Answer:
The product of the digits of n is 8
Step-by-step explanation:
An arithmetic series is of the form
The nth term of an arithmetic series = aₙ + (n - 1)d
Therefore, for the series, we have;
n!, (n+1)!, (n+19)n!
Therefore;
n! + (n - 1)·d = (n+1)! = (n + 1)·n! = n·n! + n!
n·n! = (n - 1)·d
n! + (n + 1 - 1)·d = (n+19)n!
n! + n·d = n·n!+19·n! = (n - 1)·d +19·n! = n·d - d + 19·n!
n! - 19·n! = n·d - n·d - d
-18·n! = -d
Therefore, d = 18·n!
n! + d = (n + 1)!
n! + 18·n! = (n + 1)·n!
n!·(18 + 1) = (n + 1)·n!
18 + 1 = n + 1
∴ n = 18
Hence the product of the digits of n = 1 × 8 = 8
WHAT IS THE LENGTH OF B QUICK HELP
Answer:
2 cm.
Step-by-step explanation:
The entire base is 10 cm and the top is 8 cm, so b is 10 - 8 = 2 cm.
Hope this helps!
I hope this helps you
b+8=10
b=2
Two terms of an arithmetic sequence are a7 = 32 and a19 =140. Find a rule for the nth term.
Answer:
aₙ = 9n - 31
Step-by-step explanation:
If we call the common difference as d, since 19 - 7 = 12, we can write:
32 + 12d = 140
12d = 108
d = 9 which means that a₁ = a₇ - 6d = 32 - 6 * 9 = -22.
Explicit formula for arithmetic sequence: aₙ = a₁ + (n-1)d so the answer is
aₙ = -22 + (n - 1) * 9
= -22 + 9n - 9
= 9n - 31
40 cm³ of mercury weighs 544 g. Calculate the density of mercury. pls answer question
Answer:
13.6
Step-by-step explanation:
density= mass/volume
= 544g/40cm3
=13.6
Matthew wants to estimate the mean height of students attending his collage. He records the heigjts of 100 randomly selected students attending the college. What is the population?
Answer:
ned more info
Step-by-step explanation:
The correct option that shows the population of the research carried out by Matthew is Option D; all the students attending the college.
What is the mean?Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.
We are told that Matthew wants to estimate the mean height of students attending his college.
Now, let us say the total number of students in his college is x.
If he decides to select 100 students randomly to record their height, it means this 100 student is a sample out of the total number of students which is x that is the population.
In conclusion, we can say that the population of this research by Matthew is the total number of students that attend the college.
Hence, The correct option that shows the population of the research carried out by Matthew is Option D; all the students attending the college.
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Which rule describes the composition of transformations
that maps ABC to A'B'C"?
Answer:
Step-by-step explanation:
To get from ABC to A'B'C', ABC is reflected across line m.
To get from ABC to A"B"C", ABC need to first be reflected across line m. Then, it needs to be rotated 90° clockwise to get to A"B"C".
I'm not exactly sure which one you were trying to get (so I just added both), because you said A'B'C", instead of A'B'C' or A"B"C", but I really hope this answers your question!
The rule which describes the composition of transformations that maps ABC to A'B'C' is,
⇒ reflect across the line m.
We have to given that,
To find the rule which describes the composition of transformations that maps ABC to A'B'C'.
Here, The triangle ABC and it's image A'B'C' is shown in image.
Clearly, Image of triangle ABC is reflect across the line m.
Thus, the rule which describes the composition of transformations that maps ABC to A'B'C' is,
⇒ reflect across the line m.
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Rob is making a scale model of the Solar System on the school field. He wants the distance from the Sun to Jupiter to be 8 metres on his scale model. The real distance from the Sun to Jupiter is 7.8 × 10 8 kilometres. Find the scale of the model. Give your answer in the form 1 : n , where n is written in standard form.
