If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ .
The volume of the cube with side length "a" can be calculated using the formula
Volume = a³ ,
For Example : if the side length of the cube is 2m , then the volume of the cube will be
Volume = 2³ = 8m³ .
In the question ,
it is given that ,
the side length of the cube is x⁻² inches ,
So, substituting the value of side length in the Volume formula , we get
volume = (x⁻²)³
= x⁻⁶ ....(as (xᵃ)ᵇ = (x)ᵃˣᵇ = xᵃᵇ )
Therefore , If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ inches³ .
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A house purchased for $265,100 gains 2% of its value every year. If this growth rate continues, in how many years will the house be worth twice its original value
The price of the house will double the original value in 35 years
How to determine the number of years?The given parameters from the question are
Initial value of the house = $265,100
Rate of gain = 2% of its value every year
An exponential function is represented as
y = a *(1 + r)^x
Where
y represents the current valuea represents the initial valuer represents the growth or decay ratex represents the number of years, in this caseThis means that
a = 265,100
r = 2%
So, we have
y = 265,100 *(1 +2%)^t
When the price doubles, we have
2 * 265,100 = 265,100 *(1 +2%)^t
Divide both sides by 265,100
So, we have
2 = (1 +2%)^t
Evaluate the sum
So, we have
2 = 1.02^t
Take the logarithm of both sides
t * log(1.02) = log(2)
Divide
t = log(2)/log(1.02)
Evaluate
t = 35
Hence, the number of years is 35
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The diameter of the bicycle wheels is 22 inches what is the radius of the bicycle wheels what is the circumference of the bicycle wheels what is the area of the bicycle wheels
The radius, area, and circumference of the given bicycle wheels are:
Radius = 11 inCircumference = 69.14 inArea = 380.29 inWhat are the area and circumference of a circle?The circle is a two-dimensional rounded figure in which all the points on the boundary of the circle maintain a fixed distance from a definite point called the center of the circle and the fixed distance is called the radius of the circle.The area of the circle is the total space taken by the circle.If r is the radius of the circle, the area of the circle is calculated by the formula:Area = πr²The circumference of the circle is the length of the boundary of the circle.If r is the radius of the circle, the circumference of the circle is calculated by the formula:Circumference = 2πrSo, the Diameter of the bicycle wheel = is 22 inches
Radius of bicycle wheel = 22/2 = 11 inchesCircumference of a bicycle wheel:
2πr2 × 22/7 × 11184/769.14 inArea of bicycle wheel = πr²
22/7 × 11 × 112662/7380.29 inTherefore, the radius, area, and circumference of the given bicycle wheels are:
Radius = 11 inCircumference = 69.14 inArea = 380.29 inTo learn more about the area and circumference of the circle, refer to the link:
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HELP THIS IS DUE SOON!
The maximum height the ball reaches is 80 feet
The ball stayed in the air for 1 second
What is a function?A function can be defined as a law, rule or expression that shows the relationship between two known variables:
The dependent variableThe independent variableGiven the function:
h(t) = -16t² + 96
Where;
h is the maximum height measured in feett is the time in secondsTo determine the maximum height in feet that the ball reached, we have to substitute the value of t as
We have:
h(1) = -16(1)² + 96
expand the bracket
h = -16 + 96
Add the values
h = 80 feet
The time it took the ball to stay in the air would be 1 second, this is so because the ball reached it maximum height as t = 1 sec
Hence, the maximum height is 80 feet
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What does standard deviation measure in a probability distribution?
Answer:
omg what is standard deviation that was on my psat today
Please help I’ll mark you as brainliest if correct!!
Answer:
y (y + x)
Step-by-step explanation:
Simplify the following:
y^2 + x y
Factor y out of y^2 + x y:
Answer: y (y + x)
Amber sold 23.4 pounds of chocolate. She sells the chocolate for $4.76 per pound. How much money did she collect?
Use the table below to determine whether f(x) could represent a linear function. If it could, write f(x) in the form f(x)=mx + b
Answer:
Step-by-step explanation:
1)
f(x) = m*x + b
x = 0
5 =m*0 + b
b = 5
2)
2 = m*2 + 5
2*m = - 3
m = - 3/2
3)
f(x) = - 3/2*x + 5
The water level in a lake was 22 inches below normal at the beginning of March. The water level decreased by 3 1/6 inches in March and increased by 1 6/7 inches in April. What was the water level compared to normal at the end of April? Enter your answer as a mixed number.
The water level compared to normal at the end of April is 23 13/42 inches below normal.
How to calculate the fraction?From the information, the water level in a lake was 22 inches below normal at the beginning of March and rhe water level decreased by 3 1/6 inches in March and increased by 1 6/7 inches in April.
