The dimensions of the playing field the width is 54 yards and the length is 210 yards.
Given that the perimeter of the rectangular playing field is 528 yards and the length of the field is 6 yards less than quadruple the width.
Let the width of the rectangular playing field is x yards and it is given that the length of the field is 6 yards less than quadruple the width means the length is 4x-6.
As we know that the perimeter of the rectangle is two times the sum of length and breadth so.
P=2(l+w)
As it is given that the perimeter is 528 yards.
So, we will substitute all the values in the formula, we get
528=2(4x-6+x)
528=2(5x-6)
528=10x-12
528+12=10x-12+12
540=10x
540/10=10x/10
54=x
Now, substitute this values in l=4x-6 to find the length, we get
l=4(54)-6
l=216-6
l=210
Hence, the dimension of the playing field when the perimeter of the rectangular playing field is 528 yards is width is 54 yards and length is 210 yards.
Learn more about the perimeter of rectangle from here brainly.com/question/1746672
#SPJ9
Todd wants to make a cheesecake for a birthday party. The recipe calls for a 9-inch diameter round pan. Todd only has square pans. He has an 8 -inch square pan, a 9-inch square pan, and a 10 -inch square pan. Which pan comes closest in area to the one that the recipe suggests?
The pan that comes closest in area is the 8-inch square pan.
What pan comes closest?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 22/7
R = radius = diameter / 2 = 9/2 = 4.5 inches
22/7 x 4.5² = 63.64 in²
A square is a quadrilateral with four equal sides.
Area of a square = length²
8² = 64 in²
9² = 81 in²
10² = 100 in²
To learn more about the area of a circle, please check: https://brainly.com/question/14351152
#SPJ1
248 miners need to ride the elevator to the bottom of the mine. The elevator can hold 9 miners at a time. How many miners will be in the elevator on its last trip?
Check
ху
Triangle DEF has vertices D(-2, -1), E(0, 1), and F(1, -3). Graph the
triangle and its image after a dilation with a scale factor of 3.
The image after a dilation with a scale factor of 3 is A(-6, -3), B(0, 3), and C(3, -9) of triangle ABC.
Here, the coordinates are,
D = (-2, -1)
E = (0 , 1)
F = (1, -3)
After dilating triangle DEF using a scale factor of 3 and a center of dilation at the origin to form triangle ABC.
A = (-2 x 3, -1 x 3) = (-6, -3)
B = (0 x 3, 1 x 3) = (0, 3)
C = (1 x 3, -3 x 3) = (3, -9)
Line segments,
AB = 8.48
BC = 12.36
CD = 10.81
Therefore, after dilation by using a scale factor of 3 is A(-6, -3), B(0, 3), and C(3, -9).
Learn more about dilation here -
https://brainly.com/question/13437953
#SPJ9
which of the following values is not a soliution to -4x - 6.8<34
A. X=-9
B. X=-10.2
C. X=-11
D. X=-10
The value not in the solution is x = -10.2
How to determine the value not in the solution?The inequality expression is given as:
-4x - 6.8<34
Add 6.8 to both sides of the inequality
So, we have:
-4x < 40.8
Divide both sides by -4
x > -10.2
This means that only values greater than -10.2 are in the solution set
Hence, the value not in the solution is x = -10.2
Read more about inequality at:
https://brainly.com/question/25275758
#SPJ1
The following table presents the time taken to review articles that were submitted for publication to a particular journal during a recent year. A few articles took longer than 6 months to review; these are omitted from the table. Consider the data to be a population.
A) Variance = 10.24
B) Standard Deviation = 3.2
One of the measurements of dispersion is the standard deviation, which is exclusively used for quantitative data. It aids in determining if the data's mean is a suitable measurement to reflect the core value.
