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Shalnov [3]
3 years ago
12

Abdul's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Abdul per pound, and type B coff

ee costs per pound. This month, Abdul made pounds of the blend, for a total cost of . How many pounds of type A coffee did he use
Mathematics
1 answer:
xenn [34]3 years ago
7 0

Complete question :

Abdul's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Abdul $4.25 per pound, and type B coffee costs $5.90 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $337.05 . How many pounds of type A coffee were used?

Answer:

21 pounds

Step-by-step explanation:

Pounds of coffee A used = x

Pounds of coffee B = 2x

Cost per pound of A = $4.25

Cost per pound of B = $5.90

Total cost of coffee = $337.05

4.25x + 2x(5.90) = 337.05

4.25x + 11.8x = 337.05

16.05x = 337.05

x = 337.05 / 16.05

x = 21

Hence, 21 pounds of coffee A was used

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In cylindrical coordinates, we have r^2=x^2+y^2, so that

z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}

correspond to the upper and lower halves of a sphere with radius \sqrt2. In spherical coordinates, this sphere is \rho=\sqrt2.

1 \le r \le \sqrt2 means our region is between two cylinders with radius 1 and \sqrt2. In spherical coordinates, the inner cylinder has equation

x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)

This cylinder meets the sphere when

x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)

which occurs at

\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi

where n\in\Bbb Z. Then \frac\pi4\le\phi\le\frac{3\pi}4.

The volume element transforms to

dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi

Putting everything together, we have

\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3

4 0
2 years ago
How do you know that 4/11 is a repeating decimal?
Leokris [45]

Answer:

by dividing it= 4/11

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3 0
3 years ago
Extreme cold and hot temperatures are known to affect the operation of electronic components. Winter is approaching and you are
Musya8 [376]

Answer:

A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

Test statistic(Z) = 2.31

P-value = 0.0104

Step-by-step explanation:

Step 1

Null hypothesis: The average damaging temperature of nine iPods is 5°F

Alternate hypothesis: The average damaging temperature of nine iPods differs from 5°F

Step 2

Mean=5°F, Sd=3, df=n-1=9-1=8

The t-value corresponding to 8 degrees of freedom and 95% confidence level (5% significance level) is 2.306

Confidence Interval(CI) = (mean + or - t×sd/√n)

CI = (5 + 2.306×3/√8) = 5 + 6.918/2.828= 5+2.45=7.45°F

CI = (5 - 2.306×3/√8) = 5-2.45 = 2.55°F

Z = (sample mean - population mean)/(sd÷√n) = (5-2.55)/(3÷√8) = 2.45/1.061 = 2.31

Step 3

Using the standard distribution table, the cumulative area to the left of Z = 2.31 is 0.9896

P-value = 1 - 0.9896 = 0.0104

Step 4

Conclusion: A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

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agasfer [191]

Answer:

50

Step-by-step explanation:

.80n = 40

n = 40 divided by .80

40/8/10  = 400 / 80 = 50

Best Of Luck,

- I.A. -

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g100num [7]
ANSWER:
128.79 x .30 = $38.64
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