The water level compared to normal at the end of April will be:
= -22 - 3 1/6 + 1 6/7
= - 22 - 3 7/42 + 1 36/42
= -22 - 1 13/42
= -23 13/42
There, it is 23 13/42 below normal.
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or
Jacob and Diego are racing to see who can get his community service hours for scouting completed first. Jacob, who has already completed 50 hours, plans to volunteer for 5 hours per week going forward. Diego hasn't started yet, but plans to dedicate 6 hours per week to his volunteer project from now on. Before too long, the boys will be tied, with the same number of volunteer hours. How long will that take?
Using system of equation, the solution shows that it will take 50 weeks before Jacob and Diego will be tied in the race to complete community service hours for scouting.
As given,
let us assign the unknown quantity (number of weeks) a variable x.
Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.
Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.
For Jacob and Diego to tie in the race, their volunteer hours should be equal.
Solution of the system of equation is given by:
6x = 5x+50
=> 6x-5x = 50
=> x = 50
Therefore, using system of equation, the solution shows that it will take 50 weeks before Jacob and Diego will be tied in the race to complete community service hours for scouting.
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plelaleasldle help aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
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Which fraction is not equivalent to 12/20 6/10 3/5 24/40 2/3
A fraction which is not equivalent to 12/20 is: D. 2/3
What is a fraction?A fraction simply refers to a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
The parts of a fraction.In Mathematics, a fraction comprises two (2) main parts and these include the following:
DenominatorNumeratorNext, we would evaluate the given fractions as follows:
Dividing the fraction by 2, we have:
12/20 = 6/10
Dividing the fraction by 3, we have:
12/20 = 4/5
Dividing the fraction by 4, we have:
12/20 = 3/5
Multiplying the fraction by 2, we have:
12/20 = 24/40
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Can someone help me understand this question please and thank you
The value of x for the given parallel line d || e is x = 20.
What is defined by the term linear pair?Linear pairs of angles are generated when two lines intersect at a single point. If the angles formed are adjacent to one another after the two lines intersect, the angles are referred to as linear. When two angles form a linear pair, their measures add up to 180°. As a result, a linear pair of angles everytime sum to 180°.From the given question;
The lines d || e.
Thus, both sum of both angles will be 180 by linear pair.
2x - 3 + 7x + 3 = 180
Solving;
9x = 180
x = 20
Thus, the value of x obtained for the given parallel lines is 20.
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Translate the phrase into an algebraic expression the sum of b and 9
It should be noted that translating the phrase into an algebraic expression the sum of b and 9 will be b + 9.
What is an algebraic expression?It should be noted that an algebraic expression in mathematics simply refers to the expression which is made up of constants and variables.
From the information given, we want to translate the sum of b and 9 into an expression. This will be:
= b + 9
Therefore, the expression is b + 9.
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Isaac's parents borrow $3600.00 from the bank for new appliances for their kitchen. The simple interest rate is 9% per year. How much interest will they have to pay if it takes them 4 years and 3 months to repay the loan?
The interest that they will they have to pay if it takes them 4 years and 3 months to repay the loan is $1377.
How to illustrate the information?From the information, Isaac's parents borrow $3600.00 from the bank for new appliances for their kitchen and the simple interest rate is 9% per year.
Principal = $3600
Rate = 9%
Time = 4 years 3 months = 4.25
It should be noted that simple interest is calculated as:
= Principal × Rate × Time / 100
= (3600 × 9 × 4.25) / 100
= 137700 / 100
= $1377
Therefore, the interest is $1377.
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The graph shows the temperature of a liquid that is being heated during an experiment. Three of the statements are true. Which is NOT?
The statement that is not true is that at this rate, it would take less than 10 mins for the temperature of the liquid to rise to 52 degrees.
Which statement is not true?We know that in a graph we see the presentation of a data set by the use of the Cartesian coordinates. There is the vertical axis and there is the horizontal axis. The vertical axis is the axis where we have to plot the time while the vertical axis is the axis where we have to plot the temperature as we can see from the image attached to this answer.
The graph as show has to the points which are; (0, 0) and (6.5, 26). Thus we can use the both points to obtain the slope of the graph and this would give us;
m = 26 - 0/ 6.5 - 0
m = 4
This implies that the rate at which the temperature rise with time is 4 degrees centigrade per hour. In a quarter hour, the temperature would rise to;
y = mx
y = 4(15)
y = 60 degrees centigrade.
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The tutorial doesn't say anything about this and I need help. What is the slope and how do you find it
Answer:
i cannot see the lines very well, but i can tell you how to find slope
Step-by-step explanation:
slope is rise/run. find where the line hits a intersection on the graph, and count the squares across the graph where it hits another intersection. it should not be on the line though, because that is only the run. then count how many squares up it takes till you touch where the line hits another intersection. that is the rise. then divide the rise by the run.
