Answer:
9 terms
Step-by-step explanation:
Given:
1, 8, 28, 56, ..., 1
Required
Determine the number of sequence
To determine the number of sequence, we need to understand how the sequence are generated
The sequence are generated using
[tex]\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]
Where n = 8 and r = 0,1....8
When r = 0
[tex]\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1[/tex]
When r = 1
[tex]\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8[/tex]
When r = 2
[tex]\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8[/tex]
When r = 3
[tex]\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56[/tex]
When r = 4
[tex]\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70[/tex]
When r = 5
[tex]\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56[/tex]
When r = 6
[tex]\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28[/tex]
When r = 7
[tex]\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8[/tex]
When r = 8
[tex]\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1[/tex]
The full sequence is: 1,8,28,56,70,56,28,8,1
And the number of terms is 9
The area of a circle is increasing at a rate of 0.4 cm square per second. What is the rate of change of the circumference of the circle when its radius is 5cm?
Answer: 4π cm^2/minute
Step-by-step explanation:
Rate of change :
Change with respect to time (dr/dt)
dr/dt = 0.4cm^2/s
r = 5cm
The rate of change when the Radius is 5cm
Area / Circumference of a circle (A) = πr^2
From chain rule of differentiation:
dA/dt = (dr/dt) * (dA/dr)
If A = πr^2
dA/dr = 2πr
dA/dr = 2π * 5 = 10π
However,
dA/dt = (dr/dt) * (dA/dr)
dA/dt = (0.4) * (10π)
dA/dt = 4π cm^2/minute
Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
-
1
5.75 cm
1
1
The area of the shape is __
square centimeters.
Answer:
shape AREA= 35cm^2
Step-by-step explanation:
you should know that this shape is a combination of triangle and trapezoid. therefore you have to find the area of each shape and add them.
A=h/2(b1 + b2) for trapezoid
A=2/2((4+4)+4)
A=1*12
A=12cm^2
A=bh/2. for TRIANGLE
A=1/2((4+4)*5.75)
A=1/2(46)
A=23cm^2
shape AREA= triangle AREA + trapezoid AREA
shape AREA=12cm^2 + 23cm^2
shape AREA= 35cm^2
Jim and Krutika win some money and share it in the ratio 2:3. Jim gets £10. How much did Krutika get?
Answer:
£15
Step-by-step explanation:
The 2 part of the ratio represents the £10 that Jim gets.
Divide the amount by 2 to find the value of one part of the ratio.
£10 ÷ 2 = £5 ← value of 1 part of the ratio, thus
3 parts = 3 × £5 = £15 ← amount Krutika gets
if you horizontally strech the quadratic parent function, f(x)=x^2, by a factor of 4, what is the equation of the new function?
Answer:
g(x) = x^2/16
Step-by-step explanation:
To stretch a function horizontally by a factor of k, replace x with x/k.
You want a stretch factor of 4, so your function is ...
g(x) = f(x/4) = (x/4)^2
g(x) = x^2/16
__
The attached graph shows the horizontal stretch.
pls help me with this question
Answer:
32 cm
Step-by-step explanation:
The volume of the container is:
V= area of the base * the heigth
Since the container has a rectangular base the area of it is:
A = length * width
Let L be the missing length
A = L * 10
V = 10* 25 * L
The container can hold 8 Liters when it's completely full to its brim.
8 liters is 8000 cm^3 ( multiply by 1000)
8000 = 10*25*L
8000 = 250 *L
L = 8000/250
L = 32 cm
v=8litres which is 8 × 1000
l=?
b=10
h=25
since, v=lbh (volume of cuboid)
8000=l × 10 × 25
l=8000/250
l=32
therefore the length is 32cm
Does this graph represent a function? Why or why not?
Answer:
Yes
Step-by-step explanation:
This graph represents a continuous function. That means that the line can be drawn without lifting your pen/pencil from the graph. You can tell that it is a function by doing the vertical line test. Since there is only one output for every input on the graph, it would be a function.
