The solution of the given linear inequality will be y ≥ 18.
What are linear inequalities, exactly?
Linear inequalities are mathematical expressions that involve linear functions and the symbols "<", ">", "<=", ">=", or "≠". They are used to describe a range of possible values that a variable can take.
For example, the inequality 3x + 2 > 10 is a linear inequality, where x is a variable. It means that the possible values of x that satisfy the inequality are those that make the expression 3x + 2 greater than 10. The solution set for this inequality is x > 2.
Now,
To solve the inequality y - 6 ≥ 12, we need to isolate y on one side of the inequality sign. We can do this by adding 6 to both sides of the inequality:
y - 6 + 6 ≥ 12 + 6
Simplifying the left side, we get:
y ≥ 18
So the solution set for this inequality is all values of y that are greater than or equal to 18. We can represent this graphically on a number line by shading all values to the right of and including 18:
---|================================>
18
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a quality control specialist at a plate glass factory must estimate the mean clarity rating of a new batch of glass sheets being produced using a sample of 18 sheets of glass. the actual distribution of this batch is unknown, but preliminary investigations show that a normal approximation is reasonable. the specialist should use a: group of answer choices t-distribution none of the distributions listed. z-distribution chi-square distribution f distribution
The quality control specialist should use a t-distribution for estimating the mean clarity rating of the new batch of glass sheets being produced using a sample of 18 sheets of glass.
The quality control specialist at a plate glass factory must estimate the mean clarity rating of a new batch of glass sheets being produced using a sample of 18 sheets of glass.
Since the actual distribution of this batch is unknown, but preliminary investigations show that a normal approximation is reasonable, the specialist should use a t-distribution.
1. The sample size (n) is 18, which is relatively small.
2. The population standard deviation (σ) is unknown.
In such cases, the t-distribution is more appropriate than the z-distribution, chi-square distribution, or f distribution.
The t-distribution is a statistical distribution that is used when the sample size is small, and the population standard deviation is unknown.
The z-distribution is used when the population standard deviation is known, and the sample size is large enough (typically, n > 30).
The chi-square distribution is used for testing the goodness-of-fit of a distribution or for testing the independence between two categorical variables.
The f distribution is used for comparing the variances of two populations.
It is not suitable for estimating the mean clarity rating in this case.
In conclusion, the quality control specialist should use a t-distribution for estimating the mean clarity rating of the new batch of glass sheets being produced using a sample of 18 sheets of glass.
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in a term 1 maths test , whitney scored 55 marks and amir scored 40 marks in a term 2 maths test whitney increased her score by 2o percent and amir increased jis score by 20 marka who had the higher mark in term 2
Answer:
whitney
Step-by-step explanation:
so amir in term 2 has 40+20=60
and whitney has 55+11=66
11 because 20% of 55 is 11 and when you add that two numbers you got the answer that whitney have higher mark
10% of 55=5.5
20% = 10%×2
5.5×2=11
Part II:
a. What is the domain of Marco's mapping diagram?
b. What is the range of Marco's mapping diagram?
Answer:
1.yes it's a function
a.1,2,3,4,5
b.40,80,120,160,200
5x^2-15x-50 factor the polynomial
Answer:
5(x - 5)(x + 2)
Step-by-step explanation:
5x² - 15x - 50
5(x² - 3x - 10)
5(x - 5)(x + 2)
a swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its deepest point. a cross-section is shown in the figure. if the pool is being filled at a rate of 0.9 ft 3 /min , how fast is the water level rising when the depth at the deepest point is 5 ft ? (round your answer to five decimal places.)
The water level is rising at a rate of 0.0075 ft/min when the depth at the deepest point is 5 ft.
Let's call the depth at the deepest point of the pool "y" and the volume of
the water in the pool "V".
We want to find the rate at which the water level is rising, which is the
rate of change of "y" with respect to time.
We know the rate at which the pool is being filled, which is 0.9 ft3/min,
and we can find the rate at which the volume of the water is increasing
using the formula for the volume of a rectangular prism:
V = lwh
where l is the length, w is the width, and h is the height.
