The largest figure that Ash can built with 61 toothpicks is of:
A composition of 12 hexagons.
How to obtain the largest figure?The number of toothpicks needed is modeled with a linear function, defined as follows:
y = mx + b.
The coefficients of the function are given as follows:
m is the slope, representing the number of toothpicks per new figure.b is the y-intercept, representing the number of toothpicks of the first figure.The number of toothpicks in each figure is represented by the following sequence:
(6, 11, 16, ...).
Hence the parameters are given as follows:
m = 5, b = 6.
Thus the definition of the function is of:
T(n) = 5(n - 1) + 6. (as the first figure is with n = 1).
T(n) = 5n + 1.
Then the number of hexagons with 61 toothpicks is obtained as follows:
5n + 1 = 61
5n = 60
n = 60/5
n = 12 hexagons.
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please help, answers only!!
The linear function in slope intercept form is y = -3x + 6
What is a linear function?A linear function is a function represented by a straight line.
What is slope intercept form?Slope intercept form of a linear function is y = mx + c where
m= slope and c = y-interceptHow to write the linear function in slope-intercept form?To write the linear function in slope intercept form, we need to know its slope, which is given by
m = (y₂ - y₁)/x₂ - x₁) where
y₁ = f(2) = 0, y₂ = f(4) = -6, x₁ = 2 and x₂ = 4Substituting the values of the variables into the equation, we have
m = (y₂ - y₁)/x₂ - x₁)
m = (-6 - 0)/4 - 2)
m = -6/2
m = -3
Next we find the equation of the linear function in slope-point form which is
m = (y - y₁)/x - x₁) where
m = -3y₁ = f(2) = 0 and x₁ = 2Substituting the the values of the variables into the equation, we have
m = (y - y₁)/x - x₁)
-3 = (y - 0)/x - 2)
-3 = y/(x - 2)
-3(x - 2) = y
-3x + 6 = y
y = -3x + 6 which is the slope-intercept form
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Serenity has 58 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 210 square meters. Solve for the dimensions (length and width) of the field.
The dimensions of the rectangular( length and width) are 14m and 15m.
Here we have to find the dimension of the length and width.
Data given:
Fencing = 58m
Area = 210 m²
Let us assume the length be x
By this, we get the width as:
width = 58 - 2x / 2
= 29-x
As the area is 210 m²
The formula to find the area of the rectangular is:
Area = length ×width
210 = x ( 29 -x)
x² - 29 x + 210 = 0
Formula to find the value of x from the quadratic equation:
x = -b ±[tex]\sqrt{b^{2} - 4ac }[/tex]
For the general equation ax² + bx + c =0
As the equation is:
x² - 29x + 210 = 0
a = -1
b = -29
c = -210
So,
x = 29 ±[tex]\sqrt{(29)^{2} - 4(-1)(-210) }[/tex] / 2(-1)
= 29± 1/-2
= 14, 15
29 - x = 15, 14 (for the value of x = 14 and 15 respectively)
Therefore the dimensions are 14m and 15m.
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How do you write a limit of a function?
The limit of a constant times a function is equal to the constant times the limit of the function. lim x →a(c f(x)) = c lim x →a f(x).
limit of a function
The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input.
the right-hand limit of a function is the value of the function approaches when the variable approaches its limit from the right. The left-hand limit of a function is the value of the function approaches when the variable approaches its limit from the left.
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(a) find a basis for the row space of a and the row rank of a. (b) find a basis for the column space of a and the column rank of a. (c) find a basis for the null space of a and the nullity of a. (d) find a basis for the null space of at and the nullity of at .
The four fundamental subspaces of a matrix are the row space, column space, null space, and left null space.(a) A basis for the row space of A is {{1,2,3}, {2,3,4}}. The row rank of A is 2.(b) A basis for the column space of A is {{1,2}, {2,3}, {3,4}}.
(c) A basis for the null space of A is {{-1,1,0}, {1,-2,1}, {0,1,-1}}. The nullity of A is 3.
(d) A basis for the null space of At is {{1,-1,0}, {-1,1,1}, {0,-1,-1}}. The nullity of At is 3.The four fundamental subspaces of a matrix are the row space, column space, null space, and left null space. The row space is the set of all linear combinations of the rows of the matrix, and its dimension is the row rank. The column space is the set of all linear combinations of the columns of the matrix, and its dimension is the column rank. The null space is the set of all vectors that are solutions to the system of equations Ax = 0, and its dimension is the nullity. The left null space is the set of all vectors that are solutions to the system of equations A^T x = 0, and its dimension is the nullity.
