The combination is solved and the number of ways of choosing the contestants is 10
What are Combinations?The number of ways of selecting r objects from n unlike objects is given by combinations
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Out of the 7 people in the front row, we need to choose 3 people to be contestants, and we want to count the number of ways that both you and your friend are chosen.
Since we are choosing 3 people, there are 3 positions to be filled. We can think of this as a combination problem, where we need to choose 2 people out of the 5 remaining people in the front row, to fill the two remaining positions after you and your friend are chosen.
The number of ways to choose 2 people out of 5 is given by the combination formula:
C(5, 2) = 5! / (2! (5 - 2)!) = 10
Hence , there are 10 ways to choose you and your friend, and then choose two additional people to fill the remaining positions
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Express 18 hours as a percent of 3 days
Answer:
25%
Step-by-step explanation:
Convert days into hours
3 days = 3×24 = 72 hours
18/72 × 100 = 25%
% is the correct percentage conversion for 2/5
Answer:
%40
Step-by-step explanation:
Step 1: Divide 2/5
2/5 = 0.4
Step 2: Convert to Decimal by multiplying by 100
0.4 * 100 = %40
Answer: %40
Answer: 0.025%
Step-by-step explanation:
Why might you need to use the addition or subtraction property of equality more than once after you have used the distributive property and combined like terms? Explain.
Answer:Use the properties of equality and the distributive property to solve equations ... Although multi-step equations take more time and more operations, they can still be ... First “undo” the addition and subtraction, and then “undo” the multiplication and ... We need to “move” one of the variable terms in order to solve the equation.
Step-by-step explanation:
Answer:
If there is a variable term and a constant on each side of the equation, then you will need to use the addition or subtraction property of equality once to isolate the variable term and once to isolate the constant.
Step-by-step explanation:
In the figure above, square ABCD and triangle EFG have the same areas. If AB =6 and EG =8, what is the height o triangle EFG?
Answer:
The height of triangle EFG is 9 units
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the area of a square ABCD
The area of a square is equal to
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]b=AB=6\ units[/tex]
substitute
[tex]A=6^2=36\ units^2[/tex]
step 2
Find the height of triangle EFG
The area of triangle EFG is equal to
[tex]A=\frac{1}{2}(b)(h)[/tex]
where
b is the base of triangle
h is the height of triangle
we have
[tex]b=EG=8\ units[/tex]
[tex]A=36\ units^2[/tex] ---> area of triangle EFG is the same that the area of square ABCD
substitute the given values in the formula
[tex]36=\frac{1}{2}(8)(h)[/tex]
solve for h
[tex]36=4h\\h=9\ units[/tex]
therefore
The height of triangle EFG is 9 units
Use the coordinate grid to determine the coordinates of point P:
A coordinate grid shown from negative 2 to positive 2 on x-axis and negative 2 to positive 2 on y-axis. There are 4 grid lines between a whole unit of the grid. A point labeled P is shown at the intersection of 8 grid lines to the left of the y-axis and 4 grid lines above the x-axis.
What are the coordinates of point P?
(0.8, −0.4)
(−0.8, 0.4)
(1.6, −0.8)
(−1.6, 0.8)
Option D: [tex](-1.6,0.8)[/tex] are the coordinates of the point P
Explanation:
It is given that "A coordinate grid shown from negative 2 to positive 2 on x-axis and negative 2 to positive 2 on y-axis. There are 4 grid lines between a whole unit of the grid".
Thus, the value of each grid is [tex]0.2[/tex]
It is also given that, "A point labeled P is shown at the intersection of 8 grid lines to the left of the y-axis and 4 grid lines above the x-axis".
Since the point P lies on the left of the y-axis and above the x-axis, the x-value will be negative and y-value will be positive.
Thus, the value of x-axis is given by
[tex]8\times0.2=-1.6[/tex]
And the value of y-axis is given by
[tex]4\times0.2=0.8[/tex]
Thus, the coordinates of the point P is [tex](-1.6,0.8)[/tex]
Hence, Option D is the correct answer.
