Tanisha has 51 m of fencing to build a
three-sided fence around a rectangular
plot of land that sits on a riverbank. (The
fourth side of the enclosure would be the
river.) The area of the land is 304 square
meters. List each set of possible
dimensions (length and width) of the
field.
Possible dimensions #1:
meters by
meters.
Possible dimensions #2:
meters by
meters.
Answers
Answer:
Two sets of dimensions are possible:
L(m) W(m) Area(m^2) Fence (m) Perimeter
Set 1 19 16 304 51
Set 2 32 9.5 304 51
Step-by-step explanation:
Let's set L and W for the Length and Width of the perimeter. We know that:
Area = L*W
Area = 304 m^2
Perimeter = 51 m
Let's say that the side bounded by the river is the length side. No fence is required for that portion, so the fencing for the perimeter is given by:
Perimeter, P = L + 2W
P = 51 m
We can write: L+2W=51 m
Rearrange to isolate one of the two variables. Lets pick L:
L+2W=51
L=51-2W
L = (51-2W)
Now use this in the area equation:
304 m^2 = L*W
304 m^2 = (51-2W)*W
304 m^2 = (51-2W)*W
304 m^2 = 51W-2W^2
Arrange this in the standard form of a quadratice equation and solve:
-2W^2+51W-304 m^2 = 0
W = 16 and 9.5 meters
W = 16 m
Since L=51-2W
L=51-2*(16)
L = 51-32
L = 19 m
Area = L*W
L*W = 304 m^2
(19m)W = 304 m^2
W = 16 m
Check:
Does a length (L) of 19 m and a width (W) of 16 m give an area of 304 m^2 and a fencing perimeter of 51 m if one of the L sides is the river?
Area = (19 m)*(16 m) = 304 m^2 YES
Per. = 2*(16)+ 19 = 51 m YES
W = 9.5 m
Ding the same calculation for a width of 9.5 m also satisfies all the equations, as per above.
Both values of W are valid, so the twos sets of possible dimensions are:
L(m) W(m) Area(m^2) Fence (m) Perimeter
Set 1 19 16 304 51
Set 2 32 9.5 304 51
Related Questions
Eve knits scarves for her online store. This week she has already knitted 9 scarves. There are 2 days left in the work week. She set a goal for herself to knit at least 15 scarves and at the most 19 scarves this week. Eve wants to know how many scarves she should knit each day to meet her goal.
Which inequality represents the given situation?
• A. 15 ≤ 2x - 9 _> 19
• B. 15 ≤ 2x - 9 ≤ 19
• C. 15 ≤ 2x + 9 ≤ 19
• D. 15 _>2x+9 _>19
Answers
Answer: C. 15 ≤ 2x + 9 ≤ 19
Step-by-step explanation:
We know that her goal is to knit at least 12 scarves and, at the most, 19 scarves
So it has to be bigger or equal to 15 and smaller or equal to 19, so it can't be A or D.
We also know that she has already knitted 9, so our equation has to have a +9
So the answer is C. 15 ≤ 2x + 9 ≤ 19
The solution to an inequality is given in set builder notation as {x 1 x > 2/3}. What is another way to represent this solution set?
Answers
Answer:
Step-by-step explanation:
34/5=p2
11. Natalee wanted to write a function which shows a 40% increase in bacteria growth.
There were 100 bacteria to start. She wrote y = 100 (40)* but she felt that she was
wrong because her y-values were extremely high when she graphed it. Identify Natalee's
mistake, and write the actual function for this scenario.
Answers
Natalee's mistake is that she has written the function incorrectly. In her function, she has multiplied the starting number of bacteria, 100, by the growth rate, 40%, to get the final number of bacteria. However, this is not correct because a growth rate of 40% means that the number of bacteria increases by 40% of the starting number, not by 40 itself.
To write the correct function, we can use the fact that a growth rate of 40% means that the final number of bacteria is 1.4 times the starting number. Therefore, the correct function for this scenario is y = 1.4 * 100 = <<1.4*100=140>>140. This function shows that the number of bacteria increases to 140 after experiencing a 40% increase in growth.
