The ratio of j to 40 is 1 to 2. What is the value of j?<br> A) 1<br> B) 10<br> C) 20<br> D) 80

Explain how to find the value of the digit 7 in the number 3,684,591.74.

alisha [4.7K]

Step-by-step explanation:

every position in a number stands for a different power of 10, which is then multiplied by the digit in that position.

and the value of the whole number is the sum of these little individual calculations.

left of the decimal point we start with 10⁰ = 1 as basic value.

then the second position left of the decimal point stands for 10¹ = 10.

the third position left of the decimal point stands for 10² = 100.

and so on.

now, right of the decimal point we go in the other direction. the first position right of the decimal point stands for 10^-1 = 1/10.

the second position stands for 10^-2 = 1/100.

and so on.

so, the 7 in this number has the value of 7/10 or 7 tenths.

the given number would be fully written

3×10⁶ + 6×10⁵ + 8×10⁴ + 4×10³ + 5×10² + 9×10¹ + 1×10⁰ + 7×10^-1 + 4×10^-2

the decimal point tells us for a number where to begin counting with 10⁰ and 10^-1.

7 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20%5Clarge%5Cbegin%7Bbmatrix%7D%20%5Cbegin%7Barray%7D%20%7B%20l%20l%20%7D%20%7B%202%20%7D%20%

SVETLANKA909090 [29]

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

$\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix} \begin{bmatrix} \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \end{bmatrix}$

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

$\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix} \begin{bmatrix} \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \end{bmatrix}$

In matrix multiplication, the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.

$\left(\begin{matrix}2&3\\5&4\end{matrix}\right)\left(\begin{matrix}2&0&3\\-1&1&5\end{matrix}\right)$

Multiply each element of the 1st row of the 1st matrix by the corresponding element of the 1st column of the 2nd matrix. Then add these products to obtain the element in the 1st row, 1st column of the product matrix.

$\left(\begin{matrix}2\times 2+3\left(-1\right)&&\\&&\end{matrix}\right)$

The remaining elements of the product matrix are found in the same way.

$\left(\begin{matrix}2\times 2+3\left(-1\right)&3&2\times 3+3\times 5\\5\times 2+4\left(-1\right)&4&5\times 3+4\times 5\end{matrix}\right)$

Simplify each element by multiplying the individual terms.

$\left(\begin{matrix}4-3&3&6+15\\10-4&4&15+20\end{matrix}\right)$

Now, sum each element of the matrix.

$\large\boxed{\boxed{\left(\begin{matrix}1&3&21\\6&4&35\end{matrix}\right) }}$

7 0

3 years ago

There are 680 raisins in 8 bags. If each bag has the same number of raisins, how many raisins are in 12 bags?

Marta_Voda [28]

Answer:

1020 raisins

Step-by-step explanation:

Let's set up a proportion using the following setup:

raisins/bags= raisins/ bags

We know there are 680 raisins in 8 bags.

680 raisins/8 bags= raisins/bags

We don't know how many raisins are in 12 bags, so we can say x raisins are in 12 bags.

680 raisins/ 8 bags= x raisins / 12 bags

680/8=x/12

We want to find x. To do this, we must get x by itself.

x is being diveded by 12. The inverse of division is multiplication. Multiply both sides of the equation by 12.

12*(680/8)= (x/12)*12

12*680/8=x

12*85=x

1020=x

x= 1020 raisins

There are 1020 raisins in 12 bags.

3 0

3 years ago

In a certain city, 30 percent of the people are conservatives, 50 percent are liberals, and 20 percent are independents. records

nignag [31]

If the person did not vote it can be:
30/100 (30%) people in the city are conservatives, and only 65/100 voted - so 45/100 did not voted.

Liberals are 50% of the city population (1/2), and 82/100 of them voted, so 100/100-82/100=8/100 did not voted!

So let’s make 2 probability events:
1) A person did not voted
2) a person is liberal

Probability that the person is a liberal: 1/2
Person didn’t voted and it’s a liberal:
1/2*8/100= 8/200=4/100 [*]

[*] To count the probability of two probability events you need to multiply them.

6 0

3 years ago

What is the distance between the points (4,5) and (10,13) on a coordinate plane?

Readme [11.4K]

The distacne between the points (x1,y1) and (x2,y2) is
$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
so the distance between (4,5) and (10,13) is
well, first
x1=4
y1=5
x2=10
y2=13
so

$D=\sqrt{(10-4)^2+(13-5)^2}$
$D=\sqrt{(6)^2+(8)^2}$
$D=\sqrt{36+64}$
D=√100
D=10
the distance is 10 units

7 0

3 years ago

The ratio of j to 40 is 1 to 2. What is the value of j? A) 1 B) 10 C) 20 D) 80