Steps to solve:
f(x) = 3x+5/x; x = 2
~Substitute
f(2) = 3(2)+5/2
~Simplify
f(2) = 6+5/2
~Add
f(2) = 11/2
~Simplify
f(2) = 5.5
Best of Luck!
An open-top box is to be made from a 70-centimeter by 96-centimeter piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume? Enter the area of the square and do not include any units in your answer. Enter an improper fraction if necessary.
Answer:
[tex]177 \frac{7}{9} cm^2[/tex]
Step-by-step explanation:
Length of the Plastic Sheet= 96cm
Width of the plastic Sheet =70cm
If a square of side x is cut from each corner of the plastic sheet to form the box.
Length of the box=96-2x
Width of the box=70-2x
Height of the box =x
Volume of the box = LWH
Volume=(96-2x)(70-2x)x
The maximum volume of the box is obtained at the point where the derivative is zero.
[tex]V=(96-2x)(70-2x)x\\V^{'}=4(x-42)(3x-40)[/tex]
Setting the derivative to 0.
[tex]4(x-42)(3x-40)=0\\x-42=0\: 3x-40=0\\x=42\:or\: x=\frac{40}{3}[/tex]
Since we are looking for the minimum value of x,
[tex]x=\frac{40}{3}\\\text{Area of the Square} = x^2\\=\frac{40}{3} X \frac{40}{3}\\=177 \frac{7}{9} cm^2[/tex]
Gabe is twenty years older than his children. Laura is forty years older than her grandchildren. All members ages add to 290. Write an equation that would represent this scenario.
Answer:
290=(20+c)+(40+g)
Step-by-step explanation:
c=Gabe's children's age
g=Laura's grandchildren's age
all add up to 290
"A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 90 miles. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train."
The rate of the passenger train is 100 miles per hour.
Given:
1. The passenger train traveled 100 miles in the same amount of time it took the freight train to travel 90 miles.
2. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train.
We can set up equations based on the distances traveled and the rates:
1. For the passenger train:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\[ 100 = r_p \times \text{Time} \]2. For the freight train:\[ 90 = r_f \times \text{Time} \]Since we know that the rate of the freight train (\( r_f \)) is 10 miles per hour slower than the rate of the passenger train (\( r_p \)), we can express \( r_f \) in terms of \( r_p \):\[ r_f = r_p - 10 \][/tex]
Now, we need to find the time it took for both trains to travel their respective distances. Since the time is the same for both trains, we can equate the expressions for time:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]For both trains, time is the same, so:\[ \frac{100}{r_p} = \frac{90}{r_f} \]Substitute \( r_f = r_p - 10 \):\[ \frac{100}{r_p} = \frac{90}{r_p - 10} \]Now, let's solve for \( r_p \):\[ 100(r_p - 10) = 90r_p \]\[ 100r_p - 1000 = 90r_p \]\[ 10r_p = 1000 \]\[ r_p = \frac{1000}{10} \]\[ r_p = 100 \][/tex]
So, the rate of the passenger train is 100 miles per hour.
What is the value of f(12)-f(8) when f(x)=3x+9
Answer:
12
Step-by-step explanation:
f(x)=3x+9
f(12) = 3*12 +9
36+9
45
f(8) = 3*8+9
=24+9
= 33
f(12) - f(8) = 45-33
12
Mrs. Benton selects one student's work to display on a bulletin board each week. Each student's name is placed in a bag from which Mrs. Benton draws a name. What is the probability that an eighth grade student will NOT be selected? A) 3 /10 B) 2/ 5 C) 1 /2 D) 2/ 3
Answer:
1/2
Step-by-step explanation:
can you solve this equation?
Answer:
x=31
Step-by-step explanation:
(x-31)/4=0
multiply each side by 4 so that you have x-31=0.
x-31=0
add 31 to each side.
x=31
Answer:
No, unless you set it equal to zero.
Step-by-step explanation:
(x-31)/4=0
((x-31)/4) times 4 = 0 times 4
x-31=0
x-31 +31 =0 + 31
x=31
F (x) = 5x-10 determine x when f (x) = 15
Answer: 5=x
Step-by-step explanation:
Ok, so if F(x)=15, then the equation would look like this: [tex]15=5x-10[/tex]
The next step would be to add the 10 over from the right to the left side to get [tex]25=5x[/tex]
Now divide both sides by 5 to get the answer.
A newborn child receives a $20,000 gift toward college education from her grandparents. How much will the 20,000 be worth in 17 years if it is invested at 7% and compounded quarterly?
Answer:
The amount the $20.000 will be worth in 17 years at compound interest is $65068.443
Step-by-step explanation:
Here we have the Principal, P = $20,000.00
The annual interest rate, r = 7% = 0.07
Time , t = 17 years
Number of compounding period per year, m = quarterly = 4
The compound interest can be found from the following formula;
[tex]Amount, \ A = P \left (1 + \frac{1}{r} \right )^{mt}[/tex]
Therefore, by plugging the values of the equation parameters, we have;
[tex]Amount, \ A = 20000 \left (1 + \frac{0.07}{4} \right )^{4 \times 17} = \$ 65068.443[/tex]
Therefore, the amount the $20.000 will be worth in 17 years at compound interest = $65068.443.
