Using the least common multiple, it is found that the least possible number of coins that each of them has is of 24.
What is the least possible number of coins that they have?They have the same number of coins, with Betty sorting the coins in groups of 6 and Jane sorting the coins in groups of 8, and none of them having coins remaining.
Thus, the least possible number of coins they have is the least common multiple of 6 and 8, found factoring both these numbers into prime factors, as is done below:
6 - 8|2
3 - 4|2
3 - 2|2
3 - 1|3
1
Hence the least common multiple of 6 and 8 is given by:
lcm(6,8) = 2 x 2 x 2 x 3 = 2³ x 3 = 24.
Thus, it is found that the least possible number of coins that each of them has is of 24.
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Four cards are dealt at random without replacement from an ordinary deck of 52 cards. If it is known that the four cards have different face values, what is the probability that the first two cards are spades
Step-by-step explanation:
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
Part b assume the statement is true for n = k. prove that it must be true for n = k + 1, therefore proving it true for all natural numbers, n. t hint: since the total number of dots increases by n each time, prove that d (k) + (k + 1) = d(k+1).
The he statement d(k) + (k + 1) = d(k+1) is true for all natural numbers, n, by mathematical induction.
To prove that the statement is true for all natural numbers, n, we can use mathematical induction.
The statement we want to prove is that d(k) + (k + 1) = d(k + 1), where d(n) represents the total number of dots in a pattern of n squares.
Base Case (n = 1):
First, let's prove the statement for the base case, n = 1.
For n = 1:
d(1) + (1 + 1) = d(1) + 2
Now, consider a single square with 1 dot.
In this case, d(1) = 1.
So, we have:
1 + 2 = 3
Now, let's consider a pattern of 2 squares (n = 2).
The first square has 1 dot, and the second square has 2 dots. So, d(2) = 1 + 2 = 3.
So, the statement is true for n = 1.
Inductive Hypothesis (Assume true for n = k):
Now, assume that the statement is true for some arbitrary natural number k.
That is, assume that: d(k) + (k + 1) = d(k + 1)
Inductive Step (Prove true for n = k + 1):
To prove that the statement is true for n = k + 1.
d(k + 1) + (k + 2) = d(k + 2)
Now, consider a pattern of (k + 1) squares.
By the inductive hypothesis, assume that the statement is true for k squares:
d(k) + (k + 1) = d(k + 1)
Now, let's add one more square to the pattern.
This square will have (k + 2) dots.
So, the total number of dots in the pattern of (k + 1) squares plus the (k + 2) dots in the additional square is:
d(k + 1) + (k + 2)
And by the inductive hypothesis, d(k) + (k + 1) = d(k + 1).
Therefore:
d(k + 1) + (k + 2) = (d(k) + (k + 1)) + (k + 2) = d(k) + (k + 1) + (k + 2)
Now, simplify:
d(k + 1) + (k + 2) = d(k + 1) + (k + 1 + 1)
So, it is shown that for n = k + 1, d(k + 1) + (k + 2) = d(k + 1) + (k + 1) + 1.
Since it is assumed the statement to be true for k and proved it for k + 1, it is shown that the statement is true for all natural numbers, n, by mathematical induction.
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Please help For 50 points
Answer:
m = 0.875
Step-by-step explanation:
the 3 angles lie on a straight line and sum to 180° , that is
4m + 83 + 4m + 90 = 180
8m + 173 = 180 ( subtract 173 from both sides )
8m = 7 ( divide both sides by 8 )
m = [tex]\frac{7}{8}[/tex] = 0.875
A group of researchers wanted to measure the impact of playing classical music at bedtime to infants. They choose 20 infants to play music from 6:30 7:30 pm at bedtime and 20 infants to not play music at all. For each day for 3 months they observed them for 4 hours and recorded exactly how long it took for them to fall asleep. At the end of the 3 months they calculated the percentage of awake time to the time they slept for the 4 hours and compared the percentages to infants that had music played versus infants that did not. None of the answer choices Experimental Survey Observational Study A group of researchers wanted to measure the impact of playing classical music at bedtime to infants . They choose 20 infants to play music from 6:30 7:30 pm at bedtime and 20 infants to not play music at all . For each day for 3 months they observed them for 4 hours and recorded exactly how long it took for them to fall asleep . At the end of the 3 months they calculated the percentage of awake time to the time they slept for the 4 hours and compared the percentages to infants that had music played versus infants that did not . None of the answer choices Experimental Survey Observational Study
Using statistical concepts, it is found that it is an experimental study, as the music played corresponds to an experiment.
