Answer:
0.09
Step-by-step explanation:
So if you use the Simple interest equation it will begin with:
Interest total = Initial Amount of money x Interest rate per year x Years money is invested for.
Then substitute the values you have been given so:
$6300 = 7000 x Interest rate per year x 10.
This is simplifies to 6300 = 70,000 x Annual Interest rate
You can rearrange this to find the annual interest rate by dividing by 70,000:
Simplifying this would be:
= Interest rate.
The interest rate is 0.09.
To find the maximum or minimum value of a function, we can find the derivative of the function, set it equal to 0, and solve for the critical points.
H'(t) = -32t + 64
Now find the critical numbers:
-32t + 64 = 0
-32t = -64
t = 2 seconds
Since H(t) has a negative leading coefficient, we know that it opens downward. This means that the critical point is a maximum value rather than a minimum. If we weren't sure, we could check by plugging in a value for t slightly less and slighter greater than t=2 into H'(t):
H'(1) = 32
H'(3) = -32
As you can see, the rate of change of the object's height goes from increasing to decreasing, meaning the critical point at t=2 is a maximum.
To find the height, plug t=2 into H(t):
H(2) = -16(2)^2 +64(2) + 30 = 94
The answer is 94 ft at 2 sec.
To answer question 12, you first need to know the definition of a <em>prism</em> and a<em> pyramid.
</em>A <em>pyramid </em> is a 3-D structure with one base, whose outer faces are made of triangles, and meet at a single point at the top.
A <em>prism</em> is any 3-D shape with a base of any number of sides, another base with the same amount of sides, and faces joining the two together on every side of the bases.
12.
Shape A is a <em>pyramid</em>, because it has one base, and all the faces join together in at one point.
Shape B is a <em>prism</em>, because it has two bases, and faces joining every side of the bases.
Shape C is a <em>prism.</em>
Shape D is a <em>pyramid.
</em>For #13, you have to know the definition of a cube to figure out the math of how many cubes there are.
A cube is a 3-D shape with six sides, all made up of squares of the same size.
The box has a volume of 120 cubic inches, and each cube is 1 inch. Since every side of a cube is equal, a 1-inch cube is one cubic inch.
This means that a box with a volume of 120 cubic inches will fit 120 of the 1 inch cubes.
1 layer of the cubes, in the diagram, is 8 cubes by 3 cubes, or 24 cubes total.
To find the number of layers needed to fill the box, you divide 120 by 24.
120 ÷ 24 = 5
The answer to #13 is 5 layers.
There are 130 pennies in the jar
Step-by-step explanation:
We have a jar of coins
- All coins are pennies and dimes
- There are 309 coins in the jar
- The total value of all coins in the jar is $ 19.2
We need to find the number of pennies in the jar
Assume that there are p pennies and d dimes in the jar
∵ There are p pennies and d dimes in the jar
∵ There are 309 coins in the jar
∵ All the coins in the jar are pennies and dimes
∴ p + d = 309 ⇒ (1)
∵ The total value of all coins in the jar is $ 19.2
∵ $1 = 100 cents
∴ $19.2 = 19.2 × 100 = 1920 cents
∵ 1 penny = 1 cent
∵ 1 dime = 10 cents
∴ p + 10 d = 1920 ⇒ (2)
Now we have system of equations, we can solve them to find p
∵ p + d = 309 ⇒ (1)
∵ p + 10 d = 1920 ⇒ (2)
- Multiply equation (1) by -10 to eliminate d
∵ (-10)(p) + (-10)(d) = (-10)(309)
∴ -10 p - 10 d = -3090 ⇒ (3)
Add equations (2) , (3)
∴ -9 p = -1170
- Divide both sides by -9
∴ p = 130
There are 130 pennies in the jar
Learn more:
You can learn more about the system of equations in brainly.com/question/3739260
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Answer:
8
Step-by-step explanation:
