The fully factored form of the equation is 2x(x + 3) (2x - 1) that is option B.
Synthetic division and the rational root theorem can be used to demonstrate this. According to the rational root theorem, p must divide the constant term and q must divide the leading coefficient if p/q is a rational root of the polynomial f(x). The constant term in this example is -6, the leading coefficient is 4, and the potential rational roots are 1, 2, 3, and 6.
When we divide 4x3 + 10x2 - 6x by 2x - 1 using synthetic division, we arrive at the following result:
4x^3 + 10x^2 - 6x = (2x - 1) (2x^2 + 8x + 6)
We can then factor the remaining quadratic, 2x^2 + 8x + 6, as (x + 3)(2x + 2).
Thus, the completely factored form of 4x^3 + 10x^2 - 6x is:
4x^3 + 10x^2 - 6x = 2x(x + 3)(2x - 1)
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Work out:
2 x 2.2 x 10^12 × 1.5 × 10^12/
2.2 x 10^12 - 1.5 x 1012
Give your answer in standard form correct to 3 significant figures.
The index forms is expressed as 9. 40 × 10¹²
What are index forms?Index forms are simply described as representation of a number in the form of an exponential expression or a single number that is raised to a number or variable.
Other names for index forms are standard form and scientific notation.
It also explains how many times a number contains itself.
From the information given, we have that;
2 x 2.2 x 10^12 × 1.5 × 10^12/2.2 x 10^12 - 1.5 x 1012
Represented as;
2(2.2) × 10¹² × 1.5 × 10¹²/ 2.2 × 10¹² - 1. 5 × 10¹²
We can add or subtract the index forms because they have the same exponential value, we have;
4.4(1.5)× 10²⁴/0.7 × 10¹²
Find the quotient
9. 4 × 10¹²
Hence, the value is 9. 4 × 10¹²
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when commercial aircraft are inspected, wing cracks are reported as nonexistent, detectable, or critical. the history of a particular fleet indicates that 69% of the planes inspected have no wing cracks, 21% have detectable wing cracks, and 10% have critical wing cracks. five planes are randomly selected. (round your answers to three decimal places.) (a) find the probability that one has a critical crack, two have detectable cracks, and two have no cracks. 0.063 correct: your answer is correct. (b) find the probability that at least one plane has critical cracks.
The probability of two planes having no cracks is 0.063 and The probability of no plane having critical cracks is 0.405.
(a) The probability of one plane having a critical crack is 10% or 0.10. The probability of two planes having detectable cracks is (0.21)^2 = 0.0441. The probability of two planes having no cracks is (0.69)^2 = 0.4761. So, the desired probability is 0.10 * 0.0441 * 0.4761 = 0.063.
(b) To find the probability that at least one plane has critical cracks, we can use the complementary probability approach, i.e., finding the probability that no plane has critical cracks and then subtracting it from 1. The probability of no plane having critical cracks is (0.90)^5 = 0.595. So, the desired probability is 1 - 0.595 = 0.405.
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find the local minimum of and local maximum of values for the function: f ( x ) = { − x , x < − 1 2 − x 2 , x ≥ − 1
The local minimum of the of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(-1) = -1 and the local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(0) = 0.
The local minimum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 occurs when x = -1. This is because when x = -1, the value of the function is f(-1) = -1. This is the lowest the function can get since the function is decreasing for x < -1 and increasing for x > -1.
The local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 occurs when x = 0. This is because when x = 0, the value of the function is f(0) = 0. This is the highest the function can get since the function is increasing for x < 0 and decreasing for x > 0.
Therefore, the local minimum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(-1) = -1 and the local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(0) = 0.
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Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine and it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag. The additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.50 each. Team B will sell the cotton candy for $0.75 per stick.
How many bags of popcorn will Team A need to sell to reach their goal?
Answer:
255
Step-by-step explanation:
Let's call the number of bags of popcorn sold by Team A as "x".
The total cost for the popcorn machine rental and supplies is $15 + 0.05x.
The revenue from selling the popcorn is 0.5x.
To reach their goal of $100, they need to satisfy the equation:
$100 = 0.5x - ($15 + 0.05x)
Expanding and solving for x:
$100 = 0.5x - $15 - 0.05x
$115 = 0.45x
x = $115 / 0.45 = 255 bags of popcorn
So, Team A needs to sell 255 bags of popcorn to reach their goal of $100.
