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Gelneren [198K]
4 years ago
8

If a sport-shop sold 1500 dozen golf balls, how many individual gold balls did the shop sell?

Mathematics
2 answers:
hichkok12 [17]4 years ago
8 0

Answer:

18000

Step-by-step explanation:

12 is a dozen,

1500 x 12 = 18000

Lelu [443]4 years ago
4 0

Answer:

18000

Step-by-step explanation:

Since 1 dozen is 12, I multiplied 1500 by 12.

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Write a story problem that includes both integers −8 and 12.
IceJOKER [234]

Answer:

Sea level is 0 meters. A cliff by the ocean is 12 meters above sea level. Around that area, the seafloor is 8 meters below sea level. How many meters  is the top of the cliff to the seafloor?

How to solve:

8 below zero is -8

The expression 12 - (-8) is the same as the expression 12 + 8

12 + 8 = 20

20 meters

8 0
3 years ago
Find \(\int \dfrac{x}{\sqrt{1-x^4}}\) Please, help
ki77a [65]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2867785

_______________


Evaluate the indefinite integral:

\mathsf{\displaystyle\int\! \frac{x}{\sqrt{1-x^4}}\,dx}\\\\\\ \mathsf{=\displaystyle\int\! \frac{1}{2}\cdot 2\cdot \frac{1}{\sqrt{1-(x^2)^2}}\,dx}\\\\\\ \mathsf{=\displaystyle \frac{1}{2}\int\! \frac{1}{\sqrt{1-(x^2)^2}}\cdot 2x\,dx\qquad\quad(i)}


Make a trigonometric substitution:

\begin{array}{lcl}
\mathsf{x^2=sin\,t}&\quad\Rightarrow\quad&\mathsf{2x\,dx=cos\,t\,dt}\\\\
&&\mathsf{t=arcsin(x^2)\,,\qquad 0\ \textless \ x\ \textless \ \frac{\pi}{2}}\end{array}


so the integral (i) becomes

\mathsf{=\displaystyle\frac{1}{2}\int\!\frac{1}{\sqrt{1-sin^2\,t}}\cdot cos\,t\,dt\qquad\quad (but~1-sin^2\,t=cos^2\,t)}\\\\\\
\mathsf{=\displaystyle\frac{1}{2}\int\!\frac{1}{\sqrt{cos^2\,t}}\cdot cos\,t\,dt}

\mathsf{=\displaystyle\frac{1}{2}\int\!\frac{1}{cos\,t}\cdot cos\,t\,dt}\\\\\\
\mathsf{=\displaystyle\frac{1}{2}\int\!\f dt}\\\\\\
\mathsf{=\displaystyle\frac{1}{2}\,t+C}


Now, substitute back for t = arcsin(x²), and you finally get the result:

\mathsf{\displaystyle\int\! \frac{x}{\sqrt{1-(x^2)^2}}\,dx=\frac{1}{2}\,arcsin(x^2)+C}          ✔

________


You could also make

x² = cos t

and you would get this expression for the integral:

\mathsf{\displaystyle\int\! \frac{x}{\sqrt{1-(x^2)^2}}\,dx=-\,\frac{1}{2}\,arccos(x^2)+C_2}          ✔


which is fine, because those two functions have the same derivative, as the difference between them is a constant:

\mathsf{\dfrac{1}{2}\,arcsin(x^2)-\left(-\dfrac{1}{2}\,arccos(x^2)\right)}\\\\\\
=\mathsf{\dfrac{1}{2}\,arcsin(x^2)+\dfrac{1}{2}\,arccos(x^2)}\\\\\\
=\mathsf{\dfrac{1}{2}\cdot \left[\,arcsin(x^2)+arccos(x^2)\right]}\\\\\\
=\mathsf{\dfrac{1}{2}\cdot \dfrac{\pi}{2}}

\mathsf{=\dfrac{\pi}{4}}         ✔


and that constant does not interfer in the differentiation process, because the derivative of a constant is zero.


I hope this helps. =)

6 0
3 years ago
According to Wine-Searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative qualit
Romashka-Z-Leto [24]

Answer:

a

\= x  =  82

b

s =  9.64

Step-by-step explanation:

From the question we are told that

    The data is  87  91  86  82  72  91   60  77  80  79  83  96

Generally the point estimate for the mean is mathematically represented as

    \= x  =  \frac{\sum  x_i }{n}

=>  \= x  =  \frac{87 +91 + 86 + \cdots  + 96}{12}

=>    \= x  =  82

Generally the point estimate for the standard deviation  is mathematically represented as

      s =  \sqrt{\frac{ \sum ( x_i  - \= x )^2 }{ n -1 } }

=>     s =  \sqrt{\frac{ ( 87 - 82  )^2 +( 91 - 82  )^2 + \cdots + ( 96 - 82  )^2  }{ 12 -1 } }

=>     s =  9.64

8 0
4 years ago
Find the length of a photograph whose width is 10 inches and whole proportions are the same as a 5-inch by 8-inch photograph.
Naily [24]

5 inch is the width, 8 inch is the length.

Find to scale between the two widths:

10 /5 = 2 the larger photo is 2 times larger,

Multiply the known length by 2:

8 x 2 = 16

The length would be 16

4 0
3 years ago
Read 2 more answers
What is the interest earned based upon a principal of $1,000 at a rate of 6% over 8 years????
Nata [24]
1000*(1.06)^8. I'm lazy and don't want to type this into a calculator, but what you get out is the answer.
4 0
3 years ago
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