The radius of the Sphere that submerged in the water is 178.9 mm.
Volume of the Cuboid:
Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space.
The general form of the Volume of the Cuboid is,
Volume of a cuboid = l × b × h [cubic units]
Where,
l = length
b = breadth
h = height
Given,
A water tank is a cuboid 45cm long, 30cm wide and 26cm high.
It contains water to a depth of 21cm.
A sphere is placed in the tank and is fully submerged. the water level rises by 1.8cm.
Here we need to find the radius of the Sphere and we have to use the Volume of the sphere as 4/3πr³.
First, we need to find the volume of the water,
For that, we have to take the measurement of it.
l = 45 cm
b = 30 cm
h = 21 cm
( here we have to find the volume of water, so we have take the water depth as its height)
Now, the volume of the water is,
V₁ = 45 x 30 x 21
V₁ = 28350 cm³
After placed the sphere on the tank the water level is increased as 1.8 cm,
So, the new height = 21 + 1.8 = 22.8
Now the new volume is,
V₂ = 45 x 30 x 22.8
V₂ = 30780 cm³
So, the Volume of the increased water level is,
=> 30780 - 28350
=> 2430 cm³
Now we have to consider this as the Volume of the Sphere and calculate the radius through it,
=> 4/3πr³ = 2430
=> r³ = 2430 x 3/4 x π
we know that the value of π = 22/7
So,
=> r³ = 2430 x 3/4 x 22/7
=> r³ = 5727.86
=> r = ∛5727.86
=> r = 17.89
Therefore, the radius of the sphere is 17.89 cm
Now we have to convert it into mm,
=> 1 cm = 10 mm
So,
=> 17.89 cm = 178.9 mm
Therefore, the radius of the sphere is 178.9 mm.
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Is the statement the solution set of a linear system involving variables is a list of numbers that makes each equation in the system a true statement when the values are substituted for respectively true or false? explain.
False, because The singles answer fits the description. All potential solutions are included in the solution set.
There might not be a solution to a set of linear equations that makes sense. False. There is at least one answer for a consistent system.What makes up a linear system's solution set?
The answer to a system of equations is a set of values for a variable that concurrently satisfy each equation. Finding every feasible combination of the variable values that make up the system's solutions is necessary to solve an equation system.Is it true that a linear system's existence and uniqueness are two key issues? False or true?
In a linear system, existence and uniqueness are crucial considerations. Both conceptually and practically, it is frequently essential to know whether a system has a solution (exists) and, if it does, whether this solution is the only one available (uniqueness).Learn more about linear system.
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Explain what is meant by confounding. what is a lurking variable? what is a confounding variable?
Explain what is meant by confounding. what is a lurking variable? what is a confounding variable?
Answer:
A Confounding is the variable that is considered in a research study, and could overall influence the relations between the variables in the study. For example, students wanting to join AP English next semester were told to write a six page essay. When the students turned in their papers and teachers say the difference and grades they believed that the variable was the time that the students handed in the paper. They thought that if the student handed in their paper later than another student that they would receive a lower score, but this was not the case. When asking the students how they prepared for the paper, students replied with different answers. Those who outlined and used other literature for reference scored much higher than those who only used prior knowledge to write their essays. In this study, the lurking variable would be the presence of an outline.
Lurking variable: A variable that is not considered in a research study that could influence the relations between the variables in the study
Confounding variable: A variable that is considered in a research study that could influence the relations between the variables in the study
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You invested a total of $50,000 in 2 funds earning 6.5% and 9% simple interest. during 1 year, the 2 funds earned a total of $3625 in interest. how much did you invest in each fund? amount at 6.5%
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The person has invested $35,000 in the fund returning at a rate of 6.5%.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT = (R% of P)T
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
Let the amount invested in the first fund be represented by x, then the amount invested in the second fund will be ($50,000 - x).
Now, if the 2 funds earn 6.5% and 9% simple interest. Also, in the first year, they earned a total of $3625 from the interest. Therefore, we can write the equation to represent the given situation as,
6.5% of x + 9% of ($50,000 - x) = $3625
0.065x + 0.09(50,000 - x) = 3625
0.065x + 4,500 - 0.09x = 3,625
0.065x - 0.09x = 3625 - 4500
0.025 = 875
x = 875/0.025
x = 35,000
Therefore, the person has invested $35,000 in the fund returning at a rate of 6.5%.
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James has a square garden with sides of length 8feet. he plans to enlarge it to a rectangle by increasing the length by 4 feet and the width by 1 feet. how many square feet in area will be added to the garden?
The area in square feet that will be added to the garden is 44 square feet.
Length of square garden = 8 feet
Area of Square garden = [tex](side)^{2}[/tex] = [tex](8)^{2}[/tex] = 64 square feet
On enlarging the square to a rectangle, length rectangular garden is (8+4)feet i.e.,12feet and width of rectangular garden is (8+1)feet i.e.,9feet.
