Answer:
257/16
Step-by-step explanation:
Given :
x¹ = 4Then :
x² + 1/x²(x¹)² + 1/(x¹)²(4)² + 1/(4)²16 + 1/16257/16Evaluate:
[tex]\bf{\sum^{10}_{n-1}\:8(\cfrac{1}{4})^{n-1}[/tex]
[tex]\bf{\overline{\underline{\overline{\underline{Please\:show\;work!}}}}[/tex]
Let S be the given sum, so
[tex]S = 8 + 8 \left(\dfrac14\right) + 8 \left(\dfrac14\right)^2 + \cdots + 8 \left(\dfrac14\right)^9[/tex]
[tex]\displaystyle S = 8 \left(1 + \dfrac14 + \frac1{4^2} + \cdots + \frac1{4^9}\right)[/tex]
Multiply both sides by 1/4.
[tex]\displaystyle \frac S4 = 8 \left(\frac14 + \frac1{4^2} + \frac1{4^3} + \cdots + \frac1{4^{10}}\right)[/tex]
Subtract this from S to eliminate all the but the first term in S and the last term in S/4 :
[tex]\displaystyle S - \frac S4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]
Solve for S :
[tex]\displaystyle \frac{3S}4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]
[tex]\displaystyle S = \frac{32}3 \left(1 - \frac1{4^{10}}\right) = \boxed{\frac{349,525}{32,768}}[/tex]
PLEASE HELP ILL MAKE YOU THE BRAINIEST
write the ratio for sin A
Answer:
In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
Flying against the wind, an airplane travels 4620 kilometers in 7 hours. Flying with the wind, the same plane travels 8640 kilometers in 8 hours. What is the rate of the plane in still air and what is the rate of the wind?
The rate of the plane in still air is 870km/h and the rate of the wind 210km/h.
What is speed?Speed has the dimensions of distance divided by time.
Let Speed of airplane be x km/h and Speed of Wind be y km/h
Speed direction of wind (x+y)
Speed in opposition of wind (x-y)
Now, using speed x time= distance
7( x-y)=4620
(x-y)=4620/7
=660------------------(1)
Similarly,
8(x+y)=8640
(x+y) =8640/8=1080-----------------------(2)
Adding (1) and (2)
2x=1740
x=870 km/h
Subtracting (1) from (2)
2y=420
=>y=210 km/h
So rate of airplane =870km/h
rate of wind=210km/h
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help me thank you ill give brainlyies
Answer:
-5 degrees is colder than -3 degrees farienheight.
Step-by-step explanation:
Let's take this and eliminate every answer-
"The lowest temperature is -3 degrees."
-5 is lower than -3.
"The highest temperature is -5 degrees."
-5 degrees is the lowest temperature, not the highest!
"-5 is warmer than 3 degrees."
-5 is the LOWEST TEMPERATURE.
This leaves us with "-5 is colder than -3 degrees," which is correct because -5 is the smallest temperature and therefore, it is the coldest.
Which solids have a round base? Select two options.
cone
cone
cylinder
cylinder
pyramid
pyramid
sphere
sphere
cube
Hey! Could someone help me with this question as quick as possible? Hope everyone is having a great day/night.
9x?=3/2+ 3/2 + 3/2 10 pts for correct answer
A fraction is a way to describe a part of a whole. The fraction that can replace the question mark is 1/2.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The fraction that can replace the question mark is,
9 × ? = (3/2) + (3/2) + (3/2)
9 × ? = 3(3/2)
9 × ? = 9/2
9 × ? = 9/2
? = 9/(2×9)
? = 1/2
Hence, the fraction that can replace the question mark is 1/2.
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Karen pays $487.56 for a company luncheon. This included a 16% gratuity. Karen needs to report the cost of the lunch without the gratuity to receive a reimbursement from her manager. How much was the cost of the luncheon without the gratuity?
(Please show how to solve it)
Answer: $409.55
Step-by-step explanation:
100% - 16% = 84%
84% of 487.56 = 409.5504.
