This graph tracks the distance travelled from home over an 8 hour time period. Which of the following is NOT the rate of change for one of the legs(A, B, C, D, or E) shown above? A. 0B. 80C. 40D. -60
Answers
The question is about the rate of change of the graph, out of the options we need to find the option that is not a slope of the lines that compose the graph. Since it is a graph that is composed by multiple lines, we can analyze the rate of change for each line. In this case, the rate of change correspond to the slope of the line, which at the same time, tells us "how much" the values in the y axis changes as the x-axis changes. In here, we denote a change positive if the value of the axis increases and negative if the change in the axis is negative.
Consider, for instance, part A of the graph.
Note that this part goes from hour 0 to hour 2. So, in the x axis the variable increased in 2 units. That is, a positive change. Now, noticed that at hour 0 the value of distance was 0. After two hours, the distance was 80. Then, the value in y increased in 80. So, in this case we have a positive change. Now, to calculate the rate of change in this part, we divide the change of Y by the change of X.
That is, 80/2, which is 40. In this case, the rate of change for the part A is 40.
For part B,
note that at hour 2 we are at 80, and then at hour 3 we are at 80. In this case, the change in the x axis is still 1 unit. However, the change in y is 0, since we are at 80 at time 2 and at time 3. So the slope of this part is the change of y, divided by the change in x, which is 0/1 =0.
Using this principle, we can determine that D has also a rate of change of 0.
Now, let us continue with part C.
Note that at time 3, we are at 80. Then, at time 4 we are at 120. In the x-axis the cahnge was of 1 unit. In the case of Y, we changed from 80 to 120. That is, the change was 120-80 =40. So, in this case, the slope is the change in y (40) divided by the change in x (1). That is 40/1 = 40. So part C also has a rate of change of 40.
Finally, we will calculate the rate of change for part E. At time 6, we are at 120 and at time 8 we are at 0. In the x axis, we got from 6 to 8. So it is an increase of 2 units. In Y, however, we go from 120 to 0. That is, we decrease in 120 units. Since it is a decrease, we consider this a change of -120.
So, the rate of change would be the change in y (-120) divided by the change in x (2). So the rate of change of E is -120/2 = -60. So the rate of change for E is -60.
Then, the only correct option is B. 80, since no line in the graph has that rate of change.
Related Questions
Find the missing number. 390 × ___ = 390 , 000
Answers
Answer:
1000Step-by-step explanation:
Find the missing number. 390 × ___ = 390,000
390.000 : 390 = 1000
Answer:
C
Step-by-step explanation:
c is 10^4 if you look at the numbers 390.000 there are 4 0 and as a teacher would teach you is how many 0 there are that the answer so 10^4 would be the anwser
Hope this helps
What is the area of this pool rounded to the tens place?
Answers
First, let's calculate the area of each circular sector, using the formula below:
\(A=\frac{r^2\theta}{2}\)Where r is the radius and theta is the central angle.
So, using theta = 2.21 and r = 30, we have:
\(A_1=\frac{30^2\cdot2.21}{2}=994.5\text{ ft^^b2}\)Both circular sectors have the same area, so A2 = A1.
The area of a triangle is given by:
\(A=\frac{b\cdot h}{2}\)Where b is the base and h is the height relative to this base.
Using b = 20 and h = 25, we have:
\(A_3=\frac{20\cdot25}{2}=250\text{ ft^^b2}\)The area of the triangles is the same, so A4 = A3.
Now, adding all areas, we have:
\(\begin{gathered} A_{total}=A_1+A_2+A_3+A_4\\ \\ A_{total}=994.5+994.5+250+250\\ \\ A_{total}=2489\text{ ft^^b2} \end{gathered}\)Rounding to the tens, we have an area of 2490 ft², so the correct option is D.
The average profit/loss of a company (in thousands of dollars) was documented for 30 months. The 5th month showed a loss of $3000, however the 25th month
showed a profit of $5000. Assuming the profitloss is linear, write the equation of the line, in slope-intercept form, that represents the profit/loss for each month x. Use
this result to predict the profit/loss after 60 months
Hint: Use the ordered pairs (5. - 3) and (25,5).
2
The equation of the line in slope-intercept form is y= 5x -5.
