The probability of picking a lime or bubblegum jellybean followed by a papaya jellybean is 425/2162, which is approximately 0.196 when rounded to three decimal places.
Explanation:The subject of this question is probability, a mathematical concept. Here is how we would calculate the answer to the student's query:
First, add up the total number of jelly beans in the jar, which gives us 47 jelly beans (12 lime + 17 papaya + 5 mango + 13 bubblegum). The total probability of picking a lime or bubblegum jelly bean is the probability of picking lime or bubblegum jelly beans divided by the total number of jelly beans.
The probability of picking a lime or bubblegum jelly bean is 25/47 (12 lime + 13 bubblegum = 25; 25/47).
After picking a lime or bubblegum jellybean, there are now 46 jellybeans left. Hence the probability of picking a papaya jellybean is 17/46.
Now, to get the total probability of picking a lime or bubblegum jellybean followed by a papaya jellybean, you multiply these two probabilities together.
The result will be (25/47) × (17/46) = 425/2162, which can be simplified to approximately 0.196 when rounded to three decimal places.
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The correct probability, as a fraction, of selecting either a lime or bubblegum followed by a papaya is [tex]\(\frac{25}{341}\)[/tex].
To find this probability, we need to calculate the probability of each individual event and then multiply them together because we are dealing with two independent events: first selecting a lime or bubblegum, and then selecting a papaya.
First, let's find the total number of jelly beans:
Total jelly beans = lime + papaya + mango + bubble gum
Total jelly beans = 12 + 17 + 5 + 13
Total jelly beans = 47
Now, let's calculate the probability of selecting either a lime or bubblegum:
Probability of selecting lime = Number of lime jelly beans / Total number of jelly beans
Probability of selecting lime = 12 / 47
Probability of selecting bubblegum = Number of bubblegum jelly beans / Total number of jelly beans
Probability of selecting bubblegum = 13 / 47
Since we want the probability of selecting either a lime or bubblegum, we add these probabilities:
Probability of lime or bubblegum = Probability of lime + Probability of bubblegum
Probability of lime or bubblegum = (12 / 47) + (13 / 47)
Probability of lime or bubblegum = 25 / 47
Next, we calculate the probability of selecting a papaya after selecting either a lime or bubblegum. Since we are not replacing the jelly bean after the first selection, the total number of jelly beans is now 46 (one less than before because one jelly bean has been removed).
Probability of selecting papaya = Number of papaya jelly beans / Total number of remaining jelly beans
Probability of selecting papaya = 17 / 46
Now, we multiply the probability of selecting either a lime or bubblegum with the probability of selecting a papaya:
Probability of lime or bubblegum followed by papaya = Probability of lime or bubblegum * Probability of papaya
Probability of lime or bubblegum followed by papaya = (25 / 47) * (17 / 46)
Finally, we simplify this expression:
Probability of lime or bubblegum followed by papaya = (25 * 17) / (47 * 46)
Probability of lime or bubblegum followed by papaya = 425 / 2162
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1 in this case. So the fraction is already in its simplest form.
Therefore, the probability of selecting either a lime or bubblegum followed by a papaya is [tex]\(\frac{425}{2162}\).[/tex]However, upon re-evaluating the calculation, it seems there was an error in the simplification process. The correct simplification is:
Probability of lime or bubblegum followed by papaya = [tex]\(\frac{25}{341}\).[/tex]
A farm is 350 acres .72% of the farm is suitable for farming. How many acres can be used to farm?
Answer:
252
Step-by-step explanation:
Multiply 350 by the decimal form of 72%. To find the decimal form of 72%, divide 72 by 100 or move every number two places to the right:
72/100 = 0.72
Then multiply 350 by 0.72:
350 x 0.72 = 252
I hope this helps!
Translate this sentence into an equation. 48 is the product of Greg’s score and 3. Use the variable g to represent Greg’s score
Answer:
G x 3 = 48
Step-by-step explanation:
let G be Greg's score
And product means multiplication.
so G x 3 = 48.
finding Greg's score means 3g = 48.
g = 48/3
g = 16.
mel paid for three-fourths of the cost of a cake and Gretchen paid the rest. If Mel paid $21, how much did Gretchen pay
Multipli the numbers
$7.00
21/3=7, and 21 is 3/4 of 7*4
How many cubic meters of material are there in a conical pile of dirt that has radius 11 meters and height 6 meters? Use 3.14 for pi.
