Answer:
22.5 minutes
Step-by-step explanation:
Initially, there were 9 students with 30 minutes to clean up the mess. This means they had a total of 9 · 30 = 270 student minutes to clean up the mess.
After the 3 additional students were added, there were a total of 9 + 3 = 12 students on the clean-up crew.
Now, let's assume the time they need to clean up the mess is "t" minutes. Since the number of students and the time are inversely proportional to the amount of work done, we can set up the following equation based on the idea that the amount of work done is the same before and after the addition of the 3 students:
9 · 30 = 12 · t
Solving for "t":
270 = 12t
t = 270 / 12
t = 22.5
So, the principal should give them approximately 22.5 minutes to complete the job with the new crew of 12 students.
Events A and B are independent, P(A)=P(B) and P(A∪B)=0.63 . Find P(B) .
Answer:
the probability of event B is approximately 0.48.
Step-by-step explanation:
P(A) = P(B) (given)
P(A∪B) = P(A) + P(B) - P(A∩B) (probability rule for the union of two events)
Since events A and B are independent, we know that P(A∩B) = P(A) × P(B).
Substituting the given values, we get:
0.63 = P(A) + P(B) - P(A) × P(B)
Since P(A) = P(B), we can substitute P(B) for P(A):
0.63 = 2P(B) - P(B)^2
Rearranging this equation, we get:
P(B)^2 - 2P(B) + 0.63 = 0
This is a quadratic equation that we can solve using the quadratic formula:
P(B) = [2 ± sqrt(4 - 4×0.63)] / 2
P(B) = [2 ± sqrt(1.48)] / 2
P(B) ≈ 1 or P(B) ≈ 0.48
Since probabilities must be between 0 and 1, we can discard the solution P(B) = 1, and the only possible solution is:
P(B) ≈ 0.48
Therefore, the probability of event B is approximately 0.48.
7 1/3 divided by 1 2/9
Answer:
6
Step-by-step explanation:
7 1/3 ÷ 1 2/9
7 1/3 = 22/3
1 2/9 = 11/9
22/3 ÷ 11/9
= 22/3 x 9/11
= 198/33
= 66/11
= 6
OPEN-ENDED Write an algebraic expression using more than one
operation. When you evaluate the expression, how do you know
which operation to perform first?
Answer:
9(4+5)-16=
Explanation:
P (parenthesis) E (exponents) M (multiply) D (divide) A (add) S (subtract)
HOPE THIS HELPS
a)2/5 t=6
t=___
b)-4.5= a-8
a=___
c) 1/2+p=3
p=___
d)-12=-3y
x=___
Solving the equations for each given variables, we have:
a. t = 15
b. a = 12.5
c. p = 5/2
d.
y = 4
How to Find the Value of a Variable in an Equation?Finding the value of a variable in an equation involves solving the equation for that variable. This process typically involves several steps, including isolating the variable on one side of the equation, using inverse operations to simplify the expression, and substituting known values into the equation to find the value of the variable.
Therefore:
a. 2/5t = 6
Multiply both sides by 5/2:
t = 6 * 5/2
t = 15
b. -4.5 = a - 8
Add 8 to both sides:
-4.5 + 8 = a
12.5 = a
a =12.5
c. 1/2 + p = 3
p = 3 - 1/2
p = 5/2
d. -12 = -3y
-12/-3 = y
4 = y
y = 4
Learn more about equations on:
https://brainly.com/question/17145398
#SPJ1
Is 59 a Prime or Composite Number?
59 is a prime number.
This means that it cannot be divided evenly by any other number except for 1 and itself. A composite number, on the other hand, can be divided evenly by at least one other number besides 1 and itself.
To determine if a number is prime or composite, you can use a simple test. Start by dividing the number by 2. If the result is a whole number, then the number is composite.
If the result is not a whole number, try dividing by 3, 4, 5, and so on until you find a whole number result or until you reach the square root of the original number. If you reach the square root without finding a whole number result, then the number is prime.
For example, with the number 59:
59 / 2 = 29.5 (not a whole number)
59 / 3 = 19.67 (not a whole number)
59 / 4 = 14.75 (not a whole number)
59 / 5 = 11.8 (not a whole number)
59 / 6 = 9.83 (not a whole number)
59 / 7 = 8.43 (not a whole number)
59 / 8 = 7.38 (not a whole number)
Since we have reached the square root of 59 without finding a whole number result, we can conclude that 59 is a prime number.
