The length of the diagonal of the garden with 19.6 square feet and 4.3 length is : 6.3 feet
What is a rectangle?A rectangle is a quadrilateral with four sides and four vertices each of angle 90°.
Analysis:
Area of rectangle: 19.6 square feet
length of one side = 4.3 feet
width of one side = Area/length = 19.6/4.3 = 4.6 feet
the diagonal and width and length of a rectangle for a right angle triangle.
To find the diagonal, we use Pythagoras theorem
[tex](diagonal)^{2}[/tex] = [tex](length)^{2}[/tex] + [tex](width)^{2}[/tex]
[tex](diagonal)^{2}[/tex] = [tex](4.3)^{2}[/tex] + [tex](4.6)^{2}[/tex]
[tex](diagonal)^{2}[/tex] = 39.7
diagonal = [tex]\sqrt{39.7}[/tex] = 6.3 feet
in conclusion, the diagonal of the rectangular garden is 6.3 feet
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A bag contains 4 red pencils, 6 blue pencils, and 5 green pencils. A pencil is randomly selected, its color is recorded, and it is returned to the bag. This is repeated 1350 times.
The expected number of times to select a green pencil when the pencils are selected 1350 times is 450
How to determine the number of times?The distribution of the pencils is given as:
Red = 4
Blue = 6
Green = 5
The total number of pencil is:
Total = 4 + 6 + 5
Evaluate the sum
Total = 15
The probability of selecting a green pencil is:
P(Green) = 5/15
Evaluate
P(Green) = 1/3
So, the expected number of times is:
E(x) = 1/3 * 1350
Evaluate
E(x) = 450
Hence, the expected number of times to select a green pencil is 450
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Answer: The Answer is 450
Explanation: I took the test and got it right
Hope this helps :)
Please Help! Look at the picture down below. I don't understand this question at all.
A taste test asks people from Texas and California which pasta they prefe
brand A or brand B. This table shows the results.
Brand A
Brand B Total
Texas
80-
45
125
California
90
60
150
Total
170
105
275
9
A person is randomly selected from those tested.
What is the probability that the person is from Texas, given that the person
prefers brand A? Round your answer to two decimal places.
Using it's concept, it is found that there is a 0.4545 = 45.45% probability that the person is from Texas, given that the person prefers brand A.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 176 people who prefer brand A, and of those 80 are from Texas, hence the probability is given by:
p = 80/176 = 0.4545.
0.4545 = 45.45% probability that the person is from Texas, given that the person prefers brand A.
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Hurry pls with the answer
Answer:
C
Step-by-step explanation:
Plug in x, for example if you plug in x in 3x+1 you will get y which is 4, and the same for the rest.
How long is it:
a) from 18 00 until 09 45 the next day?
b) from 07 30 until 01 45 the next day?
c) from 18 50 until 09 20 the next day?
d) from 08 10 until 00 35 the next day?
Answer:
a) 15h 45m gap
b) 06h 15m gap
c) 14h 30m gap
d) 16h 25m gap
Answer:
a) 3 hours and 45 mins
b) 18 hours and 15 minmins
c) 2 hours and 30 mins
d) 16 Hours and 20 mins
I might be wrong...
I) find, in terms of π, the curved surface area of a cone with circular base diameter 10cm and height 12cm.
Ii) if the cone is made of paper, and the paper is flattened out into the sector of a circle, what is the angle of the sector?
[tex]\pi[/tex]
Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
( i )
given - a cylinder with base diameter = 10 cm ! And , height = 12 cmTo find - CSA of conenow ,
since diameter = 10 cm
[tex]\implies \: radius = \frac{10}{2} = 5 \: cm \\ [/tex]
now ,
[tex]slant \: height \: ( \: l \: ) = \sqrt{h {}^{2} + r { }^{2} } \\ \\ \implies \: \sqrt{(12) {}^{2} + (5) {}^{2} } \\ \\ \implies \: \sqrt{144 + 25} \\ \\ \implies \: \sqrt{169} \\ \\ \implies \: 13 \: cm[/tex]
now ,
[tex]CSA \: of \: cone = \pi \: \times r \times l \\ \\ \implies \: \pi \: \times 5 \times 13 \\ \\ \implies \: 65\pi \: cm {}^{2} [/tex]
_____________________________
_____________________________
( ii )
now when we flatten the cone ,
the slant height becomes the radius of the sector , while the arc becomes the circumference of cone !
