The expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
How to rewrite the number?The number is given as:
Number = 675,360.41
Express the numbers using their place values
Number = 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
The above expression represents the expanded notation
Hence, the expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
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Alana bought 2 5/8 pounds of mixed nuts for the school picnic. Her classmates ate 3/4 of the mixed nuts. How much of the mixed nuts did her classmates eat
Final answer:
Alana's classmates ate 1 31/32 pounds of the mixed nuts.
Explanation:
To determine how much of the mixed nuts Alana's classmates ate, you need to multiply the total amount of nuts by the fraction that was eaten.
Alana bought 2 5/8 pounds of mixed nuts and her classmates ate 3/4 of them. To find out how much was eaten, you multiply 2 5/8 by 3/4.
First, convert 2 5/8 to an improper fraction:
(2 * 8) + 5 = 21/8.
Now, multiply this improper fraction by 3/4:
(21/8) * (3/4) = 63/32 pounds.
This is an improper fraction, which you can convert to a mixed number.
63 divided by 32 is 1 with a remainder of 31, so the mixed number is 1 31/32 pounds.
Therefore, Alana's classmates ate 1 31/32 pounds of the mixed nuts.
You buy a new laptop for
$299.99
$299.99
.
The sales tax is
6%
6%
.
What is the total cost for the laptop including the sales tax?
What is the volume of a sphere with a surface area of 64π cm²? 16π cm³ 2113π cm³ 48π cm³ 8513π cm³
Answer:
Literally just finished the test its 83 1/3
Step-by-step explanation:
What is the median of this data set?
Answer:
7
Step-by-step explanation:
Median is middle, the middle is 7. So the median is 7.
Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97, how much of his first payment went toward note reduction(reducing principal)? Show your work.
Answer:
$66.97 is his first payment went toward reduction.
Step-by-step explanation:
Given : Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97.
To find : How much of his first payment went toward note reduction(reducing principal)?
Solution :
First we find the interest of 1 month on a loan of $85,000 at 7.2% interest.
[tex]I=85000\times \frac{7.2}{12\times 100}[/tex]
[tex]I=85000\times 0.006[/tex]
[tex]I=510[/tex]
Interest of 1 month is $510.
Monthly payment = $576.97
Now, first payment or reducing principal is given by
F= monthly payment - interest of 1 month
F=$576.97- $510
F=$66.97
Therefore, $66.97 is his first payment went toward reduction.
Corey spent 20% of his savings on a printer at Louie's ElectronisHow much did Corey have in his savings account before he bought the printer?
Answer:
5
Step-by-step explanation:
PLEASE HELP AND SHOW ALL WORK
7.04
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
(4 points each.)
1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six
2. 12 + 42 + 72 + ... + (3n - 2)2 = quantity n times quantity six n squared minus three n minus one all divided by two
For the given statement Pn, write the statements P1, Pk, and Pk+1.
(2 points)
2 + 4 + 6 + . . . + 2n = n(n+1)
Answer
answer C
Step-by-step explanation:
A semi-truck is carrying 555 bags of chips. If each bag of chips has 321 chips, how many chips are in the semi-truck?
In the diagram below, m = 96 and m = 114. What is the measure of
JPM?
Answer:
C.Apex(105)
Step-by-step explanation:
What is the area of the composite figure whose vertices have the following coordinates?
(−2, −2) , (4, −2) , (5, 1) , (2, 3) , (−1, 1)
Final Answer:
The estimated total area of the composite figure is approximately 23.415 square units.
Explanation:
To calculate the area of the composite figure made by the vertices (−2, −2), (4, −2), (5, 1), (2, 3), and (−1, 1), we can divide the figure into simpler shapes, such as triangles and rectangles, whose area we know how to calculate. We will consider the vertices in the given order to create a polygon and find its area.
Let’s follow these steps:
1. Draw the figure by plotting the points on the coordinate plane and connecting them in the order given.
2. Divide the figure into simpler shapes (for example, a combination of triangles and rectangles).
3. Calculate the area of each part.
4. Sum the areas to find the total area of the composite figure.
Dividing the figure:
A simple way to divide this figure is into two triangles and one trapezoid.
Let’s name the vertices as follows:
A (−2, −2), B (4, −2), C (5, 1), D (2, 3), E (−1, 1).
- Triangle ABE and triangle BCD can be identified.
- Trapezoid ABED can be identified (alternatively, one could see it as a rectangle plus a triangle).
Calculating the area of each part:
Triangle ABE:
Using the coordinates (−2, −2), (−1, 1), (4, −2), we can calculate the base and height of the triangle. The base (AB) is the distance between points (−2, −2) and (4, −2), which is 6 units. The height (from point E) is the y-coordinate difference of points E and AB, which is 3 units (from y = 1 to y = -2). Thus, the area of triangle ABE is:
Area = 1/2 * base * height = 1/2 * 6 * 3 = 9 square units.
Triangle BCD:
For triangle BCD, we take CD as the base and find the perpendicular height from point B to line CD. However, since we cannot directly measure this height on the coordinate system without further calculations, we could use another method. Since the area calculations can get complicated with this arbitrary triangle, and since the coordinates given suggest that this is actually part of a grid system (not arbitrary points), we can instead calculate the area of trapezoid ABCD by treating AB as one base and CD as the other.
Trapezoid ABCD:
The bases of the trapezoid are AB and CD. Base AB is 6 units long (as before). To calculate the length of CD, we use the distance formula (distance = sqrt((x2 - x1)² + (y2 - y1)²)):
CD = sqrt((5 - 2)² + (1 - 3)²) = sqrt(3² + (-2)²) = sqrt(9 + 4) = sqrt(13) ≈ 3.61 units.
The height of the trapezoid (distance between the bases) is 3 units (from y = 1 to y = -2). Thus, the area of trapezoid ABCD is:
Area = (1/2) * (AB + CD) * height = (1/2) * (6 + sqrt(13)) * 3 ≈ (1/2) * (6 + 3.61) * 3 ≈ (1/2) * 9.61 * 3 ≈ 14.415 square units.
Summing up the areas:
Area of Triangle ABE + Area of Trapezoid ABCD = 9 + 14.415 = 23.415 square units.
Please note that in slight geometric figures, the area calculations might be complicated with non-right triangles or irregular shapes. In this case, a more advanced method such as breaking the figure into more regular pieces or using determinants (the Shoelace formula) for polygons might be required.
So the estimated total area of the composite figure is approximately 23.415 square units.
The number of gallons of water,y, in a swimming pool is modeled by the equation y=7.5x+500,where x represents the time in minutes after the pump is turned on. How many gallons of water are in the pool if the pump is on for 200 minutes.
Consider the net of a triangular prism where each unit on the coordinate plane represents five feet. If a can of spray paint covers 25 square feet, how many cans of spray paint are needed to paint the outside of the prism blue?
Part 1.] Indicate the general rule for the arithmetic sequence with [tex] a_{3}=-4[/tex] and [tex] a_{8}=-29[/tex]
A.] [tex] a_{n}=-6+(n-1)(-5)[/tex]
B.] [tex] a_{n}=-6+(n-1)(5)[/tex]
C.] [tex] a_{n}=6+(n-1)(-5)[/tex]
D.] [tex] a_{n}=6+(n-1)(5)[/tex]
Part 2.] Which of the following is the general term for the sequence m, -m, m, -m, . . .?
A.] [tex]m(-1)^{n-1}[/tex]
B.] [tex](-m)^{n}[/tex]
C.] [tex](-1)m^{n+1}[/tex]
D.] [tex](-1)m^{n-1}[/tex]
Part 3.] Indicate a general rule for the [tex] n^{th}[/tex] term of the sequence when [tex] a_{1}=5[/tex] and [tex]r= \sqrt{3}[/tex]
A.] [tex] a_{n}=( \sqrt{3})(5)^{n+1}[/tex]
B.] [tex] a_{n}=( \sqrt{3})(5)^{n-1}[/tex]
C.] [tex] a_{n}=(5)( \sqrt{3})^{n-1}[/tex]
D.] [tex] a_{n}=(5)( \sqrt{3})^{n+1}[/tex]
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I NEED HELP ASAP!!!!!! WILL GIVE BRAINLIEST IF ANSWER IS CORRECT
which of the binomials below is a factor of this trinomial
5x^2+14x-3
a. x-3
b. x+3
c. 5x+3
d. 5x-3
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
[tex]5x^2+14x-3[/tex]
As we know "Split the middle term":
[tex]5x^2+15x-x-3\\\\=5x(x+3)-1(x+3)\\\\=(5x-1)(x+3)[/tex]
Since it is quadratic equation so, it has 2 roots.
So, the roots are (x+3) and (5x-1).
Hence, Option 'B' is correct.
Select all the situations that can be modeled with an equation.
The sale price of a television is $125 off of the original price.
Anna gave away 5 hats.
Marco spent twice as much as Owen.
Susan earns $25 per day for d days.
Ben paid a total of $75 for a shirt and a pair of shoes.
The situations that can be modeled with an equation are:
1. The sale price of a television is $125 off of the original price.
Let the original price of TV be=x
Sale price = [tex]x-125[/tex]
Let sale price be S so equation is : S= [tex]x-125[/tex]
3. Marco spent twice as much as Owen.
Let Owen spent = x
Then Macro spent = 2x
Let Macro spends $y , So, equation becomes
y = 2x
5. Ben paid a total of $75 for a shirt and a pair of shoes.
Let 'x' represent the cost of a shirt and 'y' represents the cost of a pair of shoes then equation becomes:
[tex]x+y=75[/tex]
Can someone please solve this problem
ANSWER
[tex] \boxed { \sqrt{} }30 \degree[/tex]
[tex] \boxed { \sqrt{} }210 \degree[/tex]
EXPLANATION
We want to solve
[tex] \cot( \theta) = \sqrt{3} [/tex]
where
[tex]0 \degree \: \leqslant x \leqslant 360 \degree[/tex]
We reciprocate both sides of this trigonometric equation to obtain:
[tex] \tan( \theta) = \frac{1}{ \sqrt{3} } [/tex]
We take arctangent of both sides to get;
[tex] \theta = \tan ^{ - 1} ( \frac{1}{ \sqrt{3} } ) [/tex]
[tex] \theta = 30 \degree[/tex]
This is the principal solution.
The tangent ratio is also positive in the third quadrant.
The solution in the third quadrant is
[tex]180 + \theta = 180 + 30 = 210 \degree[/tex]
The graph of [tex]y= \sqrt[3]{x} [/tex] was shifted 5 units down and 4 units to the left. What is the equation of the resulting graph?
Please answer quickly!
Using translation concepts, it is found that the equation of the resulting graph is given by:
[tex]y = \sqrt[3]{x + 4} - 5[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the changes are given as follows:
Shift down of 5 units, hence y -> y - 5.Shift left of 4 units, hence x -> x + 4.Hence the equation of the resulting graph is given by:
[tex]y = \sqrt[3]{x + 4} - 5[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
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The equation of the graph \\sqrt[3]{x} shifted down by 5 units and to the left by 4 units is \\sqrt[3]{x + 4} - 5.
Explanation:The transformation of the graph of y = \\sqrt[3]{x} down by 5 units and to the left by 4 units is represented by the function y = \\sqrt[3]{x + 4} - 5. When a graph is shifted to the left by 'a' units, we replace 'x' in the equation with (x + a). Similarly, when a graph is shifted down by 'b' units, we subtract 'b' from the function, resulting in f(x) - b. Therefore, incorporating both transformations into the original function, we get y = \\sqrt[3]{x + 4} - 5.
Learn more about Graph Transformation here:https://brainly.com/question/19040905
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A parachutist’s speed during a free fall reaches 13 miles per hour. What is this speed in feet peer second? At what speed, how many feet will the parachutist fall during 10 seconds of free fall? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answer
Carrie has 32 ounces of ice cream to divide equally among 10 people how much ice cream will each person get? SHOW WORK
Which answer describes the function f(x) = x^6−x^4 ?
neither
even
odd
to determine if it is even replace x with -x and see if the answer is identical.