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In ΔPQR, q = 7.1 inches, ∠Q=37° and ∠R=12°. Find the length of p, to the nearest 10th of an inch.
p = 9
see explanation in image
using law of sines
Hope this helps :)
If you need any more explanation, feel free to ask. If this really helps, consider marking brainliest.
- Jeron
Length of p to the nearest 10th of an inch is 8.9 inches.
What is Sines Law of a Triangle?Sines law of a triangle defines that the ratio of the side lengths of a triangle to the sine of the opposite angles to the side lengths are equal.
a / sin A = b / sin B = c / sin C
where a, b and c are the sides opposite to A, B and C respectively.
Given is a triangle ΔPQR.
Given, ∠Q = 37° and ∠R = 12°.
Sum of the interior angles of a triangle is 180°.
∠P = 180° - (37° + 12°)
= 131°
Using the sine law,
p / sin P = q / sin Q
p / sin (131°) = 7.1 / sin (37°)
p = (7.1 / sin (37°)) × (sin (131°))
= 8.9 inches
Hence the length of p is 8.9 inches.
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The Sugar Sweet Company is going to transport its sugar to market. It will cost $5000 to rent trucks, and it will cost an additional $200 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S, and then graph your equation using the axes below.
The linear function relating the variables C and S is given as follows:
C(S) = 5000 + 200S.
The graph of the linear function is given by the image at the end of the answer.
How to define the linear function?The linear function in this problem is defined in the slope-intercept as follows:
y = mx + b.
In which the coefficients of the function are defined as follows:
m is the slope, representing the rate of change of the output y relative to the input x.b is the y-intercept, representing the initial value of the output y.In the context of this problem, the variables are given as follows:
Output: Cost.Input: Tons of Sugar.It will cost $5000 to rent trucks, hence the intercept is of:
b = 5000.
It will cost an additional $200 for each ton of sugar transported, hence the slope is of:
m = 200.
Then the equation is defined as follows:
C(S) = 5000 + 200S.
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7. Brad is planning a garage sale. To direct customers to his house, he is painting six
arrow signs.
a) Calculate the area of one sign.
b) Each can of paint can cover 1 m².
How many cans of paint
should Brad buy for all six signs. Explain your answer.
The solution is
a) The area of the sign is 3950 cm²
b) The total number of cans of paint is 3 cans of paint
What is the Area of a Rectangle?
The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the total area of the sign be = S
Now , the area of the triangle be = T
Let the area of the rectangle be = R
The height of the triangle = 50 cm
The base of the triangle = 50 cm
So , the area of the triangle = ( 1 / 2 ) Height x Base
Area of Triangle T = ( 1/2 ) x 50 x 50
Area of Triangle T = 1250 cm²
Length of the rectangle = 90 cm
Width of the rectangle = 30 cm
Now , the area of rectangle R = Length x Width
Area of the rectangle R = 90 x 30
Area of the rectangle R = 2700 cm²
And , the area of the sign = Area of the rectangle R + Area of Triangle T
Substituting the values in the equation , we get
Area of the sign = 2700 cm² + 1250 cm²
Area of the sign = 3950 cm²
b)
Each can of paint covers = 1m²
So , Each can of paint covers = 10000 cm²
The number of signs = 6 signs
So , the total area of 6 signs = 6 x Area of the sign
The total area of 6 signs = 6 x 3950
The total area of 6 signs = 23700 cm²
And , the number of cans of paint for 6 signs = The total area of 6 signs / Area covered by each can
Substituting the values in the equation , we get
The number of cans of paint for 6 signs = 23700 / 10000
The number of cans of paint for 6 signs = 2.37 cans
The number of cans of paint for 6 signs ≈ 3 cans
Hence ,
a) The area of the sign is 3950 cm²
b) The total number of cans of paint is 3 cans of paint
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Find the equation of the least squares regression line. State the value of the slope of the regression line rounded to the nearest hundredth
y=10x+235 is the equation of the least squares regression line.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We need to find the equation of the least squares regression line.
The value of the slope of the regression line can be find by using any two points from the table.
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
(58, 335) and (70, 450)
Slope of line = 450-335/70-58
=115/12
=10
The equation of line is y=10x+b
335=10(10)+b
335=100+b
335-100=b
235=b
Hence, the equation of the least squares regression line is y=10x+235.
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For positive acute angles A and B, it is known that sin A = 21/29 and tan B = 24/7
Find the value of cos(A - B) in simplest form.
The value of cos(A - B) in simplest form is 651/203.
