In summary, the upper and lower bounds for the volume of the box are:
Upper bound: 382.125cm³
Lower bound: 238.375cm³
The volume of the box is calculated by multiplying the length, width, and height together. In this case, the measurements of the box are given as 10cm x 7cm x 4cm, so the volume of the box is:
volume = 10cm x 7cm x 4cm = 280cm³
However, since the measurements are given to the nearest centimeter, there is a slight degree of uncertainty in the exact measurements of the box. To calculate the upper and lower bounds for the volume of the box, we need to consider the possible variations in the measurements.
The upper bound for the volume would be calculated by taking the highest possible measurements for each dimension. So, if the length could be as much as 10.5cm, the width could be as much as 7.5cm and the height could be as much as 4.5cm. Then the upper bound for the volume would be:
Upper bound = 10.5cm x 7.5cm x 4.5cm = 382.125cm³
The lower bound for the volume would be calculated by taking the lowest possible measurements for each dimension. So, if the length could be as little as 9.5cm, the width could be as little as 6.5cm and the height could be as little as 3.5cm. Then the lower bound for the volume would be:
Lower bound = 9.5cm x 6.5cm x 3.5cm = 238.375cm³
In summary, the upper and lower bounds for the volume of the box are:
Upper bound: 382.125cm³
Lower bound: 238.375cm³
And the exact volume is 280cm³
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Solve for x. Round to the nearest tenth, if necessary.
The value of x is 3.67 in the given right angled triangle.
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
In the given triangle ,
Triangle STU ,
T = 90
S = 69
So, U = 180 - 90-69
U = 180 - 159
U = 21
And US = 10
sin69 = TU/US
sin69 = TU / 10
0.93 = TU/ 10
93 / 100 = TU / 10
93/10 = TU
TU = 9.3
So, in the triangle
as per pythagores theorem ,
SU^2 = ST^2 + TU^2
10*10 = x*x + 9.3*9.3
x*x = 100-86.49
x*x = 13.51
x = 3.67 (Approx)
Hence, The value of x is 3.67 in the given right angles triangle.
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Why are complex fractions called complex?.
Complex fractions are called complex because they contain one or more fractions within the numerator and/or denominator of the fraction. These fractions within the fraction make the fraction more complex or difficult to simplify than a regular fraction, which only has a single numerator and denominator.
The term "complex" in mathematics often refers to something that is composed of multiple parts or layers, and that requires more steps or understanding to work with or solve.
In this case, the presence of one or more fractions within the fraction makes it more complex than a regular fraction, hence the name "complex fraction."
Another reason for the term complex is that the fractions in the numerator and denominator may have different or even the same variables, making it difficult to cancel them or simplify the expression.
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Chandler, the owner of a boutique, kept track of which sizes were worn by the store's customers. small 3 medium 32 large 22 What is the experimental probability that the next customer to come into Chandler's boutique wears a size small? Write your answer as a fraction or whole number.
The experimental probability that the next customer to come into Chandler's boutique wears a size small is; 1/19
How to find the experimental probability?Theoretical probability is defined as the term used to describe what we expect to happen based on math theory, while experimental probability refers to what actually happens when the actual situation is tried out as an experiment.
In this question, we are given;
Number of small wears = 3
Number of medium wears = 32
Number of large wears = 22
Thus;
Total number of wears = 3 + 32 + 22
= 57
Probability that next customer wears small size = 3/57 = 1/19
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How many solutions does Y =- 3x 5 have?.
The given equation y = -3x + 5 has infinitely many solutions.
We have linear equation y = -3x + 5
We need to encounter how many solutions can satisfy the given equation.
We know that,
y = -3x + 5 is a linear equation in two variables in the form ax + by + c = 0
For x = 0, y = 0 + 5 = 5. Therefore, (0, 5) is one solution.
For x = 1, y = -3 × 1 + 5 = 2. Therefore, (1, 2) is another solution.
For y = 0, -3x + 5 = 0, x = 5/3. Therefore, (5/3, 0) is another solution.
Clearly, for different values of x, we get different values for y. Thus, any value substituted in the place of x in the given equation will form another solution for the given equation. So, there is no limitation to the number of different solutions obtained by substituting real values for x in the given linear equation. Thus, a linear equation in two variables can have infinitely many solutions.
