Surface area of the box measuring 5 inches by 3 inches by 7 inches is 142 square inches.
What is surface area ?The surface area of the object that refers to the overall space that is filled by its surfaces. Different 3D shapes in the geometry have various surface areas, which can be quickly estimated using the formulas. Two categories are used to classify the surface area:
Curved surface area or Lateral surface area
Surface area in total
Surface area of rectangle = 2 ( lb + bh + hl )
Dimensions of box = 5 inches by 3 inches by 7 inches
Hence,
Length = 5 inches
Breadth = 3 inches
Height = 7 inches
By putting it in formula of surface area of rectangle
= 2 ( lb + bh + hl )
= 2 ( 5*3 + 3*7 + 7*5 )
= 2 ( 15 + 21 + 35 )
= 2 * 71
= 142 square inches
Hence, the total surface area of the box is 142 square inches.
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Consider the function
f(x,y) = y\sqrt x - y^2 - 3 x + 11 y.
Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank.
f_x =
f_y = f_{xx} = f_{xy} = f_{yy} = The critical point with the smallestx-coordinate is
(__,__) Classification:
(local minimum, local maximum, saddle point, cannot be determined)
The critical point with the next smallestx-coordinate is
(__,__) Classification:
(local minimum, local maximum, saddle point, cannot be determined)
The critical point with the next smallestx-coordinate is
(__,__) Classification:
(local minimum, local maximum, saddle point, cannot be determined)
By using the concept of maxima, it can be determined that
[tex]f_x(x, y) = \frac{y}{2\sqrt{x}} - 3[/tex]
[tex]f_y(x, y) = \sqrt{x} - 2y +11[/tex]
[tex]f_{xx}(x, y) = -\frac{1}{4}x^{-\frac{3}{2}}[/tex]
[tex]f_{yy} = -2[/tex]
[tex]f_{xy} = \frac{1}{2\sqrt{x}}[/tex]
Critical point with the smallest x - coordinate
(0, [tex]\frac{11}{2}[/tex])
Classification cannot be determined
Critical point with the next smallest x - coordinate
(1, 6)
Classification is local maxima
What is maxima of a function?
Maxima of a function gives the maximum value of a function in a given interval or within the whole domain.
f(x, y) = [tex]y\sqrt{x} -y^2 -3x + 11y[/tex]
[tex]f_x(x, y) = \frac{y}{2\sqrt{x}} - 3[/tex]
[tex]f_y(x, y) = \sqrt{x} - 2y +11[/tex]
Putting x = 0 in [tex]f_y(x, y) = 0[/tex],
-2y + 11 = 0
[tex]y = \frac{11}{2}[/tex]
[tex](0, \frac{11}{2})[/tex] is a critical point
Putting [tex]f_x(x, y) = 0[/tex] and [tex]f_y(x, y) = 0[/tex]
[tex]\frac{y}{2\sqrt{x}} - 3 = 0\\\frac{y}{2\sqrt{x}} = 3\\y = 6\sqrt{x}[/tex]
[tex]\sqrt{x} - 2y+11 = 0\\\sqrt{x} -2\times 6\sqrt{x}+11=0\\\sqrt{x}-12\sqrt{x} + 11 = 0\\11\sqrt{x} = 11\\\sqrt{x} = \frac{11}{11}\\\sqrt{x} = 1\\x = 1[/tex]
When x = 1, y = [tex]6 \times \sqrt{1} = 6[/tex]
(1, 6) is a critical point
[tex]f_{xx}(x, y) = -\frac{1}{4}x^{-\frac{3}{2}}[/tex]
[tex]f_{yy} = -2[/tex]
[tex]f_{xy} = \frac{1}{2\sqrt{x}}[/tex]
The point (0, [tex]\frac{11}{2}[/tex]) is undefined in the second order partial derivative
For the critical point (1, 6)
[tex]f_{xx}(1, 6) = -\frac{1}{4}\\f_{yy}(1, 6) = -2\\f_{xy}(1, 6) = \frac{1}{2}[/tex]
[tex]f_{xx}f_{yy}-(f_{xy})^2[/tex]
[tex]-\frac{1}{4}\times -2-(\frac{1}{2})^2\\\frac{1}{2} - \frac{1}{4}\\\frac{1}{4} > 0[/tex]
[tex]f_{yy} = -2 < 0[/tex]
Hence (1, 6) is a point of local maxima
So it can be determined that
[tex]f_x(x, y) = \frac{y}{2\sqrt{x}} - 3[/tex]
[tex]f_y(x, y) = \sqrt{x} - 2y +11[/tex]
[tex]f_{xx}(x, y) = -\frac{1}{4}x^{-\frac{3}{2}}[/tex]
[tex]f_{yy} = -2[/tex]
[tex]f_{xy} = \frac{1}{2\sqrt{x}}[/tex]
Critical point with the smallest x - coordinate
(0, [tex]\frac{11}{2}[/tex])
Classification cannot be determined
Critical point with the next smallest x - coordinate
(1, 6)
Classification is local maxima
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belmont records sends a disk jockey 13 new cd releases for possible use. in how many ways can the disk jockey select no more than 11 cds?
