Mathematics College

√7, 2, √8/2
order the number from least to greatest

Answers

Answer 1
To get a feel for where those two radicals fall on the number line, take a look at the perfect square roots they fall between. Both sqrt(7) and sqrt(8) fall between the perfect square roots sqrt(4) and sqrt(9); since sqrt(4) = 2 and sqrt(9) = 3, we know that sqrt(7) and sqrt(8) are somewhere in between 2 and 3. This means we know that sqrt(7) > 2. What about sqrt(8)/2 though? Well, sqrt(4)/2 = 2/2 = 1, and sqrt(9)/2 = 3/2 = 1 1/2, so sqrt(8)/2 has to be between 1 and 1 1/2, both of which are less than 2. Putting those all in order:

sqrt(8)/2, 2, sqrt(7)
Answer 2
Final answer:

To order the numbers √7, 2, √8/2 from least to greatest, simplify √8/2 to √2. Then compare √2, 2, and √7 to find the order.

Explanation:

To order the numbers √7, 2, √8/2 from least to greatest, first simplify √8/2. We know that √8 = √(4*2) = 2√2, so √8/2 = (2√2)/2 = √2. Now we have √7, 2, and √2. Comparing these numbers, √2 < 2 < √7.

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Related Questions

Use the cosine double-angle identity cos(2θ) = 1 − 2sin2θ to derive an identity for 2sin2θ

Answers

then is just a matter of linear simplification

[tex]\bf cos(2\theta )=1-2sin^2(\theta )\implies 2sin^2(\theta )=1-cos(2\theta )[/tex]
Final answer:

To derive an identity for 2sin2θ using the cosine double-angle identity cos(2θ) = 1 − 2sin²θ, we can rearrange the equation and substitute the value of sin²θ to obtain the identity 2sin²θ = 1 - cos(2θ).

Explanation:

To derive an identity for 2sin2θ using the cosine double-angle identity cos(2θ) = 1 − 2sin²θ, we can start by rearranging the equation to solve for sin²θ. This gives us sin²θ = (1 - cos(2θ))/2.

Next, we can substitute this value into the expression for 2sin²θ. This gives us 2sin²θ = 2(1 - cos(2θ))/2 = 1 - cos(2θ).

Therefore, the identity for 2sin²θ is 1 - cos(2θ).

True or false​: the population proportion and sample proportion always have the same value.

Answers

Answer: false

The sample is a randomly selected representation of the population, therefore it cannot represent the true data with 100% accuracy.
As the sample size increases, the sample proportion approaches the population proportion.
The population proportion and sample proportion always have the same value

- Flase

If u is a square matrix such that u^tu = i what can we say about det(u)

Answers

Recall that

[tex]\det(\mathbf{AB})=\det\mathbf A\det\mathbf B[/tex]

[tex]\det\mathbf A=\det\mathbf A^\top[/tex]

for any square matrices [tex]\mathbf A,\mathbf B[/tex]. So if

[tex]\mathbf U^\top\mathbf U=\mathbf I[/tex], and [tex]\det\mathbf I=1[/tex], we have

[tex]\det(\mathbf U^\top\mathbf U)=(\det\mathbf U)^2=1\implies\det\mathbf U=\pm1[/tex]

Write the following comparison as a ratio reduced to lowest terms.

34 quarters to 10 dollars

Answers

Well 34 quarters = $8.50 

34 Quarters : $10

$8.50 : $10

$4.25 : $5

A wooden crate is a cube with edge lengths of 18 inches. The crate contains tiny plastic tubes with edge lengths of 3 inches. How many plastic cubes can fit inside the wooden crate. PLEASE EXPLAIN

Answers

18^3 = 5832 (volume of crate)

3^3 = 27 ( volume of small cubes)

5832/27 = 216 cubes ( divide volumes to get number of cubes)

The number of plastic cubes which fit into the create 

                                 =  volume of the crate / volume of one plastic cube.

                                 =     18^3  / 3^3 =  5832 / 27 = 216 Answer

Multiply and give the answer in scientific notation: (2.3 x 10^-3) (3 x 10^8 =

A. 6.9 x 10^5
B. 6.9 x 10^11
C. 6.9 x 10^-5
D. 6.9 x 10^24

PLEASE HELP!!