(Type an equation using x and y as the variable. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
..There would be a of safter 60 months
Answers
Answer:
Step-by-step explanation: slope is (9-(-3))/(25-5)
12/20=0.6
point slope formula y-y1=m(x-x1), m slope (x1, y1) point
y-9=0.6(x-25)
y=0.6x-15+9
y=0.6x-6, x months and y profit.
for 60 months, y=0.6*60-6 or 36-6=$30000 profit
create a hanger to represent 7 = 4x + 2
Answers
4x + 2 = 7 or, 4x = 7 - 2 or, 4x = 5 or, x = 5/4 = 1.25
true/false.
____1.When the non-Standard unit used is small few unit's are
needed to fill a container when the non-standard the non-standard units used is bigger more units are needed to fill the container.
____2.Objects with shape can have the same volume.
____3. To find the volume of rectangular prism multiply the length,width and height.
_____4. Volume is measured in square unit's.
_____5. the amount of space inside an object is called the volume of the object.
____6. The volume of a rectangular prism is equal to the product of its length, width, and height V = 1xwxh cubic units.
____7. Standard units give a consistant and accurate measure of a container.
____8. Non-Standard units cannot be used to measure volume.
____9. Volume is measured in cubic units, such as cubic centimeters.
Answers
1. It is false that when non-Standard unit used is small few unit's are
needed .
2. Objects with different shapes can have the same volume. True
3. Length, width and height and multiplied to find volume of a rectangular prism. True
4. It is false that volume is measured in square unit.
5. It is true that Volume is a measure of the amount of space inside an object.
6. The formula for volume of a rectangular prism is V = l × w × h. True
7. It is true that Standard units give a consistent and accurate measure of a container.
8. It is false that Non-Standard units cannot be used to measure volume.
9. Volume is measured in cubic units. True
What is volume of an object?Volume can be defined as the amount of space inside and object. the object can be in different form such as cone, rectangular prism, cylinder and many other shapes. Even though shapes are different, It is possible for different shapes or objects to have the same volume when measure.
Measurement of volume can be through standard measurement and non standard measurements such as a cup of rice. However, for consistency and the sake of accuracy, it is advisable to always use standard measurements of volume where possible to avoid error that may occur in non standard measurement. The acceptable and recognized unit of volume is cubic meter (\(m^3\)).
Learn more on Volume on https://brainly.com/question/27710307
#SPJ1
Graph the parabola y=-3x^2+24x-42
Answers
graph y+2=2(x+3). What is the x intercept?
x intercept :
Answers
The given equation is y + 2 = 2(x + 3) and the x-intercept is -2.
To find the x-intercept of the equation y + 2 = 2(x + 3), we need to set y equal to zero and solve for x. The x-intercept occurs when the value of y is zero, meaning the graph crosses the x-axis.
Let's substitute y with 0 in the equation:
0 + 2 = 2(x + 3)
Simplifying the equation:
2 = 2(x + 3)
Dividing both sides by 2:
1 = x + 3
Subtracting 3 from both sides:
-2 = x
The x-intercept is -2. This means that the graph of the equation y + 2 = 2(x + 3) crosses the x-axis at the point (-2, 0).
The x-intercept represents the value of x where the graph intersects or crosses the x-axis. In this case, it occurs when x is equal to -2, and the y-value is zero.
For more such questions on x-intercept
https://brainly.com/question/17932786
#SPJ8
Hello! Would you please explain if Questions 7 and 8 are the same? I'm confused if I need to sub x for 23 for number 8
Answers
In question 7, the exercise only wants an explanation, in text form, of the meaning of the substitutions. That is, that the value of x=5 indicates the time that has passed, 5 hours, and that f(5)=32 indicates the number of riders.
In question 8, you need to pick some values for x, make a table with those values and the respective values of the function when you substitute those values of x, and put the points on the graph.
{ (2,3) , (4,5) , (6,6) }
Answers
Answer:
???? did u type it correctly?
(Pic) How many tablets, please help!
Show steps please
Answers
The number of tablets that should be taken each day by the patient who needs Synthroid is 1 tablet.
How to find the number of tablets ?To find the number of tablets of Synthroid that should be taken, you convert the requirements from micrograms ( μg ) to milligrams ( mg).
