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3 years ago

How do you know a relationship is proportional

Mathematics

1 answer:

Nadya [2.5K]3 years ago

4 0

Answer:

One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional

Ratios are proportional if they represent the same relationship.

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Please help with this

KonstantinChe [14]

I believe the answer is 32

4 0

3 years ago

The derivative of y with respect to x, when y = 3e^5x - 2 is:

Ede4ka [16]

Answer: 15e^5x

Step - by - step

y=3e^5x - 2

By the sum rule, the derivative of 3e^5x - 2 with respect to x is d/dx [ 3e^5x ] + d/dx [-2].

d/dx [ 3e^5x ] + d/dx [ -2 ]

Evalute d/dx [ 3e^5x ]

Since 3 is constant with respect to x , the derivative of 3e^5x with respect to x is
3 d/dx [ e^5x ].

3 d/dx [ e^5x ] + d/dx [ -2 ]

Differentiate using the chain rule, which states that d/dx [ f(g(x))] is f' (g(x)) g' (x) where f(x) = e^x and g(x) = 5x.

To apply the Chain Rule, set u as 5x.
3 ( d/du [ e^u] d/dx [5x] ) + d/dx [ -2]

Differentiate using the Exponential rule which states that d/du [ a^u ] is a^u ln(a) where a=e.

3( e^u d/dx[5x] ) + d/dx [ -2 ]
Replace
3(e^5x d/dx [5x] ) + d/dx [ -2 ]
3(e^5x( 5 d/dx [x] )) + d/dx [ -2 ]

Diffentiate using the Power Rule which states that d/dx [x^n] is nx^n-1 where n=1.
3(e^5x(5*1)) + d/dx [-2]
3 ( e^5x * 5 ) + d/dx [-2]

Multiply 5 by 3
15e^5x + d/dx [-2]

Since -2 is constant with respect to x, the derivative of -2 with respect to x is 0.
15e^5x + 0
15e^5x

5 0

10 months ago

Solve the system of equations.

Alenkasestr [34]

Step-by-step explanation:

<u>Step 1: Substitute x from the second equation into the second one</u>

$2x - 9y = 14$

$2(-6y + 7) - 9y = 14$

$(2 * -6y) + (2 * 7) - 9y = 14$

$-12y + 14 - 9y = 14$

$-21y +14 - 14 = 14 - 14$

$-21y/-21 = 0 / -21$

$y = 0$

<u>Step 2: Substitute y into the second equation</u>

$x = -6y + 7$

$x = -6(0) + 7$

$x = 0 + 7$

$x = 7$

Answer: $x = 7, y = 0$

4 0

3 years ago

Read 2 more answers

Required information An article presents a new method for timing traffic signals in heavily traveled intersections. The effectiv

Natasha2012 [34]

Answer:

$652.6-2.01\frac{311.7}{\sqrt{50}}=563.997$

$652.6+2.01\frac{311.7}{\sqrt{50}}=741.203$

So on this case the 95% confidence interval would be given by (563.997;741.203)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=652.6$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=311.7 represent the sample standard deviation

n=50 represent the sample size

Soltuion to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=50-1=49$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that $t_{\alpha/2}=2.01$

Now we have everything in order to replace into formula (1):

$652.6-2.01\frac{311.7}{\sqrt{50}}=563.997$

$652.6+2.01\frac{311.7}{\sqrt{50}}=741.203$

So on this case the 95% confidence interval would be given by (563.997;741.203)

6 0

3 years ago

If a clock takes 2 seconds to strike twice at 2’o clock, then how much time will it take to strike thrice at 3’o clock ?

zzz [600]

Clock strikes once at one o clock, twice at two o clock, thrice at three o clock and so on. how many times will it strikes for 24 hours. this is a question for time word problem. if u know the answer please write it here.

5 0

3 years ago