The equations which represents the minimum and maximum scores of the students is x = 87 ± 1.8.
Mean is defined as the average equal to the ratio of the total number of values in a particular set of values to the total number of values in the set. The average of a set of approximately equal values is calculated. The term average describes a number that represents a large amount of data.It is given that average score on a lab report is 87 points with all the students scoring within 1.8 points
According to the question if x represents a student score then , it is given by [tex]x=87\pm1.8[/tex]
The equation which represent maximum score is given by
[tex]x=87+1.8\\x=88.8[/tex]
The equation which represent minimum score is given by
[tex]x=87-1.8\\x=85.2[/tex]
Hence, maximum and minimum scores are 88.8 and 85.2 respectively.
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Tell which set or sets the 8 belongs to: natural numbers, whole, numbers, integers, rational numbers, irrational numbers, or real
numbers.
The number 8 is a natural number, whole number, integer, rational number, real number.
All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well. In this post, let's study all there is to know about whole numbers.
The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.
Irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers.
Real number is a value of a continuous quantity that can represent a distance along a line. Real numbers can be defined as the union of both rational and irrational numbers.
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Raj wrote -(5^4) = (-5^4). Is Raj correct? Why or why not?
Raj is incorrect as the negative signs are put in different place.
What are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
given:
-(5^4) = (-5^4).
Raj is incorrect because the in LHS part the negative sign is out of the exponent term and in RHS part the negative sign is within exponent.
-(5^4) gives - 625
and, (-5^4) gives 625
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Identify the type of fallacy being used in the statement.
Gone with the Wind is the top grossing movie of all time, so it must be the greatest movie of all time.
The type of fallacy which is being used in the statement is: Dicto Simpliciter.
What is a fallacy?A fallacy can be defined as a mistaken or false belief that are based on illogical arguments or reasoning.
The types of fallacy.In English literature, there are different types of fallacy and these include the following:
Appeal to authoritySlippery slopeFallacy of generalization.Ad HominemPost Hoc, Ergo Propter Hoc Non Sequitur Dicto Simpliciter Straw Man Appeal to Popularity (Ad populum)Fallacy of exclusionFalse Dilemma Petitio Principii What is Dicto Simpliciter?Dicto Simpliciter can be defined as a type of fallacy in which a general observation or rule is taken and assumed as generally (universally) true, regardless of the circumstances involved.
In this context, we can reasonably infer and logically deduce that the type of fallacy which is being used in the statement is Dicto Simpliciter.
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Complete Question:
Identify the type of fallacy being used in the statement. Gone with the Wind is the top grossing movie of all time, so it must be the greatest movie of all time.
Post Hoc, Ergo Propter Hoc
Non Sequitur
Dicto Simpliciter
Straw Man
Ad Hominem
False Dilemma
Petitio Principii
Argumentum ad populum
Solve each equation. Check for extraneous solutions. 5(3 x+1)¹/₄=10
The extraneous solution for the equation 5(3 x + 1)^ ( 1 / 4) = 10 is x = 5.
We are given an equation:
5(3 x + 1)^ ( 1 / 4) = 10
Divide each side by 5, we get that:
⁴√3 x + 1 = 2
Raise both sides to the power 4, we get that:
3 x + 1 = 2⁴
3 x + 1 = 16
3 x = 16 - 1
3 x = 15
x = 15 / 3
x = 5
Therefore, we get that, the extraneous solution for the equation 5(3 x + 1)^ ( 1 / 4) = 10 is x = 5.
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Solve. Check for extraneous solutions. √3-x+ √x+2=3 Solve.
Which length of time is between 11.20 am and 2.05 pm ?
Answer:
2 hours 45 minutes.
Step-by-step explanation:
12.00 - 11.20 = 40 minutes
2. 05 = 14.05
14.05 - 12.00 = 2.05 = 2 hours 5 minutes
Answer = 2 hours 45 minutes.
what relationship must hold for the point to be equidistant from the origin and the xz-plane? make sure that the relationship you state is valid for positive and negative values of a, b, and c
The relationship must hold for the point to be equidistant from the origin and the x z-plane is a^2+b^2+c^2 > b^2.
What is equidistant point:
A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.