Round to nearest hundredth.
$409.55
OA. Graph D
OB. Graph B
OC. Graph A
OD. Graph C
A
C
& I
of
B
D
SUBMIT
Answer:
My sister is doing this, I if remember correctly graph B?
Find the angle of CD. Round to the nearest tenth. 12.7 cm 45.5° 9/06 cm mCD= [?]°
Using the information in the diagram, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°
Calculating the angle subtended by an arcFrom the question, we are to determine the measure of [tex]\overset{\LARGE\frown}{CD}[/tex]
Consider the right triangle
The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is twice the measure of the unknown angle
Let the unknown angle in the right triangle be x
∴ The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2x
Then,
x + 90° + 45.5° = 180° (Sum of angles in a triangle)
x = 180° - 90° - 45.5°
x = 44.5°
Thus,
The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2×44.5°
The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 89°
Hence, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°
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the atlanta braves are offering bobblehead to every 10th person who enters your fundraiser. the nashville predators are offering a free ticket to every 15th person who enters the fundraiser. how many attendees must come before someone receives both bobblehead and a ticket?
In this situation, attendee number thirty will be the first one o receive both the bobblehead and the ticket.
Which attendees will receive the bobblehead and the ticket?Bobblehead:
Attendee number 10Attendee number 20Attendee number 30Ticket:
Attendee number 15Attendee number 30What can be concluded?It can be concluded the attendee number 30 will be the first one to receive both the ticket and the bobblehead.
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A regular polygon with n sides has n(n-3)/2 diagonals. Find the number of sides of a regular polygon that has 44 diagonals.
[tex]\dfrac{n(n-3)}{2}=44\\\\n(n-3)=88\\n^2-3n-88=0\\n^2+8n-11n-88=0\\n(n+8)-11(n+8)=0\\(n-11)(n+8)=0\\n=11 \vee n=-8[/tex]
Therefore, the number of sides is 11.
Solve 4|3x-1| + 3 > 11.
4|3x-1| + 3 > 11
4|3x-1| > 11-3
4|3x-1| > 8
|3x-1| > 2
3x-1>2 or 3x-1<-2
3x>2+1 3x<-2+1
3x>3 3x<-1
x>1 x<-1÷3
Solution: ]-♾️ , -1÷3 [ U ] 1,+♾️ [
Find the area of the shaded region round to the nearest tenth
Answer: 818.4
Step-by-step explanation:
Using the area of a sector formula, we get the area of the entire sector is [tex](\pi)(27.8^{2})\left(\frac{150}{360} \right)[/tex].
Using the formula [tex]A=\frac{1}{2} ab \sin C[/tex], we get the area of the triangle is [tex]\frac{1}{2}(27.8)(27.8)(\sin 150^{\circ})[/tex].
So, the area of the shaded sector is [tex](\pi)(27.8^{2})\left(\frac{150}{360} \right)-\frac{1}{2}(27.8)(27.8)(\sin 150^{\circ}) \approx \boxed{818.4}[/tex]
Which of the following is most likely the next step in the series?
A.
Answer:
D.
Step-by-step explanation:
If you look at the pattern, the first shape (square) has four sides. Then, you have 5 sides, and finally, 6 sides.
Thus, a pattern of 4, 5, 6. So, the next shape must have 7 sides, leaving the only possible answer as D.
PLS HELP!!! 80PTS PHOTO ATTACHED
The answer is no solution.
what is Simplify 6.920.
Answer:
6 23/25
Step-by-step explanation:
[tex]0.92\\\\\frac{0.92\cdot \:100}{100}\\\\=\frac{92}{100}\\\\= \frac{4\cdot \:23}{4\cdot \:25}\\\\=\frac{23}{25}\\\\= 6+\frac{23}{25}\\\\=6\frac{23}{25}[/tex]
Select the correct answer.
A mistake was made in the steps shown to simplify the expression. Which step includes the mistake?
