Mathematics College

Which number is an irrational number?

a) square root of 100
b)1/8
c)-2.2675
d)exponent 3 square root of 16

Answers

Answer 1
1. To solve this problem, you must keep on mind the followinwg information:

 You know that, by definition, an irrational number is a number that cannot be expressed as a fraction.

 2. Therefore, the correct answer is the option D. 

 3. To verify the answer you have:

 ∛16=2.51

 As you can see, the result is 2.51 and the decimal number 2.51 cannot be expressed as a fraction.
Answer 2

Answer:

D

Step-by-step explanation:

Related Questions

If the train that Megan is riding covers 80 miles in 2 hours, how fast is the train traveling?

Answers

The train is traveling at 40 mph (miles per hour).

To find this, you divide both 80 and 2 by 2 to find how many miles in a single hour the train travels. Thus giving you 40 miles in an hour (40 mph) as a ginal answer.

I hope this helps!

Final answer:

The average speed of the train Megan is traveling on is 40 miles per hour. It's obtained by dividing the total distance of 80 miles by the total time of 2 hours.

Explanation:

To find the average speed of the train that Megan is riding, which covers 80 miles in 2 hours, we will use the formula for average speed, which is total distance divided by total time. The train travels 40 miles one way and 40 miles back, totaling 80 miles.

Here is the step-by-step calculation:

Calculate the total distance the train travels: 40 miles one way + 40 miles back = 80 miles.

Calculate the total time of the journey: 2 hours.

Divide the total distance by the total time to find the average speed: 80 miles / 2 hours = 40 miles per hour.

This means the average speed of the train is 40 miles per hour.

what is the equation of the axis of symmetry of a parabola if its x-intercepts are -3 and 7?

Answers

this is a parabola, meaning the equation is a quadratic, so it has 2 roots or x-intercepts, keeping in mind that vertex will lie half-way between those intercepts.

so what's the x-value halfway between -3 and 7?  yeap, you guessed it, 2.

so the axis of symmetry for this vertical parabola will be at x = 2.

Based on the concept of the axis of symmetry, the equation of the axis of symmetry of the parabola is x = 2.

How the Equation of the axis of symmetry is determined?

To find the equation of the axis of symmetry of a parabola given its x-intercepts, we can use the fact that the axis of symmetry is the vertical line that passes through the midpoint of the x-intercepts.

The midpoint formula is given by:

x-coordinate of midpoint = (x-intercept1 + x-intercept2) / 2

In this case, the x-intercepts are -3 and 7. Let's calculate the midpoint:

Midpoint = (-3 + 7) / 2

Midpoint = 4 / 2

Midpoint = 2

Therefore, the x-coordinate of the midpoint (and the equation of the axis of symmetry) is x = 2.

Hence, in this case, it is concluded that the equation of the axis of symmetry of the parabola is x = 2.

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-7y to the third (4y + y - 3)

Answers

Hello,

So if we have the equation: -7y^3(4y + y - 3), we're essentially distributing "-7y^3" to everything of what's in the parenthesis. When you distribute -7y^3, know that you add exponents but you multiply the numbers. After simplifying you get:

-28y^4 - 7y^4 + 21y^3

**We can still simplify this expression because there are still like terms:

-35y^4 +21y^3

Hope this helps!

May

hey can you please help me posted picture of question

Answers

We have the following function:
 C (f) = (5/9) (f -32)
 Clearing f we have:
 (f-32) = (9/5) c
 Rewriting:
 f = (9/5) c + 32
 f (c) = (9/5) c + 32
 Answer:
 The inverse function for this case is given by:
 f (c) = (9/5) c + 32
 option B

i need help working this problem?

Answers

Let p represent the number of people originally in the fort. Then the quantity of provisions is 90p (person-days). The scenario can be described by
  90p = 20p +50(p+600)
  90p = 70p +30000 . . . . . . . eliminate parentheses
  20p = 30000 . . . . . . . . . . . . subtract 70p
  p = 1500 . . . . . . . . . . . . . . . . divide by 100

There were originally 1500 people in the fort.

Daisy is cooking pasta. The recipe says she needs 480 grams of pasta for 4 people. How many kilograms will she need for 14?

Answers

480 grams of pasta = 480 grams x (1 kilogram / 1,000 grams) = 0.48 kilograms

Rule of three:

    Pasta            People 
(kilograms)     
    0.48         →     4
       x           ←    14

x=(14 * 0.48)/4
x=1.68

Answer: She will need 1.68 kilograms of pasta for 14 people

Answer:

1.68 kilo grams are required for 14 people.

