Answer:
7
Step-by-step explanation:
The common ratio of the geometric sequence is 7.
What is geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.
According to the question,
First term = a = 5
Third term = a×r²
= 245
⇒ ar² = 245
⇒ 5×r² =245
⇒ r² = 245/5
⇒ r² = 49
⇒ r = 7.
Hence the common ratio = 7
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A committee of 3 men and 4 women , is to be formed from 5 men and 7 women . How many different committees can be formed if :
A. a particular man must be on the seat
B .two particular must not be on the committee
C. There are no restrictions.
Topic : Permutation and combination
Answer:
Part AA particular man on the seat, then 2 men are out of 4:
4C2 = 4!/(4-2)!2! = 4*3*2/2*2 = 64 women out of 7:
7C4 = 7!/(7-4)!4! = 7*6*5*4!/3!4! = 35Total combinations:
6*35 = 210Part BOption 1. 2 men excluded
3 men out of 3 and 4 women out of 7
Total ways:
7C4 = 35 (as above)Option 2. 2 women are excluded
3 men out of 5 and 4 women out of 5
5C3*5C4 = 5!/3!(5-3)! * 5!/4!(5-4)! = 5*4/2 * 5/1 = 10Option 3. 1 man and 1 woman excluded
3 out of 4 men and 5 out of 6 women:
4C3*6C5 = 4!/3!(4-3)! * 6!/5!(6-5)! = 4*6 = 24 Part CNo restrictions, so the number of ways:
3C5 * 7C4 = 5!/3!(5-3)! * 35 = 4*5/2 * 35 = 10*35 = 350Hal says the volume of the sphere shown below is 36 cm3. Find the correct volume, using 3.14 for π. Round to the nearest hundredth. What was Hal's likely error? Use the drop-down menus to explain your answer.
This question is incomplete
Complete Question
Hal says the volume of the sphere shown below is 36 cm³.Find the correct volume, using 3.14 for π. Round to the nearest hundredth. What was Hal's likely error? Use the drop-down menus to explain your answer.
Radius of the sphere = 3 cm
Answer:
a) The volume of the sphere = 113cm³
b) Hal's likely error was :
He used the wrong formula and did not make use of π = 3.14 in his calculation.
Step-by-step explanation:
a) The Volume of a Sphere = 4/3πr³
The radius of the sphere = 3cm
π = 3.14
The volume of the sphere = 4/3 × 3.14 × 3³
= 113.04 cm³
Approximately to the nearest hundredth = 113cm³.
b) Hal's likely error comes in two forms:
1) He used the wrong formula which is Surface area of the sphere(4πr²) in his calculation instead of the right formula which was the Volume of a Sphere(4/3πr³)
ii) Also he did not use π in his calculation.
This means Hal's calculation=
Surface Area of a Sphere = 4πr²
But Hal's used = 4r²
Where r = 3cm = 4 × (3cm)²= 36 cm³
This is wrong.
How many factors of 10 are in 1000, only answer are three, two, four
Answer:
Step-by-step explanation:
The number 1000 has prime factors: 2, 2, 2, 5, 5, 5.
The factors of 1000 include 1 and combinations of these numbers multiplied together (in any arrangement):
1, 2*2*2*5*5*5 or 1, 1000
1*2, 2*2*5*5*5 or 2, 500
1*2*2, 2*5*5*5 or 4, 250
. . . (You already did these)
But, a “factor” is “a number or quantity that when multiplied with another produces a given number or expression,” so you should consider the following:
How many 1's? How many 5's? How Many 2's? [and any others ...]
1 = 1 0 0
2 = 1 0 1
4 = 1 0 2
8 = 1 0 3
5 = 1 1 0
10 = 1 1 1
20 = 1 1 2
40 = 1 1 3
25 = 1 2 0
50 = 1 2 1
100 = 1 2 2
200 = 1 2 3
125 = 1 3 0
250 = 1 3 1
500 = 1 3 2
1000 = 1 3 3
There are 4*4=16 factors because there can be 4 (that is, 0-3) 5's and 4 (that is 0-3) 2's.
Answer:
the answer to the question is four
Write 4 ⅔ as a decimal.
Answer:
4.6667
Step-by-step explanation:
Answer:
4.66666667
Step-by-step explanation:
I was never sure about the amount 6's in it, but 2/3 is just .6666666... (so on) and 4 is a whole number so you'll just place it before like so: 4.66666..
f(x)=3x2−12x+5, what would be the axis of symmetry for this function?
