Complete Question:
Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters. This year he wants to make the garden three times as long and two times as wide.
Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.
How many more meters of fencing is needed for this year’s garden than last year’s?
Answer:
26 meters of fencing needed
Step-by-step explanation:
Given
Last Year:
[tex]Width = 5m[/tex]
[tex]Area = 20m^2[/tex]
This Year:
[tex]Length = 3\ times\ longer[/tex]
[tex]Width = 2\ times\ wider[/tex]
Required
Determine how many more meters is needed
Represent last year's length of Fence with L and last year's width with W
First, we need to calculate L
[tex]Area = L * W[/tex]
Where
[tex]Area = 20m^2[/tex]
[tex]W = 5m[/tex]
[tex]20m^2 = L * 5m[/tex]
Divide both sides by 5m
[tex]\frac{20m^2}{5m} = \frac{L * 5m}{5m}[/tex]
[tex]\frac{20m^2}{5m} = L[/tex]
[tex]L = \frac{20m^2}{5m}[/tex]
[tex]L = 4m[/tex]
So, we have that:
For Last Year
[tex]Length = 4m[/tex] and [tex]Width = 5m[/tex]
For this year:
[tex]Length = 3\ times\ longer[/tex]
[tex]Length = 3 * 4m[/tex]
[tex]Length = 12m[/tex]
[tex]Width = 2\ times\ wider[/tex]
[tex]Width = 2 * 5m[/tex]
[tex]Width = 10m[/tex]
So, for this year, we have:
[tex]Length = 12m[/tex] and [tex]Width = 10m[/tex]
Next, we calculate perimeter of fencing in both years.
[tex]Perimeter = 2 * (Length + Width)[/tex]
Last Year:
[tex]Perimeter = 2 * (4m + 5m)[/tex]
[tex]Perimeter = 2 * 9m[/tex]
[tex]Perimeter = 18m[/tex]
This Year:
[tex]Perimeter = 2 * (12m + 10m)[/tex]
[tex]Perimeter = 2 * 22m[/tex]
[tex]Perimeter = 44m[/tex]
To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.
[tex]Difference = 44m - 18m[/tex]
[tex]Difference = 26m[/tex]
Hence, there are 26 meters of fencing needed
A random sample of 2,500 people was selected, and the people were asked to give their favorite season. Their responses, along with their age group, are summarized in the two-way table below.
Among those whose favorite season is spring, what proportion are adults?
1.)250/1000
2.)250/2500
3.)475/2500
4.)250/475
5.)225/475
Answer:
250/475
Step-by-step explanation:
If m<1=55, find m<8.
A store bought a shirt for $20 dollars.
They sold it for some $23 dollars.
What is the percent of change here?
[tex]\mathrm {Hey, there!}[/tex]
Thanks for posting your question! Let's solve your problem:
The answer to your question is: 280% increase!
When we do percent of change, we will set up this ratio.
CHANGE IN QUANTITY (23 - 20)
------------------------------------------
ORIGINAL QUANTITY (3)
The change in quantity is : 23 - 20
The original quantity would be 3, 23 - 20 = 3.
Now, we will convert that into a fraction.
20 / 2 = 10
23 - 20 = 3
Fraction - 3/10
Make the fraction into a decimal.
3/10 = 0.15
Make the decimal into the percent.
0.15 = 15% increase
Best of Luck!
7. The vertices of a triangle are P(-7, -1). Q(-7, -8), and R(3. -3). Name the vertices of the
image reflected across the line y=x.
OPX4,7). Q18. 7), R3.-3)
OP/4.-7). Q18. -7). R33)
OP(-7). QI-S.-7), R(-3.3)
OPT+7). Q1-8. 7). R(-3, -3)
The vertices of the image triangle reflected across the line y = x are P'( -1, -7), Q'( -8, -7), and R'( -3, 3).
Therefore, the correct answer is:
P'( -1, -7), Q'( -8, -7), R'( -3, 3)
Here,
To find the image of the triangle vertices reflected across the line y = x, we need to swap the x-coordinates with the y-coordinates.
Original vertices of the triangle:
P(-7, -1)
Q(-7, -8)
R(3, -3)
Now, swap the x and y coordinates to get the reflected image:
Reflected image vertices:
P'( -1, -7)
Q'( -8, -7)
R'( -3, 3)
So, the vertices of the image triangle reflected across the line y = x are P'( -1, -7), Q'( -8, -7), and R'( -3, 3).