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10 ≤ 2x ≤ x+9
I need an explanation in how to solve this step by step?
The solution to the given inequality, 10 ≤ 2x ≤ x+9, is 5 ≤ x ≤ 9
Solving Linear inequalitiesFrom the question, we are to solve the given inequality
The given inequality is
10 ≤ 2x ≤ x+9
Then,
We can write that
10 ≤ 2x and 2x ≤ x+9
First, solve the inequality 10 ≤ 2x
10 ≤ 2x
Divide both sides by 2
5 ≤ x
Now, solve
2x ≤ x + 9
2x - x ≤ 9
x ≤ 9
Thus,
5 ≤ x and x ≤ 9
5 ≤ x ≤ 9
Hence, the solution is 5 ≤ x ≤ 9
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find the indefinite integral and check the result by differentiation. (use c for the constant of integration.) 2 x5 dx
The indefinite integral is [tex]\frac{x^6}{3} +c[/tex].
What is indefinite integral?
An integral is considered to be indefinite if it has no upper or lower bounds.
The most generic anti-derivative of f(x) is known as an indefinite integral and denoted, in mathematics, by F(x), which is any anti-derivative of f(x).
[tex]\int[/tex]f(x) = F(x) + C
Here the given integral is [tex]\int{2x^5} dx[/tex]
=> [tex]\int{2x^5} dx[/tex]
=> [tex]2\int x^5 dx[/tex]
We know that [tex]\int x^n dx = \frac{x^{n+1}}{n+1}+c[/tex] where c is constant then,
=> [tex]2[\frac{x^{5+1}}{5+1} ]+c[/tex]
=> [tex]2\frac{x^6}{6} +c[/tex]
=> [tex]\frac{x^6}{3} +c[/tex]
Now take [tex]\frac{x^6}{3}[/tex] and differentiate to check the results then,
=> [tex]\frac{d}{dy}[\frac{x^6}{3} ][/tex]
=> [tex]\frac{1}{3} \frac{dx^6}{dy}[/tex]
We know that [tex]\frac{d}{dy} x^n = nx^{n-1}[/tex] then
=> [tex]\frac{1}{3}\times6x^{6-1}[/tex]
=> [tex]2x^5[/tex]
Hence the indefinite integral is [tex]\frac{x^6}{3} +c[/tex].
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Is or Is Not? what is the correct answer?
The ordered pair (-2, 1) is not a solution
How to determine if the ordered pair is a solution or notFrom the question, we have the following parameters that can be used in our computation:
6x + 5y = -7
2x - 4y = -8
The ordered pair is given as
(-2, 1)
Substitute the known values in the above equation, so, we have the following representation
6(2) + 5(-1) = -7 == false
The above equation is false
Hence, the ordered pair is not a solution
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Can anyone solve 21x>5y+49x>2y>2-28x>2y for me?
A point in the solution of the system of inequalities is (2, 0.5)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
21x>5y+49x>2y>2-28x>2y
Express properly
So, we have the following representation
21x > 5y+49
x > 2y
2 - 28x > 2y
Next, we plot the graphs of the inequality expressions on a plane
(See attachment for the graph)
The shaded region represent the solution
And a point in this region is (2, 0.5)
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What does it mean if the graph is skewed to the right?
If the histogram is skewed to the right, the graph's peak will be to the left of the center.
What happens when the distribution is skewed to the right?The peak of the graph is located to the left of the center if the histogram is skewed to the right. The frequency of observations is less frequent on the right side of the graph than it is on the left.
The mean is typically higher than the median when the distribution is right-skewn. We anticipate that the mean and median will be roughly identical in value in symmetric distributions. There is a significant link between the distribution's form and how the mean and median are related.
A positively skewed distribution, sometimes referred to as a right-skewed distribution, is a type of distribution where the majority of values are concentrated around the left tail and the right tail is longer. The distribution that leans positively is the exact opposite of one that leans negatively.
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does this interval give convincing evidence of a difference between the population proportions? justify your answer. no. because the interval does not contain 0, there is not convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. yes. because the interval does not contain 0, there is convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. no. because the interval does not contain negative numbers, there is not convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. yes. because the interval does not contain negative numbers, there is convincing evidence that the true proportion of men who can identify egypt on the map is different than the true proportion of women that can identify egypt on a map. no. because the conditions were not met, we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify egypt on the map is different from the true proportion of women that can identify egypt on a map.
