Plz help me :(
Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
Answers
PROOF:
\(y^4-(y^2-9)(y^2+9)\\=y^4 -(y^4-81)\\=y^4-y^4+81\\=81\)
And 81 is ALWAYS divisible by 9
Answer:
Its 9*9
Step-by-step explanation:
The equation equals 81 and 9*9=81.
Have a great day! :)
Related Questions
A group of friends wants to go to the amusement park. They have no more than $125 to spend on parking and admission. Parking is $15, and tickets cost $12.50 per person, including tax. Write and solve an inequality which can be used to determine pp, the number of people who can go to the amusement park.
Answers
Answer:
100
Step-by-step explanation:
A recipe requires 3 cups of flour to make 15 servings and 7 cups of flour to make 35 servings how many cups of flour are needed to make 20 servings?
Answers
Answer:
a = 8
b = 2
c = 48
Step-by-step explanation:
3 cups of flour is needed to make 24 servings.
3:24
Simplify. First, divide 3 from both sides of the ratio.
(3)/3 : (24)/3
1:8
Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1
1 x 2 = b = 2
Finally, multiply 8 to 6 to get c.
8 x 6 = c = 48
~
Question 6 of 19 Step 1 of 1 Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4. Using Chebyshev's Theorem, state the range in which at least 75% of the data will reside. Please do not round your answers. Answer(How to Enter) 4 Points to
Answers
Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4, the range in which at least 75% of the data will reside is from 6.3 to 7.9.
Chebyshev's Theorem is a statistical tool that provides a range for how much data is likely to fall within a certain number of standard deviations from the mean.
Specifically, it tells us that, for any set of data, no matter how it is distributed, at least 1 - (1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.
In this case, we want to find the range in which at least 75% of the data will reside. We can use Chebyshev's Theorem to determine the minimum value of k that will give us this range. We know that at least 75% of the data should fall within two standard deviations from the mean, so we can set k = 2.
Using Chebyshev's Theorem, we can say that at least 1 - (1/2^2) = 75% of the data will fall within 2 standard deviations from the mean. The standard deviation is 0.4, so two standard deviations would be 2 * 0.4 = 0.8.
To learn more about range click on,
https://brainly.com/question/30657711
#SPJ4
to make one cup of hot chocolate, 1 1/2 tablespoons of hot cocoa mix must be used. if a snack bar wants to make 70 cups of hot chocolate, how much mix will they need?
Answers
Given:
1 cup of hot chocolate = 1½ tablespoons of cocoa mix.
70 cups of hot chocolate = x tablespoons of cocoa mix.
Note that 1½ = 1.5
Let's find how much mix will they need below:
\(\begin{gathered} \frac{1}{1.5}=\frac{70}{x} \\ \text{Cross multiply} \\ x\text{ = 70 }\ast\text{ 1.5 } \\ \text{ = }105 \end{gathered}\)Therefore the amount of hot cocoa mix they will need is 105 tablespoons
ANSWER:
105 tablespoons of hot cocoa mix
Example # 2:
Find
Za
for the confidence level 90%.
2
Example # 3:
Find 2, for the confidence level 99%.
Answers
Answer:
(a) 1.645
(b) 2.5758
Step-by-step explanation:
The complete question is: Find Z(\(\alpha\)/2) for the confidence level 90% and for the confidence level 99%.
Firstly, as we know that \(\alpha\) represent the level of significance, i.e;
Level of significance = 1 - confidence level
(a) We are given the confidence level of 90%, so;
Level of significance = 1 - 90%
= 1 - 0.90 = 0.10 or 10%
Now, \(Z_(_\frac{\alpha}{2}_)\) = \(Z_(_\frac{0.10}{2}_)\) = \(Z_(_0_._0_5_)\)
This means that we have to look for a critical value in the z table at a 5% level of significance which gives us a value of 1.645.
