

Margin of error = 1.96 * √[(0.1803 * (1 - 0.1803)) / 2290]

Calculating the margin of error:

Margin of error ≈ 1.96 * √[(0.1803 * 0.8197) / 2290]

Margin of error ≈ 0.0214 (rounded to four decimal places)

Confidence interval = 0.1803 ± 0.0214

Lower bound = 0.1803 - 0.0214 ≈ 0.1589 (rounded to four decimal places)

Upper bound = 0.1803 + 0.0214 ≈ 0.2017 (rounded to four decimal places)

Therefore, the 95% confidence interval for the proportion of adults in the country who have donated blood in the past two years is approximately 0.1589 to 0.2017 (or 15.89% to 20.17%, rounded to two decimal places).

(c) Interpret the confidence interval in the context of the problem.

The confidence interval provides a range of values within which we can be 95% confident that the true proportion of adults in the country who have donated blood lies. Based on the survey data, the estimated proportion is 18.03% (from part a). The 95% confidence interval for this proportion is approximately 15.89% to 20.17%.

This means that we are 95% confident that the true proportion of adults in the country who have donated blood in the past two years falls within this range. In other words, if we were to repeat the survey multiple times and construct confidence intervals, approximately 95% of those intervals would contain the true proportion.

Therefore, based on this survey, we can conclude that the proportion of adults who have donated blood in the past two years in the country is likely to be between 15.89% and 20.17%, with a confidence level of 95%.

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The measure of the angle ∠S is 95°

Let's call angle Q as x. Then we can express the other angles in terms of x as follows:

Angle R = x + 25 (since angle R is 25° more than angle Q)

Angle S = x + 65 (since angle S is 65° more than angle Q)

We know that the sum of the angles in a triangle is always 180°, so we can write:

x + (x + 25) + (x + 65) = 180

Simplifying this equation, we get:

3x + 90 = 180

Subtracting 90 from both sides, we get:

3x = 90

Dividing both sides by 3, we get:

x = 30

Therefore, angle S is:

x + 65 = 30 + 65 = 95 degrees

So the measure of angle S is 95 degrees.

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The derivative of the inverse trigonometric function is equal to f'(x) = (2 · e²ˣ) / √(1 - e⁴ˣ). (Correct choice: D)

In this problem we find the case of the inverse trigonometric function, whose derivative must be found. This can be done by means of derivative rules and chain rules. First, write the entire function:

f(x) = sin⁻¹ (e²ˣ)

Second, find the derivative of the inverse trigonometric function:

f'(x) = [1 / √[1 - (e²ˣ)²]] · (2 · e²ˣ)

f'(x) = (2 · e²ˣ) / √(1 - e⁴ˣ)

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a)The concentration will be 0.5 mg/L at approximately 1.18 hours.

c) [0, ∝) is a reasonable domain for this function.

d) The patient must receive the next intravenous dose of the drug between 0.75 and 1.35 hours after the initial dose.

e) The concentrations of the two drugs cannot be compared

A. To find when the concentration will be 0.5 mg/L, we can set the function equal to 0.5 and solve for t:

20t c(t)-20 2 +4 = 0.5

20t c(t)-20 2 = 3.5

20t c(t) = 2

3.5c(t) = 1.175

So the concentration will be 0.5 mg/L at approximately 1.18 hours.

B. Using the given formula, we can complete the table as follows:

| t    | c(t)         |

0    | 4            |

2    | 2.86        |

4    | 2.14         |

6    | 1.62         |

8    | 1.23         |

10   | 0.95         |

12   | 0.74         |

14   | 0.57         |

16   | 0.44         |

18   | 0.34         |

20   | 0.27        

C. Because time cannot be negative and the function has no imaginary values, the domain of the function is all non-negative real numbers.

As a result, [0,] is a reasonable domain for this function.

D. To maintain a concentration above 1 mg/L and below 8 mg/L, we need to solve the inequality:

1 < 20t

c(t)-20 2 +4 < 8

Simplifying this inequality, we get:

0.75 < t < 1.35

To maintain the desired concentration, the patient must receive the next intravenous dose of the drug between 0.75 and 1.35 hours after the initial dose.

E. Without additional information, we cannot compare the concentrations of the two drugs.

The information provided only allows us to analyze the intravenous drug concentration

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Angle 1 and angle 2 are corresponding angles since they are in the same relative position. Corresponding angles are congruent. So, to solve, we will need to set the given expressions equal to each other and then solve for the value of x algebraically.

