Answer:
a.
[tex]\begin{gathered} 0.000041\leq\sigma^2\leq0.00015 \\ 0.0064\leq\sigma\leq0.0125 \end{gathered}[/tex]b. The standard deviation is at an acceptable level
Explanation:
The confidence interval for the variance can be calculated as:
[tex]\frac{(n-1)s^2}{\chi^2_{\frac{\propto}{2}}}\leq\sigma^2\leq\frac{(n-1)s^2}{\chi^2_{1-\frac{\propto}{2}}}[/tex]Where n is the size of the sample, s² is the variance of the sample, (1-∝) is the level of confidence, and χ² is the value of chi-square with n-1 degrees of freedom.
In this case, we get that n is 14 tablets, s² is 0.000071, and 1-∝ = 90%, so ∝ is 10%.
Then, the values of chi-square with 13 (14 -1) degrees of freedom is:
[tex]\begin{gathered} \chi^2_{\frac{\propto}{2}}=22.36 \\ \chi^2_{1-\frac{\propto}{2}}=5.89 \end{gathered}[/tex]Therefore, the interval of confidence for the population variance is:
[tex]\begin{gathered} \frac{(14-1)(0.000071)}{22.36}\leq\sigma^2\leq\frac{(14-1)(0.000071)}{5.89} \\ 0.000041\leq\sigma^2\leq0.00015 \end{gathered}[/tex]Then, the standard deviation is the square root of the variance, so the interval of confidence for the population standard deviation is:
[tex]\begin{gathered} \sqrt[]{0.000041}\leq\sigma\leq\sqrt[]{0.00015} \\ 0.0064\leq\sigma\leq0.0125 \end{gathered}[/tex]Finally, since the upper limit of the interval for the standard deviation is less than 0.15 milligrams, we can say that the population standard deviation is at an acceptable level with a confidence level of 90%
A line with a slope of -2 passes through the point (3,-2). Which of the
following is the equation of the line?
The equation of the line with slope -2 and passing through the point (3,-2) is y+2x-4=0.
What is the equation of a line with a given slope and a point?The point-slope formula is used to find the equation of the line passing through a point (a,b) and having a slope of m.
A straight line equation of the form (y-b) = m(x-a), where m is the slope of the line and (a,b) are the coordinates of a given point on the line, is the standard form given for the point-slope form of the line.
A point (3,-2) and a slope -2 are given.
Use the standard Point-slope form of the line to find the equation of the line.
(y-b) = m(x-a)
Put the given values in the Point-slope equation.
y-(-2)=-2(x-3)
Simplify the equation to get the equation of the line.
y+2=-2x+6
y+2x-4=0
So, the equation of the line is y+2x-4=0.
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3. Describe the similarities and differences among the following experiments. (a) Slips of paper are marked with the numbers 1, 2, 3, 4, and 5 and placed into a box. After being mixed, two slips are drawn simultaneously. (b) Slips of paper are marked with the numbers 1, 2, 3, 4, and 5 and placed into a box. After being mixed, one slip is drawn then put back into the box, then a second slip is drawn. (c) Slips of paper are marked with the numbers 1, 2, 3, 4, and 5 and placed into a box. After being mixed, one slip is drawn and not put back into the box, then a second slip is drawn.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Describe the first experiment
Two slips were drawn simultaneously, this means that the outcome of the first slip drawn will be multiplied by the outcome of the second slip drawn. The probability will follow the "and rule of probability".
STEP 2: Describe the second experiment
Since one slip is drawn and then put back into the box before a second slip is drawn, this is a PROBABILITY WITH REPLACEMENT. The outcome of the first event will not affect the outcome of the second event since the paper slips are replaced hence not reduced.
STEP 3: Describe the third experiment
Since one slip is drawn and not put back into the box before a second slip is drawn, this is a PROBABILITY WITHOUT REPLACEMENT. The outcome of the first event will affect the outcome of the second event since the paper slips reduce.