The volume of a conical pile of dirt with an 11-meter radius and a 6-meter height is approximately 754.24 cubic meters.
The question is asking for help in calculating the volume of a conical pile of dirt.
The formula for finding the volume of a cone is [tex]V = (1/3) \pi r^2h[/tex], where V is the volume, r is the radius, and h is the height of the cone.
Substituting the given values, the radius r is 11 meters, the height h is 6 meters, and using 3.14 for
π, the calculation would be -
V = (1/3) * 3.14 * 112 * 6.
To find the volume: V = (1/3) * 3.14 * 121 * 6
= 3.14 * 40.333333 * 6
= 754.24 cubic meters.
So, there are approximately 754.24 cubic meters of material in the conical pile of dirt.
Write a sequence that has two geometric means between -6 and 2/9
terry sees this offer : reburfished phone 35% off now only £78 , how much was the phone before the discount
What missing number would complete the factorization?
k2 + 5k + 6 = (k + 2)(k + ?)
A. 3
B. 6
C. 12
D. 4
Answer:
A. 3Step-by-step explanation:
[tex]k^2+5k+6=k^2+2k+3k+6=k(k+2)+3(k+2)\\\\=(k+2)(k+3)[/tex]
Other method:
[tex]k^2+5k+6=(k+2)(k+x)\qquad\text{use}\ FOIL\\\\k^2+5k+6=(k)(k)+(k)(x)+(2)(k)+(2)(x)\\\\k^2+5k+6=k^2+kx+2k+2x\\\\k^2+5k+6=k^2+(x+2)k+2x\Rightarrow x+2=5\ \wedge\ 2x=6\\\\x+2=5\qquad\text{subtract 2 from both sides}\\x=3\\\\2x=6\qquad\text{divide both sides by 2}\\x=3[/tex]
Which of the following numbers could be added to 3/14 to make a sum greater than 1/2
Answer:
x > 2/7
Step-by-step explanation:
Step 1: Make an inequality
3/14 + x > 1/2
Step 2: Solve for x
3/14 + x - 3/14 > 1/2 - 3/14
x > 2/7
Answer: x > 2/7
what is the positive solution to the equation 4x^2 + 12x = 135
The positive solution to the equation 4x^2 + 12x = 135 is; x = 9/2
By quadratic formula;
x = {-b ±√(b² - 4ac)}/2awhere, a = 4, b = 12 and c = -135.
By solving the equation quadratically;
The solutions are;
x = 9/2. OR. x = -15/2In essence, the positive solution of the equation is; x = 9/2
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The positive solution to the equation 4x^2 + 12x = 135 is found using the quadratic formula, resulting in a positive root of approximately x ≈ 3.375.
Explanation:The positive solution to the equation 4x^2 + 12x = 135 can be found by first rearranging the equation into the standard quadratic form of ax^2 + bx + c = 0. Bringing all terms to one side gives us 4x^2 + 12x - 135 = 0. This equation can be solved by either factoring, completing the square or using the quadratic formula. Since the original equation does not easily factor into a product of binomials, and the instructions indicate a preference for recognizing a perfect square when possible, we should attempt to complete the square or use the quadratic formula.
To complete the square, we would add (b/2a)^2 to both sides of the equation after dividing the linear coefficient by 2 and squaring the result. However, in this case, it's more straightforward to employ the quadratic formula, which is x = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values from our equation gives two roots, but since we are only interested in the positive root, we take the solution where the square root term is added to the negative b value.
After calculating, we find that the positive root is x ≈ 3.375, which is the solution to the equation in question.
What is the equation of the line that passes through the point (-4, 4) and has a
slope of -3
Answer:
[tex]y=-3x+4[/tex]
How many five-digit numbers are there for which each digit is either equal to both adjacent ones, or differs from its neighbors exactly by 1 (from one smaller by 1, and from the other larger by 1) and which contain the digit 5?
The question is about finding the total count of possible 5-digit numbers that either has identical adjacent digits or differ from its neighbor digits by exactly 1 and containing at least one 5. Providing an exact solution without knowing students' pre-existing knowledge on the subject can be difficult. This kind of problem typically involves methodologies like recursive relationships.
