The average rate of change of the function f(x) is found as -3.75.
Explain the term average rate of change?The rate about which one value in a function evolves in proportion to another is known as the average rate of change. The slope of a graphical representation function is typically calculated using the average rate of change.The formula for the average rate of change (A(x)) of f(x) over the interval [a,b] is:
A(x) = f(b) - f(a) / b - a
The function being:
f(x) = 20.(1/4)ˣ
Its average rate of change between x = 1 to x = 2 must be determined.
At x = 1
Then;
f(x) = 20.(1/4)¹
f(1) = 5
At x = 2
Then;
f(x) = 20.(1/4)²
f(2) = 1.25
Add these to the formula above to get;
A(x) = f(2) - f(1) / 2 - 1
A(x) = - 3.75
Consequently, the average rate of change of a function f(x) between x = 1 and x = 2 is -3.75.
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a rectangle is constructed with its base on the diameter of a semicircle with radius 12 and with its two other vertices on the semicircle. what are the dimensions of the rectangle with maximum area?
As describes in geometry the area of the rectangle = 288cm
what is geometry ?
The area of mathematics known as geometry is concerned with the characteristics of the surrounding space as well as the shapes of individual objects and their spatial relationships.
solution
radius of semicircle = 12
diameter will be = 24 and this is the length of rectangle s given in the question
area of the rectangle = l*b
= 24*12
area of the rectangle = 288cm
Hence the area of the rectangle = 288cm
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a runner is participating in half marathon he has run 12 of the 15 miles course what percent of the course has he run so far?
find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm. what is the maximum volume?
The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.
The maximum volume of right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.
How to find volume of Right Circular Cylinder?
Right cylinders are cylinders with axes that are perpendicular to the bases.
Volume of a Right Circular Cylinder= πr²h
where,
r = radius of the base
h = height of right circular cylinder
Maximum volume of right circular cylinder that can be inscribed in a sphere will be,
[tex]\pi r^{2} h-\frac{\pi }{4} h^{3}\\\\= \frac{4\pi r^{3} }{3\sqrt{3} }[/tex]
given that, radius=70cm=0.0.7 m
so,
[tex]Maximum\ volume=\frac{4\pi r^{3} }{3\sqrt{3} } \\\\= \frac{4\pi (70)^{3} }{3\sqrt{3} }\\\\=2640.4\pi \ m^{3}[/tex]
Using volume of right circular cylinder,
[tex]h=\frac{2r}{\sqrt{3} }\\\\ h = \frac{2(0.07)}{\sqrt{3} }\\\\h= 0.08\ m[/tex]
Hence, The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.
The maximum volume of right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.
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The length of a rectangle is 5 more than twice the width. The perimeter is 130 in. What is the area?
Answer:
900
Step-by-step explanation:
l = 2w + 5
2(2w + 5) + 2w = 130
4w + 10 + 2w = 130
6w + 10 = 130
6w = 120
w = 20
l = 2(20) + 5
l = 40 + 5
l = 45
130 = 2(45) + 2(20)
130 = 90 + 40
130 = 130
A = l × w
A = 45 × 20
A = 900
Could you please give me brainliest for this? Thank you!
the number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals
By using the concept of complex number, it can be calculated that
There is only one complex number which satisfies |z – 1| = |z + 1| = |z – i|
What is a complex number?
Any number of the form a+ib where, a and b are real numbers and i = [tex]\sqrt{-1}[/tex] are called complex number.
Let z = x + iy
[tex]|z - 1|^2 = |z + 1|^2 = |z - i|^2[/tex]
[tex]|x + iy - 1|^2 = |x+iy + 1|^2 = |x+iy - i|^2\\(x-1)^2+y^2 = (x+1)^2+y^2 = x^2+(y -1)^2[/tex]
So the point (x, y) is equidistant from (1, 0), (-1, 0) and (0, 1)
(0, 0) is the only point which is equidistant from (1, 0), (-1, 0) and (0, 1)
z = 0 is the only complex number which satisfies |z – 1| = |z + 1| = |z – i|
There is only one complex number which satisfies |z – 1| = |z + 1| = |z – i|
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number of days absentprobability 00.60 10.20 20.12 30.04 40.04 50.00 what is the standard deviation of the number of days absent?