1 milligram = 1, 000 micrograms ( μg )
25. 0 μg in milligrams is therefore:
= 25 / 1, 000
= 0. 025 mg
This means that the number of tablet to take is:
= Mg requirement / Mg of tablet
= 0. 025 / 0. 025
= 1 tablet
Find out more on tablets at https://brainly.com/question/11217552
#SPJ1
What is |4|? I need help
Answers
Answer: It is just 4
Step-by-step explanation: That means the absolute value of 4 and it is just 4
Answer 4
calculate the value of 12-3×0
Answers
this one kinda makes no sense but uhm- here ya go
12-3 is 9, but 9x0 is 0. So your answer would be 0.
PLEASE GIVE BRAINLIEST LOL
What is 1/10 of 0.002
Answers
1/10 of 0.002 IS 0.0002 that is the answer to your question
P=x-2 ÷ x+1 for whar value of x is P equal to zero
Answers
Answer:
x = 2
Step-by-step explanation:
P = \(\frac{x-2}{x+1}\)
P will equal zero when the numerator is equal to zero , that is
x - 2 = 0 ( add 2 to both sides )
x = 2
P = 0 when x = 2
The equation x3 + 3x2 + 5x + 15 = 0 has real and imaginary solution(s).
need help really fast
Answers
Use the properties of exponents to simplify the expression:
Answers
The simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.
How can you simplify → aˣ/aⁿ?We can write the simplified form of the given expression using the exponent rule as -
{aˣ/aⁿ} = {aˣ a⁻ⁿ} = {aˣ ⁻ ⁿ}
Given is the expression as -
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\)
We can simplify the expression as -
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (27)^{\frac{1}{2} \times \frac{2}{3} }\)
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 27^{\frac{1}{3} }\)
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (3)^{3}^{\frac{1}{3} }\)
\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 3\)
Therefore, the simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.
To solve more questions on exponents, visit the link below -
brainly.com/question/12431044
#SPJ1
Adam is planning
a rectangular patio that will have an area of
16x2 1 20x square feet. The length of the patio
will be x 1 5 feet. Write an expression to
represent the width of the patio.
Answers
Answer:
The width of the patio is 15 feet
Step-by-step explanation:
We can start by using the formula for the area of a rectangle:
Area = length x width
In this case, we know that the area of the patio is given by:
16x^2 + 20x square feet
And we also know that the length of the patio is x + 5 feet. So we can substitute these values into the formula to get:
16x^2 + 20x = (x + 5) x width
Simplifying the right-hand side by multiplying x + 5 by width, we get:
16x^2 + 20x = width x^2 + 5x
To solve for the width, we can move all the terms with width to the left-hand side and all the other terms to the right-hand side:
width x^2 - 16x^2 + 20x - 5x = 0
Simplifying the left-hand side by combining like terms, we get:
width x^2 - 16x^2 + 15x = 0
Factoring out x, we get:
x (width x - 16x + 15) = 0
Now we can solve for the width by setting each factor equal to zero and solving for x:
x = 0 or width x - 16x + 15 = 0
Since the length and width of the patio must be positive values, we can disregard the solution x = 0. So we are left with:
width x - 16x + 15 = 0
We can factor this quadratic equation by finding two numbers whose product is 15 and whose sum is -16. These numbers are -1 and -15, so we can write:
(width x - 1)(x - 15) = 0
Setting each factor equal to zero and solving for x, we get:
width x - 1 = 0 or x - 15 = 0
width x = 1 or x = 15
Since the length of the patio is x + 5, which is 20 feet, we know that x = 15 is the correct solution. So we can substitute x = 15 into the expression for the width:
width x = 1, x = 15, so we choose x = 15
width x - 16x + 15 = (15) x - (16)(15) + 15 = 15 feet
Therefore, the width of the patio is 15 feet.
5.A Nathan decided he wanted to go to a theme park. The theme
park charges $ 7.00 for entry and $ 1.50 for each ride. Part A : Write an
expression to represent this scenario where R represents the number of
rides.
5.B Refer to problem 5. Part B: Write and solve an equation to determine
how many rides Nathan can ride if his Dad give him $ 28.00. Show your work.
Answers
Answer:
5a. $1.50R + $7
5b. 14 rides
Step-by-step explanation:
5b. $28 - $7= $21/1.50= 14
He can go on 14 rides
If rides be x
Initial price=7Rate of change=1.5The equation is
y=1.5x+7#B
Put y=28
1.5x+7=281.5x=28-71.5x=21x=14Total 14 rides
Listed below is a table showing the number of employees. 20 years or older by gender in the United states
Answers
The total number of workers that were studied can be found to be 139,340,000.