In this case, this function is even
Answer:
The function [tex]f(x)=x^6-x^4[/tex] is:
Even
Step-by-step explanation:
A function f(x) is even if:
f(-x)= f(x)
A function f(x) is odd if:
f(-x)= -f(x)
Here, we are given a function f(x) as:
[tex]f(x)=x^6-x^4[/tex]
[tex]f(-x)=(-x)^6-(-x)^4\\\\ =x^6-x^4\\\\=f(x)[/tex]
f(-x)=f(x)
Hence, the function [tex]f(x)=x^6-x^4[/tex] is:
Even
Which postulate or theorem can be used to prove that △PQR is similar to △PST?
Answer: SAS similarity theorem.
Step-by-step explanation:
In the given picture , we have two triangles △PQR and △PST with common vertex P and common angle ∠P.
Also, the ratio of sides that include the common angle ∠P of ΔPQR and ΔPST is given by :-
[tex]\frac{PS}{PQ}=\frac{45}{20}=\frac{9}{4}\\\\\frac{PT}{PR}=\frac{36}{16}=\frac{9}{4}[/tex]
Therefore, SAS similarity postulate ΔPQR is similar to ΔPST.
SAS similarity postulate says that if an angle of one triangle is equal to the corresponding angle of another triangle and the sides that include this angle are proportional, then the two triangles are similar.
Lines p and q are perpendicular. If the slope of line p is 2, what is the slope of line q?
A. 1/2
B. -1/2
C. -2
D. 2
Answer:
- 1/2
Step-by-step explanation:
I just did it
Match each as a Compound (C) or Element (E)
Cu
HCI
CCI4
Co
HI
CH4
I need help fast. Identify the apothem (a), the radius (r), and the perimeter (p) of the regular figure.
The apothem (a), radius (r), and perimeter (p) of a regular figure are defined as follows: the apothem is the perpendicular distance from the center of the figure to one of its sides, the radius is the distance from the center of the figure to any point on its circumference, and the perimeter is the total length of all its sides.
Explanation:The apothem (a) of a regular figure is the perpendicular distance from the center of the figure to one of its sides.
The radius (r) of a regular figure is the distance from the center of the figure to any point on its circumference.
The perimeter (p) of a regular figure is the total length of all its sides.
If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?
Answer:
(5,-2).
Step-by-step explanation:
First, let's find the original center of the circle, we have
[tex]x^2 - 4x + y^2 + 2y = 4[/tex]
we are going to complete square adding and subtracting 4 for the x terms and 1 for the y terms
[tex]x^2 - 4x+4-4 + y^2 + 2y+1-1 = 4[/tex]
[tex](x-2)^2 - 4 + (y+1)^2 - 1 = 4[/tex]
[tex](x-2)^2+ (y+1)^2 - 5 = 4[/tex]
[tex](x-2)^2+ (y+1)^2 = 4+5[/tex]
[tex](x-2)^2+ (y+1)^2 = 9.[/tex]
The canonical formula of a circumference is [tex](x-h)^2+(y-k)^2=r^2[/tex]
Then, we have a circle with [tex]r^2 =9[/tex] and center (h,k)=(2,-1).
Now, if we translate the circle 3 units to right and 1 unit down, then all the points in the circle will be translated including the center. Especifically, the x values will be added 3 units and the y-vaues will be subtracted 1 unit, then the new center will be
(2+3,-1-1) = (5,-2).
Jade is painting a rectangular wall. The wall is 4 1/4 yards long and 2 2/3 yards high. The formula for the area of a rectangle is A=bh. What is the area of the wall?
Answer:
11 1/3
Step-by-step explanation:
How do you do number 38 to 40 please help
What is the greatest common factor of 8xy^5−16x^2y^3+20x^4y^4 ?
A. 8xy^5
B. 2xy^3
C. 4xy^3
D. 4x^4y^5
The answer is C 4xy^3