The sum of two numbers is 32. One number is 3 times as large as the other. What are the numbers?
Answer:
Let the greater number be x and the smaller number be y
A.T.Q,
x+y=32 ...(1)
x=3y ...(2)
putting the value of x from (2) in (1)
(3y)+y=32
4y=32
y= 32/4=8
x=3y
x=3(8)=24
x=24 , y=8
The boxed definition of absolute value states that |a|=-a if a is a negative number. Explain why |a| is always nonnegative, even though |a|=-a for negative values of a.
Final answer:
Since absolute values determine the distance between the number and the value whether the value is positive or negative. As distance is always positive.
Thus, |a| is always nonnegative, even though |a|=-a for negative values of a.
Step-by-step explanation:
Step 1
It is said that |a| is always nonnegative even though even though |a|=-a for negative values of a.
Step 2
This is because by the definition of an absolute value, any real number inside an absolute value symbol || will always be positive.
Select the correct answer.
What is the solution to this equation?
(z
(x + 6) - 5 = -2
OA.
OB. 7
OC. 21
OD. -139
Answer:
-3
Step-by-step explanation:
Equation: (x + 6) - 5 = -2
we want to isolate x
(x + 6) - 5 = -2
+ 5 + 5 (add 5 to start getting x on its own)
x + 6 = 3
- 6 - 6 (subtract 6 to isolate x)
x = -3
so, this answer was not provided, but is the correct answer.
The solution to this equation is -3,
so, the correct answer is: -3.
Here, we have,
given that,
Equation is:
(x + 6) - 5 = -2
we want to isolate x
(add 5 to start getting x on its own)
(x + 6) - 5+ 5 = -2 + 5
(subtract 6 to isolate x)
x + 6 - 6 = 3 - 6
so, we get,
x = -3
so, the solution to this equation is -3,
so, the correct answer is: -3.
To learn more on equation click:
brainly.com/question/24169758
#SPJ7
The following stem-and-leaf plot represents the test scores for
26 students in a class on their most recent test. Use the data provided to find the quartiles.
Stem
Leaves
6 0 1 2 2 4 7 8
7 0 1 2 5 8
8 3 6 6 7 9 9
9 0 1 2 2 2 4 5 8
Key:
6|0=60
To find the second quartile, we must first divide the data in half. There are an even number of data values, so the 50th percentile, or median, is the arithmetic mean of the two values in the middle of the set. Thus, the median is the mean of the 13th data value,
83 and the 14th data value, 86
83+86/2=84.5
Therefore, the second quartile is 84.5
Step 2 of 3 : Find the first quartile.
Considering the given stem-and-leaf plot, the quartiles are given as follows:
The first quartile is of 67.5.The second quartile, which is the median, is of 84.5.The third quartile is of 91.5.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, which are 83 and 86, hence:
Me = (83 + 86)/2 = 84.5.
The first half has 12 elements, hence the first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:
Q1 = (67 + 68)/2 = 67.5.
The third half also has 12 elements, starting at the second 86, hence the third quartile is the mean of the 6th and 7th elements of this half, hence:
Q3 = (91 + 92)/2 = 91.5.
More can be learned about the quartiles of a data-set at https://brainly.com/question/28017610
#SPJ1
3,5,12,55,648? vwhat is the next number
Hello,
Answer:
The next number is 35 585
Step-by-step explanation:
3 × 5 - 3 = 12
5 × 12 - 5 = 55
12 × 55 -12 = 648
55 × 648 - 12 = 35 585
The next number for the given series is 35,585.
What is number series?A number series is a number-based sequence. In the number series questions, we must identify the rules that lead to the formation of a number series. These series vary in nature, as do the questions that may arise from them.
Given that the series is 3,5,12,55,648. The next number will be calculated by decoding the series as below,
3 × 5 - 3 = 12
5 × 12 - 5 = 55
12 × 55 -12 = 648
55 × 648 - 12 = 35,585
Therefore, the value of the next number for the series is 35,585.
