solve for inequality
|x-1/2| + 4 ≤ 5/2

Answer:

Question 1.) The rate is 198 feet per second.
Question 2.) The parachutist will fall 396 feet in 2 seconds of free fall.

Step-by-step explanation:

We have to first convert 60 meters into feet.
According to the question, we know that 1 meter is 3.3 feet. So use this equation to get 60 meters into feet.
3.3 x 60 = 198

This is in 1 second of free fall. We have to find 2 seconds of freefall so we multiply this by 2.
198 x 2 = 396 feet in 2 seconds of free fall.

I hope this was able to help you :D

250 adults and 195 children swam at the public pool on that day.

What is the system of linear equations?

A system of linear equations is a set of two or more equations that contain two or more variables. The goal is to find the values of the variables that will satisfy all of the equations in the system.

This is a system of equations problem. We can start by using two variables, x for the number of children and y for the number of adults, and then set up two equations based on the information given.

The first equation is for the total number of people: x + y = 445

The second equation is for the total amount of money collected: 1.75x + 2.5y = 964.75

We can now use the first equation to solve for one of the variables in terms of the other, and then substitute that expression into the second equation.

x + y = 445

x = 445 - y

Now we substitute x = 445 - y into the second equation

1.75(445 - y) + 2.5y = 964.75

after solving this equation we get

y = 250

x = 195

Hence, 250 adults and 195 children swam at the public pool on that day.

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Answer:

c

Step-by-step explanation:

The sound of the alarm clock will become fainter as the air is removed from the space around it. As the air is removed, the sound waves will be unable to travel and will become more and more muffled until you can only hear a faint sound from the clock. The appearance of the clock will not change.

As the air is slowly removed from the space around an alarm clock, the sound of the clock will become fainter. This is because the sound waves will be unable to travel properly through the airless space, and will become more and more muffled until you can only hear a faint sound from the clock. The appearance of the clock will not change, however. This phenomenon is caused by sound waves being unable to travel through airless spaces, which is why sound can be muffled when you cover your ears or put something between you and the sound source. Although the clock will become quieter and its sound will become fainter, the appearance of the clock will remain the same.

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Answer:

First let 'A' stand for area.

So, there's 3 areas so we write it like this:

A1: 14 ft × 3ft = 42 ft

A2: (14 ft - 2 ft) × 2 ft = 24 ft

A3: 8 ft × 3 ft = 24 ft

So when you add all of them = 90 ft

Have a wonderful day! :-)

By taking a quotient we will see that the percent is 24%.

The percent will be given by the quotient between the number of cars that have a speed above the speed limit, and the total number of cars (and we multiply that by 100%)

There are 25 cars in total, and 6 of these have a speed above the speed limit, then the percent is:

p = (6/25)*100% = 24%

So 24 percent of the cars are travelling above the speed limit.

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Answer: The zeros of the function f(x) are the values of x that make f(x) equal to zero. To find the zeros of the function, we can set f(x) equal to zero and solve for x.

f(x) = x^3 - 2x^2 - 3x = 0

One way to find the zeros of the function is to factor it:

x(x-3)(x+1)=0

Thus the zeros of the function are x=0, x=3, x=-1

The largest zero of the function is 3.

Another way to find the zeros of the function would be using synthetic division or other root-finding techniques like the Newton-Raphson method.

Step-by-step explanation:

h(x) = g(x) + 200, which means the average  new income tax is the sum of the original income tax and an additional flat fee of 200 dollars per taxpayer.

h(x) = g(x) + 200

h(x) is the new income tax for a single person with taxable income x dollars.

g(x) is the 2010 federal income tax for a single person with taxable income x dollars.

Therefore, h(x) = g(x) + 200, which means the new income tax is the sum of the original income tax and an additional flat fee of 200 dollars per taxpayer.

