Answer:
The company should make 0 jumbo and 300 regular biscuits.
The maximum income is $42.
Step-by-step explanation:
Let's say J is the number of jumbo biscuits and R is the number of regular biscuits.
The oven can bake at most 300 biscuits. So:
J + R ≤ 300
Each jumbo biscuit uses 2 oz of flour, and each regular biscuit uses 1 oz of flour. There is 500 oz of flour available. Therefore:
2J + R ≤ 500
Income from jumbo biscuits is $0.12, and income from regular biscuits is $0.14. So the total income is:
I = 0.12J + 0.14R
Graph the two inequalities under the condition that J ≥ 0 and R ≥ 0:
desmos.com/calculator/aea00cmpwm
The region where the inequalities intersect has 4 corners:
(J, R) = (0, 0); (0, 300); (250, 0); (200, 100)
Find the income at each point:
(0, 0): I = 0
(0, 300): I = 42
(250, 0): I = 30
(200, 100): I = 38
The company makes maximum profit of $42 by baking 0 jumbo biscuits and 300 regular biscuits.
Seems all good to me at least!
Answer: 24 tests
Step-by-step explanation:
Ms. Carey graded 1/3 of the tests and still had 16 tests to go.
This means that the 16 tests represent the remaining proportion of the total number of tests:
= 1 - 1/3
= 2/3
2/3 of the total is equal to 16 tests. Assuming the total is x, the expression would be:
2/3x = 16
x = 16 ÷ 2/3
x = 16 * 3/2
x = 24 tests
We use the Pythagorean theorem
x^2=7^2+24^2
x^2=49+576
x^2=625
x=sqrt(625)=25
The correct order to express cos3x in terms of cosx is; As shown in steps 1 to 9 below.
<h3>How to simplify Trigonometric Identities?</h3>
The steps to simplify the trigonometric identities cos 3x in terms of cos x are as follows;
Step 1; cos x = cos(2x + x)
Step 2; cos(2x) cosx - sin(2x) sinx
Step 3; 1 - 2sin^2x(cosx) -(2sinxcosx)sinx
Step 4; cosx - 2sin²x cosx - 2sin²x cosx
Step 5; cosx - 4sin²x cosx
Step 6; cosx( 1 - 4sin²x)
Step 7; cosx{1 - 4(1 - cos²x)}
Step 8; cosx{-3 + 4cos²x}
Step 9; 4cos³x - 3cosx
Read more about Trigonometric Identities at; brainly.com/question/7331447
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