To know more about the number series follow
https://brainly.com/question/6561461
#SPJ2
Dont Really need explanation Simply answer
Considering the given graph, the profit during the period was of -2 dollars.
How to add negative numbers along with positive?We add all the negative numbers, all the positive numbers, then keep the signal of the higher absolute value, and subtract the values.
From the graph, we have that:
The sum of the negative numbers is of 8.The sum of the positive numbers is of 2 + 4 = 6.8 > 6, hence the profit is negative given by:
-(8 - 6) = -2 dollars.
More can be learned about the addition of negative numbers at https://brainly.com/question/572656
#SPJ1
graph y(t) = 13.5t - 4.9t^2
Answer:
here
Step-by-step explanation:
Is the relationship between red sox away games and average daily revenues significant at the 95% confidence level? choose the correct answer with the corresponding correct reasoning.
Answer:
Yes, because the p-value of the independent variable is less than 0.05
Step-by-step explanation:
The relationship between Red Sox away games and average daily revenues significant at the 95% confidence level because the p-value ( X) < 0.05 , Option C is the correct answer.
What is Probability ?Probability is the study of chances of an event to happen.
It has a range form 0 to 1 , where 0 indicates uncertainty while 1 indicates certainty.
The data is given and on the basis of it
It can be seen that for 95 % confidence Level
P value =0.0005
So , the relationship between Red Sox away games and average daily revenues significant at the 95% confidence level because the p-value of the independent variable is less than 0.05.
Therefore Option C is the correct answer.
The complete question is
Is the relationship between Red Sox away games and average daily revenues significant at the 95% confidence level? Choose the correct answer with the corresponding correct reasoning.
No, because R Square is less than 50%
Yes, because the slope is positive.
Yes, because the p-value of the intercept is less than 0.05
Yes, because the p-value of the intercept is less than 0.95
Yes, because the p-value of the independent variable is less than 0.05
Yes, because the p-value of the independent variable is less than 0.95
The data table is attached with the answer.
To know more about Probability
https://brainly.com/question/11234923
#SPJ2
(02.02 LC)
If h(x) = −2x − 10, find h(−4).
Group of answer choices
−2
−18
−3
−16
The value of the function h(-4) is (a) -2
How to determine the h(-4)?The function is given as
h(x) = -2x - 10
When x = -4, we have:
h(-4) = -2 * -4 - 10
Evaluate the product
h(-4) = 8 - 10
Evaluate the difference
h(-4) = -2
Hence, the value of the function h(-4) is (a) -2
Read more about functions at:
https://brainly.com/question/12431044
#SPJ1
How many significant figures does 119.3 have
! PLS HELP ! There are a total of 30 white and black marbles in a box. There are 14 more white marbles than black marbles. How many black marbles are in the box?
Answer:
There are 8 black marbles.
Step-by-step explanation:
First, set up your equation. You have black (b) and white (w) marbles, total of 30, so those will be your variables to set in your equation.
w + b = 30
You mentioned that there are 14 more white marbles then black. Therefore, white marbles will have b many marbles + 14, creating the equation:
w= b + 14
If w = b + 14 and w can be easily substituted in the first equation, substitute w for b + 14. This will result in having the equation of:
(b +14) + b= 30
Simplify this equation, combine like terms to break down the equation, making it easier for you to solve for b.
-Subtract 14 from both sides.
-Add b + b = 2b
Then, you will have your resulting equation in which you divided 2 from both sides to get b by itself.
2b = 16
b=8
There are 8 black marbles.
Choose the best selection for the
quadrilateral with vertices at the
following points:
(1,0), (1,4), (6,0), (6,4)
Hint: Start by graphing the points.
