The equivalent expression for a*(b*c) is (a*b)*c.
What is Associative Property?when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.
The given expression is a*(b*c).
The associative property is holds for multiplication.
According to the definition of associative property when more than two numbers are multiplied the result remains the same, irrespective of how they are grouped.
The equivalent expression for a*(b*c) is (a*b)*c.
For example a=2,b=3 and c=1 then
a*(b*c) =2*(3*1)=6
(a*b)*c=(2*3)*1=6
a*(b*c)=(a*b)*c
Therefore (a*b)*c is equivalent expression for a*(b*c).
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I have 6 quarts of paint. How many shelves can be painted if each one takes one third of a quart.
The perimeter of the figure below is 110 cm. Find the length of the missing side.
Answer:
6.1 cm
Step-by-step explanation:
You want to know the remaining side of the irregular figure such that the perimeter is 110 cm.
PerimeterThe perimeter of a plane figure is the sum of the lengths of the sides. Working clockwise from the upper left corner, we have ...
34.6 +8.6 +17.3 +11.6 +? +11.6 +11.6 +8.6 = 110
103.9 +? = 110 . . . . collect terms
? = 6.1 . . . . . . . . . subtract 103.9
The length of the missing side is 6.1 cm.
__
Additional comment
If the angles that appear to be right angles actually were right angles, the perimeter would be 109.6 cm. The perimeter is longer than this, so at least three of the angles are not right angles.
Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: , where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing
If Wilson produces only one 1 bag, then his profit starts decreasing
How to determine the pointGiven the function;
Let f ( x ) = [tex]2x^4 - 4x^3 + 7[/tex]
Where;
x is the number of bags of cereal produced
[tex]f'x = 2x^4 - 4x^3 + 7[/tex]
[tex]f'(x) = 8x^3 - 12x^2[/tex]
Factorize the expression
[tex]f'(x) = 4x^2(2x - 3)[/tex]
If the value of x is decreasing, we have;
f ′ ( x ) ≤ 0
4x² (2x - 3) ≤ 0
If x² ≥ 0, then;
2x - 3 ≤ 0
x ≤ 3/ 2
With x as the number of bags
x ∈ N
x = 1 is the only possibility
Thus, if Wilson produces only one 1 bag, then his profit starts decreasing
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The complete question:
Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: pi = 2x ^ 4 - 4x ^ 3 + 7, where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing
Hello! I need help with #2 and #3 please!
The banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.
Principal 1 = $ 50,000
Rate 1 = 4 %
Let principal 2 be x
Rate = 6 %
Time = 1 year
Interest = 3800
Using simple interest, we get that:
SI = p × r × t
3800 = ( 50,000 × 0.04 × 1) + ( x × 0.06 × 1)
3800 = 2000 + 0.06 x
0.06 x = 3800 - 2000
0.06 x = 1800
6 x = 180000
x = 180000 / 6
x = 30,000
Therefore, we get that, the banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.
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find the value of ...B
Answer:
b=–2
Step-by-step explanation:
we've got:
(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243
and we've also got the coefficient of x³ as –720
90b³=–720===> b³=–8===> b=–2
a movie theater has a seating capacity of 329. the theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. there are half as many adults as there are children. if the total ticket sales was $ 2392, how many children, students, and adults attended?
Taking into account the definition of a system of linear equations, 178 children, 62 students and 89 adults attended to the movie theater.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be found, with which when are replaced in the equations, they must give the solution proposed.
This caseIn this case, a system of linear equations must be proposed taking into account that:
C is the number of children who attended the movie theater.S is the number of students who attended the movie theater.A is the number of adults who attended the movie theater.On the other hand, you know:
A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. The total ticket sales was $ 2392.There are half as many adults as there are children.So, the system of equations to be solved consists of the following equations:
Equation 1: C + S + A= 329
Equation 2: 5C + 7S + 12A= 2392
Equation 3: A= C÷2= 1/2C
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Replacing equation 3 in equation 1 and isolating the variable S you get:
C + S + 1/2C= 329
3/2C + S= 329
S= 329 - 3/2C
Replacing this expression and equation 3 in equation 2 you get:
5C + 7(329 - 3/2C) + 12×1/2C= 2392
Solving:
5C + 7×329 - 7×3/2C + 12×1/2C= 2392
5C + 2303 - 21/2C + 6C= 2392
5C - 21/2C + 6C= 2392 -2303
1/2C= 89
C= 89÷ 1/2
C= 178
Remembering that S= 329 - 3/2C, you get S= 329 - 3/2×178 → S= 62
Finally, substituting the value of C in Equation 3: A= 1/2C= 1/2×178 → A=89
In summary, 178 children, 62 students and 89 adults attended to the movie theater.
