Answer:
The smallest area the field could be is 6,400 m²The largest area the field could be is 8,250 m²Step-by-step explanation:
Given;
smallest possible length of the international soccer field, L₀ = 100 m
smallest possible breadth of the international soccer field, B₀ = 64 m
Largest possible length of the international soccer field, L₁ = 110 m
Largest possible breadth of the international soccer field, B₁ = 75 m
Area of a rectangle is given by;
A = L x B
The smallest area the field could be is calculated as;
A₀ = L₀ x B₀
A₀ = 100 m x 64 m
A₀ = 6,400 m²
The largest area the field could be is calculated as;
A₁ = L₁ x B₁
A₁ = 110 m x 75 m
A₁ = 8,250 m²
PLEASE HELP IM CONFUSED
If angle ACB is 1 degree 25 minutes (1°25’) what is angle ACD. Please give your answer as degrees and minutes.
Answer:
178° 35'
Step-by-step explanation:
∠ACB and ∠ACD are supplementary, so they add up to 180°.
First, convert to degrees (there are 60 minutes in a degree).
∠ACB = 1°25' = 1° + (25/60)° = 1.4167°
Now find the supplementary:
∠ACD = 180° − 1.4167°
∠ACD = 178.5833°
∠ACD = 178° 35'
-38 - 7y = 2 - 7(y + 6)
Answer:
No solution
Step-by-step explanation:
[tex]-38 - 7y = 2 - 7(y + 6)\\\\\mathrm{Expand\:}2-7\left(y+6\right):\quad -7y-40\\-38-7y=-7y-40\\\\\mathrm{Add\:}38\mathrm{\:to\:both\:sides}\\-38-7y+38=-7y-40+38\\\\Simplify\\-7y=-7y-2\\\\\mathrm{Add\:}7y\mathrm{\:to\:both\:sides}\\-7y+7y=-7y-2+7y\\\\Simplify\\\\0=-2\\\mathrm{The\:sides\:are\:not\:equal}\\No\: solution[/tex]
Answer:
No solution
Step-by-step explanation:
First do distribute property
-38-7y=2-7y-42
then combine like terms the 2 and the -42
-38-7y=-40-7y add 7y from both sides
-38+y=-40 add 38 to -40 you get -2
0=-2 no solution
Please help me with this
Answer:
OPTION D
Step-by-step explanation:
The bracket is part of bodmas and the only thing it does is to divide equations to make it easier, so thereby I testify that the answer is 2.5/7
A come and a pyramid has equal heights and volumes.if the base area of the pyramid is 154cm2.find the radius of the cone.
Answer:
Radius = 8.575 cm
Step-by-step explanation:
Formula for volume of a pyramid is;
V_p = ½Ah
Where A is area of base and h is height
Also, formula for volume of cone is given as;
V_c = ⅓πr²h
Now, we are told that V_p = V_c and that h is the same for both shapes.
Thus ;
½Ah = ⅓πr²h
h will cancel out to give;
½A = ⅓πr²
Cross multiply to give;
3A/2π = r²
Base area of pyramid is given as 154 cm². Thus;
(3 × 154)/2π = r²
r = √((3 × 154)/2π
r = 8.575 cm
Find the inverse of the function f(x)= 6x^3-8
Hello, please consider the following.
[tex](\forall x \in \mathbb{R}) \\ \\ x=(f^{-1}of)(x)\\\\=(fof^{-1})(x)\\\\=f(f^{-1}(x))\\\\=6\left( f^{-1}(x) \right) ^3-8 = x\\\\\text{We need to express }f^{-1}(x) \text{ in function of x.}\\\\\text{Let's do it!}[/tex]
[tex]6\left( f^{-1}(x) \right) ^3-8 = x\\\\\left( f^{-1}(x) \right) ^3 =\dfrac{x+8}{6}\\\\\Large \boxed{\sf \bf \ \ f^{-1}(x)=\sqrt[3]{\dfrac{x+8}{6}}\ \ }[/tex]
Thank you
The amount of paint used on new tractors averages 18.2 gallons with a standard deviation of 0.8 gallons. A new nozzle is used on 20 tractors and averaged 17.9 gallons. What is the probability that is was just random chance
Answer:
17.9/18.2 =0.984 to 3 decimal places
Step-by-step explanation:
The initial mean/average = 18.2 gallons
A standard deviation of 0.8 gallons implies a lower-upper limit of (17.4 - 19) gallons of paint used on new tractors.
New mean/average = 17.9 gallons
It is noticeable that this value 17.9 falls within the lower range of the standard deviation of the initial mean; hence the question
What is the probability that this happened by chance?
17.9 ÷ 18.2 = 0.9835
Therefore, there is a high probability that this happened by chance. 0.9 is closer to 1 than to 0.