What is an experimental study?It is an study where an intervention is applied to a sample, and the effect of this intervention is studied.
In this problem, the music played is the intervention, and it's effect on the time that it takes for the infants to be asleep, hence it is an experimental study.
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4 mark please help me
Answer:
There are 4 red counters
Step-by-step explanation:
1. Add the known decimals
[tex]0.25+0.35+0.3=0.9[/tex]
2. Subtract that amount from one
[tex]1-0.9=0.1[/tex]
3. multiply the result by 40
[tex](40)(0.1)=4[/tex]
Hope this helps
Step-by-step explanation:
a probability is always desired cases / total cases.
from the table and given information we know :
there are 40 blue counters.
0.25 = 40/x
x being the total number of counters in the box.
x = 40 / 0.25 = 160
the sum of all probabilities must be 1 (the always true probability), as there are only counters in the box, and one of the 4 colors is always the result.
so,
1 = 0.25 + 0.35 + 0.3 + red-probability
1 = 0.9 + red-probability
red-probability = 1 - 0.9 = 0.1
0.1 = red counters / 160
red counters = 0.1 × 160 = 16
there are 16 red counters in the box.
Where s is the distance traveled by an object (in meters) with an initial velocity u (in m/s) and final velocity v (in m/s), t
seconds later.
Find s when u is 6 m/s, v is 20 m/s, and t is 5 seconds.
B. 25 m
C. 130 m
= 1/2 (u + v) t
OD. 65 m
S=
The distance travelled by the object in meters is 65 meters.
How to find distance?using the formula,
s = 1 / 2 (u + v)t
where
u = initial velocityv = final velocitys = distancet = timeTherefore, the distance can be found as follows;
s = 1 / 2 (6 + 20)5
s = 1 / 2 (26)5
s = 13(5)
s = 65 m
Therefore, the distance travelled by the object in meters is 65 meters.
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Answer:
D.
Step-by-step explanation:
I had the same question
Please help ill give whoever answers the best the brainliest answer :00
Answer: If for every independent unit(aka x), you multiply the dependent unit by the same amount(aka y).
Step-by-step explanation:
EXAMPLE:
(0,2) (1,6) (2,18) (3,54) (4,162)
As you can see, each time x increases by unit, you multiply the y unit by 3.
As an example, if you increase x by 4, you multiply the y unit by 3^4 = 81.
If this pattern is consistent with your whole table, you have an exponential function.
Hope this is useful.
6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp 6xp
Answer:
6xp^24
Step-by-step explanation:
Basically, there is 24 6xp's which is 6xp^24.
Hope I explained well enough.
A box contains 72 cups of fruit juice. one serving size is 12 cup. how many servings can be made from the fruit juice?
Answer:
6 servings
Step-by-step explanation:
Box = 72 cups
1 serving size = 12 cups
72 ÷ 12 = 6
For every 5 minutes that Scarlett plays on the computer, she plays outside for 12 minutes. What is the ratio of minutes Scarlett plays on the computer to minutes she plays outside?
Answer:
5:12
Step-by-step explanation:
because of the new wife
Determine the slope-intercept form (y = mx + b) of the equation of the line that contains the
points (3, 5) and (5, 6)
Hello,
We have A(3, 5) and B(5, 6)
[tex]m=\frac{y_{B}-y_{A}}{x_{B}-x_{A}} =\frac{6-5}{5-3} =\frac{1}{2}[/tex]
We know the line contain the point (3, 5)
y = 1/2x + b
⇔ 5 = 1/2 × 3 + b
⇔ 5 = 3/2 + b
⇔ 5 - 3/2 = b
⇔ b = 10/2 - 3/2
⇔ b = (10 - 3)/2
⇔ b = 7/2
[tex]\boxed{y = \frac{1}{2}x + \frac{7}{2} }[/tex]
Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60%, percent of their plants are flowers and 40%, percent are vegetables. They have 50 plants growing in the garden. How many vegetable plants do they have?
