which number is a rational number?A. √3B. √36C. √7D. π

Answers

Answer 1

We have to identify the rational number.

Any number that can be expressed as a fraction is a rational number.

In this case the options are:

A. The square root of 3. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.

B. The square root of 36, unlike the square root of 3, does have a rational solution: 6. So the square root of 36 is a rational number.

C. The square root of 7. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.

D. The number π has an infinite number of decimals, so it can not be represented as a fraction. Thn, it is not a rational number.

nswer: O√36 [ption B]

Related Questions

Find a degree 3 polynomial having zeros -8, 2 and 8 and the coefficient of x3 equal 1.

Answers

The degree 3 polynomial is "x³-2x²-64x+128".

We have to find a polynomial of degree 3.We are given that the polynomial has -8, 2, and 8 as its roots.We are also given that the coefficient of x³ equals 1.If x = -8 is a root, then:(x+8) is a factor of the polynomial.If x = 2 is a root, then:(x-2) is a factor of the polynomial.If x = 8 is a root, then:(x-8) is a factor of the polynomial.All the three roots are of the same polynomial.So, the polynomial is the product of these factors.(x+8)(x-8)(x-2)(x²-64)(x-2)x³-2x²-64x+128The required polynomial is "x³-2x²-64x+128".

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Graph the image of ∆KLM after a dilation with a scale factor of 4, centered at the origin.

Answers

The red triangle is the original figure

The green triangle is the image

Scale factor is 4

Three cubes of side 10 cm are joined end to end to form a cuboid as given in the figure. Find is total surface area.

Answers

Solution:

The cuboid is a solid-shaped figure formed by six faces. A cuboid is a simple figure. It has three dimensions - width, length, and height. Thus, the cuboid is a parallelepiped. Now, the surface area of the parallelepiped is the sum of the areas of all sides, that is:

[tex]S\text{ =2(}lw+lh+wh\text{)}[/tex]

where

l is the lenght

w is the width

and

h is the height

According to the figure given in the problem, we have that:

l = 30

w = 10

h = 10

thus, the surface area of the given cuboid would be:

[tex]\begin{gathered} S\text{ =2(}lw+lh+wh\text{)} \\ \text{ = 2((}30\cdot10\text{)+(30}\cdot10\text{)+(10}\cdot10\text{))=}1400 \end{gathered}[/tex]

So that, we can conclude that the correct answer is:

[tex]1400[/tex]

Drop down options for 1 2 and 4 are Forest A or Forest B

Answers

Given :

[tex]A(t)=107(1.015)^t[/tex]

[tex]B(t)=88(1.025)^t[/tex]

Set t=1 we get

[tex]A(t)=107(1.015)^t[/tex]

In 5 minutes, a conveyor belt moves 100 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans thesame distance in 9 minutes. If both belts are used, find how long it takes to move the cans to the storage area.The conveyor belts can move the 100 pounds of recyclable aluminum from the delivery truck to a storage area in minutes.(Simplify your answer. Type an integer, fraction, or a mixed number.)

Answers

we know that

a greater conveyor belt moves 100 pounds ------------> 5 minutes

Applying proportion

1-minute ---------> move 100/5=20 pounds

a smaller conveyor belt moves 100 pounds ------> 9 minutes

Applying proportion

1-minute --------> move 100/9 pounds

therefore

If both belts are used

then

1-minute --------> move 20+(100/9)=(180+100)/9=280/9 pounds

Applying proportion

Find out how long it takes to move 100 pounds

[tex]\begin{gathered} \frac{1}{\frac{280}{9}}=\frac{x}{100} \\ \\ solve\text{ for x} \\ x=\frac{100}{\frac{280}{9}}=\frac{900}{280} \end{gathered}[/tex]

Simplify the fraction

45/14

Convert to a mixed number

45/14=42/14+3/14=3 3/14 minutes

The answer is 3 3/14 minutes

The graph below plots the values of y for different values of x: plot the ordered pairs 1, 3 and 2, 4 and 3, 9 and 4, 7 and 5, 2 and 6, 18 What does a correlation coefficient of 0.25 say about this graph? (1 point) x and y have a strong, positive correlation x and y have a weak, positive correlation x and y have a strong, negative correlation x and y have a weak, negative correlation

Answers

The presented data for x and y show a significant, positive correlation with 0.78 serving as the coefficient of correlation.

The intensity and direction of a relationship between two variables are indicated by a correlation coefficient, which is a number between -1 and 1. In other words, it shows how comparable two or more variables' measurements are across a dataset. The other variables shift in the same direction when one changes.

