(n! + (n + 1)!) / n! = n!/n! + (n + 1)!/n! = 1 + (n + 1) = n + 2
because (n + 1)! = (n + 1)n!.
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 749. Find a linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course. Round your answer to the tenths place.
Given:
30-hour review course average a score of 620 on that exam.
70-hour review course average a score of 749.
To find:
The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.
Solution:
Let x be the number of hours of review course and y be the average score on that exam.
30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).
70-hour review course average a score of 749. So, the linear function passes through the point (70,749).
The linear function passes through the points (30,620) and (70,749). So, the linear equation is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]
[tex]y-620=\dfrac{129}{40}(x-30)[/tex]
[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]
[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]
Adding 620 on both sides, we get
[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]
[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]
[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]
We need to find the y-value for [tex]x=57[/tex].
[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]
[tex]y=183.825+523.25[/tex]
[tex]y=707.075[/tex]
[tex]y\approx 707.1[/tex]
Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.
Using the net below, find the surface area
of the pyramid.
sto
5 in
5 in.
Surface Area
=
[?] in?
Enter
Answer:
Using the net below, find the surface area
of the pyramid.
sto
5 in
5 in.
Surface Area
=
[?] in?Step-by-step explanation:
Question
The quotient of a number and 5 has a result of 2. What is the number
Answer:
Probably 10
Step-by-step explanation:
10/5=2
For the geometric series 2 + 6 + 18 + 54 + ... , find t n
Answer:
i believe its 162
Step-by-step explanation:
hope it helped :>
a square pyramid A is similar to pyramid the volume of pyramid are 1224 cubic.meters and 73 cubic meters the height of pyramid A is 18 meters. what are the possible lengths of one side if pyramid B's base? plz help
Answer:
i dont know tryna get points
Step-by-step explanation:
use the figure at the right the complete inequality statements
What are equivalent expressions please explain
Answer:
Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.
Step-by-step explanation:
What does 8 represent in the decimal 478.92?
Answer:
ones
Step-by-step explanation:
Easy
a) -2,-5.-8.-11,...
Step-by-step explanation:
???????? what is easy??
evaluate log25+log8 _log2
Step-by-step explanation:
log 25 + log 8 = log (25 × 8) = log 200
log 200 - log 2 = log (200 ÷ 2) = log 100
logarithm base 10 of 100 is 2.
Please answer fast!!!!!
Explain the steps you would use to solve the equation. Find the solution.
8^2x=4096
Answer:
x = 2
Step-by-step explanation:
note that 4096 = [tex]8^{4}[/tex] , then
[tex]8^{2x}[/tex] = [tex]8^{4}[/tex]
Since bases on both sides are equal, both 8 , then equate the exponents
2x = 4 ( divide both sides by 2 )
x = 2
Answer:
x = 2
Step-by-step explanation:
[tex]8^{2x} = 4096[/tex]
Step 1 :- Write 4096 in the exponential form with the base of 8.
[tex]8^{2x} = 8^4 [/tex]
Step 2 :- Since the base of both equation is same , set the exponents equal.
2x = 4
Step 3 :- Divide both side by 2
[tex]{2x}{2} = \frac{4 }{2}[/tex]
x = 2
4(1\:-\:2b)\:+\:7b\:-\:10
[tex]4(1\:-\:2b)\:+\:7b\:-\:10[/tex]
Answer:
-6 -b
Step-by-step explanation:
I have attached the explanation above. hopefully this will help you
What is 4 and 2/3 written as a radical?
Answer:
14/3
Step-by-step explanation:
4 and 2/3 = 4 2/3 = 4 + 2/3 = 4/1 + 2/3 = 12/3 + 2/3 = 14/3
what is the measure of < B ? help !!
The choose (C) 60
The measure of the angles of a triangle is 180, and this triangle is equilateral, so 180/3=60, each angle is 60°
please help me to solve this
Answer: x= 112°, y = 34°
Step-by-step explanation:
"Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle."
That means the angle adjacent to 56° = 90° - 56° = 34°"The angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points."
The angle adjacent to the left of ∠X = 2(34°) = 68°x = 180° - 68° = 112°
The angle adjacent to the right of ∠X = the angle adjacent to the right of ∠X = 68°y = 68 ÷ 2 = 34°
Circle theorems source: https://revisionmaths.com/gcse-maths-revision/shape-and-space/circle-theorems#:~:text=Angles%20formed%20by%20drawing%20lines%20from%20the%20ends,the%20point%20on%20the%20circumference%20our%20triangle%20touches.