The standard deviation of the number of days absent is found as 1.1616.
Define the term standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.For the stated question-
Number of Days Absent/Probability
0 - 0.601 - 0.202 - 0.123 - 0.044 - 0.045- 0.00Thus, the mean is found as;
Mean = (0x0.60) + (1x0.20) + (2x0.12) + (3x0.04) + (4x0.04)
Mean = 0.72
Standard deviation σ = (0-0.72)² x 0.60 + (1-0.72)² × 0.20 + (2-0.72)² × 0.12 + (3-0.72)² × 0.04 + (4-0.72)² × 0.04
Standard deviation = 1.1616
Thus, the standard deviation of the number of days absent is found as 1.1616.
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The complete question is-
A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.
Number of Days Absent/Probability
0 0.60
1 0.20
2 0.12
3 0.04
4 0.04
5 0.00
What is the standard deviation of the number of days absent?
PLEASE HELP ASAPPP. WILL GIVE BRAINLIEST AND 5.0 STAR RATING.
Answer:
0.40
Step-by-step explanation:
.04 x 10 = .40
Answer: $0.40
Step-by-step explanation: The sales tax will be 4% of the selling price
The end price will be 10.40
Kelli walks no more than 25 dogs on Mondays. Ms. Lincdan has 5 dogs that Kelli walks. The inequality shown can be
used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs.
x + 5 ≤ 25
Which inequality represents all possible values of x?
A x ≥ 20
B x ≤ 20
C x ≥ 30
D x ≤ 30
X is 19 units to the left of 0. Use the drop-down menus to complete the statement about −X.
Options:
-19
-9
0
9
19
The value of ''- X'' will be;
⇒ - X = 19
What is Number line?
Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
Given that;
X is 19 units to the left of 0.
Now,
Since, X is 19 units to the left of 0.
Hence, The value of X = - 19
So, We get;
The value of - X = - (- 19)
= 19
Thus, The value of ''- X'' will be;
⇒ - X = 19
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A new car is purchased for 22600 dollars. The value of the car depreciates at 11. 5% per year. To the nearest tenth of a year, how long will it be until the value of the car is 5200 dollars?.
When the car is acquired for $22600 and depreciates at an 11.5% rate, it will take 6.7 years for its worth to reach $5200.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Here,
Cost of car=$22600
Rate of depreciation=11.5%
After n years, value of car=$5200
Annual depreciation expense=22600*11.5%
=$2599
Value of the Car = Purchase cost - (Annual depreciation expenses * n)
5200=22600-(2599*n)
2599n=22600-5200
2599n=17400
n=6.695
n=6.7 years
The number of years until the value of the car is 5200 dollars at depreciation rate of 11.5% when purchased at 22600 dollars will be 6.7 years.
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A line join A (3,2) and B (3,-3) on a half centimetre grid. P i a point on the line AB uch that AP:PB =3:2
ue the x tool to plot point P
The co-ordinates of the point P that divides the line segment AB in the ratio 3:2 are (3,0)
What is Line Geometry?
A line is an endlessly long object with no breadth, depth, or curve in geometry. Lines are thus one-dimensional objects, even if they can exist in two, three, or higher dimensions. In ordinary language, the term line can also refer to a line segment with two points denoting its endpoints.
Solution:
To find the co-ordinates of point P we wil use section formula
(x,y) = (m*x2 + n*x1 / m+n), (m*y2 + n*y1 / m+n)
(x,y) = (3*3 + 2*3)/5 , (3*2 + 2*(-3))/5
(x,y) = 15/5 , 0/5
(x,y) = 3,0
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If the function f (x) is the absolute value of 3 more than the value of x. Select all the true statements.
