Answer:
Common difference: 30
General term formula: [tex]a_n=30n-9[/tex]
52nd term: 1551
Step-by-step explanation:
Given sequence:
21, 51, 81, 111
Calculate the difference in terms:
[tex]21 \underset{+30}{\longrightarrow} 51 \underset{+30}{\longrightarrow} 81 \underset{+30}{\longrightarrow} 111[/tex]
The sequence is increasing by 30 each time, so as there is a common difference, this is an arithmetic sequence with a common difference of 30.
General form of an arithmetic sequence
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between consecutive termsGiven:
a = 21d = 30Substitute the given values into the formula to find the general term formula:
[tex]\implies a_n=21+(n-1)30[/tex]
[tex]\implies a_n=21+30n-30[/tex]
[tex]\implies a_n=30n-9[/tex]
To find the 52nd term, simply substitute n = 52 into the found general term formula:
[tex]\implies a_{52}=30(52)-9[/tex]
[tex]\implies a_{52}=1560-9[/tex]
[tex]\implies a_{52}=1551[/tex]
Jeremy is reading a 60-page book. He read the first 20 pages in 30 minutes. If Jeremy continues to read a the same rate, how long will it take him to finish the book?
It will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.
What is Ratio and Proportion ?When two numbers can be written as p/q is called a Ratio , and when two ratios are equal they are said to be in proportion .
It is given that
Jeremy is reading a 60-page book.
The time taken to read 20 pages is 30 minutes
Then it can be written as 20:30 = 2:3
The rate of reading is same so To read the rest 40 pages is given by
40:x
40: x = 2:3
40*3/2 = x
x = 60 minutes
Therefore it will take total 90 minutes to finish the book and 60 minutes to read the left 40 pages.
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A football team carried out a report to see the impact of stretching on preventing injury. Of the 45 footballers in the squad 36 stretch regularly. Of those who stretch, 6 got injured last year. There was a total of 10 injured players last year.
The results can be presented in a frequency tree. What fraction of players who don't stretch get injured?
The fraction of players who don't stretch and get injured = 4/9.
The frequency tree is shown in the image attached.
The total number of footballers = 45.
The total number of footballers who stretch = 36.
Therefore, the number of footballers who don't stretch = 45 - 36 = 9.
The total number of injured footballers = 10.
The number of injured footballers from the players who stretch = 6.
Therefore, the number of injured footballers from the footballers who don't stretch = 10 - 6 = 4.
The total number of footballers who don't get injured = 45 - 10 = 35.
The number of footballers who stretch and don't get injured = 36 - 6 = 30.
The number of footballers who don't stretch and don't get injured = 9 - 4 = 5.
Therefore, the frequency tree can be shown in the image attached.
The fraction of players who don't stretch and get injured = 4/9.
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What is the range of the function y=-x² +1?
A) y≤ -1
B) y²-1
C) y≤ 1
D) y≥ 1
Answer:
Option (C)
Step-by-step explanation:
The minimum value of x² is 0, and the maximum value is unbounded, so therefore, the maximum value of -x² is 0, and the minimum value is unbounded.
So, this means that adding 1 to this, the range matches with option C.
PLS HELP ME AND PLEASE GIVE ME THE ANSWER EXPLAINED THANK YOU!!
The coordinates of the vertices of the reflected image are (-3,4) (0,4) (-3, 2) (0,2).
What is reflection?Reflection is a mathematical transformation of a shape by moving the vertices of the shape across a line of reflection.
Analysis:
coordinates of the shape before transformation are: (-3, 0) (0,0) (-3, -2) 0, -2)
Across the line of transformation, the corresponding vertices(old and new) must be equal distance from the line of reflection.
Also for reflection on y-axis only y-coordinates are affected.
so for point(-3, 0) 0 is 1 unit away from y = 1 so the other coordinate 1 unit away from y = 1 is y = 2 making the new point (-3, 2) same as others .
Find the image in the attached file below.
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The fuel for a lawn mower is a mixture of 8 parts petrol to one part oil. How much oil is required to make 1 litre of fuel?
The amount of oil required for 1 liter of fuel is 111.11 mL.
Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.
Given that the fuel is the mixture where 8 parts are petrol and 1 part is oil in the whole part of the fuel.
The total part of the fuel is 8+1=9
the portion of the petrol is = parts of petrol/total parts of the fuel= 8/9
the portion of the oil = parts of oil /total parts of the fuel= 1/9
Now we have to calculate the amount of oil required for 1 liter of fuel.
As discussed before, 1/9 parts of the fuel is oil.
So the amount of oil is= (1/9)*1 liter= (1/9)litre= 1/9* 1000 mL= 111.11 mL
Similarly, we can calculate the amount of petrol which will be
the amount of petrol= (8/9)*1 liter= (8/9) liter= 8/9*1000 mL= 888.88 mL
Therefore the amount of oil required for 1 liter of fuel is 111.11 mL.
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Let
f(x) = (x − 3)−2.
Find all values of c in (1, 4) such that
f(4) − f(1) = f '(c)(4 − 1).
(Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
c =
Based off of this information, what conclusions can be made about the Mean Value Theorem?
This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 4) such that
f '(c) =
f(4) − f(1)
4 − 1
.
This does not contradict the Mean Value Theorem since f is not continuous at x = 3.
This does not contradict the Mean Value Theorem since f is continuous on (1, 4), and there exists a c on (1, 4) such that
f '(c) =
f(4) − f(1)
4 − 1
.
This contradicts the Mean Value Theorem since there exists a c on (1, 4) such that
f '(c) =
f(4) − f(1)
4 − 1
,
but f is not continuous at x = 3.
Nothing can be concluded.
Answer:
3/4 = -3* 2*(c-
I hope it helps!
if it does pls mark me brainliest answer
please help and answer it in a sentence :)
Answer:
x = $1 & y = $2.
Each doughnut cost $1 and hot chocolate cost $2.
Determine the linear function for a graph that is a line with a slope of 1/7
and contains the point
(−4, 1).
The linear equation is y = (1/7)*x + 11/7.
How to get the linear equation?
The general linear equation is:
y = a*x + b
Where a is the slope.
Here we know that a = (1/7), then the line is:
y = (1/7)*x + b
We also know that the line contains the point (-4, 1), this means that when x = -4, we must have y = 1.
Replacing that, we get:
1 = (1/7)*(-4) + b
1 + 4/7 = b
7/7 + 4/7 = b
11/7 = b
So the linear equation is:
y = (1/7)*x + 11/7.
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The equation of the linear function of the line is: y = 1/7x + 11/7.
What is a Linear Function Equation?A linear function equation is modelled as, y = mx + b, where m is the slope and b is the y-intercept.
Slope (m) = 1/7, and the line passes through (-4, 1), therefore, substitute (x, y) = (-4, 1) and m = 1/7 into y = mx + b:
1 = 1/7(-4) + b
1 = -4/7 + b
1 + 4/7 = b
11/7 = b
b = 11/7
Plug in the values of m and b into y = mx + b:
y = 1/7x + 11/7
The equation of the linear function is: y = 1/7x + 11/7
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Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-1, 2]? A. Both functions are increasing, but function f increases at a faster average rate. B. Only function f is increasing, but both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Only function f is increasing, and only function f is negative.
The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.
Given the table
x f(x)
-2 -46
-1 -22
0 -10
1 -4
2 -1
We have to choose which statement describes better about function
Let us assume [tex]f(x)=ab^x+c[/tex]
at x=0, f(0)=-10
So, -10 =a+c
Similarly, by satisfying the above table in the f(x)
[tex]f(x)=\frac{33}{5} (\frac{1}{11})^x-\frac{17}{5}[/tex]
[tex]f'(x) > 0[/tex]
So we can say that f(x) is an increasing function.
