Lily made $75.36 more than Layla did. If Layla raised her price to $1.00, she would still not make more money than Lily.
Use a proportion to find the number of cupcakes Lily makes in 8 hours. She bakes 7 cupcakes in 10 minutes; we want to know how many she makes in 8(60)=480 (since there are 8 hours and each hour is 60 minutes):
7/10 = x/480
Cross multiply:
7*480 = 10*x
3360 = 10x
Divide both sides by 10:
3360/10 = 10x/10
336 = x
Lily bakes 336 cupcakes.
She sells 2/3 of these; 2/3(336) = 2/3(336/1) = 672/3 = 224 cupcakes sold.
Each cupcake is sold for $1.29; 224(1.29) = 288.96
To find the number of cupcakes Layla makes in 8 hours, we set up a different proportion. We know she bakes 8 cupcakes in 12 minutes; we want to know how many she bakes in 8(60) = 480 minutes:
8/12 = x/480
8*480 = 12*x
3840 = 12x
Divide both sides by 12:
3840/12 = 12x/12
320 = x
She bakes 320 cupcakes. She sells 75% of those; 75% = 75/100 = 0.75:
0.75(320) = 240
Each of those 240 cupcakes sells for $0.89:
0.89(240) = 213.60
This means Lily makes 288.96-213.60 = 75.36 more than Layla.
If Layla raised her price to $1.00, she would make 1(240) = $240; this is still less than Lily.
Answer:
39.9
Step-by-step explanation:
a/sinA = c/sinC
a/sin(77) = 16/sin(23)
a = sin(77) × 16/sin(23)
a = 39.89935764
<h3>
Answer:</h3>
- 3,200 + 560 + 16 √ [ True ]
- (400 × 8) + (70 × 8) + (2 × 8) √ [ True ]
- (400 × 8) × (70 × 8) × (2 × 8) X [ False ]
- 3,776 √ [ True ]
- 3,200 × 560 × 16 √ [True ]
- (400 + 70 + 2) × 8 √ [ True ]
- (400 × 70 × 2) × 8 X [ False ]
- 28,672,000 X [ False ]
<h3>
Step-by-step explanation:</h3>
3,200 + 560 + 16 √
(400 × 8) + (70 × 8) + (2 × 8) √
(400 × 8) × (70 × 8) × (2 × 8) X
3,776 √
3,200 × 560 × 16 √
(400 + 70 + 2) × 8 √
(400 × 70 × 2) × 8 X
28,672,000 X
I assume you're just solving for x. Factorize the left side as
3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0
Recall that
sin²(x) + cos²(x) = 1
so that the equation further reduces to
3 sin²(x) cos²(x) = 0
Also recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0
Solve for x :
3/4 sin²(2x) = 0
sin²(2x) = 0
sin(2x) = 0
2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ
(where n is any integer)
2x = 2nπ or 2x = (2n + 1) π
x = nπ or x = (2n + 1)/2 π
Notice that this means the solution set is
{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}
so we can condense the solution further to
x = nπ/2
with any integer n.
A = L * W
P = 2(L) + 2(W) or P = 2(L + W)
7 * 10 + 7 * 2 = 7(10 + 2) = 7 * 12.....this will get u the area
2 * 7 + 2 * 12 = 2(7 + 12) = 2(19)...this will get u the perimeter
7 + 12....this gets u neither
2(7 + 12).....this will get u perimeter
7 + 12 + 7 + 12......this will also get u perimeter
7 * 12....this will get u area
