The are of the triangle below is 9/20 square centimeters. What’s is the length of the base? Express your answer as a fraction in simplest form.
Answers
Answer:
6/5
Step-by-step explanation:
For this you need to clear the formula for the area which is bxh/2=A, now you need to clear the base and the formula would be b=Ax2/h, and would be (9/20)x2/ 3/4 equal to 18/20 / 3/4 and gives the result of 72/60,now you need to simplify and the simplest form is 6/5
The base of the triangle with area of 9 / 20 centimetres squared and height of 3 / 4 centimetres is 6 / 5 centimetres.
Area of a trianglearea of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area = 9 / 20 cm²
height = h = 3 / 4 cm
b = ?
Hence.
area of the triangle = 1 / 2 bh
9 / 20 = 1 / 2 × 3 / 4 × b
9 / 20 = 3 / 8 b
cross multiply
9 × 8 = 20 × 3b
72 = 60b
b = 72 / 60
b = 12 / 10 = 6 / 5
learn more on triangle here: https://brainly.com/question/2773823
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[tex] \frac{3}{2} [/tex]
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Step-by-step explanation
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Convert to the given unit. 65 m = cm
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Answer:
65m = 6500 Cm.
Step-by-step explanation:
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A cylindrical tank has a base of diameter 12 ft and height 5 ft. The tank is full of water (of density 62.4 lb/ft3).(a) Write down an integral for the work needed to pump all of the water to a point 4 feet above the tank.(b) Write down an integral for the fluid force on the side of the tank.(c) How would your answer to part (a) change if the tank was on its side
Answers
Answer:
a. 71884.8 π lb/ft-s²∫₀⁵(9 - y)dy
b. 23961.6 π lb/ft-s²∫₀⁵(5 - y)dy
c. 99840π lb/ft-s²∫₀⁶rdr
Step-by-step explanation:
.(a) Write down an integral for the work needed to pump all of the water to a point 4 feet above the tank.
The work done, W = ∫mgdy where m = mass of cylindrical tank = ρA([5 + 4] - y) where ρ = density of water = 62.4 lb/ft³, A = area of base of tank = πd²/4 where d = diameter of tank = 12 ft.( we add height of the tank + the height of point above the tank and subtract it from the vertical point above the base of the tank, y to get 5 + 4 - y) and g = acceleration due to gravity = 32 ft/s²
So,
W = ∫mgdy
W = ∫ρA([5 + 4] - y)gdy
W = ∫ρA(9 - y)gdy
W = ρgA∫(9 - y)dy
W = ρgπd²/4∫(9 - y)dy
we integrate W from y from 0 to 5 which is the height of the tank
W = ρgπd²/4∫₀⁵(9 - y)dy
substituting the values of the other variables into the equation, we have
W = 62.4 lb/ft³π(12 ft)² (32 ft/s²)/4∫₀⁵(9 - y)dy
W = 71884.8 π lb/ft-s²∫₀⁵(9 - y)dy
.(b) Write down an integral for the fluid force on the side of the tank
Since force, F = ∫PdA where P = pressure = ρgh where h = (5 - y) since we are moving from h = 0 to h = 5. So, P = ρg(5 - y)
The differential area on the side of the tank is given by
dA = 2πrdy
So. F = ∫PdA
F = ∫ρg(5 - y)2πrdy
Since we are integrating from y = 0 to y = 5, we have our integral as
F = ∫ρg2πr(5 - y)dy
F = ∫ρgπd(5 - y)dy since d = 2r
substituting the values of the other variables into the equation, we have
F = ∫₀⁵62.4 lb/ft³π(12 ft) × 32 ft/s²(5 - y)dy
F = 23961.6 π lb/ft-s²∫₀⁵(5 - y)dy
.(c) How would your answer to part (a) change if the tank was on its side
The work done, W = ∫mgdr where m = mass of cylindrical tank = ρAh where ρ = density of water = 62.4 lb/ft³, A = curved surface area of cylindrical tank = 2πrh where r = radius of tank, d = diameter of tank = 12 ft. and h = height of the tank = 5 ft and g = acceleration due to gravity = 32 ft/s²
So,
W = ∫mgdr
W = ∫ρAhgdr
W = ∫ρ(2πrh)hgdr
W = ∫2ρπrh²gdr
W = 2ρπh²g∫rdr
we integrate from r = 0 to r = d/2 where d = diameter of cylindrical tank = 12 ft/2 = 6 ft
So,
W = 2ρπh²g∫₀⁶rdr
substituting the values of the other variables into the equation, we have
W = 2 × 62.4 lb/ft³π(5 ft)² × 32 ft/s²∫₀⁶rdr
W = 99840π lb/ft-s²∫₀⁶rdr
Can you pleaseee help me I beg u !
