Final answer:
The volume of Kathy's stacks is 24 cm³ greater than Marco's stacks. Each cube has a volume of 8 cm³, and after multiplying by the number of cubes each person has and subtracting, we find the difference in volume.
Explanation:
To calculate how much greater the volume of Kathy's stack of cubes is compared to Marco's, we need to determine the volume of both sets of cubes and then subtract the smaller volume from the larger one. Each cube has a volume of 2 cm × 2 cm × 2 cm, which equals 8 cm³.
Kathy has 8 cubes, so her total volume is:
8 cubes × 8 cm³ per cube = 64 cm³.
Marco has 5 cubes, so his total volume is:
5 cubes × 8 cm³ per cube = 40 cm³.
To find out how much greater Kathy's volume is:
Kathy's volume – Marco's volume = 64 cm³ – 40 cm³ = 24 cm³.
Therefore, the volume of Kathy's stacks is 24 cm³ greater than Marco's stacks.
One city has a population of about 11,566,740. Another city has a population of about 6,978,730. What would the combined population be?
Answer:
Step-by-step explanation:
11,566,740
+6,978,730
--------------------
18545470
Not much explaining, just add. A calculator can be used.
The combined population of the city will be 18,545,470.
What is addition?Addition is the mathematical operation of adding two numbers to get total.
We have,
Population of One city = 11,566,740
And,
Population of another city = 6,978,730
Now,
To get combined population,
Add population of both city,
i.e.
Combined population = Population of One city
+ Population of another city
= 11,566,740 + 6,978,730
i.e.
Combined population = 18,545,470
Hence, we can say that the combined population of the city will be 18,545,470.
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What is the volume of the portion of the aquarium with water in it?
101 cm³
14000 cm³
32,200 cm³
46,200 cm³
I think the answer is 32,2000cm^3
Answer: C
Step-by-step explanation: i got 100% on test
A month of the year is chosen at random. What is the probability that the month starts with the letter J or m
5/24
1/6
1/4
5/12
solve 9(x + 1)^2 = 144
Answer:
x = 3
x = -5
Step-by-step explanation:
(9)(x+1)(x+1) = 144
(9)(x²+2x+1) = 144
9x²+18x+9 = 144
9x²+18x = 135
x²+2x = 15
x(x+2) = 15
x = 3
x= -5
Answer: [tex]x_1=3\\x_2=-5[/tex]
Step-by-step explanation:
Divide boht sides of the eqeuation by 9:
[tex]\frac{9(x+1)^2}{9}=\frac{144}{9}\\\\(x+1)^2=16[/tex]
Remembert that:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Then, applying this, you get:
[tex]x^2+2(x)(1)+1^2=16\\x^2+2x+1=16[/tex]
Subtract 16 from both sides:
[tex]x^2+2x+1-16=16-16\\x^2+2x-15=0[/tex]
Factor the quadratic equation. Find two numbers whose sum be 2 and whose product be -15, then:
[tex](x-3)(x+5)=0\\x_1=3\\x_2=-5[/tex]
You can solve the following proportion by cross multiplying what will the equation be after you cross multiply x/7 = 4/14
x in (-oo:+oo)
2/7 = x/14 // - x/14
2/7-(x/14) = 0
2/7-1/14*x = 0 // - 2/7
-1/14*x = -2/7 // : -1/14
x = -2/7/(-1/14)
x = 4
x = 4
i hope this helps
Answer:
x*14 = 7*4
Step-by-step explanation:
what is the volume of the cylinder below?
Hello There!
To find a cylinder, we use the formula Pi*radius “squared” *height
First, let’s put in our values. Our radius is 5 but in our formula, we have to square 5 so we get a product of 25.
Then we multiply 25 by 9 because you will see in our formula we have to multiply by the height. 25*9 equals 225
Now, we are putting our value in terms of pi so our answer would be 225
Answer “C”
Answer:
175
Step-by-step explanation:
APEXX!!!!
Help with this question
Answer:
-2
Step-by-step explanation:
2x + y = 10 Subtract 2x from both sides.
2x-2x + y = 10 - 2x Combine the left.
y = 10 - 2x
The slope is the number in front of the x -- in this case - 2
The answer is - 2
Lines CB and CA are tangents to circle O at B and A. We can conclude that, for circle O, angle BOA and angle BCA are ___, and angle BOC and angle BCO are ____.
Blank 1 options: equal, complementary, supplementary
Blank 2 options: equal, complementary, supplementary
Answer:
Blank 1 ⇒ supplementary
Blank 2 ⇒ complementary
Step-by-step explanation:
* Lets revise some facts to solve the problem
- The tangent to a circle is a line touch the circle at one point
- The tangent and the radius of a circle are perpendicular to each
other at the point of contact
- If the two angles are supplementary, then the sum of their measure
is 180°
- If the two angles are complementary, then the sum of their measure
is 90°
* Now lets solve the question
∵ CB and CA are two tangents to the circle O at B and A
∵ OB and OA are radii
∴ OB ⊥ BC at point B and OA ⊥ AC at point A
∴ m∠OBC = 90° and m∠OAC = 90°
- In figure CBOA is a quadrilateral
∴ The sum of the measures of its interior angles is 360°
∵ m∠CBO + m∠BOA + m∠OAC + m∠BCA = 360°
∵ m∠CBO = 90° , m∠OAC = 90°
∴ 90° + m∠BOA + 90° + m∠BCA = 360°
∴ 180° + m∠BOA + m∠BCA = 360° ⇒ subtract 180 from both sides
∴ m∠BOA + m∠BCA = 180°
∴ ∠BOA and ∠BCA are supplementary
- In Δ CBO
∵ The sum of the measures of the interior angles of any triangle is 180°
∴ m∠BOC + m∠BCO + m∠CBO = 180°
∵ m∠CBO = 90°
∴ m∠BOC + m∠BCO + 90° = 180° ⇒ subtract 90° from both sides
∴ m∠BOC + m∠BCO = 90°
∴ ∠BOC and ∠BCO are complementary
Answer:
Blank 1: Supplementary
Blank 2:Complementary
Step-by-step explanation: I picked these and got it right
How do you figure this out?
Answer:
∠g and ∠h are complementary angles∠g and ∠h are acute anglesStep-by-step explanation:
Use the given information to determine what the angles can be.
g = 2x -90 . . . . given
g > 0 . . . . . . . . . given
2x -90 > 0
2x > 90 . . . . . add 90
x > 45 . . . . . . divide by 2
__
h = 180 -2x
h > 0
180 -2x > 0
180 > 2x
90 > x
__
The requirement that both angles be greater than zero puts limits on x:
45 < x < 90
We can put this back into the given relations for g and h:
g = 2x -90
x = (g +90)/2
45 < (g +90)/2 < 90 . . . . substitute for x
0 < g/2 < 45 . . . . . . . . . . subtract 45
0 < g < 90 . . . . . . . . . . . . g is an acute angle
Similarly, ...
h = 180 -2x
x = (180 -h)/2 = 90 -h/2
45 < (90 -h/2) < 90 . . . . substitute for x
-45 < -h/2 < 0 . . . . . . . . . subtract 90
90 > h > 0 . . . . . . . . . . . multiply by -2; h is an acute angle
__
We can add the angle measures to see if they are supplementary or complementary:
g + h = (2x -90) +(180 -2x)
g + h = 90 . . . . . simplify; the angles are complementary
__
The relevant observations are ...
∠g and ∠h are complementary angles∠g and ∠h are acute angleswhat expression is equivalent to ( X 3 ) 4 ?
Answer:
4
Step-by-step explanation:
Final answer:
The expression equivalent to (X^3)^4 is X^12. You calculate this by multiplying the exponents, resulting in X raised to the power of 3 times 4, which equals 12.
Explanation:
The expression (X^3)^4 is equivalent to X^(3*4), which is X^12. This follows the rule that when you raise a power to a power, you multiply the exponents. A number raised to the fourth power, like in this case, means that number is multiplied by itself four times. Generalizing this, for any base 'n' and exponents 'a' and 'b', the expression (n^a)^b is equal to n^(a*b).
For example, similar to (5^3)^4 being 5^(3*4) or 5^12, which is twelve fives multiplied together. Therefore, our given expression simplifies to X multiplied by itself a total of twelve times.
What is the volume of the rectangular solid?
A) 11 cubic centimeters
B) 22 cubic centimeters
C) 30 cubic centimeters
D) 40 cubic centimeters
Answer:
40 cm
Step-by-step explanation:
Multiply the length, the width, and the height. You can multiply them in any order to get the same result. The formula for finding the volume of a rectangular solid is:
Volume = Length * Height * Width,
or V = L * H * W.
by car john traveled from his house to miami florida in 6 hours going 14 mph faster elliot can drive from his house to miami florida in 5 hours what is the distance from johns house to miami florida calculating spped distance and tiem
Answer:
420 miles
Step-by-step explanation:
Distance = rate × time
Let's say that the distance is D and that John's speed is S. We know that:
D = S × 6
When Elliot drives at speed S+14:
D = (S+14) × 5
Setting D = D:
S × 6 = (S+14) × 5
6S = 5S + 70
S = 70
Therefore, the distance D is:
D = 70 × 6
D = 420
The distance from John's house to Miami is 420 miles.
