The ribbon cost $0.60 per foot.
Solution:[tex]\text{Total number of ribbon used} = (5.75 + 11.75) = 17.50 \ \text{feet}[/tex]
[tex]\text{17.50 feet of ribbon cost} = \$10.50[/tex]
[tex]\text{1 foot of ribbon cost = x}[/tex]
Cross Multiply[tex]17.50 \times x = 1 \ foot \times \$10.50[/tex]
[tex]x = 1 \ foot \times 10.50\div17.50[/tex]
[tex]x = \$0.60[/tex]
Therefore, The ribbon cost per foot $0.60 per foot.
Combine like terms to simplify the expression completely. 2x + 5 - y + 6x + 4y =
Thus, the simplification of linear expression is : 8x + 3y +5 .
Explain about the simplification of linear equation?A linear equation is an integer number of the form y=mx+b, where m represents the slope when b is the y-intercept, and only a constant alongside a first-order (linear) term are included.
To simplify the linear equation-
Add or remove like terms from a linear expression to make it simpler. Contrary terms are not added to or withdrawn from. Reduce common factors and add brackets to factorise. Add like terms together and multiply all terms inside brackets by the term outside to expand.
Given linear equation-
= 2x + 5 - y + 6x + 4y
Add like term with same variable.
= 8x + 3y +5
Thus, the simplification of linear expression is : 8x + 3y +5 .
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Use the discriminant to determine the number of solutions.
10. y=x²-3x+2
11. y = 2x² - 4x +3
13. y = x’−5x−10
14. y=x²+2x-1
12. y=-3x² + 5x-1
15. y = 4x²-9
In response to the stated question, we may state that y = 4x²-9 The discriminant is (-9)² - 4(4)(0) = 81. Since the discriminant is positive, there are two real solutions.
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Basic Theorem of Algebra implies that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. The formula "ax2 + bx + c = 0" is a common solution for quadratic equations. where a, b, and c are numerical coefficients or constants. where the variable "X" is unnamed.
y=x²-3x+2
The discriminant is (-3)² - 4(1)(2) = 1. Since the discriminant is positive, there are two real solutions.
y = 2x² - 4x +3
The discriminant is (-4)² - 4(2)(3) = -8. Since the discriminant is negative, there are no real solutions.
y=-3x² + 5x-1
The discriminant is (5)² - 4(-3)(-1) = 29. Since the discriminant is positive, there are two real solutions.
y = x’−5x−10
The discriminant is (-5)² - 4(1)(-10) = 65. Since the discriminant is positive, there are two real solutions.
y=x²+2x-1
The discriminant is (2)² - 4(1)(-1) = 8. Since the discriminant is positive, there are two real solutions.
y = 4x²-9
The discriminant is (-9)² - 4(4)(0) = 81. Since the discriminant is positive, there are two real solutions.
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suppose that you wanted to predict the price of a house based on where the house was located (northeast, northwest, southeast, or southwest) as well as square footage. how many indicator variables would you need? group of answer choices 4
Suppose that you wanted to predict the price of a house based on where the house was located (northeast, northwest, southeast, or southwest) as well as square footage, then the northwest indicator variable would be set to 1, and the other three indicator variables would be set to 0.
What is a variable indicator?Indicator variable An indicator variable is a binary variable that indicates whether or not a specific condition or category is present. Indicator variables are typically used in statistical models to represent categorical data or conditions, and they are also known as dummy variables or binary variables.
Example suppose you want to conduct a statistical analysis to determine the impact of location and size on the price of a house. There are four possible locations: northeast, northwest, southeast, and southwest. We can use four indicator variables (one for each location) to represent this information.
For instance, if a house is in the northeast, the northeast indicator variable would be set to 1, while the other indicator variables would be set to 0. Similarly, if the house is in the northwest, the northwest indicator variable would be set to 1, and the other three indicator variables would be set to 0. We would use similar logic for the other two locations.
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What is the total cost of order number four if the customer received 10% off and paid a 15% gratuity and 4.5% sales tax?
The cost of order number four would be $12.60.
What does US sales tax mean?
Sales taxes are levied on the purchase or leasing of products and services inside the United States. There is no federal general sales tax, and sales tax regulation is handled at the state level. Think about this sales tax illustration.
You want to know how much your purchase will cost after taxes before you check out at The Clothes Boutique. Your cart contains goods with a combined price of $100 after totaling up all the charges. You would calculate 9.5% of $100 since the sales tax in that county is 9.5%. (100 x 0.095).