(a) We are given the confidence level of 99%, so;
Level of significance = 1 - 99%
= 1 - 0.99 = 0.01 or 1%
Now, \(Z_(_\frac{\alpha}{2}_)\) = \(Z_(_\frac{0.01}{2}_)\) = \(Z_(_0_._0_0_5_)\)
This means that we have to look for a critical value in the z table at a 0.5% level of significance which gives us a value of 2.5758.
A factory manager wishes to install types of machines, small and large. A small machine needs 2 operators and occupies 4m² of floor space. A large machine needs 3 operators and accupies 8m³of floor space. There are up to 30 operators available and 72m² of floor space. At Least 4small machines and at least 5 large machines must be installed.
a) Taking X to be the number of small machine, and y as the number of large machine to be installed, write down. the four major inequalities required.
b) Draw a graph to show the region satisfying the inequalities
c) Determine the maximum number of machines he can install .
d) If the profit made by each small machine is 250,000 and by the large type is 300,000 per week, find the maximum profit the factory can make in one week and the number of machines of each type that should be installed.
Answers
a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72
b) We have drawn the graph.
c) The maximum number of machines that can be installed is 11.
d) The maximum profit is 2,500,000.
What is inequality?
An inequality is a mathematical statement that shows the relationship between two values where one value is either greater than or less than the other value. It is represented by symbols such as >, <, ≥, or ≤. For example, if x is a variable and we want to express that x is greater than 5, the inequality would be written as x > 5.
a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72
b) To graph the region, we can plot the lines that define the inequalities and shade the area that satisfies all of them.
c) Solving the system of inequalities graphically, we find the maximum number of machines that can be installed is 11 (6 small and 5 large).
d) To find the maximum profit, we need to substitute the number of machines into the profit equation. P = 250,000X + 300,000Y. Plugging in X = 6 and Y = 5, we find the maximum profit to be 2,500,000.
Hence,
a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72
b) We have drawn the graph.
c) The maximum number of machines that can be installed is 11.
d) The maximum profit is 2,500,000.
To learn more about the inequalities, visit:
https://brainly.com/question/24372553
#SPJ1
What’s the correct answer for this question?
Answers
Answer:
B:
Step-by-step explanation:
If we rotate the 3-D figure around y-axis we'll obtain a cone with a radius of 3 units
solve above question
Answers
2 Substitute
y
=
2
−
3
x
y=2−3x into
x
+
y
=
7
x+y=7.
−
2
x
+
2
=
7
−2x+2=7
3 Solve for
x
x in
−
2
x
+
2
=
7
−2x+2=7.
x
=
−
5
2
x=−
2
5
4 Substitute
x
=
−
5
2
x=−
2
5
into
y
=
2
−
3
x
y=2−3x.
y
=
19
2
y=
2
19
5 Therefore,
x
=
−
5
2
y
=
19
2
x=−
2
5
y=
2
19
Together,two boxes of spices weigh 4 pounds 8 ounces. Each pound is worth $400. How much are the boxes worth in all.
Answers
The total worth of the 4 pounds and 8 ounces of box is $1800
Total costWeight of the boxes:
4 pounds8 ouncesCost of each pound = $400Convert ounces to pounds:
8 ounces to pounds = 0.5 pounds
Total cost of the boxes = 4 pounds (400) + 0.5 pounds (400)
= 1600 + 200
= $1,800
Learn more about ounces to pounds:
https://brainly.com/question/10618309
#SPJ1
206) A recipe for cupcakes calls for 3-
3
10
200
7
sugar. Julio accidentally put in 4-
10
How many extra cups did he put in?
cups of
cups.
Answers
Julio accidentally put in an extra 1/10 cup of sugar.
To calculate the number of extra cups of sugar that Julio put in, we need to find the difference between what the recipe called for (3/10 cups) and what he actually added (4/10 cups).
The difference can be calculated as follows:
Actual amount - Required amount = Extra amount
= 4/10 - 3/10
= 1/10
Therefore, Julio accidentally put in an extra 1/10 cup of sugar.