Therefore, the correct answer is:
P'( -1, -7), Q'( -8, -7), R'( -3, 3).
To learn more on reflection click:
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Find the midpoint of the segment with the following endpoints.
(-4,-9) and (4, -1)
Answer:
[tex](0,-5)[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Point (-4, -9)
Point (4, -1)
Step 2: Find midpoint
Substitute: [tex](\frac{-4+4}{2},\frac{-9-1}{2})[/tex]Add/Subtract: [tex](\frac{0}{2},\frac{-10}{2})[/tex]Divide: [tex](0,-5)[/tex]Standardization of Normal Distribution is the process of
Answer:
Step-by-step explanation:
Standardizing a normal distribution is to convert a normal distribution to the standard normal distribution. In real-world applications, a continuous random variable may have a normal distribution with a value of the mean that is different from 0 and a value of the standard deviation that is different from 1.
It is assumed that the test results for a class follow a normal distribution with a mean of 78 and a standard deviation of 36. If you know that a student's grade is greater than 72, what is the probability that it is greater than 84? What do I know? What do I want to find out? What do we expect the answer to be? How do I go from what I know to what I want to find? Does this answer seem reasonable?
Answer:
0.7143
- You know the minimum possible grade of the student
- You want to find out the probability that that grade which is greater than 72 is also greater than 84
- Expect the answer to be 0.7143
- The explanation/steps is given below
- The answer seems (and is) reasonable. You only created a new lower limit.
Step-by-step explanation:
Distribution Type: Normal
Mean: 78
Standard deviation: 36
Range of marks: [78 - 36], [78 + 36] = [42 to 114]
If you know that a student's grade is greater than 72, what is the probability that it's greater than 84?
In this case, the full probability level is between 72 and the upper limit of 114 (instead of between 42 and 114). First, find the fraction of this probability.
[114 - 72] ÷ [114 - 42] = 42/72 = 0.5833
So, the probability of a student's mark falling between 72 and 114 is 0.5833.
Now making this a whole interval, 114 - 72 = 42
What fraction of this interval of 42 will bear marks between 84 and 114?
[114 - 84] = 30
30/42 = 0.7143
Because of the first part of the question "If you know (are sure) that a student's grade is greater than 72...", your answer stops at 0.7143, since 72 was used as the lower limit.
At a carnival, Tammy bought 9 packs of 17 tickets each. She has used 36 of the tickets so far. How many tickets does she have left?
Answer: 117 tickets left
Step-by-step explanation:
The degree of the expression 4x5ymz is 10. What is the value of m?
Answer:
the answer is 4
Step-by-step explanation:
If the average price of a new one-family home is $246,300 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 60% of the market. Assume that the variable is normally distributed.
Answer:
Step-by-step explanation:
P(-a<z<a)=0.60, from the symmetry of normal distribution, P(z<a) = 0.60+ (1-0.60)/2 =
0.60+0.4/2
0.60+0.2
= 0.8
Considering the standard normal distribution table, we have a = 0.80, thus
z =(x-m)/std = 0.80
the maximum x = m + 0.80×std =
Where m = 246300
Std = 15000
246300+0.80×15000
= 246300+12000
= 258300
For the minimum x
x = m - 0.80×std
x = 246300-0.80×15000
246300-12000
= 234300
The difference between a number y and 9 is -34. What is the number?
Answer:
y-9=34
y=34+9
y= 43
Step-by-step explanation:
please Mark as brainliest
Answer:
y= -25 because if you add -25 to 9 it gives you -34
If the x-values of the table shown above are doubled and the y-values stay the same, it represents the function g(x). Construct the equation for g(x)
Answer:
The maximum value of the table t(x) has a greater maximum value that the graph g(x)
Step-by-step explanation:
Hope this helps :P
A city is approximately circular with a radius of 10.6 miles. Approximately 90,000 people live there. What is the population density of this city?
Answer:
513 people per square mile
Step-by-step explanation:
because
The list below shows the results of a survey of favorite ice-cream flavors among middle-school students.
• 18 students voted for chocolate.
• 12 students voted for strawberry.
20 students voted for vanilla.
What percentage of the students chose chocolate as their favorite ice-cream flavor?
Answer:36%
Step-by-step have 12+18+20 which equals 50 and 18 out of 50 is 36%
The percentage of the students who chose chocolate as their favorite ice cream flavor will be 36%
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
It is given that, there are 18 students voted for chocolate,12 students voted for strawberry and 20 students voted for vanilla.