Answer:
x=2 is the axis of symmetry
Step-by-step explanation:
Find the error & explain why it is wrong: Megan wanted to solve this problem: given that sin 0=-divided2/2, and cos =divided3/2, find tan 0
What did she do wrong
Answer:
As seen on the picture, all the steps A to D are correct.
Step A. Identity is correctStep B. The fraction is correctStep C. Simplification is correctStep D. Solution is correctNote:
It could be more simplified by adding a step and multiplying both the numerator and denominator by √3: [tex]\frac{-\sqrt{2} }{\sqrt{3} } = - \frac{\sqrt{6}}{3}[/tex]Simplify expression and can you explain how
Answer: 64r^36
Step-by-step explanation:
On picture below
HELPPPPP PLEASEEE!!!!
Answer:
X= - 3
Step-by-step explanation:
Multiply both sides by 2 to remove the division on the LHS
3X - 15=8X
Move 3X to the RHS
-15 =8X - 3X
-15= 5X
Divide both sides by 5
-3 =X
[tex]\boxed{c.\:x\:=\:-3}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{3x - 15}{2} = 4x \\ ⇢ 3x - 15 = 4x \times 2 \\ ⇢ 3x - 15 = 8x \\ ⇢ 3x - 8x = 15 \\ ⇢ - 5x = 15 \\ ⇢ x = \frac{15}{ - 5} \\ ⇢ x = - 3[/tex]
[tex]{ \bf{ \underbrace{To\:verify :}}}[/tex]
[tex] \frac{3x - 15}{2} = 4x \\ ⇢ \frac{3 \times (- 3) - 15 }{2} = 4 \times - 3 \\ ⇢ \frac{ - 9 - 15}{2} = - 12 \\ ⇢ \frac{ - 24}{2} = - 12 \\ ⇢ - 12 = - 12 \\ ⇢ L.H.S.=R. H. S[/tex]
Hence verified.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
Can anyone help me with this plz
There is a prism with a pentagonal base the height is 8 cm the area of the pentagonal base is 30.5cm what is the volume of the prism
Answer:
244 cm³
Step-by-step explanation:
Step 1: Given data
Height of the prism with a pentagonal base (h): 8 cm
Area of the pentagonal base (A): 30.5 cm²
Step 2: Calculate the volume of the prism with a pentagonal base
We have a regular pentagonal prism, that is, the 5 sides of the base are equal and we know the area of the base and the height of the prism. We can calculate its volume using the following expression.
V = A × h
V = 30.5 cm² × 8 cm = 244 cm³
What is the equation of the circle with a diameter whose endpoints are (-3,-9) and (-7,1)?
Answer:
12
Step-by-step explanation:
Answer:
( x + 5 )² + ( y + 4 )² = 29
Step-by-step explanation:
Equation of the circle is
( x - h )² + ( y - k )² = r²
( h, k ) are coordinates of the center
~~~~~~~~~~~~~~~~~~~~~
Coordinates of the center of the circle are
( [tex]\frac{-3-7}{2}[/tex] , [tex]\frac{-9+1}{2}[/tex] ) = ( - 5 , - 4 )
d = 2√29 ⇒ r = √29
( x + 5 )² + ( y + 4 )² = 29
4. Elsa mixed 2 cups red paint with 1 cup blue paint to make purple paint. If she needs more purple
paint and uses 2 cups cup red paint, how much blue paint should she mix with it?
Solve for x if:
y = 7
x = 5y + 2
Solve for y if:
k = 2
8k - 3y 10
Solve for y if:
m = 3
y = 5x - 15
Solve for x and y if:
y = -3x + 9
y = 8x - 2
Answer:
Step-by-step explanation:
Please the number given in place of its letter in your equation
x = 5y + 2 if y = 7
x = 5*7 + 2
x = 35 + 2
x = 37
Apply the same principle to the others
Is the question below a statistical question?
Do teachers make more money than nurses?
Yes or no please answer !!
Answer:
no
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
Write a proportion. What is x in the image above
Answer:
X IS A WORD TE-PAHADI
Step-by-step explanation:
Answer:
proportion: 6/8 = 3/x
x = 4
Step-by-step explanation:
6/8 = 3/x
6/2 = 3
8/2 = x
8/2 = 4
x = 4
What is the length of QR?