The new income tax plan consists of the 2010 income tax plus an additional 200 dollars per taxpayer. To represent this mathematically, we let g(x) be the function such that g(x) is the 2010 federal income tax for a single person with taxable income x dollars, and let h(x) be the corresponding function for the new income tax plan. By examining the new income tax plan, we can see that the new income tax is the sum of the original income tax plus an additional flat fee of 200 dollars per taxpayer. Thus, h(x) = g(x) + 200, which is a concise formula that captures the essence of the new income tax plan. This formula shows that the new income tax is simply the original income tax increased by a fixed amount of 200 dollars.

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Answer:

Step-by-step explanation:

46

A negative correlation coefficient indicates that as one variable increases, the other variable decreases. This means that the points on the scatterplot are spread in a downward direction, which suggests a negative correlation between the two variables.

A scatterplot is a graph that shows the relationship between two variables by plotting points that represent the values of the two variables. When reviewing a scatterplot, one can look for the correlation coefficient, which is a statistical measure that describes the strength of the relationship between the two variables. A negative correlation coefficient indicates that as one variable increases, the other variable decreases. This means that the points on the scatterplot are spread in a downward direction, which suggests a negative correlation between the two variables. A scatterplot with several negative coefficients indicates that the correlation between the two variables is negative, meaning that when one variable increases, the other one decreases. The strength of the correlation is determined by how close the points on the scatterplot are to the line of best fit. A strong negative correlation means that the points are close to the line of best fit and are spread in a downward direction, while a weak negative correlation means that the points are further away from the line of best fit and are spread in a more random pattern.

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Brand and product quality are the factors account for the dramatic difference in watch prices.

The factors of production are resources that are the building blocks of the economy they are what people use to produce goods and services.

Given that the Timex watch is $45.

Rolex watch is $10000.

We have to find the factors account for the dramatic difference in watch prices.

The rolex watch quality is better than the Timex, so the price of Rolex watch is high compared to Timex.

The brand and product quality are the factors account for the dramatic difference in watch prices.

Hence, brand and product quality are the factors account for the dramatic difference in watch prices.

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Answer:

Step-by-step explanation:

a. To find the percentage of the weight limit that 33 pounds is, we can use the following formula:

(Weight / Weight Limit) x 100 = Percentage

So, for 33 pounds:

(33 / 60) x 100 = 55%

b. To find the percentage of the weight limit that 114 pounds is:

(114 / 60) x 100 = 190%

c. To find what weight is 95% of the limit, we can use the following formula:

Weight Limit x (Percentage / 100) = Weight

So, for 95%:

60 x (95 / 100) = 57 pounds

Therefore, 95% of the weight limit is 57 pounds.

Answer:

Exact Form:

14/25

Decimal Form:

0.56

Step-by-step explanation:

The trigonometric equation has the following roots: x₁ = ± i · π, x₂ = π / 6 ± i · π, where i are integers. (Correct choice: D)

Trigonometric equations are equations that involve trigonometric functions. Trigonometric functions are periodic trascendent functions. In this problem we must determine the roots of a trigonometric equations by means of algebra properties and trigonometric formulas:

3 · tan² x = √3 · tan x

3 · tan² x - √3 · tan x = 0

tan x · (3 · tan x - √3) = 0

The roots of the equation are tan x = 0 or tan x = √3 / 3, whose angles are: x₁ = ± i · π, x₂ = π / 6 ± i · π, where i are integers.

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Answer: You want to ship 80 items, and each case holds 7 items. To find the number of cases needed to ship the 80 items, you can use the formula:

Number of cases = (Number of items) / (Items per case)

So in this case, the number of cases needed to ship 80 items is:

Number of cases = 80 / 7

Which simplifies to 11.428571428571429, so you will need 12 cases to ship 80 items.

Step-by-step explanation:

The rotation of the image given 180° clockwise around the point (-2, 1) gives the image in the second option.

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

The coordinates of the given image are :

(-1, 1), (-2, 1), (-1, 4) and (-2, 4).

Point of rotation is (-2, 1).

The points are not rotated around the origin.

