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olga_2 [115]
3 years ago
15

A cookbook cost 3 times as a storybook.A cookbook and 4 storybook cost $112.How much did a storybook cost?

Mathematics
2 answers:
Alexxx [7]3 years ago
6 0

Answer:

Cost of storybook is $16

Step-by-step explanation:

Let's assume that the Cost of storybook= ‘x’

If the cost of the cookbook is 3 times the cost of storybook then the cost of the cookbook will be ‘3x’

The cost of 1 cookbook and 4 storybooks = $112

The cost of cookbook and storybook can be calculated by the equation:

3x+4x=112

7x=112

Divide both sides by 7 to isolate x:  

7x/7=112/7

x=16

Therefore, the cost of storybook is $16

Reptile [31]3 years ago
3 0
1c+4s=112
1c=3s
3s+4s=112
7s=112
Storybook= $16
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3 years ago
Sum of all natural numbers from100to300 which are divisible by 4and 5 is​
My name is Ann [436]

If x is a number that is both divisible by 4 and 5, then

\begin{cases}x\equiv0\pmod4\\x\equiv0\pmod5\end{cases}

4 and 5 are coprime, so we can use the Chinese remainder theorem to solve this system and find that x=20n is a solution to the system, where n is any integer. Simply put, any multiple of 20 fits the bill.

Now, there are 11 numbers between 100 and 300 that are divisible by 20 (100, 120, 140, and so on). We have 20n=100 when n=5, so the sum we want to compute is

\displaystyle\sum_{n=5}^{15}20n=\boxed{2200}

4 0
3 years ago
Recall, we have five connectives in propositional logic ¬, ∧, ∨, →, ↔ (negation, conjunction, disjunction, conditional and bicon
Free_Kalibri [48]

Answer:

(a) ¬(p→¬q)

(b) ¬p→q

(c) ¬((p→q)→¬(q→p))

Step-by-step explanation

taking into account the truth table for the conditional connective:

<u>p | q | p→q </u>

T | T |   T    

T | F |   F    

F | T |   T    

F | F |   T    

(a) and (b) can be seen from truth tables:

for (a) <u>p∧q</u>:

<u>p | q | ¬q | p→¬q | ¬(p→¬q) | p∧q</u>

T | T |  F  |   F     |    T       |  T

T | F |  T  |  T      |    F       |  F

F | T |  F  |  T      |    F       |  F

F | F |  T  |  T      |    F       |  F

As they have the same truth table, they are equivalent.

In a similar manner, for (b) p∨q:

<u>p | q | ¬p | ¬p→q | p∨q</u>

T | T |  F  |   T     |    T    

T | F |  F  |   T     |    T    

F | T |  T  |   T     |    T    

F | F |  T  |   F     |    F    

again, the truth tables are the same.

For (c)p↔q, we have to remember that p ↔ q can be written as (p→q)∧(q→p). By replacing p with (p→q) and q with (q→p) in the answer for part (a) we can change the ∧ connector to an equivalent using ¬ and →. Doing this we get ¬((p→q)→¬(q→p))

4 0
3 years ago
In equilateral ΔABC, AD, BE, and CF are medians. If FO = 4, then AE = A) 4 B) 4 3 C) 8 D) 12
vampirchik [111]

Firstly, we need to draw triangle

we know that

O is a centroid

and centroid divides median into 2:1

so,

\frac{CO}{FO} =\frac{2}{1}

we have FO=4

so, we can plug it

\frac{CO}{4} =\frac{2}{1}

CO=8

now, we can find CF

CF=OC+FO

CF=8+4

CF=12

now, we can see triangle ACF is a right angled triangle

so, we can use pythagoras theorem

x^2=(\frac{x}{2} )^2+12^2

now, we can solve for x

\frac{3x^2}{4}=144

x^2=192

x=8\sqrt{3}

Since, it is equilateral triangle

so,

AC=x=8\sqrt{3}

we know that

E is a mid-point

so,

AE=\frac{AC}{2}

now, we can plug values

AE=\frac{8\sqrt{3}}{2}

AE=4\sqrt{3}................Answer


5 0
3 years ago
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