Distance Formula: d= √(x2-x1)² + (y2 − ₁)²
A. Rectangle
C. Rhombus
B. Square
D. Trapezoid
Answer: a rectangle
Step-by-step explanation:
If you graph the points out you will see that it is four points high and six points wide
Answer:
It is A.Rectangle. from the given points.
Step-by-step explanation:
the graph is given in the image.
I hope it to be helpful ^=^
The height of a triangle is 4 m less than its base. The area of the triangle is 48 m². What is the length of the base? Enter your answer in the box.
The length of the base of the triangle is 12m
Area of a triangleThe formula for calculating the area of a triangle is expressed as:
A = 0.5 * base * height
If the height of a triangle is 4 m less than its base, then;
h = b - 4
Substitute
A = 0.5(b)(b-4)
48 = 0.5b²-2b
b²-4b - 96 = 0
Factorise
b² - 12b + 8b - 96 = 0
b(b-12)+8()b-12) = 0
b - 12 = 0
b = 12
Hence the length of the base of the triangle is 12m
Learn more on area of triangle here: https://brainly.com/question/17335144
#SPJ1
Margaret makes bracelets and sells them to tourists. the function s(t) approximates how many bracelets margaret makes per hour. the function w(h) represents how hours per week margaret spends making bracelets. what are the units of measurement for the composite function s(w(h))?
The units for the composite function s(w(h)) is bracelets over a week when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.
To define the unit of the composite function s(w(h)), we first need to find the units of the functions s(t) and w(h).
The function s(t) represents the number of bangles per hour, so its unit will be bangles over an hour.
The function w(h) represents the hours per week spent on making the bracelets, so its unit will be hours over a week.
Now, we can define the unit of the composite function s(w(h)).
To find the unit of the composite function we follow these steps:-
s(w(h)),
= s(hours over a week) {replacing the function w(h) by its units},
= (bangles over an hour(hours over a week)) {replacing the function s(t) with its units},
= bangles over a week {Simplifying}.
Thus, the units for the composite function s(w(h)) is bracelets over a week when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.
Learn more about the units of a composite function at
https://brainly.com/question/15056566
#SPJ4
Which benchmark fraction is
Please help I’m stuck
Hello,
Step-by-step explanation:
6/7 ≈ 0,857
we have 4/4 = 1 and 3/4 = 0,75
| 0,75 - 0,857| = 0,107
| 1 - 0,857 | = 0,143
→ Answer is 3/4
Answer:
the bench mark is 1/4 and the lower range is 3/4.
Step-by-step explanation:
Estimate the fraction 6/7 using 1/4 as our benchmark: Display the fraction bar for 6/7 The lower range is 3/4 and the upper range is 1
On March 4, Micro Sales makes $13,500 in sales on bank credit cards which charge a 3% service charge and deposits the funds into Micro Sales' bank accounts at the end of the business day.
Required:
Journalize the sales and recognition of expense. Refer to the Chart of Accounts for exact wording of account titles. Round your answers to two decimal places.
Based on the sales made by Micro Sales on bank credit cards, the journal entries would be:
Date Account Title Debit Credit
March 4 Cash $13,095
Card Service expense $ 405
Sales Revenue $13,500
How is the transaction by Micro Sales recorded?The cash account will be debited with:
= 13,500 x (1 - 3%)
= $13,095
The Card service expense is:
= 13,500 x 3%
= $405
Sales revenue will be credited by the amount of sales which is $13,500.
Find out more on recording credit card sales at https://brainly.com/question/24038076.
#SPJ1
A baker purchased 13 lb of wheat flour and 14 lb of rye flour for a total cost of $14.85. A second purchase, at the same prices, included 15 lb of wheat flour and 12 lb of rye flour. The cost of the second purchase was $14.85. Find the cost per pound of the wheat flour and of the rye flour.
An equation is formed when two equal expressions. The cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the cost of a pound of wheat flour be x and the cost of a pound of rye flour be y.
A baker purchased 13 lb of wheat flour and 14 lb of rye flour for a total cost of $14.85.