If 4(a+3)=2a+12, then a= [blank] −−−−−−
Answer:
a=0
Step-by-step explanation:
Solve for a
4a + 12 = 2a +12
4a-2a=12-12
2a=0
a=0/2
a=0
You mix 2 1/2 quarts of juice with 6 2/3 quarts of ginger ale to make fruit punch. What is the ratio of the amount of juice to the amount of ginger ale in simplest form
The ratio of the amount of juice to the amount of ginger ale is 3 : 8
Step-by-step explanation:
Fruit punch = amount of juice + amount of gingle ale
(convert the mixed fraction into proper fraction)
amount of juice = 2 1/2 = 5/2 amount of ginger ale = 6 2/3 = 20/3Ratio of the amount of juice to the amount of ginger ale = (5/2) / (20/3)
⇒ (5/2)[tex]\times[/tex](3/20)
⇒ (1/2)[tex]\times[/tex](3/4)
⇒(3/8)
∴ The ratio of juice to ginger ale is 3 : 8
June’s multivitamin contains 1500mg of calcium. Convert this to grams
Answer:
What is the best definition of a biohazard?
Step-by-step explanation:
Answer:
1.5g
you need to find out how many miligrams (mg) are in a gram (g).
1mg = .001g therefore move the decimal point over three times to the left
Step-by-step explanation:
given a sphere with a radius of 2 cm find the volume of the nearest whole number
Answer:
34cm3
Step-by-step explanation:
Volume of sphere = 4/3 pi x cube of radius
Radius =2cm , pi = 3.142
Volume = 4/3 x 3.142 x 2 x 2 x 2
Volume = 1.3333 x 3.142 x 8
Volume = 33.5cm3
Volume = 34cm3 to the nearest whole number
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the rise and the run between each set of points
Answer:
The rise would be 4 the run would be 5.
Answer: Rise = 4, Run = 5
Step-by-step explanation:
Rise is how many it goes up
Run is how many is goes right
3) 4x -8y=-24
4x - 10y=-12
To the nearest tenth, what is the population density of bacteria at the end of the third hour in petri dish A?
Answer:
The question is not complete or missing details. Here is a similar question ; Suppose the rate of growth of bacteria in a Petri dish is given by q(t)=2t, where t is given in hours and q(t) is given in thousands of bacteria per hour. If a culture starts with 3,000 bacteria, find a function Q(t) that gives the number of bacteria in the Petri dish at any time t. How many bacteria are in the dish after 4 hours? Round your answer to the nearest thousand and do not include units.
Step-by-step explanation:
The detailed steps are as shown in the attachment.
q(t)=2t
dq/dt = 2t
Integrating both sides as shown in the attachment.
Any other question can be approached the same way.
Simplify (x^2y)(xy^4)
Answer:
y^4x^1+2y
Step-by-step explanation:
Answer:
8xsquareysquare (square=2 on right hand corner)
Step-by-step explanation:
2yx4xy
The store offers a 20% discount. The regular price of a T-shirt is $18. What is the discount price?
Answer:
$16.40
Step-by-step explanation:
First we find the how much the discount takes off
$20 × .18 = $3.60
So, the discount takes off $3.60, we then subtract that from $20
$20 - $3.60 = $16.40
Which then gives the price of the shirt as $16.40
how to multiply and divide algebraic fractions
Answer:
Step-by-step explanation:
Multiplying two algebraic fractions produces a new algebraic fraction. Multiply the two numerators to get the new numerator and multiply the two denominators to get the new denominator. Then simplify by reducing the new fraction to lowest terms.
for example:
[tex]\frac{x}{y} \\[/tex]×[tex]\frac{a}{b}[/tex] = [tex]\frac{xa}{yb}[/tex]
Division of algebraic fractions
The procedure for dividing algebraic fractions is the same as the procedure for dividing common fractions. Replace the division by a fraction by the multiplication by the reciprocal of that fraction, like this. Then carry out the multiplication of the two fractions as described above.
for example:
[tex]\frac{\frac{a}{b} }{\frac{x}{y} }[/tex]
can be written as
[tex]\frac{a}{b}[/tex]×[tex]\frac{x}{y}[/tex]= [tex]\frac{ax}{by}[/tex]
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Can you guys please answer this question 20 ASAP
Answer:
a the answer is a
Step-by-step explanation:
how many packs of pencils can you get if there is 1,440 pencils and 6 in each pack
Divide 1440 by 6 to get 240 packs.
A baker started out with 12 cups of flour. She had 9 1/4 cups of flour left after the first batch of batter she made. She had 6 1/2 cups of flour left after the second batch of batter she made. If she makes two more batches of batter, how many cups of flour will be left?