Answer:
The actual function for this scenario would be:
y = 100 * 1.40
Step-by-step explanation:
Natalee's mistake was that she didn't add 1 to the value of the increase. When you multiply a number by 1 plus the percentage increase, you get the correct result. In this case, the correct function would be:
y = 100 * 1.40
This function will show a 40% increase in the number of bacteria, starting with 100 bacteria. When graphed, the y-values will not be extremely high.
if you have any question let me know!
Ciara Walker was earning $47,100 and received a 13% raise. Find her new annual earnings directly.
Answers
The annual earnings for Walker will be $53223.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this case, Ciara Walker was earning $47,100 and received a 13% raise.
Her new annual earnings directly will be:
= $47100 + (13% × $47100)
= $47100 + $6123
= $53223
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The volume of a one i 125(pi) in3. The height i three time the length of the radiu. What i the height of the cone
Answers
The volume of a cone is 125(pi) in3. The height is three time the length of the radius. The height of the cone = 3 × 125π = 375π inches
Given:
Volume of cone = 125π in3
Height = 3 times the radius
To find:
Height of the cone
Height of the cone = 3 × 125π = 375π inches
The given information is the volume of a cone, which is 125π in3, and the height of the cone which is 3 times the radius. To find the height of the cone, we need to multiply the volume by 3. Using the given information, we can calculate the height of the cone by multiplying 125π by 3, which gives us 375π inches as the height of the cone.
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Micaela has $0.20 worth of pennies and nickels. She has a total of 8 pennies and
nickels altogether. Determine the number of pennies, a, and the number of nickels,
y, that Micaela has.
Micaela has
pennies and
nickels.
Answers
Answer:
3 nickels and 5 pennies
Step-by-step explanation:
3 nickels = 15¢
5 pennies = 5¢
15+5=20
Angles 1 and 7 are what type of angles?
A. Same side interior angles
B. Alternate exterior angles
C. Alternate interior
D. Corresponding angles
Answers
Answer:
B. Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are pairs of angles on the outer side of the two parallel lines but on the opposite side of the transversal. They also have the same degree. So, the answer is B.
Determine the sign of the solution of
ax+b=cx+d in each situation. Justify your
reasoning with a graph.
a. 0
b. d
Answers
Answer:
ax+b=cx+d
Step-by-step explanation:
true or false: in a probability model, the sum of the probabilities of all outcomes must equal 1.
Answers
Answer:
Step-by-step explanation:
false that is not at all true
Use synthetic division to find the result when x4 - 11x³ +26x² + 10x + 28 is
divided by x - 7.
Answers
Answer: x³-4x²-2x-4
Tips:
Bring down top values, then multiply by the outside value, then put it under the next value, add, and repeat
at the beginning of a semester an anonymous survey was conducted on students in a statistics class. two of the questions on the survey were about gender and whether or not students have equal, more, or less energy in the afternoon compared to the morning. below are the results. what test should we perform to see if gender and energy level are associated? 1 point z test hypothesis test for a single mean anova chi-square test of independence f test comparing two means chi-square test of goodness of fit comparing two proportions
Answers
Chi-square independence test.
What is Chi-square?A test that evaluates how well a model matches real observed data is the chi-square (2) statistic.
A chi-square statistic can only be calculated with data that is random, unprocessed, mutually exclusive, obtained from independent variables, and drawn from a sizable enough sample.
The outcomes of a fair coin toss, for instance, satisfy these requirements.
To test hypotheses, chi-square tests are frequently employed.
Given the size of the sample and the number of variables in the relationship, the chi-square statistic examines the size of any discrepancies between the expected results and the actual results.
According to the total number of variables and samples used in the experiment, degrees of freedom are utilized in these tests to assess whether a particular null hypothesis can be rejected. as well.
According to our question-
The independence of two variables, each of which is categorized into a variety of categories or attributes, is also tested using the chi square statistic.
