Answers
Answer:
The answer is 2240m².
Step-by-step explanation:
Given that the formula of area of trapezium is A = 1/2×(a+b)×h where a and b represents the length and h is height :
[tex]area = \frac{1}{2} \times (a + b) \times h[/tex]
[tex]let \: a = 50 \\ let \: b = 90 \\ let \: h = 32[/tex]
[tex]area = \frac{1}{2} \times (50 + 90) \times 32[/tex]
[tex]area = \frac{1}{2} \times 140 \times 32[/tex]
[tex]area = 70 \times 32[/tex]
[tex]area = 2240 \: {m}^{2} [/tex]
Answer:
2,240 square meters
Step-by-step explanation:
The shape above is a trapezoid. Therefore, we can use the area formula for a trapezoid:
A=1/2(a+b) *h
where a is the short base, b is the long base is h is the height.
In this trapezoid, the short base is 50 meters , the long base is 90 meters and the height is 32 meters.
a= 50
b=90
h=32
A=1/2(50+90)*32
Add inside the parentheses first.
A=1/2(140)*32
Multiply 1/2 and 140, or divide 140 by 2.
A=70*32
Multiply 70 and 32
A=2240
Add appropriate units. In this case, the units are meters^2
A=2240 meters^2
The area of the playground is 2,240 meters^2
Related Questions
Find the focus and directrix of the parabola y = {(x + 2)2 – 3.
Answers
Answer:
focus: (-2, -2.75)directrix: y = -3.25Step-by-step explanation:
For focus-to-vertex distance "p", the equation of a parabola with vertex (h, k) can be written as ...
y = 1/(4p)(x -h)^2 +k
Comparing this to your equation, we see that ...
1/(4p) = 1
h = -2
k = -3
Solving for p, we find ...
1/(4p) = 1
1/4 = p . . . . . multiply by p
The parabola opens upward, so this means the focus is 1/4 unit above the vertex, and the directrix is 1/4 unit below the vertex.
focus: (-2, -2.75)directrix: y = -3.25Answer:
The focus is at (–2,–212) and the directrix is at y = –312.
Step-by-step explanation:
Find the focus and directrix of the parabola y=12(x+2)2−3.
got the answer right in the test.
Dan buys a car for £2100.
It depreciates at a rate of 2.2% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate.
Answers
Answer:
£472.92
Step-by-step explanation:
£2100(0.78)^6
Assume that in a statistics class the probability of receiving a grade of A equals .30 and the probability of receiving a grade of B equals .30. The probability that a randomly selected student from this class will receive either an A or a B equals.
a. .09
b. .6
c. .9
d. .3
Answers
Answer:
Answer D is correct
In a village
The number of houses and the number of flats are in the ratio 9:5
The number of flats and the number of bungalows are in the ratio 10:3
There are 30 bungalows in the village.
How many houses are there in the village?
Note: please make sure your final answer clear by writing ... houses
Answers
The number of houses are 180, and the number of flats are 100.
It is given that the number of houses and the number of flats ratio is 9:5 the number of flats and the number of bungalows ratio is 10:3.
It is required to find the number of houses in the village if the number of bungalows is 30.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The ratio of the number of houses and the number of flats:
= 9:5 and
The ratio of the number of flats and the number of bungalows :
=10:3
It means we can write the ratio of the number of houses and the number of flats = 18:10
And the ratio of the number of:
Houses : Flats : Bungalows = 18:10:3
But the number of bungalows are 30.
Then the ratios are:
180:100:30
Thus, the number of houses are 180, and the number of flats are 100.
Learn more about the fraction here:
brainly.com/question/1301963
there are 47 students in the science club. all but 5 of them went on a field trip to the planetarium. what is the total cost if each student who went on the field trip paid $7?
Answers
47-5=42
42*7=294
Answer:
$294
Step-by-step explanation:
First do 47-5=42
Next do 42x7=294
so the total is 294
You have $150 to spend at a store. If you shoes cost $30 and belts cost $25, write an equation that represents the different ways that you could spend a total of $150
Answers
Answer:
you could buy a pair of shoes and a belt still have 95 dollars to spend
Given that the area of a rectangle is 36 square cm and its length is 12 cm. Find the
width of the rectangle.
