The maximum number of plants Sophie can have in each pot is 18.
Highest Common factor:
The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
Here it is given that Sophie plants 36 violas, 54 sweet peas, and 72 fuchsias. She wants to plant them in pots.
So we have to find the maximum number of plants she could have in each pot.
For that, we have to find the Highest common factor of the given different-different plant she has.
HCF of 36, 54, 72 = 18
So the maximum number of plants she can pot is 18.
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TWO trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train
travels at 95 miles per hour. How long will It take for the two trains to be 396 miles apart?
Do not do any rounding.
Rupert has a bag containing 2 green, 3 purple and 2 orange marbles. He selects two marbles from
his bag in succession, without replacement.
Using a tree diagram, determine the probability that Rupert picked the two green marbles.
The probability that Rupert picked 2 green balls is 1/21.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. It's value ranges from 0 to 1.
Main Body:
total balls = 7 , green balls =2
1st try:
probability of getting green ball = 2/7
As there is no replacement so now,
total balls = 6 , green balls = 1
2nd try:
probability of getting green ball = 1/6
total probability = (2/7)*(1/6)
= 1/21
Hence the answer is 1/21.
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range of 17,21,14,17,12,15,16
Answer:
The range is 9.
Step-by-step explanation:
The range of a data set is the difference between the maximum and the minimum values.
Let's begin by putting the set of values in order from lowest to highest.
12, 14, 15, 16, 17, 17, 21
The lowest value is 12, and the highest value is 21.
Let's subtract the minimum value from the maximum value to determine the range:
21 - 12 = 9
Hope this helps :)
Answer:
Step-by-step explanation:
Put them in order (lowest to highest)
so,
12, 14, 15, 16, 17, 17, 21
to find the range : highest - lowest
21 - 12 which is 9
Thanks
how many cards must be selected from the standard 52 deck to guarantee that at least 3 cards of the same suit are chosen
Nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.
What is the pigeon-hole approach?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. For instance, if one possesses three gloves but none of them are ambidextrous or reversible, then there must be at least two right-handed gloves or at least two left-handed gloves since there are three items but only two categories of handedness. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.
The standard 52 deck has 4 suits of 13 cards each, thus as per n pigeons need to be extracted from p = 4 pigeon-holes; as per established literature above.
∴ [(n - 1) / p] + 1 = 3 ⇒ [(n - 1) / 4] + 1 = 3 ⇒ n - 1 = 8 ⇒ n = 8 + 1 ⇒ n = 9
Therefore, nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.
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which of the following is a linear equation
The option that is a a linear equation is B. 4x - 2 = 20.
What is an equation?An 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.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign
This is illustrated as 4x - 2 = 20
4x = 20 + 2
4x = 22
x = 22/4 = 5.5
This illustrates an equation.
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a=4 b=2, find value of a) 3ab
b) a+5b
Answer:a. 24
b. 14
Step-by-step explanation:
a. 3ab=
3*a*b=
3*4*2=
12*2=24
b. a+5b=
a+5*b=
4+5*2=
4+10=14
Answer: a) 24
b) 14
Step-by-step explanation:
step1: We have to substitute the numbers.
step2: Then finish the answer.
a) 3ab = 3 x 4 x 2 = 24
b) a+5b = 4 + 5 x 2 = 4 + 10 = 14
Solve the following system of linear equations ( Step-by-step)(Tell me, what is x,y,z):
2x - 3y + 6z = -12
5x + 2y - 8z = 29
7x + 6y + 4z = 49
The solution to the linear system of equation is x = 3, y = 5, and z = -0.5
What is a linear system of equation?A system of linear equations is a set of linear equations that involve the same variable and which work or are operated (simultaneously) together
The system of linear equation is presented as follows;
2·x - 3·y + 6·z = -12...(1)
5·x + 2·y - 8·z = 29...(2)
7·x + 6·y + 4·z = 49...(3)
Multiplying equation (1) by 5 and equation (2) by 2, we get;
5 × Equation (1) ⇒ 10·x - 15·y + 30·z = -60...(4)
2 × Equation (2) ⇒ 10·x + 4·y - 16·z = 58...(5)
Subtract equation (4) from equation (5), to get;
10·x - 10·x + 4·y - (-15·y) - 16·y - 30·z = 58 - (-60) = 118
19·y - 46·z = 118...(6)
Multiplying equation (1) by 7 and equation (3) by 2, we get;
7 × Equation (1) ⇒ 14·x - 21·y + 42·z = -84...(7)
2 × Equation (3) ⇒ 14·x + 12·y + 8·z = 98...(8)
Subtracting equation (7) from equation (8), we get;
14·x - 14·x + 12·y - (-21·y) + 8·z - 42·z = 98 - (-84) = 182
33·y - 34·z = 182...(9)
Multiplying equation (6) by 33 and equation (9) by 19, we get;
627·y - 1,518·z = 3,894...(10)
627·y - 646·z = 3,458...(11)
Subtracting equation (10) from equation (11), we get;
627·y - 627·y -646·z - (-1,518·z) = 3,458 - 3,894 = -436
872·z = -436
z = -436 ÷ 872 = -0.5
z = -0.5
From equation (6), we have;
19·y - 46·z = 118
19·y - 46 × (-0.5) = 118
19·y - 46 × (-0.5) = 118
19·y = 118 + 46 × (-0.5) = 95
y = 95 ÷ 19 = 5
y = 5
From equation (1), we get;
2·x - 3·y + 6·z = -12
2·x - 3 × 5 + 6 × (-0.5) = -12
2·x = -12 + 3 × 5 - 6 × (-0.5) = 6
x = 6 ÷ 2 = 3
x = 3
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y=3/4x−1/2 linear equation
The equation's graph is a straight line: y= 3/4x - 1/2.
What is a straight line?A straight line is a line with an infinite length and no curves. A straight line can also be drawn between any two places, but its endpoints must stretch into the infinite.When two places A (x1, y1) and B (x2, y2) are connected by the shortest path possible, and the line ends are stretched to infinity, a straight line is the result.acc to our question-
There are an endless number of solutions to a linear equation with two variables, and we can obtain each one as a pair of numbers.
Draw the two-variable linear equation's graph by plotting these values on a coordinate plane.
Using the slope and y-intercept is the simplest approach to graph something in slope-intercept form because that information is already available.
Follow all of the instructions listed below to plot the equation's graph.
Step 1: When x = 0, the y-intercept is 0, and y would then equal -1/2. (0, -1/2) are the points.
Step 2: Since the slope is 3/4 rise over run, go three up (rise) and four across (run).
Step 3: The slope of the line is upward since the slope in the equation, not negative.
Step4; There are two points, draw a line connecting the two points.
hence,The equation's graph is a straight line: y= 3/4x - 1/2.
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The temperature dropped to 24 degrees in 8 days. what was the average daily change in temperature? a) 3 degrees b) -8 degrees c) -3 degrees d) 16 degrees
The average daily change in temperature will be 3 degrees The temperature dropped to 24 degrees in 8 days
Since we know an average could be a single number taken as an agent of a list of numbers, as a rule, the whole of the numbers divided by how numerous numbers are within the list. We are said the temperature dropped to 24 degrees in the 8 days
So the average of it will be =24 /8 = 3, which means the temperature needed to drop for at least 3 degrees in order to get the sum of 28 in 8 days.
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1/4(8x+12)=-15 ''solve''
After solving the value of x in the equation is x [tex]=[/tex] -9 .
In the question ,
it is given that ,
the equation is 1/4(8x+12) = -15
Applying the associative property of multiplication ,
we get ,
8x/4 + 12/4 = -15
cancelling out the common factor 2 from numerator and denominator ,
we get ,
2x + 3 = -15
Subtracting the number 3 from both sides of the equation ,
we get ,
2x = -15 - 3
2x = -18
Dividing both sides of the equation above by the number 2 ,
we get ,
x = -18/2
x = -9
Therefore , After solving the value of x in the equation is x [tex]=[/tex] -9 .
