The average speed of this particle over the interval 2 ≤ t ≤ 10 is 25 , the correct option is (b)25 .
In the question ,
it is given that
the position of the particle that travels along the x-axis at time t is given by the function
x(t)=2t²+t
the average speed of the particle can be calculated by using the formula
average speed = (change is distance)/(change in time)
particle position at t=2
x(2) = 2(2)²+2 = 2*4+2 = 10
particle position at t=10
x(10) = 2(10)²+(10)
= 2*100+10
= 200+10
= 210
So, change in distance = 210-10= 200
change in time = 10-2 = 8
Putting the values in the average speed formula we get
average speed = 200/8
= 100/4
=25
Therefore , the average speed of this particle over the interval 2 ≤ t ≤ 10 is 25 , the correct option is (b)25 .
The given question is incomplete , the complete question is
A particle travels along the x-axis such that its position at time t is given by the function x(t)=2t²+t . What is the average speed of this particle over the interval 2 ≤ t ≤ 10?
(a) 4
(b) 25
(c) 32
(d) 200
Learn more about Speed here
https://brainly.com/question/12084203
#SPJ1
-3+n ≥ -4n-3 or 3n-4≥4n + 1
Answer:
-3+n ≥ -4n-3
Step-by-step explanation:
its good to use a number for n
if n = 5
-3+n ≥ -4n-3 or 3n-4≥4n + 1
for
-3+n ≥ -4n-3
-3+5 ≥ -4(5)-3
-2 ≥ -20-3
-2 ≥ -23
true
for
3n-4≥4n + 1
3(5)-4≥4(5) + 1
15-4≥20 + 1
11 ≥20 + 1
11 ≥21
not true
21. What are the modes of the following sets of numbers?
a. 3, 13, 6, 8, 10, 5, 6
b. 12, 0, 15, 15, 13, 19, 16, 13, 16, 16
Answer:
a. 6
b. 16
Step-by-step explanation:
a.
The mode is the number that appears the most
3 appears once
13 appears once
6 appears twice
8 appears once
10 appears once
5 appears once
Since 6 appears the most, it is the mode in this set of numbers
b.
Again, The mode is the number that appears the most
12 appears once
0 appears once
15 appears twice
13 appears twice
19 appears once
16 appears three times
Since 16 appears the most, it is the mode in this set of numbers
The correct answers are: [A]: "6 " ; and: [B]: " 16 ."
____________________
Step-by-step explanation:
The question asks to find the modes of the following sets of numbers:
Set a) "{3, 13, 6, 8, 10, 5, 6}."
Set b) "{12, 0, 15, 15, 13, 19, 16, 13, 16, 16}."
Note that the mode is the number that occurs most frequently within a data set.
To begin: let's find the mode of Set: a:
_____
First, let's list all the values within Set: a: in order of smallest to largest—to simplify matters:
→ " { 3, 5, 6, 6, 8, 10, 13 }."
In this data set, there is only one value that occurs more than once—
which is 6. As such, the mode of "Data Set: a" is 6 .
Then: To continue: let's find the mode of Set: b:
_____
Second, Let's list all the values within Set: b: in order of smallest to largest—again; to simplify matters:
→ " { 0, 12, 13, 13, 15, 15, 16, 16, 16, 19 } ."
In this data set, we see the following:
Each of the three values: 0, 12, and 19 appear only once;
13 and 15 individually, appear twice; and:
16 appears "three times".
As such:
The value, 16 appears the most in this data set; and:
→ The mode of "Data Set: b"—is 16.
_____
The correct answers are: [A]: "6 " ; and: [B]: " 16 ."
_____
Hope this is helpful to you!
If you have any questions—Please "comment" below!
_____
I'm not good with graphs so I really need help solving and understanding this
4x + 3y = -24 (option D)
Explanation:To determine the orrect option, we would find the equation of the line.
Equation of line: y = mx + c
m = slope, c = y-intercept
Using the slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]We would use any two points on the graph.