Answers
Explanation: since the formula for area of a rectangle is length*width= area, plug the numbers in. 12*x=36. So, what times twelve equals 36? 3! You can also view it like this, 36/12, which would also get you three.
Answer:
is 3
Step-by-step explanation:
because to find the area for a ractangle you have to multiply LxW and 12x3=36
Enter the y-coordinate of the solution. Round to the nearest tenth. 5x+2y=7 -2x+6y=9
Answers
Answer:
59/34
Step-by-step explanation:
5x+2y=7
-2x+6y=9
Multiply the top equation by 3:
15x+6y=21
Subtract the second equation from the first:
17x=12
x=12/17
Plug this back into one of the other equations to find y:
5(12/17)+2y=7
60/17+2y=7
2y=59/17
y=59/34
Hope this helps!
Adrian is training for a 5K race. She
ran 5.5 miles the first week, 7.25
miles the second week and 10 miles
the third week. On the average, how
many miles did she run per week?
Round to the nearest hundredth.
PLZ HELP PLZ!!!!!
Answers
To get this we divide the total miles she ran for the weeks by the no of weeks she ran.
Total miles =5.5 +7.25+10= 22.25 miles altogether.
no of weeks =3.
Average miles = 22.75 /3=7.583333≅7.58(nearest hundredth)
Please help! Correct answer only, please! Which of the following is one of the cheapest routes to pass through each vertex once starting and ending with Vertex "A" and using the Nearest Neighbor Algorithm. A. ABDCA, $890 B. ACDBA, $900 C. ABCDA, $960 D. None of the Above
Answers
Answer: c) ABCDA, $960
Step-by-step explanation:
The nearest Neighbor Algorithm states to choose the next vertex based only on the weights of the neighbor of that vertex.
Starting at A: Options are B = 220, C = 240, D = 310
Choose B because it has the smallest value.
From B: Options are C = 200, D = 210
Choose C because it has the smallest value.
From C: There is only one option --> D = 230 (we cannot choose A because it was our starting point and we haven't touched every vertex, yet).
From D: We touched all of the vertices so return to the starting point, A = 310
A → B → C → D → A --> 220 + 200 + 230 + 310 = 960
Notice that if we looked at the entire circuit first, this is NOT the optimum path. But this is the result using the Nearest Neighbor Algorithm.
Write down the 1st term in the sequence given by:t(n) =n^2+4
Answers
Answer:
5
Step-by-step explanation:
t(1) = [tex]1^{2} + 4 = 5[/tex]
if you’re good with set theory and word problems in math 30 please help with questions 42 and 43 !! real answers only !!
Answers
Answer: 42) 2, 3 43) 144
Step-by-step explanation:
42)
1. n(P) = 8 + 5 = 13 (not 8) This statement is False.
2. n(Q but not P) = 9 This statement is True!
3. n(neither P nor Q) = 2 This statement is True!
4. n(Q') --> (n (not Q) = 8 + 2 = 10 (not 8) This statement is False.
5. P ∪ Q = 8 + 9 - 5 = 12 (not 5) This statement is False.
43)
Fill in the Venn Diagram as follows (from left to right):
M only = 55 --> 89 - (17 + 4 + 13) = 55
M ∩ E = 17 --> 30 - 13 = 17
E only = 5 --> 46 - (17 + 13 + 11) = 5
B ∩ M = 4 --> 17 - 13 = 4
M ∩ E ∩ B = 13 --> given
B ∩ E = 11 --> 24 - 13 = 11
E only = 35 --> 63 - (13 + 4 + 11) = 35
(M ∪ E ∪ B)' = 4 --> given
Total = 144
find the next two terms in this sequence. 5,-5,10,-10,15,?,?
Answers
Answer:
I think the answer is -15
Evaluate 3(x - 1) + 2 when x= 5.