What is acute angles?An acute angle is an angle that is less than 90 degrees, or less than a right angle. Acute angles are typically found in everyday life, such as the shape of a slice of pizza or the corner of a triangle. Acute angles are also found in shapes such as pentagons, hexagons, and octagons. Acute angles are important for engineering, architecture, and construction, as angles that are too wide or too small can affect the structural integrity of a building or other structure. Acute angles are also important in geometry, as they can be used to solve for the area, perimeter, and interior angles of a given shape.
We can use the formula for cos(A - B):
cos(A - B) = cos A cos B + sin A sin B
cos(A - B) = (21/29) * (24/7) + (21/29) * (7/24)
cos(A - B) = (504 + 147)/29 * 7
cos(A - B) = (651/203)
Therefore, the value of cos(A - B) in simplest form is 651/203.
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(2x² + 15x+20) ÷ (x+5)
Answer:
To divide polynomials, we need to use polynomial long division. First, we divide the first term of the dividend by the first term of the divisor to get the first term of the quotient, which we write above the division bar. In this case, the first term of the dividend is 2x² and the first term of the divisor is x, so the first term of the quotient is 2x. We then multiply the divisor by the quotient and subtract it from the dividend to get the remainder.
Here's how the long division would look:
2x² + 15x + 20
===
x + 5
2x
_______
15x - 10x
15x + 20 - 10x - 20
___________
5x - 20
After we perform the polynomial long division, we get the quotient 2x + 5 and the remainder -20. Therefore, the final result of the division is:
(2x² + 15x + 20) ÷ (x + 5) = 2x + 5 + (-20)/(x + 5)
Note that the remainder -20 is written as a fraction with the divisor x + 5 in the denominator. This is the correct way to write the remainder because it tells us that the remainder has a degree that is one less than the degree of the divisor. In this case, the degree of the divisor is 1, so the degree of the remainder is 0.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). The mean score on a biology exam taken by all undergraduate students in a college in a particular year is 67. 8 with a standard deviation of 11. 5. The standard error of the mean for a sample of 70 students is , and the margin of error of the mean is. (round off your answers to the nearest hundredth. ).
Standard error of the mean is 1.375 and margin of error of the mean is 2.694.
Based on the provided information, mean µ = 67.8 and standard deviation σ = 11.5. The sample size n = 70
The standard error (SE) of a statistic refers to the standard deviation of its sampling distribution or an estimate of that standard deviation.
Standard error (SE) is given by:
SE = σ/√n = 11.5/√70 = 1.375
The margin of error (MOE) refers to a statistic demonstrating the amount of random sampling error in the results of a survey.
Margin of error (MOE) is the standard error multiplied by a Z value that correspondence to a confidence percentage. Assuming a 95% confidence the Z value is 1.96. Hence,
MOE = z * σ/√n = 1.96 x 1.374 = 2.694
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→Will give 80 points and brainliest!!←
Please don't give a link, and give the full answer, not just half.
Thank you!
A; The distance between the starting point to Obstacle 2 is 13 meters
B; There are 10 meters around one lap of course.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²]
Part A;
Starting point: (-12, 5); Obstacle 2: (0, 0)
(x₁, y₁) and (x₂, y₂)
Therefore,
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(0 - (-12))² + (0 - 5)²
d = √(12)² + (- 5)²
d = √144 + 25
d = √169
d = 13 meters
B. Starting point: (-12, 5); Obstacle 2: (0, 0);
Obstacle 1: (-12, 0)
(Starting Point + Obstacle 2)
Now,
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(0 - (-12))² + (0 - 5)²
d = √(12)² + (- 5)²
d = √144 + 25
d = √169
d = 13 meters
Therefore, (Starting Point + Obstacle 1)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(-12 - (-12))² + (0 - 5)²
d = √(0)² + (-5)²
d = √25
d = 5 meters
(Obstacle 2 + Obstacle 1)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(-12 - 0)² + (0 - 0)²
d = √(-12)² + (0)²
d = √144
d = 12 meters
Total = 12m + 5m + 13m = 30
30 ÷ 3 = 10 meters
we can conclude that 10 meters around one lap of course.
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Please help pleasee 40 points
which inequality do I pick for the word problem
The height to ride the roller coaster mist be at least 3 feet but no more than 6 feet
tall
A)x< 3 or x > 6
B) 3 < x < 6
C) 3 <= x <= 6
D) x <= 3 or x => 6
the <= means greater than or equal too
If 3x + 7 = 20, what is 3x + 10?