Answer:
First batch: 12 - 9 1/4 = 2 3/4 cups
Second batch: 9 1/4 - 6 1/2 = 2 3/4 cups
(2 batches)(2 3/4 cups per batch) =
2(11/4) = 11/2 = 5 1/2 cups
6 1/2 - 5 1/2 = 1 cup of flour left
Find the volume of this prism:
5 cm
4 cm
6 cm
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw EXAMPLE
put that into a formula.... and boom solved just comment on this for the answer
State your first and last name. Use the letters in your first name and last name to write an equation of a line in slope-intercept form, y=mx + b as follows:
1. Let x = the number of letters in your first name. Write down the coordinates of the x-intercept using this value for x (If your first name is hyphenated, you may use only the first or last part).
2. Let y = the number of letters in your last name. Write down the coordinates of the y-intercept using this value of y (If your last name is hyphenated, you may use only the first or last part).
3. Find the slope of your line using the x and y intercepts from #1 & #2.
Part Two (3 points): Write the equation of the line using y = mx + b. Replace the m with the slope from #3 and the b with the y value from #2. Use the equation generated to complete a table of at least four ordered pairs. You already have two ordered pairs from #1 and #2.
Part Three (5 points): Use graph paper to sketch a graph of the line in part two. Please be sure to write the coordinates of all points on the graph, label the x and y axes, place arrows on your graph.
My name has 6 letters and my last name 9
Answer:
i) b = 9
ii) m = -3/2
iii) another two ordered pairs on the graph can be (2, 6) and (8, -3).
Step-by-step explanation:
i.) equation of the line is y = mx + b
ii) x = number of letters in my first name = 6 is the x-intercept
iii) y = number of letters in my last name = 9 is the y-intercept
iv) if x = 0 then y-intercept is b. then 9 = (0 [tex]\times[/tex] m) + b. Therefore b = 9
v) if y = 0 then x -intercept is given by 0 = (6 [tex]\times[/tex] m) + 9.
Therefore 0 = 6m + 9 [tex]\Rightarrow[/tex] 6m = -9, m = -3/2
vi) another two ordered pairs on the graph can be (2, 6) and (8, -3).
Write a word phrase for the expression 10+(6-4)
Answer:
Ten added to the difference of six and four. Or, the difference of six and four added to ten.
Step-by-step explanation:
The word phrase for the mathematical expression 10+(6-4) is 'Ten plus the difference of six and four'. It is the representation of the arithmetic operation in a sentence format.
Explanation:The word phrase for the mathematical expression 10+(6-4) is 'Ten plus the difference of six and four'. In this phrase, 'Ten plus' corresponds to the 10+ part of the expression. 'The difference of six and four' means you subtract 4 from 6, which corresponds to the (6-4) part of the expression.
The expression 10+(6-4) can be simplified using the order of operations. First, we need to subtract 4 from 6, which equals 2. Then, we add the result 2 to 10, which equals 12. Therefore, the word phrase for the expression 10+(6-4) is "Ten plus the difference of six and four."
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Find algebraically in RxR using substituting method the S.S. of the two equations:
X + y = 4
,
2 x - y = 5
Answer:
x=3 y=1
Step-by-step explanation:
x+y=4
y=-x+4
plug in the y
2x-(-x+4)=5
2x+x-4=5
3x=9
x=3
plug in x=3 into first equation to find y
y=-(3)+4
y=-3+4
y=1
Answer:
Step-by-step explanation:
x + y = 4 equation 1
2x - y = 5 equation 2
using substitution method,
x= 4 - y equation 3
substitute equation 3 into equation 2
2(4-y) -y = 5
8 - 2y - y = 5
8 - 3y = 5
-3y = 5 - 8
-3y = -3
divide through by -3
-3y/-3 = -3/-3
y = 1
substitue the value of y into equation 1
x + y = 4
x + 1 = 4
x = 4 - 1
x = 3
Hence, x = 3 and y = 1
This soda can is going to be made from aluminum. How many square centimeters of aluminum are needed if the radius r = 3.5 cm and the height h = 6 cm? (Use π = 3.14 and round answer to the hundredths' place.)
