The area of the rectangular field is 120,000 square meters.
How do we find the area of the rectangular field?We shall multiply the length by its width, to find the area of the rectangular field.
We can calculate like this:
Area = Length x Width
Area = 0.4 kilometers x 0.3 kilometers
Next, we convert the measurements to square meters, recalling that 1 kilometer = 1000 meters:
Area = (0.4 km * 1000 m/km) x (0.3 km * 1000 m/km)
Area = (400 m) x (300 m)
Then, multiplying the values, we have:
Area = 120,000 square meters
Hence, the area of the rectangular field is 120,000 square meters.
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Four friends split equally a lunch bill of 36.96 plus 20% tip. How much did each person pay
Jack is mowing a lawn that has a shed. Jack wants to know the area of the lawn he has to mow. here are the dimensions of the yard and the shed. 13x-4 length 5x withd shed is 2x+4length withd is 2x
find a polynomial that describes the area of the lawn he has to mow. i.e. find the area of the area of the shed.
We know that the formula for area is simply:
area = l w
where l is length and w is width
yard dimensions: l = 13x – 4, w = 5x
Ayard = (13x – 4) 5x = 65x^2 – 20x
shed dimensions: l = 2x + 4, w = 2x
Ashed = (2x + 4) 2x = 4x^2 + 8x
Therefore the area to mow is:
Amow = Ayard – Ashed
Amow = 65x^2 – 20x – (4x^2 + 8x)
Amow = 65x^2 – 20x – 4x^2 – 8x
Amow = 61x^2 – 28x
George spent 70 % of his saving to buy a camera. The camera cost $574 . How much did he originally have in savings?
which of the following steps were applied to abc obtain a'b'c'
Answer:
Shifted 2 units left and 4 units up
Step-by-step explanation:
Given are two triangles
ABC is having vertices as (4,6) (7,6) and (5,9)
The transformed image A'B'C' has vertices as
(2,10) (5,10) (3,13)
On comparing the vertices corresponding we find a certain pattern.
X coordinate is reduced by 2 and y coordinate is increased by 4.
This implies the transformation is
Shifted 2 units left and 4 units up
Find the product of 4×7×25tell which strategy you used
The length of a rectangle is given by 5t+4sqrt(t), and its height is sqrt(t), where t is time in seconds and the dimensions are in centimeters. Fine the rate of change of the area of the rectangle with respect to time when the length of the rectangle is 9 centimeters.
Answer:
11.5 cm²/s
Step-by-step explanation:
We must solve two problems to answer this question:
find the time at which the length is 9 cmfind the rate of change of area with respect to time (at that time)For the first problem, we have ...
... 9 = 5t +4√t
... 9 -5t = 4√t . . . . . subtract 5t
... 81 -90t +25t² = 16t . . . . square both sides
... 25t² -106t +81 = 0 . . . subtract 16t
... (t -1)(25t -81) = 0 . . . . factor
... t = 1 or 3.24 . . . . . . t=3.24 is an extraneous solution
_____
For the second problem, we have area (a(t)) is ...
... a(t) = length×height = (5t +4√t)(√t) = 5t^(3/2) +4t
Then the derivative is ...
... a'(t) = (3/2)(5√t) +4
and
... a'(1) = (3/2)(5√1) +4 = 11.5 . . . . . cm²/s
_____
Comment on the attachment
A graphing calculator can help solve both problems. It can help find the time at which length is 9 cm by solving ... length-9 = 0. (The nice thing here is that there is no extraneous solution.) It can compute the derivative of a function, too.
if 2 out of every 20 ducks were banded, What percent were not banded?
if 2 were banded that means 18 out of 20 were not banded
18 divided by 20 = 0.9
so 90% were not banded
after taking 1/4 pound of flour from a canister to make muffins, maria has 7/8 of the flour left. If each batch of muffins requires 2/5 pound of flour, find the greatest number of batches of muffins that Maria can make using the remaining flour/
Based on the graph of the line below, which describes the relationship between the value of the y-intercept and the value of the slope?
