Answer:
C. Less than or equal to
Step-by-step explanation:
The floor function is a function used to return an integer value that is great than the input number.
More often than not, the input number is a real number.
Take for instance.
Floor(3.2).
Going by the explanation above, the result of this will be 3
How about floor(-3.2)
The result of this will be -4.
This is so because -4 is less than or equal to -3.2.
The floor function maps any number to the greatest integer that is C.) less than or equal to the number.
The floor function maps any number to the greatest integer that is less than or equal to the number. This means that for any real number \( x \), the floor function, denoted as [tex]\( \lfloor x \rfloor \),[/tex] will produce the largest integer that does not exceed \( x \). For example, \( \lfloor 3.7 \rfloor = 3 \) and \( \lfloor -2.3 \rfloor = -3 \).
The floor function is widely used in mathematics and computer science for rounding down numbers to the nearest integer. It is especially useful in discrete mathematics, algorithms, and number theory. When working with the floor function, it is essential to understand that it always rounds down towards negative infinity, not necessarily towards zero. Thus, for any real number \( x \), \( \lfloor x \rfloor \leq x \).
Therefore, the correct phrase to complete the statement about the floor function is:
C.) less than or equal to.
Please help. worth 60 points
Answer:
What am I supposed to help you with?
Step-by-step explanation:
An equation for the depreciation of a car is given by y = A(1-r)^twhere y = current value of the car, A = original cost, r = rate of
depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately
how old is the car?
Answer: The car is 6.6 years old.
Step-by-step explanation:
Hi, to answer this question we have to replace the values in the equation given:
Y = 1/2 (half the value)
A = 1 (total value)
r =10% = 0.10 (decimal form)
Replacing:
y = A(1-r)^t
1/2 = 1 (1-0.10)^t
Solving for t:
(1/2)/1 = 0.9^t
1/2 = 0.9^t
log 1/2 = log 0.9^t
log 1/2 = (t) log 0.9
(log 1/2)/ log 0.9 = t
6.57 =t
6.6 years (rounded)
The number of students enrolled at a college is 14,000 and grows 5% each year.
Answer:
14000/100*105 = 14,700
Step-by-step explanation:
Cameron sent a chain letter to his friends, asking them to forward the letter to more friends.
The relationship between the elapsed time t, in days, since Cameron sent the letter, and the number of people, P(t), who receive the email is modeled by the following function:
P(t) = 100 · (1.83) ^ t/2.5
Complete the following sentence about the rate of change in the number of people who receive the email.
Every _______ days, the number of people who receive the email increases by 83%.
A.) 0
B.) 1.83
C.) 100
D.) 2.5
Answer:
Step-by-step explanation:
Answer:
2.5
Step-by-step explanation:
What is the simplified form of the expression?
Answer:
The answer is A - a. -6a^2/b b. 5y^3
risha wants to buy a computer for $775. She already has $275 saved and earns $100 a week babysitting. a. Use w to represent weeks and write an inequality that could be used to determine how many weeks she would have to work to afford the computer. b. How many weeks does she have to work?
Answer
Inequality=100x+275≥775 Answer=5 or more
Step-by-step explanation:
The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% pure fruit juice. The company is
attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 160
pints of a mixture that is 70% pure fruit juice?
Answer: 96 pints of the first fruit drink (60% pure fruit juice) and 64 pints of the second fruit drink (85% pure fruit juice).
Step-by-step explanation:
This question is a system of equations. First, we will define our variables:
Let x= number of pints of the first fruit drink (60% pure fruit juice), and then y = the number of pints of the second fruit drink(85% pure fruit juice).
We know that there are 160 total pints of the mixture. Therefore,
x + y = 160 .......... equation i
We are also aware that 70% of those 160 pints will be pure fruit juice, and they will come from either x or y.
