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rosijanka [135]
3 years ago
7

8. An online bank statement reads as follows: Account balance: $986.24 Car payment: $203.34 Gas bill: $96.67 Check deposit: $128

9.60 Cash deposit: $45 Debit card transaction: $67.12 ATM withdrawal: $30 Find the current account balance to date. A. $937.47 B. $1,726.52 C. $1,555.33 D. $1,923.71
Mathematics
1 answer:
Lunna [17]3 years ago
8 0
Starting balance : 986.24

deductions :
car payment : 203.34
gas bill : 96.67
debit card : 67.12
ATM : 30
total deductions : 203.34 + 96.67 + 67.12 + 30 = 397.13

deposits :
check : 1289.60
cash : 45
total deposits : 1289.60 + 45 = 1334.60

Balance to date : 986.24 + 1334.6 - 397.13 = 1923.71 <==
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A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above an
slega [8]

Answer:

The equation of the parabola that models the path of the long jumper through the air is y = -x^{2}+12\cdot x -27.

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

y = a\cdot x^{2}+b\cdot x + c

Where:

x - Horizontal distance from the start line, measured in meters.

y - Height of the long jumper, measured in meters.

a, b, c - Polynomial constants, measured in \frac{1}{m}, dimensionless and meters, respectively.

If we know that (x_{1},y_{1}) = (3\,m, 0\,m), (x_{2},y_{2}) = (8\,m, 0.05\,m) and (x_{3}, y_{3}) = (9\,m, 0\,m), this system of linear equations is presented below:

9\cdot a + 3\cdot b + c = 0 (Eq. 1)

81\cdot a + 9\cdot b + c = 0 (Eq. 2)

64\cdot a + 8\cdot b + c = 0.05 (Eq. 3)

The coefficients of the polynomial are, respectively:

a = -\frac{1}{100}, b = \frac{3}{25}, c = -\frac{27}{100}

The equation of the parabola that models the path of the long jumper through the air is y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}.

But we need y measured in centimeters, then, we use the following conversion:

y = 100\cdot y'

Then, we get that:

y = -x^{2}+12\cdot x -27

Where x and y are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is y = -x^{2}+12\cdot x -27.

4 0
3 years ago
Is -2.54 greater or less than -2 and 27/50
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-2.54 is equal to -2 27/50
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50/2=L is the a expression 
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Cody was
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On the first day of school last year, Cody was 148.5 cm tall.
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3 years ago
Cube-shaped blocks are packed into a cube-shaped storage container. The edge of the storage container is 2 1/2 feet. The edge le
GarryVolchara [31]

Answer:

Volume of one cube shaped block is, 0.125 cubic feet

Step-by-step explanation:

Volume of a cube(V) is given by:

V = a^3                 .....[1]

where a is the edge length of the cube.

As per the statement:

Cube-shaped blocks are packed into a cube-shaped storage container. The edge of the storage container is 2 1/2 feet.

⇒\text{Edge length of storage} = 2\frac{1}{2} = 2.5 ft

It is also given that:

The edge length of each block is 1/5 the edge length of the storage container

⇒\text{Edge length of each block (a)} = \frac{1}{5} \cdot 2.5 = 0.5 ft

Substitute this in [1] we have;

V = (0.5)^3 = 0.125 ft^3

Therefore,  volume, in cubic feet, of one cube-shaped block is, 0.125

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