Difference between b and c is that b is with replacement and the total outcomes does not change while c is without replacement and the total outcomes change(reduce) after the first slip is drawn.
On a map of Europe, the cities of Berlin, Budapest, and Vienna form a triangle. Berlin is 329 miles from Vienna, and Vienna is 129 miles from Budapest. Berlin is closer to Vienna than to Budapest. Based on these facts, which of the following best describes the possible values of d, the distance between Berlin and Budapest in miles?
The possibles values of d i.e., the distance between Berlin and Budapest will be as follows
200 miles < d < 458 miles
What is the triangle inequality theorem?The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side.
Case 1
129 miles + d > 329 miles
⇒ d > 200 miles
Case 2
129 miles + 329 miles > d
⇒ 458 miles > d
From Case 1 and Case 2, for d we can say
200 miles < d < 458 miles
Therefore, The possibles values of d i.e., the distance between Berlin and Budapest will be as follows
200 miles < d < 458 miles
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Ai Mi was out at a restaurant for dinner when the bill came. Her dinner came to $9. After adding in a tip, before tax, she paid $11.79. Find the percent tip.
The percent tip paid on the Ai Mi's $9 dinner is 31%.
What is the percent tip?Tip increases the price paid for a service rendered. Percentage is the rate of amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to percentage, multiply the number by 100.
The first step is to determine the tip paid : $11,79 - $9 = $2.79
Now, express the tip as a ratio of the cost of the dinner and multiply by 100
(2.79 / $9) x 100 = 31%
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Please help! Will give brainliest!
Step-by-step explanation:
[tex]\sqrt[3]{t^{2} } + 4\sqrt{t^{3} } \\=t^{\frac{2}{3} } + 4t^{\frac{3}{2} }\\\\then, \\u` = \frac{2}{3}t^{-\frac{1}{3}} + 6t^{\frac{1}{2} }[/tex]
Armando kicks a football into the air. The function f(x) = - 7x² + 38x+0.22 models the height of the football from the ground, in feet, with respect to the time x inseconds. Use a graph or table to estimate the time for the ball to return to the ground after being kicked
Hi there. To solve this question, we'll have to remember some properties about parabolas and its roots.
Given the function:
[tex]f(x)=-7x^2+38x+0.22[/tex]that models the height of the football Armando kicked from the ground, in feet, with respect to time x in seconds, we have to determine:
The time it takes for the ball to return to the ground after being kicked.
Let's suppose that the ball was kicked from x = 0, since the times x is given in seconds and we can't have negative time.
Before supposing it, in fact we have to determine which moments the ball was at the ground, that is, f(x) = 0. We're finding the roots of the function:
[tex]\begin{gathered} -7x^2+38x+0.22=0 \\ \end{gathered}[/tex]To solve this quadratic equation, remember the general solution to a quadratic equation
[tex]ax^2+bx+c=0,a\text{ not equal to 0.}[/tex]Is given by the formula:
[tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Plugging a = -7, b = 38 and c = 0.22, we get:
[tex]x=\frac{-38\pm\sqrt{38^2-4\cdot7\cdot0.22}}{2\cdot(-7)}[/tex]Multiply the values, square the number and add inside the radical.
[tex]x=\frac{-38\pm\sqrt{1444-6.16}}{-14}=\frac{-38\pm\sqrt{1437.84}}{-14}[/tex]Separing the solutions and calculating their values, we get
[tex]\begin{gathered} x=\frac{-38\pm37.92}{-14} \\ \\ x_1=\frac{-38+37.92}{-14}=0.006 \\ \\ x_2=\frac{-38-37.92}{-14}=5.423 \end{gathered}[/tex]In this case, we before had supposed the ball started from x = 0. This is not really necessary because we found that the roots of this functions are contained in the positive x-axis.
To find the time for the ball to return to the ground, we make:
[tex]|x_2-x_1|=|5.423-0.006|=|5.417|=5.417[/tex]Or 5.42 seconds.