Answers
I need to get to twenty characters so
Answer:
[tex]x < - 7[/tex]
the answer is option C
The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the association's name. The association's by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if meeting is necessary. Suppose the association decided to conduct a test of hypothesis using the following null and alternative hypotheses:
H0: p = 0.6
HA: p > 0.6
Define a Type II Error in the context of this problem.
A.They conclude that more than 60% of the association wants a name change when, in fact, that is not true.
B.They conclude that exactly 60% of the association wants a name change when that is, in fact, true.
C.They conclude that more than 60% of the association wants a name change when that is, in fact, true.
D.They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.
Answers
Answer:
D.They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.
Step-by-step explanation:
Type 2 error results in a statistical analysis when a false null is incorrectly accepted.
The hypothesis Given :
H0: p = 0.6
HA: p > 0.6
The null in this context is that, the percentage of members who wants a name change is 60% ; while the alternative is that more than 60% wants a name change.
In this context, accepting a false null means Making a conclusion that exactly 60% wants a name change while it is actually FALSE.
PLZ HELP I SHALL GIVE BRAINLIESST
Answers
fjdjdjdjdjcj random letters, work in picture
Answer:
610m^2
Step-by-step explanation:
break the polygon into two rectangles as shown in attachment
I have labeled the new length A
A = 50 - 18
A = 32 m
area of rectangle 1 = l x w
= 5 x 32
= 160m^2
area of rectangle 2 = l x w
= 18 x 25
= 450 m^
area of polygon = rectangle 1 + rectangle 2
= 160 + 450
= 610m^2
Please help me with this
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Answer:
πr2
Step-by-step explanation:
Answer:
i think the answer is
Step-by-step explanation:
πr^2
Write the equation of the graph
Answers
Answer:
x + 2y - 5 = 0
Step-by-step explanation:
We can see that , the graph passes through (0,2.5) and (5,0) . Therefore the ,
x intercept is 5 y intercept is 2.5We can use the intercept form of equation as ,
=> x/a + y/b = 1
=> x/5 + y/2.5 = 1
=> x + 2y/5 = 1
=> x + 2y = 5
=> x + 2y -5 = 0 .
This equation can be verified by plotting the graph .[ Refer to attachment ]
Hence the equation of the line is x + 2y - 5 = 0 .HELP HELP JIMTHOMPSON5910
Answers
Note: I had to write FA in that order, and not the other way around, due to the filter.
Part 1
There are 2 answers and they are
Choice 2) FA/AB = FG/BCChoice 3) AB/FA= BC/FG------------------
Explanation:
For any of the answer choices we are involving the following segments
ABFABCFGSo we're only involving four segments. They are paired up to form fractions which are then set equal to one another. Notice how segment FA is smaller than AB, and how they correspond together. Going from FA to AB means go from small to big. If we write the ratio FA/AB, then can think of it as small/big.
Also note that FG is smaller than BC, and both segments also correspond as they are both going downhill from left to right. So we can write FG/BC to set equal to the first fraction we set up.
Overall, the proportion FA/AB = FG/BC is one valid answer.
The other valid answer is AB/FA= BC/FG. This equation is formed by applying the reciprocal to both sides of the first equation mentioned.
We can rule out choice 1 because FA/AB is small/big, but BC/FG is big/small. The two don't match up. Choice 4 is ruled out because AB does not correspond to FG.
=====================================================
Part 2
Answer: 27------------------
Explanation:
Through similar ideas mentioned in part 1, we can form this proportion
FA/AB = AG/AC
we have the format small/big = small/big
We are given these values either in word form or through the diagram
FA= 15AB = FA+FB = 15+30 = 45AC = 81Plug in those given values and isolate AG
FA/AB = AG/AC
15/45 = AG/81
15*81 = 45*AG .... cross multiply
1215 = 45AG
45AG = 1215
AG = 1215/45 .... divide both sides by 45
AG = 27
Segment AG is 27 inches long.