(Thanks to the users who caught my previous error :)
Can someone help me solve this :): ?
( brainliest to the correct answer/explanation)
Answer:
1and1/2yrs ago
Step-by-step explanation:
price dis year= 56545
reduction per year= 11309
...number of years ago = 73810-56545=17265
and is about 20% of annual deductions
so if 56545 +20% + 1/2 20% = 1nd1/2 yrs
What else would need to be congruent to show that ABC= ADEF by SAS?
A. ZCE ZF
B. BC = EF
O C. ZA= ZD
D. AC = DF
Answer:
The correct option is;
c. ∠A ≅ ∠D
Step-by-step explanation:
The given information are;
[tex]\overline{AB}\cong \overline{DE}[/tex]
[tex]\overline{AC}\cong \overline{DF}[/tex]
Therefore, for Side Angle Side, SAS, condition of congruency, we have;
The included angle should be congruent that is ∠C ≅ ∠D
Two triangles, triangle ABC and triangle XYZ for example, having two adjacent sides, AB and AC in triangle ABC and XY and XZ in triangle XYZ of corresponding length such that AB ≅ XY and AC ≅ XZ and also having congruent included angles between the two sides (∠A ≅ ∠X), the two triangles are said to be congruent.
For triangles ABC and DEF to be considered congruent triangles, the additional information that is needed to be congruent is: C. ∠A ≅ ∠D
What is the SAS Congruence Theorem?SAS means, side-angle-side congruence theorem, which states that two triangles are congruent if they have two pairs of congruent sides and a pair of congruent angles that are included angles (in between the two congruent sides).
Therefore, for triangles ABC and DEF to be considered congruent triangles, the additional information that is needed to be congruent is: C. ∠A ≅ ∠D
Learn more about SAS congruence theorem on:
https://brainly.com/question/14252518
how to do this question plz answer me step by step plzz plz
Answer: 4cm
Step-by-step explanation:
Ok so no matter the orientation of the carton, it will contain the same volume of milk. We can use the fact it's volume of milk will stay constant to find out it's new depth.
Before being turned over the milk volume is:
5 * 8 * 12 = 480. This is because the volume of a cuboid is length * width * height (depth).
Therefore the volume of the milk once turned over is 480
When on it's side, the volume of the milk equals
8 * 15 (the base) * depth
120 * depth
120 * depth = 480
so the depth = 4cm
If k is a negative even integer that is greater than -7.86 what is the least possible value of k step by step explanation
Answer: The least possible value of k is -6.
Step-by-step explanation:
Let 'k' be the negative even integer that is greater than -7.86 .
On number line, -7.86 lies between -7 and -8 such that
-7 > -7.86 > -8
So, -7 is the least integer that is greater than -7.86.
Since, -6 > -7 . That means -6 is the least negative even integer that is greater than -7.86 .
Hence, the least possible value of k is -6.
Social Networking Sites
In a survey of 2255 randomly selected US adults (age 18 or older), 1787 of them use the Internet regularly. Of the Internet users, 1054 use a social networking site.7 Find and interpret a 95% confidence interval for each of the following proportions:________
(a) Proportion of US adults who use the Internet regularly.
(b) Proportion of US adult Internet users who use a social networking site.
(c) Proportion of all US adults who use a social networking site. Use the confidence interval to estimate whether it is plausible that 50% of all US adults use a social networking site.
Answer:
(a). ( 0.776 ,0.809).
(b). (0.567 , 0.613).
(c). 0.600.
Step-by-step explanation:
Okay, we are given the following set of values or data or parameters;
=> "A survey of 2255 randomly selected US adults (age 18 or older)"
=> "1787 of them use the Internet regularly. Of the Internet users, 1054 use a social networking site".
=> Also, "95% confidence interval for each of the following proportions"
Therefore, we are going to make use of one (major ) mathematical formula in solving this particular Question and it is given below;
Confidence Interval = p +/- z* × [ √p( 1 - p) / n].