The answer to the question is no, there is not convincing evidence of a difference between the population proportions.
Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.
In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.
Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.
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The answer to the question is no, there is not convincing evidence of a difference between the population proportions.
Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.
In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.
Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.
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If F and f are differentiable function such that F(x) = integral^x_0 f(t) dt and if F(a) = -2 and F(b) = -2 where a < b which must be true? a. f(x) = 0 for some x such that a < X < b b. f(x) < 0 for all X such that a < X < b c. f(x) = 0 for some X such that a < X < b d. f(x) > 0 for all X such that a < X < b e. f(x) less than or equal to 0 for all X such that a < X < b
By differentiable polynomial f(x) = 0 for some x such that a < X < b , A is correct
What is an example of a differentiable function?
If a function's derivative is present at every location inside its domain, the function is said to be differentiable. If a function f(x) is differentiable at x = a, in particular, then f′(a) exists in the domain.
Let's examine a few instances of differentiable polynomial and transcendental functions, such as f(x) = x4 - 3x + 5.
A is correct
F receives two equal values in different places .
consider the line between them .
it cannot be in a coustant ascent nor descent, since it must return to the minimal value .
therefore, A, either coutant or has an surprising and descending area ,
thus from Fermat's rule the derivate must be equal to zero .
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The mean is the measure of central tendency most likely to be affected by an outlier.true or false
The mean is the measure of the central tendency most likely to be affected by an outlier.
The following statement is correct.
The term "mean" is another synonym for "average." When there is an outlier in the data set, the mean suffers the most. The only measure of central tendency on which an outlier will always have an effect is the mean.
The mean is the only measure of central tendency that is affected by all values since it is calculated by dividing the total of the values by the number of observations.
The arithmetic mean is the average quantity in a given set of data. It is defined as the sum of all observations in the data divided by the total number of observations in the data. As a result, because it comprises all of the data in a series, the mean is influenced by the extreme values.
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evaluate the following. give your answers as exact fractions. 2 x2−4 dx −2 = 2 x2−4 dx −2 =
After evaluating the given equation ∫(x²-4)dx, we get -32/3.
Integration is the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up their areas. The sum approaches a limit that is equal to the region under the curve of a function. Integration is the process of finding the antiderivative of a function. If a function is integrable and if its integral over the domain is finite, with the limits specified, then it is the definite integration. If F(x) is a particular anti-derivative of f(x) on an interval I, then every anti-derivative of f(x) on I is given by ∫ f(x) dx = F(x) + C.
Here, ∫ f(x) dx represents the whole class of integral.
C is the arbitrary constant, and all the antiderivatives of f(x) on I can be obtained by assigning a particular value to C.
Here f(x) is the integrand,
The variable x in dx is called the integrator and the whole process of finding the integral is called the integration. The ∫ sign stands for the sum.
The given equation is:
∫(x²-4)dx for interval (-2,2).
Integrate the above equation, we get
∫(x²-4)dx = x³/3 -4x +c
Now, solving this for the interval (-2,2), we get
= (2³/3 - 4×2) - ((-2)³/3 - 4×-2)
= (8/3)-8 + 8/3 - 8 = -32/3
Thus, after evaluating the given equation ∫(x²-4)dx, we get -32/3.
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An elevator went up 20 floors, down 13 floors, up 10 floors, and down 19 floors. Find its location.
Note: 1st floor (1) - Ground floor
Zero (0) - Parking Lot
Negative one (-1) - Underground
Negative two (-2) - Basement
Answer: -2 (basement)
Step-by-step explanation:
20-13=7
7+10=17
17-19= -2
Answer:
the basement
20-13=7+10=17-19=-2
You have a total of 200 Coins, Consisting of nickels and dimes. The total value of the 200 Coins is $16.85. How many of each do you have?
Answer:
Below
Step-by-step explanation:
n = # nickels value = 5n
(200-n) = # dimes value = 10(200-n)
summed, these equal 1685
5n + 10(200-n) = 1685
5n + 2000 -10 n = 1685
-5n = -315
n = 63 then dimes = 137
COMPOUND INTEREST You depoit $100 i n an account that pay 6% annual
interet. How long will it take for the balance to reach $1000 for each given
frequency o f compounding?
