mr. jones has a patio in the sahpe of a trapezoid. a round fountain having a circumference of 14 pi linear feet is placed in the corner as showin in the accompanying diagram. to the nearest square foot, how much of the patio s area ins not taken up by the fountanin? reall tha the circumferencie of a circle is calculated using c = 2
Answers
The area of the patio not taken up by the fountain is 241ft²
Please find attached an image of the patio
Area of the patio not taken up by the fountain = area of patio - area of fountain
The patio is in a shape of a trapezoid. Thus, the area of the patio can be determined by using the formula for the area of a trapezoid
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Characteristics of a trapezoid
It has 4 vertices It has 4 edges If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogramArea of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height
Taking a look at the image, we are not provided with the height of the trapezoid, just the parallel sides and the hypotenuse.
Pythagoras theorem can be used to determine the the height of the trapezoid
The Pythagoras theorem : a² + b² = c²
where a = height
b = base = 20 ft - 12 ft = 8ft
8ft / 2 = 4
c = hypotenuse
a² + 4² = 25²
a² = 625 - 16
a² = 609
√609 = 24.68 ft
Area of the trapezoid = 0.5 x (20 + 12) x 24.68 = 394.88 ft²
The fountain is in the shape of a circle.
Area of a circle = πr²
Where : = π = pi = 22/7
R = radius
The radius would have to determined from the circumference
circumference of a circle = 2πr
14π = 2πr
r = 14π / 2π
r = 7
Area of the circle = [tex]\frac{22}{7}[/tex] × 7²
[tex]\frac{22}{7}[/tex] × 49 = 154 ft²
Area of the patio not taken up by the fountain = 394.88 ft² - 154 ft² = 240.88ft²
To round off to the nearest square, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.
The tenth digit is greater than 5, so one is added to 0. The number becomes 241ft²
Learn more about how to determine the area of a trapezoid here : https://brainly.com/question/23814640?referrer=searchResults
Related Questions
For the partially complete factorization, find the other binomial which will complete the factorization n^2-8n-20=(n+2)(_____)
Answers
Answer:
(n-10)
Step-by-step explanation:
Jdjdjdhbejdudjkdff
PLEASE HELP
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
Y=-3x+1
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Answers
The equation is already solved for y
It's in y = mx+b form where
m = -3 = slope
b = 1 = y intercept
The graph is shown below. It's a straight line through the two points (0,1) and (1,-2).
Note that (0,1) is the y intercept. We use the slope = -3 = -3/1 to move 3 units down and 1 unit to the right to arrive at (1,-2).
F(x)=x^2 what is g(x)
Answers
Answer:
stop spamming
Step-by-step explanation:
Is the following polynomial or not
5xy^2+3x^2y-2x^2y^2
Answers
9514 1404 393
Answer:
is a polynomial
Step-by-step explanation:
The expression is a sum of products.
Each product involves a numerical value and a product of variables to positive integer powers.
These meet the requirements for an expression to be a polynomial, so ...
the given expression is a polynomial
According to the website www.costofwedding, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U. S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767.
Choose the statement that is the best interpretation of the confidence interval.
I. That probability that the flowers at a wedding will cost more than $698is greater than 5%.
II. In about 95%of all samples of size 40,the resulting confidence interval will contain the mean cost of flowers at weddings.
III. We are extremely confident that the mean cost of flowers at a wedding is between $701and $767
A) II only
B) I only
C) III only
D) II and III are both correct
Answers
Answer:
D) II and III are both correct.
Step-by-step explanation:
The Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The cost of flowers for a wedding is $698. The 95% of all samples of size is 40 and the confidence interval will be mean cost of flowers at wedding. There is confidence that mean cost of wedding flowers is between $701 to $767.