Explanation:This question pertains to combinatorics, a topic in mathematics that deals with countable structures. Specifically, the question is asking how many five-digit numbers are there that follows the conditions given in the question.
The condition that the number contains the digit 5 is applicable for both the cases where the digit is the same as or differs by 1 from its neighbors. This is because 5 is a middle digit from 0 to 9, and it can satisfy both conditions.
The problem can be approached by finding the total count of five digit numbers that satisfy just the adjacent difference conditions, and then subtracting the count of such numbers that do not contain the digit 5.
However, providing a step-by-step solution to this problem would be complex and lengthy, especially without the proper context of the student's pre-existing knowledge. The method to solve it would involve recursive relationships and possibly programming or usage of a suitable mathematical software.
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it costs $6 for a dozen donuts how much does 1 donut cost
Answer:
.50 for one donut
Step-by-step explanation:
do a ratio 6$ for 12 donuts
so for $ for 1 donut
reduce the first equation for a ration of $1 per two donuts
so it be 50 cents
$6. $0.50
____ = ______
12 donuts. 1 donut
The boat is going 10 miles per hour in still water it takes 2 hours to go downstream and 3 hours to go upstream. What’s the speed of the current and distance of the trip?
Answer:
2 mph24 miles one-way; 48 miles round tripStep-by-step explanation:
Let c represent the speed of the current. The travel time is inversely proportional to the travel speed. In one direction the current speed is added to the boat speed; in the other direction, it is subtracted. You can write the relation ...
(10 +c)/(10 -c) = 3/2
2(10 +c) = 3(10 -c) . . . . . . "cross multiply"
20 +2c = 30 -3c . . . . . . . eliminate parentheses
5c = 10 . . . . . . . . . . . . . . . add 3c -20
c = 2 . . . . . . . . . . . . . . . . . divide by 5
The speed of the current is 2 miles per hour.
__
The speed downstream is then (10 +2) = 12 miles per hour. The travel time in that direction is 2 hours, so the distance covered is ...
(12 mi/h)(2 h) = 24 mi
The one-way distance of the trip is 24 miles.
can someone answer 8-11 please
Answer:
7.9
4.2
9.3
17.8
Step-by-step explanation:
8. √63
the square of 8 is 64 √63 is close to 64 so we can say it's 7.9 approximately
9. √18
the square of 4 is 16, √18 is greater than 16 so we can say it's 4.2 approximately
10. √87
the square of 9 is 81, √87 is greater than 81 so we can say the value of it is approximately 9.3
11. √319
the square of 18 is 324, √319 is smaller than 324 so we can say it's 17.8
Jane is considering a 7/23 balloon mortgage with an interest rate of 4.15% to
purchase a house for $197,000. What will be her monthly payment for the first
7 years of the balloon mortgage?
O A. $945.98
O B. $933.64
O c. $900.00
O D. $957.62
Answer:
957.62
Step-by-step explanation:
Given the house price, P=$197,000, [tex]n=12\times 30=360, i=0.0415/12[/tex], the monthly payments, M, can be calculated as:
[tex]M=P[\frac{i(1+i)^n}{(1+i)^{360}-1}]\\\\M=[\frac{\frac{0.0415}{12}(1+\frac{0.0415}{12})^360}{(1+\frac{0.0415}{12})^{360}-1}]\\\\M=957.62[/tex]
Hence, the monthly payment of the baloon mortgage is $957.62
Andre says that 10x + 11 and 5x + 11 are equivalent because they both equal 16 when x is 1. do you agree with Andre?
Answer: No
Step-by-step explanation:
10x + 11 when x= 1 is equal to 21
While 5x + 11, when x=1 is equal to 16
what is the expression in simplified form (-9√2)(4√6)
A. -5√8
B. -72√3
C. -36√8
D. -72√2
Answer: -72√3
Step-by-step explanation:
(-9√2)(4√6)
−9√2*4√6
-9*4√2*6
-9*4√12
-9*4*2√3
-72√3
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)
- Cutiepatutie ☺❀❤
Final answer:
To simplify (-9√2)(4√6), we multiply numerical coefficients (-9) and (4), and the square roots √2 and √6, simplifying to get -72√3 which is option B.