Area of rectangular garden = (length × width)
= (12 × 9) square feet
= 108 square feet
The area in square feet that will be added to the garden = (Area of rectangular garden - Area of Square garden)
= (108 square feet - 64 square feet)
= 44 square feet
The area in square feet that will be added to the garden is 44 square feet.
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The function h is defined by the following rule
h(x)=-5x+5
Complete the function table down below
Will give brainliest
answer:
3/4
explanation:
the side lengths of preimage abcd are all four units, whereas image abcd's lengths are all three. from this, we can surmise the scale factor is 3/4.
how to calculate scale factor:
scale factor = dimension of the new shape ÷ dimension of the original shape
please help i’m literally so stressed out
Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $209.67.
•He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.
•He plans to spend some or all of the money he has left to buy new biking outfits
for $37.16 each.
Which inequality can be used to determine x, the maximum number of outfits Luis
can purchase while staying within his budget?
The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
How to solve inequality?Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
He buys a new bicycle for $209.67.He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.He plans to spend some or all of the money he has left to buy new biking outfits for $37.16 each.Therefore,
x = maximum number of outfits Luis can purchase while staying within his budget.
Hence, the inequality that can be used to represent the situation is as follows;
209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420
235.44 + 12.08 + 37.16x ≤ 420
247.52 + 37.16x ≤ 420
37.16x ≤ 420 - 247.52
37.16x ≤ 172.48
divide both sides by 37.16
x ≤ 4.64155005382
x ≤ 4
Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
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For the function g defined above, a is a constant and g(4)=8. What is the value of g(-4)?
The value of g(-4) is 8.
A set of inputs and outputs that are connected to one another in some way is referred to as a relation. We refer to the relations as a function when each input results in a single output. However, you must be certain that no input leads to more than one output in order to determine if a relation is a function or not.
Only when each element of a nonempty set M has a single range to a nonempty set N is a function a relation.
g(x) = ax^2 + 24
⇒ g(4) = a (4)^2 + 24
⇒ 8 = 16a + 24
⇒ 8 − 24 = 16a
⇒ −16 = 16a
⇒ a = −1
Since, g(−4) = a(−4) ^2 + 24
∴ g(−4) = 16(−1) + 24
⇒ g(−4) = 8
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find the measure of angle B.
Answer:
m <B = 41°
Step-by-step explanation:
Fact: complementary angles measures add to 90 degrees
Given: m < A = 2x-19, and m <B = x+7
Find: m <B = ?
Find x
2x-19 + x+7 = 90
2x+x = 90 +19-7
3x = 102
x = 34
Find m <B
m <B = x+7
m <B = 34+7
m <B = 41
Show ([tex]\frac{\sqrt{11} }{6} ,[/tex][tex]\frac{5}{6}[/tex]) is or is not on the unit circle. State the unit circle definitions and definitions in terms of other trig functions.
By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.
Is a given point on Cartesian plane lying on the unit circle?
We find a point in rectangular form, that is, a point of the form (x, y). Unit circles are circles with a radius 1 that are commonly used to represent graphically angles. The given point is in the units if and only if its norm is equal to 1. The norm of the point is determined by using the Pythagorean theorem:
r = √[(√11 / 6)² + (5 / 6)²]
r = √[(11 / 36) + (25 / 36)]
r = √(36 / 36)
r = √1
r = 1
By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.
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If you want to use the sin function in the math library, as x = math.sin(3.14), how should you write the import statement?
We use import math when we want to use the sin function in the math library, x= math. sin(3.14).
Similar to #include header_file in C/C++, that how to import function in python. The import statement brings in code from one module into another program, where modules are files that contain python code, and modules are used to group related code in a program, instead of rewriting the code again, you can reuse the same code in different files. To import code from a module a parameter is to be followed import module name ( where the import word is the keyword and the module name is the module you want to import ).
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HELP me ill give brainlist or whatever its called
Answer:
1 cm
Step-by-step explanation:
you multiply 3 by 1/3 and you get 3/3 which is 1
2y-4+5y=4-3y+5
How to solve this?
Answer:
You would first move all of the y numbers to one side so it should look like this: 2y-4+5y+3y=4+5. Then you would all the numbers that don't have y at the end to the other side: 2y+5y+3y=4+5+4.
Then you would add them all up: 10y=13
So your answer is 10y=13
Step-by-step explanation:
Luis has 1/2 quart of grape juice. he pours the same amount into each of 5 glasses. which equation represents the fraction of a quart of grape juice n that is in each glass?ll
The equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
Luis has 1/2 quart of grape juice. he pours the same amount into each of 5 glasses. which equation represents the fraction of a quart of grape juice n that is in each glass?
n = (1/2)(1/5)
n = (1/2)(5/1)
n = (1/2)(5)
n = (1/2)
From the data given in the question:
Let n be the fraction of a quart of grape juice n that is in each glass:
n = (1/2)(1/5)
Thus, the equation n = (1/2)(1/5) represents the fraction of a quart of grape juice n that is in each glass option (A) is correct.