When the cell probabilities rely on the unknown parameters, the goodness of fit test is relevant as long as the unknown parameters are substituted by their estimates and as long as one degree of freedom is subtracted for each estimated parameter.
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high school has 36 players on the football team. the summary of the players' weights is given in the box plot. how many players weigh between 169 and 194 pounds?
Answers
There are 8 players who weigh between 169 and 194 pounds.
To answer this question, we can look at the box plot to understand the distribution of weights on the football team. The box plot shows us the minimum, maximum, median, and quartiles of the team's weights. The left quartile is 169 pounds, and the right quartile is 194 pounds. This means that 25% of the team's players weigh between 169 and 194 pounds. Since the team has 36 players, 25% of 36 is 9. However, since we are looking at the number of players between 169 and 194 pounds, we need to subtract 1 since the right quartile of 194 pounds is included in the number of players. Thus, there are 8 players who weigh between 169 and 194 pounds.
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a goat rancher has 25% of her cows aborting and many of the cows have arthrogryposis? what other lesion are you likely to see when you dissect the fetus that would lead to the limb deformities such as these
Answers
Arthrogryposis, also called arthrogryposis multiplex congenita (AMC), is a term used to describe a variety of conditions involving multiple joint contractures (or stiffness).
Arthrogryposis is a general or descriptive term for the development of non progressive contractures affecting one or more areas of the body prior to birth (congenitally). A contracture is a condition in which the joint becomes permanently fixed in a bent (flexed) or straightened (extended) position, completely or partially restricting the movement of the affected joint. When congenital contractures occur only in one body area which means it is not referred to as arthrogryposis but rather as an isolated congenital contracture. The most common form of an isolated congenital contracture is clubfoot. When arthrogryposis affects two or more different areas in the body, it may be referred to as arthrogryposis multiplex congenita (AMC).
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PLS HELP 100 POINTS
....................................
Answers
Answer: i know how to do it but i can't really see it pls bring it closer
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
Consider the given density curve. a uniform density curve is at startfraction 1 over 12 endfraction. what is the value of the median? 8 12 14 20
Answers
The median of the probability density curve is (c) 14
How to determine the median of the density curveFrom the question, we have the following parameters that can be used in our computation:
Initial position = 1/12
Suppose we have a set {x₁, ..., xₙ}
The median is the number at the middle.
The difference between a set and a density curve is that the density curve is continuous, so getting the exact middle value can be harder.
In the given graph, we have
Constant density curve that goes from 8 to 20.
Because it is constant, the median will just be equal to the mean,
So, the median is the average between the two extreme values.
The average of two numbers a and b is calculated as
(a + b)/2
So we have
Median = (a + b)/2
Substitute the known values in the above equation, so, we have the following representation
Median = (20 + 8)/2
Evaluate
Median = 14
Hence, the median is 14
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What is the range of this function?
6802
10
12
OA. (-8, -3, 5, 7}
B. (-3, 7, 8, 12)
C. (-8, -3, 5, 6, 7, 8, 10, 12}
D. (6, 8, 10, 12)
or wo
-7
Answers
Answer:
Step-by-step explanation:
it is
Consider the figure shown below (not drawn to scale). Both of the triangles are RIGHT triangles. y X(0,13) Y(0,7) Z(0,3) (0,0) J The length of vertical segment XY is: W(3,13) P 0 T(9,9) S(9,3) -X
Answers
Both of the triangles are RIGHT triangles. y X(0,13) Y(0,7) Z(0,3) (0,0) J. the length of vertical segment XY is 6.
What is a vertical segment?Generally, A part of a line that is totally vertical is referred to as a vertical line segment. This means that the two vertices that make up the segment's ends have the same x- and y-coordinates but different z-coordinates than one another.
The length of vertical segment XY can be found by subtracting the y-coordinate of point X from the y-coordinate of point Y.
In this case, the y-coordinate of point X is 13 and the y-coordinate of point Y is 7, so the length of vertical segment XY is
13 - 7 = 6.
