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2 years ago

112 is the product of 7 and Raj’s score.

Mathematics

2 answers:

Alla [95]2 years ago

7 0

Answer:

Raj´s score = 16

Step-by-step explanation:

112 = 7R

R = Raj´s score

112/7 = R

R = 16

Brut [27]2 years ago

4 0

Answer: 16

Step-by-step explanation: 112 is equal to the product of 7 and Raj's score. Therefore, Raj's score score is 112 divided by 7 which is 16.

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What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 2197 cm cubed?

Zarrin [17]

Answer:

radius = height ≈ 8.88 cm

Step-by-step explanation:

If the weight is proportional to the surface area, then we need to find the minimum surface area for the given volume.

The volume of the can is given by ...

V = πr²h . . . . . . for radius r and height h

The surface area includes that of the bottom and the sides:

SA = πr² +2πrh

Solving the first equation for h, we can write the second equation as ...

SA = πr² +2πr(V/(πr²)) = πr² +2V/r

The minimum area for the volume will be found where the derivative is zero.

d(SA)/dr = 2πr -2V/r² = 0

πr³ = V . . . . . multiply by r²/2 and add V

Then the can radius is ...

r = ∛(V/π)

and the height is ...

h = V/(π(V/π)^(2/3)) = ∛(V/π) = r

For the given volume, the dimensions are ...

r = h = ∛(2197/π) ≈ 8.8762 cm

The lightest can with that volume has a radius and height of about 8.88 cm.

_____

Comment on cylinder aspect ratio

You may notice that the lateral area is equal to twice the bottom area for this cylinder. If the can had a top, the minimum weight would be such that the lateral area is twice the total of top and bottom area. In that case, the height is equal to the diameter, not the radius.

4 0

3 years ago

The equation y =

-Dominant- [34]

Answer:

The constant of proportionality k = 12

Hence, option A is true.

Step-by-step explanation:

We know that when 'y' varies directly with 'x', we get

y ∝ x

y = kx

Where 'k' is called the constant of proportionality.

In our case,

The given equation is

y = 12x

comparing with the equation y = kx, we can say

k = 12 which is the constant of proportionality.

Therefore, we conclude that:

The constant of proportionality k = 12

Hence, option A is true.

6 0

3 years ago

⦁ In a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football. Construct a 95% confiden

fomenos

Answer:

95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

Step-by-step explanation:

We are given that in a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football.

Firstly, the pivotal quantity for 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = proportion of adults in the United States whose favorite sport to watch is football in a sample of 1219 adults = $\frac{354}{1219}$

n = sample of US adults = 1291

p = population proportion of adults

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

significance level are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }$ ]

= [ $\frac{354}{1219}-1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} }$ , $\frac{354}{1219}+1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} }$ ]

= [0.265 , 0.316]

Therefore, 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

5 0

3 years ago

Find the area of the following rectangle in square feet. 44 ft 2 11 ft 2 14.7 ft 2 132 ft 2

uysha [10]

The picture in the attached figure

we know that
area of rectangle=base*height
in this problem
base is 22 ft
height is 2 yd

convert yd to ft
1 yd is equal to 3 ft
2 yd--------> 2*3-----> 6 ft

area of rectangle=22*6-----> 132 ft²

the answer is
132 ft²

8 0

3 years ago

Read 2 more answers

Help fast and now plz

Stella [2.4K]

35 is the answer35 is the answer35 is the answer

5 0

3 years ago