Thus, y = -3x + 5 has infinitely many solutions.
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7x-2y+5 xy + x 2 for x= -1and y= 2
Answer:
= - 23.
Step-by-step explanation:
7x - 2y + 5 xy + x 2
From the question
x = -1
and
y = 2
7(-1) - 2(2) + 5 (-1)(2) + (-1) 2
= -7 - 4 + 5 (-2) - 2
= -7 - 4 -10 - 2
= - 11 - 12
= - 23.
if you want to make a figure 9x larger what scale factor do you use?
Mateo is making bookmarks with different colored ribbon.The amount of color he has is shown in the table.Each bookmark will be 1/6 yard long.How many more orange bookmarks can he make than aqua bookmarks.
color length(yd)
Aqua 3/4
orange 9/10
yellow 15/16
use reciprocals pls
The orange bookmarks that Mateo can make than aqua bookmarks is 1.
How to calculate the number of bookmark?Based on the information given, let x = number of aqua bookmarks
(1/6) × x = 3/4
x = (3/4) × (6/1)
x = 18/4
x = 4.5
Rounding down shows that we can make 4 aqua bookmarks.
y = number of orange bookmarks
(1/6)y = 9/10
y = (9/10)*(6/1)
y = 54/10
y = 5.4
This rounds down to 5 orange bookmarks.
Therefore, Mateo can make 5-4 = 1 extra orange bookmark compared to aqua.
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Mateo is making bookmarks with different colored ribbon. The
amount of each color he has is shown in the table. Each bookmark
will be yard long. How many more orange bookmarks can he make
than aqua bookmarks?
Table:
Color: Length (yd):
———————————-
Aqua. 3/4
Orange. 9/10
Yellow. 15/16
How do you graph inverse operations?.
The inverse operations can be graphed by determining the inverse of the function by swapping the x and y variables,
Not all functions have inverses, and in order for a function to have an inverse, it must be a one-to-one function that is, there must not be repeated output for many inputs which indicates that not all functions have inverses. The various steps to graph inverse functions can be noted as -
By switching the x and y variables, first determine the function's inverse, and then solve for y. The inverse function, for instance, will be x = f-1 if the original function is y = f(x) (y).By switching the original function's x and y values, plot the inverse function's points. For instance, if the original function is y = 2x + 1, the inverse function would be x = (y-1)/2, and instead of plotting the point (0,1), you would plot (1,0), (2,-1) and so on (-1,2)Over the line y = x, reflect the original function's graph. You will then be shown the inverse function's graph.Lastly, it is required to correctly identify the axes and the points.Read more about inverse operations on:
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What is commutative property of real numbers?.
The commutative property applies only to addition and multiplication of real numbers.
What is commutative property in math?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT commutative.
The commutative property of real numbers states that for any real numbers a and b, a + b = b + a and a * b = b * a. In other words, the order in which two real numbers are added or multiplied does not change the result. This property applies to both addition and multiplication of real numbers.
Therefore, the commutative property applies only to addition and multiplication of real numbers.
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Attendance i decreaing at a rate of 0. 5% per year. If there are 1200 people attending now how many will be attending in 4 year?
So, in 4 years, there will be 1176 people attending.
To find out how many people will be attending in 4 years, you need to determine the total decrease in attendance over that time period. The attendance is decreasing at a rate of 0.5% per year, so over 4 years, the decrease in attendance will be 4 years x 0.5% = 2%
To find out how many people will be attending in 4 years, you can then subtract the 2% decrease from the current attendance of 1200 people:
1200 x (1 - 0.02) = 1176 people
So, in 4 years, there will be 1176 people attending.
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You must ascertain the overall drop in attendance over that time span in order to calculate the number of attendees in 4 years. If enrollment drops by 0.5% annually, it will drop by 2% over the course of four years (4 years x 0.5%).
Then, from the present attendance of 1200 people, subtract the 2% decline to determine how many attendees there will be in 4 years:
1200 times (1-0.02) ≈ 1176 individuals
Therefore, there will be 1176 attendees in 4 years.