[tex]\therefore \: radius = l = 13 \: cm \\ \\ arc \: length = circumference = 2\pi \: r[/tex]
now ,
[tex]s = d \: \theta \: ( \: for \: a \: sector \: ) \\ \\ \therefore \: l\theta \: = 2\pi \: r \\ \\ \implies \: \theta = \frac{2\pi \: r}{l} \\ \\ \implies \: \theta = \frac{2 \times \pi \times 5}{13} \\ \\ \implies \: \theta \: = \frac{10\pi}{13} \\ \\ \implies \theta \: = \: 0.77 \pi [/tex]
hope helpful :D
Step-by-step explanation:
i)
remember, the radius is half the diameter !
the overall surface area of a cone (base circle + "mantle", the lateral, curved surface) is
A = pi×r × (r + sqrt(h² + r²))
so, only the "mantle" or lateral curved stave area is
pi×r × sqrt(h² + r²) = pi×5 × sqrt(12² + 5²) = pi×5×sqrt(169) =
= pi×5×13 = 65×pi cm²
ii)
the length of the arc of the sector is the circumference of the circle, that was the base of the original cone.
that is
2×pi×r = 2×pi×5 = 10×pi cm
the total circumference of the large circle containing that sector is
2×pi×r' = 2×pi×sqrt(h² + r²)
as the radius r' of the circle containing the sector (representing the "mantle" of the cone) is the lateral height of the cone (the distance along its side from the base to the top). and that is per Pythagoras simply the square root of the sum of the square of the inner height and the square of the base radius.
in our case that is
2×pi×sqrt(12² + 5²) = 2×pi×13 = 26×pi cm
the angle of the sector is then 10/26 of the total of 360° for the whole circle :
360 × 10/26 = 138.4615385...°
or, if you need this in terms of pi too, remember that 360° are represented by 2×pi (the arc length of the standard circle).
2×pi × 10/26 = pi × 20/26 = pi × 10/13 =
= 0.769230769... × pi
The first four numbers of a sequence are 3,9,27, and 81. If this sequence continues, what are the next two numbers?
Answer:
243 and 729
Step-by-step explanation:
next will be 81 x 3= 243
next will be 243 x 3= 729
Answer:
243 729
Step-by-step explanation:
r = common ratio = 3 means multiply each number by 3 to get the next number
3 9 27 81 (81*3 ) ( 81*3)*3
3 9 27 81 243 729
Another teacher has a monthly salary of $2000 She spends $943 per month on rent Her monthly salary then increases by 15% What percentage of her new monthly salary does the teacher spend on rent?
Answer:
47.15%
Step-by-step explanation:
Getting a raise of 15% would increase the teacher's salary by 300. 943 of 2300 is 47.15%.
hi lots of work today
Answer:
x-axis
Step-by-step explanation:
The lateral line on a graph is known as the x-axis
Choose the inequality that represents the following graph.
Answer:
The correct answer is B
Step-by-step explanation:
The blue line points to the left and has a closed circle, so the value of x has to be less than or equal to -4.
Please explain, too! Thank you :)
Answer:
∠POS = 128°
Step-by-step explanation:
Angles on a straight line always add up to 180°
Therefore:
∠POS + ∠POQ = 180° (as they are the angles on line SOQ)
∠POS + 52° = 180°
∠POS = 180° - 52°
∠POS = 128°
[tex]\huge{\color{magenta}{\fbox{\textsf{\textbf{Answer}}}}}[/tex]
To find :-
The value of ∠POS
Given :-
∠POQ = 52°
Solution :-
The ∠POQ + ∠POS lies on same line SOQ. So they are linear pair and linear pair angle forms sum of 180°.