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Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?.
πr2 is an example of (D) a model.
What is a model?A mathematical model is a system description that employs math ideas and language. Mathematical modeling is the process of creating a mathematical model. Mathematical models are used in the natural sciences (physics, biology, earth science, chemistry), engineering disciplines (computer science, electrical engineering), and non-physical structures such as the social sciences (such as economics, psychology, sociology, political science). A large part of the field of operations research is the use of statistical equations to solve problems in business or military operations. Music, linguistics, and philosophy all use mathematical models (for example, intensively in analytic philosophy). A model is, for example, the method for the area of a circle, πr2.Therefore, πr2 is an example of (D) a model.
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The complete question is given below:
Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?
A. a robot
B. a car
C. a telescope
D. a model
WILL GIVE THE BRAINLIEST
A graph of a quadratic function is shown. Use the graph for questions 1 through 4.
1. Use the graph to determine the value of for the function.
2. Write the equation of the parabola in vertex form.
3. Convert the vertex form of the parabola to standard form.
4. Use standard form of the parabola to identify the y-intercept of the function.
5. The factored form of a quadratic function is represented by () = 2(―4)(―6).
Write the equation in standard form.
For questions 6 through 9, a graph and table of values for () are shown.
6. Use the table or the graph to determine the value of for the function.
7. Write the equation in vertex form.
8. Write the equation in factored form.
9. Write the equation in standard form.
10. The function () is represented by () = 2(+ 3)^2 +4. Rewrite the function in
standard form.
The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 3.9 and 6.1
How to write the equation of the parabola in vertex formThe vertex v is at v ( 5, -4 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 5 )^2 + {-4)
substituting point ( 4, -1 ) from the graph we have:
-1 = a ( 4 - 5 )^2 - 4
-1 = a - 4
a = 3
substituting the known values to y = a ( x- h ) + k
y = 3 ( x - 5 )^2 - 4
How to write the equation of the parabola in factored formy = 3 ( x - 5) ( x - 5 ) - 4
How to write the equation of the parabola in standard formy = 3 ( x - 5) ( x - 5 ) - 4
y = 3 ( x^2 - 10x + 25 ) - 4
y = 3x^2 - 30x + 75 - 4
y = 3x^2 - 30x + 71
Graph BHow to find the roots of the the function
The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 2 and 4
How to write the equation of the parabola in vertex form
The vertex v is at v ( 3, 2 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 3 )^2 + 2
substituting point ( 0, -16 ) from the graph we have:
-16 = a ( 0 - 3 )^2 + 2
-16 = a - 9 + 2
-16 = a - 7
a = -9
substituting the known values to y = a ( x- h ) + k
y = -9 ( x - 3 )^2 + 2
How to write the equation of the parabola in factored formy = -9 ( x - 3) ( x - 3 ) + 2
How to write the equation of the parabola in standard formy = -9 ( x - 3) ( x - 3 ) + 2
y = -9 ( x^2 - 6x + 9 ) - 4
y = 3x^2 - 54x - 81 - 4
y = 3x^2 - 54x - 85
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3. Solve the formula v + f -e = 2 for e
O Ae-v-f-2
O BC v+f-2
O ce-v-f+2
O De-u+f+2
Answer:
B is the correct answer.
Step-by-step explanation:
Add -2+e to both sides
v + f − e -2+e = 2 -2+e
Which will give you v + f -2 = e.
Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?.
πr² an example of a model.
What are mathematical models?A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Here, the area of a circle is calculated by the use of formula πr² where π is a constant 3.14 and r is a variable. Therefore this formula is used to find the area.
Thus, πr² an example of a model.
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I need help on this one question, anyone know the answer?
PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING
Answer:
12/15
Step-by-step explanation:
What is the side length of a square with an area of 121 square centimeters?
In centimeters
The answer to this question is:
Size of a square's side = 11 cm
A Square is a flat geometric shape with four right angles and equal sides. The square's four sides are equal to one another or congruent. The square's opposing sides run parallel to one another. The square's diagonals form a 90° angle with one another. The two diagonals of the square are equivalent to one another. The square is made up of four vertices and four sides.