To know more about prime number click on below link:
https://brainly.com/question/30358834#
#SPJ11
The area of a square is one third the area of a triangle. If the base of the triangle and a side of the square are equal, what is the ratio of the height of the triangle to the side of the square ?.
The ratio of the height of the triangle to the side of the square is 6.
A triangle is a three-sided polygon with three vertices and three angles. Triangles can have different shapes and sizes, including equilateral, isosceles, and scalene triangles.
Let's call the side of the square x. Since the base of the triangle is equal to the side of the square, we can use x for both. The area of the square can then be found by x² and the area of the triangle can be found by (x)(h)/2, where h is the height of the triangle.
We know that the area of the square is one-third the area of the triangle, so we can set up an equation:
x² = (1/3)(x)(h)/2
Expanding the right side of the equation:
x² = (1/3)(xh)/2
Now we can isolate the height of the triangle by multiplying both sides by 6 and dividing by x:
6x² = (xh)
Finally, we can divide both sides by x to find the ratio of the height of the triangle to the side of the square:
6x = h
To know more about triangle here.
https://brainly.com/question/8587906
#SPJ4
Pleaseee help now please help nowwww
The length of JM is given as follows:
JM = 16.875.
What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.The polygons for this problem are similar, hence the proportional relationship for the segment lengths is given as follows:
16/15 = JM/18
Then the length of JM is obtained applying cross multiplication as follows:
16JM = 15 x 18
JM = 15 x 18/16
JM = 16.875.
More can be learned about similar polygons at brainly.com/question/14285697
#SPJ1
The flat rate for your service runs $9.50 per hour. To cover costs, you charge the flat rate plus 15% of that rate for the first 8 hours, and 10% of that rate on the second 8 hours. You estimate that a particular job will take 16 hours. Write the equations and the total estimate.
(9.50 + 0.15 x 9.50) x Hours and (9.50 + 0.10 x 9.50) x Hours are the equation to and the total cost estimate is $173.04.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
For the first 8 hours: The flat rate is $9.50 per hour, so 15% of that rate is 0.15 x 9.50 = $1.43.
The cost for the first 8 hours is (9.50 + 1.43) x 8 = $96.64.
For the next 8 hours: The flat rate is still $9.50 per hour, so 10% of that rate is 0.10 x 9.50 = $0.95.
The cost for the next 8 hours is (9.50 + 0.95) x 8 = $76.40.
Total cost estimate = $96.64 + $76.40 = $173.04
We can also write the equations for the costs as follows:
For the first 8 hours: Cost = (9.50 + 0.15 x 9.50) x Hours = 1.15 x 9.50 x Hours
For the next 8 hours: Cost = (9.50 + 0.10 x 9.50) x Hours = 1.10 x 9.50 x Hours
Using these equations, we can calculate the cost for any number of hours up to 16.
Hence, (9.50 + 0.15 x 9.50) x Hours and (9.50 + 0.10 x 9.50) x Hours are the equation to and the total cost estimate is $173.04.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Answer:
(9.50 + 0.15 x 9.50) x Hours and (9.50 + 0.10 x 9.50) x Hours are the equation to and the total cost estimate is $173.04.
Step-by-step explanation:
A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $55. The total cost to rent 6 chairs and 2 tables is $28. What is the cost to rent each chair and each table?
Chair:
Table:
I truly would appreciate if someone could help me understand or solve this quickly :)
The solution is: the cost of renting one chair is $2.25
the cost of renting one table is $8.25.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Let x represent the cost of renting one chair.
Let y represent the cost of renting one table.
The total cost to rent 3 chairs and 5 tables is $48. This means that
3x + 5y = 48 - - - - - - - - - -1
The total cost to rent 6 chairs and 2 tables is $30. This means that
6x + 2y = 30 - - - - - - - - - -2
Multiplying equation 1 by 6 and equation equation 2 by 3, it becomes
18x + 30y = 288
18x + 6y = 90
Subtracting, it becomes
24y = 198
y = 198/24 = 8.25
Substituting y = 8.25 into equation 1, it becomes
3x + 5 × 8.25 = 48
3x + 41.25 = 48
3x = 48 - 41.25
= 6.75
x = 6.75/3
= 2.25
To learn more on equation click:
brainly.com/question/24169758
#SPJ1
Help me please I need someone’s help on this hmh
Note that the area of the smaller square will be depicted by: 20inches.