Learn more about Unitary Method here:
https://brainly.com/question/28276953
#SPJ1
X^2 + 18x + 81 = 25
what are the solutions
Answers
Answer:
Step-by-step explanation:
use quadratic formula answers -4,-14
9. Kyoko plans to put a new wood floor in her den, which is shown in the floor plan.
a. What is the area of the floor?
b. At a cost of $11 per square foot, how much will it
cost to put down the new floor?
c. Kyoko plans to put a rectangular area rug in the
room. The rug will be large enough so that only
a 2-foot wide section of the wood floor will be
exposed on each side. Find the dimensions of the
area rug.
d. What is the area of the area rug?
Den
17 ft x 14.5 ft
e. Find the area of the wood floor that will be exposed once the area rug is laid down.
Answers
a.) The area of the floor = 246.5ft²
b.) The amount that it will cost to put down the new floor would be = $2,711.5
C.) The new dimensions of the area rug would be= Length= 21ft, width = 18.5 ft.
d.) The area of the area rug would be = 388.5ft²
How to calculate the area of the floor?For question a.)
The floor has a rectangular shape. The area of a rectangle = length×width
area of the floor= 17×14.5
= 246.5ft²
For question b.)
For a square foot(1ft²) = $11
246.5ft² = 246.5×11 = $2,711.5
For question c.)
Since the rug will be extended by 2ft at each side, the new dimensions would be:
length = 2+2+17 = 21ft
width = 2+2+14.5 = 18.5ft
For question d.)
The area of the floor with the new dimensions = 21×18.5 = 388.5ft²
Learn more about area here:
https://brainly.com/question/25292087
#SPJ1
Sue-Lee scored 93 points on a science test on Monday and 77 points on a science test on Friday. What was the difference between her two scores?
Answers
Answer:
16
Step-by-step explanation:
93 - 77 = 16
Answer:
16
Step-by-step explanation:
Difference is a key word for subtraction in problems like this/ So take Sue-Lee's two test scores and subtract them, 93-77 is equal to 16. The difference between the two scores is 16
What is 5% of 345? ......
Answers
Answer:
17.25
Step-by-step explanation:
5/100 x 345 = 1725/100 = 17.25
An employee of the department store receives 10% off all purchases. The employee purchases a shirt for $46.99. Determine the cost of this purchase.
Answers
The cost of purchase of the employee for a shirt worth $46.99 is $42.30 .
In the question , It is given that
amount of discount employee receives = 10%
Price of the shirt = $46.99 ...(i)
amount of discount the employee got for the shirt = 10% of 46.99
= 0.10*46.99 ...(as 10%=0.10 )
= 4.699 ...(ii)
So the amount of discount the employee got for the shirt = $4.699
The cost of purchase = Price of shirt - discount
Substituting the values from equation (i) and equation (ii) we get,
cost of purchase = 46.99 - 4.699
= 42.291
≅ 42.30
Therefore , the cost of purchase of the employee for a shirt worth $46.99 is $42.30 .
Learn more about Discount here
https://brainly.com/question/13887247
#SPJ1
Two buildings are 18 m part. The shorter building is 12 m high while the taller one is 19 m high. Find the distance, x m between the top of the buildings.
Answers
The distance between the tops of the buildings is 28.5 meters.
To find the distance between the top of the buildings, we can use the concept of similar triangles.
Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).
We can set up a proportion based on the similar triangles formed by the buildings:
a/c = b/x
Substituting the known values:
12/18 = 19/x
To find "x," we can cross-multiply and solve for "x":
12x = 18 * 19
12x = 342
x = 342/12
x = 28.5 m
Therefore, the distance between the tops of the buildings is 28.5 meters.
for such more question on distance
https://brainly.com/question/12356021
#SPJ8
What is 3.65 x 5
♀️
Answers
Answer:
18.25
Step-by-step explanation:
Amo has three times as many marbles as
Effah. Amo gives Effah 15 marbles, and
Then Effah has twice as many as Amo.
