Question:
A computer can sort x objects in t seconds, as modeled by the function below:
t=0.005x^2+0.002x
How many objects are required to keep the computer busy for exactly 9 seconds?
Round to the nearest whole object.
Answer:
42 objects are required to keep the computer busy for exactly 9 seconds
Solution:
Given function is:
Computer can sort x objects in t seconds, as modeled by the function below:
[tex]t = 0.005x^2+0.002x[/tex]
We have to find number of objects required to keep the computer busy for exactly 9 seconds
Therefore t = 9
Substitute t = 9 in given function
[tex]9 = 0.005x^2+0.002x\\\\0.005x^2+0.002x - 9 = 0[/tex]
Let us solve the above equation by quadratic formula,
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Using the above formula,
[tex]\text{ for } 0.005x^2+0.002x - 9 = 0 , \text{ we have } a = 0.005 ; b = 0.002 ; c = -9[/tex]
Substituting the values of a = 0.005 ; b = 0.002 ; c = -9 in above quadratic formula we get,
[tex]\begin{aligned}&x=\frac{-0.002 \pm \sqrt{0.180004}}{0.01}\\\\&x=\frac{-0.002 \pm 0.4242}{0.01}\\\\&x=\frac{-0.002+0.4242}{0.01} \text { or } x=\frac{-0.002-0.4242}{0.01}\\\\&x=42.22 \text { or } x=-42.62\end{aligned}[/tex]
Ignoring negative value,
x = 42.22 ≈ 42
Thus 42 objects are required to keep the computer busy for exactly 9 seconds
1. During a field trip, 60 students are put into equal-sized groups.
- Describe two ways to interpret 60:5 in this context.
- Find the quotient.
- Explain what the quotient would mean in each of the two interpretations you
described.
Help me plzz
The ratio 60:5 can be described as follows :
60 students are divided into equal groups of 5 student each. Groups of 5 students per group totaled up to 60 students. The quotient in both expression is 60:5 = 12 students per group .The ratio expression is a way of expressing the division of numerator by a denominator.
Here,
The total number of students is the numerator = 60
The denominator is the number of students per group = 5
Hence, the quotient is the value of the divison obtained which is (60/2) = 12
Therefore, there are 12 groups of 5 students.
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PLEASE HELP ASAP! WORTH 8 POINTS
"Four-fifths of the pieces of fruit in Maria's basket are apples. Three-fourths of the apples are McIntosh apples.
This model represents the fraction of the fruit in Maria's basket that are McIntosh apples.
What fraction of the fruit in Maria's basket are McIntosh apples?"
Answer:
3/5
Step-by-step explanation:
4/5 * 3/4 = 12 / 20 = 3 / 5
which set of side lengths can be used to form a right triangle?
Answer:
30, 40, 50
Step-by-step explanation:
30 x 30 + 40 x 40 = 900 + 1600 = 2500
500 x 500 = 2500
sum of two legs² equals hypotenuse²
Answer:
Step-by-step explanation:
30,50,40
The cost of renting a bicycle is $9 for the first hour plus another $4 for each
additional hour. Which of the following represents this situation, where Cis
the total cost of renting a bicycle for h hours?
The missing choices are:
A. C = 9h + 4
B. C = 4h + 9
C. C = 4(h - 1) + 9
D. C = 13h
C = 4(h - 1) + 9 represents this situation ⇒ answer C
Step-by-step explanation:
The given is:
The cost of renting a bicycle is $9 for the first hourAnother $4 for each additional hourC is the total cost of renting a bicycle for h hoursWe need to find which of the following represents this situation
∵ The cost of renting a bicycle is $9 for the first hour
∵ Another $4 for each additional hour
∵ h represents the number of hours
- Add the cost of the first hour to the cost of the remaining hours
∵ The remaining hours = h - 1
∴ The cost of the remaining hours = 4(h - 1)
∵ C is the cost of renting the bicycle for h hour
- Add 9 to 4(h - 1) to find C
∴ C = 4(h -1) + 9
C = 4(h - 1) + 9 represents this situation
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The tables represent the functions fx) and g(x). Which input value produces the same output value for the two functions? X=-3 x=-1 x=0 x=1
Answer: Last option.
Step-by-step explanation:
By definition, a relation is a function if and only if each input value has an unique output value.