Without looking Elna chooses a colored marble from a mixed bag of marbles writes down the color and returns it to the bag then she draws another Marble without looking are these 2 events dependent or independent
The 2 events are independent because the outcome of the first draw doesn't affect the outcome of the second.
ANSWER
independent
Question
Find the equation of the line with slope m = - 1/3 and passing through the point (1, 1/3)
(Write the equation in standard form.)
answer has to be in the form ax+by=c
The equation of the line is x + 3y = 2
What are linear equations?Linear equations are equations that have constant average rates of change.
How to determine the equation of the line?The given parameters are
Slope, m = -1/3
Points (x, y) = (1, 1/3)
A linear equation is represented as
y = slope * (x - x₁) + y₁
Where
(x₁, y₁) = (1, 1/3)
Substitute (x₁, y₁) = (1, 1/3) and Slope, m = -1/3 in the equation y = slope * (x - x₁) + y₁
So, we have
y = -1/3* (x - 1) + 1/3
Multiply through by 4
So, we have
3y = -(x - 1) + 1
Remove the brackets
3y = -x + 1 + 1
So, we have
x + 3y = 2
Hence. the linear equation is x + 3y = 2
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GHJ PQR and PQR – STU. Complete the following using a side or angle of STU
(a)
The angle R of triangle PQR is congruent to the angle U of triangle STU. So
[tex]\angle R\cong\angle U[/tex](b)
The angle H of triangle GHJ is congruent to angle Q of triangle PQR and angle Q of triangle PQR is congruent to angle T of triangle STU, which means
[tex]\begin{gathered} \angle H\cong\angle Q \\ \angle Q\cong\angle T \end{gathered}[/tex]So,
[tex]\angle H\cong\angle T[/tex](c)
The side QR of triangle PQR is congruent to the side TU of triangle STU. So
[tex]QR\cong TU[/tex]
(d)
The side JG of triangle GHj is congruent to side RP of triangle PQR and side RP of triangle PQR is congruent to side US of triangle STU. So
[tex]JG\cong US[/tex]the total cost of renting a car is $35 for each day the car is rented plus 42.5 cents for each mile the car is driven what is the total cost of renting the car for 6 days and driving 350 miles
The total cost of renting the car for 6 days and driving 350 miles is $358.75 .
What is renting car?
An organisation known as a car rental, hire car, or car hire agency lends out cars to the general public for brief periods of time, typically from a few hours to a few weeks. Usually situated close to airports or busy city centres, it is frequently structured with a number of local branches that let customers return vehicles to multiple locations. A website that allows online reservations is sometimes added on top of this.
Car rental businesses generally cater to customers who need a short-term vehicle, such as those who don't own their own car, tourists who are out of town, or owners of damaged or totaled vehicles who are awaiting repairs or insurance settlement.
The cost of renting the car is $35 for each day .
And for each mile the car is driven we have to pay 42.5 cents .
Therefore 6 days the rent is = $35 x 6
= $210
And for 350 miles we have to pay = 350 x 42.5 cents
= 14875 cents = $148.75
In total $ 358.75
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Tanisha earns $4,000 per month
after taxes. She saves $730. What
percent of her budget is savings?
Answer:
18.25%
Step-by-step explanation:
730/4000 = 0.1825
Plot (−3 1/2, −1 1/4) on the coordinate plane.
The plot of the points on a coordinate plane is added as an attachment
How to plot the point on a coordinate plane?The coordinate of the point on a coordinate plane is given as
Point = (-3 1/2, -1 1/4)
As a general rule, we express the above coordinate as follows:
(x, y) = (-3 1/2, -1 1/4)
The next step is to remove the bracket
So, we have the coordinates into x and y coordinates
This is represented as
x = -3 1/2 and y = -1 1/4
The interpretation of the above equations is:
(-3 1/2, -1 1/4) is at a point that is 3 1/2 points to the left of the origin (-3 1/2, -1 1/4) is at a point that 1 1/4 points below the originNext, we plot the points
See attachment for the plot of the points on a coordinate plane
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what are the names of these polygons ?
Answer:
Types of Polygons
3 sides - Triangle.
4 sides - Quadrilateral.
5 sides - Pentagon.
6 sides - Hexagon.
7 sides - Heptagon.
8 sides - Octagon.
9 sides - Nonagon.
10 sides - Decagon.
a group of students asked Pythagoras how many students were in his class. "One half study mathematics, one quarter study natural philosophy, one seventh observe silence and there are three others", How many students did he have?
the total number of students in class is given by the equation x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3 and is equal to 28.
