Ellie made a cube-shaped cardboard box with side-length s. The area of cardboard she used is given by the formula A = 6s2, where s represents the side length of the cube.
if a crate contains 25,500 ounces of rice , about how many kilograms does it contain?
After 7 years, Abner earned $1575 in simple interest from a CD into which he initially deposited $6000. What was the annual interest rate of the CD?
The annual interest rate of the CD was 3.75 %
Explanation
Simple Interest formula is : [tex] I =P*r*t [/tex] , where [tex] I= [/tex] Amount of interest, [tex] P= [/tex] Principal/Initial amount, [tex] r= [/tex] rate of interest in decimal form and [tex] t= [/tex] time in years
Here Abner earned $1575 in simple interest and he initially deposited $6000. So, [tex] I=1575 [/tex] dollar and [tex] P= 6000 [/tex] dollar
Also given that, [tex] t = 7 [/tex] years
Now according to the formula...
[tex] I= P* r*t\\ \\ 1575= 6000*r*7\\ \\ 1575= 42000*r\\ \\ r= \frac{1575}{42000}= 0.0375 [/tex]
For getting the interest rate in percentage, we will multiply it by 100%. So... (0.0375 × 100) % = 3.75 %
So, the annual interest rate of the CD was 3.75 %
Bonnie can complete her paper route in 45 min. when her sister jean helps her it takes them 18 min to complete the route. how long would it take jean alone?
Which equation does not represent a function? A) y = 2x + 3 B) x = 4y + 7 C) 6x - 5y = 8 D) y2 = -5x - 8
Answer:
D) y2 = -5x - 8
Step-by-step explanation:
A function is a rule between two sets A and B so that each element of set A (Domain) corresponds to a single element of set B (Range). Mathematically they can be expressed as:
[tex]f: A\rightarrow B\\\\a\rightarrow b =f(a)[/tex]
So:
[tex]y^2=-5x-8\\\\y=\pm \sqrt{-5x-8}[/tex]
Isn't a function because the elements of the domain don't corresponds to a single element of the range.
We can see this in an easier way using the vertical line test, which is a visual way to determine if a curve is a graph of a function or not. If a vertical line intersects a curve in an xy plane more than once, then for a value of x the curve has more than one value of y, and then the curve does not represent a function.
I attached you the graphs, so you can corroborate the results visually.
The figure has 60 edges and 30 vertices. Use Euler’s formula to find the number of faces in the given polyhedron.
Solve the quadratic in form equation x^4-14x^2+45=0
What is the range of f(x)
The range of f(x) is a single value which is the y-coordinate of any point on the horizontal line representing f(x).
The range of a function is the set of possible values its output can have. In this case, the function f(x) is a horizontal line. Since f(x) is restricted to the portion between x = 0 and x = 20, inclusive, the range of f(x) is the set of all y-values within that range. Since the graph of f(x) is a horizontal line, the range of f(x) is a single value, which is the y-coordinate of any point on the line.
Based on the graph shown below, the range of f(x) include the following: B. { f(x)| –∞ < f(x) ≤ 4}
In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following range:
Range = (-∞, 4] or {f(x)| –∞ < f(x) ≤ 4}
Complete Question;
What is the range of f(x)?
{ f(x)| –∞ < f(x) < ∞}
{ f(x)| –∞ < f(x) ≤ 4}
{ f(x)| 4 < f(x) < ∞}
{ f(x)| 0 ≤ f(x) < ∞}
identify the type of conic section that has the equation 4x^2+25y^2=100 and identify its domain and range.
4x^2+25y^2=100
[tex]4x^2+25y^2=100 \\\\ Dividing \;both \;sides \;by \;100 \\\\ \frac{4x^2}{100}+ \frac{25y^2}{100}= \frac{100}{100} \\\\ \frac{x^2}{25}+ \frac{y^2}{4}= 1 \\\\ \frac{x^2}{5^2}+ \frac{y^2}{2^2}= 1 \\\\ This \;is \;an \;ellipse. \\\\
\frac{x^2}{a^2}+ \frac{y^2}{b^2}= 1 [/tex]
Domain of an ellipse is x ∈ [-a,a] and Range of an ellipse is y ∈ [-b,b].