What is the rationale for the above response?Area of the larger square - Area of the 4 Right Angled Triangles
Since the Area of the larger square = is 36inches; and
Area of the one of the Right Angled Triangles = 4inches
Thus, the Boxes will be completed as follows;
[36in] - (4) [4] or [20in]
Since
36 - 16 = 20 inches.
Note that a square is a closed two-dimensional form having four equal sides and four vertices. Its opposing sides are perpendicular to one other. A square can alternatively be thought of as a rectangle with equal length and width.
Learn more about squares;
https://brainly.com/question/14198272
#SPJ1
Write the other side of this equation so it has MANY solutions.
6x - 5 =
Answer:
6x - 5 = 6x - 5
Step-by-step explanation:
If we have the same quantity on both sides of the equation, then the equation becomes an identity — an equation that is true for any value of the present variables.
If we set 6x - 5 equal to 6x - 5, then there are infinite solutions.
For example,
when x is 3:
6(3) - 5 = 6(3) - 5
18 - 5 = 18 - 5
13 = 13 ✔
when x is 5:
6(5) - 5 = 6(5) - 5
30 - 5 = 30 - 5
25 = 25 ✔
Which graph represents the solution -1/2(8x-32)< -4
The solution set for the given inequality is {6, 7, 8, 9, 10,.....}.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -1/2(8x-32)< -4
Multiply by -2 on both the sides of an inequality, we get
(8x-32)>8
Add 32 on both the sides of an inequality, we get
8x>40
Divide 8 on both the sides of an inequality, we get
x>5
So, solution set is {6, 7, 8, 9, 10,.....}
Therefore, the solution set for the given inequality is {6, 7, 8, 9, 10,.....}.
To learn more about the inequalities visit:
https://brainly.com/question/20383699.
#SPJ9
What percent of 72 is 68.4
68.4 is approximately 95% of 72.
Here, we have,
To find out what percent of 72 is 68.4, we can follow these steps:
Step 1: Divide 68.4 by 72.
68.4 / 72 = 0.95
Step 2: Convert the decimal to a percentage by multiplying by 100.
0.95 * 100 = 95
Therefore, 68.4 is approximately 95% of 72.
To learn more on percentage click:
brainly.com/question/13450942
#SPJ6
The equation m=35g
m
=
35
g
gives the distance in miles, "m," that a truck can travel using "g" gallons of gas. What is the inverse function that represents the gallons as a function of miles?
The inverse function that represents the gallons g as a function of miles m is:
g = m/35.
What is meant by the inverse of a function?
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.
A function that can reverse into another function is known as an inverse function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as " f ⁻¹ " or " F ⁻¹."
Given a function m = 35g
where m = distance in miles travelled by the truck
g = gallons of gas used to travel m distance
If the function is m = 35g
Then the inverse function is g = m/35.
The inverse of the given function tells us how many gallons of gas are needed for a given number of miles.
Therefore the inverse function that represents the gallons g as a function of miles m is:
g = m/35.
To learn more about inverse functions, follow the link.
brainly.com/question/3831584
#SPJ1
Engineers want to measure the distance from P to Q, but the span from P to Q is across the tip of a lake. So they select a point R on land and fine that the distance from R to Q is 100 feet and from R to P is 120 feet. Angle QPR measures 47 degrees. How far is it from P to Q?
The distance of P to Q is given as follows:
89.6 feet.
What is the law of cosines?The law of cosines states that we can find the side c of a triangle as follows:
c² = a² + b² - 2abcos(C)
In which:
C is the angle opposite to side c.a and b are the lengths of the other sides.The parameters for this problem are given as follows:
a = 120, b = 100, C = 47º.
Hence the distance is obtained as follows:
c² = 120² + 100² - 2 x 120 x 100 x cosine of 47 degrees
c² = 8032
c = sqrt(8032)
c = 89.6 feet.
More can be learned about the law of cosines at https://brainly.com/question/4372174
#SPJ1
A circular pizza is divided into eight equal slices. The outer edge of the crust from one piece measures 5. 5 inches. What is the diameter of the pizza to the nearest inch?.
The diameter of the pizza to the nearest inch is 11 inches.