Now,
distance from P(a, b, c) and the Origin (0,0,0)
[tex]\sqrt{(a-0)^2+(b-0)^2+(c-0)^2} =\sqrt{a^2+b^2+c^2}[/tex]
distance from p(a ,b, c) and the x-z plane
[tex]\sqrt{(0-0)^2+(b-0)^2+(0-0)^2} = |b|[/tex]
Here,
P is equidistant from the Origin and the x - z plane
[tex]\sqrt{a^2+b^2+c^2} = |b|[/tex]
[tex]a^{2} +b^2+c^3 = b^2[/tex]
[tex]a^{2} +c^2 = 0[/tex]
Hence a=c=0 ,thus the point P must be of the form (0,b,0) for any b ∈R
Again,
point P far the from the origin than from the x z plane
[tex]\sqrt{a^2+b^2+c^2} > |b|[/tex]
[tex]a^{2} +b^2+c^2 > b^2[/tex]
[tex]a^{2} +c^2 > 0[/tex]
Hence a, c ∈R such that atleast one of the a ,b ,c is non-zero.
Therefore,
(a ,b ,c) for any b∈ R and for a, c ∈ R with atleast one of the a and c is non-zero.
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6. The Golden Gate Bridge was built at a height of 300 m over San Francisco
Bay. From the ends of the bridge, the angles of depression to a tugboat in
the middle of the river are 25° and 32° respectively.
Find the length of the bridge.
The length of the golden gate bridge is -163.250975.
What is trigonometry?
Trigonometry is the branch of mathematics that deals with particular functions of angles and how to apply them in calculations. There are six widely used angles-related trigonometric functions. Their respective names and acronyms are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
What is length?
Length is a measure of distance. According to the International System of Quantities, length has the dimension of distance. Most measurement systems select a length base unit from which all other units are derived. The International System of Units' fundamental unit of length is the meter.
Given that,
The height of the bridge is 300m,
The angle of depression in the middle of the river are 25⁰ and 32⁰ respectively.
[tex]\frac{300}{tan(32)}[/tex] -[tex]\frac{300}{tan(25)}[/tex],
[tex]\frac{300}{0.624869}[/tex]-[tex]\frac{300}{0.466308}[/tex],
= -163.250975.
The length of the golden gate bridge is -163.250975.
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Jackson has a points card for a movie theater. • He receives 35 rewards points just for signing up. • He earns 8.5 points for each visit to the movie theater. • He needs 154 points for a free movie ticket. Write and solve an equation which can be used to determine x, the number of visits Jackson must make to earn a free movie ticket.
The number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35 = 154.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Jackson has a points card for a movie theater. He receives 35 reward points just for signing up. He earns 8.5 points for each visit to the movie theater.
Let x be the number of visits Jackson must make to earn a free movie ticket.
8.5x + 35 = 154
8.5x = 154 - 35
8.5x = 119
x = 119/8.5
x = 14
Thus, the number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35 = 154.
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What is the value of ?
Answer:
25.49
Step-by-step explanation:
[tex]5^2 + 0.7^2 \\ \\ =25+0.49 \\ \\ =25.49[/tex]
answer this and u will get 20 points
The rate of increase in the water pressure will be
0.000993 atmosphere per kilometers.
How to illustrate the information?From the information given,it should be noted that the water pressure on Mustafa was illustrated by 0.993 atmosphere per meter.
Therefore, it should be noted that the rate of increase per kilometers will be illustrated as:
1000 meters = 1 kilometer
This will be
= 0.993 / 1000
= 0.000993
This will be illustrated as 0.000993 atmosphere per kilometers.
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-can someone help me 4d+3 if d=-1
Answer:
7
Step-by-step explanation:
-4d+3
-4(-1) + 3 Insert -1 for d
4+3=7
92x 4.6 divided by 2.3
Answer:
184
Step-by-step explanation:
92 x 4.6 is 423.2 then you divide it by 2.3 which gets you 184.
Answer:
184
92 times 4.6 = 423.2
423.2 divided by 2.3 = 184
Step-by-step explanation:
Hope it helps! =D
Which angle number represents the linear pair of \angle FHC∠FHC?
The angle number that represents the linear pair of angle FHC is: angle 5.
What is the Linear Pair?The linear pair consists of two adjacent angles that are on a straight line, whose sum will be equal to 180 degrees when added together.
Thus, the two adjacent angles share a common side and a common vertex, and they are supplements of each other. That is, they have a sum of 180 degrees.
Angle 4 represents angle FHC. Angle 5 is adjacent to angle 4, and both lie on a straight line.
