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Svetradugi [14.3K]
3 years ago
9

The number of calories you burn depends on your weight. A 160​-pound person burns 237 calories during 30 minutes of tennis. Find

the number of calories that a 190​-pound person would burn during the same​ activity, assuming they burn calories at the same rate.
Mathematics
1 answer:
larisa [96]3 years ago
5 0

Answer:

A 190-pound person would burn 285 calories at the same rate.

Step-by-step explanation:

<em>Calories burn depends on the weight</em>

<em>Weight of first person = 160</em>

Calories burn for 160 pounds in 30 mins =  237

Calories burn rate for 1 pound in 30 mins = \frac{237}{160} = 1.5


<em>Calories burn for 190 Pound person would be:</em>

Weight of second person = 190

Calories burn for 190 pounds in 30 min:

As the burn rate of calories is same for the two persons:

= rate × weight

= 1.5 * 190

= 285 calories

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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
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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

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Use the drop-down menus to complete the proof. by the unique line postulate, you can draw only one segment,
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The reflection of BC over I is shown below.

<h3>What is reflection?</h3>
  • A reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is known as the reflection's axis (in dimension 2) or plane (in dimension 3).
  • A figure's mirror image in the axis or plane of reflection is its image by reflection.

See the attached figure for a better explanation:

1. By the unique line postulate, you can draw only one line segment: BC

  • Since only one line can be drawn between two distinct points.

2. Using the definition of reflection, reflect BC over l.

  • To find the line segment which reflects BC over l, we will use the definition of reflection.

3. By the definition of reflection, C is the image of itself and A is the image of B.

  • Definition of reflection says the figure about a line is transformed to form the mirror image.
  • Now, the CD is the perpendicular bisector of AB so A and B are equidistant from D forming a mirror image of each other.

4. Since reflections preserve length, AC = BC

  • In Reflection the figure is transformed to form a mirror image.
  • Hence the length will be preserved in case of reflection.

Therefore, the reflection of BC over I is shown.

Know more about reflection here:

brainly.com/question/1908648

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The question you are looking for is here:

C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, Using the definition of, reflect BC over l. By the definition of reflection, C is the image of itself and is the image of B. Since reflections preserve , AC = BC.

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