Graphically, what we have is:
A client of Susan's has asked her to create a new wood floor for his living room. The design will be created by laying wood strips in different directions, as shown on the coordinate grid. Determine whether Quadrilateral can best be described as a trapezoid, a rhombus, a rectangle, or a square. Explain your reasoning.
The Quadrilateral can best be described as a trapezoid with it's two parallel sides and two non- parallel sides.
What is a Quadrilateral?A Quadrilateral is a type of polygon that is known to have four sides from which the name is being derived.
Examples of quadrilateral include the following:
Trapezoid: This is a type of quadrilateral that has two parallel sides with two non parallel sides.Rhombus: This is the type of quadrilateral that has all its four sides equal.Rectangle: This is the type of quadrilateral that has four sides with two equal opposite sides each.Square: This is the type of quadrilateral that has four equal sides with four equal right angles.The quadrilateral represented in the coordinate grid is a trapezoid because it has two parallel sides which are AB and DC and two non parallel sides such as AD and CB.
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c) 2.5-1.4 x 1.4 x 1.4 2.5 x 2.5 x (2.5)² + 2.5 x 1.4+ (1.4)²
We will have the following:
[tex]\begin{gathered} \frac{2.5\ast2.5\ast2.5-1.4\ast1.4\ast1.4}{(2.5)^2+2.5\ast1.4+(1.4)^2}=\frac{15.625-2.744}{6.25+3.5+1.96} \\ \\ =1.1 \end{gathered}[/tex]So, the simplification is equal to 1.1.
***Explanation***
[tex]\frac{2.5\operatorname{\ast}2.5\operatorname{\ast}2.5-1.4\operatorname{\ast}1.4\operatorname{\ast}1.4}{(2.5)^2+2.5\operatorname{\ast}1.4+(1.4)^2}[/tex]First, we multiply all the values that are asked to be multiplied, and we also operate all the exponents. [We recall that a value at the power of a number is the number of times the value is multiplied by itself], then we get that:
[tex]\frac{2.5\ast2.5\operatorname{\ast}2.5-1.4\operatorname{\ast}1.4\operatorname{\ast}1.4}{(2.5\ast2.5)+2.5\operatorname{\ast}1.4+(1.4\ast1.4)}=\frac{15.625-2.744}{6.25+3.5+1.96}[/tex]Finally we operate the simpler and lower in the hierarchy of operations expressions:
May I receive help? Find the surface area of the solid. round to the nearest tenth.
The diagram of the solid is shown below:
The surface area ould be the sum of the area of each face
The area of the first rectangular face = 1.5 * 3.3 = 4.95 cm^2
The area of the middle rectangular face = 2.5 * 3.3 = 8.25 cm^2
The area of the third rectangular face = 2.0 * 3.3 = 6.6 cm^2
Area of each triangle is 1/2 * base * height = 1/2 * 2 * 1.5 = 1.5
Since the faces are 2, area of both triangular faces = 1.5 * 2 = 3 cm^2
Total surface area of the solid is
4.95 + 8.25 + 6.6 + 3 = 22.8 cm^2
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee !!
Answer: 600
Step-by-step explanation:
I did not check your work from parts a and b.
Assuming they are correct,
You have found the total amount after the first year and the total amount after the first two years.
To find the total amount for only the second year,
you subtract the second year totals from the first year totals.
So,
(b) - (a) = 1000 - 400 = 600
If f(x) = x² - 6x + 2 and g(x) = -2x, find the following composition (g o f)(5)
The composite function's value, (gof)(5), is equivalent to 6.
What are composite functions?A mathematical procedure called composite combines two functions, f and g, to produce a third function, h(x), where g(x) is the sum of f(x) and h(x).
Given the aforementioned functions,
f(x) = x^2-6x+2 and;
g(x) = -2x
The composite function is known as the gof (5)
(gof) = g(f(x)) where;
f(x) = g(x2-6x+2) and;
f(x) = -2(x2-6x+2).