Therefore, angle FHC + angle 5 = 180 degrees.
In conclusion, we can state that, the angle number that represents the linear pair of angle FHC is: angle 5.
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For questions 4-7, find the measures of the angles in the picture below.
(Questions shown in image)
Answer:
Measures of each angle are as follows:
4. ∠BXC = 20°
5. ∠FXE = 85°
6. ∠GXD = 75°
7. ∠BXF = 75°
Step-by-step explanation:
#4
∠BXC is opposite ∠EXD and so it is the same as ∠EXD = 20°
#5
∠FXE is opposite ∠CXG and so it is the same as ∠CXG = 85°
#6
Angles ∠CXG, ∠GXD and ∠EXD line on a straight line so the sum of these angles must be 180°
∴ m∠CXG + m∠GXD + m∠EXD = 180°
Substituting known values for ∠CXG and ∠EXD we get
85 + ∠GXD + 20 = 180°
105 + m∠GXD = 180°
m∠GXD = 180-105 = 75°
#7
∠BXF is opposite ∠GXD which we computed in #6 to be 75°
So m∠BXF = m∠GXD = 75°
a. What is the solution of √5 x-1 +3=x ? Check your results.
The solution is 10
Firstly rewriting the equation to frame the steps of solution -
√(5x-1) + 3 = x
Shifting 3 to the Right Hand Side of the equation -
√(5x-1) = x - 3
Now taking square of both sides of the equation
(√(5x-1))² = (x - 3)²
On solving the square we get the equation -
(5x - 1) = x² + 9 - 6x
Further solving the equation -
5x - 1 - 9 = x² - 6x
5x - 10 + 6x = x²
x² - 11x + 10 = 0
Solving the equation by factorizing -
x² - 1x - 10x + 10 = 0
x (x - 1) - 10(x - 1) = 0
(x - 1) (x - 10) = 0
x = 1, 10
Keeping the value of x in equation to find the solution and check the results-
x = 1
√(5×1-1) +3 = 1
√(5 - 1) + 3 = 1
√4 + 3 = 1
2 + 3 = 1
5 = 1
x = 10
√(5×10-1) +3 = 10
√(50 - 1) + 3 = 10
√49 + 3 = 10
7 + 3 = 10
10 = 10
Since, 10 = 10, the result is correct.
Hence, the solution is 10
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Charlotte is visiting Brazil and is looking at souvenirs to purchase. She finds a jersey that costs 110 Brazilian real. If the current exchange rate is 1 dollar:5.43 Brazilian real, how much does the jersey cost in U.S. dollars?
a. $4.94
b. $20.26
c. $104.57
d. $597.30
What is each logarithm expanded?
a. log₃ 250/37
We need to know about logarithm to solve this problem. The logarithm expanded is [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]
Logarithm is the power to which a base should be raised to get a given number. Expanding logarithm is writing logarithms usisng addition, subtraction, simplifying the logarithm. In logarithm, log ab can be written as log a+ log b and log a/b can be written as log a -log b, [tex]log_{a} b[/tex] can be written as log b/log a. We will be using these rules to expand the given logarithm. In the given logarithm we have the base of the log as 3 and we have logarithm of fraction, which we can expand.
[tex]log_{3} \frac{250}{37} =log_{3} 250 - log_{3} 37=\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex]
So we found the expansion of the given algorithm using the rules for expansion of algorithm to be [tex]\frac{log 250}{log 3} -\frac{log 37}{log 3}[/tex].
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estimate 180 x 586 rounding
Answer:
12,000
Step-by-step explanation:
Since we're just estimating, we can just round the two numbers.
180 rounded to the nearest hundred is 200.
586 rounded to the nearest hundred is 600.
200 * 600 = 12,000
Therefore, 180 * 586 is roughly 12,000.
4xsquared-1 factories
Answer:
That is a quadratic equation and must be factorized using two brackets. It is just a little confusing to recognize it as a quadratic as the middle x value is not there so we treat it as 0 - which means the two numbers must cancel each other out:
(2x + 1) (2x - 1)
Step-by-step explanation:
help
Answer:
(2x - 1)(2x + 1)
Step-by-step explanation:
4x² - 1
is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
4x² - 1
= (2x)² - 1²
= (2x - 1)(2x + 1)
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Assessment
Math
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Analytics
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Some salespeople earn a commission that pays them a percentage of the price of the items
they sell. The equation I = hr + ps gives the income of a salesperson who receives an hourly
wage plus commission, where h is the number of hours worked, r is the hourly rate of pay, p
is the percent commission, and s is the dollar amount of the salesperson's sales.
