The common sum is 18 as "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same".
What is sum?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. The outcome or conclusion we arrive at when we add two or more numbers is known as the SUM. Addends are the numbers that are added.
Here,
The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these 8 numbers represent all of the vertices of the cube.
=(1+2+3+4+5+6+7+8)/2
=18
Since "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same," the common sum is 18.
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1. The following data represents the amount of time Algebra II students at NVLA prepare for their math exams. Study Time (min) 7 14 17 23 27 33 38 43
Test Score 61 54 63 65 70 69 75 77 I Find the quadratic regression model of the data. Then, predict the test score of a student who studies for 60 minutes. Show your work.
The quadratic regression model of the data is 0.007x² + 0.168x + 56.63 and the the test score of a student who studies for 60 minutes is 94.114
Quadratic regression model:
Quadratic regression refers the process of determining the equation of a parabola that best fits a set of data.
The set of data is a given set of graph points that make up the shape of a parabola.
The general equation of the parabola is y = ax² + bx + c, where a can never equal zero.
Given,
Here we have the following data represents the amount of time Algebra II students at NVLA prepare for their math exams.
Now, we need to find the the quadratic regression model of the data and then, predict the test score of a student who studies for 60 minutes. Show your work.
When we plot these value of the graphing calculator, then we get the following graph.
Through the graph we have identified that the value of
a = 0.007
b = 0.168
c = 56.63.
Therefore, the quadratic regression model of the data is 0.007x² + 0.168x + 56.63
And through the graph we have identified that test score of a student who studies for 60 minutes is approximately 94.114.
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what are the roots of the following function? f(x) (4x-1)(x+9)
please answer due today.
Answer:
[tex]x=-9, \quad x=\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=(4x-1)(x+9)[/tex]
The roots of a function are the x-values for which the function equals zero. Therefore, to find the roots, set the function to zero and solve for x.
Set the function to zero:
[tex]\implies f(x)=0[/tex]
[tex]\implies (4x-1)(x+9)=0[/tex]
Zero Product Property
If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Apply the zero product property:
[tex](4x-1)=0 \implies x=\dfrac{1}{4}[/tex]
[tex](x+9)=0 \implies x=-9[/tex]
Therefore, the roots of the given function are:
[tex]x=-9, \quad x=\dfrac{1}{4}[/tex]
in a recent study, it was found that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected. the data follows a binomial distribution. a) what is the mean of the distribution? (round your answer to 3 decimals.)
The mean of the distribution is 24.444.
Given, that 87.3% of all homes have a large-screen tv. a sample of 28 homes is selected.
Now, we have to find the mean of the distribution
As, we know
E(x) = np
where, n is the sample and p is the probability of success
So, n = 28 and p = 87.3% = 0.873
Now, on using the formula we get,
E(x) = (28)(0.873)
E(x) = 24.444
So, the mean of the distribution is E(x) = 24.444
Hence, the mean of the distribution is 24.444.
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the price of popcorn is $0.50 per box and the price of peanuts is $0.25 per bag, and you have $10. the maximum number of bags of peanuts that you can purchase is: question 8 options: a) 20. b) 5. c) 10. d) 40.
Answer:
d is correct
Step-by-step explanation:
[tex].25p = 10[/tex]
[tex]p = 40[/tex]
So d is correct.
astudy showed that 33% of allfirms in couniry a are owned by women. you are phoning local businesses, assuming that the national percentage is true in your area. you call 3 fims. what is the probability that all three are owned by women?
There is a 0.33 percent chance that a woman is the owner of each of the firms identified. Therefore, there is a 0.036 percent chance that women own ALL three of the called businesses.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The probability that each of the firms called is owned by a woman is 0.33. Therefore, the probability that ALL three of the firms called are owned by women is:
percentage=0.33*0.33*0.33
percentage=0.035937
=0.036
There is a 0.33 percent chance that each of the businesses is run by a woman. As a result, there is a 0.036 percent chance that women own ALL three of the businesses mentioned.
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If f is continuous everywhere, f'(3) = 0 and f" (3) = 4, then there must be a local minimum at z = 3.
Answer:
True
Step-by-step explanation:
f'(3) = 0 says the tangent line at x = 3 is horizontal.
f"(3) = 0 means the graph of f is concave up at x = 3.
Together, these tell you the graph has a local minimum at x = 3. The graph is U-shaped at the point where x = 3.
Factorise the following
4x²-25y²
Answer:
= (2x + 5y) * (2x - 5y)
Step-by-step explanation:
4x²-25y²
= (2x)² - (5y)²
= (2x + 5y) * (2x - 5y)
Answer:
[tex]\huge\boxed{\sf (2x + 5y)(2x - 5y)}[/tex]
Step-by-step explanation:
Given expression:[tex]4x^2-25y^2[/tex]
Both of the terms are perfect squares.
[tex](2x)^2-(5y)^2[/tex]
Using formula: a² - b² = (a + b)(a - b)= (2x + 5y)(2x - 5y)
[tex]\rule[225]{225}{2}[/tex]
I WILL MARK BRAINLY BE QUICK
Answer:
B
Step-by-step explanation:
Use the slope-intercept form to find the slope and y-intercept.
Slope: 5
y-intercept: (0,-10)
Answer:
Step-by-step explanation:
The slope is 5
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A rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.
In the given question we have to find the maximum area of the rectangular area.
Liana has 3200 yards of fencing to enclose a rectangle.
So we know that the perimeter of rectangle is
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 3200
Divide by 2 on both side we get
x+y = 1600................(1)
As we know the area of rectangle is
A = xy
From the equation the value of y is 1600-x.
Now putting the value of y
A = x(1600-x)
A = 1600x-x^2
On differentiating
dA/dx = 1600-2x
Putting dA/dx=0
1600-2x=0
Subtract 1600 on both side we get
-2x= -1600
Divide by -2 on both side we get
x = 800 yards
Now putting the value of x in the y=1600-x
y=1600-800
y=800 yards
So the maximum area is
A= 800*800
A= 640,000 square yards
Hence, a rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.
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Which equation correctly applies the Associative Property of Addition?
8.9+(6.4 +7.2) (8.9 + 6.4) +7.2
1/6 + 4/6 = 5/6
=
1/3(1/2+3/4)= (1/3 x 1/2) + (1/3 X 3/4)
6-18 = 6 + (-18)
Answer:The equation 8.9+(6.4 +7.2) is correctly applying the Associative Property of Addition.
Step-by-step explanation:
The Associative Property of Addition states that when adding three or more numbers, the order in which the numbers are added does not affect the sum.
Length of a rectangle is 7 cm more than the width. The perimeter is 78 cm. Find the rectangles dimensions
Answer:
let the width be x
perimeter= 2(l+b)
78= 2(7 +x)
78-14= 2x
32= x
this must be the ans
At the craft store, Tara bought 12 yards of fabric to make tote bags. Each bag requires 1.25 yards of fabric.
Write an equation that shows how the number of yards of fabric remaining, y, depends on the number of tote bags Tara sews, x.
The number of yards of fabric remaining, y, depends on the number of tote bags Tara sews, x is y = 12 - 1.25x.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, Tara bought 12 yards of fabric to make tote bags and each bag requires 1.25 yards of fabric.
The equation that describes the number of yards of fabric remaining, y, depends on the number of tote bags Tara sews, x is
y = 12 - 1.25x.
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A, B , C or D ???????? help
Answer:
The Answer is B
Step-by-step explanation:
Since 1.8 times 10 is bigger than 18% meaning its the only one that would be in correct descending order.
Answer:
Pretty sure it’s A
Step-by-step explanation:
18% is 18/100 which is then .18
1/8 is .125
1.8x10 is 18
And .188 is just .188
Does this scatter plot show a linear association explain yes or no
No, The scatter plot does not show a linear association
What is graph?A graph is way of presenting data used by several disciplines.
There are many types of graphs and scatter plot is one of them.
scatter plot can be defined as set of dots plotted on a horizontal and vertical axis.
scatter plots can demonstrate the degree of connection, if any, between the values of observed quantities or events, they are crucial in statistics
The scatter plot does not show a straight line graph or a linear function. tracing the line shows a inverted shape of "s" which is not associated with linear functions.
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A class trip consists of 84 students and 6 teachers.
What is the student to teacher ratio?
I need help please!
Answer:
All answers other than {7, 11, 15, 19}
Step-by-step explanation:
If we have a Set A, it is a subset of Set B if every element in A is also in B. Set A is a proper subset of Set B if it is a subset of Set B but not equal to Set B.
Using the above information, we know that the proper subset of {7, 11, 15, 19} cannot be itself, so we can rule out the second option.
All of the other options are sets where every element of that set is also an element of {7, 11, 15, 19}. The 3rd option is an empty set, which is a proper subset of any set other than itself, so it is a proper subset of {7, 11, 15, 19}.
Therefore, all of the options except for {7, 11, 15, 19} are valid.
What does negative 3 over 5 > −2 indicate about the positions of negative 3 over 5 and −2 on the number line? (1 point) a negative 3 over 5 is located on the right of −2 b negative 3 over 5 is located on the left of −2 c negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 d negative 3 over 5 is located on the left of 0 and −2 is located on the right of 0
This is worth 40 points pls help
Answer:
−2 c negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 d negative 3 over 5
Step-by-step explanation:
Solve the system by substitution.
Answer:
(-7, -7)
Step-by-step explanation:
y = x; x = y
9x - 2y = -49
9(y) - 2y = -49
9y - 2y = -49
7y = -49
÷7 ÷7
----------------
y = -7
y = x
-7 = x
or
9x - 2y = -49
9x - 2(-7) = -49
9x + 14 = -49
-14 -14
-------------------
9x = -63
÷9 ÷9
---------------
x = -7
(-7, -7)
I hope this helps!
The difference between 2 times an angle's
supplement and 120 is 30. Find the measure of
the angle.
Answer:
105
Step-by-step explanation:
Kirty count the number of pea in a ample of pea pod. Number of pea in a pod: 4 5 6 7 8
Number of pod: 2 10 18 14 6
What wa the mean number of pea in a pod?
The following measure's values are based on the number of peas provided.
Peas in a Pod mode is not possible.
Peas in a pod's median number is equal to 6
the average number of peas in a pod is 6
What is the number?
The definition of a number is "the count of the specified quantity."
utilized formula
Mean = sum of number of observation / toatal number present there
The answer to the query is
Considering counts of peas,
How many peas are in a pod = 4,5,6,7,8
Quantity of pods = 2,10,18,6,14
The number that represents the highest frequency is called the mode.
All of the numbers in the list have a frequency of one.
For the provided data, mode is not feasible.
If all the numbers are odd, the middle value, after placing them in ascending or descending order, is the median.
The supplied numbers' median is.
To obtain the mean value, replace the values in the formula.
Mean = 4+5+6+7+8/5 = 30/5 = 6
Consequently, the following measure's values are as follows based on the number of peas given:
Peas in a Pod mode is not possible.
Peas in a pod's median number is equal to 6
the average number of peas in a pod is 6
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23X-17 = 15X+7 give me the solution
Answer: x=3
Step-by-step explanation:
Simplify equation to get 8x=24. Divide 24 by 8 to get x=3. Please give brainliest :D
Answer:
Step-by-step explanation:
23X - 17 = 15X + 7First add 17 to both sides to isolate the variable (usually the one with the bigger coefficient is best)
23X = 15X + 24subtract 15x from both sides to combine 23X and 15X terms
8X = 24Divide by 8 to solve
X = 32000*5/100 pls help me
Answer:
100
Step-by-step explanation:
2000*5 = 10000/100 = 100
Can someone please explain how to factor X^2 + 2x - 15?
The factored form of x² + 2x - 15 is (x + 5)(x - 3).
What is factorisation?Factorisation is a process of finding the factors of algebraic equations and representing them in simple form instead of expanded form.
Therefore, let's factor x² + 2x - 15
x² + 2x - 15
let's find two numbers we can add to get 2 and multiply to get - 15. The two numbers are -3 and 5.
Therefore,
x² - 3x + 5x - 15
x(x - 3) + 5(x - 3)
(x + 5)(x - 3)
Therefore,
x² + 2x - 15 = (x + 5)(x - 3)
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A line is subdivided according to the golden ratio, with a smaller piece having a length of 5 meters. What is the length of the entire line?
The length of the entire line which is subdivided according to golden ratio is 13.09 meters.
What is Golden Ratio?
The golden ratio is a special number approximately equal to 1.618
We find the golden ratio when we divide a line into two parts so that, the whole length divided by the long part is also equal to the long part divided by the short part
Let smaller part of a line be b and long part be a
Golden ratio = a + b/a = a/b = 1.618
According to the given question:
Length of smaller part of line = 5 meters
Let the longer length of the line be x
∴ Total length of line = 5 + x
Using Golden ratio to find the entire length of line
x/5 = 1.618
x = 8.09
Calculating length of entire line = 5 + x = 5 + 8.09 = 13.09
∴ Length of entire line is 13.09 meters
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An athlete ran a total of 1,500 kilometer in race before retiring. The athlete finihed thirty-two 15-kilometer race. The ret were 10-kilometer race. How many of the race were 10-kilometer race?
The number of races that were 10-kilometer long is 102.
An athlete ran a total of 1,500 kilometers in a race before retiring. The athlete completed 32 races that were at least 15 kilometers in length. The rest were 10-kilometer races. We need to find out the number of races that were 10-kilometer long.
Let the number of races that were 10-kilometers long be denoted by the variable "x". An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign. We can write the equation as given below.
32×15 + 10x = 1,500
480 + 10x = 1,500
10x = 1,500 - 480
10x = 1,020
x = 1,020/10
x = 102
Hence, the number of races that were 10-kilometer long is 102.
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39 Points, need this ASAP
If a = -9 and b = -4, what is the value of a + b ?
-5
5
13
-13
If polygon A is the original shape, what is the scale factor to get polygon B?
Answer:
scale factor = 2
Step-by-step explanation:
the scale factor is the ratio of corresponding sides , polygon B to polygon A
in figure A the vertical side RS = 2 units
the corresponding vertical height in figure B = 4 units , then
scale factor = [tex]\frac{4}{2}[/tex] = 2
Use the following diagram for questions 1-3.
1. Find x.
2. Find y
3. Find z
Answer:
x= 40° y= 66° z=106° ....
The value of angles are x = 40° , y = 66°, z = 106°
Since there are two parallel lines and two intersecting lines forming a triangle we will use the properties of lines and triangles to find out the value of x,y,z. First of all y = 66° because of the vertical angle theorem, which means that adjacent angles formed by the intersection of two lines are supplementary or equal to 180° degrees. The third angle of the triangle formed is 74°. Using the sum of all angles of the triangle is equal to 180° we can find the third angle of triangle x which is equal to 40°. Now z can be found using the property sum of two opposite interior angles which will come out to be 106°. Hence by this, we can find all the angles.
I hope this answer helps.
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light bulbs are packed in boxes of 10. inspectors randomly select 3 of the 10 light bulbs. the box contains exactly 4 defective light bulbs. using a hypergeometric probability distribution, find the following to four decimals. a defective bulb is considered a success. what is the probability that exactly four of the selected is defective? enter the answer as a number to one decimal.
The probability that exactly four of the selected bulbs from the pack of 10 bulbs is defective is 1/120.
Define the hypergeometric probability distribution?When sampling from such a low population without replacement, the hypergeometric distribution represents a discrete probability distribution which determines the likelihood that an event occurs k times in n trials. In terms of the aspect of sampling without replacement, this distribution is equal to the binomial distribution.For the given question;
Total bulbs = 10Defective bulbs = 4Selected bulbs = 3Thus, the probability that exactly four of the selected is defective.
P = ⁴C₄ / ¹⁰C₃
P = 1/120
Thus, the probability that exactly four of the selected is defective is 1/120.
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probabilities of a part need to be painted and galvanized are 0.20 and 0.30, respectively. what is the probability of the part needs both painted and galvanized?
The probability that the component requires both painting and galvanizing is 0.06.
Considering the values provided in the question,
P(Painted) = 0.20
P(Galvanized) = 0.30
Both the events are independent of each other.
The probability of the part needs both painted and galvanized is
= P(Painted and Galvanized)
= P(Painted) × P(Galvanized)
= 0.20 × 0.30
= 0.06
Therefore, The probability of the part needs both painted and galvanized is 0.06.
The possibility of an event happening is determined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us. In these circumstances, we say if there is a chance the event will happen or not.
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