To determine the number of different ways a math teacher can select 6 students from a class of 30, we use the combination formula C(30, 6) = 30! / (6! * (30 - 6)!), which gives us 593,775 different possibilities. Therefore, the correct answer is C, 593,775.
The math teacher needs to select 6 students from a class of 30 students to go to the library, which is a combinatorial problem in mathematics. The number of ways to choose k students from a group of n students without regard to the order is given by the combination formula:
C(n, k) = n! / (k! * (n - k)!), where n! is the factorial of n and equals n multiplied by all positive integers less than n, and k is the number of students chosen.
Applying the formula for our situation:
C(30, 6) = 30! / (6! * (30 - 6)!)
= (30 * 29 * 28 * 27 * 26 * 25) / (6 * 5 * 4 * 3 * 2 * 1)
= 593,775
So there are 593,775 different ways the teacher can select 6 students from a class of 30. Hence, the correct answer is C, 593,775.
Tony has $10 to buy apples and bananas for a fruit salad. Apples cost $2 per pound and bananas cost $1 per pound. Write and graph an inequality to describe the situation. Then give two possible combinations of pounds of apples and bananas that Tony can buy. HELP
The equation of inequality would be = 2 x + y ≤ 10 for the process of purchase.
Explanation:
Total amount of money tony have , T = $10
Thus the cost of apple, (We can represent as Ca) = $2
Also the cost of banana,(We can represent as Cb) = $1
Let x be the number of apples bought
Let y be the number of bananas bought
Total expenditure to buy fruits, E = $2 x + $1 y
So,The equation of inequality would be = 2 x + y ≤ 10 for the process of purchase.
Solve proportion S/84=3/21
Answer:
S=21
Step-by-step explanation:
First cross multiply, next divide. I hope this helped!
Answer: S = 12
Step-by-step explanation:
S/84 =3/21
Cross multiply to find the value of S
21 x S= 84 x 3
21S= 252
S= 252/21
S= 12
A wise man once said, “400 reduced by 4 times my age is 168.” What is his age?
Answer: the man is 58!
Step-by-step explanation: please mark brainliest
we could use this equation
168=400-4a an a= uknown age
-400 -400
-232=-4a
divide by -4 on both sides to get the variable by itself
58=a
a=58
and to double check we can do this
168=400-4(58) by susbtuting the variable
168=400-232
168=168 correct
2x+15=145
Solve for x
Answer:
Step-by-step explanation:2x=145-15
2x=130
X=130/2
X=65
If i have 6 bottles of water and each weigh 3/5 pounds how much do i have
You have 3 and 3/5 pounds of water.
To find this, simply multiply 3/5 by 6/1 (multiplying straight across). 6 times 3 is 18 and 5 times 1 is 5. Thus meaning you have 18/5 pounds, which simplified is 3 and 3/5 pounds.
I hope this helps!
Answer:
if you multiply 3/5 ×6 that would be 3.6 or in mix number that would be 3⅗
How do you multiply 342 and 13.5
Answer:
Step-by-step explanation: first multiply 342 and 135
then put the decimal just before the ones digit.
answer is
4617.0
please mark as brainliest
How should I prove this???
What is 926 divided by 38? and also what is its remainder
Hello!
The answer to your problem is 24 R 14 (R for remainder)
Here is my work show.
Answer: 24.37
Step-by-step explanation:
926/36 = 24.3684
Rounded = 24.37
The measure of Mis 57°. What is the measure of its complementary angle?
A 33
B90°
C123
D180°
Answer:
A 33°
Step-by-step explanation:
Complementary angle of 57° = 90° - 57° = 33°
How many interior angles does a star have
five acute angles: the rest of this text does not matter.
Brandy drove three times as far as Trisha. Together, they drove 48 miles. Which equation below can be used to find the number of miles Trisha drove?
48=4x can be used to determine the miles covered by Trisha that is 12 miles.