Answer:
1 : 9.75 * 10⁷
Step-by-step explanation:
To find n, we have to divide the real distance by the scale distance. This is 7.8 * 10⁸ / 8 = 0.975 * 10⁸ = 9.75 * 10⁷ which means that the ratio is 1 : 9.75 * 10⁷.
Answer:
1:9.75x10^10
Step-by-step explanation:
780000000km/0.008km=97500000000
=9.75×10^10Which one of the following is the graph of:
Answer:
B
Step-by-step explanation:
Correct if wrong
Please answer this question fast in two minutes
Answer:
(7, 8)
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
Simply set our midpoint and given point equal into a formula to find the other endpoint:
4 = (1 + x)/2
8 = 1 + x
x = 7
6 = (4 + y)/2
12 = 4 + y
y = 8
Solve algebraically for x: -23(x + 12) + 23x = −54x + 2
Answer:
[tex]x=\frac{139}{27}[/tex]
Step-by-step explanation:
-23(x+12)+23x=-54x+2
-23x-276+26x=-54+2
-276=-54x+2
54x=2+276
54x=278
[tex]x=\frac{139}{27}[/tex]
Answer:
Use mathaway <3
Step-by-step explanation:
Jeanine is selecting various albums to be displayed in the front of her music coffee house. She will be choosing 4 albums for
one part of the display. This part of the display is very prominent and she is really trying to promote jazz. There are five albums
from Diana Kroll, seven albums from Harry Connick Jr. and four albums from Michael Bublé. In how many ways can she choose
four albums for display and at least two albums are from Diana Kroll? Evaluate using both the direct and indirect method.
Gt11.2014
Answer:
The number of ways she can choose four albums for display with at least two from Diana Kroll is from the sixteen albums is 665 ways
Step-by-step explanation:
1) The number of ways she can choose 2 albums of Diana from the 5 Diana Kroll albums is 5!/(2!(5 - 2)!) = 10 ways
Choosing the other 2 albums from the remaining 11 albums gives;
11!/(2!(11 - 2)!) = 55 ways
Total number of ways is then 10 × 55 = 550 ways
Choosing 3 from the 5 Diana Kroll albums is 5!/(3!(5 - 3)!) = 10 ways
Choosing the other 1 album from the remaining 11 albums gives;
11!/(1!(11 - 1)!) = 11 ways
Total number of ways is then 10 × 11 = 110 ways
Choosing 4 from the 5 Diana Kroll albums is 5!/(4!(5 - 4)!) = 5 ways
Choosing the other 0 album from the remaining 11 albums gives;
11!/(0!(11 - 0)!) = 1 way
Total number of ways is then 5 × 1 = 5 ways
Total number of ways = 550 + 110 + 5 = 665 ways
2) In the indirect method, we first find the number of ways to choose 4 albums out of the 16 albums, then we subtract the number of cases where there are 1 and 0 Diana Kroll albums as follows;
16!/(4!(16 - 4)!) = 1820 ways
With 1 Diana Kroll album gives
5!/(1!(5 - 1)!)×11!(3!(11 - 3)!) = 825 ways
With 0 Diana Kroll album gives
5!/(0!(5 - 0)!)×11!(4!(11 - 4)!) = 330 ways
Total number of ways with at least 2 Diana Kroll albums = 1820 - 825 - 330
Total number of ways with at least 2 Diana Kroll albums = 665 ways.
1) Lynda runs the 400 meter for her school's track team. She beat her best time by 3.6
seconds in the meet today with a time of 49.3 seconds. What was her previous best time?
Lynda previous best time was 52.9 second.
Calculations:Given that, Lynda runs the 400 meter for her school's track team.
She beat her best time by 3.6 seconds in the meet today with a time of 49.3 seconds.
It means that, previous best time of Lynda was 3.6 second more than as compared to todays time.
So that,
Previous best time is, [tex]=49.3+3.6=52.9seconds[/tex]
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In order for the parallelogram to
be a square, x=?
