The option that can be used to support the idea that the set of polynomials is closed under multiplication is; Option C: (10x^(0.5) - 8)(5x^(0.5) + 4)
What is the Closure property under multiplication?When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. It is pertinent to note that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Thus, we can also say that the polynomials are closed under multiplication.
Now, looking at the options, we can say that option C is the only polynomial that is closed under multiplication because its' variables and exponents will not change;
(10x^(0.5) - 8)(5x^(0.5) + 4)
The output will retain the same thing.
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Graph the equation:
Y = 1/3x + 2
Please help!!
please explain in a way a middle schooler would understand!!
ty!
Find the hourly wage for a person with an income of $44762, who works 54
hours a week for 47 weeks.
Round your answer to 2 decimal places.
Answer:17.64
Step-by-step explanation:44762/54/47= 17.6367 or 17.64
2- (ITA-2007) Dentre 4 moças e 5 rapazes deve-se formar uma comissão de 5 pessoas com, pelo menos , 1 moça e 1 rapaz. De quantas formas distintas tal comissão poderá ser formada?
Answer:
Step-by-step explanation:
√(2x+1)
Evaluate the integral
2
(2x + 1) In (2x + 1)
dx.
Substitute [tex]y=\ln(2x+1)[/tex] and [tex]dy=\frac2{2x+1}\,dx[/tex], so that
[tex]\displaystyle \int \frac2{(2x+1) \ln(2x+1)} \, dx = \int \frac{dy}y = \ln|y| + C = \boxed{\ln|\ln(2x+1)| + C}[/tex]
The probability that a rental car will be stolen is. 4. if 3500 cars are rented, what is the approximate poisson probability that 2 or fewer will be stolen?
Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:
[tex]\mu = 3500 \times 0.0004 = 1.4[/tex]
The probability that 2 or fewer cars will be stolen is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466[/tex]
[tex]P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452[/tex]
[tex]P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335[/tex]
0.8335 = 83.35% probability that 2 or fewer will be stolen.
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solve math problem plsss LOTS OF POINTS
The solution to 0.5^(x + 2) > 9 is x > -5.170
How to solve the inequality expression?The inequality expression is given as:
0.5^(x + 2) > 9
Take the logarithm of both sides of the inequality expression
log(0.5^(x + 2)) > log(9)
Rewrite the inequality expression as
(x + 2)log(0.5) > log(9)
Divide both sides by log(0.5)
x + 2 > -3.170
Subtract 2 from both sides
x > -5.170
Hence, the solution to 0.5^(x + 2) > 9 is x > -5.170
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sixteen thousand, four hundred eighty-two. Write this number in standard
In a recent year, the population of Springfield, Illinois was one hundred
form. Show your work in the space below. Remember to check your solutic
Answer:
16482 this is the answer
Expand and simplify (2+√3)² - (2-√3)²
Answer:
8√3
I hope this helps you
Find the area of the parallelogram?
A. 13.5
B. 18
C. 16
D. 12
Answer:
12 ft²
D
Step-by-step explanation:
Area of parallelogram = Base × Height
Here, base = 3ft
height = 4ft
So, Area = 3×4 ft² = 12 ft²
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Area of parallelogram is:}[/tex]
[tex]\rm{\bold{b}ase\times\bold{h}eight = \bold{a}rea}[/tex]
[tex]\huge\text{Your equation should look like: }[/tex]
[tex]\rm{3\times4 = \boxed{\bf area}}[/tex]
[tex]\huge\text{Simplify the equation above \& you will have}\\\\\huge\text{the answer to the area of the parallelogram.}[/tex]
[tex]\mathsf{3[base] \times 4[height] = ?[area]}[/tex]
[tex]\huge\text{Simplify it:}[/tex]
[tex]\rm{12\ ft^2}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\frak{12\ ft^2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the probability distribution of X when X~B(1,1/25)?
P(X= 0) = 0.96
P(X= 1) = 0.04
P(X= 0) = 0.75
P(X= 1) = 0.25
P(X= 0) = 0.04
P(X= 1) = 0.96
P(X= 0) = 0.25
P(X= 1) = 0.75
The probability distribution of X when X~B(1,1/25) is (Option A)
P(X= 0) = 0.96P(X= 1) = 0.04See the explanation below.