Let's call the diameter of the pizza "d". The circumference of the pizza can be calculated using the formula:
C = πd
And since the outer edge of the crust from one piece measures 5.5 inches, that length is equal to 1/8 of the circumference of the pizza:
5.5 = (1/8)C
So we can substitute the formula for the circumference into this equation:
5.5 = (1/8)(πd)
Solving for d, we can multiply both sides by 8/π:
d = (5.5)(8/π)
Calculating the approximate value of π as 3.14, we get:
d ≈ (5.5)(8/3.14) = 11 inches
So the diameter of the pizza is approximately 11 inches, rounded to the nearest inch.
To learn more about diameter here:
https://brainly.com/question/5501950
#SPJ4
Seven subtracted from fives times a number, and then the difference added to nine times a number.
Step-by-step explanation:
Let n= The first number
Let x= The second number
(5n-7)+9x
This is if the number are different numbers.
If they are the same:
Let n= a number
(5n-7)+9n=
7n-7
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 5 liters of synthetic oil. In order to make 855 liters
of Petrolyn oil, how many liters of natural oil are needed?
380 liters of natural oil is needed
How to calculate the amount of natural oil that is needed?
The ratio of natural oil to synthetic oil is 4:5
Total number of petrolyn oil is 855
4x + 5x= 855
9x= 855
x= 855/9
x= 95
The number of natural oil is 4x
= 4(95)
= 380
Hence the number of liters of natural oil that is needed is 380
Read more on liters here
https://brainly.com/question/29400126
#SPJ1
What is 46 kg in lbs ?
Answer: 101.41 lbs.
Step-by-step explanation:
46 kilograms can be converted to pounds by multiplying the number of kilograms by 2.20462.
So, 46 kg = 46 * 2.20462 = 101.41 lbs.
The graph shows the amount of a chemical in a patient's body at different times measured in hours since the levels were first checked.
Which equation best represents the graph?
Answer: please look at the image for the answer
Step-by-step explanation:
How would you solve this problem?
Measure of angle V is 103°.
What is Polygons?Polygons are closed figures which has at least three set of line segments joined together.
The polygon with least number of sides is triangle.
Here is a six sided polygon, which is hexagon.
Sum of interior angles of a polygon = (n - 2) 180, where n is the number of sides of the polygon.
Sum of the interior angles of the given polygon = (6 - 2) 180 = 720
So,
∠S + ∠T + ∠U + ∠V + ∠W + ∠X = 720°
90° + (9x - 19)° + 111° + (5x + 8)° + 128° + (7x + 3)° = 720°
9x + 5x + 7x + 90 - 19 + 111 + 8 + 128 + 3 = 720
21x + 321 = 720
21x = 399
x = 19
∠V = (5 × 19) + 8 = 103°
Hence the angle V is of measure 103°.
Learn more about Polygons here :
https://brainly.com/question/28276384
#SPJ1
What is the rule for derivative of trigonometric functions?
The derivative of y = sin(x)cos(x) is 2sin(x)cos(x).Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x)
The rule for derivatives of trigonometric functions states that the derivative of a trigonometric function is the product of the coefficient and the derivative of the other function in the product. This rule can be expressed mathematically using the following formula: (f(x)g(x))' = f'(x)g(x) + f(x)g'(x) For example, let's say that we want to calculate the derivative of the function y = sin(x)cos(x). Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x) Therefore, the derivative of y = sin(x)cos(x) is 2sin(x)cos(x).
Learn more about derivatives here:
https://brainly.com/question/8791755
#SPJ4
Download
Stations - Applicatio....pdf
2.) If you add Ginger and her
grandmother's
ages together it
would be 66. Her grandmouer
is ten times older than Ginger.
What are the ages of each
person?
Answer:
Step-by-step explanation:
Let us consider the Ginger to be x years old.
Therefore, her grandmother will be 10x years old(10 times Ginger's age)
So,
10x+x=66
(adding both Ginger and her grandmother's age)
11x=66
(adding x and 10x)
x=66/11
x=6
Ginger's age is 6.
Her grandmother is 10 times her age.
Therefore she is 60 years old.
Mandisa interpreted the range of the data set, 5, as meaning half the cats at the shelter weigh no more than 5 pounds. Do you agree with mandisa's interpretation
No, Mandisa's interpretation is incorrect because range does not describes the weight of the cats.
The range of a data set is the difference between the largest and smallest values in the set. In this case, the range of the data set is 5, which means the difference between the highest value and the lowest value is 5. This does not necessarily mean that half the cats at the shelter weigh no more than 5 pounds.