The distance from John's house to Miami, Florida is 420 miles, calculated by first determining John's speed using the given information and then applying the formula distance = speed times time.
To calculate the distance from John's house to Miami, Florida, we need to use the formula distance = speed times time. John's travel time is 6 hours. We are not directly given John's speed; instead, we know that Elliot drives 14 mph faster than John and it takes him 5 hours to cover the same distance. Let's denote John's speed as 's'. Therefore, Elliot's speed is 's + 14 mph'. Setting up an equation based on Elliot's travel information, we have distance = (s + 14 mph) times 5 hours.
Since they both travel the same distance, we can also write John's travel information as distance = s times 6 hours. Equating both expressions for distance, we get: s times 6 = (s + 14) times 5. Simplifying, we have 6s = 5s + 70, which leads to s = 70 mph. This means John's speed is 70 mph.
To find the distance to Miami, we return to the distance formula and substitute John's speed: distance = 70 mph times 6 hours = 420 miles. Hence, the distance from John's house to Miami, Florida is 420 miles.
which of the following is most likely the next step in the series ?
Answer:
C.
Step-by-step explanation:
Answer:
The correct answer is C.
Step-by-step explanation:
We have given some pattern in the series.
We need to find the next step which follows and continue the series.
We know that, we have three given patterns in the question. In the first we have given a pattern which is made by the joining of three dots, and in the second pattern made by the joining of five dots and in the third pattern made by the joining of the five dots.
In the following way, we can say that the next step in the series and fourth pattern follows same pattern as given in the above. That's why next pattern made by the joining of seven dots, but in the following given options next to next pattern is given which is joining by nine dots, therefore we choose option which is the next step in the series.
Simplify the expression
3a(3-a)+3(a^2-3)+3a
Answer:
12a−9
Step-by-step explanation:
Distribute:
=(3a)(3)+(3a)(−a)+(3)(a2)+(3)(−3)+3a
=9a+−3a2+3a2+−9+3a
Combine Like Terms:
=9a+−3a2+3a2+−9+3a
=(−3a2+3a2)+(9a+3a)+(−9)
=12a+−9
Answer:
3 (4 a - 3)
Step-by-step explanation:
Simplify the following:
3 a (3 - a) + 3 (a^2 - 3) + 3 a
3 a (3 - a) = 9 a - 3 a^2:
9 a - 3 a^2 + 3 (a^2 - 3) + 3 a
3 (a^2 - 3) = 3 a^2 - 9:
3 a^2 - 9 - 3 a^2 + 9 a + 3 a
Grouping like terms, 3 a^2 - 3 a^2 + 9 a + 3 a - 9 = (9 a + 3 a) - 9 + (-3 a^2 + 3 a^2):
(9 a + 3 a) - 9 + (-3 a^2 + 3 a^2)
9 a + 3 a = 12 a:
12 a - 9 + (-3 a^2 + 3 a^2)
3 a^2 - 3 a^2 = 0:
12 a - 9
Factor 3 out of 12 a - 9:
Answer: 3 (4 a - 3)
The mass of a clownfish is 2.5 x 10 to the negative 1 power kilograms. The mass of a pilot whale is 3 x 10 to the third power kilograms. About how many times as massive is the pilot whale than the clownfish?
Answer:
Mass of pilot whale is 1.2 X 10 ^4 times massive than Mass of clownfish.
Step-by-step explanation:
Mass of clown fish = 2.5 X 10 ^-1 kg
Mass of pilot whale = 3 X 10 ^ 3 kg
Find the ratio of Mass of pilot whale to the ratio of Mass of clown fish
Mass of pilot whale : Mass of clown fish
3 X 10 ^ 3 : 2.5 X 10 ^-1
It can be written as
3 X 10 ^ 3 / 2.5 X 10 ^-1
1.2 x 10^4
So, Mass of pilot whale is 1.2 X 10 ^4 times massive than Mass of clownfish.
Suppose you roll a 6-faced die 90 times. About how many times would you expect to get a 5?