(a).
Where p = 1787/2255 = 0.793.
95% confidence Interval = z* = 1.96.
= 0.793 +/- 1.96 × [√0.793 ( 1 - 0.793)/ 2255] .
= 0.793 +/- 0.0167.
= ( 0.776 ,0.809).
(b). Where p = 1054/ 1787 = 0.5900
95% confidence Interval = z* = 1.96.
= 0.5900 +/- 1.96 × [√0.5900 ( 1 - 0.5900)/ 1787]
= 0.5900 +/- 0.0228.
= (0.567 , 0.613).
(c). 1054/1787 = 0.59 = 0.600.
Answer:
your answer is the third one
Step-by-step explanation:
Check all that apply. If tan theta = 15/8 then:
Answer:
B, C, D
Step-by-step explanation:
if tan theta = 15/8 then the hypotenuse is 17
therefore the correct answers are B, C, D
calculate EG if a=5 and b=15
PLEASE HELP IMMEDIATELY!!!! Find x when – Negative one-half + x = –Negative StartFraction 21 over 4 EndFraction. – Negative StartFraction 23 over 4 EndFraction – Negative StartFraction 19 over 4 EndFraction 19/4 23/4
Answer:
-61/4
Step-by-step explanation:
-1/2 + x = - 21/4 - 23/4 - 19/4
-1/2 + x = -(21+23+19)/4
x = -63/4 + 1/2
x= -63/4 + 2/4
x = -61/4
Hope that helps, tell me if you need further explanation. =)
Answer:
B. -19/4
Step-by-step explanation:
-1/2 + x = -21/4
x = -21/4 + 2/4
x = -19/4
Answer: B. -19/4
Select the correct answer.
What is the justification for step 2 in the solution process?
10x − 25 − 3x = 4x − 1
Step 1: 7x − 25 = 4x − 1
Step 2: 7x = 4x + 24
A.
the multiplication property of equality
B.
the division property of equality
C.
the addition property of equality
D.
the subtraction property of equality
Answer:
The answer is C addition property of equality.
Step-by-step explanation:
In step 1, 7x − 25 = 4x − 1 there are the numbers -25 and -1
In step 2, 7x = 4x + 24 The -25 is removed and -1 is replaced with 24
Meaning that in step 2 25 was added to those numbers meaning the answer C addition property of equality.
Answer:
C
Step-by-step explanation:
Answer this in two minutes
Answer:
900
Step-by-step explanation:
a heptagon has 7 sides, so we take the hexagon's sum of interior angles an and add 180 to it's getting us, 720 + 180 = 900 degrees
Convert the following to Slope-Intercept Form: 4x – 3y = 24.
The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
4x – 3y = 24
Convert the equation from standard form to slope-intercept form. Then we have
4x – 3y = 24
3y = 4x - 24
y = (4/3)x - 24 / 3
y = (4/3)x - 8
The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
Which is not a property of a parallelogram? a: Diagonals are perpendicular. b: Opposite sides are congruent. c: Opposite angles are congruent. d: Opposite sides are parallel.
Answer:
A
Step-by-step explanation:
Diagonals are perpendicular.
This means that there have to be 90 degree angles in the parallelogram which is not true at all. They can be slanted as well!
Hope this helped :) good luck!
simplify
[tex](xy) ^{ - 1} [/tex]
Answer:
Below
Step-by-step explanation:
●(xy)^(-1)
● x^(-1) * y^(-1)
● (1/x)*(1/y)
● 1/xy
Calculate the perimeter of this trapezoid
Answer:
31 cm
Step-by-step explanation:
The perimeter is the sum of the sides so the answer is 8 + 10.5 + 9 + 3.5 = 31 cm.
