Answer:
9x-4y=17
-4y=-9x+17
y=9/4x+17
Step-by-step explanation:
Suppose you are building a storage box of volume 4368in^3. the length of the box will be 24 in. the height of the box will be 1 in. more than its width. find the height and the width of the box.
Answer:
height: 14 incheswidth: 13 inchesStep-by-step explanation:
The volume formula can be used to find the height and width of a box with volume 4368 in³ and height 1 in greater than width.
SetupThe volume formula is ...
V = LWH
Substituting given information, using w for the width, we have ...
4368 = (24)(w)(w+1)
SolutionWe want to find the value of w.
182 = w² +w . . . . . . . . divide by 24
182.25 = w² +w +0.25 = (w +0.5)² . . . . . . add 0.25 to complete the square
13.5 = w +0.5 . . . . . . . . take the positive square root
w = 13 . . . . . . . . . . . . subtract 0.5
h = w+1 = 14
The height of the box is 14 inches; the width is 13 inches.
__
Additional comment
By "completing the square", we can arrive at the exact dimensions of the box, as we did above. Note that we only added 0.25 to the equation to do this.
For numbers close together, the geometric mean (root of their product) is about the same as the arithmetic mean (half the sum):
\(\sqrt{w(w+1)}\approx\dfrac{w+(w+1)}{2}=w+\dfrac{1}{2}\\\\w\approx\sqrt{182}-\dfrac{1}{2}\approx12.99\)
Using this approximation to arrive at the conclusion w=13 saves the steps of figuring the value necessary to complete the square, then adding that before taking the root.
answer for 14+3y < 65
Answer:
The answer is y<17
Step-by-step explanation:
First, move the constant to the right.
3y<65-14
Then, subtract 65 and 14
3y<51
Lastly, divide both sides by 3.
y<17
Is it possible to ride a bike 200 miles in 13 hours
Answer:
no
Step-by-step explanation:
because even going back to back it would take you about one or two days
A test of H0: =55 versus H1= 55 is performed using a significance level of . The P-value is 0.048. If the true value of μ is 59, does the conclusion result in a Type I error, a Type II error, or a correct decision?
The conclusion results in a correct decision when test of H0: =55 versus H1= 55 is performed using a significance level of the P-value is 0.048
The given null hypothesis is H0: μ = 55 and the alternative hypothesis is H1: μ ≠ 55.
The significance level is not given in the question.
Given P-value is 0.048.
If the true value of μ is 59, and the P-value is 0.048, then we would reject the null hypothesis at a significance level of α = 0.05.
Since the true value
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One endpoint of a line segment is (10,-1). The point (7,-2) i s one-third of the way from that endpoint to the other endpoint. Find the other endpoint
The coordinates of the other endpoint of the Line segment is (-2,-5).
If M(x.y) divides the line formed by two points A(a,b) and B(c,d) into a ratio m:n. Then the coordinates of the point M can be found out by using the formula,
x = (mc + na)/(m+n)
y = (md + nb)/(m+n)
This above mentioned formula is known as The section Formula.
The one of the End point of the line is (10,-1) and the point (7,-2) is dividing the line in the ratio of 1:3.
Let us assume the other end point to be (a,b).
Now, applying Section Formula,
7 = [(1)(a)+(3)(10)]/4 and
-2 = [(1)(b)+(3)(-1)]/4
Further solving,
a = -2 and
b = -5
So, the coordinates of the endpoint is (-2,-5).
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Observa la siguiente figura y responde la pregunta.
¿Cuál es la expresión que representa el perímetro de la figura?
A.
(2x+5)+(7x+3)
B.
2(2x+5)(7x+3)
C.
4(2x+5+7x+3)
D.
2(2x+5)+2(7x+3)
The perimeter of the rectangle can be calculated as 2(2x + 5)(7x + 3) which is option B.
