The degree of the given polynomial [tex]3x^5[/tex] is quintic that is 5 and this can be determined by comparing the given polynomial with the generalized quintic equation.
Given :
Polynomial -- [tex]3x^5[/tex]
The following points should be remembered in order to determine the degree of any polynomial:
The generalized quadratic equation is represented by: [tex]ax^2 + bx + c =0[/tex]The generalized cubic equation is represented by: [tex]ax^3 + bx^2 + cx + d =0[/tex]The generalized quartic equation is represented by: [tex]ax^4 + bx^3 + cx^2 + dx+e =0[/tex]The generalized quintic equation is represented by: [tex]ax^5 + bx^4 + cx^3 + dx^2+ex + f =0[/tex]So, from the above points, it can be concluded that the degree of the given polynomial [tex]3x^5[/tex] is quintic that is 5. Therefore, the correct option is C).
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Nelson finds a video game for $38.50. The game is on sale for $31.57. What is the percent of discount on the game?
Enya is building a storage cupboard in the shape of a rectangular prism. The rectangular prism has a square base with side lengths of 2.3 feet and a height of 3.6 feet. Use percentage to compare the amount of paint she would use to paint all but the bottom surface of the prism to the amount she would use to paint the entire prism. Round your final answer to the nearest tenth.
Enya will paint
________% of the surface area of the storage cupboard.
PLEASE HELP!!!
To compare the amount of paint Enya would use to paint all but the bottom surface of the storage cupboard to the amount she would use to paint the entire prism, calculate the surface area of the prism and the surface area of all but the bottom surface of the prism. Then, divide the surface area of all but the bottom surface by the surface area of the entire prism and multiply by 100. Round the final answer to the nearest tenth.
Explanation:To compare the amount of paint Enya would use to paint all but the bottom surface of the storage cupboard to the amount she would use to paint the entire prism, we need to calculate the surface area of the prism and the surface area of all but the bottom surface of the prism.
Step 1: Calculate the surface area of the prism by adding the areas of all its faces. The prism has two rectangular faces with dimensions 2.3 ft by 3.6 ft, two rectangular faces with dimensions 2.3 ft by 2.3 ft, and one rectangular face with dimensions 3.6 ft by 2.3 ft.
Step 2: Calculate the surface area of all but the bottom surface of the prism by subtracting the area of the bottom surface from the total surface area of the prism. The bottom surface has dimensions 2.3 ft by 2.3 ft.
Step 3: Calculate the percentage by dividing the surface area of all but the bottom surface of the prism by the surface area of the entire prism and multiplying by 100. Round the final answer to the nearest tenth.
PLS PLS HELP, WILL GIVE BRAINLIEST-Kenard takes a square piece of cardboard and cuts 4 in. by 4 in. squares out of each corner. He folds the sides up to make a box without a top.
What equation can Kenard use to determine the volume of the box, where x is the side length of the original piece of cardboard?
Express the equation in standard form.
Enter your answer in the box.
1.) Four teachers bought an old boat for $60.
The first teacher paid one-half of the sum of the amounts paid by the other teachers.
The second teacher paid one-third of the sum of the amounts paid by the other teachers.
The third teacher paid one-fourth of the sum of the amounts paid by the other teachers.
How much did the fourth teacher pay?
2.) What is the smallest number of coins that you need so that you can give exact change for any amount from 1 cent to 99 cents?
Show your work please. Any improper answers will be reported and removed- thanks!
:) Have fun!
The diameter of the circle above is 98 cm. What is the circumference of the circle?
Answer Check!! Which domain restrictions apply to the rational expression.
helppppppppppppppppppppp
Simplify: (8x4)(4x3)/7x2
A. 32x5/7
B. 1/28x
C. 1/3x
D. 7/9x4
Step-by-step explanation:
The answer is A: (32 × ^5)/7
help me please ASAP !!!!!
Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need…
to make 1.5% of syrup
Help with this Geometry problem please
Which of the following is equivalent to log7 50 rounded to three decimal places?
2.010
1.772
0.854
0.497
Answer:
Option A - [tex]log_7 50=2.010[/tex]
Step-by-step explanation:
Given : The expression [tex]log_7 50[/tex]
To find : Which of the following is equivalent and rounded to three decimal places.
Solution :
We solve the given expression [tex]log_7 50[/tex] using calculator
We get, [tex]log_7 50=2.0103821378[/tex]
Rounded to three decimal places
[tex]log_7 50=2.010[/tex]
Therefore, Option A is correct.
