Answer:
His actual score is 15
Step-by-step explanation:
Here, we are interested in calculating Wayne’s actual score on the ACT
when we say the scores have being standardized, it means the score was reported in terms of the z-score and not the initial raw scores.
Now, mathematically, for the scores to have a negative z-score, it means it is actually below the mean.
The formula for the z-score or standard score is given below;
z-score = (x - mean)/SD
where in this case, x = ? which is the score we are looking for , z-score = -0.5 , mean score = 18 and standard deviation of the scores = 6
So, substituting these values into the z-score equation, we have;
-0.5 = (x-18)/6
x-18 = 6(-0.5)
x -18 = -3
x = -3 + 18
x = 15
Final result :
9y - 17z - 2
Step by step solution :
Step 1 :
1
Simplify —
3
Equation at the end of step 1 :
1
— • (27y - 51z - 6)
3
Step 2 :
Pulling out like terms :
3.1 Pull out like factors :
27y - 51z - 6 = 3 • (9y - 17z - 2)
Final result :
9y - 17z - 2
Answer:
x = s/2
Step-by-step explanation:
● s states have joined the union in 1788
● half of s have joined in 1889
Let x be the number of states that have joined in 1889
● x = (1/2)× s
● x = s/2
Answer:
133.33 years
Step-by-step explanation:
Given that:
Principal = $500
Interest rate (r) = 1.5% = 0.015
Triple amount of principal = $500 * 3 = $1500 = final amount (A)
Number of years (t) =?
Using the relation :
A = P(1 + rt)
1500 = 500(1 + 0.015t)
1500 / 500 = 1 + 0.015t
3 = 1 + 0.015t
3 - 1= 0.015t
2 = 0.015t
2 / 0.015 = 0.015t / 0.015
133.333 = t
133.33 years
Answer:
0.25g + 0.05g + 500g = 500.30g
Step-by-step explanation:
The first step is converting everything to grams, by rules of three. Then we add.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
Unit conversion problems, like this one, is an example of a direct relationship between measures.
First step: 0.5kg to g
Each kg has 1000g. So
1kg - 1000g
0.5kg - xg
x = 1000*0.5
x = 500g
0.5kg = 500g
Second step: 50mg to g
Each g has 1000mg. So:
1g - 1000mg
xg - 50mg
1000x = 50
x = 0.05g
50mg = 0.05g
Third step: 2.5dg to g
Each g has 10dg. So:
1g - 10dg
xg - 2.5dg
2.5x = 10
x = 0.25g
2.5 dg = 0.25g
Final step: Add
0.25g + 0.05g + 500g = 500.30g
