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luda_lava [24]
3 years ago
14

There are (2^4)^2 ⋅ 2^0 books in a cupboard. What is the total number of books in the cupboard?

Mathematics
1 answer:
irinina [24]3 years ago
5 0
Hey there!

First of all, we can get rid of that 2 ^{0}. Anyting to the power of 0 is equal to one.

Now, we can apply our rule of a power to a power which states that:

(x^{a})^y =  x^{ay}

Therefore, since we have two to the fourth raised to the second power, we just multiply the powers to get 2^8, or C.

Hope this helps!
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Justin had $24 to buy a gift card for his cousin Julie and he found a gift for $22 with 5% sales tax is added on will Justin hav
Aloiza [94]
Yes he would have enough money.

8 0
3 years ago
Simplify the expression by combining like
viva [34]

Answer:

Below

Step-by-step explanation:

First we combine your first set of terms,

7b^2 + 2b^2 = 9b^2

There's a subtraction hidden in there!

9b^2 - 3b^2 = 6b^2

Next we do the same thing for the second term,

3b + 7b = 10b

but there's a subtraction in the expression!

10b - b = 9b

Then we finish with our third term

6 + 5 = 11

Answer:

6b^2 + 9b + 11

4 0
3 years ago
[15 Points] Solve for x.<br> <img src="https://tex.z-dn.net/?f=45x%2B34%3D24x%2B16" id="TexFormula1" title="45x+34=24x+16" alt="
sergiy2304 [10]

Answer:

6/7

Step-by-step explanation:

45x+34=24x+16

collect like terms, we now have;

45x-24x=16-34

21x=-18

X=18/21

X=6/7

8 0
3 years ago
Keegan is priting and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total p
Damm [24]

Complete question is;

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

Answer:

Number of t-shirts to make maximum profit = 2790 shirts

Maximum profit = $12,209

Step-by-step explanation:

From the question, we are given that the profit function is;

p(x) = -x³ + 4x² + x

For the maximum value of the profit function,

(dp/dx) = 0 and (d²p/dx²) < 0

Since, p(x) = -x³ + 4x² + x

Then,

(dp/dx) = -3x² + 8x + 1

at maximum point (dp/dx) = 0, thus;

-3x² + 8x + 1 = 0

Solving this using quadratic formula, the roots are;

x = -0.12 or 2.79

Also, (d²p/dx²) = -6x + 8

Now, let's put the roots of x into -6x + 8 and check for maximum value conditon;

at x = -0.12

(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0

At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0

Maximum has to be d²p/dx² < 0

So, the one that meets the condition is -8.74 < 0 at x = 2.79

Thus, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousands) = 2790

Now, the maximum profits that corresponds to this number of t-shirts of 2.79(in thousands) is obtained by putting 2.79 for x in the profit function;

So,

p(2.79) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.7176 + 31.1364 + 2.79

p(x) = 12.2088 (in thousand dollars) ≈ $12,209

6 0
2 years ago
Help on these 2 please!!
gladu [14]
Hope this helps
7 \frac{1}{5}  - 2 \frac{3}{5}  =  \frac{36}{5}  -  \frac{13}{5}  =  \frac{23}{5}  = 4 \frac{3}{5}

8 \frac{2}{5}  - 4 \frac{3}{5}  =  \frac{42}{5}  -  \frac{23}{5}  =  \frac{19}{5}  = 3 \frac{4}{5}
good luck
6 0
3 years ago
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