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tester [92]
3 years ago
15

If a table and a bench is $1000 combined. The cost of the table is three times the cost of the bench. What is the cost of the be

nch
Mathematics
1 answer:
attashe74 [19]3 years ago
5 0
1,000= 3x+x. 1,000=4x. 250=x. 1,000= 3(250) +250. 1,000=750+250. The bench costs $250.
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Find the doubling time of an investment earning 7% interest if interest is compounded continuously
Alex

Answer:

The doubling time of this investment would be 9.9 years.

Step-by-step explanation:

The appropriate equation for this compound interest is

A = Pe^(rt), where P is the principal, r is the interest rate as a decimal fraction, and t is the elapsed time in years.

If P doubles, then A = 2P

Thus, 2P = Pe^(0.07t)

Dividing both sides by P results in 2 = e^(0.07t)

Take the natural log of both sides:  ln 2 = 0.07t.

Then t = elapsed time = ln 2

                                       --------- = 0.69315/0.07 = 9.9

                                         0.07

The doubling time of this investment would be 9.9 years.

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3 years ago
In a triangle, one of the angle measures 70°
Tanya [424]

Answer:

the two angles are 55° each

Step-by-step explanation:

Let the two equal angles be y each

Therefore,

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Collect like terms

2y = 180 — 70

2y = 110

Divide both side by the coefficient of y i.e 2

y = 110/2

y = 55°

Therefore, the two angles are 55° each

4 0
3 years ago
If a coin is tossed three times, find probability of getting
Assoli18 [71]

{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}

‣ A coin is tossed three times.

{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}

‣ The probability of getting,

1) Exactly 3 tails

2) At most 2 heads

3) At least 2 tails

4) Exactly 2 heads

5) Exactly 3 heads

{\large{\textsf{\textbf{\underline{\underline{Using \: Formula :}}}}}}

\star \: \tt  P(E)= {\underline{\boxed{\sf{\red{  \dfrac{ Favourable \:  outcomes }{Total \:  outcomes}  }}}}}

{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}

★ When three coins are tossed,

then the sample space = {HHH, HHT, THH, TTH, HTH, HTT, THT, TTT}

[here H denotes head and T denotes tail]

⇒Total number of outcomes \tt [ \: n(s) \: ] = 8

<u>1) Exactly 3 tails </u>

Here

• Favourable outcomes = {HHH} = 1

• Total outcomes = 8

\therefore  \sf Probability_{(exactly  \: 3 \:  tails)}  =  \red{ \dfrac{1}{8}}

<u>2) At most 2 heads</u>

[It means there can be two or one or no heads]

Here

• Favourable outcomes = {HHT, THH, HTH, TTH, HTT, THT, TTT} = 7

• Total outcomes = 8

\therefore  \sf Probability_{(at \: most  \: 2 \:  heads)}  =  \green{ \dfrac{7}{8}}

<u>3) At least 2 tails </u>

[It means there can be two or more tails]

Here

• Favourable outcomes = {TTH, TTT, HTT, THT} = 4

• Total outcomes = 8

\longrightarrow   \sf Probability_{(at \: least \: 2 \:  tails)}  =  \dfrac{4}{8}

\therefore  \sf Probability_{(at \: least \: 2 \:  tails)}  =   \orange{\dfrac{1}{2}}

<u>4) Exactly 2 heads </u>

Here

• Favourable outcomes = {HTH, THH, HHT } = 3

• Total outcomes = 8

\therefore  \sf Probability_{(exactly \: 2 \:  heads)}  =  \pink{ \dfrac{3}{8}}

<u>5) Exactly 3 heads</u>

Here

• Favourable outcomes = {HHH} = 1

• Total outcomes = 8

\therefore  \sf Probability_{(exactly \: 3 \:  heads)}  =  \purple{ \dfrac{1}{8}}

\rule{280pt}{2pt}

8 0
1 year ago
If x. 5x and 6x are the measures of the
max2010maxim [7]

Answer:

<em>Since one of the angles is 90°, the triangle is right.</em>

Step-by-step explanation:

<u>Angles in a Triangle</u>

The sum of angles in a triangle is 180°. We are given the angles are x, 5x, and 6x, thus:

x + 5x + 6x = 180

Simplifying:

12x = 180

Dividing by 12:

x = 180/12 = 15

x = 15°

5x = 75°

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Since one of the angles is 90°, the triangle is right.

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We can select any two points

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we can use slope formula

m=\frac{y_2-y_1}{x_2-x_1}

now, we can plug points

m=\frac{7-4}{5-0}

m=0.6

we know that slope of line is always constant irrespective of any value of t

so, acceleration will always be same irrespective of any value of t

so, we will get acceleration

a(t)=0.6m/s^2............Answer

(b)

we can see that acceleration is constant

and we know that

derivative of constant is always 0

so, instantaneous rate of acceleration at t=10s is 0........Answer

7 0
3 years ago
Read 2 more answers
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