work out the length of the container. Giver your answer to the nearest whole centimetre.
Dennis is making a container for tomato plant. The container will be in the shape of a cuboid.

missing length ? 40cm by 55cm.
The capacity of the container will be 180 litres.
1 Litre =1000cm cuboid.

Answers

Answer 1

Answer:

Length of the container = 82 cm

Step-by-step explanation:

Given:

Breadth of the container is 40 cm and height of the container is 55 cm

Volume of the container is 180 litres

To find: length of the container

Solution:

A container is in the shape of the cuboid.

Volume of cuboid = length × breadth × height

Put breadth = 40 cm , height = 55 cm and volume = 180 litres = 180000 [tex]cm^3[/tex]

(as 1 litre = 1000 [tex]cm^3[/tex] )

Therefore,

[tex]180000=length\,\times \,40\times 55\\length = \frac{180000}{40\times 55}=81.82\approx 82\,\,cm[/tex]


Related Questions

NEED GEOMETRY HELP ASAP PLEASE (12 POINTS)

Answers

Answer:

2 times the square root of 10

Step-by-step explanation:

If you make a right triangle and solve for the hypotenuse (the distance between P1 and P2), you will get 2 times the square root of 10.

Please mark this brainliest.

Answer: [tex]2\sqrt{10}[/tex]

Step-by-step explanation:

if you draw a triangle starting from P1 and go up to the y value of P2, the change in y is equal to 6.

From that point, go to the right until you hit P2 to get a change in x of 2.

Youre basically missing the hypotenuse of this triangle that you drew. Which is where the distance formula is derived from. 6^2 + 2^2 = s^2

You get √40 = s. It appears that they want you to simplify this square root. What are the two greatest numbers that multiply to equal 40 and atleast one of them has a perfect square root? That's 10 and 4. you can perfectly take the square root of 4, so go ahead and do that. Put that 2 outside of the square root. That gives you [tex]2\sqrt{10}[/tex]

Patrick’s luck had changed over night – but not his skill at mathematical reasoning. The day after graduating from college he used the $20 that his grandmother had given him as a graduation gift to buy a lottery ticket. He knew his chances of winning the lottery were extremely low and it probably was not a good way to spend this money. But he also remembered from the class he took in business analytics that bad decisions some-times result in good outcomes. So he said to himself, "What the heck? Maybe this bad decision will be the one with a good outcome." And with that thought, he bought his lottery ticket.The next day Patrick pulled the crumpled lottery ticket out of the back pocket of his bluejeans and tried to compare his numbers to the winning numbers printed in the paper. When his eyes finally came into focus on the numbers they also just about popped out of his head. He had a winning ticket! In the ensuing days he learned that his share of the jackpot would give him a lump sum payout of about $500,000 after taxes. He knew what he was going to do with part of the money, buy a new car, pay off his college loans, and send his grandmother on an all expenses paid trip to Hawaii. But he also knew that he couldn’t continue to hope for good outcomes to arise from more bad decisions. So he decided to take half of his winnings and invest it for his retirement. So what do you think? Who is right, Josh or Peyton? And more important, why?

Answers

Answer:

I assume Josh and Peyton are his friends and both gave him advice on what to do with half of the money from the big lottery win.

Let's say Josh said "save it or invest it for your retirement" and Peyton said "use it to keep playing the lottery.

We will now look at the sense in each piece of advice!

Step-by-step explanation:

JOSH

By investing the $250,000 (half of the money won), Patrick will be sure that the money is available for him anytime and would even have gotten interest, by the time he's ready to use it.

PEYTON

By playing the lottery continuously, Patrick could get lucky once in a while and win big again. How big though?

Analyzing with the figures given,

$20 gets Patrick a lottery ticket.

$250,000 will get him 12,500 lottery tickets!

Whether he's buying the tickets at once or he'll play the lottery once in a while, I'll say he has good chances of winning big again.

So if the probability of winning big after purchasing up to 12,500 tickets is close to 1, Patrick should play the lottery with the $250,000

If the probability of winning big after purchasing 12,500 lottery tickets is close to 0 (closer to 0 than it is to 1) then Patrick should invest the $250,000 in retirement.

In a sample of real estate ads, 62% of homes for sale have garages, 19% have swimming pools, and 15% have both features. What is the probability that a home for sale has a pool, a garage or both? State your answer as a decimal, not as a percent.