Answers

It is A. 6.9 x 10^5 Because 
2.3(10−3)(3(108))=2.3(11000)(3(108))=0.0023(3(108))=0.0023(3)(100000000)=(0.0023)(300000000)=690000

then 6.9*10^5 = 690000

its a i did test and got it right

You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?

using a paid membership card to buy it at a 10 percent discount

buying it online at a 10 percent discount with a $5 shipping charge

buying it at a 10 percent discount without sales tax

Answers

Buying it 10% discount without tax is the best option. With card you still have the tax plus the card fee you pay annually to add to it. On the online purchase, you still have the tax plus the 5 shipping charge.

Answer:

C.  

buying it at a 10% discount without sales tax

Step-by-step explanation:

Let z ∼ norm(0, 1). use the normal table and also r's "pnorm" function to find (a) p r(z ≤ 1.45) (b) p r(z > −1.28) (c) p r(−0.674 ≤ z < 1.036) (d) p r(z > 0.836)

Answers

If z~N(0,1), and using R, 
(a) P(z<=1.45)=pnorm(1.45)=0.9264707
(b) P(z>-1.28)=pnorm(-1.28,lower.tail=FALSE)=0.8997274
(c) P(-0.674<=z<1.036)=pnorm(1.036)-pnorm(-0.674)=0.5997433
(d) P(z>0.836)=pnorm(0.836,lower.tail=FALSE)=0.2015775

Using normal probability tables (find one on the Internet if you don't have a book) use the normal table of left probabilities, i.e. the shaded part is on the left.
(a) Go to line 1.4, and column 0.5 to find the value 0.9265
(b) Go to line -1.2 and column 0.8 to find 0.1003, subtract from 1 to get the right tail (i.e. z>-1.28), or 1-0.1003=0.8997
(c) The probability between two values of z is found be the difference of the left tails
Here P(-0.674)=0.2502 (interpolate between P(-0.67) and P(-0.68).
P(1.036)=0.8499 (interpolate between P(1.03)=0.8485 and P(1.04)=0.8499
So P(-0.674<=z<1.036)=0.8499-0.2502=0.5997
(d) P(z<0.836)=interpolate between P(z<0.83)=0.7967 and P(z<0.84) =0.7995 to get 0.7894
P(z>0.836)=1-P(z<0.836)=1-0.7984=0.2016

Final answer:

To find the probabilities using the normal table and R's pnorm function, follow these steps: (a) p r(z ≤ 1.45) is 0.9265 or 92.65%. (b) p r(z > −1.28) is 0.8997 or 89.97%. (c) p r(−0.674 ≤ z < 1.036) is 0.6017 or 60.17%. (d) p r(z > 0.836) is 0.2013 or 20.13%.

Explanation:

To find the probabilities using the normal table and r's pnorm function, we can follow these steps:

For (a) p r(z ≤ 1.45), we can use the normal table or the pnorm function in R to find the area to the left of 1.45. The area is 0.9265 or 92.65%.

For (b) p r(z > -1.28), we can find the area to the left of -1.28 using the normal table or the pnorm function in R, which is 0.1003 or 10.03%. To find the area to the right of -1.28, we subtract this value from 1. The area is 0.8997 or 89.97%.

For (c) p r(-0.674 ≤ z < 1.036), we can find the area to the left of -0.674 using the normal table or the pnorm function in R, which is 0.2514 or 25.14%. To find the area to the left of 1.036, we can use the normal table or the pnorm function in R, which is 0.8531 or 85.31%. The difference between these two values gives us the area between the z-scores, which is 0.8531 - 0.2514 = 0.6017 or 60.17%.

For (d) p r(z > 0.836), we can find the area to the left of 0.836 using the normal table or the pnorm function in R, which is 0.7987 or 79.87%. To find the area to the right of 0.836, we subtract this value from 1. The area is 0.2013 or 20.13%.

Suppose that a person rolls two balanced dice three times in succession. determine the probability that on each of the three rolls, the sum of the two numbers that appear will be 7.

