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2 years ago

Select all radical expressions that are equivalent to 3 4/7 Sorry for the bad quality!!

Mathematics

2 answers:

tatuchka [14]2 years ago

7 0

Answer:

Correct \/

Step-by-step explanation:

I just took the test

AnnZ [28]2 years ago

5 0

Answer:

$(\sqrt[7]{3} )^{4}$

Step-by-step explanation:

The only radical that matches the equivalent answer is the fifth one down. We can easily eliminate the radicals without exponents on the outside, since we know they won't create leftover fractions. So that leaves us with the second, fourth and fifth answers to contemplate.

Let's look at $(\sqrt[4]{3} )^{7}$ and $\sqrt[4]{3^{7} }$ first. It's good to know that these are equivalent radicals. The numbers are the same, and they will produce the same answers.

When you do the math, the exponent rule gives us fractions of $\frac{7}{4}$ for exponents, and eventually, a $3 * 3^{\frac{3}{4} }$ for both answers. So these are eliminated.

Now, for $(\sqrt[4]{3}^{7}$ , we can easiy simplify by changing the 7th root to a fraction in our exponent. Use the rule: $\sqrt[n]{x} = x^{\frac{1}{n} }$

$(3^{\frac{1}{7} } )^{4}$
Multiply the exponents: $\frac{1}{7} * 4 = \frac{4}{7}$
Insert the product into the exponent: $3^{\frac{4}{7} }$

And we can see the answer we're looking for! If you use this method to look at the other problems, you'll see that this is the only radical that simplifies to the required answer.

You might be interested in

-5 + 3g + (-3) - 8g = -18

Greeley [361]

Answer:

the answer is g=2

Step-by-step explanation:

hope this helps!!!

3 0

1 year ago

The parallel dotplots below display the girths (belly

liraira [26]

Answer:

The standard deviation for the distribution of girths is

about the same for both male and female pigs.

Step-by-step explanation:

Step 1

We will interprete the dotplots

For the Male pigs

24, 26, 26, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 32

Range

Maximum value - Minimum value

= 32 - 24

= 8

IQR = Interquartile range = Q3 - Q1

Q1 formula = 1/4(n + 1)th

=n = 25

= 1/4(25 + 1)

= 1/4(26)

= 26/4

= 6.5

This mean the value is between the 6th and 7th value

6th value = 26

7th value = 26

Q1 = 26 + 26/2

Q1 = 26

Q3 formula = 3/4(n + 1)th

=n = 25

= 3/4(25 + 1)

= 3/4(26)

= 78/4

= 19.5

This mean the value is between the 19th and 20th value

19th value = 30

20th value = 30

Q3= 30+ 30/2

= 30

IQR = 30 - 26

= 4

Standard deviation

Mean

First we find the mean

= 24+ 26+26+ 26+ 26+ 26+26+28+ 28+ 28+ 28+28+ 28+ 28+28+ 28+28+28+30+ 30+30+ 30+30+30+32/28

= 700/25

= 28

Standard deviation Formula = √(x - mean)²/n - 1

= √[(24-28)² + (26- 28)² + (26 -28)² + (26 - 28)² +................ (32 - 28)²]/25 - 1

= √(16 + 4 + 4+ 4+ 4+4+ 4+0+ 0+ 0+ 0+0+ 0+ 0+ 0+0+0+0+ 4+ 4+4+4+4+ 4+ 16)/25 - 1

= √80/25 - 1

=√3.333333333

1.825741858

Female Pigs

21, 23, 23, 23,23,23,23,25, 25, 25, 25, 25, 25, 25, 25, 25, 25,25, 27, 27, 27, 27,27, 27, 29

Range:

Maximum value - Minimum value

= 29 - 21

IQR

IQR = Interquartile range = Q3 - Q1

Q1 formula = 1/4(n + 1)th

=n = 25

= 1/4(25 + 1)

= 1/4(26)