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A traffic cone with a height of 20 in. is ideal for traffic control. Find the lateral area of a cone with a height of 20 in. and a diameter of 12 in. Round the answer to the nearest whole number. (Hint: The height given is not the slant height.)
The lateral area of the cone is 394 square inches
How to determine the value
The formula for lateral area of a cone is expressed as;
Lateral area = πr √h² + r²
Given that;
height = 20 inDiameter = 12 in, radius = 12/ 2 = 6 inSubstitute the values into the formula
Lateral area = 3. 142(6) √20² + 6²
Lateral area = 18. 85 √436
Lateral area = 18. 85 × 20. 8
Lateral area = 394 square inches
Thus, the lateral area of the cone is 394 square inches
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How do you express without exponents [tex](3a^3)^2[/tex]
__________________________________________________________
Hello! In this question, we were given an expression and would have to express it without the use of exponents.
__________________________________________________________
Explanation:
In the question, we were given:
(3a³)²
In order to express the expression without the exponents, we would have to first simplify it and then expand the expression.
__________________________________________________________
Solve:
[tex](3a^3)^2[/tex]
Simplify by "squaring" the variable inside the parenthesis, in which in this case we would multiply the "2" to the "3".
[tex]3a^6[/tex]
Now in this step, we would have to expand the expression in a different form to get rid of the exponent.
To get rid of the exponent, we would expand the " [tex]a^6[/tex] " term.
Note that the term [tex]a^6[/tex] is the same thing as a · a · a · a · a · a, it is just the expanded version of the exponent.
This means that our expressed expression without exponents, including our constant "3" would be:
3 · a · a · a · a · a · a
__________________________________________________________
Answer:
3 · a · a · a · a · a · a
__________________________________________________________
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2 m - 54 cm equals????????
Answer:
146 centimeters or 1.46 meters.
Step-by-step explanation:
1m = 100cm
2m = 200cm
200 - 54 =146
Hope this helps!
question is in the photos
Answer:
n(AuB)=15
n(AnB)=8 is the answer!
true or false???????
Answer:
False
Step-by-step explanation:
3 x 1/3
3/1 x 1/3 = 1
Answer:false
Step-by-step explanation: i did the test
The upper arm length of males over 20
years old in the United States is approximately Normal with mean 39.1
centimeters (cm) and standard deviation 5.1
cm. Use the 68−95−99.7
rule to answer the following questions. (Start by making a sketch of the Normal distribution for upper arm lengths for this population.)
A normal plot shows the range of Iowa test scores for 68% of the data, 95% of the data and 99.7% of the data. About 68% of the distribution of scores ranges from 5.29 to 8.39. About 95% of the distribution of scores ranges from 3.74 to 9.94. About 99.7% of the distribution of scores ranges from 2.19 to 11.49. There is an annotation that One standard deviation is 1.55 and another annotation that 2.5% of sores are below 3.74.
What percentage of men over 20
have upper arm lengths greater than 44.2 cm?
Provide your answer to one decimal place.
Using the Empirical Rule, it is found that 16% of men over 20 have upper arm lengths greater than 44.2 cm.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For the distribution in this problem, we have that:
The mean is of 39.1 cm.The standard deviation is of 5.1 cm.Hence, 44.2 is one standard deviation above the mean, as 44.2 = 39.1 + 1 x 5.1.
The normal distribution is symmetric, meaning that 50% of the measures are above the mean and 50% are below. Of those measures above the mean, 68% are less than 44.2 and 32% are more than 44.2 cm, hence:
0.5 x 32 = 16%.
16% of men over 20 have upper arm lengths greater than 44.2 cm.
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Which of the following equations represents a linear function?
Question 8 options:
y =[tex]\sqrt4{x}[/tex]
y =6/x
2x – 4y = 6
x3 – y = –2
Answer:
2x – 4y = 6
x3 – y = –2
Step-by-step explanation:
When graphing these two are linear.
Answer:
2x - 4y = –2
x3 – y = –2
Step-by-step explanation:
'cause they both have two unknown digits and this can be worked out with 3 methods;
1. substitution method
2. elimination method
3. grahical method
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Find the greatest common factor of the expressions.
12y1329, -16y6z9
Answer:
2 and 3 and y
Step-by-step explanation:
2x2x4x y x 1x2x3x3x3
-2x7x y x 2x3x z x3x3
Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.
4 x + 8 = negative 24 , 9 x + 18 = negative 24 are equations have the same value of x .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.A - 4 x + 8 = negative 24
E - 4 x = negative 32
ARE CORRECT ON EDGE.
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The complete question is-
Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.
4 x + 8 = negative 24
9 x + 18 = negative 24
4 x = negative 16
StartFraction 18 x + 36 over 2 EndFraction = negative 24
4 x = negative 32
12. If √1225 = 35 then √12.25
[tex] \sqrt{12.25 } = 3.5[/tex]
A small class has 9 students, 4 of whom are girls and 5 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the first student chosen will be a boy and the second will be a girl? Write your answer as a fraction in simplest form.