The x-intercept of the function is 3.
The range of the function is (f (x) f(x) E R).
The function is positive in the interval -3 < x < 00.
The function is increasing in the interval -3 < x < [infinity]0.
The function is negative in the interval -[infinity]o < x < -3.
The function is decreasing in the interval -[infinity]o < x < -3
Answer:
The function is positive in the interval -3 < x < ∞.The function is increasing in the interval -3 < x < ∞.The function is decreasing in the interval -∞ < x < -3.Step-by-step explanation:
You want to identify the true statements about the function f(x) = |x+3|.
GraphA graph of the function is attached. It shows the function is decreasing to the left of x = -3, increasing to the right of that point, and has an x-intercept at x = -3. The function is positive everywhere.
The true descriptions are ...
The function is positive in the interval -3 < x < ∞.The function is increasing in the interval -3 < x < ∞.The function is decreasing in the interval -∞ < x < -3.In the league, the Leos play 8 games. Their win to loss ratio is 5:3. The Tigers play 11 games. Their win to loss ratio is 7:4. a) Which team has the better record? Explain.
Answer:
The Tiger has the better record, because the Leo won 5 games out of 8 and the Tiger won 7 games out of 11. When we change both denominator to the same number, the Leo's is 55/88 and the Tiger is 56/88, so the Tiger has the better record
find the f-test statistic to test the claim that the population variances are equal. both distributions are normal. the standard deviation of the first sample is 2.1971 7.32 is the standard deviation of the second sample.
the f-test statistic to test the claim that the population variances are equal is F test = 2.54
We are given two samples
Standard deviation of the first sample = 2.1971
Standard deviation of the second sample = 7.32
F test statistic = Variance of the Larger sample/ Variance of the smaller sample
Variance = (Standard deviation)²
Variance for the first sample = 2.1971²
= 4.8272
Variance for the second sample = 7.32² = 53.5824
F test = 53.5824/4.8272
= 11.100
Therefore, the F test approximately = 11.100
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simplify the expression 8s−11s+6
analyze the solution to the system to determine whether there is a catapult arm length that aiden and natalie can both use to launch their tennis balls the same distance. explain your reasoning.
There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.
From the graph,
x axis represents the arm length of the catapult and the y axis represents the distance.
The point at which the catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance is the intersecting point of the both line
The coordinates of the intersecting point = (-30, 90)
Here arm length represents -30, but the arm length cannot be a negative value
Therefore, there is no arm length that gives equal distance
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Answer:
There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.
Step-by-step explanation:
If you invest $1,500 at 3% annual compound interest for 30 years, how much
interest would you earn? Round your answer to two decimal places.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
sus
if angles of a triangle are congruent then are the sides also congruent
Answer:
yes
Step-by-step explanation:
You want to know if the sides are congruent in a triangle with congruent angles.
Law of sinesThe Law of Sines tells us the sides of a triangle are proportional in length to the sines of the opposite angles.
If the angles are congruent, their sines are equal, and the sides are congruent.
Congruent anglesA triangle with congruent angles has all angles 60°. Such a triangle is called an equilateral triangle. The name "equilateral" refers to the fact that the sides are the same length.
Work out 2.151 x 10²
Answer:
215.1x
Step-by-step explanation:
2.151x(102)
=2.151*x*100
=215.1*x
=215.1x
Answer:
The answer would be 215.1x
Step-by-step explanation:
2.151 x 10^2 = 215.1x
10^2 = 100
Then multiply 100 and 2.151x
100 x 2.151x = 215.1x
question professor liu gave the same quiz to the students in her morning class and in her afternoon class. the average (arithmetic mean) score for the two classes combined was 84. which class had more students?
From the given average the number of students are more in the afternoon quiz as compare to the morning quiz .