Answers

The number of combinations that will result in a sum of 7 is:

1 + 6

6 + 1

2 + 5

5 + 2

3 + 4

4 + 3

For a total of 6 combinations per roll. While the total number of combinations per roll are:

6 * 6 = 36

Hence the probability that the sum is 7 would be:

Probability = 6 / 36 = 1 / 6

 

For a succession of three times, the overall probability that each three rolls will be a sum of 7 is:

Overall probability = (1/6) * (1/6) * (1/6)

Overall probability = 1/216 = 4.63 x 10^-3 = 0.463%

Final answer:

The probability of rolling a sum of 7 three times in succession using two balanced dice is 1/216.

Explanation:

To determine the probability that on each of the three rolls of two balanced dice, the sum of the two numbers that appear will be 7, we first need to identify the probability of rolling a sum of 7 with a single roll of two dice. There are six ways to roll a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of possible outcomes when rolling two dice is 6*6 = 36. Therefore, the probability of rolling a sum of 7 on one roll is P(sum=7) = 6/36 = 1/6.

Since each roll is independent of the others, the probability of this event occurring three times in succession is the product of the individual probabilities. Thus:

P(First roll is 7) = 1/6P(Second roll is 7) = 1/6P(Third roll is 7) = 1/6

Therefore, the probability of all three rolls resulting in a sum of 7 is:

P(Three 7's in a row) = P(First roll is 7) * P(Second roll is 7) * P(Third roll is 7) = (1/6) * (1/6) * (1/6) = 1/216.

f(x)=12sinx+12cosx. Find f'(x)

Answers

[tex]\bf f(x)=12sin(x)+12cos(x)\implies \cfrac{df}{dx}=12cos(x)-12sin(x)[/tex]

A rectangular flower box holds 1232 in3 of soil. Find the height of the box if it is 22 in. long and 7 in. wide

Answers

the anwser is 21in because if you add all the length and width than multipy that by how many inches of soil there is you get your anwser. But make sure to change inches into cm

Ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores.

88%, 73%, 97%, 76%, 90%, 80%

Answers

To find the mean you: add up all the numbers, then divide by how many numbers there are.  So the mean for these numbers would be: 84%

To find the median: You put the numbers in order (From least to greatest), and then find the number exactly in the middle. Here it is an even amount of numbers. No problem, just add the two numbers in the middle and then divide by 2. The answer here is: 84%

Answer: The Mean

The mean is when you add up all of those grades and divide by the amount of exams.

can someone please help me

Answers

Sam makes sweeter coffee.

Mario puts 4 packets in 16 ounces.

For the coffee to be equally sweet, if he had a 32 cup,
just multiply both numbers by 2.
If he put 4 packets in 16 ounces,
you'd put 8 packets in 32 ounces.
By doubling the packets and the coffee, the coffee is equally sweet.
There is just more of it.

Sam puts 8 packets in only 31 ounces of coffee.
Since Sam puts as much sugar in less coffee, Sam's coffee is sweeter.

A linear function has a slope of -7/9 and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y+11=-7/9(x-18)

Answers

the answer is that they're equal, one is just in point-slope form and the other is in slope-intercept form

Answer:

A

Step-by-step explanation:

it has the same slope and the same y-intercept

Tan (pi/5) - tan (pi/30) / 1+tan (pi/5)tan (pi/30)

Answers

Find the value using the definition of tangent.tan(+)=opposite/adjacent tan(+)= opposite/adjacentSubstitute the values into the definition.tan(+)=0/1 tan(+)=0/1Divide 0/0 by 1/1 to get 0/0.Answer is 0
[tex]\bf \textit{Sum and Difference Identities} \\ \quad \\ sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}}) \\ \quad \\ [/tex]

[tex]\bf tan({{ \alpha}} + {{ \beta}}) = \cfrac{tan({{ \alpha}})+ tan({{ \beta}})}{1- tan({{ \alpha}})tan({{ \beta}})}\qquad tan({{ \alpha}} - {{ \beta}}) = \cfrac{tan({{ \alpha}})- tan({{ \beta}})}{1+ tan({{ \alpha}})tan({{ \beta}})}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{tan\left( \frac{\pi }{5} \right)-tan\left( \frac{\pi }{30} \right)}{1+tan\left( \frac{\pi }{5} \right)tan\left( \frac{\pi }{30} \right)}\implies tan\left( \frac{\pi }{5} -\frac{\pi }{30} \right)\implies tan\left( \frac{6\pi -\pi }{30} \right)[/tex]