Answers

Answer:

66%

Step-by-step explanation:

15% of homes have both features.

The percentage of homes that have a pool and no garage is:

Pool only = 19% - 15% = 4%

The percentage of homes that have a garage and no pool is:

Garage only = 62% - 15% = 47%

Therefore, the percentage of homes that have a pool, a garage or both is:

[tex]P = 4\%+47\%+15\%\\P=66\%[/tex]

A survey found that​ women's heights are normally distributed with mean 63.3 in. and standard deviation 2.7 in. The survey also found that​ men's heights are normally distributed with a mean 67.3 in. and standard deviation 2.8. Complete parts a through c below.
a) most of the live characters at an amusement park have height requirements with a minimum of 4ft 9in and a maximum of 6ft 4in find the percentage of women meeting the height requirement
the percentage of woment who meet the height requirement?
(round to two decimal places as needed)
b) find the percentage of men meeting the height requirement
the percentage of men meeting the height requirement
(round to two decimal places as needed )
c) If the height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women what are the new height requirements
the new height requirements are at least ___ in. and at most ___ in.
(round to one decimal place as needed)

Answers

a) The percentage of women meeting the height requirement is approximately 99.99%.

b) The percentage of men meeting the height requirement is approximately 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) To find the percentage of women meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we need to calculate the proportion of women within this range using the normal distribution.

First, we standardize the height requirement using the formula:

Z = (X - μ) / σ

where X is the value (height), μ is the mean, and σ is the standard deviation.

For the lower limit (57 inches):

Z_lower = (57 - 63.3) / 2.7 ≈ -2.33

For the upper limit (76 inches):

Z_upper = (76 - 63.3) / 2.7 ≈ 4.70

Using a standard normal distribution table or calculator, we can find the area between -2.33 and 4.70. This represents the percentage of women meeting the height requirement.

The percentage of women meeting the height requirement is approximately 99.99%.

b) Similarly, for men meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we standardize the values:

For the lower limit (57 inches):

Z_lower = (57 - 67.3) / 2.8 ≈ -3.68

For the upper limit (76 inches):

Z_upper = (76 - 67.3) / 2.8 ≈ 3.11

Using the standard normal distribution table or calculator, we find the area between -3.68 and 3.11.

The percentage of men meeting the height requirement is approximately 99.95%.

c) To find the new height requirements that exclude the tallest 5% of men and the shortest 5% of women, we need to determine the corresponding Z-scores.

For men:

Z_upper_men = Z(0.95) ≈ 1.645

For women:

Z_lower_women = Z(0.05) ≈ -1.645

Using these Z-scores, we can calculate the new height requirements:

For the new lower limit:

X_lower = Z_lower_women * σ + μ

For the new upper limit:

X_upper = Z_upper_men * σ + μ

Substituting the values:

X_lower = -1.645 * 2.7 + 63.3 ≈ 58.53 inches

X_upper = 1.645 * 2.8 + 67.3 ≈ 71.78 inches

Therefore, the new height requirements are at least 58.5 inches and at most 71.8 inches.

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a) The percentage of women meeting the height requirement is 99.99%.

b) The percentage of men meeting the height requirement is 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) For women meeting the height requirement:

Given: Mean (μ) = 63.3 in.

Standard Deviation (σ) = 2.7 in.

So, Minimum height requirement:

= 4 ft 9 in

= 4 * 12 + 9

= 57 inches

and, Maximum height requirement:

= 6 ft 4 in

= 6 * 12 + 4

= 76 inches

We will calculate the Z-scores for these heights using the formula:

Z = (x - μ) / σ

For the minimum height requirement:

[tex]Z_{min[/tex] = (57 - 63.3) / 2.7 ≈ -2.33

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 63.3) / 2.7 ≈ 4.70

So, the the area between -2.33 and 4.70.

Thus, the percentage is  99.99%.

b) For men meeting the height requirement:

Given: Mean (μ) = 67.3 in., Standard Deviation (σ) = 2.8 in.

Minimum height requirement: 4 ft 9 in = 57 inches

Maximum height requirement: 6 ft 4 in = 76 inches

For the minimum height requirement:

[tex]Z_{min[/tex]= (57 - 67.3) / 2.8 ≈ -3.68

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 67.3) / 2.8 ≈ 3.11

So, the area between -3.68 and 3.11.