To make it seem like around the origin, subtract the point of rotation from the points.

So the new points are :

(1, 0), (0, 0), (1, 3) and (0, 3)

Now rotate the image with the new coordinates around the origin 180° clockwise.

Rotation is -180°, which is equivalent to rotation of 180° counterclockwise.

Coordinates (x, y) when rotated 180° clockwise becomes (-x, -y).

New coordinates after rotation about origin are :

(-1, 0), (0, 0), (-1, -3) and (0, -3).

Now add the point of rotation (-2, 1) again.

Points are :

(-3, 1), (-2, 1), (-3, -2) and (-2, -2).

Image with these points is the second option.

Hence the required image is the second option.

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The range of this set of data is 30 ≤ y ≤ 80.

In Mathematics, a range is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown above, we can reasonably and logically deduce the following domain and range:

Domain = 0 ≤ x ≤ 24 or [0, 24].

Range = 30 ≤ y ≤ 80 or [30, 80].

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The maximum and minimum number of hikers from the given frequency table are 17 and 4 respectively.

What is a frequency table?

One approach to display data is in a frequency table. To summarise bigger collections of data, the data are organised and counted. You can examine the distribution of the data across various values using a frequency table.

From the given frequency table, we can see that

Between 0 and 5 miles, there are 3 hikers

Between 5 and 10 miles, there are 4 hikers

Between 10 and 15 miles, there are 7 hikers

Between 15 and 20 miles, there are 6 hikers

Between 20 and 25 miles, there is only 1 hiker.

So the maximum number of hikers between 8 miles and 19 miles is the total number of hikers between 5 and 20 miles = 4 + 7 + 6 = 17

The minimum number of hikers who could have walked between 8 miles and 19 miles is 4 hikers.

Therefore the maximum and minimum number of hikers from the given frequency table are 17 and 4 respectively.

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Answer: 9.25

For this equation you will need to use division. 74min. divided by 8mi.

To double check your answer is correct you have to multiply. 9.25min times 8mi.

Answer: a. First-in, first-out (FIFO) method:

Under FIFO, the first units purchased are assumed to be the first units sold.

9 units were sold at $39 each for a total cost of $351

9 units were sold at $41 each for a total cost of $369

6 units were sold at $42 each for a total cost of $252

So the total cost of goods sold is $351 + $369 + $252 = $972

The 7 units remaining in inventory at the end of the year were purchased at $41 each, so their cost is 7*41 = $287

b. Last-in, first-out (LIFO) method:

Under LIFO, the most recent units purchased are assumed to be the first units sold.

6 units were sold at $42 each for a total cost of $252

9 units were sold at $41 each for a total cost of $369

9 units were sold at $39 each for a total cost of $351

So the total cost of goods sold is $252 + $369 + $351 = $972

The 7 units remaining in inventory at the end of the year were purchased at $39 each, so their cost is 7*39 = $273

c. Weighted average cost method:

Under the weighted average cost method, the average cost of all the units is used to determine the cost of goods sold and ending inventory.

The total cost of the units available for sale is $351 + $369 + $252 = $972 and the total number of units available for sale is 24. So, the average cost per unit is $972 / 24 = $40.50

The cost of goods sold is $40.50 * 24 = $970.

The cost of the units remaining in inventory at the end of the year is $40.50 * 7 = $283.50

Note: The final answers were rounded to the nearest whole dollar.

Step-by-step explanation:

The value of `near twentyfive` is approximately equal to 25.3 and is calculated by taking the square root of the product of `e` raised to the power of[tex]$2\pi$[/tex], and 30[tex]$\pi$[/tex].

The designation "e" for the natural logarithm's base, which is around 2.71, is provided by the math module. We must take the square root of the product of "e" raised to the power of $2 pi and of "30 pi" in order to determine the value of "near twentyfive." The mathematical notation for this is sqrt(e(2)pi, pi). 'near twentyfive' has a value that is roughly equivalent to 25.3. This is due to the fact that $e2pi$ is roughly equivalent to 19.7, and $30pi$ is roughly equivalent to 94.2. 1867.4 is the result of adding these two integers together, while 43.4 is the result of taking 1867.4 as its square root. Finally, when 43.4 is divided by 2, the result is 25.3

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A correct answer is an option (C); both statements together are sufficient.

Although k < n, no details are given about the value of k or n; not sufficient.

Since the median of the numbers in the list is 10 and there are 5 numbers in the list, 10 is one of these 5 numbers. Hence, n = 10 or k = 10. If n = 10, then the value of n has been decided. However, if k = 10, then n can be any number that is 10 or less, so the value of n cannot be found out; not sufficient.

Taking (1) and (2) together, if k < n and the median of the list are 10, then 12 and 17 are to the right of the median and the list in ascending order is either 6, k, n, 12, 17 or k, 6, n, 12, 17. In this case, n is the middle number, and since the median is 10, n = 10.

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The complete question is:

Given the list k, n, 12, 6, 17, What is the value of n in the list above?

(1) k < n

(2) The median of the numbers in the list is 10.

Which option is correct?

A) Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

B) Statement (2) alone is sufficient, but Statement (1) alone is not sufficient.

C) Both statements together are sufficient, but neither statement alone is sufficient.

D) Each statement alone is sufficient.

Answer:

Step-by-step explanation:

can u send the story or did you lie?

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The expressions using only addition are (a) 4x + (-7y) + (-5z) + 6 and (a) -3x + (-8y) + (-4) + (-8/7z)

Expression 1

From the question, we have the following expression that can be used in our computation:

4x - 7y - 5z + 6

When represented using only addition, we have

4x + (-7y) + (-5z) + 6

Expression 2

From the question, we have the following expression that can be used in our computation:

-3x - 8y - 4 - 8/7z

When represented using only addition, we have

-3x + (-8y) + (-4) + (-8/7z)

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The total distance that rob ran and walked for 60 minutes is; 8820 meters

The parameter for the constant speed is that Rob runs at a speed of 3.4 meters per second for one half hour.​ Thus;

V1 = 3.4 m/s

t1 = 1.5 hours =

30 * 60 = 1,800 seconds.

The distance he runs at that speed and time is;

S1 = V1 * t1

= 3.4 * 1,800

= 6,120 meters

He walks at V2 = 1.5 m/s for t2 = 1,800 seconds.

The distance he walks;

S2 = V2 * t2

= 1.5 * 1,800

= 2,700 meters

The total distance he runs and walks;

S = S1 + S2

= 6120 + 2700

= 8820 meters

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The equation on the interval [0, 2π).x is 4π / 3 ,5π / -2

Intervals are expressed using parentheses or rectangular brackets, and a comma is used to separate two integers. The two numbers are referred to as the interval's endpoints. The least element or lower bound is shown by the number on the left. The biggest element or upper bound is shown by the number on the right.

As a result, when x = 4 and 5 4, f (x) has its maximum value of 1, which is 1.

A range of numbers between two specified numbers that include all real numbers in that range is known as an interval.

2sinx+ [tex]\sqrt{}[/tex]3 =0

⇒sinx= [tex]\sqrt{}[/tex] 3− 2

⇒x=nπ+(−1) ^-n  4π /3 (∵sin3 4π  = [tex]\sqrt{}[/tex]3/-2 )

X =?]π5TT

x = 4π / 3 ,5π / -2

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The three consecutive integers are given as follows:

-4, -3 and -2.

The three consecutive integers are obtained using a system of equations, for which the variables are given as follows:

x, y and z.

They are consecutive, thus:

Triple the sum of the first two integers is 19 less than larger integer, hence:

3(x + y) = z - 19

Replacing into the equation, the value of x is obtained as follows:

3(x + x + 1) = x + 2 - 19

6x + 3 = x - 17

5x = -20

x = -4.

Hence the remaining integers are -3 and -2.