No: of ways can the disk jockey select no more than 11 CDs is 1012
What is a combination in math?Combinations are mathematical operations that count the number of possible configurations for a set of items where the order of the selection is irrelevant. You can choose the components of combinations in any order. Permutations and combinations can be mixed up.
What are the two types of combinations?Combinations with Repetition. ...
Combinations without Repetition. ...
Combinations with Repetition.
There are more options for him to pick from than just 11 CDs when choosing "no more than 8 CDs," including 11,10,9,8,7, 6, 5, 4, 3, and 1.
Ways to choose 9 CDs: 13C9=10
Ways to choose 8 CDs: 13C8= 45
Ways to choose 7 CDs: 13C7 = 120
Ways to choose 6 CDs: 13C6= 210
Ways to choose 5 CDs: 13C5 = 252
Ways to choose 4 CDs: 13C4 = 210
Ways to choose 3 CDs: 13C3= 120
Ways to choose 2 CDs: 13C= 45
Ways to choose 1 CD: 13C1 = 10
10+45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 = 1012
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Please help mee
I need this for math homework pleass
Answer: -2x + 3
Step-by-step explanation:
Subtract like terms. But first, there is a negative in front of the parenthesis of (-6x+2), use the distributive property.
-(6x+2), multiply each number inside of the parenthesis by -1:
-1 * -6x + -1 * 2
6x - 2
Now remove the parenthesis and add (or subtract) like terms.
-8x + 5 + 6x - 2
-8x + 6x = -2x
5 - 2 = 3
-2x + 3
two trains leave stations miles apart at the same time and travel toward each other. one train travels at miles per hour while the other travels at miles per hour. how long will it take for the two trains to meet? do not do any rounding.
Time taken for the both train to meet each other is 1.8 hours
The distance between two stations = 360 miles
The speed of one train = 95 miles per hour
The speed of the second train = 105 miles per hour
The relative speed of the trains = 95 + 105
Add the numbers
= 200 miles per hour
We know
Speed = Distance / Time
The time = Distance / Speed
The time taken for the two trains to meet = Distance / relative speed
Substitute the values in the equation
= 360 / 200
= 1.8 hours
Therefore, both trains will meet each other after 1.8 hours
I have answered the question in general, as the given question is incomplete
The complete question is:
Two trains leave stations 360 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 105 miles per hour. How long will it take for the two trains to meet?
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taylor ran a study with a 2x2 factorial design and found a significant main effect associated with one of the independent variables. he decides that he need to run a post-hoc test to find out exactly which conditions are constituting the significant difference. for which of the following reasons is this a foolish idea?
Taylor conducted a study using a 2x2 factorial design, and one of the independent variables was linked to a substantial main effect with significant difference.
A post-hoc test is not appropriate in this situation because it cannot provide reliable information about the conditions that are causing the significant difference. Post-hoc tests are only appropriate for small sample sizes and cannot be used to draw any definitive conclusions about the causes of a significant main effect.
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30 bottles of water for $4.80
Answer: unit rate is $0.16
1 bottle cost $0.16
Step-by-step explanation:
Find an equation for the parabola that has its vertex at the origin and has its focus at the point: ( − 7.32 , 0 ) .
Step-by-step explanation:
1.What is the equation of a parabola with a vertex at (0, 0)?
y = ax²; y = -ax²; x = ay²; x = -ay² where a = [½, 1 , 2]
Also an infinity of others at various values of a and various angles.
