The number of gold balls in the given bag is determined as 25 gold balls.
How many of the 40 balls are gold?Let's use the formula for calculating probability:
Probability of an event = Number of favorable outcomes / Total number of outcomes
The total number of possible ways to choose 2 balls from a bag of 40 is:
40C2 = (40 x 39) / (2 x 1) = 780
Now we need to find the number of ways to choose 2 gold balls from the bag.
Let's say there are "g" gold balls in the bag. Then the number of ways to choose 2 gold balls is:
gC2 = (g x (g-1)) / (2 x 1)
We want to find the probability that 2 gold balls are removed, so we use the formula above to get:
Probability of choosing 2 gold balls = Number of ways to choose 2 gold balls / Total number of ways to choose 2 balls
Therefore, we have:
Probability of choosing 2 gold balls = gC2 / 40C2
We are given that this probability is 12/95, so we can set up an equation:
(g x (g-1)) / (2 x 1) / (40 x 39) / (2 x 1) = 12/95
Simplifying, we get:
g x (g-1) = (12/95) x (40 x 39)
g x (g-1) = 624
Expanding and rearranging, we get a quadratic equation:
g² - g - 624 = 0
Solving this quadratic equation, we get:
g = 25 or g = -24
We discard the negative solution, as the number of gold balls must be a positive integer. Therefore, there are 25 gold balls in the bag.
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How many three-digit positive integers x are there, such that subtracting
the sum of digits of × from x gives a three-digit number whose digits are all
the same?
Answer:
Let's call the three-digit number whose digits are all the same "n". We know that n must be between 111 and 999, inclusive.
Now let's consider a three-digit number x. We can write x as:
makefile
Copy code
x = 100a + 10b + c
where a, b, and c are the hundreds, tens, and one's digits of x, respectively. The sum of the digits of x is:
CSS
Copy code
a + b + c
If we subtract this sum from x, we get:
CSS
Copy code
100a + 10b + c - (a + b + c) = 99a + 9b
We want this to be equal to n, which means:
Copy code
99a + 9b = n
We know that n has three identical digits, so we can write:
makefile
Copy code
n = 111p
where p is a digit between 1 and 9. Substituting this into the equation above, we get:
CSS
Copy code
99a + 9b = 111p
11a + b = 37p
Since a and b are digits between 0 and 9, we can see that 37p must be between 0 and 99. The possible values of p are therefore 1, 2, and 3.
If p = 1, then 37p = 37, and we need to find two digits a and b such that 11a + b = 37. This gives us the solutions (a, b) = (3, 4) and (a, b) = (4, 3), which correspond to the numbers 343 and 434.
If p = 2, then 37p = 74, and we need to find two digits a and b such that 11a + b = 74. There are no such solutions since the largest possible value of 11a + b is 99.
If p = 3, then 37p = 111, and we need to find two digits a and b such that 11a + b = 111. This gives us the solution (a, b) = (10, 1), which corresponds to the number 1001. However, 1001 is not a three-digit number, so it does not count.
Therefore, the only two three-digit numbers that satisfy the conditions of the problem are 343 and 434. There are 2 such numbers.
Step-by-step explanation:
g(x)= 0.5|x+1|. Edit the transformation Function. Use y= +A|x-C| + D
The transformation of the function G(x) in the form of y = +A| x - C| + D is -
y = 0.5| x + 1| + 0.5
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
To write the transformation of the function G(x) = 0.5|x+1| in the form y = +A |x - C| + D, we need to find the values of A, C, and D.
First, let's rewrite the given function in the form of |x - C| -
G(x) = 0.5 | x + 1| = 0.5| x - (-1)|
Comparing with the standard form y = A | x - C| + D, we have -
A = 0.5, C = -1
To find the value of D, we need to substitute a point on the graph of G(x) into the function and solve for D.
Let's use the point (-2, 1) -
G(-2) = 0.5|-2+1| = 0.5
So, we get D = 0.5.
Therefore, the transformation of the function is y = 0.5| x + 1| + 0.5.
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20. There are 100 packs of 100 sheets of paper on a table. Melissa must transfer 82 sheets from each
pack onto a cart. She can count at a maximum speed of 3 sheets per second and needs a minimum of 3
seconds more for putting each pack onto a cart. What is the minimum amount of time she will need to
accomplish the task?
a) 15 minutes
b) 8 minutes
c) 10 minutes
d) 12 minutes
e) 13 minutes
The minimum time that Melissa will need to accomplish the task are 15 minutes.
How much time will Melissa require to complete this task?To start let's calculate the time she needs to count the sheets Melissa will transfer:
Sheets to be counted: 18 (Melissa can just count 18 sheets rather than 82 as there are 100 sheets in a pack) 100 - 82 = 18.
Time to count 3 sheets: 1 second
1 second = 3 sheets
x = 18 sheets
x = 18 x 1 / 3 = 6 seconds
6 seconds + 3 seconds to transfer the package = 9 seconds
Finally, let's calculate the total time by multiplying by the number of packs.
9 x 100 = 900 seconds / 60 = 15 minutes.
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Question 7 of 10
Which equation matches the graph of the greatest integer function given
below?
8
6
t
et
1
-8-6-4-20 2 4
-2
-4
-6
-8
1
OA. y-1x1-3
OB. y-[x]-1
OC. y-[x]+3
OD. y-[x]+1
6 8
The graph represents B) y = [x] - 1.
What is equatiοn?In algebra, an equatiοn is defined as a mathematical assertiοn that shοws the equality οf twο mathematical expressiοns. Fοr example, the equatiοn 3x + 5 = 14 is made up οf the twο equatiοns 3x + 5 and 14, which are divided by the wοrd "equal."
The Greatest Integer Functiοn is denοted by y = [x].
Fοr all real numbers, x, the greatest integer functiοn returns the largest integer less than οr equal tο x. In essence, it rοunds dοwn a real number tο the nearest lοwest integer.
In the plοt οf y = [x], the plοt starts frοm οrigin because
y = [0] = 0.
But, in the questiοn, all the line are shifted 1 units dοwnward, as it starts frοm (0, -1).
i.e fοr every values οf x, y decreases 1 units. Hence, 1 must be subtracted.
Therefοre, this graph represents B) y = [x] - 1.
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If h(x) = 5 + x and k (x) = StartFraction 1 Over x EndFraction, which expression is equivalent to (k circle h) (x)?\
A: StartFraction (5 + x) Over x EndFraction
B: StartFraction 1 Over (5 + x) EndFraction
C: 5 + (StartFraction 1 Over x EndFraction)
D: 5 + (5 + x)
Answer:
B: (k circle h)(x) = StartFraction 1 Over (5 + x) EndFraction
Step-by-step explanation:
To find the expression that is equivalent to (k circle h)(x), we first need to find k(h(x)).
k(h(x)) = k(5 + x) = 1/(5 + x)
Therefore, the expression that is equivalent to (k circle h)(x) is 1/(5 + x), which is option B:
(k circle h)(x) = StartFraction 1 Over (5 + x) EndFraction
Solve the inequality 8k−(2k−1)≥7k−21, and write the solution in interval notation.
Answer:
k∈(-∞;22]
Step-by-step explanation:
I added a photo of my solution
Help me please 15 points
In given Histogram, The fraction of shows that was more than half full was 2/3 i.e. C.
What exactly is a histogram?
A histogram is a graphical depiction of numerical data distribution. It entails splitting the data range into intervals or bins and counting how many data points fall into each bin. Bins are often stated as non-overlapping, sequential intervals of a variable. The count or frequency of data points in the respective bin is represented by the height of each bar on the graph. Histograms are often used in statistics to illustrate data distribution and to find trends, outliers, and other data properties.
Now,
Given that
Total shows shown were=3+0+7+10+7+3=30
Show which has more than 150 viewers=1+7+3=20
then,
The fraction of shows that was more than half full =20/30⇒2/3.
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Write four tasks that you can do using you Computer
what is the answer to this math equation i am very bad at division and dont understand it (564873 / 5) * 2 + 6
Answer:
225955.2
Step-by-step explanation:
Kimmy is at track practice she starts by walking 0.25 km as a warm-up then she runs 2 km she feels tired after running that far so she only walk 0.15 km to cool down if the truck is 400 m long how many times did Kimmy go around the track
Kimmy went around the track 6 times.
What is Track practice ?Track practice typically refers to a training session or practice session for athletes who participate in track and field events such as running, jumping and hurdling.
Kimmy's total distance covered during her warm-up, run, and cool-down is:
0.25 km + 2 km + 0.15 km = 2.4 km
To find how many times Kimmy went around the track, we need to convert the total distance to laps.
Since the track is 400 m long, we can divide 2.4 km by 0.4 km to get:
2.4 km ÷ 0.4 km/lap = 6 laps
Therefore, Kimmy went around the track 6 times.
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Y=6-x4/3algebraic method
Answer:
Step-by-step explanation:
Two brothers, Mark and Brian, each inherit $39000 . Mark invests his inheritance in a savings account with an annual return of 2.1% , while Brian invests his inheritance in a CD paying 5.6% annually. How much more money than Mark does Brian have after 1 year?
Answer: 4.2
Step-by-step explanation:
solve for x show ur work pls
The value of the variable x for the similar triangle ∆MST is 9 which makes option D correct.
How to solve for the value of x for the triangle ∆MSTThe triangles MLK and MST are similar, this implies that the length MS of the smaller triangle is similar to the length MK of the larger triangle
and the length MT of the smaller triangle is similar to the length ML of the larger triangle
so;
14/21 = (x + 5)/21
by comparison of both sides of the equation, we have that;
14 = x + 5
x = 14 - 5 {subtract 5 from both sides}
x = 9
Therefore, the value of the variable x for the similar triangle ∆MST is 9.
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Root of the equation
Answer:
A fancy way of saying "solutions" of the equation
Here’s the question
The value of 2 miles = 3520 yards and 3 miles = 5280 yards. 2 yards = 6 feet and 3 yards = 9 feet. 2 feet = 2 x 12 inches = 24 inches and 3 feet = 36 inches.
What is SI unit conversion?The International System of Units (SI) units may be used in trade and commerce, grants and other business-related activities, educational information, and as guidelines in publications to improve understanding of the metric system. The SI units may be interpreted or modified for use in the United States by the Secretary of Commerce through the National Institute of Standards and Technology.
Multiply the number of miles by 1760:
1 mile = 1760 yards
2 miles = 2 x 1760 yards = 3520 yards
3 miles = 3 x 1760 yards = 5280 yards
Multiply the number of yards by 3, since there are 3 feet in a yard.
1 yard = 3 feet
2 yards = 2 x 3 feet = 6 feet
3 yards = 3 x 3 feet = 9 feet
Multiply the number of feet by 12, since there are 12 inches in a foot.
1 foot = 12 inches
2 feet = 2 x 12 inches = 24 inches
3 feet = 3 x 12 inches = 36 inches
Hence, the value of 2 miles = 3520 yards and 3 miles = 5280 yards. 2 yards = 6 feet and 3 yards = 9 feet. 2 feet = 2 x 12 inches = 24 inches and 3 feet = 36 inches.
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PLEASE HELP! DUE TODAY!!
SHOW WORK!!!!
Answer:
Step-by-step explanation:
The sum of the measures of angles DAC and CAB must equal the measure of angle DAB, since they are adjacent angles that share a common vertex, A. Therefore, we have:
(DAC) + (CAB) = (DAB)
Substituting the given values, we get:
(2y - 7) + (3y + 2) = (DAB)
Simplifying and solving for y, we get:
5y - 5 = (DAB)
y = (DAB + 5) / 5
Now we can find the measure of angle CAB by substituting y back into the given expression for CAB:
<CAB = (3y + 2) = 3[(DAB + 5)/5] + 2 = (3DAB + 17)/5
Therefore, the measure of angle CAB is (3DAB + 17)/5 degrees.
If it is 10:41 now what time will it be in 18 hours 17 minutes
Answer : 04:48 AM
:)
Answer:
4:58
Step-by-step explanation:
10+18 = 28
28/12 = 2 r4
41+17 = 58
here's the picture pls help
The volume of the square based cuboid is 160 cm³.
What is the volume of the square based cuboid?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Since the cuboid has a squared base.
Width w = 4cmLength l = 4cmHeight h = 10cmPlug in the given values and solve for the volume.
Volume = w × h × l
Volume = 4cm × 10cm × 4cm
Volume = 160 cm³
Therefore, the volume is 160 cubic centimeters.
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A patient has a choice between four different prescription plans through their health insurance. The options are:
Option A: $105 monthly premium with a $15 co-pay per prescription
Option B: $100 monthly premium with a $20 co-pay per prescription
Option C: $115 monthly premium with a $10 co-pay per prescription
Option D: $110 monthly premium with a $12 co-pay per prescription
Which option is the most expensive if the patient fills 7 prescriptions each month?
O Option A
O Option B
O Option C
O Option D
Option B is the most expensive, with a total cost of $240 per month if the patient fills 7 prescriptions per month.
Which option is the most expensive if the patient fills 7 prescriptions each month?To determine which option is the most expensive, we need to calculate the total cost for each option if the patient fills 7 prescriptions per month.
For Option A, the total cost would be:
(7 x $15) + $105 = $210
For Option B, the total cost would be:
(7 x $20) + $100 = $240
For Option C, the total cost would be:
(7 x $10) + $115 = $185
For Option D, the total cost would be:
(7 x $12) + $110 = $194
Therefore, Option B is the most expensive, with a total cost of $240 per month if the patient fills 7 prescriptions per month. The other options are cheaper, with Option C being the least expensive at $185 per month.
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Use appropriate formulas to find (a) the perimeter and (b) the area of the figure.
(a) The perimeter is
(b) The area is
17 cm
17 cm
Answer:
perimeter=68cm
area=289cm^2
Step-by-step explanation:
the perimeter is 17+17+17+17=68cm
the area is 17×17=289cm^2
La raíz cuadrada de 81 dividida en el cuadrado de 3
Answer:
27 duh lord help them please and me
In a circle with radius 7, an angle measuring π radians intercepts an arc. Find the length of the arc in simplest form.
Answer: the length of an arc intercepted by an angle in a circle is L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.
Using this formula, we can find the length of the arc intercepted by an angle of π radians in a circle with radius 7:
L = rθ = 7π/1 = 7π
Therefore, the length of the arc is 7π units. This is already in its simplest form since π is a constant that cannot be simplified further.
Step-by-step explanation:
a distribution of values is normal with a mean of 128.3 and a standard deviation of 80.9.find p36, which is the score separating the bottom 36% from the top 64%. p36 = ___
The score separating the bottom 36% from the top 64%. p36 = 97.43
To find the score that separates the bottom 36% from the top 64%, we need to find the z-score corresponding to the 36th percentile and then use it to calculate the corresponding raw score.
First, we find the z-score using a standard normal table or calculator:
z = invNorm(0.36) = -0.379
Next, we use the formula:
z = (x - mu) / sigma
where x is the raw score, mu is the mean, and sigma is the standard deviation.
Plugging in the given values, we get:
-0.379 = (x - 128.3) / 80.9
Solving for x,
x = -0.379 * 80.9 + 128.3 = 97.43
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I need help Area of a circle
Answer:
The formula
Step-by-step explanation:
just do pi times the circle's radius squared.
(pi x r squared)
I need help with this please
The snow that will be gotten daily of the line plot is redistributed equally will be 1/2.
What is a line plot?A line plot, also known as a line graph, is a type of graph that displays information as a series of data points connected by straight lines. Line plots are often used to show how a particular variable changes over time or to compare two or more variables.
To create a line plot, you typically need to have a set of data points that represent the variable you want to graph. You then plot each data point on a graph, with the x-axis representing time or some other variable, and the y-axis representing the value of the variable you're graphing.
The snow that will be gotten daily of the line plot is redistributed equally will be:
= (1/8 + 2/8 + 3/8 + 4/8 + 5/8 + 6/8 + 7/8 + 8/8) / 9
= 36/8 / 9
= 1/2
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Help me solve this. Thank you
the total area under the normal distribution curve is 0.9632.
How to find total area under the normal distribution curve?
To find the total area under the normal distribution curve, we can use the standard normal distribution table or a calculator with a normal distribution function. We need to find the areas to the left and right of the given z-scores and add them together.
First, we can find the area to the left of z = -2.15 using the standard normal distribution table or a calculator with a normal distribution function. The area to the left of z = -2.15 is the same as the cumulative probability of a standard normal distribution with a z-score of -2.15. Using a standard normal distribution table or a calculator, we find this area to be 0.0158.
Next, we can find the area to the right of z = 1.62 using the standard normal distribution table or a calculator with a normal distribution function. The area to the right of z = 1.62 is the same as the complement of the cumulative probability of a standard normal distribution with a z-score of 1.62. Using a standard normal distribution table or a calculator, we find the complement to be 0.0526. Therefore, the area to the right of z = 1.62 is 1 - 0.0526 = 0.9474.