Step-by-step explanation:

First of all the answer is required in kilo grams and the data given is in grams.

Lets convert the given value to kilo grams;

480 grams = 0.48 kilo grams

If 0.48 kilo grams are required to cater 4 people then how many kilo grams are required to cater 14 people?

⇒[tex]\frac{0.48}{4} *14[/tex] kilo grams

1.68 kilo grams.



A leak in a water tank causes the water level to decrease by 3.6×10−2 millimeters each second.

About how many millimeters does the water level in the tank decrease in 5 hours, or 1.8×104 seconds?



Drag and drop the values to the boxes to express the answer in scientific notation.

Answers

(3.6×10⁻² mm/s) × (1.8×10⁴ s) = (3.6×1.8) × 10⁻²⁺⁴ mm = 6.48×10² mm

Answer:

just to sum up the answer it is 6.5*10^2

What is the length of AA' , rounded to the nearest hundredth? Type a numerical answer is the space provided. Do not type spaces in your answer

Answers

Coordinate of A are (0,0)
Coordinates of A' are (5,2)

We can find the distance from A to A' using the distance formula:

[tex]AA'= \sqrt{(5-0)^{2}+ (2-0)^{2} } \\ \\ AA'= \sqrt{25+4} \\ \\ AA'= \sqrt{29} \\ \\ AA'=5.39 [/tex]

Thus, rounded to nearest hundredth, AA' is equal to 5.39

Select all that apply. In a linear function: Δy = 0 Δx = 0 Δy = n Δx = n Δy = -n Δx = -n

Answers

Answers: All the options are right and have a special meaning.

Explanation:

1) Δy = 0

Means y is constant, which is also that the slope is zero.

The function is a horizontal line (paralell to the x-axis)

2) Δx = 0

Means x is constant, the slope is not defined (∞).

The function is a vertical line (parallel to the y-axis)

3) Δy = n

Means that the change in y is constant. So, only if the change in x is also constant the slope is constant and the function is linear.

This is because the slope is Δy / Δx.

4) Δx = n

Means the change in x is constant. So, only if Δy is constant it is a linear function, for the same reason explained above

5) Δy = -n and and 6) Δx = -n

Same reasoning of 3 and 4.

Answer:

All options are correct except Δx = 0.

So select: Δy = 0 Δy = n Δx = n Δy = -n  Δx = -n

Step-by-step explanation:

Δy can be positive, negative, or zero. The value of  Δx can be positive or negative but not zero. From Odyssey ware.

need help please.I forgot this.

Answers

The associative property lets you move the parentheses.

6. (-20×50)×-29 = -1000×-29 = 29,000

7. (5×10)×18 = 50×18 = 900

8. 400 + (60 + 98) = 400 +158 = 558

9. 3×(20×5) = 3×100 = 300

10. (18 + 9) +91 = 27 +91 = 118

A cartoon in the shape of a cube measuring 8 inches tall is filled with colored plastic cubes measuring 1 inch across each face. The cubes sell for 25cent each. How much would it cost to buy all of the cubes in the carton? Enter your answer in the box?

Answers

The entire package is a cube, so its volume is 8 x 8 x 8 = 512 in^3. Each small cube is 1 x 1 x 1 = 1 in^3. Therefore, there are 512 in^3 / 1 in^3 = 512 cubes, and since each cube is 25 cents, it would cost (512 cubes)($0.25) = $128 to buy all the cubes in the carton.

Ted determined that there are 50000 millimeters in 5 meters. Was he correct? Why or why not?

Answers

Ted is incorrect because if you use the formula mm/1000, 50,000 millimeters would equal to 50 meters, which makes 5 meters equal to 5,000 millimeters.

simplify this problem

Answers

Try the suggested solution (in the attachment).

Use the Change of Base Formula to evaluate log3 58. Then convert log3 58 to a logarithm in base 4. Round to the nearest thousandth.

Answers

[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]
[tex]\log_358=\dfrac{\log_458}{\log_43}\approx\dfrac{2.929}{0.792}\approx3.698[/tex]



Suppose f(x)=x^2-2. Find the graph of f(5x).

Answers

The function f (x) = x ^ 2 - 2 is given
 It is asked to find the graph of f (5x)
 So where the x goes we must now place "5x"
 In this way the function is as shown below:
 f (5x) = (5x)² -2
 f (5x) = 25x² -2
 The graph of this function is shown in the attached image.