208.81 square centimeters of aluminium are needed
Solution:
Given that,
Radius = 3.5 cm
Height = 6 cm
We have to find the square centimeters of aluminum needed
So we have to find the surface area of cylinder
The surface area of cylinder is given by formula:
[tex]A = 2 \pi r(h+r)[/tex]
Where "r" is the radius and "h" is the height of cylinder
Substituting the values we get,
[tex]A = 2 \times 3.14 \times 3.5 \times (6+3.5)\\\\A = 21.98 \times 9.5\\\\A = 208.81[/tex]
Thus 208.81 square centimeters of aluminium are needed
The soda can requires approximately 208.51 square centimeters of aluminum.
To determine the amount of aluminum needed to make the soda can, we need to calculate the surface area of the cylinder. The formula for the surface area of a cylinder is:
Surface Area = 2πr(h + r)
Given the radius (r) = 3.5 cm and the height (h) = 6 cm, we substitute these values into the formula:
Surface Area = 2 * 3.14 * 3.5 * (6 + 3.5)
First, calculate the term inside the parentheses:
6 + 3.5 = 9.5
Next, multiply by the radius:
3.5 * 9.5 = 33.25
Finally, multiply by 2π:
2 * 3.14 * 33.25 ≈ 208.51
So, the total surface area of the soda can is approximately 208.51 square centimeters of aluminum.
A dog is standing 5 feet from the base of a tree, looking up at a cat that has climbed 16 feet up the tree. What is the angle of elevation from the point the dog is standing on the ground to the cat?
Answer:
x=72.6
Step-by-step explanation:
use inverse trig because your finding a missing angle. use tan because you haved opp/adj
tan-1=(16/5)
x=tan-1(16/5)
*use a calculator
x=72.6
The the angle of elevation from the point the dog is standing on the ground to the cat is 72.6 degrees
We have given that a dog is standing 5 feet from the base of a tree, looking up at a cat that has climbed 16 feet up the tree
We have to find the angle of elevation
We can see in a figure.
What is the angle of elevation?The angle between the horizontal line of sight and the object.
use inverse trig because we are finding a missing angle.
use tan because we have given height of tree (one side) and a distance between dog and tree(second side)
[tex]tab(\theta)}= opp/adj[/tex]
Apply [tex]tan^-1[/tex] on both side we get,
[tex]\theta=tan-1(16/5)[/tex]
[tex]\theta=tan-1(16/5)[/tex]
[tex]\theta=72.6[/tex]
Therefore,the the angle of elevation from the point the dog is standing on the ground to the cat is 72.6 degrees
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Determine if the three given side lengths would form a right triangle
9 ft, 12 ft, 16 ft
Answer:
Yes.
Step-by-step explanation:
You can use the triangle inequality theorem: the sum of any two sides must be greater than the third side. You can also just check the two smallest sides.
9+12=21
21>16 --> yes it is a triangle.
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If the sum of the lengths of any two sides of a triangle is less than or equal to the length of the third side, then the triangle is not possible.
If a triangle has sides with lengths of 9, 12, and 16, notice that 9 + 12 or 21 is greater than 16. So the sum of the lengths of two sides of the triangle is greater than the length of the third side.
This means that the triangle with sides of lengths
9, 12, and 16 is possible.
If 6 workers can paint a house in 2 days; how
many days will it take for 3 workers to paint the same house?
Answer:
0, because the house is already painted. If this isn't a riddle then, it should take 4 days because that is half the people, two times the workload per person.
Answer:
4 days
Step-by-step explanation:
6 workers takes 2 days.
That means that each worker works 6*2 = 12 worker days.
To get the same amount it takes 3 workers 4 days to get 12 worker days.
One fifth of the sum of a number and -3 is twice the number
Answer:
the number is -1/3
Step-by-step explanation:
The given statement can be written in math terms as ...
(1/5)(n -3) = 2n . . . the problem statement, using n to represent the number
n -3 = 10n . . . . . . . . . multiply by 5
-3 = 9n . . . . . . . . . . . subtract n
-1/3 = n . . . . . . . . . . . divide by 9 and reduce the fraction
The number is -1/3.
_____
Check
-1/3 -3 = -3 1/3 = -10/3
1/5 of -10/3 = -2/3
-2/3 is twice the number -1/3 . . . . . answer checks OK
How many centimeters equal 39.4 meters?
Answer:
Step-by-step explanation:
100CM equal 1m
Therefore
39.4*100=3940cm
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Answer:
attached below
Step-by-step explanation:
Check 56 divided 16 using multiplication
Answer:
3.5
Step-by-step explanation:
3.5x16=56