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3 years ago

Find the real solution(s) of the equation. Round your answer to two decimal places when appropriate. 5x^6=30

Mathematics

1 answer:

Elina [12.6K]3 years ago

7 0

Answer:

The real solutions are

$x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35$

Step-by-step explanation:

The solution, or root, of an equation is any value or set of values that can be substituted into the equation to make it a true statement.

To find the real solutions of the equation $5x^6=30$ :

$\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5x^6}{5}=\frac{30}{5}\\\\\mathrm{Simplify}\\\\x^6=6\\\\\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)}\\\\x=\sqrt[6]{6}\approx 1.35\\\\\:x=-\sqrt[6]{6}\approx -1.35$

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Rent-An-SUV charges an $80 fee to rent a truck and $12 per mile. Another rental company charges a $150 fee to rent a truck

almond37 [142]

The linear equation that can be used to calculate daily car rentals is f(x) = -20x + 320

Since we are not told what to find, we can look for the linear equation that can be used to calculate daily car rentals;

Let the charge amount be y

Let the amount per mile of the truck rent be x.

If rent-An-SUV charges an $80 fee to rent a truck and $12 per mile, this can be expressed in coordinate form as (12, 80)

Similarly, if another rental company charges a $150 fee to rent a truck and $8.50 per mile, this can also be written in a coordinate form as (8.50, 150)

The standard linear expression is given as f(x) = mx + b

m is the rate of change

b is the y- intercept

Get the rate of change;

$m=\frac{150-80}{8.5-12}\\m=\frac{70}{-3.5}\\m= -20\\$

Get the y-intercept;

80 = -20(12) + b

80 = -240 + b

b = 320

Get the required linear equation;

f(x) = mx + b

f(x) = -20x + 320

Hence the linear equation that can be used to calculate daily car rentals is f(x) = -20x + 320

Learn more on linear equation here: brainly.com/question/12788590

4 0

3 years ago

The sum of two positive integers is 97 and their difference is 37. What is their product?

LuckyWell [14K]

Answer:

2010

Step-by-step explanation:

If the numbers are x and y, you have ...

x +y = 97

x -y = 37

Adding these two equations gives ...

2x = 134

x = 67

y = 67 -37 = 30

The product is then ...

xy = (67)(30) = 2010

Alternate solution

There is no need to find the actual numbers. We can go directly to their product.

(x+y)² = x² +2xy +y² = 97² = 9409

(x-y)² = x² -2xy +y² = 37² = 1369

Subtracting the second equation from the first gives ...

4xy = 9409 -1369 = 8040

xy = 8040/4 = 2010

Of course the difference of squares can be factored, so we could compute ...

(97² -37²)/4 = (97 +37)(97 -37)/4 = 134(60)/4 = 134(15) = 2010

8 0

2 years ago

It is believed that 43% of the US population can play the piano, 28% can play the guitar, 15% can play the harmonica, 12% can pl

melomori [17]

Answer:

The smallest sample size to satisfy the conditions is n=500.

Step-by-step explanation:

The condition for performing the inference related to the sample size is that, for all the categories, the expected success and failures in the sample are at least 10:

$np\geq10\\\\n(1-p)\geq10$

The largest sample size required will be for the minimum p or (1-p).

This happens to be the proportion that can play other instruments: 2%.

Then, we can calculate the minimum sample size as:

$np\geq10\\\\n(0.02)\geq10\\\\n\geq(10/0.02)\\\\n\geq500$

6 0

3 years ago

Wild fruit flies have red eyes. A recessive mutation produces white-eyed individuals. A researcher wants to assess the proportio

svlad2 [7]

Answer:

a. The conditions are met to use a large-sample confidence interval.

b. [0.048; 0.171]

c. Decision: Not reject the null hypothesis.

d. Check explanation.

Step-by-step explanation:

Hello!

You have the following study variable:

X: red-eyed fruit fly that shows to be heterozygous due to producing mixed progeny after being crossed with s white-eyed fruit fly.

n= 100

x= 11

sample proportion 'p= 0.11

Binomial criteria:

1. The number of observation of the trial is fixed (In this case n = 100)

2. Each observation in the trial is independent, this means that none of the trials will affect the probability of the next trial

3. The probability of success in the same from one trial to another (In this case our "success" is that the fruit fly show heterozygous trough its progeny)

So X≈ Bi (n;ρ)

Considering that the sample is big enough (n≥30), you can apply the Central Limit Theorem and approximate the distribution of the sample proportion to normal. So you can use the large-sample confidence interval.

b. The formula for the confidence interval is:

'p ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{'p(1-'p)}{n} }$

$Z_{1-\alpha /2} = Z_{0.975} = 1.96$

0.11 ± 1.96* $\sqrt{\frac{0.11*0.89}{100} }$

[0.048; 0.171]

At a confidence level of 95%, you'd expect that the interval [0.048; 0.171] will contain the value of the population proportion of heterozygous red-eyed flies.

H₀: ρ = 0.10

H₁: ρ ≠ 0.10

α: 0.05

Z= $\frac{'p - p}{\sqrt{\frac{p(1-p)}{n} } }$

Z= $\frac{0.11 - 0.10}{\sqrt{\frac{0.10*0.90}{100} } }$

Z= 0.33

The two tailed p-value for this test is 0.7414. The p-value is greater than the level of significance so the decision is to not reject the null hypothesis.

To be able to compare a Confidence Interval several conditions shoud be met.

1) The interval and the hypothesis test should be made for the sale population parameter.

2) The hypothesis has to be two-tailed

3) Both levels (confidence and significance) should be complementary.

4) Both have to be made with the information of the same sample. (Remember that the variable is random and the values will change from sample to sample therefore it makes no sense to compare an interval and hypothesis of different samples. You could reach a wrong conclusion)

If the conditions are met, you check the calculated interval to see if it contains the value of the parameter under the null hypothesis. If the interval contains the value (In this case 0.10) then the hypothesis is to be supported. If the interval doesn't include the value, then the hypothesis is to be rejected.

I hope this helps!

7 0

3 years ago

The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations b

Anna007 [38]

Answer:

2 hours, 142 miles

Step-by-step explanation:

Given;

equation of motion of car A as;

y = 55x + 32

equation of motion of car B as;

y = 42x + 58

where;

y is distance measured in miles

x is time measured in hours

When the distance of the two cars are equal, we will have the following equation;

55x + 32 = 42x + 58

collect like terms and solve for x

55x - 42x = 58 - 32

13x = 26

x = 26 /13

x = 2 hours ( x is time measured in hours)

Now substitute in the value of x into any equation of the cars;

y = 55x + 32

y = 55 (2) + 32

y = 110 + 32

y = 142 miles ( y is distance measured in miles)

Thus, the correct option is 2 hours, 142 miles

8 0

3 years ago