The intensity and direction of a relationship between two variables are indicated by a correlation coefficient, which is a number between -1 and 1. In other words, it shows how comparable two or more variables' measurements are across a dataset.

Given x and y values in this case

x 1 2 3 4 5 6

y 3 4 9 7 2 18

xy 3 8 27 28 10 108

x² 1 4 9 16 25 36

y² 9 16 81 49 4 324

∑x = 21,

∑y = 43,

∑xy = 194,

∑x² = 91,

∑y² = 483,

n = 6

the relationship between x and y now:

r = (n∑xy - ∑x.∑y)/ √[{n∑x²- (∑x)²}{n∑y² - (∑y)²}]

r = ( 6 X 194 - 21 X 43 ) / √[ {6 X 91 - (21)²}{ 6 X 483 - (43)²}]

r = ( 1164 - 903) / √( 546 - 441)(2898 - 1849)

r = 261 / √ 105 X 1049

r = 261 / √110145

r = 261 / 331.88

r = 0.78

As a result, the x and y data's correlation coefficient is 0.78.

The strong, positive association between x and y

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PLEASEEE HELPP
Megan is in a musical production. She was at practice for 2 hours yesterday and 3 hours today. Altogether she spent of her practice hours dancing. How many total hours did Megan spend dancing yesterday and today?

Answers

Answer:

2.0833

Step-by-step explanation:

2 3/4 + 3 1/2 =6.25

6.25(1/3)=2.0833

Find the rates of change in population for both parks between 2009 and 2014, and determine which park showed faster population growthduring those years.

Answers

The table and graph given show the information about two national parks.

It is required to find the rate of change of the population of the two parks between 2009 and 2014, and then determine the park that shows faster population growth during those years.

Notice that the variable x represents the number of years after 2005.

Hence, the years 2009 and 2014 represent, x=4 and x=9, respectively.

The formula for the rate of change of a function f(x) between x=a and x=b is given by the formula:

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Calculate the rate of change for park A:

Substitute a=4 and b=9 into the formula:

[tex]\frac{f(9)-f(4)}{9-4}[/tex]

Substitute f(9)=2870 and f(4)=2370 from the table for park A into the expression for the rate of change:

[tex]\frac{2870-2370}{9-4}=\frac{500}{5}=100\text{ swallows per year}[/tex]

Calculate the rate of change for park B:

[tex]\frac{f(9)-f(4)}{9-4}[/tex]

Substitute f(9)=2800 and f(4)=2200 from the graph of park B:

[tex]\frac{2800-2200}{9-4}=\frac{600}{5}=120\text{ swallows per year}[/tex]

Notice that the rate of change in population for park B is higher than that of park A.

Hence, park B showed faster population growth during those years.

Answers:

Rate of change for park A= 100 swallows per year.

Rate of change for park B= 120 swallows per year.

Park B showed faster population growth during those years.

A student incorrectly simplifies an expression. The expression and work is shown below.

-(-6)(-3) - 2/3 (22 - 7)
3/5

Step 1: -(-6) (-3) - 2/3 (15)
3/5

Step 2: 18 - 2/3 (15)
3/5

Step 3: 18 - 10
3/5

Step 4: 8_3_5

Answer they got: 4 4/5

Idetnfiy which step is incorrect.

.
PLSSS HELP MEEEEEE

Answers

Answer:

so in the second step you see how the 18 is a positive

its supposed to be a negative

in the step 1, the part is -(-6)(-3), right?

so the negative symbol outside the negative 6 cancels out the negative, making it a positive number

it becomes 6(-3), which them multiplies into -18

so, i think the explanation is "the person forgot to change the 18 to a negative in the second step"
yea lol i think thats it

I need help with this practice Please read below ‼️‼️Use pencil and paper to graph the function, if you can’t, please use a drawing/writing tool that is *NOT* a graphing tool. If you cannot do this let me know

Answers

Answer:

Step-by-step explanation:

The trigonometric functions are represented by the following function form:

[tex]\begin{gathered} f(x)=\text{Atrig(Bx-C)}+D \\ \text{where,} \\ A=\text{ amplitud} \\ B,C=\text{ phase shift} \\ D=\text{ vertical shift} \end{gathered}[/tex]

Then, for the following function:

[tex]f(x)=-\cot (x+\frac{\pi}{6})[/tex]

Since it is an arctan function reflected the y-axis:

What is the image of ( − 8 , 0 ) after a dilation by a scale factor of 1/4 centered at the origin?

