The volume of the sand pit is V = 694.6 feet²
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the volume of the rectangle be represented as V
Now , the length of the sand pit = 30.2 feet
The width of the sand pit = 9.2 feet
The depth of the sand pit = 30 inches = 2.5 feet
Now , the volume of the rectangular pit = L x W x H
On simplifying the equation , we get
The volume of the rectangular pit V = 30.2 x 9.2 x 2.5
The volume of the rectangular pit V = 694.6 feet²
Hence , the volume of the rectangular sand pit is 694.6 feet²
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write the system as a vector equation where the first equation of the system corresponds to the first row. select the correct choice below and fill in any answer boxes to complete your choice.
The system of equations can be represented as a vector equation A x = b, where A is the coefficient matrix, x is the variable vector, and b is the constant vector.
Using matrices and vectors, a system of linear equations can be expressed as a vector equation. Consider a set of n variables and m linear equations. It may be written as follows:
A x = b
where A is a m x n matrix of the coefficients of the variables, x is a n x 1 column vector of the variables, and b is a m x 1 column vector of the constants on the right-hand side of each equation.
To match the rows of the system of equations to the corresponding row of the matrix A and vector b in the vector equation, we can represent the system of equations as:
a 21 x 1 + a 22 x 2 +... + a 2n x n = b 2 a 11 x 1 + a 12 x 2 +... + a 1n x n = b 1
a mn x n = b m, where a m1 x 1 = a m2 x 2 +...
The vector form of this is as follows:
Beginning with "a 11" and "a 12," adding "cdots and a 1n," going on to "a 21" and "a 22," adding "cdots and a 2n," adding "vdots and vdots and ddots and vdots," ending with "a m1" and "a m2," adding "cdots and a mn,"
With A serving as the coefficient matrix, x serving as the variable vector, and b serving as the constant vector, the system of equations can thus be expressed as a vector equation, A x = b.
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Maureen has a Jump rope that is 62 inches long nancys jump rope is 10 inches longer how long is nancys jump rope?
Answer: 6 feet long
Step-by-step explanation:
1ft. = 12 in
62 inches = 5 feet and 2 inches
Break down 62 into 60 and 2
60 divided by 12 = 5 (12x5=60)
60in. = 5ft.
2in. = 2in.
5ft. and 2in.
10in.= 10in.
Add the inches
10in. + 2 in. = 12 in.
12in.= 1ft.
5ft. + 1ft. = 6ft.
Answer: Nancy’s rope is 6ft. long
If is between 4 and 5, then x is
Answer:
X=4.5, or X=4 1/2
Step-by-step explanation:
HELPPPPP
i need the answer for this today
Answer:
Below
Step-by-step explanation:
The quations are both equal to 'y' so the equations are equal
5x-10 = -3x+ 14
8x = 24
x = 3 <====== use this value of 'x' in one of the equations to calculate y
y = 5x-10
y = 5(3)-10 = 5
5x+5y=18
Determine the missing coordinate in the order pair (2,?) so that it will satisfy the given equation
Answer: (2,1.6)
y=1.6
Step-by-step explanation:
you have the x coordinate, so that means x=2.
Plug in values for x:
5(2) + 5y = 18
10 + 5y = 18
Solve for y.
Answer:
The missing coordinate is 1.6.
Step-by-step explanation:
What is a coordinate?A coordinate is two points, x value and y value, on a graph. Ex: 1, 4. 1 is on the x axis, and 4 is on the y axis. In some Math problems, the point in the x value will be replaced with x.
5x + 5y = 18
5(2) + 5y = 18
10 + 5y = 18
10 - 10 + 5y = 18 - 10
5y = 8
5y/5 = 8/5
y = 1.6
To check this, we need to input 2 and 1.6 into the original problem.
5(2) + 5(1.6) = 18
10 + 5(1.6) = 18
10 + 8 = 18
18 = 18
This is true, so we know 1.6 is correct.
according to kepler's third law, a hypothetical planet that is twice as far from the sun as earth should hvae an orbital period of
Orbital period of the planet is 2√2 earth years
What is Kepler's third law?According to Kepler's third law, the square of a planet's orbital period is proportional to the cube of its semi major axis.
T² α a³
where, T is orbital period and a is length of semi-major axis.
