Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.
Are all rational numbers also whole numbers:#Every Rational number is not a whole number because A whole number is a component set of zero and all positive numbers such as 0, 1, 2, 3, 10, 15,… include only positive integers. It excludes negative integer, decimal, and fractional values .
Rational Number includes all the fractions, integers as well as decimal numbers.
Here set of whole number like 3, 4, 5 we can write this number as a fraction of 1 like 3/1, 4/1, 5/1… in ratio of two integers. Therefore every whole number is a rational number but every rational number is not a whole number.
Are all whole numbers is a rational number :#Whole numbers are that starts from 0 to infinity. Whole numbers can be written in the form of 0/1, 1/1, 2/1, … Thus, every whole number is a rational number but every rational number is not a whole number.
Solve. Check for extraneous solutions. √√x+25 = √x+5
-1 is the extraneous solution
To know the value of x first we need to remove the square root of the equation
[tex]\sqrt \sqrt{x +25}[/tex] = [tex]\sqrt{x + 5}[/tex]
So to get the value we have to square both sides of the equation
[tex](\sqrt\sqrt{x +25})^{2}[/tex] = [tex](\sqrt{x + 5} )^{2}[/tex]
We get
[tex]\sqrt{x +25}[/tex]= x + 5
Now again we have to square both sides of the equation
x + 25 = [tex](x + 5)^{2}[/tex]
x + 25 =[tex]x^{2}[/tex] + 10x + 25( As we know [tex](a + b)^{2}[/tex]= [tex]a^{2}[/tex] + [tex]b^{2}[/tex] + 2ab )
[tex]x^{2}[/tex] + 9x = 0
x( x + 9) = 0
Therefore x = 0, -9
1 = [tex]\sqrt{-1}[/tex]
9 = [tex]\sqrt{81}[/tex]
The square root of 81 is 9 but the square root of -1 is an imaginary number
so the correct choice is " 9 is the solution of the equation " and -1 is the extraneous solution
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The elevation of city A is 96 feet below sea level; the elevation of city C is 24 feet below sea level. The elevation of city D is [tex]\frac{1}{4}[/tex]of the elevation of city C.
Answer: (A) -24x1/4 (B) Negative multiplied by a positive equals a negative
Step-by-step explanation:
The question says below sea level, so the whole number is negative. we don't need city A its a distraction so city C is multiple by city D. why do we multiply because the word of means multiple there for the expression is
write the product into one single fraction
-24x1
4 canceled the 4 in the fraction -24x1
4
-6x1 any expression divided by one remains the same -6x1
1
solution
x1=0
6(2c - cd² + d)
Answer
Answer:
(2)(6)+3
?
=
15
15=15
True
Step-by-step explanation:
help
what is the mean of −26,39,−10,−16,12,31
The mean of of −26,39,−10,−16,12,31 is 5 which is determined by summing up the numbers and dividing by 6
What is the mean?
The mean is the sum of the integers divided by the number of integers therein, in other words, the mean is determined sum , having computed the sum we divide by 6 since there are six numbers in the distribution
sum=-26+39-10-16+12+31
sum=30
mean=sum/n
n=6(there are six numbers)
mean=30/6
mean=5
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Help please 10 points
For the given statement conclusion it was drawn using the law of syllogism.
Option A is our correct answer
What is the law of syllogism?The Law of Syllogism states that,
If the following two statements are true:
- If p, then q.
- If q, then r.
Then the third statement is true:
- If p, then r.
We have,
p - If you do the unit review, q - you will do well on the test.
q - If you do well on the test, r - then you will do well in the course.
Therefore, p - if you do the unit review, r - then you will do well in the course.
This is in the form of:
- If p, then q.
- If q, then r.
Then the third statement is true:
- If p, then r.
Thus this conclusion was drawn using the law of syllogism.
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The slope of line a is 2/3 . The slope of line b is 2/3 .
Which statement is true?
Responses
The lines are perpendicular.
The lines are neither perpendicular nor parallel.
The lines are parallel.
Since lines a and b have the same slope, then: the lines are parallel.
What are the Slopes of Parallel Lines?The slope of a line is the rise/run or change in y / change in x. When two lines lie parallel to each other, they will have equal slope value.
