There are only red beads and green beads in a bag.
The ratio of the number of red beads to the number of green beads is 5 : 9
(a) What fraction of the beads are red?
There is a total of 84 beads in the bag.
(b) How many of the beads are green?
Susie is going to put some more beads in the bag.
There will still be only red beads and green beads in the bag.
Susie wants to have twice as many green beads as red beads in the bag.
(c) What beads should she put in the bag?
You must explain your answer
Answers
Answer:
(a) 5/14
(b) 54 beads
(c) 6 green beads
Step-by-step explanation:
(a) Find the total number of units for red and green beads.
5 + 9 = 14
Since red beads is 5, it is 5/14.
(b) Find the units for red and green beads altogether.
5 + 9 = 14
14 units = 84 beads
Find one unit.
1 unit = 84 ÷ 14 = 6 beads
Since green beads have 9 units, find how many beads there are in 9 units.
9 units = 6 x 9 = 54 beads
(c) As there are 54 green beads and Susie wants to have twice as much green beads as red beads, she have to find how many red beads there are first.
Since red beads have 5 units, find how many beads there are in 5 units.
5 units = 6 x 5 = 30 beads
After that, since she wants twice, she have to find x2 of 30 beads which are red.
30 x 2 = 60
After that, find the remaining amount of green beads needing to make x2 of 30.
60 - 54 = 6 beads (green)
Part(a),
5/14 of the beads are red.
Part(b),
There are 54 green beads in the bag.
Part(c),
Add 18 red beads and 36 green beads to the bag to get the desired ratio.
How to get the solution?(a) There are five times as many red beads as green beads, or a 5:9 ratio. Therefore, there are 9 green beads in the bag for every 5 red beads. Therefore, the fraction of the beads that are red can be expressed as:
5/(5+9) = 5/14
So, 5/14 of the beads are red.
(b) The bag contains 84 beads, and the proportion of red to green beads is 5:9. Let G equal the number of green beads and R equals the number of red beads. Next, we have:
R/G = 5/9
And we also know that:
R + G = 84
We can use the first equation to express R in terms of G:
R = (5/9)G
This results from substituting this into the second equation:
(5/9)G + G = 84
Simplifying:
(14/9)G = 84
G = (9/14) * 84 = 54
So there are 54 green beads in the bag.
(c) Let's assume that the bag currently contains G-green beads and R red beads. So that there are twice as many green beads as red beads, we wish to add a few more beads.
G = 2R
We also know that the total number of beads in the bag should be:
R + G + X = 84
Where X is the required number of beads. G = 2R is substituted into this equation to produce:
R + 2R + X = 84
3R + X = 84
Finding R and X numbers that meet both this equation and the prerequisite that G = 2R is necessary. One potential answer is:
R = 18, X = 30
This gives:
G = 2R = 36
And:
R + G + X = 18 + 36 + 30 = 84
Hence, to get the correct ratio, we can add 18 red beads and 36 green beads to the bag. There might be other workable alternatives as well, though.
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Related Questions
What is the area of a rectangle that is \dfrac1{2} 2 1 start fraction, 1, divided by, 2, end fraction of a meter long and \dfrac38 8 3 start fraction, 3, divided by, 8, end fraction of a meter wide?
Answers
Answer:
\(Area = \frac{3}{16} m^2\)
Step-by-step explanation:
Given
Shape: Rectangle
\(Length = \frac{1}{2}\ m\)
\(Width = \frac{3}{8}\ m\)
Required
Determine the area of the rectangle;
Area is calculated as thus;
\(Area = Length * Width\)
Substitute values for Length and Width
\(Area = \frac{1}{2} * \frac{3}{8}\)
\(Area = \frac{1 * 3}{2 * 8}\)
\(Area = \frac{3}{16}\)
Hence, the area of the rectangle is \(\frac{3}{16}m^2\)
HELPP I need the answer
Answers
Answer:
H(1 , 0.5)
F(3 , 2,5)
G(5 , 0.5)
Step-by-step explanation:
First step is to get the coordinates of the points.
H(2,1)
F(6,5)
G(10,1)
To find the vertices after a dilation, we multiply the coordinates by the scale factor of the dilation. Since the scale factor is 0.5, its the same as dividing by two.