Answers

Step-by-step explanation:

it is then simply scanned (multiplied).

the new point is

(-8 × 1/4, 0 × 1/4) = (-2, 0)

Points B and C are on parallel lines with s and T, respectively. The size of the angle BAC is 96 degrees. Find the acute angle between straight AC and straight t if it is known that it is three times the size of the acute angle between straight AB and straight S.

Answers

Answer:

72°

Step-by-step explanation:

Let the acute angles be B and C.

If we add a parallel line through the point A, we'll see that:

m∠BAC = B + C

And we know that:

m∠BAC = 96C = 3B

Plug in the known parameters to get:

B + 3B = 964B = 96B = 24

We are looking for the value of C:

C = 3*24 = 72

The figure shows a circle inscribed into a regular pentagon.Cis the center of the circle and the regular pentagon.G and H are on the edge of both the circle and the regular pentagon.The radius of the circle is 3 inches.GHCPart A. Find the area of the dark shaded region. Show your work.Part B. Find the area of the light shaded region. Show your work.

Answers

Solution

Part A: The area of the dark shaded region = S1,

where

The radius of the circle is 3 inches.

[tex]\begin{gathered} S_1=\frac{4}{5}\pi r^2 \\ =\frac{4}{5}\pi.3^2 \\ S_1=\frac{36}{5}\pi in^2 \end{gathered}[/tex]

Part B: The area of the light shaded region = S,

[tex]\begin{gathered} S=S_2-S_1 \\ S=5\times\frac{1}{2}r.rtan36 \\ S=\frac{45}{2}\sqrt{5-2\sqrt{5}} \\ S=\frac{45}{2}\sqrt{5-2\sqrt{5}}-\frac{36}{5}\pi in^2 \end{gathered}[/tex]

IS THIS A FUNCTION YES OR NO?? (ALGEBRA 1)

Answers

Answer: Yes

Step-by-step explanation:

Yes, the numbers in the table are a function. The equation for the equation would be

y = 2x

Yes the numbers in the table are a function the equation for this would be y = 2x

Oscar drew a scale drawing of a house. The garage, which is 8 meters long in real life, is 4centimeters long in the drawing. What is the drawing's scale factor?Simplify your answer and write it as a fraction.

Answers

Answer:

1/200

Explanation:

Length of the garage in the drawing = 4 centimeters

Length of the garage in real life = 8 meters

The ratio of the lengths = 4 cm : 8m

Divide both sides by 4

[tex]\begin{gathered} \frac{4\operatorname{cm}}{4}\colon\frac{8m}{4} \\ 1\operatorname{cm}\colon2m \end{gathered}[/tex]

1 m =100cm

2m= 2 x 100 =200cm

Converting both to the same unit, we have:

[tex]\begin{gathered} 1\operatorname{cm}\colon200\operatorname{cm} \\ =\frac{1}{200} \end{gathered}[/tex]

The drawing's scale factor in fraction form is 1/200.

Triangle BCD is similar to triangle EFG. Find the measure of side EF. Round youranswer to the nearest tenth.

Answers

Triangle BCD is similar to triangle EFG.

A rectangular garden has one side with a length of x + 7 and another with a length 2x + 3. Find the perimeter of the garden.

Answers

A rectangular garden has one side with a length of x + 7 another with a length 2x + 3

We are asked to find the perimeter of the garden

Let me draw this rectangular garden to better understand the problem

Recall that the perimeter of a rectangular shape is given by

[tex]P=2(W+L)[/tex]

Where W is the width and L is the length of the rectangular garden

Let us substitute the given values into the above formula

[tex]P=2(x+7+2x+3)[/tex]

Now simplify the equation

[tex]\begin{gathered} P=2(x+2x+7+3) \\ P=2(3x+10) \\ P=6x+20 \end{gathered}[/tex]

Therefore, the perimeter of the rectangular garden is equal to 6x + 20.

Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x)).

Answers

The x–intercept of g(h(x)) is the option;

[tex] \displaystyle {-\frac{2}{3}}[/tex]

What is a The x–intercept of a function?

The x–intercept of a function is given by the point where the function intersects the x–axis.