The cost of order number four would be $12.60.
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40 percent of employess judge their peers by their cleaniliness of the workspace
The number of employees who judge their cleanliness in their workplaces are: P(x=0) = 0.0168, P(x=1)= 0.0896, P(x=2) =0.2090, P(X=3)= 0.2787,
P(X=4)= 0.2322, P(X=5)= 0.1239, P(X=6)= 0.0413, P(x= 7)= 0.0079 and P(x=8)= 0.0007.
Binomial distribution :
A binomial distribution is a distribution whose experiment has two possible outcomes, a success and failure. The outcomes of the experiment do not depend on each other. In probability theory and statistics, the binomial distribution with the parameters n and p is a discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes or no question, each with its own Boolean result. : success (with probability p) or failure (with probability q=1-p). A pass/fail experiment is also called Bernoulli's trial or Bernoulli's experiment, and a sequence of results is called Bernoulli's process; for a single trial, i.e. n = 1, the binomial distribution is the Bernoulli distribution.
According to the Question:
For n trials in a binomial distribution, the probability of getting success:
[tex]P(X=x) = \frac{n!}{(n-x)!x!} * p^x *q^{(n-x)}[/tex]
Where p = success
q = failure
n = 8, p= 40% = 0.4
q = 1-0.4 = 0.6
After calculating, we get the values:
P(x=0) = 0.0168, P(x=1)= 0.0896,
P(x=2) =0.2090, P(X=3)= 0.2787,
P(X=4)= 0.2322, P(X=5)= 0.1239,
P(X=6)= 0.0413, P(x= 7)= 0.0079
and P(x=8)= 0.0007.
Complete Question:
40% of employees judge their peers by the cleanliness of their workspaces. You randomly select 8 employees and ask them whether they judge their peers by the cleanliness of their workspaces. The random variable represents the number of employees who judge their peers by the cleanliness of their workspaces.
P(x)=0,1,2,3,4,5,6,7, 8
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Pablo needs to memorize words on a vocabulary list for Latin class he has 12 words to memorize and he is 3/4 done how many words has Pablo memorized so far
Answer:
9 words
Step-by-step explanation:
We know
He has 12 words to memorize, and he is 3/4 done.
How many words has Pablo memorized so far?
We Take
12 x 3/4 = 9 words
So, Pable has memorized 9 words.
Our class is planning to paint a rectangular mural with an area of 60 square feet, it has to be at least 4 feet high but no more than 6 feet the length and width have to be hold numbers list of possible width for the
The possible widths for the rectangular mural are between 10 and 15 feet. We can also list the number of possible widths within this range, which is six. They are 10 feet, 11 feet, 12 feet, 13 feet, 14 feet, and 15 feet.
To determine the possible widths for the rectangular mural with an area of 60 square feet, we can use the formula for the area of a rectangle, which is length multiplied by width. Since the area is given as 60 square feet and the length should be between 4 and 6 feet, we can set up inequality as follows:
4w ≤ 60 ≤ 6w
where w is the width of the mural in feet. Solving this inequality for w, we get:
10 ≤ w ≤ 15
It is important to consider the dimensions carefully to ensure that the mural meets the requirements and fits in the desired space. By having multiple possible widths, the class can select the most suitable one based on the available resources and space.
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Complete question:
Our class is planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list a number of possible widths for our class. Planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list the number of possible widths for it.
pls solve it. it's urgent
Rounding to the nearest cm², the area of the shaded region is 32 cm².
Describe Area of triangle?The area of a triangle is the measure of the region enclosed by the three sides of a triangle. It is measured in square units. The formula to find the area of a triangle is given as:
Area = 1/2 x base x height
where "base" is the length of the side of the triangle that is perpendicular to the height and "height" is the distance between the base and the opposite vertex.
The base and height can be any two sides of the triangle as long as the height is perpendicular to the base. If the base and height are not known, they can be found using the Pythagorean theorem or other trigonometric functions.
We can find the area of the shaded region by subtracting the area of triangle ABD from the area of rhombus ABCD.
To find the area of triangle ABD, we need to first find the length of BD. Since angle BAD is 70 degrees and ABCD is a rhombus, we know that angle BCD is also 70 degrees. Therefore, angle BXD is 70 degrees / 2 = 35 degrees.
