Scott and Harry went cycling every day. They increased the number of minutes of cycling every week as described below:
Scott: Cycled for 10 minutes every day in the first week, 15 minutes in the second week, 20 minutes in the third week, and 25 minutes in the fourth week.
Harry: Cycled for 10 minutes every day in the first week, 20 minutes in the second week, 40 minutes in the third week, and 80 minutes in the fourth week.
Which statement best describes the methods used by Scott and Harry to increase the time they spent cycling?
A. Scott's method is linear because the number of minutes increased by an equal number every week.
B. Harry's method is linear because the number of minutes increased by an equal factor every week.
C. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal factor every week.
D. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal number every week.
Answers
Answer:
(A)
Step-by-step explanation:
Scott cycled for 10 minutes in first week, 15 minutes in second week,20 minutes in third week and 25 minutes in the fourth week which maintains a consistency in the line as there is consistent slope when drawn on a graph.
On, the other hand, harry cycled for 10 minutes in first week, 20 minutes in second, 40 minutes in third and 80 minutes in fourth week in which there is no consistency in the timings according to the weeks. Therefore, only, scott's method is linear as the number of minutes increased by an equal factor every week.
Related Questions
Work out tan(19pi/4) without a calculator
Answers
sin of 3/4π is √2/(2)
cos of 3/4π is -√2/2
so if you were to divide them up it would be
√2 * -2
2 √2
equal to -1
Solve for x.
x/2≥−4
x≥−8
x≥−2
x≤−2
x≤−8
Answers
x/2>= -4
x>= -4.2
x>= -8
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 ...?
Answers
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.
Simplify
sqrt(3 + 2 sqrt 2) ...?
Answers
sqrt(2) is [tex] \sqrt{2} [/tex]
sqrt(3 + 2 sqrt 2) is [tex] \sqrt{3 +2 \sqrt{2} } [/tex]
Now, let's simplify [tex] \sqrt{3 +2 \sqrt{2} } [/tex].
We will use square of sum: (a + b)² = a² + 2ab + b²
[tex]\sqrt{3 +2 \sqrt{2} } = \sqrt{1+2+2 \sqrt{2} }= \sqrt{1+2 \sqrt{2}+2 }= \\ = \sqrt{1^{2} +2*1* \sqrt{2} + (\sqrt{2} ) ^{2} } = \sqrt{(1+ \sqrt{2}) ^{2}} =1+ \sqrt{2}[/tex]
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].
Expand and simplify 2 (x+7)+3(x+1)
Answers
Explain the correlation between the graph of a line, direction of the line and the positive or negative slope of the line.
Answers
carl is paid $10 plus $8 an hour he was paid $66 how many hours did he work?
Answers
minus 10 both sides
8h=56
divide both sides by 8
h=7
worked 7 hours
10 + 8h = 66
8h = 56 Subtract 10 from both sides
h = 7 Divide both sides by 8
In other words, he worked 7 hours.
Fiona has to choose a bouquet for her wedding. The probability that she uses red roses is 98%, the probability that she uses orchids is 87%, and the probability that she uses Gerber daisies is 94%. Given the probability that she has both roses and orchids is 0.87 and the probability that she has both Gerber daisies and roses is 0.97 what is the probability that her bouquet contains roses or Gerber daisies?
Answers
the answer would be b.) .84
betty has a cow.the cow produces 5 liters of milk in a day. if the cows diet is improved the cow will produce 200% more milk.how much milk would the cow make in a day.
Answers
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?
Answers
Hope this helps :)
let f=cos^2x and g=sin^2x which of the following lie in the space spanned by f and g
a)cos2x
b)3+x^2
c)1
d)sinx
e)0 ...?
Answers
Math test assesment chapter 5 answer #9
Answers
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
Answers
the converse: If 2 lines do not intersect, they are parallel
the converse is false, the lines could be skew.
Hope this helped :)
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.
Learn more about Converse of a Conditional Statement here:https://brainly.com/question/2386083
#SPJ2
What fraction of an hour is 46 minutes??
Answers
46/60=23/30
4 x plus= equals what
Answers
dF=0dF=0
d⋆F=⋆J
Fab=2∇[aAb]Fab=2∇[aAb]
∇[aFbc]=0∇[aFbc]=0
∇aFab=
∇⋅B⃗=0∇⋅B→=0
∇⋅E⃗=4πρ∇⋅E→=4πρ
∂B⃗∂t=−∇×B⃗∂B→∂t=−∇×B→
∂E⃗∂t=+∇×B⃗−4πJ⃗.
∇⋅v⃗=∂vi∂xi∇⋅v→=∂vi∂xi
and the curl is defined as
(∇×v⃗)i=ϵijk∂vk∂xj.