What is the value of 1/6 + 1/12 + 2/6
Answers
Answer:
7/12
Step-by-step explanation:
1/6 +1/12+2/6
=1×2/6×2 +1/12+2×2/6×2
=2/12+1/12+4/12
final answer is
= 7/12
1/6 + 1/12 + 2/6
= 2/12 + 1/12 + 4/12
= (2 + 1 + 4)/12
= 7/12
On May 1st, Jay’s mom gives him 1 cent. Each day, she pays him double the amount she paid the day before. How much money did Mike earn in total by May 15?
Answers
Answer: $1.83
Step-by-step explanation:
1. Solve this problem: 1+2+4+6+8+10+12+14+16+18+20+22+24+26. There are 15 numbers for 15 days. You want to solve this because each day is doubled. For example: first day is 1 cent, second day is 2 cents, third day is 4 cents, and so on.
2. Answer is 183 cents.
3. Convert 183 cents to dollars.
4. Your answer is $1.83.
Hope it helps!
Answer:
$1.83.
You start with one cent, and add two more cents after that day.
please solve quick
Answers
Answer:
x = 5
AC = 6
DC = 8
Step-by-step explanation:
∆ABC ~ ∆CDE
Therefore, [tex] \frac{AB}{ED} = \frac{AC}{DC} [/tex]
AB = 3
ED = 4
AC = x + 1
DC = x + 3
Plug in the values and solve for x:
[tex] \frac{3}{4} = \frac{x + 1}{x + 3} [/tex]
Cross multiply
[tex] 3(x + 3) = 4(x + 1) [/tex]
[tex] 3x + 9 = 4x + 4 [/tex]
[tex] 3x - 4x = -9 + 4 [/tex]
[tex] -x = -5 [/tex]
[tex] x = 5 [/tex]
Plug in the value of x and find AC and DC
AC = x + 1 = 5 + 1 = 6
DC = x + 3 = 5 + 3 = 8
0.3,1/5,1/2,0.706,7/8,57.1%
Place following in ascending order
Answers
Answer:
the answer is 0.31/ 5.1/8.57.1% /207067
Step-by-step explanation:
ascending order from the smallest to the largest
what is the graph of −36≤2x+4(x−3)
Answers
Solve for x: 2x – 1] + 5 < 13 please send help
Answers
Answer:
Step-by-step explanation:
2|x-1|+5 < 13
2|x-1| < 8
|x-1| < 4
-4 < x-1 < 4
-3 < x < 5
Find the equation of the tangent line at the point (0,1) of the graph of the function f(x) = x^3 - 2x + 1 ?
Answers
9514 1404 393
Answer:
y = -2x +1
Step-by-step explanation:
The derivative of the function is ...
f'(x) = 3x^2 -2
so the slope at x=0 is f'(0) = -2. In slope-intercept form, the equation of the tangent line is ...
y = -2x +1
if (ax+b)(x-3) = 4x^2+cx-9 for all values of x, what is the value of c? a) -9 b) -6 c) 6 d) 9
Answers
Answer:
c=-9
Step-by-step explanation:
Hello,
[tex](ax+b)(x-3)=ax(x-3)+b(x-3)=ax^2-3ax+bx-3b\\\\=ax^2+(b-3a)x+(-3b) \\\\\text{And it should be equal to } 4x^2+cx-9[/tex]
We can identify the like terms so:
a = 4
b-3a = c
3b = 9 <=> b = 3
So c = 3 - 3*4 = 3-12 = -9
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Monique makes $11 per hour delivering pizzas. Monique works Monday
through Friday, and on average she earns $20 a day in tips. If Monique
made no less than $450 for one week, find an inequality for the number
of hours she worked
Answers
Answer:
x > 39 hours
Step-by-step explanation:
Let x be the number of hours she worked.
11x - is how much she would get paid for working for x hours
11x + 20 > 450
11x > 430
x > 39 hours
Hope that helped!!! k
Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on 3 trips, and for each trip Lennox gets 300 dollars. On a single trip, a truck delivers 50 packs, and each pack contains 12 kilograms of apples. Overall, Lennox sells 4500 dollars worth of apples in a week. How much does Lennox get for a single kilogram of apples?
