\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)
\(\large\sf\:3 \frac { 5 } { 6 } - 1 \frac { 1 } { 3 }\\\)\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)
\(3 \frac { 5 } { 6 } - 1 \frac { 1 } { 3 } \\ \)
Multiply 3 and 6 to get 18.
\(\frac{18+5}{6}-\frac{1\times 3+1}{3} \\ \)
Multiply 1 and 3 to get 3.
\(\frac{23}{6}-\frac{3+1}{3} \\ \)
Add 3 and 1 to get 4.
\(\frac{23}{6}-\frac{4}{3} \\ \)
The least common multiple of 6 and 3 is 6. Convert 23/6 and 4/3 to fractions with denominator 6.
\(\frac{23}{6}-\frac{8}{6} \\ \)
Because 23/6 and 8/6 have the same denominator, subtract them by subtracting their numerators.
\(\frac{23-8}{6} \\ \)
Subtract 8 from 23 to get 15.
\(\frac{15}{6} \\ \)
Reduce the fraction 15/6 to its lowest terms by extracting and cancelling out 3.
\( \frac{5}{2} \\ \)
5/2 as a mixed fraction will become :-
\( \huge \boxed{\boxed{ \bf \: \frac{5}{2} = 2\frac{1}{2} }} \\ \)
\( {x}^{2} + 2x = 0\)
Answer:
\(\textbf{Hello!}\)
\(\Longrightarrow2^2+2z=0\)
\(\Longrightarrow x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \:0}}{2\cdot \:1}\)
\(\Longrightarrow \sqrt{2^2-4\cdot \:1\cdot \:0}\)
\(\Longrightarrow =\sqrt{2^2-0}\)
\(\Longrightarrow =\sqrt{2^2}\)
\(\Longrightarrow=2\)
\(\Longrightarrow x_{1,\:2}=\frac{-2\pm \:2}{2\cdot \:1}\)
\(\Longrightarrow x_1=\frac{-2+2}{2\cdot \:1},\:x_2=\frac{-2-2}{2\cdot \:1}\)
\(\Longrightarrow\frac{-2+2}{2\cdot \:1}\)
\(\Longrightarrow =\frac{0}{2\cdot \:1}\)
\(\Longrightarrow =\frac{0}{2}\)
\(=0\)
\(\Longrightarrow\frac{-2-2}{2\cdot \:1}\)
\(\Longrightarrow =\frac{-4}{2\cdot \:1}\)
\(\Longrightarrow =\frac{-4}{2}\)
\(\Longrightarrow =-\frac{4}{2}\)
\(=-2\)
\(x=0,\:x=-2\Longleftarrow\)
\(\underline{HOPE ~IT~HELPS}\)
A rectangular painting is bordered on all sides by a frame. Write an
expression to describe the area of the frame.
A. 6x + 4
B. 4x2 + 3
C. 5x + 3
D. 4x2 + 5x + 3
I think it is a 6x+4
The required area of the frame shown is 5x + 3. Option C is correct.
What is surface area?The surface area of any shape is the area of the shape that is faced or the surface area is the amount of area covering the exterior of a 3D shape.
Here,
The area of the picture is given as,
= 2x × x
= 2x²
The area of the whole painting with frame.
= (x + 1)(2x+ 3)
= 2x² + 5x + 3
The area of the frame is given as,
= area of picture with frame - an area of the picture,
= 2x² + 5x + 3 - 2x²
= 5x + 3
Thus, the required area of the frame shown is 5x + 3. Option C is correct.
Learn more about the surface area here: https://brainly.com/question/2835293
#SPJ2
Ty bought a new computer for $499. This brand depreciates at a rate of 12% of the original price per year. The value y of Ty's computer, x years after he purchased it, is found using an equation in the form y = mx + b. What is the approximate value of m?
Answer:
the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.
Step-by-step explanation:
o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").
Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:
m = -12% / 100 = -0.12
The average low temperatures in international falls minnesota are shown in the graph f(x) represents the function that contains these points find each of the following
The Relative Maximum will be (7, 50) and minimum is (12, 0).