Solve for s in terms of I, h, r, and p.
Submit
Skill plans
You have prizes to reveal!
Quest
answ
12
Tim
elap:
01
03
HR MI
Smarts
out of 1
in
Answer:
hope it helped!
Step-by-step explanation:
With the SmartScore, the learning process is rewarded and your students are constantly reassessed. When a student starts practicing a skill, the SmartScore ...
Missing: s h, r, p. Quest 12th Leap: MI
When finding the intersection of two lines from both Algebra I and Geometry, you first "set the linear equations equal to each other. Find the intersection Doint of the two lines whose equations are shown below. Be sure to find both the x and y coordinates. y=5x+1 and y=2x -11
The intersection point of two lines are (-4 , -19)
The intersection point are those point where two line met of cut each other are called intersection point.
the given line of equation are
y = 5x + 1
y = 2x - 11
On solving these two equation we get the values as follow,
value of x = -4
value of y = -19
hence by this we can say the the intersection point of the above lines are
( -4 , -19 )
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Find the amount in a continuously compounded account for the given conditions.principal: $ 1000 annual interest rate: 4.8% time: 2 years
A = $ 1100.76 the amount in a continuously compounded account for the given conditions.
What does compound interest entail?
Compound interest is when you receive interest on both your interest income and your savings. Let's imagine you invest $1,000 (your principal) and it earns 5% once a year in interest or profits (the compounding frequency).principal: $ 1000 annual
interest rate: 4.8%
time: 2 years
We know that continuously compound interest
A = [tex]P_{0} e^{rt}[/tex]
= [tex]1000 e_{(0.048)(2)}[/tex]
= [tex]1000 (e)^{0.096}[/tex]
= [tex]1000 ( 1.10075906 )[/tex]
= 1100 . 75906
A = $ 1100.76
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put these numbers in least to greatest form7.25, -9.8, 0
Answer:
7.25, 0, -9.8
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST!!!!
Answer: 36 degrees
Step-by-step explanation: 180 degrees - 144 degrees = 36 degrees
Answer:
A = 54 d and x = 45 B = 45 so a = 54 and x= 45 and b= 45 and x = 45
The points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2. If HK=45, find HJ.
Will give brainliest
When the points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2 ,the value of HJ is 27.
How to illustrate the information?Fronxrye information, the points H, I, J and K all lie on the same line segment, in that order, such that the ratio of HI: IJ: JK is equal to 1:2:2.
Therefore, the value of HJ will be:
= (1 + 2)/(1 + 2 + 3) × 45
= 3/5 × 45
= 27
Therefore, the value of HJ is 27.
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guys please help plsssssssss
Answer:
b = 15
Step-by-step explanation:
[tex]\frac{5\left(\frac{b-1}{2}-1\right)+2b}{3}\\5\left(\frac{b-1}{2}-1\right)+2b\\5\left(\frac{b-1}{2}-1\right)\\5\cdot \frac{b-1}{2}-5\cdot \:1\\5\cdot \frac{b-1}{2}\\\frac{\left(b-1\right)\cdot \:5}{2}\\\frac{5b-5}{2}\\\frac{5b-5}{2}-5\\\frac{5b-5}{2}-5+2b\\=\frac{5b-5}{2}+\frac{2b\cdot \:2}{2}\\=\frac{5b-5+2b\cdot \:2}{2}\\5b-5+4b\\5b+4b-5\\9b-5\\\frac{9b-5}{2}\\=\frac{9b-5}{2}-5\\=\frac{\frac{9b-5}{2}-5}{3}\\\frac{9b-5}{2}-5\\\frac{9b-5}{2}-\frac{5\cdot \:2}{2}\\[/tex]
[tex]=\frac{9b-5-5\cdot \:2}{2}\\9b-5-5\cdot \:2\\9b-5-10\\9b-15\\=\frac{9b-15}{2}\\=\frac{\frac{9b-15}{2}}{3}\\=\frac{9b-15}{2\cdot \:3}\\=\frac{9b-15}{6}\\\frac{3\left(3b-5\right)}{6}\\\frac{3b-5}{2}\\=\frac{3b}{2}-\frac{5}{2}\\\frac{3b}{2}-\frac{5}{2}=5+b\\=\frac{3b}{2}\cdot \:2-\frac{5}{2}\cdot \:2=5\cdot \:2+b\cdot \:2\\\frac{3b}{2}\cdot \:2\\\frac{3b\cdot \:2}{2}\\=3b\\-\frac{5}{2}\cdot \:2\\=\frac{5}{2}\cdot \frac{2}{1}\\=-\frac{5}{1}\\=-5\\5\cdot \:2\\=10\\=3b-5=10+b\cdot \:2[/tex]
[tex]\mathrm{Add\:5--both\:\:sides\:of\:the\:expression}\\3b-5+5=10+b\cdot \:2+5\\3b=2b+15\\\mathrm{Subtract}\\3b-2b=2b+15-2b\\\mathrm{Thus,}\\b=15[/tex]
Hope it helps. :-)
A school trip uses a 42-seater coach (excluding the driver’s seat).