O A. 14
OB. 16
O c. 4
O D. 18
Answers
Answer:
A
Step-by-step explanation:
[tex]3(x-1)+2= \\\\3((5)-1)+2= \\\\3(4)+2= \\\\ 12+2=\\\\14[/tex]
Hope this helps!
Answer:
[tex]14[/tex]
Step-by-step explanation:
[tex]3(x - 1) + 2[/tex]
[tex]x= 5[/tex]
[tex]3(5 - 1) + 2[/tex]
[tex]3(4) + 2[/tex]
[tex]12 + 2[/tex]
[tex]=14[/tex]
(Bonus) A rectangular box has its edges changing length as time passes. At a par-ticular instant, the sides have lengthsa= 150 feet,b= 80 feet, andc= 50 feet.At that instant,ais increasing at 100 feet/sec,bis decreasing 20 feet/sec, andcisincreasing at 5 feet/sec. Determine if the volume of the box is increasing, decreasing,or not changing at all, at that instant.
Answers
Answer:
the volume of the box is increasing
dV = +310,000 ft^3/s
Step-by-step explanation:
Volume of a rectangular box with side a,b and c can be expressed as;
V = abc
The change in volume dV can be expressed as;
dV = d(abc)/da + d(abc)/db + d(abc)/dc
dV = bc.da + ac.db + ab.dc ......1
Given:
a= 150 feet,
b= 80 feet, and
c= 50 feet
ais increasing at 100 feet/sec,bis decreasing 20 feet/sec, andcisincreasing at 5 feet/sec
da = +100 feet/s
db = -20 feet/s
dc = +5 feet/s
Substituting the values into the equation 1;
dV = (80×50×+100) + (150×50×-20) + (150×80×+5)
dV = +400000 - 150000 + 60000 ft^3/s
dV = +310,000 ft^3/s
Since dV is positive, the volume of the box is increasing at that instant.
In a recent year, the Better Business Bureau settled 75% of complaints they received. You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Suppose your sample size is 113. What is the probability that the sample proportion will be at most 2 percent more than the population proportion
Answers
Answer:
what
Step-by-step explanation:
Function c(x) = 5x
If your input was 2, what is your output?
Answers
QUESTION 23 What does a BER of 10-5 mean? a. there will be no errors during transmission since the BER is so low b. does not mean anything unless associated with a transmission data rate (bit rate) c. there is a probability of one error for every 100,000 bits transmitted d. None of the above
Answers
Answer:
c. there is a probability of one error for every 100,000 bits transmitted
Step-by-step explanation:
What does a BER of 10-5 mean?
a. there will be no errors during transmission since the BER is so low b. does not mean anything unless associated with a transmission data rate (bit rate) c. there is a probability of one error for every 100,000 bits transmitted d. None of the above
BER is an abbreviation for bit error rate.
BER is the percentage of bits with errors divided by the total number of bits that have been transmitted, received or processed over a given time period.
The rate is typically expressed as 10 to the negative power.
BER is the digital equivalent to signal-to-noise ratio in an analog system.
In this case [tex]10^{-5}[/tex] is the same as writing [tex]1 \times10^{-5}[/tex] which means there is a probability of 1 error for every 100,000 bits transmitted.
Use the Law of Cosines to determine the length of the third side of the triangle.
4.1 cm
350
6.7 cm
a 1 = 4.9cm
b. 1 = 5.3cm
C.
1 = 5.5cm
d. 1 = 4.1cm
Answers
Corrected Question
Given a triangle with two sides 4.1 cm and 6.7cm and an Included angle of [tex]35^\circ[/tex]. Use the Law of Cosines to determine the length of the third side of the triangle.
Answer:
(D) 4.1cm
Step-by-step explanation:
Given a triangle with two sides 4.1 cm and 6.7 cm and an included angle of [tex]35^\circ[/tex].
Using Law of Cosines
[tex]a^2=b^2+c^2-2bc\cos A\\a^2=4.1^2+6.7^2-2*4.1*6.7\cos 35^\circ\\a^2=16.6958\\a=\sqrt{16.6958}\\a=4.09\\a \approx 4.1$ cm[/tex]
The correct option is D.