[tex]g(x) = - 18 (\frac{1}{3} )^ x + 2[/tex]
[tex]g^ \prime (x) = - 18 (\frac{1}{3} )^ x ln(1/3)[/tex]
ln(1/3) < 0
So, g^ \prime (x) > 0
So, g(x) is an increasing function.
For any x∈f(x) and x∈g(x) [tex]g'(x) > f'(x)[/tex]
So, g increases at a faster average rate
Thus, Both functions are increasing, but function g increases at a faster average rate.
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Consider a political discussion group of 8 democrats, 8 republicans and 6 independent suppose the teo groups meme bet are randomly selected in succession to attend a policial convection find the probability of selecting two demo
Answer:
The probability of selecting two democrats is 1/380
Step-by-step explanation:
Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur.Probability of an event = Number of favourable outcomes / Total number of outcomes.Here we are given the people as,
8 democrats, 8 republicans and 6 independent.
So total number of people are: 8+6+6=20
Probability of choosing first democrat = 1/20
Probability of choosing first democrat = 1/19
Thus P( two democrats in succession ) = 1/20 ×1/19
= 1/380
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The star shape is made from a regular hexagon and six congruent equilateral triangles The area of the star shape is 96cm squared Work out the area of the regular hexagon.
Answer:
48 Square Centimeters
Step-by-step explanation:
The red triangular exterior pieces are all equilateral triangles with some side length.
We don't need to know what that side length is. It doesn't matter.
The area of one red equilateral triangle is some area A.
There are 6 of these red triangles, so the red exterior triangular parts combine to a total area of 6*A.
The hexagon is composed of equilateral triangles as well.
Each of these blue equilateral triangles is congruent to any outer red triangle because the side length is the same.
Therefore, the 6 blue equilateral triangles composing this hexagon combine to get a total area of 6*A
The area of the star overall is 12*A because we have 6 blue triangles combining with the 6 red triangles.
There is a total of 12 triangles.
What is the coefficient of the third term in the binomial expansion of (a b)6? 1 15 20 90
All of the details to the question are in the picture that is attached in this question, please help
Answer: 10
The arc length of the semicircle is
a+(a+1)+(a+2)+(a+3)+(a+4)=5a+10
As x = 42, this means a+4 is 42/180 of the arc length of the circle, 5a+10.
So,
(42/180)(5a+10)=a+4
42(5a+10)=180(a+4) [multiply both sides by 180]
210a+420=180a+720 [distributive property]
30a+420=720 [subtract 180a from both sides]
30a=300 [subtract 420 from both sides]
a=10 [divide both sides by 30]
On a number line, 1.43 would be located ______. Choose all answers that make a true statement.
1.43
《--|----|----|----|----|----|----|----|----|----|--》
A. to the left of 1.41
B. between 1 and 2
C. between 1.42 and 1.44
D. to the right of 1.45
Answer:
B and C
Step-by-step explanation:
Given right triangle QRS, what is the value of sin(30°)?
The value of sin(30°) is 1/2.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations.
The diagram is attached below:
We know,
sin 30= Perpendicular/ Hypotenuse.
As, the hypotenuse is the opposite side of the right angle and the perpendicular is opposite to the given angle.
So,
sin 30 = 5/10
sin 30 = 1/2
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Mike has 21 pounds of tomatoes and 9 pounds of mixed peppers from his garden that he will use to make salsa and tomato sauce. The graph represents the system of equations shown.
A system of equations. x plus 5 y equals 21. x plus y equals 9.
The variable x represents the number of batches of salsa that can be made and y represents the number of batches of tomato sauce that can be made.
Answer:
x= 6 , y = 3
Step-by-step explanation:
x + 5y = 21
i am using trail and error method and i got the answer easily
the logic behind this is simple
the first equation is x + 5y = 21 so we can say that y will be 5 x 1 , 5 x 2 , 5 x 3 , 5 x 4
first i did 5 x 4 = 20
x + 5 x 4 = 21
x= 1 but the equation x + y = 1 + 4 = 5 which is not equal to 9
second i tried with 5 x 3 =15
and the equation will be
x + 5 x 3 = 21
6 + 15 = 21
this time the second equation became true
x + y = 9
6 + 3 = 9
the no of pounds of salsa = 6
no of pounds of tomato = 3
Find the distance between 4.5 and -1.4.?
