The table shows the amount of species of birds and the amount of species of frogs that have been collected in Georgia.
Animal Population Birds
Birds 3.4 x 10^2
Frogs 2.2 x 10^1
How many times more birds species are there than frogs? (1 point)
20 times more bird species
4 times more bird species
15.5 times more bird species
1.6 times more bird species
20 times more bird species
Two students have bank accounts:
Sama: $ 4^3 ⋅ 4^−4/(4^2)^-5
Jimena: $ 3 ⋅ (3^8)^2/(3^2)^3 ⋅ 3^0
Which person has the most money in their account? (1 point)
Sama
They have the same amount of money
You cannot compare the total amount because the bases are different.
Jimena
To compare the amounts of money in their accounts, we need to simplify the expressions.
Sama: $ 4^3 ⋅ 4^(-4) / (4^2)^(-5)
Sama: $ 64 ⋅ 1/ 2^(-5)
Sama: $ 64 ⋅ 1 / 32
Sama: $ 2
Jimena: $ 3 ⋅ (3^8)^2 / (3^2)^3 ⋅ 3^0
Jimena: $ 3 ⋅ 6561^2 / 9^3 ⋅ 1
Jimena: $ 3 ⋅ 43046721 / 729
Jimena: $ 3 ⋅ 59201
Jimena: $ 177603
Therefore, Jimena has the most money in her account.
What is the missing exponent that would make this equation true? k^−5 ⋅ k^2/k^x = (k^0)^−2 (1 point)
x = -5
x = 0
x = 2
x = -3
To find the missing exponent "x" that would make the equation true, we simplify both sides of the equation:
k^(-5) ⋅ k^2 / k^x = (k^0)^(-2)
Using the properties of exponents, we can rewrite the equation as:
k^(-3) / k^x = k^0
Since any non-zero number raised to the power of 0 is 1, we have:
k^(-3) / k^x = 1
Now, we bring k^x to the left side by taking the reciprocal:
1/k^x = k^3
Solving for x, we have:
k^x = 1/k^3
Thus, x = -3
Therefore, the missing exponent that would make the equation true is x = -3.
Which inequality represents the graph below (1 point)
The number line shows the numbers -10 through 1 filled in with a closed circle
−3x − 7 ≥ −10
3x + 7 > 10
3x − 7 < −10
−3x + 7 < 10
The graph described with the filled-in circle represent -10 to 1. This means that the solution includes -10 and 1. Hence, the inequality that represents this graph would have either "≥" or "≤" (greater than or equal to, less than or equal to) symbols, with -10 and 1 inside brackets or circles.
Looking at the options provided:
-3x - 7 ≥ -10 is the inequality that best represents the graph described.