Which set of ordered pairs represents a function?
A {(2, 7), (2, 8), (3, 8)}
B {(3, 2), (3, 3), (3, 4)}
C {(4, 1), (5, 1), (4,4)}
D {(5, 6), (8, 6), (9, 6)}
does anyone know the answer
Answers
Answer:
Its D
Step-by-step explanation:
becasue the X is not repeating. the other are.
State whether the growth (or decay) is linear or exponential, and answer the associated question.
The value of a house is increasing by $1500 per year. If it is worth $120,000 today, what will it be worth in three
years?
Answers
Answer:
The growth is linear.
It will be worth $124,500 in three years.
Step-by-step explanation:
The value of a house is increasing by $1500 per year.
Fixed increase, that is, each year the value increases the same. So the growth is linear.
Value after t years:
The equation has the following format:
[tex]V(t) = V(0) + a*t[/tex]
In which V(0) is the current value and a is the yearly increase.
The value of a house is increasing by $1500 per year. It is worth $120,000 today.
Then [tex]V(0) = 120000, a = 1500[/tex]
So
[tex]V(t) = V(0) + a*t[/tex]
[tex]V(t) = 120000 + 1500*t[/tex]
What will it be worth in three years?
This is V(3).
[tex]V(t) = 120000 + 1500*t[/tex]
[tex]V(3) = 120000 + 1500*3[/tex]
[tex]V(3) = 124500[/tex]
It will be worth $124,500 in three years.
The growth is linear. The worth of the house after 3 years from now will be $124500.
Given information:
The value of a house is increasing by $1500 per year.
It is worth $120000 today.
The value of the house increases at a fixed rate of $1500 per year. So, it is a linear growth function.
Let the worth of the house after t years be V. The given situation can be written in equation form as,
[tex]V=V_0+rt\\V=120000+1500t[/tex]
Above equation represents the worth of house after t years.
So, the worth of the house after 3 years will be calculated as,
[tex]V=120000+1500t\\V(3)=120000+1500\times 3\\V(3)=120000+4500\\V(3)=124500[/tex]
Therefore, the worth of the house after 3 years from now will be $124500.
For more details, refer to the link:
https://brainly.com/question/24972665
Each limit represents the derivative of some function f at some number a. State such an f and a in each case.
lim √9 + h - 3 / h
h-->0
Answers
Answer:
a = 0f(h) = [tex]\frac{\sqrt{9+h} - 3}{h}[/tex]limit of the function is 1/6Step-by-step explanation:
The general form representing limit of a function is expressed as shown below;
[tex]\lim_{h \to a} f(h)[/tex] where a is the value that h will take and use in the function f(h). It can be expressed in words as limit of function f as h tends to a. Comparing the genaral form of the limit to the limit given in question [tex]\lim_{h \to 0} \frac{\sqrt{9+h} - 3}{h}[/tex], it can be seen that a = 0 and f(h) = [tex]\frac{\sqrt{9+h} - 3}{h}[/tex]
Taking the limit of the function
[tex]\lim_{h \to 0} \frac{\sqrt{9+h} -3}{h}\\= \frac{\sqrt{9+0}-3 }{0}\\= \frac{0}{0}(indeterminate)[/tex]
Applying l'hopital rule
[tex]\lim_{h \to 0} \frac{\frac{d}{dh} (\sqrt{9+h} - 3)} {\frac{d}{dh} (h)}\\= \lim_{h \to 0} \frac{1}{2} (9+h)^{-1/2} /1\\=\frac{1}{2} (9+0)^{-1/2}\\= \frac{1}{2} * \frac{1}{\sqrt{9} } \\= 1/2 * 1/3\\= 1/6[/tex]
A board of directors consists of 10 people, in how many ways can a chief executive officer, director, a treasurer, and a secretary be selected?
Answers
Answer:
The correct answer to the following question will be "5040".
