Answer:
The 27th term is 73.5.
Step-by-step explanation:
We want to find the 27th term of the arithmetic sequence:
15, 17.25, 19.5, 21.75, ...
We can write a direct formula. Recall that the direct formula for an arithmetic sequence is given by:
[tex]x_n=a+d(n-1)[/tex]
Where a is the initial term and d is the common difference.
From the sequence, we can see that our initial term a is 15.
To find the common difference, subtract a term and its previous term. Thus, the common difference will be:
[tex]d=17.25 - 15 = 2.25[/tex]
Thus, our direct formula is:
[tex]x_n=15+2.25(n-1)[/tex]
To find the 27th term, let n = 27. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} x_{27} &=15+2.25((27)-1) \\ &= 15+2.25(26) \\&= 15+58.5 \\ &= 73.5\end{aligned}[/tex]
Thus, the 27th term is 73.5.
What is the scale factor of this dilation?
A 2/3
B 1 1/2
C 3
D 5
Answer:
B. 1 1/2
Step-by-step explanation:
The post-image is clearly larger than the pre-image. The ratio of the post to the pre is 9 : 6 and 10 : 15, which are equal to 3 : 2, and equal to 1 1/2.
Margaret bought a video game, her father gave her 0.2 of the money, her aunt gave 0.5 of the money and she saved the rest. She saved $168 so what amt of money did her father give
Answer:
if Im correct it should be $8.40
Step-by-step explanation:
why well if you think of breaking down by say 1/4 of 168 all you do is divide 4 which is the whole amount by 0.2 which is the amount the father gave her so 4/0.2= 20 the you take your whole 168 and divide by 20 which the whole number for 0.2 the your answer should be this 168/20= 8.4 which then i assumed it was $8.40 hopefully that is correct hehe
Identify the vertex of this absolute value function: f(x) = -2|x + 1| + 2. Type the correct answer in each box. Use numerals instead of words.
Answer:
Step-by-step explanation:
x+1=0
then f(x)=2
x=-1
vertex is (-1,2)
Answer:
-1,2
Step-by-step explanation:
Plato
Surveys were sent to a random sample of owners of all-wheel-drive (AWD) vehicles and to a random sample of owners of front-wheel-drive (FWD) vehicles. The proportion of owners who were satisfied with their vehicles was recorded for each sample. The sample proportions were used to construct the 95 percent confidence interval for a difference in population proportions (FWD minus AWD) for satisfied owners. The interval is given as (−0.01,0.12). A car company believes that the proportion of satisfied owners of AWD vehicles differs from the proportion of satisfied owners of FWD vehicles. Does the confidence interval provide evidence that this belief is plausible?
Answer:
No, the confidence interval does not provide evidence that this belief is plausible as the confidence interval range contains the null value (0)
Step-by-step explanation:
Given that the confidence interval for the mean difference of AWD and FWD vehicles is :
(−0.01,0.12)
When defining the hypothesis for mean difference :
H0 : μ1 - μ2 = 0
H1 : μ1 - μ2 ≠ 0
Using the confidence interval result, reject the Null if the confidence interval value at the given α - level does not contain 0 ; otherwise fail to reject the Null ;
Since the (−0.01,0.12) contains 0 ; then we fail to reject the Null and conclude that there is no statistically significant difference between the two groups
tìm tất cả giá trị thực của tham số m để đồ thị hàm số y=x³-mx²+4 cắt trục hoành tại ba điểm phân biệt
Answer:
실례합니다?
Step-by-step explanation:
질문이 뭔가요??? 이해가 안가요? 어느 언어?
a local community college has 860 students. Of these 860 students, 220 ride bicycles. Write the number of bike riders as a fraction of the number of students at the college in simplest form
Answer:
11/43
Step-by-step explanation:
A local community college has 860 students
Out of this 860 students, 220students ride bikes
Therefore the fraction of bike riders to the number of students can be calculated as follows
= 220/860
= 11/43
I AM GIVING BRAINLISEST AND 20 POINTS! Write the equation of the circle in standard form.
Answer:
[tex](x-4)^2+(y)^2=9[/tex]
Step-by-step explanation:
The general format for the equation of a circle is the following:
[tex](x-n)^2+(y-m)^2=a[/tex]
This circle will have a radius of ([tex]\sqrt{a}[/tex]), moreover, this circle will have its center at point [tex](n,m)[/tex]. Please note that its center is shifted (n) units to the right of the origin, and (m) units up. Apply this knowledge to the given problem.
The circle in the given problem has its center at (4, 0). Therefore the following can be stated,
[tex]n=4\\\\m =0[/tex]
Since one knows the center of the circle is at (4, 0), and (the circle has (4, 3) on its circumference, the distance between the coordinates will produce the radius of the circle. The following formula can be used to find the distance between two points on a number line,
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Where ([tex](x_1,y_1)[/tex]) and ([tex](x_2,y_2)[/tex]) are the points one is trying to find the distance between. Substitute the given points into the formula and solve for the distance between them.
