Factor the polynomial.
3x³-300x
The result to the factorization of the polynomial is 3x (x + 10) (x - 10).
Polynomial FactorizationFactoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.
Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.
= 3x³ - 300x
= 3x(x²) - 300x
= 3x(x²) - 3x(100)
= 3x(x² - 100)
= 3x(x² - 10²)
Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );
where
a = x and b = 10= 3x (x+10) (x−10)
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amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answer:
25 minutes
Step-by-step explanation:
Subtract the two times to find the duration.
working alone, Ted can install a new deck in 15 hours. Jimmy can install the same deck in 16 hours. How long would it take them to install the deck if they worked together
The time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.
What is the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value.
Let W be the total work to be done, which is installing a new deck.
Given Ted alone can complete the work W in 15 hours.
Using unitary method,
So in one hour, work done by Ted = W/15
Also given Jimmy alone can complete the work W in 16 hours.
So in one hour, work done by Jimmy = W/16
Using unitary method,
In one hour the work done by Jimmy and Ted together = W/15 + W/16 = 31W/240
ie 31W/240 = 1 hour
So W = 240/31 = 7.7 hours
Therefore the time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.
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Sasha is bisecting a segment. First, she places the compass on one endpoint, opens it to a width larger tha the compass the same width and places it on the other endpoint. What is her next step?
Swing arcs on both sides to intersect the first two arcs created.
Swing an arc that intersects the segment.
Swing arcs that intersect a point that is not on the segment.
Swing an arc that intersects the opposite endpoint.
When bisecting a segment using a compass, Sasha's next step would be to swing an arc that intersects the segment. Correct option is B.
To bisect a segment, Sasha needs to find the midpoint of the segment. The compass can help her achieve this by creating two arcs with the same radius from each endpoint of the segment. The intersection of these arcs will be the midpoint of the segment.
Sasha's first step is to place the compass on one endpoint of the segment and open it to a width larger than the length of the segment. Then, she places the compass on the other endpoint and draws an arc that intersects the first arc.
The next step is to swing an arc with the same radius from the other endpoint of the segment, again intersecting the first arc. The intersection of these two arcs will give the midpoint of the segment, which can be marked with a straightedge.
Therefore, Sasha's next step in bisecting a segment using a compass is to swing an arc that intersects the segment.
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who has a better chance of winning the super bowl 2023
The Kansas City Chiefs has a better chance of winning the super bowl 2023.
In 1967's Super Bowl I, Las Vegas sportsbooks gave the Green Bay Packers a 14-point advantage against the Kansas City Chiefs. Nevada was the only state up until 2018 to allow legal Super Bowl sports betting.
The reigning champion Kansas City Chiefs are the early favorited in the Super Bowl 58 odds, according to the top NFL betting companies. At BetMGM, the Super Bowl 58 odds for the Kansas City Chiefs are +600. You can evaluate the odds on a team you prefer to discover the best price because competing sportsbooks provide different odds for each team to win the Super Bowl.
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Hiro painted his room. After 333 hours of painting at a rate of 888 square meters per hour, he had 282828 square meters left to paint.
The solution is, the situation can be modeled as y = 52 - 8x.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
So, the total area to be painted is (28 + 3 × 8) = 52 square meters.
Let y represent the area (in square meters) left to paint after x hours of painting then the situation can be modeled as
y = 52 - 8x ................ (1) (Answer)
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If 3 garbage trucks can collect the trash of 24 homes in a day, how many trucks are needed to collect in 72 houses?
Answer:
9
Step-by-step explanation:
72/24 = 3
72 is 3 times 24, so you need 3 times as many garbage trucks.
Answer: 9
Find the greatest whole number which divides 372 & 324 without leaving remainder
The greatest whole number that divides both 372 and 324 without a remainder is 4.
To find the greatest whole number that divides both 372 and 324 without a remainder, we can use the concept of the greatest common divisor (GCD).
One method to find the GCD is to factor each number into its prime factors and then find the product of the common prime factors.
372 can be factorized as 2 * 186, and 324 can be factorized as [tex]2^2 * 3^4[/tex]
The greatest common divisor is [tex]2^2[/tex], which is equal to 4.
So, the greatest whole number that divides both 372 and 324 without a remainder is 4. This means that 4 is the largest number that can divide both 372 and 324 evenly, leaving no remainder.
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A rectangle flower garden is 9 2/5 feet long and 6 1/2 feet wide.What is the area of the flower garden?