∠POS + ∠POQ = 180° {linear pair}
∠POS + 52° = 180°
∠POS = 180° - 52°
∠POS = 128°
Result :-
The angle ∠POS is 128°.
What is the explicit arithmetic sequence formula for 72, 48, 24,....?
Answer:
f(x)=x-24
Step-by-step explanation:
It is decreasing by 24. Hope this helps!
Answer:
The formula is f(x) = x-24
Step-by-step explanation:
72-24=48
48-24=24 and so on
If x = -6, which inequality is true? question 1 options: -5 - 3x > 10 -3 - 5x < -14 1 - 2x > 13 2 - x < -3
Answer:
The inequality true is -5-3x > 10-3 (I hope thats the selection kinda hard to tell with spaces.
Step-by-step explanation:
By solving each side of each inequality your able to compare if the statements are true. -5-3x Is 13 and 10-3 is seven making that inequality the only true one in the selection.
help me asap i need help i dont understand
Answer:
∠A + ∠B = 90°
Step-by-step explanation:
Complementary angles are angles which, combined, add to 90°. Therefore, an equation displaying the relationship between two complementary angles may look like this: ∠A + ∠B = 90°.
Ok but... what's 6+6? i've been stuck on this forever and i can't see to find the answer. 0-0
Answer:
12
Step-by-step explanation:
How much cardboard is needed to make the tissue box above? Square inches 8 3 3
The amount of cardboard needed to make a cuboid box of dimensions 8 inch, 3 inches and 3 inches is 114 sq. inches.
What is the surface area of cuboid?Let the three dimensions(height, length, width) be x, y,z units respectively.
The surface area of the cuboid is given by
[tex]S = 2(a\times b + b\times c + c\times a)[/tex]
For this case, tissue box is almost cuboid shaped.
Also, its dimensions are given being 8 inches, 3 inches and 3 inches.
Suppose we measure the amount of cardboard needed in terms of area, then, the amount of cardboard needed to make that box(without any whole, full cuboid) is equal to the area of its surface(either outer or inner if we assume 0 inches thickness of cardboard),
Thus, we get:
Amount of cardboard needed = surface area of cuboid box with dimensions 8 by 3 by 3 (in inches)
= [tex]2(8 \times 3 + 3 \times 3 + 3 \times 8) = 114 \: \rm in^2[/tex]
Thus, the amount of cardboard needed to make a cuboid box of dimensions 8 inch, 3 inches and 3 inches is 114 sq. inches.
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Can someone help on these two?, Its okay if you can only do one.
Answer:
5 shaded region area = 100 - 78.5 = 21.5 sqm
6 c
Step-by-step explanation:
5. area of square = 10 x 10 = 100 sqm
area of circle = pi * r^2 = pi (5)^2 = 78.5 sqm (take pi as 3.14)
shaded region area = 100 - 78.5 = 21.5 sqm
6. for a straight line, equation is y = mx + b
m = 5, b = -12 in this case
10 more than the difference of 6m and 3. Write the sentence as a numerical expression
NEED HELP ASAP
Answer:
10 + 6 - 3
Step-by-step explanation:
a lot is 50m by 38m. A house 30m by 9m is built on the lit. How much area is left over
Answer:
1480m^2
Step-by-step explanation:
1. Fine the area of the full lot: 35 x 50 = 1750
2. Find the area of the house: 270
3. Subtract the area of the house from the lot: 1750 - 270 = 1480
Your answer is 1480m^2.
What is the midpoint for a segment with endpoints (3,5) and (7,-1)?
(10.4)
B
(5,2)
С
(1,3)
D
(4,4)
Answer:
B
Step-by-step explanation:
took the test >:)
What value of f makes the equation f+4.02=6.5 true?
