Answer:
A)
The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first.
For example, the polynomial f(x)=x5+2x3−x2+2x+1 is in standard form because the highest degree terms are kept first.
B)
The problem 3 + 6 = 9 demonstrates the closure property of real number addition.
Observe that the addends and the sum are real numbers.
The closure property of real number addition states that when we add real numbers to other real numbers the result is also real.
In the example above, 3, 6, and 9 are real numbers
Part(A),
The standard form of the polynomial is 3x⁴ - 2x³ + 5x² + 7x - 1.
Part(B),
This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.
2x³ - 4x² - x + 8
What is a polynomial?A polynomial is a mathematical statement made up of exponents, coefficients, and variables, which are frequently denoted by the symbol x. (numbers that indicate the power to which the variable is raised).
Part A:
An example of a polynomial in standard form is:
3x⁴ - 2x³ + 5x² + 7x - 1
This polynomial is in standard form because the terms are written in descending order of degree, and each term has a coefficient and a variable raised to a power.
Part B:
The closure property of polynomials states that if we add, subtract, or multiply two polynomials, the result is always another polynomial.
For example, consider the polynomials:
f(x) = 2x³- 5x² + 3x + 1
g(x) = x² - 4x + 7
If we add these polynomials, we get:
f(x) + g(x) = 2x³ - 4x² - x + 8
This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.
The closure property is important in algebra because it ensures that the operations we perform on polynomials are always well-defined and meaningful.
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Suppose 10 tosses of a coin were all heads, and you switch to a new coin. What is the probability of tossing this new coin and getting another head?
Answer:
50% or 1/2 Could be 100% but i think it is 50%
Step-by-step explanation:
Because Changing the coin will make no difference.
The probability of getting heads is same as the probability of tails which is [tex]\frac{1}{2}[/tex].
What is the probability?
The concept of probability is used to assign a numerical description to the likelihood of occurrence of an event.
Probability can be defined as the number of favorable outcomes divided by the total number of possible outcomes of an event.
Here given that,
The [tex]10[/tex] tosses of a coin were all heads, and you switch to a new coin.
So, the probability of getting all heads is [tex]2^{-n}[/tex]
And we have [tex]n=10[/tex],
Then, the probability of getting the heads is
[tex](^{n}C_k)(\frac{1}{2})^k(\frac{1}{2})^{n-k}=2^{-n}(^nC_k)[/tex]
Hence, the probability of getting heads is same as the probability of tails which is [tex]\frac{1}{2}[/tex].
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What is the positive solution to the equation 2x2 + 3x = 2?
Answer:
x(2x+3)
Step-by-step explanation:
Answer:
X= -2
2. x = 1/2 = 0.500
Step-by-step explanation:
someone pls help I'm genuinely confused
I've literally been trying to figure out all three of these for like two hours now but I can't figure it out
Answer:
the area is 50
Step-by-step explanation:
Answer:
its 0.09637 but round it by urself . please like my answer and brainliest me hshsshhs
1) Red City is 6 cm away from Blue City on a map but the two cities are actually 240 miles
apart in real. What is the scale on the map?
If x varies inversely as y and x=16 when y=5, find x when y=20.
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Answer:
x = 4
Step-by-step explanation:
The inverse variation means that when y goes up by a factor of 20/5 = 4, the value of x goes down by the same factor.
x = 16/4
x = 4
g(x) = 2x – 4
h(x)=x²-3
Find (g.h)(5)
Answer:
40
Step-by-step explanation:
This is asking you to plug in the value of h(5) into g(x). First solve for h(5)
x^2-3 = h(x)
5^2-3= 22
h(5) = 22
h(5) is 22. So now, plug that into g(x).
g(h(5)) = 2(22)-4
44-4=40
(g.h)(5) is 40.
PLEASE HELP, anything is very appreciated
Answer:
117.8097 [tex]in^{2}[/tex]
Step-by-step explanation:
Depending on how you're math is going there are two ways to solve this, find the are by the arc or just figure out the whole cookie and divide by 6. Let's try the latter is seems easier to say. I mean easier for me to say.
area of a circle is pi * r^2
the diameter is 30 inches so the radius is half of that or 15 inches
then the whole cookie is
pi*15^2 = 706.858 [tex]in^{2}[/tex]
now divide by 6 or each piece
706.858 [tex]in^{2}[/tex] / 6 = 117.8097 [tex]in^{2}[/tex]
now eat your cookie :p
Find the area of the shape shown below. 2 4 1. 2 2 2 2 units
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Answer:
10 square units
Step-by-step explanation:
The shape is a trapezoid with bases of 2 units and 8 units. Its height is 2 units, so its area is ...