+3(41)
7+2³
Step 1: =
=
+ 3(3) - 7 + 23
Step 2:
=
+3(3) - 7 + 8
Step 3: =
(3) - 7+8
Step 4: =
Step 5: = 31+8
Step 6: =
= 47
A.
Step 4
B.
Step 1
C.
Step 5
D. Step 3
The mistake made in the step 3 option(D) step 3 is correct and the simplification form of the expression is 29/2,
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
The question is incomplete.
The complete question is in the picture please refer to the picture.
We have given an arithmetic expression:
[tex]=\dfrac{9}{2}+3\left(4-1\right)-7+2^3[/tex]
Step 1:
[tex]=\dfrac{9}{2}+3(3)-7+2^3[/tex]
Step 2:
[tex]=\dfrac{9}{2}+3(3)-7+8[/tex]
Step 3 should be:
[tex]=\dfrac{9}{2}(3)-7+8[/tex]
The mistake made in the step 3
Thus, the mistake made in the step 3 option(D) step 3 is correct and the simplification form of the expression is 29/2,
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rearrange the equation so b is the independent variable
a - 7 = 3(b+2)
a = ?
I want pictures of how you took the answer
The value of x in both case is 17 and 10.
What is complementary and supplementary angle?If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
1. As the given angle is 90 degree i.e., complementary angle.
So,
22+4x=90
4x= 90-22
4x= 68
x= 17
2. As the figure for the linear pair i.e., supplementary angle
So,
110+7x=180
7x=70
x=10
Hence the value of x in both case is 17 and 10.
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In the solid figure below, what is the volume of the bottom section of the figure?
48
24
36
12
The volume of the bottom section of the figure is:
V = 48 cm³
How to get the volume of the bottom section?Remember that for a rectangular prism of length L, width W, and height H, the volume is V.
V = L*W*H
For the bottom section the dimensions are:
Length = 6cm
Width = 4cm
Height = 4cm - 2cm = 2cm
Replacing these in the volume equation we get:
V = (6cm)*(4cm)*(2cm) = 48cm³
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Answer:
Step-by-step explanation:That’s t up to you STOP CHEATING!!
A survey asked 20 mobile phone dealers how many mobile phones were sold during the previous week. Their answers are displayed in the Box-and-Whisker Plot and the Stem-and-Leaf Plot shown. Which graph can be used to find the mode? What is the mode of the data set? A. Stem-and-Leaf Plot, Mode: 34 B. Stem-and-Leaf Plot, Mode: 42 C. Box-and-Whisker Plot, Mode: 43 D. Box-and-Whisker Plot, Mode: 38
ASAP 100 POINT AND BRAINLIST
The best type of chart for quickly deriving the mode of a sample data is called the Stem-and-Leaf Plot.
What is a Stem-and-Leap Plot?
In statistics, the Stem-and-Leaf Plot is an easy-to-make easy-to-read kind of graph that is derived from the table holding the sample data.
The Box-and-Whisker Plot on the other hand is best for visually depicting the five-number summary of any set of data, which are:
MinimumFirst QuartileMedian (Second Quartile) Third Quartile; andMaximum.It is to be noted that referenced plots are not indicated hence, the general answer.
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The best type of chart for quickly deriving the mode of a sample data is called the Stem-and-Leaf Plot.
What is a Stem-and-Leap Plot?
In statistics, the Stem-and-Leaf Plot is an easy-to-make easy-to-read kind of graph that is derived from the table holding the sample data.
The Box-and-Whisker Plot on the other hand is best for visually depicting the five-number summary of any set of data, which are:
Minimum
First Quartile
Median (Second Quartile)
Third Quartile; and
Maximum.
It is to be noted that referenced plots are not indicated hence, the general answer.