The new points are
H(1 , 0.5)
F(3 , 2,5)
G(5 , 0.5)
Robbert wants to put lights around the edge of his yard.The yard if 40 feet long and 23 feet wide.How many yards of light does he need
Answers
Answer:
102.222 square yards of light.
Step-by-step explanation:
From the above question, the yard had the dimensions 40 feet long and 23 feet wide.
Hence, the yard is rectangular in shape.
We have to find the area of the yard.
The formula is given as:
Area = Length × Width
= 40 feet × 23 feet
= 920 square feet
Converting to yards
1 square foot = 0.111 square yard
920 square feet = x
Cross Multiply
x = 920 × 0.111 square yard
x = 102.222 square yards.
Therefore, Robbert would need 102.222 square yards of light.
What are the x and y intercepts for this equation? 2x - 3y = 6
Then, write each intercept in coordinate form. Show ALL your work
Answers
Answer:
So standard form is 2x-3y=6
Slope intercept form is y=2/3x-2
In the diagram below, AB || DF, m/DCE = 104 ° and m/CEF = 145 °. Find m/B.
(I put some parts I could figure out, but now I'm stuck).
Answers
Explanation: Line AE=180°, and angle C = 104°. To find its supplementary angle, subtract it from 180. 180-104=76. Using the alternate interior angle theorem, you can conclude that angle B also equals 76°
a sequence is given by the rule 4n - 5. what is the 20th term in the sequence?
Answers
Answer:
a₂₀ = 75
Step-by-step explanation:
Substitute n = 20 into the n th term rule , that is
a₂₀ = 4(20) - 5 = 80 - 5 = 75
how fast must a meterstick be moving if its length is measured to shrink to 0.737 m?
Answers
The meterstick must be moving at a velocity of approximately 0.836 times the speed of light (or about 251,547,246 m/s) for its length to be measured as 0.737 m.
According to this theory, the length of an object moving relative to an observer appears to be shorter than its rest length. The amount of length contraction depends on the relative velocity between the observer and the object, as well as the direction of motion.
The formula for length contraction is given by:
\(L' = L \times \sqrt{(1 - v^2/c^2)}\)
where L is the rest length of the object, L' is its length as measured by the observer, v is the relative velocity between the observer and the object, and c is the speed of light.
In this case, we are given that the measured length of the meterstick is 0.737 m. We can assume that the rest length of the meterstick is the standard length of a meterstick, which is 1.0 m. We want to find the velocity v at which this length contraction occurs.
So, we can rearrange the formula above to solve for v:
\(v = c \times \sqrt{(1 - (L'/L)^2)}\)
Plugging in the values given, we get:
\(v = c \times \sqrt{(1 - (0.737/1.0)^2)} \\= c \times \sqrt{(1 - 0.542^2)} \\= c \times \sqrt{v} \\= 0.836c\)
where c is the speed of light (299,792,458 m/s).
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Answer:
Step-by-step explanation:
Simplify to create an equivalent expression. −3(2+4k)+7(2k−1)
Answers
Answer:
\(\huge\boxed{2k-13}\)
Step-by-step explanation:
\(\sf -3(2+4k)+7(2k-1)\\Expanding \ brackets\\-6-12k+14k-7\\Combining \ like \ terms\\-12k+14k-6-7\\2k -13\)
First step= -3(2+4K)+7(2k-1)
Second step= -6 - (12k) + 14k- 7
Third step= -12k+14k - 6 -7= 2k-13
Dropping a piece of buttered toast will theoretically land butter-side down with a probability of 0.65. Some students decided to test this theory and dropped five pieces of buttered toast. All five landed butter-side down. One of the students claims that the next piece of buttered toast dropped will land butter-side up because it is due to happen.
Is the student’s reasoning correct?
Yes, the students need to start dropping buttered toast to land butter up to get back to 0.65.
No, the probability of buttered toast landing butter-side down is 0.65 over a large number of trials.
No, if buttered toast lands butter-side down five times in a row, the probability must be higher than 0.65.
Yes, it is unlikely that five pieces of dropped buttered toast will land butter-side down, so butter up must be due.
Answers
The correct statement regarding the probability and the student's reasoning is given as follows:
No, the probability of buttered toast landing butter-side down is 0.65 over a large number of trials.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
On five trials, the piece landed butter side down on all trials, representing the experimental probability.
Over a small number of trials, it is expected for there to be a discrepancy between the experimental probability and the theoretical probability, both over a large number of trials, they are expected to be close.
The theoretical probability for this problem is of 0.65, meaning that the correct statement is given by the second statement.
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Katherine is a waitress at a restaurant. Each day she works, Katherine will make a guaranteed wage of $20, however the additional amount that Katherine earns from tips depends on the number of tables she waits on that day. From past experience, Katherine noticed that she will get about $7 in tips for each table she waits on. How much would Katherine expect to earn in a day on which she waits on 11 tables? How much would Katherine expect to make in a day when waiting on tt tables?
Answers
If Katherine’s wage is $20 the whole day and if she averages about $7 from each table and waits 11, she would get $97. 11 x 7 = 77 + 20 = 97.
best anwser gets brain make sure show anwser thank you
Answers
Answer:
2187
Step-by-step explanation:
1594323/729
basically and you just need to divide and your good.
tommy wait, a minor league baseball pitcher, is notorious for taking an excessive amount of time between pitches. in fact, his times between pitches are normally distributed with a mean of 36 seconds and a standard deviation of 2.5 seconds. what percentage of his times between pitches are a. longer than 39 seconds? b. between 29 and 34 seconds?
Answers
(a) 11.51 percent of tommy's times between pitches are longer than 39 seconds.
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell-shaped curve represents the probability.
How to use z-table?
Step 1: In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.9 1.4, 2.2, 0.5, etc.)
Step 2:Then look up at the top of the z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.95 then go for the 0.05 column)
Step 3:Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2. We want to find out the probability that what percentage of his times between pitches are longer than 31 seconds.
Here, In the given question: we have,
Mean=36 seconds
Standard deviation = 2.5 seconds
So,
For x>39
We want to find out the probability that what percentage of his times between pitches are longer than 39 seconds.
\(\begin{aligned}&P(X > 39)=1-P(X < 39) \\&P(X > 39)=1-P\left(Z < \frac{x-\mu}{F}\right) \\&P(X > 39)=1-P\left(Z < \frac{39-36}{2.5}\right) \\&P(X > 31)=1-P\left(Z < \frac{3}{2.5}\right) \\&P(X > 39)=1-P(Z < 1.2)\end{aligned}\)
The z-score corresponding to 1.2 is 0.8849
\(\begin{aligned}&P(X > 39)=1-0.8849 \\&P(X > 39)=0.1151 \\&P(X > 39)=11.51 \%\end{aligned}\)
Therefore, 11.51% of his times between pitches are longer than 39 seconds.
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Jack and Jill each opened accounts that earn 5% interest compounded annually. Jack deposited $2500 and Jill deposited $3000. No additional money was deposited or withdrawn. At the end of 6 years, what will be the combined balance of these two accounts? (Round to the nearest cent)
Answers
Answer:
3,850
Step-by-step explanation:
have a good day!!
19/13 Rewrite as a decimal with repeating line.
1.46153846153846153846153846153846153846
Answers
Answer:
Write it like the image below. The reason we put the line there is because the digits in the exact order of 461538 repeats.
What is the effect on the graph of f (x) = |x| when the function is changed to g(x) =-2|x|
Answers
Here the graph shows reflection across x - axis by 2 units.
f(x) = |x| => g(x) = -2|x|.
Solution:Graph transformation is the process of modifying an existing graph or graphed equation to produce a variation of the following graph.The modification of algebraic equations is a common type of problem in algebra.Here given the parent function, f(x)=|x|
The translation is , g(x)= -2|x|
Which is an absolute function.
Here the transformation is .
f(x)=|x| => g(x)= -2|x|
The value of f(x) is reflecting over x- axis and value of y changes by 2 units.
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172 students went on a field trip. seven buses were filled and 25 students traveled in cars. how many students were in each bus? i need an equation with the steps
Answers
The number of students in each bus is 21
Given data
Total number of students on the trip = 172
25 students traveled in cars
7 buses were filled
let the number students on each bus be x
number of students on the bus is gotten by
172 - 25 = 147
so 147 students travelled by bus and the total number of buses is 7.
to get the number of students in each bus we solve as follows
147 / 7 = 21
Hence each bus contains 21 students.
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Solve logx^8 = -3
I need help trying to solve this ;-;
Answers
Answer:
ans: x= 1/2
Step-by-step explanation:
i need the volume, the numbers put into the volume and the answer :))
Answers
The volume of the triangular prism on top is:
\(\begin{gathered} V1=(\frac{b\cdot h}{2})\cdot l \\ where\colon \\ b=20ft \\ h=25ft \\ l=22ft \\ V1=\frac{20\cdot25}{2}\cdot22 \\ V1=5500ft^3 \end{gathered}\)The volume of the rectangular prism underneath is:
\(\begin{gathered} V2=l2\cdot w\cdot h2 \\ where\colon \\ l2=22ft \\ w=20ft \\ h2=10ft \\ so\colon \\ V2=22\cdot20\cdot10 \\ V2=4400ft^3 \end{gathered}\)Therefore, the total volume will be:
\(\begin{gathered} V=V1+V2 \\ V=5500ft^3+4400ft^3 \\ V=9900ft^3 \end{gathered}\)Learn with an example
While working at the drugstore, Zachary earns $17 per hour. How many hours will it take
Zachary to earn $34?
Answers
Answer:
2 hours
Step-by-step explanation:
1 hour = $17
To find out how long for Zachary to earn $34..
34 ÷ 17 = 2
Which inequality does the given graph represent?
A) y > x + 2
B) y ≤ −x − 2
C) y < x − 2
D) y ≥ x − 12
Answers
The given inequality in the graph is represented by the inequality y < x - 2. The correct option is C.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Given that the graph is attached to the question and shows one of the inequalities from the options.
When the inequalities are plotted on the desmos graph it is observed that the inequality which represents the graph is y < x − 2.
Therefore, the given inequality in the graph is represented by the inequality y < x - 2. The correct option is C.
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As the project progresses, the actual finish times (AFs) of completed activities will determine
the earliest start and earliest finish times for the remaining activities in the network diagram, as well as the total slack.
Answers
As the project progresses, the actual finish times (AFs) of completed activities play a crucial role in determining various aspects of the project schedule.
The AFs are used to calculate the earliest start and earliest finish times for the remaining activities in the network diagram. These calculations are based on the dependencies between activities and the actual durations of completed activities.
By considering the AFs, the project team can determine the earliest possible start and finish times for the remaining activities, taking into account the sequence of activities and any imposed constraints. This information helps in managing the project schedule and identifying any potential delays or critical paths.
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If f(x) = x, which of the following describes the graph of RX) - 52
OB.
OA. The graph of (x) - 5 Is a horizontal shift of Rx) = x five units to the right.
The graph of RX) - 5 is a vertical shift of AX) = five units down.
OC. The graph of RX) - 5 is a horizontal shift of R43 = x five units to the left.
The graph of AX) - 5 is a vertical shift of (x) = xfive units up.
OD.
Answers
One of the numbers, 14, cannot be used to write related number sentences because it is not an odd number.
The given numbers are 5, 7, 9, and 14. To write related number sentences, we need to use a pattern or relationship between the numbers. We can see that the first three numbers are consecutive odd numbers, so we can write related number sentences such as:
5 + 7 = 12
7 + 9 = 16
5 + 9 = 14
However, the number 14 is not an odd number, so we cannot use it to write related number sentences with the other given odd numbers. For example, we cannot write 9 + 14 = 23 as a related number sentence because 14 is not an odd number. Therefore, the number 14 cannot be used to write related number sentences with the other given numbers.
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need help to this what would the variance be?
Answers
The variance of the set of data is 10. Option A
What is variance?Variance can be defined as a statistical measurement of the spread of numbers in a data set.
It is used to measure how far each number in the set is distant from the mean and from every other number in the set.
It is sometimes described as the measure of variability.
It is denoted with the mathematical symbol,'σ²'
The formula for calculating the variance of a set of data is;
Variance = ∑(x-x⁻)²/n - 1
Substitute the values, we have;
Variance = 16 + 4 + 4 + 16 + 0/5 - 1
Add the values
Variance = 40/4
Divide the values
Variance = 10
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What is a potential problem that can arise from the continual remodeling of bone matrix?
Answers
A potential problem that can arise from the continual remodeling of bone matrix is an imbalance between bone resorption and bone formation, leading to weakened or compromised bone structure.
The continual remodeling of bone matrix is a dynamic process in which old bone tissue is resorbed by specialized cells called osteoclasts, and new bone tissue is formed by osteoblasts. This remodeling process allows for the renewal and repair of bone, as well as the adaptation of bone structure to changing mechanical demands.
However, if there is an imbalance between bone resorption and bone formation, it can lead to potential problems. Excessive bone resorption without adequate bone formation can result in a net loss of bone mass, leading to conditions such as osteoporosis, where bones become weak and brittle. On the other hand, excessive bone formation without sufficient bone resorption can lead to abnormal bone growth and density, which may contribute to conditions like osteopetrosis.
Maintaining a balance between bone resorption and bone formation is crucial for healthy bone remodeling. Factors such as hormonal imbalances, nutritional deficiencies, certain medications, and aging can disrupt this balance, leading to potential problems with bone health and structure. Regular monitoring and appropriate interventions are important in managing and preventing these issues.
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Translate 1 unit right and 2 units up
Answers
Answer:
Step-by-step explanation:
It basically means move from the spot you are at 1 step/square right. Moving up means to go two steps/squares up/forwards.
if the discriminant of a quadratic is zero determine the number of real solutions
Answers
Answer:
2 real and equal solutions
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
the discriminant of the quadratic equation is
b² - 4ac
• if b² - 4ac > 0 , the 2 real and irrational solutions
• if b² - 4ac > 0 and a perfect square , then 2 real and rational solutions
• if b² - 4ac = 0 , then 2 real and equal solutions
• if b² - 4ac < 0 , then 2 not real solutions
HELP DUE IN 15 MINS!
x = ?? degrees
Answers
Answer:
148°Step-by-step explanation:
Inscribed angle is half the intercepted arc measure.
m∠PQR = 1/2xx = 2m∠PQRx = 2(74°) = 148°An assembly line has 16 hours to make 1.000 units. What is the required cycle time? (slide 23) 72sec 216sec 57.65sec 14,4sec
Answers
The required cycle-time is approximately 57.6 seconds.
To find the required cycle time, we need to divide the total available time by the number of units to be produced.
Total available time: 16 hours = 16 * 60 minutes = 960 minutes = 960 * 60 seconds = 57,600 seconds
Number of units to be produced: 1,000 units
Required cycle time: Total available time / Number of units
Cycle time = 57,600 seconds / 1,000 units
Cycle time ≈ 57.6 seconds
Therefore, the required cycle time is approximately 57.6 seconds.
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Correct Answers only!
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Round your answer to the nearest dollar.
Answers
Answer:
128,000
Step-by-step explanation:
I=prt
I=80,000 x 15 x 4
I=128,000
Answer:
$128000
Step-by-step explanation:
Using the given formula :
I = P × R × T
I = 80000 × 15/100 × 4
I = $48000
He saves = 48000 +80000 = $128000
now suppose neither consumption nor investment are affected by changes to the interest rate. show how will this affect the slope of the is curve and explain the economic intuition.
Answers
If neither consumption nor investment are affected by changes in interest rates, the slope of the IS curve will be vertical.
The IS (Investment-Saving) curve represents the relationship between real output (Y) and the interest rate (r) in the goods and services market. In a standard macroeconomic model, the IS curve has a negative slope because a decrease in the interest rate leads to an increase in investment and consumption, which in turn leads to an increase in real output. However, if neither consumption nor investment are affected by changes in the interest rate, then the slope of the IS curve will be vertical.
The economic intuition behind this is that if consumption and investment are not affected by changes in the interest rate, then the interest rate has no impact on the demand for goods and services. Therefore, changes in the interest rate will not affect the level of real output. In other words, the vertical IS curve implies that the level of real output is fixed and independent of the interest rate.
This situation is often referred to as a "liquidity trap," where monetary policy becomes ineffective in stimulating economic growth because interest rates cannot be lowered enough to boost consumption and investment. This can happen when interest rates are already at or close to zero and cannot be lowered further. In a liquidity trap, fiscal policy (government spending and taxation) may be used to stimulate the economy instead of monetary policy
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