Which inequalities have the solution set graphed on the number line? Select two options. A number line going from negative 6 to positive 2. An open circle is at negative 4. Everything to the left of the line is shaded. x less-than negative 4 Negative 4 less-than x Negative 4 less-than-or-equal-to x Negative 4 greater-than x x greater-than negative 4
Answers
Answer:
[tex]x < -4[/tex]
[tex]-4 > x[/tex]
Step-by-step explanation:
Given
Description of number line
Range: -6 to 2
Open circle on -4
Left shaded
Required
Select the number line
From the question, we understand that the left side of the number line is shaded.
This means that the inequality is [tex]\le[/tex] or [tex]<[/tex]
Also, the open circle on -4 means that we discard [tex]\le[/tex].
So, the inequality is:
[tex]x < -4[/tex]
The opposite of the above inequality is:
[tex]-4 > x[/tex]
Answer:
A, D.
Step-by-step explanation:
good luck with edge :)
A model of a house uses a scale of 1 inch : 5 feet. The height of the model is 5 5/8
inches. What is the height of the actual house?
Answers
Answer:
scale = 1 in: 5 ft
= 1inch x 5 5/8 = 5.625
5 ft x 5 5/8 28.125 ft
The actual height of the house is 28.125 ft
The area of a rectangle is 99 ft”, and the length of the rectangle is 7 ft more than twice the width. Find the dimensions of the rectangle
Answers
Answer: Width = 5.5ft
Length = 18ft
Step-by-step explanation:
Let the width of the rectangle be x
Since the length of the rectangle is 7 ft more than twice the width. This mean that the length will be:
= (2 × x) + 7 = 2x + 7.
Therefore, length × width = area
x × (2x + 7) = 99
2x² + 7x = 99
2x² + 7x - 99 = 0
2x² + 18x - 11x - 99 = 0
2x(x + 9) - 11(x + 9) = 0
(2x - 11) = 0
2x = 0 + 11
2x = 11
x = 11/2
x = 5.5
The width is 5.5ft
Length = 2x + 7 = 2(5.5) + 7 = 11+7 = 18ft
Osa is trying to estimate V8. So far she has 2.8, but she wants one more digit to make it more accurate. What value would you add to Osa's estimate of V8? How can you tell that your estimate is more accurate than Osa's
[tex] \sqrt{8} [/tex]
[tex]2.8[/tex]
?
Answers
If you rotated the shape around the line, which three-dimensional figure would be formed?
O A cone
O B. sphere
O C. cylinder
D. pyramid
Answers
Answer:
c cylinder
Step-by-step explanation:
Solve for z.
z
7
= 8
z =
Answers
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Exact Form:
z=0,7√8
Decimal Form:
z=0,1.34590019…
Hope this helps!
Have a great day!
- Hailey : )
Henry is mixing concrete.To make
concrete he needs to mix cement,
sand and gravel in the ratio 4:3:1 by
weight. Henry needs to make 120 kg
of concrete. He has 65 kg of cement,
40 kg of sand and 15 kg of gravel.
Which ingredient is Henry short of?
Answers
Answer:
Sand
Step-by-step explanation:
120kg = (4 + 3 + 1) units = 8 units
1 unit = 120 ÷ 8 = 15kg
Calculating required quantities:
Cement: 4 units = 4(15) = 60kg
Sand: 3 units = 3(15) = 45kg
Gravel: 1 unit = 1(15) = 15kg
Comparing these values to those given in the question, he is short of sand.
WHATS THE ANSWER?? answer ASAP NO FILE AT ALL
Answers
Answer:
A
Step-by-step explanation:
Answer:
it is A because the shape is the same and is just facing a different way
Step-by-step explanation:
What is 7845 times 3000^[2] divided by 90+3^85×(2)
Answers
Answer: 7.1835091
Step-by-step explanation:
Back to Content
QUIZ:
Foundations - Systems of Equations
Which expression is equivalent
Please help
Answers
Answer:
3
Step-by-step explanation:
Solve this system of linear equations. Separate
the x- and y-values with a comma.
-2x = 8 - 6y
-15x = 21 - 6y
Answers
Answer:
Your solution is (-1, 1).