The given question is incomplete , the complete question is
Solve the given equation for x ?
1/4(8x+12)= -15
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Determine whether the function is one-to-one. If it is, find a formula for its inverse.
f(x) = 4/9x+8
Answer:
87c
Step-by-step explanation:
helppppppppppppp can you tell me where to put the answers
After applying the distributive property, Ezra's expression was 8y + 16.
After he used the commutative property, his expression was 16 + 8y.
How to use the distributive and commutative properties?When using the distributive property, we are able to expand an expression with a bracket by multiplying the things in the bracket with the things outside:
8( y + 2) becomes:
= (8 x y) + (8 x 2)
= 8y + 16
The commutative property on the other hand, means that when adding, the position of the number does not matter. For instance, a + b = b + a
When the commutative property is applied therefore, we get:
8y + 16 = 16 + 8y
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Andrew has 8 cassettes. Mary has x cassettes and Jim has twice as many as Andrew. Together they have four times as Mary has. Form an equation and find how many cassettes Mary has.
Answer:
mary=x
andrew=8
jim=2*8=16
together=4*mary
total=8+16=24
24/4=x
x=6
Step-by-step explanation:
You exercise for 3/4 of an hour. You jump rope for 1/3 of that time. What portion of the hour do you spend jumping rope?
Answer:
15 minutes
Step-by-step explanation:
The 3/4 of an hour is,
→ 60 × (3/4)
→ 180/4 = 45
Now required time spend on rope is,
→ 45 × (1/3)
→ 45/3 = 15 minutes
Hence, he had spend 15 minutes.
Solve the following problems using the concept of multiples. Justify your work with a table.
3. María is shopping for party supplies. She finds that paper plates come in packages of 8,
napkins come in packages of 10, and paper cups come in packages of 12. What is the
least number of packages of plates, napkins, and cups she has to buy so that she
has the same number of each item for her party?
8
10
4. For the month of November, Jaime plays basketball every other day and he goes to sc
practice every four days.
If he starts on November 2 on what days will he do both sports?
For Maia's birthday celebration, the bare minimum amount of packets of plates, napkins, and cups she needs to purchase is 15, 12, and 10, respectively.
What is a Fraction?A portion of a whole is referred to as a fraction. such as 0.25 can be used to describe the fraction 1/4.Given that paper plates, napkins, and cups are sold in quantities of eight, ten, and twelve each, respectively, Therefore, we need to take the LCM of the following in order to determine how many packets of plates, napkins, and cups Maria needs to purchase in order to have the same quantity of each item for her birthday celebration.acc to our question-
LCM of 8, 10, and 12 = 120Now, the number of packages,Hence, the least number of packages of plates, napkins, and cups Maia has to buy so that she has the same number of each Item for her birthday party is 15, 12, and 10, respectively.Learn more about Fraction:
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5x - 4 ≥ 4x + 3 or 9 + 4x2-1 + 9x
Answer:
9x3
Step-by-step explanation:
x+9
/4
9x=8
x=2
+2=4
x=1+4234
Use the diagram of AlL where k, S and are midpoints or the sides, RK = 3, KS = 4, and JK
Is perpendicular to KL.
Find the length of RS
Find the length of JK
Find the length of RT
Find the perimeter of JKL
1. The length of RS is 5.
2. The length of JK is 6.
3. The length of RT is 4.
4. The perimeter of triangle JKL is 24.
What do you mean by right angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
According to data in the diagram of the given question:
We have :
The ΔJKL, ΔRKS and ΔRTS are right-angle triangle.
The length of RK=3 and KS=4
We are using pythagoras theorem for determine the length of RS,
(RK)²+(KS)²=(RS)²
(3)²+(4)²=(RS)²
9+16=(RS)²
25=(RS)²
(5)²=(RS)²
RS=5
∴ The the length of RS is 5.
Now, we need to find the length of JK,
JK=2(RK)=2(3)=6
JK=6 [Because RK is midpoint of the side JK]
We have given value of KS=4 and the side KS is the opposite side of RT,
So, that's why the value of RT=4.