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
[tex]D=\sqrt{(4-4)^2+(3-0)^2}[/tex]
Simplify,
[tex]D=\sqrt{(4-4)^2+(3-0)^2}[/tex]
[tex]D=\sqrt{(0)^2+(3)^2}[/tex]
[tex]D=\sqrt{0+9}[/tex]
[tex]D=\sqrt{9}[/tex]
[tex]D=3[/tex]
The parameter (a) is equal to ([tex]D^2[/tex]) are per the format of the equation, thus one must do the following to find the value of (a):
[tex]a = D^2[/tex]
[tex]a=3^3[/tex]
[tex]a = 9[/tex]
Substitute all of the information into the general formula for the equation of a circle, then simplify,
[tex](x-n)^2+(y-m)^2=a[/tex]
[tex](x-4)^2+(y-0)^2=9[/tex]
[tex](x-4)^2+(y)^2=9[/tex]
please help me
solve (x+3) (x+7)
Step-by-step explanation:
Here, we'll need to multiply these two values together. I'll use the expansion formula, which goes as follows:
[tex](a+b)(c+d)[/tex]
Expand[tex]ac + ad + bc + bd[/tex]
Lets apply this to the following equation:
[tex](x+3) (x+7)[/tex]
Expand.[tex](x*x) + (x * 7) + (3 * x) + (3 * 7)[/tex]
Simplify.[tex](x^2) + (7x) + (3x) + (21)[/tex]
Remove parenthesis and add.[tex]x^2+10x+21[/tex]
Answer:
x^2+10x+21
Nishi invests £3500 at 4% interest per year. Work out how much she will have altogether after: 2 years
Answer:
£3780
Step-by-step explanation:
P= £3500, R=4%, t=2years
I = PRT/100
I= (3500×4×2)/100 =£280
Amount in 2years = P+I = £3500+ £280= £3780
When a certain number is divided by 48,72 or 100 the remainder in each case is 3.... Find the number
Answer:
The number is 4875
Step-by-step explanation:
What is the answer to the question 3x+5x
Answer:
8x
Step-by-step explanation:
=3x+5x
=8x
find the measure of one exterior angle for the following regular polygon
Answer:
36 degrees
Step-by-step explanation:
10 corners/sides.
the sum of all exterior angles in a polygon is always 360 degrees.
so, one exterior angle here is 360/10 = 36 degrees
(-1,6),(3,-4) find the slope and y intercept.
Answer:
Y =-2.5X +3.5
Step-by-step explanation:
x1 y1 x2 y2
-1 6 3 -4
(Y2-Y1) (-4)-(6)= -10 ΔY -10
(X2-X1) (3)-(-1)= 4 ΔX 4
slope= -2 1/2
B= 3 1/2
Y =-2.5X +3.5
5/√2+9/√8-2√50+√32 rationalise the denominator and simplify
The simplification of the expression is [tex]\frac{15\sqrt{2} }{4}[/tex]
How to rationalize the denominatorFirst, find the factors of the number that ahs square root
Given,
= [tex]\frac{5}{\sqrt{2} } + \frac{9}{\sqrt{6} } - \frac{2}{\sqrt{50} } + \sqrt{32}[/tex]
Multiply the numerators by the surd of the denominators
= [tex]\frac{5 *\sqrt{2} }{\sqrt{2}*\sqrt{2 } } + \frac{9 *\sqrt{8} }{\sqrt{8}* \sqrt{8} } - \frac{2 *\sqrt{50} }{\sqrt{50 * \sqrt{50} } } + \sqrt{32}[/tex]
Multiply through and find their square root
= [tex]\frac{5\sqrt{2} }{2} + \frac{18\sqrt{2} }{8 } - \frac{10\sqrt{2} }{50} + 16\sqrt{2}[/tex]
To simply, we have
= [tex]\frac{5\sqrt{2} }{2}+ \frac{9\sqrt{2} }{4} + \frac{1\sqrt{2} }{5} + 16\sqrt{2}[/tex]
Find the LCM
= [tex]\frac{10\sqrt{2} + 45\sqrt{2}+ 4\sqrt{2} + 16\sqrt{2} }{20}[/tex]
Add through
= [tex]\frac{75\sqrt{2} }{20}[/tex]
= [tex]\frac{15\sqrt{2} }{4}[/tex]
Thus, the simplification of the expression is [tex]\frac{15\sqrt{2} }{4}[/tex]
Learn more about surds here:
https://brainly.in/question/4594146
#SPJ1
find the value of the trigonometric ratio. make sure to simplify if its needed.
Answer:
12/5
Step-by-step explanation:
Tan Z
= opposite/adjacent
= 24/10
= 12/5
Answered by GAUTHMATH
Factor 4n4 + n3. find the factor
Answer:
n^3( 4n+1)
Step-by-step explanation:
4n^4 + n^3
2*2*n^3*n + 1*n^3
Factor out the common terms
n^3( 4n+1)
Which equation can be used to solve the problem?
495 is 55 percent of what number?
Answer:
55/100 * x = 495
Step-by-step explanation:
The unknown number is x.
55% of x = 495
55/100 * x = 495
I just really need to finish this math stuff so plz help
Answer:
wx/5
Step-by-step explanation:
Divide the denominator and the numerator by 7y.
Answer:
wx / 5
Step-by-step explanation:
here..
7wxy / 35y
7/35 is 1/5
and wxy /y is wx as we can cancel out y
thus..
7wxy/35y = wx/5
Which of the following best describe(s) the slope of a linear function?
Select all that apply.
rise over run
run over rise
average rate of change
intersection with the y-axis
CKPenny is selling 50 coats. Each coat with a hood have 5 buttons and each coat without a hood have 10 buttons. If there are 400 buttons among all the coats, how many coats don't have hoods?
Answer:
40 coats don't have hoods
Find the surface area of the composite solid.
A.
502 m2
B.
574 m2
C.
646 m2
D.
720 m2
Answer:
A is the answer I pretty sure
Answer:
i think the answer is 502 m2
Simplify this expression.
I need u again pls
Answer:
The answer is the Second Option
Step-by-step explanation:
Answer:
the second one sqrt(10) + sqrt(15) -sqrt(14) - sqrt(21)
Step-by-step explanation:
Please help me with this problem.
Answer:
Step-by-step explanation:
Remark
The cos(60) = 1/2
The radii marked 6 is the adjacent side. You have to solve for the hypotenuse.
Why?
Because the hypotenuse is the distance from the center of the circle to the point of intersection of the angle. Once you have the hypotenuse, you can find the length of the tangent, which will lead to the area of the kite. Then take away 1/3 the area of the circle.
Hypotenuse
Cos(60) = 1/2
cos(60) = adjacent / hypotenuse Multiply both sides by the hypotenuse
hypotenuse * cos(60) = adjacent Divide by Cos(60)
hypotenuse = adjacent / cos(60)
adjacent = 6
hypotenuse = 6/0.5
hypotenuse = 12
Tangent
tangent^2 = 12^2 - 6^2
tangent^2 = 144 - 36
tangent^2 = 108
tangent = sqrt(108)
tangent = 6sqrt(3)
Triangles
The area of the triangle = 1/2 6sqrt(3) * 6
The area of the triangle = 18 sqrt(3)
There are two triangles so the area = 36 sqrt(3) That's the area of the kite.
Circle sector.
Area of the circle sector = 1/3 * pi * r^2
r = 6
Leave pi as it is.
Area of the circle sector = 1/3 * pi * 6^2
area of the circle sector = 12 pi
Answer
Area of the red part = area of the triangles - the area of circle sector
Area of the red part = 36*sqrt(3) - 12* pi
What is the number when 4is subtracted from the Sum of 4 and 7 multiplied by one-fourth of 20?
Answer:
one fourth of 20 = 5
(4+7)-4*5
11-4*5
11-20
-9
please answer this!!
Answer:
16
Step-by-step explanation:
if angle c is 45 then angle A is 45 also
Hence AB is equal to BC
8
20
х
18
Solve for x.
O A) 40
B) 38
C) 45
D) 46
Answer:
its A
Step-by-step explanation:
a car can complete journey of 300 km with the average speed of 60 km per hour how long does it take to complete the journey what is the speed of the car if it covers only 200 km in the same interval of the time
please I need help urgent
Answer:
a. 5 hours
b. 40 kph
Step-by-step explanation:
300 km ÷ 60 km = 5 hours
200 km ÷ 5 hours = 40 kilometers per hour
Write an inequality to describe the region represented on the number line.
H
-4 -3 -2 - 1 0 1 2 3 4
O x>-3
O x>-3.5
O x<-3
O x<-3.5
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the required number line is not included in the question.
A general explanation is as follows:
An open circle means > or <
A closed circle means >= or <=
Take, for instance, the attached number line:
The open dot on -3 means >-3 or <-3
The arrow points to the right direction, means >-3 i.e. greater than -3
Hence, the inequality is:
[tex]x > -3[/tex]
You and six friends play on a basketball team. A sponsor paid $100 for the league fee, x dollars for each player’s T-shirt, and $68.25 for trophies. Write an expression for the total amount paid by the sponsor
Answer:
Total amount paid by the sponsor = 175 + 6d
Step-by-step explanation:
You and 5 friends = 6 people
Cost of renting a bus = $75
Team entry fee = $100
Cost of each student t shirts = $d
Cost of 6 student t shirts = $d × 6= $6d
Write an expression for the total amount the sponsor paid.
Total amount paid by the sponsor = Cost of renting a bus + Team entry fee + Cost of 6 student t shirts
= $75 + $100 + $6d
= $175 + $6d
Total amount paid by the sponsor = 175 + 6d
Where,
d = cost of each student t shirts
A motorboat travels 81 miles in 3 hours going upstream. It travels 135 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Answer:
27, 18
Step-by-step explanation:
Here's why