Thus, the percentage is 99.95%.

c) For the new height requirements:

For men:

[tex]Z_{upper_{men[/tex] = Z(0.95) ≈ 1.645

For women:

[tex]Z_{lower_{women[/tex] = Z(0.05) ≈ -1.645

For the new lower limit:

[tex]X_{lower} = Z_{lower}_{women} \sigma+ \mu[/tex]

For the new upper limit:

[tex]X_{upper} = Z_{upper}_{men} \sigma+ \mu[/tex]

Substituting the values:

[tex]X_{lower} = -1.645 * 2.7 + 63.3[/tex]

           = 58.53 inches

and, [tex]X_{upper} = 1.645 * 2.8 + 67.3[/tex]

                     = 71.78 inches

Therefore, the new height at least 58.5 inches and at most 71.8 inches.

Learn more about z score here:

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A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36 stores this year shows mean sales of 53 units of a small appliance with a standard deviation of 12 units. During the same point in time last year, a random sample of 49 stores had mean sales of 41 units with standard deviation 6 units.

It is of interest to construct a 95 percent confidence interval for the difference in population means ?1??2, where ?1 is the mean of this year's sales and ?2 is the mean of last year's sales.

Enter values below rounded to three decimal places.

(a) The estimate is: _________ .

(b) The standard error is: ____________________ .

Answers

Answer:

The 95% confidence interval for the difference of means is (7.67, 16.33).

The estimate is Md = 12.

The standard error is sM_d = 2.176.

Step-by-step explanation:

We have to calculate a 95% confidence interval for the difference between means.

The sample 1 (this year's sales), of size n1=36 has a mean of 53 and a standard deviation of 12.

The sample 2 (last year's sales), of size n2=49 has a mean of 41 and a standard deviation of 6.

The difference between sample means is Md=12.

[tex]M_d=M_1-M_2=53-41=12[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12^2}{36}+\dfrac{6^2}{49}}\\\\\\s_{M_d}=\sqrt{4+0.735}=\sqrt{4.735}=2.176[/tex]

The degrees of freedom are:

[tex]df=n_1+n_2-1=36+49-2=83[/tex]

The critical t-value for a 95% confidence interval and 83 degrees of fredom is t=1.989.

The margin of error (MOE) can be calculated as:

[tex]MOE=t \cdot s_{M_d}=1.989 \cdot 2.176=4.328[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = 12-4.328=7.67\\\\UL=M_d+t \cdot s_{M_d} = 12+4.328=16.33[/tex]

The 95% confidence interval for the difference of means is (7.67, 16.33).

Please help me with this math problem, urgent please

Answers

Answer:

see below

Step-by-step explanation:

To find the x intercept set y =0 and solve for x

6x+5y = -30

6x = -30

Divide by 6

x = -30/6 = -5

The x intercept is (-5,0)

To find the y intercept set x =0 and solve for y

6x+5y = -30

5y = -30

Divide by 5

y = -30/5 = -6

The y intercept is (0,-6)

To find the x-intercept set y =0. Solve for x.

6x+5y=-30

6x+5(0)=-30

6x+0=-30

6x=-30

x=-30/6

x=-5

The x-intercept is at (-5, 0)

To find the y-intercept set x =0. Solve for y.

6x+5y=-30

6(0)+5y=-30

0+5y=-30

5y=-30

y=-30/5

y=-6

The y-intercept is at (0, -6)

Write a simplified expression for the area of the rectangle below

Answers

Answer:

12x+40

Step-by-step explanation:

A=l*w

A=20(3/5x+2)

A=4*3x+20*2

A=12x+40

Answer:

[tex] = 12x + 40[/tex]

Step-by-step explanation:

[tex]area = l \times b \\ = 20 \times (\frac{3}{5} x + 2) \\ = \frac{60x}{5} + 40 \\ = 12x + 40[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

A pair of shoes usually sells for $70. If the shoes are 30% off, and sales tax is 5%, what is the total price of the shoes, including tax?

Answers

the answer to your question is 51.45$

Answer:

The total price of the shoes including tax is 51.45

Step-by-step explanation:

You could go about this 2 ways.

One way is if the shoes originally cost $70 and they are now 30% off, it basically means that the discounted price of the shoes is 70% of the original cost, which is $49. Then to find the total price including tax, you need to find 105% of 49, because you are adding 5% to the discounted price(100). When you do the math, you should get the answer 51.45.