Since the pool is not rectangular, we can find the volume of the water as
a function of "y" using similar triangles:
h/y = (9 - 3)/(40 - 20) = 0.3
where h is the height of the pool at the deepest point. Solving for h, we get:
h = 0.3y
Substituting this expression for h into the formula for the volume, we get:
V = lw(3 + 0.6y)
Taking the derivative with respect to time, we get:
dV/dt = lw(0.6 dy/dt)
Now we need to find the values of l and w. The width is given as 20 ft,
and the length is a function of "y":
l = 40 - 2(40 - y) = 2y
Substituting these values into the expression for dV/dt, we get:
dV/dt = 40y(0.6 dy/dt)
Finally, we can find the rate at which the water level is rising when y = 5 ft
by plugging in the values:
0.9 = 40(5)(0.6 dy/dt)
Solving for dy/dt, we get:
dy/dt = 0.9/(4050.6) = 0.0075 ft/min
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I have 30 eggs, I broke ten, I sold five, I cook ten, and I fry ten. How many are remaining?
Answer:
Step-by-step explanation:
ER=(5) [A single,1-tuple]. You start with 30 eggs. After selling 5 eggs, cooking 10, and frying 10 eggs 5 eggs remain.
PREMISES
ER=(E-S)-(C+F)
ASSUMPTIONS
Let E=the number of eggs at the start (30)
Let S=the number of eggs that were sold (5)
Let C=the number of eggs that were “cooked” i.e., hard-boiled, poached, and so forth (10)
Let F=the number of eggs that were fried (10)
Let ER=the number of eggs that remain having not been sold, cooked, or fried
CALCULATIONS
ER=(E-S)-(10+10)
ER=(30–5)-(20)
ER=25–20
ER=
5 eggs
PROOF
If ER=5, then the mathematic sentence ER=(E-S)-(C+F) returns
ER=(30–5)-(C+F)
5=25-(10+10)
5=25–20 and
5=5 verifies the result ER=5 of the sentence
Find the shaded area. Round your answer to the nearest tenth, if necessary.
Area of of the Triangle =
Area of the whole Rectangle =
Total Shaded Area =
Answer: For the triangle area you do= base*height what gives you 198in
For the rectangle area you do= side*lenght what gives you 756in
An for the shaded area you do triangle area-rectangle area, what gives you 558 in
(3) Two cylinder of equal volume have
heights in the ratio 1:16. Find the
ratio of their radii.
The ratio between their radii of cylinder is therefore 1:4.
WHAT IS RADIUS?The distance between a circle's or sphere's centre and its edge is referred to in geometry as its radius1. It is known as "r" and is a crucial component of spheres and circles3.
For instance, if a circle has a radius of 5 cm, that indicates that the circle's center to edge distance is 5 cm3.
When two cylinders have 1:16 ratios for their volumes and heights, it is possible to calculate their radii as follows:
Assume that one cylinder has a radius of r and a height of h. The other cylinder will have a radius of R and a height of 16h.
As the volumes of both cylinders are equal, we may write:
πr²h = πR²(16h) (16h)
r²/R² = 1/16
r/R = √(1/16) = 1/4
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Write the equation for a quadratic function that has x-intercepts of (-2,0) and (7,0) and passes through the point (5,-42).
The quadratic equation for a function having the x-intercepts of (-2,0) and (7,0) and passing through the point (5,-42) is:
f(x) = -2(x - 7)(x + 2)
The quadratic function has x-intercepts of (-2,0) and (7,0).
The function passes through the point (5,-42).Let's try to find the quadratic equation using the above information:
Since the quadratic function has x-intercepts of (-2,0) and (7,0), the function can be written as:
f(x) = a(x + 2)(x - 7)
Since the quadratic function passes through the point (5,-42), we can substitute the x and y coordinates into the above
equation to get the value of 'a':-
42 = a(5 + 2)(5 - 7)-42 = a(7)(-2)-42 = -14a => a = 3
So, the quadratic equation for the given function is:
f(x) = 3(x + 2)(x - 7)
Simplifying the equation:
f(x) = 3(x² - 5x - 14)f(x) = 3x² - 15x - 42
Therefore, the quadratic equation for a function having the x-intercepts of (-2,0) and (7,0) and passing through the point
(5,-42) is: f(x) = -2(x - 7)(x + 2)
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using gradient=rise/run find the gradient of ab in the following (0,6) and (3,2)
The gradient of the line segment AB is -4/3.
What is the gradient?
The gradient is a measure of the steepness of a curve or surface at a particular point. It is a vector quantity that points in the direction of the greatest increase in the function value and whose magnitude gives the rate of change of the function in that direction.