Using points: (-6, 0) and (0, -8)
[tex]\begin{gathered} x_1=-6,y_1=0,x_2=0,y_2\text{ = -}8 \\ m\text{ = }\frac{-8-0}{0-(-6)} \\ m\text{ =}\frac{-8}{0+6}=\frac{-8}{6}=-\frac{4}{3} \end{gathered}[/tex]The y intercept is the point where the line crosses the y axis and the value of x is zero. It crosses the line at y = -8
The equation of line becomes:
y = -4/3 x + (-8)
y = -4/3x - 8
Multiply both sides by 3:
3(y) = 3(-4/3 x) - 3(8)
3y = -4x - 24
3y + 4x = -24
4x + 3y = -24 (option D)
Determine which angles are right triangles. Select all that apply
Answer:
[tex]A,B[/tex]Explanation:
Here, we want to get the right triangles
Mathematically, for us to have a right triangle, the square of the hypotenuse (which is the longest side) equals the sum of the squares of the two other sides. This is Pythagoras' theorem
We shall be testing this principle out on the given options
We proceed as follows:
[tex]\begin{gathered} a)\text{ 24}^2\text{ + 143}^2\text{ = 145}^2 \\ b)\text{ 28}^2\text{ + 195}^2\text{ = 197}^2 \\ c)\text{ 135}^2\text{ + 140}^2\text{ }\ne\text{ 175}^2 \\ d)\text{ 56}^2+\text{ 16}^2\ne\text{ 65}^2 \end{gathered}[/tex]What this means is that only options A and B is correct
12 nights camp accommodation costs #6720. What will be the cost of a)7 nights number b)4 nights
EXPLANATION :
The cost of a 12 nights camp accommodation is 6720.
We need to divide the cost by 12 to get the cost per day.
[tex]6720\div12=560[/tex]Now, we are asked to find the cost of 7 nights and 4 nights.
We just need to multiply the daily rate by the number of nights.
a. 7 nights :
7 x 560 = 3920
b. 4 nights :
4 x 560 = 2240
ANSWER :
a. 3920
b. 2240
The vertical distance is
. The horizontal distance is
. So the slope can be represented by the ratio
. The ordered pair for the red point on the line is
. If we substitute the numbers from the ordered pair in for x and y in the ratio, it will equal
please help ill give brainly
.
Answer:
. The horizontal distance
Step-by-step explanation:
The vertical distance is
. The horizontal distance is
. So the slope can be represented by the ratio
. The ordered pair for the red point on the line is
. If we substitute the numbers from the ordered pair in for x and y in the ratio, it will equal
please help ill give brainly
.
Tell whether x and y show direct variation. Explain your reasoning.
y - x = 0. Find the value of k
In the given equation x and y show a direct variation of the form:
y = x
Where the value of k is 1.
Is there a direct variation?
A direct variation between two variables x and y is written as:
y = k*x
Where k is called the constant of proportionality.
Here we have the equation:
y - x = 0
moving x to the right side we get:
y = x
This is a direct variation with k = 1.
y = 1*x
Learn more about direct variation.
https://brainly.com/question/6499629
#SPJ1
WATER DEPTH An echo sounder is a device used to determine the depth of water by measuring the time it takes a sound produced just below the water surface to return, or echo, from the bottom of the body of water. The accuracy of an echo sounder is the positive difference between the depth of water reading on the echo sounder and the actual depth of water w. Write two absolute value expressions equivalent to the accuracy of an echo sounder.
The absolute value expressions of the echo sounder are |r - w| and |w - r|
How to determine the absolute value expressions of the echo sounder?The statement in the question is represented as
The accuracy of an echo sounder is the positive difference between ...
To solve further, we use the following representations
Depth of water reading = r
Actual depth = w
So, the statement becomes
The accuracy of an echo sounder is the positive difference between r and w
The difference can be represented as
Difference = r - w or Difference = w - r
Represented as absolute value expressions
Difference = |r - w| or Difference = |w - r|
Hence, the expressions are |r - w| and |w - r|
Read more about absolute value at
https://brainly.com/question/28943520
#SPJ1
In a bar graph the length of the bar need not be in proportion to the information being shown.