2.The focus lies above the vertex, so the parabola is vertical and the focal length p=10.25
Equation for up-opening parabola with vertex (h,k) and focal length p:
y=14p(x−h)2+k
y=14p(x−0)2+0y=141x2
3.Since the directrix is the line y=−10.25 , a point (x,y) is on the parabola if, and only if,
x2+(y−10.25)2=(y+10.25)2.
Therefore, x2−20.5y=20.5y and y=141x2.
hope I helped
Which of the following is located 2/3 the distance from the vertex?
Circumcenter
Incenter
Centroid
Orthocenter
Answer:centroid
Step-by-step explanation:
Answer:Centroid I hope this helpful to you mark me brainlist if correct
Step-by-step explanation:
Hence, the correct statement is "The Centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side."The centroid is the centre point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangleCentroid theorem: the distance between the centroid and its corresponding vertex is twice the distance between the barycenter and the midpoint of the opposite side. That is, the distance from the centroid to each vertex is 2/3 the length of each median. This is true for every triangleThe centroid of a triangle is the intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side).
Carol,dan and eli each had ome coin
dan had twice a many a eli
carol had twice a many a dan
write down the ratio carol had to the number of coin eli had
give your anwer in it implet form
Carol had four times as many coins as Eli had, or a 4:1 ratio.
What is ratio?An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, if there is 1 male and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every guy), meaning that there are 1 in 4 boys and 3 in 4 girls. A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
Here,
Dan has twice what Eli has ( D= 2 x E )
Carol had twice what Dan had ( C = 2 x D )
for example , let's suppose Eli had 2 coins
this means Dan had 4 coins,
and Carol had 8 coins .
carol 8 : 2 Eli
=4:1
The ratio in which carol had to the number of coin eli had will be 4:1.
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in the big bucks lottery, the chances of winning a $10.00 prize is 1%. what is your best guess about how many people would win a $10.00 prize if 1,000 people each buy a single ticket to big bucks?
In the big bucks lottery, there are chances that 10 out of 1000 people will win the lottery.
If there are 1000 people in the Big Bucks lottery and there is a 1 percent chance of winning 10 dollars prize if all 1000 people buy the lottery ticket of 10 dollars. If every person buys 10 dollar lottery ticket, then the chances of winning people would be calculated as follows:
Total number of People = 1000
Chances of winning the lottery = 1%
How many people would win 10 dollar lottery = 1000 * 1%
= 1000 * 0.01
= 10 People.
So there are chances that 10 out of 1000 people will win the lottery.
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How long will the air in the tank last at this rate
Answer:
60 minutes. (1 hour)
Step-by-step explanation:
An average recreational tank containing 200 bars or 12 L of air should last you for 60 minutes. However, several factors come into play while determining the lifespan of a scuba air cylinder. The amount of air that a diver needs depends on their air consumption rate, which in turn is based on their physical exertion level.
Answer: you have to say at what rate. we cant answer this question. there is part of this question that is missing.
A clothing store offers customers a holiday sale of 30% off the price of x items. A customer then has an additional 15% off coupon that can be used whe checking out. Which of the following functions represents the final price Px) of the items purchased?
a. P(x) = 0.045x b. P(x) = 0.45X c. P(x) = 0.595x
d. P(x) = 0.15x
A clothing store offers customers a holiday sale of 30% off the price of x items. A customer then has an additional 15% off coupon that can be used when checking out then the function is P(x) = 0.595x
Original price = x
Sale price = 30% off:
x - 30% =
x - 0.3x =
0.7x
Further discount 15% off:
0.7x - 15% =
0.7x - 0.7x*0.15 =
0.7x - 0.105x =
0.595x
The function is:
P(x) = 0.595x
Correct choice is C
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The point g(2,1) is translated 3 units left. What are the coordinates of the resulting point, g'?.
The coordinates of the resulting point, g' is :
(-1,1)
Given:
The coordinate plane allows for the translation of any object both horizontally (left/right) and vertically (up/down).
Rules are:
Replace x with x - k when the form is moved k units to the left.Replace x with x + k when the form is moved k units to the right.Replace y with y + k when the form is raised by k units.Change y to y - k when the form is shifted down by k units.The point g(2,1) is translated 3 units left.
we are asked to find the coordinates of the resulting point, g'.
By translating 2 units left, it means the x-axis value is made more negative by 2 units
So we are going to subtract two from the x-coordinate
So we have;
(2-3,1)
= (-1,1)
Hence we get the required coordinates.