Find the ratio of the area inside the square but outside the circle to the area of the square in the picture
Answer:
0.2146
Step-by-step explanation:
From the picture:
The radius of the circle = r. This means that the area of the circle = πr²
Also For the square, the length of the square = 2r, Therefore the area of the square = Length × length = 2r × 2r = 4r²
The area inside the square but outside the circle = Area of square - Area of circle = 4r² - πr² = r²(4 - π) = 0.8584r²
The ratio of the area inside the square but outside the circle to the area of the square = r²(4 - π) / 4r² = (4 - π) / 4 = 1 - π/4 = 0.2146
Can someone help ! Please !!!! I don’t understand!
Answer:
(A∩B')∪(A'∩B)(A∩B)'Step-by-step explanation:
Here, we'll use an apostrophe to signify the complement of a set.
__
(a) The shaded portion is two disjoint (non-overlapping) sections, so must be the union of something. The shaded space on the left is that part of A that is not in B, so it is A∩B'. Similarly, the shaded space on the right is that part of set B that is not in set A: A'∩B. Then the shaded area altogether is the union of these sets:
(A∩B')∪(A'∩B)
__
(b) For this one, it might be easier to identify the unshaded area. That is where the sets A and B overlap, so it is A∩B. Then the area that is not that area is the complement of this:
(A∩B)'
8*10^4 is how many times as large as large as 4*10^-5
Answer:
D. 2 . 10^9
Step-by-step explanation:
( 8 * 10^4 ) / ( 4* 10^-5 )
( 8*10^4 ) 10^5 / ( 4 )
2 * 10^ 9
which expression is equivalent to 2(x-3) + 4
Answer:
2x - 2
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Distribute parenthesis
2x - 6 + 4
Step 2: Combine like terms
2x - 2
And we have our answer!
Answer:
[tex]2( x -3) + 4 \\ 2x - 6 + 4 \\ [/tex]
HELP PLEASE ! Due tonight! A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of
7% of sales. Write a linear equation for the salesperson's monthly wage W in terms of monthly sales S
Answer:
w=5000+0.7s
Step-by-step explanation:
if its possible give me 5 start I need it
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
Freshmen 83
Sophomores 68
Juniors 85
Seniors 64
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
Answer:
There has been no change in the classifications between the last school year and this school year.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
The expected values are computed using the formula:
[tex]E_{i}=p_{i}\times N[/tex]
Here, N = 300
Use Excel to compute the values.
The test statistic value is:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=1.662[/tex]
The test statistic value is, 1.662.
The degrees of freedom of the test is:
n - 1 = 4 - 1 = 3
The significance level is, α = 0.05.
Compute the p-value of the test as follows:
p-value = 0.6454
*Use a Chi-square table.
p-value = 0.6454 > α = 0.05.
So, the null hypothesis will not be rejected at 5% significance level.
Thus, concluding that there has been no change in the classifications between the last school year and this school year.
Y=12x
Do x and y vary directly ?
Answer:
Yes, they vary directly
Step-by-step explanation:
y=kx; k is the constant (12 in this case) and as x increases y increases, so they vary directly
Find the measure of ∠ 1 in O.
Answer:
10°
Step-by-step explanation:
The angle subtended at the circumference is half the angle subtended at the centre of the circle i.e. 20°÷2=10°
The following is a list of 5 measurements. 16,13,5,20,14 Suppose that these 5 measurements are respectively labeled
=====================================================
Explanation:
The fancy or strange looking E symbol is the greek uppercase letter sigma, to mean sum. So they want you to add the terms in the form x^2. The x values are from the list given to us.
x = 16 leads to x^2 = 256
x = 13 leads to x^2 = 169
etc etc
After squaring all the x values, we have this new list {256, 169, 25, 400, 196}
Lastly, you add up all the squared values to get the final answer of 256+169+25+400+196 = 1046
Stavros is 1.6m tall. His sister is 95cm tall. How many centimeters taller is Stavros than his sister?
Carla enjoys collecting baseball cards Her album contains 115 pages . Each page holds 9 baseball cards How many baseball cards are will there be in her album in all?
Answer:
1035 cards
Step-by-step explanation:
the total number of baseball cards can be calculate by multiplying amount of pages and how many cards each page can hold.
115*9=1035 cards
Answer:
1035 cards
Step-by-step explanation:
Step 1: State what is known
The album contains 115 pages
Each page has 9 cards
Step 2: Assume the pages are full, calculate how much cards are in the album
115 pages x 9 cards per page = 1035 cards
Therefore there are 1035 cards in the album
Find the value of x.