A = 1/2(b1 +b2)h
A = (1/2)(2 +8)(2) = 10
The area of the shape is 10 square units.
Riley's grandparents drive from city A to city B every spring. It takes them several days. Each day they use the expression 2+ distance over 54 to figure out how many hours they will be on the road. The first day they were on the road for 7 hours. How far did they travel on the first day?
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Answer:
270 miles
Step-by-step explanation:
For h hours of driving the distance d is covered:
h = 2 +d/54
Solving for d, we find the distance covered in h hours is ...
d = 54(h -2)
In 7 hours, the distance they traveled is ...
d = 54(7 -2) = 270 . . . miles
They traveled 270 miles on the first day.
A news report states that the 90% confidence interval for the mean number of daily calories consumed by participants in a medical study is (1920, 2140). Assume the population distribution for daily calories consumed is normally distributed and that the confidence interval was based on a simple random sample of 22 observations. Calculate the sample mean, the margin of error, and the sample standard deviation based on the stated confidence interval and the given sample size. Use the t distribution in any calculations and round non-integer results to 4 decimal places.
1. What is the sample mean?
2. What is the margin of error?
3. What is the sample standard deviation?
Answer:
ddXvffggf
Step-by-step explanation:
vvzgsgygsv gdhvsysgvs gsvysvvs6sg he's) v gateways tsgsyysgd Yacc subs USB GA t gsd
Answer this and I’ll give you a sticker
F(x)-mx+ b, f(-2)=3 and f(4)=1 , what is the value of m and b
Answer: [tex]m=\dfrac{-1}{3}, b=\dfrac{7}{3}[/tex]
Step-by-step explanation:
Given
Function is [tex]f(x)=mx+b[/tex]
[tex]f(-2)=3[/tex]
[tex]\therefore 3=m(-2)+b\\\Rightarrow b-2m=3\quad \ldots(i)[/tex]
[tex]f(4)=1\\\therefore 1=4m+b\quad \ldots(ii)[/tex]
from (i) and (ii) we get
[tex]m=\dfrac{-1}{3}, b=\dfrac{7}{3}[/tex]
A cold water tap can fill a tub in 6 minutes, and a hot water tap can fill the tub in 8 minutes. A drain can empty a full tub in 10 minutes. If both taps are on and the drai is open, how long will it take to fill the tub? It will take
how many minutes?
Answer:
12 minutes
Step-by-step explanation:
The Hot tap fills 1/30th of the bath in 1 minute. The cold tap fills 1/20th of the bath in one minute. In one minute both taps together will fill (1/30 + 1/20) of the bath, which is 5/60ths or 1/12th of the bath. Since it takes one minute to fill 1/12th of the bath, it’ll take 12 minutes to fill the bath
100Points! show work
Using angle sum property
[tex]\\ \sf\longmapsto x+43+73+70=180[/tex]
[tex]\\ \sf\longmapsto x+43+143=180[/tex]
[tex]\\ \sf\longmapsto x+186=180[/tex]
[tex]\\ \sf\longmapsto x=180-186[/tex]
[tex]\\ \sf\longmapsto x=-6[/tex]
Option C is correct
Sum of angles of any triangle is 180°
x+43+73+70=180x+186=180x=180-186x=-6Option C
which is a true statement about the two rectangular prism shown below
For the following right triangle, find the side length x, Round your answer to the nearest hundredth.
12
x
6
Answer:
x=12
Step-by-step explanation:
Pls help 10 ptsssssssssssss
NO LINKS
Answer:
it is actually a very simple question first you add 4+9=13 then you multiply 5 times 13 which gets you the answer of 65
how do i find the polar form of
1-2i
Answer:
9
Step-by-step explanation:
(1 point) An open-top box is to be constructed from a 8 \ \mbox{in} by 14 \ \mbox{in} rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let x denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, V, of the box as a function of x. \ \ V(x)
Answer:
Volume=[tex]4x^3-44x^2+112x[/tex]
Step-by-step explanation:
Let x denotes the length of the side of each cut
After Cutting square length will be=8-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)
After cutting square width will be=14-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)
Height = x
Volume=Length*width*Height
Volume=(8-2x)*(14-2x)*x
On solving we will get:
Volume=[tex]4x^3-44x^2+112x[/tex]
pls help me somebody
Answer:
it is 36 inches
Step-by-step explanation:
¿cuales tienen solo un eje de simetría?
English:Which have only one axis of symmetry?