Using trigonometry, we can find BD:
tan(35) = BD/9
BD = 9 tan(35)
BD ≈ 5.458 cm
To find the area of triangle ABD, we use the formula:
Area of triangle = (base x height) / 2
The base of triangle ABD is BD, which we just found, and the height is the perpendicular distance from A to BD. We can find this distance using trigonometry and the fact that angle BAC is 20 degrees:
tan(20) = height/9
height = 9 tan(20)
height ≈ 3.170 cm
Therefore, the area of triangle ABD is:
Area of triangle ABD = (BD x height) / 2
Area of triangle ABD = (5.458 x 3.170) / 2
Area of triangle ABD ≈ 8.661 cm²
The area of rhombus ABCD is:
Area of rhombus ABCD = (diagonal 1 x diagonal 2) / 2
Area of rhombus ABCD = (9 x 9) / 2
Area of rhombus ABCD = 40.5 cm²
Therefore, the area of the shaded region is:
Area of shaded region = Area of rhombus ABCD - Area of triangle ABD
Area of shaded region = 40.5 - 8.661
Area of shaded region ≈ 31.839 cm²
Rounding to the nearest cm², the area of the shaded region is 32 cm².
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3x≥12.
resultats ???
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
x >= 4
Step-by-step explanation:
3x >= 12
x >= 4
this is nothing but → x ≈ (∞ , 4]
Hope it helps you ~In square $ABCD$ with sides of length 4 cm, $N$ is the midpoint of side $BC$ and $M$ is the midpoint of side $CD$. What is the area of triangle $AMN$,
Consequently, the area of triangle $AMN$ is equal to $A = \frac{1}{2}bh = \frac{1}{2}(4)(2) = 4$ cm2.
The area of triangle $AMN$ in square $ABCD$ can be calculated using the formula for area of a triangle, $A = \frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the height of the triangle.
Since side $BC$ has a length of 4 cm, we can determine that $N$ is located 2 cm away from point $B$ and 2 cm away from point $C$.
Similarly, we can conclude that $M$ is located 2 cm away from point $C$ and 2 cm away from point $D$.
Therefore, the base of triangle $AMN$ is equal to 4 cm, and the height of triangle $AMN$ is equal to 2 cm.
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Work out the total area of the shape below:
The total area of the given shape is 71cm².
What is area?The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. A shape's area can be calculated by contrasting it with squares of a known dimension. The square meter (abbreviated as m²), which is the area of a square whose sides are one metre long, is the common measure of area in the International System of Units (SI). Three such squares would be the same size as a shape with a three square metre surface.
The following figure can be divided into a rectangle 7cm x 8cm and a triangle of height and base 6 cm and 5 cm respectively.
Area of rectangle= 7*8= 56 cm²
Area of triangle= 1/2* base*height= 1/2*6*5 = 15 cm²
Total area of shape = 56+15= 71 cm²
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One characteristic of all exponential functions is that they change by
One characteristic of all exponential functions is that they change by a constant factor at each step, which means that they exhibit exponential growth or decay.
The constant factor by which an exponential function changes is called the base, which is usually denoted by the symbol "b". If b is greater than 1, the function exhibits exponential growth, and if b is between 0 and 1, the function exhibits exponential decay.
For example, the function f(x) = 2^x is an exponential function with a base of 2. At each step, the function increases by a factor of 2. For instance, f(0) = 1, f(1) = 2, f(2) = 4, f(3) = 8, and so on.
On the other hand, the function g(x) = (1/2)^x is an exponential function with a base of 1/2. At each step, the function decreases by a factor of 1/2. For instance, g(0) = 1, g(1) = 1/2, g(2) = 1/4, g(3) = 1/8, and so on.
Therefore, exponential functions exhibit a characteristic change by a constant factor at each step, which leads to either exponential growth or decay.
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Maricopa's Success scholarship fund receives a gift of $ 75000. The money is invested in stocks, bonds, and CDs. CDs pay 3.75 % interest, bonds pay 3.8 % interest, and stocks pay 10.3 % interest. Maricopa Success invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 4142.5 , how much was invested in each account?
$____ in stocks, $____ in bonds, and $____ in CDs.
Answer: Maricopa Success invested $13,350 in CDs, $38,350 in bonds, and $23,300 in stocks.
Step-by-step explanation:
Let x be the amount invested in CDs.
Then, the amount invested in bonds would be (x + $25,000) and the amount invested in stocks would be ($75,000 - x - (x + $25,000)) = ($50,000 - 2x).