The coordinates of point A are (0, 6), and the coordinates of point B are (3, 2). We can find the gradient of the line connecting these two points using the formula:
gradient = rise/run
where "rise" is the difference in the y-coordinates of the two points, and "run" is the difference in the x-coordinates.
So, we have:
rise = 2 - 6 = -4
run = 3 - 0 = 3
Plugging these values into the formula, we get:
gradient = -4 / 3
Therefore, the gradient of the line segment AB is -4/3.
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Write the slope-intercept form of the equation of the line passing through the point (4, 5) and perpendicular to the line y =3/8x + 3.
Answer:
Step-by-step explanation:
Because the lines are perpendicular the slopes will be negtive
reciprocals of each other. Thus slope of 3/8 becomes -8/3.
Using point slope formula: y - y1 = m(x - x1)
Substitute the point given with the new slope and solve.
y - 5 = -8/3(x - 4)
y - 5 = -8/3x - - 32/3
y - 5 = -8/3x + 32/3
y - 5 + 5 = -8/3x + 32/3 + 5
y = -8/3x + 47/3
or
y = -8/3x + 15 2/3
0.416 (6 repeating) into fration
Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n
Answer:
24 = 31.4n + (–8.4)
Step-by-step explanation:
24=31.4n-8.4
At a toy store, a small bag contains 25 marbles, and a medium sized bag contains 7S marbles. The ratio of the number of marbles in the small bag to the number of marbles in the medium bag is equivalent to the ratio of the number of marbles in the medium bag to the number of marbles to the large bag. How many marbles are in the large bag?
Answer:
Let the number of marbles in the large bag be L. Then we have: 25 : 7S = 7S : L Multiplying both sides by 7S, we get: 25(7S) = (7S)^2 : L 175S = 49S^2 : L L = (49S^2) / 175 L = (7S^2) / 25 Therefore, the number of marbles in the large bag is (7/25) times the number of marbles in the medium bag.
I need help finding A
The value of a in the given parabola is a = 4/5.
What is parabola?A quadratic function's graph is a parabola. A parabola, according to Pascal, is a circle's projection. Galileo described the parabolic route that projectiles take when they fall under the influence of uniform gravity. Several bodily movements have a curvilinear course that has the form of a parabola. In mathematics, a parabola is any planar curve that is mirror-symmetrical and typically resembles a U shape.
We know that the parabola passes through (-3, 0) and (5, 0), so we can write:
0 = a(-3)² + b(-3) + c (equation 1)
0 = a(5)² + b(5) + c (equation 2)
We also know that the parabola passes through (1, -32), so we can write:
-32 = a(1)² + b(1) + c (equation 3)
Equating the equation 1 and 2 we have:
9a - 3b + c = 25a + 5b + c
16a + 2b = 0 (equation 4)
Now, equation i can be written as:
c = - 9a + 3b
Substituting in equation 3 we have:
-32 = a + b - 9a + 3b
-32 = -8a + 4b
-8 = -2a + b (equation 5)
b = -8 + 2a
Substitute the value of b in equation 4:
16a + 2(-8 + 2a) = 0
16a - 16 + 4a = =
20a = 16
a = 16/20 = 4/5
Hence, the value of a in the given parabola is a = 4/5.
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find the surface area of the composite figure/ triangular prism 10, 5, 10 height of 8cm/ rectangular prism 4, 5, 12, 4
Answer:
Therefore, the surface area of the composite figure is 368 cm².
Step-by-step explanation:
To find the surface area of the composite figure, we need to find the areas of each individual face and add them together.
The triangular prism has two triangular faces and three rectangular faces.
The area of each triangular face is 1/2(base × height).
Area of each triangular face = 1/2(10 × 5) = 25 cm²
The area of each rectangular face is length × width.
Area of the rectangular face with dimensions 5 cm by 10 cm = 5 × 10 = 50 cm²
Area of the rectangular face with dimensions 5 cm by 10 cm = 5 × 10 = 50 cm²
Area of the rectangular face with dimensions 10 cm by 8 cm = 10 × 8 = 80 cm²
Total area of the triangular prism = 2 × 25 + 3 × 50 + 80 = 280 cm²
The rectangular prism has two rectangular faces and four square faces.
The area of each rectangular face is length × width.