For x pints of the first juice, there is
0.6x of pure fruit juice and for y pints of first juice, there is 0.85y of pure fruit juice. Therefore, we will have:
0.6x + 0.85y = 160 × 0.7
0.6x + 0.85y = 112
Multiply through by 100 to remove decimal. This will be:
60x + 85y = 11200 ........... equation ii
Combine both equations
x + y = 160 .......... i
60x + 85y = 11200 ........ ii
Multiply equation i by 60
Multiply equation ii by 1
60x + 60y = 9600 ........ iii
60x + 85y = 11200 ......... iv
Subtract iv from iii
-25y = -1600
y = 1600/25
y = 64
Since x + y = 160
x = 160 - 64
x = 96
Therefore , we will need 96 pints of the first fruit drink (60% pure fruit juice) and 64 pints of the second fruit drink (85% pure fruit juice).
What is the radius of the circle x^2+6x + y^2– 12y = 36?
Answer:
Step-by-step explanation:
hello :
x²+6x + y²– 12y = 36
completed to suqard :(x²+6x) + (y²– 12y) = 36 means :
(x²+6x+9)-9 + (y²– 12y+36)-36 = 36
(x+3)²+(y-6)² = 9².... standard form when the radius is : 9
May I please get help with this question?
Simplify 5+ W equals eight
Answer:
3
Step-by-step explanation:
5+3=8
8-5=w
In an assembly line, 56 out of 60 randomly selected parts have no faults. Predict the number of parts that will have no faults in a similar batch of 12,000 parts.
We have been given that in an assembly line, 56 out of 60 randomly selected parts have no faults. We are asked to predict the number of parts that will have no faults in a similar batch of 12,000 parts.
We will use proportions to solve our given problem.
[tex]\frac{\text{Not faulty parts}}{\text{Total parts}}=\frac{56}{60}[/tex]
[tex]\frac{\text{Not faulty parts}}{12,000}=\frac{56}{60}[/tex]
[tex]\frac{\text{Not faulty parts}}{12,000}\times 12,000=\frac{56}{60}\times 12,000[/tex]
[tex]\text{Not faulty parts}=56\times 200[/tex]
[tex]\text{Not faulty parts}=11,200[/tex]
Therefore, approximately [tex]11,200[/tex] parts will have no faults in a similar batch of 12,000 parts.
The circumference of a circle is 24π ft. What is the area, in square feet? Express your answer in terms of
π
π.
Answer:
[tex]144\pi[/tex]
Step-by-step explanation:
Circumference = [tex]\pi d[/tex]
Diameter = [tex]2r[/tex]
Area of a circle = [tex]\pi r^2[/tex]
From our first equation, we can find our value for our diameter:
We do this by dividing [tex]24 \pi[/tex] by [tex]\pi[/tex] to get 24.
[tex]c=\pi d[/tex]
[tex]d=\frac{c}{\pi } = \frac{24\pi }{\pi } =24[/tex]
Using our second equation, we can find out the value for our radius:
[tex]d=2r[/tex]
[tex]r=\frac{d}{2} =\frac{24}{2} =12[/tex]
Now we have a value for our radius, we can use our third equation to find out our area:
[tex]A=\pi 12 ^2 = 144 \pi[/tex]
Given that:
The circumference of a circle is 24π ft.To Find:
What is the area, in square feet?We know that:
Circumference of a circle = 2πRArea of a circle = πR²Where,
Radius is denoted as R.Finding the radius of the circle:
Circumference of a circle = 24π
⟶ 2πR = 24π
⟶ 2πR = 2π × 12
Cancelling 2π.
⟶ R = 12
∴ Radius of the circle = 12 ft.
Finding the area of the circle:
⟶ Area = πR²
⟶ Area = π(12)²
⟶ Area = π × 12 × 12
⟶ Area = π × 144
⟶ Area = 144π
Hence,
Area of the circle is 144π square feet.which set of side lengths form a right triangle?
A. 8 cm, 17 cm, 14 cm
B. 50 in., 48 in., 14 in.
C. 53 m, 48 m, 24 m
D. 3 ft, 6 ft, 5 ft
Answer:
I think the answer is B.
Answer:
b.) [tex]50,48,14[/tex]
Step-by-step explanation:
To find if a set of lengths makes a right triangle, use the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
If a and b squared equal c squared, then the set makes a right triangle. C (the hypotenuse) is the largest number of the set because the hypotenuse is always the largest side in a right triangle.