What is the explanation to the above solution?Given X~B(n,p)
P(x=1) = C¹ₙ * P¹ * (1-P)ⁿ⁻¹ (n≥1)
Thus, X~B [1, 1/25]
1/25 = 0.04
hence, p(x=0)
= C⁰₁ * 0.04⁰ (1 - 0.04)¹
= 0.96
P (x=1)
= C¹₁ 0.04¹ (1-0.04)⁰
= 0.04
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If NR is parallel to OQ AND OQ = 130m, what is the length of NR?
Answer: 260 m
Step-by-step explanation:
Let's say the length of NR is x m, using the similarity rule, we get the equation
175/130 = (175+175)/x
x = 260
So NR is 260 m
What is the correct sequence of organs for the formation and elimination of urine?.
The analysis of the kidney exists named urology. The kidney exists as a bean-shaped organ. The Kidney exists metanephric in nature and is located retroperitoneal in position.
What is a kidney?The organ current in the body which regulates the fluid concentration of the body exists named the kidney.
The nephron exists as the structural and operational unit of the kidney.
The sequence of the appearance of the kidney exists as pursues:-
Minor calyxMajor calyxCollecting ductNephronUreterUrethraTo learn more information about the kidney refers to:
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help me pls like srsly
The time it will take the thermometer to hit the ground is 22 seconds
Calculating TimeFrom the question, we are to determine the how long it would take the thermometer to hit the ground
From the given information,
The equation for the height as a function of time is
h(t) = -16t² + initial height
From the given information,
The thermometer falls from a weather balloon at a height of 7744 ft
∴ Initial height = 7744 ft
When the thermometer hits the ground, h(t) = 0
Thus, we get
0 = -16t² + 7744
16t² = 7744
t² = 7744/16
t² = 484
t = √484
t = 22 seconds
Hence, the time it will take the thermometer to hit the ground is 22 seconds
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A cylinder has a radius of 1 inch and height of 1 inch.what is the approximate volume of the cylinder? round to the nearest hundredth. use 3.14 for π.1.05 cubic inches1.57 cubic inches3.14 cubic inches6.28 cubic inches
The volume of the cylinder is [tex]3.14 inch^3[/tex]
Given that
radius = 1 inch
height = inch
we know that volume =[tex]V = \pi \times r^2 \times h[/tex]
now put the value in the above equation we get
[tex]V = 3.14 \times 1 ^2\times 1\\V = 3014inch ^3[/tex]
What is Volume?Volume is a measurement of three-dimensional space that is occupied.Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch).The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes.If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects with dimensions of zero, one, and two have no volume;To know more about volume with the given link
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A radioactive material has a half life of 10 years. What is the fraction of the initial isotope is left after 60 years
Answer:
1/2^6 = 1/64
Step-by-step explanation:
Half life = 10 years
Time = 60 years
No of half life = T/t
= 60 / 10 = 6
Remaining fraction = 1/2^(no of half life)
= 1/2^6
= 1/64
The linear density in a rod 5 m long is 10 x + 4 kg/m, where x is measured in meters from one end of the rod. Find the average density ave (in kg/m) of the rod.
The average density of the rod is 0.704 kg/m.
For given question,
We have been given the linear density in a rod 5 m long is 10 / x + 4 kg/m, where x is measured in meters from one end of the rod.
We need to find the
The length of rod is, L = 5 m.
The linear density of rod is, ρ = 10/( x + 4) kg/m
To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 5,
The expression for the average density is given as,
⇒ ρ'
[tex]=\int\limits^5_0 {\rho} \, dx\\\\=\int\limits^5_0 {\frac{m}{L} } \, dx\\\\=\int\limits^5_0 {\frac{10}{5(x+4)} }\, dx\\\\=\int\limits^5_0 {\frac{2}{x+4} }\, dx[/tex] ......................(1)
Using u = x + 4
du = dx
u₁ = x₁ + 4
u₁ = 0 + 4
u₁ = 4
and
u₂ = x₂ + 4
u₂ = 5 + 4
u₂ = 9
By entering the values above into (1), we have:
⇒ ρ'
[tex]=2\int\limits^9_4 {\frac{1}{u} } \, du\\\\ = 2[(log~u)]_4^{9}\\\\=2[(log~9-log~4)]\\\\=2\times[0.352][/tex]
= 0.704
Thus, we can conclude that the average density of the rod is 0.704 kg/m.
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A small manufacturer constructs refrigerators. the fixed monthly cost is $200,000, and it costs $450 to produce one refrigerator. the average cost function to produce x refrigerators is represented by: what is the horizontal asymptote of c(x)? y =
Horizontal asymptote of c(x) is 450.