Area of the rectangular face with dimensions 4 cm by 5 cm = 4 × 5 = 20 cm²
Area of the rectangular face with dimensions 4 cm by 5 cm = 4 × 5 = 20 cm²
The area of each square face is side × side.
Area of each square face with side length 4 cm = 4 × 4 = 16 cm²
Total area of the rectangular prism = 2 × 20 + 4 × 16 = 88 cm²
The total surface area of the composite figure is the sum of the surface areas of the triangular prism and the rectangular prism.
Total surface area = surface area of triangular prism + surface area of rectangular prism
= 280 cm² + 88 cm²
= 368 cm²
I need to know the steps too I’ve been struggling with this all week:/
Answer:
The answer would be 28.96
Step-by-step explanation:
Sorry I was'nt to explain step by step But I know the answer
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Answer:
(what is your question)
Hattie is on a boat 74 metres away from the foot of a vertical cliff. The height of the cliff is 94 metres. Calculate the angle of depression of the boat from the top of the cliff.
The angle of depression of the boat from the top of the cliff = 51.78 degrees
To calculate the angle of depression of the boat from the top of the cliff, we need to draw a diagram to visualize the situation.
In this instance, we can draw a right-angled triangle with one side representing the cliff's height (94m) and the other representing the horizontal distance between the boat and the cliff's foot. (74m). This triangle's hypotenuse depicts the line of sight from the top of the cliff to the boat.
The angle of depression is defined as the angle formed by the horizontal line and the line of sight from the cliff's summit to the boat.
We can use the tan function to determine this angle.
tan(angle of depression) = (height of cliff) / (horizontal distance from the boat to the foot of the cliff)
tan(∅) = (h/x)
tan(angle of depression) = 94 / 74
angle of depression = [tex]tanx^{-1} (94/74)[/tex]
angle of depression = 51.788974574 degrees
Therefore, the angle of depression of the boat from the top of the cliff is approximately 51.78 degrees.
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The angle of depression of the boat from the top of the cliff is approximately 50.67 degrees.
To calculate the angle of depression of the boat from the top of the cliff, we can use trigonometry. The angle of depression is the angle formed between the horizontal line (parallel to the ground) and the line of sight from the top of the cliff to the boat.
In this scenario, we have a right triangle formed by the cliff, the boat, and the horizontal line connecting them.
Let's denote the angle of depression as θ.
Using trigonometric ratios, we can use the tangent function to calculate the angle of depression:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the cliff (94 meters) and the adjacent side is the horizontal distance from the foot of the cliff to the boat (74 meters).
tan(θ) = 94/74
To find θ, we can take the inverse tangent (arctan) of both sides:
θ = arctan(94/74)
Using a calculator or trigonometric table, we can find that θ is approximately 50.67 degrees.
Therefore, the angle of depression of the boat from the top of the cliff is approximately 50.67 degrees.
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4-23 use the data in problem 4-22 and develop a regression model to predict selling price based on the square footage and number of bedrooms. use this to predict the selling price of a 2,000-square-foot house with three bedrooms. compare this model with the models in problem 4-22. should the number of bedrooms be included in the model? why or why not?
A regression model can be created to predict selling price based on square footage and number of bedrooms using available data. The model equation includes coefficients that can be estimated to predict the selling price of a house. The number of bedrooms is a significant predictor of selling price and should be included in the model.
To develop the regression model to predict selling price based on the square footage and number of bedrooms, the following steps can be taken:
Collect data on the selling price, square footage, and number of bedrooms for a sample of houses.
Create a scatter plot to visually inspect the relationship between selling price and square footage, and between selling price and number of bedrooms.
Use regression analysis to create a model that predicts selling price based on square footage and number of bedrooms. The model equation will be:
Selling price = b0 + b1(Square footage) + b2(Number of bedrooms)
where b0, b1, and b2 are coefficients to be estimated from the data.
To predict the selling price of a 2,000-square-foot house with three bedrooms, substitute the values into the model equation and solve for selling price:
Selling price = b0 + b1(2000) + b2(3)
Comparing the performance of this model with the models in problem 4-22. The number of bedrooms should be included in the model because it is a significant predictor of selling price. However, further analysis could be conducted to determine if other variables could improve the model's predictive power.
Overall, this regression model can provide a useful estimate of the selling price of a house based on its square footage and number of bedrooms.
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Chen subtracted two polynomials as shown. Explain Chen’s error.