The probability that the first student chosen will be a boy and the second will be a girl is 0.28.
What is probability?Probability is also called the chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
Total students = 9
Number of girls = 4
Number of boys = 5
Probability of choosing first boy = Number of boys / total students
⇒ 5/9
Now since 1 boy extract so remaining students = 9 - 1 = 8
Probability of choosing second girl = Number of girls / Total students
⇒ 4//8
Probability of A and B = P(A) × P(B)
Therefore,
The probability that the first student chosen will be a boy and the second will be a girl = (5/9) × (4/8) = 0.28
Hence "The probability that the first student chosen will be a boy and the second will be a girl is 0.28".
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Absolute value of 4 is
Answer: -4
Step-by-step explanation:
it is -4 because we are looking for like the opposite so the opposite of 4 is -4
Answer:
Absolute value of |4| = 4
Step-by-step explanation:
The absolute value of a number is always positive
P₁ 1:23:55 AM
Jatch help video
an is preheating his oven before using it to bake. Fabian wants to predict the final
perature after a minutes. He wrote the equation y 50x+78, where y
resents the final temperature in degrees Fahrenheit. What could the number 50 in
bian's equation represent?
-
Number 50 in the Jack's equation represents the rate of change in the oven's temperature over time (per minute) or with respect to time by using the slope form concept.
As per the question statement, Jack is preheating his oven before using it to bake. He wants to predict the final temperature after [tex]x[/tex] minutes.
He wrote the equation [tex]y =50x+78[/tex] , where [tex]y[/tex] represents the final temperature in [tex]fahrenheit[/tex]. We are supposed to tell the significance of number 50 in the given equation.
As we know that the equation which is in the form of [tex]y=mx+c[/tex], or the slop form equation, m is called the slope or the rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].
And the given equation [tex]y =50x+78[/tex] is also of the form of [tex]y=mx+c[/tex] hence we conclude that 50 is the slope or the rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].
As y is the temperature in Fahrenheit therefore x is the time hence "50 Degrees Fahrenheit change of temperature per unit minute" is the significance of 50.
Slop Form Equation: [tex]y=mx+c[/tex] where m is the slope and c is called as the intercept of the lineTo learn more about Slop Form Equation, click on the link given below:
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i need the scientific notation of 0.0000018(430,000,000) over 0.00008(0.0075)
Answer:
1.29 x [tex]10^{9}[/tex]
Step-by-step explanation:
{(1.8 x 10^-6) x (4.3 x 10^8)} / [(8 x 10^-5) x (7.5 x 10^-3)]
[(1.8 x 4.3)x(10^-6 x 8)] / [(8 x 7.5) x(10^-5 x 10^ -3)]
(.129 x 10^[2-(-8)]
.129 x 10^10
1.29 x 10^-1 x 10^10
1.29 10^9
Find the quotient. Do not round your answer 58.543/10,000
Answer:
0.0058543
Step-by-step explanation:
58.543/10,000 = 58.543 divide 10,000
A jar contains 100 marbles. There are 21 blue marbles, 19 green marbles, 37 red marbles, and 23 yellow marbles. What is the probability of randomly selecting a yellow marble? Enter the correct answer
Answer:
23% or 23/100
Step-by-step explanation:
Since there are 23 in 100 is is 23/100 or 23%
Answer:
4.348%
Step-by-step explanation:
blue marbles = 19
yellow marbles = 23
probably of getting yellow = 23/100
= 4.34782608696
then you round then number to three decimal places and there you go
two classes each with 21 students were given a physical fitness test. the result of the number of pull ups performed in 30 seconds were recorded in the table below
Based on the results of the physical fitness test, the reason why we are unable to calculate the mean number of pull-us done by the students in each class is that we don't have the exact number of pull-ups done by each student.
What is needed to calculate mean?To calculate the simple mean of a distribution of numbers, we would need the value of all the numbers to be known. These numbers will then be summed up and divided by the number of the distribution.
In this case of the physical fitness test, the number of pull-ups is not known for all the students as there are some that either did below 5 or above 10 and we don't know the exact number of pull-ups done.
As a result, we are unable to calculate the mean.
Question is:
Explain why we are unable to calculate the mean number of pull-ups done by the students in each class.
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Kaleb determined how much money he would spend if he stopped at McDonalds each day after school. His cost can be modeled using c(m)=2.3m+2.50, where m is the number of McGriddle he orders each time. What is the cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles?
Answer:
The cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles would be 11.50.
Step-by-step explanation:
We know this is the answer because, when solving for c(3), we would get c(3)=2.3(3)+2.50=11.50.
the quotient of 10 and a number in math terms
Question
The following data set represents the dollar amounts of donations collected at the entrance to a free museum during one hour.
