The manager of the toy store at the mall is curious about why nobody is buying the new robot toys. He's very annoyed because he paid a lot of money for inventory, and wants to know how to get the merchandise sold. What is the best method of sampling for him to get his answers?
A.
use a convenience sample of customers in other toy stores
B.
survey customers as they leave the store
C.
survey the toy store employees
D.
random sampling of people walking in the mall

Given:

Given that the figure is a triangular prism.

The length of the prism is 4 m.

The base of the triangle is 2.5 m.

The height of the triangle is 2.25 m.

We need to determine the volume of the triangular prism.

Volume of the triangular prism:

The volume of the triangular prism can be determined using the formula,

[tex]V=\frac{1}{2}bhl[/tex]

where b is the base of the triangle,

h is the height of the triangle and

l is the length of the prism.

Substituting b = 2.5, h = 2.25 and l = 4 in the above formula, we get;

[tex]V=\frac{1}{2}(2.5)(2.25)(4)[/tex]

[tex]V=\frac{1}{2}(22.5)[/tex]

[tex]V=11.25 \ m^3[/tex]

Thus, the volume of the triangular prism is 11.25 m³

The region represented by the shaded area has 25% and accounts for one-quarter of the overall circle.

The area is the space occupied by any two-dimensional figure in a plane. The area of the circle is the space occupied by the circle in a two-dimensional plane.

The formula for calculating circle area is r2, where r is the radius of the circle.

The entire area of the circle in the accompanying figure is r2. The shaded area accounts for one-fourth of the circle's overall area.

Total area =  πr²

Shaded area = ( 1 / 4 )πr²

The percentage of the shaded area will be calculated as

Shaded area = ( 1 / 4 )πr²

Shaded area = ( 0.25 )πr²

To convert it into a percentage multiply by 100.

Shaded area = ( 0.25 x 100 )πr²

Shaded area =25% πr²

Put πr² as the total area.

Shaded area =25% of Total area.

Therefore, the region represented by the shaded area has 25% and is 1/4th of the total circle.

Answer:

1) We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 5[/tex]  

Alternative hypothesis:[tex]\mu > 5[/tex]  

2) [tex]df=n-1=8-1=7[/tex]  

Since is a one sided test the p value would be:  

[tex]p_v =P(t_{(7)}>2.233)=0.0304[/tex]  

3) For this case is we use a significance level of 1% or 99% of confidencewe see that [tex]p_v >\alpha[/tex] and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance [tex]\alpha=0.05[/tex] or 95% of confidence we see that [tex]p_v <\alpha[/tex] and we have enough evidence to conclude that the specification is satisfied.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=6.5[/tex] represent the sample mean

[tex]s=1.9[/tex] represent the sample standard deviation

[tex]n=8[/tex] sample size  

[tex]\mu_o =5[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

Part 1: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 5[/tex]  

Alternative hypothesis:[tex]\mu > 5[/tex]  

If we analyze the size for the sample is <30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{6.5-5}{\frac{1.9}{\sqrt{8}}}=2.233[/tex]    

Part 2: P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=8-1=7[/tex]  

Since is a one sided test the p value would be:  

[tex]p_v =P(t_{(7)}>2.233)=0.0304[/tex]  

Part d: Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant higher compared to the height of men in 1960 at 1% of signficance.  

Part 3

For this case is we use a significance level of 1% or 99% of confidencewe see that [tex]p_v >\alpha[/tex] and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance [tex]\alpha=0.05[/tex] or 95% of confidence we see that [tex]p_v <\alpha[/tex] and we have enough evidence to conclude that the specification is satisfied.

Answer:

y=25

Step-by-step explanation:

10*2=20

20+5=25

Final answer:

When x=10, the value of the function y=2x+5 is 25, found by substituting 10 for x and following the order of operations.

Explanation:

The value of the function y=2x+5 when x=10 can be found by substituting the value of x into the equation. To do this, multiply 2 by 10 and then add 5 to the result:

y = 2(10) + 5

y = 20 + 5

y = 25

Therefore, when x equals 10, the value of the function is 25.

Answer:

5

Step-by-step explanation:

f(-4) f(x)=-2x-3

f(-4)=-2(-4)-3

f(-4)=8-3

f(-4)=5

Answer:

5

Step-by-step explanation:

you imput -4 for x then you proceed as normal solving the equation

-2(-4) - 3 since two negatives when multiplied make a positive

8 - 3

5

Given:

In the given triangle ΔABC,

AB = 9 unit

AC = 2 unit

To find the value of ∠ABC.