The percent of workers unemployed would be 5. 4 %.
Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.
How to find the employment figures ?Number of employed workers :
= 74,624,000 + 64, 716, 000
= 139,340,000
Percentage unemployed :
= ( 4, 209,000 + 3,314,000 ) / 139,340,000
= 5. 4 %
Percentage of unemployed men :
= 4,209,000 / 74,624,000
= 5.6 %
Percentage of unemployed women:
= 3,314,000 / 64, 716, 000
= 5. 1 %
Find out more on unemployment at https://brainly.com/question/13280244
#SPJ1
The full question is:
a. How many workers were studied?
b. What percent of the workers were unemployed?
c. Compare the percent unemployed for the men and the women.
a recipe calls for 2 cups of flour for every 3 cups of sugar. If you are planning to use 5 cups of flour, how many cups of sugar should you use
Answers
Answer:
7½ cups of sugar
Step-by-step explanation:
2 cups of flour needs 3 cups of sugar
1 cups of flour needs 3/2=1.5 cups of sugar
1×5 cups of flour needs 1.5×5=7.5 cups of sugar=7½ cups of sugar ANS
An investment portfolio is shown below.
Investment Amount Invested ROR
Money Market Account $3,200 2.1%
Government Bond $1,750 4.4%
Preferred Stock $1,235 −7.8%
Common Stock $2,300 10.5%
Using technology, calculate the difference between the arithmetic average ROR and the weighted average ROR. Round to the nearest tenth of a percent.
0.5%
1.1%
2.3%
3.5%
Answers
Using technology, the difference between the arithmetic average ROR and the weighted average ROR is 0.52%
What is arithmetic mean?The Arithmetic Mean will be called the Simple Arithmetic Mean when it is calculated as the quotient between the sum of all the different related values and the number of observations involved in this sum.
Given An investment portfolio
Since arithmetic average ROR:
The average arithmetic average ROR is the sum of the rate of returns divided by the number of investments arithmetic average:
ROR = (2.1%+ 4.4%+ 7.8% + 0.5%)/4
arithmetic average ROR=6.20%
total amount invested=$3200+$1750+$1235+$2,300
total amount invested=$8,485
weighted average:
ROR = (3200/8485 * 2.1%+ 1750/8485 * 4.4%+ 1235/8485 *7.8% + 2300/8485 *0.5%)
weighted average:
ROR=5.68%
difference=6.20%-5.68%
difference=0.52%
Learn more about ROR on:
brainly.com/question/28683603
#SPJ1
Answer: it’s 1.1%
Step-by-step explanation: just got it right on the test
Hi can someone who is great at math please help me with these math questions. I'm struggling with them!!
Answers
The value of x will be 18.67 for the given data of the triangle.
We have,
Thale's theorem:
When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.
Given that the sides of the triangle are divided into two parts,
For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.
The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-
x / ( x + 7 ) = 16 / 22
22x = 16x + 112
6x = 112
x = 112 / 6
x = 18.67
Therefore, the value of x will be 18.67.
To know more about Thale's theorem follow
brainly.com/question/14417137
#SPJ1
complete question;
Find the values of x and y. Find value of x.
What will be the new position of the given point (3, 5) after translation of 2 units left and 3 units up?
Answers
Answer:5 8
Step-by-step explanation:left 2 up 3
A car advertisement states that a certain car can accelerate from rest to 72 km/h in 12.5 seconds.
Initially the car is at rest, so the initial velocity is ______
m/s.
The car speeds up to 72 km/h which is equivalent to _______
m/s. Find the car’s average acceleration.
The acceleration of the car is _______
m/s2
Answers
The initial velocity is 0 m/sec
The car speed up to 72km/h which is equivalent to 36m/sec
The acceleration of the car is 2.88 m/sec².
What is acceleration?Acceleration is the rate of change of the velocity of an object with respect to time. Vector quantities are accelerations. Acceleration = (Final Velocity - Initial Velocity)/ Time taken
Given that car can accelerate from rest to 72km/h in 12.5 seconds. Therefore, we can write:
Initial Velocity = 0 m/sec
Final Velocity = 72 km/hr = 72×(0.50) m/sec = 36m/sec
Time taken = 12.5 second
Now, the car’s acceleration in m/s can be written as,
Acceleration = (Final Velocity - Initial Velocity)/ Time taken
(36 m/sec - 0 m/sec)/12.5 seconds
= 2.88 m/sec²
Hence, the car’s acceleration in m/s is 2.88 m/sec².