13x + 14y = $14.85
x = (14.85-14y)/13
A second purchase, at the same prices, included 15 lb of wheat flour and 12 lb of rye flour.
15x + 12y = $14.85
Substitute the value of x from the above equation and solve for y,
[tex]\dfrac{15(14.85-14y)}{13} + 12y = 14.85\\\\222.75-210y+156y = 193.05\\\\y = 0.55[/tex]
Substitute the value of y in any one of the equations formed,
13x + 14(0.55) = 14.85
13x = 7.15
x = 0.55
Hence, the cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
The probability all of the students in this class will be present and on time is 3/10. The probability all of the students are present is 2/5. What is the probability that everyone is on time given that everyone is present? Give your answer as a simplified fraction.
Answer:
3/4
Step-by-step explanation:
A: students present
B: students on time
P(all students present and on time) = P(A and B) = 3/10
P(all students present) = P(A) = 2/5
P(A and B) = P(A).P(B|A) where P(B|A) is the probability of everyone being on time given that everyone is present
So P(B|A) = P(A and B) /P(A) = 3/10 ÷ 2/5 = 3/10 * 5/2 = 15/20 which can be reduced to 3/4 by dividing numerator and denominator by 5
A box contains 162 marbles which are either red or blue. There are 42 more blue marbles than red marbles. How many blue marbles are in the box? Blue marbles=
The number of the blue marbles are in the box will be 102.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
A box contains 162 marbles which are either red (r) or blue (b).
r + b = 162 ...1
There are 42 more blue marbles than red marbles.
b = r + 42 ...2
Then from equation 1 and 2, we have
r + r + 42 = 162
2r = 120
r = 60
Then the number of blue marble will be
b = 60 + 42
b = 102
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
Choose the number sentence that applies the commutative property to the example.
3 × 4 = 12
6 + 6 = 12
12 × 1 = 12
6 × 2 = 12
4 × 3 = 12
Simplify (x^2)^3*5x/6x^2*15x^3
When we Simplify [(x^2)^3 × 5x] / [6x^2 × 15x^3], the result obtained is (1/18)x^2
Data obtained from the question[(x^2)^3 × 5x] / [6x^2 × 15x^3]Simplification =?How to simplify [(x^2)^3 × 5x] / [6x^2 × 15x^3][(x^2)^3 × 5x] / [6x^2 × 15x^3]
Recall
(M^a)^b = M^ab
Thus,
(x^2)^3 = x^6
[(x^2)^3 × 5x] / [6x^2 × 15x^3] = [x^6 × 5x] / [6x^2 × 15x^3]Recall
M^a × M^b = M^(a+b)
Thus,
x^6 × 5x = 5x^(6 + 1) = 5x^7
6x^2 × 15x^3] = (6×15)x^(2 + 3) = 90x^5
[x^6 × 5x] / [6x^2 × 15x^3] = 5x^7 / 90x^5Recall
M^a ÷ M^b = M^(a - b)
Thus,
5x^7 ÷ 90x^5 = (5÷90)x^(7 - 5) = (1/18)x^2
Therefore,
[(x^2)^3 × 5x] / [6x^2 × 15x^3] = (1/18)x^2Learn more about algebra:
https://brainly.com/question/2768008
#SPJ1
Which
graph shows a dilation?
What is a possible value for the missing term of the geometric sequence? 25,_,874,…
Answer:
The middle term is 5√874======================
Given sequence25, x, 874, ...To findThe missing term xSolutionSince the given is the GP, find the common ratio in terms of given values:
r = x/25r = 874/xEquate the two values and solve for x to find the missing term:
x/ 25 = 874/xx² = 874*25x² = 21850x = √21850x = 5√874Over the past five years, an analyst records the annual returns (in percent) for a mutual fund as: 13, −2, 3, 18, and −14. Construct the 95% confidence interval for μ.