Formula

From trigonometric ratio we get,

[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]

Let us take, ∠ABC = [tex]\theta[/tex]

With respect [tex]\theta[/tex], AC is the opposite side and AB is the hypotenuse.

So,

[tex]sin \theta = \frac{AC}{AB}[/tex]

or, [tex]sin \theta[/tex] = [tex]\frac{2}{9}[/tex]

or, [tex]\theta = sin^{-1} (\frac{2}{9} )[/tex]

or, [tex]\theta= 12.84^\circ[/tex]

Hence,

The value of ∠ABC is 12.84°.

Answer:

a movie, m is 3

a video game, v is 5.5

Brainliest would be really appreciated. (need it to unlock chat)

Feel free to ask further questions if you feel like it.

Till then, have a nice day

Step-by-step explanation:

I 5m+2v=26

II 3m+8v=53

I 5m+2v=26 devide by 2 on both sides

5/2m+v=13 subtract 5/2m om both sides

v=13-5/2m

Now put this whole thing in the other equation II, replacing the v there

3m+8(13-5/2m)=53 just calculate it

3m+104-20m=53

-17m+104=53 subtract 53 on both sides

-17m+51=0 add 17m on both sides

51=17m devide by 17

3=m

we found m, v is easy

now put m in an equation from the start, let's take equation I here

I 5m+2v=26

5*(3)+2v=26

15+2v=26 subtract 15 on both sides

2v = 11 devide by 2

v = 5.5

So we found m and v, prices for single items. we can proof this when we put m and v into a given equation and the if it equals a true value

m & v in II

II 3m+8v=53

3*(3)+8*(5.5)=53

9+44=53

53=53

Seems legit.

To find the rental cost for each movie and video game, set up a system of equations based on the given information and solve for the variables.

To find the rental cost for each movie and video game, we can set up a system of equations based on the given information.

Let's assign variables to represent the rental cost for each movie and video game. Let's use 'm' for the cost of a movie and 'g' for the cost of a video game.

Based on the first month's information, we can write the equation: 5m + 2g = 26

Based on the second month's information, we can write the equation: 3m + 8g = 53

Now we can solve this system of equations to find the values of 'm' and 'g'.

By solving the system of equations, we find that the rental cost for each movie is $4 and the rental cost for each video game is $5.

https://brainly.com/question/22393405

#SPJ2

Answer:

141 cookies

Step-by-step explanation:

amount of cookies

= 9(15) + 6

= 135 + 6

= 141

Answer:

No

Step-by-step explanation:

3x + 9 = 13

Subtract 9 from each side

3x + 9-9 = 13-9

3x = 4

Divide each side by 3

3x/3 = 4/3

x = 4/3

8 is not a solution

Answer:

36

Step-by-step explanation:

[tex] \frac{c}{4} - 5 = 4 \\ \\ \frac{c}{4} = 4 + 5\\ \\ \frac{c}{4} = 9 \\ \\ c = 9 \times 4 \\ \\ \huge \red{ \boxed{ c = 36}}[/tex]

Answer:

Step-by-step explanation:

There are 5numbers and 3 letters. Each number can be one among the 10 possible.

Each letter is 1 among the 26 available.

a)The number of possible unique serial numbers are

10^5x 26³

The number of 5 number combinations each different (order important) is 5!(10/5)= 30240

The number of 3 letter combinations each different (order important) is 3!(26/3)=15600

The required probability (that all symbols are different if one laptop is picked at random with equal probability) is

15600x3240/ 10^5x 26³=0.2684

b) The first letter must be at least 4 to be largest among the 5 numbers. So the first letter can be one of . 4,5,6,7,8,9..

The number of 5 number combinations each different and starting with 4 (order important) is .

4!=24

The number of 5 number combinations each different and starting with 5 (order important) is .

4!(5/4)= 120

The number of 5 number combinations each different and starting with 6 (order important) is .

4!(6/4)= 360

The number of 5 number combinations each different and starting with 7 (order important) is .

4!(7/4)= 840

The number of 5 number combinations each different and starting with 8 (order important) is

4!(8/4)= 1680

The number of 5 number combinations each different and starting with 9 (order important) is .

