2/3 (m + 4) = 1/5 (3m+9)
Answers
\(\frac{2}{3} (m+4) = \frac{1}{5} (3m+9)\)
\(\frac{2m+8}{3} = \frac{3m+9}{5}\)
10m + 40 = 9m + 27
10m - 9m = 27 - 40
m = -13
Answer:
m = - 13
Step-by-step explanation:
2/3 (m + 4) = 1/5 (3m+9)
2/3m + 8/3 = 3/5m + 9/5
2/3m - 3/5m = 9/5 - 8/3
10/15m - 9/15m = 27/15 - 40/15
1/15m = - 13/15
m = - 13/15 / 1/15
m = - 13/15 * 15
m = - 195/15
m = - 13
Related Questions
what is the probability of observing the expected value for the distribution of binomial(100, 0.20)?
Answers
The probability of observing the expected value for the distribution of a binomial (100, 0.20) is 0.20 (or 20%).
The probability of observing the expected value for a binomial distribution can be calculated using the following formula:
Probability = (n C r) p^r (1-p)^(n-r)
where n = number of trials,
r = expected value,
p = probability of success
For the given distribution, binomial (100, 0.20), we know that n = 100 and p = 0.20.
The expected value is given by:E(X) = np = 100 * 0.20 = 20
So, to find the probability of observing the expected value of 20, we need to plug in the values of n, r, and p into the formula:
Probability = (n C r) p^r (1-p)^(n-r)=
(100 C 20) (0.20)^20 (0.80)^80≈
0.1875 ≈ 0.20 (rounded to two decimal places)
Therefore, the probability of observing the expected value for the distribution of binomial (100, 0.20) is approximately 0.20 (or 20%).
To learn more about “probability” refer to the https://brainly.com/question/13604758
#SPJ11
Show the work please! Thanks!!
Answers
Simplifying
2x + 5y = 2
Solving
2x + 5y = 2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5y' to each side of the equation.
2x + 5y + -5y = 2 + -5y
Combine like terms: 5y + -5y = 0
2x + 0 = 2 + -5y
2x = 2 + -5y
Divide each side by '2'.
x = 1 + -2.5y
Simplifying
x = 1 + -2.5y
Simplifying
5X + 10y = 17
Solving
5X + 10y = 17
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-10y' to each side of the equation.
5X + 10y + -10y = 17 + -10y
Combine like terms: 10y + -10y = 0
5X + 0 = 17 + -10y
5X = 17 + -10y
Divide each side by '5'.
X = 3.4 + -2y
Simplifying
X = 3.4 + -2y
Let R be a relation on a set A and suppose R is symmetric
and transitive. Prove the following: If for every x in A
there is a y in A such that x R y, then R is an equivalence
relation.
please state proof technique and explain
Answers
R is transitive. it is an equivalence relation. We used direct proof technique to prove this.
To prove that R is an equivalence relation, we need to show that it is reflexive, symmetric, and transitive.
Since for every x in A there is a y in A such that x R y, we know that R is reflexive. This is because every element in A is related to itself by R, as given by the premise of the problem.
To show that R is symmetric, let x and y be arbitrary elements in A such that x R y. Since R is symmetric, we know that y R x. But since x R y, and R is transitive, it follows that x R x. Therefore, R is symmetric.
Finally, to show that R is transitive, let x, y, and z be arbitrary elements in A such that x R y and y R z. Since R is transitive, it follows that x R z. Therefore, R is transitive.
Since R is reflexive, symmetric, and transitive, it is an equivalence relation. We used direct proof technique to prove this.
Learn more about transitive here
https://brainly.com/question/24606230
#SPJ11
The area of a rectangular field is 4368 m.
If the width of the field is 56 m, what is its length?
Length of the field:
Answers
Answer:
78m
Step-by-step explanation:
We can use the formula of area of rectangle which is the product of length and breadth.
=> A = l * b
=> 4368m² = 56m * l
=> l = 4368m²/56m
=> l = 78m .
Hence the length of the rectangle is 78m.A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 10 granola bars and each large box has 12 granola bars. The camp bought a total of 9 boxes that have 100 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Answers
The system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased is b + s = 9 and 10s + 12s = 100
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the small box be represented as s.
Let the big box be represented as b.
Each small box has 10 granola bars and each large box has 12 granola bars. The The camp bought a total of 9 boxes that have 100 granola bars altogether.