Answer:
7°Step by step explanation
We know that the diagonals of a square bisects it's angles and every angles of square are 90°
m<BCD = 90°
m<BCA = m< DCA = 4x + 17
m<BCA + m<DCA = m <BCD
4x + 17 + 4x + 17 = 90
4x + 4x + 17 + 17 = 90
8x + 34 = 90
8x = 90 - 34
8x = 56
X = 56/8
x = 7
Hope this helps...
Good luck on your assignment...
In square, the angle between the diagonal and the sides of the square is 45°. Then the value of x is 15.5°.
What is a square?
It is a polygon with four sides. The total interior angle is 360 degrees. In a square, opposite sides are parallel, all side are equal, and each angle is 90 degrees.
In square, the angle between the diagonal and the sides of the square is 45°.
4x + 17° = 45°
4x = 62°
x = 15.5°
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What does Cos mean in geometry
Answer:
cosine
Step-by-step explanation:
"Cos" is the abbreviation usually applied to the name of the cosine function. That function gives the x-coordinate of the point on a unit circle that is at some angle measured counterclockwise from the x-axis. A unit circle is a circle with a radius of 1 unit, centered at the origin.
What is the slope and y-intercept of the equation 3(y − 2) + 6(x + 1) − 2 = 0
Which of the following is the correct factored form of the given equation?
Answer: 3
Step-by-step explanation:
Evaluate the expression for the given value(s) of the variables(s).
m-8 when m= 12
Replace m with 12 and simplify.
m-8 = 12-8 = 4
Find the solutions to the equation below.
16x2 - 64 = 0
A. X=-4
B. X= 4
C. X = -2
D. X=-8
E. X= 2
F. X=-64
Answer:
C. X = -2
E. X = 2
Step-by-step explanation:
16(-4)² = 64
16(16) = 64
256 = 64 (false)
16(4)² = 64
16(16) = 64
256 = 64 (false)
16(-2)² = 64
16(4) = 64
64 = 64 (true)
16(-8)² = 64
16(64) = 64
1024 = 64 (false)
16(2)² = 64
16(4) = 64
64 = 64 (true)
16(-64)² = 64
16(4096) = 64
65356 = 64 (false)
What is the nth term rule of the quadratic sequence below? 7, 14, 23, 34, 47, 62, 79
Answer:
Tn = Tn-1 + 2(n-1) + 5
Kindly note that Tn-1 means T subscript n-1
Step-by-step explanation:
Here, we want an expression for the nth term.
First term is 7
Then first common difference is 7
second common difference is 7 + 2
Third common difference is 9 + 2
So within the common differences, the nth term is 7 + (n-1) 2
Now, the nth term of the series would be;
Tn = Tn-1 + 7 + 2(n-1)
Tn = Tn-1 + 7 + 2n -2
Tn = Tn-1 + 2n + 5
Now there is a fix to this,
n for the term is not the same n for the common difference.
the 7th term works with the 6th common. difference, while the 8th term work for the 7th common difference.
So we might need to rewrite the final expression as follows;
Tn = Tn-1 + 2(n-1) + 5
Here
are
two
rectangles:
4x
2= -3
A
2.5
av
All measurements (cm)
Both
rectangles
hake
area.
Work out perimeter of shape B.
same
Answer:
Perimeter of rectangle B = 29cm
Step-by-step explanation:
Area of A = 4x x 2.5
Area of B = (2x - 3) x 7
The area of A and B are equal so
4x x 2.5 = (2x - 3) x 7
10x = 14x - 21
-4x = -21
4x = 21
x = 5.25
Work out the perimeter of B:
2x - 3
= (2 x 5.25) - 3
= 7.5
7.5 x 2 = 15
15 + (7 x 2) = 29
Therefore, the perimeter of rectangle B = 29cm
The area of Rectangle is length times of width. Perimeter of rectangle A is 47cm
What is Area of Rectangle?The area of Rectangle is length times of width.