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Complete Question not found
Image not found
Help me I don’t know
Answers
AU is 20 degrees and ∠QPA is 35 degrees and ∠ARU is 40 degrees are the unknown measures.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle.
In the given triangle A is the incenter for triangle PQR.
By observing figure, AR is angle bisector of angle URK.
So, ∠ARU = ∠ARK = 40 degree
Since, incenter point is equidistant from the sides of a triangle.
AT = AU = AK = 20
Since, PA is angle bisector of angle QPU.
So, ∠QPA = ∠UPA
3x + 2 = 4x - 9
Subtract 3x and add 2 on both sides of equation.
4x - 3x = 9 + 2
x = 11
Now plug in x value in ∠QPA=3(11)+2
=33+2=35 degrees.
Hence, Measures ∠ARU is 40 degrees, AU is 20 degrees and ∠QPA is 35 degrees.
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Rewrite the following equation in standard form. y= 10x-9
Answers
The equation y = 10x - 9 is rewritten in standard form as: -10x + y = -9.
What is the Equation of a Line in Standard Form?A line's equation can be expressed in standard form as Ax + By = C. Here, A, B, and C are integers.
How to Write the Equation of a Line in Standard Form?We are given the equation of a line as y = 10x - 9, which is expressed in slope-intercept form. We are asked to rewrite the equation in standard form. Follow the steps below:
y = 10x - 9 [given]
Subtract 10x from both sides of the equation:
y - 10x = 10x - 9 - 10x [subtraction property of equality]
y - 10x = -9
Rearrange the equation to fit the standard form:
-10x + y = -9
Therefore, in standard form, the equation, y = 10x - 9 is rewritten as -10x + y = -9.
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please help me answer this question
Answers
Answer:
The two equations are true for the same value because when you substitute 7 for x both of them are correct
Step-by-step explanation:
1) 3(7) - 5 = 16 3(7) = 21
27 - 5 = 16 21 = 21
16 = 16 True
True
PLEASE GIVE ME RIGHT ANSWERS HELP ME FAST I BEG YOU
Answers
Reason 1: Given
Reason 4: Reflexive Property
Reason 5: ASA
Proof 2:
Reason 2: Alternate Interior Angles Theorem
Reason 3: Given
Reason 4: Reflexive Property
Reason 5: AAS
Proof 3:
Reason 2: Given
Reason 3: Symmetric Property
Reason 4: Hypotenuse-Leg Theorem
Reason 5: CPCTC
Proof 4:
Reason 2: Definition of bisector
Reason 3: Given
Reason 4: Reflexive Property
Reason 5: SAS
PLEASE HELP ASAP, DUE TONIGHT! 5th grade math
Answers
The result of subtractions with mixed fractions are listed below:
71 / 2827 / 105 / 65 / 425 / 12How to make subtractions with mixed fractions
In this question we have five case of subtractions with mixed fractions, the procedure is summarized below:
Transform all mixed fractions into improper fractions.Subtract the resulting expression by algebra properties.Simplify the resulting fraction if necessary.Case 1
[tex]5 \frac{1}{4} - 2\frac{5}{7}[/tex]
(5 + 1 / 4) - (2 + 5 / 7)
(20 / 4 + 1 / 4) - (14 / 7 + 5 / 7)
(21 / 4) - (19 / 7)
(21 · 7 - 19 · 4) / (4 · 7)
71 / 28
Case 2
[tex]4\frac{1}{2} -1\frac{8}{10} \\[/tex]
(4 + 1 / 2) - (1 + 8 / 10)
(8 / 2 + 1 / 2) - (10 / 10 + 8 / 10)
9 / 2 - 18 / 10
9 / 2 - 9 / 5
(9 · 5 - 9 · 2) / (2 · 5)
(45 - 18) / 10
27 / 10
Case 3
[tex]3\frac{1}{2} - 2\frac{2}{3}[/tex]
(3 + 1 / 2) - (2 + 2 / 3)
(6 / 2 + 1 / 2) - (6 / 3 + 2 / 3)