The equation will be:
b + s = 9
10s + 12s = 100
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Answer:
10x + 12y = 100
x + y = 9
Step-by-step explanation:
Define Variables:
Let x = the number of small boxes purchased
Let y = the number of large boxes purchased
Each small box has 10 granola bars, so small boxes have 10x granola bars.
Each large box has 12 granola bars, so large boxes have 12y granola bars. Therefore, the total number of granola bars 10x + 12y equals 100:
10x + 12y = 100
Since a total of 9 boxes were purchased, we know x + y must equal 9.
x + y = 9
If you're good with area or you're good with rhombus' can you help me out? 2 PARTS
Answers
The area of a rhombus with the given diagonals measure is 48 square units.
Given that, the length of two diagonals are 8 units and 12 units.
We know that, Area of rhombus = 1/2 × (product of the lengths of the diagonals)
Here, Area = 1/2 × 8 × 12
= 48 square units
Therefore, the area of a rhombus with the given diagonals measure is 48 square units.
Learn more about the area here:
https://brainly.com/question/27683633.
#SPJ1
it's all on the picture
Answers
Answer:
1. 6 square feet 2. 32ft
Step-by-step explanation:
1. 2x3=6
2. 8 times how many sides so that would be 8x4 which would equal 32
cos 15 - sin 15 = 1/2
prove that :
Answers
Answer:
Cos(15) = Cos(45-30)
Sin(15) = Sin(45-30)
Cos(45-30) - Sin(45-30)
Simplifying both brackets
Recall
Cos(A+B) = CosACosB - SinASinB (For cosine... The sign is always the opposite during expansion. If you look... Cos(A+B) became negative during its expansion;So if It was Cos(A–B)... Its expansion is CosACosB + SinASinB)]
Sin(A+B) = SinACosB + CosASinB
Now let's go!
Cos(45-30) = Cos45Cos30 + Sin45Sin30
From Trig
Cos45 = 1/√2
Cos30 = √3/2
Sin45 = 1/√2
Sin30 = 1/2
Substituting
Cos(45-30) = (1/√2).(√3/2) + (1/√2).(1/2)
= √3/(2√2) + 1/(2√2)
= 1 + √3/(2√2).
For
Sin(45 - 30)
= Sin45cos30 – Cos45Sin30
= (1/√2).(√3/2) – (1/√2).(1/2)
= √3/(2√2) – 1/2√2
= √3 – 1/(2√2)
So the question was
Cos15 - Sin15
Substituting...
1 + √3 / 2√2 – (√3 - 1)/ 2√2
When the Minus interacts with the parenthesis
We have
1 + √3 - √3 + 1 / (2√2)
= 2/2√2
= 1/√2.
THE ANSWER IS 1/√2 AND NOT 1/2.
YOU CAN VERIFY THIS WITH YOUR CALCULATOR ALSO.
YOU'LL HAVE 0.7071 WHICH IS SAME AS 1/√2.
HAVE A GREAT DAY!
Pls explain ur aswer and hsow he steps!
Answers
First find the areas of each shape. So the area for both triangles (a=(b•h)/2) is equal to 20. The second triangle is also 20. 20+20=40.
Now for the rectangles (a=bh), so multiply each height by the base of 4. You end up getting 20, 32, and 36. Now add all those up: 20+32+36+40=128
A state trooper used a radar gun to measure the speed (in miles per hour) of all the cars that drove past her stretch of highway in a twenty minute period. She separated the results by whether the cars were traveling northbound or southbound. The histograms show the speed of each car that she recorded.
Which statement is an appropriate inference based on the median of each data set?
Question 4 options:
1.)The northbound cars were generally faster because the median for the northbound cars is less than the median for the southbound cars.
2.)The northbound cars were generally faster because the median for the northbound cars is greater than the median for the southbound cars.
3.)The southbound cars were generally faster because the median for the northbound cars is less than the median for the southbound cars.
4.)The southbound cars were generally faster because the median for the northbound cars is greater than the median for the southbound cars.
Answers
Answer:
2.
Step-by-step explanation:
There are more boxes towards the highest numbers which means that the medians for northbound cars are generally high while the medians for southbound cars are located more on the smaller numbers representing the speed.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find mZ1 and mZ3 in the kite. The diagram is not drawn to scale.
Answers
The values of angles are m∠1 = 39° and m∠2 = 51° from the given kite.
What is triangle ?
triangle can be defined in which it consists of three sides , three angles and sum of the angles is 180 degrees
Given figure is a kite.