Substitute the given functions into the composite;
g(f(5)) = -2(5^2-6(5)+2)
g(f(5)) = -2(-3) = 6
The comparable composite value is provided by this.
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Answer:
A) y = 4B) ∠A = 66°, ∠C = 114°, ∠D = 114°Step-by-step explanation:
Angles A and B, same as angles C and D are vertical angles and have equal measure according to definition of vertical angles:
Part Am∠A = m∠B = 66°6y + 42 = 666y = 66 - 426y = 24y = 24/6y = 4Part BFind the measure of angles C and D.
∠C and ∠D are supplementary with ∠A or ∠B, so the pair sums to 180°.
m∠C = m∠Dm∠A + m∠C = 18066 + m∠C = 180m∠C = 180 - 66m∠C = 114So the angle measures are:
m∠A = 66°, m∠C = 114°, m∠D = 114°Which is the better buy: 18 oz. of rice for $6.30, 12 oz. of rice for $4.56, or 7 oz. of rice for $2.59? steps
Using unitary method, it is better to buy 18 ounce of rice for $6.30
There are three types of rice
Rice 1
The cost of 18 ounce of rice = $6.30
Here we have to use the unitary method
The cost of 1 ounce of rice = 6.30/18
= $0.35
Rice 2
The cost of 12 ounce of rice = $4.56
Apply unitary method
The cost of 1 ounce of rice = 4.56/12
= $0.38
Rice 3
The cost of 7 ounce of rice = $2.59
Apply unitary method
The cost of 1 ounce of rice = 2.59/7
= $0.37
So It is better to buy rice 1
Hence, unitary method, it is better to buy 18 ounce of rice for $6.30
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DeMarcus multiplies all of the intergers from -10 to -1, including -10 and -1. Should his answer be positive or negative
Multiplication of all of the integers from -10 to -1, including -10 and -1 is positive.
What is integer?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 3/4, 3.14.
According to question,
multiplication of all of the integers from -10 to -1, including -10 and -1 is
-10 × -9 × -8 × -7 × -6 × -5 × -4 × -3 × -2 × -1 = +3628800
Answer is positive because - × - gives + and there are five such pairs of number, all of the minus sign become positive after multiplication.
Hence, multiplication of all of the integers from -10 to -1, including -10 and -1 is positive.
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The area of the rectangle shown above is 17.36 square yards. What's the perimeter?
Answer:
D. 17.4 yards
Step-by-step explanation:
Since the area of the rectangle is 17.36 square yards, and the width is 3.1 yards, we set up and solve this equation to find the length:
17.36 = 3.1h, so h = 5.6 yards.
From this, the perimeter of the rectangle is 2(3.1 + 5.6) = 2(8.7) = 17.4 yards.
So D is the correct answer.
Given: ABCD is a parallelogram A = (3x + y) B = (5x + 10) C = (5y + 20) Find x, y, and mB. x y The measure of angle B =
we know that
In a paralleogram opposite angles are congruent and consecutive angles are supplementary angles
That means
and
so
substitute the given values
(3x+y)=5y+20
3x-4y=20 ------> equation 1
substitute
(3x+y)+(5x+10)=180
8x+y=170
y=170-8x ------> equation 2
solve the system
substitute equation 2 in equation 1
3x-4(170-8x)=20
solve for x
3x-680+32x=20
35x=20+680
35x=700
x=20
Find the value of y
y=170-8(20)
y=10
step 2
Find the measure of angle B
Challenge:
Aisha's mother is 5 times older than Aisha. In 15 years
Aisha's mother will be twice the age her daughter. How old
are both ladies now?
Aisha age is 5 year and Aisha's mother age is 25 year.
What is a linear equation?The formula for a linear equation is the way in which a linear equation is expressed. It can be expressed in the standard form, the slope-intercept form or the point-slope form. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is the coefficient of x, and B is a constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, and A, B, and C are any real numbers.
Given that,
Aisha's mother is 5 times older than Aisha.
Let Aisha age = x year
Aisha's mother = 5x year
After 15 years Aisha's mother will be twice the age her daughter.
