Answer:
Step-by-step explanation:
Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.
A) The polynomial in standard form is therefore - 3x⁸ + 2x⁵ + 4x³. We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.
B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8
C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵, 4x³ and - 3x⁸.
D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as -3x⁸ + 2x⁵ + 4x³, the leading term will be - 3x⁸
E) Given the leading term to be - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3
Someone help me understand
Answer:
f¯¹(x) = 23/ (6x + 3)
Step-by-step explanation:
f(x) = (23 – 3x)/6x
The inverse, f¯¹, for the above function can be obtained as follow:
f(x) = (23 – 3x)/6x
Let y be equal to f(x)
Therefore, f(x) = (23 – 3x)/6x will be written as:
y = (23 – 3x)/6x
Next, interchange x and y.
This is illustrated below:
y = (23 – 3x)/6x
x = (23 – 3y)/6y
Next, make y the subject of the above expression. This is illustrated below:
x = (23 – 3y)/6y
Cross multiply
6xy = 23 – 3y
Collect like terms
6xy + 3y = 23
Factorise
y(6x + 3) = 23
Divide both side by (6x + 3)
y = 23/ (6x + 3)
Finally, replace y with f¯¹(x)
y = 23/ (6x + 3)
f¯¹(x) = 23/ (6x + 3)
Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is
f¯¹(x) = 23/ (6x + 3)
If Tristan wants to stretch the spring by 9 inches, how many kilograms of weight must he apply to it? I need help with it please.
Answer:
9/3 = 3x/3
3 = x
The spring stretches 9 inches with 3 kilograms of weight attached to it
Step-by-step explanation:
Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:
y = 3x
9 = 3x.
Divide both sides of the equation by 3
Answer:The spring stretches 9 inches with 3 kilograms of weight attached to it.
Step-by-step explanation:
Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:
y = 3x
9 = 3x.
Divide both sides of the equation by 3:
The spring stretches 9 inches with 3 kilograms of weight attached to it.
How to solve this question
hopefully this answer can help you to answer the next question. can you choose this answer as the brainliest answer and give five stars
What is the value of x to the nearest tenth?
Answer:
x=9.6
Step-by-step explanation:
The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.
The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.
Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:
[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]
Factor of
x2 – 14x + 24
A. (x - 6)(x - 4)
B. (x - 8)(x - 3)
C. (x - 12)(x - 2)
D. (x - 24)(x - 1)
Answer: The answer is C.
Step-by-step explanation:
Hi, there!!!
The answer is option C.
The solution is in picture.
I hope it helps....
Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7
Rewrite 3 3/4 as an improper fraction
3 3/4 = 15/4
Now you have
15/5 / 5/7
When you divide fractions, change the division to multiplication and flip the second fraction over:
15/4 x 7/5
Now multiply the top numbers together and the bottom numbers together:
( 15 x 7) / (4 x 5) = 105/20
Write as a proper fraction:
105/20 = 5 1/4
find the dimension of the swimming pool if the sum must be 50 feet and the length must be 3 times the depth.
Answer:
depth 5 8.3 ft, length 5 24.9 ft, width 5 16.8 ft
find the missing side. round your answer to the nearest tenth. PLEASE HURRY!
Answer:
44.8
Step-by-step explanation:
Using the Cosine formula, we first have Cos 48 = 30/x. So then we just solve for x and get 44.8342965, which rounds to 44.8
I hope this helped! :D
a lottery offers one $1000 prize one $500 and two $50 prizes. one thousand tickets are sold at $2.50. what is the expectived profit
Answer:
$900
Step-by-step explanation:
To begin with let us estimate the total cash value of the prices
$1000 x 1= 1000
$500 x 1= 500
$50 x 2= 100
Total = $1600
Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets
2.5*1000= $2,500
Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600
Then the expected profit is = $2,500-$1600= $900
Please help brainliest will be given
Complete the equation describing how
x and y are related.
x
-1
5
0 1 2 3 4
3 8
V 2
13
18
23
28
y = 5x + [?]