Use the options:
a.) insert values:
[tex]8^2+14^2=17^2\\64+196=289\\260\neq 289[/tex]
260 does not equal 289, so a is wrong.
b.) insert values:
[tex]14^2+48^2=50^2\\196+2304=2500\\2500=2500[/tex]
2,500 equals 2,500, so b is correct.
Finito.
2/3+q=1/2 what is Q
Q=rational number=1/6
2/3+q=1/2=1/6
Need this answer in fraction form these are the answer choices
A.8/15
B.15/16
C.16/15
D.15/8
Answer:
Option B 15/16
Step-by-step explanation:
calculate the volume of the cone and the volume of the cylinder and then put them in a fraction with the cone over the cylinder, afterwards put that fraction in a calculator and see what you get. once you get the answer input each one of the options into the calculator until one of the fractions gives you the same product as the cone/cylinder fraction.
please mark brainliest :)
Shwetha comes to the swimming pool once every 12 days. Vinnie comes once every 4 days and Olga comes once every 10 days. Last Monday all of them were in the pool. In how many days all of them will meet at the swimming pool again? What day of the week will it be?
Answer:
60 days, Friday
Step-by-step explanation:
This problem is solved using concept of LCM.
LCM is the least number which is the common multiple of given set of different number.
To find the LCM we method of prime factors, the steps are given below
get all the all the prime factor of the given set of numberselect all the prime factors as many times they occur in given set of numbermultiply together the numbers selected together to get LCM________________________________________________
Given
frequency of visiting swimming pool by Shwetha = once in 12 days
factors of 12 = 2 * 2 * 3
frequency of visiting swimming pool by Vinnie = once in 4 days
factors of 2 = 2 * 2
frequency of visiting swimming pool by Olga = once in 10 days
factors of 10 = 2 * 5
minimum no of days after which they will be visiting together will be least common multiple of number of days after which they visit swimming pool individually.
Selecting the prime numbers with their highest occurrence
we have 2, 2, 3 ,5
multiplying them together we have
2 * 2 * 3* 5 = 60
therefore 60 is the LCM of 12, 4, 10
it means that Shwetha, Vinnie and Olga will visit swimming pool together once in 60 days
It is given that they visited on Monday and now they will visit after 60 days again.
since in one week there are seven days, every eighth day will be monday
so we divide 60 days by 7 to see how many cycles of monday has passed.
60/7 = 8 4/7
It suggest that 8 weeks has passed and they will meet on 4 days after Monday which will be Friday.
Thus they will meet meet at the swimming pool again in 60 days.
It will be Friday.
Answer:
60 days, friday
Step-by-step explanation:
The measure of XYZ is 45. The length of radius YZ is 6 inches. What is the area of sector XYZ?
(Use 3.14 for I.)
Answer:
area of a sector = 14.13 yards²
Step-by-step explanation:
XYZ is a sector of a circle. The radius YZ is 6 inches .The angle of the sector is given as 45°. The area of the sector can be solved as follows.
area of a sector = ∅/360 × πr²
where
r = radius
∅ = center angle
r = 6 inches
∅ = 45°
area of a sector = 45/360 × 3.14 × 6²
area of a sector = 45/360 × 3.14 × 36
area of a sector = 45/360 × 113.04
area of sector = 1/8 × 113.04
area of a sector = 14.13 yards²
Answer:
14.13
Step-by-step explanation:
i know
For which value of x would this model make the least sense
to use? A.-2.75 B.0.25 C.1.75 D.2.25
Answer: A
Explanation: x is your independent variable and is time, so it is unlikely to have negative amounts of time.
The time will be 2.25 seconds. Then the correct option is D.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function is given below.
h(x) = – 16x² + 100
Where x is the time in seconds and h(x) is the height at x.
Let the height is y feet.