In a large population, very close to 25% of the observations will fall below the 25th percentile (Q1), and close to 75% fall below the 75th percentile (Q3). The Web site of the Educational Testing Service reports that on the SAT Verbal test, with a possible perfect score of 800, the 89th percentile of 1,475,623 scores nationwide is a score of 670. What is the best estimate of exactly how many scores were below 670?

Answers

Solving:

 .89 * 1,475,623 = 1,313,304.47 

So, the answer would be: 
approximately equal to 1,313,305 number of scores were below 670

Answer:

1,313,000

Step-by-step explanation:

a rectangle box is twice as long as it is wide. the height of the box is 3 feet less than the width. if the box is x feet wide, what polynominal represents its volume in cubic feet

Answers

The width is given as x.
The length is twice the width, so is 2x.
The height is 3 less than the width, so is x-3.

The volume is (length)*(width)*(height), so is (2x)(x)(x -3). Eliminating parentheses, the volume in cubic feet is represented by the polynomial ...
  2x³ -6x²

What is the measure of < L ? Need help

Answers

Hello!

Looking at the image above, we can see that the two “legs” of the triangle both have a length of 7 units. Consequently, this triangle can be classified as an isosceles triangle. An isosceles triangle has two sides of equal length (in this case, KJ and KL) and two corresponding angles of equal measure (in this case, ∠J and ∠L).

∠J has a measure of 25 degrees. Consequently, with our knowledge of isosceles triangles, we can conclude that ∠L has a measure of 25 degrees as well.

I hope this helps!

Final answer:

Length contraction is the shortening of an object's measured length when it is moving relative to the observer's frame. The formula for length contraction is L = L0√(1 - (v^2/c^2)).

Explanation:

Length contraction (L) is the shortening of the measured length of an object moving relative to the observer's frame. It occurs when an object is moving at a significant fraction of the speed of light. The formula for length contraction is L = L0√(1 - (v2/c2)), where L0 is the rest length of the object, v is its velocity, and c is the speed of light.

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rewrite 5/6 with the denomintaior of 12

Answers

To change 5/6 to a fraction with a denominator of 12, you need to do one step.  Since 12 is a multiple of 6 (meaning that it can be multiplied by 6 and another number), you multiply 5/6 by 2 to get 10/12. 10/12 is your answer.

Write the sum as a product of the GCF and a sum: 39+91

Answers

[tex]\bf 39+91\qquad \begin{cases} 39=3\cdot \underline{13}\\ 91=7\cdot \underline{13} \end{cases}\implies \underline{13}(3+7)[/tex]

Suppose we want to form five digit numbers using the set of digits 0 1 2 3

Answers

Final answer:

The question pertains to creating five-digit numbers using the digits 0, 1, 2, and 3, with the restriction that the digit 0 cannot be used as the first digit. We consider the choices for each digit, leading to a total of 768 different combinations.

Explanation:

The student is asking about forming five-digit numbers with a set of digits 0, 1, 2, 3. To create five-digit numbers with these digits, we need to consider that each digit position can be one of these four digits. The fact that 0 is included as one of the possible digits is significant because it means 0 cannot be used as the first digit in a five-digit number as that would create a four-digit number.

Since there are restrictions on the use of 0 in the first position, the first position can only be filled with digits 1, 2, or 3, providing us with three choices for the first digit. The remaining four positions can be filled by any of the four digits (0, 1, 2, 3) without restriction. Thus, for each of the remaining four positions, we have four choices.

To calculate the total number of different five-digit numbers that can be formed, we would multiply the number of choices for each position, which yields 3 choices for the first digit and 4 choices for each of the remaining four digits. Therefore, the formula becomes 3 * 4 * 4 * 4 * 4, which equals 768 different five-digit numbers.

There are 768 five-digit numbers that can be formed using the digits {0, 1, 2, 3}.

To find out how many five-digit numbers can be formed using the set of digits {0, 1, 2, 3}, we can use the concept of permutations.

Since we want to form a five-digit number, we have 5 positions to fill. For each position, we have 4 choices: 0, 1, 2, or 3.

However, since the number cannot start with 0, we have only 3 choices for the first digit.

After choosing the first digit, the remaining four positions can be filled with any of the digits {0, 1, 2, 3}.

So, the total number of five-digit numbers that can be formed using the given set of digits is:

3 (choices for the first digit) × 4 (choices for each of the remaining four digits) × 4 (choices for each of the remaining four digits) × 4 (choices for each of the remaining four digits) × 4 (choices for each of the remaining four digits)

This simplifies to:

3 × 4^4 = 3 × 256 = 768

Therefore, there are 768 five-digit numbers that can be formed using the digits {0, 1, 2, 3}.

