Answers
Suppose that the corrals are rectangular in shape. The formula of the area of a rectangle is
[tex]\begin{gathered} A=lw \\ l\to\text{ length} \\ w\to\text{ width} \end{gathered}[/tex]Therefore, the areas of the four different corrals are
[tex]\begin{gathered} A_1=50\cdot40=2000 \\ A_2=60\cdot35=2100 \\ A_3=55\cdot45=2475 \\ A_4=65\cdot40=2600 \end{gathered}[/tex]Then, divide each area by its corresponding population,
[tex]\begin{gathered} \frac{A_1}{110}=18.1818\ldots<20 \\ \frac{A_2}{115}=18.2608\ldots<20 \\ \frac{A_3}{125}=19.8<20 \\ \frac{A_4}{110}=20=20 \end{gathered}[/tex]Therefore, the only corral that meets the requirement is corral 4, the answer is option D.
Related Questions
help! its due tomorrow
Answers
For Question 1,
(a) Teammates eye-level depths in order from lowest to highest:
-3.5 ft < -3 ft < 0 ft < 1.5 ft
(b) Comparison between Teammate B and teammate D depths:
-3.5 ft < -3 ft
so, eye level depth of Teammate B < Teammate D.
For Question 3,
The options given to the designer are:
1 3/4 and 1 5/12
On simplifying these fractions,
1 3/4 = 7/4
1 5/12 = 17/12
On taking the LCM of the denominator of 4 and 12, we get LCM as 12,
So, 7/4 = 21/12
Now, on comparing the two distances,
21/12 > 17/12
(a) So, the distance of 17/12 is closest to the slide.
(b) On comparing the two distances,
we get, 21/12 > 17/12
(c) 17/12 will lie in between 1 and 1 1/2 on the number line whereas 21/12 will lie in between 1 1/2 and 2 on the number line.
What is Number Line?A number line, used to represent the real numbers visually in early mathematics, is a drawing of a graduated straight line. It is presumptively true that each real number and each point on a number line relate to one another. A line with carefully marked equally spaced-out points on it is frequently used to represent integers. Especially when negative numbers are involved, it is frequently used as a teaching tool for basic addition and subtraction. The set R of all real numbers, considered as a geometric space, namely the Euclidean space of dimension one, is the formal definition of the number line, often known as the real line or real number line in advanced mathematics.To learn more about the Number line, refer to:
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Evaluate. [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) What is the value of the expression? Enter your answer as a simplified fraction in the box.
Answers
The value of given expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) is 1/5
In this question, we have been an expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9)
We need to evaluate given expression.
First we write an improper fraction as proper fraction.
1 1/5 = 6/5
So given expression becomes,
[(1 1/5−2/5)⋅(− 3/4)3]÷(−9)
= [(6/5 − 2/5) × (− 3/4) 3] ÷ (−9)
= [(4/5) × (-9/4)] ÷ (−9)
= (-9/5) ÷ (-9)
= 1/5
Therefore, the value of given expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) is 1/5
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Given the sum of the interior angles is 12,600 of a regular polygon, determine the following:
The number of sides =
Each interior angle =
Each exterior angle =
Sum of the exterior angles =
Answers
Answer:
72 sidesinterior angle: 175°exterior angle: 5°exterior angle total: 360°Step-by-step explanation:
Given a regular polygon whose interior angles total 12,600 degrees, you want to know the number of sides, the measures of each interior and exterior angle, and the sum of the exterior angles.
Angle sumThe sum of angles of a convex polygon is given by the formula ...
angle sum = 180° × (n -2)
where n is the number of sides.
ApplicationSubstituting the given angle sum, we can solve for n:
12,600 = 180(n -2)
70 = n -2 . . . . . divide by 180
72 = n . . . . . . . add 2
The regular polygon has 72 sides.
Interior angleThe interior angles of a regular polygon are congruent, so each one is ...
12,600°/72 = 175°
Each interior angle = 175°.
Exterior angleThe exterior angle at a vertex is the supplement of the interior angle there:
180° -175° = 5°
Each exterior angle = 5°.
Sum of exterior anglesThe 72 exterior 5° angles have a total of ...
72 × 5° = 360°
Sum of the exterior angles = 360°.
__
Additional comment
The invariant with convex polygons, regular or not, is that the sum of exterior angles is 360°. This fact is what gives rise to the formula for interior angles.