The other way to do it is by first finding 30% of 70, which is 21, and then subtracting that from the original price(70) to get the discounted price, $49. Then you need to find 5% of 49 and then add that to 49 to find the total cost w/ tax, which is 51.45.

A population of protozoa develops with a constant relative growth rate of 0.7781 per member per day. On day zero the population consists of six members. Find the population size after four days. (Round your answer to the nearest whole number.) P(4)

Answers

Answer:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Step-by-step explanation:

For this case we can use the following function to model the population of protzoa:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Find the m∠YAX in the figure below

Answers

Answer:

76

Step-by-step explanation:

The two angles are vertical angles so they are equal

3x+7 = 4x-16

Subtract 3x from each side

3x-3x+7 = 4x-3x-16

7 = x-16

Add 16 to each side

7+16 = x-16+16

23 =x

We want YAX

YAX = 3x+7

3*23+7

69+7

76

URGENT!! MY LAST 2 QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!

13. Assume that you have a square. What can you conclude from applying the law of detachment to this conditional?

If you have a square, then you have a rectangle.

A) You have a quadrilateral.
B) All sides are the same length.
C) Squares and rectangles are the same.
D) You have a rectangle.


14. Which two theorems would justify that m∠4 = m∠6, given that m∠5 = m∠6 in the diagram below?
IMAGE BELOW
A) vertical angles theorem, consecutive interior angles theorem
B) vertical angles theorem, alternate interior angles theorem
C) right angles theorem, exterior angles theorem
D) corresponding angles theorem, angle addition theorem

Answers

Answer:

d: please note I am not sure about this but look at my reasoning and maybe you can find your own answer that you are sure about.

D: i am sure about this.

Step-by-step explanation:

From what I looked up, i believe what you are talking about is deductive reasoning, which is based off of facts. It can't be a or b because that wasn't defined in the statement. Squares and rectangles are not the same thing since you can have a square that is a rectangle, but a rectangle that is not a square, so D is correct.

corresponding angles i believe since they are matching

I know that the 2 lines are parallel because 5 and 6 are alternate interior angles since they are on opposite sides.

4 and 6 are not vertical or right angles, so it must be d, also they follow what a corresponding angle is, which is them being matching.

Answer:

13. B

14. D

Step-by-step explanation:

13. Law of Detachment says that if two statements are true then we can derive a third true statement. So, for example, say the first statement is that you are a human. Say the second statement is that you breathe. You can write this as: if you are a human, you breathe. In this case, if you have a square, then you have a rectangle. You have a quadrilateral.

14. 4 and 6 are corresponding angles, since you can tell that there are two parallel lines from angle 5 = angle 6. You can also use angle addition theorem.

What’s the correct answer for this?

Answers

Answer:

s = 4.43

Step-by-step explanation:

Using formula for bigger circle

s =r∅

Where s is the Arc length, r is rdius and ∅ is theta(angle)

8.84=5∅

∅= 8.84/5

Angle = 1.77 radians

So both angles equal to 1.77 radians

Now again

Using formula

s = r∅

Where s is the Arc length, r is rdius and ∅ is theta(angle)

s = (2.5)(1.77)

s ≈ 4.43

Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate? Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of
return of 6%? Explain.

Answers

Answer:

The simple interest rate is 5%.

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?

We have that [tex]P = 4200, E = 630, t = 3[/tex]. We have to find I.

[tex]E = P*I*t[/tex]

[tex]630 = 4200*I*3[/tex]

[tex]I = \frac{630}{4200*3}[/tex]

[tex]I = 0.05[/tex]

The simple interest rate is 5%.

Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of  return of 6%?

We have to find T when [tex]P = 4200, t = 4, I = 0.06[/tex]

So

[tex]E = P*I*t[/tex]

[tex]E = 4200*0.06*4[/tex]

[tex]E = 1008[/tex]

[tex]T = E + P = 4200 + 1008 = 5208[/tex]

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

For the given central angle, determine the distance traveled along the unit circle from the point (1, 0). 210 degrees a. 3.67 units c. 1.83 units b. 1.17 units clockwise d. 7.33 units

Answers

Answer:

3.67 units

Step-by-step explanation:

The central angle is at the point (0,0).

Then it's at the point (1,0)

Then it moved 210 degrees.