Answer:
[tex]\sqrt{205}[/tex]
Step-by-step explanation:
Using the pythagorean theorem, [tex]x^{2} +18^{2} =23^{2} \\[/tex] so that means [tex]x^{2} = 23^{2} -18^{2} =205[/tex] so x = [tex]\sqrt{205}[/tex]
What is lim x→3 x^2 - x - 6/ x - 3
=======================================================
Explanation:
If we plugged x = 3 into the expression, then we'd get x-3 = 3-3 = 0 in the denominator. That's not allowed. But we can simplify first
x^2-x-6 factors to (x-3)(x+2). The key here is that (x-3) is a factor. It cancels with the x-3 in the denominator
So, [tex]\frac{x^2-x-6}{x-3} = \frac{(x-3)(x+2)}{x-3} = x+2[/tex]
Allowing us to say,
[tex]\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}\frac{(x-3)(x+2)}{x-3}\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}(x+2)\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 3+2\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 5\\\\\\[/tex]
The solution is 5
The value of the equation lim x tends to 3 ( x² -x - 6 ) / ( x - 3 ) is A = 5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = lim x tends to 3 ( x² -x - 6 ) / ( x - 3 ) be equation (1)
On simplifying the equation , we get
Taking the common factors on numerator , we get
A = lim x tends to 3 ( x² + 2x - 3x - 6 ) / ( x - 3 )
A = lim x tends to 3 ( x ( x + 2 ) - 3 ( x + 2 ) ) / ( x - 3 )
Taking the common factor as ( x + 2 ) , we get
A = lim x tends to 3 ( x + 2 ) ( x - 3 ) / ( x - 3 )
So , the equation is
A = lim x tends to 3 ( x + 2 )
Substitute the value of x = 3 , in the equation , we get
A = ( 3 + 2 )
A = 5
Therefore , the value of A is 5
Hence , the equation is A = 5
To learn more about equations click :
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Reed wants to have a square garden plot in his backyard. He has covered enough compost to cover an area of 214 square feet.To the nearest tenth of a foot how long can a side of his garden be?
Answer:
o the nearest tenth of ft
Length of one of the side= 14.6 ft
Step-by-step explanation:
Reed wants to have a square garden plot in his backyard. He has covered enough compost to cover an area of 214 square feet.
His square garden is a square one, and the area of a square is the square of one of it's sides .
So if the area= 214 ft²
Length of one of the side = √(214 ft²)
Length of one of the side= 14.6287 ft
To the nearest tenth of ft
Length of one of the side= 14.6 ft
Three spherical balls with radius r are contained in a rectangular box. two of the balls are each touching 5 sides of the rectangular box and the middle ball. the middle ball also touches four sides of the rectangular box. What is the volume of the space between the balls and the rectangular box? This is a SAT question and is no calculator. Show all the work Answer is 4r^3(6-pi)
Answer:
[tex]\bold{4r^3 (6-\pi)}[/tex]
Step-by-step explanation:
Let us try to visualize the given situation in the form of 2 Dimensional image as shown in the attached diagram.
Let the Diameter of spherical balls be D.
As the spherical balls are completely fit in the rectangular box, the sides of box become:
[tex]D \times D\times (3 \times D)[/tex] OR [tex]D\times D\times 3D[/tex]
We know that Diameter is twice of radius.
Therefore [tex]D = 2r[/tex]
So, the dimensions of rectangular box becomes:
[tex]2r \times 2r \times 6r[/tex]
Volume of a rectangular box is given as:
[tex]V = Length \times Width \times Height\\\Rightarrow V = 2r\times 2r\times 6r = \bold{24r^3}[/tex]
Now, let us find out the volume of each spherical ball.
Volume of a sphere with radius 'r' is given as:
[tex]V_{sphere} = \dfrac{4}{3}\pi r^3[/tex]
Volume of 3 spheres = [tex]3\times \frac{4}{3}\pi r^3 =4\pi r^3[/tex]
Now, the volume of space between the balls and rectangular box is = Volume of rectangular box - Volume of 3 balls
[tex]24r^3 - 4\pi r^3\\\Rightarrow \bold{4r^3 (6-\pi)}[/tex]
Mr. Coelho and Ms. Steiner are grading math and science tests of sixth-grade and seventh-grade students, respectively,
Mr. Coelho graded 25 science tests in 50 minutes and 30 math tests in 40 minutes. Ms. Steiner graded 20 science tests in
50 minutes and 12 math tests in 30 minutes.
Whose grading shows a proportional relationship between the number of tests graded and the time spent grading?
The answer is only ms.Steiner’s grading
Answer:
Ms. Steiner
Step-by-step explanation:
Mr. Coelho
science = 25 / 50 = 1/2
math = 30 / 40 = 3/4
not the same rate
Ms. Steiner
science = 20 / 50 = 2/5
math = 12 / 30 = 2/5
It is the same rate, so they are proportional
Mr. Coelho: Science: 50 minutes / 25 tests = 2 minutes per test
Math: 40 minutes / 30 tests = 1.33 minutes per test.
