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3 years ago

9

A punch recipe that serves 24 people calls for 4 liters of lemon soda, 2 pints of sherbert, and 6 cups of ice. How much of each

ingredient would you need to make an identical recipe that serves 12 people? 36 people?

1 answer:

Vitek1552 [10]3 years ago

8 0

For 12 people it would be 2 liters of soda, 1 pint of sherbet, &3 cups of ice. you wanna make half as much as his recipe says so just divide everything by 2. then you can multiply what the half recipe calls for to serve 36 people by three. so it would be 6 liters of soda, 3 pints of sherbet and 9 cups of ice. I hope that made sense to you, it was kind of hard to out the explanation into words

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Steve earns $8 per hour. His older brother earns $2 more per hour than Steve. What is the ratio of the money Steve earns in an h

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Answer: 4:5

Explanation:

Steve earns 8 dollars an hour. His brother earns 10 dollars an hour.

The ratio is Steve:Brother, which is 8:10.

This can be treated the same was as a fraction and simplified, dividing both sides by 2, which becomes 4:5

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4 years ago

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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100100 engin

Margaret [11]

Answer:

Null hypothesis: $\mu \geq 7.3$

Alternative hypothesis: $\mu < 7.3$

$z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so then we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=7.2$ represent the sample mean

$\sigma=0.81$ represent the population standard deviation

$n=100$ sample size

$\mu_o =7.3$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean pressure is lower than the specificated value 7.3, the system of hypothesis are :

Null hypothesis: $\mu \geq 7.3$

Alternative hypothesis: $\mu < 7.3$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235$

4) P-value

Since is a one-side lower test the p value would given by:

$p_v =P(z$

5) Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.

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3 years ago

A solid object is dropped into a pond with a temperature of 20 degrees Celsius. The function f(t)=Ce(−kt)+20 represents the situ

LenaWriter [7]

Answer:

The initial temperature of the object was 37.6 degrees Celsius

The initial temperature of the object was 37.6 (without units)

Step-by-step explanation:

we have

$f(t)=Ce^{(-kt)} +20$

where

f(t) represent the temperature of the object in degree Celsius

t is the time in minutes

<em>Find the value of the constant C</em>

we have the ordered pair (4,35)

substitute in the equation and solve for C

$35=Ce^{(-0.0399*4)} +20$

$Ce^{(-0.0399*4)}=15$

$C=15/e^{(-0.0399*4)}$

$C=17.6$

Find the initial value of the object

we know that

The initial temperature is the value of f(t) when the value of t is equal to zero

so

For t=0

$f(0)=(17.6)e^{(-k*0)} +20$

$f(0)=17.6 +20$

$f(0)=37.6\ degrees\ Celsius$

therefore

The initial temperature of the object was 37.6 degrees Celsius

The initial temperature of the object was 37.6 (without units)

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