The total number of students = 18+12+20 = 50
A percentage of the students chose chocolate as their favorite ice cream flavor is,
%choclate = (Number of students voted for chocolate / Total student)×100
%choclate =(18/50)×100
%choclate =36%
Learn more about the percentage here:
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Solve for the values of x and y
SOLVING LEFT-SIDED RIGHT TRIANGLE
Answer:
The value of the missing length of the side x=26 units
Step-by-step explanation:
The Pythagorean theorem states
[tex]\:a^2\:+\:b^2\:=\:x^2[/tex]
We will use the Pythagorean Theorem to solve for the missing side length.
[tex]24^2\:+\:10^2\:=\:x^2[/tex]
switch both sides
[tex]x^2=24^2+10^2[/tex]
[tex]x^2=576+100[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]x=\sqrt{676},\:x=-\sqrt{676}[/tex]
[tex]x=26,\:x=-26[/tex]
As x can not be negative.
Therefore, the value of the missing length of the side x=26 units
SOLVING LEFT-SIDED RIGHT TRIANGLE
Answer:
The value of the missing length of the side y=15 units
Step-by-step explanation:
Considering the right-sided right triangle
The Pythagorean theorem states
[tex]a^2\:+\:b^2\:=\:c2[/tex]
We will use the Pythagorean Theorem to solve for the missing side length.
[tex]15^2\:+\:y^2\:=\:\left(15\sqrt{2}\right)^2[/tex]
[tex]225+y^2=450[/tex] ∵ [tex]\left(15\sqrt{2}\right)^2=450[/tex]
[tex]y^2=225[/tex]
[tex]y=\sqrt{225},\:y=-\sqrt{225}[/tex]
[tex]y=15,\:y=-15[/tex]
As y can not be negative.
Therefore, the value of the missing length of the side y=15 units
can someone help me with this?
Answer:haha no
Step-by-step explanation:
Which term describes the figure? Please help
Answer:
C . None of these
Is the answer.
Step-by-step explanation:
Because parallel lines do not intersect.
And perpendicular lines form angle of 90°.
Answer:
None of the above.
Step-by-step explanation:
Those lines are intersecting lines. Parallel lines face each other and never meet. Perpendicular lines do meet, but they form a 90 degree angle, which this doesn't. Intersecting lines meet, but don't form a 90 degree angle.
Hope this helps!
Help me pleaseeeeeee
The answer is the second one
Explanation above
Answer:
The correct answer is "y = 3/4x"
Step-by-step explanation:
Slope-intercept form is y2-y1/x2-x1. If you place the points into slope-intercept form you get 6-3/8-4. After reducing the fractions you will get 3/4. So the equation is y = 3/4x.
PLEASEEE HELPPPPPPP :))))))))
Answer:
False
Explanation
The x-intercept of a line occurs when the line intersects with the x-axis.
Find the area of the parallelogram.
Answer:
Step-by-step explanation:
Area of parallelogram = base * height
= 3 * 3
= 9 square units
When the following quadratic equation is written in standard form, what is the value of "c"?
Answer:
it's 2
Step-by-step explanation:
a= -3/4
b=0
c=2
About 7% of the population has a particular genetic mutation. 400 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 400.
Answer:
5.10 people
Step-by-step explanation:
Calculation to Find the standard deviation for the number of people with the genetic mutation
Using this formula
Standard deviation = √ ( n * p * q)
Where,
n = 400
p = .07
q = 100%-7% = 93% or .93
Let plug in the formula
Standard deviation =√400*07*.93
Standard deviation =√26.04
Standard deviation = 5.10 people
Therefore the standard deviation for the number of people with the genetic mutation is 5.10 people.
What are the answers and explain
Answer:
Step-by-step explanation:
answers to what
1.2, 1.05, 1.5, 1.005
In order from smallest to largest
Answer:
1.005, 1.05, 1.2, 1.5
Step-by-step explanation:
think of it as:
1.200
1.050
1.500
1.005
then we can see that from least to greatest, it is: 1.005, 1.05, 1.2, 1.5
Which shows the best estimate of the quotient of 4,346 +82?
between 50 and 60
between 60 and 70
between 500 and 600
between 600 and 700
Answer:
between 500 to 600 because I like
Select the scenario below that demonstrates sampling bias. Select the correct answer below:
A. Justin wants to estimate the ethnic background distribution of residents of his town. He collects data from 1000 randomly selected town residents by using a random number generator.