Area of square = ( Side )²
Given that:
Area of square = ( Side )² = 121 cm²
Dimensions of a square's side = √ Area
so, the length of the square's side = √ 121
= √ 11*11
= √ ( 11 )²
= 11
Thus, side of the square = 11 cm
Therefore, side length of square = 11cm
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b) The angle of elevation of a tower at a distance of 27 meter from the foot of the tower is 60°, find the height of the tower. Speedy Additional Mathematics - Book VIII 98
The height of the tower is approximately 46.765 feet
Step-by-step explanation:
The given parameters are;
The distance from the foot of the tower where the angle of elevation is
measured = 27 feet
The angle of elevation to the top of the tower from a point 27 feet from the foot of the tower, θ = 60°
Therefore, by trigonometric ratio, we have;
tan 60= the height of tower / distance from foot of tower
[tex]\sqrt{3}[/tex]= height of tower /27
1.73205 *27 = height of tower
46.765 feet is the height of tower
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A scale that allows us to rank individuals or objects, but not to say anything about the meaning of the differences between the ranks, is a(n)?
A scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.
What is an ordinal scale?An ordinal scale is one that allows us to rank individuals or objects without saying anything about the significance of the differences between the ranks. The ordinal scale is the second level of measurement that reports data ranking and ordering without determining the degree of variation between them. Cases in the same class are regarded as equivalent. Movie ratings, political affiliation, military rank, and other variables that use ordinal scales are examples."Movie ratings" is an example of an ordinal scale. Students in a class, for example, could rate a movie using the scale below.Therefore, a scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.
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a line with a slope equal to -2/3 passes through (-1, -4) and (3,y) what’s the value of y
Answer:
-20/3
Step-by-step explanation:
Using point-slope form, the equation is
[tex]y+4=-\frac{2}{3}(x+1) [/tex]
Substituting x=3,
[tex]y+4=-\frac{2}{3}(3+1) \\ \\ y+4=-\frac{8}{3} \\ \\ y=-\frac{20}{3}[/tex]
What is the converse of the following statement?
"If cows make milk, then chickens make eggs. "
Answer:
"If chickens make eggs, then cows make milk."
Step-by-step explanation:
Answer: A: If chickens make eggs, then cows make milk.
Step-by-step explanation: Hope that helped
solve 2x-9y=14 for y
The value of y in expression is 14-2x/-9
How to calculate the value of y ?The expression is written as
2x - 9y = 14
We are asked to calculate the value of y in the expression
2x - 9y = 14
-9y= 14-2x
Divide by the coefficient of y which is -9
y= 14-2x/-9
Hence the value of y is 14-2x/-9
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pls help find interval notation
Step-by-step explanation:
-2x - 7 > 1
-2x > 8
-x > 4
x < -4
that is a continuous line from -4 all the way to the left, and the dot on -4 is empty (meaning : it is not included due to the "<" symbol).
x - 2 >= -1
x >= 1
that is a continuous line from +1 all the way to the right, and the dot on +1 is filled (meaning : is IS included due to the ">=" symbol.
i’m confused please help
L is the midpoint of JM. K is the midpoint
of JL. JL = 1. What is the length of KM?
Answer:
KM = 1.5
Step-by-step explanation:
The first piece of info we get is that L is the midpoint of JM. This means that L = JM/2. The second piece of information provided is that K is the midpoint of JL, which means K = JL/2. We know that JL = 1, so we can plug it into the equation to help us figure out the problem. You can also illustrate to solve this problem, as I do here.
Since JL = 1...
K = 1/2, K = 0.5
________________________________________________
J K(0.5) L M
___________ __________
0.5 0.5
Now with this information, we know that 0.5 represents the distance of 1/4 of JM. We know that KM is 3/4 of the number line, and we know that 1/4 of the line is 0.5. We multiply 0.5 * 3 to get our final answer.
FINAL ANSWER: KM = 1.5
8. Olivia's brother is twice her age
minus 9 years. He is also as old
as half the sum of the ages of
Olivia and both of her 12 year-
old twin brothers. Write and
solve an equation to find the
ages of Olivia and her brother.
The ages of Olivia and her brother are 10 years and 11 years respectively
Let x₁, and x₂ be the ages of Olivia and her brother respectively.
Given that Olivia's brother is twice her age minus 9 years.
⇒ x₂ = 2x₁ - 9 → equation 1
Also given that Olivia's brother is as old as half the sum of the ages of Olivia and both of her 12-year-old twin brothers.
⇒ x₂ = 1/2 × (x₁ + 12) → equation 2
Using equation 1 in equation 2, we get
2x₁ - 9 = 1/2 × (x₁ + 12)
⇒ 4x₁ - 18 = x₁ + 12 (multiplying by 2 on both sides)
⇒ 4x₁ - x₁ = 12 + 18
⇒ 3x₁ = 30
⇒ x₁ = 10 (dividing by 3 on both sides)
Using the value of x₁, in equation 1,
⇒ x₂ = 2(10) - 9
⇒ x₂ = 20 - 9
⇒ x₂ = 11
Therefore the ages of Olivia and her brother are 10 years and 11 years respectively.
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