The surface area of the largest sphere that could fit into the rectangular box of dimensions 12 in x 14 in x 18 in is 324π inches²
The surface area of sphere = 324π inches²
What is a Sphere?
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the surface area of the Sphere be = S
Let the dimensions of the rectangular box be L x W x H
12 inches x 14 inches x 18 inches
Now , for the surface area of the sphere to have the largest surface area , the radius should be maximum
From the rectangular box , we can see that the height of the rectangle is best suited as the diameter of the sphere
So , Height of the Box = Diameter of the Sphere
And , Radius of the sphere = Height of the Box / 2
= 18 / 2
Radius of the sphere = 9 inches
Now ,
Surface Area of a Sphere = 4πr²
r = 9 inches
Substituting the values in the equation , we get
Surface Area of a Sphere S = 4 x π x ( 9 )²
= 4 x π x 81
= 324π inches²
Therefore , the value of S is 324π inches²
Hence , The surface area of sphere = 324π inches²
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Consider the equation and the following ordered pairs: (−3,y) and (x,2).
y=−3x−1
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Complete the table below.
x y
row 1−3 Answer
row 2 Answer
2
The missing values of the ordered pairs using the given equation are:
x = -1; y = 8
The table is:
x | y
-3 8
-1, 2
How to Find the Values that Satisfies an Equation?To find the missing values of an ordered pair that satisfies a given equation, plug n the given value of one of the variables into the equation and solve to find the value of the other variable.
The equation given is y = -3x - 1
Find the missing value of the ordered pair (-3, y) by plugging in x = -3 into the equation given:
y = -3(-3) - 1
y = 8
Find the missing value of the ordered pair (x, 2) by plugging in y = 2 into the equation given:
2 = -3x - 1
2 + 1 = -3x - 1 + 1
3 = -3x
x = 3/-3
x = -1
The ordered pairs are: (-3, 8) and (-1, 2).
Therefore, we would have:
x | y
-3 8
-1, 2
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Evaluate (6x+3y)-z2 divided by (2x) when X = -3 , y=4 , z=-6
The evaluated expression of (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6 is 5.3
How to evaluate an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators.
Therefore, let's evaluate the expression, (6x+3y) - z² divide by 2x when x = -3, y = 4 and z = -6.
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
In other words, to evaluate the expression, we have to substitute the given value of the variable and simplify the expression.
Therefore,
(6x+3y) - z² = (6(-3)+3(4)) - (-6)² = (-18 + 12) - 36 = -32
2x = 2(-3) = -6
Hence,
- 32 / -6 = 5.3
Therefore,
(6x+3y) - z² / 2x when x = -3, y = 4 and z = -6 is 5.3
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HELP ASAP PLEASEEEEEEEEEE
A possible perimeter for the rectangular table that was built by Irene is 50 inches.
My thinking was gotten by getting the dimensions and then using the perimeter formula to solve it.
How to calculate the perimeter?From the information given, it should be noted that the area of the rectangle is given as 114 square inches. A dimension that can give this is 19 inches and 6 inches
The perimeter of a rectangle is calculated as:
= 2(Length + Width)
= 2(19 inches + 6 inches)
= 2(25 inches)
= 2 × 25
= 50 inches
The perimeter is 50 inches.
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A T-shirt company can produce and sell x T-shirts per day. The total cost C (in dollars) for producing x T-shirts is
C = 1,780 + 7x,
and the total revenue R (in dollars) is
R = 14x.
Find the profit (in dollars) obtained by selling 275 T-shirts per day.
Answer:
The profit from selling 275 shirts is 3,995
Step-by-step explanation:
P= R-C
P=14x- (1,780+7x)
since we are producing 275 shirts substitute that for x
P=14(275)-1,780+7(275)
P=3850-1780+1925
P=2070+1925
P=3995
What is the reason for each step in the solution of the equation?
18−2x=4x
Drag and drop the reasons into the boxes to correctly complete the table.
Answer:
Given
Addition property of equality
Division property of equality
Step-by-step explanation:
The first line is given.
Next 2x was added to each side. The addition property of equality says that for an equation to stay in balance, it you add something to one side of the equation, you have to add that same thing to the other side of the equation.
The same is true for the division property.
will give u brainliest
Answer:
224 in²
Step-by-step explanation:
The formula for the area of a triangle is 0.5bh, where b is the base and h is the height. Here the base is '4t' and the height is '7t'. Subbing in 4 for t, we get
Base = 4(4) = 16
Height = 7(4) = 28
Subbing this values into our formula for the area of a triangle, and we have:
Area = 0.5(16)(28) = 224 in²
The graph of a linear function passes through the points ; negative one; negative 1 over 4. and ; one, negative 3 over 4.. Y; X. Which equation represents the function? A Y equals negative one over 2 X. minus one over four. B Y equals 1 over 2 X. plus 1 over 4. C Y equals negative 1 over 4 X. minus 1 over 2. D Y equals 1 over 4 X. plus 1 over 2.