The gym teacher is told that the average height of the girls in her physical education class is 5’4”, and the heights follow the normal distribution. She is told that 68% of the girls are 5’2” to 5’6” tall. She measures the height of each girl and finds that the heights do follow the normal distribution. Based on her findings, she determines that 95% of the girls will be 5’0” to 5’8” tall. Use your knowledge of normal distribution to select two options that will justify the gym teacher’s belief.
Final answer:
The gym teacher's belief is justified by using the empirical rule, which describes the distribution of data in a normal distribution. Since 68% of the girls fall within 1 standard deviation of the mean, it's likely that 95% fall within 2 standard deviations, supporting her height range belief.
Explanation:
The gym teacher's belief can be justified by understanding the properties of the normal distribution and the empirical rule. The empirical rule states that for a normal distribution:
Approximately 68% of the data will fall within 1 standard deviation (±1σ) of the mean.
Approximately 95% of the data will fall within 2 standard deviations (±2σ) of the mean.
Approximately 99.7% of the data will fall within 3 standard deviations (±3σ) of the mean.
In the teacher's class, 68% of the girls are between 5'2” and 5'6”, which is within 1 standard deviation of the mean height of 5'4”. Therefore, it's likely that 95% of the girls would fall within 2 standard deviations, which explains her belief that 95% of the girls would be between 5’0” to 5’8”.
Use the substitution method to solve the system of equations. Choose the correct ordered pair. x + 2y = 12 –x = –y – 6
A. (9, 3)
B. (7, 1)
C. (6, 0)
D. (8, 2)
Answer: D
Step-by-step explanation:
The ordered pair of the system of equations is (8, 2).
Option D is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x + 2y = 12 _____(1)
x = 12 - 2y _____(2)
-x = -y - 6 _______(3)
Putting (2) in (3) we get,
-(12 - 2y) = -y - 6
-12 + 2y = -y - 6
-12 + 6 = -y - 2y
-6 = -3y
y = 2
Now,
y = 2 in (2)
x = 12 - 2 x 2
x = 12 - 4
x = 8
Thus,
The ordered pair is (8, 2).
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The three sides of a triangle are in the ratio 2:3:5. If the longest side of the triangle is 45m, find the perimenter of the triangle
which of these equations represent functions where x is the input and y is the output? Select each correct answer.
A- x=5
B- y=4
C- y=3x
D- x=3y
E- x+y=5
Scott signed a two-year lease for a monthly rent of $505. How much will
he pay in rent over the term of his lease?
a. $13,130
b. $1,212
c. $6,060
d. $12,120
AGAIN WILL GIVE BRAINEST TO FIRST PERSON WHO ANSWERS
Does the point ( 3 , 3 ) lie on the circle that is centered at the origin and contains the point (3, 0)? Why?
A) Yes, because ( 3 )2 + ( 3 )2 = 9
B) Yes, because you can create always create a circle through two given points. C) No, because ( 3 , 3 ) is less than 3 units away from the origin.
D) No, because ( 3 , 3 ) is greater than 3 units away from the origin.
Answer:
Its actually C his whole explanation is wrong
Step-by-step explanation:
Can someone tell me if the answer is correct?
[tex]1,\frac{1}{8},\frac{1}{27},\frac{1}{64},...,\frac{1}{n^{3}},...[/tex]
The denominator of the seventh term is
A.] 125
B.] 216
C.] 343
D.] 513
Answer:
the answer is C.] 343
Three weeks ago John bought stock at 49 1/4 ; today the stock is valued at 49 7/8. We could say the stock is preforming at which of the following?
Solution:
Value of Stock three weeks ago = [tex]49 \frac{1}{4}[/tex]
Current value of stock = [tex]49 \frac{7}{8}[/tex]
Total increase= [tex]49 \frac{7}{8}[/tex]-[tex]49 \frac{1}{4}[/tex]=[tex]\frac{5}{8}[/tex]
So, we can conclude from above two observation, that
The market value of that stock or bond has rose higher the reason being value of the organization or product i.e stock is slanting in upward direction.Why value of organization has increased because company has cordial relationship with it's employees, clients and the people attached with this organization, means distribution of profit is equally shared between owner and people attached with this organization.
Anne had 28 pens, but 23 of them ran out of ink. How many of Anne's pens still have ink?
___of Anne's pens still have ink.
Describe the end behavior of the function f(x) = 3 − 4x + 6x2 − 5x3.
we are given
[tex]f(x)=3-4x+6x^2-5x^3[/tex]
we can see that this is polynomial
so, firstly we will find degree and leading coefficients
Degree:
It is the highest exponent of the polynomial
highest exponent is 3
so, degree=3
which is odd
Leading coefficient:
It is the constant term multiplied to highest exponent term
we can see that
constant term is -5
so, leading coefficient is -5
which is negative
End behavior:
degree is odd and leading coefficient is negative
so, it rises to left and falls to right
or we can also write as
[tex]x-->-\infty, y-->\infty[/tex]
[tex]x-->\infty, y-->-\infty[/tex]
Answer:
Ends up in Quadrants II and IV
Step-by-step explanation:
Since the leading coefficient is −5 and the degree is 3, the function has the behavior described.