B. To estimate the mean salary of accountants at her bank, Patricia collects data by recording the salaries of all accountants included in 12 randomly selected bank sites.
C. Elizabeth wants to estimate the mean vacation days of coworkers at her company. She collects data by selecting a random group of coworkers within her department.
D. To estimate the mean satisfaction level of coworkers at her company, Annie collects data by recording the satisfaction level of every 25th coworker on the list of coworkers after a randomly selecting first coworker.
Answer:
C. Elizabeth wants to estimate the mean vacation days of coworkers at her company. She collects data by selecting a random group of coworkers within her department.
Step-by-step explanation:
Sampling Bias is case, in which some section of population have higher or lower chance of being selected in sample than others.
'Elizabeth wants to estimate the mean vacation days of coworkers at her company. She collects data by selecting a random group of coworkers within her department'. This case is of Convenience Sampling, where person selects sample only as per his/ her convenience.
Elizabeth has conveniently chosen sample workers from her department, so they have higher chance of being in sample, others have lesser chance. Hence, this is Sampling Bias
In the diagram below, triangle A is similar to triangle B. What is the value of n?
In the diagram below, triangle A is similar to triangle B. What is the value of n?
Answer:
n = 2
Step-by-step explanation:
Since ∆A is similar to ∆B, therefore, the ratio of their corresponding sides would be equal.
Thus:
[tex] \frac{10}{n + 2} = \frac{6}{3} [/tex]
[tex] \frac{10}{n + 2} = 2 [/tex]
Multiply both sides by (n + 2)
[tex] \frac{10}{n + 2}(n + 2) = 2(n + 2) [/tex]
[tex] 10 = 2n + 4 [/tex]
Subtract 4 from each side
[tex] 10 - 4 = 2n + 4 - 4 [/tex]
[tex] 6 = 2n [/tex]
Divide both sides by 2
[tex] \frac{6}{2} = \frac{2n}{2} [/tex]
[tex] 3 = n [/tex]
n = 2
A friend gives you two baseball cards for your birthday. Afterward you begin collecting them. You buy the same number of cards once each week. The equation y=4x +2 describes the number of cards ,y, you have after x weeks.
Answer: x and y have the same absolute value. Also, x is a positive number, and y is a negative number.
Step-by-step explanation:
Answer:
The slope is 2, while the y-intercept is 4. This equation represents starting with 4 cards and adding 2 cards each week.
Step-by-step explanation:
Given the equation which describes the number of cards, y, you have after x weeks: y=2x+4
Comparing this with the slope intercept form of the equation of the line: y=mx+b, where:
m is the slope
b is the y-intercept.
We have that:
Slope, m=2.
A slope of 2 indicates that you buy 2 cards per week.
The y-intercept of the line, b=4.
This is the starting value. In this case, it represents the number of cards you were given by your friend.
The slope is 2, while the y-intercept is 4. This equation represents starting with 4 cards and adding 2 cards each week.
What compound inequality describes the graph shown below?
You have asked to design a rectangle box with a square base and an open top. The volume of the box must be620 cm to the 3rd power. the cost of the material for the base is $0.40 per square cm and the cost of the material for the side is $0.10 per square cm.How to determine the dimension of the box that will minimize the cost of manufacturing. What is the minimum cost? in dollars and rounded to the nearest cent.
Answer:
$69.21
Step-by-step explanation:
Since the box has a square base the length and breadth of the box will be equal. Let it be [tex]x[/tex]
Let h be the height of the box
V = Volume of the box = [tex]620\ \text{cm}^3[/tex]
[tex]x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}[/tex]
Now surface area of the box with an open top is given
[tex]s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}[/tex]
Differentiating with respect to x we get
[tex]\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}[/tex]
Equating with zero
[tex]0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74[/tex]
Double derivative of the function
[tex]\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0[/tex]
So, x at 10.74 is the minimum value of the function.
[tex]h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37[/tex]
So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.
The total area of the sides is [tex]4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2[/tex]
The area of the base is [tex]x^2=10.74^2=115.35\ \text{cm}^2[/tex]
Cost of the base is $0.40 per square cm
Cost of the side is $0.10 per square cm
Minimum cost would be
[tex]230.7\times 0.1+0.4\times 115.34=\$69.21[/tex]
The minimum cost of the box is 69.21 dollars.