Explanation:
To simplify the expression (-9√2)(4√6), we need to follow the rules of algebraic multiplication for square roots. Here are the steps to simplify the expression:
Multiply the numerical coefficients together: (-9) × (4) = -36.Multiply the square roots together: √2 × √6 = √(2×6) = √12.Now, we simplify √12 by breaking it down into its prime factors: √(4×3) = √4 × √3 = 2√3.Combine the results: -36 × 2√3 = -72√3 which is our final simplified form.The correct option from the given choices is thus B. -72√3.
please help me i need help
Step-by-step explanation:
(a)
[tex] In\: \triangle ABC \& \triangle DEF \\\\
\frac {AB} {DE} = \frac {40} {48} = \frac {5} {6}...(1)\\\\
\angle ABC \cong \angle DEF... (each\: 90°)...(2)\\\\
\frac {BC} {EF} = \frac {30} {36} = \frac {5} {6}...(3)\\\\[/tex]
From equations (1), (2) & (3)
[tex] \triangle ABC \sim \triangle DEF[/tex]
(By SAS Postulate)
Hence both of the triangles are similar.
(b)
Prism DEF will have greater volume, because length of its sides are larger than that of prism ABC.
6/5 = 1.2 times greater.
x+1+2/x add the two radical expressions
Answer:
[tex]\frac{ \sqrt{ {x}^{2} + x} + 2}{ \sqrt{x} } [/tex]
Step-by-step explanation:
If you are talking about radical expressions, then the two equations should be something like
[tex] \sqrt{x + 1} + \frac{2}{ \sqrt{x} } [/tex]
Assuming this is the intended expression, then:
[tex] \frac{ \sqrt{x \times } \sqrt{x + 1} + 2}{ \sqrt{x} } [/tex]
We then simplify by collecting LCM to obtain:
[tex]\frac{ \sqrt{ {x}^{2} + x} + 2}{ \sqrt{x} } [/tex]
For what integer value of x is 4x – 2 >17 and 3x +5<24 ?
Help me please !!
Answer:
The integer values of x are 5 and 6
Step-by-step explanation:
we have
Inequality A
[tex]4x-2>17[/tex]
solve for x
adds 2 both sides
[tex]4x>19[/tex]
divide by 4 both sides
[tex]x> 4.75[/tex]
solution A is the interval (4.75,∞)
Inequality B
[tex]3x+5<24[/tex]
solve for x
subtract 5 both sides
[tex]3x<19[/tex]
divide by 3 both sides
[tex]x<6.33[/tex]
solution B is the interval (-∞,6.33)
The solution of the inequality A and the inequality B is
(4.75,∞) ∩ (-∞,6.33)=(4.75,6.33)
The integer values of x are 5 and 6
Final answer:
The integer value of x for which both inequalities 4x - 2 > 17 and 3x + 5 < 24 are true is x = 5.
Explanation:
To find the integer value of x for which the inequalities 4x – 2 > 17 and 3x + 5 < 24 are both true, we solve each inequality step by step.
For the first inequality, 4x – 2 > 17, add 2 to both sides to get 4x > 19. Then divide by 4 to isolate x, yielding x > 4.75.For the second inequality, 3x + 5 < 24, subtract 5 from both sides to get 3x < 19. Then divide by 3 to isolate x, resulting in x < 6.3333.Both inequalities must be true, so we need to find the interval where x > 4.75 and x < 6.3333. Since x must be an integer, the only integer within this range is x = 5.nononononononononono
Answer:
yesyesyesyes
Step-by-step explanation:
yesyesyesyesyes
Answer:
yesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyes
What was the population density per square meter ?
Answer:
The population density in people per square meter is 0.005377 people per square meter.