Enter the answer that belongs in [?].
How many gallons of a 5% bleach solution must be
added to 10 Gallons of a 20% bleach solution to
produce that is 15% bleach
Answer:
Step-by-step explanation:
10 gallons of the 20% solution contain 2 gallons of bleach.
x gallons of the 5% solution contain 0.05x gallons of bleach.
If the two are combined, the resulting 10+x gallons contain 2+0.5x gallons of bleach. The concentration is (2+0.05x)/(10+x).
(2+0.05x)/(10+x) = 15%
2+0.05x = 0.15(10+x)
2+0.05x = 1.5+0.15x
0.5 = 0.10x
x = 5
5 gallons of 5% solution is added to the 10 gallons of 20% solution.
Find 900 ÷ 90.
plz help
Answer:
the answer is 10
Step-by-step explanation:
900 ÷ 90
=> 10 [tex]\sf{}[/tex]
Answer:
The answer is 10.
Step-by-step explanation:
900/90=cut 0 of numerator and denominator then 90 divide by 9 is 10.
a theater has (2x+1) rows of seats, with (x-3) seats in each row. how many seats are in the theater?
A. 2x^2- 5x- 3
B. 2x^2+ 5x- 3
C. 2x^2- 7x+ 3
D. 2x^2- 7x- 3
(2x+1)(x-3)
y(x-3) .... let y = 2x+1
y*x+y(-3) .... distribute
xy - 3y
x( y ) - 3( y )
x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1
2x^2 + x - 6x - 3 ..... distribute
2x^2 - 5x - 3
Answer is choice A
Write each expression in a simpler form that is equivalent to the given expression. Let g be a nonzero number. 1/g^1 or 1/g-1
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
Apply rule : [tex]a^1 =a[/tex]
[tex]\displaystyle \frac{1}{g^1 } =\frac{1}{g}[/tex]
[tex]\displaystyle \frac{1}{g^{-1}}[/tex]
Apply rule : [tex]\displaystyle a^{-b}=\frac{1}{a^b}[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }[/tex]
Apply rule : [tex]\displaystyle \frac{1}{\frac{1}{a} } =a[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }=g[/tex]
Answer:
[tex]\frac{1}{g^1}[/tex]
= [tex]\frac{1}{g}[/tex]
[tex]\frac{1}{g - 1}[/tex]
= [tex]\frac{g^1}{1}[/tex]
= [tex]\frac{g}{1}[/tex]
= g
Hope this helps!
John runs a computer software store. Yesterday he counted 140 people who walked by the store, 63 of whom came into the store. Of the 63, only 25 bought something in the store.
(a) Estimate the probability that a person who walks by the store will enter the store. (Round your answer to two decimal places.)
(b) Estimate the probability that a person who walks into the store will buy something. (Round your answer to two decimal places.)
(c) Estimate the probability that a person who walks by the store will come in and buy something. (Round your answer to two decimal places.)
(d) Estimate the probability that a person who comes into the store will buy nothing. (Round your answer to two decimal places.)
Answer:
.................
Step-by-step explanation:
............
What is the lateral surface area of a right hexagonal prism whose base is a regular hexagon with sides measuring 8 inches long and altitude measuring 6 inches tall?
Answer:
288 square inches
Step-by-step explanation:
Assuming your "altitude" is the height of the prism--the distance between bases, the lateral area is the sum of the areas of the six rectangular faces. Each of those has an area of ...
(8 in)(6 in) = 48 in^2
so the 6 of them will have an area of ...
lateral area = 6×48 in^2 = 288 in^2
_____
Comment on nomenclature
'Altitude' is usually associated with the height of a triangle. In the case of a regular polygon, the 'altitude' of a triangular section of the polygon is called the 'apothem', and is often designated using the letter 'a'. If the polygon is regular, the apothem can be calculated from the side length and the number of sides, but it is often given in problems involving area, perimeter, and/or volume.
The distance between the parallel bases of a prism is often referred to as the prism height or length. The use of the word 'altitude' is confusing in this case.