HELPPPP I need help finding x a and b pleaseeee
Answer:
5x-18 this angle is equal to 92
3x+22 this angle is equal to 88
angle a=88
angle b=92
Step-by-step explanation:
set 5x-18 and 3x+22 equal to 180 and solve to get x=22. Now look for ways to fill in a and b. A is an alternate interior angle that will be equal to 3x+22
angle b will be equal to the angle 5x-18
Answer:
The value of x is22°, a is 88° and b is 92°.
Hope it helps..
plz plz, answer it hurry.
Answer:
c
Step-by-step explanation:
Answer:
I think it's b.
Step-by-step explanation:
Let's just say that in the first square, all sides equal 4. In this square, if you cut out a piece the perimeter will stay the same. Let's check:
First square: 4+4+4+4=16
Second square: 3+4+4+2+1+2=16
So yes, it's b.
Which value of m will create a system of parallel lines with no solution? y=mx-6 8x-4y=12 A coordinate grid with one line labeled 8 x minus 4 y equals 12. The line passes through a point at (0, negative 3), (1, negative 1) and a point at (1.5, 0). -2 - 2
Answer:
A system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2
Step-by-step explanation:
The equation of the given line is 8·x - 4·y = 12
Which gives;
8·x- 12= 4·y
y = 2·x - 3
Given that the line passes through the points (0, -3) and (1, -1), we have;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
When (x₁, y₁) = (0. -3) and (x₂, y₂) = (1, -1), we have;
[tex]Slope, \, m =\dfrac{(-1)-(-3)}{1-(0)} = 2[/tex]
y - (-3) = 2×(x - 0)
y = 2·x - 3 which is the equation of the given line
For the lines 8·x - 4·y = 12, which is the sane as y = 2·x - 3 and the line y = m·x - 6 to have no solution, the slope of the two lines should be equal that is m = 2
Given that the line passes through the point (1.5, 0), we have;
y - 0 = 2×(x - 1.5)
y = 2·x - 3...................(1)
For the equation, y = m·x - 6, when m = 2, we have;
y = 2·x - 6..................(2)
Solving equations (1) and (2) gives;
2·x - 3 = 2·x - 6, which gives;
2·x - 2·x= - 3 - 6
0 = 9
Therefore, a system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2.
Answer:
short answer is 2 or d
Step-by-step explanation:
Help urgently please❤️
Answer:
1. 677 inches = 18.056 yards
677 inches = 56.416 feet
677 inches = 677 inches
2. QP = 23.5 cm
3. The perimeter = 53.5 cm
Step-by-step explanation:
1. To convert, 677 inches to yards, we have;
1 inch = 0.0277778 yards
677 inches = 677*0.0277778 = 18.056 yards
To convert, 677 inches to feet, we have;
1 inch = 0.083333 feet
677 inches = 677*0.083333 = 56.416 feet
To convert, 677 inches to inches, we have;
1 inch = 1 inch
677 inches = 677*1 = 677 inches
2. We have that ∠PRQ and ∠PRS are supplementary angles (angles on a straight line
Given that ∠PRS = 90°, ∠PRQ = 180° - 90° = 90°;
∠PRQ + ∠PQR + ∠RPQ = 180°, sum of angles in a triangle
∠PQR = 24° given
∠PRQ = 90°
∴ ∠RPQ = 180° - 90° - 24° = 66°
∴∠SPQ = ∠SPR + ∠RPQ = 36° + 66° = 102°
∠QSP + ∠SPQ + ∠PQS = 180° (sum of angles in a triangle)
∠QSP = 180° -∠SPQ - ∠PQS = 180° -102° - 24 = 54°
By sine rule, we have;
a/(sin(A)) = b/(sin(B))
Therefore, we have;
11.8/(sin(24)) = QP/(sin(54°))
QP = (11.8/(sin(24))) × (sin(54°)) = 23.5 cm
3. From trigonometric ratios, we have;
tan(43°) = BC/CA = BC/(16.2 cm)
BC = 16.2 cm × tan(43°) = 15.1
By Pythagoras theorem, we have;
AB = √(15.1² + 16.2²) = 22.2
The perimeter = 15.1 + 16.2 + 22.2 = 53.5 cm
PLEASE HELP ME!!! I will give the BRAINLIEST for whoever answers it CORRECTLY!