So, given equation is an Ellipse where Domain is x ∈ [-5,5] and Range is y ∈ [-2,2].
A number that divides evenly into another number is known as which of the following?
A.) prime number
B.)factor
C.) multiple
D.) Integer
A number that divides evenly into another number is known as factor.
The correct answer is
B.) factor.
A factor is a number that divides evenly into another number. To find the factors of a number, you can perform a process of division or use other mathematical methods.
Let's take an example to illustrate:
If we consider the number 12, its factors are the numbers that divide it evenly without leaving a remainder. We can start by dividing 12 by 1:
12 ÷ 1 = 12
Since there's no remainder, 1 is a factor of 12. Now, let's try dividing 12 by 2:
12 ÷ 2 = 6
Again, there's no remainder, so 2 is also a factor of 12. Continuing this process, we find that 3 is also a factor of 12:
12 ÷ 3 = 4
And finally, 12 ÷ 4 = 3
So, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Each of these numbers divides evenly into 12, making them factors. Therefore, the correct answer is B.) factor.
Factors are essential in various mathematical concepts, including prime factorization, finding greatest common divisors, and simplifying fractions. Understanding factors helps in solving problems related to divisibility and multiplication. By identifying factors, we can break down complex numbers into simpler components, aiding in various mathematical computations and analyses. Hence, recognizing factors is fundamental in mathematics.
Complete question:
A number that divides evenly into another number is known as which of the following?
A.) prime number
B.)factor
C.) multiple
D.) Integer
Find the center, vertices, and foci of the ellipse with equation 2x2 + 9y2 = 18.
If VX = WZ = 40 cm and m∠ZVX = m∠XWZ = 22°, can ΔVZX and ΔWXZ be proven congruent by SAS? Why or why not?
Yes, along with the given information, ZX ≅ ZX by the reflexive property.
Yes, the triangles are both obtuse.
No, the sides of the triangles intersect.
No, there is not enough information given.
No, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
The given information only provides the lengths of two sides and the measures of two angles in the triangles, but we do not know if the third side is congruent, and we cannot assume that it is by the given information.
Additionally, the given information does not specify that one of the congruent sides is included between the congruent angles, which is necessary for the SAS postulate to be used to prove congruence.
Therefore, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.
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(x^ 3 + y ^3) divided by (x - y)
When wrapping a birthday gift for his mother kemji adds additional 2.5 square feet of gift wrap to allow for overlap. how many squares feet of gift wrap will kenji use to wrap a gift 3.5 ft long 18 in wide and 2 ft high?
The base is a 45 45 90 triangle with a leg of 5 in. The height is 1.8 what’s the volume of the prism
The volume of the prism is 22.5 cubic inches.
Explanation:To find the volume of the prism, we need to first find the area of the base and then multiply it by the height. In this case, the base is a 45-45-90 triangle with a leg of 5 inches. The area of a triangle is given by the formula 1/2 * base * height, so the area of the base is 1/2 * 5 * 5 = 12.5 square inches. The height of the prism is given as 1.8, so we can now calculate the volume by multiplying the area of the base by the height: 12.5 * 1.8 = 22.5 cubic inches.
How many different ways can you choose a council with exactly 3 sophomores, 1 junior, and 2 seniors?
At 59 F, crickets chirp at a rate of 76 times per minute, and at 65 F they chirp 100 times per minute. Write an equation in slope-intercept form that represents the situatio.
The rate of crickets chirping is linearly dependent on the temperature and can be represented by the equation y = 4x -100, whereby y is the number of chirps per minute, and x is the temperature in °F.