TIME FREQUENCY(f) MIDPOINT(x) d d² fd fd²
0 - 0.9 43 0.45 -3 9 -129 387
1.0 - 1.9 17 1.45 -2 4 -34 68
2.0 - 2.9 19 2.45 -1 1 -19 19
3.0 - 3.9 18 3.45 0 0 0 0
4.0 - 4.9 14 4.45 1 1 14 14
5.0 -5.9 16 5.45 2 4 32 64
∑f = 127
∑fd = -136
∑fd² = 552
[tex]d = \frac{x - 3.45}{1}[/tex]
Standard Deviation = [tex]\sqrt \frac{fd^{2} }{N} - \sqrt \frac{(fd)^{2} }{N} * i[/tex]
[tex]\sqrt \frac{552}{127} -\sqrt (\frac{-136}{127})^{2} * 1[/tex]
√4.35 - √1.15
Standard Deviation = 3.2
(SD)² = (3.2)² = 10.24
Variance = 10.24
To know more about standard deviation, refer to this link :
https://brainly.com/question/12402189
#SPJ1
What is the appropriate analysis to use when there are two independent variables that are measured and one dependent variable that is measured?
If there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use
Given,
The conditions
There are two independent variablesThe two independent variables are measured and one dependent variable that is measuredWe know
In multiple regression method the dependent variables are predicted by using the known independent variables. This method is usually used to analyze the relationship between multiple independent variables and one independent variables,
So here multiple regression method is using.
Hence, if there are two independent variables that are measured and one dependent variable that is measured, then the multiple regression method will use
Learn more about multiple regression here
brainly.com/question/3737733
#SPJ4
Two pounds of grapes cost `\$5`. jordan says that's `2.5` pounds per dollar. emika says it's `0.4` pounds per dollar. which rate is correct?
The rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.
We know that the rate is nothing but the ratio of two different quantities which have different units.
In this question, we have been given two pounds of grapes cost $5
First we find the rate in pounds per dollar.
2 pounds of grapes = $5
As rate is the ratio of two different quantities, we find the ratio (pounds per dollar).
= 2 pounds /5 dollars
= (2/5) pounds per dollar
= 0.4 pounds per dollar .......(1)
This means the rate of grapes is 0.4 pounds per dollar.
In this question, we have been given Jordan says that's 2.5 pounds per dollar and Emika says it's 0.4 pounds per dollar.
From (1), we can clearly say that Emika is correct.
Therefore, the rate of grapes said by Emika i.e., 0.4 pounds per dollar is the correct rate.
Learn more about the rate here:
https://brainly.com/question/199664
#SPJ4
b. a quality control randomly selects two of five parts to test for defects. in a group of five parts, how many combinations of two parts can be selected?
10 combinations of two parts can be selected.
Combination is defined as the number of arrangements in a collection of items where the order of selection does not matter.
denoted by C(n,x)= ⁿcₓ=[tex]\frac{n!}{(x!)(n-x)!}[/tex] ,
where n is the total number of elements in the set.
x is the number of selected objects.
According to the Question
Total number of elements = 5 = n
Number of objects to be selected = 2 = x
Substituting the values in the above formula
C(5,2)=[tex]\frac{5!}{2!*3!}[/tex]
[tex]=\frac{5*4*3!}{2*3!} \\ \\ =\frac{20}{2} \\ \\ =10[/tex]
Therefore , 10 combinations of two parts can be selected.
Learn more about Combinations here https://brainly.com/question/17091293
#SPJ4
609+283+97 pls help help helpp
Answer:
989
Step-by-step explanation:
Answer:
986
DO NOT HAVE A GOOD DAYHAVE A GREAT DAY\Which set does not contain –3?
the set of all real numbers
the set of all integers
the set of all whole numbers
the set of all rational numbers
Answer:
The set of all whole numbers
Step-by-step explanation:
Real numbers, integers, and rational numbers can all contain negative numbers. Whole numbers include numbers from 0 and up.
Hope this helps!