On the other hand, when two lines lie perpendicularly to each other, their slopes will be negative reciprocal.
For example, if a line has a slope of 2/3, the slope of the line that is parallel to it will be 2/3 also, while the slope of the line that is perpendicular to it will be -3/2.
Thus:
The slope of line a = 2/3
The slope of line b = 2/3
Therefore, since lines a and b have the same slope, then: the lines are parallel.
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Answer: the lines are parallel.
A manufacturer produces a large number of toasters. From past experience, the manufacturer knows that approximately 2% are defective. In a quality control procedure, we randomly select 20 toasters for testing. We want to determine the probability that no more than one of these toasters is defective.
The probability that a randomly selection of 20 toasters for testing, no more than one is defective is: 0.9401
To solve this exercise the formula and the procedure that we have to use for binomial distribution is:
P(x) = n! /[x! *(n-x)!] * pˣ * (1 - p)ⁿ⁻ˣP = P(0) + P(1)Where:
n = number being sampled or trialsp = probability of getting a success in one trial1 - p = probability of getting a failure in one trialx = number of successes desiredInformation about the problem:
n = 20 toastersp = 2% = 0.021 - p = 1 - 0.02 = 0.98x = no more than oneApplying the binomial distribution formula, we get:
P(x) = n! /[x! *(n-x)!] * pˣ * (1 - p)ⁿ⁻ˣ
P(x) = 20! /[x! *(20-x)!] * 0.02ˣ * (1 - 0.02)²⁰⁻ˣ
Using the P formula to calculate the probability that no more than one of these toasters is defective, we have:
P = P(0) + P(1)
P(0) = 20! /[0! *(20-0)!] * 0.02⁰ * (1 - 0.02)²⁰⁻⁰
P(0) = 20! /(0!*20!) * 0.02⁰ * (0.98)²⁰
P(0) = 1/0! * 1 * 0.6676
P(0) = 1/1 * 1 * 0.6676
P(0) = 0.6676
P(1) = 20! /[1! *(20-1)!] * 0.02¹ * (1 - 0.02)²⁰⁻¹
P(1) = 20! /(1!*19!) * 0.02¹ * (0.98)¹⁹
P(1) = (20*19!) / (1!*19!) * 0.02¹ * (0.98)¹⁹
P(1) = 20/1! * 0.02 * 0.6812
P(1) = 20 * 0.02 * 0.6812
P(1) = 0.2725
P = P(0) + P(1)
P = 0.6676 + 0.2725
P = 0.9401
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
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In the sentence 52 = 15∙3 + 7, 7 is the ________________.
In the sentence 52 = 15∙3 + 7, 7 is equal to 36.7
In mathematics, equality is a relationship that states that two quantities have the same value or that two mathematical expressions represent the same mathematical object.
Someone or something that is equal to another has the same quantity, value, or rights as that other thing. One cup and eight ounces are equivalent, for instance. Equal pay for equal work performed by men and women is an illustration of equality.
If both operands have the same value, the equal-to operator (==) returns true; otherwise, it returns false. If the operands do not have the same value, the not-equal-to operator (!=) returns true; otherwise, it returns false.
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4. Is it appropriate to use an absolute value inequality to represent how a player wins this game? Why? (2
points: 1 point for an answer, 1 point for an explanation)
Answer: yes, because you can't score negative numbers in a game and the absolute value is really just making all numbers positive unless there is a negative variable outside of the absolute value symbols
Step-by-step explanation: brainliest?
Which function represents the value after x years of a new delivery van that costs $ 25,000 and depreciates 15 % each year?
(A) y=-15(25,000) x (C) y=25,000(0.85)x (B) y=25,000(0.15)x D) y=25,000(1.15) x
The function that represents the value after x years of a new delivery van that costs $ 25,000 and depreciates 15 % each year is option (C) y = 25000(0.85)ˣ.
Consider the compound interest formula:
y = P(1 + r/n)ⁿˣ
y here stands for the car's potential value.
P represents the value of the new car.
r is a measure of how quickly a car's value declines.
The number n indicates how frequently the car's value depreciates each year.
x represents the number of years.