Step-by-step explanation:
-2x = 8 - 6y
-15x = 21 - 6y
Let's solve this through elimination.
Right away I can see that our y-values are the same. We want to eliminate one variable at a time, so let's make one of the -6y's a positive by multiplying each term in the equation by -1.
-15x = 21 - 6y
-1(-15x = 21 - 6y)
15x = -21 + 6y
Now we have a new equation in our system.
-2x = 8 - 6y
15x = -21 + 6y
Now, eliminate by performing each action given by the terms.
-2x = 8 - 6y
15x = -21 + 6y
___________
13x = -13
Divide both sides by 13 to isolate x.
x = -1
Now that we know x, plug it back into one of the original equations to find y.
-2x = 8 - 6y
-2(-1) = 8 - 6y
Multiply.
2 = 8 - 6y
Subtract 8 from both sides.
-6 = -6y
Divide both sides by -6.
y = 1
Your solution is (-1, 1).
Check your answer by plugging both values into one of the original equations.
-15x = 21 - 6y
-15(-1) = 21 - 6(1)
Multiply.
15 = 21 - 6
Add 6 to both sides.
15 = 15
Your answer is correct.
Hope this helps!
Answer:
(-1,1)
Step-by-step explanation:
-2x = 8 -6y *
-15x = 21 - 6y
Solve for -6y:
-6y = -8 - 2x *
-15x = 21 - 6y
Substitute the given value of 6y into second equation, you get:
-15x = 21 -8 - 2x
Solving this equation for x gets you:
x = -1
Substitute this value (x = -1) into the equation (-6y = -8 - 2x):
-6y = -8 - 2x (-1)
This provides y:
y = 1
Ms. Medina gives 9 students each 3 Jolly Ranchers. Then she divides
the rest of the Jolly Ranchers in her bag up between those 9 students.
if she started with 72 Jolly ranchers, how many extra Jolly Ranchers
did she give them?
Answers
Answer:
45
Step-by-step explanation:
9 × 3 = 27
started with 72
72 - 27 = 45
Please help me with my math guys really need it
Answers
Answer:
The answers are given in the pictures. One of them was an opinionated question, so you can just put whatever you want there. I put my opinion just in case.
Step-by-step explanation:
19 less than 28
Write as a algebraic expression
Answers
Choice A ) 28 - 19
Answer:
A
Step-by-step explanation:
A sphere shaped orange has a diameter of 7 centimeters. Find the volume of the orange to the nearest tenth.
Answers
22cm^3
Step-by-step explanation:
My education system is different so I dont know what nearest tenth would mean in this .
But going mathematically:
Its diameter is 7 centimetres.
So to find its volume we can use the formula pi/d or pi/r^2
Now, 22/7÷7 would be 22cm³.
Two analysts are going to compute confidence intervals for the unknown population mean lifetime of batteries being used in a particular brand of cellphones. The 1st analyst selects a random sample of batteries and computes a 95% confidence interval that has a margin of error of .85 hours. The 2nd analyst selects a random sample of batteries and computes a 99% confidence interval that has a margin of error of .70 hours. Both samples have the same standard deviation of 4 hours. Which analyst will have a wider interval
Answers
Answer:
Due to the higher margin of error, the 1st analyst will have a wider interval.
Step-by-step explanation:
Width of a confidence interval:
The width of a confidence interval is twice its margin of error, meaning that the sample with the largets margin of error will be wider.
1st analyst:
Margin of error of 0.85, so width of 0.85*2 = 1.7
2nd analyst:
Margin of error of 0.7, so width of 0.7*2 = 1.4
Which analyst will have a wider interval?
Due to the higher margin of error, the 1st analyst will have a wider interval.
A 40-inch piece of rope is cut into 4 equal pieces. How long is each piece in feet?
Answers
Answer:
10!
Step-by-step explanation:
Because 40*10= 4
and we all know 4/10=40 so there you go! Go succeed!
Answer: 5/6
Step-by-step explanation:
If you chose \(\frac{5}{6}\) foot, you are correct. If you chose 10 feet, you forgot to convert inches to feet. If you chose 1 foot, you thought that there were 10 inches in a foot. If you chose \(\frac{1}{10}\)foot, you wrote 1 over the number of inches because you were unsure how to write fractions in terms of feet.