Let the total number of students be x
Mathematics = 1 / 2 x
natural philosophy = 1 / 4 x
Silence = 1 / 7 x
Remaining = 3
So, we get the equation as:
x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3
(28 x - 14 x - 7 x - 4 x) / 28 = 3
3 x / 28
x = (3 × 28) / 3
x = 28
Number of students in class = 28.
Therefore, the total number of students in class is given by the equation x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3 and is equal to 28.
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Can someone help me with this
Answer:
650,000÷10^3 = 650
40,000÷10^4 = 4
7,000÷10^2=70
Step-by-step explanation:
(Look at picture) 8th grade pre-algebra math question, super easy!
The true statements about the solutions to this number line include the following:
A. -1 is a solution.
E. -1.5 is a solution.
F. All negative numbers are solutions.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to determine the difference between two numbers such as 23 and 12. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
In conclusion, we can reasonably infer and logically deduce that an inequality which represent the solutions to this number line in interval notation is given by: -1 ≤ x ≤ ∞.
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This right rectangular prism is filled with 1/3
foot unit cubes.
N
a. What are the actual dimensions of the prism?
b. How many unit cubes are in this prism?
C What is the total volume of the prism, in cubic feet?
UPLOAD
The most appropriate choice for right rectangular prism will be given by
a) Dimension of the prism = [tex]\frac{4}{3}[/tex] ft [tex]\times[/tex] [tex]1[/tex] ft [tex]\times[/tex] 1 ft
b) There are 36 unit cubes
c) Volume of prism = [tex]\frac{4}{3}[/tex] [tex]ft^3[/tex]
What is a right rectangular prism?
A geometrical figure which has 6 faces, 12 edges and 8 vertices is called a right rectangular prism.
If l is the length, b is the breadth and h is the height of right rectangular prism, volume will be l [tex]\times[/tex] b [tex]\times[/tex] h .
a) The right rectangular prism is filled with [tex]\frac{1}{3}[/tex] ft of unit cubes
Length of right circular prism = [tex]4 \times \frac{1}{3} = \frac{4}{3}[/tex] ft
Breadth of right circular prism = [tex]3 \times \frac{1}{3} = 1[/tex] ft
Height of right circular prism = [tex]3 \times \frac{1}{3} = 1[/tex] ft
Dimension of the prism = [tex]\frac{4}{3}[/tex] ft [tex]\times[/tex] [tex]1[/tex] ft [tex]\times[/tex] 1 ft
b) Number of unit cubes = [tex]4 \times 3 \times 3[/tex]
= 36 ft
c) Total volume = [tex]\frac{4}{3} \times 1 \times 1[/tex]
= [tex]\frac{4}{3}[/tex] [tex]ft^3[/tex]
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Complete Question
The diagram has been attached here
Please help. When forming a marching band the leader wants the number so the greatest number of arrangements can be made. She has to choose between 18 and up to 42 members. Which number will produce the greatest number of rectangular arrangements?
The number that will produce the greatest number of rectangular arrangements is 6.
How to illustrate the information?From the information, when forming a marching band the leader wants the number so the greatest number of arrangements can be made and she has to choose between 18 and up to 42 members.
It should be noted that the question simony relate to the highest common factor of the values that are given. This will be illustrated as:
18 = 1, 2, 3, 6, 9 and 18
42 = 1, 2, 3, 6, 7, 14 and 42
Therefore, the highest common factor is 6 and this is the greatest number.
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The area of a rectangular painting is 1/6 square yard. The width is 2/3 yard. What is the length of the painting use the formula A=e x w
The length of this rectangular painting is equal to 1/4 yard.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.Making L the subject of formula, we have:
L = A/W
Given the following data:
Width of rectangular painting = 2/3 yard.
Area of rectangular painting = 1/6 square yard.
Substituting the given parameters into the formula, we have;
L = 1/6/(2/3)
L = 1/6 × 3/2
L = 3/12
Length, L = 1/4 yard.
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Over the last three evenings, Karen received a total of 130 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. How many phone calls did she receive each evening?
CORRECT ANSWERS ONLY!!! HELP
The number of phone calls that Karen can be said to have received in these evenings are: 30 , 80 , and 20 calls
How to solve for the phone callsWr have x, y , z as the number of phone calls that have been received
Such that
x + y + z = 130
On the second day she received 4 calls more than the 3rd day
y = 4z
On the first evening she had 10 more calls than the last
x = 10 + z
We have to substitute the equations in the first equation
10 + z + 4z + z = 130
10 + 6z = 130
6z = 120
divide through by 6
z = 20
Then x = 10 + 20
x = 30
y = 4z
= 4 x 20 = 80
Therefore on the first day the phone call was 30 minutes, the second day was 80 and the third was 20
To check, 20 + 30 + 80 = 130. the solution is correct
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