Given,
Distance between the sun and the planet
= twice the distance of sun and earth
Let distance between sun and earth a₁ = d
then distance between planet and sun a₂= 2d
Orbital period of earth T₁ = 1 earth year
By Kepler's third law
T² α a³
(T₁/T₂)² = (a₁/a₂)³
(1/T₂)² = (D/2D)³
1/T₂² = 1/8
T₂ = 2√2 earth years
Hence, 2√2 earth years is the orbital period of other planet.
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The equation y = 1.55x + 110,419 approximates the total cost, in dollars, of raising a child in the United States from birth to 17 years, given the household’s annual income, 78,300.
$231784 is the to raise a child from birth to 17 years in a household with an annual income of $78,300.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Let y represents the total cost in dollars f raising a child in the United States from birth to 17 years
x represents the households annual income
We have y = 1.55x + 110,419
We need to find the value of y for x=78300
y=1.55(78300) + 110,419
y=231784
Hence, $231784 is the to raise a child from birth to 17 years in a household with an annual income of $78,300.
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A right cone has radius 2 ft and slant height 5 ft. The radius and slant height are both multiplied by 1/4. Which of the following correctly describes the effect on the surface area?
a. The surface area is multiplied by 8.
b. The surface area is multiplied by 1/16.
c. The surface area is multiplied by 16.
d. The surface area is multiplied by 1/8.
The surface area will be multiplied by 1/8.
What is a cone:A cone is a three-dimensional geometric shape that has a circular base and a curved surface that tapers to a point called the apex or vertex.
The height of a cone is the perpendicular distance from the vertex to the base. The radius of the base is the distance from the center of the circle to its edge.
The slant height is the distance from the vertex to any point on the edge of the base, The formula for the surface area of the cone is given by
Surface Area of the cone = πr(r + l) square unitsHere we have
A right cone has a radius of 2 ft and a slant height of 5 ft.
As we know, the total Surface Area of the cone = πr(r + l) square units
Surface Area of cone = π(2)(2 + 5) ft² = 44 ft²
Given that both the radius and slant height are multiplied by 1/4.
Radius, r = (1/4)(2) = 1/2 ft
Slant height, h = (1/4)5 = 5/4 ft
Surface Area of cone will be = π(1/2)(1/2 + 5/4) ft²
= π(1/2)(7/4) ft²
= 11/4 ft²
Let the surface area is multiplied by 'x'
=> 44x = 11/4
=> 4x = 11/4
=> x = 1/8
Therefore,
The surface area will be multiplied by 1/8
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During a snowstorm, Kaylee tracked the amount of snow on the ground. When the storm began, there were 4 inches of snow on the ground. Snow fell at a constant rate of 3 inches per hour until another 6 inches had fallen. The storm then stopped for 5 hours and then started again at a constant rate of 2 inches per hour for the next 7 hours. Make a graph showing the inches of snow on the ground over time using the data that Kaylee collected. Click twice to plot a segment. Click a segment to delete it. 0 Time Since Storm Began (Hours) Snow on the Ground (Inches) x y
The snowstorm resumes at a consistent rate of 2 inches per hour after 5 hours. Draw a second diagonal line with a slope of 2 as a result. Points 7 and 10 should be the beginning and finish of this line, respectively (14,18).
The resulting graph should include a horizontal line at y=10 from (0,4) to (2,10), a diagonal line with a slope of 2 from (7,10) to (0,4), and a horizontal line at y=3 from (0,4) to (0,10). (14,18).
Describe Graph?Graphs are visual representations of data that show how any two variables relate to one another. Without requiring a lot of words, they are frequently used to communicate complex and large amounts of data. A specific amount of data must be gathered through surveys or experiments before a graph may be created.
To create the graph of the snow on the ground over time, we can follow these steps:
Start with a point at (0,4) since at the beginning of the storm there were 4 inches of snow on the ground.
From this starting point, draw a diagonal line with a slope of 3, representing the constant rate of snowfall of 3 inches per hour. This line should have a y-intercept of 4 and an x-intercept of 2 (since 6 inches of snow fell in 2 hours).
After the 6 inches of snow have fallen, the snowstorm stops for 5 hours. During this time, the snow on the ground remains the same. So, draw a horizontal line at the y-value of 10 (since there are 10 inches of snow on the ground after the first 6 inches fall).
