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____ [38]
3 years ago
13

Travon had a balance of $345.28 in his checking account. During the week amounts: $65.08, $24.50, and $118.95. He then made a de

posit of $56.00. What was his balance after the deposit?
Mathematics
1 answer:
Vladimir79 [104]3 years ago
8 0

Select Is a Function or Is not a Function to correctly classify each relation.

<span><span>Title Is a Function Is not a Function</span><span><span><span><span>{<span><span>(<span>3, 7</span>)</span>,<span>(<span>3, 6</span>)</span>,<span>(<span>5, 4</span>)</span>,<span>(<span>4, 7</span>)</span></span>}</span></span> </span><span><span><span>{<span><span>(<span>1, 5</span>)</span>,<span>(<span>3, 5</span>)</span>,<span>(<span>4, 6</span>)</span>,<span>(<span>6, 4</span>)</span></span>}</span></span> </span><span><span><span>{<span><span>(<span>2, 3</span>)</span>,<span>(<span>4, 2</span>)</span>,<span>(<span>4, 6</span>)</span>,<span>(<span>5, 8</span>)</span></span>}</span></span> </span><span><span><span>{<span><span>(<span>0, 4</span>)</span>,<span>(<span>3, 2</span>)</span>,<span>(<span>4, 2</span>)</span>,<span>(<span>6, 5</span>)</span></span>}</span></span> </span></span></span>
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Explain which variables would be included when using technology to calculate the present value of a lump sum and to calculate th
koban [17]

Answer:

a. Present value of a lump sum =

PV = FV / ( 1 + i )ⁿ

b. Present value of an annuity =

P = PMT x ((1 – (1 / (1 + r)⁻ⁿ )) / r)

Step-by-step explanation:

a. Present Value of a Lump sum =

PV = FV / ( 1 + i )ⁿ

Where variables in the formula are explained as follows

PV = Present Value of the given amount today

FV = Future Value of the given amount

i = Discount rate

n = Number of periods

b. Present value of an annuity is given as:

P = PMT x ((1 – (1 / (1 + r)⁻ⁿ)) / r)

The variables in the equation are explained as the follows:

P = the present value of annuity

PMT = Payment per period or the amount in each annuity payment

r =  the interest or discount rate

n = total number of periods or the number of payments left to receive

8 0
3 years ago
How is this solved using trig identities (sum/difference)?
GenaCL600 [577]
FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

cos \beta = -\frac{1}{2}  \sqrt{3}

tan \beta= \frac{1}{3}  \sqrt{3}

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2}  \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )
sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )
sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )
cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )
cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )

Find tan (α - β)
tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha  tan \beta }
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}

Simplify the denominator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5\sqrt{3}}{24})}
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the numerator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }
tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the fraction
tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})
tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}

7 0
3 years ago
Each tree in the orchard had exactly 118 apples on it. The number of apples in the whole orchard was 2,242. How many apple trees
sergejj [24]
118×2242
= 264,556
this is the answer
7 0
3 years ago
Read 2 more answers
A pool holds 19,900 gallons of water. There are two
Vaselesa [24]

Answer:

396010000

Step-by-step explanation: You multiply 19,900 * 19900 because there are 2 pools and you will get your answer

5 0
3 years ago
Read 2 more answers
Can any one help with y = 2x + 4
geniusboy [140]

Answer:

It's in the screenshot hope it helpsss

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
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