Answer: 15
Step-by-step explanation: because there are 6 sides. 1/6*90=15
Hoped this helped!
When rolling a fair six-sided die 90 times, the expected number of times you would roll a 5 is about 15, calculated by multiplying the probability of rolling a 5 (1/6) by the number of rolls (90).
If you roll a fair six-sided die 90 times, you would expect each number to appear with equal probability because the die is fair. For each individual roll, the probability of getting a 5 is 1 in 6, as there are six possible outcomes. To find the expected number of times you would get a 5 in 90 rolls, you simply multiply the probability of rolling a 5 by the total number of rolls.
Expected number of fives = Probability of rolling a 5 × Total number of rolls
= (1/6) × 90
= 15
Therefore, you would expect to roll a 5 approximately 15 times out of 90 rolls.
What is the value for f(x) = 42x - 100 when x= 2 ?
Final answer:
To find the value of f(x) when x=2 for the function f(x) = 42x - 100, substitute 2 for x, giving f(2) = 84 - 100, which simplifies to f(2) = -16.
Explanation:
The student is asking to evaluate the function f(x) = 42x - 100 when x = 2. To do this, we simply substitute 2 for x in the equation, which gives us f(2) = 42(2) - 100. Performing the multiplication first, we get 84 - 100. Thus, f(2) equals -16.
The subject is mathematics, specifically related to the evaluation of functions, which is a topic typically covered in high school algebra courses. This is a straightforward example of how to evaluate a function at a given point.
2 Points
What is the slope of the line shown below
(3,9)
(1,1)
ANSWER
The slope is 4
EXPLANATION
We want to find the slope of the line goin through (3,9) and (1,1)
We use the slope formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
We substitute the points into the slope formula to get;
[tex]m = \frac{1 - 9}{1 - 3} [/tex]
This simplifies to:
[tex]m = \frac{ - 8}{ - 2} [/tex]
[tex]m = 4[/tex]
Hence the slope of the line is 4.
The table below shows 10 data values:
224 245 203 290 217
236 262 216 224 245
What values of minimum, Q1, median, Q3, and maximum should be used to make a box plot for this data?
Minimum = 203, Q1 = 245, median = 230, Q3 = 217, maximum = 290
Minimum = 203, Q1 =217, median = 230, Q3 = 245, maximum = 290
Minimum = 216, Q1 = 236, median = 240, Q3 = 245, maximum = 262
Minimum = 216, Q1 =245, median = 240, Q3 = 236, maximum = 262
Answer:
The answer is the second option
Minimum = 203, Q1 =217, median = 230, Q3 = 245, maximum = 290
Step-by-step explanation:
First order the data from lowest to highest
203, 216, 217, 224, 224, 236, 245, 245 ,262 ,290
Minimun = 203
Maximum =290
Now divide the data in half
203, 216, 217, 224, 224, 236, 245, 245 ,262 ,290
Divide half of the first half of the data. The data of the medium is the first quartile
1) 203, 216, [217], 224, 224
Q1
Divide half of the second half of the data. The data of the medium is the third quartile
2) 236, 245, [245] ,262 ,290
Q3
The average between the two values that are in the center of the 10 ordered data is the median
203, 216, 217, 224, [224, 236], 245, 245 ,262 ,290
[tex]Median =\frac{224+236}{2}=230[/tex]
Median=230
The answer is the second option
Minimum = 203, Q1 =217, median = 230, Q3 = 245, maximum = 290
Answer:
the answer is B :D
Step-by-step explanation:
Which algebraic expression represents the phrase “six less than a number”?
Answer:
x-6
Step-by-step explanation:
Let the number be x
Then the algebraic expression “six less than a number” can be represented as:
x - 6
So, "six less than a number” can be represented as: x - 6
Use ΔDEF to complete the statements. Angle E is the included angle between sides . The included angle between sides FE and DF is angle .
Answer:
second choice
third choice
Step-by-step explanation:
righty whighty edg 2020
From the given diagram of triangle DEF:
Included angle E is between sides DE and FE.Included angle F is between sides FE and DF.Triangle DEF is shown in the image attached below/.
Triangle DEF has the following sides:
Side FESide DFSide DEThe triangle also shows that:
Angle E, as an included angle is between side sides DE and FE. Both sides meet at point E.Also,
The angle that lie between side FE and side DF is angle F. Both sides meet at point F.In summary, from the given diagram of triangle DEF:
Included angle E is between sides DE and FE.Included angle F is between sides FE and DF.Learn more here:
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Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. There are 2 sizes, 4 colors, 7 phrases, and 4 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.)