Have a nice day
Write the following solution in interval notation:
x≥-3
Answer:
[-3,∞)
Step-by-step explanation:
Since x is on the left side and is greater than -3, we will use a bracket in front of the -3. Since we do not know when the interval ends, we finish it with a positive infinity because we know that x is GREATER than (or equal) to -3. If it were less than -3, it would be negative infinity. Similarly, we use a rounded bracket because infinity is a positive value greater than -3.
Which statement about the product is true? (1 point)
5.643 x 4.6
O The product is irrational.
The product is neither rational nor irrational.
O The nature of the product cannot be determined.
O The product is rational.
Answer:
The product is rational.
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
On simplifying the given expression the no. that goes in green box is -7
The rule of addition of two numbers
(+) (+) = (+)adding two positive integers result in positive integer.
(-)(-) = (+)adding two negative integers results in the sum with a negative sign.
(+)(-) = (-) (-)(+) = (-)addition of two different signed Integer will result in subtraction only and the sign of the result is same as the larger number sign.
so
2 + 16x - 9 - 10x
6x + [-7] HERE [ 2 + (-9) = -7 ]
On simplifying the given expression the no. that goes in green box is -7
To know more about simplify
https://brainly.com/question/1014802
#SPJ1
marvin was completing the square, and his work is shown below. identify the line where he made his mistake. (2 points) f(x)
It can be seen that the mistake that was made by Marvin was on line 1.
How to illustrate the information?2x² - 8x + 5.... move the 5 to the other side
2x² - 8x = -5
Now divide by 2
x² - 4x = -5/2
x² - 4x + 4 = -5/2 + 4
(x - 2)² = -5/2 + 8/2
(x - 2)² = 3/2
x - 2 = (+-)sqrt 3/2
x = 2 + sqrt 3/2 or x = 2 - sqrt 3/2
Therefore, he made his mistake on line 1.
Learn more squares on;
https://brainly.com/question/1566484
#SPJ4
Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake. f(x) = 2x2 − 8x + 5. Line 1: f(x) = 2(x^2 − 8x) + 5 Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32 Line 3: f(x) = 2(x − 4)^2 − 27
-4b+5=-27 is what because i have no idea
Answer:
b=8
Step-by-step explanation:
-4b + 5 = -27
Move the 5 to the right side by subtraction, subtract five from the right side as well.
Now you should have:
-4b = -32
Now divide by -4 to get ‘b’ isolated, do this on both sides.
You should be left with:
b=8
PLEASE HELP ASAP! Solve the system of equations by graphing on your own paper. Write the solution as an ordered pair (x, y)
y=2x+1
y=4x-5
Answer:
Step-by-step explanation:
its 6 2 + 5 = 9-2 = 6
Do the two functions below appear to be inverses of each other
Answer:
yes
Step-by-step explanation:
if (a,b) is on the graph of f(x) then (-a,-b) is on the graph of f^-1(x)
State the domain and range of the sin, cos, tan, functions. State the domain
and range of the inverse sin, cos, and tangent functions.
The domain and range of trigonometric functions are as follows;
Function Domain Range
sin(x). All real numbers [-1, 1]
cos(x). All real numbers [-1, 1]
tan(x). {x| x ≠ -3•π/2, -π/2, π/2, } R
The domain and range of the inverse sine, cosine, and tangent are;
Function Domain Range
arcsin(x). (-1, 1) [-π/2, π/2]
arccos(x). (-1, 1) [0, π]
arctan(x) (-∞, ∞). [-π/2, π/2]
What are the domains and ranges of the trigonometric functions?sin(x)
The domain of sin(x) is the set of possible values for x, for which sin(x) is defined, which is;
All real numbers.The range of sin(x) is the set of possible values output values of sin(x) is, which is; -1 ≤ sin(x) ≤ 1
The range is therefore; [-1, 1]cos(x)
Similarly;
The domain of cos(x) is the set of all real numbersThe range of cos(x) is; -1 ≤ cos(x) ≤ 1tan(x)
tan(x) = sin(x)/cos(x), however, cos(x) = 0, when x = -3•π/2, -π/2, π/2, 3•π/2...