Now, we will find the perimeter of ΔJKL,
JK=6, KL=8 and we need to find the side JL,
(JK)²+(RL)²=(JL)²
(6)²+(8)²= (JL)²
36+64=(JL)²
100=(JL)²
(10)²=(JL)²
JL=10
The perimeter of the triangle ΔJKL,
Perimeter=6+8+10=24
Therefore, the perimeter of the triangle is 24.
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After 3 new kids came to the park, a total of 18 kids played at the park. Write an equation that could be used to find x, the number of kids at the park before the 3 new kids came.
Please help, please
Answer:
x + 3 = 18
Step-by-step explanation:
original number of kids: x
additional kids: 3
new total number of kids: x + 3
actual total number of kids: 18
Equation: x + 3 = 18
A sample of gas is enclosed in a container of fixed volume. Identify which of the following statements are true. Check all that apply. If the container is heated, the gas particles will lose kinetic energy and temperature will increase. If the container is cooled, the gas particles will lose kinetic energy and temperature will decrease. If the gas particles move more quickly, they will collide more frequently with the walls of the container and pressure will increase. If the gas particles move more quickly, they will lose energy more rapidly and collide with the walls of the container less often, and pressure will decrease. If the gas particles move more quickly, they will collide with the walls of the container more often and with more force, and pressure will increase.
The true statement about the sentence 'sample of gas is enclosed in a container of fixed volume' are:
If the container is cooled, the gas particles will lose kinetic energy and temperature will decrease. If the gas particles move more quickly, they will collide more frequently with the walls of the container and pressure will increase.What will happen to 'sample of gas is enclosed in a container of fixed volume?When a sample of gas is been enclosed in a container of fixed volume then then if the container temperature is been reduced then the kinetic energy of the gas will reduce.
Therefore the first and the third option are correct.
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Darnel and Tammy deposited $4,890.00 into a savings account which earns interest
compounded continuously. After 10 months, they had $5,067.00 in the account which they
used to go on a trip. What was the interest rate on the account?
Round your answer to the nearest tenth of a percent.
The interest rate on the account would be 0.4.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
Compound interest
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Where,
A = amount,
P = principal
t = no. of years
r = annual interest rate
n = no of times compounded in a year.
By putting the values in the equations we get,
[tex]5067=4890(1+\frac{r}{10} )^{8.3}\\[/tex]
Solving this, we get
[tex]r = 0.356[/tex]
Rounding off to the nearest tenth of a percent we get
[tex]r=0.4[/tex]
Hence, the interest rate on the account will be [tex]0.4[/tex].
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the mean cost of domestic airfares in the united states rose to an all-time high of $385 per ticket. airfares were based on the total ticket value, which consisted of the price charged by the airline plus any additional taxes and fees. assume domestic airfares are normally distributed with a standard deviation of $110. answer to four decimals. what is the probability domestic airfare is $250 or less.
The probability 11.1% of domestic airfares within the United States are $250 or less.
Define the term standard deviation?A square root of variance is used to calculate the standard deviation, a statistic that illustrates how distributed widely a dataset is in relation to its mean. By evaluating the deviation of each data point from the mean, the standard deviation may be approximated as the square root of variance.The formula for the z score is -
z = (x - μ)/σ
In which,
μ = mean = $385 per ticketσ = standard deviation = $110x = sample value = $250 or less.Substitute the value in formula.
P(x ≤ 250) = (250 - 385)/100
P(x ≤ 250) = -1.22
Select the p value from negative z score table;
P(x ≤ 250) = 0.111
P(x ≤ 250) = 11.1%
Thus, 11.1% of domestic flights within the United States are $250 or less.
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. a trough has ends shaped like isosceles triangles, with width 3 m and height 4 m, and the trough is 10 m long. water is being pumped into the trough at a rate of 5m3/min. at what rate does the height of the water change when the water is 1 m deep?