P^2+7mp+4-(-2p^2-mp+1)
P^2+2p^2+7mp-mp+4+1
3p^2+6m+5
The correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.
What is a polynomial?
In mathematics, a polynomial is an expression consisting of variables (also known as indeterminates) and coefficients, which involves only the operations of addition, subtraction, and multiplication. Polynomials can have one or more terms, and each term can have one or more variables with non-negative integer exponents.
Chen's error is in the second line where they added the terms -(-2p²-mp+1) without distributing the negative sign to each term inside the bracket. The correct way to subtract a polynomial is to change the sign of each term inside the bracket and then add them to the other polynomial. So, the correct simplification would be:
P²+7mp+4-(-2p²-mp+1)
= P²+7mp+4+2p²+mp-1 (Distributing the negative sign)
= 3p²+8mp+3
Therefore, the correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.
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11. Alina is flying a kite. The kite string is fully extended and measures 37 feet in length.
The kite is 12 feet east of Alina. Which equation can be used to find the height of the kite?
How high is the kite? Select all that apply.
a. 12² + b² = 37²
b.
37 = 0.5(12)(b)
c. 12 feet
d. 25 feet
Answer: A | 12² + b² = 37²
Step-by-step explanation:
The height can be found by using the Pythagoras Theorem
h² = b² + p²
A total of 70 tickets were sold for a concert and earn the organizers $804. If the cost of each ticket is either $10 or $12, how many tickets of each type were sold?
Answer:
Step-by-step explanation:
18 tickets cost $10 and 52 tickets cost $12.
Use Figure 1 to answer the following question
Name a set of collinear points
Name a set of parallel lines
Name a set of concurrent lines
Name a ray
Name an obtuse angle
Name a right angle
Name a pair of adjacent angles
Name a pair of complementary angles
Name a pair of supplementary angles
Name a pair of vertical angles
The set of points and lines when named are listed below
Naming the set of points and linesUsing the figure as a guide, we have the following:
Name a set of collinear points: B and EName a set of parallel lines: AO and BEName a set of concurrent lines: SM and HNName a ray: OWName an obtuse angle: JBTName a right angle: BECName a pair of adjacent angles: BEC and BENName a pair of complementary angles: AOW and WOPName a pair of supplementary angles: AOB and WOPName a pair of vertical angles: TBG and PBERead more about points and lines at
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under 21
21-34
35-54
55 and
older
Total
Basketball Football Soccer Baseball
10
9
8
5
32
N
7
10
5
7
29
10
5
10
8
Sport
33
9
9
5
9
29
Other/Hate
Sports
6
10
7
6
29
Total
42
32 133
43
35
32
152
What percent of the people between the ages of 35 and 54 prefer baseball? Round
your answer to the nearest whole number percent.
The percentage of the people between the ages of 35 and 54 that prefer baseball is 17.14%.
What does a preference means?A preferences means the certain characteristics that any person wants to have in a good/service to make it preferable to him.
In the table, the total number of people between the ages of 35 and 54 is 35. Out of the 35 people, the people that prefer baseball is known to be 6.
Now, the percentage between the ages of 35 and 54 that prefer baseball will be:
= Baseball preference / Total number of people aged 35 and 54
= 6/35
= 0.17142857142
= 17.14%
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A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.
The first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. What is the equation for the situation, written in standard form?
a. x2 – 99 = 0
b. x2 – 99x = 0
c. x2 + 5x + 104 = 0
d. x2 + 5x – 104 = 0
Answer:
d. x² + 5x - 104 = 0
Step-by-step explanation:
(x+5)x = 104
x² + 5x = 104
x² + 5x - 104 = 0
Use the box plot. It shows the number of days on the market for single family homes in a city.
Home Sales: Days on the Market
+
0 20 40 60 80 100 120
What is the interquartile range of the data?
F. 70
G. 40
H. 90
I. 120
The interquartile range (IQR) of the data is 70 and the third and the first quartile of the data is (90, 20).
What is the interquartile range of the data?The second and third quartiles, or the middle half of your data collection, are contained in the interquartile range (IQR). The interquartile range provides the range of the middle half of a data set, whereas the range provides the spread of the entire data collection.
The given plot shows the number of days on the market for single-family homes in the city.
The figure shows the first quartile = 20 and the third quartile 90
Therefore the interquartile range of the data is equal to the difference between the third quartile and the first quartile i.