[tex]\bf tan\left( \frac{5\pi }{30} \right)\implies tan\left( \frac{\pi }{6} \right)\implies \cfrac{sin\left( \frac{\pi }{6} \right)}{cos\left( \frac{\pi }{6} \right)}\implies \cfrac{\quad \frac{1}{2}\quad }{\frac{\sqrt{3}}{2}} \\\\\\ \cfrac{1}{2}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{1}{\sqrt{3}}\implies \cfrac{\sqrt{3}}{3}[/tex]

I thought of a number, then divided it by another number, and got a result of 7. Think of the possible values for my number and the number I divided it by. What number is impossible to divide by? What number can my original number not be?

My number is a multiple of ?
The number I divided my number by can be any number but ?
My number cannot be a number which we cannot divide by ?

Answers

Let the first unknown number be [tex]x[/tex]
And the second unknown number be [tex]y[/tex]

We know that [tex]x[/tex] ÷ [tex]y[/tex] = 7

My number is a multiple of 7 and also multiple of [tex]y[/tex]
This is because of 7 × [tex]y[/tex] = [tex]x[/tex]
-----------------------------------------------------------------------------------------------------------

The number I divided my number by can be any number but ZERO
Because [tex]x[/tex] ÷ 0 is undefined
--------------------------------------------------------------------------------------------------------------

My number cannot be a number which we cannot divide by SEVEN
Because [tex]x[/tex] ÷ [tex]y[/tex] = 7, so [tex]x [/tex] must be divisible by 7 to obtain [tex]y[/tex]

[tex] \frac{x}{y} =7[/tex]
[tex] \frac{x}{7} =y[/tex]
[tex]7y=x[/tex]


solve the following system of equations 3x+4y=17 -4x-3y=-18

Answers

3x + 4y = 17.....multiply by 4
-4x - 3y = -18 ...multiply by 3
------------------
12x + 16y = 68 (result of multiplying by 4)
-12x - 9y = - 54 (result of multiplying by 3)
------------------add
7y = 14
y = 14/7
y = 2

3x + 4y = 17
3x + 4(2) = 17
3x + 8 = 17
3x = 17 - 8
3x = 9
x = 9/3
x = 3

ur solution is (3,2)

Use the distributive property to simplify the following expression 4x(2x-6)

Answers

4x (2x - 6)

8x - 24x 

= -16x

[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]

- - - - - - - - - - - - - - - - - - -

[tex]\textsf{Using the distributive property, \textbf{a(b+c)=ab+ac}, expand the given expression:}[/tex]

[tex].\qquad\bullet\sf{4x(2x-6)=4x*2x-4x*6=8x^2-24x}[/tex]

[tex]\sf{\bf{$Answer: 8x^2-24x}}[/tex]

[tex]\Large\underbrace{\overbrace{\boldsymbol{Reflection - RoSe}}}^\star_\star[/tex]

C = 2πr; If r = 4.6, find C.

Answers

4.6 x 2 = 9.2. 9.2 x 3.14 = 28.8. so your answer is C= 28.8


Hello there!

C = 2πr

For r = 4.6

C = 2 * 3.14 * 4.6

C = 28.888

Best of luck with your studies!

Find the value of x and the value of y.

A.
x = 10, y = 130
B.
x = 65, y = 10
C.
x = 65, y = 130
D.
x = 130, y = 10

Answers

The answer is C. Lol

the 2 angls need to equal 180 degrees

 so 2x-y +  60 = 180

 and 2x+y + 40 = 180


 using the choices you have

 answer is B x = 65, y = 10

 when you use those values they both equal 180


Cassie has 1/2 pound of sugar in her cabinet. Her cake recipe calls for 2/10 of a pound of sugar. How many cakes can she make?

Answers

she can make 2 cakes and half . so your answers is 2.5
Cassie could make two cakes and one half of one.

assume heights of adult men are normally distributed. the average height of adult men in a certain country is 68.9 inches. the standard deviation of the heights is 2.4 inches. based on this data, what percentage of men in this country are taller than 73.7 inches?