True
False
In a bar graph the length of the bar need not be in proportion to the information being False.
Bar graph. A bar chart is frequently used to compare values of different things at a specific time. It presents information visually using rectangles (bars). It generally serves as a visual aid for proportions, patterns, comparisons, and contrasts.
How do you describe a bar graph?To represent value, it makes use of bars that stretch to various heights. Vertical bars, horizontal bars, grouped bars (several bars that compare values in a category), and stacked bars can all be used to construct bar graphs (bars containing multiple types of information).
A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.
comparisons of several variables that are simple. clarity in the presentation of data trends. Simple value determination.
To learn more about bar graph refer to:
https://brainly.com/question/24741444
#SPJ1
Lisa is putting money into a savings account, she starts with $350 in the savings account, and each week she adds $60
The total amount of money in the savings account after 11 weeks is $1010.
What is the total amount in the savings account?The from of the equation that can be used to determine the total amount of money in the savings account is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one. When a linear equation is drawn on a coordinate graph, it is usually a straight line.
The form of the linear equation is:
Total amount = amount she starts with + (number of weeks x amount of money she adds each week)
S = $350 + ($60 x W)
S = $350 + $60W
Amount she would have in 11 weeks : $350 + ( 11 x $60)
$350 + 660 = $1010
Here is the complete question:
Lisa is putting money into a savings account. She starts with $350 in the savings account, and each week she adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Jenny has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.
To learn more about linear functions, please check: https://brainly.com/question/26434260
#SPJ1
answer pls
1. A surfer paddles out past breaking waves, rides a
wave, paddles back out past the breaking waves,
rides another wave back to the beach. Draw a sketch
of a graph (with labels) that shows the surfer’s
possible distance from the beach over time.
2. For the table, identify the independent and
dependent variables, Represent the relationship
using words, an equation and a graph.
# of cases of
bottled
water, c
# of bottles
of water,
b
1 24
2 48
5 120
10 240
20 480
for this one i only need the graph cannot find it out
3. Sketch a graph of the function shown by the table. Is
its linear or nonlinear?
x y
1 0
2 1
3 8
4 20
5. Write a function rule to represent the situation:
The volume, V, remaining in a 243 ft3 pile of gravel
decreases by .2 ft3 with each shovelful, s, of gravel
spread in a walkway
Tell whether the relation is a function. Explain your
reasoning.
{(-1, 7), (9, 4), (3, -2), (5, 3) , (9, 1)
7. Tell whether the relation is a function. Explain your
reasoning. find graph below
Describe the pattern in the sequence. Find the next
two terms of the difference.
-2, -5, -8, -11,
the graph for 7
Answer:
V = 243 - 0.2s
Step-by-step explanation:
See attached document for questions 1 - 3.
5. Write a function rule to represent the situation:
The volume, V, remaining in a 243 ft3 pile of gravel
decreases by .2 ft3 with each shovelful, s, of gravel
spread in a walkway.
Volume Remaining (V) = Initial - Used
Volume Remaining (V) = 243 ft^3 - (0.2 ft^3/shovel)(s shovels)
V = 243 - 0.2s
6. Tell whether the relation is a function. Explain your
reasoning.
{(-1, 7), (9, 4), (3, -2), (5, 3) , (9, 1)
This is not a function. When x = 8, it results in more than one output.
7. Pattern:
-2
-5
-8
-11
Each step decreases by 3
-14
-17
8.
Which of the following describes the graph of y 3 -3 in a coordinate plane?
ANSWER
The boundary line is a solid horizontal line that passes through (0, -3). The half-plane that does not contan the origin is shaded.
(the answer is the second option)
EXPLANATION
The graph is
Is this function continuous or discrete? How far can you get on 20 gallons? What is the domain and range of this function? How many gallons to get 500 miles? Where do the labels on the graph go?
EXPLANATION
The equation of the function can be represented as shown as follows:
[tex]G(m)=12m[/tex]-This function is discrete.