How many had each as first?
Answers
Step-by-step explanation:
amo tenia 9 canicas y efhha 3
If anyone can help with any of these probability questions, I'll give more points and brainiest!! Idaho Jones regains consciousness and next to her are 4 blodegradable packing peanuts. 5 seconds later each peanut has split in half, and each half grows into a full-size peanut. This repeats in the next 5 seconds. She sees a door with a keypad. A sign next to it has a timer indicating 10 seconds have passed and says the code is the number of peanuts when the timer reaches 100. (After 10 secords there were 16 peanuts.) Idaho realizes she must escape before then or the peanuts could suffocate her. Show how she figures out the code to open the door, and write what the code is
A mans
Idaho gets out and closes the door behind her. She is in a room with one exit, and the lock requires a key. There's a table with a briefcase that is also locked. It has a three-digit combination. The first part of the combination is on a wheel with all 10 digits. The second wheel has only 5 digits, and the third has 3 digits. How many combinations are possible?
150
combinations
The briefcase holds a key and out Idaho goes. She is met by an enchanted skeleton that directs her to a wall where a shelf has room for 5 books. The 5 ancient books are on the floor. She puts them on the shelf, but nothing happens. She realizes they must be put in the correct order. How many attempts will Idaho need to make if she doesn't get it right until her last attempt
Answers
Answer: let me explain!
Step-by-step explanation: So this might seem really confusing at first, but it’s actually suuuuuuper easy :P
So, if you think about it, every five seconds the amount of peanuts…well I don’t know how to explain it but let me show you this with numbers.
(4x2)x2x2x2 and so on. The number multiplies by two every five seconds from there. So figure out how many groups of five second there are in 100 seconds by dividing!
It’s 20!
So since 5 happens 20 times, and every time 5 happens, 2 happens, 2 also happens 20 times! (If that makes any sense)
So that answer would be 8x*twenty twos*
Which is…*drumroll please*
8,388,608
I even double checked!
And for the briefcase skeleton thing
She needs to try it 25 times because there are 5 books and each book can be switched with the other 4 times if the first one doesn’t work, therefore you need to multiply and the equation would be 5^2, or in other words, 25.
Don’t forget ur units!
Hope this helps :P
Joey is putting all of his trophies onto 7 shelves. If he places 7 trophies on each shelf but still has 4 trophies left over, how many
trophies does he have?
OA. 53
OB. 35
OC. 18
OD. 49
Answers
Answer:
53
Step-by-step explanation:
7 * 7 = 49 + 4 = 53
Answer:
A. 53
Step-by-step explanation:
Find number of trophies on shelves:
7 shelves x 7 trophies each = 49 trophies on shelves
Find total number of trophies:
49 trophies on shelves + 4 leftover = 53 trophies overall
So the answer is A. 53
Solve 2/3x-1/5>1.
x>
Answers
Answer:
x> 9/5
Step-by-step explanation:
is 1 over 3 = to 3 out of 3
Answers
the correct answer is No
Step-by-step explanation:
it's not equal
Answer:
\(\frac{1}{3}\neq\frac{3}{3}\)
Step-by-step explanation:
The two numbers are different
If <2 is equivalent to (2x-8)• what is the value of c?
A 62•
B 35•
C 28•
D 18•
Answers
Reason:
\(\angle 1 = 62^{\circ}\) because of the vertical angles theorem.
Then angle 1 and angle 2 add to 90 degrees (the angles are complementary).
\(\angle 1 + \angle 2 = 90\\\\62 + (2x-8) = 90\\\\2x + 54 = 90\\\\2x = 90 - 54\\\\2x = 36\\\\x = 36/2\\\\x = 18\\\\\)
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
Answers
Answer:
They will meet after 4 hours from the departure------------------------
The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.