Then the value of y will be
y = 84 – 65
y = 19 feet
Then the time will be
19 = – 16x² + 100
16x² = 100 – 19
16x² = 81
4x = 9
x = 2.25 seconds
Then the correct option is D.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ2
A golfer hits a ball from a starting elevation of 7 feet with a velocity of 70 feet per second down to a green
with an elevation of -2 feet. The number of seconds t it takes the ball to hit the green can be represented
by the equation - 16t2 + 70t +7=-2. How long does it take the ball to land on the green?
It takes the ball ___
seconds to land on the green.
Answer:
[tex]t \approx 4.501\,s[/tex]
Step-by-step explanation:
The second-grade equation must be rearragend into its standard form:
[tex]-16\cdot t^{2} + 70\cdot t + 9 = 0[/tex]
Roots can be found with the help of the General Equation for Second-Order Polynomial:
[tex]t = \frac{-70\pm \sqrt{70^{2}-4\cdot (-16)\cdot (9)}}{2\cdot (-16)}[/tex]
[tex]t = 2.188 \pm 2.313[/tex]
[tex]t_{1} \approx 4.501\,s[/tex]
[tex]t_{2} \approx -0.125\,s[/tex]
Only the first root offers a reasonable solution.
[tex]t \approx 4.501\,s[/tex]
Question: Solve it using the proportion method.
log8x=2 solve for x by converting the logarithm to an exponential equation. (i already know the answer is 12.5 but i need the written steps that it takes to solve this problem in order for my answer to count.) please help!!!!1
Answer:
pooooooo
Step-by-step explanation:
I WILL GIVE BRAINLIEST
Solve the inequality:
10x - 3 ≥ 2
A. x ≤ 1/2
B. x ≤ 2
C. x ≥ 1/2
D. x ≥ 2
10x−3+3≥2+3
10x≥5
(10x10)/2≥(5/10)
x≥1/2
If the product of two integers is positive, their signs are positive or negative
Lauren owes her friend $32.50 for a concert ticket. She doesn’t have the cash now, but she’ll earn it babysitting this weekend. If Lauren gets paid $8 an hour to babysit, the equation that represents y, how much money will she have after paying back her friend, in terms of x, the number of hours she spends babysitting this weekend, is y = x .
Answer:
y=8x-32.5
Step-by-step explanation:
8 dollars an hours = slope
-32.5 owed = y-intercept
Observe the graph below and determine the exponential function.
PLEASE HELP FAST
Step-by-step explanation:
I think the exponential function is 4,-8
Answer:
f(x) = 1/4
Step-by-step explanation:
I used google, and I wish there were some answer choices!! If there are, let me know!!
The diameter of a golf ball is about 4 centimeters. Which of these is the closest to the volume of a golf ball?
16.75 cm^3
33.51 cm^3
100.53 cm^3
268.08cm^3
The volume is approximately 33.51 [tex]cm^3[/tex], option B.
The question asks us to determine the closest volume to a golf ball with a diameter of approximately 4 centimeters. To find the volume of a sphere (which is the shape of a golf ball), we use the formula:
V = (4/3)π[tex]r^3[/tex],
where r is the radius of the sphere. Since the diameter of the golf ball is given as 4 cm, the radius would be half of that, which is 2 cm. Plugging in the radius into the formula, we have:
[tex]V = (4/3)\pi(2 cm)^3 = (4/3)\pi(8 cm^3) = (32/3)\pi cm^3,[/tex]
Now, we calculate the value using the approximation π = 3.14:
V = (32/3) × 3.14 [tex]cm^3[/tex] = 33.51 [tex]cm^3[/tex] (approximately).
Therefore, the volume that is closest to the actual volume of the golf ball is 33.51 [tex]cm^3[/tex], option B.
Ice cream sandwiches are wrapped in white paper before they are put in
a box to be sold. How many ice cream sandwiches can be wrapped with
500 square inches of paper?
I need help pleaseee (10 points)
Answer:
(x+9) (x+9)
Step-by-step explanation:
hope this helps ;/
Answer:
(x+9)(x+9)
Step-by-step explanation:
How many significant digits are there in the product of 0.005 and 25.725
a. 0
b. 1
c. 2
d. 3
Answer:
its D 3
Step-by-step explanation:
Plz help me love you
Answers)
27=6
30=82
33=24