The linear equation that passes through the two given points is:
y = (-1/4)*x - 2/4
Which is the equation of the line?A general linear equation is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
m = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through (-1, -1/4) and (1, -3/4)
Then the slope is:
m = (-3/4 + 1/4)/(1 + 1)
m = (-2/4)/2 = -2/8 = -1/4
the line is:
y = (-1/4)*x + b
To find the value of v we can replace the point (1, -3/4) so we get:
-3/4 = (-1/4)*1 + b
-3/4 + 1/4 = b
-2/4 = b
The linear equation is:
y = (-1/4)*x - 2/4
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why are 0.8 and 0.80 are equivalent?
0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
In mathematics, the decimal representation of numbers allows for the use of trailing zeros after the decimal point. When a decimal number has trailing zeros, such as in the case of 0.8 and 0.80, they are considered equivalent because they represent the same value.
The trailing zeros after the decimal point do not change the numerical value of the number. The number 0.8 represents eight tenths, and adding a trailing zero to make it 0.80 does not change its value; it still represents eight tenths. The zero after the decimal point in 0.80 is simply a placeholder, indicating that there are no hundredths or smaller fractional parts.
It is common to use trailing zeros in decimal representations to indicate the precision or accuracy of a measurement. For example, if a measurement is known to be accurate to two decimal places, it is common to represent it as 0.80 rather than 0.8 to indicate the level of precision.
Therefore, mathematically speaking, 0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
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To adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.
a. Write an expression in the simplest form that represents the amount (in dollars) it costs to adopt x dogs.
An expression is (?) dollars.
Question 2
b. What does the coefficient of the expression in part (a) represent?
Responses
the total cost (in dollars) of adopting one dog
the total cost (in dollars) of adopting one dog
the total amount (in dollars) the veterinarian is paid when one dog is adopted
the total amount, (in dollars), the veterinarian is paid when one dog is adopted
the total cost (in dollars) of adopting x dogs
the total cost (i, n dollars), of adopting x dogs
the total amount (in dollars) the animal shelter earns when x dogs are adopted
the total amount (, in dollars) the animal shelter earns when , x, dogs are adopted
please and thank you!
Answer:$190
Step-by-step explanation:
for an expression is $80+$65+$50=190 per dog to adopt a from the animal shelter.
The equation: -2(x - 5) = 4x is solved in several steps below. For each step, select the reason that best justifies it.
Equations:
2x + 10 = 4x
-2x + 10 + 2x = 4x + 2x
10 = 6x
10/6 = 6x/6
5/3=x
Options:
Simplifying
Subtraction Property of Equality
Multiplication Property of Equality
Addition Property of Equality
Distributive Property
Division Property of Equality
The order of reasons that best justifies each step of the equation's solution is as follows;
-2x + 10 = 4x (Distributive property)-2x + 10 + 2x = 4x + 2x (Addition property of Equality)10 = 6x (Simplifying)10/6 = 6x/6 (Division property of Equality)5/3 = x (Simplifying).What are the reasons that justify the steps of the solution?It follows from the task content that the reasons which best justify each step of the solution be identified.
Therefore; Given the equation; -2(x - 5) = 4x; we have;
-2x + 10 = 4x (Distributive property)-2x + 10 + 2x = 4x + 2x (Addition property of Equality)10 = 6x (Simplifying)10/6 = 6x/6 (Division property of Equality)5/3 = x (Simplifying).Ultimately, the reasons which best justifies each of the steps as required are as provided above.
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Answer: Justification for each step is provided below.
Step-by-step explanation:
Original Equation: -2(x - 5) = 4x
-2x + 10 = 4x --> Distributive property - simplify the left side
-2x + 10 + 2x = 4x + 2x --> Addition property of Equality - add 2x to both sides
10 = 6x --> Simplifying
10/6 = 6x/6 --> Division Property of Equality - divide each side by 6
5/3 = x --> Simplifying
Raise the powers of all variables and numbers indicated, and then turn the following expressions in radical form into exponential expressions in rational form. You do not need to evaluate or solve any of the expressions, just put them in simplest exponential form. [All sets of similar base variables and numbers are meant to be under the same radical sign]
The radical expression [tex]\sqrt[5]{x^3}^8.x^4[/tex] simplifies to [tex]x^\frac{44}{5}[/tex].
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, [tex]\sqrt[5]{x^3}^8.x^4[/tex].
= [tex]x^3(^\frac{8}{5}).x^4[/tex].