Answer:
Step-by-step explanation:
maybe 2 by 4 and 7 by 4 then add sorry if i'm wrong
9 please help with 9
10 what is P
Answer:
9.
The probabilities are the same
10.
1/3
Step-by-step explanation:
9.
Assuming the coin is fair;
The probability of getting heads in a single toss is, P(H) = 1/2
The probability of getting tails in a single toss is, P(T) = 1/2
Now, P(H,H,H) is the probability of obtaining 3 heads in the e tosses. Since each toss is independent of the others,;
P(H,H,H) = P(H)*P(H)*P(H)
= 1/2 * 1/2 * 1/2 = 1/8
On the other hand, P(H,T,H) is the probability of obtaining a head followed by a tail followed by a final head. Using the independence property;
P(H,T,H) = P(H)*P(T)*P(H)
= 1/2 * 1/2 * 1/2 = 1/8
Therefore, P(H,H,H) = P(H,T,H)
10.
We are informed that a coin is tossed and a number cube is rolled. We are to determine the following probability;
P(heads, a number less than 5)
Assuming the coin is fair;
The probability of getting heads in a single toss is, P(H) = 1/2
Assuming the number cube is fair as well, the probability of rolling a number less than 5 is;
4/6 = 2/3
This is because there are 4 numbers less than 5, (1, 2, 3, 4) while the cube has 6 sides.
P(heads, a number less than 5), the events presented here are independent since the outcome from tossing the coin does not in any way determine the outcome from rolling the number cube. Therefore,;
P(heads, a number less than 5) = P(heads)*P(a number less than 5)
= 1/2 * 2/3 = 1/3
HURRY ANSWER ASAP!
A rectangular prism with a volume of 3 cubic units is filled with cubes with side lengths of 1/4 unit. How many 1/4
unit cubes does it take to fill the prism?
So, 1 cube equals 1/4 unit.
4 cubes will equal 1 whole unit.
If the volume of the rectangular prism is 3 cubic units, all you have to do is multiply.
4*3=12
So it would take a total of 12 cubes to fill the prism.
Hope this helps.
A total of 119 golden tickets were sold for an NBA match. A hundred general tickets and 6 platinum tickets were also sold. The price of a general ticket was three-fourth the cost of the golden ticket. The price of a platinum ticket was twice that of the golden ticket. How much was priced at, if the total collection from-ticket sales was $6,592? a golden ticket
Pls show steps...
Answer:
Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.
119g + 100t + 6p = 6592
t = 3/4g
p = 2g
119g + 100(3/4)g + 6(2g) = 6592
g = 32
t = 3/4(32) = 24
p = 32(2) = 64
A golden ticket costs $32. A regular ticket costs $24. A platinum ticket costs $64. Hope this helps!
Answer:
Let g be the golden ticket; t be the regular ticket; p be the platinum ticket.
119g + 100t + 6p = 6592
t = 3/4g
p = 2g
119g + 100(3/4)g + 6(2g) = 6592
g = 32
t = 3/4(32) = 24
p = 32(2) = 64
Step-by-step explanation:
Which equation could be used to calculate the sum of the geometric series?
1/3 + 2/9 + 4/27 + 8/81 + 16/243
Answer:
The equation is:
[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]
[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]
The sum is:
[tex]S=\frac{211}{243}[/tex]
--------------------------------------------------------------------
If the sequence is infinite, the formula is:
[tex]S = \frac{a_1}{1-r}[/tex]
-------------------------------------------------------------------
Step-by-step explanation:
We must calculate the radius of the geometric series
[tex]r =\frac{a_{n+1}}{a_n}\\\\r=\frac{\frac{2}{9}}{\frac{1}{3}}\\\\r=\frac{2}{3}[/tex]
The first term of the series is: [tex]a_1=\frac{1}{3}[/tex]
The last term of the series is: [tex]a_n=\frac{16}{243}[/tex]
If the sequence is finite then the formula is:
[tex]S=\frac{a_n*r-a_1}{r-1}[/tex]
[tex]S=\frac{\frac{16}{243}*\frac{2}{3}-\frac{1}{3}}{\frac{2}{3}-1}[/tex]
[tex]S=\frac{211}{243}[/tex]
If the sequence is infinite then by definition as the radius are [tex]0 <| r | <1[/tex] then the formula for the sum of the geometric sequence is:
[tex]S = \frac{a_1}{1-r}\\\\S = \frac{\frac{1}{3}}{1-\frac{2}{3}}\\\\S =1[/tex]
Answer:
A
Step-by-step explanation:
got it right on edge
A square piece of plastic has sides that are 4 centimeters long. What is the plastics perimeter?
