Is it possible that<br> 1952<br> is the remainder of 375139654

Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar pe

Arlecino [84]

From the given data, we can generate two equations with two unknowns.

We let x = number of loaves of bread
y = number of batches of muffins

For the equation of the flour requirement:
17 = 3.5x + 2.5y

<span>For the equation of the sugar requirement:
</span>4.5 = 0.75x + 0.75y

We evaluate the solutions by manipulating one of the equations into terms of the other. We use the first equation.We write x in terms of y.

x = (4.5/0.75) - y

Substitute the third equation to the second equation.

17 = (3.5((4.5/0.75)-y)) + 2.5y

Evaluating y and x, we have,

y = 4 and x = 2

Thus, from the amounts she has in hand, she can make 4 loaves of bread and 2 batches of muffins.

4 0

2 years ago

Read 2 more answers

Jordan wants to play a basketball game at a carnival. The game costs the player $5 dollar sign, 5 to play, and the player gets t

Alinara [238K]

Answer:

The expected value of Jordan gains is -1 dollar.

Step-by-step explanation:

Consider the following random variables. X := #of shots that Jordan makes. Then, we can can define the random variable Y of the earnings of Jordan in a game as follows

Y = 5 if X=2 (since he gets 10, but invested 5), Y=0 if X=1(since he gets the 5 back) and Y=-5 if X=0(since he doesn't get the money back). Then, in this case, we can define the probability as follows.

P(Y=5) = P(X=2), P(Y=0) = P(X=1), P(Y=-5)= P(X=0).

By definition, the expected value of Y is given by

$E[Y] = 5\cdot P(Y=5)+0\cdot P(Y=0)-5 P(Y=-5)$ . By the previous analysis, we have that

$E[Y] = 5\cdot P(X=2)-5P(X=0)$

We only need to calculate the probabilities for X. In this case, we can consider each shot independt from each other. Then, we can consider X to be distributed as a binomial random variable with n=2 trials and p=0.4 of success (since he has a 40% chance of winning).

Then, by definition

$P(X=k) = \binom{n}{k}p^k(1-p)^{n-k} = \binom{2}{k}0.4^{k}0.6^{2-k}$

where $\binom{n}{k}=\frac{n!}{k!(n-k)!}$

Then,

$P(X=0) = \frac{2!}{0!2!}0.4^{0}0.6^{2} = 0.36$

$P(X=2)=\frac{2!}{0!2!}0.4^{2}0.6^{0} = 0.16$

Then,

$E[Y] = 5\cdot 0.16-5\cdot 0.36 = -1$

8 0

2 years ago

A farmer is having problems with birds eating her crops. She tries putting up different numbers of scarecrows to keep the birds

Alexeev081 [22]

Answer:

The value of the intercept is a=216.

Step-by-step explanation:

We define "s" as the number of scarecrows and "C" the number of crops eaten.

The farmer finds the linear regression equation:

$C=a-0.8s$

We have a linear function, for which we only know the slope (m=0.8) and a point within it (when s=20, C=200).

We can find a replacing the variables C asn s with the known point (20, 200):

$C=a-0.8s\\\\C(20)=a-0.8(20)=200\\\\a=200+0.8*20=200+16\\\\a=216$

The value of the intercept is a=216.

3 0

2 years ago

the surface area of two similar figures are 25 in ^2 and 36 in ^2 if the volume of the smaller figure is 250 in ^3 then what is

k0ka [10]

Answer:

432 in^3

Step-by-step explanation:

The ratio of linear dimensions is the square root of the ratio of the areas, so is ...

scale factor = √(36/25) = 6/5

The ratio of volumes is the cube of the ratio of linear dimensions, so is ...

volume ratio = (scale factor)^3 = (6/5)^3 = 216/125

Then the volume of the larger figure is ...

larger volume = (250 in^3)·(216/125) = 432 in^3

8 0

2 years ago

A total of 8,644 people went a football game 5,100 sat on the home side rest sat on visitors side if people on visitors side fil

gregori [183]

First do this to find out the total amount of people sitting in the visitor side:
8644-5100= 3544

then you divide 3544/8= 443
so 443 people sat in each section in all 8 sections

so final answer is 443 people per section

6 0

2 years ago

Is it possible that 1952 is the remainder of 375139654 - 1953?