Given P = 25000
r = -15% = -0.15 (Since the value of the car depreciates)
n = 1
x = x
Using the given values, we get the function as,
y = 25000(1 + (-0.15)/1)ˣ
⇒ y = 25000(1 - 0.15)ˣ
⇒ y = 25000(0.85)ˣ
Therefore, the function that represents the value after x years of a new delivery van that costs $ 25,000 and depreciates 15 % each year is option (C) y = 25000(0.85)ˣ.
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The sum of 4 consecutive numbers odd numbers is 56.
Find the greatest of the 4 numbers.
A=1 b= 1/2 what would be the answer to the picture attached
Answer:
B/a
Step-by-step explanation:
Because 1/a is still the same as a to power negative one and so 1/b. 1/a divided by 1/b is b/a
Which of the following represents an algebraic expression?
4 + (5 - 2)
4x + 5y - 2
4x + 5 = 2
None of the above
Answer:
4x + 5y - 2
Step-by-step explanation:
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
look for relationships (an elevator decends at a constant speed what is the change in elevation after 19 seconds)
An elevator descends at a constant speed, the change in elevation after 19 seconds will be an elevation of distance
d= 19v where acceleration remains constant
What is elevation?Generally, An angle is created when a horizontal line and a line of sight are placed side by side.
In conclusion, This angle is known as the angle of elevation. If the line of sight rises above the horizontal line, the angle that is generated is known as an angle of elevation.
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in the right angled triangle abc below ab =bc. the size of C is..
Answer:
45°
Step-by-step explanation:
AB and BC are congruent which mean ∠BAC and ∠BCA are congruent.
We already know ∠ABC is 90°.
We cans set up the equation with what is given.
180 = 90 + 2c
Subtract 90 from both sides.
90 = 2c
Divide both sides by 2
45 = C
So angle C is 45°
Which of the following vectors has the greatest magnitude? Explain.
a= (3,4)b = (-4, 3)c = (4,-3)
The Magnitude of all the vectors is the same.
As you know, a vector is an object with both Magnitude and direction. To find the size of a vector, we need to calculate the length of the vector. Variables such as velocity, distance, force, and momentum are vector variables. But velocity, mass, distance, volume, temperature, etc., is a scalar quantities. A vector has both Magnitude and direction, while a scalar has only one Magnitude.
The Magnitude of a vector is the length of the vector. The Magnitude value of vector a is represented by ∥a∥.
The formula for its Magnitude is given below for a two-dimensional vector a= (a1, a2).
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The PTA at Greenville High School is having its annual dinner and auction to raise money for music and art programs. Last year, the event raised $42,890. This year, it raised 30% less. How much was raised this year?
The amount the PTA at Greenville High School raised this year is $30,023.
What is percentage?The percentages are also called the centesimal ratio, and are usually accompanied by the symbol “%”, which reads “percent”.
What percentage of the last year's funds are raised this year?The fact that the PTA at Greenville High School raises 30% less funds this year compared to last year means that the amount raised this year is 70% of last year's funds, in essence, 70% multiplied by last year's:
amount gives this year funds raisedfunds raised this year=funds raised last year*70%funds raised this year=$42,890*70%funds raised this year=$30,023Find out more about percentages on: brainly.com/question/18706090
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SOMEONE HELP MEEE PLEASEEEEE
Answer:
∠ 10 = 86°
Step-by-step explanation:
∠ 7 and ∠ 10 are same- side interior angles and sum to 180° , that is
∠ 7 + ∠ 10 = 180°
94° + ∠ 10 = 180° ( subtract 94° from both sides )
∠ 10 = 86°
A restaurant has the following items on its two-course menu.
List all the possible two-course meals that could be ordered assuming diners must order one meal from each category.
Starters Mains
Garlic bread
Prawns
Soup Chicken
Risotto
The possible two-course meals that could be ordered assuming diners must order one meal from each category are;
Garlic and BreadGarlic and soupGarlic and RisottoPrawns and BreadPrawns and soupPrawns and RisottoChicken and BreadChicken and soupChicken and RisottoWhat are the possible two-course meals that could be ordered assuming diners must order one meal from each category?It follows from the task content that the categories are as indicated below;
Starters Mains
Garlic Bread
Prawns Soup
Chicken Risotto
The condition that diners must order one meal from each category simply leaves the diners with;
3 options for the first course and 3 options for the second.Consequently, the expected number of possible two-course meal combination is; 3 × 3 = 9.