The Jacksons have a scaled down model of a football field on their property. The measurements of an actual sized field
are shown below.
50 yds
120 yds
The length of the field in the backyard is 30 yards. What is the width?
18.75 yards
6.25 yards
25 yards
12.5 yards
Answer:
Scale model width = 12.5 yards
Step-by-step explanation:
Given:
Actual length of field = 120 yards
Actual width of field = 50 yards
Scale model length = 30 yards
FInd:
Scale model width
Computation:
Scale model width = [Scale model length / Actual length of field] Actual width of field
Scale model width = [30/120]50
Scale model width = [1/4]50
Scale model width = 0.25 x 50
Scale model width = 12.5 yards
Aditi has $50.00 in her wallet. She buys a shirt for $12.00 and also wants to buy some bracelets that are on sale for $0.60 each. The inequality below relates x, the number of bracelets she can buy, with her shirt purchase and the money in her wallet.
what is the greatest number of bracelets she can buy?
You use a cone-shaped cup to drink water. The cup
has a diameter of 6 centimeters and a height of
12 centimeters. What is the volume of the cup?
Use 3.14 to approximate pi. Round your answer
to the nearest tenth.
Answer:
V = 133 cm³
Step-by-step explanation:
The formula for the volume of a cone is V = (πr²h) / 3, which is just the formula for the volume of a cylinder but divided by 3, by the way.
If the diameter is 6, divide that by 2 to get a radius of 3 cm. The height and pi are already given.
V = ((3.14)(3)²(12)) / 3
V = (339.12) / 3
V = 113.04 cm³, or if rounded, it should just be 133 cm³
Answer:
113.0
Step-by-step explanation:
You have to round. Also its correct on Imagine Math.
Two sides of a triangle have the following measures, Vind the range of possible measures for
the third side,
13) 8,7
14) 12,6
A) 1
B) 2 < x < 14
C) 1
D) 1
A) 8
B) 9
C) 8 < X < 18
D) 6 < X < 18
Answer:
[tex](13)\ 1 <x < 15[/tex]
[tex](14)\ 6 <x < 18[/tex]
Step-by-step explanation:
Question 13:
[tex]a,b = 8,7[/tex] -- the two sides
Using triangle inequality theorem, we have:
[tex]a + b > x[/tex]
[tex]a + x > b[/tex]
[tex]x + b > a[/tex]
So, we have:
[tex]a + b > x[/tex]
[tex]8 + 7 > x[/tex]
This gives:
[tex]15 > x[/tex]
[tex]a + x > b[/tex]
[tex]8 + x > 7[/tex]
Collect and evaluate like terms
[tex]x > -1[/tex]
[tex]x + b > a[/tex]
[tex]x + 7 > 8[/tex]
Collect and evaluate like terms
[tex]x > 1[/tex]
Ignore the inequality with a negative value.
So, we have:
[tex]x > 1[/tex] and [tex]15 > x[/tex]
Rewrite as:
[tex]1< x[/tex] and [tex]x < 15[/tex]
Merge
[tex]1 <x < 15[/tex]
Question 14:
[tex]a,b = 12,6[/tex] -- the two sides
Using triangle inequality theorem, we have:
[tex]a + b > x[/tex]
[tex]a + x > b[/tex]
[tex]x + b > a[/tex]
So, we have:
[tex]a + b > x[/tex]
[tex]12 + 6 > x[/tex]
This gives:
[tex]18 > x[/tex]
[tex]a + x > b[/tex]
[tex]12 + x > 6[/tex]
Collect and evaluate like terms
[tex]x > -6[/tex]
[tex]x + b > a[/tex]
[tex]x + 6 > 12[/tex]
Collect and evaluate like terms
[tex]x > 6[/tex]
Ignore the inequality with a negative value.
