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anastassius [24]
2 years ago
11

A spherical ball has a diameter of 8 inches. The ball has a slow leak in which the air escapes at the rate of 2.5 inches per sec

ond. How long would it take for the ball to deflate? Round to the nearest tenth.
Mathematics
1 answer:
s344n2d4d5 [400]2 years ago
4 0

Answer:

107.2 seconds

Step-by-step explanation:

Step one:

given

the diameter of ball 8 inches

radius= 8/2 = 4 in

The volume of the ball

v=4/3 \pi r^3

v= 4/3*3.142*4^3\\\\v= 4/3*3.142*64\\\\v= 804.35/3\\\\v=268.12 in^3

Step two:

we know that

rate= quantity/time

rate= 2.4 in per second

quantity= 268.12

time=?

time= quantity/rate

time= 268.12/2.5

time= 107.2 seconds

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The linear function f i with values f(-1) = 10 and f(5) = -1 is f(x)
zhenek [66]
Answer:

Use the two points to compute the slope, m, then use one of the points in the form <span>y=m<span>(x)</span>+b</span> to find the value of b.

Explanation:

The equation for the slope, m, of a line is:

<span>m=<span><span><span>y1</span>−<span>y0</span></span><span><span>x1</span>−<span>x0</span></span></span> [1]</span>

The equation <span><span>f<span>(2)</span></span>=−1</span> tells us that <span><span>x0</span>=2and<span>y0</span>=−1</span>; substitute this into equation [1]:

<span>m=<span><span><span>y1</span>−−1</span><span><span>x1</span>−2</span></span> [2]</span>

The equation <span><span>f<span>(5)</span></span>=4</span> tells us that <span><span>x1</span>=5and<span>y1</span>=4</span>; substitute this into equation [2]:

<span>m=<span><span>4−−1</span><span>5−2</span></span> [3]</span>

<span>m=<span>53</span></span>

Substitute <span>53</span> for m into the equation <span>y=m<span>(x)</span>+b</span>

<span>y=<span>53</span>x+b [4]</span>

Substitute 2 for x and -1 for y and the solve for b:

<span>−1=<span>53</span><span>(2)</span>+b</span>

<span>b=−<span>133</span></span>

Substitute <span>−<span>133</span></span> for b in equation [4]:

<span>y=<span>53</span>x−<span>133</span> [5]</span>

Check:

<span>−1=<span>53</span><span>(2)</span>−<span>133</span></span>
<span>4=<span>53</span><span>(5)</span>−<span>133</span></span>

<span>−1=−1</span>
<span>4=<span>4</span></span>

<span><span>
</span></span>

<span><span>Hope this helps </span></span>

3 0
2 years ago
Solve. (x + 3)^1/2– 1 = x
Natali [406]

Answer:

x=1

Step-by-step explanation:

(x + 3) ^{ \frac{1}{2} }  - 1 = x  \\  \sqrt{x  + 3}   - 1 = x \\  \sqrt{x + 3}  = x + 1 \\ square \: both \: sides \\ x + 3 =  {x}^{2}  + 2x + 1 \\  {x}^{2}  + 2x - x + 1 - 3 = 0  \\  {x}^{2}  + x - 2 = 0  \\ x ^{2}  + 2x - x - 2 = 0  \\ (x^{2}  + 2x) - (x  + 2) = 0 \\ x(x + 2) - 1( x + 2) = 0 \\ (x - 1)(x + 2) = 0 \\ x - 1 = 0 \\ x = 1 \\  \\  \\ x  +  2 = 0 \\ x =  - 2

8 0
3 years ago
The answer and how to do it
inessss [21]
Alright, here is how to do it:
First you are going to want to multiply 4x4. [That is Dino's Charges for 4 Sandwiches.] So once you've done that, you should get 16

Now, you're going to want to multiply 8x4. [That is Carla's charges for 4 Sandwiches.] So once you've done that, you should get 24.

Now, to find the difference you will have to subtract them. 24-16 = 18.
Now that we've done this we now know your answer is:
Carla's sandwiches cost more than Dino's sandwiches. The difference is 18 dollars.
-------------------------
I hope I helped, if I did; please give me brainliest. :)
4 0
2 years ago
2.The mean area of several thousand apartments in a new development is advertised to be 1,100 square feet. A consumer advocate h
KiRa [710]

Answer:

Null Hypothesis, H_0 : \mu = 1,100 square feet

Alternate Hypothesis, H_A : \mu < 1,100 square feet

Step-by-step explanation:

We are given that the mean area of several thousand apartments in a new development is advertised to be 1,100 square feet.

A consumer advocate has received numerous complaints that the apartments are smaller than advertised.

<u><em>Let </em></u>\mu<u><em> = mean area of several apartments.</em></u>

So, Null Hypothesis, H_0 : \mu = 1,100 square feet

Alternate Hypothesis, H_A : \mu < 1,100 square feet

Here, <u>null hypothesis states that</u> the mean area of apartments are same as advertised.

On the other hand, <u>alternate hypothesis states that</u> the mean area of apartments are smaller than advertised.

So, this would be the appropriate null and the alternative hypothesis to test this claim.

4 0
2 years ago
Consider the expression. (StartFraction 2 m Superscript negative 1 baseline n Superscript 5 Baseline Over 3 m Superscript 0 Base
suter [353]

Answer:

The correct option is option (3) 4 ÷ 25.

Step-by-step explanation:

The expression in terms of <em>m</em> and <em>n</em> is:

F(m,n)=[\frac{2m^{-1}n^{5}}{3m^{0}n^{4}}]^{2}

Exponent rule of division:

a^{x}\div a^{y}=a^{x-y}

Compute the value of the expression for <em>m</em> = -5 and <em>n</em> = 3 as follows:

F(m,n)=[\frac{2m^{-1}n^{5}}{3m^{0}n^{4}}]^{2}

F(-5,3)=[\frac{2\csdot (-5)^{-1}\cdot (3)^{5}}{3\cdot (-5)^{0}\cdot (3)^{4}}]^{2}

             =\{\frac{2}{3}\times [(-5)^{-1-0}\times (3)^{5-4}}]\}^{2}\\\\=\{\frac{2}{3}\times \frac{-1}{5}\times 3\}^{2}\\\\=\{-\frac{2}{5}\}^{2}\\\\=\frac{4}{25}

Thus, the correct option is option (3) 4 ÷ 25.

8 0
3 years ago
Read 2 more answers
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