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2 years ago

14

A recipe uses 21/4 cups flour for a batch of cookies.Henry makes 10 batches of cookies for the bake sale. How many cups of flour

does Henry use?

1 answer:

gulaghasi [49]2 years ago

8 0

If you are using 2.25 cups for each batch and there are 10 batches. He would use 22 1/2 cups of flour for the cookies.

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Rewrite this inequality so y is by itself:<br><br> 3x − 4y ≥ 24.

vazorg [7]

Answer:

y $\leq$ 6 + $\frac{3x}{4}$

Step-by-step explanation:

3x - 4y $\geq$ 24

-3x -3x

(-4y $\geq$ 24 - 3x ) / -4

y $\leq$ 6 + $\frac{3x}{4}$

8 0

2 years ago

Suppose you toss a fair coin 10 times, let X denote the number of heads. (a) What is the probability that X=5? (b) What is the p

zubka84 [21]

Answer: The required answers are

(a) 0.25, (b) 0.62, (c) 6.

Step-by-step explanation: Given that we toss a fair coin 10 times and X denote the number of heads.

We are to find

(a) the probability that X=5

(b) the probability that X greater or equal than 5

(c) the minimum value of a such that P(X ≤ a) > 0.8.

We know that the probability of getting r heads out of n tosses in a toss of coin is given by the formula of binomial distribution as follows :

$P(X=r)=^nC_r\left(\dfrac{1}{2}\right)^r\left(\dfrac{1}{2}\right)^{n-r}.$

(a) The probability of getting 5 heads is given by

$P(X=5)\\\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}\\\\\\=\dfrac{10!}{5!(10-5)!}\dfrac{1}{2^{10}}\\\\\\=0.24609\\\\\sim0.25.$

(b) The probability of getting 5 or more than 5 heads is

$P(X\geq 5)\\\\=P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}+^{10}C_6\left(\dfrac{1}{2}\right)^6\left(\dfrac{1}{2}\right)^{10-6}+^{10}C_7\left(\dfrac{1}{2}\right)^7\left(\dfrac{1}{2}\right)^{10-7}+^{10}C_8\left(\dfrac{1}{2}\right)^8\left(\dfrac{1}{2}\right)^{10-8}+^{10}C_9\left(\dfrac{1}{2}\right)^9\left(\dfrac{1}{2}\right)^{10-9}+^{10}C_{10}\left(\dfrac{1}{2}\right)^{10}\left(\dfrac{1}{2}\right)^{10-10}\\\\\\=0.24609+0.20507+0.11718+0.04394+0.0097+0.00097\\\\=0.62295\\\\\sim 0.62.$

(c) Proceeding as in parts (a) and (b), we see that

if a = 10, then

$P(X\leq 0)=0.00097,\\\\P(X\leq 1)=0.01067,\\\\P(X\leq 2)=0.05461,\\\\P(X\leq 3)=0.17179,\\\\P(X\leq 4)=0.37686,\\\\P(X\leq 5)=0.62295,\\\\P(X\leq 6)=0.82802.$

Therefore, the minimum value of a is 6.

Hence, all the questions are answered.

3 0

3 years ago

Find the perimeter of a triangle with sides 12 inches, 9 inches, and 15 inches.

Artist 52 [7]

If its perimeter, it should be quite easy to find. Just add 12+9+15. Which equals 36. So the perimeter is 36 inches. -Hope it helps!

7 0

3 years ago

Read 2 more answers

Which of the following ordered pairs is a solution of 2x-y=-9?

Ann [662]

Answer:

(4,-1)

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

S = vt + 16t^2, solve for v.

Phoenix [80]

$S=vt+16t^2\ \ \ \ \ | subtract\ 16t^2\\\\
S-16t^2=vt\ \ \ \ \ | divide\ by\ t\\\\
\frac{S-16t^2}{t}=v\\\\\Solution\ is\ v=\frac{S-16t^2}{t}.$

7 0

3 years ago