The rate at which the height of the water changes when the water is 1m deep is; dh/dt = 1.5m/min
We are given;
width; w = 3m
Height; h = 4m
Length of trough; L = 10m
According to similar triangle property; w =3/4h
volume of water; V = 1/2×w×h×L = 1/2 × 3/4h × h × 10 = 15/4 h²
Differentiate using chain rule for both sides with respect to t gives;
dV/dt = (1/2)(15/2)h(dh/dt).
Now, we are given dV/dt = 5m³/min and we want to find the rate at which the height of water changes when the water is 1 m deep.
Thus;
5 = ×dh/dt
At h = 1m; 5 = 15(1)/2 × dh/dt
⇒ dh/dt = 2/3
dh/dt = 1.5 m / min
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please help me with this problem.
Answer:
(- 25, 5 )
Step-by-step explanation:
- 3x - 6y = 45 → (1)
- 5y = x → (2)
substitute x = - 5y into (1)
- 3(- 5y) - 6y = 45
15y - 6y = 45
9y = 45 ( divide both sides by 9 )
y = 5
substitute y = 5 into (2)
- 5(5) = x , then
x = - 25
solution is (- 25, 5 )
Which inequality is equivalent to 2/3x -5 < 11
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] x - 5 < 11 ( multiply through by 3 to clear the fraction )
2x - 15 < 33 ← equivalent inequality
to solve add 15 to both sides
2x < 48 ( divide both sides by 2 )
x < 24
While shopping with her husband (see practice e), Mrs. Garantua
bought 2 garden hoses (one to use as a neclace and the other to
use a leash for her pet whatchamacallit) and 2 giant flowerpots
(both to use as summer hats). If the hoses cost $30 each, and
the bill for all the items (hoses and flowerpots combined) was
$96, how much did each flowerpot cost?
Answer:
$18
Step-by-step explanation:
She bought 2 garden hoses which both cost $30, so she already spent $60. The subtract 60 from 90, and get $36 left. Divide that by 2 because she buys 2 flower pots, and you arrive at the answer of $18 per flower pot.
What is the value of log10 1000000000
Answer:
9 i think
Step-by-step explanation:
Find the geometric mean between ab³ and a³b?
[tex]{ \green{ \sf{G = \sqrt{ ab}}}}[/tex]
[tex]{ \green{ \sf{G = \sqrt{ (ab³)(a³b)}}}}[/tex]
[tex]{ \green{ \sf{G = \sqrt{ a⁴b⁴}}}}[/tex]
[tex]{ \red{ \boxed{ \pink{ \sf{G = \sqrt{ a².b²}}}}}}[/tex]
1. Perform Gauss-Jordan elimination on the augmented matrix shown.
O
-261
3
A. 0 1 -7
00 0
3
B. 0 -1 7
0
[102]
C.0 17
001
2370
[100]
D. 0 1 0
00
Answer:
Step-by-step explanation:
Isabella, do you know how to do the "elementary row operations"?
Also, when did they begin teaching linear algebra in H.S. :DDD nice work getting there.
Gauss Jordan, just mean get your matrix in RREF (Reduced Row Echelon Form)
I suggest using Matlab to do this. it's got the "RREF(x) function to do this exact thing.
Your teacher probably wants you to do this by hand. thou, huh. :/
here is my Matlab code and the answer
clc
close all
clear
format compact
A=[3 -4 2;0 -1 7]
mymatx=rref(A)
A =
3 -4 2
0 -1 7
mymatx =
1.0000 0 -8.6667
0 1.0000 -7.0000
Yes, maybe it's totally cheating, but it seems fair nowadays to use technology that is commonly available. :)
So answer A) looks right
Is 4 ÷ 3/2 the same as 4 ÷ 2/3. Explain
olumide plays the piano and guitar.for every 5 min of piano practice,he spends 8 min practicing guitar.how many minutes will olumide practice piano if he spends 64 minutes practicing guitar?
Answer:
Olumide will practice 40 minutes of playing the piano
Step-by-step explanation:
Olumide practices piano and guitar in the ratio of 5:8
64 minutes of guitar playing means that Olumide has had 8 individual practicing sessions of guitar (64 / 8 = 8), so he has also had 8 practicing sessions of piano.
5 x 8 = 40 minutes of piano practice