4!(9/4)= 3024

Thus, there are

The required probability ( that all symbols are different and the first number is the largest among the numbers) is

15600* 6040/10^5x 26³= 0.0537

Answer:

False

Step-by-step explanation:

Common sense

Answer:

think 23 pot

Step-by-step explanation:

Answer:

Step-by-step explanation:

23

Answer:

2.47 times more likely.

Step-by-step explanation:

16 out of 178 cases were reported for exposure.

And 8 out of 220 control reported for exposure.

Chances that a case would be reported for exposure = (16/178) = 0.0898876404

Chances that one control would report for exposure = (8/220) = 0.0363636364

Comparing both, how likely were cases to report an exposure compared with controls

= (0.0898876404) ÷ (0.0363636364)

= 2.4719101085 = 2.47 times more likely.

Hope this Helps!!

Answer:

P(Fewer than 3) = 0.05.

Step-by-step explanation:

We are given that a student takes a true-false test that has 10 questions and guesses randomly at each answer.

The above situation can be represented through Binomial distribution;

[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]

where, n = number of trials (samples) taken = 10 questions

            r = number of success = fewer than 3

           p = probability of success which in our question is probability

                that question is answered correctly, i.e; 50%

LET X = Number of questions answered correctly

So, it means X ~ Binom(n = 10, p = 0.50)

Now, Probability that Fewer than 3 questions are answered correctly is given by = P(X < 3)

P(X < 3)  = P(X = 0) + P(X = 1) + P(X = 2)

=  [tex]\binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0}+ \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1}+ \binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}[/tex]

=  [tex]1 \times 0.50^{10} + 10 \times 0.50^{10} +45 \times 0.50^{10}[/tex]

=  0.05

Hence, the P(Fewer than 3) is 0.05.

To find the probability of the student passing the test with at least a 70 percent, we can use the binomial probability formula. The probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).

To find the probability of the student passing the test with at least a 70 percent, we need to find the probability of the student answering 7, 8, 9, or 10 questions correctly out of the 10 questions. Since the student randomly guesses at each answer, the probability of guessing correctly is 0.5. Now we can calculate the probability using the binomial probability formula:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

P(X = k) = C(10, k) * (0.5)^k * (0.5)^(10-k), where C(n, r) is the binomial coefficient (n choose r).

Calculating each probability and summing them up, we get P(X ≥ 7) = 0.171875. Therefore, the probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).

Answer:

20

Step-by-step explanation:

Of means multiply and is means equals

80% * 25 = ?

Change to decimal form

.80 *25 =

20

Answer:

79.45

Step-by-step explanation:

Answer: o Subtract 7 tens from 8 tens.

Step-by-step explanation: you subtract

Answer:

Step-by-step explanation:subtract 7 tens from 8 tens

Answer:

Uhhhhhhhhhhhhh  yes most recipies do call for that

Step-by-step explanation:

have a nice day

Answer:

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

Step-by-step explanation:

We have to write the transition matrix M for the population.

We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.

We can write the transition matrix, in which the rows are the actual state and the columns are the future state.

- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. Then, the probability of staying in the same state is 90%.

-  For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. Then, the probability of staying in the same state is 80%.

- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. Then, the probability of staying in the same state is 82%.

The transition matrix becomes:

[tex]\begin{vmatrix} &NS&P1&PM\\NS& 0.90&0.08&0.02 \\ P1&0.10&0.80 &0.10 \\ PM& 0.08 &0.10&0.82 \end{vmatrix}[/tex]

The actual state matrix is

[tex]\left[\begin{array}{ccc}5,000&2,500&2,500\end{array}\right][/tex]

We can calculate the next month state by multupling the actual state matrix and the transition matrix:

[tex]\left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4950&2650&2400\end{array}\right][/tex]

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:

[tex]\left[\begin{array}{ccc}4950&2650&2400\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4912&2756&2332\end{array}\right][/tex]

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:

[tex]\left( \left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] \right)^{12} =\left[\begin{array}{ccc}4792.63&3005.44&2201.93\end{array}\right][/tex]

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

Answer:

7  2/3

Step-by-step explanation:

Multiply 4/3 by 23/4

Answer:

A prism that has a length of 2, height of 1 and one-half, and width of 2.

Step-by-step explanation:

The formula for calculating the area of a prism is base area × height

Volume = L×W×H

L is the length of the prism

W is the width

H is the height.

To determine the prism that has an area of 6 cubic units, we will substitute the values in the option in the formula.

Using option D i.e prism that has a length of 2, height of 1 and one-half, and width of 2.