The time it takes for the balance to reach $1000 depends on the frequency of compounding:
If compounding is done annually (once per year), it will take approximately 12.68 years for the balance to reach $1000.If compounding is done semi-annually (twice per year), it will take approximately 12.44 years for the balance to reach $1000.If compounding is done quarterly (four times per year), it will take approximately 12.33 years for the balance to reach $1000.If compounding is done monthly (twelve times per year), it will take approximately 12.25 years for the balance to reach $1000.This is calculated using the formula for compound interest: A = P * (1 + r/n)^(nt), where P is the initial deposit, r is the annual interest rate, n is the number of times compounded in a year, and t is the number of years.
Compound Interest CalculationI calculated the time it takes for the balance to reach $1000 using the formula for compound interest:
A = P * (1 + r/n)^(nt),
where A is the final balance, P is the initial deposit ($100), r is the annual interest rate (6%), n is the number of times compounded in a year (annually, semi-annually, quarterly, or monthly), and t is the number of years.
I solved for t, keeping all other variables constant, by taking the natural logarithm of both sides of the equation and rearranging the terms:
t = (ln(A/P)) / (ln(1 + r/n) * n)
I used a mathematical software or calculator to perform the calculations and obtain the values for t for each given frequency of compounding.
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how to find area of a triangle
Answer:
To find the area of a triangle you got A=1\2×b×h
The distribution of ph levels for all community swimming pools in a large county is approximately normal with mean 7. 5 and standard deviation 0. 2. According to swimming pool studies, the safest ph levels for water in swimming pools are between 7. 2 and 7. 8. (a) one community swimming pool in the county will be selected at random. What is the probability that the selected pool has a ph level that is not considered safe?.
The probability that the selected pool has a ph level not considered safe is approximately 0.22 (or 22%). This can be calculated using the cumulative probability of a normal distribution with a mean of 7.5 and a standard deviation of 0.2.
1. Calculate the z-score for the lower limit of 7.2: (7.2 - 7.5) / 0.2 = -1.5
2. Calculate the z-score for the upper limit of 7.8: (7.8 - 7.5) / 0.2 = 1.5
3. Calculate the cumulative probability of the lower limit: P(-1.5) = 0.0668
4. Calculate the cumulative probability of the upper limit: P(1.5) = 0.9332
5. Calculate the probability that the selected pool has a ph level not considered safe: P(not safe) = 1 - (P(1.5) - P(-1.5)) = 0.22
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In isosceles ABC, AC is the base, Points D. Band
Fare the midpoints of AB. A and BC
respectively. The length of BD is 13 inches and
ZBFD 65. Find each measure
a. A
b. DE
G. AD
d. M EDF
According to the question
Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.
a. In a triangle sum of all the sides is equals to 180 degrees.
So the following formula may be used to get the value of angle A:
∴ A = 180 - (2 * ZBFD)
⇒ A = 180 - (2 * 65/2)
⇒ A = 115 degrees.
b. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to get the length of DE:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ DE = AD/2
⇒ DE = √(x^2 + (x/2)^2) / 2
⇒ DE = √((13^2) + (13/2)^2) / 2
⇒ DE = √338 / 4
c. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to determine the length of AD:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ AD= √(13^2 + (13/2)^2)
⇒ AD = √338 / 2
d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.
EDF = A/2
⇒ EDF = 115/2
⇒ EDF = 57.5 degrees
The measure of each of the following are as follows :
the measure of A = 115 degree.
the measure of DE = √338/4.
the measure of AD = √338/2.
the measure of DEF = 57.5 degrees.
According to the question
Given an isosceles triangle, ABC with AC as its base, points D and F are the midpoints of AB and BC, respectively. Let's refer to the length of BD as x.
a. In a triangle sum of all the sides is equals to 180 degrees.