Someone help me please
The dots are the shaded parts
Answer:
1 [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Both blocks contain 9 stars
left block has all 9 shaded = [tex]\frac{9}{9}[/tex] = 1
right block has 5 shaded = [tex]\frac{5}{9}[/tex]
mixed number = 1 + [tex]\frac{5}{9}[/tex] = 1 [tex]\frac{5}{9}[/tex]
For a company picnic, Kenny ordered a box of fresh-baked gingerbread cookies and sugar cookies. The box included a total of 90 cookies, and 70% of them were gingerbread. How many gingerbread cookies did Kenny get
Answer: 63 gingerbread cookies
Step-by-step explanation: Okay, to find the answer to this problem, we shall use this formula:
Final amount = Whole # * Part % / 100
So, now let's plug in the numbers to find the answer:
Final amount = 90 * 70 / 100
= 6300/ 100
= 63
Therefore, Kenny ordered a total of 63 gingerbread cookies. I hope this helped!
You are trying to save $540 for your trip to New York. You started with $54 that you saved up and you earn $9 per hour of babysitting. How many hours will you have to babysit in order to have the money you need?
Answer:
54 Hours
Step-by-step explanation:
first of all 540-54 he started with is 486 and 486/9 is 54 since you get 9 per hour
Answer: 54 Hours of babysitting
Step-by-step explanation: 540-54=486 Then you take 486 and you divide it by 9 to see how many hours you have to work and that would be 54 hours.
Write y = 2x + 5 in standard form
The equation y = 2x + 5 is already in standard form.
Standard form of a linear equation is Ax + By = C, where A, B, and C are constants and A and B cannot be both zero. In this case, A=2, B=1 and C=5, which meets the standard form equation, y = 2x + 5 is already in standard form.
Answer: y = 2x + 5 in standard form is 2x - y = -5
Step-by-step explanation: I hope this helps!
What is the solution to the system of equations y equals 1. 5 x 4 and y equals negative x?.
The solution to the system of equations is y equals 1. 5 x 4 and y equals negative x is-= (1.6,-1.6)
In this case option A is correct
The coordinates of the ordered pair (s) that satisfy all of the equations in the system are the solution set to a system of equations. To put it another way, those x and y values will make the equations true. As a result, when a system of equations is graphed, the intersection points of the graphs are the system's solution.
y = 1.5x – 4...........(1)y = –x...........(2)-----------------------Since equation 2's y is -x, we can substitute this into equation 1 as follows: y = 1.5x - 4 -x=1.5x-4 -2.5x=-4 x=1.6Now, when x=1.6, equation 2's result for "y" is -1.6. (1.6,-1.6)To know more about solutions here
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What is the solution to the system of equations y equals 1. 5 x 4 and y equals negative x?.
(1.6,-1.6)(1.5,-1.6)(1.6,-1.5)0HELP PLEASE THIS IS OVERDUE!!!!!!!!!!!!!!!
The high school tennis team is made up of boys and girls. The team has a total of 25 players. 12 of the players are girls. If a player is chosen at random, what is the probability that the player will be a boy?
A. 0.52
B.0.26
C.0.13
D.0.048 (will mark brainliest)
Answer:
0.52
Step-by-step explanation:
25-12=13
boys are equal to 13
the probability of picking a boy at random will be;
13/25=0.52
george places a mirror on the ground 45ft from the base of building. He walks backward until he can see the top of the building in the middle of the mirror. At that point, George’s eyes are 6th above the ground and he is 7.5ft from the mirror. Use similar triangles to find the height of the building.
The height of the building is given as follows:
36 ft.
How to obtain the height of the building?In this problem, we have two similar triangles, meaning that their side lengths are proportional.
As the triangles are similar, the equation involving proportions for the equivalent side lengths is given as follows:
x/6 = 45/7.5.
Applying the division on the right side of the equality, we have that:
45/7.5 = 6.
Hence:
x/6 = 6.
Applying cross multiplication, the height is given as follows:
x = 6(6) = 36 ft.
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a total of 516 tickets were sold for the school play. they were either adult tickets or student tickets. there were 66 more student tickets sold than adult tickets. How many adult tickets were sold
In the word problem the number of the adult ticket is 225.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here total number of tickets = 516.
