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2 years ago

Which unit rate is higher 24 for 5 or 5 for 24

Mathematics

1 answer:

frez [133]2 years ago

3 0

Answer:

24 for 5 is higher because you have to divide 24 by 5 and if you do that it gives you $4.8, while 5 for 24 gives you a unit rate of $0.20.

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Help! If you know this can you tell me how to do it?

aleksandr82 [10.1K]

Answer:

Step-by-step explanation:

Here's how this works:

Get everything together into one fraction by finding the LCD and doing the math. The LCD is sin(x) cos(x). Multiplying that in to each term looks like this:

$[sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?$

In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

$\frac{sin^2(x)}{sin(x)cos(x)}+\frac{cos^2(x)}{sin(x)cos(x)}=?$

Put everything over the common denominator now:

$\frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)}=?$

Since $sin^2(x)+cos^2(x)=1$ , we will make that substitution:

$\frac{1}{sin(x)cos(x)}$

We could separate that fraction into 2:

$\frac{1}{sin(x)}$ × $\frac{1}{cos(x)}$

$\frac{1}{sin(x)}=csc(x)$ and $\frac{1}{cos(x)}=sec(x)$

Therefore, the simplification is

sec(x)csc(x)

5 0

3 years ago

An aircraft factory manufactures airplane engines. The unit C(the cost in dollars to make each airplane engine) depends on the n

blsea [12.9K]

34,590 because even if 0 engines are made, then 34,590 is still expected as a base price

5 0

2 years ago

A sales person is given a choice of two salary plans. Plan 1 is a weekly salary of 700 plus 4% commission of sales. Plan 2 is a

bezimeni [28]

Let 's' represent the amount of sales.

Plan 1:

$\text{ \$700 + (4\% of s)}$ $\begin{gathered} \text{ \$700+(}\frac{\text{4}}{100}\times s) \\ \text{ \$700+(0.04}\times s)=\text{ \$700}+0.04s \end{gathered}$

Plan 2:

$12\text{ \% of s}$ $\begin{gathered} \frac{12}{100}\times s \\ 0.12\times s=0.12s \end{gathered}$

Equating the two plans together and solving for the amount of sales,

$\begin{gathered} \text{Plan 2=Plan 1} \\ 0.12s=\text{ \$700+0.04s} \\ \end{gathered}$

Collecting like terms,

$\begin{gathered} 0.12s-0.04s=\text{ \$700} \\ 0.08s=\text{\$700} \end{gathered}$

Divide both sides by 0.08,

$\begin{gathered} \frac{0.08s}{0.08}=\frac{\text{ \$700}}{0.08} \\ s=\text{ \$8750} \end{gathered}$

Hence, the amount of sales is $8,750.

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1 year ago

Given: △ACM, m∠C=90°, CP ⊥ AM

larisa86 [58]

Answer: The answer is $3\dfrac{4}{7}.$

Step-by-step explanation: Given in the question that ΔAM is a right-angled triangle, where ∠C = 90°, CP ⊥ AM, AC : CM = 3 : 4 and MP - AP = 1. We are to find AM.

Let, AC = 3x and CM = 4x.

In the right-angled triangle ACM, we have

$AM^2=AC^2+CM^2=(3x)^2+(4x)^2=9x^2+16x^2=25x^2\\\\\Rightarrow AM=5x.$

Now,

$AM=AP+PM=AP+(AP+1)\\\\\Rightarrow 2AP=AM-1\\\\\Rightarrow 2AP=5x-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(A)$

Now, since CP ⊥ AM, so ΔACP and ΔMCP are both right-angled triangles.

So,

$CP^2=AC^2-AP^2=CM^2-MP^2\\\\\Rightarrow (3x)^2-AP^2=(4x)^2-(AP+1)^2\\\\\Rightarrow 9x^2-AP^2=16x^2-AP^2-2AP-1\\\\\Rightarrow 2AP=7x^2-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(B)$