80 - 2x = 93 - 3x

80 + x = 93

x = 13

Answer: x = 13

Hope this helps!

Answer:

x = 10

Step-by-step explanation:

m<1 = m<2

(80-2x) = (90-3x)

80 - 2x = 90 - 3x

80 = 90 - x

-10 = -x, x = 10

The pythagorean theorem says a^2 + b^2 = c^2 when a and b are the sides of the right triangle and c is the hypotenuse (longest side, opposite the 90 degree angle).

so if  8^2 + 6^2 = 10^2, then it's a right triangle.

8^2 + 6^2 = 64 + 36 = 100 = 10^2, so yes, this is a right triangle.

The distance d between A and B is √(68), and the square of the distance in the y direction is 64.

To find the distance d between points A and B, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values of A and B, we get:
d = sqrt((4 - 2)^2 + (5 - (-3))^2)
d = sqrt(2^2 + 8^2)
d = sqrt(4 + 64)
d = sqrt(68)
Next, to calculate the square of the distance in the y direction, we need to find the difference between the y-coordinates of A and B and square it. So:
(y2 - y1)^2 = (5 - (-3))^2 = 8^2 = 64
Therefore, the square of the distance in the y direction is 64.
I'm here to help you with your question. To find the distance d between two points A(x1, y1) and B(x2, y2), we can use the distance formula:
d = √((x2-x1)² + (y2-y1)²)
Given the points A(2, -3) and B(4, 5), let's plug in the values:
d = √((4-2)² + (5-(-3))²)
Now, calculate the difference for each coordinate:
d = √((2)² + (8)²)
Next, square the differences:
d = √(4 + 64)
Finally, calculate the square root:
d = √(68)
ow, let's find the square of the distance in the y direction, which is (y2-y1)²:
(y2-y1)² = (5-(-3))²
Calculate the difference:
(y2-y1)² = (8)²
Square the difference:
(y2-y1)² = 64
So, the distance d between A and B is √(68), and the square of the distance in the y direction is 64.

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Step 1: Find a common denominator.

The denominators are 3y, 4, and 8. The least common multiple (LCM) of these is 24y.

Step 2: Adjust each term to have a denominator of 24y.

To do this, we multiply the numerator and denominator of each term by the appropriate factor:

For the term 8/3y, multiply numerator and denominator by 8: (8/3y) * (8/8) = 64/24y.

For the term 5y/4, multiply numerator and denominator by 6y: (5y/4) * (6y/6y) = 30y^2/24y.

For the term 5/8, multiply numerator and denominator by 3: (5/8) * (3/3) = 15/24y.

Step 3: Combine the terms.

Now that all terms have a common denominator of 24y, we can add them together:

(64/24y) + (30y^2/24y) - (15/24y)

Step 4: Combine the numerators.

Add the numerators of the fractions:

(64 + 30y^2 - 15) / 24y

Step 5: Simplify the numerator.

Combine like terms in the numerator:

(49 + 30y^2) / 24y

Thus, the simplified expression is (49 + 30y^2) / 24y, considering all permissible values of y.

Answer:

(-1, 3 1/4) and (3, 12 3/4)

Step-by-step explanation:

These are the only two pairs that will work for the graph.

The area of the triangle in the shaded region is derived to be 12.5 square units.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

For the triangle in the shaded region;

base = 5 units

height = 5 units

area of the triangle = 1/2 × 5 units × 5 units

area of the triangle = 25/2

area of the triangle = 12.5 square units

Therefore, the area of the triangle in the shaded region is derived to be 12.5 square units.

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75 chairs expected to be understaffed.

Given : number of common problems found during one such spot check. manufacturer makes 1500 beanbag chairs per day.

To Find : how many of those chairs would they expect to be understaffed?

Common Problems   Frequency

Open seam                  4

Cuts in upholstery       14

Understaffed                15

None                             267

Total                              300

Probability of understaffed  = Understaffed   / Total

= 15/300

= 1/20

manufacturer makes 1500 beanbag chairs per day,

Number of chairs expected to be understaffed = (1/20) x 1500 = 75

Hence 75 chairs expected to be understaffed.

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The theoretical probability of exactly 4 students from your school being selected as contestants out of 10 possible contestant spots is approximately 0.009.