The annual income from the investments is $4,142.5, so we can set up the following equation:
0.0375x + 0.038(x + $25,000) + 0.103($50,000 - 2x) = $4,142.5
Simplifying the equation, we get:
0.0755x + $5,150 = $4,142.5
0.0755x = -$1,007.5
x = -$1,007.5 / 0.0755
x = $13,350
Therefore, the amount invested in CDs is $13,350.
The amount invested in bonds is $13,350 + $25,000 = $38,350.
The amount invested in stocks is $75,000 - $13,350 - $38,350 = $23,300.
So, Maricopa Success invested $13,350 in CDs, $38,350 in bonds, and $23,300 in stocks.
Which derived character is placed immediately after that group on the cladogram?
Answer:
Step-by-step explanation:
One that has the next least in common with the rest.
What's 5/6 ÷ 7/9 ÷ 8/9 ÷0/7
Answer: The expression is undefined.
Step-by-step explanation:
Division by zero is undefined in mathematics. In this expression, there is a division by zero in the term 0/7. Therefore, the entire expression is undefined.
In the above video lecture, we verified the following result: Computing the gradient of n
Rn (θ) = 1/n Σ (y^(t) - θ.x^(t)^2 / 2
t=1
we get ΔRn (θ) = Aθ-b (=0) where A= n n
A = 1/n Σ x^(t) (x^(t))^T , b = 1/n Σ y^(t) x^(t)
t=1 t=1
Now, what is the necessary and sufficient condition that Aθ - b = 0 has a unique solution?
- None of A's entries is 0. - A is invertible.
- A's dimension is the same as that of θ's
The direction of the steepest descent, which is used to find the minimum value of a function.
The necessary and sufficient condition that Aθ-b = 0 has a unique solution is: A is invertible.What is computing?Computing is a part of computer science that focuses on computer programs, including their software and hardware. It is concerned with designing algorithms to solve problems and creating software that will run these algorithms. As a result, computing is a field of study that is concerned with the process of creating algorithms and software.InvertibleAn invertible matrix is a matrix in which the determinant is not zero. An invertible matrix is also referred to as a non-singular matrix. An invertible matrix has a unique inverse. The rank of an invertible matrix is equal to its dimension. An invertible matrix can be used to solve a system of linear equations.GradientA gradient is a vector field in which the direction of the vector points to the steepest increase in a function, and the magnitude of the vector is the rate of increase in that direction. The gradient of a function is a vector field that is a derivative of the function. The gradient is used in multivariable calculus to solve optimization problems. The gradient is used to find the direction of the steepest ascent, which is used to find a maximum value of a function. It is used to find the direction of the steepest descent, which is used to find the minimum value of a function.
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If P(A)=0. 3, P(B)=0. 2, and P(A∩B)=0. 1, find the probability
a. P(
)
b. P(A∪B)
c. P(
∩B)
d. P(A∩
)
e. P(
∪B)
P(∅) = 0, P(A∪B) = 0.4 , P(A∩B) = 0.1 ,Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').and P(A∪B) = 0.4. are the required solutions ofgiven probability check .
a. The probability of an empty set is always zero. Therefore, P(∅) = 0.
b. The probability of the union of two events, A and B, is given by the formula P(A∪B) = P(A) + P(B) - P(A∩B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
c. The probability of the intersection of A and B is given by the formula P(A∩B). Substituting the values given in the question, we get:
P(A∩B) = 0.1
Therefore, P(A∩B) = 0.1.
d. The probability of the intersection of A and the complement of B is given by the formula P(A∩B'). The complement of B is the set of all outcomes that are not in B. Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').
e. The probability of the union of A and B is given by the formula P(A∪B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
In probability theory, the union of two events A and B is the set of outcomes that belong to either A or B or both. The intersection of two events A and B is the set of outcomes that belong to both A and B. The complement of an event A is the set of outcomes that do not belong to A. These concepts are fundamental in probability theory and are used extensively in solving various problems.
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Write the expression in complete factored form.
5a(b + 1) + 3(b + 1) = please help!
Answer: (5a + 3)(b + 1)
Step-by-step explanation:
We can factor out the common factor of (b + 1) from both terms:
5a(b + 1) + 3(b + 1) = (5a + 3)(b + 1)
Therefore, the expression in complete factored form is (5a + 3)(b + 1).
A plane takes off 500 feet away from a tower. The plane takes off at an angle of
elevation of 20°. In its path is the tower of 200 feet.