For this exercise it is important to remember that the input values are the values of "x" and the ouput values are the values of "y"
Knowing this and given the tables attached which represent the functions [tex]f(x)[/tex], and [tex]g(x)[/tex],, you can identify that:
1. In the table that represents the function [tex]f(x)[/tex], the input value 1 produces the output value 3.
2. In the table that represents the function [tex]g(x)[/tex], the input value 1 produces the output value 3.
Therefore, based on this, you can determine that the input value that produces the same output value for the two functions is:
[tex]x=1[/tex]
Sue drives 12 kilometers and passes 24 street lights set along the road. Find the number of street lights she passed in 1 kilometer.
Answer:
2
Step-by-step explanation:
You have to find unit rate (I feel like this is wrong, sorry in advance!)
Answer:
she passes 2 per 1 kilometer
Step-by-step explanation:
24 / 2 = 12
12 x 2 = 24
24 / 12 = 2
What is 3(23d+4d)-18d=
Given f(x)=2x^2+3x-5 for what values of x is f(x) positive
Answer:
x< -2.5 or x>1
Step-by-step explanation:
Please see attached picture for full solution.
To find the values of x for which f(x) is positive, we can set f(x) greater than zero and solve for x using factoring or the quadratic formula.
Explanation:
To determine the values of x for which f(x) is positive in the quadratic function f(x) = 2x^2 + 3x - 5, we need to find the values that make the function output positive values.
First, let's set f(x) greater than zero: f(x) > 0.Next, we can factor the quadratic function to solve for the roots: 2x^2 + 3x - 5 = 0.Using factoring or the quadratic formula, we can find the roots which are x = -1 and x = 2.5.We can see that the quadratic function is positive in the intervals (-∞, -1) and (2.5, ∞).Therefore, the values of x that make f(x) positive are x < -1 and x > 2.5.
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what is the mean proportion between 10 and 40?
Answer:
Step-by-step explanation:
10, 20, 30, 40
Answer:25
Solve the radical equation. q-6=sqrt(27-2q). What is the extraneous solution to the radical equation?
Answer:
the answer is 9
Step-by-step explanation:
the answer is 9
-13g+12g+9=15 solve for g
A population of 45 foxes in a wildlife preserve triples in size every 13 years. The function y equals 45 * 3to the x power, where x is the number of 13-year periods, models the population growth. How many foxes will there be after 39 years?
Answer:
1,215
Step-by-step explanation:
39/13=3
45*(3)^x
45*(3)^3
45*(27)
1,215
Final answer:
To find the number of foxes after 39 years, use the population growth function y = 45 *[tex]3^x[/tex]. Since 39 years corresponds to 3 periods of 13 years each, the equation becomes y = 45 * [tex]3^3,[/tex] resulting in 1215 foxes.
Explanation:
The student has asked how many foxes will there be after 39 years, given the population growth function y equals 45 times 3 to the x power, where x represents the number of 13-year periods. To solve this, we calculate the value of x by dividing the total time of population observation (39 years) by the duration of one population tripling period (13 years). This gives us:
x = 39 years / 13 years/period = 3 periods
We then substitute x into the equation and get:
y = 45 *[tex]3^3,[/tex] = 45 * 27 = 1215 foxes
Therefore, there will be 1215 foxes in the wildlife preserve after 39 years.
Three workers have to do a certain job. The first worker can finish the job in 8 hours. The second worker can finish the job in 4 hours. The third worker can also finish the job in 4 hours. How long will it take the three workers to finish the job if they work together?
PLS help
Working together three workers would take 1 hour 36 minutes to finish the job
Solution:
Given that first worker can finish the job in 8 hours
So in one hour, first worker can do [tex]\frac{1}{8}[/tex] th of the work
The second worker can finish the job in 4 hours
So in one hour, second worker can do [tex]\frac{1}{4}[/tex] th of the work
The third worker can also finish the job in 4 hours
So in one hour, third worker can do [tex]\frac{1}{4}[/tex] th of the work
The three workers working together in 1 hour can do:
[tex]\frac{1}{8} + \frac{1}{4} + \frac{1}{4} = \frac{1 + 2 + 2}{8} = \frac{5}{8}[/tex]
The three worker can thus do [tex]\frac{5}{8}[/tex] th of the work in one hour
Hence the three of them together can finish the work in [tex]\frac{8}{5}[/tex] hours
[tex]\frac{8}{5} = 1\frac{3}{5}[/tex] hours
Thus working together three workers would take 1 hour 36 minutes to finish the job
Is angle ABC congruent to angle DCE
Answer:
I do not think I can answer this without any pictures.