Scott is 72 inches tall and Chris is 185 centimeters tall. Who is taller? Show your work. How do we convert this?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Scott is 72 inches tall and Chris is 185 centimeters tall.
Who is taller? Show your work.
Step 2:
Scott is 72 inches tall
and
Chris is 185 centimeters tall
Converting cm to inches, we have that:
[tex]\begin{gathered} 1\operatorname{cm}\text{ = }0.393701\text{ inch} \\ 185\text{ cm = 185 x 0.393701 = }72.\text{ 834685 }\approx\text{ 72. 8 inch} \end{gathered}[/tex]CONCLUSION:
Since Chris' height = 72.8 inch tall and Scott's height = 72 inch tall
Hence, Chris is taller.
The business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344. 12 were written the store manager then made a deposit of $955.30. Findthe current checkbook balance.
Answers
Solution
For this case we can solve the problem with the following operation:
7349.44 -1348.67 -344.12 + 955.30 = 6611.95$
What are the correct answers the drop down both say negative or positive
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Given the data set:
(-8,-10) (6, -1), (-5,-7),(3, -2) (10, 0) (4,-3) (-3,-6) , (9, 1)
We will graph the points to find the slope of the line of best fit for the data
The graph will be as shown in the following figure:-
As shown, the given points are the dots of blue color
The line of best fit is the dashed red line
As shown, the line has a positive slope and a negative y-intercept
So, the answer will be:
The line of best fit for the data will have a positive slope and a negative y-intercept value.
Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q8
Answers
Part A (Domain and Range)
Domain
The domain is the set of all the values of x for which the function represented by the graph is defined. From the graph:
(A)The domain of the function is:
[tex]\lbrace x|-\inftyRangeThe range is the set of all the values of y for which the function represented by the graph is defined. From the graph:
(A)The range of the function is:
[tex]\lbrace y|-\inftyPart B (Intercepts)(A)The x-intercepts of the function are:
[tex]x=1.4,-1.4[/tex](A)The y-intercept of the function is:
[tex]y=-1[/tex]Part C
The horizontal asymptote is at:
[tex](A)y=-2[/tex]Part D
The vertical asymptotes are at:
[tex](A)x=-2,2[/tex]Part E
The oblique asymptote is usually slant.
From the graph, there are no obliques asymptotes.
Option B is correct here.
Find the missing coordinates to complete the following ordered-pair solutions to the given linear equation.y + 4x = 6(a) (-1, )(b) (4, )....
Answers
SOLUTION
Write out the given linear equation
[tex]y+4x=6[/tex]For the first ordered pair,
[tex]\begin{gathered} (-1,\text{?)} \\ x=-1,y=\text{?} \end{gathered}[/tex]Substitute the value of x into the linear equation to find the value of y
[tex]\begin{gathered} y+4x=6 \\ y+4(-1)=6\ldots\text{.}\ldots(\text{expand the paranthesis )} \\ y-4=6\ldots\ldots(\text{add 4 to both sides )} \\ y-4+4=6+4 \\ y=10 \\ \text{The ordered pair is (-1,10)} \end{gathered}[/tex]a). Therefore For the first ordered pair, the missing coordinate y is 10
Similarly, for the second ordered-pair
[tex]\begin{gathered} (4,\text{?)} \\ x=4,y=\text{?} \end{gathered}[/tex]Substitute the value of x into the linear equation to obtain the value of y
[tex]\begin{gathered} y+4x=6 \\ y+4(4)=6 \\ \text{Expand the parenthesis} \\ y+16=6 \\ \text{subtract 16 from both sides } \\ y+16-16=6-16 \\ y=-10 \\ \text{Ordered pair=(4,-10)} \end{gathered}[/tex]b). Therefore for the second ordered pair, the missing coordinates y is -10
positive exponents.2) (22). 2)
Answers
To find the result we are going to use the following rule:
[tex](a^m)^n=a^{mn}[/tex]and
[tex]a^m\cdot a^n=a^{m+n}[/tex]Then:
[tex]\begin{gathered} ((2^2)^4\cdot2^3)^4=(2^8\cdot2^3)^4 \\ =(2^{11})^4 \\ =2^{44} \end{gathered}[/tex]Therefore the result is:
[tex]2^{44}[/tex]Find the volume of the sphere. Either enter an exact answer in terms of ar or use 3.14 for pi and round your final answer to the nearest hundredth.