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[tex]\huge\fbox\purple{question}[/tex]
#Write the member of the following sets=
a)V={vowels of English alphabets}
b){cube numbers between 0 to 50
c)M={y:y is a multiple of 3 less than 20}
#a
V={Vowels of English alphabets}
V={a,e,i,o,u,A,E,I,O,U}#b
C={cube numbers between 0 to 50}
C={0,1,8,27}#c
M={y:y is a multiple of 3 less than 20}
M={0,3,6,9,12,15,18}
A cube has side length 3 inches. A sphere has a radius of
3 inches. (Lesson 5-16)
a. Before doing any calculations, predict which solid has greater surface
area to volume ratio.
b. Calculate the surface area, volume, and surface area to volume ratio for
each solid.
I predict that the solid with the greater surface area to volume ratio would be the cube.
The volume of the cube is 27in³
The surface area of the cube is
The ratio of surface area to volume for the cube is 2.
The volume of the sphere is 113.14 in³
The surface area of the sphere is 113.14 in²
The ratio of surface area to volume is 1.
What is the surface area and volume of each solid?The volume of a cube = side length³
3³ = 27 in³
The surface area of a cube = 6a²
a = side length
6 x (3²) = 54 inches²
Ratio of surface area to volume = 54 / 27 = 2
The volume of the sphere= 4/3πr³
4/3 x 22/7 x 3³ = 113.14 in³
The surface area of the sphere = 4πr²
4 x 22/7 x 3² = 113.14 in²
Ratio of surface area to volume = 113.14 / 113.14 = 1
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can someone help me with this question? thank ou!
Answer:
11
Step-by-step explanation:
2x-13=9
2x=9+13
2x=22
x=11
a pair of dice is rolled what is the probability of getting a sum of seven or eleven
Answer:
Step-by-step explanation:
this year you earned $75500. Last year you earned $72400. What the rate of change on your earnings since last y?
If two sides of a triangle are 10 cm and 6 cm long, which of the
following cannot be the perimeter of this triangle?
Answer:
J
Step-by-step explanation:
To find perimeter we add. 10+6 is 16. The third side has to be much bigger than this. So, J is the answer and J is 19 which wouldnt make sense as the length of the third side.
In trapezoid ABCD, Line AB is parallel to CD. If AE=5.2, AC=11.7 and CD=10.5, what is the length of AB to the nearest tenth?
In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
What is trapezoid?" Trapezoid is defined as the quadrilateral whose one pair of opposite side is parallel."
According to the question,
Given
Length of AE=5.2
Length of AC=11.7
Length of CD=10.5
As shown in figure
In trapezoid ABCD,
AB is parallel to CD, AC is the transversal.
AC and BD intersect at point E.
In ΔABE and ΔCDE,
∠BAE ≅∠ECD
∠ABE ≅∠EDC
By AA theorem,
ΔABE ~ ΔCDE
Therefore,
[tex]\frac{AE}{EC}=\frac{AB}{CD}[/tex]
AE + EC = AC
⇒ 5.2 + EC = 11.7
⇒ EC = 11.7 - 5.2
⇒ EC = 6.5units
Substitute the value in the given proportion we get,
[tex]\frac{5.2}{6.5}=\frac{AB}{10.5}[/tex]
⇒ [tex]AB = \frac{(10.5)(5.2)}{6.5}[/tex]
⇒[tex]AB = 8.4[/tex] units
Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
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help me, please ist question 1
Answer:
432
Step-by-step explanation:
To find the volume of a rectangular prism you multiply, L × W × H
L = 6 W = 8 H =9 you plug that in 6 × 8 × 9= 432
so the volume is 432in²
Answer with an algebraic equation too!!
Four years from now the combined ages of a set of twins will be 50. How old are they now?
Answer:
The twins are 21 years old right now.
(x+4) + (x+4) = 50
Step-by-step explanation:
Let x = the current age of one of the twins.
They are twins, that means they are the same age. So the other twin is also x years old.
In four years, the age will be x+4.
Both of them together will be:
(x+4) + (x+4)
The question says that total (of their ages in 4 years) will be 50.
(x+4) + (x+4) = 50
Combine like terms.
2x + 8 = 50
Subtract 8.
2x = 42
Divide by 2.
x = 21
The twins are currently 21.
To check: in four years they will be 25; then the sum of their ages will be 50. Check! Hope this helps!