Assuming that each member of the audience has an equal chance of being selected as a contestant, the total number of possible ways to select 10 contestants from the audience is:

[tex]150 $ choose 10 = 150! / (10! \times (150 - 10)!) = 2,535,316,699,000[/tex]

To calculate the probability of exactly 4 students from your school being selected as contestants, we need to count the number of ways this can happen and divide it by the total number of possible outcomes.

There are 30 students from your school and 120 students from other schools in the audience.

We need to choose 4 students from your school and 6 students from other schools for the contestant spots.

The number of ways to do this is:

[tex]30 $ choose 4 \times 120 $ choose 6 = (30! / (4! \times 26!)) \times (120! / (6! \times 114!)) = 23,400,140,040,000[/tex]

Therefore, the probability of exactly 4 students from your school being selected as contestants is:

P(4 students selected) = (number of ways to select 4 students from your school and 6 students from other schools) / (total number of ways to select 10 contestants from the audience)

P(4 students selected) = 23,400,140,040,000 / 2,535,316,699,000.

P(4 students selected) ≈ 0.00923 (rounded to 3 decimal places).

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Answer:

[tex]\sqrt[2]{(m)^1}[/tex]

Step-by-step explanation:

denominator = the root number ___

numerator = to the power of ___

The expression simplifies to |2x| = -2x, when x<0 by definition of absolute value

If x<0, then the expression |2x| simplifies to -2x.

The absolute value of a number is the distance of the number from zero on the number line.

Since x is negative in this case, 2x will be negative as well.

Taking the absolute value of -2x will give us the opposite of -2x, which is 2x.

However, since we know that x<0, this means that -2x will always be a positive number.

Hence, the expression simplifies to |2x| = -2x, when x<0.

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Complete question

Simplify the expression |2x|  when x is less than 0, x<0

The measurement is the same for Charles and Jermod are lower quartile and upper quartile. Therefore, options C and D are the correct answer.

From the given dot plot.

The number of minutes Charles spent on homework.

15, 15, 20, 20, 25, 30, 30, 30, 30, 30, 45, 50, 55, 60, 60.

Here, lower quartile = 20

Upper quartile = 50

Median = 30

Range = 60-15

= 45

The number of minutes Jermod spent on homework.

15, 15, 15, 20, 20, 30, 35, 45, 45, 45, 50, 50, 55, 55.

Here, lower quartile = 20

Upper quartile = 50

Median = 45

Range = 55-15

= 40

Therefore, options C and D are the correct answer.

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Answer:

The equation of a line that is perpendicular to y = 3x + 3 is option A y equals negative one-third times x plus 1(-1/3x + 1)Given,The equation of line, y = 3x + 3The line passes through (-6, 3)We have to find the equation of the line that is perpendicular to y = 3x + 3Slope of the line, m = 3Here, in perpendicular case, slope is negative of its reciprocal.That is, m = -1/3Now, we can find the equationy - y₁ = m(x - x₁)

Here,

y₁ = 3x₁ = -6m = -1/3

So,y - 3 = -1/3(x - (-6))

y - 3 = -1/3(x + 6)

y - 3 = -1/3x + -1/3(6)

y - 3 = -1/3x - 6/3

y - 3 = -1/3

x - 2y = -1/3

x - 2 + 3

y = -1/3x + 1

That is, the equation of a line that is perpendicular to y = 3x + 3 is y equals negative one-third times x plus 1(y = -1/3x + 1)

Step-by-step explanation:

Answer:

1890ml<10litres

1.72m=172cm

Step-by-step explanation:

10 x 1000 = 10000 ml which is greater than 1890 ml.

1.72 x 100 = 172 cm

Answer:

The average cost is 4400

Step-by-step explanation:

c=800+40x

where x=number of items

c=800+4x;when x=90

c=800+40(90)

c=800+3600

c=4400

Answer:

4400

Step-by-step explanation:

The actual side length of the house is 240 feet long.

The scale factor is 1 inch on the blueprint represents 60 actual feet.

The side of the house measures 4 inches on the blueprint. To find the actual length, we multiply the blueprint length by the scale factor:

Actual side length = 4 inches * 60 feet/inch = 240 feet

So, the actual side length of the house is 240 feet.

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The inverse of the function f(x) = 1/x is B. f⁻¹(x) = 1/x

The inverse of a function f(x) written as f⁻¹(x) is such that ff⁻¹(x) = f⁻¹f(x)

Given the function f(x) = 1/x,we desire to find its inverse. We proceed as follows.