For example, if the smallest value is 2 and the largest value is 7, the range would be 7 - 2 = 5. This means that the range of the data set is 5, and yet the weight of a cat can be 7 pounds (more than 5 pounds). It does not mean that half the cats weigh no more than 5 pounds.
Learn more about range here: https://brainly.com/question/24326172.
#SPJ11
PLEASE HELP THE PROBLEM BELOW
Answer: x = 11
Step-by-step explanation:
divide both sides by 12
12x/12 = 132/12
simplify it and you get your answer :)
x = 11
How many multiples does 19 have?
19 has an infinite number of multiples since we can multiply 19 by any positive integer to get a new multiple.
A multiple of number is product of that number and other integer.
To find the multiples of 19, we need to multiply 19 by every positive integer. So, the multiples of 19 are:
19 × 1 = 19
19 × 2 = 38
19 × 3 = 57
19 × 4 = 76
19 × 5 = 95
19 × 6 = 114
19 × 7 = 133
19 × 8 = 152
19 × 9 = 171
19 × 10 = 190
and so on.
Learn more about multiples here: brainly.com/question/96515
#SPJ4
Bailey is asked to draw a circle. She is given the center and two points on the circle, but she isn't told which point is which. The points are (-6, 3), (-15, 3), and (3,3). Bailey draws an accurate circle from this information. What is the equation of the circle she drew?
O (= - 6)3 + (3 - 3)? = 3
O (= - 3)? + (y - 3)? = 3
O (* + 6)3 + (y - 3)? = 81
О (= - 3)3 + (y - 3)? = 81
〇(c+15)+(- 3) = 81
O (= - 6)? + (3 - 3)? = 81
The equation of circle with center ( -6 , 3 ) is ( x + 6 )² + ( y - 3 )² = 9² , where the radius of circle r = 3 units
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the radius of the circle be represented as r
Now , the first point is A ( -6 , 3 )
Let the second point be B ( -15 , 3 )
Let the third point be C ( 3 , 3 )
And , from the distance formula ,
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
The distance of AB = √ ( -15 + 6 )² + ( 3 - 3 )² = 9 units
The distance of AC = √ ( 3 + 6 )² + ( 3 - 3 )² = 9 units
The distance of BC = √ ( -15 - 3 )² + ( 3 - 3 )² = 18 units
So , the measure of AB = AC and the radius of the circle r = 3 units
Now , the center of the circle is A ( -6 , 3 )
where the standard form of a circle is
( x - h )² + ( y - k )² = r²,
On simplifying , we get
( x + 6 )² + ( y - 3 )² = 9²
Hence , the equation of circle is ( x + 6 )² + ( y - 3 )² = 9²
To learn more about circle click :
https://brainly.com/question/28391204
#SPJ1
Aubrey opened a savings account and deposited $100.00. The account earns 2% interest, compounded annually. If she wants to use the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike? nt P(1 + 2)", where A is the balance (final amount), P is the principal Use the formula A = P (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
In 3 years, Aubrey will be able to spend $106.08 on a new bicycle.
To find out how much Aubrey will be able to spend on the bike in 3 yearsFirst we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount (balance)
P = principal (starting amount) = $100.00
r = interest rate as a decimal = 2% = 0.02
n = number of times per year that the interest is compounded = 1 (annually)
t = time in years = 3
Plugging in these values, we get:
A = $100.00 * (1 + 0.02/1)^(1 * 3)
A = $100.00 * (1.02)^3
A = $100.00 * 1.0608
A = $106.08
Therefore, in 3 years, Aubrey will be able to spend $106.08 on a new bicycle.
Learn more about compound interest here : brainly.com/question/12325365
#SPJ1
What is the solution to the inequality 3n-12> 4n-16, using interval notation?
Answer:
the answer is D (4,∞)
Step-by-step explanation:
3n-12>4n-16
C.L.T.
3n-4n>-16+12
-n>-4
n>4
Ayuda las necesito para mañana y no le entiendo
Supplementary angles are important in mathematics because they have a sum of 180 degrees.
This property is used in various geometric constructions and proofs, as well as in solving real-world problems involving angles. For example, in trigonometry, the concept of supplementary angles is used to determine the values of trigonometric functions for angles greater than 90 degrees.
Learn more about Angles:
https://brainly.com/question/16307055
#SPJ1