From the given table, the slope of the graph of g(x), [tex] m_1 [/tex] is given by the equation;

[tex] \displaystyle{ m_1 = \frac{ - 4 - ( - 8)}{ - 4 - ( - 6))} = \frac{4}{2} = 2}[/tex]

The equation of g(x) in point slope form is therefore;

g(x) - (-4) = 2×(x - (-4)) = 2•x + 8

g(x) = 2•x + 8 - 4 = 2•x + 4

g(x) = 2•x + 4

The slope of the function h(x), [tex] m_2 [/tex] is found using the equation;

[tex] \displaystyle{ m_2 = \frac{ 8 - 14}{ - 4 - ( - 6))} = \frac{ - 6}{2} = - 3}[/tex]

h(x) presented in point and slope form is therefore;

h(x) - 8 = (-3)×(x - (-4)) = -3•x - 12

h(x) = -3•x - 12 + 8 = -3•x - 4

h(x) = -3•x - 4

g(h(x)) = 2•h(x) + 4

Plugging in the value of h(x) gives,;

g(h(x)) = 2×(-3•x - 4) + 4 = -6•x - 8 + 4

g(h(x)) = -6•x - 4

The x–intercept of g(h(x)) is given by the point where g(h(x)) = 0, which gives;

At the x–intercept, g(h(x)) = 0 = -6•x - 4

[tex] \displaystyle{ x = \frac{4}{-6} = -\frac{ 2}{3} }[/tex]

The x–intercept is [tex] \displaystyle{ -\frac{ 2}{3} }[/tex]

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Analyzing Graphs of Functions
Which graph shows a function where f(2)= 4?
21
12
12y
12ty
8
8
8
8
4
4
4
х
4 8 12
-12-8 -4
4 8 12
-12-8-4
4 8 12
12-48-4
4 8 12
4
-12-84
8-44
-8
-12
8
-8
-12
-12 V
Intro
Done

Answers

From the graphs we can conclude:

[tex]undefined[/tex]

A journal on how to determine a quadratic equation given the roots

Answers

Answer:

this is your answer hope this helps you

What the roots of the equations?

The roots of an equation is "solutions" of the equation. Solutions are the numerical values equal to the variable after solving it.

To determine the sum and product of the roots of a quadratic equation, the equation has to be written in the form ax²+bx+c = 0

From that form, the sum of the roots is given by -b/c and the product is c/a

For example, we want to find the sum and product of the roots of the quadratic equation 3x²-x = 2

Notice that the equation is not written in the form described above. So, it has to be written as 3x²-x - 2 = 0

From this form, we see that and a = 3, b = -1 and c = -2

Therefore, the sum is -b/a = 1/3 while the product is c/a = -2/3 = -2/3

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Which four groups make up nearly one half of the male population?

Answers

We are given the percentages for males on the left side and the percentages for females on the right side.

We are trying to find four groups that make up nearly 1/2 of the male population, so we want the percentages for these groups to add up to nearly 50%.

Let's take a look at the lowest age groups of the male population, which in turn make up the highest proportion of the male population.

We have the age group 0-4, which makes up roughly 12%.

We have the age group 5-9, which makes up roughly 11%.

We have the age group 10-14, which makes up roughly 11%.

We have the age group 15-19, which makes up roughly 12.5%.

If we add all of these percentages together, we get:

12% + 11% + 11% + 12.5% = 46.5%

Since we cannot go any smaller than 46.5% because this is the closest percentage to 50%, the four groups that make up nearly one half of the male population must be:

Ages 0-4, 5-9, 10-14, and 15-19

What is the magnitude (size) of -7.5?_______________________________O A. -7.5, because |-7.5| = 7.5O B. 7.5, because |-7.5 = 7.5O C. 7/5, because |-7.5| = 7/5O D. 7.5, because | -7.5| = - 7.5

Answers

it is given that the expression is -7.5

the magnitude of -7.5 is,

I-7.5I = 7.5

thus, the answer is option A

in the figure shown Line O is parallel to line P and line M is Parallel to linea N

Answers

we have that

In this problem angle x and angle of 62 degrees are supplementary angles

that means

x+62=180

solve for x

x=180-62

x=118 degrees

find volume of hemisphere who’s great circle has an area of 12.5 ft squared

Answers

The surface area of a hemisphere is given as 12.5 square feet. It is required to find the volume of the hemisphere.

To do this, equate the given surface area to the formula, find the radius, and then substitute the radius into the volume formula to find the volume.

The surface area of a hemisphere radius, r is given as:

[tex]S=3\pi r^2[/tex]

Substitute S=12.5 into the formula and solve for r in the resulting equation:

[tex]\begin{gathered} 12.5=3\pi r^2 \\ \Rightarrow3\pi r^2=12.5 \\ \Rightarrow\frac{3\pi r^2}{3\pi}=\frac{12.5}{3\pi} \\ \Rightarrow r^2=\frac{25}{6\pi} \\ \Rightarrow r=\sqrt{\frac{25}{6\pi}} \end{gathered}[/tex]

The volume of a hemisphere is given as:

[tex]V=\frac{2}{3}\pi r^3[/tex]

Substitute the calculated value of r into the volume formula:

[tex]\begin{gathered} V=\frac{2}{3}\pi\left(\sqrt{\frac{25}{6\pi}}\right)^3 \\ \text{ Substitute }\pi=3.14\text{ into the equation:} \\ \Rightarrow V=\frac{2}{3}(3.14)\left(\sqrt{\frac{25}{6(3.14)}}\right)^3\approx3.2\text{ square feet} \end{gathered}[/tex]

The required volume is about 3.2 square feet.