Answer:
if your looking for a shape it would be a kite if your looking for a line it would be a parabolas.
si buscas una forma sería una cometa, si buscas una línea sería una parábola.
Step-by-step explanation:
Shanna is planning a trip from Dallas, Texas, to San Diego, California. She knows that the distance she will travel is
about 1400 miles. If she looks at a map with a scale of 1 in. = 300 mi, about how far will the trip be on the map?
3
14
in
0 2 in.
in.
WIN
in
Answer:
4.67 inches
Step-by-step explanation:
Shanna is planning a trip from Dallas, Texas, to San Diego, California.
She will travel about = 1,400 miles
The scale of a map is 300 miles = 1 inches
The trip of 1,400 miles = [tex]\frac{1400}{300}[/tex]
= 4.66666 inches ≈ 4.67 inches
Her trip is 4.67 inches far on the map.
Find the greatest common factor of the following monomials: 20a 46a^2 48a^6
Determine the missing factor in ■ × 4.2 = 16.8.
A triangle flower bed has a perimeter of 15cm the drawing has a scale of 1:200. What is the perimeter of the actual flower bed
Answer:
300cm
Step-by-step explanation:
scale 1:200 means 1cm on drawing represent 200cm on ground so 15cm will be 15×200 which is 3000cm
Help me I need this really bad and I need a good grade I’m behind on school
Answer:
If you share 7 apples equally with 3 people, then there are 2 1/3 apples per person.
The number 2 represents the number of whole apples each individual gets.
The denominatior, 3, represents how many times an apple will have to be split to divide equally
The numerator, 1, represents how many 3rds each person gets.
can someone help me with this please
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Answer:
1. attendance (y), time (x)
2. 1,2: increasing; 3: constant; 4: decreasing
3. attendance increases, remains constant, then decreases
4. increasing; pre-heating the oven
Step-by-step explanation:
It is always difficult to read the mind of the author of questions like these. Usually, specific wording is expected. If your curriculum material has examples you can copy from, you should do that.
__
1. The variables and what they stand for are listed on the axes of the graph. The y-variable stands for attendance. The x-variable stands for time. It isn't clear whether the desired answer is "y and x" or "attendance and time".
__
2. The graph slopes upward in intervals 1 and 2. It can be described as "increasing."
The graph remains level in interval 3. It can be described as "constant."
The graph slopes downward in interval 4. It can be described as "decreasing."
__
3. The attendance is adequately described in question 2. Attendance increases, remains constant, then decreases. It isn't clear how general or specific the answer is supposed to be.
__
4. The graph of the function is "increasing." We don't know if the indicated temperature is the temperature of the bread, the oven, or the room containing the oven. If we assume the indicated temperature is that of the oven, we expect an increase during the oven pre-heat interval.
If the indicated temperature is that of the bread, then the increase would be following insertion of the bread into the oven.
Using the same scenario as above, but now you do not know the population variance. You collect a random sample of n = 21 cereal boxes and find the sample mean is 12.8 and the sample standard deviation to be 0.5. Test the null hypothesis H0: µ = 13 against the alternative hypothesis HA: µ < 13 at level of significance α = 0.01.
Required:
a. Find the test statistic.
b. Using the rejection region, do you reject or not reject the null hypothesis?
c. Find the p-value.
d. Using the p-value, do you reject or not reject the null hypothesis?
e. In context of your problem, what is your conclusion about the ounces contained in cereal boxes?
Answer:
-1.833 ; we do not reject the Null.
Pvalue = 0.0409 ; We do not reject the Null
There is no significant evidence to conclude that the number of ounces contained in the cereal boxes is less than 13
Step-by-step explanation:
H0 : μ = 13
HA : μ < 13
Test statistic :
(xbar - μ) ÷ s/sqrt(n)
(12.8 - 13) ÷ 0.5/sqrt(21)
-0.2 / 0.1091089
= - 1.833
The critical value at α = 0.01 ; df = 21 - 1 = 20 = 2.528
-1.833 > - 2. 528 (left tailed test) ; Hence we do not reject the Null.
Test statistic :
Pvalue from Test statistic at DF = 20 ; α = 0.01
Pvalue = 0.0409
Pvalue > α
0.0409 > 0.01 ; Hence, we do not reject H0.
There is no significant evidence to conclude that the number of ounces contained in the cereal boxes is less than 13
What would be the new median if 21 was added to the list
Answer:
52 is the correct answer
Please help me btw if I see links I’ll report
Answer:
bro that is easy its 15*1/2
Step-by-step explanation: