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bixtya [17]
3 years ago
8

A customer placed an order with a bakery for muffins.The Baker has completed 37.5% of the order after baking 81 muffins.How many

muffins did the customer order.
Mathematics
1 answer:
likoan [24]3 years ago
6 0

Answer:

The total muffins ordered are <em>216</em>

Step-by-step explanation:

Let the total number of muffins ordered by customer be <em>"x"</em>

It is given that, baker has completed 37.5% of total muffins,

That is, \frac{37.5(x)}{100}

It is also said that he has finished baking 81 muffins.

thus,

<em>\frac{37.5(x)}{100} = 81</em>

<em>x = \frac{(81)(100)}{37.5} = 216</em>

Thus, the total muffins are 216.

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How many permutations of the 26 letters of the English alphabet do not contain any of the strings fish, rat, or bird
NARA [144]

The number of permutations of the 26 letters of the English alphabet that do not contain any of the strings fish, rat, or bird is 402619359782336797900800000

Let

\mathcal{E}=\{\text{All lowercase letters of the English Alphabet}\}\\\\B=\overline{\{b,i,r,d\}} \cup \{bird\}\\\\F=\overline{\{f,i,s,h\}} \cup \{fish\}\\\\R=\overline{\{r,a,t\}} \cup \{rat\}\\\\FR=\overline{\{f,i,s,h,r,a,t\}} \cup \{fish,rat\}

Then

Perm(\mathcal{E})=\{\text{All orderings of all the elements of } \mathcal{E}\}\\\\Perm(B)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing bird}\}\\\\Perm(F)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing fish}\}\\\\Perm(R)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing rat}\}\\\\Perm(FR)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing both fish and rat}\}\\

Note that since

F \cap R=\varnothing, Perm(F)\cap Perm(R)\ne \varnothing

But since

B \cap R \ne \varnothing, Perm(B)\cap Perm(R)= \varnothing

and

B \cap F \ne \varnothing , Perm(B)\cap Perm(F)= \varnothing

Since

|\mathcal{E} |=26 \text{, then, } |Perm(\mathcal{E})|=26! \\\\|B|=26-4+1=23 \text{, then, } |Perm(B)|=23!\\\\|F|=26-4+1=23 \text{, then, } |Perm(F)|=23!\\\\|R|=26-3+1=24 \text{, then, } |Perm(R)|=24!\\\\|FR|=26-7+2=21 \text{, then, } |Perm(FR)|=21!\\

where |Perm(X)|=\text{number of possible permutations of the elements of X taking all at once}

and

|Perm(F) \cup Perm(R)| = |Perm(F)| + |Perm(R)| - |Perm(FR)|\\= 23!+24!- 21! \text{ possibilities}

What we are looking for is the number of permutations of the 26 letters of the alphabet that do  not contain the strings fish, rat or bird, or

|Perm(\mathcal{E})|-|Perm(B)|-|Perm(F)\cup Perm(R)|\\= 26!-23!-(23!+24!- 21!)\\= 402619359782336797900800000 \text{ possibilities}

This link contains another solved problem on permutations:

brainly.com/question/7951365

6 0
2 years ago
What is an equation of the line that is perpendicular to -x+2y=4 and passes through the point (-2, 1)?
KATRIN_1 [288]
First: Slope of -x+2y=42y=x+4y=x/2+2So, m=1/2.
Second: Slope  of the perpendicular line: mp=-2.
Third: Find the line with slope -2 and passes through the point (−2, 1)y-y1=m(x-x1)y-1=-2(x+2)y=-2x-4+1y=-2x-3 

Read more on Brainly.com - brainly.com/question/7942650#readmore

5 0
3 years ago
If y varies inversely as x2 and y = 100 when
love history [14]
Ans: (c)

y = k/x^2

when y = 100, x = 1
100 = k/1^2
k = 100

when x = 2,
y = 100/2
= 50

(u/rachelmarrons already gave you the answer but here’s a step-by-step explanation in case you needed it haha)
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Rosa recorded the height (in centimeters) of a pea plant over a 10-day period for a science experiment. Please help me with this
katrin [286]

Answer:

option a)

y = m(0.5) + 1.8

Step-by-step explanation:

Equation

<h3>y = mx + c</h3>

represent the equation of straight line

here m = gradient of straight line

         c = y-intercept

First find the gradient of the graph

<h3>m = y2 - y1 / x2 - x1</h3>

    = 4 - 3 / 4 - 2

    = 1 / 2

Put the values in the equation of straight line

y =mx + c

4 = 1/2(4) + c

c = 2

y = 1/2x + 2

which is approximately equal to y = 0.5x + 1.8

7 0
3 years ago
3 tens+ 7 thousands +5 ten thousands + 2 ones +6 hundreds
Natali [406]

I'm not sure I understand your question, but I believe the answer you're looking for is 57632.

8 0
3 years ago
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