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n200080 [17]
2 years ago
10

Two numbers are in a ratio 11:7. If the smaller number is 700, what is the larger number? Pls tell with steps

Mathematics
2 answers:
Nutka1998 [239]2 years ago
6 0

Answer:

The larger number is 1100

Step-by-step explanation:

Let larger number be x

We have

\frac{x}{700} =\frac{11}{7} \\\\x=100\times11\\\\=1100

andre [41]2 years ago
4 0

Answer:

The larger number is <u>1100</u><u>.</u>

Step-by-step explanation:

<u>Solution</u> :

Let the,

  • >> Larger number be <em>11x</em><em>.</em>
  • >> Smaller number be <em>7x</em><em>.</em>

Now, According to the question :

\begin{gathered} \dashrightarrow\sf{Smaller \:  number} =  \tt{700} \end{gathered}

\begin{gathered} \dashrightarrow\sf{7x}= \tt{700} \end{gathered}

\begin{gathered} \dashrightarrow\sf{x}= \tt{700 \div 7} \end{gathered}

\begin{gathered} \dashrightarrow\sf{x}= \tt{ \dfrac{700}{7} } \end{gathered}

\begin{gathered} \dashrightarrow\sf{x}= \tt{\cancel{\dfrac{700}{7}}} \end{gathered}

\begin{gathered} \dashrightarrow  \sf{x}= \tt{100} \end{gathered}

Hence, the value of x is 100.

Now, calculating the larger number :

\begin{gathered} \dashrightarrow\sf{Larger \:  number} =  \tt{11x} \end{gathered}

\begin{gathered} \dashrightarrow\sf{Larger \:  number} =  \tt{11 \times 100} \end{gathered}

\begin{gathered} \dashrightarrow\sf{Larger \:  number} =  \tt{1100} \end{gathered}

Hence, the larger number is 1100

\rule{300}{1.5}

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Which of the following are valid (necessarily true) sentences? a. (∃x x = x) ⇒ (∀ y ∃z y = z). b. ∀ x P(x) ∨ ¬P(x). c. ∀ x Smart
Phantasy [73]

Answer:

b; ∀x   P(x) ∨ ¬P(x)

Step-by-step explanation:

Suppose that we have a proposition p

Such that p can be true or false.

We can define the negation of p as:

¬p

Such that, if p is false, then ¬p is true

if p is true, then ¬p is false.

Also remember that a proposition like:

p ∨ q

is true when, at least one, p or q, is true.

Then if we write:

p ∨ ¬p

Always one of these will be true (and the other false)

Then the statement is true.

And if the statement depends on some variable, then we will have that:

p(x) ∨ ¬p(x)

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from this, we can conclude that the statement that is always true is:

b; ∀x   P(x) ∨ ¬P(x)

Where here we have:

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7 0
2 years ago
Plzz anyone solve all answers plzzzzzzzz​
algol13

You posted a lot of problems here. In the future please only post one problem at a time. Thank you.

I'll do the first two problems to get you started. Hopefully it will help you finish off the rest of the questions.

==========================================

Problem 1

{18, a, b, -3} is an arithmetic sequence or arithmetic progression (AP).

This means we have some number d added on to each term to get the next term.

first term = 18

second term = first term + d = 18+d = a

third term = second term + d = (18+d)+d = 18+2d = b

fourth term = third term + d = (18+2d)+d = 18+3d = -3

----

Let's solve that last equation for d

18+3d = -3

18+3d-18 = -3-18

3d = -21

3d/3 = -21/3

d = -7

----

The value d = -7 tells us to add -7 to each term to get the next term. In other words, we subtract 7 from each term to get the next term

first term = 18

second term = first term + d = 18+d = 18+(-7) = 18-7 = 11

third term = second term + d = 11+d = 11+(-7) = 11-7 = 4

fourth term = third term + d = 4+d = 4+(-7) = 4-7 = -3

----

We see that a = 11 and b = 4 are the second and third terms respectively.

Therefore, a+b = 11+4 = 15

-------------

<h3>Answer: 15</h3>

==========================================

Problem 2

A multiple of 4 is in the form 4*n for some integer n, ie n is a whole number.

We want to know which values of 4*n are between 10 and 250.

----

Divide both 10 and 250 by 4 to get the following

10/4 = 2.5

250/4 = 62.5

If n = 2, then 4*n = 4*2 = 8 is not between 10 and 250; however n = 3 will make 4*n = 4*3 = 12 to be between 10 and 250. We see that n = 3 is the smallest possible allowed value.

If n = 62, then 4*n = 4*62 = 248 is between 10 and 250; while n = 63 will make 4*n too big because 4*63 = 252. The largest n can get is n = 62

----

The question posed in question 2 is equivalent to asking the following: "How many values are in the set {3, 4, 5, ..., 60, 61, 62}?"

You could count all of the values in the set, but that exercise is very tedious busywork. There's a much faster way. First lets consider the set below

{a, a+1, a+2, ..., b-2, b-1, b}

where a,b are integers. Basically this set starts at 'a', counts up until we get to 'b'. The handy formula

c = b-a+1

will provide the exact count of values in the set {a, a+1, a+2, ..., b-2, b-1, b}

----

In this case, a = 3 and b = 62, making

c = b-a+1

c = 62-3+1

c = 60

There are 60 values in the set {3, 4, 5, ..., 60, 61, 62}

There are 60 multiples of four that are between 10 and 250.

-------------

<h3>Answer: 60</h3>
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