After 5 hours, the snowstorm starts again at a constant rate of 2 inches per hour. So, draw another diagonal line with a slope of 2. This line should start at the point (7,10) and end at the point (14,18).
The resulting graph should have a diagonal line with a slope of 3 from (0,4) to (2,10), a horizontal line at y=10 from (2,10) to (7,10), and a diagonal line with a slope of 2 from (7,10) to (14,18).
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help pls!
A homeowner would like to spread shredded bark (mulch) over her flowerbeds. She has three flowerbeds measuring 24 ft by 3.1 ft, 14 ft by 4.3 ft, and 30 ft by 1.5 ft. The recommended depth for the mulch is 4 inches, and the shredded bark costs $27 per one cubic yard. How much will it cost to cover all of the flowerbeds with shredded bark? (Note: You cannot buy a portion of a cubic yard of mulch. Assume that there are 27 ft³ in a yd³.)
If a homeowner would like to spread shredded bark (mulch) over her flowerbeds. it will cost $65.07 to cover all the flowerbeds with shredded bark.
How to find the cost?To calculate the amount of mulch needed, we need to find the volume of each flowerbed and add them together. The recommended depth for the mulch is 4 inches, which is equal to 4/12 = 1/3 feet.
For the first flowerbed, the volume of mulch needed is:
24 ft x 3.1 ft x 1/3 ft = 24.8 cubic feet
For the second flowerbed, the volume of mulch needed is:
14 ft x 4.3 ft x 1/3 ft = 20.87 cubic feet
For the third flowerbed, the volume of mulch needed is:
30 ft x 1.5 ft x 1/3 ft = 15 cubic feet
The total volume of mulch needed to cover all three flowerbeds is:
24.8 cubic feet + 20.87 cubic feet + 15 cubic feet = 60.67 cubic feet
Since there are 27 cubic feet in a cubic yard, the total amount of mulch needed is:
60.67 cubic feet / 27 cubic feet per cubic yard = 2.25 cubic yards
At a cost of $27 per cubic yard, the total cost of the mulch is:
2.25 cubic yards x $27 per cubic yard = $60.75
Therefore, it will cost $60.75 to cover all of the flowerbeds with shredded bark.
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In the rhombus shown below, Angle 1 has a measure of 140 degrees. What are the measures of Angles 2 and 3? Be sure to explain how you know.
The measure of angle 2 is 140 and <3 is 20 degree.
What is Rhombus?A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.
As, Rhombus have angles which are opposite to each other are equal.
So, <1 = <2 = 140
Also, Consecutive angles are equal to 180° which shows the angle between <1 and <2 measure
= 180- 140
= 40
and, <3 = 1/2 <1
<3 = 1/2(40)= 20
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The changes in Mr. Connor's bank account for five days are $50.25, (-$22.50), $50.25, (−$22.50), and (−$22.50). What is the mean change in his bank account? Show your work. (4 pts)
The mean change in Mr.60. Connor's bank account is $6.
According to given condition :To find the mean change in Mr. Connor's bank account, we need to add up all the changes and divide by the total number of changes.
First, we can simplify the given list of changes by combining the positive changes and the negative changes separately:
$50.25 + $50.25 = $100.50 (total positive change)
-$22.50 + (-$22.50) + (-$22.50) = -$67.50 (total negative change)
Then, we can find the total change in Mr. Connor's account by subtracting the total negative change from the total positive change:
$100.50 - $67.50 = $33.00 (total change)
Finally, we can find the mean change by dividing the total change by the number of changes:
$33.00 ÷ 5 = $6.60 (mean change)
Therefore, the mean change in Mr.60. Connor's bank account is $6.
What is mean ?In mathematics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is also known as the arithmetic mean or simply the average.
To find the mean of a set of numbers, you add up all the numbers in the set and then divide by the total number of numbers. For example, to find the mean of the numbers 2, 5, 7, and 10, you add them up (2 + 5 + 7 + 10 = 24) and then divide by the total number of numbers (4), which gives a mean of 6.
The mean is often used in statistics to describe the typical or average value of a data set. It is a useful measure of central tendency because it takes into account all the values in the data set, not just a few extreme values. However, the mean can be affected by outliers, or extremely high or low values in the data set that can skew the average.
There are different types of means, including the arithmetic mean, the geometric mean, and the harmonic mean, each with different methods of calculation and specific applications.