Total distance covered comprises the sum of distances covered by individual entities. Sum means adding like terms in mathematics.
Given, the total number of miles covered by both of them, t= 48 miles
If miles covered by Trisha = x
Then, miles covered by Brandy = 3x (as Brandy drove three times as far as Trisha ).
The total distance covered comprises miles covered by Trisha as well as Brandy.
t=x+3x
On adding the like terms.
t=4x
Substituting t=48,
48=4x
Dividing 4 both sides of the equation,
48/4=4x/4
12=x
x=12 miles
So, the Number of miles Trisha drove is 12.
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22.4 divide by 134.4
the point A ( 5,3) translate 3 to the right and 1 down. what is the new point? (x,y)----> (x+3,4-1)
Answer:
(8, 2) OR (x + 3, y - 1)
Step-by-step explanation:
Step 1: Add 3 to 5 and subtract 1 from 3
(5 + 3, 3 - 1)
(8, 2) OR (x + 3, y - 1)
Answer: (8, 2) OR (x + 3, y - 1)
An electronics store reduced the price of a TV from $1000 to $880. What was the percent of decrease?
Answer:
12% decrease
Step-by-step explanation:
think of 1000 as 100% and thin 880 as 88% subtract those 12%
The price decrease from $1000 to $880 represents a 12% decrease. This is figured out by taking the difference in price, dividing it by the original price, and then multiplying by 100%.
Explanation:The percentage decrease is calculated by taking the difference in price divided by the original price, and then multiplying by 100 to get a percentage. In this case, the difference in price is the original price minus the sale price. This would be $1000 - $880 = $120. So, the formula would be ($120/$1000)*100. The calculated percentage decrease is 12%, meaning the price of the TV has been reduced by 12%.
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How do u graph y=15x+35?
Hey there!
This is slope intercept form, where y=mx+b, where b is the y-intercept (where the line hits the y-axis) and the slope (rate of change).
If you wanted to graph this line, we can see that the y intercept in 35. Therefore, our line is going have one point on (0,35). Our slope is 15, which is positive, showing that our line will go up. Because the slope is fifteen, for every single increase of 1 there is in x, there will be an increase of 15 in y. This will give us points like (1,15) (2,30) (3,45). Therefore, this will be a very steep line.
You can use this info to graph your line.
Answer:
PLS PASS BRAINLIEST
Step-by-step explanation:
put the first point on 35 on y axis
now count 15 from 35 which is 50 and move one to the right
which is (50,1)
and keep on reapeting that
What is the value of x ?
A : 15
B : 30
C: 45
D : 60
Answer:
A
Step-by-step explanation:
So that is a 90 degree angle and there is an angle of 30. 30-90 is 60. 60 divided by 4 is 15. So thus the answer is A,15.
Answer:
15
Step-by-step explanation:
90 is right angle
90 - 30 = 60
60 / 4 = 15 <---- theres the answer
hope i helped
A movie theater sells small and large boxes of popcorn.
• A small box of popcorn costs $1.50.
• A large box of popcorn costs $4.00.
• A total of 25 boxes of popcorn were sold totaling $75.00.
How many large boxes of popcorn were sold?
A 6
B. 10
C.
12
D.
15
There 15 large boxes of popcorn were sold. The option D is correct.
We need to determine the number of large boxes of popcorn sold. Let's denote the number of small boxes as s and the number of large boxes as l. We are given the following information:
The cost of a small box of popcorn is $1.50.
The cost of a large box of popcorn is $4.00.
A total of 25 boxes of popcorn were sold.
The total revenue from popcorn sales was $75.00.
We can set up two equations based on this information:
s + l = 25 (the total number of boxes sold)
1.50s + 4.00l = 75.00 (total revenue from sales)
Let's solve for l using these equations. Multiplying the first equation by 1.50 gives us:
1.50s + 1.50l = 37.50
Subtracting this from the second equation:
(1.50s + 4.00l) - (1.50s + 1.50l) = 75.00 - 37.50
2.50l = 37.50
l = 37.50 / 2.50
l = 15
The length of a rectangle is 4 more than 3 times the width. If the perimeter of the rectangle is 18.4 cm, what is the area of the rectangle?