Donation Amount ($) Frequency
1 1
5 5
10 3
15 1
600 1
Is the median a reasonably good measure of central tendency for this data set? What if the outlier were removed from consideration?
Select the correct answer below:
The median is a good measure regardless of whether the outlier is included.
The median is a very poor measure regardless of whether the outlier is included.
The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.
The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.
In the given situation (A) the median is a good measure regardless of whether the outlier is included.
What do we mean by media?The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in a data set. The basic difference between the median and the mean in describing data is that the median is not skewed by a small proportion of extremely large or small values, and thus provides a better representation of a "typical" value.To find the median:
1, 5, 5, 5, 5, 5, 10, 10, 10, 15, 600The number of terms is 11, so the middle number will be the 5th term from both ends.The 5th term is 5.So, regardless of whether the outlier is included, the median is a good measure in the given situation.Therefore, in the given situation (A) the median is a good measure regardless of whether the outlier is included.
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The correct question is given below:
The following dataset represents the dollar amounts of donations collected at the entrance to a free museum for one hour.
(Refer to the table given below)
Is the median a reasonably good measure of central tendency for this dataset? What if the outlier were removed from consideration?
Select the correct answer below:
(A) The median is a good measure regardless of whether the outlier is included.
(B) The median is a very poor measure regardless of whether the outlier is included.
(C) The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.
(D) The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.
Are these fractions equivalent or
nonequivalent?
The two fractions are equivalent.
When two fractions have the same value, they are said to be equivalent, meaning that even though the numbers in the two fractions are different, their overall value is the same.
Fractions that are not equal to one another are referred to as nonequivalent fractions. The same cross multiplication procedure must be used to determine whether two fractions are comparable or not.
Consider these two fractions,
x = ( m / 4n ) and y = ( 2m / 8n )
Now when the fraction x is multiplying and dividing by 2.
We get,
x = ( m / 4n ) × ( 2 / 2 )
x = 2m / 8n
Therefore, x = y
Hence, the fractions are equivalent.
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Consider the relationship chart for the a fast-food restaurant,
Assume that the areas required for each department are:
Department Area Required (Square feet)
(CB) 300
(CF) 200
(PS) 200
(DD) 200
(CS) 300
Assume facility dimension of 6 (horizontal) by 8 (vertical) squares, where each square is 5 feet on a side. As a result, for example the CB department requires 12 squares. Develop a layout for the fast-food restaurant.
The layout of the fast-food restaurant of dimensions 6 by 8 5 feet squares is presented in the attached table created with Sheets.
How can the required layout be found?The dimensions of the facility are;
Horizontal = 6 squares
Vertical = 8 squares
The side length of each square = 5 feet
Therefore;
Area of each square = 5² ft.² = 25 ft.²
Number of squares, n, required by each dependent are therefore;
CB department, n = 300 ÷ 25 = 12 squares
CF department, n = 200 ÷ 25 = 8 squares
PS department, n = 8 squares
DD department, n = 8 squares
CS department, n = 12 squares
A layout for the fast-food restaurant is therefore;
The first three vertical columns of 8 squares each are occupied by the CF, PS, and DD departments. The remaining 3 by 8 squares are occupied by the CB department, (3 by 4 squares), and the CS department, (3 by 4 squares)Please see the attached table layout created using Sheets.
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Helpppp meeeee!!!! Ayudaaamee
Determine whether the quadratic function shown below has a minimum or
maximum, then determine the minimum or maximum value of the functio
ƒ(x) = x² + 6x + 7
Answer:
Minimum = (-3, -2)
Step-by-step explanation:
Standard form of a quadratic function:
[tex]f(x)=ax^2+bx+c[/tex]
If a > 0 the parabola opens upwards and the curve has a minimum point.
If a < 0 the parabola opens downwards and curve has a maximum point.
Given function:
[tex]f(x)=x^2+6x+7[/tex]
As a > 0, the parabola opens upwards and so the curve has a minimum point.
The minimum/maximum point of a quadratic function is its vertex.
Vertex form of a quadratic function:
[tex]f(x)=(x-h)^2+k[/tex]
Where (h, k) is the vertex.
To rewrite the given function in vertex form, complete the square.
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=x^2+6x+7 +\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2[/tex]
[tex]\implies f(x)=x^2+6x+7 +9-9[/tex]
[tex]\implies f(x)=x^2+6x+9+(7 -9)[/tex]
[tex]\implies f(x)=x^2+6x+9-2[/tex]
Factor the perfect square trinomial formed by x²+6x+9:
[tex]\implies f(x)=(x+3)^2-2[/tex]
Compare with the vertex form:
h = -3k = -2Therefore, the vertex is (-3, -2) and so the minimum value of the given function is (-3, -2).