We have the graph showing average low temperatures in international falls minnesota.
From the graph the maximum y coordinate is 50.
So, the Relative Maximum will be (7, 50).
and, the minimum y coordinate is 0.
So, the Relative minimum is (12, 0)
Learn more about Relative Maximum and Minimum here:
https://brainly.com/question/29158306
#SPJ1
The lines A and B are parallel. Identify a pair of corresponding angles?
Answer:
2 and 5............................
Answer:
Yes. 2 & 5 / 4 & 8 / 1 & 6 / 3 & 7 (Choose one yourself)
Step-by-step explanation:
Corresponding angles are angles that have one angle outside a pair of parallel lines and one angle within it and they are equal to each other.
HELP PLS!!!!!!!!!!!!!!!!!!!!!!!!!!! n
We can split 200 into 100 x 2.
100 is a perfect square and its square root is 10. The 2 will remain under the radical.
ANSWER: 10 sqrt(2)
(Option 2)
Hope this helps!
The population of a city grew from 43,209 to
45,687 in just five years. What was the percent
increase in the population to the nearest whole
percent?
Answer:
5 percent or 5.7349percent
divide 43209 by 45687 and get 1.0573491 subtract one
and get 0.0573491 make into a percentage 5.7percent depending on where you need to round.
In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.
Answer: The percentage of people surveyed who liked blue cars is 50%.
Step-by-step explanation:
Total number of people partaking in survey= 36
number of people who like blue cars= 18
therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)
hence, percentage of people who liked blue cars= (18/36)*100 %
= 50%
To learn more about percentages visit the link below:
https://brainly.com/question/30399396
Answer:
Percentage of people who like blue-coloured cars is 50%
Number of people who were surveyed=36
Number of people who like blue-colored cars=18
Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100
=(18/36)*100
=50%
Read more about percentage
https://brainly.in/question/21062337#:~:text=Answer%3A,has%20no%20unit%20of%20measurement.
A survey of 400 students yielded the following information: 262 were seniors, 215 were commuters, and 150 of the seniors were commuters. How many of the 400 surveyed students were seniors or were commuters?
Out of the 400 surveyed students, 327 were either seniors or commuters.
To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.
According to the information given:
There were 262 seniors.
There were 215 commuters.
150 of the seniors were also commuters.
To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.
Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters
= 262 + 215 - 150
= 327
Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.
It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.
This ensures an accurate count of the students who fall into either category.
For similar question on surveyed.
https://brainly.com/question/14610641
#SPJ8
When 1370 subjects were asked, "On how many days in the past 7 days have you felt lonely?" the mean was 1.5 and the standard deviation was 2.16. The margin of error for a 95% confidence interval for the population mean is 0.12. Construct that confidence interval, and interpret it. The confidence interval goes from nothing to nothing. (Round to two decimal places as needed.)
Answer:
Confidence Interval = (1.41, 1.59)
Step-by-step explanation:
To construct a confidence interval for the population mean, we can use the following formula:
Confidence Interval = sample mean ± (margin of error * standard error)
where the standard error is equal to the standard deviation divided by the square root of the sample size.
Given the information provided, we can calculate the standard error as:
standard error = 2.16 / sqrt(1370) = 0.058
Then, we can calculate the margin of error as 0.12.
Substituting these values into the formula, we get:
Confidence Interval = 1.5 ± (0.12 * 0.058)
Confidence Interval = (1.41, 1.59)
Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.
A worker bee has a mass of 0.00011 \text{ kg}0.00011 kg0, point, 00011, start text, space, k, g, end text.
Choose the best approximation of the mass of a worker bee.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
1 \cdot 10^{-4}\text{ kg}1⋅10
−4
kg1, dot, 10, start superscript, minus, 4, end superscript, start text, space, k, g, end text
(Choice B, Checked)
B
1 \cdot 10^{-3}\text{ kg}1⋅10
−3
kg1, dot, 10, start superscript, minus, 3, end superscript, start text, space, k, g, end text
An African elephant has a mass of 8139 \text{ kg}8139 kg8139, start text, space, k, g, end text.
Choose the best approximation of the mass of an African elephant.