Which is contains adult and students tickets. Then let us take x is number of adult ticket and y is number of student tickets then,
=> x + y = 516 ------> 1
Now there were 66 more student tickets sold than adult tickets then
=> y = x+66 -----> 2
Now put 2 into 1 then
=> x+66+x = 516
=> 2x = 516-66 = 450
=> x = 225.
Now put x = 225 into then
=> y = 225+66 = 291.
Hence the number of adult tickets is 291.
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A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 12400 kilograms have already been loaded into the container. Which inequality can be used to determine x, the greatest number of
120-kilogram crates that can be loaded onto the shipping container?
Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is 8000 + 120C <= 27500
What is inequality?An inequality is a relationship that allows us to contrast two or more mathematical expressions.
Knowing that;
Each carton weighs 120 kg.
The container's maximum weight when loaded is 27500 kg.
Weight of the container as it is currently loaded: 8000 kg
Now that we have merged, we have;
Solution
because 8000 grams have already been loaded kilograms
into the container
each crate weighs 120 kilograms.
so 8000 + 120C <= 27500
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Keiha i a oftware alewoman. Let y repreent her total pay (in dollar). Let x repreent the number of copie of Hitory i Fun he ell. Suppoe that x and y are related by the equation =1600110xy
Keiha sells computer software she sells 1800 if no books are sold.
Let y signify her overall salary (in dollars).
Let x be the volume of History is Fun that she sells.
Keep in mind that a change can be an improvement or a problem. Use a positive number to indicate an increase. Use a negative integer to indicate a reduction.
Consider the case when the equation =y+180070x connects x and y.
The number of books sold will affect the variable 70x in equation y=1800 + 70x.
Y=70x+1800=70(0)+1800=1800 if no books are sold.
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Full question
Keiko is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of History is Fun she sells. Suppose that x and y are related by the equation 2200 + 90x = y. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What is the change in Keiko's total pay for each copy of History is Fun she sells?
PLEASE HELP ASAP
which expression can be used to find the sum of the polynomials?
The correct expression to solve te sum of polynomials is [(-3x)+(-8x)]+4x+[9+5] (D).
To solve any polynomials problems, it is important for us to take a close look on the orders of each number. For the sum and substraction operation, we need to categorize each number based on its orders.
From the case, we have a problem as:
(9 - 3x²) + (-8x² + 4x + 5)
We can categorize each order:
Order 2 = (-3x²) and (-8x²)
Order 1 = 4x
Order 0 = 9 and 5
Hence, we can solve the problem as:
(9 - 3x²) + (-8x² + 4x + 5)
= [(-3x²) + (-8x²)] + 4x + (9 + 5)
= -11x² + 4x + 14
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Rewrite f(x)= x as a piecewise function
The piecewise function will be written as y= -x { x < 0 } and y = x { x > 0 }.
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
Given that the function is f(x)= x. The piecewise function of the given function will vary from x being less than zero and x being greater than zero. The function can be written as y= -x { x < 0 } and y = x { x > 0 }.
The graph of the piecewise function of the given function is attached with the answer below.
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the slope-intercept form is used to write a linear equation.
What is the range of the function f x − x 3 2 7?.
Answer:
Step-by-step explanation:
nhbjbjhbnjbjnjnjny6778899
College tudent are randomly elected and arranged in group of three. The random variable x i the number in the group who ay that they take one or more online coure. Determine whether a probability ditribution i given. If a probability ditribution i given, find it mean and tandard deviation. If a probability ditribution i not given, identify the requirement that are not atified. X P(x)
0 0. 108
1 0. 354
2 0. 390
3 0. 148
Yes, a probability distribution is given.
The mean of this probability distribution is 1.62 and the standard deviation is 0.84.