36 students, 3 teachers and 3 parents go on the coach.
Each student pays £4.25 towards the cost of the coach. Each parent pays twice as much
as a student pays. The teachers travel for free.
The coach company charges £195 for the trip.
a Show that the money paid by the students and parents is not enough to pay for the
coach.
b How much should each teacher pay so that the cost of the coach is covered exactly?
c On the day of the trip, 8 students are ill and they get their money back. The
passengers on the coach share the extra cost equally. What is the extra payment for
each passenger?
Step-by-step explanation:
the total charge is £195.
we have 36 students. each paying £4.25.
we have 3 parents. each paying 2×£4.25 = £8.50
we have 3 teachers. each paying £0.
a.
the payments are
36×4.25 + 3×8.50 = 153 + 25.5 = £178.50
that is clearly below the total charge of £195.
there is a deficit of 195 - 178.5 = £16.50
b.
3 teachers.
so, each should pay
16.5 / 3 = £5.50
c.
8 students drop out.
that means
8× 4.25 = £34.00 are not paid.
we have now
28 students
3 parents
3 teachers
on the bus.
these are 34 persons.
34 / 34 = £1.00
they each would have to pay £1.00 as extra payment.
Please help please I'll give brainlyest
[tex]\bf \implies{The \: correct \: option \: is \: (c) \: 240}[/tex]
Step-by-step explanation:[tex] \large \frac{40}{5} . \: 6 \: . \: \frac{10}{2} [/tex]
Step 1) : Cross out the common factor
[tex] \bf \longrightarrow\frac{ \cancel{40}}{ \cancel{5}} . \: 6 \: . \: \frac{ \cancel{10}}{ \cancel{2} } \\ \\ \bf \longrightarrow8 \times 6 \times 5[/tex]
Step 2 : Multiply it
[tex] \bf \longrightarrow8 \times 6 \times 5 \\ \bf \longrightarrow8 \times 5 \times 6 \\\bf \longrightarrow 40 \times 6 \\ \bf \longrightarrow240[/tex]
Solve. (x+1)³/₂-2=25
The values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2
[tex] {(x + 1) }^{3/2} [/tex] - 2 = 25
Adding 2 on both the sides of the equation we get
[tex] {(x + 1) }^{3/2} [/tex] - 2 + 2 = 25 + 2
[tex] {(x + 1) }^{3/2} [/tex] = 27
On squaring both the sides of the equation we get
[tex] {x + 1}^{3/2 \times 2} [/tex] = 27²
(x + 1)³ = 729
Now, using the identity (a + b)³ = a³ + b³ + 3ab(a + b), we get
x³ + 1 + 3x² + 3x = 729
x³ + 3x² + 3x - 728 = 0 : Equation 1
By hit and trial method x = 8 is the solution of the equation 1.
Now, by remainder theorem we can write the equation 1 as
x³ + 3x² + 3x - 728 = (x - 8)(x² + 11x + 91) + 0
On solving quadratic equation x² + 11x + 91, we get
x = -b+✓(b² - 4ac)/2a and -b-✓(b² - 4ac)/2a
x = -11+✓(11² - 4×1×91)/2×1 and -11-✓(11² - 4×1×91)/2×1
x = -11+✓(121 - 364)/2 and -11-✓(121 - 364)/2
x = -11+✓(-243)/2 and -11-✓(-243)/2
x = -11/2 + ✓243i/2, -11/2 - ✓243i/2
Thus, the values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2
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