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
8 \cdot 10^{3}\text{ kg}8⋅10
3
kg8, dot, 10, cubed, start text, space, k, g, end text
(Choice B)
B
8 \cdot 10^{4}\text{ kg}8⋅10
4
kg8, dot, 10, start superscript, 4, end superscript, start text, space, k, g, end text
Approximately how many times as large is the mass of an African elephant as the mass of a worker bee?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
8\cdot 10^68⋅10
6
8, dot, 10, start superscript, 6, end superscript
(Choice B)
B
8\cdot10^78⋅10
7
8, dot, 10, start superscript, 7, end superscript
(Choice C)
C
8\cdot10^88⋅10
8
Answer:
Answer:
1). Option (A)
2). Option (A)
Step-by-step explanation:
1). A worker bee has the mass = 0.00011 kg
In scientific notation we can convert the mass of bee as,
0.00011 =
=
Since 1.1 ≈ 1,
Therefore, 1.1 × 10⁻⁴ ≈ 1 × 10⁻⁴ kg
Option (A) is the answer.
2). An African elephant has a mass = 8139 kg
In scientific notation,
8139 = 8.139 × 10³
Since, 8.139 ≈ 8
Therefore, 8139 kg = 8.139 × 10³ kg
Option (A) is the answer.
Step-by-step explanation:
Can someone please help with question 2 for my little brother in 4th grade?
Answer:
Susie is correct. And Sammy rounded to the nearest thousand.
Step-by-step explanation:
Susie rounded 39,090 to 39,000 because for thousands you round to the hundredth. And Sammy rounded the 90 to 1,000, but really it should have been rounded to the hundredth. Short story short Susie rounded right and Sammy got it wrong because he/she rounded the the nearest thousand not the hundredth.
Company Holdings in Marks Brothers
Total number of shares: 78,000
USS Oil 8%
Harp Pensions 12%
Marks Family Trust 32%
PRH 19%
Live Fund 24%
Marks Brothers is paying a dividend of $56.25 on each share. How much will PRH
receive in dividends?
$14,820
$43,875
$83,363
$638,725
$833,625
Answer:
Amount of dividend that PRH will receive is $833,625.
Step-by-step explanation:
The following are given in the question:
Total number of shares of Marks Brothers = 78,000
Percentage of shares of Marks Brothers held by PRH = 19%
Dividend per share = $56.25
Therefore, we can now proceed as follows:
Number of shares of Marks Brothers held by PRH = Total number of shares of Marks Brothers * Percentage of shares of Marks Brothers held by PRH = 78,000 * 19% = 14,820
Amount of dividend that PRH will receive = Number of shares of Marks Brothers held by PRH * Dividend per share = 14,820 * $56.25 = $833,625
The amount of dividend that PRH will receive is $833,625.
The calculation is as follows;
Number of shares of Marks Brothers held by PRH is
= Total number of shares of Marks Brothers × Percentage of shares of Marks Brothers held by PRH
= 78,000 × 19%
= 14,820
Now
Amount of dividend that PRH will receive = Number of shares of Marks Brothers held by PRH × Dividend per share
= 14,820 × $56.25
= $833,625
Learn more: brainly.com/question/16911495
find the equation of the line that contains the point (-4,-4) and is perpendicular to the graph of y=-4/5x-1
The equation of the line that contains the point P(−4, −4) and is perpendicular to the graph of y = − 4/5x − 1 is y+4 = 5/4(x+4)
Equation of a line in point slope formThe equation of a line in point slope form is expressed as;
y-y1 = m(x-x1)
where
m is the slope
(x1, y1) is any point on the line
Given the following
(x1, y1) = (-4, -4)
perpendicular lope = 5/4
Substitute
y-(-4) = 5/4(x-(-4))
y+4 = 5/4(x+4)
Hence the equation of the line that contains the point P(−4, −4) and is perpendicular to the graph of y = − 4/5x − 1 is y+4 = 5/4(x+4)
Learn more on equation of a line here: https://brainly.com/question/19417700
#SPJ1
I need help!
Question 1 and 2 have the same questions so HELP!!