Answer:
20 vegetable plants
Step-by-step explanation:
In order to figure this out, you need to find 40% of 50. You can solve that by doing 0.40 * 50, which gives you 20. I hope that helps!
Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.
GX =
mABX = °
The value of GX is 13 and m ∠ABX is 22°
How to determine the angles
With the information, we have
EX = 4z + 1 and XF = 2z + 7
It is important to note that EX = XF = GX are congruent, that is, they are equal
Equate EX = XF to determine z
4z + 1 = 2z + 7
Collect like terms
2z = 6
z = 3
We know that EX = XF = GX and x = 3, substitute into the value of any one
EX = 4(3) + 1
EX = 13
EX = GX
GX = 13
To determine m ∠ABX, we divide m ∠ABC by 2
We have
m ∠ABX = 44/2
m ∠ABX = 22°
Therefore, the value of GX is 13 and m ∠ABX is 22°
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Answer: 13, 22°
Step-by-step explanation: Trust Me!
Answer is correct on Edge. Good Luck! :)
GX = 13
mABX = 22°
help me please maths
A. 64
B. 1/12
C. 1/64
D. 12
Answer:
Step-by-step explanation:
First, since they have the same base, you can join them. Because it is division, you have to subtract the exponents.
4^(-11/3 -(-2/3)) = 4^-9/3 = 4^-3
Negative exponents turn the base into a fraction and 4^3= 64
so the answer is C. 1/64
Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth.
From the least to the greatest, the solutions are:
From the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2
the answers are -2.1 and 0.2.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two systems of the equation:
y = log (−5.6x + 1.3)
y = −1 − x
After plotting the above equation on the graph we will see two intersections point:
(-2.12, 1.12) and (0.221, -1.221)
So the least value is x = -2.12 ≈ -2.1
The greatest value is x = 0.221 ≈ 0.2
Thus, from the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2
the answers are -2.1 and 0.2.
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40 points please help!!!!
use the 3rd icon to measure 30 and 60 degrees, Then connect them with a line and add a right angle.
Answer:
Not Possible
Step-by-step explanation:
It is not possible. While it does add up to 180, if one is 90 degrees, the rest must be 45 and 45, or your not getting anything.
Let me know if this helped !!
Which of the following graphs shows the
solution set to 2x < 6 and 3x + 2 >
-4?
Answer:
The third picture
Step-by-step explanation:
Solve for x in both equations
2x<6
Divide both sides by 2:
x<3
3x+2>-4
Subtract 2 from both sides:
3x>-6
Divide both sides by 3:
x>-2
There is this trick you can use when x is on the left side of the equation to find out which way to shade in you graph. Keep in mind this is only for the left side, it will not work if your variable is on the right.
When the symbol is facing left < then shade left, imagine it is pointing which way to shade. x<3 is represented by the 3 picture on the left. When the symbol is facing right > then shade right, again it is pointing which way to shade. x>-2 is represented by the 3 picture on the right.
The circles are not filled in because the symbol is < and > rather than [tex]\leq and \geq[/tex]. When it is greater than or equal to or less than and equal to (represented by the line under the symbol), then the circle is shaded in.
What is the volume of this rectangular prism? A rectangular prism with a length of 6 and one-fourth foot, width of 14 feet, and height of 3 feet.
Answer:
V = 262.5 ft.
Step-by-step explanation:
Volume = length × width × height
6.25 × 14 × 3
6.25 × 42
262.5
\Triangles A C B and M Q R are shown. Sides A B and M R are congruent. Angles C A B and M R Q are 42 degrees. Angle C B A is 53 degrees. Angle M Q R is 85 degrees.