Answers
Answer:
$0.50
Step-by-step explanation:
Each trip transports 50 packs at 12 kg each, for a total of 600 kg. That trip nets $300 in income.
Lennox gets paid ($300)/(600 kg) = $0.50/kg, or 50¢ for 1 kg of apples
Answer:5 trucks
Step-by-step explanation: in kahn it’s 4500 divided by 900 because she makes 300 a trip which makes 900$ a truck
i will rate you brainliest
Answers
Answer:
Option (2)
Step-by-step explanation:
In an arithmetic progression,
[tex]a_1,a_2,a_3.........a_{n-1},a_n[/tex]
First term of the progression,
a = [tex]a_1[/tex]
Common difference 'd' = [tex](a_2-a_1)[/tex]
Recursive formula for the sequence,
a = [tex]a_1[/tex]
[tex]a_n=a_{n-1}+d[/tex]
By applying these rules in the recursive formula,
[tex]a_1=\frac{4}{5}[/tex]
[tex]a_n=a_{n-1}+\frac{3}{2}[/tex]
Common difference 'd' = [tex]\frac{3}{2}[/tex]
Therefore, Option (2) will be the answer.
A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are given below where x denotes seed density, and y denotes lawn quality.x 1 1 2 3 3 3 4 5y 30 40 40 40 50 65 50 50The sample linear correlation coefficient is r=0.600. At the 1% significance level, do the data provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated?
Answers
Answer:
I think it -1.50 to 10.58
Step-by-step explanation:
Emily thinks the perfect tomato sauce has 8 cloves of garlic in every 500 mL, of sauce. Raphael's tomato sauce has 121 cloves of garlic in every 900 mL of sauce. What will Emily think of Raphael's tomato sauce? Choose 1 answer: Choose 1 answer: (Choice A) A It is too garlicky. (Choice B) B It is not garlicky enough. (Choice C) C It is perfect.
Answers
Answer:
A
Step-by-step explanation:
Let's find the ml per garlic for each sauce. Emily's has 1 clove of garlic for 62.5 ml. Raphael's has 1 clove of garlic for 7.438... ml. So, A, it will be too garlicky.
-8 + (-15)
Evaluate this expression
Answers
Answer:
-23
Step-by-step explanation:
-8+(-15) means that you are subtracting 15 from -8. So you end up with -8-15=-23.
In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
a. Convenience sampling
b. Cluster sampling
c. Stratified sampling
d. Systematic sampling
Answers
Answer:
C Stratified sampling
Step-by-step explanation:
Stratified sampling : Stratified sampling is a type of sampling technique in which the total population is divided into smaller groups or strata to complete the sampling process. The strata is formed based on some common characteristics in the data of the population.
One of the advantage of stratified random sampling is that it covers important population characteristics in the sample.
Which property is not used to simplify the following expression 2* (x+5)+7x=(2x+10)+7x
Answers
Hence, the commutative property of addition is not used.
What is an expression?
A mathematical expression is in form of variables and constants separated by their arithmetic operation.
As we know that, there are three types of properties they are associative property which is [tex](a+b) + c = a + (b+c)[/tex],
Distributive property which is [tex]a(b+c) = ab + ac[/tex],
Commutative property which is [tex]a + b = b + a[/tex].
Here given that,
[tex]2 (x+5)+7x=(2x+10)+7x[/tex]
[tex](2x+10)+7x=(2x+10)+7x[/tex] ( distributive property of multiplication)
[tex](2x+7x)+10=(2x+7x)+10[/tex] ( it is associative property of addition)
[tex](8x)+10=(8x)+10[/tex] ( it is a commutative property)
Hence, the commutative property of addition is not used.
To know more about the distributive property
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Help me please! thanks
Answers
9514 1404 393
Answer:
5. (a) Polygon Angle-Sum Theorem
6. (c) 360°
Step-by-step explanation:
5. The sum of the angles is shown as 540°. The theorem that tells you the sum of angles in an n-gon is the "polygon angle sum theorem."