Answer:
4.5-1.4=3.1
Step-by-step explanation:
Hope this answers your question!
If not, I am sorry.
Please help!!
Construct the circle that circumscribes image DEF.
Answer:
See below
Step-by-step explanation:
General outlineConstruct the perpendicular bisectors of DE, EF, and DF.Identify the circumcenter. Draw the circumcircle.Circles & CircumcirclesTo construct a circle, one must know the center point of the circle, and the circle's radius.
The circle that circumscribes a triangle (called a circumcircle), has a circumcenter (center point) that is the point of concurrency (a point where more than two lines intersect at the same point) of all three perpendicular bisectors (perpendicular lines that happen to cut a given line segment exactly in half) of the sides of the triangle.
Construct the circle with a center at the circumcenter, and a radius out to any one of the vertices of the triangle. The circumcenter is equidistant from all three vertices, so the circle draw will contain all three vertices.
Constructing perpendicular bisectorsTo construct perpendicular a bisector, recall that a perpendicular bisector is a line containing all points that are equidistant the end points of a line segment (each point on the line is the same distance from both segment endpoints simultaneously).
So, if we can find two points that are the equidistant from the two segment endpoints, we'll have two points on the line, and to draw any line, one only needs two distinct points, and the straightedge.
Finding a point that is equidistant from two given points
Set the compass to any radius that is larger than half the distance between the two endpoints. If uncertain of a "good" choice, one can simply choose the length of the line segment itself as a radius.
Setting the center of the compass circle on one endpoint, draw an arc such that the arc will pass through the perpendicular line we're trying to construct twice. If uncertain, draw the entire circle. Keeping the radius saved.
With the same radius, setting the center of the compass circle to the second endpoint, draw and arc such that the arc intersects the first circle two times. If it doesn't intersect two times, the radius chosen at the beginning was too small. Start the entire process over with a larger radius.
These two points of intersection are equidistant from the two endpoints of the line segment, and thus, they are on the perpendicular bisector of the line segment.
Using those two points, and a straightedge, draw the line containing those two points, and extend it generously in both directions.
ProcessSteps 1-5 in pink; steps 6-10 in green; steps 11-15 in blue (see diagram):
Set compass radius to length DEDraw circle, centered at D, through E. Keep radius set.Draw circle, centered at E, through D.Identify points of intersection of the circles from steps 2 & 3, M & NDraw line MNSet compass radius to length EFDraw circle, centered at E, through F. Keep radius set.Draw circle, centered at F, through E.Identify points of intersection of the circles from steps 7 & 8, Q & RDraw line QRSet compass radius to length DFDraw circle, centered at D, through F. Keep radius set.Draw circle, centered at F, through D.Identify points of intersection of the circles from steps 12 & 13, S & TDraw line STIdentify point of concurrency of line MN, line QR, and line ST; label it point PSet compass radius to length DP (or EP, or FP)Draw circle, centered at P, through points D, E, and F.Note: Since all three perpendicular bisectors intersect at the same point, it is only necessary to find two of three, not all three. So, one could skip constructing one of those three perpendicular bisectors (either steps 1-5, 6-10, or 11-15), and still be able to construct the circumcircle correctly.
How many grains of Fermiun will remain after 15 days? 50 25 12.5 6.25
Answer:
0.00305 (rounded)
Step-by-step explanation:
this is a geometric sequence so the formula is
an=a×r×n-1
PLEASE HELP I WILL GIVE 20 POINTS
Function g can be thought of as translated (shifted) version of f(x)=x^2
What is the value of x?
to
x = [? ]°
36°
Enter
I will give you points
Answer:
54 degrees!