What is the perimeter of a rectangleThe perimeter of a rectangle is the total length of all its sides. In a rectangle, the opposite sides are equal in length, so to find the perimeter, we can add up the lengths of two adjacent sides and then multiply that sum by 2.
If we denote the length of the rectangle as L and the width as W, then the perimeter P is given by:
P = 2(L + W)
In the problem given, the perimeter of the rectangle is given as;
P = 2[(7x + 3) + (2x + 5)]
P = 2[9x + 8]
P = 18x + 16
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Translation: Which option represents the perimeter of the figure?
lots of point n brainliest SO help rq
Bruce invested a certain amount of money for five years at a rate of 2.25%. At the end of that time, he had earned $675 in interest. How much money was invested? (See Example 3 from your notes.)
a
$6000
b
$6675
c
$6750
d
$5645
Answer:
A. $6000Step-by-step explanation:
Let the invested amount is x.
Then the interest amount is:
x*5*2.25/100 = 6750.1125x = 675x = 675 / 0.1125x = 6000Correct choice is A
Point A is at -7, -3. There are 12 points between A and B. What are possible coordinates for point B?
Answer:
(5,9)
(-19, - 15)
(5, - 15)
(-19, 9)
Step-by-step explanation:
Given that :
Coordinate of point A = - 7, - 3
Number of points between point A and B = 12
Possible coordinate of point B
Possible coordinates of point B:
(-7, - 3) + 12 = (5, 9)
(-7, - 3) - 12 = (-19, - 15)
(-7, - 3) = (-7 +12, -3 - 12) = (5, - 15)
(-7, - 3) = (-7 - 12, - 3 + 12) = (-19, 9)
Hence possible coordinates of be are :
(5,9)
(-19, - 15)
(5, - 15)
(-19, 9)
describe and correct the error in using properties of parallelograms.
Error: The error in using properties of parallelograms is assuming that all quadrilaterals with opposite sides that are parallel are parallelograms.
Correction: Not all quadrilaterals with opposite sides that are parallel are parallelograms. To determine if a quadrilateral is a parallelogram, both pairs of opposite sides must be parallel and equal in length. Additionally, the opposite angles must be congruent. These conditions must be satisfied for a quadrilateral to be classified as a parallelogram.
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HELP PLEASE I WILL GIVE BRAINLIST
Answer:
19
Step-by-step explanation:
it’s the only one within Q3
Name the types of angles shown.
G
F
Н
E
Answer:
obtuse acute straight obtuse
Step-by-step explanation:
how many ternary strings (digits 0,1, or 2) are there with exactly seven 0's, five 1's and four 2's? show at least two different ways to solve this problem.
1441440 ternary strings (digits 0,1, or 2) are there with exactly seven 0's, five 1's, and four 2's.
What is permutation?
A permutation of a set in mathematics is a loosely defined organization of its members into a sequence or linear order, or, if the set is already ordered, a rearranging of its elements. The term "permutation" also refers to the act or process of shifting the linear order of a set.
Here, we have
We have to find the ternary strings (digits 0,1, or 2) that are there with exactly seven 0's, five 1's and four 2's.
There are a total of 7 + 5 + 4 = 16 characters in the string.
The total number of ways to permute seven 0's, five 1's and four 2's is :
= 16!/(7! 5!4!)
= 1441440
Hence, 1441440 ternary strings (digits 0,1, or 2) are there with exactly seven 0's, five 1's and four 2's.
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What percentage of a radioactive isotope remains after 3 half-lives?
Answer:
12.5%------------------------
After 3 half-lives the remaining amount becomes:
(1/2)³ = 1/8 of the initial amountConvert 1/8 to percent:
1/8 * 100% = 12.5%Find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon round of the nearest tenth if necessary162430142240
The required formula to calculate exterior angle and an interior angle are 360°/n and (n-2) * 180°/n.
What is polygon?In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides). To create a closed figure, a minimum of three line segments must be connected end to end.