Since the lateral area is the product of the perimeter of the base and the distance between bases, we have to assume that your 'altitude' refers to the distance between bases. Otherwise, there is not sufficient information to work the problem.
What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)?
k = –k equals negative StartFraction 3 Over 2 EndFraction.
k = –k equals StartFraction 2 Over 3 EndFraction.
k = k equals StartFraction 2 Over 3 EndFraction.
k = k equals StartFraction 3 Over 2 EndFraction.
Answer: k = 2/-3
Step-by-step explanation: Option (B)
Taking the test as we speak
In a triangle ABC,AB=9 and BC =12 which of the following Cannot be the length of AC.
Step-by-step explanation:
mark it as the brainliest
Answer:
i need help with this too
Step-by-step explanation:
In a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard. Compute the test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
Answer:
The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.
Step-by-step explanation:
We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.
In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.
Let [tex]p_1[/tex] = population proportion of cars driven at high altitudes who exceeded a standard of 10 grams.
[tex]p_2[/tex] = population proportion of cars driven at low altitudes who exceeded a standard of 10 grams.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1>p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}
The test statistics that will be used here is Two-sample z-test statistics for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of cars driven at high altitudes who exceeded a standard of 10 grams = [tex]\frac{24}{90}[/tex] = 0.27
[tex]\hat p_2[/tex] = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = [tex]\frac{42}{380}[/tex] = 0.11
[tex]n_1[/tex] = sample of cars driven at high altitudes = 90
[tex]n_2[/tex] = sample of cars driven at low altitudes = 380
So, the test statistics = [tex]\frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }[/tex]
= 3.234
The value of z-test statistics is 3.234.
g Which of the following is equivalent to P( A|B)? a. P(A and B) b. P(B|A) c. P(A)/P(B) d. None of these choices.
Answer:
The correct option is D.
But option B is correct if P(A) = P(B).
Step-by-step explanation:
P(A|B) is read as "The probability of A given B".
It is different from the options A, B, and C.
It is equal to option B only if the probability of A is equal to the probability of B. That is P(A|B) = P(B|A) if P(A) = P(B).
For the regression equation, Ŷ = +20X + 200 what can be determined about the correlation between X and Y?
Answer:
There is a positive correlation between X and Y.
Step-by-step explanation:
The estimated regression equation is:
[tex]\hat Y=20X+200[/tex]
The general form of a regression equation is:
[tex]\hat Y=b_{yx}X+a[/tex]
Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.
The formula of slope is:
[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]
Here r (X, Y) is the correlation coefficient between X and Y.
The correlation coefficient is directly related to the slope.
And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.
Here the slope is positive.
This implies that the correlation coefficient must have been a positive values.
Thus, it can be concluded that there is a positive correlation between X and Y.
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Task: Population of a Species
The population of a species in the wild in Asia has been decreasing exponentially since 1980. This function represents the wild population of the species t years after 1980: W(t)=20000(0.95)t.
The Wildlife Refuge Foundation noticed this trend before 1980
and decided to try to help reduce the population decline by
breeding the species in captivity. The graph shows the number
of these animals that have been born in captivity since 1980.
(Note: The function W(t) and the graph are not the same function!)
[15 points] Use the graph to create a function to represent the number of the species that have been born in captivity, C(t).
Answer:
C(t) = 20t
Step-by-step explanation:
The graph of C(t) appears to be linear
The y intercept is 0
The slope is 200/10 = 20
y = mx+b where m is the slope and b is the y intercept
y = 20x+0
y = 20x
C(t) = 20t
Answer:
the answer is c (t) = 20 t
Step-by-step explanation:
[tex]\sf{}[/tex]
:,-)
♛┈⛧┈┈•༶♛┈⛧┈┈•༶
a radion station usa 1\6 of its time for the news. in a 12 hour day, how many hours are used for music & entertainment?
