Which value plotted on the number line rounds up when rounded to the nearest tenth?

At the park, 4/7 of the children are boys. if there are 8 boys at the park, how many are girls?

Oksana_A [137]

There are 4/7 boys, so there are 3/7 girls.

Let the total number of children be x.

4/7x = 8
1/7x = 8 ÷ 4
1/7x = 2
3/7x = 2 x 3
3/7x = 6

There are 6 girls.

4 0

3 years ago

Read 2 more answers

Solve the system of equations.

guajiro [1.7K]

Answer:

Option 2: (1, 0) and (0, -5)

Step-by-step explanation:

Let's solve this system of equations using the elimination method.

Start by labelling the two equations.

5x -y= 5 -----(1)

5x² -y= 5 -----(2)

(2) -(1):

5x² -y -(5x -y)= 5 -5

Expand:

5x² -y -5x +y= 0

5x² -5x= 0

Factorise:

5x(x -1)= 0

5x= 0 or x -1= 0

x= 0 or x= 1

Now that we have found the x values, we can substitute them into either equations to solve for y.

Substitute into (1):

5(0) -y= 5 or 5(1) -y= 5

0 -y= 5 or -y= 5 -5

y= -5 or -y= 0

y= 0

Thus, the solutions are (0, -5) and (1, 0).

3 0

2 years ago

Can somebody prove this mathmatical induction?

Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

$\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2$

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

3 step:

Check for n=k+1 whether the statement

$\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)$

is true.

Start with the left side:

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)$

According to the 2nd step,

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

Substitute it into the $\ast$

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)$

So, you have proved the initial statement

4 0

3 years ago

What is 7 devided by 245 and show work

agasfer [191]

1. Set up the long division.

245/7

2. Calculate 700 ÷ 245, which is 2 with a remainder of 210.

0.02245/7.4.902.10

3. Bring down 0, so that 2100 is large enough to be divided by 245.

0.02245|/.4.902.100

4. Calculate 2100 ÷ 245, which is 8 with a remainder of 140.

0.028245|/.4.902.1001.960140

5. Bring down 0, so that 1400 is large enough to be divided by 245.

0.028245/7.4.902.1001.9601400
6. Calculate 1400 ÷ 245, which is 5 with a remainder of 175.

0.0285245|7.4.902.1001.96014001225175

7. Therefore, 7 divided by 245 approximately equals 0.0285
7÷245≈0.0285

8. Simplify
0.0285 <------------- Answer :)

8 0

3 years ago

Solve x Log 10×=5.9 ×=

Alja [10]

Answer:

x=0.59

Step-by-step explanation:

because if u divide 5.9 by 10 it will give u 0.59

and isolate x

8 0

3 years ago