According to question:The measure of an exterior angle of a regular polygon with n sides is given by 360°/n. The measure of an interior angle of a regular polygon with n sides is given by (n-2) * 180°/n.
So if you provide the number of sides of the polygon, I can give you the measures of the exterior and interior angles rounded to the nearest tenth if necessary.
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Order the following numbers from least to greatest.
Put the lowest number on the left.
0
0
18
-53
-24
Answer: -53, -24, 0, 0, 18
Step-by-step explanation:
A rain gauge had 0.6 centimeter of rain after 2 hours, 0.9 centimeter after 3 hours, 1.2 centimeters after 4 hours, and 1.5 centimeters after 5 hours. At what rate (cm per hour) did it rain?
Answer: 0.3 cm per hour
Step-by-step explanation:
got it off of quizizzes
A basketball team has 15 players on its roster. How many possible starting lineups does the team have? (There are 5 players on a basketball court.)
120
1,200
3,003
5,576
360,360
Answer:
3003
Step-by-step explanation:
This is just basically choosing 5 players out of 15 people.
15 choose 5 is \(\frac{15!}{10!*5!}\)
\(\frac{15*14*13*12*11}{5*4*3*2}\)
3*7*13*11=1001*3=3003
Feel free to tell me if I did anything wrong! :)
The basketball team has 3,003,600 possible starting lineups. Given that there are 15 players on the roster and 5 players on the basketball court, this calculation involves determining the number of ways to select 5 players out of the total 15.
To calculate the number of possible starting lineups, we can use the concept of combinations. We have 15 players on the roster, and we need to select 5 players to form a starting lineup.
The number of ways to choose 5 players out of 15 can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, n represents the total number of players (15) and r represents the number of players needed for the lineup (5).
Plugging these values into the formula, we get:
C(15, 5) = 15! / (5! * (15 - 5)!)
= (15 * 14 * 13 * 12 * 11 * 10!) / (5! * 10!)
= (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)
= 3,003,600
Therefore, there are 3,003,600 possible starting lineups for the basketball team. This means that the team has a vast number of combinations to choose from when selecting the starting lineup from the 15 players on its roster.
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Does anyone know this?!?
(If you know the answer please type it as how i will need to put it into the box)
which of the following is quotient obtained on dividing (x²-b) (x-a) by - (x-a)
Answer:
Step-by-step explanation:
x²-b
Emily has 13 candies and wants to give an even amount to each of her 3 friends. How many candies do each of Emily's friends get, and how many candies are left over?
Answer:
4 with 1 left over
Step-by-step explanation:
* Let D and T be sets, and let X:D→T be a function from D to T. Let T be a σ-algebra of subsets of T, and define D={X−1(B):B∈T}, the collection of subsets A⊂D of the form A=X−1(B) for B∈T. (a) ∗ Show directly that D is a σ-algebra of subsets of D. [3 marks] Now let T=R and T=B, the Borel σ-algebra. Let Ω=D, let F be a σ-algebra of subsets of Ω, and let P be a probability measure on (Ω,F). (a) * Suppose that X is a random variable on the probability space (Ω,F,P). Show that D⊂F.
The set D, defined as D = {X^(-1)(B) : B ∈ T}, is a σ-algebra of subsets of D. If X is a random variable on a probability space (Ω, F, P), then D is a subset of the σ-algebra F.
To show that D is a σ-algebra of subsets of D, we need to verify three conditions:
1. D is non-empty: Since X is a function from D to T, the pre-image of the entire space T is D itself, so D is non-empty.
2. D is closed under complementation: For any set A ∈ D, there exists a corresponding set B ∈ T such that A = X^(-1)(B). Taking the complement of A, we have A^c = X^(-1)(B^c), where B^c is the complement of B in T. Since T is a σ-algebra, B^c ∈ T, and therefore A^c ∈ D.
