The new number in the sequence is found to be 7.
What is the term of the sequence?In mathematics, a sequence is a list of components, usually numbers, where the components' order is important. Here, everything fits into a predetermined pattern.
A sequence can be arranged in either ascending or descending order.
There are certain unique sequences, including the triangular number series, square number sequence, cube number sequence, geometric sequence, Fibonacci sequence, and harmonic sequence.
According to the question, the sequence follows the pattern:
Next number=2(Previous number)-2
On substituting the values,
48=2(Previous number)-2
50=2(Previous number)
Previous number=[tex]\frac{50}{2}[/tex]=25
New number=sum of digits of the previous number in the sequence
=2+5
=7
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The value of an investment portfolio decreased by 8 % in 2010. In 2011, its value increased by 5% of
its value in 2010. Given that the value of the portfolio at the end of 2011 was $ 61 824, find its
original value.
Answer:
$63422.42
Step-by-step explanation:
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Find the vertex of the function given below.
y= 2x² + 8x+1
A. (-2,-7)
B. (-2,-1)
OC. (3,-4)
D. (1,7)
Answer:
A
Step-by-step explanation:
given a quadratic function in standard form
y = ax² + bx + c (a ≠ 0 ) then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 2x² + 8x + 1 ← is in standard form
with a = 2 , b = 8 , then
x = - [tex]\frac{8}{4}[/tex] = - 2
substitute x = - 2 into the equation for corresponding y- coordinate
y = 2(- 2)² + 8(- 2) + 1 = 2(4) - 16 + 1 = 8 - 16 + 1 = - 7
vertex = (- 2, - 7 )
IJ=
Help me please thanks
Answer: 11
Step-by-step explanation:
By the secant-secant theorem,
[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]
Find a in degrees.
a
6
√11
5
? ]°
Round to the nearest hundredth.
Answer:
33.55
Step-by-step explanation:
[tex]sin \alpha = \sqrt{11} \div 6 \\ [/tex][tex] \alpha = {sin}^{ - 1} 0.5527[/tex][tex] \alpha = 33.55[/tex]Answer:
α = 33.56° (nearest hundredth)
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta=\alpha[/tex]O = [tex]\sf \sqrt{11}[/tex]A = 5H = 6As all sides of the right triangle have been given, any of the trigonometric ratios can be used to find α.
Sine Ratio
[tex]\begin{aligned}\sf \sin(\alpha) & = \sf \dfrac{\sqrt{11}}{6}\\\implies \alpha & = \sf \sin^{-1}\left(\dfrac{\sqrt{11}}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]
Cosine Ratio
[tex]\begin{aligned}\sf \cos(\alpha) & =\sf \dfrac{5}{6}\\\implies \alpha & = \sf \cos^{-1}\left(\dfrac{5}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]
Tangent Ratio
[tex]\begin{aligned}\sf \tan(\alpha) & =\sf \dfrac{\sqrt{11}}{5}\\\implies \alpha & = \sf \tan^{-1}\left(\dfrac{\sqrt{11}}{5}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]
Therefore, α = 33.56° (nearest hundredth)
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Can you please find the value of x
Answer:
14
Step-by-step explanation:
when two lines intersect, the opposite angles are equal: vertical angles rule
this means that 88 and 6x + 4 are the same, therefore we get the equation 6x+4 = 88.
subtracting 4 from both sides, we find that 6x = 84
we get our final answer by dividing each side of the equation by 6:
x = 14
Find two numbers such that one number is 3 less than twice as big as the other number and the two numbers sum to 21.
Answer:
The two numbers are:
8 and 13
Step-by-step explanation:
a = 2b - 3 Eq. 1
a + b = 21 Eq. 2
Replacing Eq. 1 in Eq. 2:
(2b-3) + b = 21
3b - 3 = 21
3b = 21 + 3
3b = 24
b = 24/3
b = 8
from Eq. 1
a = 2*8 - 3
a = 16 - 3
a = 13
Check:
From Eq. 2:
a + b = 21
13 + 8 = 21
The coordinates of C are (4,4), and the midpoint of CD is at M(-2,-6), what are the coordinates of point D?
The coordinates of D is (-8 , -16 )
What are Coordinates ?Coordinates are the location of a point on the x-y plane.
It is given that the coordinates of C are (4,4)
the midpoint of CD is at M(-2,-6)
The distance between D to the midpoint is equal to distance between C and the mid point M .
The distance between C and M is
( -2 - 4 , -6 -4 )
( -6 , -10)
Adding this to the mid point will give the location of D
(-2 -6 , -6 , -10 )
(-8 , -16 )
Therefore the coordinates of D is (-8 , -16 ).
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Answer:
-8, -16
Step-by-step explanation:
got it right on the est.
I am not able to solve this question
First, we multiply the numbers : 10 x 5 = 50
Now, we multiply r squared to r^6. To do this, we add the index numbers together : r^2 x r^6 = r^(2+6) = r^8
So, the answer is 50r^8, or b.
Call a number quasi-prime if it is composite but not divisible by 2, 7, or 11. For instance, the five smallest quasi-prime numbers are 5, 9, 15, 25, 27, and 39. There are 95 prime numbers less than 500. How many quasi-prime numbers are there less than 500
The number of quasi-prime numbers that are less than 500 = 92
What are quasi-prime numbers?Quasi-prime numbers are those numbers that are also known as semi prime numbers which can not be divided by 2,7 or 11.
They are often derived from prime numbers which are 95 in number from 2 - 499. ( less than 500).
The 95 prime numbers - 3 numbers( such as 2,7 or 11) = 92
Therefore, the number of quasi-prime numbers that are less than 500 = 92
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The slope of the line below is -3. Which of the following is the point-slope form of the line?
Answer:
Step-by-step explanation:
Is there a graph or more information?
Determine the length of the missing sides for each special right triangle. Leave answer in exact (reduced radical) form. Geometry!! pls help!!
Answer:
[tex]a = 18 \sqrt{3} [/tex]
[tex]c = 36[/tex]
Can someone help me out on this problem and show work
Step-by-step explanation:
1. multiply by 8
2. divide by 2
Answer:
4096, 125
Step-by-step explanation:
In the first sequence, notice that each term increases by a factor of 8 (multiplied by 8 each time). Therefore, the fourth term would be 64*8 = 512, so the fifth term is 512*8 = 4096.
In the second sequence, each term decreases by a factor of 2 (divided by 2 each time). The fourth term would be 500/2 = 250, so the fifth term is 250/2 = 125.
Which equation represents the line that is perpendicular to and passes through (-40,20)?
The equation of the perpendicular line to the given line is: y = -5/4x - 30.
What is the Equation of Perpendicular Lines?The slope values of two perpendicular lines are negative reciprocal of each other.
Given that the line is perpendicular to y = 4/5x+23, the slope of y = 4/5x+23 is 4/5. Negative reciprocal of 4/5 is -5/4.
Therefore, the line that is perpendicular to it would have a slope (m) of -5/4.
Plug in m = -5/4 and (x, y) = (-40, 20) into y = mx + b to find b:
20 = -5/4(-40) + b
20 = 50 + b
20 - 50 = b
b = -30
Substitute m = -5/4 and b = -30 into y = mx + b:
y = -5/4x - 30
The equation of the perpendicular line is: y = -5/4x - 30.
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On the number line above, point L (not
shown) is located on line segment JK so that
JL = LK. What is the position of point L?
The position of point L is halfway between points K and L
How to determine the position?The line segment is given as:
JK
This means that the endpoints of the line are:
J and K
Also, we have:
JL = LK
So, we have:
JK = JL + LK
Substitute JL = LK
JK = JL + JL
This gives
JK = 2JL
Divide by 2
JL = 1/2 JK
Hence, the position of point L is halfway between points K and L
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look at images........
Answer:
[tex] \pink{ \rule{1pt}{3000000pt}}[/tex][tex] \red{ \rule{1pt}{3000000pt}}[/tex][tex] \purple{ \rule{1pt}{3000000pt}}[/tex]
A(n) Blank______ is a data characteristic that stands for a value that changes or varies over time. Multiple choice question. information fact variable
Variable is a data characteristic that stands for a value that changes or varies over time.
A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables.
Information is that portion of the content of a signal or message which conveys meaning. (so this is the wrong option)
A fact is a quantitative piece of information - such as a sale or a download. (so this is also the wrong option)
Hence, a Variable is a data characteristic that stands for a value that changes or varies over time.
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Area =
Help me please :)
Answer:
24 unit²
Step-by-step explanation:
use Pythagoras to calculate the height of triangle
which gives you 6 √100-64
then half hight x base
Write down a multiple of 9 that is between 60 and 80
Answer:
72
Step-by-step explanation:
9×8 = 72 which means that 72 is a multiple of 9 lying between 60 and 80.
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Answer:
m=months
clark= 10000-105m
lois= 7500-50m
10000-105m=7500-50m
+50m
10,000-55m=7500
-10000
-55m=-2500
simplify
55m=2500
divide by 55
m=45.45
so i would say b
Hope This Helps!!!
The question "How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes?" is a type of
The question posed in the task content is a goal seeking analysis type of question.
How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes is a goal seeking analysis question.
Goal seeking analysisA goal seeking analysis question is a type of question which helps to determine the efficient and effective measure of achieving a goal either individually or in a group.
The question will help the manager of the restaurant to determine how many servers is needed in order to reduce the waiting time of customers.
Complete question:
The question "How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes?" is a type of
a. goal-seeking analysis.
b. what-if analysis.
c. sensitivity analysis.
d. utility modeling.
a. goal-seeking analysis.
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could you show me what sin D is?
Answer:
sin D = 28/53
Step-by-step explanation:
sin D = opp/hyp
For angle D, the opposite leg is FE with length 28.
The hypotenuse is DE with length 53.
sin D = 28/53
Answer: sinD=28/53.