So, we have:
[tex]x > 6[/tex] and [tex]18 > x[/tex]
Rewrite as:
[tex]6< x[/tex] and [tex]x < 18[/tex]
Merge
[tex]6 <x < 18[/tex]
3. Can a regular polygon have an interior angle of 160°
the sum of interior angle is 180:
[tex]x + 160 = 180 \\ x = 180 - 160 \\ x = 20[/tex]
f(x)=3x^2 and g(x)=x+2 find (f.g)(x)
Answer:
3[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex]
Step-by-step explanation:
(f · g )(x) = 3[tex]x^{2}[/tex] · (x + 2) = 3[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex] (Multiply the two terms by distributing)
Max can travel 100 miles in 2 hours. At this rate, how many hours will it take him to travel 650 miles?
The local skating rink pays Mary a fixed rate per pupil plus a base amount to work as a skating instructor. She earns $90 for instructing 15 students on Monday afternoon. Last Friday, she earned $62 for working with 8 students. Lisa is also a skating instructor. She receives half the base amount that Mary does, but she is paid twice as much per student. Who would earn more money instructing a class of 20 students?
answer choice
1. 120
2. 65
3. 15
4. 10
Answer:
ok so lets divide 90 by 15 to get 6 so she gets paid 6 per student and that means lisa gets paid 12 so lets just multiply
6*20=120 so mary gets paid 120
and lisa gets paid doable that so 420
but i don't know there base pay so the i can't answer this problem
Hope This Helps!!!
You have 3 pounds of egg whites. You need 8 oz to make one serving of consommé.How many servings can you make?
The number of servings you can make is 6
How to determine the number of servings?The given parameters are:
Available = 3 poundsContent per serving = 8 ozNext, we convert oz to pounds
Content per serving = 8 * 0.0625 pound
This gives
Content per serving = 0.5 pound
The number of serving is then calculated as:
Number = Available/Content per serving
This gives
Number = 3/0.5
Evaluate
Number = 6
Hence, the number of servings is 6
Read more about proportions at:
https://brainly.com/question/1781657
#SPJ9
10 − 3(2a − 1) = 3a + 1
Answer:
4/3 =a
Step-by-step explanation:
10 − 3(2a − 1) = 3a + 1
Distribute
10 -6a +3 = 3a+1
Combine like terms
13 -6a = 3a+1
Add 6a to each side
13-6a+6a = 3a+6a +1
13 = 9a+1
Subtract 1 from each side
13-1 = 9a+1-1
12 = 9a
Divide by 9
12/9 = 9a/9
4/3 =a
a = 4/3
Step-by-step explanation:10 - 3( 2a - 1 ) = 3a + 1
use the distributive property to multiply -3 by 2a -110 - 3 × 2a -3 × -1 = 3a + 1
10 - 6a + 3 = 3a + 1
collect like terms10 + 3 - 6a = 3a + 1
13 - 6a = 3a + 1
Subtract 3a from both sides13 - 6a - 3a = 3a - 3a + 1
13 - 9a = 1
subtract 13 from both side13 - 13 - 9a = 1 - 13
- 9a = - 12
divide both side by -9-9a / - 9 = - 12 / - 9
a = 4/3
please help me please
Answer:
that thing is not seeing properly and you can capture it again and resend it
PLEASE I NEED THIS NOW 50 POINTS
Write your answer as a function
Andy is wrapping gifts for his family. He ties 25 inches of ribbon around each gift. Which function gives the relationship between the number of
gifts (g) and the length of ribbon used (9)?
The function representing the relationship between the length of ribbon and the number of gifts is ?
Just Question B!
One of the numbers in the diagram is chosen at random, find the probability that the number is in set B, giving your answer as a decimal.
Gibing brainlist!
Answer:
0.4 or 0.40
Step-by-step explanation:
There are 10 total numbers. 4 of them are in set B.
So, 4/10 are in set B.
The probability is 0.4 because 4 divided by 10 is 0.4.
On a piece of paper graph f(x) 2x(3)^x then determine which graph represents the function
Answer:
ok
What do you want me to answer ?
find the value of x and HI. H and J are the endpoints
Answer:
x = 6
HI = 29
Step-by-step explanation:
✔️HI = ½(AB) => Triangle Mid-segment Theorem
HI = 5x - 1
AB = 58
Plug in the values and solve for x
5x - 1 = ½(58)
5x - 1 = 29
Add 1 to both sides
5x - 1 + 1 = 29 + 1
5x = 30
Divide both sides by 5
5x/5 = 30/5
x = 6
✔️HI = 5x - 1
Plug in the value of x
HI = 5(6) - 1
HI = 30 - 1
HI = 29