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Write the equation of the line passing through the points (0, 0), (2, 1), and (-2, − 1).
Answer:
y = 0.5x
Step-by-step explanation:
Slope = m = (2-0)/(1-0) = 1/2 or 0.5
y-intercept = b = 0 since it passes through (0,0)
Slope-Intercept form of a line is y = mx + b
So the equation is
y = 0.5x + 0
or
y = 0.5x
What is the answer to 2+2?
A- 4
B- 5
C- 22
D- 8
PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5.0 STAR RATING
Answer:
Step-by-step explanation: 347000 * 6.5% * 20%= 347000*0.065*0.2=4511
Answer is 4511
Answer:
$4,511
the agency makes 6.5% of 347000 which is 22,555 and the agent makes 20 percent of what the agency makes.
so 20% of 22,555 is 4511
PLEASE HELP! (WILL MARK BRAINLIEST.)
The cost to rent a scooter is $24 plus $1.25 per mile traveled on the scooter. Paula rented a scooter and paid a total of $48. How many miles did she ride?
*please provide an explanation! *
Answer:
answer = 19.2
Step-by-step explanation:
48 = 24 + 1.25x
48 - 24 = 1.25x
24 = 1.25x
24/1.25 = x
19.2 = x
can someone do this and show work plsss xx
Answer:
Here is the work
Step-by-step explanation:
solve for y : -9=-7x+10
Answer: x=-19/7 or -2.71428571
Step-by-step explanation:
first you have to subtract 10 from each side to isolate the variable x. So -9-10=-19, and 10-10=0. Then to find x, you divide both sides by its coefficient, in this case 7.
Which expression makes the equation true for
the values of x?
16x16= 4(?)
a. 4x - 4
b. 4x - 16
C. 2x - 2
d. 12x -12
Answer:
Step-by-step explanation:
answer is c
Maya worked 41 hours this week at a local hospital. She makes $12. 00 per hour. Anytime over 40 hours is paid at time and half or 1. 5 times her hourly wage. How much will maya earn for her 41 hours of work this week?.
We know that Maya's earnings will be $498 for working 41 hours using simple mathematical operations.
What do we mean by mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
So, earnings of Maya when she works for 41 hours are:
We know that Maya works for $12.00 per hour.
She's paid 1.5 times her hourly income when she works for more hours after 40 hours.
That will be: 12 × 1.5 = $18
Hence, Maya's income for 41 hours will be:
40 hours + 1 hour (Extra hour)
(12 × 40) + 18
480 + 18
$498
Therefore, we know that Maya's earnings will be $498 for working 41 hours using simple mathematical operations.
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Question inside if the picture
The value of the function, f(g(x)), is [tex]f(g(x)) = 2(\sqrt{x+7} )- 3[/tex]. The correct option is the second option [tex]2(\sqrt{x+7} )- 3[/tex]
Evaluating a functionFrom the question, we are to determine the value of the given function, f(g(x))
From the given information,
The given functions are
[tex]f(x) = 2x- 3[/tex]
and
[tex]g(x) = \sqrt{x+7}[/tex]
To determine the value of f(g(x)), we will substitute the value of g(x) into the function, f(x)
That is,
[tex]f(x) = 2x- 3[/tex] becomes
[tex]f(g(x)) = 2(\sqrt{x+7} )- 3[/tex]
Hence, the value of f(g(x)) is [tex]2(\sqrt{x+7} )- 3[/tex]
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Find the ditance from the point A(-2,3) to the line y =1/2x1. Round your anwer to the nearet tenth
The distance in units of 2√5 between the point A(-2,3) and the line y =1/2x1.
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line.
The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.
We will comprehend the slope-finding method and its applications in this article.
According to our question-
10/√5 *√5/√5*105/√5
Hence, The distance in units of 2√5 between the point A(-2,3) and the line y =1/2x1.
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Which of the following fractions have repeating decimal representations? Which have terminating decimal representations?
a) 3/16 b) 4/125 c) 3/13 d) 7/24
Repeating decimal representation will be 3/13, 7/24. Terminating decimal representation will be 3/16, 4/125.
What is decimal?The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system. The base-10 number system, arguably the most widely used number system, is referred to as decimal. The decimal number system consists of ten single-digit numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The number following nine is 10.