Answer:
[tex]f = 2.48[/tex]
Step-by-step explanation:
Step 1: Subtract 4.02 from both sides
[tex]f + 4.02 = 6.5[/tex]
[tex]f + 4.02 - 4.02 = 6.5 - 4.02[/tex]
[tex]f = 2.48[/tex]
Answer: [tex]f = 2.48[/tex]
Hope this helps! Let me know if you have any questions
PLEASE HELP ASAP WILL GIVE BRAINLIEST !!
You are planning to join a gym. Muscles Gym costs $100 to join and $25 each month (C= 100 + 25x) and Cardio Gym costs
nothing to join and $50 each month (C = 50x).
Solve this linear system and choose the true statement below. (Look carefully at the order of the numbers in the solution.)
A.) The solution is (200, 4). This means that it will cost me $200 to go to either gym 4 times.
B.) The solution is (4, 200). This means that it will cost me $200 to go to either gym 4 times.
C.) The solution is (4, 200). This means that at 4 months of
membership, either gym will cost $200.
D.) The solution is (200, 4). This means that at 4 months of
membership, either gym will cost $200.
One figure models 1/4 as 4 of 12 equal parts of a whole. The other models 1/3 as 1 of 3 equal parts of a whole. What is true about the equal parts for the two fractions?
The correct option for this questions is Option C
Equivalent Fractions for 4/12:
1/3, 2/6, 3/9, 4/12, 5/15, 6/18, 7/21, 8/24, 9/27, 10/30, 11/33, 12/36, 13/39, 14/42, 15/45, 16/48, 17/51, 18/54, 19/57, 20/60, and so on ...
How do you find equivalent fractions?Two frations are equivalent when they have the same value when written in lowest terms. The fraction 8/24 is equal to 1/3 when reduced to lowest terms. To find equivalent fractions, just multiply the numerator and denominator of that reduced fraction (1/3) by any interger number, ie, multiply by 2, 3, 10, 30.
2/6 is equivalent to 4/12 because 1 x 2 = 2 and 3 x 2 = 63/9 is equivalent to 4/12 because 1 x 3 = 3 and 3 x 3 = 94/12 is equivalent to 4/12 because 1 x 3 = 4 and 3 x 3 = 12Equivalent fractions may look different, but when you reduce then to the lowest terms you will get the same value. If any fraction is not reduced to lowest terms, you can get other equivalent fractions just dividing both numerator and denominator by the same number.
Thus, option c is your answer
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Evaluate i=∫c(sinx 9y)dx (3x y)dy for the nonclosed path abcd in the figure. A=(0,0),b=(4,4),c=(4,8),d=(0,12)
The value of the integration for a non closed path abcd will be -88
What is cyclic integration?
Cyclic integration is the integration over a closed loop.Close the path by connecting D to A. Then by Green's theorem, the integral over the closed path ABCDA - which I'll just abbreviate C - is
[tex]\oint_c(Sin(x)+9y)dx+(4x+y)dy\\\\\\[/tex]
[tex]=\int\int \dfrac{\partial (4x+y)}{\partial x} -\dfrac{\partial (Sin(x)+9y)}{\partial y}dxdy[/tex]
[tex]=-5\int\int dxdy[/tex]
(where int(C ) denotes the region interior to the path C )
The remaining double integral is -5 times the area of the trapezoid, which is
[tex]-5 \int\int dxdy=\dfrac{-5}{2}\times (12+4)\times 4=-160[/tex]
To get the line integral you want, just subtract the integral taken over the path DA. On this line segment, we have x = 0 and dx = 0, so this integral reduces to
[tex]\int _{DA} ydy=\int\limits^0_{12} y dy=-\int\limits^{12}_0ydy =-72[/tex]
Then
[tex]\int_{ABCD}9Sin(x)+9y)dx+(4x+y)dy=-160-(-72)=-88[/tex]
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The histogram below shows the estimated monthly salaries of company employees with different years of experience. a bar graph entitled estimated monthly salary has years of experience on the x-axis, and estimated monthly salary on the y-axis. with 13 to 15 years of experience, an employee makes 3,000 dollars; with 16 to 18 years, they make 4,000; with 19 to 21 years, they make 5,000. how might the graph be misleading? the scale on the y-axis overemphasizes the difference in salaries between different experience levels. the scale on the y-axis underemphasizes the difference in salaries between different experience levels. the scale on the x-axis overemphasizes the difference in salaries between different experience levels. the scale on the x-axis underemphasizes the difference in salaries between different experience levels.