Step-by-step explanation:
Sorry, but could you attach a link or maybe sketch it out?
You prepare 8 scoops of dog food for 4dogs and prepare 12.5 scoops of dog food for 5 dogs is there a propositional relationship between the number of scoops and the number of dogs?
Answer:
The relationship between the number of scoops and the number of dogs is not proportional
Step-by-step explanation:
Let
x ----> the number of scoops
y ----> the number of dogs
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
First situation
You prepare 8 scoops of dog food for 4 dogs
x=8, y=4
Find the constant of proportionality k
[tex]k=\frac{y}{x}[/tex]
substitute the values of x and y
[tex]k=\frac{4}{8}=0.5[/tex]
Second situation
You prepare 12.5 scoops of dog food for 5 dogs
x=12.5, y=5
Find the constant of proportionality k
[tex]k=\frac{y}{x}[/tex]
substitute the values of x and y
[tex]k=\frac{5}{12.5}=0.4[/tex]
Compare the values of k
[tex]0.5\neq 0.4[/tex]
The values of k are not equal
therefore
The relationship between the number of scoops and the number of dogs is not proportional
Determine the point that lies on the equation y = -5x - 3.
(4, 12)
(4, -12)
(4, 23)
(4, -23)
Answer:
(4, -23)
Step-by-step explanation:
To see if a point is on the equation, substitute its "x" and "y" coordinates into the equation. The points are written as (x, y). If the left side equals the right side, the point is on the line. (LS = RS)
Try (4, 12)
y = -5x - 3
12 = -5(4) - 3
12 = -20 - 3
12 = -23
LS ≠ RS
The point is not on the line.
Try (4, -12)
y = -5x - 3
-12 = -5(4) - 3
-12 = -20 - 3
-12 = -23
LS ≠ RS
The point is not on the line.
Try (4, 23)
y = -5x - 3
23 = -5(4) - 3
23 = -20 - 3
23 = -23
LS ≠ RS
The point is not on the line.
Try (4, -23)
y = -5x - 3
-23 = -5(4) - 3
-23 = -20 - 3
-23 = -23
LS = RS
The point (4, -23) is on the line.
a film canister in the shape of a cylinder has a height of 8 centimeters and a volume of the film canister. write an equation for the volume of the film canister.
Answer:
Part a) The equation for the volume of the film canister is
[tex]32\pi=\pi r^{2}(8)[/tex]
Part b) The radius of the film canister is [tex]2\ cm[/tex]
Step-by-step explanation:
The complete question is
A film canister in the shape of a cylinder has a height of 8 centimeters and a volume of 32π cubic centimeters.
a. Write an equation for the volume of the film canister.
b. What is the radius of the film canister?
Part a) Write an equation for the volume of the film canister
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
where
r is the radius of the circular base
h is the height of the cylinder
we have
[tex]V=32\pi\ cm^3[/tex]
[tex]h=8\ cm[/tex]
substitute
[tex]32\pi=\pi r^{2}(8)[/tex] ----> equation for the volume of the film canister
Part b) What is the radius of the film canister?
we have
[tex]32\pi=\pi r^{2}(8)[/tex]
[tex]32\pi=8\pi r^{2}[/tex]
Simplify
Divide by 8π both sides
[tex]4=r^{2}[/tex]
square root both sides
[tex]r=2\ cm[/tex]
express the ratio in its simpilest form
4:2:2
To simplify the ratio 4:2:2, divide each part by the greatest common factor, which is 2, resulting in a simplest form of 2:1:1.
To express the ratio 4:2:2 in its simplest form, you need to divide each term of the ratio by the greatest common factor of all the terms. In this case, the greatest common factor of 4, 2, and 2 is 2. Therefore, when you divide each part of the ratio by 2, the simplest form of the ratio is 2:1:1.
Here's a step-by-step breakdown:
Identify the greatest common factor (GCF) of the numbers in the ratio. GCF of 4, 2, and 2 is 2.
Divide each term of the ratio by the GCF. So, 4 divided by 2 is 2, and 2 divided by 2 is 1.
Write down the simplified ratio: 2:1:1.