Area of rectangle A is 4x x 2.5
Area of B = (2x - 3) x 7
The area of A and B are equal so
4x x 2.5 = (2x - 3) x 7
10x = 14x - 21
Take common variables on one side
10x-14x=-21
-4x = -21
Multiply minus on both sides
4x = 21
Divide both sides by 4
x = 5.25
So 4x=4(5.25)=21
2x-3=2(5.25)-3=7.5
Let us find the perimeter of a rectangle with length 21 and width 2.5
2(21+2.5)
2(23.5)=47
The perimeter of rectangle A is 47
Hence the perimeter of rectangle A = 47cm
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Which one of the following statements expresses a true proportion?
O A. 7:9 = 8:9
OB. 3:4 = 9:12
O C.54:9 = 6:3
OD. 2:1 1:2
Answer:
The answer is B.
Step-by-step explanation:
A true proportion is a set of ratios that equal each other.
For example, 1:2=2:4 is a proportion.
As we look through the list, we observe only B equals each other. Imagine 3:4 and 9:12 as a fraction. (¾ and 9/12). If we reduce 9/12, we get ¾. Thus, 3:4 = 9:12:)
I hope this helps!
A map has a scale of 1 cm to 2.3 km. The real-life distance between two towns is 69 km. What is the distance between the two towns on the map?
Answer:
Step-by-step explanation:
Cm : km
1 : 2.3
x : 69 Cross multily
2.3x = 69
x =[tex]\frac{69}{2.3}[/tex]
x = 30cm
the distance between the two towns on the map is 30cm
Answer:
30 cm
Step-by-step explanation:
69/2.3 = 30
Stacey wishes to make a hamburger which is lower in fat without having to give up the great taste. She purchases 5 pounds of ground beef which is 15% fat and combines it with 7 pounds of ground turkey which is only 3% fat. What is the percentage of fat in the mixture?
Answer:
%P = 8%
the percentage of fat in the mixture is 8%
Step-by-step explanation:
Given;
The percentage of fat in the mixture is;
%P = total mass of fat in mixture/total mass of mixture × 100%
%P = F/T × 100% ….....1
Mass of fat in mixture is;
She purchases 5 pounds of ground beef which is 15% fat
F1 = 15% of 5 pounds = 0.15×5 pounds
F1 = 0.75 pound
and combines it with 7 pounds of ground turkey which is only 3% fat
F2 = 3% of 7 pounds = 0.03 × 7
F2 = 0.21 pound
Total mass F = F1 + F2
F = 0.75+0.21
F = 0.96 pound
Total mass of mixture T = 5 + 7 pounds
T = 12 pounds.
From equation 1,
%P = F/T × 100%
%P = 0.96/12 × 100%
%P = 0.08×100%
%P = 8%
the percentage of fat in the mixture is 8%
Reduce the fraction
72/120
Enter your answer as a fraction in simplest form, using the / symbol, like this: 42/53
Or, if the denominator is 1. enter your answer as a number, like this: 42
Answer:
3/5
Step-by-step explanation:
72/2 =36
120/2 =60
=36/60
36/2 = 18
60/2 = 30
=18/30
18/2=9
30/2 =15
= 9/15
9/3=3
15/3 =5
= 3/5
The points A (-3, b), and B (1, 3) are 5 units apart. Find the value of b.
Answer:
b = 0
Step-by-step explanation:
To find the value of b, we will follow the steps below;
Using the distance formula:
D = √(x₂-x₁)² + (y₂-y₁)²
from the question given,
A (-3, b), this implies
(-3, b) = (x₁ ,y₁)
x₁=-3 and y₁ = b
similarly
B (1, 3)
(1, 3) = (x₂,y₂)
this implies
x₂ = 1 and y₂=3
D= 5
we can now proceed to insert the values into the formula and then solve for b
D = √(x₂-x₁)² + (y₂-y₁)²
5 = √(1+3)² + (3-b)²
5 = √4² + (3-b)²
5=√16 + (3-b)²
take the squares of both-side of the equation
5² = 16 + (3-b)²
25 = 16 + (3-b)²
subtract 16 from both-side of the equation
25 - 16 = (3-b)²
9 = (3-b)²
Take the square root of both-side
√9 = 3-b
3 = 3-b
add b to both-side of the equation
3 + b = 3 - b+ b
3 + b = 3
subtract 3 from both-side of the equation
3+b-3 = 3-3
b = 0
Therefore, the value of b is 0
Determine the intercepts of the line.