Answer:
22.9
Step-by-step explanation:
22.9
3x+7=20
-7 -7
3x=13
/3 /3
x= 4.3
3(4.3)+10
12.9+10
22.9
(i think you put something in wrong. the answer usually shouldnt have a decimal)
in a scientific research, a statistical test resulted in a -value of 0.026. match each value with the correct decision. (a) do not reject h0 (b) reject h0 group of answer choices significance level equals 0.01 (a) significance level equals 0.05
Any p-value less than 0.05 is a cause to reject the null hypothesis.
What is Null Hypothesis?
The statement "The null hypothesis is a claim about population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.
Explanation:
In this case, 0.015 is the only option for p-value that would lead to a rejection of the null hypothesis (if the level of significance for the test is 0.05).
Any p-value less than 0.05 is a cause to reject the null hypothesis.
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Answer now with steps and I will give Brainliest! Use picture below.
Answer:
Step-by-step explanation: Here is your answer 97
PLEASE HELP I NEED HELP FASTT!!
20 POINTS
Triangle a is reflected in the x-axis to give b which is the reflected in the line y=x.
Triangle a is reflected in the x-axis to give b which is reflected in the line y=x. The coordinates of triangle C are (-5,4) , (-2,2) and (-2,4)
Coordinates for Triangle A are (4,5), (2,2), and (4,2)
Triangle B is created by reflecting triangle A along the x-axis.
The x-axis coordinates stay the same after reflection in the x-axis, while the y-axis coordinates go negative with the same magnitude.
Consequently, triangle B's coordinates are (4, -5), (2, -2), and (4,-2)
The x and y coordinates of triangle B are now reversed as it is reflected by the line y = x to create triangle C.
Triangle C's coordinates are (-5,4), (-2,2), and (-2,4)
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customers depart from a bookstore according to a poisson process with rate a per hour. each customer buys a book with probability p, independent of everything else. (a) find the distribution of the time until the first sale of a book.
Let X be a random variable representing the time until the first sale of a book. Then X has a Poisson distribution with rate a*p per hour.
Let X be a random variable representing the time until the first sale of a book. This random variable is the sum of the times that customers take to arrive and purchase a book. Since customers arrive at a bookstore according to a Poisson process with rate a per hour, the time until the first customer arrives has an exponential distribution with rate a per hour. Moreover, each customer buys a book with probability p, independently of everything else. Thus, the time until the first sale of a book is the sum of the time until the first customer arrives and the time until the first successful purchase. This sum of two independent exponential random variables is a Poisson random variable with rate a*p per hour. Therefore, the distribution of the time until the first sale of a book is a Poisson distribution with rate a*p per hour.
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there is a line that includes the point ( 0, 10 ) and has a slope of 10. what is its equation in slope-intercept form?
Answer:
y=10x+10
Step-by-step explanation:
Remember, y=mx+b, where m is the slope and b is the y-intercept.
In this case, the slope, or m, is 10 and the y-intercept, or b, is 10. We then substitute m=10 and b=10 in and get the equation y=10x+10.
Find the standard deviation for the binomial distribution which has the stated values of n and p.
n = 48
p = 3/5
The standard deviation for the binomial distribution is 3.39
The standard deviation for the binomial distribution is given by,
σ = [tex]\sqrt{n * P(1-P}[/tex]
where n = Number of trials
P = probability of success of an individual trail
If n = 48 and P = 0.6
σ = [tex]\sqrt{48 *0.6(1-0.6})[/tex]
= [tex]\sqrt{48*0.24}[/tex]
=[tex]\sqrt{11.52}[/tex]
=3.39
Therefore, the standard deviation for the binomial distribution will be 3.36.
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the new malthusians worry that of the population will lead to a scarcity of food. a. exponential decline b. exponential growth c. steady growth d. steady decline
Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.
Given that,
The new Malthusians worry that ______ of the population will lead to a scarcity of food.
We have to fill the blank.
We know that,
What is exponential growth?A pattern of data that exhibits larger increases over time, forming the curve of an exponential function, is said to exhibit exponential growth.
The formula for the exponential growth is
V=S×(1+R[tex])^{T}[/tex]
The starting value, S, of an initial starting point subject to exponential growth can be multiplied by the sum of one plus the interest rate, R, raised to the power of T, or the number of periods that have passed, to get the current value, V.
Therefore, Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.
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sovle bpleaseeeeeeeeeedeeeeeeeeeeeeeeeeeeeeeeeeeese
Answer:
24 divided by 6 equals 4
Step-by-step explanation:
Answer: I think is 4
Step-by-step explanation:
Emma has 3 1/8 slices of pizza in her lunch box. Ryan has 1/4 the amount of pizza that Emma does. How much pizza do they have together?
Please Help!
Emma and Ryan both have 125/32 pizzas.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given, Emma has [tex]3\frac{1}{8}[/tex] slices of pizza.
