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Tresset [83]
2 years ago
5

A grocery store owner budgets $5,000 to buy and maintain a booth for 300 days to give out samples of food. If she bought the boo

th for $1,400, how much money, in dollars, can she spend on food each day for samples and stay within budget? Write an inequality that represents this situation and indicate what the solution to the inequality will look like.
Mathematics
1 answer:
serious [3.7K]2 years ago
7 0

Answer:

x ≤ $12 a day

Step-by-step explanation:

5000-1400=3600

3600/300=12

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Use integration by parts to find the integrals in Exercise.<br> ∫(4x-12)e-8x dx.
stepladder [879]

Answer:

e(2x^{2} -12x)-4x^{2}+C

Step-by-step explanation:

We have been given an indefinite integral as \int \left(4x-12\right)e-8x\:dx. We are asked to find the given integral.

Let us solve our given problem.

\int \left(4x-12\right)e\:dx-\int 8x\:dx

Take out constant:

e\int \left(4x-12\right)\:dx-8\int x\:dx

e(\int 4x\:dx -\int 12\right\:dx)-8\int x\:dx

e(\frac{4x^{1+1}}{2} -12x)-8*\frac{x^{1+1}}{1+1}+C

e(\frac{4x^{2}}{2} -12x)-8*\frac{x^{2}}{2}+C

e(2x^{2} -12x)-4x^{2}+C

Therefore, our required integral would be e(2x^{2} -12x)-4x^{2}+C.

5 0
3 years ago
Find the measure of one interior angle for the following regular polygon ​
kipiarov [429]

Answer:

144 degrees

Step-by-step explanation:

We can use the formula (n-2)(180), where n = number of sides, to find the sum of all the interior angles in the decagon. Since a decagon has 10 sides:

(n-2)(180) = ?

(10-2)(180) = ?

(8)(180) = 1440.

Now, to find one interior angle in the decagon, divide 1440 by the number sides in our polygon (10).

1,440/10 = 144

               = <u>144 degrees</u>

7 0
3 years ago
Use the given information to write an equation and solve the problem.<br> (28-31 in the picture)
tia_tia [17]

Answer:

28. 120 degrees

29. 30 degrees

30. 56 degrees & 124 degrees

31. 72 degrees, 108 degrees, and 18 degrees

Step-by-step explanation:

We assign variable x for the answer we are looking for (28-29).

28.

Supplement means x + y = 180 degrees. We also know x = 2y. Substitution gives us 3y = 180 degrees, so y = 60 degrees and x = 120 degrees.

29.

Complement means x + y = 90 degrees. We are given 2x = y. Substitution brings us 3x = 90 degrees, x = 30 degrees.

30.

Supplement means x + y = 180 degrees. We are told that y = 2x + 12, so we substitute. This gives 3x + 12 = 180 degrees, x = 56 degrees. Substituting that back into the equation for y, we get 124 degrees.

31.

Supplement means x + y = 180 degrees. Complement means x + z = 90 degrees.  Using our given info, we know y = 6z. We can substitute that in to get x + 6z = 180. Subtracting our second and third equations, we get 5z = 90, z = 18 degrees.  Therefore, x = 72 degrees, y = 108 degrees.

3 0
2 years ago
Read 2 more answers
Giselle works as a carpenter and as a blacksmith. She earns $ 2 0 $20dollar sign, 20 per hour as a carpenter and $ 2 5 $25dollar
dem82 [27]
She worked as a carpenter for 12 hours and as a blacksmith for 18 hours.

Assuming you mean she earned $20 as a carpenter and $25 as a blacksmith per hour, with a total of 30 hours for $690,
let c represent carpenter hours and b for blacksmith hours.

20c + 25b = 690
c + b = 30
Subtract b from each side so that c = 30 - b
Plug this value into the first equation

20(30 - b) + 25b = 690
600 - 20b + 25b = 690
600 + 5b = 690
5b = 90
b = 18

To find c, plug this value of b into the other equation
c + 18 = 30
c = 12


3 0
3 years ago
Read 2 more answers
Solve the following inequality. n/3&gt;1
lbvjy [14]
N/3>1
n>1*3
n>3    or    (3,+∞)

Solution: n>3    or    (3, +∞)
3 0
3 years ago
Read 2 more answers
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