Let's bear in mind that we start moving the degree from it's current position.

So moving 210 degrees is moving 180 degrees plus 30 degrees.

Moving 180 degrees I like transforming linearly.

Now the location is at (-1,0)

But the distance covered will be

= 2πr*210/360

r = 1

= 2*3.142*1*(210/360)

= 6.144*0.5833333

= 3.67 units

2. The width of a rectangle is 12 inches less than its length. The perimeter of the rect-
angle is 56 inches. Find the length and width of the rectangle.​

Answers

Answer:

[tex] P= 2*Lenght + 2*Width[/tex]

Since the perimeter is 56 inches we can solve for the lenght with this equation:

[tex] 56 in = 2*12in + 2*Length[/tex]

And solving for the length we got:

[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]

So then the lenght = 16 inhes and the width of 12 inches

Step-by-step explanation:

For a rectangle of width 12 inches and lenght y inches we know that the perimeter is given by:

[tex] P= 2*Lenght + 2*Width[/tex]

Since the perimeter is 56 inches we can solve for the lenght with this equation:

[tex] 56 in = 2*12in + 2*Length[/tex]

And solving for the length we got:

[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]

So then the lenght = 16 inhes and the width of 12 inches

I need help please help

Answers

Answer:

Step-by-step explanation:

Note that 28 + 110 + 42 = 180, and that 28 + 42 + 110 = 180 also.

Since all three angles of one triangle are the same as the corresponding angles of the other triangle, the triangles are similar.

A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters.



A smaller cylinder is cut out of a larger cylinder. The smaller cylinder has a diameter of 6 millimeters. The larger cylinder has a diameter of 8.4 millimeters. Both cylinders have a height of 10 millimeters.



What is the volume of metal in the pipe? Use 3.14 for and round the answer to the nearest tenth of a cubic millimeter.

Answers

Answer:

[tex]271.3 mm^3\\[/tex]

Step-by-step explanation:

We have to find the volume of the hole and subtract it from the volume of the cylinder.

The volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

where r = radius

h = height

A cylindrical metal pipe has a diameter of 8.4 mm and a height of 10 mm.

Its radius is 4.2 mm. Therefore, its volume is:

[tex]V = 3.14 * 4.2^2 * 10 = 553.9 mm^3[/tex]

A hole cut out of the center has a diameter of 6 mm. Its height is also 10 mm.

Its radius is 3 mm. Therefore, its volume is:

[tex]V = 3.14 * 3^2 * 10 = 282.6 mm^3[/tex]

Therefore, the volume of metal in the pipe is:

[tex]553.9 - 282.6 = 271.3 mm^3[/tex]

Answer:

B

Step-by-step explanation:

CAN SOMEONE HELP ME IN THIS INTEGRAL QUESTION PLS
''Find the surface area between the z = 1 and z = 4 planes of z = x ^ 2 + y ^ 2 paraboloid.''

Answers

Due to the symmetry of the paraboloid about the z-axis, you can treat this is a surface of revolution. Consider the curve [tex]y=x^2[/tex], with [tex]1\le x\le2[/tex], and revolve it about the y-axis. The area of the resulting surface is then

[tex]\displaystyle2\pi\int_1^2x\sqrt{1+(y')^2}\,\mathrm dx=2\pi\int_1^2x\sqrt{1+4x^2}\,\mathrm dx=\frac{(17^{3/2}-5^{3/2})\pi}6[/tex]

But perhaps you'd like the surface integral treatment. Parameterize the surface by

[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u^2\,\vec k[/tex]

with [tex]1\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex], where the third component follows from

[tex]z=x^2+y^2=(u\cos v)^2+(u\sin v)^2=u^2[/tex]

Take the normal vector to the surface to be

[tex]\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial u}=-2u^2\cos v\,\vec\imath-2u^2\sin v\,\vec\jmath+u\,\vec k[/tex]

The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:

[tex]\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|=u\sqrt{1+4u^2}[/tex]

Then the area of the surface is

[tex]\displaystyle\int_0^{2\pi}\int_1^2\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\int_0^{2\pi}\int_1^2u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]

which reduces to the integral used in the surface-of-revolution setup.

which shows the equation below written in the form ax^2 + BX + C=0
x+10=3(x - 1)^2

Answers

Answer:

C

Step-by-step explanation:

Given

x + 10 = 3(x - 1)² ← expand (x - 1)² using FOIL

x + 10 = 3(x² - 2x + 1) ← distribute

x + 10 = 3x² - 6x + 3 ← subtract x + 10 from both sides

0 = 3x² - 7x - 7 → C

Answer:

     

Step-by-step explanation:

Please answer this correctly

Answers

Answer: 363 cm squared

Step-by-step explanation:

So we can split the shape into 1 triangle and 3 rectangles.