What is Horizontal asymptote?A horizontal asymptote is a line that guides the graph of a function for x-values but is not itself a part of the graph. "far," either "far" to the right or "far" to the left. Eventually, whether the graph is large enough or little, it may intersect.
According to the information:Since we have given that
Cost to produce one refrigerator = $450
Fixed monthly cost = $200,000
Thus, the following formula represents the average cost to produce x refrigerators:
C(x) = (200000 + 450x)/x
Horizontal asymptote of c(x) would be
= 450x/x
= 450
Hence, Horizontal asymptote of c(x) is 450
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Circle X is shown. Line segments W X and Y X are radii. Tangents W Z and Y Z intersect at point Z outside of the circle. Arc W Y is 109 degrees.
What is the measure of angle WZY?
54.5°
71°
125.5°
180°
From the calculations below, it is seen that the measure of angle WZY is gotten to be 71°
How to find the angle from a circle tangent?The lines ZY and ZW are tangents to the attached circle which is centered at x.
From the properties of circles, the tangents (ZY and ZW) from an external point to the circle make an angle of 90° to the radius of the circle. i.e. XW and ZY respectively.
From the attached diagram, we see that angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.
Out of the four angles of the quadrilateral, the three angles are seen as 109°, 90°, 90°. Therefore, the fourth angle is;
∠WZY = 360° - (90° + 90° + 109°)
∠WZY = 360° - 289°
∠WZY = 71°
Therefore, we can conclude from the calculations above that the measure of angle WZY is gotten to be 71°
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Answer: B. 71°
Step-by-step explanation: TRUST ME!!! Answer is correct on Edge!!! :)
I got it right!
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
numbers
Step-by-step explanation:
numbers
help pls i will give brainleast no links
Answer: 100 square cm
Step-by-step explanation: the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.
Answer: 104
Step-by-step explanation:
area of trangle =33 because 6*11/2=33
area of rectangle 9*7=63
area of rectangle 2*2=4
33+63+4=100^2
A certain amount of concentrate is mixed with water to create a juice. The table shows the amount of concentrate, in ounces remaining, in the original container after x ounces of juice are made. How many ounces of concentrate were in the original container before any juice was made? PLEASE HELP ME
TheThe number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.
Number of ouncesA. Let assume the two are linear relationship
Let y represent juice made
Let x represent the concentrate remaining
Hence:
Slope=600-200/200-280
Slope=400/-80
Slope=-5
y=-5x+b
Where:
x=200
y=-5(200)+b=600
y=-1000+b=600
b=1600
Thus,
y=-5x+1600
y=0. -5x+1600=0
-5x=-1600
divide both side by 5x
x=-1600/-5
x=320 ounces
B. x=0
y=1600 ounces
Therefore the number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.
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i don’t understand graphs
Answer:
y ≤ 2.5x + 5
Step-by-step explanation:
first step is to obtain the equation of the line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line
m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = 2.5x + 5 ← equation of line
since the line is solid then inequality will be ≤
the solution to the inequality is the blue region below the line , then
y ≤ 2.5x + 5 ← inequality represented by graph
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and prefers cola.
The probability that the person is over 40 and prefers cola exists at 1.3725.
What is probability?The probability of an event exists in the ratio of the size of the event space to the size of the sample space.
The size of the sample space exists the entire number of possible outcomes.
The event space exists the number of outcomes in the event you exists interested in.
So, P = size of the event space/size of the sample space
To estimate the probability that the person exists over 40 years.
Size of the sample size = 255
Size of the event space = 85
P = 85/255
P = 1/3
To estimate the probability that they drink cola.
Size of the sample size = 255
Size of the event space = 95
P = 95/255
P = 19/51
To estimate the probability that the person exists over 40 years of age or that they drink cola
So, P = (1/3) + (19/51)
[tex]$P = (51*3+3*19)/153[/tex]
P = 1.3725
Therefore, the probability that the person is over 40 and prefers cola exists at 1.3725.
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Helpppppp show your work
(-3²)-2(-3-4)-(-1³)
=9-2(-7)+1
=9+14+1
=24
Hope it helps!
Answer: look at the picture
Step-by-step explanation:
What is the exponent of x in in the expression -4x^3y^2 + 6
Answer:
3
Step-by-step explanation:
- 4x³y² + 6
the x is raised to the power of 3 , that is exponent of x is 3
A soccer ball is kicked across a field at an angle of 45° with an initial speed of 16m/s.
Determine how long the soccer ball was in the air.