-If we have 20 gallons, we can obtain the number of miles by plugging in the value into the equation, as shown as follows:
[tex]20=12m[/tex]Dividing both sides by 12:
[tex]\frac{20}{12}=m[/tex]Simplifying:
[tex]\frac{5}{3}=m[/tex]We can make 1.67 miles with 20 gallons.
-The domain of the function are all the Real Numbers and the Range are also the Real numbers.
-Finally, drawing the graph of the function:
The points of the table are the following:
Gallons Miles
2 24
4 48
6 72
8 96
-We can get the number of gallons needed to, make 500 miles by plugging the value 500 into the equation, as shown as follows:
[tex]500=12m[/tex]Isolating m:
[tex]\frac{500}{12}=m[/tex]Simplifying:
[tex]41.7=m[/tex]The number of gallons to make 500 miles is equal to 41.7 gallons
Finally, labeling the graph:
what is the range of :
-6
-2.
11
8
10
12
Answer:
18
Step-by-step explanation:
The range is the biggest number minus the smallest number.
The biggest number is 12.
The smallest number is -6 .
Range = 12-(-6) = 18
Which of these is a perfect square? Responses 29/ 78/ 144/ -6/
Here, 144=12×12=12². Therefore, 144 is a perfect square.
The given numbers are 29, 78, 144 and -6.
What is a perfect square?A perfect square is a positive integer that is obtained by multiplying an integer by itself. In simple words, we can say that perfect squares are numbers that are the products of integers by themselves.
By perfect square definition
29=29×1
78=2×2×17
144=2×2×2×2×3×3=12×12
-6=-2×3
So, from the above factors it is clear that, 144 is a perfect square.
Here, 144=12×12=12². Therefore, 144 is a perfect square.
To learn more about a perfect square visit:
https://brainly.com/question/11358616.
#SPJ1
Ple help me with Problems 2 & 3 ASAP
2) w = 16.5 mis the equation represents the relationship shown in the table.
3) The number of minutes is proportional to the number of pages, with a unit rate of 2.25 minutes per page is the best statement describes the relationship in the table.
How is a proportion determined?When determining if two ratios or fractions are equivalent, the proportion formula is utilized. We can calculate the missing value by dividing the given values. One way to express the percentage formula is as a: Whereas a and d are the extreme terms and b and c are the mean terms, a:b::c: d = a/b = c/d.
2) Divide the number of gallons of water with number of minutes
66/4 = 16.5
So, the equation represents the relationship shown in the table is
w = 16.5 m
3) Divide number of minutes by number of pages, we get
9/4 = 2.25
13.5/6 = 2.25
So, option (B) best describes the relationship in the table.
To know more about proportions visit:
https://brainly.com/question/7096655
#SPJ13
Eric ordered a set of red and yellow pins. He received 70 pins in all. 21 of the pins were red. What percentage of the pins were red?
The percentage of red pins in total pins ordered by Eric is 30%.
According to the question,
We have the following information:
Eric received 70 pins in all.
21 of the pins are red.
Now, we will find the percentage of red pins:
Percentage of red pins = (Number of red pins*100/total number of pins)
Percentage of red pins = (21*100)/70
Percentage of red pins = 2100/70
Percentage of red pins = 30%
(In the same way, we can also find the number and percentage of yellow pins from the total pins.)
Hence, the percentage of red pins in total pins ordered by Eric is 30%.
To know more about percentage here
https://brainly.com/question/28269290
#SPJ1
Vince and Wendy share $2000 in the ratio Vince : Wendy = 19 : 21. Calculate the amount of money that Vince receives
workout:
19+21=40
2000÷40=50
Vince=50×19=950
Wendy=50×21=1050
-u can check by adding 950+1050=2000 (which means the ratio is correct)
Answer:
(vince:wendy)= 950:1050
Answer:
V:W
19:21
19 + 21 = 40
19 over 40 × 200
Vince received $950
ASAP PLEASE HELP *20 POINTS*
1.If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, what transformation occurs from f(x) to h(x)?
A.Shift left 3 units
B.Shift right 3 units
C.Shift up 3 units
D.Shift down 3 units
2. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the vertex affected? Select all that apply.