Answer:
Add equations A + B to eliminate y
Then add equations A and C to eliminate y
Step-by-step explanation:
Since all the equations have y with a coefficient of 2, I would eliminate y
Add equations A + B to eliminate y
Then add equations A and C to eliminate y
Answer:
the 3rd choice
I) Construct a triangle PQR such that |PQ|=8cm,{RPQ=90°{PQR=30°.Measure |RQ|
Answer:
6.93 cm
Step-by-step explanation:
You have a right triangle (90°), so you do as follow:
If I understand correctly, you are looking for the hypotenuse so
[tex]cos(30) = \frac{PQ}{QR} = \frac{8 cm}{QR}[/tex]
That is equal to [tex]QR = cos(30)*8 cm = 6.928 cm[/tex]
Which expression is equivalent to 17s-10+3(25+1)?
23s-9
23s-7
115-7
115-9
Answer:
17s + 68.
Step-by-step explanation:
17s - 10 + 3(25 + 1)
= 17s - 10 + 3 * 26
= 17s - 10 + 78
= 17s + 68.
Hope this helps!
Answer:
its b 23s - 7
Step-by-step explanation:
took the test
ASAP! Please help me!!!
Answer:
120 cm³Step-by-step explanation:
First we have to find out area of the base
[tex]s = \frac{a + b + c}{2} [/tex]
[tex] = \frac{5 + 12 + 13}{2} [/tex]
[tex] = \frac{30}{2} [/tex]
[tex] = 15[/tex]
Area of base = [tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex] = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} [/tex]
[tex] = \sqrt{15 \times 10 \times 3 \times 2} [/tex]
[tex] = \sqrt{5 \times 3 \times 5 \times 2 \times 3 \times 2} [/tex]
[tex] = 2 \times 3 \times 5[/tex]
[tex] = 30 \: {cm}^{2} [/tex]
Now, let's find the volume of triangular pyramid
[tex] = \frac{1}{3} \times a \times h[/tex]
[tex] = \frac{1}{3} \times 30 \times 12[/tex]
[tex] = 120 \: [/tex] cm³
Hope this helps..
best regards!!
HELP!
Please answer i)
Answer:
(i) The increase expected in the share price between the first year and the third year is $0.90
(ii) The 10th year
Step-by-step explanation:
(i) The given relation is [tex]V = 2.95+2\cdot log_{10}\left (10\cdot t + 1 \right )[/tex]
In the first year, we have t = 1, which gives;
[tex]V = 2.95+2\cdot log_{10}\left (10\times 1 + 1 \right ) = 2.95+2\cdot log_{10}\left (1 1 \right ) = \$5.03[/tex]
In the third year, we have t= 3 which gives;
[tex]V = 2.95+2\cdot log_{10}\left (10\times 3 + 1 \right ) = 2.95+2\cdot log_{10}\left (31 \right ) = \$5.93[/tex]
Therefore, the increase expected in the share price between the first year and the third year is $5.93 - $5.03 = $0.90
(ii) When the share price value becomes >$7.00, we have;
[tex]7 = 2.95+2\cdot log_{10}\left (10\cdot t + 1 \right )[/tex]
Which gives;
7 - 2.95 = 2·㏒(10·t + 1)
4.05/2 = ㏒(10·t + 1)
2.025 = ㏒(10·t + 1)
[tex]10^{2.025} = 10 \cdot t + 1[/tex]
105.93 = 10·t + 1
104.93 = 10·t
t = 104.93/10 = 10.493 ≈ 10.5 years which is within the 10th year.
what is 3x^3 - 11x^2 - 26x + 30 divided by x-5?
Answer:
Most likely the answer is
3x^2+4x-6
Answer:
3x^2+4x-6 is correct