1.94 s
3.89 s
2.16 s
O2.30 s
Answer:
it's C. 2.26s
but you wrote 2.16s nearly
The soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds, option D.
How to determine how long the soccer ball was in the airTo determine how long the soccer ball was in the air, we can use the vertical motion of the ball. When a projectile is launched at an angle, its vertical motion can be analyzed separately from its horizontal motion.
In this case, the initial velocity of the soccer ball can be divided into vertical and horizontal components. The initial velocity in the vertical direction can be calculated using the sine of the launch angle:
Vertical component (Vy) = initial speed (v) * sin(angle)
Vy = 16 m/s * sin(45°)
Vy = 11.31 m/s
Now, we can use the vertical motion equation to find the time the ball spends in the air:
Vertical displacement (y) = Vy * time - (1/2) * gravity * time^2
Since the ball reaches the same vertical position when it lands as when it was launched, the vertical displacement is 0. Therefore, we can set the equation equal to zero:
0 = (11.31 m/s) * time - (1/2) * 9.8 m/s^2 * time^2
Simplifying the equation:
4.9 * time^2 = 11.31 * time
Dividing both sides by time:
4.9 * time = 11.31
time = 11.31 / 4.9
time ≈ 2.31 seconds
Therefore, the soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds, which corresponds to option D.
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Use the quadratic formula to find the solutions to the equation.
3x^2- 10x+ 5 = 0
Answer:
[tex]x =\frac{5}{3} \pm \frac{\sqrt{10}}{3} \\\\x=2.72076\\x=0.612574\\[/tex]
Step-by-step explanation:
The quadratic equation is:
[tex]3x^2 - 10x + 5 = 0[/tex]
The roots (solutions) of a quadratic equation of the form
[tex]a^2 + bx + c = 0\\[/tex]
are
[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
in this case we have a = 3, b = -10, and c = 5
So, substituting for a, b and c we get
[tex]x = \frac{ -(-10) \pm \sqrt{(-10)^2 - 4(3)(5)}}{ 2(3) }[/tex]
[tex]x = \frac{ 10 \pm \sqrt{100 - 60}}{ 6 }\\[/tex]
[tex]x = \frac{ 10 \pm \sqrt{40}}{ 6 }[/tex]
Simplifying we get
[tex]x = \frac{ 10 \pm 2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 10 }{ 6 } \pm \frac{2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 5}{ 3 } \pm \frac{ \sqrt{10}\, }{ 3 }\\\\\frac{ 5}{ 3 } + \frac{ \sqrt{10}\, }{ 3 } = 2.72076\\\\\\[/tex] (First root/solution)
[tex]\frac{ 5}{ 3 } - \frac{ \sqrt{10}\, }{ 3 } = 0.612574[/tex] (Second root/solution)
Geometry: complete this proof, ASAP!!!!!!!!
Answer:
1. Given
2. Definition of Congruent Angles
3. Triangle Interior Angle Sum Theorem
4. Transitive Property of Equality
5. Substitution Property of Equality
6. Definition of Congruent Angles
Arrange the Fractions in Descending order
Step-by-step explanation:
How can these fractions be arranged in descending order?Arranging fractions in descending order means arranging the fractions starting from the highest to the lowest.
Finding the LCM of 3, 16, 12, 24,
[tex] \frac{2}{3} \: \frac{5}{16} \frac{7}{12} \frac{11}{24} \\ \\ \frac{32 + 15 + 28 + 22}{48} \\ \\ Arranging \: the \: fractions \: in \: descending \: order \\ \frac{2}{3} \frac{7}{12} \frac{11} {24} \frac{5}{16} [/tex]
Consider the quadratic equation x² 20x + 13 = 0.
-
Completing the square leads to the equivalent equation (x-
—)² = —
The analogous equation for the square will be; (x-10)²=87.
What is Equivalent equation?Algebraic equations with equivalent solutions or roots are called equivalent equations.
Based on information provided, an equivalent equation is created by adding or deleting the same quantity or expression from both sides of a given equation;
Using the original equation as a starting point as;
-20x+ x² + 13 = 0
Now x² - 20x = -13.
We need to take the "x" term's coefficient, or b, to complete the square.
Then Divide by 2 and write the equation in the quadratic formula (ax² + bx + c = 0).Then,
B = -20
b/2 = -10
(b/2)² = 100
x² - 20x +100 = -13 + 100
On the left side,
LHS: (x + b/2)² = (x-10)2
RHS: -13 + 100 = 87
(x-10)² = 87
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