A.The vertex will not change.
B.The vertex will shift right 3 units.
C.The vertex will shift left 3 units.
D.The vertex will shift up 3 units.
E.The vertex will shift down 3 units.
F.The vertex will not move up or down.
G.The vertex will not move right or left.
3. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the range affected?
A.The range will not change.
B.The range will be all real numbers.
C.The range will change from y ≥ 0 to y ≥ -3.
D.The range will change from x ≥ 0 to x ≥ -3.
if the parent function f(x) = |x| is transformed to h(x) = |x| - 3,
1. The transformation occurs from f(x) to h(x) is D. Shift down 3 units
2. The vertex is affected by:
E. The vertex will shift down 3 unitsG. The vertex will not move right or left3. The range will C. change from y ≥ 0 to y ≥ -3.
What is transformation?This is an ordered movement of image or object as seen in geometry. The instance here the movement is done by the graph f(x) and h(x) as described.
The type of movement described is called translation.
What is the range?The range refers to the output of the graph and is typically the y direction.
The range here changed from the origin which is the initial vertex and included point y ≥ -3
It should be noted that the origin of the graph refers to the point y ≥ 0
Learn more on transformation: https://brainly.com/question/1548871
#SPJ1
Which set of ordered pairs (x, y) could represent a linear function?
A = {(-3,5), (0, 2), (3,-1), (7,-4)}
B = {(0,3), (1,5), (2,7), (4,9)}
C= {(-3,8), (-1,7), (1,6), (3,5)}
D = {(-5, -1), (-2,2), (1,4), (4,7)}
OA
C
B
D
Submit Answer
The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
How is a linear function written?The equation y = mx + b, where y is the y-coordinate, denotes a linear function. m represents the line's slope, or how steep it is. The coordinate for x is x.
The equation y = mx + b, where y is the y-coordinate, denotes a linear function.
m represents the line's slope, or how steep it is.The coordinate for x is x.the point where the line intersects the y-axis, or b.To learn more about Linear function refer to:
https://brainly.com/question/15602982
#SPJ13
Sylas loves cookies! If he bought 5 cookies for $6.65, how many cookies
could he buy with $20?
Answer:
15
Step-by-step explanation:
6.65:5=1.33
1.33х15=19.95$
we need to around the 19.95 and we get a 20$
have a nice day
A circle has a radius of 5 units, 3 students tried to calculate the circumference of the circle, put their answers in order from most accurate to least accurate31.4π units 10π units 31.4 units
A circle has a radius of 5 units, 3 students tried to calculate the circumference of the circle, put their answers in order from most accurate to least accurate
31.4π units
10π units
31.4 units
we know that
the circumference of a circle is equal to
[tex]C=2\pi r[/tex]we have
pi=3.14
r=5 units
substitute
[tex]\begin{gathered} C=2\pi(5) \\ C=10\pi\text{ units} \end{gathered}[/tex]the exact value is 10pi units
the approximate value (assume pi=3.14)
C=31.4 units
so
order from most accurate to least accurate is
10π units
31.4 units
31.4π units
order from least accurate to most accurate is31.4π units31.4 units10π units1/3x - 7 = -8 what is x
Answer:
x = -3
Step-by-step explanation:
Add 7 to -8 = -1
1/3x = -1
Divide -1 by 1/3
x = -3
Answer:
x=-3
Step-by-step explanation:
Rewrite as x/3 -7 = -8Multiply the entire equation by 3 which results in : x -21 = -24Isolate the variable: x = -24 + 21Solve for x: x=-3Can a triangle have sides with the given lengths?a2 in, 4 in, 6 inYesNo
In general, if the sides of a triangle are a, b, and c, they must satisfy the inequalities below
[tex]\begin{gathered} a,b,c\rightarrow\text{ sides of a triangle''} \\ \Rightarrow a+b>c \\ b+c>a \\ c+a>b \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} 2+4>6\Rightarrow6>6\rightarrow False \\ 4+6>2\Rightarrow10>2\rightarrow True \\ 6+2>4\Rightarrow8>4\rightarrow True \end{gathered}[/tex]The first inequality is false; thus, the triangle cannot exists. The answer is No.Use the appropriate compound interest formula to compute the balance in the account after the stated period of time
$19,000 is invested for 2 years with an APR of 4% and daily compounding.