Answer:
10 hours
Step-by-step explanation:
In order to answer this question, you must assume that all air time not spent on news is spent on music & entertainment. That would usually not be the case, as there would usually be advertisements and public service programming along with everything else.
The time spent on news is ...
(1/6)(12 hours) = 2 hours
If the rest is spent on music and entertainment, then ...
12 -2 = 10 . . . hours are used for music and entertainment
Find the slope of the line whose x-intercept is 4 and the y- intercept is -9
Answer:
y = (9/4)x - 9
Step-by-step explanation:
The x-intercept is (4, 0) and the y-intercept is (0, -9).
As we move from (0, -9) to (4, 0), x (the 'run' increases by 4 and y (the 'rise' increases by 9. Thus, the slope of the line connecting these two points is m = rise/run = 9/4, from which we can write the desired equation in the form y = mx + b:
y = (9/4)x - 9
According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that fewer than 13 have vcrs?
Answer:
The probability is [tex]P(x < 13) = 0.8732[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.70
The sample size is [tex]n = 15[/tex]
Generally the distribution of U.S. households have vcrs follow a binomial distribution given that there are only two outcome (household having vcrs or household not having vcrs )
The probability of failure is mathematically evaluated as
[tex]q = 1- p[/tex]
substituting values
[tex]q = 1- 0.70[/tex]
[tex]q = 0.30[/tex]
The probability that fewer than 13 have vcrs is mathematically represented as
[tex]P(x < 13) = 1- [P(13) + P(14) + P(15)][/tex]
=> [tex]P(x < 13) = 1-[( \left 15 } \atop {}} \right. C_{13} *p^{13}* q^{15-13})+ (\left 15 } \atop {}} \right. C_{14} *p^{14}* q^{15-14}) +( \left 15 } \atop {}} \right. C_{15} *p^{15}* q^{15-15}) ][/tex]
Here [tex]\left 15 } \atop {}} \right. C_{13}[/tex] means 15 combination 13 and the value is 105 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{14}[/tex] means 15 combination 14 and the value is 15 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{15}[/tex] means 15 combination 15 and the value is 1 (obtained from calculator)
So
[tex]P(x < 13) = 1-[(105 *p^{13}* q^{2})+ (15 *p^{14}* q^{1}) +(1*p^{15}* q^{0}) ][/tex]
substituting values
[tex]P(x < 13) = 1-[(105 *(0.70)^{13}* (0.30)^{2})+ (15 *(0.70)^{14}* (0.30)^{1}) +(1*(0.70)^{15}* (0.30)^{0}) ][/tex]
[tex]P(x < 13) = 0.8732[/tex]
Find the measure of a.
A. 20
B. 70
C. 80
D. 40
A circle is a curve sketched out by a point moving in a plane. The measure of a is 70°. The correct option is B.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
In the given circle, the line AC is the diameter of the circle, therefore, the measure of ∠ABC will be 90°.
∠ABC = 90°
This is because a triangle formed on the diameter of the circle such that all the vertices of the triangle intersect the circle, then the angle opposite to the diameter is a right angle.
Now, in ΔABC, the sum of all the angles of the triangle can be written as,
∠ABC + ∠BCA + ∠BAC = 180°
90° + a + 20° = 180°
110° + a = 180°
a = 180° - 110°
a = 70°
Hence, the measure of a is 70°.
Learn more about Circle:
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what is ap in math abreviation and explain my math teacher was drunk so he couldn't teach nothing
Step-by-step explanation:
n mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. ... For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.
find the HCF of 72,108 and 180
Answer:
36 is the answer
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
72: 2×2×2×3×3
108: 2×2×3×3×3
180: 2×2×3×3×5
here, common factors are 2,2,3 and 3 ..
so.. HCF: 2×2×3×3
•°•HCF=36 ..
Question 19 of 20:
Select the best swer for the question
19. The distance from the center of a round table top to the edge of the table top is 4 ft what is the area of the table top
Answer:
50.26 ft^2
Step-by-step explanation:
Area=pi*r^2
Area=pi*(4)^2=pi*16=50.26