Area of the rectangle is 10.27 cm²
Step-by-step explanation:
Step 1: Let the width of the rectangle be x, then length = 4 + 3x. Find the dimensions if perimeter = 18.4 cmPerimeter = 2(length + width)
⇒ 18.4 = 2 (x + 4 + 3x)
⇒ 18.4 = 2(4x + 4)
⇒ 18.4 = 8x + 8
⇒ 8x = 10.4
⇒ x = 10.4/8 = 1.3
∴ 4 + 3x = 4 + 3×1.3 = 7.9
Step 2: Find area of the rectangle.Length = 7.9 cm and width = 1.3 cm
⇒ Area = length × width
= 7.9 × 1.3 = 10.27 cm²
Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A E, B F, and C D. The length of line segment A G is 2 x + 10, the length of line segment F G is 2 x minus 1, and the length of line segment G B is 3 x + 6.
G is the centroid of triangle ABC.
What is the length of AE?
units
Answer:
The length of AE is 39 units.
Step-by-step explanation:
Given:
G is the centroid of a triangle ABC.
Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments AE, BF, and CD.
The length of line segment A G is 2 x + 10, the length of line segment F G is 2 x minus 1, and the length of line segment G B is 3 x + 6
To Find: Length of the AE.
The centroid of the triangle is always cut the line in the ratio of 2:1. For clarification, the image is provided.
Hence,
G divides the line BF into a 2:1 ratio.
Thus,
[tex]\begin{aligned}&2FG=BG\\&2(2x-1)=3x+6\\&4x-2=3x+6\\&x=8 \end{aligned}[/tex]
Also,
G divides the line AE into a 2:1 ratio.
Therefore,
[tex]AG=2GE\\GE=AG/2[/tex]
Line segment AE is the sum of AG and GE.
Thus,
[tex]AE=AG+GE\\AE=AG+AG/2\\AE=3AG/2\\AE=3(2x+10)/2\\AE=39[/tex]
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The length of AE is 9 units.
Given that G is the centroid, it divides each median into two segments with the ratio of 2:1, where the longer segment is toward the vertex and the shorter segment is toward the midpoint of the opposite side.
Let's denote the length of AG as a, the length of BG as b, and the length of FG as c. According to the given information:
1. AG = 2x + 10
2. FG = 2x - 1
3. BG = 3x + 6
We know that AG = 2GE and BG = 2GE. Thus:
[tex]\[ AG = 2GE \implies GE = \frac{AG}{2} = \frac{2x + 10}{2} = x + 5 \]\[ BG = 2GE \implies GE = \frac{BG}{2} = \frac{3x + 6}{2} = \frac{3}{2}x + 3 \][/tex]
Since GE is common, we can equate the expressions:
[tex]\[ x + 5 = \frac{3}{2}x + 3 \][/tex]
Solving for x:
[tex]\[ \frac{1}{2}x = 2 \][/tex]
x = 4
Now that we've found the value of x, we can substitute it back into the expressions for AG and FG to find their lengths:
AG = 2x + 10 = 2(4) + 10 = 18
FG = 2x - 1 = 2(4) - 1 = 7
Now, we know that AE = AG - GE:
AE = AG - GE = 18 - (x + 5) = 18 - (4 + 5) = 18 - 9 = 9
So, the length of AE is 9 units.
A 20 packet box of detergent sells for $5.49. What is the unit rate
Answer:$0.27
Step-by-step explanation:
20=$5.49
1=20/5.49
1=$0.2745
Which statement is correct?
A kilometer is 100 times the length of a meter.
A kilometer is 1,000 times the length of a meter.
A centimeter is 100 times the length of a meter.
A meter is 10 times the length of a centimeter.