The domain of tan(x) is therefore;
{x| x ≠ -3•π/2, -π/2, π/2, 3•π/2...}sin(x) increases as cos(x) decreases, therefore;
The range of tan(x) = sin(x)/cos(x) is therefore;
-∞ < tan(x) < ∞ which is {-∞, ∞}arcsin(x)
The input of arcsin(x) is sin(x)
sin(x) = opposite/hypotenuse
Given that the magnitude of hypotenuse > opposite, the ratio, opposite/hypotenuse is < 1 in magnitude
The domain of arcsin(x) is therefore;
-1 < sin(x) < 1, which is (-1, 1)The range is the set of possible outputs, which is [-π/2, π/2], given that sin(x) is positive and negative from -π/2, π/2
The range is [-π/2, π/2]arccos(x)
Similarly;
The domain of arccos (x) is (-1, 1) The range is [0, π]arctan(x)
The input of arctan(x) is tan(x)
tan(x) = sin(x)/cos(x)
The domain of arctan(x) is therefore;
{-∞, ∞}The range is [-π/2, π/2]Learn more about the domain and range of functions here:
https://brainly.com/question/1942755
#SPJ1
Mobius, incorporated, has a total debt ratio of .48. a.what is its debt-equity ratio?
debt-equity ratio is 0.92.
What is debt equity ratio?A firm's total liabilities and shareholder equity are compared using the debt-to-equity (D/E) ratio, which may be used to determine how heavily reliant a company is on debt. D/E ratios vary by sector and are most useful for comparing a firm to its closest rivals or tracking changes in its reliance on debt over time. When comparing similar organizations, a larger D/E ratio denotes greater risk, whereas a very low one can signify that a company is not utilizing debt funding to grow. Since long-term debt entails greater risk than short-term commitments, investors frequently change the D/E ratio to simply take it into account.
Debt-equity ratio is computed as follows:
= total debt ratio / (1 - total debt ratio)
= 0.48 / (1 - 0.48)
= 0.48 / 0.52
= 0.92
To know more about debt equity ratio, visit;
https://brainly.com/question/25651634
#SPJ4
consider a clock with an hour hand and a minute hand. what is the measure of the angle the minute hand traces in 36 minutes. your answer should be in radians.
The measure of the angle the minute hand traces in 36 minutes is 3.77 radians
Calculating AngleFrom the question, we are to determine the measure of the angle the minute hand traces in 36 minutes
The minute hand makes a complete rotation after 60 minutes.
Thus,
The angle the minute hand would have traced in 36 minutes is
36/60 × 360°
= 12960/60
= 216°
Now, convert to radians
216° = 216 × π/180 rad
= 3.77 rad
Hence, the measure of the angle the minute hand traces in 36 minutes is 3.77 radians
Learn more on Calculating angles here: https://brainly.com/question/82007
#SPJ4
The height, in meters, of a machine piston can be modeled by the regression equation y = 4.4sin(0.4x -1.7) +2.3,
where x represents time, in seconds.
To the nearest tenth of a meter, what is the height of the piston after 10 seconds?
O 1.6 m
O 25m
O 3.3 m
O
5.6 m
The height of the machine piston after 10 seconds is 2. 5m . Option B
How to determine the value
Given the function;
y = 4.4 sin (0.4x -1.7) +2.3,
Where;
x represents time in secondsy is the height of the machine pistonGiven x as 10 seconds
y = 4. 4 sin ( 0.4(10) - 1. 7) + 2. 3
y = 4. 4 sin ( 4 - 1. 7) + 2. 3
y = 4. 4 sin (2. 3) + 2. 3
y = 4. 4(0. 04013) + 2. 3
y = 2. 47
y = 2. 5 meters in the nearest tenth
Thus, the height of the machine piston after 10 seconds is 2. 5m . Option B
Learn more about functions here:
https://brainly.com/question/2328150
#SPJ1
Answer:
D. 5.6 m
Step-by-step explanation:
Use your context clues.