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The result is close to the 1:1 ratio of red to white flowering plants, so the genotype must be Rr and rr. Option A is correct.

Mendel's law of dominance states that in a heterozygote, one trait will conceal the presence of another trait for the same characteristic.

According to this law, the offspring of the first generation from pure breed parents will show only dominant traits.

When a Heterozygous dominant parent mates with a pure recessive parent the ratio of the dominant and recessive characters will be 1:1.

The cross:

           r            r

R         Rr          Rr

r          rr           rr

Therefore, the result is close to the ratio of red to white flowering plants, so the genotype must be Rr and rr.

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The complete option are:

A. The results are close to a 1:1 ratio of plants with red flowers to plants with white flowers. Therefore, the genotypes of the

Rr and ir

B.

The results should yield plants with red flowers and plants with white flowers in a 3:1 ratio due, so the geneotype of each parent is Rr.

The number of offspring was not large enough to produce the expected results

C. The results differ from the predicted values. Therefore, the genotypes of the parents cannot be determined.

D

. The results should show a ratio of 3 plants with white flowers to 1 plant with red flowers, so the genotypes of the parent plants are RR

The measure of the numbered angles of the quadrilaterals in the question are presented as follows;

14. m∠1 = 54°, m∠2 = 36°, m∠3 = 54° m∠4 = 108°, m∠5 = 72°

15. m∠1 = 90°, m∠2 = 45°, m∠3 = 45°, m∠4 = 45°, m∠5 = 45°

16. m∠1 = 64°, m∠2 = 64°, m∠3 = 26°, m∠4 = 90°, m∠5 = 64°

A quadrilateral is a four sided polygon.

14. The figure is a rectangle

The two diagonals of a rectangle are the same length and the diagonals of a rectangle bisect each other, therefore;

The triangles formed by the diagonals of the rectangle are isosceles triangles.

The angle at the vertex of the isosceles triangle that has 36° as the base angle of the triangle is therefore; (180° - 2 × 36°) = 108°

The angle ∠4, is a vertical angle to the angle calculated above, therefore;

m∠4 = 108°

m∠5 = (360° - 2 × 108°) = 72°

m∠5 = 72°

The similar triangles formed by the diagonals indicates that we get;

m∠2 = 36°

m∠1 = (180° - m∠5)/2

Therefore; m∠1 = (180° - 72°)/2 = 54°

m∠1 = 54°

∠1 ≅ ∠3

Therefore; m∠3 = m∠1 = 54°

m∠3 = 54°

15. The quadrilateral is a square, therefore;

The diagonals bisect each other and are perpendicular.

m∠1 = 90° (Definition of perpendicular angles)

m∠5 = (180° - 90°)/2 = 45°

m∠5 = 45°

∠3 ≅ ∠5, therefore;

m∠3 = m∠5 = 45°

m∠3 = 45°

m∠3 + m∠2 = 90° (The vertex angles of a square are 90°)

m∠2 = 90° - m∠3

m∠2 = 90° - 45° = 45° (Substitution property)

m∠2 = 45°

16. The quadrilateral is a rhombus, therefore;

The diagonals of a rhombus perpendicular

Adjacent angles are supplementary

The opposite angles of a rhombus are congruent

The opposite sides of a rhombus are parallel

Diagonals of a rhombus bisect the interior angles

The above properties indicates that we get;

90° + m∠1 + 26° = 180°

m∠1 = 180° - 26° - 90° = 64°

m∠1 = 64°

m∠4 = 90°

The angle ∠3 and the 26° angle are alternate interior angles. Alternate interior angles between parallel lines are congruent, therefore;

m∠3 = 26°

m∠1 = m∠2 (definition of bisected angle), therefore;

m∠2 = m∠1 = 64°

m∠2 = 64°

∠2 and ∠5 are alternate interior angles, therefore;

∠2 ≅ ∠5

m∠5 = m∠2 = 64°

m∠5 = 64°

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