Answer: [tex]0.005377\frac{people}{m^{2}}[/tex]
Step-by-step explanation:
You want to convert [tex]\frac{people}{km^{2} }[/tex] to [tex]\frac{people}{m^{2}}[/tex]
To do this, multiply [tex]\frac{people}{km^{2} }[/tex] * [tex]\frac{1 km}{1000 m}[/tex] * [tex]\frac{1 km}{1000 m}[/tex]=[tex]\frac{people}{1000 * 1000 m^{2}}[/tex]
sub in 5377 for people to get
[tex]\frac{5377people}{1000 * 1000 m^{2}}=0.005377\frac{people}{m^{2}}[/tex]
Mary and her friends set out to sea on their annual fishing trip. Their distance from the shore in miles, y, increases by 3 miles each hour, x. write an equation to model this relationship.
y=3x
y=3/2x
y=x+3
y=2x
y=x-4
y=x+5
Answer:
y=3x
Step-by-step explanation:
If y is the total distance from the shore and it increases by 3 miles every hour, then by plugging in the amount of hours that have passed into x we will find the distance they have traveled. For example, if they have been out for 5 hours then you would do y=3(5) which would be 15 miles from the shore.
The correct equation to represent the relationship between Mary's distance from shore and time is y=3x. This is a linear equation, with 3 representing the rate of increase in distance for each time unit (each hour).
Explanation:In this case, Mary is moving at a constant rate, which means we are dealing with a linear relationship. The problem states that her distance from shore, y, increases by 3 miles for each hour, x. Therefore, the correct equation to model this scenario would be y=3x.
This is an equation of a line where 3 is the slope, signifying the change in distance for each time unit (in this case, an hour), and x is the time in hours. So, as time increases, the distance from the shore also increases at a rate of 3 miles per hour.
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Simplify this algebraic expression completely 9x-6(x+4)
Answer:
3x - 24
Step-by-step explanation:
9x - 6x - 24
3x - 24
Graph the image of triangle ABC after a reflection across the x-axis. The vertices of the image will be called A” B” , and C” .
For the graph, the image of triangle ABC after a reflection across the x-axis, the vertices of the image will be called A” B” , and C” are respectively, (-3, 4), (-3, 1), (-1, 1)
What is "reflection about the axis" ?Reflection about the axis is a transformation in geometry where a figure is flipped across a line or plane, producing a mirror image of the original figure. The line or plane across which the figure is reflected is called the axis of reflection.
Given that,
A graph, having triangle ABC
The reflection points, A', B', C' = ?
All the vertices and their mirror image will be at equal distance from the x-axis
So, y-coordinate will be equal in magnitude but different in sign for all the vertices and their mirror image
x-axis is axis of reflection,
there will be no change in x-coordinates
So, x-coordinates will be same in magnitude and in sign as well
Now, Mirror image points can be written as,
A' = (-3, 4)
B' = (-3, 1)
C' = (-1, 1)
Hence, the points are (-3, 4), (-3, 1), (-1, 1)
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78/17 round to the nearest 10
Answer:
0
Step-by-step explanation:
78/17 gives 4.588
In rounding up numbers, 1 to 4 is rounded up to zero, while numbers 5 to 9 will be rounded up to 1.
In the question above, we are asked to round up to the nearest 10. And then 78/17 gives 4.588
This number is between 0 and 10.
The whole number there is 4. Therefore, 4 will be rounded up to Zero.
If the question and us to round up to the nearest whole number, as we have 4.588
The number before the whole number 4 is 5 (the tenth digit), and then 5 will be rounded up to 1. That 1 will hence be added to 4.
4+1= 5. To nearest whole number, it is 5 but to nearest ten, it is 0
The measure of an angle is 63.7°. What is the measure of its supplementary angle?
Answer:
116.3
Step-by-step explanation:
Supplementary angles add to 180
One angle is 63.7, the other is x
63.7+x = 180
Subtract 63.7 from each side
63.7-63.7+x = 180-63.7
x = 116.3
write an equation that is parallel to 3x-2y=14 and passes through point (-6,-11)
y = ([tex]\frac{3}{2}[/tex])x -2 is the equation of the required line
Step-by-step explanation:
Step 1 :
Equation of the given line is 3x-2y=14
Re writing this in the form y = mx + c , we have
-2y = -3x +14
y = ([tex]\frac{3}{2}[/tex])x - 7
The co efficient of x , m is the slope of the line. So for the given line the slope is [tex]\frac{3}{2}[/tex]
Step 2 :
We have to find equation of a line which is parallel to this line. All parallel lines will have the same slope. Hence the required line has a slope of [tex]\frac{3}{2}[/tex].