The required confidence interval for μ is (-12.07, 19.27 )
Annual returns (in percent) for a mutual fund as: 13, −2, 3, 18, and −14
95% Confidence interval
The statistic is the study of mathematics which deal with relations between comprehensive data.
Mean(x) = 13-2+3+18-14/5
x = 3.6
Standard deviation = [tex]\sqrt{\frac{\sum(x_i- x)^2}{n-1} }[/tex]
S = 12.6214
Point estimate of (μ) = 3.6
Confidence interval = mean (+,-) Tc x S/√5
= 3.6 (+,-) 2.7764 x 12.62/√5
=3.6 (+,-) 15.671
= (-12.07, 19.27)
Thus, the required confidence interval for μ is (-12.07, 19.27 ).
Learn more about Statistics here:
https://brainly.com/question/23091366
#SPJ1
On a coordinate plane, a line goes through (negative 4, 0) and (0, 2). The graph of the equation y = 12 x + 2 is displayed. Which equations would intersect the orange line at the y-intercept? Check all that apply. y = 7x + 2 y = 3x + 5 y = 2 minus StartFraction 7 Over 3 EndFraction x y – 2 = 4x 3y = –9x – 6
The equation of line which would intersect be
y = 7x + 2 y = 2- 7/3x y-2 = 4xWhat is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given:
y = 12 x + 2
and, a line passes through (-4, 0) and (0, 2)
Equation of line
y = -1/2 (x+ 4)
y= -x/2 - 2
The equations which would intersect the line will be
y = 7x + 2 y = 2- 7/3xy-2 = 4xLearn more about equation here:
https://brainly.com/question/10413253
#SPJ1
Suppose 4y – 1 = 15 and y = 5x – 3.
Which of the following equations is equivalent to 4y – 1 = 15, but written only in terms of x?
The equivalent equation of 4y – 1 = 15 is 20x - 13 = 15
How to determine the equivalent equation?The equations are given as:
4y – 1 = 15 and y = 5x – 3.
Substitute y = 5x – 3. in 4y – 1 = 15
4(5x – 3) – 1 = 15
Expand
20x- 12 - 1 = 15
Evaluate the like terms
20x - 13 = 15
Hence, the equivalent equation of 4y – 1 = 15 is 20x - 13 = 15
Read more about equivalent equation at:
https://brainly.com/question/2972832
#SPJ1
linear pairs of angles are always adjacent true or false
The statement that linear pairs of angles are always adjacent is true.
What are Linear Pairs?
The pair of angles formed when two lines intersect each other at a point, are called Linear Pairs, the angles formed are adjacent to each other and they share a common arm.
It is asked in the question that linear pairs of angles are always adjacent and the answer is yes, it is a true statement as they have a common arm and an uncommon arm, the sum of the angles is equal to 180 degrees.
Hence, the statement that linear pairs of angles are always adjacent is true.
To know more about Linear Pairs
https://brainly.com/question/1757859
#SPJ1
Two cars leave town at the same time one travels West at 56 miles per hour and the other travel south at 42 miles per hour after 1 hour how far apart are the cars
Ulises lives 11 miles from school. Convert the distance to feet
Answer:
58080
Step-by-step explanation:
You just have to multiply it by 5280. So, 11*5280 is 58080. The answer is 58080.
A can do a piece of work in 40 days. He works at it for 5 days and then B finishes it in 10 days.
In what time can A and B together finish it ?
Answer:Given
a can do a piece of work = 40 days
so, A's 1 day work =1/4
so, A's 8 day's work =8/40=1/5
remaining work = 1- 1/5= 4/5
Now, B can do 4/5 piece of work in =16 days
So, B’s 1 day's work = (4/5) /16= 4/ 5x6=1/20
Therefore, (A+B)’s 1 day's work = 1/40+1/20 =
1+2/40=3/40
∴ Both (A+B) can do a piece of work in =
1/days (3/40) = 40/3 days
= 13 1/3 days