Ms. Steiner: Science: 50 minutes / 20 tests = 2.5 minutes per test.
Math: 30 minutes / 12 tests = 2.5 minutes per test.
The answer is Ms. Steiner.
Calculate the value of the sample correlation coefficient. Based on this value, how would you describe the nature of the relationship between the two variables
Answer:
Explained below.
Step-by-step explanation:
The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.
The formula to compute correlation coefficient is:
[tex]r(X,Y)=\frac{Cov(X,Y)}{\sqrt{V(X)\cdot V (Y)}}[/tex]
[tex]=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot\sum X^{2}-(\sum X)^{2}][n\cdot\sum Y^{2}-(\sum Y)^{2}]}}[/tex]
Positive correlation is an association amid two variables in which both variables change in the same direction.
A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.
Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa.
In statistics, a perfect positive correlation is represented by +1 and -1 indicates a perfect negative correlation.
coordinates easy - please help me :)
Answer:
Step-by-step explanation:
starting after after after
coordinates reflection rotation translation
(x,y) (x,-y) (-y,-x) (-y-2,-x-4)
A (-2,1) (-2,-1) (-1,2) (-3,-2)
B (2,1) (2,-1) (-1,-2) (-3,-6)
C (2,-1) (2,1) (1,-2) (-2,-6)
D (-2,-1) (-2,1) (1,2) (-2,-2)
Note: Enter your answer and show all the steps that you use to solve this problem.
*btw the note is the same thing for question 6*
1. 7x=42
6.simplify the expression 8to the 2power +9(12÷3×2)-7.
Answer:
1) x = 6
2) 129
Step-by-step explanation:
For equation 1:
[tex]7x=42\\\\\frac{7x=42}{7}\\\\ \boxed{x=6}[/tex]
Expression 2:
Apply PEMDAS Rule.
[tex]8^2+9((12/3)*2)-7\\\\8^2+9(4*2)-7\\\\8^2+9(8)-7\\\\64+9(8)-7\\\\64+72-7\\\\136-7\\\\\boxed{129}[/tex]
Hope this helps.
Milo receives a commission of 8% on all sales. If his commission on a sale was $97.84 find the cost of the item he sold
Answer:
Cost of the item sold= $1,223
Step-by-step explanation:
Let
x= cost of the item sold
$97.84=commission on the item
Percentage of the commission=8%
To find the cost of the item sold
Commission=8% of cost of the item
97.84=0.08 * x
97.84=0.08x
Divide both sides by 0.08
97.84 / 0.08 = 0.08x / 0.08
1,223=x
x=$1,223
Therefore, cost of the item sold= $1,223
PLEASE HELP! A) 7 B) 5.7 C) 4.7 D) 8.2
Answer:
[tex]\Large \boxed{\mathrm{A) \ 7}}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions to solve the problem.
tan(θ) = opp/adj
tan(35) = x/10
Multiply both sides by 10.
10 tan(35) = x
x = 7.00207538...
5. Which of the following illustrates the Distributive
Property?
F. 3(2x + 4) = 5x + 4
G. 3(2x + 4) = 5x + 7
H. 3(2x + 4) = 6x + 4
I. 3(2r + 4) = 6 + 12
plz answer quickly yikess
Answer: Hi!
Option I is correct. 3(2x + 4) = 6x + 12
When you use the distributive property, you multiply the term outside of the parentheses (in this case, 3) by the terms inside of the parentheses (in this case, 2x and 4.)
Hope this helps!
Adam was curious if quadrilaterals ABCDABCDA, B, C, D and GFEHGFEHG, F, E, H were congruent, so he tried to map one figure onto the other using transformations:
Adam concluded:
"It's not possible to map ABCDABCDA, B, C, D onto GFEHGFEHG, F, E, H using a sequence of rigid transformations, so the quadrilaterals are not congruent."
What error did Adam make in his conclusion?
Answers reflection (b)
Step-by-step explanation:
it’s right on 8th grade khan ywwww
So he tried to reflect(b) map one figure onto the other using transformations.
Are quadrilaterals congruent?If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Are two quadrilaterals congruent?Both the theorems are proved now which states that quadrilaterals are congruent to one another. Note: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles and the opposite sides of a parallelogram are congruent.
Learn more about the quadrilaterals are not congruent at
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Linear function g is shown in the graph. Write the slope-intercept form of the equation representing this function.
Answer:
y = -2x + 1
Step-by-step explanation:
First, find the slope with rise/run (y2 - y1) / (x2 - x1)
We can use the points (-1, 3) and (0, 1)
Plug in the points:
(1 - 3) / (0 + 1)
-2/1
= -2
The y-intercept is (0, 1) because that is the point where the line intercepts the y axis. So, we can plug in the slope and y-intercept into the equation:
y = mx + b
y = -2x + 1