The scale on the y-axis overemphasizes the difference in salaries between different experience levels.
What is a histogram?The histogram is one of the ways of data presentation. Usually, it utilizes rectangles plotted on the x and the y axis.
In this case, the graph is misleading in the sense that; the scale on the y-axis overemphasizes the difference in salaries between different experience levels.
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Answer:
A
Step-by-step explanation:
Henry deposited $1700 in a savings account
that earned 2.1% compound interest. If he
made no more deposits, how much would he
have in his account after 72 months?
The amount that will be there in Henry's account after a period of 6 years will be $1,925.765.
What is compound interest?Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
The amount that Henry put in the account is $1700, while the compound interest on that account is 2.1% annually. Also, the time for which the amount is kept in the account is 72 months which is equal to 6 years.
Now, the total amount in Henry's account after a period of 6 years will be,
[tex]\rm Account\ Balance = \$1700(1+0.021)^6[/tex]
[tex]= \$1700(1.021)^6\\\\= \$1,925.765[/tex]
Hence, the amount that will be there in Henry's account after a period of 6 years will be $1,925.765.
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Katrina's ski boots cost 8%more than her skis.her ski boots cost $162 .Which equation can be used to find the cost c,of Katrina's skis.
A. C + 0.08c=162
B C +0.8c =162
C C+ 0.08c =162
D C+ 0.8c=162
please help me
PLSSS I NEED HELP I’LL MARK BRAINLYESS OR WTV IS CALLED
Answer: y= -7 y= -5 y= -3 y= -1
Step-by-step explanation:
Given p = (6,6) and q = (-5,- 3) find the magnitude of 2p + 3q
A. 2√3
B. 3√2
C.√144
D.14
[tex]\begin{cases} p= < 6,6 > \\ q= < -5,-3 > \end{cases}\qquad \qquad \stackrel{2p}{2 < 6,6 > }~~ + ~~\stackrel{3q}{3 < -5,-3 > } \\\\\\ \stackrel{2p}{ < (2)(6)~~,~~(2)(6) > }~~ + ~~\stackrel{3q}{ < (3)(-5)~~,~~(3)(-3) > } \\\\\\ < 12~~,~~12 > ~~ + ~~ < -15~~,~~-9 > \implies < 12-15~~,~~12-9 > \\\\\\ \stackrel{2p~~ + ~~3q}{\boxed{ < -3~~,~~3 > }}\qquad \qquad ||\stackrel{magnitude}{ < -3,3 > }||\implies \sqrt{(-3)^2 + (3)^2}\implies 3\sqrt{2}[/tex]
PLEASE ANSWER AS FAST AS U CAN
Answer:
1) 14π
2) 47.1
Step-by-step explanation:
1)
Circumference = 2πr
where r = radius
given radius is 7mi
So we have C = 2πr and r = 7
==> plug in 7
C = 2π(7)
==> multiply 2 and 7
C = 14π
we leave our answer in terms of pi so this is our final answer.
2)
Again Cicumference = 2πr
The given radius here is 7.5
So C = 2πr
R = 7.5 and π = 3.14
==> plug in values
C = 2(3.14)(7.5)
==> multiply 2 and 3.14
C = 6.28(7.5)
==> multiply 6.28 and 7.5
C = 47.1