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Please add all of these together, so look at both attachments.
p.s the 1,2,3,4,5,6,7,8,9 is the order to do it in
Thank you
18x+30 is the solution of the expression which we get by adding all the expressions.
What is Expression?An expression is combination of variables, numbers and operators.
The given expressions from 1 to 9 are -4(x-5), 6(x+1), 4x-20,3x+12, -1(x-9), -x-12, 8-x, -2x, 7(2x+1)
Add all the nine expressions.
-4(x-5)+6(x+1)+4x-20+3x+12-1(x-9)-x-12+8-x -2x+ 7(2x+1)
-4x+20+6x+6+4x-20+3x+12-x+9-x-12+8-x-2x+14x+7
Combine the like terms
18x+30
Hence, 18x+30 is the solution of the expression which we get by adding all the expressions.
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The length of a room is 583 cm. Express the length in metres. *
Your answer
Calculate *
Answer:
5.85m
Step-by-step explanation:
1 meter is 100 centimeters.
583 divided by 100
Round 2.77247497243 to the nearest millionth.
Answer:
3.00000000000
Step-by-step explanation:
2.77247497343 is closer to 3.00000000000 than 2.00000000000
Convert 59°C to degrees Fahrenheit. If necessary, round your answer to the nearest tenth. Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answer: Using the formula F=9/5C+32, we can convert 59°C to degrees Fahrenheit:
F = 9/5 * 59°C + 32
F = 118.2°F + 32
F ≈ 150.8°F
Therefore, 59°C is approximately equal to 150.8°F.
Step-by-step explanation:
3. The following data below represents the running times of six movies. Find
the standard deviation of the running times. Give your answer to the
nearest hundredth of a minute.
Movie
Running
Time
A
1 hr
47 min
B
1 hr
32 min
C
2 hr
14 min
D
1 hr
56 min
2 hr
32 min
F
3 hr
2 min
3.
The standard deviation of the movie times is given as follows:
27.7 minutes.
How to obtain the standard deviation of the data-set?Considering that an hour has 60 minutes, the time in minutes of each movie is given as follows:
107 minutes, 92 minutes, 134 minutes, 116 minutes, 152 minutes, 182 minutes.
The mean of a data-set is given by the sum of all observations divided by the number of observations, hence:
Mean = (107 + 92 + 134 + 116 + 152 + 182)/6
Mean = 130.5 minutes.
The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, hence:
s = sqrt([(107-130.5)² + (92-130.5)² + (134-130.5)² + (116-130.5)² + (152-130.5)² + (182-130.5)²]/7)
s = 27.7 minutes.
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Given (x – 7)2 = 36, select the values of x.x = 13x = 1x = –29x = 42
Answer:
The values of x are 1, 13, -29, and 42.
Points (-2,-6)
Solve for a
Y=a(x²-2x-3)
Please help me its linear equations.
Answer:
A: -5B: -6greaterStep-by-step explanation:
You want the y-intercepts of the relation y -5 = -5/2(x +4) and the one shown in the graph.
Y-interceptThe y-intercept of a function is its value when x=0. It is the y-value where the graph crosses the y-axis.
ASetting x=0, we can solve for y:
y -5 = -5/2(0 +4) = -10
y = -5 . . . . . . . . add 5; this is the y-intercept
The y-intercept of Line A is -5.
BThe graph crosses the y-axis at y = -6.
The y-intercept of Line B is -6.
The y-intercept of Line A is greater than the y-intercept of Line B.
can somebody please help me
find the value of x
Answer:
x = 40
Step-by-step explanation:
Alternate exterior angles are congruent (equal).
2x + 16 = 96 Subtract 16 from both sides
2x + 16 -16 = 96 - 16
2x = 80 Divide both sides by 2
x = 40
Answer:
x=40
Step-by-step explanation:
Suppose you are working on your taxes using a Microsoft Excel spreadsheet. Cell B3 shows the total amount of income tax you paid. Cell B2 shows the total amount of tax for which you are responsible. You want to write a formula that looks to see if the amount that you paid is greater than the amount that you were responsible for.
If it is, then subtract the amount you were responsible from the amount you paid and round this difference to the nearest whole number.
Otherwise, display zero
A. =IF(B3>B2, ROUND(B2 – B3, 0), 0)
B. =ROUND(IF(B3>B2, B3 – B2, 0), 0)
C. =IF(B3>B2, ROUND(B3 – B2, 0), 0)
D. =IF(B2>B3, ROUND(B3 – B2, 0), 0)
The correct formula for this scenario is A. =IF(B3>B2, ROUND(B3 - B2, 0), 0).