The interquartile range = Q3 - Q1
= 90 - 20
= 70
The third and first quartiles of the data are (90, 20).
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A rectangular container 6.5 ft long, 3.2 ft wide and 2 ft high is filled with sand to a depth of 1.3 ft. How much sand is in the container?
Answer:
Therefore, there are 27.04 cubic feet of sand in the container.
Step-by-step explanation:
We can start by calculating the volume of the rectangular container:
Volume = length x width x height
Volume = 6.5 ft x 3.2 ft x 2 ft
Volume = 41.6 cubic feet
Since the sand fills the container to a depth of 1.3 feet, we can calculate the volume of the sand as follows:
Volume of sand = length x width x depth of sand
Volume of sand = 6.5 ft x 3.2 ft x 1.3 ft
Volume of sand = 27.04 cubic feet
Therefore, there are 27.04 cubic feet of sand in the container.
a certain medical test is known to detect 84% of the people who are afflicted with the disease y. if 10 people with the disease are administered the test, what is the probability that the test will show that: all 10 have the disease, rounded to four decimal places? 0.1749 at least 8 have the disease, rounded to four decimal places? at most 4 have the disease, rounded to fo
Rounding to four decimal places, the probability is (a) 0.3273 (b) 0.8423, and (c) 0.0446.
We can model this problem using a binomial distribution, where the probability of success (having the disease) is p = 0.84, and the number of trials (people tested) is n = 10.
(a) To find the probability that all 10 people have the disease, we can calculate the:
P(X = 10) = (10 choose 10) * (0.84)^10 * (1-0.84)^(10-10) = 0.3273
Rounding to four decimal places, the probability is 0.3273.
(b) To find the probability that at least 8 people have the disease, we can calculate the:
P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)
We can find each term using the binomial probability formula and then add them up:
P(X = 8) = (10 choose 8) * (0.84)^8 * (1-0.84)^(10-8) = 0.2018
P(X = 9) = (10 choose 9) * (0.84)^9 * (1-0.84)^(10-9) = 0.3132
P(X = 10) = (10 choose 10) * (0.84)^10 * (1-0.84)^(10-10) = 0.3273
P(X ≥ 8) = 0.2018 + 0.3132 + 0.3273 = 0.8423
Rounding to four decimal places, the probability is 0.8423.
(c) To find the probability that at most 4 people have the disease, we can calculate:
[tex]P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
We can find each term using the binomial probability formula and then add them up:
P(X = 0) = (10 choose 0) * (0.84)^0 * (1-0.84)^(10-0) = 0.000004
P(X = 1) = (10 choose 1) * (0.84)^1 * (1-0.84)^(10-1) = 0.0001
P(X = 2) = (10 choose 2) * (0.84)^2 * (1-0.84)^(10-2) = 0.0012
P(X = 3) = (10 choose 3) * (0.84)^3 * (1-0.84)^(10-3) = 0.0084
P(X = 4) = (10 choose 4) * (0.84)^4 * (1-0.84)^(10-4) = 0.0348
P(X ≤ 4) = 0.000004 + 0.0001 + 0.0012 + 0.0084 + 0.0348 = 0.0446
Rounding to four decimal places, the probability is 0.0446.
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Factor out the greatest common factor (GCF) from 6x^4 + 8x^3
Required factor form is 2x³(3x + 4).
What is GCF?
GCF stands for Greatest Common Factor, also known as the Greatest Common Divisor (GCD). In mathematics, the GCF of two or more numbers is the largest positive integer that divides each of the numbers without a remainder. For example, the GCF of 12 and 18 is 6 because 6 is the largest integer that divides both 12 and 18 without a remainder. The concept of GCF is important in many areas of mathematics, including algebra, number theory, and calculus, and is used in various problem-solving applications.
Given form is 6x⁴+8x³.
Here is two term 6x⁴ and 8x³.
By factorisation,
6x⁴ = 2×3×x⁴ and 8x³ = 2×2×2×x³
The greatest common factor (GCF) of 6x⁴ and 8x³ is 2x³.
To factor it out, we can divide each term by 2x³:
Now,
6x⁴ ÷ 2x³ = 3x
8x³ ÷ 2x³ = 4
So, we can write:
6x⁴ + 8x³ = 2x³(3x + 4)
Therefore, the factored form of 6x⁴ + 8x³ is 2x³(3x + 4).
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