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Anastaziya [24]
3 years ago
8

Yuma needs a singer. Singer A is offering her services for an initial $50 in addition to $20 per hour. Singer B is offering his

services for initial $100 in addition to $10 per hour. When will the two singers charge the same amount of money?
Mathematics
1 answer:
hoa [83]3 years ago
8 0
Initial charge charged by the Singer A = $50
Hourly charge of Singer A = $20
Initial amount charged by Singer B = $100
Hourly rate charged by Singer B = $10
Let us assume the time after which both singers will charge the smae amount of money = x
Then
50 + 20x = 100 + 10x
20x -10x = 100 - 50
10x = 50
x = 50/10
   = 5
So after 5 hours both Singer A and Singer B will charge the same amount of money. I hope the procedure is clear to you and you can attempt such problems in future without needing any kind of help.
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Saturn is 8.867 × 10^8 miles away from the Sun. Uranus is 1.787 × 10^9 miles away from the Sun. Approximately how many times far
Over [174]

Answer:

<em>2 times </em>

<em></em>

Step-by-step explanation:

Please refer to the image attached of our <em>solar system </em>in which Saturn and Uranus are clearly visible.

Distance of Saturn from Sun, D_{1} = 8.867 \times 10^{8}\ miles

Distance of Uranus from Sun, D_{2} = 1.787 \times 10^{9}\ miles

We have to find, how many times the Uranus is far from Sun than Saturn is far from Sun.

Let us begin by multiplying the distance of Saturn from Sun by 2: D_{1} \times 2 = 8.867 \times 10^{8}\ miles \times 2\\\Rightarrow 17.734 \times 10^{8}\ miles\\\Rightarrow 1.7734 \times 10^{1} \times  10^{8}\ miles\\\Rightarrow 1.7734 \times 10^{8+1}\  miles\\\Rightarrow 1.7734 \times 10^{9} $\approx$ D_{2}

From above, we can say that D_{2} is approximately <em>twice </em>of D_{1}.

In other words, we can say that Uranus is at approximately twice distance from Sun than that of Saturn is.

3 0
3 years ago
Donna fed 1/8 of the chickens at the farm which decimal is equal to the fraction of chickens Donna fed (Must Show Long Divison)
nalin [4]

0.125 is the decimal of 1/8

4 0
3 years ago
Is #5 correct please check it. Write each equation in slope intercept form.
Nata [24]
I think it is right!!!
3 0
3 years ago
Find the first four terms of the sequence given ai<br> 31 and an+1<br> an<br> 3.
Leno4ka [110]

Answer:

he arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence

Step-by-step explanation:

In an arithmetic sequence,

a_1=2a

1

=2

a_i=a_{i-1}-3a

i

=a

i−1

−3

To find:

The sum of the first 335 terms in the given sequence.

Solution:

The recursive formula of an arithmetic sequence is:

a_i=a_{i-1}+da

i

=a

i−1

+d ...(i)

Where, d is the common difference.

We have,

a_i=a_{i-1}-3a

i

=a

i−1

−3 ...(ii)

On comparing (i) and (ii), we get

d=-3d=−3

The sum of first i terms of an arithmetic sequence is:

S_i=\dfrac{i}{2}[2a+(i-1)d]S

i

=

2

i

[2a+(i−1)d]

Putting i=335,a=2,d=-3i=335,a=2,d=−3 , we get

S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)]S

335

=

2

335

[2(2)+(335−1)(−3)]

S_{335}=\dfrac{335}{2}[4+(334)(-3)]S

335

=

2

335

[4+(334)(−3)]

S_{335}=\dfrac{335}{2}[4-1002]S

335

=

2

335

[4−1002]

S_{335}=\dfrac{335}{2}(-998)S

335

=

2

335

(−998)

On further simplification, we get

S_{335}=335\times (-499)S

335

=335×(−499)

S_{335}=-167165S

335

=−167165

Therefore, the sum of the first 335 terms in the given sequence is -167165.

7 0
3 years ago
Please tell me the answer with explanation.​
nikitadnepr [17]

Answer:

HELLO DEAR,

GIVEN:-

10sin⁴A + 15cos⁴A = 6

=> 10(sin²A)² + 15cos⁴A = 6

=> 10{(1 - cos²A)²} + 15cos⁴A = 6

=> 10{1 + cos⁴A - 2cos²A} + 15cos⁴A = 6

=> 10 + 10cos⁴A - 20cos²A + 15cos⁴A = 6

=> 25cos⁴A - 20cos²A + 4 = 0

=> 25cos⁴A - 10cos²A - 10cos²A + 4 = 0

=> 5cos²A(5cos²A - 2) - 2(5cos²A - 2) = 0

=> (5cos²A - 2)(5cos²A - 2) = 0

=> cos²A = 2/5

=> cosA = √2/√5 [ secA = √5/√2]

therefore,

sinA = √[1 - 2/5] = √3/√5 [ cosecA = √5/√3]

now,

27cosec^6A + 8sec^6A

=> 27 × {(√5/√3)²}³ + 8 × {(√5/√2)²}³

=> 27 × 125/27 + 8 × 125/8

=> 125 + 125

=> 250.

HENCE, 27cosec^6A + 8sec^6A = 250.

I HOPE IT'S HELP YOU DEAR,

THANKS

Step-by-step explanation:

7 0
3 years ago
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