Answer:
B
Step-by-step explanation:
5/8 + 3/4
_______
-2/3 - 5/6
Answer:
- 11/12
Step-by-step explanation:
5/8 + 3/4
_______ x 24/24
-2/3 - 5/6
15+18
= ______
-16-20
33
= _____
-36
= - 11/12
A report states that the mean household income last year for a certain rural county was $46,200 and the median was $54,500. If a histogram were constructed for the incomes of all households in the county, would you expect it to be skewed to the right, to the left, or approximately symmetric
Answer:
skewed to the left
Step-by-step explanation:
A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval. the frequency is usually on the vertical axis while the class interval is usually on the horizontal axis.
If the mean is greater than the median, the histogram would be skewed to the right
If the mean is less than the median, the histogram would be skewed to the left.
The mean in this question is $46,200 while the median is $54,500. So, the histogram would be skewed to the left
2
Cameron has 6 pounds of pears.
A roasted-pears recipe requires
13 pounds of pears.
How many batches can he make?
Number sentence:
Solution:
Answer:
0.4 batches
Step-by-step explanation:
6 / 13 = 0.4
The ratio of the number of laps Tonya swam last week to the number of laps Randy swam last week is 3:10. If Randy swam 84 MORE laps last week, how many did Tonya swim?
Answer:
The number of laps Tonya swam last week were:
36 laps.Step-by-step explanation:
To understand the ratio, you must know that 3:10 means that each time Tonya swam 3 laps, Randy swam 10 laps, by this reason, to identify the total number of laps you can divide the total difference given in the exercise (84 laps) into the difference indicated by the ratio (10 - 3 = 7 laps):
84 / 7 = 12This number obtained is the number of times the ratio had to be met so that the difference in laps swam was 84. Now, you must multiply the obtained value (12) by the number of laps from Tonya given in the ratio (3):
Tonya's total number of laps = 12 * 3Tonya's total number of laps = 36 lapsAs you can see, with the calculates, we obtained 36 laps in total. You could also do the iterations 12 times, subtracting the number of turns given by Tonya from the number of turns made by Randy and you would get the same result:
10 - 3 = 720 - 6 = 1430 - 9 = 2140 - 12 = 2850 - 15 = 3560 - 18 = 4270 - 21 = 4980 - 24 = 5690 - 27 = 63100 - 30 = 70110 - 33 = 77120 - 36 = 84In a right triangle, if the length of the hypotenuse is 10 and the length of one of the other sides is 6, what is the length of the third side? (Simplify Answer)
Answer:
8
Step-by-step explanation:
10^2=100 6^2=36 100-36=64 sqrt64=8
Find the center and radius of a circle with the equation x² + y2 +6x–8y +16= 0.
a. (-3, 4);r=3
b. (3,-4);r=3
c. (-3, 4);r=9
d. (3,-4);r=9
Someone please help me thank you
Answer:
It represents polynomial expression
What is the value of x in this figure?
10
O 5
o 5V2
30°
103
O
X
o 513
18
19 20 21
22 23 24 25 26
Answer:
5√3
Step-by-step explanation:
Thanks to the given information we can say that the smallest leg is 5 because the triangle is half of an equaliteral one.
for the same reason we can say that x is 5√3 that is the simplest from of the result of the Pytaghorean theorem
Explain how making a table helps to compare two or more sets of data that have been presented in different ways.
Answer:
By easing the ranking and colerration of the data
Answer: a table is an organized way of displaying data
all data in a table has the same format
you can see how output of a data set changes by looking at a column
you can compare outputs of different functions that have the same input by looking at rows
Step-by-step explanation: edge 2022
Please help this is for a project: The stimulus check is a one time $1,200 pay out and the unemployment check is $600 per week
for a maximum of 16 weeks. Make an equation that can be used to find y, the amount of money in your
account after x number of weeks of getting unemployment checks.
Can b an x be greater than 16? What is a mathematical way to show that?
PLEASE HELP ME ASAP Given the following polynomial function, find f(-1): 2x^3 - 3x^2+7x-10
F(-1)=?
Answer:-22
Step-by-step explanation:Just put the value -1 wherever there is x.
Answer:
f(-1) = -22
Step-by-step explanation:
f(x): 2x^3 - 3x^2 + 7x - 10
Repace x = -1
f(-1) = 2(-1)^3 - 3(-1)^2 + 7(-1) - 10
f(-1) = -2 - 3 - 7 - 10
f(-1) = -22
please help me quick will give any award
you dont need to show work
Answer:
Q1. A. 209.8
Q2. B. 313.6
Q3. 448.22 (not in ur options)
Step-by-step explanation:
Matthew has 30 Starbursts. Twelve are yellow and the rest are red. What is the ratio of yellow starbursts to red?
Answer is 2:3.
~Refer to the attachment for the solution.