7 / 2 - 8 / 3
(7 · 3 - 8 · 2) / (2 · 3)
(21 - 16) / 6
5 / 6
Case 4
[tex]2\frac{3}{4} - 1 \frac{1}{2}[/tex]
(2 + 3 / 4) - (1 + 1 / 2)
(8 / 4 + 3 / 4) - (2 / 2 + 1 / 2)
11 / 4 - 3 / 2
(11 · 2 - 3 · 4) / (4 · 2)
(22 - 12) / 8
10 / 8
5 / 4
Case 5
[tex]3\frac{1}{3} - 1 \frac{1}{4}[/tex]
(3 + 1 / 3) - (1 + 1 / 4)
(9 / 3 + 1 / 3) - (4 / 4 + 1 / 4)
10 / 3 - 5 / 4
(10 · 4 - 5 · 3) / (4 · 3)
(40 - 15) / 12
25 / 12
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b(t)=1000 times e^.03t how long to reach $1500
Answers
Answer:
Below
Step-by-step explanation:
1500 = 1000 e^.03t
1.5 = e^.03t
take LN of both sides
.405465 = .03 t t =13.5 yrs
Little help here? Also say why you got the answer…?
Answers
Answer: B
Step-by-step explanation:
Equation: S=KT
Just do S divided by T to get K and you get 7
Answer: s=7t
Step-by-step explanation:
you have to multiply every answer in the t column by 7 to get the number across in the s column
What is the slope of the line that passes through the points (2, 3) and (0, 11)? Write
your answer in simplest form.
Answers
Answer:
The slope is -4.
Step-by-step explanation:
[tex]m = \frac{11 - 3}{0 - 2} = \frac{8}{ - 2} = - 4[/tex]
Writing Equations of Lines of Best Fit
Answers
Answer: y=-2x+36
Step-by-step explanation:
slope intercept form
Y=mx+b
m= slope
b= Y-intercept
to find the slope, use the slope formula
y2-y1=x2-x1
(4,28),(11,14)
14-28/11-4
-14/7
-2
Slope is -2
y=-2x+b
Substiute in (11,14) to find b
14=-2(11)+b
14=-22+b
b=36
y=-2x+36
question 3 how many elements are there in this object called sample means small? 0 / 1 point 0 3 25 100 5,000
Answers
In the given sample mean, there are total 5 elements present.
What is a sample mean?An average of a group of data is called a sample mean.
A data set's central tendency, standard deviation, and variance can all be determined using the sample mean.
A population average can be determined using the sample mean, among other things.
Both the sample mean and sample median are helpful statistics for outlining a data set's core tendency.
The sample mean uses all of the data values because it is the arithmetic average.
Extreme values have no impact on the sample median, which simply uses one or two middle values.
So, we have the sample mean:
0 | 3 | 25 | 100 | 5,000
Now, in the given sample mean we can count that the number of values or the elements is 5.
Therefore, in the given sample mean, there are total 5 elements present.
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Correct question:
How many elements are there in this object called a sample means small?
Sample mean:
0 | 3 | 25 | 100 | 5,000
c) Write as a power of 10: (10 x 10 x 10 x 10 x 10) (10 x 10) ÷
Answers
10^7 ÷
your question is incomplete, please comment the full question for a more accurate answer
Written as a mixed number, the improper fraction 113⁄8 would appear as
Answers
[tex]\displaystyle\\Answer:\ \frac{113}{8} =14\frac{1}{8}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\\frac{113}{8}=\\\\\frac{112+1}{8}=\\\\\frac{112}{8} +\frac{1}{8} =\\\\14+\frac{1}{8} =\\\\14\frac{1}{8}[/tex]
Use square roots to solve the equation x² = -36 over the complex numbers.
Answers
Answer:
x=+/- i 6
Step-by-step explanation:
x²=+/- rad(i²*36) i²= -1
x²=+/-i rad(36) [rad = square roots]
x²=+/- i 6