= [tex]x^\frac{24}{5}.x^4[/tex].
= [tex]x^\frac{24}{5}^{+4}[/tex].
= [tex]x^\frac{24 + 20}{5}[/tex].
= [tex]x^\frac{44}{5}[/tex].
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Determine the interval(s) on which the function is (strictly) increasing.
Write your answer as an interval or list of intervals.
When writing a list of intervals, make sure to separate each interval with a comma and to use as few intervals as possible.
Click on "None" if applicable.
Answer:1341
Step-by-step explanation:
1342123
(ASAP Please)
Find the area of the sector. Use 3.14 for the value of pi. Round your answer to the nearest tenth.
A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.
The area of a circle is given as:
Area = πr²
The total sector of a circle is 360°
The area of the sector of 270° is 37.68 square meters.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.
The area of a circle is given as:
Area = πr²
We have,
The radius of the circle = 4 m
The total sector of a circle is 360°
The area of the sector with 270°.
= (270°/360°) x πr²
= 0.75 x πr²
= 0.75 x 3.14 x 4²
= 37.68
= 37.7 square meters
Thus,
The area of the sector of 270° is 37.68 square meters.
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Water , Tonya drinks the recommended 8 cups of water per day how many gallons of water dose she drink per year ?Hint:( 1gallon = 16 cups)
Step-by-step explanation:
your teacher gave you the solution to the real problem of this question : how many cups are in 1 gallon. 16 cups.
and if you remember that a year has 365 days, then the rest is rant simple and straight forward :
8 cups per day
so
365 × 8 = 2920 cups per year.
2920 cups = 2920/16 = 182.5 gallons
therefore, she drinks 182.5 gallons of water per year.
At 12 noon it was discovered that a driver has travelled 3/8 of the distance from Kano to lagos ,while another driver had travelled 3/10 of that distance from lagos,travelling at the same rate .if the two drivers are 390km apart .find the distance from Kano to lagos
The distance from Kano to Lagos is 1200 km
How to determine the distance from Kano to LagosThe problem involves addition of fractions
The fraction required are:
let the distance form kano to Lagos be x
it was discovered that a driver has travelled 3/8 = 3x/8
another driver had travelled 3/10 of that distance = 3x/10
The drivers are still 390 km apart
total distance, x
x = 390 + 3x/8 + 3x/10
x - 3x/8 - 3x/10 = 390
0.325x = 390
x = 390 / 0.325
x = 1200 km
From the driving distance information 1200 km is the distance from Kano to Lagos
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PLEASE SOMEONE HELP ME GIVING BRAINLIEST!!!
Answer:
23/5 > (sqrt(18)
Step-by-step explanation:
there are many ways you could go about this,
I subtracted (sqrt(18)) from (23/5) and because the answer i got was greater than 0, 23/5 must be bigger than sqrt18
Birdseed costs $0.67 a pound and sunflower seeds cost $0.97 a pound. Angela Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for $0.79 per pound. How many pounds of each type of seed should she use?
All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Birdseed that costs $0.67 a pound and sunflower seeds that cost $0.97 a pound. Angela Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for $0.79 per pound.
Assume that she used [x] pound and [y] pound of each type. We can write -
0.67x + 0.97y = 0.79 x 30
0.67x + 0.97y = 23.7
Plot the graph of this function. All the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.
Therefore, all the coordinates on the line represent the possible quantities in pounds which she can take to prepare the mixture.
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Ali had 457 pieces of clothes for her dolls. She had 235 dresses and 125 shirts. How many pairs of shoes and pants did she have?
Answer:
Step-by-step explanation:
457-235= 222
222-125=97
97÷2= 48.5
≈49 pairs of pants and shoes
Find the x- and y-intercepts of the graph of 3x−8y=39. State each answer as an integer or an improper fraction in simplest form.
The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.
Given that,
The equation is 3x-8y=39.
We have to find the x- intercept and y- intercept of the equation.
We know that,
x/a + y/b = 1 is the intercept form of the line's equation. One of the key types of line equations is this one. In this equation, the sign of the intercepts also enables us to determine where the line is in relation to the coordinate axes.
To find the x- intercept of the equation.
We have to take y as 0.
3x-8(0)=39
3x=39
x=39/3
x=13
To find the y- intercept of the equation.
We have to take x as 0.
3(0)-8y=39
-8y=39
x=-39/8
Therefore, The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.
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please answer 25 points
The number of miles (m) between the two cities as represented in the equation given 2[(4m * 3.5) / 400] = 171.5 is 2450 miles
EquationsThe definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.