The diagram is not drawn to scale.
We have to find the measure of angle 1 and 3 in the kite.
From the figure,
Kites have two sets of equivalent adjacent sides and one set up of congruent opposite angles.
So, sides AB and AD are equivalent adjacent sides.
m∠1 = 39°
AC and BD are diagonals.
Diagonals of a kite always meet at right angles.
Let the diagonals intersect at point O.
From right triangle AOB,
m∠1 + m∠2 + m∠O = 180°
39° + m∠2 + 90° = 180
m∠2 = 180° - 90° - 39°
m∠2 = 90° - 39°
m∠2 = 51°
Therefore, m∠1 = 39° and m∠2 = 51°.
To learn more about triangle from the given link.
https://brainly.com/question/2773823
#SPJ1
Which graph represents a function with direct variation?
Answers
is it
A) X || Z
B) A T Z
C) A || B
D) X T A
Answers
Answer:
Well I would say the answer is A
Step-by-step explanation:
Because there is no metion of line A
Hope this helps have an awsome day!
Use one of these team benefits and costs to best complete the following sentences. Use each term no more than once.
Enhanced performance Lower stress Lower turnover
Lower absenteeism Fewer injuries Cost reductions
Greater flexibility Improved customer service Frustration
Threat of job loss Slow process to get to high team productivity Risking lost confidence in management
If top management is impatient with the slow process in moving to self-managing teams, teams may be disbanded, returning the organization to its original hierarchical form and .
As empowered teams reduce scrap, make fewer errors, and file fewer worker compensation claims, organizations based on teams are showing significantwhere must change start for a team implementation to be successful?
Answers
Because of the slow process to get to high team productivity, organizational productivity may fall before it rises.
Because teams give employees the freedom to manage themselves and gain respect and dignity, employees in teams often experience organizational productivity, this is known as enhanced performance.
How do most firm enhanced performance of its employees?Firms offer various training and development programs to their employees to enhance their skills and knowledge. These programs could be on-the-job training, coaching, mentoring, workshops, and seminars. The aim is to equip employees with the necessary skills and knowledge required to perform their job functions effectively.
They also set performance goals and expectations for their employees to help them stay focused on achieving specific objectives. These goals are typically aligned with the firm's overall objectives and may include performance metrics, such as productivity, quality, efficiency, and customer satisfaction. Incentives and benefits are offered to motivate employees to perform at their best.
Missing words "Because of the may fall before it rises Because teams give employees the freedom to manage themselves and gain respect and dignity, employees in teams often experience organizational productivity Use your knowledge of how to effectively move to a team-based organization to answer the following question."
Read more about performance
brainly.com/question/1532968
#SPJ1
solve the equation by factoring. check your solution. if there are multiple solutions, list the solutions from least to greatest separated by a comma. 27 x 2^5
Answers
The Solutions of the equation 27x² + 5 = 48x are x = 1/9 , x = 5/3 . .
In the question ,
it is given that ,
the equation is 27x² + 5 = 48x ,
we have to find the solution for it ,
27x² + 5 = 48x
rewriting it , we get ,
27x² - 48x + 5 = 0
27x² - 45x + 5 = 0
27x² - 3x - 45x + 5 = 0
Simplifying further , we get ,
3x(9x - 1) -5(9x - 1) = 0
taking (9x-1) common from both the terms ,
(9x - 1)(3x - 5) = 0
So , either (9x - 1) = 0 or (3x - 5) = 0
x = 1/9 or x = 5/3
Therefore , the solution of the given equation are x = 1/9 , x = 5/3 .
The given question is incomplete , the complete question is
Solve the equation by factoring. check your solution. if there are multiple solutions, list the solutions from least to greatest separated by a comma.
27x² + 5 = 48x .
Learn more about Equations here
https://brainly.com/question/25615696
#SPJ4
Write down the two inequalities that define the shaded region in the diagram
Answers
The two inequalities that define the shaded region in the diagram are:
y ≥ 4 and y < x
How to Write Inequalities that define the Shaded Region?For the solid vertical line, the slope (m) is 0. The inequality sign we would use would be "≥" because the shaded region is to the left and the boundary line is solid.