Compound interest exists as the interest you gain on interest. The balance in the account after 2 years is $42266.
What is meant by compound interest?Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.
'Compound interest' simply indicates earning interest on your savings, and also, eventually, on the interest that those savings earn.
The appropriate formula is
A = P(1 +r/n[tex])^{(nt)[/tex]
where P = 19,000, r = 0.4, n = 365, t = 2.
substitute the values in the above equation, we get
A = 19,000(1 +0.4/365[tex])^{(365 \times2)[/tex]
simplifying the above equation, we get
A = 42266.7592
The balance in the account after 2 years is $42266.
To learn more about Compound interest refer to:
https://brainly.com/question/24924853
#SPJ13
a group of friends is taking part in a two-day walking event for charity. yesterday, they walked 28 miles in 9 hours and 44 minutes. today, they finished the last 10 miles in 2 hours and 55 minutes. what was the group's average speed for the two-day event?
Average speed of the group for the two day event is 0.105 miles\min.
The average is defined as the mean value that is equal to the ratio of the total sum of the number of a given set of values to the total number of values present in that set.
Time taken on day 1 in minutes = 9x60 + 44
= 540 + 44 = 584 minutes.
Time taken on day 2 in minutes = 2x60 + 55
= 120 + 55 = 157 minutes
Now we will be applying speed-distance formula we get,
Speed= Distance/time
On day 1,
[tex]Speed_{1}[/tex]= 28/584 = 0.0479 miles/min
On day 2,
[tex]Speed_{2}[/tex]= 10/175 = 0.0571 miles/min
Thus,the average speed is:
Average = [tex]Speed_{1} + Speed_{2}[/tex] = 0.0479 + 0.0571= 0.105 miles/min
Hence,the average speed is 0.105 miles/min
To learn more about Average visit:
https://brainly.com/question/130657
#SPJ4
Paula measured the auditorium and made a scale drawing. The stage, which is 56 feet long in real life, is 84 inches long in the drawing. What scale did Paula use?
3 inches= ? feet
There are 2 feet in real life be 3 inches long in the scale drawing.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The stage, which is 56 feet long in real life, is 84 inches long in the scale drawing.
Let the x feet in real life be 3 inches long in the drawing.
According to the given question, we can write a ratio as
56 feet : 84 inches = x feet : 3 inches
⇒ 56 / 84 = x / 3
Apply the cross-multiplication operation,
⇒ 56 × 3 = x × 84
⇒ 168 = 84x
⇒ 84x = 168
⇒ x = 168 / 84
⇒ x = 2
Therefore, there are 2 feet in real life be 3 inches long in the scale drawing.
Learn more about Ratio here:
brainly.com/question/1504221
#SPJ1
Find 3 ratios that are equivalent to 5:13
a ball dropped from rest and falls for 8 seconds
whats the final velocity
and whats te average velocity
how far did it fall
On the map, 0.1 inches represents
25 miles. If the real distance between
two cities is 112.5 miles, what is the
distance between their locations on
the map?
A. 0.45 in
B. 2 in
C. 0.2 in
D. 1 in
The distance between the two cities on the map is 0.45 inches , the correct option is (A) 0.45inches .
In the question ,
it is given that
the scale factor of the map is 25 miles = 0.1 inches
So, 1 mile = 0.1/25 inches
= 0.004 inches
So , on the map 1 mile is represented by 0.004 inches
Given that the real distance between the two cities is 112.5 miles
So , on the map 112.5 miles = 112.5*0.004 inches
= 0.45 inches
Therefore , the distance between the two cities on the map is 0.45 inches , the correct option is (A)0.45inches .
Learn more about Scale Factor here
https://brainly.com/question/4526389
#SPJ1