All the other answers had O, like an X, so I put D, which was correct. *Wink*
simplify three square root of five end root minus two square root of seven end root plus square root of forty five end root minus square root of twenty eight. (1 point)
The expression is simplified to 6√5 - 4√7
How to simplify the expressionFrom the information given, we have that;
[tex]3\sqrt{5} - 2\sqrt{7} + \sqrt{45} - \sqrt{28}[/tex]
Let's find the surd forms with perfect squares and add into the formula
3√5 - 2√7 + √9 ×5 - √7× 4
Find the perfect squares of the expression
3√5 - 2√7 + 3√5 - 2√7
collect like terms
3√5 + 3√5 - 2√7 - 2√7
Add like terms
6√5 - 4√7
Thus, the expression is simplified to 6√5 - 4√7
Learn more about surds here:
https://brainly.com/question/840021
#SPJ4
Solve for x. Please show work.
2x + 6 = -3x - 14
A) 16 Miss Violet was in the cafeteria.
B) -16 Mrs. Teal was in the library.
C) 3.2 Mr. Brown was in the auditorium.
D) -4 Ms. Ivory was in the student center.
E) 4 Prof. Gray was in the library.
Answer:
D
Step-by-step explanation:
2x+6=-3x-14
2x+3x=-14-6
5x=-20
x=-4
Answer:
X = -4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
A certain school's enrollment increased 6% this year over last year's enrollment. If the school now has 1378 students enrolled, how many students were enrolled last year?
A. 1295
B. 1300
C. 1350
D. 1460
E. 1500
If the school now has 1,378 students enrolled, last year, the number of students enrolled was B. 1,300.
How is the number of students determined?Using the mathematical operations of addition, subtraction, division, and multiplication, we can determine the number of students.
Mathematical operations help us to determine unknown values, given a known domain.
Data and Calculations:Increase in school enrollment over last year's = 6%
Enrollment for the current year = 1,378
Let last year's enrollment = 100%
And the current year's = 1.06 (100 + 6)
Therefore, the enrollment last year = 1,300 (1,378/1.06)
Thus, the enrollment (number) last school year was B. 1,300.
Learn more about mathematical operations at https://brainly.com/question/28294142
#SPJ1
11. The circlex²+y² = 26 and the line y = x + 4 meet at two points P and Q
a) show that the x co-ordinates of P and Q satisfy the equation x² + 4x-5=0
b) hence find the co-ordinates of P and Q
a)The x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.
b)The co-ordinates of P and Q are (-5, -1) and Q = (1, 5).
What is defined as the equation of the circle?(x-h)² + (y-k)² = r² is the equation for a circle with (h, k) center and r radius. This is the equation's standard form. Thereby, if we recognise the coordinates of the circle's center and radius, we can usually find its equation.The given equation of the circle is;
x² + y² = 26.
Th circle satisfies the line y = x + 4.
Thus, Put the value of y in the main equation.
x² + (x + 4)² = 26.
Simplify the equation;
x² + x² + 16 + 8x = 26
2x² + 8x - 10 = 0
Divide the equation by 2.
x² + 4x - 5 = 0
Part a: This shows that x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.
Part b: Now, do the factorization of x² + 4x - 5 = 0.
(x + 5)(x - 1) = 0
x = -5 and 1.
For x = -5; y = -1
Point P = (-5, -1)
For x = 1; y = 5
Point Q = (1, 5)
Thus, the requires points P and Q are obtained.