Step-by-step explanation:
Given:
The number of directors,
n = 10
and they select on 4 peoples, then
Number of ways will be:
⇒ [tex]10_{P}_{4}[/tex]
⇒ [tex]\frac{10!}{10-4!}[/tex]
⇒ [tex]\frac{10!}{6!}[/tex]
⇒ [tex]\frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1!}{6\times 5\times 4\times 3\times 2\times 1!}[/tex]
⇒ [tex]5040[/tex]
A trip took you 5 hours and you traveled 283.5 miles. If you averaged 49 mph
for the first part of the trip and 60 mph for the 2nd part, how long did you drive
at each rate?
Answers
Answer:
1.5 hr and 3.5 hr
Step-by-step explanation:
Time in the first part= x
Time in the second part= 5 - x
49x+60(5-x)=283.549x+300-60x=283.511x=300-283.511x= 16.5x= 16.5/11x= 1.5 hrand5-x= 5-1.5= 3.5 hrsay true or false with explanation if both sin teta and cos tetanus are negative then teta is thrid quadrant angle.
Answers
Answer:
true
Step-by-step explanation:
hope it helps .
all the best
Justin and Hayley conducted a mission to a new planet, Planet X, to study arm length. They took a random sample of 100 Planet X residents. Then they calculated a 95% confidence interval for the mean arm length.
Answers
Answer:
The correct answer is I am 95% sure that this interval includes the population mean arm length.
Note: Kindly find an attached image or copy of the complete question to this solution below:
Sources: The complete question was researched from Quizlet and Course hero sites.
Step-by-step explanation:
Solution
From the given question, i will say that I am 95 % confident interval that this interval include the population mean arm length is correct because using sample mean and confidence level we can obtain an interval which gives us the certain level of confidence that population mean is within this interval and here we are 95% confident that population mean is within this interval.
John Calipari, head basketball coach for the national champion University of Kentucky Wildcats, is the highest paid coach in college basketball with an annual salary of million (USA Today, March 29, 2012). The following sample shows the head basketball coach's salary for a sample of schools playing NCAA Division basketball. Salary data are in millions of dollars.
University Coach's Salary University Coach's Salary
Indian 2.2 Syracuse 1.5
Xavier .5 Murry State .2
Texas 2.4 Florida State 1.1
Connecticut 2.7 South Dekota State .1
West Virginia 2.0 Vermont .2
A. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division 1 basketball (to 2 decimal).
B. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches (to 4 decimals).
C. what is the 95% confidence interval for the population variance (to 2 decimals)?
D. what is the 95% confidence interval for the population standard deviation (to 2 decimals)?
Answers
Answer:
A) sample mean = $1.36 million
B) standard deviation = $0.9189 million
C) variance confidence interval = ($0.40 million, $2.81 million)
D) standard deviation confidence interval = ($1.93 million , $0.79 million)
*since the sample size is very small, the confidence interval is not valid.
Step-by-step explanation:
samples:
$2.7 million$2.4 million$2.2 million$2 million$1.5 million$1.5 million$0.5 million$0.5 million$0.2 million$0.1 millionsample mean = $1.36 million
the standard deviation:
$2.7 million - $1.36 million = 1.34² = 1.7956$2.4 million - $1.36 million = 1.04² = 1.0816$2.2 million - $1.36 million = 0.84² = 0.7056$2 million - $1.36 million = 0.64² = 0.4096$1.5 million - $1.36 million = 0.14² = 0.0196$1.5 million - $1.36 million = 0.14² = 0.0196$0.5 million - $1.36 million = -0.86² = 0.7396$0.5 million - $1.36 million = -0.86² = 0.7396$0.2 million - $1.36 million = -1.16² = 1.3456$0.1 million - $1.36 million = -1.26² = 1.5876total $8.444 million / 10 = $0.8444 millionvariance 0.8444
standard deviation = √0.8444 = 0.9189
in order to calculate the confidence interval for the population variance we are going to use a chi-square distribution with 2.5% on each tail ⇒ table values 2.7004 and 19.023 enclose 95% of the distribution.