Choose the answer. 3. (1 pt) Suzanne cut a ribbon into 9 equal pieces. She sewed 5 pieces onto her quilt. Which number line shows a dot representing the fraction of the ribbon that was sewn onto the quilt? A. B. C. D.
Use place value to find the product 3x600=3x
Prove the quotient of any two rational numbers is a rational number
The quotient of any two rational numbers is always a rational number. This can be proved by expressing the division as multiplication by the reciprocal and demonstrating that the result is a rational number. Therefore, the property of being rational is preserved under division.
Let's define rational numbers first. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. Mathematically, if a and b are integers and b ≠ 0, then r = a/b is a rational number.
Consider two rational numbers r1 and r2.Thus, we have proved that the quotient of any two rational numbers is a rational number.
Write an equation for "eight less than a number is seventy-five". What is the number? n - 8 < 75; -67 n - 8 = 75; 67 n - 8 = 75; 83 n - 8 < 75; 67
n-8=75
n is the number
so number minus 8 equals 75
Richard estimates that he can apply fertilizer to 4,485 square feet of grass in 3/4 of an hour. How many square feet of grass can Richard fertilize per hour?
We know that Richard can apply fertilizer to 4485 square feet = 3/4 hour
To solve this problem, one approach is to find 1/4 then multiply by 4 to get the whole 4/4 or 1 hour.
So the solution would be:
4485/3=1495
Then multiply this by 4.
1495 multiplied by 4 is equal to 5980 square feet.
So Richard can apply fertilizer to 5980 square feet in 1 hour.
How to determine if the function has x-axis sym, y-axis sym, and origin sym
y^2 -xy =2
To check for symmetry on the x axis, replace y with –y
-y^2 –x(-y) =2
Apply the product rule, since the equation is not identical tot eh original equation it is not symmetric about the x axis
Now do the same for y axis by replacing x with –x
Again using product rule the equations are not identical, so it is not symmetric about the y axis
To check the origin,
Replace both x & y with –x & -y
Again using product rule, the equations are not identical so it is not symmetric about the origin
To check for symmetry, replace x with -x and y with -y in the equation. Upon doing that for y^2 -xy =2, we find it lacks x-axis, y-axis, and origin symmetry.
Explanation:To determine whether a function has x-axis symmetry, y-axis symmetry, or origin symmetry, we have to replace x with -x and y with -y and see whether we get the same function.
X-axis symmetry: Replace y with -y. The equation becomes (-y)^2-(-y)x=2 which simplifies to y^2+xy=2. This is different from the original function, so there is no x-axis symmetry.Y-axis symmetry: Replace x with -x. The equation becomes y^2-(-x)y=2 which simplifies to y^2+xy=2. This is different from the original function, so there is no y-axis symmetry.Origin symmetry: Replace x with -x and y with -y. The equation becomes (-y)^2-(-y x -x)=2, which simplifies to y^2+xy=2. This is different from the original function, so there is no origin symmetry.Learn more about Symmetry of Functions here:https://brainly.com/question/16710816
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the difference of twice a number and 3
Find two consecutive odd integers such that their product is 71 more than 3 times their sum.
Round 354,738 to the nearest thousand?
354,738 rounded to the nearest thousand is 355,000.
What is a place value?In Mathematics and Euclidean Geometry, a place value is a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.The number in the thousand place in the number 354,738 is 7 and it is greater than or equal to 5. This ultimately implies that, we would round up the number 4 to 5.
354,738 ≈ 355,000.
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A car is traveling at a rate of 40 miles per hour. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
1 mile = 1.6 kilometers
multiply 40 mph by 1.6 = 64
car's rate = 64 kilometers per hour
multiply kilometers per hour by 4 = 256
car will travel 256 kilometers in 4 hours
Ahmad is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 12 feet and its width is 10 feet. Suppose each bag of fertilizer covers 30 square feet. How many bags will he need to cover the garden?
after 9 months, the simple interest earned on an investment of $1200 is $72. find the interest rate.
what is the value of this expression when x = -1 and y = 2?
4x³y²
Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 8 min and standard deviation 3 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)
What is the domain of the function f(x)= 1/3x+2
The answer is the last one
x≥-6
I hope this helps, and God bless <3
Find the simple interest. Principal $2300 rate 20% time 27 months The interest is $ ?