Answer:
A centimeter is 100 times the length of a meter.
A kilometer is 1,000 times the length of a meter.
The statement that asserts a true claim would be:
B). A kilometer is [tex]1,000[/tex] times the length of a meter.
Metric System
The metric system is a measurement system that employs the meter, liter, and gram as base units of length (distance), capacity (volume), and weight (mass).Kilometers are [tex]1,000[/tex] meters. In the metric system, the meter is the basic unit for measuring length or distance.[tex]1[/tex] kilometer [tex]=1000[/tex] metersSo, a kilometer is [tex]\boldsymbol{1,000}[/tex] times the length of a meter.Find out more information about "mathematical units" here:
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The sum of three consecutive even numbers is 522.find the number
Answer: 172, 174 and 176
Step-by-step explanation:
Since they are even numbers,
Let x be the number, x + 2 be the second number and x +4 the third number
can think of this as x+(x+2)+(x+4)=522
so you get 3x=522-6
3x= 516
so x=172
If x is 172, second number is 174 and third number is 176
PLEASE ANSWER
For Saturday’s debate tournament, Sarah ordered 3 cookies for each student participant and a tray of 30 cookies for the sponsors’ hospitality room. This relationship can be expressed by the function C = 3s + 30, where s is the number of student participants and C is the number of cookies ordered. Which is the dependent quantity in this functional relationship?
A. The number of cookies ordered
B. The number of trays ordered
C. The number of student participants
D. The number of sponsors
Answer:
A
Step-by-step explanation:
The cookies ordered is the dependent quantity/variable because the other variables don't depend on anything that is quantifiable.
The dependent quantity in this functional relationship is A. The number of cookies ordered.
A dependent quantity simply refers to the quantity that depends on another quantity or is determined by another quantity.
Based on the information given, the dependent quantity in this functional relationship is the number of cookies ordered since it depends on other factors such as the number of trays and students.
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What is the stretch or shrink of the graph g(x) = 2 |x + 3| − 5
It's a stretch by coefficient of two.
Hope this helps.
Determine whether the two expressions are equivalent. If so, tell what property is applied.
(20 – 4) – 2 and 20 – (4 – 2)
Both expressions (20 – 4) – 2 and 20 – (4 – 2) are equivalent, simplifying to 14. The equivalence exemplifies the Associative Property of Addition.
The question asks to determine whether the two expressions (20 – 4) – 2 and 20 – (4 – 2) are equivalent, and if so, to identify the property applied. To determine equivalence, we need to simplify both expressions. The first expression, (20 – 4) – 2, simplifies to 16 – 2 which equals 14. The second expression, 20 – (4 – 2), simplifies to 20 – 2 which also equals 14. Therefore, both expressions are equivalent, and the property applied here is the Associative Property of Addition, which allows us to change the grouping of the numbers we're adding (or subtracting, in this case) without changing the result.
What must be the length of ZY in order for ZY to be tangent
to circle X at point Y?
14 units
15 units
16 units
17 units
Answer:
15 units
Step-by-step explanation:
The picture of the question in the attached figure
we know that
Triangle XYZ is a right triangle, because segment ZY is tangent to circle X at point Y
so
Applying the Pythagorean Theorem
[tex]XZ^2=XY^2+ZY^2[/tex]
we have
[tex]XZ=8+9=17\ units\\XY=8\ units[/tex]
substitute the given values
[tex]17^2=8^2+ZY^2[/tex]
[tex]ZY^2=289-64\\ZY^2=225\\ZY=15\ units[/tex]
Answer:
15
Step-by-step explanation:
What is the change that occurs to the parent function f(x) = x^2 given the function f(x) = (x + 1)^2 - 5.
One yard crew works four times faster than the other yard crew. If they work together they can finish a job in 60 minutes. How fast each yard crew works?
Time taken by both crew is 48 min and 12 min , when they work together !