L = 2units, H = 1 1/2 units , W = 2units

Substituting in the formula for finding the volume

V = 2×2×3/2

Volume of the prism = 6cubic units

Answer:

B

Step-by-step explanation:

Answer:

a) The test statistic is z=-0.94

b) The p-value is 0.1736

c) The null hypothesis is [tex]H_0:p=0.10[/tex], we can conclude that, if the result is not significant at 0.01 level, we fail to reject the null hypothesis

d) We fail to reject the null hypothesis at 0.01 significance level.

e) We do not have sufficient  evidence to reject the claim that, less than 10​% of the treated subjects experienced headaches.

Step-by-step explanation:

The test statistic is defined by:

[tex]Z=\frac{\hat p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }[/tex]

It was given that, 23 of 277 treated in the clinical trial of the​ drug subjects experienced headaches.

This means that:

[tex]\hat p=\frac{23}{277}\approx 0.083[/tex]  and n=277

The  claim is that, less than 10​% of treated subjects experienced headaches. This means:

[tex]p_0=\frac{10}{100}=0.1[/tex]

We substitute the values into the formula to obtain:

[tex]Z=\frac{0.083-0.1}{\sqrt{\frac{0.1(1-0.1)}{277} } }[/tex]

The test statistics becomes:

[tex]Z=-0.94[/tex]

b) From the normal distribution table, the p-value corresponds to Z=-0.94 .

Since this is a left-tailed test, the p-value corresponds to area under the normal curve that is to the left of z=-0.94

P(Z<-0.94)=0.173609.

c) Since the claim is that, less than 10​% of treated subjects experienced headaches, the null hypothesis is

[tex]H_0:p=0.10[/tex]

The alternate hypothesis will be:

[tex]H_1:p\:<\:0.10[/tex]

This implies that, the result is not significant at 0.01 alpha level.

d) We need to compare the p-value to the significance level. If the significance level is greater than the null hypothesis, we reject the null hypothesis.

Since 0.01<0.1736, we fail to reject the null hypothesis.

d) Conclusion: There is no enough evidence to reject the claim that, less than 10​% of treated subjects experienced headaches.

Answer:

(a)Test statistic[tex]z_{score}=-0.94[/tex]

(b) p-value=0.1736

(c)Null hypothesis,

    [tex]H_0:p=0.10[/tex]

(d)[tex]\alpha>p[/tex], we reject the null hypothesis.

(e)We have experimental values to reject the claim.

Step-by-step explanation:

Given information;

n=277

Significance level [tex]\alpha[/tex]=0.01

By normal distribution,

[tex]z_{score}=\frac{\widehat{p}-p_0}{\frac{\sqrt {p_0(1-p_0)}}{n}}[/tex]

[tex]\widehat{p}=\frac{23}{277}=0.83[/tex]

[tex]p_0=10[/tex]%=0.1

On substitution,

[tex]z_{score}=\frac{{0.83}-0.1}{\frac{\sqrt {0.1(1-0.1)}}{277}}[/tex]

Test static,

[tex]z_{score}=-0.94[/tex]

b)From the table normal distribution,

for,[tex]z_{score}=-0.94,[/tex]

[tex]P(z<-0.94)=0.173609[/tex]

(c)Null hypothesis,

    [tex]H_0:p=0.10[/tex]

     Alternate hypothesis,

    [tex]H_1:p<0.10[/tex]

It implies result is not significant at

[tex]\alpha=0.01[/tex]

(d) On compare value if

[tex]\alpha>p[/tex], we reject the null hypothesis.

For more details please refer link:

https://brainly.com/question/5286270?referrer=searchResults

Answer:

1, [tex]\frac{m}{n}[/tex], [tex]\frac{1-m}{n}[/tex].

Step-by-step explanation:

probability = [tex]\frac{Number of Possible Outcomes}{Total Outcomes}[/tex]

Total number of persons in the party = n

a) Pr ( every person gets their phone back) = Pr (each person picks his phone ) multiplied by number of person

   = [tex]\frac{1}{n}[/tex] × n = 1.

     No of first m persons to pick = m

     No of last m persons to pick = 1 - m

b) Pr (first m persons to pick each gets their phones back) = [tex]\frac{m}{n}[/tex]

c) Pr( first m persons get a phone belonging to last m persons) = [tex]\frac{1-m}{n}[/tex]

Given:

It is given that the measurements of the triangle.

The measure of ∠2 is (3x + 3)°

The measure of ∠3 is (3x - 4)°

The measure of ∠4 is (5x + 8)°

We need to determine the measure of ∠1 and ∠4.