The y-intercept is at 4, therefore, substitute m = 0 and b = 4 into y ≥ mx + b:
y ≥ 0(x) + 4
y ≥ 4
For the dashed line:
m = change in y / change in x = 1/1 = 1
b = 0
the inequality sign to use is: "<"
Substitute m = 1 and b = 0 into y < mx + b:
y < 1(x) + 0
y < x
Thus, the two inequalities are:
y ≥ 4 and y < x
Learn more about Inequalities on:
https://brainly.com/question/24372553
#SPJ1
The percentage of measurements that are above the 39th percentile is.
Answers
The percentage of measurements that are above the 39th percentile is 61%.
To calculate the percentage of measurements above the 39th percentile, we need to find the complement of the percentile value. The 39th percentile represents the value below which 39% of the measurements fall. Therefore, the complement of the 39th percentile is the percentage of measurements above that value. Since the total percentage adds up to 100%, subtracting 39% from 100% gives us the percentage of measurements above the 39th percentile, which is 61%.
In summary, the percentage of measurements that are above the 39th percentile is 61%. This means that 61% of the measurements are higher than the value corresponding to the 39th percentile.
Learn more about percentile here
brainly.com/question/32171834
#SPJ11
What is the percentage of measurements that fall above the 39th percentile?
PLEASE HELP
What is the measure of the unknown acute angle on the face of this
pyramid?
Answers
Answer:
80°
Step-by-step explanation:
let make suppose angle x°
x°+45°+55°= 180 { the sum of angle of triangle is 180°}
or, x° + 100° = 180°
or, x° = 180° - 100°
or, x° = 80°
x°= 80°
6 1/4×2 1/5 as an improper fraction
Answers
The product of the fractions is 275/20
What is a fraction?
A fraction can simply be defined as the part of a given whole variable, a whole number or a whole element.
In mathematics, there are different types of fractions, namely;
Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
To determine the product of the fraction
6 1/4×2 1/5
convert to improper fractions, we get;
25/4 × 11/5
Multiply the numerators
275/4(5)
Multiply the denominator
275/20
Learn more about fractions at: https://brainly.com/question/11562149
#SPJ1
unding decimals to the nearest whole number, Adam traveled a distance of about
miles.
Answers
In a case whereby Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles Adam traveled a distance of about 335 miles.
How can the distance be calculated?The distance traveled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction.
Speed = Distance/ time
speed =72.4 miles
time=4.62 hours
Distance =speed * time
= 72.4 *4.62
Distance = 334.488 miles
Read more about speed
https://brainly.com/question/13590103
#SPJ1
complete question;
Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles. Rounding decimals to the nearest whole number, Adam traveled a distance of about miles.
Round 18 people in 3 vans round to the nearest hundred
Answers
Answer:
I think the answer will be 18.3
Answer:
6 in each van
Step-by-step explanation:
(a) (5 pts) prove the following identity: n 1 log n = 2
Answers
This proof by induction shows that n + 1 log n = 2 for all positive integers n. This holds true since S(1) = 2, and S(k + 1) = 2 for any integer k ≥ 1.
Proof:
Let S(n) = n + 1 log n
We will prove S(n) = 2 by induction.
Base Case:
Let n = 1. Then S(1) = 1 + 1(log 1) = 1 + 0 = 1 = 2.
Inductive Step:
Assume S(k) = 2 for some arbitrary integer k ≥ 1. We must show that S(k + 1) = 2.
S(k + 1) = (k + 1) + 1(log(k + 1))
= k + 1 + 1(log k + log 1)
= k + 1 + 1(log k + 0)
= k + 1 + 1(log k)
= k + 1 + log k
= 2 + log k
= 2 (by induction hypothesis)
Therefore, S(n) = 2 for all positive integers n.
This proof by induction shows that n + 1 log n = 2 for all positive integers n. This holds true since S(1) = 2, and S(k + 1) = 2 for any integer k ≥ 1.
Learn more about integer here
https://brainly.com/question/15276410
#SPJ4
(01.08 mc) a high school's student council wants to purchase spirit shirts for its upcoming homecoming event. purchases of 25 shirts or less cost $20 per shirt, plus $20 shipping and handling. when more than 25 shirts are ordered, the price is $15 per shirt, plus $15 shipping and handling. if $720 was spent on shirts, how many shirts did the student council order?
Answers
When more than 25 shirts are ordered, the price is $15 per shirt, plus $15 shipping and handling. If $720 was spent on shirts, the student council ordered 47 shirts.
Let x be the number of shirts ordered. We can set up an equation based on the given information:
If x ≤ 25, then the cost of the shirts is 20x + 20.
If x > 25, then the cost of the shirts is 15x + 15.