Answer: 61 1/10
Step-by-step explanation:
9 2/5 x 6 1/2
A plumber cut a pipe into 5 equal pieces and had 27 cm of the pipe left. For a second
pipe 15m long, he cut 11 pieces of the same length as that of each piece cut from the
first pipe and had 15 cm of the second pipe left. What was the length, in cm, of each
shorter piece of the second pipe? What was the length of the first pipe originally?
Please input your answer:
Answer:
Step-by-step explanation:
Let's call the length of each shorter piece of the first pipe x. Then the total length of the first pipe would be 5x + 27 cm.
Similarly, the length of each shorter piece of the second pipe would be x and the total length of the second pipe would be 11x + 15 cm.
Since both pipes were cut into the same length pieces, we can set the two equations equal to each other:
5x + 27 = 11x + 15
Solving for x, we can find the length of each shorter piece:
6x = -12
x = -2
This means that each shorter piece of both pipes was -2 cm long, which is not physically possible. So, this solution is not valid. This means that the problem is underdetermined and that we cannot determine the length of each piece.
f(x)=x^2-4x+3 find the quadratic function
Answer:
Step-by-step explanation:
3. Find the height of the tree below to the nearest foot.
The height of the tree to the nearest foot is 27 feet.
How to find the height of a tree?The height of the tree can be found as follows:
The height of the tree can be found using trigonometric ratios. Therefore,
let
tan ∅ = opposite / adjacent
Therefore,
opposite side = adjacent tan ∅
Hence,
height of the tree = 20 + x tan 45° = x tan 75°
20 + x tan 45° = x tan 75°
20 tan 45 + x tan 45° = x tan 75°
20 tan 45 = x tan 75° - x tan 45°
20 tan 45 = x(tan 75 - tan 45)
20 tan 45 = x(3.73205080757 - 1)
2.73205x = 20
x = 20 / 2.73
x = 7.32600732601
x = 7.34
Therefore,
height of the tree = x tan 75°
height of the tree = 7.34 × tan 75°
height of the tree = 27.3186119114
height of the tree = 27 ft
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A pet toy company performed an experiment to see how
many toys dogs might play with. Each of the 60 dogs
involved was put in a room with its owner and 4 different
toys.
The researchers recorded how many toys each of the 60
dogs used.
Fill in the blanks to complete the probability
distribution.
Do not round your answers.
Toys used
Frequency
Probability .05
0
3
1 2
2
0.25
3
3 4
21 12
9
0.35 0.2 0.15
The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
What is the probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
To fill in the blanks, we need to use the given information to complete the probability distribution table.
We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
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Two factory plants are making TV panels. Yesterday, Plant A produced 4000 fewer panels than Plant B did. Four percent of the panels from Plant A and 2% of
the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 500 defective panels?
14
The number of panels that Plant B produced is; 11000 panels
How to solve algebra word problems?We are told that Plant A produced 4000 fewer panels than Plant B did.
Thus;
A = B - 4000 -----(1)
Four percent of the panels from Plant A and 2% of the panels from Plant B were defective. Thus;
0.04A + 0.02B = 500 ------(2)
Put eq 1 in eq 2 to get;
0.04(B - 4000) + 0.02B = 500
0.04B - 160 + 0.02B = 500
0.06B = 660
B = 660/0.06
B = 11000 panels
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PLEASE!!! Someone, please help test tomorrow!! Just explain how to get this please!
The correct value of the expression is,
⇒ (2²)³ - (8 - 4)² × 4 = 0
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (2²)³ - (8 - 4)² × 4
Now, We can solve as;
⇒ (2²)³ - (8 - 4)² × 4
⇒ (4)³ - (4)² × 4
⇒ 4³ - 4³
⇒ 64 - 64
⇒ 0
Thus, We get;
⇒ (2²)³ - (8 - 4)² × 4 = 0
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2 + cscsecx/cscsecx = (sinx+cos)
Answerk bzijnjlngljntgojengojnetgihnrtgkte4wg
please help im kinda failing in math
Answer:
Step-by-step explanation:
c
a
Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days. She also paid $18 for a guided waterfall tour. Tara paid $94 in all. What was the rental cost of each day Tara used the kayak?
Answer:
$19
Step-by-step explanation:
calculate 94-18/4 = 19
32 Ounces of Juice for $7.04. How much per ounce
Answer:
$0.22.