Joshua earns $8.20 per hour when he works at the college library. How much money does he earn by working at the library for $4.5 hours.
PLEASE HELP!!!
the value of the 7 in 507,264 is 10 times the value of the 7 in which number?
Answer:
The value of the 7 in 507,264 is 10 times the value of the 7 in number 2
Step-by-step explanation:
Given Number : 507,264
To find : Number in which the value of the 7 in 507,264 is 10 times the value of the 7 .
Starting from the left ,
4 is in ones place
6 is in tens place
2 is in hundreds place
7 is in thousands place
0 is in ten thousands place
5 is in lakhs place
Here, 7 is in thousands place
7000 = 10 x 700
2 is in hundreds place
200 = 2 × 100
Therefore, the value of the 7 in 507,264 is 10 times the value of the 7 in number 2 .
A protective cover for a wireless tablet has a height of 8 inches and base of 7 inches. What is the area of the cover?
Answer: The area of the cover = 56 square inches.
Step-by-step explanation:
We know that the shape of a tablet is rectangle.
Thus to calculate the area of the protective cover we apply the formula to calculate area of rectangle.
The area of rectangle is given by :-
[tex]\text{Area}=\text{Length*width}\\\\\Rightarrow\text{Area}=8\times7\\\\\Rightarrow\text{Area}=56\text{ inches}^2[/tex]
Therefore, the area of the protective cover is 56 square inches.
A data firm records a large amount of data. historically, 1.0% of the pages of data recorded by the firm contain errors. if 200 pages of data are randomly selected?
a. what is the probability that six or more pages contain errors?
b. what is the probability that more than 10 pages contain errors?
c. what is the probability that none of the pages contain errors?
d. what is the probability that fewer than five pages contain errors?
a) P(X >= 6) = 0.0160
b) P(X > 10) ≈ 6.88 x 10^-6
c) P(X = 0) ≈ 0.1339
d) P(X < 5) ≈ 0.9482
a. Probability of six or more pages with errors:
This is the sum of probabilities for 6, 7, 8, ..., 200 errors:
P(X >= 6) = 1 - [P(X < 6)] = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]
Using a calculator or statistical software, we can find these individual probabilities and sum them up. Alternatively, we can use binomial distribution tables or functions available in programming languages.
P(X >= 6) ≈ 0.0160
b. Probability of more than 10 pages with errors:
Similar to part (a), but calculating from 11 errors onwards:
P(X > 10) = 1 - [P(X=0) + P(X=1) + ... + P(X=10)]
P(X > 10) ≈ 6.88 x 10^-6 (very small probability)
c. Probability of none of the pages containing errors:
P(X = 0) = (0.99)^200 ≈ 0.1339
d. Probability of fewer than five pages containing errors:
P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)
P(X < 5) ≈ 0.9482
A six-sided rectangular box is to hold 1/2 cubic meter; what shape should the box be to minimize surface area?
A circle is an object which has the lowest surface area to volume ratio. So in this case, the shape should be like that of a circle but we cannot have a circle here because we want to form a 6 sided box. So the next thing closer to circle is a square. Hence the shape should be a square:
Answer:
square
To minimize surface area for a given volume of 1/2 cubic meter, the box should be shaped as a cube with each side measuring approximately 0.7937 meters. This cube shape offers the smallest surface area for the given volume.
Explanation:To minimize the surface area of a six-sided rectangular box with a volume of 1/2 cubic meter, it is best to make the box in the shape of a cube. This shape has the smallest surface area for a given volume. To find the dimensions of the box, let's denote the side of the cube as 's'. We know that volume V of a cube is given by V = s³. So, if the volume is 1/2 cubic meter, we have:
s³ = 1/2
s = ∛(1/2) ≈ 0.7937 meters
Each side of the cube should be approximately 0.7937 meters to achieve the minimal surface area. The surface area SA of the cube can be calculated as:
SA = 6s²
SA = 6 × (0.7937)² ≈ 3.770 meters²
Thus, a cube with sides of about 0.7937 meters will have the minimal surface area for a volume of 1/2 cubic meter.
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