As given in the question,
Combined average score of the two classes = 84.
Average score of students in the morning quiz = 80
Let 'x' be the number of students in the morning quiz
80 = ( Sum of all number of students in the morning quiz) / x
⇒ Sum of all number of students in the morning quiz = 80x __(1)
Average score of students in the afternoon quiz = 86
Let 'y' be the number of students in the afternoon quiz
86 = ( Sum of all number of students in the afternoon quiz) / y
⇒ Sum of all number of students in the afternoon quiz = 86y __(2)
Average score of combined classes = ( 80x + 86y ) / (x + y)
⇒ 84 = ( 80x + 86y ) / (x + y)
⇒ 84x + 84y = 80x + 86y
⇒4x = 2y
⇒ y = 2x
Number of students in the afternoon are double the number of students in the morning.
Therefore, from the given averages afternoon class has more number of students than morning class
The complete question is :
Professor Liu gave the same quiz to the students in her morning class and in her afternoon class. The average (arithmetic mean) score for the two classes combined was 84. Which class had more students?(1) The average score for the students in the morning class was 80
(2) the average score for the students in the afternoon class was 86
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17/-2n=-8.5 (with steps please)
ten points labeled a, b, c, d, e, f, g, h, i, j are arranged in a plane in such a way that no three lie on the same straight line. (a) how many straight lines are determined by the ten points?
Total number of straight lines are 45 and it can be found out using combination.
What is combination?
A combination could be a choice of things from a collection that has distinct members, such the order of choice doesn't matter.
Main body:
Total points = 10
we need to find no three lie on the same straight line.
so , to find we can select 2 lines out of 10 and assume packing them together so no 3 points lie on a line .
selection of 2 points out of 10.
C(10,2) = ¹⁰C₂
= 10!/2!8!
= 10*9/2
= 45 lines.
Hence ,Total number of straight lines are 45 .
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recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quart of grape juice, how much grape juice would you need for 15/4 quarts of sparkling water
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
15/8 quart of grape juice is needed for 15/4 quart of sparkling water.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The recipe for sparkling grape juice calls for 1(1/2) quart of sparkling water and 3/4 quart of grape juice,
This means,
1(1/2) quart of sparkling water = 3/4 quart of grape juice
3/2 quart of sparkling water = 3/4 quart of grape juice
Multiply 15/6 on both sides.
15/6 x 3/2 quart of sparkling water = 15/6 x 3/4 quart of grape juice
15/4 quart of sparkling water = 15/8 quart of grape juice
Thus,
15/8 quart of grape juice is needed for 15/4 quart of sparkling water.
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Please help me ASAP!!
Create a graph of this situation.
Show that the equation (y = mx + b) of this graph equals an= -30 + (n - 1)5
The equation (y = mx + b) of this graph is equal to the equation for this arithmetic sequence aₙ = a₁ + (n - 1)d
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.For the 10th term, the equation for the arithmetic sequence is given by;
a₁₀ = a₁ + (n - 1)d
15 = a₁ + (10 - 1)d
15 = a₁ + 9d
For the 14th term, the equation for the arithmetic sequence is given by;
a₁₄ = a₁ + (n - 1)d
35 = a₁ + (14 - 1)d
35 = a₁ + 13d
Next, we would determine the common difference as follows;
a + 9d = 15
a + 13d = 35
-4d = -20
Common difference, d = -20/-4
Common difference, d = 5.
For the first term of this arithmetic sequence, we have;
a + 9d = 15
a + 9(5) = 15
a = 15 - 45
First term, a = -30
Finally, we would write an equation for the nth term of an arithmetic sequence as follows;
aₙ = a₁ + (n - 1)d
aₙ = -30 + (n - 1)5
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Anita started making sugar cookies for her friends at 9:55 A.M. It took her 1 hour and 15 minutes to make the dough and 40 minutes to bake all of the cookies. Then, Anita spent 15 minutes decorating the cookies with icing and sprinkles. What time was it when Anita finished making the cookies?
