Both the leftmost digit and the rightmost digit of a four-digit numberN are equal to 1. When these digits are removed, the two-digit number
thus obtained is N ÷ 21. Find N.

Answers

Answer 1

Answer: $N=1000w+100x+10y+z\nw=z=1\nx,y\in\{0,1,2,\ldots,7,8,9\}\n10x+y=(N)/(21)\n10x+y=(1000w+100x+10y+z)/(21)\n10x+y=(1000+100x+10y+1)/(21)\n10x+y=(100x+10y+1001)/(21)\n210x+21y=100x+10y+1001\n110x+11y-1001=0\n10x+y-91=0\ny=-10x+91\n\n\hbox{The above equation meets the condition }x,y\in\{0,1,2,\ldots,7,8,9\}\n\hbox{only for } x=9:\ny=-10\cdot9+91\ny=-90+91\ny=1\n\n\hbox{Therefore:}\nN=1000\cdot1+100\cdot9+10\cdot1+1\nN=1000+900+10+1\nN=\boxed{1911}$

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Determine the smallest 6 digit number which is exactly divisible by 8,15,and21

Answers

Find the least common multiple of 8, 15, and 21. . . . . . It's 280 .

So all the numbers divisible by 8, 15, and 21 are all the multiples of 280.

The smallest 6-digit number is 100,000 .

100,000 / 280 = 357.1 , so the next whole-number multiple is the 358th one.

280 x 358 = 100,240 .

You can tell right away that this is the smallest one that qualifies,
because if you take away 280 and go to the next smaller multiple,
it won't have 6 digits anymore.

If x2=y3, what is the value of z does x3z=y9?

Answers

If x² = y³ , for what value of z does $x^(3z)$ = $Y^(9)$ ?

Answer:

z= 2

Step-by-step explanation:

To solve the question given, we will follow the steps below;

$X^(3z)$ = $Y^(9)$ -----------------------------------------------------------------(1)

but applying the law of indices mᵃᵇ = (mᵃ)ᵇ

then

$Y^(9)$ = $(Y^(3))^(3)$

replace $Y^(9)$ by $(Y^(3))^(3)$ in equation (1)

$X^(3z)$ = $Y^(9)$

$X^(3z)$ = $(Y^(3))^(3)$ --------------------------------------------------------------------(2)

but from the question x² = y³

replace y³ by x² in equation (2)

$X^(3z)$ = $(Y^(3))^(3)$

$X^(3z)$ = $(X^(2))^(3)$

$X^(3z)$ = $X^(6)$

3z = 6

divide both-side of the equation by 3

3z/3 = 6/3

On the left-hand side of the equation, 3 at the numerator will cancel-out 3 at the denominator leaving us with just z while on the right-hand side of the equation 6 will be divided by 3

z= 2

Given a conditional statement p → q, which statement is logically equivalent? ~p → ~q
~q → ~p
q → p
p → ~q

Answers

Hello,
p=>q is equivalent to ~q → ~p

p-------q-------p=>q--~q ----- ~p----~q → ~p
0-------0-------1-------1 ------- 1------- 1
0-------1-------1-------0------- 1------- 1
1-------0-------0-------1------- 0-------0
1-------1-------1-------0------- 0-------1

Column 3= column 6 ==>equivalent

Answer B

The logically equivalent statement to p → q is:

~q → ~p

How to find the logically equivalent statement?

The conditional statement:

p → q

p and q are propositions, then the conditional statement is can be written as:

if p is true, then q is also true.

So, always that p is true, q is also true, this means that if q is not true, then p must also not be true.

Then we can rewrite this using the negation propositions, which are:

~p and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

If you want to learn more about statements, you can read:

brainly.com/question/1601404

The work of a student to solve a set of equations is shown:Equation A: y = 4 − 2z
Equation B: 4y = 2 − 4z
Step 1: −4(y) = −4(4 − 2z) [Equation A is multiplied by −4.]
4y = 2 − 4z [Equation B]
Step 2: −4y = 4 − 2z [Equation A in Step 1 is simplified.]
4y = 2 − 4z [Equation B]
Step 3: 0 = 6 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 6
Step 5: z = 1
In which step did the student first make an error?
Step 1
Step 3
Step 4
Step 2

Answers

in step 2 .. because when you multiple by -4 in step 1 , the equation in step 2 will be ( -4y =-16 + 8z)

Five Easter eggs or added to my initial collection of Easter eggs I share them between myself and two friends each person get exactly 4 find how many X there were initially by solving and approximate equation?

Answers

I am sorry that I don’t know what you mean by approximate equation but I can help with the actual question. So first of all you gotta start by times ing the number of Easter eggs the people get by the number of people to get the amount. 4eggsx3people=12 eggs now we have to add five to the 12 eggs because at the start of the equation is says they added 5 to the original number of eggs so 12eggs+5eggs=17eggs. This is the number of eggs the person gets at the start. 17.

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