So the following formula may be used to get the value of angle A:
∴ A = 180 - (2 * ZBFD)
⇒ A = 180 - (2 * 65/2)
⇒ A = 115 degrees.
b. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to get the length of DE:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ DE = AD/2
⇒ DE = √(x^2 + (x/2)^2) / 2
⇒ DE = √((13^2) + (13/2)^2) / 2
⇒ DE = √338 / 4
c. The Pythagorean theorem,i.e.,
Perpendicular^2 + base^2 = Hypoteneuse^2
can be used to determine the length of AD:
∴ (AD)^2 = x^2 + (x/2)^2
⇒ AD= √(13^2 + (13/2)^2)
⇒ AD = √338 / 2
d. We utilize the fact that the angles at a triangle's midpoints are half its angle measurements to get the measure of angle EDF.
EDF = A/2
⇒ EDF = 115/2
⇒ EDF = 57.5 degrees
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If f(x) = 4x2 - 3x + 2, evaluate f(-1) and If f(x) = 4x + 3, evaluate f(x+h)
The value of f(-1) is 9
The value of f(x+h) is 4x + 4h + 3
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
f(x) = 4x² - 3x + 2 Now replace x with -1.
f(-1) = 4(-1)² -3(-1) + 2
f(-1) = 4 + 3 + 2
f(-1) = 9
f(x) = 4x + 3 Now replace x with x + h.
f(x+h) = 4(x+h) + 3
Distribute and simplify
= 4x + 4h + 3
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. STATE YOUR ASSUMPTION Breelyn is making cookies using a cookie cutter in the shape of a parallelogram. What are the perimeter and area of each cookie? Explain any assumptions that you make. Round your answers to the nearest hundredth, if necessary. order of get
The perimeter and area of a parallelogram can be determined if the length and width are known.
How to explain the perimeterThe perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.
Without additional information, it is not possible to determine the exact perimeter and area of each cookie. Assuming the length and width are given, we can use the formula for the perimeter of a parallelogram (2 times the sum of the length and width) and the formula for the area of a parallelogram (length times width) to find the desired quantities.
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a vector has initial point 1=(−3,1) and terminal point 2=(,7). find all numbers so that has length 10
The terminal point of the vector for a length of 10 is (x, y) = (-15.8, 7).
The length of a vector can be calculated using the Pythagorean Theorem. The formula for calculating the length of a vector can be expressed as:
Length (vector) = √((x2 - x1)² + (y2 - y1)²).
In this case, the initial point is (x1, y1) = (-3, 1) and the terminal point is (x2, y2) = (x, y) = (x, 7). Substituting these values into the formula, we get:
Length = √((x - (-3))² + (7 - 1)²)
As we need the length of the vector to be 10, we can solve for x.
10 = √((x + 3)² + 6²)
100 = (x + 3)² + 36
164 = (x + 3)²
12.8 = x + 3
x = -15.8
Therefore, the terminal point of the vector for a length of 10 is (x, y) = (-15.8, 7).
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PLSSS HELP IF YOU TURLY KNOW THISSS
Answer: 12
Step-by-step explanation:
Answer:
[tex] \sf \: x = 12[/tex]
Step-by-step explanation:
Given equation,
→ x - 9 = 3
Now the value of x will be,
→ x - 9 = 3
→ x = 3 + 9
→ [ x = 12 ]
Hence, the value of x is 12.
There are 2 red, 5 green, 3 blue and 4 white point on a circle. Find the number of line egment which have endpoint of different color at the given point
The number of those line segments which have endpoints of different colors is 40.5.
What is permutation?A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to organise the components of set A, as you can see.Given data :
There are 2 red, 5 green, and 3 blue points on a circle.
There are different colored endpoints on each line segment that starts at a red point and travels to either a green point or a blue point.
There are 2 red points and 7 segments from each of them, making a total of 14 segments.
There are different colored endpoints on each line segment that leaves at a green point and travels to either a red or blue point.
There are 5 green points and 8 segments from each, for a total of 40 segments.
There are different colored endpoints on each line segment that leaves at a blue point and travels to either a green point or a red point.
Each blue point has 9 segments, and there are a total of 3 blue points.
Add all the ways = 14 + 40 + 27
= 81 segments.
Number of segment = 81/2 = 40.5 Segments
Thus, the number of those line segments which have endpoints of different colors is 40.5.
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This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Below are two dot plots containing sample means from the same population
How many samples are represented in each plot?
There are __ samples in both plot A and plot B. Each dot represents one sample.
The number of samples for each dot plot is given as follows:
32.
What is shown by the dot plot?The dot plot shows the number of times that each measure appears in the data-set.