∇⋅v⃗=∂vx∂x+∂vy∂y+∂vz∂z∇⋅v→=∂vx∂x+∂vy∂y+∂vz∂z
and curl is defined as
(∇×v⃗)z=∂vy∂x−∂vx∂y
= meaning of life 42
The triangles below are similar. Find the value of x.
9
8
10.5
11
Answers
This is the answer because the relationship is dividing by 2.
14÷2=7 so 18÷2=9
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
Answers
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.
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?
Answers
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.
Learn more about Direct and Inverse Proportion here:https://brainly.com/question/1266676
#SPJ12
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.
Learn more about IQ and mental age here:https://brainly.com/question/19131213
#SPJ3
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.
...?
Answers
1J, 2J, 3J, ...............29D, 30D, 31D = 365 days
2 4 6 ........................................
let be S the value of entire savings
S= Sum 2K= 2 Sum K = 2 [365(365+1) / 2],
1<K<365 1<K<365
because Sum K = n(n+1) /2
1<K<n
finally S= 133590 pennies
Answer:
1335.90
Step-by-step explanation:
The dimensions of a smaller rectangle are 3 ft. by 9 ft. The dimensions of a larger rectangle are 5 ft. by 11 ft. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle. Options are 11:9, 3:4, 4:3, and 5:3 ...?
Answers
Answer:
Option 3rd is correct
4: 3
Step-by-step explanation:
Perimeter(P) of rectangle is given by:
[tex]P =2(l+w)[/tex]
where, l is the length and w is the width of the rectangle respectively.
Given that:
The dimensions of a smaller rectangle are 3 ft. by 9 ft.
Perimeter of smaller rectangle= 2(3+9) =2(12) = 24 ft.
It is also given that: The dimensions of a larger rectangle are 5 ft. by 11 ft.
Perimeter of Larger rectangle = 2(5+11) =2(16) = 32 ft.
We have to find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.
[tex]\frac{\text{Perimeter of the larger rectangle}}{\text{Perimeter of the Smaller rectangle}}[/tex]
Substitute the given values we have;'
[tex]\frac{32}{24}=\frac{4}{3}[/tex]
Therefore, the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle is, 4 : 3
if the tank is half full, approximately how many miles has troy driven since last filling up his tank
BTW troy truck has a 30 gallon gas tank and gets an average of 21 miles per gallon
ASAP plz I really need help
Answers
30 Gallon Tank on Half: 30 / 2 = 15.
21 miles per gallon: 21 x 15 = 315 Miles.
I hope this helps!
Answer:
Toy truck will drive 315 miles since last the tank was filled.
Step-by-step explanation:
BTW troy truck has tank of capacity = 30 gallons
Since the toy truck is half filled so gas in the tank = [tex]\frac{30}{2}[/tex]
= 15 gallons of gas
Average of the toy truck is given as = 21 miles per gallon
That means in 1 gallon truck travels = 21 miles
Therefore in 15 gallons of gas truck will travel = 21 × 15
= 315 miles
Toy truck will drive 315 miles since last the tank was filled.
solve for x enter your answer in interval notation using grouping symbols x²+2x<8
Answers
Write the function in slope-intercept form. Then graph the function.
2x - 5y = -6
Answers
-5y=-2x-6 and then multiply each side by a -1 to get
5y=2x+6 divide by 5
y=2/5x+6/5
To graph this just put a point on 6/5 on the y axis then to find the next point move over to the right 2 and up 5. After you have two points draw the line connecting them.
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 ...?
Answers
The area (A) of the rectangle is:
A = l * w (l - length, w - width)
We have:
l = x - 7
w = x + 3
Therefore:
A = (x - 7)(x + 3)
Now, multiply each factor with another:
A = (x - 7)(x + 3) = x * x + x * 3 - 7 * x - 7 * 3 = x² + 3x - 7x - 21 = x² - 4x - 21
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 .
To know more about Area
https://brainly.com/question/27683633
#SPJ5
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 ...?
Answers
Given:
L=6-√2 feet; W= 12-√2
Area = L*W = 6-√2ft * 12-√2 ft = 74-18√2 square feet
The best and most correct answer among the choices provided by your question is letter B. 74-18√2 square feet.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Whut is 2 pus 2 i dount no
Answers
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
Answers
6x-4 (x+2)= -10x
6x-4x-8= -10
2x= 2
x= 1
y=1+2=3
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).
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
#SPJ6
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?
Answers
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
When f is defined by
f(x) = sqrt(x) ,
find a so f'(a) is two times the value of f'(4).
Answers
how many times does 28 go into 126
Answers
It would be:126/28 = 4.5
So, your final answer is 4.5
Hope this helps!