We can start with the top right rectangle which is a 4 by 5.

4*5 = 20 cm squared

We can now do the horizontal rectangle. We need to find the dimensions firs by subtracting 4 from 31 to find the length and add 4 and 5 to find the height.

This means the dimensions are 27 by 9.

27 * 9 = 243 cm squared

Now the final square toward the bottom left will be a 10 by 7.

10 * 7 = 70 cm squared.

Now for the final piece is the triangle in the bottom left. We need to first find the height which we can determine by taking the the right hand side values of 10 , 4 and 5 and adding those together then subtracting that number by 13 to get the missing length that will add to 6 to find the height.

10 + 4 + 5 = 19

19 - 13 = 6

6 + 6 = 12

Now that we have the height and base of the triangle we solve for the area.

0.5 * 5 * 12 = 30 cm squared

Now we add all the areas together to find the total area.

20 + 243 + 70 + 30 = 363 cm squared

Which of the following statements best describes the concept of a function?

Group of answer choices
For a given input value, there is, at most, one output value.

For a given output value, there is, at most, one input value.

For a given input value, there may be more than one output value.

There is no relationship between the input and output values.

Answers

Answer:

For a given output value, there is, at most, one input value

Step-by-step explanation:

Given: the concept of function

To find: the statement that best describes the concept of a function

Solution:

A function is a relation in which every value of the domain has a unique image in the codomain.

Input value belongs to the domain and output value belongs to the codomain.

The statement ''For a given output value, there is, at most, one input value'' describes the concept of a function

The statement best describes the concept of a function is

For a given output value, there is, at most, one input value.

Function :

A relation is a function when each input has exactly only one output

Concept :

Domain x is the input and range y is the output

In a function , each input x must have exactly only one output.

Input x cannot have two outputs.

The statement best describes the concept of a function is

For a given output value, there is, at most, one input value.

Learn more information about 'functions' here :

brainly.com/question/1593453

B
ABC is a right-angled triangle.
AC = 16 cm
Angle C = 90°
А.
size of angle B : size of angle A = 3:2
С
16 cm
Work out the length of AB.
Give your answer correct to 3 significant figures.​

Answers

Answer:

  19.8 cm

Step-by-step explanation:

Angle B is the complement of angle A, so we have this relation for the angles:

  B/A = 3/2 = (90°-A)/A

  2(90° -A) = 3A . . . . . cross multiply

  180° = 5A . . . . . . . . . eliminate parentheses, add 2A

  36° = A . . . . . . . . . . . divide by 5

The relations expressed by the mnemonic SOH CAH TOA remind you that ...

  Cos = Adjacent/Hypotenuse

  cos(A) = AC/AB

  AB = AC/cos(A) = (16 cm)/cos(36°)

  AB ≈ 19.8 cm

11. List and describe three factors that may affect body temperature.​

Answers

it is age heart rate and weather

A tree was 9 feet tall. One year later, the tree was 16 feet tall. Write an equation and use mental math to find how many feet f the tree grew.

Answers

Answer:

7 ft

Step-by-step explanation:

let the height height of the tree be "h"

Hence the tree's height h=9 ft

one year later,let the height of the tree increased by x ft

hence

[tex]9 + x = 16[/tex] --------This is the equation for the growth of the tree

In order to solve for the added height(growth) of the tree we need to solve for x

[tex]9 + x = 16\\x=16-9\\x=7ft[/tex]

If triangles DEF and NPQ are similar, what is the length of side d? As fraction or whole number.

Answers

The length of the side d would be 77/18.

What is the ratio of two quantities?

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or

[tex]\dfrac{a}{b}[/tex]

If triangles DEF and NPQ are similar, then

7/9 = d/ (11/2)

By cross multiply

9d = 7 x 11/2

d = 77/2 ÷ 9

d = 77/18

Thus, The length of the side d would be 77/18.