3. D is closed under countable unions: Let {A_n} be a countable collection of sets in D, with corresponding sets {B_n} in T such that A_n = X^(-1)(B_n) for each n. Taking the union of all the A_n's, we have ∪A_n = X^(-1)(∪B_n), where ∪B_n is the union of all the B_n's in T. Since T is a σ-algebra, ∪B_n ∈ T, and therefore ∪A_n ∈ D.
Now, if X is a random variable on the probability space (Ω, F, P), it means that X is measurable with respect to the σ-algebra F. Since D is a σ-algebra of subsets of D, and X^(-1)(B) ∈ D for any B ∈ T, we can conclude that D ⊂ F.
Therefore, D is a subset of the σ-algebra F when X is a random variable on the probability space (Ω, F, P).
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Becca scored 10, 10, 15, 15, 18, 20, 20, and 20 points in her first 8 basketball games of the season. By how much will her mean score improve if she scores 25 points in her 9th game? Explain.
Answer:
Her mean score increased by 3.125 or 3 1/8 (just use whatever your teacher wants)
Step-by-step explanation:
Let's calculate the mean of Becca's first eight:
Mean = sum of items/# of items
(10 + 10 + 15 + 15 + 18 + 20 + 20 + 20)/8 = 16
Now let's see the mean when she scores 25 (add this to the top) in her 9th game (new # of items)
(10 + 10 + 15 + 15 + 18 + 20 + 20 + 20 + 25)/8 = 19 1/8 or 19.125
Improvement is new mean - old mean, so 19 1/8 - 16 = 3 1/8 or 3.125
2,167 divided by 6 equals
Peter gets paid $20 just for accepting a yard job. He then earns $3 for every hour spent on gardening. He wants to buy a mountain bike which costs $800. How many hours does he need to work on gardening to earn enough money
Answer:
260 hours
Step-by-step explanation:
first take out the 20 fixed cost that doesn't change no matter how long he gardens from 800
divide the remainder which is 780 by 3 which is the amount he gets paid for every hour he gardens. He would have to work 260 hours for the bike if he only takes one yard job
Find the area and perimeter of a square that has a side length of 4. Remember area is a length times width and perimeter is when you add all the sides together.
Answer:
Area= 16
Perimeter= 16
Answer:
A = l*w
P = 2l + 2w
A = 4*4 = 16
A = area
l = length
l = 4
w = width
w = 4
The area is equal to 16.
P = 2*4 + 2*4 = 16
P = perimeter
2l = 2*length
2l = 2*4
2w = 2*width
2w = 2*4
The perimeter is equal to 16.
It can be concluded both are equal to each other.
Hope this helps
A beaker has a mass of 129 g. What is the mass of this beaker in kilograms?
Answer: 0.129 kg
Step-by-step explanation:
A gram to a kilogram can be found by dividing the value of grams by 1000, or multiplying the value by 0.001
Complete the inequality. 13/18___ 11/14 < > =
Answer:
Your answer is <, Hope it helps.
john has walked 15% of the way home from school. if he has walked 54 yards so far, how far does he walk home from school
Answer: John walks a total of 360 yards from school.
Step-by-step explanation:
Let's represent the total distance John walks from school as "x".
According to the problem, John has already walked 15% of the way, which can be written as:
0.15x
We also know that he has walked 54 yards so far, which means:
0.15x = 54
To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:
x = 54 ÷ 0.15
x = 360
Therefore, John walks a total of 360 yards from school.
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which one is greater -6 or 6
Answer:
6 is greater than -6
Explanation:
Hope it helps you..
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I'M SO SICK OF BOTS SOMEONE PLSS HELP
=====================================================
Explanation:
Angles ABC and angle EBD are vertical angles. Vertical angles form when we have an X shape and the angles are opposite one another. These types of angles are always the same measure.
Once we set up statements 2, 3 and 4, we can then use the ASA (angle side angle) rule to prove the triangles are congruent.
Statement 2 handles the "S" in the middle while statements 3 and 4 handle the two "A"s. The order doesn't matter as long as the side is between the angles.
Refer to the diagram below.