What is the use of IF and ROUND functions in Microsoft Excel?The IF and ROUND functions are two commonly used functions in Microsoft Excel. Here's a brief explanation of each:
IF Function:
The IF function allows you to test whether a certain condition is true or false, and then perform a specific action based on the result of that test. The basic syntax of the IF function is as follows:
=IF(logical_test, value_if_true, value_if_false)
Here, the "logical_test" is the condition that you want to test. If this condition is true, then Excel will return the "value_if_true". If the condition is false, Excel will return the "value_if_false".
For example, suppose you have a cell A1 that contains a number. You could use the IF function to test whether that number is greater than 10, and then return "Yes" if it is, and "No" if it isn't, using the following formula:
=IF(A1>10, "Yes", "No")
ROUND Function:
The ROUND function allows you to round a number to a specific number of decimal places. The basic syntax of the ROUND function is as follows:
=ROUND(number, num_digits)
Here, the "number" is the number that you want to round, and the "num_digits" is the number of decimal places to which you want to round. If the "num_digits" is positive, then the function will round to the specified number of decimal places to the right of the decimal point. If the "num_digits" is negative, then the function will round to the left of the decimal point.
For example, suppose you have a number in cell A1 that contains many decimal places, and you want to round it to two decimal places. You could use the ROUND function as follows:
=ROUND(A1, 2)
This will round the number in cell A1 to two decimal places.
Here,
The correct formula for this scenario is A. =IF(B3>B2, ROUND(B3 - B2, 0), 0).
This formula uses the IF function to check whether the amount paid (B3) is greater than the amount for which the person is responsible (B2). If this is true, then it subtracts the amount for which the person is responsible from the amount paid and rounds the difference to the nearest whole number using the ROUND function. If the amount paid is not greater than the amount for which the person is responsible, then the formula displays zero.
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7
5
3
10
Find the perimeter.
8
2
8
The perimeter of the figure is 43 units.
How to find the perimeter of a figure?The perimeter of a figure is the sum of the whole sides of the figure. Therefore, the figure above is a composite figure, let's find the perimeter of the shape as follows:
Hence,
Perimeter of the figure = 8 + 3 + 5 + 7 + 10 + 2 + 8
Therefore,
Perimeter of the figure = 11 + 12 + 12 + 8
Perimeter of the figure = 23 + 20
Perimeter of the figure = 43 units
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Find the real solution(s) of the equation (x+10)5=70.
Answer:
x = 4
Step-by-step explanation:
(4 + 10)
14 x 5 = 70
~ LadyBrainiac
Katya is making rectangular table that is 3/4 meters wide.The table has an area of 1 1/5 m2
So Katya's rectangular table is 1.6 meters long and 3/4 meters wide, with an area of 1 1/5 square meters.
What is area?Area is a measure of the size of a two-dimensional surface, such as the surface of a shape or object. It is usually measured in square units, such as square meters, square centimeters, square feet, or square inches. The area of a shape tells us how much surface area it covers, and is often used in a variety of fields, such as architecture, engineering, and physics. For example, the area of a room can help determine how much flooring is needed to cover it, the area of a building facade can help determine how much material is needed to cover it, and the area of a wing can help determine its lift and drag characteristics in aerodynamics.
Here,
Let's start by using the formula for the area of a rectangle:
A = lw
where A is the area, l is the length, and w is the width.
We are given that the width of the table is 3/4 meters, so we can substitute this value into the formula and simplify:
A = l(3/4)
l = (4/3)A
Next, we are told that the table has an area of 1 1/5 m^2. We can convert this mixed number to an improper fraction by multiplying the whole number by the denominator and then adding the numerator:
1 1/5 = (5*1 + 1)/5 = 6/5
So the area of the table is 6/5 m^2. Substituting this value for A in the formula above, we get:
l = (4/3)(6/5)
l = 8/5 m
Therefore, the length of the table is 8/5 meters, or 1.6 meters when converted to a decimal.