Answers
We have a sphere of radius 4
r = 4
We know that the equation for the volume is:
[tex]V=\frac{4}{3}\pi r^3[/tex]We know that:
r = 4
and
π = 3.14
Then, we replace in the equation:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\cdot3.14\cdot4^3 \end{gathered}[/tex]Since
4³ = 64
then
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot4^3 \\ =\frac{4}{3}\cdot3.14\cdot64 \\ =267.9467 \\ =\frac{4}{3}\cdot\pi\cdot64=\frac{256}{3}\pi \end{gathered}[/tex]We want to round our answer to the nearest hundredth (two numbers after the decimal point).
For this case we have two options:
267.94 or 267.95
Since
267.9500 is nearer to 267.9467
than
267.9400
then the answer is 267.95
Answer: the volume of the sphere is 267.95 units³ or (256/3)π units³
Find the least common multiple (LCM) of 12 and 18
Answers
Answer:
0.0[infinitely reprating] 1 is the smallest
Answer:
36
Step-by-step explanation:
LCM of 12 and 18 is the smallest number among all common multiples of 12 and 18. The first few multiples of 12 and 18 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (18, 36, 54, 72, . . . ) respectively
Find the average rate of change of f(x) = x°-2x² +3+ 3x from x=1 to x=3.Simplify your answer as much as possible.
Answers
The average rate of change for a function f(x) from x=a to x=b is:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]For the given function:
[tex]f(x)=x^3-2x^2+3x[/tex]Averate rate of change from x=1 to x=3:
[tex]\begin{gathered} \frac{f(3)-f(1)}{3-1}=\frac{(3^3-2(3)^2+3(3))-(1^3-2(1)^2+3(1))}{3-1} \\ \\ =\frac{(27-2(9)+9)-(1-2+3)}{2} \\ \\ =\frac{(27-18+9)-(2)}{2} \\ \\ =\frac{18-2}{2} \\ \\ =\frac{16}{2} \\ \\ =8 \end{gathered}[/tex]Then, the averate rate of change for the given function from x=1 to x=3 is 8
How many 1/4 pound pork chops can be cut from a 9 1/2 pound boneless pork loin.
For Culinary
Answers
3.724x10^-12 convert into numerical form
Answers
A numerical expression is a mathematical statement that only consists of numbers and one or more operation symbols.
3.724x10^-12 = 3724/1000000000000000.
What is a numerical form?A numerical expression is a mathematical statement that only consists of numbers and one or more operation symbols. Thus, if someone gives you an expression, such as x + 2 - 3 + 8 = 11, and claims it is a numerical expression, you must deny it.Standard form refers to any number that can be written as a decimal number between 1.0 and 10.0 multiplied by a power of ten.A fraction is a numerical representation of a portion of something larger.A standard form is a method of writing a given mathematical concept, such as an equation, number, or expression, in a way that adheres to certain rules.3.724x10^-12 = 3.724/ 10^12
= 3.724/ 1000000000000
=3724/1000000000000000 (numerical form)
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In parallelogram STUV, VT bisects US and point G. If UG = x + 6 andGS = 2x + 6, find US.
Answers
Answer:
US = 12
Explanation:
The length of GS = UG (because TV bisected the line segment US) and
GS + UG = US
From GS = UG we have
[tex]x+6=2x+6[/tex]subtracting 6 from both sides gives
[tex]x=2x[/tex]subtracting x from both sides gives
[tex]0=x[/tex]With the value of x in hand, We now find the length of the line segment US.
[tex]US=UG+GS=x+6+2x+6=3x+12[/tex]Since x =0, the above gives
[tex]\begin{gathered} US=3(0)+12 \\ US=12 \end{gathered}[/tex]If (ax + 3)(bx + 4) = 6x 2+ cx + 12 for all values of x, and a + b = 5, what are the two possible values for c ?
Answers
Answers: c = 17 and c = 18
==================================================
Explanation:
Let's expand out the left hand side and rearrange terms like shown in the steps below.