The remainder of the distance is reducing by:
110000 + 90000 = 200000 km an hourTime to travel before they meet:
(710000 - 110000)/200000 = 600000/200000 = 3 hoursAdd the first hour to this to get total travel time of 4 hours.
Find the area of the parallelogram below
Answers
Step-by-step explanation:
area of the parallelogram = 7 × 14
=98 cm²
Explanation: To find the area of a parallelogram, you need to multiply the base and the height. The base in this case is 14, and the height is 7. The only number that will not be used is 9. This will not be used as the height since it it slanted.
Equation: 7x14=98
Hope this helps!
A middle school took all of its 6th grade students on a field trip to see a symphony at a theater that has 4980 seats. The students filled 3237 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answers
Answer: 65%
Step-by-step explanation: *using the butterfly* x over 100 equals 3237 over 4980. multiple to get 4980x=323700. divide to get x by itself. x=65
Answer:
53.85%
Step-by-step explanation:
The percentage increase from 3237 to 4980 is 53.85%.
A rectangular room is
1.5
times as long as it is wide, and its perimeter is
35
meters. Find the dimension of the room.
The length is :
meters and the width is
meters.
Answers
The dimensions of the room are approximately 7 meters by 10.5 meters.
The length is 10.5 meters and the width is 7 meters.What are dimensions?In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.
Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.
The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:
\(\text{Perimeter} = 2(\text{length} + \text{width})\)
Substituting the values we have for length and width, we get:
\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)
Simplifying the equation, we get:
\(\rightarrow35 = 2(2.5\text{x})\)
\(\rightarrow35 = 5\text{x}\)
\(\rightarrow\text{x}=\dfrac{35}{5}\)
\(\rightarrow\bold{x\thickapprox7}\)
So the width of the room is 7 meters.
To find the length, we can substitute x into the expression we have for the length:
\(\rightarrow\text{Length} = 1.5\text{x}\)
\(\rightarrow\text{Length} = 1.5(7)\)
\(\rightarrow\bold{Length=10.5}\)
So the length of the room is 10.5 meters.
To know more about dimensions, click on:
https://brainly.com/question/31677552
giving brainliest!
A can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters. Which measurement is donest to the total suratace area
of the can in square centimeters?
Answers
Answer:
radius r = 3 cm
height h = 10 cm
volume V = 282.743339 cm^3
lateral surface area L = 188.495559 cm^2
top surface area T = 28.2743339 cm^2
base surface area B = 28.2743339 cm^2
total surface area A = 245.044227 cm^2
In Terms of Pi π
volume V = 90 π cm3
lateral surface area L = 60 π cm^2
top surface area T = 9 π cm^2
base surface area B = 9 π cm^2
total surface area A = 78 π cm^2
Step-by-step explanation:
Agenda:
r = radius
h = height
V = volume
L = lateral surface area
T = top surface area
B = base surface area
A = total surface area
π = pi = 3.1415926535898
√ = square root
Formluas:
Cylinder Formulas in terms of r and h:
Calculate volume of a cylinder:
V = πr2h
Calculate the lateral surface area of a cylinder (just the curved outside)**:
L = 2πrh
Calculate the top and bottom surface area of a cylinder (2 circles):
T = B = πr2
Total surface area of a closed cylinder is:
A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
6 pizzas cost $16 What will 4 pizzas cost
Answers
Answer:
$10 2/3
Step-by-step explanation:
Answer:
$10.67
Step-by-step explanation:
First, we need to find out what one pizza costs.
16 divided by 6 will get us the cost of one pizza.
16/6=2.67 (rounded to nearest tenth)
Each pizza costs $2.67
Now to figure out the cost of 4 pizzas
4.67x4=10.67 (rounded to nearest tenth)
Four pizzas cost $10.67
Identify the x intercept and y intercept of a line with the equation 2x-4y=8
Answers
Answer:
x=6
Step-by-step explanation:
2x-4y=8
+4 +4
2x=12
--- ---
2x 2x
x=6