Step-by-step explanation:
Here we have , One yard crew works four times faster than the other yard crew. If they work together they can finish a job in 60 minutes. We need to find How fast each yard crew works . Let's find out:
One yard crew works four times faster than the other yard crew
Let speed of one crew be x , So speed of other crew is four times i.e.
⇒ [tex]4x[/tex]
If they work together they can finish a job in 60 minutes.
According to above statement , both can finish work in 60 min i.e.
⇒ [tex]4x+x=60[/tex]
⇒ [tex]5x=60[/tex]
⇒ [tex]x=12[/tex]
So , time taken by other crew is 4x = 4(12) = 48 min . Therefore , Time taken by both crew is 48 min and 12 min , when they work together !
The second yard crew works for 48 minutes.
The first yard crew works for 12 minutes which is four times faster that the second crew.
Step-by-step explanation:
Let us assume,
The second yard crew completes the work in 'x' minutes.
It is given that,
The first yard crew works four times faster than the other yard crew. Therefore, first yard crew will complete the work in 'x/4' minutes.If they work together they can finish a job in 60 minutes.
⇒ x + x/4 = 60 minutes.
⇒ 5x / 4 = 60
⇒ x = 240/5
⇒ x = 48 minutes.
Therefore, the second yard crew works for 48 minutes.
To find the first yard crew :
We already know that, they are 4 times faster that the second yard crew.
Substitute x = 48 in x/4,
⇒ 48 ÷ by 4
⇒ 12 minutes.
Therefore, the first yard crew works for 12 minutes which is four times faster that the second crew.
Philip ran 4 3/8 miles yesterday. Michael ran 1 5/8 miles yesterday.
How much farther did Philip run than Michael. fractions .with common denominators.
Philip ran 3 1/4 miles farther than Michael. We obtained this by subtracting the fraction and whole number of Michael's distance from Philip's and simplified the resultant fraction.
Explanation:To find out how much farther Philip ran than Michael, you need to subtract the distance run by Michael from Philip's distance. Since we are dealing with fractions with common denominators, this makes the subtraction process easier.
Philip's distance = 4 3/8 miles
Michael's distance = 1 5/8 miles
Subtract Michael's distance from Philip's distance: 4 3/8 - 1 5/8
Since the denominators are the same, you can simply subtract the numerators: 8 (the common denominator) stays the denominator, and subtract 3 from 5 which gives: 2/8
We subtract the whole numbers: 4 - 1 = 3. Therefore, the final difference is 3 2/8 miles. However, you can simplify 2/8 fraction to 1/4. So, the final and simplest difference is 3 1/4 miles.
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To find out how much farther Philip ran than Michael, we need to subtract the fractions representing their respective distances. After converting these to improper fractions, we subtract the numerators, giving us a result of 2 6/8 miles, which is the distance by which Philip ran farther than Michael.
Explanation:The problem involves subtracting fractions to find the difference between the distances that Philip and Michael ran. First, convert the mixed fractions into improper fractions. Philip ran 4 3/8 miles which equals 35/8 miles and Michael ran 1 5/8 miles which equals 13/8 miles. Subtracting fractions with like denominators is straightforward, so subtract the numerators: 35 - 13 equals 22. Therefore, Philip ran 22/8 or 2 6/8 miles more than Michael.
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A 12inch diameter pizza has 22 calories per square inch. About how many calories are in the entire pizza? Use 3.14 for pi. Select from the drop-down menu to correctly complete the statement
Step-by-step explanation:
Diameter of pizza = 12 inch
Therefore, radius r = 6 inch
[tex]Area \: of \: entire \: pizza \\ = \pi {r}^{2} \\ = 3.14 \times {6}^{2} \\ = 3.14 \times 36 \\ = 113.04 \: {inch}^{2} \\ \\ amount \: of \: calories \: in \: entire \: pizza \\ = area \: of \: pizza \\ \times calories \: per \: square \: inch \\ = 113.04 \times 22 \\ = 2,486.88 \\ [/tex]