[(n - 1) x variance] / 2.7004 = (9 x 0.8444) / 2.7004 = 2.81
[(n - 1) x variance] / 19.023 = (9 x 0.8444) / 19.023 = 0.40
95% confidence interval = mean +/- 1.96 standard deviations/√n:
$1.36 million + [(1.96 x $0.9189 million)/√10] = $1.36 million + $0.57 million = $1.93 million
$1.36 million - $0.57 million = $0.79 million
PLEASE HELP!!! Find the equation of the line passing through the point (6,3) that is perpendicular to the line 4x−5y=−10. Enter your answers below. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12). Solution Step 1: Find the slope of the line 4x−5y=−10. Use a forward slash (i.e. "/") for all fractions (e.g. 1/2 for 12). m= _____ What would the perpendicular slope be? m= _____ Step 2: Use the slope to find the y-intercept of the perpendicular line. b= ____ Step 3: Write the equation of the line that passes through the point (6,3) that is perpendicular to the line 4x−5y=−10 y= ____ x+ Answer
Answers
Linear equations are typically organized in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = y-interceptPerpendicular lines have slopes that are negative reciprocals.
Example: 2 and -1/2Example: 3/4 and -4/3SolutionWe're given:
Perpendicular to [tex]4x-5y=-10[/tex]Passes through (6,3)1) Determine the slope
Let's first rearrange this equation into slope-intercept form:
[tex]4x-5y=-10\\-5y=-4x-10\\\\y=\dfrac{4}{5}x+2[/tex]
Notice how [tex]\dfrac{4}{5}[/tex] is in the place of m in y = mx + b. This is the slope of the give line.
Since perpendicular lines are negative reciprocals, we know the slope of the other line is [tex]-\dfrac{5}{4}[/tex]. Plug this into y = mx + b:
[tex]y=-\dfrac{5}{4}x+b[/tex]
2) Determine the y-intercept
We're also given that the line passes through (6,3). Plug this point into our equation and solve for b:
[tex]y=-\dfrac{5}{4}x+b\\\\3=-\dfrac{5}{4}(6)+b\\\\b=3+\dfrac{5}{4}(6)\\\\b=\dfrac{21}{2}[/tex]
Plug this back into our original equation:
[tex]y=-\dfrac{5}{4}x+\dfrac{21}{2}[/tex]
Answer[tex]y=-\dfrac{5}{4}x+\dfrac{21}{2}[/tex]
Find the slope of a line perpendicular to the graph of the equation. y = –8
Answers
Answer:
undefined
Step-by-step explanation:
y = -8 is a horizontal line with a slope of zero
A line that is perpendicular is a vertical line, which has a slope of undefined
Evaluating and solving functions
Use the function f(x)=240(0.7)^x to answer the following questions. Round your nearest answers to two decimal places.
Evaluate f(7) f(7)=
Determine x when f(×)=120
Answers
Answer:
Evaluate f(7)
[tex] f(7) = 240(0.7)^7 = 19.765[/tex]
Determine x when f(×)=120
[tex] 120 = 240 (0.7)^x[/tex]
We can derive both sides by 240 and we got:
[tex] 0.5 = 0.7^x[/tex]
Now we can apply natural log on both sides and we got:
[tex] ln(0.5)= x ln(0.7)[/tex]
And if we solve for the value of x we got:
[tex] x =\frac{ln(0.5)}{ln(0.7)}= 1.943[/tex]
And then the value of x = 1.943
Step-by-step explanation:
We have the following function given:
[tex]f(x) = 240(0.7)^x [/tex]
Evaluate f(7)
And we want to find [tex] f(7) [/tex] so we just need to replace x=7 and we got:
[tex] f(7) = 240(0.7)^7 = 19.765[/tex]
Determine x when f(×)=120
And for the second part we want to find a value of x who satisfy that the function would be equal to 120 and we can set up this:
[tex] 120 = 240 (0.7)^x[/tex]
We can derive both sides by 240 and we got:
[tex] 0.5 = 0.7^x[/tex]
Now we can apply natural log on both sides and we got:
[tex] ln(0.5)= x ln(0.7)[/tex]
And if we solve for the value of x we got:
[tex] x =\frac{ln(0.5)}{ln(0.7)}= 1.943[/tex]
And then the value of x = 1.943