5x+15 = 2(x+15)
5x+15 = 2x+30
3x = 15
x = 5
Aisha age = 5 year
Aisha's mother age = 5x = 5×5 = 25 year
Hence, Aisha age is 5 year and Aisha's mother age is 25 year.
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please help me solve this problem!
(a) Josh would pay $592.48 for the television at the department store.
(b) Josh would pay $634.8 for the television at the superstore.
(c) Josh would pay less for the television at the department store.
Given:
Wholesale price of television = $529
(a) In the department store,
Television wholesale price is marked up by 40%.
Discount = 20%
Marked price = 529 × ( 1 + 40%)
= 529 × (140/100)
= $740.6
Selling price = 740.6 × (1 - 20%)
= 740.6 × (80/100)
= $592.48
(b) In the superstore,
Television wholesale price is marked up by 20%.
Marked price = 529 × ( 1 + 20%)
= 529 × (120/100)
= $634.8
He must pay the full in-store price.
Selling price = $634.8
Ignoring the tax, he must pay the full price at the superstore which is $634.8.
(c) As the selling price in the department store is less than in the superstore, $592.48 < $634.8.
So, Josh would pay less for the television at the department store.
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The width of a rectangle is 4 less than the length. If the area of the rectangle is 165cm?,solve for the length and width of the rectangle.
length:15 cm
width: 14 cm
Explanation
Step 1
Let
w represents the width of the rectangle
l represents the length of the rectangle
a)The width of a rectangle is 4 less than the length,hence
write this in math terms, replace
[tex]\begin{gathered} \text{width}=length-4 \\ w=l-4\rightarrow equation\text{ (1)} \end{gathered}[/tex]b)the area of the rectangle is 165 square cm
the area of a rectangle is given by
[tex]\begin{gathered} \text{Area}=\text{length}\cdot\text{width} \\ \text{replace} \\ 165cm^2=l\cdot w\rightarrow \\ 165=l\cdot w\rightarrow equiation(2) \end{gathered}[/tex]Step 2
now, solve the equations
[tex]\begin{gathered} w=l-4 \\ 165=lw \end{gathered}[/tex]a) replace the w from equation (1) into equation(2)
[tex]\begin{gathered} 165=lw \\ 165=l(l-4) \\ 165=l^2-4l \\ \text{subtract 165 on both sides} \\ 165-165=l^2-4l-165 \\ l^2-4l-165=0 \end{gathered}[/tex]b) now, we have a quadratic equation in the form
[tex]ax^2+bx+c=0[/tex]hence, we can use the quadratic formula to solve
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]let
a=1
b=-4
c=-165
replace
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-4)\pm\sqrt[]{-4^2-4(1)(-165)}}{2\cdot1} \\ x=\frac{4\pm\sqrt[]{676}}{2}=x=\frac{4\pm26}{2} \end{gathered}[/tex]therefore
[tex]\begin{gathered} x=\frac{4\pm26}{2} \\ x_1=\frac{4+26}{2}=\frac{30}{2}=15 \\ x_2=\frac{4-26}{2}=\frac{-22}{2}=-11 \end{gathered}[/tex]as we are searchinf for a distance, the only valid answer is 15
so, the answer is length= 15 cm
[tex]l=15\text{ cm}[/tex]c) finally, replace the l value into equation (1) to find the width
[tex]\begin{gathered} w=l-4\rightarrow equation\text{ (1)} \\ w=15-4 \\ w=11 \end{gathered}[/tex]therefore, the width is 11 centimeters
I hope this helps you
The table lists the eight human blood types.It also shows how blood types determine who a person can donate blood to and receive blood from.