Value of x:

The value of x can be determined using the exterior angle theorem.

Applying the theorem, we have;

[tex]m \angle 4=m \angle 2+m \angle 3[/tex]

Substituting the values, we get;

[tex]5x+8=3x+3+3x-4[/tex]

[tex]5x+8=6x-1[/tex]

[tex]-x+8=-1[/tex]

     [tex]-x=-9[/tex]

        [tex]x=9[/tex]

Thus, the value of x is 9.

Measure of ∠4:

Substituting the value of x in the expression of ∠4, we get;

[tex]m\angle 4=5(9)+8[/tex]

       [tex]=45+8[/tex]

[tex]m\angle 4=53^{\circ}[/tex]

Thus, the measure of ∠4 is 53°

Measure of ∠1:

The angles 1 and 4 are linear pairs and hence these angles add up to 180°

Thus, we have;

[tex]\angle 1+ \angle 4=180^{\circ}[/tex]

Substituting the values, we get;

[tex]\angle 1+ 53^{\circ}=180^{\circ}[/tex]

         [tex]\angle 1=127^{\circ}[/tex]

Thus, the measure of ∠1 is 127°

Answer:

(a)f(x)=0.8869x

(b)g(x)=143.1126x

(c)g(f(x))=126.9266x

(d)g(f(1000))=126926.6 Yen

Step-by-step explanation:

Given on a particular day

(a)If x represents the number of Dollars

Since one can purchase 0.8869 Euro with 1 USD, the function f(x) is a direct relationship where x is dollars and f(x) is in Euros.

(b)If x represents the number of Euros

Since one can purchase 143.1126 yen with 1 Euros, the function g(x) is a direct relationship where x is Euros and g(x) is in Yen.

(c)Given:

g(f(x))=143.1126(0.8869x)

(d)g(f(1000))

Answer:

Step-by-step explanation:

Answer:

a) 83%

b) 0.892

Step-by-step explanation:

percentage that attends class on friday = 74%

percentage that pass because they attend class on friday = 88%

percentage that pass but did not go to school on friday = 20%

a) percentage of students expected to pass the course

  = (74% x 88%) +(88% x 20%)

   = 0.6512 + 0.176

   = 0.8272

   = 83%

b) If a person passes the course, what is the probability that he/she attended classes on Fridays

        = 74% divided by 83%

        = 0.892

Answer:

Step-by-step explanation:

The first derivative is ...

  f'(x) = 30x^5 -40x^3 = 10x^3(3x^2 -4)

This will have zeros (critical points) at x=0 and x=±√(4/3).*

We don't need the second derivative to tell the nature of these critical points. Since the degree is even, the function is symmetrical about x=0. Since the leading coefficient is positive, it generally has a U-shape. This means the "outer" critical points will be minima, and the central one will be a local maximum.

__

However, since we're asked to use the 2nd derivative test first, we find the 2nd derivative to be ...

  f''(x) = 150x^4 -120x^2 = 30x^2(5x^2 -4)

For x=0, f''(0) = 0 -- as we expect for a function with a high multiplicity of the root at that point. For x either side of zero, both the function and the second derivative are negative, indicating downward concavity. That is, x = 0 is a local maximum.

For x² = 4/3, the second derivative is positive, indicating upward concavity. At x = ±√(4/3), we have local minima.

_____

* The "simplified" equivalent to √(4/3) is (2/3)√3.

The critical points of the function f(x) = 5x^6 − 10x^4 are x = 0, x = ±√(4/3). The point at x = 0 is a relative maximum while the points at x = ±√(4/3) are relative minima based on the second derivative test.

Given the function f(x) = 5x^6 − 10x^4, we first find the critical points. This is done by finding the derivative of the function and setting it equal to zero. For this function, the derivative, f'(x), is 30x^5 - 40x^3 = 0. Solving this equation for x, we get x = 0, and x = ±√(4/3).

Next, we apply the second derivative test by taking the second derivative of the original function, f''(x). This gives us f''(x) = 150x^4 - 120x^2. We substitute the obtained critical points into the second derivative. If f''(x) > 0, then the point is a relative minimum, if f''(x) < 0, it's a relative maximum. If neither, we need to consider higher order derivatives or other methods.

The second derivative is negative at x = 0, so that position is a relative maximum. The second derivative is positive at x = ±√(4/3), so these positions are relative minima.

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