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4 years ago

How much sugar syrup would you get by making 30% sugar syrup using 75g sugar?

Mathematics

1 answer:

seraphim [82]4 years ago

6 0

Answer:

Step-by-step explanation:

use proportions

x/100=75/30

75x=3,000

x=40

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7. The length of time (in months after maintenance) until failure of a bank’s surveillance television equipment follows a Weibul

cupoosta [38]

Answer:

The frequency by which the equipment should receive periodic maintenance is $x= 13.59$

Step-by-step explanation:

A Wellbull distribution is mathematically represented as

$f(x,\alpha, \beta ) = \left \{ { {\frac{\alpha }{\beta^{\alpha } }x^{\alpha -1} e^{-[\frac{x}{\beta } ]^\alpha} \ \ \ \ \ \ \\ \\ , x \ge0} \atop {0 \ \ \ \ \ \ \ \ Otherwise }} \right.$

Where x is the frequency that the equipment should receive periodic maintenance

probability of a breakdown before the next scheduled maintenance is mathematically represented as

$P(x) = \int\limits^x_0 {\frac{\alpha }{\beta^{\alpha } } x^{\alpha -1 } e^{-[\frac{x}{\beta } ]^{\alpha }} } \, dx$

Substituting 2 for $\alpha$ and 60 for $\beta$ 0.05 for P(x)

$0.05 = \int\limits^x_0 {\frac{2}{60^2} x^{2-1} e^{-[\frac{x}{60}]^2 } \, dx$

$0.05 = \frac{2}{3600}\int\limits^x_0 {xe^{[-\frac{x^2}{3600} ]}} \, dx$

Let $v = - \frac{x^2}{3600}$

=> $dv = \frac{-xdx}{1800}$

=> $-xdx = 1800\ dv$

Multiply both sides by minus

=> $xdx = -1800dv$

Substituting this into the equation

$0.05 = \frac{2}{3600} \int\limits^x_0 {-1800 e^u} \, du$

Integrating and substituting back for x

$0.05 = -\frac{1800}{1800} [e^{[-\frac{x^2}{3600} ]}]\left {{x} \atop {0}} \right.$

substituting for the range of x and 0

$0.05 = - [e^{-[\frac{x^2}{3600}] } -1]$

$0.05 = -e^{[-\frac{x^2}{3600} ]} +1$

$0.05 -1 = -e^{-\frac{x^2}{3600} }$

$-0.95 = -e^{[-\frac{x^2}{3600} ]}$

$0.95 = e^{[-\frac{x^2}{3600} ]}$

Taking ln of both sides

$-0.05129 = - \frac{x^2}{3600}$

making x the subject of the formula

$x = \sqrt{0.05129 * 3600 }$

$x= 13.59$

4 0

3 years ago

Multiply: (5t - 4)(4t + 5)

ANEK [815]

Answer:

A. 20t² + 9t - 20

Step-by-step explanation:

(5t × 4t) + (5t × 5) - (4 × 4t) - (4 × 5)

= 20t² + (25t - 16t) - 20

= 20t² + 9t - 20 (A)

Hope this is helpful and useful :)

5 0

4 years ago

Ann takes 70 paces to walk 50m. the number of paces ann takes to walk 3.5km is A.70 B.490. C.3900 D.4900

Shalnov [3]

<h3>Answer: 4900 (choice D)</h3>

===================================================

Work Shown:

1 km = 1000 m

3.5 km = 3500 m ............. multiplying both sides by 3.5

(70 paces)/(50 m) = (x paces)/(3500 m)

70/50 = x/3500

7/5 = x/3500

7*3500 = 5x .............. cross multiply

5x = 7*3500

x = (7*3500)/5

x = (7*5*700)/5

x = 7*700

x = 4900

Ann takes 4900 paces to walk 3.5 km

4 0

2 years ago

Simplify. (x6y3)−2x−5y−8

Elodia [21]

Answer:

18xy-2x-5y-8

Step-by-step explanation:

Просто умножьте,то что было в скобках

7 0

3 years ago

Find the value of the "?"

Andru [333]

Answer:

Step-by-step explanation:

Set up ratios for 2 similar triangles:

20/28=x/x+18

Cross multiply

28x=20x+360

8x=360

x=45

3 0

3 years ago