Step-by-step explanation:
[tex]sinD=\frac{FE}{DE} =\frac{28}{53} .[/tex]
A pillar 80 m tall casts a shadow 39 m long. Find the distance between the top of the pillar and the foot of the shadow
Answer:
89
Step-by-step explanation:
[tex] \sqrt{ {80}^{2} + {39}^{2} } = 89[/tex]
The distance between the top of the pillar and the foot of the shadow is 80 meters.
How to find the distanceLet's call the distance we want to find "x".
In particular, set up the following proportion:
pillar height / shadow length = distance / shadow length
Plugin the given values
80 / 39 = x / 39
Simplifying and solving for x
x = (80 / 39) * 39
x ≈ 80
Therefore, the distance between the top of the pillar and the foot of the shadow is 80 meters.
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Each statement describes a transformation of the graph of . Which statement correctly describes the graph of y = f(x − 7) + 3?
A.
It is the graph of f translated 3 units up and 7 units to the left.
B.
It is the graph of f translated 7 units down and 3 units to the right.
C.
It is the graph of f translated 7 units up and 3 units to the right.
D.
It is the graph of f translated 3 units up and 7 units to the right.
Answer: D. It is the graph of f translated 3 units up and 7 units to the right
Step-by-step explanation:
the +3 part of the equation makes the function translated vertical 3 units
then the x - 7 part makes it translate horizontal to the right 7 units (always the opposite of the sign)
because when
x-7=0,
x=7
Medians: Using the methods previously described, the medians of each group were found to be:
Answer:
Medians: Using the methods previously described, the medians of each
group were found to be: Low: ( , ) Medium: ( . ) High: ( . ) Use these points to find the equation of the median fit regression line. Slope: What is the slope of the median regression line? m = Jig—y" = (Round to the nearest H—xL hundredth.) Y-lntercept: What is the y-intercept of the median regression line? kW _ 3 b _ (33—(—U.01)(2300))+(27—(—0.01)(3350))+(19—(—U.01)(4400)) _ 3 m (Round to the nearest hundredth.) Regression Line: The equation of the median regression line isy= x+
To join a new fitness center, there is a $40 initiation fee. It costs an additional $10 for every spinning class you attend. What is the average cost per class if you take 10 classes in the first month of joining the fitness center
the average cost per class is $14.
Think of this as an algebraic equation, which would be expressed as 40+10s=total cost
The (s) would be the number of spinning classes you decide to take.
Therefore to find the average cost of the class, you would plug in 10 classes for s.
This brings the total cost to $140 dollars.
To find the average you must divide this cost by the number of classes you took.
This will be the price per class, which is $14.
Statement of the equality of two expressions formulated by way of making use of a set of variables the algebraic operations, particularly, addition, subtraction, multiplication, department, elevating to energy, and extraction of a root.
In arithmetic, an algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some area, regularly the field of rational numbers.
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A can of soup has a height of 10 cm. If the volume of the can is 363 cubic cm, what is its radius?
The radius of the circular cross-section of the can of soup is; 3.4cm.
What is the radius of the can of soup?Since, the can has a height of 10cm and the volume of the can is 363cm³, it follows that the area of the circular cross-section can be evaluated as;
A = 363/10 = 36.3cm²
Hence, it follows that the radius can be evaluated as follows;
36.3 = 3.14 × r²
r² = 36.3/3.14
r² = 11.56
r = 3.4cm
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Pleased help asp
Please help asp
Please help asp
A sports league has 10 teams. Each team must send at least one player to the league's annual meeting, but may send as many as 5 if space is available based on the cost of the meeting. Holding the meeting costs the league $600 for the facility, plus $50 per player for food and materials. The league cannot spend more than $1900 on the meeting. Which inequality shows the number of players, n, who could be at the meeting?
can I get your number personally
math!!
PLEASE HELP!!
what is the angle indicated in the triangle below??
a) 46 degrees
b) 65°
c) 44°
d) 35°
e) 55°
f) 90°
Answer:
e) 55°
Step-by-step explanation:
use the tangente ratio
[tex]tan\alpha =\frac{10}{7} =1.42857[/tex]
[tex]angle(?)=tan^{-1} (1.42857)=55^{0}[/tex]
Hope this helps
Answer:
55 degrees (e)
Step-by-step explanation:
This is a trigonometry problem. We are given a right triangle with an unknown angle in which the opposite and adjacent sides of the angle are known (10 and 7). We also know that the tangent of any angle is the length of the opposite divided by the length of the adjacent. If we let the unknown angle be Ф, we can say that tan(Ф) = 10/7. To isolate Ф, all we have to do is take the inverse. In other words, Ф = arctan(10/7). Using a graphing calculator, we find that arctan(10/7) is approximately 55 degrees.
help me please i dont understand
Answer:
96 ft^2.
Step-by-step explanation:
Area of shaded region = area of the original rectangle - area of the one removed
= 8 * 16 - 8*4
= 128 - 32
= 96