Perimeter of a square = side*side
4*4=16cm^2
The perimeter of a square piece of plastic with each side measuring 4 centimeters is 16 centimeters.
Explanation:The question is asking for the perimeter of a square piece of plastic with sides that are 4 centimeters long. To calculate the perimeter of a square, you multiply the length of one side by four. Since a square has four equal sides, the calculation in this case would be 4 cm (side length) times 4 (number of sides), which equals 16 cm. So, the perimeter of the square piece of plastic is 16 centimeters.
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A basket contains 6 oranges and 4 tangerines. a sample of 3 is drawn. find the probability that they are all oranges
The probability of drawing 3 oranges from a basket of 6 oranges and 4 tangerines is 1/6 or approximately 0.167.
Explanation:This problem is a probability question in the field of mathematics. It is asking us to find the probability that all three fruits drawn from the basket are oranges. This can be solved using the concept of combinations from probability theory.
The total number of fruits in the basket is 10 (6 oranges and 4 tangerines). We want to draw a sample of 3 fruits. The number of ways to draw 3 fruits from a total of 10 (regardless of type) is given by the combination formula C(n, r), where n is the total number of items and r is the number of items to choose. So we have C(10, 3) = 120 possible ways.
Next, consider the scenario we're interested in--drawing 3 oranges. The total number of ways to draw 3 oranges from a total of 6 oranges is C(6, 3) = 20 possible ways.
So, the probability of drawing 3 oranges is the number of ways to draw 3 oranges divided by the total number of ways to draw 3 fruits. So, the probability is 20/120 = 1/6 or approximately 0.167.
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Final answer:
The probability of drawing 3 oranges from a basket containing 6 oranges and 4 tangerines is found using combinations. The calculation shows that the probability of selecting all oranges in a draw of 3 fruits is 1/6.
Explanation:
The question asks to find the probability that when three fruits are drawn from a basket containing 6 oranges and 4 tangerines, all three are oranges. This is a problem of probability without replacement, which can be solved using combinations.
To find the probability of drawing 3 oranges out of 3 fruits, we calculate the combinations of choosing 3 oranges from 6 and then divide it by the combinations of choosing 3 fruits from the total 10 fruits in the basket.
The number of ways to select 3 oranges out of 6 is given by the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items, and k is the number of items to choose. So, we have:
Ways to pick 3 oranges: C(6, 3)
Total ways to pick 3 fruits: C(10, 3)
Then the probability is calculated by:
P(all oranges) = C(6, 3) / C(10, 3)
Calculating the combinations, we have:
P(all oranges) = (6! / (3! × (6-3)!)) / (10! / (3! × (10-3)!)) = (6 × 5 × 4) / (3 × 2 × 1) divided by (10 × 9 × 8) / (3 × 2 × 1) = 20 / 120 = 1/6.Thus, the probability that all three fruits are oranges is 1/6.
simplify 3 square root of 7 over 5 square root of 7
The simplified form of ratio of [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by dividing it.
Given that simplify 3 square root of 7 over 5 square root of 7 that is [tex]3\sqrt7 / 5\sqrt7.[/tex]
To find the ratio of [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by dividing it by following steps:
Step 1: Factorize the numerator and denominator.
Numerator [tex]= 3\sqrt7 = 3(\sqrt7)[/tex]
Denominator [tex]= 5\sqrt7 = 5(\sqrt7)[/tex]
Step 2: Divide both numerator and numerator by common factor gives:
Ratio = numerator/denominator
[tex]= \sqrt7(3)/\sqrt7(5)[/tex]
Divide both numerator and numerator by [tex]\sqrt7[/tex] gives:
= 3/5.
Therefore, the simplified form of ratio of [tex]3\sqrt7[/tex] and [tex]5\sqrt7[/tex] is equal to 3/5 by factorizing the numerator and denominator and by dividing it.
Learn more about ratio here:
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what is the axis of symmetry of h(x)= -x^2-2x+8
Answer:
The answer is 2.
Step-by-step explanation:
The equation for finding the axis of symmetry is:
x=-\frac{b}{2a}
Plug the numbers from the equation in:
a=1
b=-2
x=-\frac{-2}{2(1)}
Solve:
x=\frac{2}{1}
x=2
hope this helps :)