= 26/4

= 6.5

This mean the value is between the 6th and 7th value

6th value = 23

7th value = 23

Q1 = 23 + 23/2

Q1 = 23

Q3 formula = 3/4(n + 1)th

=n = 25

= 3/4(25 + 1)

= 3/4(26)

= 78/4

= 19.5

This mean the value is between the 19th and 20th value

19th value = 27

20th value = 27

Q3= 27+ 27/2

Q3 = 27

IQR = 27 - 23

= 4

First we find the Mean

=(21+23+23+23+23+23+23+25+ 25+ 25+ 25+25+ 25+ 25+ 25+25+25+25+27+27+ 27+27+27+ 27+29)/25

= 625/25

= 25

Standard deviation Formula = √(x - mean)²/n - 1

= √[(21-25)² + (23- 25)² + (23 -25)² + (23 - 25)² +................ (29 - 25)²]/25 - 1

= √(16 + 4 + 4+ 4+ 4+4+ 4+0+ 0+ 0+ 0+0+ 0+ 0+ 0+0+0+0+ 4+ 4+4+4+4+ 4+ 16)/25 - 1

= √80/25 - 1

=√3.333333333

1.825741858

Looking at the calculation above and comparing both the girths from the male and female

We can conclude that: The standard deviation for the distribution of girths is

about the same for both male and female pigs which is 1.825741858

5 0

2 years ago

On a coordinate plane, a parallelogram has points A (negative 3, 4), B (3, 4), C (1, negative 2), and D (negative 5, negative 2)

vladimir2022 [97]

Answer:

(1,-12)

Step-by-step explanation:

d starts at (-5,-2) if you add 6 to -5 and minus -2 by 10 you will end up with (1,-12)

3 0

1 year ago

Read 2 more answers

The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested, however, the m

masha68 [24]

Answer:

$1.667-2.31\frac{1.803}{\sqrt{9}}=0.2789$

$1.667+2.31\frac{1.803}{\sqrt{9}}=3.055$

So on this case the 95% confidence interval would be given by (0.2789;3.055)

The 95% confidence interval to judge whether the two indeners result in different measurements is?

Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.

Step-by-step explanation:

We have the following dataset:

specimen 1 2 3 4 5 6 7 8 9

Steel Ball 51 57 61 70 68 54 65 51 53

Diamond 53 55 63 74 69 56 68 51 56

If we calculate the differences diamond-steel ball we have this datase:

d: 2, -2, 2, 4, 1, 2, 3, 0, 3

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}=1.667$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.803$

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".

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:

$df=n-1=9-1=8$

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(0.025,9)".And we see that $t_{\alpha/2}=2.31$ .

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

$1.667-2.31\frac{1.803}{\sqrt{9}}=0.2789$

$1.667+2.31\frac{1.803}{\sqrt{9}}=3.055$

So on this case the 95% confidence interval would be given by (0.2789;3.055)

The 95% confidence interval to judge whether the two indeners result in different measurements is?

Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.

4 0

2 years ago

Carbon-141414 is an element that loses about 10\%10%10, percent of its mass every millennium (i.e., 100010001000 years). A sampl

ololo11 [35]

Answer:

Carbon-14 loses around 10% ( 0.1 in decimal form) of its mass, after one millennium.

Then if we start with a mass A of Carbon-14, after one millennium we will have a mass equal to:

A - A*0.1 = A*(0.9)

After another millennium, we will have a mass equal to:

A*(0.9) - A*(0.9)*0.1 = A*(0.9)^2

And so on, this is an exponential decay.

We already can see the pattern here, after x millenniums, the mass of carbon-14 will be:

M(x) = A*(0.9)^x

Now, in this problem we have 600 grams of carbon-14, then the equation for the mass will be:

y = M(x) = 600g*(0.9)^x

And the graph of this equation is shown below.

4 0

2 years ago

Read 2 more answers