One's intelligence quotient, or IQ, varies directly as a person's mental age and inversely as that person's chronological age. A person with the mental age of 25 and a chronological age of 20 has an IQ of 125. What is the chronological age of a person with a mental age of 40 and an IQ of 80?
The chronological age of a person with a mental age of 40 and an IQ of 80 is calculated to be 50 years by using the direct and inverse proportionality of the IQ, Mental Age, and Chronological Age.
Explanation:The subject of your question is related to a mathematical concept known as Direct and Inverse Proportion. In this scenario, the IQ is directly proportional to the Mental Age and inversely proportional to the Chronological Age. Therefore, the formula is given as: IQ = (Mental Age / Chronological Age) * 100.
From the first example that indicates a person with the mental age of 25 and a chronological age of 20 has an IQ of 125, we can determine the proportionality constant as follows: 125 = (25 / 20 ) * 100.
Now, to find out the chronological age of a person with a mental age of 40 and an IQ of 80, we use the same proportionality and solve the equation for chronological age: 80 = (40 / Chronological Age) * 100. Solving the equation, the Chronological Age equates to 50 years.
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To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. The specific chronological age depends on the value of the constant of variation, k.
Explanation:To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. Let's denote the chronological age as x. We can set up the equation as follows:
IQ = (k * mental age) / chronological age
where k is the constant of variation.
Given that the mental age is 40 and the IQ is 80, we can plug in these values into the equation:
80 = (k * 40) / x
To solve for x, we can cross-multiply and then divide both sides by 80:
80x = k * 40
x = (k * 40) / 80
Since we don't have the value of k, we can't determine the specific value of x. However, we can determine the relationship between x and the mental age:
x = 40 / k
Therefore, the chronological age of a person with a mental age of 40 and an IQ of 80 depends on the value of the constant of variation, k.
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what is the area of a park that is 100 yards square?
80 POINTS!!!
A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the given line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?
Answer:
1). Slope = (-2)
2). Midpoint = (2, -2)
3). Slope of the perpendicular bisector = (1/2)
4). Equation of perpendicular bisector will be x - 2y = 6
Step-by-step explanation:
A line segment has the endpoints at (4, -6) and (0, 2).
1). Then the slope of the given line segment will be = (y - y')/(x - x') = (2 + 6)/(0 - 4) = 8/(-4) = (-2)
2). Mid point of the line segment is given by [tex](\frac{x_{1}+x_{2}}{2}) , (\frac{y_{1}+y_{2}}{2})[/tex]
Therefore midpoints of the line segment will be [tex]\frac{4+0}{2},\frac{-6+2}{2}[/tex] = (2, -2)
3). Slope of the perpendicular bisector is represented by [tex]m_{1}.m_{2}=(-1)[/tex]
⇒ (-2)×m2 = (-1)
⇒ [tex]m_{2}=\frac{1}{2}[/tex]
4). Now we have to find the equation of perpendicular bisector passing through (2, -2) and slope (1/2).
Since standard equation of the line will be given as y = mx + c
[tex]y=\frac{1}{2}x+c[/tex] passes through (2, -2).
[tex](-2) = \frac{1}{2}(2) + c[/tex]
c = (-1) - 2 = -3
Finally the equation of perpendicular bisector will be
[tex]y=\frac{1}{2}x+(-3)[/tex]
⇒ 2y = x - 6
⇒ 2y - x = -6
⇒ x - 2y = 6
Answer: the answers are in the explanation, they are also in order
Step-by-step explanation:
-2
(2,-2)
1/2
y=(1/2)x - 3
Simplify
sqrt(3 + 2 sqrt 2) ...?
Answer:
[tex]1+\sqrt{2}[/tex]
Step-by-step explanation:
We have been given a radical expression [tex]\sqrt{3+2\sqrt{2}}[/tex]. We are asked to simplify the given expression.
We will add [tex](\sqrt{2})^2-2[/tex] to our given expression as after adding and subtracting same quantity the value of our expression will be same.
[tex]\sqrt{3+2\sqrt{2}+(\sqrt{2})^2-2}[/tex]
[tex]\sqrt{3-2+2\sqrt{2}+(\sqrt{2})^2}[/tex]
[tex]\sqrt{1+2\sqrt{2}+(\sqrt{2})^2}[/tex]
Using perfect square formula [tex](a+b)^2=a^2+2ab+b^2[/tex] we can rewrite our expression as:
[tex]\sqrt{1^2+2\sqrt{2}\cdot 1+(\sqrt{2})^2}[/tex]
[tex]\sqrt{(1+\sqrt{2})^2}[/tex]
Applying radical rule [tex]\sqrt[n]{x^n} =x[/tex], we will get,
[tex](1+\sqrt{2})^{\frac{2}{2}}=1+\sqrt{2}[/tex]
Therefore, the simplified form of our given expression would be [tex]1+\sqrt{2}[/tex].
The triangles below are similar. Find the value of x.
9
8
10.5
11
In 2010, the United States national debt was estimated to be nearly 13,000,000,000,000 dollars. Which of the following represents the national debt in scientific notation?
a. 1.3 x 10^11
b. 1.3 x 10^12
c. 1.3 x 10^13
d. 1.3 x 10^14 ...?
Answer:
option C
Step-by-step explanation:
In United States national debt in 2010 was estimated to be nearly $13,000,000,000,000.
Now we have to convert this debt in scientific notation.
In scientific notation we have to convert this number in to 10ˣ.
13000000000000 = 1.3 × 10¹³
Therefore option C is the answer.
Which is the better buy, 6 bagels for $3.29 or 8 bagels for $4.15?
How many solutions does this linear system have?
y = x+ 2
6x – 4y = –10
one solution: (–0.6, –1.6)
one solution: (–0.6, 1.6)
no solution
infinite number of solutions
The solution of a linear system of an equations is (-1, 1).
The given linear system of equations are y = x+ 2 and 6x – 4y = –10.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The system of linear equations can be solved as follows
x-y=-2 --------(1)
6x – 4y = –10 --------(2)
Multiply equation (1) by 4
That is, 4x - 4y= -8 --------(3)
Subtract equation (3) from the equation (2)
So, 6x-4y-(4x-4y)=-10-(-8)
2x=-2
⇒ x=-1
Put x=-1 in x-y=-2
Now, y=1
So, solution is (-1, 1)
Therefore, the solution of a linear system of an equations is (-1, 1).
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What fraction of an hour is 46 minutes??
Glenn has a beginning balance of $840 in his checking account. He has a deposit of $375 and withdraws $250 from the ATM. If the ATM fee is $3, what is his new balance?
$718
$212
$962
$572
Work out tan(19pi/4) without a calculator
Which is the largest religion in india? zoroastrianism hinduism daoism judaism?
If you save two pennies on January 1, four pennies on January 2, six pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars, at the end of that one year? Express your answer as a decimal without commas.
...?
Answer:
1335.90
Step-by-step explanation:
4 x plus= equals what
What is 7/50 in decimal form?
There are 35 students going to the zoo each vans can hold 6 students how many vans are needed
Ariel wants to write 8 entries for her blog. After 2 hours, she has 5 entries left. After 4 hours, she has 2 entries left. Which graph represents Ariel's remaining entries?
graph of line going through (0, 0) with a slope of 1.5
graph of line going through (0, 2) with a slope of 2
graph of line going through (0, 8) with a slope of 1.5
graph of line going through (0, 3) with a slope of 3
Answer:
Graph of line going through (0, 8) with a slope of 1.5 represents Ariel's remaining entries
Step-by-step explanation:
Ariel wants to write 8 entries for her blog.
After 2 hours, she has 5 entries left. [tex](x_1,y_1)=(2,5)[/tex]
After 4 hours, she has 2 entries left. [tex](x_2,y_2)=(4,2)[/tex]
So, now using two point slope form:
[tex]y-y_1=m(x-x_1)[/tex] ---1
where [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
So , substituting the given points we get the equation that represents the given situation .
[tex]m = \frac{2-5}{4-2}[/tex]
[tex]m = \frac{-3}{2}[/tex]
[tex]m = -1.5[/tex]
Now,
[tex]y-5 = -1.5(x-2)[/tex]
[tex]y-5 = -1.5x+3[/tex]
Thus the slope of the given situation is 1.5
Now at x = 0
[tex]y-5 = -1.5*0+3[/tex]
[tex]y=8[/tex]
So, at 0 hour 8 entries left .
So, graph of line going through (0, 8) with a slope of 1.5 represents Ariel's remaining entries
1) The data in the table below represents the pressure of the gas as the temperature changes. Plot a graph of the data, using the space below. Draw a trend line and calculate its slope. How are the variables related? What will he pressure of the gas be at 0C?
the graph looks like this
Temperature Pressure
10 723
25 763
40 800
55 845
80 900
Answer:
The pressure of the gas 0°C is about 699.
Step-by-step explanation:
The given table of values is
Temperature Pressure
10 723
25 763
40 800
55 845
80 900
The general form of a trend line is
[tex]y=a+bx[/tex]
where, b is slope and a is y-intercept.
[tex]b=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]
[tex]a=\overline{y}-b\overline{x}[/tex]
Using graphing calculator, we get
[tex]a=699.006826[/tex]
[tex]b=2.552218[/tex]
The equation of line of best bit is
[tex]y = 2.552218x + 699.006826[/tex]
where, y is pressure at x°C.
We need to find the pressure of the gas at 0°C.
Substitute x=0 in the above equation.