Mean = ΣxP(x) = 0*0.108 + 1*0.354 + 2*0.390 + 3*0.148 = 1.62
Standard Deviation = √Σ(x-mean)2P(x) = √(0-1.62)2*0.108 + (1-1.62)2*0.354 + (2-1.62)2*0.390 + (3-1.62)2*0.148 = 0.84
This is a probability distribution for a situation in which college students are randomly elected and arranged in groups of three. The number of people in the group who claim to take one or more online courses is the random variable, or x. The probability distribution is given by the values of x and the probabilities associated with them (P(x)). From the given values, we can calculate the mean and standard deviation of the distribution. The mean of the distribution is 1.62, and the standard deviation is 0.84. This means that, on average, 1.62 students in the groups of three will say that they take one or more online courses. The standard deviation of 0.84 implies that the actual number of students in the groups who say that they take online courses will vary from the mean value by about 0.84 students
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Use the vertical line test to determine if the graph represents a function.
The graph that depicts a function is graph when the vertical line test is used (b).
What is meant by vertical line test?By visually counting the number of times the curve crosses vertical lines, the vertical line test is a graphical approach for verifying whether a curve in the plane accurately depicts the graph of a function. the graph of a function can only be intersected by any vertical line in the plane once as a result.
A graph must satisfy the vertical line test in order to be considered a function representation. The vertical line test requires that the line from the x-axis only once crosses an associated y-value.
Graphs (a), (c), and (e) fail the vertical line test, indicating that they do not reflect a function.
So, graph is the name of the graph that represents a function (b)
The complete question is:
Use the vertical- line Test to determine which graph represents a function? I'm thinking it's the first one...
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Solev
solve the system of inequalities
Answer:
b.
Step-by-step explanation:
5x ≥ 15 or x + 4 > 13
5x ≥ 15
x ≥ 15/5
x ≥ 3
x + 4 > 13
x > 13-4
x > 9.
So, the answer is x ≥ 3
How do you find the equation of a function in factored form?.
Using factoring, we do the following actions to make rational expressions simpler:
As much as you can, factor the numerator and denominator. Any factors that appear in both the numerator and the denominator should be eliminated. Your expression gets simplified as a result. How is an expression factorized:
Step 1 is to identify the expression's prime factors.
Step 2: Find the GCF by enclosing the common factors.
Write each term in the expression as a combination of the GCF and the final factor in step 3.
Step 4: Simplify the equation by applying the distributive property.
Y=12(x-6)(x+2) is an illustration of a quadratic function in factored form. This shape can be examined to determine the vertex as well as the graph's x-intercepts.
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Shenelle has $25 to spend at the movie theater. She wants to see the regular admission showing of a 3D movie and buy
snacks. Define a variable and write an inequality to represent
the amount of money Shenelle can spend on snacks. Then solve the inequality and interpret the solution. Explain your reasoning.
Movie Ticket
Matinee 2D $5.50
Matinee 3D $7.25
Regular Admission 2D $8.50
Regular Admission 3D $10.25
The inequality that represents the amount of money Shenelle can spend on snacks is given as follows:
x + 10.25 ≤ 25.
The solution to the inequality is of:
x ≤ 14.75.
Meaning that she can spend at most $14.75 on the snacks.
How to define the inequality?The total amount that Shenelle has is given as follows:
$25.
Her spendings are given as follows:
$10.25 on the regular admission of the 3D movie.x on snacks.Hence the inequality is given as follows:
x + 10.25 ≤ 25.
The solution is obtained as follows:
x ≤ 25 - 10.25.
x ≤ 14.75.
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What are the possible ways in which two consecutive odd numbers are added to sum of 2023?
Possible way in which two consecutive odd numbers are added to sum of 2023 is by evaluation using the formula (2n - 1) + (2n + 1) = 2023, so that we have 1010.5 + 1012.5 = 2023
What are consecutive odd numbersConsecutive odd numbers are a sequence of numbers that are separated by a difference of 2 and are all odd numbers. For example the first four odd numbers are: 1, 3, 5, and 7. Odd numbers can be generated using the formula 2n -1.
We shall represent the first odd number with (2n - 1) so that the two consecutive odd numbers will be expressed as:
(2n - 1) + (2n + 1) = 2023
2n + 2n = 2023
4n = 2023
n = 2023/4 {divide through by 4}
n = 505.75
Therefore the two consecutive odd numbers added to sum of 2023 are derived as:
2(505.75) - 1 = 1010.5 and 2(505.75) + 1 = 1012.5
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Answer: Well, let’s consider a number, [math]n[/math], it could be even or odd, it doesn’t ...
Step-by-step explanation:
