Answer:
x = 119
Step-by-step explanation:
Solution:-
- The number of students in a marching band = x
- When they Line up in "twos" there is 1 left over, That if we mathematically express it:
Division: x / 2 , Remainder = 1
- When they Line up in "threes" there is 2 left over, That if we mathematically express it:
Division: x / 3 , Remainder = 2
- When they Line up in "fours" there is 3 left over, That if we mathematically express it:
Division: x / 4 , Remainder = 3
When they Line up in "fives" there is 4 left over, That if we mathematically express it:
Division: x / 5 , Remainder = 4
When they Line up in "sixes" there is 5 left over, That if we mathematically express it:
Division: x / 6 , Remainder = 5
When they Line up in "sevens" there are no left over, That if we mathematically express it:
Division: x / 7 , Remainder = 0
- It means that the total number of "x" students are perfectly divisible by 7. If it is not divisible by 2, then it is an odd number.
- So,
x = 7 * a
Where, x > 7 and exclude derivative multiples of (5, 4 , 6)
- So from trial and error, a = 17
x = 119
Using multiples and remainder of divisions, it is found that there were 119 students there.
-------------------------
When they line up in sevens, no students remain, thus, the number of students is a multiple of 7.When they line up in two's, there is 1 left over, thus, the number of students is odd.When they line up in three's, there are 2 left over, thus, the remainder of the division of the number of students n and 3 is 2.When they line up in fives, there are 4 left over, thus, the remainder of the division of the number of students n and 5 is 4.When they line up in sixes there are 5 left over, thus, the remainder of the division of the number of students n and 6 is 5.-------------------------
Shortening the possibilities, we look at odd multiples of 7, which are: {7, 21, 35, 49, 63, 77, 91, 105, 119, ...}
21, 63 and 105 are multiples of 3, so these are not the number of students.35 is multiple of 5, so it is also disconsidered.The remainder of the division of 119 and 3 is 2.The remainder of the division of 119 and 5 is 4.The remainder of the division of 119 and 6 is 5.Thus, 119 is the number of students.
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What is a possible measure of an angle that has a terminal side in Quadrant III and makes a 60degree angle with the x -axis
Answer:
[tex]240^\circ[/tex]
Step-by-step explanation:
See the attached picture. One possible angle measure is [tex]60^\circ+180^\circ=240^\circ[/tex]
The possible measure of an angle with terminal side in 3rd quadrant and making an angle of 60°with the X-axis is 240°.
What is the terminal side of an angle?When the vertex of an angle is at the origin and one ray is on the positive x-axis, it is said to be in standard position. The ray on the x-axis is known as the starting side, while the ray on the y-axis is known as the terminal side.
The question is shown in the figure below:
The angle made with X - axis = 60°
Angle is lying in 3rd quadrant
If we start moving in the anticlockwise direction then the measure of the total angle will be 180° + 60° = 240°.
Hence, the total angle for an angle lying in 3rd quadrant is 240°.
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What is the radius and diameter of the following circle?
7 cm
Diameter =
-
Answer:
Radius =
Diameter =
Answer:
Diameter = 7cm
Radius = 3.5cm
Step-by-step explanation:
The diameter is the distance across the circle; shown as 7cm.
The radius is half the distance of the diameter, or half the distance across the circle.
Answer:
Radius = 3.5
Diameter = 7
Step-by-step explanation:
Radius = half of diameter
Diameter is the 7 cm you see on the image.
Brenda sewed a total of 784 buttons on 90 dresses. She sewed 8 or 12 buttons on each dress. how many dresses have 12 buttons on it？please help fast
By setting up a system of equations based on the given information, we find that Brenda sewed 12 buttons on 28 dresses.
Explanation:Since there are 90 dresses in all, Brenda would have sewed 8 buttons on some and 12 buttons on the remaining. We can set up a system of equations to solve this. Let's say the number of dresses that have 8 buttons is 'x' and the number of dresses with 12 buttons is 'y'. Hence, we have two equations:
x + y = 90 (which is the total number of dresses)8x + 12y = 784 (which is the total number of buttons)From the first equation, we get x = 90 - y. Substituting this into the second equation, we have 8*(90 - y) + 12y = 784. Solving this yields, y = 28. Therefore, Brenda sewed 12 buttons on 28 dresses.
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A bag contains 100 cubes that are black, yellow, and white. A student randomly selects a cube without looking and replaces it in the bag. If the student selected 9 black cubes, 4 yellow cubes, and 7 white cubes, which of the options below show a reasonable estimate for the total number of a certain cube in the bag? Select all that apply.
A) 45 black cubes
B) 20 yellow cubes
C) 70 white cubes
D) 90 black cubes
E) 35 white cubes
Answer:
The answer is..
A) 45 black cubes
B) 20 yellow cubes
E) 35 white cubes
Step-by-step explanation:
Final answer:
To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. The estimates for the total number of a certain cube in the bag are 45 black cubes and 20 yellow cubes.
Explanation:
To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. In this case, the proportion of black cubes to the total number of cubes is 9/20. So, if there are 100 cubes in total, we can estimate that there are approximately 45 black cubes in the bag. Similarly, the proportion of yellow cubes to the total number of cubes is 4/20, so we can estimate that there are approximately 20 yellow cubes in the bag. However, the proportion of white cubes to the total number of cubes is 7/20, which is less than the proportion of yellow cubes. Therefore, we cannot estimate that there are 70 white cubes in the bag. The estimates for the total number of a certain cube in the bag are A) 45 black cubes and B) 20 yellow cubes.
Alexis is knitting a blanket 6 meters long. Every 3 decimeter, she changes the color of the yarn to make stripes. How many stripes will the blanket have?
Answer:
There are 20 color strips in the blanket.
Step-by-step explanation:
We are given the following in the question:
Length of blanket = 6 meter
A new color strip is added every 3 decimetres
We have to find the number of color strips in the blanket.
1 decimetre = 0.1 meter
Number of color strips =
[tex]=\dfrac{\text{Length of blanket}}{\text{Color strip every 3 decimeter}}\\\\=\dfrac{6}{3\times 0.1}\\\\=20[/tex]
Thus, there are 20 color strips in the blanket.
scientific notation for 778,330,000?
Answer:
7.7833 × 108
Step-by-step explanation:
Answer:
7.78×10∧8
Step-by-step explanation:
Simplify 3y -y
.
.
.
.
3y-y =2y
you have 3 ys and you are taking one y away so the answer is 2y.
think it as 3 yogurts and you eat one, then you have 2 yogurts
hope this helps!
Lucia is making invisibility potions. Each potion requires 222 eyes of newt. How many invisibility potions can Lucia make with 161616 eyes of newt? Lucia has all of the other ingredients she needs.
We have been given that Lucia is making invisibility potions. Each potion requires 2 eyes of newt. We are asked to find the number of invisibility potions that Lucia can make with 16 eyes of newt.
We will use proportions to find the number of potions that Lucia can make with 16 eyes of newt as:
[tex]\frac{\text{Invisibility potions}}{\text{Number of Newt eyes}}=\frac{1}{2}[/tex]
[tex]\frac{\text{Invisibility potions}}{16}=\frac{1}{2}[/tex]
[tex]\frac{\text{Invisibility potions}}{16}\times 16=\frac{1}{2}\times 16[/tex]
[tex]\text{Invisibility potions}=8[/tex]
Therefore, Lucia can make 8 invisibility potions with 16 eyes of newt.
In a hydraulic jack, the pipe below the load has an area of 4 m2, and the pipe through which the input force transmits has an area of 0.1 m2. What input force is necessary to balance a load of 9,000 N?
Answer:
The input force needed is 225 Newtons
Step-by-step explanation:
From hydraulic pressure laws, we have that the pressure at the same level throughout the body of a fluid is equal.
This means that for the Hydraulic Jack, input pressure = output pressure
Recall,Pressure is a ratio of force and area
i.e pressure = Force / Area
For the hydraulic jack to work properly, the pressure at the input end must be equal to the pressure at the output end.
[tex]\frac{F_{1}}{A{1}} = \frac{F_{2}}{A_{2}}[/tex]
[tex]\frac{9000}{4}=\frac{Force}{0.1}[/tex]
From this we can compute that the Input force = 225 Newtons
Answer:
Step-by-step explanation:
Since the pipe is an enclosed container, we would apply Pascal's law which states that a pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and the walls of the container,
This means that pressure at input = pressure at output
Pressure = force /area
Input force = unknown
Input area = 0.1 m²
Output force = 9000N
Output area = 4m²
Therefore
Input force/0.1 = 9000/4
Input force = 0.1 × 9000 /4 = 225N
136 / 286 Marks
78%
Daisy measured the heights of 20 plants.
The table gives some information about the heights (h in cm) of the plants.
Height of plants (h) Frequency
0< < 10
10 <n< 20
4
20 <h<30
30 <h <40
2
40 <h <50
50 <h < 60
3
|
By using the midpoints of each group, work out an estimate
for the mean height of a plant.
Will will
be
acer
The mean point of the each group can be calculated using midpoint and mean formula. The mean is sum of all the term divided by number of term.
The mean height of a plant is 30.5.
Given:
The height of plant and frequency is given in table.
Refer the attached table for the calculation of mid point and frequency of midpoint.
Now we have ,
[tex]\rm {Sum \:of\: frequencies} = 20[/tex]
[tex]{\rm Sum \:of\: frequency\: \times midpoint\: product} = 610[/tex]
Calculate the mean of height of a plant.
[tex]\rm Mean=\dfrac{610}{20}\\\rm Mean=30.5[/tex]
Thus, the mean height of a plant is 30.5.
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To estimate the mean height of 20 plants, using midpoints and frequencies, the calculation yields approximately 13.89 cm. This provides a representative value based on the distribution of heights within specified intervals.
To estimate the mean height of the plants using the midpoints of each group, we'll calculate the midpoints for each interval and then find the weighted average.
1. Midpoint for 0 < h < 10:
- Midpoint = (0 + 10)/2 = 5
2. Midpoint for 10 < h < 20:
- Midpoint = (10 + 20)/2 = 15
3. Midpoint for 20 < h < 30:
- Midpoint = (20 + 30)/2 = 25
4. Midpoint for 30 < h < 40:
- Midpoint = (30 + 40)/2 = 35
5. Midpoint for 40 < h < 50:
- Midpoint = (40 + 50)/2 = 45\)
6. Midpoint for 50 < h < 60:
- Midpoint = (50 + 60)/2 = 55
Now, calculate the weighted average using the frequencies:
[tex]\[ \text{Mean height} = \frac{\sum (\text{Midpoint} \times \text{Frequency})}{\sum \text{Frequency}} \]\[ \text{Mean height} = \frac{(5 \times 4) + (15 \times 2) + (25 \times 3) + (35 \times 0) + (45 \times 0) + (55 \times 0)}{4 + 2 + 3 + 0 + 0 + 0} \]\[ \text{Mean height} = \frac{20 + 30 + 75}{9} \]\[ \text{Mean height} = \frac{125}{9} \][/tex]
Therefore, the estimate for the mean height of a plant is approximately 13.89 cm.
The ratio of nonfiction books to fiction books in a library is 105 to 189. Which statement describes this relationship?
A)
There are 5 nonfiction books for every 9 fiction books in the library.
B)
There are 9 fiction books for every 5 nonfiction books in the library.
C)
There are 5 nonfiction books for every 14 books in the library.
D)
There are 9 fiction books for every 14 books in the library.
Answer: A)There are 5 nonfiction books for every 9 fiction books in the library.
Step-by-step explanation: If you do the math you realize that there are clearly less nonfiction books than fiction books.
105/5=21 and after 21*9 lines up and to check your work than
5*21=105 and 9*21=189 it is not B because the smaller number 105 is in front of the ratio 105:189 and 5:9
Per 5 nonfiction books there are 9 fiction books in the given library.
Given that;
Ratio of nonfiction books to fiction books = 105:189
Computation:
Ratio of nonfiction books to fiction books = 105:189
[tex]Ratio\ of\ nonfiction\ books\ to\ fiction\ books = \frac{105}{189}\\\\Ratio\ of\ nonfiction\ books\ to\ fiction\ books = \frac{35}{63}\\\\Ratio\ of\ nonfiction\ books\ to\ fiction\ books = \frac{5}{9}\\\\[/tex]
So,
we say that;
Per 5 nonfiction books there are 9 fiction books
Option "A" is the correct answer to the following question.
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PLEASE ANSWER THIS QUICKLY!! I WILL GIVE BRAINLIEST!!!
The monthly demand for a company's sports caps varies directly as the amount spent on advertising and inversely as the square of the price per cap. At $15 per cap, when $2750 is spent each week on ads, the demand is 330 caps. When advertising is increased to $3250, what price yields a demand of 330 caps? (Round your answer to the nearest cent.)
I think it's $16.432 but I'm not sure.
The price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
It is given that at $15 per cap , $2750 is spent each week on ads , and demand is 330 caps.
So , we can find how much money earn if cost is $15 per cap.
As 330 is the demand , then total earning is :
= 330 × 15
= $ 4950
Out of this , $2750 is spent per week on ads. So , total profit is :
= 4950 - 2750
= $ 2200
Now , If advertising is increased to $3250 then , money more spent on ads is :
= 3250 - 2750
= 500
So , total earning will be :
= 3250 + 2200
= 5450
And price per cap for demand of 330 caps will be :
= 5450 ÷ 330
= 16.51 per cap
Therefore , the price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.
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Perry sells TVs at an electronics store. He makes a 15% commission for every TV he sells. How much would he have to sell a single TV for to make a $72 commission?
Answer:
$480
Step-by-step explanation:
Perry makes 15% commission for each TV he sells.
How much would he have to sell a TV to get $72
First of all, let's call the unknown variable x
So 15% of x= $72
Mathematically, this would be represented as 15/100 * x= 72
15/100x= 72
Breaking down further,
15/100 can be broken down to 3/20
3/20x= 72
So to find the value of x, we divide both sides by 3/20
x= 72 ÷ 3/20
x= 72 * 20/3 (using the law of indices)
x= 1440/3
x= $480 dollars.
So, Perry would have to sell a TV for $480 to make a $72 commission.
I need to solve this system of equations, how do I do that?
3x-4y=20
y=3/4x-5
Answer:
Is is Infinitely many solutions so 0=0
Step-by-step explanation:
First we have to rearrange/simplify the equations:Equation 1: 4y - 3x = -20
Equation (2): y - 3x/4 = -5
Then you remove the fractions by multiplication:Multiply equation (2) by 4
The Equations now look like this:Equation 1: 4y - 3x = -20
Equation (2): 4y - 3x = -20
Solve for y on Equation (2):y = 3x/4 - 5
Then plug in this for the y in Equation 1 and then solve:4•(3x/4-5) - 3x = -20
Therefore the answer leads to:
Infinitely many solutions, 0=0
Hope this helped :')
Help me please!!!
Help me understand why sin2x+cos3x. Equals = 2sinxcosx+4cos³x-3cosx
Use the double identity
Step-by-step explanation:
sin(2x) + cos(3x)
Use double angle formula sin(2x) = 2 sin x cos x.
Use triple angle formula cos(3x) = 4 cos³x − 3 cos x.
Substitute:
2 sin x cos x + 4 cos³x − 3 cos x
find the value of tan (a-b) if cos a=4/5 on the interval (270, 360) and sin b=-5/13 on the interval (270, 360)
We can find a and b using inverse trig functions,
[tex]
\cos(a)=\frac{4}{5}\implies a=\arccos\Big(\frac{4}{5}\Big)\approx36.87 \\
\sin(b)=-\frac{5}{13}\implies b=\arcsin\Big(-\frac{5}{13}\Big)\approx-22.62
[/tex]
[tex]\tan(36.87-(-22.62))\approx1.7[/tex]
Hope this helps.
The following graphs show the performance of two stocks over the first five months of the year.
Which graph appears to show the best performance?
Which scale makes the graph appear to be rising more slowly?
a. Stock XYZ shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly.
b. Stock ABC shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly.
c. Stock XYZ shows the best performance. The scale of Stock XYZ makes the graph appear to be rising more slowly.
d. Stock ABC shows the best performance. The scale of Stock XYZ makes the graph appear to be rising more slowly.
Answer:
A. Stock XYZ shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly.
Step-by-step explanation:
What is the midpoint of OA ?
A: (2m, n)
B: (m, n)
C: (m – n, 0)
D: (m, 2n)
Answer:
(m,n)
Step-by-step explanation:
Since O is at the origin, we can take the coordinates of point A and divide them by 2 to find the midpoint
( 2m/2,2n/2)
The midpoint is at (m,n)
D'Naisa mixed her favorite shade of orange paint. She had 111 gallon of orange paint and added 222 quarts of yellow paint and 333 pints of red paint. How many quarts of paint did D'Naisa mix?
Answer:
7.5 Quarts
Step-by-step explanation:
D'Naisa mixed the following:
1 gallon of orange paint2 quarts of yellow paint3 pints of red paint.We are to determine in total, the number of quarts of paint that she mixed. this is done by converting each of the volume to quart.
1 gallon of orange paint
1 gallon = 4 QuartsOrange Paint=4 Quarts3 pints of red paint.
1 pint =0.5 quart3 Pints =3 X 0.5 Quart=1.5 Quart of red paintTherefore,
Total Volume of Paint Mixed in quart= Volume of Orange+Yellow+Red
=4+2+1.5
=7.5 Quarts
Lily goes to gym once every 8 days. Ann goes once every 12 days and Taylor comes once every 16 days. This Wednesday all of them were in the gym. How many days after this Wednesday will all of them meet at the gym again and what day of the week will it be?
Step-by-step explanation:
Lily goes to gym once every 8 days.
Such that she will visit on 8, 16 , 24, 32 , 40, 48th days
Ann goes once every 12 days
Such that she will visit on 12, 24, 36, 48, 60th days ....
Taylor comes once every 16 days
Such that she will visit on 16, 32, 48, 64th days....
Comparing the common days on which they will visit again after wednesday,
it will be after 48 days, (i.e) after 6 weeks and 5 days, it will be tuesday
Answer:
48 days
Step-by-step explanation:
LCM of 8, 12, 16 is 48.
The probability that a person is accepted for admission to a specific university is 0.6. Determine the probability that exactly two of the next five people who apply to that university get accepted.
Answer: the probability that exactly two of the next five people who apply to that university get accepted is 0.23
Step-by-step explanation:
We would number of people that applies for admission at the university and gets accepted. The formula is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represent the number of successes.
p represents the probability of success.
q = (1 - p) represents the probability of failure.
n represents the number of trials or sample.
From the information given,
p = 0.6
q = 1 - p = 1 - 0.6
q = 0.4
n = 5
the probability that exactly two of the next five people who apply to that university get accepted is
P(x = 2) = 5C2 × 0.6^2 × 0.4^(5 - 2)
P(x = 2) = 10 × 0.36 × 0.064
P(x = 2) = 0.23
Answer:
0.2304 or 23.04%
Step-by-step explanation:
Please kindly check the attached files for explanation
help QUICK please and thank youuu :))
Step 1: Simplify both sides of the equation.
28 = −7 /2 x
Step 2: Flip the equation.
−7 /2 x = 28
Step 3: Multiply both sides by 2/(-7).
( 2 /−7 )*( −7 /2 x) = ( 2 /−7 )*(28)
x=−8
Answer:
x=−8
[tex]28 = - \frac{7}{2} x \\ x = 28 \div ( - \frac{7}{2} ) \\ x = 28 \times ( - \frac{ 2 }{7} ) \\ x = - 8[/tex]
Let's chek
[tex] - 8 \times ( - \frac{7}{2} ) = \frac{8 \times 7}{2} \\ = 28[/tex]
Answer:
[tex]x = - 8[/tex]
An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 334 people living in East Vancouver and finds that 43 have recently had the flu. Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.03. How large a sample should she take to achieve this?
Answer:
The sample should be as large as 480
Step-by-step explanation:
Probability of having a flu, p = 43/334
p = 0.129
Margin Error, E = 0.03
Confidence Interval, CI= 95%
At a CI of 95%, [tex]z_{crit} = 1.960[/tex]
The sample size can be given by the relation:
[tex]n = p(1-p)(z/E)^{2}[/tex]
[tex]n = 0.129(1-0.129)(1.960/0.03)^{2} \\n = 479.59\\n = 480[/tex]
To determine the sample size needed to estimate the population proportion with a desired margin of error, we can use the formula n = (z^2 * p * (1-p)) / (E^2), where n is the required sample size, z is the z-score corresponding to the desired level of confidence, p is the estimated proportion of the population with the characteristic, and E is the desired margin of error. Plugging in the given values, the epidemiologist should take a sample size of approximately 3245 in order to achieve her desired margin of error.
Explanation:To determine the sample size needed to estimate the population proportion with a desired margin of error, we can use the formula:
n = (z^2 * p * (1-p)) / (E^2)
Where:
n is the required sample size z is the z-score corresponding to the desired level of confidence (in this case, 95% confidence) p is the estimated proportion of the population with the characteristic (in this case, the proportion of people with the flu in East Vancouver) E is the desired margin of error (in this case, 0.03)
Plugging in the given values:
n = (z^2 * p * (1-p)) / (E^2) = (1.96^2 * 0.129 * 0.871) / (0.03^2) ≈ 3244.42
So, the epidemiologist should take a sample size of approximately 3245 in order to achieve her desired margin of error.
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Type the correct answer in the box. Use numerals instead of words. What value of x makes this equation true? -6x + 3 = 45 x =
Answer:
x = -7
Step-by-step explanation:
-6x + 3 = 45
- 3 - 3
-6x = 42
/-6 = /-6
x = -7
The value of x to satisfy the given equation is 1/17.
Given,
-6x + 3 = 45x
We need to find x that makes that satisfy the equation.
What is numerals?A numeral is a symbol or name that stands for a number.
Find x.
-6x + 3 = 45x
Subtract 45x on both sides
-6x + 3 - 45x = 45x - 45x
-51x + 3 = 0
Subtract -3 on both sides
-51x + 3 - 3 = -3
-51x = -3
Divide both sides by 51
(51/51)x = 3/51
x = 1 / 17
This means we need x = 1/17 to make the equation true.
-6 x 1/17 + 3 = 45 x 1/17
-6/17 + 3 = 45/17
(-6 + 51) / 17 = 45/17
45/17 = 45/17
Thus the value of x to satisfy the given equation is 1/17.
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In order to answer the question correctly, please use the following image below:
Points Y and Z are points of tangency. Find the value of c.
C= (blank)
What is the value of C?
Please show all the work on how you got your answer. ( I'm not asking for an explanation. All I want is the work shown so I can understand how you got your answer)
Answer:
C = 2
Step-by-step explanation:
9c + 14 = 2c^2 + 9c + 6
-9c -9c
14 = 2c² + 6
-6 -6
8 = 2c²
4 = c²
c = 2
The value of c on the circle is 4 or -4.
What is tangent on a circle?In geometry, the tangent of a circle is a line that intersects the circle at only one point, known as the point of tangency.
The tangent line is perpendicular to the radius of the circle at that point.
We have,
XY and XZ are tangent on the same circle.
So,
XY = XZ
This means,
2c² + 9c + 6 = 9c + 14
Combining like terms.
2c² + 9c - 9c + 6 - 14 = 0
2c² - 8 = 0
2c² = 8
c² = 8/2
c² = 4
c = √4
c = ±4
Thus,
The value of c is 4 or -4.
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30+30-2 hi brainly people and I
Answer:
58
Step-by-step explanation:
Order of operations.
Additions and subtractions, in the order they appear, from left to right.
30 + 30 - 2 =
= 60 - 2
= 58
A rectangle had a length of 4.5 units and a width of 2.67 units..
How much longer was the length of the rectangle than its width? _____________________
Answer:
1.83 units
Step-by-step explanation:
To find we rest the width from the lenght. It would be 4.5 - 2.67 = 1.83, so the lenght was 1.83 units longer than the width.
The length of the rectangle is 1.83 units longer than its width. This value is calculated by subtracting the width (2.67 units) from the length (4.5 units).
Explanation:The student asked how much longer the length of a rectangle was compared to its width. The length of the rectangle is 4.5 units and the width is 2.67 units. To find how much longer the length is than the width, we subtract the width from the length.
To calculate it: 4.5 - 2.67 = 1.83
So, the length is 1.83 units longer than the width of the rectangle.
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The time t required to empty a tank varies inversly as the rate r of pumping. If a pump can empty a tank in 35 min at the rate of 800kL per minute, how long will it atake the pump to empty the same tanks at the rate of 1400kL per minute?
Answer: It will take the pump 20 min
Step-by-step explanation: Please see the attachments below
Solomon is 3D printing chess pieces. The table gives the amount of time needed to print certain numbers of
pieces.
Pieces
Print time (minutes)
16
32
128
512
What does 16 mean in this situation?
Answer:
A= It takes Solomon 16 minutes to print each chess piece.
Step-by-step explanation: Its the first one
The number 16 in this scenario signifies the amount of 3D printed chess pieces. The number indicates the quantity Solomon can print within a particular span of time.
Explanation:In this given context, 16 refers to the number of 3D printed chess pieces. This is a common type of mathematical problem dealing with ratios or rates. Here, the table suggests a ratio that compares the number of pieces printed to the time it takes to print them. Therefore, 16 essentially represents the quantity of chess pieces that Solomon can print using his 3D printer within a certain amount of time.
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A cube measures 3 meters on a side. What is it’s volume?
The volume of a cube that measures 3 meters on one side is 27 cubic meters.
Explanation:The volume of a cube is calculated by raising the length of one side to the power of three, which in mathematical notation is written as s^3. If a cube measures 3 meters on one side, you would calculate the volume as follows: 3^3 = 3 * 3 * 3 = 27 cubic meters. So, the volume of this cube is 27 cubic meters.
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