Answers

73.7 inches is 2 standard deviations above the mean of 68.9 inches. The empirical rule states that 95% of the data for a normal distribution falls within 2 standard deviations of the mean. The tails on both ends account for the remaining 5%. Symmetry of the distribution then suggests that 2.5% of men are taller than 73.7 inches.

what is the sum of 2 3/8 and 3 3/7

Answers

first off, we'd convert the mixed fractions to "improper", then get the LCD to sum them up.

[tex]\bf \stackrel{mixed}{2\frac{3}{8}}\implies \cfrac{2\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{19}{8}} \\\\\\ \stackrel{mixed}{3\frac{3}{7}}\implies \cfrac{3\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{24}{7}}\\\\ -------------------------------\\\\ \cfrac{19}{8}+\cfrac{24}{7}\impliedby \textit{so our LCD is just 56}\implies \cfrac{(7\cdot 19)~+~(8\cdot 24)}{56} \\\\\\ \cfrac{133+192}{56}\implies \cfrac{325}{56}\implies 5\frac{45}{56}[/tex]



Sadie has a blue ribbon and a red ribbon. The blue ribbon is 12 inches long. The blue ribbon is 3 times longer than the red ribbon.



Which operation would be best to use to determine the length of the red ribbon?


addition

division

multiplication

subtraction

Answers

multiplication it says time 3 so 12 times 3 is 36

what is the perimeter of (-6, 2), (3,2), (-6,-7) (3,-7)

Answers

Hello! So just by looking at the points, I already know that it’s gonna be a square. This is because when we look at the coordinates, The difference if -6 And 3 is 9 And the difference between 2 and -7 is 9. With that being said, each side is 9 inches apart. There are 4 sides. Multiply the length of the sides by 4. 9 * 4 = 36. The perimeter of the square is 36 units.

What is the total rounded to the nearest tenth of 94.23

Answers

The total is 94.2.

Hope this helps!
See 94.23 is the number you are rounding.

94.23 the 2 is in the tenth place so you look at the next number 3 since it’s less then 5 the total rounded to the nearest tenth would be 94.2 because you take off the 3

What is the slope of the line that passes through th epoints (26, 7) and (-39, 12)?

Answers

                                                 12 - 7            5
Use the slope formula:    m = ------------ = -------- = -1/13
                                                -39 - 26       -65

A population consists of all the weights of all defensive tackles on a university's football team. they are johnson, 204 pounds; patrick, 215 pounds; junior, 207 pounds; kendron, 212 pounds; nicko, 214 pounds; and cochran, 208 pounds. what is the population standard deviation (in pounds)?

Answers

The population standard deviation of the weights of the defensive tackles is approximately 3.96 pounds.

Here, we have to calculate the population standard deviation,

Calculate the mean:

Mean = (204 + 215 + 207 + 212 + 214 + 208) / 6

Mean = 1260 / 6

Mean = 210 pounds

Calculate the squared differences between each weight and the mean:

[tex](204 - 210)^2 = 36\\(215 - 210)^2 = 25\\(207 - 210)^2 = 9\\(212 - 210)^2 = 4\\(214 - 210)^2 = 16\\(208 - 210)^2 = 4[/tex]

Find the mean of the squared differences:

Mean of squared differences = (36 + 25 + 9 + 4 + 16 + 4) / 6

Mean of squared differences = 94 / 6

Mean of squared differences = 15.67

Take the square root of the mean of squared differences:

Population standard deviation = √(15.67)

Population standard deviation ≈ 3.96 pounds

So, the population standard deviation of the weights of the defensive tackles is approximately 3.96 pounds.

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An unknown number x is at most 30. Which graph best represents all the values of x?

Number line graph with closed circle on 30 and shading to the right.
Number line graph with closed circle on 30 and shading to the left.
Number line graph with open circle on 30 and shading to the left.
Number line graph with open circle on 30 and shading to the right

Answers

This would be the second option. That is because a closed circle means that x could be 30, and shading to the left means that it could also be less than 30, which matches the description.

Answer:

b

Step-by-step explanation:

Ken has 4.66 pounds of walnuts ,2.1 pounds of cashew , and 8 pounds of peanuts .he mixes them together and divides them equally among 18 bags .how many pounds of nuts are in each bag ?

Answers

walnut= 4.66 pounds cashew=2.1 pounds peanuts=8 pounds Total nuts= 4.66+2.1+8 = 14.76 pounds each bag contains= 14.76/18=0.82 pounds of nuts
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