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MaRussiya [10]
3 years ago
9

What is the solution to the equation?

Mathematics
1 answer:
ki77a [65]3 years ago
7 0

Answer:

7

Step-by-step explanation:

3 {(x + 9)}^{ \frac{3}{4} }  = 24 \\  \\ {(x + 9)}^{ \frac{3}{4} }  =  \frac{24}{3}  \\  \\  {(x + 9)}^{ \frac{3}{4} }  =  8  \\  \\  {(x + 9)}^{ \frac{3}{4} }  =   {2}^{3}   \\  \\ (x + 9) =  {2}^{3 \times  \frac{4}{3} }  \\  \\ x + 9 =  {2}^{4}  \\  \\ x + 9 = 16 \\  \\ x = 16 - 9 \\  \\ x = 7

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To get a final grade of B, a student must have an average mark on five tests that is greater than or equal to 80 and less than 9
yulyashka [42]

Answer:

Lisa must get an 88.75 or higher to stay in between 80 and 90.

Step-by-step explanation:

8 0
2 years ago
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High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers
Maurinko [17]

Answer:

The 99% of a confidence interval for the average maximum HP for the experimental engine.

(536.46, 603.54)

Step-by-step explanation:

<u><em>Step:-1</em></u>

Given that the mean of the Population = 540HP

Given that the size of the sample  'n' = 9

Given that the mean of the sample = 570HP

Given that the sample standard deviation = 30HP

<u><em>Step(ii):-</em></u>

<u><em>Degrees of freedom = n-1 =9-1 =8</em></u>

<u><em>t₀.₀₀₅ = 3.3554</em></u>

The 99% of a confidence interval for the average maximum HP for the experimental engine.

(x^{-} - t_{\frac{0.01}{2} ,8} \frac{S.D}{\sqrt{n} } ,x^{2}  + t_{\frac{0.01}{2},8 } \frac{S.D}{\sqrt{n} } )

(570-3.354\frac{30}{\sqrt{9} } , 570+3.354\frac{30}{\sqrt{9} } )

(570 - 33.54 , 570+33.54)

(536.46 , 603.54)

<u><em>Final answer</em></u> :-

<em>The 99% of a confidence interval for the average maximum HP for the experimental engine.</em>

<em>(536.46, 603.54)</em>

<em></em>

4 0
3 years ago
a spherical balloon is deflated at a rate of 256pi/3 cm^3/sec. at what rate is the radius of the balloon changing when the radiu
Hunter-Best [27]
What you need to look for is \frac { dr }{ dt } when r=8.

Now:

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\therefore \quad \frac { dV }{ dr } =\frac { 4 }{ 3 } \pi \cdot 3{ r }^{ 2 }=4\pi { r }^{ 2 }\\ \\ \therefore \quad \frac { dr }{ dV } =\frac { 1 }{ \frac { dV }{ dr }  } =\frac { 1 }{ 4\pi { r }^{ 2 } }

And:\\ \\ \frac { dV }{ dt } =-\frac { 256\pi  }{ 3 } \\ \\ Therefore:\\ \\ \frac { dr }{ dt } =\frac { dr }{ dV } \cdot \frac { dV }{ dt }

\\ \\ =\frac { 1 }{ 4\pi { r }^{ 2 } } \cdot -\frac { 256\pi  }{ 3 } \\ \\ =-\frac { 256 }{ 12 } \cdot \frac { \pi  }{ \pi  } \cdot \frac { 1 }{ { r }^{ 2 } }

\\ \\ =-\frac { 64 }{ 3{ r }^{ 2 } } \\ \\ When\quad r=8,\\ \\ \frac { dr }{ dt } =-\frac { 64 }{ 3\cdot { 8 }^{ 2 } } =-\frac { 1 }{ 3 } \\ \\ Answer:\quad -\frac { 1 }{ 3 } \quad cm/sec
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3 years ago
Approximate the value of the square root of 110 to the nearest hundredth
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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Now the ratio becomes 3:4:6

So the number of each is

3x + 4x + 6x = 520

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x = 40

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Yellow = 4*40 = 160

Blue = 6 * 40  = 240

Total =               520

7 0
3 years ago
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