__
6. The sum of exterior angles around any (convex) polygon is 360°. (This is where the angle-sum theorem comes from.)
A line contains the piont (4,5) and is perpendicular to a line with a slope of -2/3. Write an equarion of the line satisfying the given conditions. Write the answer in slope-intercept form
Answers
Answer:
[tex]y=\frac{3}{2}x-3.5[/tex] or, preferably, [tex]y=\frac{3}{2}x-\frac{7}{2}[/tex]
Step-by-step explanation:
First is to find the perpendicular slope. In this case, you swap the numerator and denominator and then multiply that fraction by -1.
In this case, -2/3's inverse slope is 3/2.
Now, the initial y=3/2 passes through 7.5,5
So, you must subtract 3.5 from that to make it pass through 4,5.
In this way, you get the answer in slope-intercept form.
Answer:
y = [tex]\frac{3}{2}[/tex] x - 1
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex] , then
y = [tex]\frac{3}{2}[/tex] + c ← partial equation in slope- intercept form
To find c substitute (4, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = [tex]\frac{3}{2}[/tex] x - 1 ← equation of line
A blue die and a red die are thrown. B is the event that the blue comes up with a 6. E is the event that both dice come up even. Write the sizes of the sets |E ∩ B| and |B|a. |E ∩ B| = ___b. |B| = ____
Answers
Answer:
Size of |E n B| = 2
Size of |B| = 1
Step-by-step explanation:
I'll assume both die are 6 sides
Given
Blue die and Red Die
Required
Sizes of sets
- [tex]|E\ n\ B|[/tex]
- [tex]|B|[/tex]
The question stated the following;
B = Event that blue die comes up with 6
E = Event that both dice come even
So first; we'll list out the sample space of both events
[tex]B = \{6\}[/tex]
[tex]E = \{2,4,6\}[/tex]
Calculating the size of |E n B|
[tex]|E n B| = \{2,4,6\}\ n\ \{6\}[/tex]
[tex]|E n B| = \{2,4,6\}[/tex]
The size = 3 because it contains 3 possible outcomes
Calculating the size of |B|
[tex]B = \{6\}[/tex]
The size = 1 because it contains 1 possible outcome
An experimental probability is ______ likely to approach the theoretical probability if the number of trials simulated is larger. A. as B. more C. less D. not
Answers
Answer:
B. More
Step-by-step explanation:
This is according to the law of large numbers
An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.
What is an experimental probability and theoretical probability?Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.
An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed
Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.
Learn more about probability here:
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The first step in a mathematical induction proof is to divide by n. (True or False).
Answers
Answer:
Step-by-step explanation:
Hello, this is false.
The first step of a mathematical induction proof is to prove the statement for the initial value, which is most of the time for n = 0 or n = 1.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What do we use mathematical induction for?
Answers
proving statements!
it's the very definition of it
Hope this helped ♥︎
7. 20x + 10 = 110
a. X= 1
b. X= 5
c. x= 12
Answers
Answer:
b x=5
Step-by-step explanation:
20x+10=110
20x+10-10=110-10
20x/20=100/20
x=5
Answer:
x=5
Step-by-step explanation:
20x + 10 = 110
Subtract 10 from each side
20x +10-10 = 110-10
20x = 100
divide by 20
20x/20 =100/20
x= 5
If the product of three identical numbers is 1000, find one of the number?
Answers
Answer:
10
Step-by-step explanation:
Three identical numbers whose product is 1000
10 * 10 * 10
Solve for x -3x-3=-3(x+1)
Answers
Step-by-step explanation:
[tex] - 3x - 3 = - 3(x + 1) \\ - 3x - 3 = - 3x - 3 \\ - 3x + 3x = - 3 + 3 \\ 0 = 0[/tex]
Step 1: Use 3 to open the bracket
Step 2 : Collect like terms and simplify
Answer = 0