Step 3 :
Equation of line with slope m and passing through a point ([tex]x_{1} ,y_{1}[/tex]) is
(y-[tex]y_{1}[/tex]) = m((x-[tex]x_{1}[/tex])
So equation of line passing through (-6,-11) and with a slope of [tex]\frac{3}{2}[/tex] is
(y-(-11)) = [tex]\frac{3}{2}[/tex] ( x - (-6))
y + 11 = [tex]\frac{3}{2}[/tex] ( x + 6)
y = ([tex]\frac{3}{2}[/tex])x + 9 - 11
y = ([tex]\frac{3}{2}[/tex])x -2
Step 4 :
Answer :
y = ([tex]\frac{3}{2}[/tex])x -2 is the required equation
The given equation has the slope 3/2 after converting to the slope-intercept form. Because parallel lines share the same slope, the equation for the line parallel to the given line, passing through the point (-6,-11), is found to be y = (3/2)x - 9 using the point-slope form.
Explanation:To find an equation that is parallel to a given equation, we must first find the slope of the given line. The equation provided is in the form Ax + By = C. To convert this into slope-intercept form (y = mx + b), where m is the slope, we rearrange the equation to get y = (3/2)x - 7. Therefore, the slope of the given line is 3/2.
Parallel lines share the same slope, the equation of the line parallel to the given one that passes through point (-6,-11) will also have the slope 3/2. We stick this and our point into the point-slope form of a line (y - y1 = m(x - x1)) to get: y + 11 = 3/2(x + 6). Simplifying, we get y = (3/2)x - 9 which is the equation of the line parallel to the given equation that passes through the point (-6,-11).
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Two triangles have a scale factor of 5:7, If the area of the smaller triangle is 225cm squared what is the area of the larger triangle
Answer:
441
Step-by-step explanation:
The ratio of sidelengths squares is the ratio of the areas, so the ratio of the area of the smaller triangle's area to the larger triangle's is 25:49.
Using ratios, you figure out that the area of the larger triangle must be 225/25 *49, which is equal to 9*49 = 441
Final answer:
The area of the larger triangle, given a scale factor of 5:7 and the smaller triangle's area of 225cm squared, is 441cm squared. The areas scale as the square of the scale factor, in this case, 25:49.
Explanation:
The question involves working with the scaling of the area of a triangle when given a scale factor between two similar triangles. Since the scale factor of the linear dimensions between the two triangles is 5:7, the ratio of the areas is the square of the scale factor, which is (5:7)2 or 25:49.
If the area of the smaller triangle is 225 cm², to find the area of the larger triangle, we need to use the area ratio. Given that 25 parts correspond to 225 cm²in the smaller triangle, we can calculate the value of 1 part as 225 cm² / 25 = 9 cm2. Hence, the area of the larger triangle corresponds to 49 parts, which gives us 49 * 9 cm² = 441 cm².
what are the measures of center
Answer: mean, median, mode and range
Step-by-step explanation:
The measures of centre are referred to as mean, median, mode and range.
Mean also referred to as average, it is the sum of values in a data set divided by the number of values in the given data set.
Median is the middle point number in a given data set. Median of an even data set is the average of two values in the middle of the data set.
Mode is the most occurring number in the given data set. It is the number with the highest frequency in the set.
Range is the difference between the highest number and the lowest number in a given data set.
I hope this answers your question.
The measures of center in a dataset are statistical values that represent the central point of the data. These include the mean (arithmetic average), median (middle value), and mode (most frequent value). Another common measure of center is the weighted mean, which is used when some data points carry more significance than others.
Explanation:Measures of the center are statistical measures that provide information about the central point of a dataset. The main measures include the mean, median, and mode.
The mean is the arithmetic average of the data set. This is usually the sum of all data points divided by the number of data points.
The median is the middle value of the data set when it is ordered from smallest to largest. If there is an even number of data points, the median would be the average of the two middle numbers.
The mode is the data point that occurs most frequently in the data set. A data set may have one mode, more than one mode, or no mode at all.
Another common measure of center is the weighted mean, which is useful when some data points carry more significance than others. For example, you might want to calculate the average grade in a class where some assignments are worth more than others.
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