(ax + 3)(bx + 4) = 6x^2 + cx + 12
ax(bx + 4)+3(bx + 4) = 6x^2 + cx + 12
abx^2 + 4ax+3bx + 12 = 6x^2 + cx + 12
abx^2 + (4a+3b)x + 12 = 6x^2 + cx + 12
Then equate the corresponding coefficients
ab = 6 .... x^2 terms4a+3b = c .... x termsWe'll use the fact that a+b = 5. Solving for 'a' gets us a = 5-b
Plug this into the equation dealing with the x^2 coefficients.
ab = 6
(5-b)b = 6
5b-b^2 = 6
0 = b^2-5b+6
b^2-5b+6 = 0
(b-3)(b-2) = 0
b-3 = 0 or b-2 = 0
b = 3 or b = 2
If b = 3, then a = 5-b = 5-3 = 2
If b = 2, then a = 5-b = 5-2 = 3
Therefore, the solutions to this system of equations
[tex]\begin{cases}a+b = 5\\ab = 6\end{cases}[/tex]
are (a,b) = (2,3) and (a,b) = (3,2)
In other words, the answer to the question "what two numbers multiply to 6 and add to 5?" is "2 and 3". The order doesn't matter which is why we can flip the 'a' and b values.
---------------------------------
Go back to 4a+3b = c which was us equating the x coefficients.
This is the same as c = 4a+3b
Plug in a = 2 and b = 3
c = 4a+3b
c = 4*2+3*3
c = 8 + 9
c = 17 is one possible value of c.
Now let's plug in a = 3 and b = 2
c = 4a+3b
c = 4*3+3*2
c = 12 + 6
c = 18 is the other possible value of c.
HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answers
Answer:
(-3)³, (-2)⁴, (-2)³, 3⁰, -3², -2⁴
Write the ratio as a ratio of whole numbers in lowest terms $2.00 to $0.80
Answers
Ratio given is $2.00 : .80
To simplify, you can move your decimal point over 2 to the right to remove the decimals and then simplify
2.00 ➡️ 200
.80 ➡️ 80
200:80 divide both by 40
5:2 is your simplified ratio
the wholesale cost of shoes is 22.60$ the markup is 45% what is the selling price
Answers
Answer:
$32.77
Step-by-step explanation:
Add 45% of the wholesale cost to the entire wholesale cost to get the selling cost:
$22.60 + (45%)($22.60) = $32.77
The selling cost is $32.77.
if log2 5=x and log2 3=y, determine an expression in terms of x ,y, and integers. the first is log 2 20
Answers
Answer:
[tex]\log _220\text{ = 2 + x}[/tex]Logarithm base 2 of a number, is the number you have to use as a power of two to get that number, for example, logatithm base 2 of 4 is 2, because 2 to the power of 2 is 4, another example, logarithm base 2 of 8 is 3, because 2 to the power or 3 is 8
[tex]\log _2(4)=2because2^{2\text{ }}=4[/tex][tex]\log _2(8)=3because2^{3\text{ }}=\text{ 8}[/tex]A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=−16t2+v0t. Find the time(s) that the projectile will (a) reach a height of 400 ft and (b) return to the ground when v0 is 128 feet per second.
Answers
At time t = 4 + 3i sec and t = 4 - 3i sec that the projectile will reach a height of 400 ft.
A projectile is launched from ground level with an initial velocity of v₀ feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s = −16t² + v₀t.
To determine the time that the projectile will reach a height of 400 ft
⇒ s = −16t² + v₀t
Here v₀ = 128 ft/s and s = 400 ft
Substitute the value of v₀ = 128 and s = 400 in the above equation,
400 = -16t² + 128 × t
16t² - 128t + 400 = 0
Which is simplified as :
t² - 8t + 25 =0
Which gives t = 4 + 3i sec and t = 4 - 3i sec
Therefore, time t = 4 + 3i sec and t = 4 - 3i sec that the projectile will reach a height of 400 ft.