X' is the set of blood types that type AB- cannot donate blood to
Y is the set of blood types that type AB+ can donate blood to
From the table, AB- cannot donate blood to:
(This is all the blood types minus the ones that can receive from AB-)
U - {AB+, AB-} = {A+, B+, A-, B-, O+, O-} = X'
Y = {AB+}
So the negations:
X = {AB+, AB-}
Y' = {A+, B+, AB-, A-, B-, O+, O-}
And this is our final answer
What is the minimum Brianna can lost the house to accommodate both of these requirements, round the the nearest hundred dollars
We are given that Brianna needs to receive $199300 and that she also needs to allow for a 3 percent commission. Let "x" be the amount Brianna needs to sell her house. We need to subtract from this amount the 3% commission. To do that we will use the following relationship:
[tex]x-\frac{3}{100}x=199300[/tex]Now, we solve for "x" first by adding the fractions using the following model:
[tex]a+\frac{b}{c}=\frac{ac+b}{c}[/tex]Therefore, we will multiply the 100 from the denominator by "x" and subtract 3 from the result, like this:
[tex]\frac{100x-3x}{100}=199300[/tex]Solving the operations we get:
[tex]\frac{97x}{100}=199300[/tex]Now we multiply both sides by 100:
[tex]97x=19930000[/tex]Now we divide both sides by 97:
[tex]x=\frac{19930000}{97}=205463.92[/tex]Therefore, the amount is $205463.92. Since we are told to round to the nearest hundred dollars we round the answer to $205500.
5.2
6.5
8
15.6 19.5 24
What is the value of y when x = 5?
X
y
1.5
3
4.5 9
According to the table of values, y has a value of 15 when equals 5
How to determine the value of y?The table of values represents the given parameter
On the table of values, we can see that:
The value of x multiplied by 3 gives the corresponding value of y
This can be represented as
y = 3 * x
Evaluate
y = 3x
As a proof, we have
1.5 * 3 = 4.5
3 * 3 = 9
5.2 * 3 = 15.6
So, when x = 5;
We have
y = 3x
This gives
y = 3 * 5
Evaluate
y = 15
Hence, the value of y when x= 5 is 15
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What is the standard deviation for the group of data items
Check the picture below.
What does the leading term of −5x^4+4x^3−6x^2+8 tell you?
1. Zacarías se tardó un semestre en escribir su proyecto final de 95,234 palabras para un curso universitario.
Zacarías escribió 35,295 palabras el primer mes y 19,240 palabras el segundo mes.
a. Redondea cada valor a la decena de millar más cercana para estimar cuántas palabras escribió
Zacarías durante la parte restante del semestre.
hi can u pls help me with my math here's the picture of it
To find the answer, we just have to look for the complement fraction of 9/10, which is found by subtracting from 1
[tex]1-\frac{9}{10}=\frac{1}{10}[/tex]Hence, the energy passed to a cow is 1/10.Observe that the complement of 9/10 is the answer because that's the amount of energy that stays in the plant.
I need help with this question but no one is helping me! Can someone please help me
Answer:
0.053
Step-by-step explanation:
the probability of taking a Boston creme first is 6/19 (19 is the total doughnuts in the box), then the probability of taking a chocolate glazed second would be 3/18 (bc there would be 18 left after taking one first). then multiply these fractions together. as a decimal you get 0.053 to 3 decimal places
is this right y = 39 z = 102 x =51
The first triangle is an Isosceles triangle:
2 equal sides
2 equal angles ( opposite to the sides)
The sum of all interior angles of a triangle is 180°
So, for the left triangle:
51+x+x2 = 180
x+x2 = 180-51
x+x2 = 129
Since both angles are equal:
129/2 = 64.5°
x= 64.5°
x+y = 90°
64.5 + y = 90
y= 90-64.5
y= 25.5°
Right triangle:
25.5+25.5 +z = 180
z= 180-25.5-25.5
z= 129°
For each relation decide whether or not it’s a function(This is ONE question I do on my math program with this is considered one question)
Relation 1:
It is a function because one point of its range (axis y) have two points in the domain (axis x).
Relation 2:
It is not a function because one point in the domain have two points in the range:
Relation 3:
It is a function because each point in the domain have a different point in the range.