Ultimately, the possible two-course meals that could be ordered assuming diners must order one meal from each category are as listed above.
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Evaluate each expression for the given value of the variable.
(x³ . x⁵ ; x=2)
After evaluating the expression x³ . x⁵, we get the result as 256.
We are given an expression:
x³ . x⁵
We can use the properties of exponents that if the base is same and two numbers are multiplied, then the powers get added.
So, the expression will become:
= x ³⁺⁵
Simplifying the expression, we get that:
= x⁸
Now, we need to evaluate the expression at x = 2
Put x = 2 in the expression, we get that:
= 2⁸
Evaluating it, we get that:
= 256
Therefore, after evaluating the expression x³ . x⁵, we get the result as 256.
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Evaluate each expression for x=-2,0 , and 2 .
(3/2)x
The value of given expression for x=0 is 1, x=-2 is 0.44 and x=2 is 2.25.
Given the expression is (3/2)ˣ.
Firstly, we will simplify the given expression (3/2)ˣ for x=0.
Substitute the value x=0 in given expression, we get
(3/2)ˣ =(3/2)⁰
As we know that something raise to power zero is 1.
So, we get
(3/2)ˣ =1
Now, we will simplify the given expression (3/2)ˣ for x=-2.
Substitute the value x=2 in given expression, we get
(3/2)ˣ =(3/2)²
Now, we will square the expression to simplify it, we get
(3/2)ˣ =9/4
(3/2)ˣ =2.25
Furthermore, we will simplify the given expression for x=-2.
Substitute the value x=-2 in given expression, we get
(3/2)ˣ =(3/2)⁻²
Now, we will square the given expression, we get
(3/2)ˣ =(9/4)⁻¹
Further, we will divide it above expression by 1 to remove negative sign, w eget
(3/2)ˣ =1/(9/4)
(3/2)ˣ =4/9
(3/2)ˣ =0.44
Hence, the value of expression (3/2)ˣ for x=0, 2 and -2 is 1, 2.25 and 0.44.
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re arrange the equation option pls help giving brainliest answers!! :)
[tex]\displaystyle\\Answer:\ C. \ f=\sqrt{\frac{B}{4} }[/tex]
Step-by-step explanation:
A box of oats cereal measures 24 cm long by 5 cm wide 25 cm high. A box of rice cereal measures 26 cm long by 4 cm wide by 28 mm high. Which box has the greater volume? How much greater?
Answer:
Box of oat:
24*5*25(all in cm)=3000 cm3
cereal:
26*4*2.8=291.2 cm3
oat is grater by 2708.8
Step-by-step explanation:
28mm was changed to 2.8 cm
There are 24 students in a spelling bee. How many ways can the students win first, second, or third place?
There are ________ ways the students can win first, second, or third place.
In 12144 ways the students can get first, second, or third place.
The permutation system is used to locate the special range of preparations that may be shaped through taking r matters from the n to be had matters. Permutations are beneficial to shape distinctive words, quantity preparations, seating preparations, and for al. of the conditions related to special preparations. As consistent with the permutation formula, the permutation of 'r' items taken from 'n' items is identical to the factorial of n divided through the factorial of distinction of n and r.
The formula for permutations is
nPr= n!/(n-r)!
From the given question let us consider,
n= 24 r=3
Now let us solve using formula
24P3= 24!/(24-3)!
=24*23*22*21......*2*1
=12144
Therefore there are 12144 ways.
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Write the lower and upper bounds for the following to the given degrees of accuracy. a 64mins (nearest 1 min) c 30m/s (nearest 5m/s) b 20g (nearest 10g) d 7500 (nearest 100mm)
The lower and upper bounds for the following to the given degrees of accuracy are: a- 64 mins (63.5 ≤ 64 < 64.5) c- 30m/s (27.5 ≤ 30 < 32.5) b- 20g (15 ≤ 20 < 25) d-7500mm (7450 ≤ 7500 < 7550)
The upper and lower bounds can be found by dividing the degrees of accuracy by 2 and then subtracting and adding with the value to give the lower and upper bounds respectively.