[tex]y = 2.552218(0) + 699.006826[/tex]
[tex]y =699.006826[/tex]
[tex]y \approx 699[/tex]
Therefore the pressure of the gas 0°C is about 699.
carl is paid $10 plus $8 an hour he was paid $66 how many hours did he work?
Write the function in slope-intercept form. Then graph the function.
2x - 5y = -6
Marcus solved for x in the quadratic equation x2 – 10x + 25 = 0.
Answer:
Option 1,3 and 4 are correct.
Step-by-step explanation:
Given is a quadratic equation
[tex]x^2-10x+25=0[/tex]
Marcus used quadratic formula to solve this
The correct use of formula is
[tex]\frac{-b+/\sqrt{b^2-4ac} }{2a}[/tex]
for the quadratic equation [tex]ax^2+bx+c=0[/tex]
Comparing we have a =1, b =-10: c=25
The student should have substituted -10 for b but he wrong did only 10
II option is wrong since 2 is substituted correctly
III option is right -4ac i.e. the product x 4 must have been subtracted
IV option is right since repeated root is there so only one solution
painter was hired to design and draw a mural for a new restaurant. before he can design the mural, he needs to know the are of the wall. the restaurant manager informs the painter that the mural wall is 6-√2 feet tall by 12-√2 feet wide. what is the total area of the mural wall? (recall that the area of a rectangle is the width multiplied by the length)
a. 70-18√2 square feet
b. 74-18√2 square feet
c. 74-6√2 square feet
d. 74+18√2 square feet ...?
What is the converse of the following true conditional? If the converse is true, rewrite the statements as a bioconditional. If either is false, give a counter example. If two lines are parallel, they do not intersect
The converse of the statement 'If two lines are parallel, they do not intersect' is 'If two lines do not intersect, they are parallel', which is false. A counterexample to this converse is skew lines that do not intersect but are not parallel. Thus, we can't write both statements as a biconditional
Explanation:The subject of your question is regarding conditional statements and their converses in mathematics. A conditional statement is often expressed in the form: 'If p, then q', where p is a hypothesis and q is a conclusion. The converse of a conditional statement switches the hypothesis and the conclusion, i.e., 'If q, then p'.
In the context of your question, the conditional statement given is 'If two lines are parallel, they do not intersect'. The converse of this statement is 'If two lines do not intersect, they are parallel'. However, this converse is not true. A counterexample can be two lines that do not intersect but are not parallel because they are skew lines, which exist in three dimensions and do not lie in the same plane. Thus, the statements can't be written as a biconditional as one is not a valid conditional.
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jill sold half her comic books then bought 16 more she now has 36 how many did she start with? help me plz ...?
Math test assesment chapter 5 answer #9
A basketball court is in the shape of a rectangle. It has a length of (x − 7) meters and a width of (x + 3) meters. The expression below represents the area of the court in square meters.
(x − 7)(x + 3)
Which of the following simplified expressions represents the area of the basketball court in square meters?
− 6x + 3
x2 − 21
x2 − 4x − 21
x2 − 7x + 3 ...?
The expression x²- 4x - 21 represents the area of the basketball court in square meters.
What is Area ?The area can be defined as the space occupied by a flat shape or the surface of an object.
The area of a figure is the number of unit squares that cover the surface of a closed figure.
It is given that the area of a rectangle is (x − 7)(x + 3)
when It has a length of (x − 7) meters and a width of (x + 3) meters.
The simplified expression of the area is equal to
(x-7)(x-3)
This can also be written as
x *(x+3) - 7*(x+3)
x²+3x-7x-21
x²- 4x - 21
Therefore x²- 4x - 21 represents the area of the basketball court in square meters .
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Solve for x.
x/2≥−4
x≥−8
x≥−2
x≤−2
x≤−8
Question 1: Describe how you would use the distributive property to simplify (39 x 5). Question 2: Your best friend tells you the solution of 375 = x - 28 is 347. Explain your best friend's error.
Which graph could represent a car that begins by increasing its speed, then travels at a constant speed, and then decreases its speed, as time increases?
What is the result of isolating y2 in the equation below?
(x - 2)^2 + y2 = 64
A. y2 = -x2 + 4x + 60
B. y2 = -x2 + 4x + 4
C. y2 = 64 - x2
D. y2 = x2 + 4x + 60
Answer with explanation:
The given equation which represents a circle having center at, (2,0) and radius =8 is,
[tex](x - 2)^2 + y^2 = 64\\\\y^2=64 - (x-2)^2\\\\y^2=64 - (x^2-4 x +4)\\\\ y^2=64 -x^2+4 x-4\\\\y^2=60+4 x-x^2[/tex]
Result of isolating y² in the equation below, gives
Option A
[tex]y^2=60+4 x-x^2[/tex]