Here,
Repeating decimal representation,
=3/13, 7/24
Terminating decimal representation,
=3/16, 4/125
3/13 and 7/24 will be repeated in decimal form. The final two decimal places are 3/16 and 4/125.
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a cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. the base of the can has an area of 75 \text{ cm}^275 cm 2 75, start text, space, c, m, end text, squared, and the height of the can is 10 \text{ cm}10 cm10, start text, space, c, m, end text. if 110 \text{ cm}^3110 cm 3 110, start text, space, c, m, end text, cubed of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?
The total volume of the fruits is 640 when Syrup is poured over fruit pieces in a cylindrical can and then the lid is closed. The can's height is 10 cm, and its base has a surface area of 75 cm².
Given that,
Syrup is poured over fruit pieces in a cylindrical can and then the lid is closed. The can's height is 10 cm, and its base has a surface area of 75 cm².
We have to find which of the following comes closest to the total volume of the fruit pieces in the can if 110 cm³ of syrup is required to fill the can completely.
We know that,
Total volume of the cylinder can is equal to the sum of the total volume of fruits and total volume of Syrup.
So,
The total volume of the fruits is we have to find take x
The total volume of the cylinder is base× height=75×10
The total volume of the syrup is 110
So,
75×10=x+110
x=750-110
x=640
Therefore, The total volume of the fruits is 640 when Syrup is poured over fruit pieces in a cylindrical can and then the lid is closed. The can's height is 10 cm, and its base has a surface area of 75 cm².
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How many solutions does this linear system have? one solution: (0, –1) one solution: (1, 4) no solution infinite number of solutions
Linear systems have no solution.
What are the solutions to the linear system?
The solution to a system of linear equations is the point that lies on both lines. In other words, the solution is the point where the two lines intersect
A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).
How do you determine a linear system?
Simplify the equation as closely as possible to the form of y = mx + b. Check to see if your equation has exponents. If it has exponents, it is nonlinear. If your equation has no exponents, it is linear
Linear means something related to a line. All the linear equations are used to construct a line. A non-linear equation is such that it does not form a straight line. It looks like a curve in a graph and has a variable slope value.
Hence, the linear systems have no solution.
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Factor each polynomial
Answer: x^2 (x+1) (4x-9)
Step-by-step explanation:
We can test the equation above x^2 (x+1) (4x-9) to see if it is true or not by rewriting it
x^2 ( 4x^2 -9x +4x -9)
x^2 (4x^2 - 5x -9)
4x^4 - 5x^3 - 9x^2
So x^2 (x+1) (4x-9) is the correct answer for this equation!
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A coat is marked down by 10% and the customer is given a second discount of 25% what is the sales price
The sales price of the coat is 67.5% of the original price
How to determine the sales price of the coat ?From the question, we have the following parameters that can be used in our computation:
Markdown rate = 10%
Second discount = 25%
The retail price of the coat can be calculated using the following equation
Retail price = original price * (1 - Markdown rate) * (1 - discount)
Substitute the known values in the above equation, so, we have the following representation
Retail price = original price * (1 - 10%) * (1 - 25%)
Evaluate the products
Retail price = original price * 0.675
Rewrite as
Retail price = 67.5% of the original price
Hence, the sales price is 67.5% of the original price
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In a school there are 875 students.
3
5 of the students are girls.
The rest are boys.
How many boys are there?
Answer:845
Step-by-step explanation:
II The small capillaries in the lungs are in close contact with the alveoli. A red blood cell takes up oxygen during the 0.5s that it squeezes through a capillary at the surface of an alveolus. What is the diffusion time for oxygen across the 1-um thick membrane separating air from blood? Assume that the diffusion coefficient for oxygen in tissue is .2x10^-11m^2/s Give your answer to 1 significant figure.
The diffusion time of the red blood cell to take oxygen through the membrane is 25uS.
The small capillaries in the lungs are in close contact and it takes a red blood cell 0.5 seconds to squeeze through the capillary.
The diffusion time for the oxygen across the 1 um thick membrane separating the air is given by,
t = x²/2D
Where,
t is the diffusion time,
x is the thickness of the membrane,
D is the diffusion coefficient.
Putting values,
t = (1 x 10⁻⁹)²/2 x 2 x 10⁻¹¹
t = 10⁻⁷/4
t = 25 x 10⁻⁹ seconds.
t = 25 uS.
so, the diffusion time is 25uS.
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