Are the triangles congruent? Why or why not?
Yes, all the angles of each of the triangles are acute.
Yes, they are congruent by either ASA or AAS.
No, AngleB is not congruent to AngleQ.
No, the congruent sides do not correspond.
By the ASA postulate, it can be said that the triangle ABC and triangle MRQ are congruent. Thus, option B is correct, Yes, they are congruent by either ASA or AAS.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Using Angle Sum Property, in ΔMRQ
<M + <R + <Q= 180
<M + 42 + 85 = 180
<M = 180 -42
<M= 53°
Now, In ΔMRQ and ΔABC
<A= <R ,
<B = <M
AB = MR
Hence, By ASA criteria ΔMRQ ≅ ΔABC.
Thus, option B is correct, Yes, they are congruent by either ASA or AAS.
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Answer: Yes, they are congruent by either ASA or AAS.
Step-by-step explanation:
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown: A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1. Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD? (1 point) Group of answer choices Counterclockwise rotation by 90 degrees about the origin followed by a translation to the right by 1 unit Counterclockwise rotation by 90 degrees about the origin followed by a translation to the left by 1 unit Reflection about the x-axis followed by a translation to the left by 1 unit Reflection about the y-axis followed by a translation to the right by 1 unit
Last option. The sequence that can be used to to get the figure A'B'C'D' is Reflection about the y-axis followed by a translation to the right by 1 unit.
How to get the reflection of the imageWe have an opposite orientation in this question. This based on the fact that (ABCD)' is counterclockwise. While its reflection ABCD is clockwise.
The reflection has to go over a vertical line given that (CD)' and CD are at the bottom. Hence this reflection has to go over a vertical line.
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[tex] {3}^{2x - 2} - 28( {3}^{x - 2} ) + 3 = 0[/tex]
solve for x.....
Answer:
x = 3, x = 0
Given expression:
[tex]3^{2x-2}-28\left(3^{x-2}\right)+3=0[/tex]
rewrite expression
[tex]3^{2x} \times 3^{-2}-28\left(3^{x} \times 3^{-2}\right)+3=0[/tex]
treat [tex]\sf \s3^{x}\:as\:u[/tex], then expression
[tex]u^2 \times 3^{-2}-28\left(u \times 3^{-2}\right)+3=0[/tex]
multiply both sides by [tex]\sf 3^{2}[/tex]
[tex]u^2-28\left u+27=0[/tex]
factor expression
[tex]u^2-27\left u - u + 27=0[/tex]
factor out common terms
[tex]u(u-27) -1( u - 27)=0[/tex]
collect into groups
[tex](u-1)( u - 27)=0[/tex]
set to zero
[tex]u =1, \ u=27[/tex]
Substitute [tex]\sf 3^x = u[/tex], to find x
[tex]3^x = 1, \ 3^x = 27[/tex]
[tex]3^x = 3^0, \ 3^x =3^3[/tex]
[tex]x= 0, \ x = 3[/tex]
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Plis help! Will give brainliest!
Answer:
Q1: 62
Q2: 13
Step-by-step explanation:
Just follow Order of operations, and you get the answers.
P arenthesis
E xponents
M ultiplication
D ivision
A ddition
S ubtraction
I need help desperately! Could someone explain this math concept for me please?
The inequality that represents the range of k so that inequality 1 has real solution is -3 < k < 5
How to determine the range?Inequality 1
x^2 + (k + 1)x + k + 4 > 0
The discriminant is calculated using
D = b^2 - 4ac
So, we have:
D = (k + 1)^2 - 4 * 1 * (k + 4)
Evaluate
D = k^2 + 2k + 1 - 4k - 16
This gives
D = k^2- 2k - 15
Factorize the equation
D = (k+ 3)(k -5)
Solve for k
k = -3 and k = 5
Express the k values as inequalities
-3 < k < 5
Inequality 2
The inequality cannot be read, because of the image quality
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Can someone help me please?
Answer:
7.6 units
Step-by-step explanation:
Use law of sines
12 / sin C = b / sin B
sin B * 12 / sin C = b
sin (32) * 12 / sin(57) = b = 7.6
Each large rectangle below represents one whole.
What percent is represented by the shaded area?
Answer:
180%
Step-by-step explanation:
Given:
Large rectangle represents one (1) wholeEach rectangle is divided evenly into 5 partsThere are 2 whole rectanglesThe rectangle on the left is fully shaded in meaning that is 1 whole (100%)
The rectangle on the right is 4 / 5 shaded, 4 / 5 = 0.8 (80%)
Combining these will be 100 + 80 = 180%
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Step-by-step explanation:
there are 2 whole rectangles 1 of them is full making it 1 whole the other has 4 shaded potions and 1 unshaded potion making 4/5Mathematically writing it: 1 ⅘ (mixed fraction)we change 1 ⅘ into an improper fractionby multiplying the whole (1) by the denominator (5) and adding the numerator (4) which gives us 9/4 (improper fraction).9/4 = 9÷4 = 2.25 (decimal)Then we convert 2.25 into percentage by multiplying 2.25 by 100 2.25 x 100 = 225%Therefore the percentage represented by the shaded area is 225%. Hope this helps.Good luck ✅.Please Help!!!
Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 5 units long. Point C is on the line x = −2. If the area of ΔABC is 12.5 square units, then find a possible y-coordinate of point C.
5
6
7
8
Answer: its 7
Step-by-step explanation: hope it helps
in poker, a royal flush is a hand with the ace, king, queen, jack and 10 of all one suit and is the best possible hand in the game. what is the probablity of a royal flush in a 5 card hand
The probability of a royal flush in a 5-card hand is 1/649740 or 0.0001539%.
The combination is a way of selecting a smaller number of sets from a larger number of sets in no particular order.
If selecting r items from a set of n items, in no particular order, we use combinations, using the formula:
nCr = n!/{r!(n - r)!}.
In the question, we are asked the probability of a royal flush in a 5 card hand.
The number of ways of selecting 5 cards from a deck can be computed using a combination, 52C5, as we have 52 cards in a deck, 5 cards are to be chosen and the order is not in concern.
52C5 = 52!/{5!(52 - 5)!} = 52!/(5!.47!) = (52*51*50*49*48)/(5*4*3*2*1) = 2598960.
The number of hands that make a royal flush is only 4. 4 from each suit.
Therefore, the probability = 4/2598960 = 1/649740 or 0.0001539%.
Therefore, the probability of a royal flush in a 5-card hand is 1/649740 or 0.0001539%.
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What's Part of a 1 minute and 5 seconds?
62.5 seconds
Step-by-step explanation:
ZA and ZB are
supplementary angles. If mA = (7x + 24)˚ and
m/B = (7x − 26)°, then find the measure of ZA.
-
The measure of ∠A is 115˚.
Given that, ∠A and ∠B are supplementary angles. ∠A=(7x + 24)˚ and ∠B=(7x − 26)°.
What are supplementary angles?Two angles are Supplementary when they add up to 180 degrees.
Now, ∠A+∠B=180°
⇒(7x + 24)˚+(7x − 26)°=180°
⇒14x− 2°=180°
⇒14x=182°
⇒14x=182°
⇒x=13°
Now, ∠A=7×13 + 24˚
⇒∠A=91˚+ 24˚=115˚
Therefore, the measure of ∠A is 115˚.
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gradients - pls help :)
The line which has a gradient of 6 is A. line A
To answer the question, we need to know what the gradient of a line is.
What is the gradient of a line?The gradient of a line is its slope. It is given by m = Δy/Δx where
Δy = change in y and Δx = change in x. How to find the line that has the gradient 6?Now, to find the line that has the gradient of 6, we see that the gradient
m ∝ Δy and m ∝ 1/Δx.So, for a high value of gradient, we need
a large change in y and a small change in x.Also, since 6 is positive, the gradient for the line will be positive.
The only line that meets these criteria is line A.
So, the line which has a gradient of 6 is A. line A
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