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3 years ago

How many minutes he does arm routine and abdominal routine

Mathematics

1 answer:

AlekseyPX3 years ago

5 0

Let $x$ be the amount of time it takes to perform an arm routine and $y$ be the amount of time it takes to perform an abdominal routine. We see:

$4x+y=70$
$4x+2y=100$

Subtracting the second equation from the first gives $y=30$ . Substituting gives $4x+30=70$ , so $4x=40$ and $x=10$ .

Thus, an arm routine takes ten minutes and an abdominal routine takes thirty minutes.

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A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour.

baherus [9]

A function that gives the amount that the plant earns per man-hour t years after it opens is $\mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}$

<h3><u>Solution:</u></h3>

Given that

A manufacturing plant earned $80 per man-hour of labor when it opened.

Each year, the plant earns an additional 5% per man-hour.

Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.

Amount earned by plant when it is opened = $80 per man-hour

As it is given that each year, the plants earns an additional of 5% per man hour

So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)

Amount earned by plant after two years is given as:

$=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052$

Similarly Amount earned by plant after three years $=80 \times 1.05^{t}$

$\begin{array}{l}{\Rightarrow \text { Amount earned by plant after } t \text { years }=80 \times 1.05^{t}} \\\\ {\Rightarrow \text { Required function } \mathrm{A}(t)=80 \times 1.05^{t}}\end{array}$

Hence a function that gives the amount that the plant earns per man-hour t years after it opens is $\mathrm{A}(t)=80 \times 1.05^{t}$

5 0

3 years ago

If y(x) = 4x, what is x when y(x) = 4? <br><br> a.2<br> b.1.<br> c.4<br> d.0

zavuch27 [327]

Answer:

b. 1

Step-by-step explanation:

Step 1: Define

y(x) = 4x

y(x) = 4

Step 2: Substitute and Evaluate

4 = 4x

x = 1

8 0

3 years ago

Please help me on this

Leni [432]

5 7/8 is the answer to the problem

4 0

3 years ago

Find the seventh term of the expansion of (3x+7y)^11

Ber [7]

13,207,982,634 x⁵y⁶

Step-by-step explanation:

We understand that in Binomial Theorem, expounding of polynomial functions, we have a rule that also involves the use of Pascal's Triangle to find the Coefficients that will be used to multiply each variable as the polynomial function is multiplied by itself several times;

(3x + 7y)^11 = ₁₁C₀ (3x)¹¹(7y)⁰ + ₁₁C₁ (3x)¹⁰(7y)¹ + ₁₁C₂ (3x)⁹(7y)² + ₁₁C₃ (3x)⁸(7y)³ + ₁₁C₄ (3x)⁷(7y)⁴ + ₁₁C₅ (3x)⁶(7y)⁵ + ₁₁C₆ (3x)⁵(7y)⁶....

The 7th term in our case is;

₁₁C₆ (3x)⁵(7y)⁶

According to the attached Pascals Triangle, the coefficient for our term should be 462, so;

462 (3x)⁵(7y)⁶

= 462 (243x⁵) (117,649y⁶)

= 13,207,982,634 x⁵y⁶

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