The time when Anita finished making the cookies is 12.05 pm.
How to calculate the time?From the information illustrated, Anita started making sugar cookies for her friends at 9:55 A.M, it took her 1 hour and 15 minutes to make the dough and 40 minutes to bake all of the cookies and then, Anita spent 15 minutes decorating the cookies with icing and sprinkle.
It should be noted that the time that she finishes will be the addition of the time given. This will be:
9.55 + 1.15 + 40 + 15
= 9.55 + 1.15 + 55
= 9.55 + 2.10
= 12.05
The time is 12.05 pm
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Trey believes there is a correlation between the number of texts sent in class and gpa. he collected data and found that the line of best fit for the data can be modeled by the equation y = 4.0 − 0.5x. identify the slope and the type of association. the slope is −4.0, which indicates a negative correlation. the slope is −0.5, which indicates a negative correlation. the slope is 4.0, which indicates a positive correlation. the slope is 0.5, which indicates a positive correlation.
Answer:
The slope is -0.5, which indicates a negative correlation.
Step-by-step explanation:
y = mx + b
Is a slope-intercept form of the equation.
The y represents the distance of the line from the y-axis. (if u were to graph the problem)
M represents the slope of the line.
An the value of b is equal to y when x = 0
The equation that was given is y = 4.0 - 0.5x, which wasn't written the normal way, like y = mx + b, they just switched the spots from y = mx + b, to y = b + mx.
So the slope is the 0.5. (which is also -0.5)
Trust me, I took a test and it had this answer, and I got it right.
Answer:
B- -0.5
Step-by-step explanation:
-.05 is a negative correlation
Negative Correlation definition- Is a situation or an event where two variables move in the opposite direction
(Plus I also Took the test and got it right)
Could someone help me understand what v is
The value of v in the triangle is 15 degrees.
How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
The exterior angle theorem is used to find the value of v.
Therefore,
31 + 4v + 44 = 9v
31 + 44 = 9v - 4v
75 = 5v
divide both sides by 5
v = 75 / 5
v = 15
Therefore,
v = 15
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Linda was selling tickets for the school play. She sold 10 more adult tickets than children tickets and she sold twice as many senior tickets as children tickets. Find an expression for the total number of tickets sold by Linda.
Answer:X+(X+10)+(2X)
Step-by-step explanation:
Lets say X is the amount of children tickets sold.
So she sold some kid tickets and we get an X
So X
and then she sold ten more than X tickets to adults
So now we have
X+(X+10)
And then she sold twice as many senior tickets than kids tickets
so now we have
X+(X+10)+(2X)
hope that helped at all!
Linda received a $25.00 gift card for a photo center. She used it to buy prints that cost 25 cents each. The remaining balance, B (in dollars), on the card after
buying x prints is given by the following.
B=25.00-0.25x
What is the remaining balance on the card if Linda bought 30 prints?
Answer:$17.50 remaining
Step-by-step explanation: 0.25 x 30 = 7.50
7.50 - 25.00 = $17.50 remaining
Answer:
$17.5
Step-by-step explanation:
B = 25 -0.25(30)
B = 25 - 7.5
B = 25.0 - 7.5
B = $17.5
hana is 4 year older than her brother. 2 years ago, her brother’s age was ¾ of her age. how old will her brother be in 5 years?
hana is 4 year older than her brother. 2 years ago, her brother’s age was ¾ of her age then brother age will be 19 years
The concept of age describes how old a person is at a particular point in time. It is defined as the measure of the time elapsed from date of live birth to a specific point in time, usually the date of collection of the data
Hana is 4 years older then her brother
let x be brother present age
and x+4 be the hana present age
2 year ago
hana was x+2
and brother was x-2
according to the question
x-2= 3/4 * ( x+2)
x= 14
after 5 years he will be 19 years
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