Question

Suppose we want to form five-digit numbers using the set of digits {0, 1, 2, 3}. For example, 30133 and 22301 are such numbers, but 03731 is not. How many such numbers are possible? There are no five-digit numbers formed by using the digits {0, 1, 2, 3}.

What is the median of the data set represented by the dot plot? A number line with line with two dots above the number 10, one dot above the number 12, one dot above the number 13, one dot above the number 14, one dot above the number 15, one dot above the number 18, and two dots above the number 19.

Answers

There are 4 dots either side of the dot above 14, so 14 is the middle value.

The median of the data set is 14.

Answer:

The median of the data set is 14.

Need help with this question please

Solve the triangle.
B = 36°, a = 38, c = 17 (5 points)


b ≈ 41.3, C ≈ 22.3, A ≈ 121.7

b ≈ 41.3, C ≈ 26.3, A ≈ 117.7

b ≈ 26.2, C ≈ 118.7, A ≈ 25.3

b ≈ 26.2, C ≈ 22.3, A ≈ 121.7

Answers

To solve for the triangle we shall proceed as follows:
B = 36°, a = 38, c = 17
using cosine rule:
b^2=a^2+c^2-2accosB
b^2=38^2+17^2-2*38*17cos36
b^2=697.7500
b=26.2

th missing angles will be evaluated using sine rule:
a/sin A=b/sin B
thus
38/sin A=26.2/sin 36
sin A=(38sin 36)/26.2
sin A=0.8525
A=58.49

since a is the longest side then A is the largest angle and it will be:
A=180-58.49=121.51
also:
c/sin C=b/sin B
17/sin C=26.2/sin 36
sin C=0.3814
C=22.42

Thus answer is:
b ≈ 26.2, C ≈ 22.3, A ≈ 121.7

find the unit price rounded to the nearest cent: $12.35 for 11 lb

Answers

The unit price is 1.12.

All you have to do is divide $12.35 / 11 = 1.12

Hope this Helps!!
Answer:
unit price = $1.1

Explanation:
We are given that 11 lb cost $12.35. To know how much does 1 lb cost (unit price), all you have to do is cross multiplication as follows:
11 lb .......................> 12.35
1 lb .........................> ??
unit price = (1*12.35) / 11 = $1.122 which is approximately $1.1 (to the nearest cent)

Hope this helps :)

QM Q4.) Find the solution set

Answers

Hello!

First you find the least common multiplier which is 2x(x + 2)

[tex] \frac{1}{x} * 2x(x + 2) + \frac{1}{x + 2} * 2x(x + 2) = \frac{1}{2} * 2x(x + 2)[/tex]

Simplify

2(x + 2) + 2x = x(x + 2)

Now you solve it algebraically

Distribute the 2

2x + 4 + 2x = x(x + 2)

Distribute the x

[tex]2x + 4 + 2x = x^{2} +2x[/tex]

Combine like terms

[tex]4x + 4 = x^{2} +2x[/tex]

Subtract 4 from both sides

[tex] x^{2} + 2x - 4 = 4x[/tex]

Subtract 4x from both sides

[tex] x^{2} - 2x - 4 = 0[/tex]

Now you put this into the quadratic formula

[tex]x = \frac{-(-2) + and - \sqrt{(-2)^{2}- 4 * 1 * (-4) } }{2 * 1} [/tex]

Simplify

[tex]x = \frac{2 + and - \sqrt{20} }{2} [/tex]

Factor the sqrt of 20

[tex]x = \frac{2 + and -2 \sqrt{5} }{2} [/tex]

Factor 2 + and - the 2 * sqrt of 5

[tex] \frac{2(1 + and - \sqrt{5}) }{2} [/tex]

The 2's cancel each other other

[tex]x = 1 + and - \sqrt{5} [/tex]

The answers are [tex]x = 1 + \sqrt{5} and x = 1- \sqrt{5} [/tex]

Hope this helps!

The square root of a negative number is imaginary, there are no real solutions to the equation x² - x = 2.

The equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Where:

a is the coefficient of the x² term

b is the coefficient of the x term

c is the constant term

In the equation x² - x = 2, we have:

a = 1

b = -1

c = 2

Plugging these values into the quadratic formula, we get:

x = (1 ± √((-1)² - 4(1)(2))) / 2(1)

Simplifying the expression, we get:

x = (1 ± √(1 - 8)) / 2

Evaluating the square root, we get:

x = (1 ± √(-7)) / 2

Since the square root of a negative number is imaginary, there are no real solutions to the equation x² - x = 2.