Hence the dot plot in this problem shows the number of samples that had means of 10, 20, 30, 40, 50, 60, 70, 80 and 90.
Hence, the total number of samples is obtained by the number of dots in each of the dot plots, which is of 32, hence the sentence is completed as follows:
There are 32 samples in both plot A and plot B. Each dot represents one sample.
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What is the domain function?
The domain of a function is the set of possible values that can be plugged into it.
What is meant by domain function?Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while using a value for x to that end, then that selected x-value is said to belong to the domain of f.
The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values. The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The entire range of possible values for the independent variable make up the domain of a function. In layman's terms, this definition states that the domain is the collection of all x-values that could possibly cause the function to "work" and produce actual y-values.
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The population of winbug beetles in 1990 was 35,000. The population each year after 1990 is shown by the equation below.
P(t) = 6,000 + 29,000(1 + 0.031)^t
Which of the following best describes what will happen to the population of winbug beetles in the years after 1990?
A) As t approaches positive infinity, P(t) approaches zero
B) As t approaches positive infinity, P(t) approaches positive infinity.
C) As t approaches positive infinity, P(t) approaches negative infinity.
D) As t approaches positive infinity, P(t) remains constant.
B) P(t) increases as t increases toward positive infinity.
An exponent is what?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
The population of winbug beetles after t years from 1990 is represented by the expression P(t) = 6,000 + 29,000(1 + 0.031)t.
We can see that when t grows, the exponential growth factor (1 + 0.031)t will eventually reach positive infinity. This implies that as t approaches positive infinity, the population of winbug beetles will similarly increase.
Consequently, the following is the best prediction of what will occur to the winbug beetle population in the years after 1990.
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Find the diameter of the circular garden whose circumference is 124.03 cm.
39.5cm the diameter of the circular garden whose circumference is 124.03 cm.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
Perimeter refers to the total outside length of an object.
here, we have,
circumference is 124.03 cm.
i.e. pi*d= 124.03 cm.
we know,
pi = 3.14
i.e. d= 124.03/3.14
=39.5cm
Hence, 39.5cm the diameter of the circular garden whose circumference is 124.03 cm.
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f the current population size is x individuals, what fraction of the resources are they using collectively?
The fraction of resources used collectively by X individuals can be represented as X/R, where R represents the total resources available. The fraction of resources not being used is represented as (R-X)/R. The per-capita growth rate can be represented as dX/dt = kX, where k is the proportionality constant. The differential equation for the population's size is dX/dt = kX.
A detailed explanation:
a) If the current population size is X individuals, then the fraction of resources they are using collectively can be calculated as X/R, where R represents the total resources available. This calculation gives us the proportion of resources used by X individuals relative to the total resources available.
b) To calculate the fraction of resources not being used, we subtract the fraction of resources used by X individuals from 1. So, the fraction of resources not being used is (R-X)/R.
c) The per-capita rate of change of X can be represented as dX/dt = kX, where k is the proportionality constant. This equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k.
d) To convert the equation into a differential equation for the population's size, we simply make X' stand alone on the left-hand side of the equation. So, the differential equation for the population's size becomes dX/dt = kX.
e) This differential equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k. This equation can be used to model the growth of a population over time and to understand the relationship between the population size and the rate of change of the population.
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Complete questin:
If the current population size is X individuals, what fraction of the resources are they using collectively? c) In the same situation, what fraction of the resources are not being used? d) The per-capita rate of change of X can be written as 7%. The key assumption mentioned above says that this quantity is pro- portional to the expression you wrote down in part (c). Call the proportionality constant 1', and write an equation for the per-capita growth rate. e) Convert this equation into a differential equation (change equa- tion) for the population's size. (Just make X' stand alone on the left-hand side of the equation.)
What is the area of the trapezoid?
43.4 m²
33.4 m²
86.8 m²
20.2 m²
Answer:
43.4 m²
Step-by-step explanation:
side 1= 4+7 m=11m
side 2=3m
height = 6.2 m
we have
the area of the trapezoid = [tex]\frac{1}{2} height*(side1+side2)[/tex]
=[tex]\frac{1}{2} *6.2*(11+3)[/tex]
=[tex]\frac{1}{2} *6.2*14[/tex]
=43.4 m²