Learn more about ratios here:

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#SPJ2

X and Y together complete a task in 4 days, Y and Z together in 5 days. If they work independently, who will finish the work in the least time? A. X B. Y C. Z D. Not enough information to decide

Answers

Answer:

c, Z

Step-by-step explanation:

x+y=4

y+z=5

y=4-x

4-x+z=5

-x+z=1

z=1+x

Match each equivalent expression with the property that it represents.
Associative Property of Multiplication
3 + (5 + 7) = (3 + 5) + 7
Identity Property of Multiplication
3 + 5 = 5 + 3
Identity Property of Addition
5(1) = 5
Commutative Property of Addition
(3 + 5) + 0 = (3+5)
Associative Property of Addition
[ 3(5) (4) = (3) 5(4)]

Answers

Answer:

Associative Property of Multiplication: [ 3(5) (4) = (3) 5(4)]Identity Property of Multiplication: 5(1) = 5Identity Property of Addition: (3 + 5) + 0 = (3+5)Commutative Property of Addition: 3 + 5 = 5 + 3Associative Property of Addition: 3 + (5 + 7) = (3 + 5) + 7

Step-by-step explanation:

The associative property lets you move parentheses in a sum or product. That is, it doesn't matter which sum or product you compute first.

The commutative property lets you swap the order of operands in a sum or product.

The identity property says the operation using the identity element gives the original value, unchanged.

Answer:

Step-by-step explanation:


ملی
A man left one-fifth of his property to his
Son , one third to his daughter
and remaining
to his wife. If his wife got 35ooo RS what was the
worth of his total property?​

Answers

Answer:

Rs 75,000

Step-by-step explanation:

Let the total value of property be x

If one-fifth of that is given to son

property with son = 1/5 of total value of property = 1/5 of x = x/5

If one-third of that is given to daughter

property with daughter = 1/3 of total value of property = 1/3 of x = x/3

remaining property after giving the portions to son and daughter

= total value of property - property with son -property with daughter

= x - x/5 - x/3

taking LCM of 5 and 3 (15)

= (15x - 3x - 5x)/15

= 7x/15

Given that remaining property was given to wife

property with wife = 7x/15

it is given that wife got 35000 Rs

thus,

7x/15 = 35,000

7x = 35,000*15 = 525,000

x =  525,000/7 = 75,000

Thus, total worth of property =Rs 75,000 Answer

Answer:

Rs 75,000

Step-by-step explanation:

Let the total value of property be x

If one-fifth of that is given to son

property with son = 1/5 of total value of property = 1/5 of x = x/5

If one-third of that is given to daughter

property with daughter = 1/3 of total value of property = 1/3 of x = x/3

remaining property after giving the portions to son and daughter

= total value of property - property with son -property with daughter

= x - x/5 - x/3

taking LCM of 5 and 3 (15)

= (15x - 3x - 5x)/15

= 7x/15

Given that remaining property was given to wife

property with wife = 7x/15

it is given that wife got 35000 Rs

thus,

7x/15 = 35,000

7x = 35,000*15 = 525,000

x =  525,000/7 = 75,000

Thus, total worth of property =Rs 75,000 Answer

What are the next two numbers in the pattern of numbers;
45, 15, 44, 17, 40, 20, 31, 25, …

Answers

Answer:

Next two numbers are 15 and 32 respectively.

Step-by-step explanation:

The given pattern is  

45, 15, 44, 17, 40, 20, 31, 25, …

Here, we have two patterns.

Odd places : 45, 44, 40, 31,...

Even places : 15, 17, 20, 25,...

In series of odd places, we need to subtract square of integers.

[tex]45-(1)^2=45-1=44[/tex]

[tex]44-(2)^2=44-4=40[/tex]

[tex]40-(3)^2=40-9=31[/tex]

So, 9th term of given pattern is  

[tex]31-(4)^2=31-16=15[/tex]

In series of even places, we need to add prime numbers.

[tex]15-2=17[/tex]

[tex]17+3=20[/tex]

[tex]20+5=25[/tex]

So, 10th term of given pattern is  

[tex]25+7=32[/tex]

Therefore, the next two numbers in the pattern of numbers are 15 and 32 respectively.

PLEASE HELP. if f(x)=x and g(x)=2, what is (f*g)(x)

Answers

Answer:

Step-by-step explanation:

hey

(f*g)(x) = f(g(x)) = f(2) = 2

second answer is correct

thanks

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