Relation 4:
It is not a function because the point -7 in the domain have three values for the range:
The answer is, the relations: 2,4 are not functions and the functions 1, 3 are functions.
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BUMP
It is an Irrational number.
Mathematics Number Types
The numbers are divided into many sorts based on their characteristics and how they are shown on a number line. To help readers comprehend each kind of number, descriptions, features, and examples are included. Here are the many kinds of numbers:
Natural Numbers
Natural numbers, which include the range of positive integers from 1 to infinity, are sometimes known as "counting numbers." The letter "N" stands for the set of natural numbers. The definition of the natural number set is:
N = {1, 2, 3, 4, 5, ……….}
For instance, 35, 59, 110, etc.
Natural Numbers' Characteristics
Natural number addition is commutative, associative, and closed.
Multiplication of Natural Numbers is closed, associative, and commutative.
Zero is the identity component of a natural number when added.
A natural number's identity component under multiplication is one.
Complete numbers
Natural numbers with a zero are another name for whole numbers. The set is made up of non-negative integers without any fractional or decimal parts. The entire set of numbers is "W" which stands for the concept. The definition of the natural number set is:
W = {0,1, 2, 3, 4, 5, ……….}
For instance, 67, 0, 49, 52, etc.
Whole-number properties:
Under addition and multiplication, whole numbers are closed.
The identity component of the whole numbers that are additive is zero.
The multiplicative identity element is 1, which.
It complies with addition and multiplication's commutative and associative properties.
The distributive property that favors multiplication over addition and vice versa is satisfied.
Here is further information about the entire numbers.
The set of all whole numbers with a negative set of natural numbers is known as an integer. The letter "Z" stands for the integer set. The definition of the set of integers is:
Z = {-3, -2, -1, 0, 1, 2, 3}
For instance: -52, 0, -1, 16, 82, etc.
Characteristics of integers
For addition, subtraction, and multiplication, integers are closed.
For integer addition and multiplication, the commutative property is met.
It abides by the addition and multiplication operations' associative feature.
For addition and multiplication, it abides by the distributive property.
The integers' additive identity is 0.
Integers have a multiplicative identity of 1.
Actual Figures
Real numbers are any number, including positive and negative integers, fractional and decimal numbers, and quantities without imaginary numbers. The letter "R" is used to signify it.
Examples are 34, 0.333, 2, 0, -10, 20.
Real Numbers' Characteristics
Under addition and multiplication, Real Numbers are commutative, associative, and distributive.
The opposite property applies to real numbers.
Real numbers have identity elements that are 0 and 1, respectively, for addition and multiplication.
Rational Numbers
Any integer that can be expressed as p/q, or as a ratio of one number to another, is referred to be a rational number. The letter "Q" can be used to signify a rational number.
Examples include 7/1, 10/2, 1/1, and 0/1.
Rational number properties include:
Addition, subtraction, multiplication, and division all result in closed rational numbers.
With regard to addition and multiplication, it meets the commutative and associative properties.
For addition and subtraction, it abides by the distributive property.
Unrealistic Numbers
The amount that cannot be represented by p/q. It denotes a number as being irrational if it cannot be expressed as a ratio of one to another. The letter "P" is used to signify it.
Examples include 2 and Euler's constant.
Irrational number characteristics include:
Irrational numbers do not meet the property of closure.
Under addition and multiplication, it complies with the commutative and associative properties.
Irrational numbers can be added to and subtracted from in distributive ways.
Large Numbers
Complex numbers are those that take the form a+bi, where a and b should be real values, and I should be an imaginary number.
Examples are 1 + 2i, -2 + 3i, and 4 + 4i.
Complex number properties include:
The complex numbers have the following characteristics:
a characteristic of addition and multiplication that is associated.
Commutative addition and multiplication properties.
Multiplication's distributive advantage over addition.
Unreal Numbers
The complex numbers category includes imaginary numbers. It is the result of adding actual numbers with the hypothetical unit "i." It defines the imaginary portion of complex numbers.
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