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3 years ago

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Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour. Jeff knows that 1 cup of that

particular vanilla powder has a mass of 128 grams. He added 2/3= of a cup of vanilla powder to the flour. Should Jeff add more vanilla powder to make the exact recipe or did he go over and by what amount? (1 point) He needs to add 1/4= of a cup He went over by 5/12= of a cup He went over by 1/4= of a cup He needs to add 5/12= of a cup

2 answers:

Elodia [21]3 years ago

6 0

He had to go over by 1/4 of a cup.
1 cup =128
1/4 of a cup =32 grams

Wewaii [24]3 years ago

6 0

Answer:

He went over by 5/12 of a cup

Step-by-step explanation:

Consider the provided information.

The recipe says that he has to mix 32 grams of vanilla powder to the flour.

Jeff knows that 1 cup of that particular vanilla powder has a mass of 128 grams. He added 2/3= of a cup of vanilla powder to the flour.

$\frac{2}{3} \cdot 128=\frac{256}{3}=85\frac{1}{3}$ grams.

That means he added $85\frac{1}{3}$ grams of vanilla but he needs to add only 32 grams of vanilla.

Now find how much he added more.

$85\frac{1}{3}-32=53\frac{1}{3}$ grams.

That means he added $53\frac{1}{3}$ grams more vanilla powder.

Lets find $53\frac{1}{3}$ is how much of a cup.

If we multiply $\frac{5}{12}$ with 128 we will get:

$\dfrac{5}{12}\cdot 128=\dfrac{5\cdot 128}{12}=\dfrac{5\cdot 32}{3}=\dfrac{160}{3}=53\dfrac{1}{3},$

Hence, He went over by 5/12 of a cup

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The Consumer Price Index (CPI) is a measure of the change in the cost of goods over time. If 1982 is used as the base year of c

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Step-by-step explanation:

Data given

1982 , CPI=100

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Let CPI the dependent variable y. And the time th independent variable x.

For this case we want to adjust a linear model givn by the following expression:

$y=mx+b$

Solution to the problem

Part a

For this case we can find the slope with the following formula:

$m =\frac{CPI_{2006}-CPI_{1982}}{2006-1982}$

And if we replace we got:

$m =\frac{191.2-100}{2006-1982}=3.8$

Let X represent the number of years after. Then for 1982 t = 0, and if we replace we can find b:

$100 = 3.8(0)+b$

And then $b=100$

So then our linear model is given by:

$y = 3.8 x +100$

Part b

For this case we need to find the years since 1982 and we got x = 2000-1982=18, and if we rpelace this into our linear model we got:

$y = 3.8(18) +100=168.4$

And the actual value is 167.5 we can compare the result using absolute change or relative change like this:

$Abs. change= |168.4-167.5|=0.9$

So the calculated value is 0.9 points above the actual value.

And we can find also the relative change like this:

$Relative. Change =\frac{|Calculated -Real|}{Real}x100$

And if we replace we got:

$Relative. Change =\frac{|168.4 -167.5|}{167.5}x100 =0.537$ %

And the calculated value it's 0.537% higher than the actual value.

Part c

For this case we can use the slope obtained from the linear model to answer this question, and we can conclude that the CPI is increasing at approximate 3.8 units per year.

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3 years ago