Step-by-step explanation:
its a right triangle so we know 2 out of the 3 angles
so 36 + 90 = 126
180 - 126 = 54!
hope this helps :)
Which expression for YYY correctly outputs that x is between 50-100? if (YYY) { // Output "50, 51, ..., 99, 100" } Group of answer choices (x >= 50) || (x <= 100) 50 <= x <= 100 50 >= x <= 100 (x >= 50) && (x <= 100)
The expression for YYY is (d) (x >= 50) && (x <= 100)
How to determine the correct expression?The instruction is given as:
If (YYY) {
// Output "50, 51, ..., 99, 100"
}
The value of x is given as:
x = 50 to 100 (inclusive)
This means that:
x must be greater than or equal to 50 AND x cannot exceed 100
The keyword AND is represented as &&.
So, the condition is:
x >= 50 && x <= 100
Hence, the expression for YYY is (d) (x >= 50) && (x <= 100)
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if pound of cheese costs $3.43, what is the cost per pound?
PLS HELP
Answer:
can you rephrase it? how many pounds are there?
Step-by-step explanation:
Sequence: 1,5,13,25
Find nth term (Equation/formula thingy)
Need answer ASAP
Answer:
Formula for a linear sequence is
Tn=a+(n-1)d
where Tn is the nth term
a is the first term
n is the number of term
d is common difference
Select the correct answer. A linear function on a coordinate plane passes through (minus 3, 2), (0, 4), and (3, 6) Which equation describes the line graphed above? A. B. C. D.
Answer:
I don't see the equation options. See below for a predicted equation.
y= (2/3)x + 4
Step-by-step explanation:
The points are (-3,2), (0,4), and (3,6). I will assume they lie in a straight line.
Find an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
m, the slope, is also known as the "Rise/Run."
Pick any two points. I'll use (0,4) and 3,6)
Rise = (6-4) = 2
Run = (3-0) = 3
Slope = 2/3
The equation becomes y = (2/3)x + b
B is easy in this case. Point (0,4) tells us that y = 4 when x = 0 (the definition of b).
The equation is y= (2/3)x + 4
See the attached graph.
Help me show your work
The value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
The value of x that will satisfy this condition can be found by simplifying the given inequality. Therefore, The given inequality can be simplified as,
4x + 1 - 1 ≥ -8
4x ≥ -8
x ≥ -2
Hence, the value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.
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write 9 430 049 in international number system
Step-by-step explanation:
9, 430, 049 = 9 million four hundred thirty thousand and fourtynine....
[tex]...[/tex] :)..
a man is 18 years older than his son. 3 years ago he was 4 times as old as his son how old is the man now
Answer:
The man is 27 years old.
Step-by-step explanation:
You can create a system of equations.
Let x = the age of the man
Let y = the age of his son
You can create the following equations based on what was given in the problem:
1. x = y + 18
2. (x - 3) = 4(y - 3)
You can simplify the second equation:
x - 3 = 4y - 12
x = 4y - 9
Then, solve the system of equations:
x = y + 18
-
x = 4y - 9
____________
0 = -3x + 27
The son's age is 9, therefore the father is 27 years old.
Find the perimeter of the triangle.
23.
7 in.
(x + 4) in.
(4x + 1) in.
Answer:
17 in.
Step-by-step explanation:
There are two same angles shown, so two sides are equal. We can form an equation x+4=4x+1. Solution is x=1, then both unknown sides are 5 in. long. Given all side lengths we add them 7+5+5+15 getting the perimeter.
hey god its me again
The statement D is false that No irrational number is rational.
What are real numbers?The set of real numbers includes integers, rational numbers, and irrational numbers.
This implies that all irrational numbers and integers are also real numbers.
Thus, statements A and B are correct.
Rational numbers are numbers that can be written as the division of two integers, which thus also include all integers.
The set of irrational numbers then contains all real numbers that are NOT rational numbers
Therefore, the set of irrational numbers does not include integers, which implies that statement D is false.
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