Finally, we can add the area to the left of z = -2.15 and the area to the right of z = 1.62 to find the total area under the normal distribution curve:
S = area to the left of z = -2.15 + area to the right of z = 1.62
S = 0.0158 + 0.9474
S = 0.9632
Therefore, the total area under the normal distribution curve is 0.9632.
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8. Compare the numbers in the following sequence and try to determine what the next number
should be.
6, 9, 18, 21, 42, 45, ?
Answer:
90
Step-by-step explanation:
this is the pattern: +3, *2, +3, *2, +3
so theoretically the next number would be 90.
The next number is 90.
If you observe the pattern the second number is +3 of the first number and the third number is ×2 of the second number following this pattern.
6+3=9
9×2=18
18+3=21
21×2=42
42+3=45
45×2=90
Therefore 90 is the right answer.
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Three grams of musk oil are required for each bottle of Mink Caress, a very popular perfume made by a small company in western Siberia. The cost of the musk oil is $1.50 per gram. Budgeted production of Mink Caress is given below by quarters for Year 2 and for the first quarter of Year 3:
Cost of Raw Materials for 4 years is = $ 297,000 $ 459,000 $ 630,000 $ 423,000
Define Budgeted productionBudgeted production refers to the expected level of production that a company plans to achieve during a specific period of time, typically a year. It is a key component of the budgeting process and involves estimating the amount of goods or services that a company will produce and sell in the upcoming period, based on various factors such as market demand, production capacity, and available resources.
Part 1:Direct Materials Budget in Bottles & Grams
Year 2
First Second Third Fourth Total
Budgeted production, 60,000 90,000 150,000 100,000 450,000
Add Desired Ending Inventory
20 % 0f the Production 18,000 30,000 20,000 14,000 82,000
Less Beginning Inventory
36,000/ 3 12,000 18,000 30,000 20,000 80,000
D.
Materials 66,000 102,000 140,000 94,000 452,000
Grams in a Bottle 3 3 3 3 3
Raw Materials 198,000 306,000 420,000 282,000 1356,000
Costs $1.50 $1.50 $1.50 $1.50 1.50
Costs Raw Materials $ 297,000 $ 459,000 $ 630,000 $ 423,000
Total Raw Material Cost is $2,034,000.
Part 2:"Unit cost of raw materials"
Direct Materials Budget in Bottles & Grams
Year 2 Year 3
First Second Third Fourth First
Budgeted production
Production = 60,000 90,000 150,000 100,000 70,000
Desired Ending Inventory
20 % of the Production = 18,000 30,000 20,000 14,000
Less Beginning Inventory
36,000/3 = 12,000/18,000 30,000 20,000 14,000 for musk oil.
D.
Materials Budget = 66,000 102,000 140,000 94,000
Grams in a Bottle = 3 3 3 3
gms = 198,000 306,000 420,000 282,000 for raw materials
Costs(given) = $1.50 $1.50 $1.50 $1.50
Costs of Raw Materials are $ 297,000, $ 459,000, $ 630,000, and $ 423,000 for 4 years.
Therefore, the correct answer are :
Total Raw Material Cost is $2,034,000.
Cost of Raw Materials for 4 years is = $ 297,000 $ 459,000 $ 630,000 $ 423,000
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The complete question is:
Three grams of musk oil are required for each bottle of Mink Caress, a very popular perfume made by a small company in western Siberia. The cost of the musk oil is $1.50 per gram. Budgeted production of Mink Caress is given below by quarters for Year 2 and for the first quarter of Year 3:
Year 2 Year 3
First Second Third Fourth First
Budgeted production, in bottles 60,000 90,000 150,000 100,000 70,000
Musk oil has become so popular as a perfume ingredient that it has become necessary to carry large inventories as a precaution against stock-outs. For this reason, the inventory of musk oil at the end of a quarter must be equal to 20% of the following quarters production needs. Some 36,000 grams of musk oil will be on hand to start the first quarter of Year 2.
Required:
Prepare a direct materials budget for musk oil, by quarter and in total, for Year 2. (Round "Unit cost of raw materials" answers to 2 decimal places.)
Simplify: 5x(5) - 2x +3
Answer:
The answer I got was 23x +3 because I multiplied the two fives together and that gives you 25x then I subtracted the 2x from the 25x and I got 23x and then I just added the +3 to the end of the 23x and that is how I got 23x +3.
How can I solve this?
Answer:
Step-by-step explanation:
linear function
straight line