To know more about the equation of the circle, here
https://brainly.com/question/10368742
#SPJ9
Cam someone help plss
Answer:
let y=0
3x+6(0)=18
3x=18
x=6
(6;0)
Answer: 3
Step-by-step explanation: If you solve the equation, like I did in the attached image, you will see that the x-intercept is 3.
I need help with 18 and 22. With a full explanation please.
The answer of 18 is y = 0.5x + 0
The answer of 22 is y = -0.4x + 0
Step-by-step explanation:
c is constant, m is gradient
18. m = 1/2
m = 0.5
1 = 0.5(2) + c
1 = 1 + c
c = 0
y = 0.5x + 0
22. m = 2/-5
m = -0.4
2 = -0.4(-5) + c
2 = 2 + c
c = 0
y = -0.4x + 0
Here is the histogram of a data distribution.
What is the shape of this distribution?
O A. Unimodal skewed
• B. Bimodal symmetric
• C. Unimodal symmetric
• D. Bimodal skewed
O E. Uniform
Answer: your answer would be unimodal skewed. This graph only has one maxima, thus it can't be bimodal. However, it's not symmetric, meaning that it is skewed
Hope this helps you
Step-by-step explanation:
The histogram is solved and it is uni-modal skewed
What is Histogram?A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable.
A histogram displays the frequency distribution of a set of continuous data. It is useful for visualizing the shape of the data distribution, such as whether it is symmetrical or skewed, and identifying any outliers or gaps in the data.
Given data ,
Let the histogram be represented as A
Now , the value of A is plotted on the graph
A. Unimodal skewed: This distribution has one peak (mode) and the tail of the distribution extends to one side. Depending on which side the tail is longer, it can be either positively skewed (tail extends to the right) or negatively skewed (tail extends to the left).
B. Bimodal symmetric: This distribution has two distinct peaks (modes) and is symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.
C. Unimodal symmetric: This distribution has one peak (mode) and is roughly symmetric, meaning the left and right sides of the distribution are roughly mirror images of each other.
D. Bimodal skewed: This distribution has two distinct peaks (modes) and the tail of the distribution extends to one side for each peak. Depending on which side each tail is longer, it can be either positively skewed (tail of one peak extends to the right and the other to the left) or negatively skewed (tail of one peak extends to the left and the other to the right).
E. Uniform: This distribution is flat and has roughly equal frequency for all values in the range of the dataset.
Hence , the histogram is unimodal skewed
To learn more about histogram click :
https://brainly.com/question/16819077
#SPJ5
A large polymeric molecule that is nonpolar over most of its structure but very polar at one end:_____.
A large polymeric molecule that is nonpolar over most of its structure but very polar at one end DNA and Phospholipid.
DNA and phospholipid were two examples of huge polymeric molecules that would be polar solely on a single end although nonpolar on the majority of their structure, as opposed to the other alternatives, which would be all monomeric compounds. Nucleotides are used to help DNA create its polymeric structure. Phosphodiester linkage aids in the arrangement of the nucleotides.
The polar molecule would only be found in one area of the vast strand-like polymeric structure. At one extremity of the strand, there is a polar phosphate link; with its assistance, some other monomeric units were joined, generating the phosphodiester bonds. Two fatty acids and the first molecule of glycerol work together to generate the structure known as the phosphodiester.
The phosphate group is present in the polar head region of the phosphate group. This help in the polarity of the phospholipid structure making the head region of the polymeric molecule hydrophilic.
Learn more about nonpolar
https://brainly.com/question/12240552
#SPJ4
Which of the following numbers are irrational?
Answer:
π/2 and ³√4
also -4.8237 and π/2
Step-by-step explanation:
number 2 and 4 are automatically out since every integer is a rational number.
√25 = 5 and 5 + 4 = 9, 9 can be expressed as 9/1 which falls under rational numbers.
π/2 on the other hand is not rational same goes for -4.8237 and ³√4 because these numbers cannot be written as a fraction with integers.
for the above numbers π/4 and ³√9 are irrational.