a fruit company delivers its fruit in two types of boxes: large and small. a delivery of 2 large boxes and 3 small boxes has a total weight of 78 kilograms. a delivery of 6 large boxes and 5 small boxes has a total weight of 180 kilograms. how much does each type of box weigh ?
weight of each large box: ? kilogram(s)
weight of each small box: ? kilogram(s)
Answers
Answer:
large box: 18.75 kgsmall box: 13.5 kgStep-by-step explanation:
The information given in the problem statement lets you write two equations relating box weights (L for the large box weight; S for the small box weight).
2L +3S = 78 . . . . . . weight of the first collection of boxes
6L +5S = 180 . . . . . weight of the second collection of boxes
We can subtract 3S from the first equation and multiply it by 3 and we have ...
2L = 78 -3S . . . . . . subtract 3S [eq3]
6L = 234 -9S . . . . . multiply by 3
Now we have an expression for 6L that can substitute into the second equation:
(234 -9S) +5S = 180
234 -4S = 180 . . . . . . . . simplify
54 -4S = 0 . . . . . . . . . . . subtract 180
13.5 -S = 0 . . . . . . . . . . . divide by 4
13.5 = S . . . . . . . . . . . . . add S
From [eq3] above, we can now find L.
2L = 78 -3(13.5) = 37.5
L = 37.5/2 = 18.75
The weight of the large box is 18.75 kg; the small box is 13.5 kg.
_____
A graphing calculator can provide an alternate means o finding the solution.
Related Questions
Suppose 15% of the apples picked one afternoon are rotten. The following simulations demonstrate how apples can be randomly chosen and then recorded as rotten or not rotten. Which simulation best models the scenario? Place 20 equally sized pieces of paper in a hat. Of the 20, 3 read "rotten," and the rest read "not rotten". Place 15 equally sized pieces of paper in a hat. Of the 15, 3 read "rotten," and the rest read "not rotten". Place 30 equally sized pieces of paper in a hat. Of the 30, 3 read "rotten," and the rest read "not rotten". Place 12 equally sized pieces of paper in a hat. Of the 12, 3 read "rotten," and the rest read "not rotten".
Answers
Answer:
Place 20 equally sized pieces of paper in a hat. Of the 20, 3 read "rotten," and the rest read "not rotten".
Step-by-step explanation:
If a+b(c+d)/e =1 which of the variable a,b,c,d, or e cannot be 0?
A.) b
B.) e
C.) a
D.) d
E.) c
Answers
Answer:
B.) e
Step-by-step explanation:
If e is zero and c + d ≠ 0, then the quotient [tex]\frac{c + d}{e}[/tex] will be an undefined number and in that case;
a + b([tex]\frac{c + d}{e}[/tex]) ≠ 1
Use the linear combination method to solve the system of equations. Explain each step of your solution. 2x-3y=13 4x-y=-9
Answers
2x -3y = 13
4x -y = -9
Multiply the second equation by -3 to make the coefficient of Y opposite the first equation.
4x -y = -9 x -3 = -12x + 3y = 27
Now add this to the first equation:
2x -12x = -10x
-3y +3y = 0
13 +27 = 40
Now you have :
-10x = 40
Divide each side by -10:
x = 40 / -10
x = -4
Now you have a value for x, replace that into the first equation and solve for y:
2(-4) - 3y = 13
-8 - 3y = 13
Add 8 to both sides:
-3y = 21
Divide both sides by -3:
y = 21/-3
y = -7
Now you have X = -4 and y = -7
(-4,-7)
Please help me with this
Answers
Answer:
26 cm
Step-by-step explanation:
Tangents drawn to a circle from a point outside the circle are equal in length.
On the left side the tangents are 4/ 4 and 3/3
On the right side the tangents are 2/ 2 and 4/4
Calculating perimeter from the bottom left clockwise
perimeter = 4 + 4 + 3 + 3 +2 + 2 + 4 + 4 = 26 cm
If f(x)=(x−3)2+1, what is f(6)?
Answers
Answer:
7
Step-by-step explanation:
If 6 is x, then it would be (6-3)2+1. 6-3 is 3, 3 times 2 is 6, 6+1=7
The answer is 7... Just Plug 6 into x and then solve
A surveyor is dividing a large plot of land that measures 27,512 square miles. He wants to divide the area into 91 equal regions. Estimate how large each area will be. Show your work.
Answers
Answer:
302 mi²
Step-by-step explanation:
Actually we're looking for the "unit rate," which here is the number of square miles are in each region:
27,512 mi²
---------------- = 302 mi² approximately (rounded up from 302.33 mi²)
91 regions
the mean (rounded to the nearest tenth if needed) of the following data set is: 110, 142, 120, 180, 151, 110, 159, 173, 173, 144, 110
A. 142.9
B. 157.2
C. 131
D. 146.8
Answers
Answer:
A
Step-by-step explanation:
Add up all of the numbers:
110+142+120+180+ 151+110+159+173+173+144+110 = 1572
Next you divide by how many number there are (there are 11 numbers)
1572 ÷ 11 = 142.9090909
142.9090909 rounded to the nearest tenth is 142.9
Answer:
A. 142.9
Step-by-step explanation:
There are 11 members in the data set, therefore:
The mean = (110+142+120+180+151+110+159+173+173+144+110) / 11
= 1572/11
= 142.9.
Please help me out :)
Answers
Answer:
A = 25√3 cm²
Step-by-step explanation:
View 5√3 cm as being the height of an equilateral triangle whose base is at the bottom of the purple figure. To find the area of one such triangle, we use the area-of-a-triangle formula A = (1/2)(b)(h).
opp
Using the sine function sin Ф = --------
hyp
we find the length of the hypotenuse, which is also the radius of the octagon, and because this is an equilateral triangle, is also the length of the base:
√3 5√3 cm
sin 60° = -------- = ------------- , which produces the value of hyp:
2 hyp
√3 5√3 cm
-------- = ------------- , which produces the value of hyp:
2 hyp
√3·hyp = 10√3, or hyp = 10 cm
Then the area of this one triangle is A = (1/2)(b)(h), or
A = (1/2) (10 cm)(5√3 cm) = 25√3 cm²
Using the DMS method to describe an angle, one degree of angle measurement can be divided into how many minutes?
Answers
Answer:
1 degree = 60 minutes
Step-by-step explanation:
The DMS method is for Degree Minutes Seconds. That allows you to give a precise location the way it's most commonly used on paper maps. Today, with the electronic maps we mostly use the numeric version (34.234 degrees for example).
So, in the DMS method, one degree is basically like an hour on your clock. It can be divided into 60 minutes. Then, those minutes can be divided into 60 seconds. Just like an hour, a degree has 60 minutes and 3600 seconds.
Final answer:
One degree in the DMS method of angle measurement is divided into 60 minutes. To convert DMS to DD, like with 118 degrees 15 minutes, divide the minutes by 60 and add the result to the degrees, giving you 118.25.
Explanation:
In the DMS method of angle measurement, one degree is equivalent to 60 minutes of angle. This is similar to how an hour of time is divided into 60 minutes. To visualize this, if you consider a full circle being 360 degrees, each degree can be further subdivided into 60 smaller parts, each of these parts is known as a minute of angle.
For example, the conversion of 118 degrees 15 minutes to decimal degrees (DD) is a simple mathematical process. You would divide the minutes by 60 since there are 60 minutes in a degree, resulting in the equation 118 + 15/60, which equals 118.25 degrees. This conversion is an important skill in coordinate conversion activities, where positions are described in DMS format and need to be converted to DD for calculations.
Select the coordinates of two points on the line y = 8. (2 points) (8, 8) and (8, 0) (8, −8) and (8, 8) (0, 8) and (8, 0) (0, 8) and (8, 8)
Answers
(8, 8) and (0, 8). If the equation is y = any number, the second coordinate will always be that number. :)
If there are initially 5000bacteria in a culture,and the number of bacteria doubles each hour,the number N of bacteria after t hours can be found using the formula N = 5000 [2 t ^]. About how long will it take the culture to grow to 40000 bacteria?
Answers
Answer:
3 hours
Step-by-step explanation:
3 hours as it takes 3 periods to be 40000
If there are initially 5000 bacteria in a culture,and the number of bacteria doubles each hour. The culture will take around 3 hours to reach 40,000 bacteria.
What is bacteria?To determine how long it will take for the culture to grow to 40,000 bacteria, we can use the given formula: N = 5000 * (2^t), where N represents the number of bacteria after t hours.
Substitute N with 40,000 and solve for t:
40,000 = 5000 * (2^t)
Divide both sides by 5000:
8 = 2^t
Since 2^3 = 8 we can conclude that t is equal to 3
Therefore it will take approximately 3 hours for the culture to grow to 40,000 bacteria.
Learn more about bacteria here:https://brainly.com/question/30638162
#SPJ3
in the 1980s, an average mortgage range was around 18.75%. how much less per month would a $125,000 30 year mortgage be today if the current rate were 5%?
Answers
Answer:
$1289.48
Step-by-step explanation:
A financial calculator tells you the payment with the higher interest rate is $1960.51, and that with the lower interest rate is $671.03. The difference in payment amounts is ...
$1960.51 -671.03 = $1289.48
Answer:
The current per month mortgages are $1289.54 less than the earlier per month mortgages.
Step-by-step explanation:
The EMI formula is = [tex]\frac{p\times r\times (1+r)^{n} }{(1+r)^{n}-1 }[/tex]
Here p = 125000
For case 1:
r = 18.75/12/100=0.015625
n = [tex]30\times12=360[/tex]
So, putting values in formula we get :
[tex]\frac{125000\times 0.015625\times (1+0.015625)^{360} }{(1+0.015625)^{360}-1 }[/tex]
= $1960.51
For case 2:
r = 5/12/100=0.004166
n = [tex]30\times12=360[/tex]
So, putting values in formula we get :
[tex]\frac{125000\times 0.004166\times (1+0.004166)^{360} }{(1+0.004166)^{360}-1 }[/tex]
= $670.97
Now we will find the difference between both EMI's
[tex]1960.51-670.97=1289.54[/tex] dollars.
Therefore, the current per month mortgages are $1289.54 less than the earlier per month mortgages.
The coordinates of point P on a coordinate grid are (?5, ?6). Point P is reflected across the y-axis to obtain point Q and across the x-axis to obtain point R. What are the coordinates of points Q and R? 1. Q(5, 6) and R(?5, ?6) 2. Q(?5, ?6) and R(5, 6) 3. Q(?5, 6) and R(5, ?6) 4. Q(5, ?6) and R(?5, 6)
Answers
Answer:
(5, −6) and R(−5, 6)
Step-by-step explanation:
Answer:
4. Q(5, -6) and R(-5, 6)
Step-by-step explanation:
In the coordinates of point P which is (-5,-6) when you reflect it on the Y axis that means that the Y would be the same but the X will change signs, thats why the point Q is (5.-6) and to reflect it on the X axis the X remains the same but the Y would change the sign this is why point R will be (-5,6).
So point Q is (5,-6) and point R is (-5,6).
If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of is . If the coordinates of point D are (5 , 5), the equation of line is y = x + .
Answers
Answer with explanation:
Equation of line Passing through two points (a,b) and (c,d) is given by:
[tex]\frac{y-b}{x-a}=\frac{d-b}{c-a}[/tex]
Equation of line Passing through two points (8,0) and (3,7) is given by:
[tex]\rightarrow \frac{y-7}{x-3}=\frac{7-0}{3-8}\\\\\rightarrow \frac{y-7}{x-3}=\frac{7}{-5}\\\\\rightarrow -5 y+35=7 x - 21\\\\\rightarrow 5 y= -7 x +35 +21\\\\ y=\frac{-7 x}{5}+\frac{56}{5}\\\\y=-1.4 x +11.2[/tex]
Comparing with slope intercept form of line,
y= m x+c, where , m is slope and c is y intercept.
⇒Y intercept = 11.2
Equation of line Passing through two points (5,5) and (3,7) is given by:
[tex]\rightarrow \frac{y-7}{x-3}=\frac{7-5}{3-5}\\\\y-7= -1 \times (x-3)\\\\y=7-x+3\\\\y=-x +10[/tex]
Comparing with slope intercept form of line,
y= m x+c, where , m is slope and c is y intercept.
⇒Y intercept = 10
Equation of line is, y= -x +10.
The y-intercept of the line passing through point A (8, 0) and B (3, 7) is 56/5. The equation of the line that passes through these points and point D (5, 5) is y = (-7/5)x + (56/5).
To determine the y-intercept and the equation of a line, we first need to find the slope of the line. The slope (m) is given by the rise over run, which can be calculated using the coordinates of two points on the line. We have point A with coordinates (8, 0) and point B with coordinates (3, 7). The slope is therefore:
m = (Y2 - Y1) / (X2 - X1) = (7 - 0) / (3 - 8) = 7 / (-5) = -7/5
Now, we use the slope-intercept form of a line equation, which is y = mx + b, where b is the y-intercept. We can determine b by substituting the slope and the coordinates of one of the given points (we'll use point A). So:
0 = (-7/5)(8) + b
b = (7/5)(8) = 56/5
Therefore, the y-intercept is 56/5.
Knowing point D with coordinates (5, 5) is also on the line, we can use our slope m and this point to write the equation of the line:
y = (-7/5)x + (56/5)
However, since we know point D lies on this line, we can check if our equation is correct by substituting x = 5 and seeing whether y = 5:
5 = (-7/5)(5) + (56/5)
5 = -7 + 56/5
5 = 5
This confirms that our calculated equation is indeed correct and passes through all given points.
Please answer this question only if you know the answer! 33 points and brainliest!
Answers
Because the teacher only picked 5 students out of all the students it was a sample.
If the teacher had asked every student, it would have been a population.
Answer:
sample
Step-by-step explanation:
The teacher only asked the five students specifically so it is a sample.
Population would be if the teacher asked every student.
Solve the system by using a matrix equation
2x-3y=3
5x-7y=9
Answers
Answer:
The correct answer would be option C
Step-by-step explanation:
Can I have some help please? Algebra 2 is not my strong suit.
Multiply: i(4−7i)
Answers
Answer:
We have the following equation:
i(4-7i)
Multiplying:
4i - 7(i^2)
So we know that i = sqrt(-1), then i^2 = -1.
For that reason:
4i - 7(i^2) = 4i - 7(-1) = 4i + 7
So the answer is: 4i +7
Answer for the problem is 4i-7i^2
Identify the volume of the sphere in terms of π. HELP PLEASE!!
Answers
Answer:
its C
Step-by-step explanation:
The length of a rectangle, I, is six meters more than it's width, w. If the perimeter of the rectangle is 36 meters what is the length of the rectangle, in meters
Answers
Answer:
Length = 12 meters
Step-by-step explanation:
Rectangle
Perimeter P = 2(L + W)
The length of a rectangle, I, is six meters more than it's width, W.
Then L = W + 6
So
P = 2(W + 6 + W)
P = 2 (2W + 6)
P = 4W + 12
Plug in P = 36 meters
36 = 4W + 12
4W = 36 - 12
4W = 24
W = 6 meters
L = 6 + 6
L = 12 meters
Marisa earns $7.50 an hour working at Panera. She wants to earn at least $250 to purchase 4 concert tickets. The cost of each ticket is $75 plus a $12.95 convenience fee per ticket. Is $250 enough to cover the cost of 4 tickets? If not, how many more hours does she need to work to cover the difference? No, she would need to work an additional 14 hours to purchase 4 concert tickets. No, she would need to work an additional 34 hours to purchase 4 concert tickets. No, she would need to work an additional 47 hours to purchase 4 concert tickets. Yes, $250 is enough to purchase 4 concert tickets.
Answers
Answer:
Part 1) [tex]\$250[/tex] is not enough to cover the cost of 4 tickets
Part 2) She would need to work an additional 14 hours to purchase 4 concert tickets
therefore
No, she would need to work an additional 14 hours to purchase 4 concert tickets
Step-by-step explanation:
step 1
Find the cost of 4 tickets
[tex]4*(75+12.95)=\$351.80[/tex]
so
[tex]\$351.80> \$250[/tex]
therefore
[tex]\$250[/tex] is not enough to cover the cost of 4 tickets
step 2
Find the number of hours needed to work to cover the difference
The difference is equal to
[tex]\$351.80-\$250=\$101.80[/tex]
Let
x-----> the number of hours needed to work to cover the difference
The inequality that represent the situation is
[tex]7.50x \geq 101.50[/tex]
[tex]x \geq 101.50/7.50[/tex]
[tex]x \geq 13.5\ hours[/tex]
The minimum number of hours is 14
Find the exact volume of the cylinder. A) 80π ft3 B) 160π ft3 C) 200π ft3 D) 400π ft3
Answers
80 ft^3 is the answer
Answer:
200ft^3
Step-by-step explanation:
Amber is on a family cell phone plan with 2 other family members. The family gets 720 shared cell phone minutes a month, each family is limited to his or her equal fair share of minutes each month and calls between family members cost zero minutes. How many minutes per day does Amber have to call her friends without going over her monthly minutes if there are 30 days in that month?
Answers
Amber plus 2 family members = 3 total people on the plan.
They share the minutes equally so divide the minutes by 3 to find how many she can use:
720 / 3 = 240 minutes per month.
Now divide the monthly minutes by 30 days:
240 / 30 = 8 minutes per day.
Evaluate cot870°.
1. - sqrt3
2. -1/sqrt3
3. 1/sqrt3
4. sqrt3
Answers
ANSWER
[tex] -\sqrt{3}[/tex]
EXPLANATION
The given angle is 870°.
870°-360°-360°=150°
This means that:
870° is coterminal with 150°, hence its terminal side is in the second quadrant.
It makes an acute angle of 30° with the x-axis.
Note that cotangent is negative in the second quadrant,
Hence,
[tex] \cot(870 \degree) = \cot(150 \degree) = - \cot(30 \degree) = - \frac{1}{ \tan(30 \degree) } = - \sqrt{3} [/tex]
The first option is correct.
Answer:
use math-way
Step-by-step explanation:
= - square root of 3
Find the values of x and y.
Answers
x = 90
y = 180 - (90 + 47)
y = 43
What is the leading coefficient of the polynomial?
23x5 + 12x2 + 19x3 + 15x6
A) 12
B) 15
C) 19
D) 23
Answers
ANSWER
B) 15
EXPLANATION
The given polynomial is
[tex]23 {x}^{5} + 12 {x}^{2} + 19 { x }^{3} + 15 {x}^{6} [/tex]
We arrange this polynomial in ascending powers of x to obtain the standard form;
[tex] 15 {x}^{6} + 23 {x}^{5} + 19 { x }^{3} + 12 {x}^{2}[/tex]
The degree of this polynomial is 6.
The coefficient of the leading term is 15
Find the value of x. Round to nearest tenth
Answers
Answer:A?
Step-by-step explanation:
Answer:
x = 55.6
Step-by-step explanation:
In this triangle, the hypotenuse is the unknownj. The sine function relates the hypotenuse, the angle and the side opposite the angle:
sin Ф = opp / hyp
Here, sin 20° = 19 / x. This can be rearranged as x = 19 / sin 20°
This works out to x = 19 / 0.342, or 55.6.
x = 55.6
PLEASE HELP DON'T UNDERSTAND THIS AT ALL AND PLEASE SHOW YOUR WORKING WILL CHOOSE THE BEST PERSON TO BE THE BRAINLIEST
Answers
Answer:
40 cm
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{4x}{x}[/tex] = [tex]\frac{48}{x+2}[/tex], simplifying gives
4 = [tex]\frac{48}{x+2}[/tex]
Multiply both sides by (x + 2)
4(x + 2) = 48 ( divide both sides by 4 )
x + 2 = 12 ( subtract 2 from both sides )
x = 10
Hence
width = 4x = 4 × 10 = 40
Help on number 6, please explain
Answers
So it's asking how many times greater is 6,000 than 600. Simply divide to find that it is 10 times greater.
Hope this helps you!
The 6 in the hundreds place is 100 and the 6 in the thousands place is 1000
So,it's 10x greaterKeith bought a baseball for 10.37 and spent 8.29 on toy trucks keith also spent 6.03 on a jacket in total how much did keith spend on toys
Answers
Answer:
$18.66
Step-by-step explanation:
Add together the amounts Keith spent on baseball and truck: $10.37 + $8.29 = $18.66. We can ignore the amount he spent on the jacket.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Suppose Company A produces packages of throat lozenges that are normally distributed with a mean of 38.2 individual lozenges and a standard deviation of 1.7 lozenges.
Company B produces packages of throat lozenges that are normally distributed with a mean of 36.9 individual lozenges and a standard deviation of 2.4 lozenges.
Select from the drop-down menus to correctly complete the statement.
CHOICES ARE COMPANY A AND COMPANY B
Answers
Answer: B, A, B
Step-by-step explanation:
Let's find the z-score for both companies using the formula: [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Company A: [tex]z=\dfrac{43-38.2}{1.7}=\large\boxed{2.8}[/tex]
Company B: [tex]z=\dfrac{43-36.9}{2.4}=\large\boxed{2.5}[/tex]
The z-score from Company B is closer to 0 than the z-score of Company A so it it more likely that a package of 43 lozenges is produced by Company B
Since the z-score from Company A is closer to zero than the z-score of Company B, the company that produced a package with 43 lozenges in it is most likely Company A.
To find which company is more likely to produce a package with 43 lozenges, we'll first calculate the z-scores for each company using the formula:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
Where:
- [tex]\( x \)[/tex] is the number of lozenges in the package (43)
- [tex]\( \mu \)[/tex] is the mean number of lozenges in the package for each company
- [tex]\( \sigma \)[/tex] is the standard deviation of the number of lozenges in the package for each company
For Company A:
[tex]\[ z_A = \frac{43 - 38.2}{1.7} = \frac{4.8}{1.7} \approx 2.82 \][/tex]
For Company B:
[tex]\[ z_B = \frac{43 - 36.9}{2.4} = \frac{6.1}{2.4} \approx 2.54 \][/tex]
Since the z-score for Company A (2.82) is higher than the z-score for Company B (2.54), it indicates that the value of 43 lozenges is relatively further away from the mean for Company A compared to Company B.
Thus, Company A is more likely to produce a package with 43 lozenges.
The correct question is:
Suppose Company A produces packages of throat lozenges that are normally distributed with a mean of 38.2 individual lozenges and a standard deviation of 1.7 lozenges.
Company B produces packages of throat lozenges that are normally distributed with a mean of 36.9 individual lozenges and a standard deviation of 2.4 lozenges.
Select from the drop-down menus to correctly complete the statement.
Since the [tex]$z$[/tex]-score from [tex]$\square$[/tex] is closer to zero than the [tex]$z$[/tex]-score of [tex]$\square$[/tex] , the company that produced a package with 43 lozenges in it is most likely [tex]$\square$[/tex] .