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.
I NEED HELP ASAP!!!!!! WILL GIVE BRAINLIEST IF ANSWER IS CORRECT
One number is 6 more than another. the difference between their squares is 192. what are the numbers?
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).
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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?
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.
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.
Johnny bought 6 movie tickets and spent $54 dollars he bought 3/6 children's tickets that cost $8 dollars each the other tickets were adult how much was adult tickets cost?
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
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]
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 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
Mrs. Isabelle is making paper and plastic foam animals for her first-grade class. She is calculating the amount of wasted materials for environmental and financial reasons. Mrs. Isabelle is cutting circles out of square pieces of paper to make paper animals in her class. Enter the polynomial that represents the amount of paper wasted if the class cuts out the biggest circles possible in squares of length l. The polynomial that represents the amount of paper wasted is
The polynomial representing the amount of paper wasted when cutting the largest possible circle out of a square of side length l is (4-π)/4 * l².
Explanation:The question at hand is concerned with finding the polynomial that represents the amount of paper wasted when cutting out the largest possible circles from square pieces of paper. The side length of each square is given as l. The area of each square is l², while the area of the circle that can be cut from the square is calculated using the formula πr², where r is the radius of the circle. Because the largest circle that fits in the square touches all four sides, the diameter of the circle equals the side length l, making the radius r equal to l/2.
To find the polynomial for the wasted paper, first we calculate the area of the circle: π(l/2)², which simplifies to πl²/4. To find the wasted area, subtract the area of the circle from the area of the square: l² - πl²/4. This difference represents the wasted paper and can be further simplified to a single polynomial: (4/4)l² - (π/4)l², which simplifies to (4-π)/4 * l². This is the polynomial representing the amount of paper wasted for each square piece of paper.
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]
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:
For the function f(x)= square root (x-5), find f^-1. What is the range of f^-1? Any explanation and answer is appreciated!!
Final Answer:
The inverse function is [tex]\( f^{-1}(x) = x^2 + 5 \)[/tex] and the range of [tex]\( f^{-1} \)[/tex] is [tex]\( y \geq 5 \)[/tex] or [5, ∞].
Explanation:
To find the inverse function, [tex]\( f^{-1} \)[/tex], for the function [tex]\( f(x) = \sqrt{x-5} \)[/tex], we'll need to follow these steps:
1. Write the function as an equation: [tex]\( y = \sqrt{x-5} \)[/tex].
2. To find the inverse, we exchange the roles of x and y. The equation now reads [tex]\( x = \sqrt{y-5} \)[/tex].
3. Our next task is to solve this equation for y. To do so, we need to eliminate the square root by squaring both sides of the equation:
[tex]\[ x^2 = (\sqrt{y-5})^2 \\\\\[ x^2 = y - 5 \][/tex]
Now, we add 5 to both sides in order to isolate y:
[tex]\[ y = x^2 + 5 \][/tex]
This is our inverse function: [tex]\( f^{-1}(x) = x^2 + 5 \)[/tex].
Regarding the range of [tex]\( f^{-1} \)[/tex], we need to consider the domain of the original function f(x). The original function [tex]\( f(x) = \sqrt{x-5} \)[/tex] is only defined for [tex]\( x \geq 5 \)[/tex], because you cannot take the square root of a negative number in real numbers.
Since the domain of f(x) becomes the range of [tex]\( f^{-1}(x) \)[/tex], the range of the inverse function must be [tex]\( y \geq 5 \)[/tex], because the smallest value of x is 5, which when inputted into the inverse gives us [tex]\( 5^2 + 5 = 25 + 5 = 30 \)[/tex], and it only grows larger for larger values of x.
So the inverse function is [tex]\( f^{-1}(x) = x^2 + 5 \)[/tex] and the range of [tex]\( f^{-1} \)[/tex] is [tex]\( y \geq 5 \)[/tex].
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]
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
How do you do number 38 to 40 please help
Carrie has 32 ounces of ice cream to divide equally among 10 people how much ice cream will each person get? SHOW WORK
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?
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:
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:
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.
HELPPPPPPP ME PLEASE!!!!!
The weight of a can of soup varies jointly with the height and the square of the diameter. a can 8 inches high with a diameter of 3 inches weighs 28.8 ounces. what is the weight of a can that is 4 inches high with a diameter of 2 ​inches?
The weight of a can of soup can be determined using the variation formula. By substituting the given values into the equation, we can find the weight of a can that is 4 inches high with a diameter of 2 inches.
To find the weight of the can that is 4 inches high with a diameter of 2 inches, we can use the given information that the weight of a can of soup varies jointly with the height and the square of the diameter. We are given that a can 8 inches high with a diameter of 3 inches weighs 28.8 ounces. This gives us enough information to set up a proportion to solve for the weight of the can we are looking for.
Let's assign variables to the height (h), diameter (d), and weight (w) of the can. From the given information, we have the following equation:
w = khd^2
Substituting the given values, we have:
28.8 = k(8)(3^2)
Here, we have one equation with one unknown. We can now solve for the constant k by dividing both sides of the equation by (8)(3^2).
After finding the value of k, we can substitute it back into the equation to find the weight of the can that is 4 inches high with a diameter of 2 inches.
w = k(4)(2^2)
Solving for w will give us the weight of the can.
Learn more about Variation here:https://brainly.com/question/34330070
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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.
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:
7s. 49
————- - —————
s^2-14s+49. s^2-14s+49
it’s supposed to be like a fraction ♀️