Answer:
(-7.5, 0) x intercept
(0, 5.5) y intercept
Step-by-step explanation:
The x intercept is where it crosses the x axis
It crosses at (-7.5, 0)
The y intercept is where it crosses the y axis
It crosses at (0, 5.5)
Answer:
the x intercept will be (-7.5,0) and the y=(5.5,0)
Step-by-step explanation:
the intercept is were the line cross the graph.
Joy makes 6.5 litres of soup, correct to the nearest 0.5 litre. She serves it the soup in 280ml portions, correct to the nearest 10ml. 22 people order this soup, Does joy definitely have enough soup to serve the 22 people
Answer:
Joy definitely does have enough soup for 22 people.
Step-by-step explanation:
Upper Bound: 285ml turn it to 0.285l 10÷2=5
280ml
Lower Bound: 275ml turn it to 0.275l
Upper Bound: 6.75l 0.5÷2=0.25
6.5 Litters
Lower Bound:6.25l
6.75÷0.275=24.54 or 25
6.25÷0.285=21.92 or 22
22 < 25 Joy definitely does have enough soup for 22 people.
Simplify the following expression (62)4
Answer:
[tex]3^{0} =1[/tex]
Step-by-step explanation:
Anita purchased apples priced at $1.79 per pound at the grocery store. Her receipt shows that she spent $5.37 on apples.
Answer:
She bought 3 pounds of apples.
Step-by-step explanation:
First we look at our given steps:
1 pound of apples=$1.79
total=$5.37
We need to divide her total by the cost per pounds of apples. So 5.37/1.79=3.
The number of pounds Anita purchased is 3.
How many pounds did Anita purchase?Given: $1.79 per pound, spent $5.37 on apples
We must divide her aggregate by the cost per pound of apples.
Number of pounds = Total Spent / Amount per pound
Number of pounds = 5.37/1.79
Number of pounds = 3.
The number of pounds Anita purchased is 3.
Therefore, the number of pounds is 3.
The completed question is,
Anita purchased apples priced at $1.79 per pound at the grocery store. Her receipt shows that she spent $5.37 on apples. Type the correct answer in the box.
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functions.
Which values are within the domain of the function?
Check all that apply.
st
x= -6
x=-4
2
1 x= -2
LED x = 0
-4
-2
2
4
I x = 2
0 x = 4
-2.
-4
Answer:
2,5 and 6
Step-by-step explanation:
The answer is going to be option 2, 5 and 6 because the line touches -4,2 and 4 on the x axis. And these are the x values so that's why this is going to be the answer.
Hope this information helps you!
x=-2, x=-4, x=2 and x=4 values are within the domain of the function
What is a function?A relation is a function if it has only One y-value for each x-value.
The domain of a function is the set of all possible inputs for the function.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.
x=2, x=4, x=5, x=-2, x=-4 are the values in domain
Hence, x=-2, x=-4, x=2 and x=4 values are within the domain of the function
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A loaf of bread that is baked today costs $7. All of the bread baked yesterday is 40% off.
Tobin has $5. He wants to know if $5 is enough to purchase a loaf of yesterday's bread.
How can Tobin find the price of a loaf of
yesterday's bread? Complete the statement
The price of ?
equals
the price of ?
minus
the discount
The price of yesterday's bread equals the price of today's bread minus the discount.
The price of yesterday's bread is equal to the price of today's bread less the dollar equivalent of the discount.
dollar equivalent of the discount = 40% X $7
= 0.4 X $7 = $2.80
Price of yesterday's bread = $7 - $2.80 = $4.20
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