Answer:
21.99 or just round to 22
Step-by-step explanation:
Radius is 3.5
Diameter is 7
Circumference is 21.99
Answer:
1st Circle
Radius = 3.5
Diameter = 7
Circumference = 2 × \(\pi\) × r = 2 × 3.14 × 3.5 = 21.98
2nd Circle
Radius = 9
Diameter = 18
Circumference = 2 × \(\pi\) × r = 2 × 3.14 × 9 = 56.52
:DDDDDDDDD
I’m doing some homework and I completely forgot how to do perimeter since 5th. Just answer the first question so I can understand it againn :’)
Answer:
You can start by changing 12 3/4 into a decimal, which would be 12.75.
The formula for perimeter of a rectangle is (l + w) x 2, so you could write it like this:
(12.75 + 6.4) x 2
Then solve the question in the parenthesis...
19.15 x 2 = 38.30
Now, the question says to write the perimeter into simplest fraction form.
38.30 = 38 3/10.
So, there you have it!
38 3/10 meters
If this helped mark me as brainliest!
16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
to know more about unitary method
https://brainly.com/question/28276953
Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
Graph this function. F(x)=3/4x-2
Answer:
Slope = \(\frac{3}4}\)
y-intercept = (0, -2)
HELP WITH ALL OF IT PLEASE I WILL GIVE BRAINLEIST
In Rebecca's neighborhood, 89% of the houses have garages and 48% have a
garage and a pool. What is the probability (in percent) that a house in her
neighborhood has a pool, given that it has a garage? Round your answer to 1
decimal place.
why are there two of these?
Answer:
53.9
Step-by-step explanation:
89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9
katie rents a car while spending her vacation travelling in australia. when she returns the car, she has driven 1400 miles and used about 56 gallons of gas. if gas costs an average of $5.099 per gallon, estimate how much she spent on fuel.
Katie spent approximately $285.544 on fuel during her vacation in Australia.
The Average Cost is the per unit cost of the product received by dividing the total cost (TC) by the total output (Q). By per unit cost of production, we mean that all the fixed and variable costs are considered for calculating the average cost. Thus, it is also called Per Unit Total Cost.
Symbolically, the average cost is expressed as:
AC = TC/Q
To estimate how much Katie spent on fuel, you need to multiply the number of gallons of gas she used (56 gallons) by the average cost of gas per gallon ($5.099):
56 gallons × $5.099/gallon = $285.544
So, Katie spent approximately $285.544 on fuel during her vacation in Australia.
To know more about Average Cost, here
https://brainly.com/question/28851877
#SPJ4
Rotate the vector (5,1) 90°
clockwise about the origin.
Answer:
(-1, 5)
Step-by-step explanation:
this is correct
The new coordinates of the vector (5,1) after rotating it 90° clockwise about the origin would be (-1,5).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
Rotating a vector 90° clockwise in a 2D coordinate system can be accomplished by "flipping" the vector's x and y coordinates and then negating one of them.
In this case, the original x-coordinate is 5 and the y-coordinate is 1.
When we negate the x-coordinate and swap the positions of x and y, we get the new coordinates of (-1,5).
To learn more about the transformations click here :
brainly.com/question/28029674
#SPJ2
Which expression is equivalent to -3(2x - 8) + 4x?
Answer:
- 2x + 24
Step-by-step explanation:
- 3(2x - 8) + 4x ← distribute parenthesis by - 3
= - 6x + 24 + 4x ← collect like terms
= - 2x + 24 or 24 - 2x
Hey there!
-3(2x - 8) + 4x
DISTRIBUTE -3 within the parentheses
= -3(2x) - 3(-8) + 4x
= -6x + 24 + 4x
COMBINE the LIKE TERMS
= (-6x + 4x) + (24)
= -6x + 4x + 24
= -2x + 24
Therefore, your answer should be:
-2x + 24
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
HEEELLLLPPP!
Whoever answers right will get brainliest!!!!!!!!!
Answer:
\(y =\frac{x}{4}\)
Step-by-step explanation:
Pre-SolvingWe are given several functions, and we want to figure out which one is linear.