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Drag one or more expression into each letter space (a,b,c,d) to create an equation that is true for all values of x. (Assume no denominator equals zero)
(3/x+2)+(4/x)+(2/x^2)=(3(a)+4(b)+2(c)/d)
X^2(x+2)
X(x+2)
X^2
X
(X+2)
The expression into each letter space (a,b,c,d) to create an equation that is true for all values of x is X(x+2),X,(X+2),X^2.
What is an expression?Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that;
The equation with a,b,c,d=(3/x+2)+(4/x)+(2/x^2)=(3(a)+4(b)+2(c)/d)
Now,
=(3/x+2)+(4/x)+(2/x^2)
=3/x + 2x/2 + 4/x + 2/x^2
=(3+2x)/x+4/x+2/x^2
Therefore, the answer of the expression will be X(x+2),X,(X+2),X^2.
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Bryan puts $200.00 into an account to use for school expenses. The account earns 3% interest, compounded monthly. How much will be in the account after 5 years?
Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 2x^2 - 4x + 6. Complete parts a through d below. Find the average rate of change of profit as x changes from 3 to 5. $ ____ per item
The average rate of change of profit as x changes from 3 to 5 is $12 per item.
How to determine the average rate of changeTo find the average rate of change of profit as x changes from 3 to 5, we need to find the change in profit divided by the change in x over that interval:
Average rate of change = (P(5) - P(3)) / (5 - 3)
We can find P(5) and P(3) by plugging those values of x into the profit equation:
P(5) = 2(5)^2 - 4(5) + 6 = 36
P(3) = 2(3)^2 - 4(3) + 6 = 12
Substituting these values, we get:
Average rate of change = (36 - 12) / (5 - 3)
Average rate of change = 24 / 2
Average rate of change = 12
Hence, the average rate is $12 per item.
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Let x be an integer. Prove: x^3 is even if and only if x is even
Let z be a real number. Prove: z is irrational if and only if - z is irrational.
Therefore, x³ must be even. Therefore, if -z is irrational, then z must also be irrational.
What is integer?In mathematics, an integer is a whole number that can be either positive, negative, or zero. It can be written without a fractional or decimal component. Some examples of integers are -3, -2, -1, 0, 1, 2, 3. Integers are used in many different areas of mathematics, including number theory, algebra, and geometry. They are a fundamental concept in mathematics and have many important properties, such as the ability to add, subtract, and multiply them.
Here,
Proof of "x³ is even if and only if x is even":
First, assume that x is even. Then x can be written as x = 2k for some integer k. Substituting this into x³, we get:
x³ = (2k)³ = 8k³ = 2(4k³)
Since 4k³ is an integer, this shows that x³ is even.
Now, assume that x³ is even. This means that x³ is divisible by 2. We can write x³ as x³ = 2m for some integer m. Taking the cube root of both sides, we get:
x = (2m)*(1/3)
If x is an integer, then (2m)*(1/3) must also be an integer. However, the only way for the cube root of an even number to be an integer is if the original number is even. Therefore, x must be even.
Proof of "z is irrational if and only if -z is irrational":
First, assume that z is irrational. By definition, this means that z cannot be expressed as the ratio of two integers. Now suppose that -z is rational. This means that -z can be expressed as the ratio of two integers, say -z = p/q, where p and q are integers and q is not equal to 0. Multiplying both sides of the equation by -1, we get:
z = -p/q
This shows that z can be expressed as the ratio of two integers, which contradicts our assumption that z is irrational. Therefore, if z is irrational, then -z must also be irrational.
Now, assume that -z is irrational. By definition, this means that -z cannot be expressed as the ratio of two integers. We can rewrite this as z = (-1)(-z), which means that z is the product of -1 and a number that is not the ratio of two integers. Multiplying a number by -1 does not change its irrationality, so z must also be irrational. Therefore, if -z is irrational, then z must also be irrational.
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105 is 33 1/3 of what number?
Answer:
≈ 315
Step-by-step explanation:
To find the number that 105 is 33 1/3 of, we can use algebra.
Let x be the number we are looking for. Then we can write the equation:
105 = (33 1/3)% of x
To solve for x, we can first convert the percentage to a decimal by dividing by 100:
33 1/3% = 33 1/3 ÷ 100 = 0.3333
Substituting this in the equation, we get:
105 = 0.3333x
To solve for x, we can divide both sides by 0.3333:
x = 105 ÷ 0.3333
Using a calculator, we get:
x ≈ 315
Therefore, 105 is 33 1/3 of 315.