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Put the number or question when You answer
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8) 17/20
9) 25/4 or 1 1/24 in mixed form
10) 27/28
11) 5/6
12) 17/48
Solve. ln(–x + 1) – ln(3x + 5) = ln(–6x + 1) –0.67 or 2 option 1 –1.58 or 0.14 option 2–0.14 or 1.58 option 3–2 or 0.67 option 4
Answers
SOLUTION
We want to solve
[tex]\ln \mleft(-x+1\mright)-\ln \mleft(3x+5\mright)=\ln \mleft(-6x+1\mright)[/tex]This becomes
[tex]\begin{gathered} \ln (-x+1)-\ln (3x+5)=\ln (-6x+1) \\ \ln (-x+1)-\ln (3x+5)-\ln (-6x+1)=0 \\ \text{From laws of logarithm } \\ \ln \frac{(-x+1)}{(3x+5)}\times\frac{1}{(-6x+1)} \\ \ln \frac{(-x+1)}{(3x+5)(-6x+1)}=0 \end{gathered}[/tex]Since ln 1 = 0, we have
[tex]\begin{gathered} \ln \frac{(-x+1)}{(3x+5)(-6x+1)}=\ln 1 \\ \text{Canceling }\ln ,\text{ we have } \\ \frac{(-x+1)}{(3x+5)(-6x+1)}=1 \\ (-x+1)=(3x+5)(-6x+1) \end{gathered}[/tex]Expanding the equation in the right hand side we have
[tex]\begin{gathered} (-x+1)=(3x+5)(-6x+1) \\ (-x+1)=-18x^2+3x-30x+5 \\ -x+1=-18x^2+3x-30x+5 \\ -18x^2+3x-30x+5=-x+1 \\ -18x^2+3x-30x+x+5-1=0 \\ -18x^2-26x+4=0 \end{gathered}[/tex]Solving the quadratic equation we have
[tex]-18x^2-26x+4=0[/tex]We have
[tex]x=-1.58\text{ or }x=0.14[/tex]Hence, the answer is option 2
Question 1-4
Rectangle ABCD is dilated into rectangle AB'C'D', as shown.
B'
B
A
3
6
C
2
D
C'
D'
What is the scale factor of dilation? Enter the answer as a whole number or a simplified fraction in the box. Use "/" for the fraction bar.
Answers
The scale factor of the dilation of Rectangle ABCD which generated rectangle AB'C'D is of:
2
What is a dilation?A dilation is when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
If the coordinates are not given, as is the case in this problem, we can observe the scale factor by the ratio of the side lengths of the dilated figure and of the original figure.
In the context of this problem, these lengths are observed as follows:
The original rectangle ABCD has side lengths of 2 and 3.The dilated rectangle AB'C'D' has side lengths of 4 and 6.Hence the scale factor of the dilation is calculated as follows:
Scale factor = 4/2 = 6/3 = 2.
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help meeee pleasee!!!
thank youu
Answers
Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Sharon makes money by commission rates. She gets 17% of everything she sells. If Sharon sold $37,000 worth of items this month, how much didshe make?O A $629O B. $5,180O C. $6,290O D. $14,800
Answers
Answer;
[tex]C;\text{ \$6,290}[/tex]Explanation;
Here, we want to get the amount of commission made by Sharon
Mathematically, we have that she makes 17% of what she sells as commission
We have this as;
[tex]\frac{17}{100}\times37,000\text{ = \$6,290}[/tex]Find the volumeof eachfigure, round to th nearest hundredth I'd necessary
Answers
Determine the base of right triangle by using pythagoras theorem.
[tex]\begin{gathered} b=\sqrt[]{(15.7)^2-(8.5)^2} \\ =\sqrt[]{174.24} \\ =13.2 \end{gathered}[/tex]Determine the area of base of figure.
[tex]\begin{gathered} A=\frac{1}{2}\cdot13.2\cdot8.5 \\ =56.1 \end{gathered}[/tex]Determine the volume of the figure.
[tex]\begin{gathered} V=A\cdot6.2 \\ =56.1\cdot6.2 \\ =347.82 \end{gathered}[/tex]So volume of the figure is 347.82 yards square.
convert into paisa RS.35.25
Answers
When RS.35.25 is converted into paise it will be :
3525 paise
How Rupee is converted into Paise? Each nation has its own currency. India's currency is the Indian Rupee. We all see and interact with rupees on a daily basis. We see various coins and notes of various denominations.A rupee contains one hundred paise. In addition, we write 1 Rupee = 100 Paise or 100 Paise = 1 Rupee. Let us first define the terms rupees and paise. We will also understand how to convert rupees to paise.Here given , RS.35.25
We know that,
1 rupee equals 100 paise.
When converting rupees to paise, multiply by 100.
For instance,
Rs 35.25 = Rs 35 + 25 paise.
= 35 x 100 paise + 25 paise
= 3500 paisa + 25 paisa
= 3525 paise.
RS.35.25 = 3525 Paise.
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PLS HELP!!! I GIVE BRAINLESS!!!! NOT FOR TEST!!!
Answers
Answer:D
Step-by-step explanation:
D (-1,-2)
Select the expressions that are equivalent to - 7(f - 4).
Answers
you can multiply each term of the parentheses by -7
[tex]\begin{gathered} -7(f-4) \\ (-7\times f)+(-7\times-4) \\ -7f+28 \end{gathered}[/tex]