Part 1.] In two or more complete sentences, describe the difference between an infinite series and a finite series.
Part 2.] In two or more complete sentences, explain why the following sequence is an example of a finite series.
2 + 4 + 8 + 16 + ... 256
Part 3.] In two or more complete sentences describe why the following series is an example of an infinite series.
1 + 2 + 3 + 4 + 5 + ...
Part 4.] The first picture
Part 5.] Express the series in summation notation.
2 + 4 + 6 + 8 + 10 + 12
Part 6.] Suppose you start an annuity where you invest $2,000 at the beginning of each year and 4% interest is paid at the end of the year. What is the value of the annuity at the end of 5 years, rounded to the nearest dollar? It is $____
Part 7.] Find the sum picture
Answer:for oddysey the answer to number 6 is 10833
Step-by-step explanation:
Mark Y inside regular pentagon PQRST so that PQY is equilateral Is RYT straight? explain
Trevor is going to Debra's Steakhouse and really wants filet for dinner and creme brulee for dessert. He knows that the probability of getting a filet at Debra's is 0.9 and the probability of creme brulee being a desert is 0.77. If he knows the two events are independent of one another, show the calculation for P(getting a steak and getting a creme brulee)
Answer:
(0.9)(0.77)
Step-by-step explanation:
(0.9)(0.77)
Since the two events are independent you can use the multiplication rule
Complete this statement: The sum of the measures of the exterior angles of an n-gon, one at each vertex, is _____ degrees.
a) 360
b) (n-2)180
c) [tex]\frac{(n-2)180}{n}
[/tex]
d) 180n
Please help ASAP.
does the function y=4^-2x represent an exponential growth or decay? what is the percent rate of change?
The function y=4^-2x represents exponential decay. The percent rate of change is 6.25%.
Explanation:The function y=4-2x represents exponential decay. In an exponential decay function, as the value of x increases, the value of y decreases. On the other hand, in exponential growth, as the value of x increases, the value of y increases.
The percent rate of change can be found by determining the decay factor, which is equal to 1 divided by the base of the exponential function raised to the power of the exponent.
In this case, the decay factor would be 4-2 = 1/16. To find the percent rate of change, we can convert the decay factor to a percentage by multiplying it by 100%, so the percent rate of change would be 1/16 * 100% = 6.25%.
How would you solve for side a? Pythagorean theorem, cause if that's the case wouldn't
a=?
b=15
c=7
But we know that 2 sides of a triangle can't be greater than the third (or am I getting that rule wrong?)
Solve for x.
3x2−6x+2=0
x=3±23√3
x=6±23√3
x=3±3√3
x=6±43√3
Answer:
[tex]\frac{3\±\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Whe have the function [tex]3x^2-6x+2=0[/tex]
To solve this equation we must factor.
To factor, we need to find the points where the function is equal to zero. So we use the quadratic formula
[tex]\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
Where:
a = 3
b = -6
c = 2
Then
[tex]\frac{-(-6) + \sqrt{(-6)^2-4(3)(2)}}{2(3)} = \frac{3+\sqrt{3}}{3}\\\\and\\\\\frac{-(-6) - \sqrt{(-6)^2-4(3)(2)}}{2(3)}= \frac{3-\sqrt{3}}{3}[/tex]
finally the correct answer is [tex]\frac{3\±\sqrt{3}}{3}[/tex]
Final answer:
To solve the quadratic equation 3x² - 6x + 2 = 0, apply the quadratic formula with a=3, b=-6, and c=2, ultimately finding the solutions x = 1 + √(3) / 3 and x = 1 - √(3) / 3.
Explanation:
To solve the quadratic equation 3x² - 6x + 2 = 0, we can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a) where a, b, and c are coefficients from the equation ax² + bx + c = 0. In this equation, it is given a = 3, b = -6, and c = 2. Substituting these values into the formula gives us:
x = (6 ± √((-6)² - 4 · 3 · 2)) / (2 · 3)
x = (6 ± √(36 - 24)) / 6
x = (6 ± √(12)) / 6
x = (6 ± 2 √(3)) / 6
x = 1 ± √(3) / 3
The two possible solutions for x are then x = 1 + √(3) / 3 and x = 1 - √(3) / 3.