We know that the total cost of the shirts is $720. So, we can write:
20x + 20 if x ≤ 25
15x + 15 if x > 25
Setting these equal to each other, we get:
20x + 20 = 15x + 15
5x = 5
x = 1
This doesn't make sense, because the number of shirts ordered must be greater than 1. Therefore, we know that the student council ordered more than 25 shirts.
Using the equation 15x + 15 = 720, we can solve for x:
15x + 15 = 720
15x = 705
x = 47
To check, we can calculate the cost of the shirts:
If 47 shirts are ordered, then the cost is 15(47) + 15 = $720.
To learn more about price click on,
https://brainly.com/question/24710811
#SPJ4
Please help me with this question.... please
Answers
Can someone pls help me with this question?
Answers
Answer:
c
Step-by-step explanation:
I think so I might not be right but I'm sure it's c
a three-digit identification card is made. find the probability that the card will contain the digits in any order.
Answers
The probability that a three-digit identification card will contain the digits in any order is 6/720 = 1/120.
Assuming that repetition of digits is not allowed in the identification card, the number of possible three-digit arrangements is 10P3 = 10 × 9 × 8 = 720. There are 3! = 6 ways to arrange three distinct digits, so the number of three-digit arrangements containing the same three digits in any order is 6. Therefore, the probability that a three-digit identification card will contain the digits in any order is 6/720 = 1/120.
Click the below link, to learn more about probability:
https://brainly.com/question/18378030
#SPJ11
A clothing company sells slacks that are either blue or gray and pleated or non-pleated. Last month, the company sold 5 times as many pairs of blue pleated slacks as gray pleated slacks, and it sold twice as many pairs of gray non-pleated slacks as blue non-pleated slacks. If it sold 333 pairs of blue slacks and 225 pairs of gray slacks, how many pairs of blue non-pleated slacks did it sell?
Answers
Answer:
138 pairs
Step-by-step explanation:
The number of blue pleated slacks is 5 times the number of gray pleated slacks, so:
\(blue\ pleated = 5 * gray\ pleated\) (eq1)
The number of gray non-pleated is twice the number of blue non-pleated slacks, so:
\(blue\ nonpleated = 2 * gray\ nonpleated\) (eq2)
The total number of blue slacks is 333, and the total number of gray slacks is 225, so we have that:
\(blue\ pleated + blue\ nonpleated = 333\) (eq3)
\(gray\ pleated + gray\ nonpleated = 225\) (eq4)
If we add (eq1) and (eq2), we have:
\(blue\ pleated + blue\ nonpleated = 5*gray\ pleated + 2*gray\ nonpleated\) (eq5)
Using (eq3) and (eq4) in (eq5), we have:
\(333 = 2*225 + 3*gray\ pleated\)
\(gray\ pleated = 117/3 = 39\)
From (eq1), we have:
\(blue\ pleated = 5*39 = 195\)
From (eq3), we have:
\(blue\ nonpleated = 333 - 195 = 138\)
Answer:
88
Step-by-step explanation:
some please help FAST
Answers
(mrh ch04-102) you are testing the weight of chocolate chip cookies produced by your new baking machine. you take the next 10 cookies off your baking line and weigh them. because cookie weight is naturally variable between cookies, you want to estimate the mean cookie weight. what kind of problem are you solving here?
Answers
The type of problem being solved is an estimation problem. This is because the aim of the problem is to estimate the mean cookie weight. The mean weight will provide an estimate of the weight of cookies produced by the new baking machine. So, it's clear that the kind of problem being solved is an estimation problem.
What is an estimation problem?
An estimation problem is a problem that involves the estimation of a parameter based on a sample statistic. The objective of estimation problems is to calculate the most likely value of the population parameter by using the sample statistic. The sample statistic is a measurable attribute of a random sample from a population, whereas the population parameter is a numerical value that describes the population as a whole. The population parameter can be a mean, standard deviation, proportion, or any other numerical value of interest. Therefore, estimation problems are designed to make a prediction about a population by analyzing a sample.
Therefore, the kind of problem being solved here is an estimation problem.
(mrh ch04-102) You are testing the weight of chocolate chip cookies : https://brainly.com/question/31056999
#SPJ11
Please help me with this
Answers
Answer:
Will
Step-by-step explanation:
Katie runs 8 feet per second
Stephanie runs 10.88 feet per second
Liz runs 12.9 feet per second
Will runs 13.45 feet per second