If each quadrilateral below is a trapezoid, find the missing measures.
#5

Answers

Applying the definition of the adjacent angles of a trapezoid, the value of x in quadrilateral TUVS is: x = 4.

What are the Adjacent Angles of a Trapezoid?

The adjacent angles of a trapezoid are the angles that are found on the same leg of the trapezoid, and they are said to be supplementary to each other because they have a sum of 180 degrees.

Given that quadrilateral TUVS is a trapezoid, where angles SVU and TSV are adjacent angles, therefore:

m∠SVU + m∠TSV = 180°

m∠SVU = 139°

m∠TSV = (14x - 15)°

Substitute

139 + (14x - 15) = 180

139 + 14x - 15 = 180

Combine like terms

124 + 14x = 180

14x = 180 - 124

14x = 56

14x/14 = 56/14

x = 4

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Questions 24-25
The scores of a standardized IQ test are normally distributed with a mean score of 100 and a standard deviation of 15.

Question 24 2
Find the probability that a randomly selected person has an IQ score higher than 105.
Question options:
0.9522
0.3694
-1.15
0.6306

Question 25
A random sample of 55 people is selected from this population. What is the probability that the mean IQ score of the sample is greater than 105?

Question options:
0.0067
0.3694
0.6306
0.9933

Answers

Using the normal distribution and the central limit theorem, it is found that the probabilities are given as follows:

24. Single person has an IQ score above 105: 0.3694.

25. Sample mean (55 people) above 105: 0.0067.

Normal Probability Distribution

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

The mean and the standard deviation of IQ scores are given as follows:

[tex]\mu = 100, \sigma = 15[/tex]

The probability that a single person has an IQ score higher than 105 is one subtracted by the p-value of Z when X = 105, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (105 - 100)/15

Z = 0.33

Z = 0.33 has a p-value of 0.6306

1 - 0.6303 = 0.3694.

For the sample of 55, the standard error is:

[tex]s = \frac{15}{\sqrt{55}} = 2.02[/tex]

Hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (105 - 100)/2.02

Z = 2.48

Z = 2.48 has a p-value of 0.9933.

1 - 0.9933 = 0.0067.

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Mary and two of her friends shared the cost of gas for a road trip if the total amount that they paid for gas was $546 and they shared it equally what amount did mary pay

Answers

Answer:

182

Step-by-step explanation:

It’s literally 546 divided by 3

АD✓32What points in Triangle 2 correspond to points A, B,and C in the original triangle?BSubin7:4610/5

Answers

Since the original triangle, which is triangle 1 has points A, B, and C.

The points in triangle 2 that corresponds to points A, B, and C are:

Points C, D, and A

Point C corresponds to point A

Point D corresponds to point B

POint A corresponds to point C

ANSWER:

Points C, D and A

HELP! Use the graph to determine the behavior of the function between the indicated points.

Answers

The behavior of the function is given as follows:

A and B - DecreasingB and C - ConstantC and D - IncreasingD and E - Decreasing.

What is a function?

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

End behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. Said differently, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +∞) and the left end of the x-axis (as x approaches -∞).

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The curve of the function for the segments AB, BC, CD, and DE is decreasing, constantly increasing, and decreasing respectively.

Given that,
A graph has been shown the behavior of the graph is to be discussed.

What is the behavior of the function?

When a function is graphed, the function must show something likewise increasing, decreasing, and contant relationship.

Here
As per the observation, the graph starts from A and seems to be decreasing up to B and further it is Constant up to C and then increases up to D, afterward it is decreasing up to E.

Thus, the curve of function for the segments AB, BC, CD, and DE is decreasing, constantly increasing, and decreasing respectively.

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This figure shows a circle with a radius of 3.

A circle with its radius labeled as 3.

What is the circumference of the circle?

Answers

The circumference of the circle has a value of 18.86 units

How to determine the circumference of the circle?

From the question, we have the following parameters:

Radius, r = 3 units

The circumference of the circle can be calculated using the following circumference formula

C = 2πr

Where

π = 22/7 (a constant)

r = 3

Substitute the known values in the above equation

So, we have the following equation

C = 2 * 22/7 * 3

Evaluate the products

So, we have the following equation

C = 18.86

Hence, the circumference is 18.86 units