A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.
SolvingLet's go through the list.
Starting with \(y=\frac{3}{x} -7\), we can see that x is in the denominator. If this is the case, it means that the power of x is -1.
Even though y has a power of 1, this is NOT linear, because x has a power of -1.
Now, with y=√x-2, this is also not linear. This is because √x = \(x^\frac{1}{2}\), even though y has a power of 1.
For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.
This leaves us with \(y = \frac{x}{4}\). x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.
This means that \(y=\frac{x}{4}\) is linear.
A line with a slope of 9/7 passes through the point (7, 14).What is its equation in slope -intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
PLEASE ANSWER ASAP!!!
Answer:
y=9/7x+5
Explanation:
We have the slope, and a point that is not an intercept. We can use Desmos graphing calculator to test y-intercepts.
Find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 75 quarts of 3% butterfat milk. The mixture should contain ___ quarts of the 4% butterfat milk.
Answer:
50
Step-by-step explanation:
The amount of 4% butterfat milk is equal to x quarts , When 1% butterfat milk is equal to 75-x. The amount of butterfat in 4% butterfat milk is x/100*4=0.04x
The amount of butterflat in 1% butterfat milk is (75-x)/100= 0,75-0.01x
1The amount of butterflat in 75 quarts of 3% butterfat milk (our desired mixture) is 75/100*3= 2.25
This quantity (2.25) is the sum of butterfat from 4% butterfat milk and 1% butterfat milk(the sum of 0.04x and 0.75-0.01x)
the equation is
0.04x+0.75-0.01x=2.25
0.03x=1.5
x=50
Candace had $20,000 to invest. She invested part the money at 5% and the remaining part of the money at 8%. If her income from the two investments was $1435, how much did she invest at each of the rates?
a
$5000 at 5% and $15000 at 8%
b
$14500 at 5% and $5500 at 8%
c
$3500 at 5% and $16500 at 8%
d
$5500 at 5% and $14500 at 8%
Answer:
D
Step-by-step explanation:
To solve this problem, we can use algebra. Let's call the amount invested at 5% "x" and the amount invested at 8% "y".
We know that:
x + y = $20,000 (because this is the total amount Candace had to invest)
We also know that:
0.05x + 0.08y = $1435 (because this is the total income from the two investments, and we need to use the percentage rates to calculate the income)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y:
y = $20,000 - x
We can substitute this expression for y into the second equation:
0.05x + 0.08($20,000 - x) = $1435
0.05x + 0.08($20,000) - 0.08x = $1435
0.05x - 0.08x = $1435 - 0.08($20,000)
-0.03x = $1435 - $1600
-0.03x = -$165
x = $5500
So, Candace invested $5500 at 5%. To find how much she invested at 8%, we can use one of the original equations:
x + y = $20,000
$5500 + y = $20,000
y = $20,000 - $5500
y = $14500
Therefore, Candace invested $14500 at 8%
The answer is d) $5500 at 5% and $14500 at 8%
Can someone help me please I need the coordinates for X , Y , W and Z
Answer --
x: -4.5,-2
y: -1,-2
w: -6,-5
z: -2.5,-5
format is x,y
Explanation --
Not completely sure if it's correct, I haven't done coordinates in a while and I could make a mistake, but I just read the dots on the x axis and y axis.
To read x and y axis, you could go to this website - https://thirdspacelearning.com/blog/what-are-coordinates-explained/#:~:text=Coordinates%20are%20written%20as%20(x,first%20and%20then%20the%20y.
Find the value of 35÷c when c= 7.
Answer:
5
Step-by-step explanation:
when c = 7,
substitute 7, into 35÷c
35 ÷ 7 = 5
Dan spent a total of $25 at the grocery store. Of this amount, he spent 14 on fruit. What percentage of the total did he spend on fruit?
Answer:
56%
Step-by-step explanation:
This is because the question you need to ask yourself is: 14 is what percent of 25? and the way you solve that is making it 14/25 and then all percents are out of 100 so you need to change the fraction to over 100 so just multiply by 4 (because 25 x 4 is 100) and you get 56/100, which means 56%.