In the equation given;
2[(4m * 3.5) / 400] = 171.5
Using changing the subject of formula to find the miles travelled;
2[(4m * 3.5) / 400] = 171.5
28m / 400 = 171.5
28m = 400 * 171.5
28m = 68600
m = 68600 / 28
m = 2450
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Factor 64+ 60. Write your answer in the form a(b + c) where a is the GCF of 64 and 60
write each system of equations as a matrix
Answer:
Step-by-step explanation:
Evaluate the expression X - 2 + 2(4) - X when x =12
Answer: 6
Step-by-step explanation: You'll need to substitute x for 12 in the expression, which will be 12 - 2 + 2(4) - 12, and using BODMAS/BIDMAS/PEDMAS (or whatever you use), you should get 6 if you did it correctly.
Answer:
18
Step-by-step explanation:
using bodmas rule by working out brackets first
ned)
Sam went to eat at Texas Roadhouse. His bill was $45. In addition, he left a 15% tip
for the waitress. He also needed to pay 5% sales tax. How much did Sam spend at
Texas Roadhouse?
The total amount of money Sam paid for his food, tip for the waitress and sales tax at the Texas Roadhouse is $54
What is the total amount Sam spent at Texas Roadhouse?Sam's bill at the Texas Roadhouse = $45Percentage tip for the waitress = 15%Percentage sales tax = 5%Amount of tip = 15% × $45
= 0.15 × 45
= $6.75
Amount of sales tax = 5% × $45
= 0.05 × 45
= $2.25
Total amount Sam spent at the Texas Roadhouse = Sam's bill at the Texas Roadhouse + Amount of tip for the waitress + Amount of sales tax
= $45 + $6.75 + $2.25
= $54
In conclusion, the total amount of money Sam paid at the Texas Roadhouse is $54
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A rectangle has an area of 20 square centimeters.
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A
B
1 cm and 20 cm
2 cm and 10 cm
3 cm and 8 cm
4 cm and 5 cm
Answer:
Most likely 4cm and 5cm
Step-by-step explanation:
Where 5cm=length
And 4cm=width
Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72. Which of the following are still outstanding?
I. A $44.09 check to the electronics store
II. A $73.98 check to the mechanic
III. A $49.96 paycheck deposit
IV. A $64.79 check deposit from Brett’s cousin
a.
I and III
b.
II and III
c.
I and IV
d.
II and IV
3. Analyze and Persevere The height of
an experimental plant after x days can be
represented by the formula 3(4x + 2) The
height of a second plant can be represented
by the formula 6(2x + 2). Is it possible that
the two plants will ever be the same height?
Explain.
their pr
Р
$1
Two plants will never be of the same height.
Given, the height of an experimental plant after x days can be
represented by the formula 3(4x + 2).
The height of a second plant can be represented by the formula 6(2x + 2).
We have to state that will the two plants ever be of the same height,
Let assume that, the height of two plants be same,
So, 3(4x + 2) = 6(2x + 12)
On simplifying, we get
12x + 6 = 12x + 72
On subtracting 12x from both the sides, we get
12x + 6 - 12x = 12x + 72 - 12x
6 ≠ 72
It is an absurd condition, so we do not have any solution for x.
So, the two plants will never be of the same height.
Hence, two plants will never be of the same height.
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I need answer please
Answer:
The rate of change is -2
Step-by-step explanation:
formula we will use: G(x)= [tex]\frac{f(b)-f(a)}{b-a}[/tex] [-1,2]
g(x)= [tex]x^3[/tex]-5x
g(-1)=[tex]-1^3[/tex]-5(-1)
g(-1)=-1+5
g(-1)=4
g(2)=[tex]2^3[/tex]-5(2)
g(2)=8-10
g(2)=-2
so g(x)= [tex]\frac{(-2)-(4)}{(2)-(-1)}[/tex]
g(x)= [tex]\frac{-6}{3}[/tex]
g(x)=-2
Tobias bought four video games for $34.10, $25.50, $13.25, and $9.99.
How much money did Tobias spend?
Pat randomly chooses marbles from an urn without replacement. The urn originally contained 55 red marbles, 30 white marbles, and 15 blue marbles. What is the probability that Pat’s second pick will be a blue marble given that the first pick was a red marble?
The probability that Pat’s second pick will be a blue marble is the fracion 5/3 considering choosing marbles without replacement.
Probability of an event without replacementProbability of an event without replacement simply means once an item is drawn, then we do not replace it back to the sample space before drawing a second item.
For the fact that a red marble was first drawn without replacement with the probability of 55/100, given that there are 55 red marbles and a total of 100 marbles in the Urn.
Hence, there will be 99 samples left for the second draw to be made.
The probability that the second pick will be a blue marble = 15/99.
Therefore, the probability that the second pick is a blue marble after the first pick without replacement is the fraction 5/33 reduced to its lowest term from 15/99.
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