Explanation:
This is essentially a linear equation problem where the rate of cricket chirps is related to the temperature.
Firstly, we list our two points: (59, 76) and (65, 100).
We can then calculate the slope (m). m = (y2-y1) / (x2-x1) = (100-76)/(65-59) = 24/6 = 4.
We have the rate of cricket chirps increasing by 4 chirps per increase in 1°F. Our equation is now of the form y= 4x + b.
Finally, we'll calculate the y-intercept (b) by plugging one of our points into the equation. If we choose the point (59, 76), we get 76 = 4*59 + b. Solving for b, we get b = -100.
So, the equation is y = 4x -100, where y is the number of chirps per minute, and x is the temperature in °F.
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1. The graph shows the distance y, in centimeters, a pendulum moves to the left (negative displacement) and right (positive displacement), for a given number of seconds x. (a) From its resting position, how long does it take the pendulum to swing one direction, then the other, and then return to its resting position? (b) What is the pendulum’s maximum displacement? (c) What percent of a full cycle is completed within 1 s? (d) How is the pendulum moving during the time period from x = 5 to x = 5.625? (e) What is the equation of the graph?
the frequency of A4 is 440.00 Hz.
what is the frequency of A6, which is two octaves above A4?
Stella has 6 pounds of chocolate. She will use 2/3 pound of the chocolate to make one cake. How many cakes can she make
The number of cakes she can make is 9.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Stella has 6 pounds of chocolate. She will use 2/3 pounds of the chocolate to make one cake.
The number of cakes will be calculated as,
Number = 6 / ( 2 / 3 )
Number = ( 6 x 3 ) / 2
Number = 9
Therefore, the number of cakes will be 9.
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The area of the circle shown below is 100π. What is the diameter (D) of the circle?
Answer: 20 units
Step-by-step explanation:
We know that the area of a circle is given by :-
[tex]\text{Area}=\pi r^2[/tex], where r is the radius of the circle.
We are given that the area of the circle = [tex]100\pi[/tex] square units.
[tex]\Rightarrow\ 100\pi=\pi r^2\\\\\Rightarrow\ r^2 =100[/tex]
Taking square root on both the sides , we get
[tex]\\\\\Rightarrow\ r=10[/tex]
The diameter of the circle is given by :-
[tex]d=2r=2(10)=20\text{ units}[/tex]
What is the negative angle that is coterminal with 120∘120∘. write your answers in radians?
The square of mark's age 3 years ago is 6 times the age he will be in 9 years. what is his age now? 9 12 15
Answer:
mos def 15
Step-by-step explanation:
Quick, anyone know the answer?
Which of the following scenarios has a lower y-intercept than y = 4x + 5 ?
(a.) A 50 gallon tub is draining. Every 2 minutes, the amount of water decreases by 2 gallons.
(b.) Reginaldo had $17 in his account and for every book he buys, it costs him $4.
(c.) Sydney has collected 8 postcards. Each time a friend comes to visit, Sydney gives her a postcard.
(d.) Owen has 3 pets. He receives a new pet each time he has a birthday.
When Mrs. Myles gave a test, the scores were normally distributed with a mean of 72 and a standard deviation of 8. This means that 95% of her students scored between which two scores?
A) 40 and 100
B) 48 and 96
C) 56 and 88
D) 64 and 80
Kristin decides to spend at most $50 for a birthday dinner at a restaurant, including a 15% tip.,
Write an inequality in one variable to represent this situation.
What is the most that her meal can cost before a tip?
Fran sells brownies $3 each she cuts pan of brownies into 6 pieces if she makes 4 pan of brownies how much money she make
Michael has $1.95 totally in his collection, consisting of quarters and nickels. The number of nickels is three more than the number of quarters. how many quarters and nickels does Michael have?
Solve the system of equations using a matrix. Separate the x and y values with a comma. 2x-y=6 & 3x-y=11