For a- 64 mins (nearest 1 min)
As the degree of accuracy is to the nearest 1 min;
1 min ÷ 2 = 0.5 min
Upper bound = 64 + 0.5 = 64.5 min
Lower bound = 64 - 0.5 = 63.5 min
For c- 30m/s (nearest 5m/s)
5m/s ÷ 2 = 2.5 m/s
Upper bound = 30 + 2.5 = 32.5 m/s
Lower bound = 30 - 2.5 = 27.5 m/s
For b- 20g (nearest 10g)
10g ÷ 2 = 5
Upper bound = 20 + 5 = 25g
Lower bound = 20 - 5 = 20g
For d- 7500(nearest 100mm)
100mm ÷ 2 = 50mm
Upper bound = 7500 + 50 = 7550mm
Lower bound = 7500 - 50 = 7450mm
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I am a 5-digit number. My ones digit is three times greater than my tens digit. My ten thousands digit is 3 more than my tens digit.
My hundreds digit is twice my ten thousands digit. My thousand digit is one less than my hundreds digit.
Read the clues. Find the number
Answer:
Hello,
Step-by-step explanation:
[tex]n=\overline{EDCBA}\\\\A=3*B\ My\ ones\ digit\ is\ three\ times\ greater\ than\ my\ tens\ digit.\\E=3+B\ My\ ten\ thousands\ digit\ is\ 3\ more\ than\ my\ tens\ digit.\\C=2*E\ My\ hundreds\ digit\ is\ twice\ my\ ten\ thousands\ digit. \\D=C-1\ My\ thousand\ digit\ is\ one\ less\ than\ my\ hundreds\ digit.\\\\A=3*B\\E=3+B\\C=2*E\\D=C-1\\\\\begin{array}{|c|c|c|c|c|}A&B&C&D&E\\--&--&--&--&--\\0&0&6&5&3\\3&1&8&7&4\\6&2&X&X&5\\9&3&X&X&6\\X&4&X&X&X\\--&--&--&--&--\\\end{array}\\[/tex]
[tex]\\\\Numbers\ are\ 35600\ or\ 47813.[/tex]
Roman saves $500 each year in an account earning interest at an annual rate of 4% compounded annually. How much interest will the account earn at the end of the first 2 years?
HELP .........................................
Answer: A and B
-3^4 = -3 × -3 × -3 × -3 = 81
When dealing with multiplying all negative numbers, the result is going to be positive.
-3^2 = -3 × -3 = 9
Step-by-step explanation:
Divide
81/9 = 9
Find an equivalent expression whose product is |+9|
A)(-3)^2 = -3 × -3 = 9
(-3)^4 = -3 × -3 × -3 × -3 = 81
81/9 = 9
A is correct, so we must find the next correct answer.
B)(-3)^6 = -3 × -3 × -3 × -3 × -3 × -3 = 729
(-3)^4 = -3 × -3 × -3 × -3 = 81
729/81 = 9
B is correct. Thus,
[tex]\frac{(-3)^4}{(-3)^2} = B)\frac{(-3)^6}{(-3)^4} = A)\frac{(-3)^2}{(-3)^4}[/tex]
Hope this helps, and have a great day.
R(2,3) S(4,-1) round to the nearest tenth
If scores on the wechsler adult intelligence scale (wais) are normally distributed, with a mean of 100 and a standard deviation of 15, what percentage of scores will fall between 85 and 115
The percentage of scores will fall between 85 and 115 is 68.26%
Given,
Scores on the Wechsler Adult Intelligence Scale (WAIS) are normally distributed with,
Mean = 100
Standard deviation = 15
We have to find the percentage of scores fall between 85 and 115.
That is,
P(85 < X < 115) = \ [tex]P[/tex] [tex](\frac{85-100}{15}[/tex] < [tex]\frac{x-mean}{standard deviation}[/tex] < [tex]\frac{115-100}{15}[/tex][tex])[/tex]
= P(-1 < Z < 1)
= \P(Z < 1) - P(Z < -1)
= 0.8413 - 0.1587
\P(85 < X < 115) = 0.6826
The probability that a person would score between 85 and 115 is 0.6826
And, the percentage of scores will fall between 85 and 115 is 68.26%
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