Learn more about acceleration on:
https://brainly.com/question/14344386
#SPJ1
Solve the following equation.
1/3 k + 80 = 1/2 k + 120
Answers
Answer:
2; 3; 80; 1; -40; 1; -240 (answered from left to right then the next line)
Step-by-step explanation:
This is a question on fractions and solving algebraic equations. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Answer:
240
Step-by-step explanation:
k/3+80=k/2+120
K/3-k/2=120-80
3k-2k/6=40
K/6=40
K=240.
So the value of k is 240.
what decimal is equivalent to 41 over 100 (pls keep it simple i am only in 5th grade )
Answers
Answer: 0.41
Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).
41 over 100 as a decimal point would be 41 divided by 100
Which produces the equivalent decimal, 0.41
P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)
0.41 = 41%
so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)
Best of luck in 5th grade :)
At the beginning of an environmental study, a forest covered an area of 1500 km^2. Since then, this area has decreased by 7.75% each year.
Let t be the number of years since the start of the study. Let y be the area that the forest covers in km^2.
Write an exponential function showing the relationship between y and t.
Answers
If "t" number of years the study started and "y" denote the forest cover area, then the exponential-function representing the relation between "y" and "t" is y = 1500 × \((0.9225)^{t}\).
An "Exponential-Function" is a mathematical expression in which a constant (called the base) is raised to a variable power.
In this case, we want to find an exponential function that relates the area of a forest (y) to the number of years since the start of an environmental study (t).
We know that the forest is decreasing by 7.75% each year, which means that the area of the forest after "t years" will be some percentage of its original area.
The formula for an exponential function is y = a × \(b^{t}\), where "a" = initial value and "b" = growth or decay factor.
In this case, the initial area of the forest is = 1500 km², and
The forest is decreasing by 7.75% each year.
So, the "decay-factor" is = 1 - 0.0775 = 0.9225,
The exponential function that relates the area of the forest (y) to the number of years since the start of the study (t) is:
⇒ y = 1500 × \((0.9225)^{t}\),
Therefore, the required "exponential-function" is y = 1500 × \((0.9225)^{t}\).
Learn more about Exponential Function here
https://brainly.com/question/26930525
#SPJ1
A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be 99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
Answers
The sample size needed to be 99% confident that the sample proportion will not differ from the true proportion by more than 4% is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
\(\pi = 0.5\)
Then the sample size for M = 0.04 is obtained as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)
\(0.04\sqrt{n} = 2.575 \times 0.5\)
\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)
\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)
n = 1037.
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
The volume of a cone is 3x* cubic units and its height is x units.
Which expression represents the radius of the cone's base, in units?
O 3x
6x
370x2
O 90X2
Mark this and retum
Save and Exit
Next
Submit
Answers
Answer:
The radius of a cone is \(\dfrac{3}{\sqrt{\pi} }\ \text{units}\).
Step-by-step explanation:
The formula of the volume of a cone is given by :
\(V=\dfrac{1}{3}\pi r^2 h\)
r is radius of cone
h is height of cone
We have,
Volume of a cone is 3x cubic units and height is x units. Putting the values of volume and height such that,
\(r=\sqrt{\dfrac{3V}{\pi h}}\\\\r=\sqrt{\dfrac{3\times 3x}{\pi x}} \\\\r=\sqrt{\dfrac{3\times 3}{\pi}}\\\\r=\sqrt{\dfrac{9}{\pi}}\\\\r=\dfrac{3}{\sqrt{\pi} }\ \text{units}\)
So, the radius of a cone is \(\dfrac{3}{\sqrt{\pi} }\ \text{units}\).
I would really appreciate it if someone could answer this I will give a brainlist:)
Answers
Steps:
72^2 + 65^2= c^2
5184 + 4225= c^2
9409= c^2
C= 97
\(97.\)
Step-by-step explanation:
By using Pythagoras theorem
AC² = AB² + BC².
Let AB = 72 and BC = 65.
AC² = 72² + 65²
AC² = 5184 + 4225
AC² = 9409.
AC = √9409
AC = 97.