Since f(x) = 1/x

Let f(x) = y

So,we have that

y = 1/x

Now, multiplying both sides by x,we have that

x × y = 1/x × x

xy = 1

Dividing though by y, we have that

xy/y = 1/y

x = 1/y

Now, relacing y with x and x with f⁻¹(x), the inverse of f(x), we have that

x = 1/y

x = 1

f⁻¹(x) = 1/x

So, the inverse is B. f⁻¹(x) = 1/x

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The result to the equation is x = 7.

To find the results of the equation √( 2x- 5) 4 = 1, we can break it step by step

Abate 4 from both sides of the equation

√( 2x- 5) = 1- 4

√( 2x- 5) = -3

Square both sides of the equation to exclude the square root

√( 2x- 5))² = (- 3)²

2x- 5 = 9

Add 5 to both sides of the equation

2x = 9 + 5

2x = 14

Divide both sides of the equation by 2

x = 14/2

x = 7

Thus, the result to the equation is x = 7.

Checking the extraneous result

Substituting x = 7 back into the original equation

√(2(7)-5)+4=1

√(14-5)+4=1

√9+4=1

3+4=1

7 = 1

This equation isn't true, which means that x = 7 is an extraneous result.

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A) the average speed  of the journey from my home town to A is 30 miles per hour

B) the average speed of the journey from my home town to B is 40 miles per hours.

C) The average time is 36 miles per hours.

Average speed = distance /   time

So the answers is

A) Average speed = 10 miles ÷ (1/3 hour) = 30 miles per hour

B) Average speed = 20 miles ÷ 0.5 hours = 40 miles per hour.

C) Average speed = 30 ÷ (50/ 60) = 30 ÷ 0.8333 = 36 miles per hour.

Average Speed is essential for understanding the rate at which a travel occurs.

The speed of a vehicle may change from time to time throughout a travel. In that instance, determining the average speed is critical in order to determine the pace at which the voyage will be completed.

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Full Question:

The diagram shows the distance between my home, H, and two towns, A and B. It also shows information about journey times. See same attached.

The approximate length of the diagonal to the nearest tenth of an inch is 32.52 inches.

To find the length of the diagonal, we can use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides.

In this case, since the sides of the square television screen are 23 inches, we can calculate the length of the diagonal using the following formula

So, if the sides of the square television screen are 23 inches, then:

[tex]Diagonal^2 = Side^2 + Side^2[/tex]

[tex]Diagonal^2 = 23^2 + 23^2[/tex]

[tex]Diagonal^2[/tex]= 529 + 529

[tex]Diagonal^2[/tex] = 1058

Diagonal = √1058

Diagonal ≈ 32.52 inches

Rounding to the nearest tenth of an inch, the approximate length of the diagonal is 32.52 inches.

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The total payment required to pay off a promissory note issued for $400.00 is $412.

Using this formula

Total payment=Promissory note+(Promissory note× Ordinary interest× 90 day term/360)

Where:

Promissory note=$400

Ordinary interest=12%

Let plug in the formula

Total payment= $400 + ($400 × 12% × 90 days ÷ 360 days)

Total payment= $400 + $12

Total payment= $412

Hence, the total payment required to pay off a promissory note issued for $400.00 is $412.

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"The correct answer is: g(x), f(x), h(x)."To determine the correct order of the functions from least to greatest according to the average rate of change on the interval from x = 0 to x = 4, we need to calculate the average rate of change for each function.

The average rate of change is calculated by finding the difference in the function's values at the endpoints of the interval (x = 4 and x = 0) and dividing it by the difference in the corresponding x-values.

For function f(x), we have:

Average rate of change = (f(4) - f(0))/(4 - 0) = (64 - 0)/(4 - 0) = 64/4 = 16

For function g(x), since it is a linear graph, the average rate of change is constant throughout. Therefore, the average rate of change for g(x) is the same as the slope of the line, which is determined by the ratio of the change in y to the change in x. In this case, it would be the slope between the given x-intercept (-2) and y-intercept (-1), which is -1/2.

For function h(x), we need to find the average rate of change between x = 0 and x = 4. Substituting the values, we get:

Average rate of change = (h(4) - h(0))/(4 - 0) = (36 - 6)/(4 - 0) = 30/4 = 7.5

Now, let's compare the average rates of change for each function:

f(x): 16

g(x): -1/2

h(x): 7.5

From least to greatest, the correct order according to the average rate of change is:

g(x), f(x), h(x).

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