This method is similar to the way coefficients in a balanced chemical equation can be simplified, or how ratios can be used in genetics to represent phenotypic distribution in a dihybrid cross. In health sciences, ratios such as 1:1000 are expressed in simplest form. Similarly, in engineering, gear ratios like 2:1 are given in the simplest way to indicate how many turns of an input gear will result in one turn of an output gear.
The dot plot represents an order of varying shirt sizes. A number line going from 8 to 26. 0 dots are above 8. 1 dot is above 10. 3 dots are above 12. 3 dots are above 14. 5 dots are above 16. 4 dots are above 18. 2 dots are above 20. 1 dot is above 22. 1 dot is above 24. 0 dots are above 26. Which histogram represents the same data?
The Answer is:
The histogram on Answer C.
The histogram will reflect the frequency of shirt sizes as shown in the dot plot, with bars representing the number of shirts for each size range; no bar for size 8, bars of height 1, 3, 5, 4, 2, 1, and 1 for sizes 10 through 24 respectively.
Explanation:The question relates to the representation of data using a histogram based on the information given for a dot plot. A histogram is a type of graph that depicts the distribution of data through contiguous boxes, where the x-axis often represents the data categories (like a number line indicating shirt sizes) and the y-axis shows frequencies or relative frequencies.
To represent the same data as the described dot plot in a histogram, we need to create intervals or bins that will encompass the range of shirt sizes, and each interval will have a frequency corresponding to the number of dots in that size range from the dot plot. We could have intervals such as 8-10, 10-12, 12-14, and so on, with the height of each bar representing the frequency of shirts in each size range.
Histogram bars will correspond to dot plot points as follows: no bar for size 8, a single bar reaching up to 1 for size 10, a bar up to 3 for both sizes 12 and 14, a bar up to 5 for size 16, a bar up to 4 for size 18, bars up to 2 and 1 for sizes 20 and 22 respectively, and a final bar reaching up to 1 for size 24.
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Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
Answer:
[tex]2x-3y=19[/tex]
Step-by-step explanation:
we have the ordered pairs
(8, –1) and (2, –5)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values in the formula
[tex]m=\frac{-5+1}{2-8}[/tex]
[tex]m=\frac{-4}{-6}[/tex]
simplify
[tex]m=\frac{2}{3}[/tex]
The equation of the line in point slope form is
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{3}[/tex]
[tex]point\ (8,-1)[/tex]
substitute
[tex]y+1=\frac{2}{3}(x-8)[/tex]
Convert to standard form
The equation of the line in standard form is equal
[tex]Ax+By=C[/tex]
where
A is a positive integer
B and C are integers
we have
[tex]y+1=\frac{2}{3}(x-8)[/tex]
Multiply by 3 both sides to remove the fraction
[tex]3y+3=2(x-8)[/tex]
apply distributive property right side
[tex]3y+3=2x-16[/tex]
Group the variables in one side and the constants in the other side
[tex]2x-3y=3+16[/tex]
[tex]2x-3y=19[/tex] ---> equation in standard form
Answer:
The answer is 2x + -3y = 19
Step-by-step explanation:
..
The answer I can’t do it I don’t understand it
Answer: -23 feet to sea level
Step-by-step explanation:
start with 0 (sea level)
he dives twenty, -20
he dives ten more, -20 - 10 = -30
he swims up twelve feet; -18
he goes down 5 more; -23 feet
Answer:
20 + 10 = 30
30 - 12 = 18
18 + 5 = 23
His elevation is 23ft below the sea level
Pls help! three arithmetic sequences are given below.
Sequence A: 5, 7, 9, 11,...
Sequence B: 34, 43, 52, 61
Sequence C: -9, -4, 1, 6..
Which of the following lists the sequences in order from least common difference to greatest common difference?
The common difference is basically the number at which the pattern increases.
A's common difference: 2
B's common difference: 9
C's common difference: 5
answer: A, C, B
Why does multiplying 37.4 times 0.01 give a product that is less than 37.4
Answer: When you multiply by 0.1 it is the same as dividing by 10. So it gives you a product that is less than 37.4.
