Answer:
There are 21 blue marbles
Step-by-step explanation:
In this question, we are asked to calculate the number of blue marbles in a bag that contains a total of 60 marbles, given the probability of choosing a blue marble.
Mathematically, the probability of choosing a blue marble can be represented as:
P(B) = number of blue marbles/ Total number of marbles
From the question, we can identify that P(B) is 0.35, number of Marbles is unknown while the total number of marbles is 60.
We insert these values in the equation;
0.35 = number of blue marbles/60
Hence, number of blue marbles = 60 * 0.35 = 21
{ x + 3 y = 7 * ( - 2)
2 x + 4 y = 8
{ - 2 x - 6 y = - 14
2 x + 4 y = 8
_______________
-2 y = - 6 * ( -1)
2 y = 6
y = 6 / 2
y = 3
For x :
2 x + 4 y = 8
2 x + 4 * ( 3) = 8
2 x + 12 = 8
2 x = 8 - 12
2 x = - 4
x = - 4 / 2
x = - 2
Solution: x = -2 and y = 3
hope this helps!
Answer:
x=34
Step-by-step explanation:
When we look triangle SQR, we have angles 3x and 68, we know that sum angles of triangle is 180.
<R=180-(3x+68)
Now, we look at the PQS:
<PQS=180-68=112°
Then :
<PSQ=180-(112+x)=68-x
Then we have :
Angles PSR= 68-x+3x=68+2x and angles TSU=4x.
We have that
PSR=TSU
68+2x=4x
4x-2x=68
2x=68
x=34
Answer:
a) 3
b) 9
c) 81
d) x
Step-by-step explanation:
We know the properties of log function as:
1) log(AB) = log(A) + log(B)
2) 
3) log(aᵇ) = b × log(a)
also,
4) 
Given:
a. y = 
Now,
taking log both sides, we get
log(y) = 
using 3, we get
log(y) = log₃(3) × log(3)
using 4, we get
log(y) =
× log(3)
or
log(y) = 1 × log(3)
taking anti-log both sides
y = 3
b. y = 
Now,
taking log both sides, we get
log(y) = 
using 3, we get
log(y) = log₃(9) × log(3)
using 4, we get
log(y) =
× log(3)
or
log(y) = log(9)
taking anti-log both sides
y = 9
c. y = 
Now,
taking log both sides, we get
log(y) = 
using 3, we get
log(y) = log₃(81) × log(3)
using 4, we get
log(y) =
× log(3)
or
log(y) = log(81)
taking anti-log both sides
y = 81
d. y = 
Now,
taking log both sides, we get
log(y) = 
using 3, we get
log(y) = log₃(x) × log(3)
using 4, we get
log(y) =
× log(3)
or
log(y) = log(x)
taking anti-log both sides
y = x
This is all about factoring. First of all, if we have the division of fractions, we can flip the second fraction and change the sign to multiplication. So now we have

. Now factor both the numerator and the denominator in the fraction on the left. Factor a 7 out of the numerator and factor completely the denominator to get this as a whole:

. The (x+3) terms cancel each other out as do the (x+2) terms, leaving you simply with