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rjkz [21]
3 years ago
12

Food costs are expected to rise 6% each month for the next year. Which series correctly depicts the cost (to the nearest cent) f

or the next three months if the current cost is $150 per month?
a. $150.00 + $159.00 + $168.00
b.$150.00 + $159.00 + $168.54
c.$159.00 + $168.00 + $177.00
d.$159.00 + $168.54 + $178.65
Mathematics
2 answers:
alexira [117]3 years ago
4 0
For this case we have the following equation:
 y = 150 * (1.06) ^ t
 For the first month we have:
 y = 150 * (1.06) ^ 1
 y = 159 $
 For the second month we have:
 y = 150 * (1.06) ^ 2
 y = 168.54 $
 For the third month we have:
 y = 150 * (1.06) ^ 1
 y = 178.65 $
 Answer:
 
d. $ 159.00 + $ 168.54 + $ 178.65
BartSMP [9]3 years ago
3 0

Answer:

the final answer is the last option, D

Step-by-step explanation:

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allsm [11]

Answer:

m∠DEC = 78°

Step-by-step explanation:

Given information: AC = AD, AB⊥BD, m∠DAC = 44° and CE bisects ∠ACD.

If two sides of a triangles are congruent then the opposite angles of congruent sides are congruent.

AC = AD                 (Given)

\angle ADC\cong \angle ACD

m\angle ADC=m\angle ACD

According to the angle sum property, the sum of interior angles of a triangle is 180°.

m\angle ADC+m\angle ACD+m\angle DAC=180

m\angle ACD+m\angle ACD+44=180

2m\angle ACD=180-44

2m\angle ACD=136

Divide both sides by 2.

m\angle ACD=68

CE bisects ∠ACD.

m\angle ACE=m\angle DCE=\dfrac{\angle ACD}{2}

m\angle ACE=m\angle DCE=\dfrac{68}{2}

m\angle ACE=m\angle DCE=34

Use angle sum property in triangle CDE,

m\angle CDE+m\angle DCE+m\angle DEC=180

68+34+m\angle DEC=180

68+34+m\angle DEC=180

102+m\angle DEC=180

Subtract 102 from both sides.

m\angle DEC=180-102

m\angle DEC=78

Therefore, the measure of angle DEC is 78°.

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3 years ago
A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the number of shoppers is 10
Ymorist [56]

Answer:

193 shoppers

Step-by-step explanation:

2nd  120 +12

3rd  132+13.2

4rd 145.2+ 14.52

5th 159.72+15.972

6th 175.692 +17.5692

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3 years ago
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Answer:

Volume of original toolbox = 180 in³

Yes, doubling one dimension only would double the volume of the toolbox.

Step-by-step explanation:

Volume = L x W x H

10 x 6 x 3 = 180 in³

proof:

double length = 20 x 6 x 3 = 360 in³, which is double the original

double width = 10 x 12 x 3 = 360 in³, which is double the original

double height = 10 x 6 x 6 = 360 in³, which is double the original

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3 years ago
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vfiekz [6]
Answer: The fourth term is -102

----------------------------------------------

Explanation:

The term after the nth term is generated by this rule  a_{n+1} = -4(a_n) + 2 which means that we first
Step 1) multiply the nth term ( a_n ) by -4
Step 2) Add the result of step 1 to the value 2 to get the next term in the sequence

Let's follow those steps above to generate the first four terms

The first term is a_1 = 2. In short, the first term is 2

The second term is...
a_{n+1} = -4(a_n) + 2
a_{1+1} = -4(a_1) + 2
a_{2} = -4(2) + 2
a_{2} = -8 + 2
a_{2} = -6
So the second term is -6

The third term is...
a_{n+1} = -4(a_n) + 2
a_{2+1} = -4(a_2) + 2
a_{3} = -4(-6) + 2
a_{3} = 24 + 2
a_{3} = 26
The third term is 26

Finally, the fourth term is...
a_{n+1} = -4(a_n) + 2
a_{3+1} = -4(a_3) + 2
a_{4} = -4(26) + 2
a_{4} = -104 + 2
a_{4} = -102
The fourth term is -102.
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