What is the answer with the remainder
Answer:
0.0007
Step-by-step explanation:
Which of the following represent the three sides of the right triangle shown below? Select all that
apply
answer choices:
-5.55
-6
-7
-10
-11.66
-12
-16
Answer:
10, 6 and 11.66
Step-by-step explanation:
10, 6 and the hypothenous is equal to : √(10^2 + 6^2)
= √(100+36)
= √136
= 11.66
Answer:
10,6 and 11.66
Step-by-step explanation:
A right angled triangle has three sides which are the adjacent, the opposite and the hypotenuse.
Looking at the triangle in question, the longest side is the hypotenuse while the other two sides are opposite and adjacent respectively.
Before we can get the hypotenuse, we need to know the value of the other sides first.
Based on the diagram the height of the triangle is (20-10) = 10
The base of the triangle = (7-1) = 6
This are gotten be subtracting the initial point from the final point on which the triangle is standing in space.
Hypotenuse is gotten using the Pythagoras theorem expressed as;
Hypotenuse² = Adjacent² + opposite²
Hypotenuse² = 10²+6²
Hypotenuse² = 100+36
Hypotenuse² = 136
Hypotenuse = √136
Hypotenuse = 11.66
The three sides of the triangles are therefore 10, 6 and 11.66
2y+8x=1 write in slope intercept form
Answer:
y=-4x+1/2
Step-by-step explanation:
2y+8x=1
2y=1-8x
2y=-8x+1
y=-8/2x+1/2
y=-4x+1/2
which expression shows a way to find 35% of 10
Answer:
10 X 0.35
OR
10 X 35%
Final answer:
To find 35% of 10, convert the percentage to a decimal (0.35) and multiply by 10, which equals 3.5.
Explanation:
The expression that shows a way to find 35% of 10 is 0.35 *10. To calculate this, you convert the percentage to a decimal by dividing by 100 and then multiplying it by the number you want to find the percentage of. So, to find 35% of 10, you calculate 0.35 *10 which equals 3.5.
To find 35% of 10, you can use the following expression:
(35/100) x 10
This can be simplified to 0.35 x 10 = 3.5. Therefore, 35% of 10 is 3.5.
Use the work shown to find the solutions of the quadratic equation. x2 – x –3/4=0 x2 – x = 3/4
Answer:
x = - [tex]\frac{1}{2}[/tex], x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given
x² - x - [tex]\frac{3}{4}[/tex] = 0
Multiply through by 4 to clear the fraction
4x² - 4x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 3 = - 12 and sum = - 4
The factors are + 2 and - 6
Use these factors to split the x- term
4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
The solutions are x = 3 and x = -7.
To solve the quadratic equation, we first need to bring it to the standard form of ax2 + bx + c = 0. In the example given, we have the equation x2 + 4x - 21 = 0, where a = 1, b = 4, and c = -21. To find the solutions for x, we will use the quadratic formula, which is x = (-b ± √(b2 - 4ac)) / (2a).
Substituting the values of a, b, and c into the quadratic formula, we get:
x = (-(4) ± √((4)2 - 4(1)(-21))) / (2(1))
x = (-4 ± √(16 + 84)) / 2
x = (-4 ± √100) / 2
x = (-4 ± 10) / 2
Which gives us two solutions:
x = (6 / 2) = 3
x = (-14 / 2) = -7
Therefore, the solutions to the quadratic equation x2 + 4x - 21 = 0 are x = 3 and x = -7.
A computer can sort x objects in t seconds, as modeled by the function
below:
t=0.007x2 + 0.003x
How many objects are required to keep the computer busy for exactly 9
seconds?
Round to the nearest whole object.
Answer:
36 objects
Step-by-step explanation:
You want the value of x when t=9, so you're solving ...
9 = 0.007x^2 +0.003x
9 = 0.007(x^2 + 3/7x)
From here, we observe that an approximation is probably sufficient.
9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2
x ≈ 3/√.007 ≈ 35.9 ≈ 36
We can check:
.007(36)(36 3/7) = 9.18
.007(35)(35 3/7) = 8.68
To keep the computer busy for 9 seconds, it needs to sort 36 objects.
Which expression is equivalent to 6(x – 4)?
6x + 4
6x-4
0 6x - 24
6x + 24
Answer:
6x-24
Step-by-step explanation:
6(x-4)=6x-24
Answer:
hi there!
The correct answer is: 6x - 24
Step-by-step explanation:
you distribute 6 into the parenthesis
you first multiply 6 by x and you get 6x
then you multiply 6 by -4 and you get -24
then you combine both to get 6x-24