Step-by-step explanation:
To find the cost per ounce of juice, divide the total cost of 32 ounces of juice by the number of ounces:
7.04 ÷ 32 ounces = 0.22 per ounce
So, the cost per ounce of juice is approximately $0.22.
Answer:
0.22
Step-by-step explanation:
find the quadratic equation whose roots are 5 and -9
The equation of the quadratic equation whose root are 5 and -9 is x² +4x -45
What is quadratic equation?quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The equation of a quadratic is given as :
x²-(alpha+beta)x + alpha×beta = 0
where alpha and beta are the roots of the quadratic equation.
alpha+beta = 5-9 = -4
alpha × beta = -9× 5 = -45
therefore the equation will be;
x²-(-4)x + ( -45) = 0
x² + 4x -45 = 0
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pls help i dont understand
The linear function giving the amount remaining after buying x cups of coffee is given as follows:
A(x) = -3x + 15.
How to obtain a linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.Each cup of coffee costs $3, hence the slope m is given as follows:
m = -3.
(for each cup purchased, the balance decays by $3).
Hence:
A(x) = -3x + b.
Buying 4 cups of coffee, the balance is of $3, hence the intercept b is obtained as follows:
3 = -3(4) + b
b = 15.
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if you randomly select a mechanical component, what is the probability that it weighs more than 11.5lbf
The probability that randomly selected mechanical component weighs: more than 11.5 lbf is 0.0099, less than 8.7 lbf is 0.3208, less than 5.0 lbf is 0.0228, between 6.2 lbf and 7.0 lbf is 0.1314, between 10.3 lbf and 14.0 lbf is 0.0436, between 6.8 lbf and 8.9 lbf is 0.3464.
We can use the standard normal distribution and z-scores to answer these questions:
P(X > 11.5) = P(Z > (11.5 - 8) / 1.5) = P(Z > 2.33) = 0.0099
Therefore, the probability that a randomly selected mechanical component weighs more than 11.5 lbf is 0.0099, or about 1%.
P(X < 8.7) = P(Z < (8.7 - 8) / 1.5) = P(Z < 0.47) = 0.3208
Therefore, the probability that a randomly selected mechanical component weighs less than 8.7 lbf is 0.3208, or about 32%.
P(X < 5.0) = P(Z < (5 - 8) / 1.5) = P(Z < -2) = 0.0228
Therefore, the probability that a randomly selected mechanical component weighs less than 5.0 lbf is 0.0228, or about 2%.
P(6.2 < X < 7.0) = P((6.2 - 8) / 1.5 < Z < (7 - 8) / 1.5) = P(-1.2 < Z < -0.67) = 0.1314
Therefore, the probability that a randomly selected mechanical component weighs between 6.2 lbf and 7.0 lbf is 0.1314, or about 13%.
P(10.3 < X < 14.0) = P((10.3 - 8) / 1.5 < Z < (14 - 8) / 1.5) = P(1.53 < Z < 2.67) = 0.0436
Therefore, the probability that a randomly selected mechanical component weighs between 10.3 lbf and 14.0 lbf is 0.0436, or about 4%.
P(6.8 < X < 8.9) = P((6.8 - 8) / 1.5 < Z < (8.9 - 8) / 1.5) = P(-0.47 < Z < 0.60) = 0.3464
Therefore, the probability that a randomly selected mechanical component weighs between 6.8 lbf and 8.9 lbf is 0.3464, or about 35%.
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____The given question is incomplete, the complete question is given below:
Suppose that the weight of a mechanical component is normally distributed with mean p = 8.0 Ibf and standard deviation = 1.5 lbf. Answer the following questions: 1. If you randomly select a mechanical component, what is the probability that it weighs more than 11.5 lbf? 2. If you randomly select a mechanical component, what is the probability that it weighs less than 8.7 lbf? 3. If you randomly select a mechanical component, what is the probability that it weighs less than 5.0 lbf? 5. If you randomly select a mechanical component, what is the probability that it weighs between 6.2 lbf and 7.0 lbf? 6. If you randomly select a mechanical component, what is the probability that it weighs between 10.3 lbf and 14.0 lbf? 7. If you randomly select a mechanical component, what is the probability that it weighs between 6.8 lbf and 8.9 lbf?
A watch salesman earns a commission of 40% of all watch sales made. Yesterday he sold 5 watches for $60 each and 4 watches for $40 each. How much did he earn in commission yesterday?