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Suppose that the dollar cost of producing x radios is c(x) = 400 + 20x - 0.2x
2. Find the marginal cost when 30
radios are produced.

Answers

cost of producing x radios is c(x) = 400 + 20x - 0.2x
where:
x=number of units
thus the cost required to produce 30 units will be given by
c(30)=400+20(30)-0.2(30)
c(30)=400+600-6
c(30)=994

Answer: Marginal cost will be $994

Find the exact value of tan5x/4

Answers

To evaluate for tan 5x/4 we proceed as follows
5x/4
=5/4*150
=225
which is in quadrant III. 
This implies that the value of tan will be positive, hence:
tan 225=tan (270-225)
tan 225=tan 45
using right angle with length of the legs being unit, then 
tan 45=1
hence
tan 5x/4=1

21$is 75% of what amount?

Answers

21 cents =75%
divide both sides by 3
7cents= 25%
multiply each side by 4
28=100%
Answer=28

Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 8 inches. How far did Chubby run? Give your answer in terms of pi. (prize is 99 points)

Answers

Answer: 800pi inches

=======================================

Explanation:

The formula to find the circumference of a circle is
C = pi*d
where
C = distance around the circle (aka circumference)
pi = 3.14 approximately
d = diameter

We know that the diameter of the wheel is d = 8, so 
C = pi*d
C = pi*8
C = 8pi
is the circumference of the wheel

One full rotation will have the wheel cover a distance of 8pi inches. Imagine that wet paint is on the outer surface of the wheel. If the wheel is rolled out in a straight line, then the wet paint would cover a linear distance of 8pi inches along the flat ground. This is one full rotation, so 100 rotations covers 100*8pi = 800pi inches

Note: if we use pi = 3.14 as the approximation, then the hamster ran approximately 800*pi = 800*3.14 = 2512 inches if the wheel could move

Answer:

6280

Step-by-step explanation:

It's 6280

A random sample of 31 charge sales showed a sample standard deviation of $50. a 90% confidence interval estimate of the population standard deviation is

Answers

The [tex]100(1-\alpha)\%[/tex] confidence interval of a standard deviation is given by:

[tex] \sqrt{ \frac{(n-1)s^2}{\chi^2_{1- \frac{\alpha}{2} } }} \leq\sigma\leq\sqrt{ \frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2} } }}[/tex]

Given a sample size of 31 charge sales, the degree of freedom is 30 and for 90% confidence interval, 

[tex]\chi^2_{1- \frac{\alpha}{2} }=43.773 \\ \\ \chi^2_{\frac{\alpha}{2} }=18.493[/tex]

Therefore, the 90% confidence interval for the standard deviation is given by

[tex]\sqrt{ \frac{(31-1)50^2}{43.773 }} \leq\sigma\leq\sqrt{ \frac{(31-1)50^2}{18.493 }} \\ \\ \Rightarrow\sqrt{ \frac{(30)2500}{43.773 }} \leq\sigma\leq\sqrt{ \frac{(30)2500}{18.493 }} \\ \\ \Rightarrow\sqrt{ \frac{75000}{43.773 }} \leq\sigma\leq\sqrt{ \frac{75000}{18.493 }} \\ \\ \Rightarrow \sqrt{1713.38} \leq\sigma\leq \sqrt{4055.59} \\ \\ \Rightarrow41.4\leq\sigma\leq63.7[/tex]

Final answer:

The 90% confidence interval estimate of the population standard deviation is (0.97, 274).

Explanation:

To estimate the population standard deviation with a 90% confidence interval, you can use the formula:

CI = [s * sqrt(n-1) / sqrt(chi-squared lower value), sqrt(chi-squared upper value))]

where s is the sample standard deviation, n is the sample size, and chi-squared lower and upper values are obtained from a chi-squared distribution table. For a 90% confidence interval, the chi-squared lower value is 0.05 and the chi-squared upper value is 0.95 for the given sample size of 31. Plugging in the values:

CI = [50 * sqrt(31-1) / sqrt(0.05), sqrt(0.95))] = [50 * sqrt(30) / sqrt(0.05), sqrt(0.95))] = [50*5.48, 0.97] = [274, 0.97]

Therefore, the 90% confidence interval estimate of the population standard deviation is (0.97, 274).

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