Simplifying to improper fraction;
Emma has 25/8 slices of pizza.
And Ryan has 1/4 x The amount of pizza Emma has, slices of pizza.
That means, Ryan has 1/4 x (25/8) slices of pizza.
Applying multiplication of fraction.
That is, 25/32 slices of pizza.
To find the total amount of pizza;
add the number of pizza,
25/8 + 25/32
To add the number:
First, we take LCM,
25/8 + 25/32
= (100+ 25) / 32
= 125/32
Therefore, they both have 125/32 pizzas.
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Complete the equation of the line through-6, 5) and(3, -3). Use exact numbers.
Answer:
To find the equation of the line through the two given points, we can use the slope-intercept form of the equation of a line, which is $y = mx + b$, where $m$ is the slope of the line and $b$ is the $y$-intercept (the point where the line crosses the $y$-axis).
We can find the slope of the line by using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the two given points. In this case, the slope is
$$m = \frac{(-3) - 5}{3 - (-6)} = \frac{-8}{9} = -\frac{4}{3}.$$
To find the $y$-intercept, we can plug the coordinates of one of the points and the slope into the equation of a line, so we have $y = -\frac{4}{3} x + b$. If we plug in the coordinates of the first point, we get
$$5 = -\frac{4}{3} (-6) + b \Rightarrow b = -\frac{4}{3} (-6) + 5 = \frac{28}{3}.$$
Therefore, the equation of the line through the two given points is
$$y = -\frac{4}{3} x + \frac{28}{3} = -\frac{4}{3} x + \frac{28}{3}.$$
Answer:
Step-by-step explanation:
(-6,5) (3,-3)
The equation of the line:
[tex]\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
x₁=-6 x₂=3 y₁=5 y₂=-3
Hence,
[tex]\displaystyle\\\frac{x-(-6)}{3-(-6)} =\frac{y-5}{-3-5} \\\\\frac{x+6}{3+6}=\frac{y-5}{-8} \\\\\frac{x+6}{9} =\frac{y-5}{-8} \\\\[/tex]
Multiply both parts of the equation by -72:
[tex]-8(x+6)=9(y-5)\\\\-8x-48=9y-45\\\\-8x-48+45=9y-45+45\\\\-8x-3=9y\\\\[/tex]
Divide both parts of the equation by 9:
[tex]\displaystyle\\-\frac{8}{9} x-\frac{1}{3} =y\\\\Thus,\ y=-\frac{8}{9}x-\frac{1}{3}[/tex]
help please, which graph is it
Answer:
it is the linear graph
hope it helps
In a game of luck, a turn consists of a player rolling 777 six-sided dice and counting how many of the dice show a 555. Let fff be the number of dice showing a 555 in a turn. What type of variable is fff?.
fff is a random variable in a game of luck
A random variable is a formula that gives each result in a sample space a numerical value.
There are two types of random variables: discrete and continuous. If a random variable only takes specified values inside an interval, it is said to be discrete. It is continuous if not.
We typically use capital letters, such X and Y, to designate the random variables
A random variable must be measured in order to be able to assign probabilities to a set of potential values. It is evident that the outcomes depend on a number of unpredictable physical elements.
According to the question,
In a game of luck, a turn consists of a player rolling 777 six-sided dice and counting how many of the dice show a 555. Let fff be the number of dice showing a 555 in a turn.
Here, fff is a Random variable.
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Help! I am struggling
Answer:
34
Step-by-step explanation:
First you arrange the data in an ascending order and the median is the middle value. if the number of values is an even number, then the median will be the average of the two middle numbers. In this case, the median is 34.
You please help me with the second part i need it to pass this by friday
The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week
What is inequality ?A relationship between two expressions or values that is not equal to one another is referred to as "inequality" in mathematics.
According to the given information
Let x be the more items that Julie will sell after First week
Number of items soled in First week = 6
So
The inequality formed will be
x + 6 > 20
Solving the inequality is
x > 20 - 6
x > 14
So
The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week
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[tex]\frac{7}{9} \\[/tex] ×5[tex]\frac{2}{5}[/tex]
The value of the expression 7/ 9 × 5 2/ 5 is 4 1/5
What is a fraction?A fraction can be described as the part of a whole element, number or expression.
There are several types of fractions which includes;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
7/ 9 × 5 2/ 5
Convert the mixed fraction to improper fraction
7/ 9 × 27/ 5
Now, reduce to simpler terms
7/ 1 × 3/ 5
Multiply the values
21/ 5
4 1/5
Hence, the value is 4 1/5
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