A. $120
B. $64
C. $40
D. $184
He earns $184 in commission yesterday on sold 5 watches for $60 each and 4 watches for $40 each.
Commission:A sales commission is a sum of money paid to an employee upon completion of a task, usually selling a certain amount of goods or services. Employers sometimes use sales commissions as incentives to increase worker productivity. A commission may be paid in addition to a salary or instead of a salary.
A salesman earns a commission 40%
He sold yesterday 5 watches for $60 each
and, 4 watches for $40 each.
We have to find the how much he earn commission?
Now, According to the question:
Price of 5 watches = 60.00 × 5 = $300
4 watches = $40.00 each
Price of 4 watches = 40.00 × 4 = $160
Total sales made = 300 + 160 = $460
His commission is 40% of the sales = 40% × 460
= 0.40 × 460 = $184
Hence, He earns $184 in commission.
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Solve -28r = 4r.
r = , r =
Step-by-step explanation:
this is very simple, we only have to divide each side by four to single out our unknown.
[tex]-28=4r[/tex][tex]-14=2r[/tex][tex]-7=r[/tex]
Answer:
the solution to the equation -28r = 4r is r = 0.
Step-by-step explanation:
To solve the equation -28r = 4r, we can isolate the variable "r" on one side of the equation and find its value. To do this, we can start by subtracting 4r from both sides of the equation:
-28r - 4r = 4r - 4r
-32r = 0
Next, we can divide both sides of the equation by -32 to find the value of "r":
(-32r) / -32 = 0 / -32
r = 0
So the solution to the equation -28r = 4r is r = 0.
What is the area of ∆AOB?
The Area of Rhombus is 97.5 cm².
What is area of Rhombus?The area of a rhombus is equal to half the product of the lengths of the diagonals. The formula to calculate the area of a rhombus using diagonals is given as, Area = (a × b )/2 where, a and b are the diagonals of the rhombus.
Given:
As, diagonals of rhombus bisect perpendicularly.
so, In triangle OAD using Pythagoras theorem
AD² = OD² + OA²
10² = 7.8² + OD²
OD= 6.25 cm
So, length of BD = 2 x 6.25 = 12.5 cm
Now, area of Rhombus = 1/2 x a x b
= 1/2 x 15.6 x 12.5
= 97.5 cm².
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The number of students enrolled at a college 18,000 and grows 5% each year. What is the initial amount
Answer:
900
Step-by-step explanation:
5% of 18,000
Please help with this question!!
According to the information, we plan to have cruising speed on for a minimum of 3 hours and a maximum of 4.1 hours.
How to calculate how many hours we are going to have the cruising speed on?To calculate how many hours we are going to have the cruising speed on we must carry out the following process:
To calculate the minimum we must subtract 35 from 215 and then divide by the speed:
215 - 35 = 180180 / 60 = 3So the minimum hours would be 3 hours.
On the other hand, to calculate the maximum we must add 35 to 215 and divide it by the speed:
215 + 35 = 250250 / 60 = 4.1So the maximum time would be 4.1 hours.
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Which is the graph of f(x) = 100(0.772)
It is not possible to graph f(x) = 100(0.772) without additional information. A function needs at least two points to graph a line. The expression f(x) = 100(0.772) represents a constant value, not a function of x, so it cannot be graphed on its own.
Answer: knvsvvs
Step-by-step explanation:
help plsplspls
Find the value of the following expression and round to the nearest integer:
34
Σ 400(0.93)n-2
n=2
The value of the expression is 5193.
How to find the value of the expression?From the question, we have the following parameters that can be used in our computation:
From the notation, we have the following values:
The first term, a = 400
The common ratio, r = 0.93
The number of terms, n = 34 - 1 = 33
The sum of the geometric progression is represented as:
Sum = a(1-rⁿ)/(1-r)
Sum = 400(1-0.93³³)/(1-0.93)
Sum = 5193
Therefore, the value of the expression is 5193
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SOMEONE, PLEASE ANSWER THESE QUESTIONS!!!
Find the y-intercept for both linear functions.
Answer:
Below
Step-by-step explanation:
The y-axis intercept occurs when x = 0
so the first one is y = 21 ( this is the value when x = 0 from table)
the second one shows every 4 increase causes a 3 decrease in y
so every 4 DECREASE in x causes a +3 INCREASE in y
decrease x = 4 to x = 0 increase y = 6 to y = 9