Will the plane clear the height of the tower? (yes/no)
How many feet (to the nearest foot) will the plane either clear or be short of the
tower. Enter a positive value if the distance represents how far over the tower the
plane will fly. Enter a negative distance if the distance represents how much lower
the plane will be than the tower.
Answer:Taking off: 2
Flying: 3
Landing: 4
Landing well enough you can use the plane again: 5
Landing well enough that your passengers will fly with you again: 6
Having the judgement and strength of character to say “I know I promised we'd fly home today, but the weather is bad so we're going to have to wait a day and miss that thing you wanted to go to”: 10
Step-by-step explanation:
Ana has a rectangular garden with the width of 2.3 meters and a length of 2.8 meters. she makes the model below to help her determine the area of her garden. What is the area of Ana's garden?
Answers 6.44, 8.6 4.38, 5.1
Answer: 6.44 square meters
Step-by-step explanation:
The area of a rectangle is given by the formula: A = L x W, where L is the length and W is the width.
Substituting the given values, we get:
A = 2.8 x 2.3 = 6.44 square meters
Therefore, the area of Ana's garden is 6.44 square meters.
what is 2 times 2x ??
Answer:
4x
Step-by-step explanation:
2 X 2x = 2x+2x= 4x
Answer:
4x
Step-by-step explanation:
So when you multiply 2×2=4
And since it's multiplication you can add the x to it giving you 4x(if it's addition you can't add them because they aren't like terms)
Jenny wants to measure the height of a tree she sites the top of the tree using a mirror that is lying flat on the ground. The mirror is 20 feet from the tree, and Jenny is standing 8 feet from the mirror as shown in the figure, her eyes are 5 feet above the ground how tall is the tree?
The Height of tree is around 8.33 feet tall.
What is the connection among Height and distance?In science, we work out the Height of an item utilizing distance and points. Distance is the even distance between the items, and point is the point over the level of the article's top, which gives the item's level.
We can utilize the rule of comparable triangles.
The hypotenuse of this triangle would be the line associating Jenny's eyes to the highest point of the tree (we should refer to this distance as "h").
We can set up the accompanying extent between the two triangles:
h / 20 = (h + 5) / 8
To solve for "h", we can cross-multiply and simplify:
8h = 20(h + 5)
8h = 20h + 100
12h = 100
h = 8.33 feet
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2. What are the values of a and b?
10
6
8
b
a
(1 point)
Answer:
a=9/3,b=15/2 using some postulate you will get answer like sss,sas,aa.
a:b=1:6
a:c=3:1
How many times is b bigger than c?
Answer:
18 times bigger
Step-by-step explanation:
[Complex Analysis] Is there a polynomial P(z) such that Pe^(1/z) is entire?
There is no polynomials such that [tex]P(z)e^{\frac{1}{z} }[/tex] is entire.
Sums of elements of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the equation 3x+2x-5. a description of polynomials.
By the Taylor expansion, [tex]e^{\frac{1}{z} }[/tex] = ∑∞n= 0.
Let P(z)= (ad)zd+.......+a0.
For n>0, the coefficient of z-n in the expansion of [tex]P(z)e^{\frac{1}{z} }[/tex] is :-
[tex]tn= n^{a0} 1 + (n+1)!+.......+(n+d)![/tex]
So the Laurent expansion of [tex]P(z)e^{\frac{1}{z} } = 0[/tex]will have terms of the form tn2-n where an is not equal to zero.
if r is the smallest non negative integer such that ar is not equal to zero, then we see that we can rewrite:-
[tex]tn= (n^{1} +r)![ar+n^{ar+1} +1+.....+(n+r+d)....(n+d)][/tex]
as we know that [tex]\lim_{n \to \infty} (n+r+1+....+(n+r+d).....(n+d)=0[/tex]
so there exists an N∈N, such that:-
[tex]/ar/ > n+r+1+....+(n+r+d)....(n+d)=0[/tex]
HenHence tn is non zero for all n>N. In other words, expansion contains terms of negative powers.
So, apart from P(z)=0, there is no polynomials such that [tex]P(z)e^{\frac{1}{z} } .[/tex]
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The perimeter of a square is 16 cm find length , diagonal and area
Answer:
Step-by-step explanation:
we have perimeter 16
for perimeter 4+4+4+4 we add together it's 16
for area we have 4 times 16
Mr. Seda has a bag with 500 marbles. The marbles are either
green or yellow. He has 20 students in his class take turns
selecting 10 marbles from the bag without looking. Each student
records the number of green marbles and then returns the
marbles to the bag.
What is a reasonable estimate for the number of green marbles
in the bag?
TRY
IT
M Math Toolkit double number lines, grid paper
Samples
5
Nu
A reasonable estimate for the number of green marbles in the bag would be around 250, since the marbles are split evenly between green and yellow. This means that for each student selecting 10 marbles, on average 5 of them should be green.
To estimate the number of green marbles in the bag, we can use the fact that the marbles are split evenly between green and yellow. This means that for each student selecting 10 marbles, on average 5 of them should be green. This means that, with 20 students selecting 10 marbles each, we can expect to have at least 100 green marbles. We can then multiply this number by two to get a reasonable estimate of 200 green marbles. Since this is a slightly conservative estimate, we can round up to 250 green marbles for our reasonable estimate.
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The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Pop is the preferred music for 35 students.
Jazz is the preferred music for 56 students.
Together, Hip Hop, Rock, and Jazz are the preferred music for less than half the students.
Together, Hip Hop and Pop are the preferred music for 260 students.
After answering the provided question, we can conclude that As a result, circle we cannot conclude that Hip Hop and Pop are incompatible.
What is circle?A circle seems to be a two-dimensional component defined as such collection of the all points in a jet that become equidistant from the hub. A circle is commonly portrayed with the capital "O" for centre and the lower section "r" for the radius, which is the distance from the origin to any point on the circle.
Girth (the distance from around circle) is given by the formula 2r, where (pi) is a proportionality constant roughly equal to 3.14159. The formula r² calculates the circle's circumference, which refers to the amount of room inside of the circle.
We can draw the following conclusions from the information in the circle graph:
Pop music is preferred by 35% of the sample, which means that 35% of 400 students, or 140 students, prefer pop music.
Jazz is the preferred music for 14% of the sample, which means that jazz is preferred by 14% of 400 students, or 56 students.
Hip Hop, Rock, and Jazz are preferred music by 52% of the sample, which means that these three genres are preferred by 52% of 400 students, or 208 students.
Hip Hop and Pop are preferred music by 60% of the sample, which means that 60% of 400 students, or 240 students, prefer these two genres together. As a result, we cannot conclude that Hip Hop and Pop are incompatible.
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A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 67. Let μ denote the true average compressive strength.
(a) What are the appropriate null and alternative hypotheses?
(b) Let X denote the sample average compressive strength for n = 12 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). If X = 1340, find the P-value. (Round your answer to four decimal places.) P-value = 0.0193
(c) What is the probability distribution of the test statistic when μ = 1350?
State the mean and standard deviation of the test statistic. (Round your standard deviation to three decimal places.)
Mean: 1350, Standard Deviation: 19.341
For a test with α = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1350 (a type II error)? (Round your answer to four decimal places.)
(a) The null hypothesis is that the true average compressive strength of the mixture is less than or equal to 1300 KN/m2.
The alternative hypothesis is that the true average compressive strength of the mixture is greater than 1300 KN/m2.
(b) To find the P-value, we need to calculate the probability of getting a sample mean of 1340 or greater, assuming the null hypothesis is true. Using the sample size n=12 and sample standard deviation σ=67, the test statistic is (1340-1300)/(67/sqrt(12)) = 2.523.
The P-value is the probability of getting a value of 2.523 or greater from a t-distribution with 11 degrees of freedom, which is 0.0193.
(c) The test statistic when μ = 1350 follows a t-distribution with 11 degrees of freedom.
The mean of the test statistic is equal to the true value of the mean, which is 1350. The standard deviation of the test statistic can be calculated as σ/sqrt(n) = 67/sqrt(12) = 19.341.
To find the probability of a type II error with α = 0.01, we need to calculate the probability of accepting the null hypothesis when the true value of the mean is 1350.
This can be calculated using the t-distribution with 11 degrees of freedom and the critical value corresponding to α=0.01, which is 2.718. The probability of a type II error is the probability that the test statistic is less than 2.718 when the true value of the mean is 1350, which is 0.2157 (rounded to four decimal places).
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What is the cost of 73 pairs of pants if each pair costs $23, with a 10% discount on every
pair ordered over 50?
Answer: $1626.10
Step-by-step explanation:
[tex]50 * 23 = 1150\\23 * 0.9 = 20.7\\20.7 * 23 = 476.1\\1150 + 476.1 = 1626.1[/tex]