So, the amount of $20,000 be worth in 17 years if it is invested at 7% and compounded quarterly is $65068.443 and this can be determined by using the compound interest formula.
Given :
A newborn child receives a $20,000 gift toward college education from her grandparents.
The formula of compound interest is given by:
[tex]\rm A= P(1+\dfrac{r}{n})^{nt}[/tex]
where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest applied per time period and t is the number of periods elapsed.
Substitute the known terms in the above formula:
[tex]\rm A = 20000(1+\dfrac{0.07}{4})^{4\times 17}[/tex]
[tex]\rm A = 20000(1.0175)^{68}[/tex]
A = $65068.443
So, the amount of $20,000 be worth in 17 years if it is invested at 7% and compounded quarterly is $65068.443.
For more information, refer to the link given below:
https://brainly.com/question/22803385
PLEASE HURRY I'M TAKING A TEST 20 PTS
Simplify the expression (in the picture)
Answer:
D
Step-by-step explanation:
2 ( x − 3 )
x ( x + 1 )
Answer:
ANSWER IS D
Step-by-step explanation:
help me please for brainliest!
Answer:
1)option b
2)option a
Step-by-step explanation:
1) circumference = 62.8 in
=> 2πr= 62.8
=> r= 62.8/(2×3.14)= 10 in
diameter = 2×10 in = 20 in
2)diameter = 14m
radius = 7 m
Area of the circle= πr² =3.14(7)²=3.14×49
= 153.86
=153.9 m²
Answer:
Q1) B
Q2) A
Step-by-step explanation:
Q1) The equation for working out the circumference of a circle is 2 × π × r or π × d, but here we are asked to do the reverse so,
π × d = 62.8
d = 62.8 ÷ π
d = 19.9
So the answer to the Q1) is 20 inches
Q2) We have to work out the area of the circle so we utilise the formula
π × r² . We only have the diameter but we can half it to find the radius so
14 ÷ 2 = 7. So 7 is the radius, now we substitute into the formula π × r²
3.14 × 7² = 153.86
Element X decays radioactively with a half life of 11 minutes. If there are 870 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 154 grams?
Answer:
It would take 27.5 minutes the element to decay to 154 grams.
Step-by-step explanation:
The decay equation:
[tex]\frac {dN}{dt}\propto -N[/tex]
[tex]\Rightarrow \R\frac {dN}{dt}=-\lambda N[/tex]
[tex]\Rightarrow \frac {dN}N=-\lambda dt[/tex]
Integrating both sides
[tex]\Rightarrow \int \frac {dN}N=\int-\lambda dt[/tex]
[tex]\Rightarrow ln|N|=-\lambda t+c[/tex]
When t=0, N=[tex]N_0[/tex] = initial amount
[tex]ln|N_0|=-\lambda .0+c[/tex]
[tex]\Rightarrow c=ln|N_0|[/tex]
[tex]ln|N|=-\lambda t+ln|N_0|[/tex]
[tex]\Rightarrow ln|N|-ln|N_0|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{N}{N_0}|=-\lambda t[/tex]
Decay equation:
[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]
Given that, the half life of of element X is 11 minutes.
For half life, [tex]N=\frac12 N_0[/tex], t= 11 min.
[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{\frac12N_0}{N_0}|=-\lambda . 11[/tex]
[tex]\Rightarrow ln|\frac12}|=-\lambda . 11[/tex]
[tex]\Rightarrow -\lambda . 11=ln|\frac12}|[/tex]
[tex]\Rightarrow \lambda =\frac{ln|\frac12|}{-11}[/tex]
[tex]\Rightarrow \lambda =\frac{ln|2|}{11}[/tex] [ [tex]ln|\frac12|=ln|1|-ln|2|=-ln|2|[/tex] , since ln|1|=0]
N=154 grams, [tex]N_0[/tex] = 870 grams, t=?
[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]
[tex]\Rightarrow ln|\frac{154}{870}|=-\frac{ln|2|}{11}.t[/tex]
[tex]\Rightarrow t= \frac{ln|\frac{154}{870}|\times 11}{-ln|2|}[/tex]
=27.5 minutes
It would take 27.5 minutes the element to decay to 154 grams.
Answer:
60.6 minutes
Step-by-step explanation:
--------------------------------
Round to 2 SF
646.42
plz
Answer:
650
Step-by-step explanation:
2sf= the first two figures
so you count to the first two sf numbers so in this case
it would be 64 then you look at the next one. But if it is 4 or below you round or if it is 5 and above you rounded up
in this case the third digit is a 6 so you would round up to 5
answer =650
The number 646.42 can be rounded to two significant figures by increasing the second significant figure up by one because the third figure is 6 which is greater than 5. Therefore, 646.42 becomes 650.
Explanation:You are requesting to round the number 646.42 to two significant figures (SF). Significant figures are the meaningful digits in a number. For example, in 646.42, there are five significant figures: 6, 4, 6, 4, 2.
To round to two significant figures, we look at the number in the third position, which is another 6. If this number is 5 or greater, we round the second significant figure up. If it is less than 5, we keep the second figure the same. Here, the next number after the two significant figure (6 and 4) is 6, which is more than 5, so you will round 4 up to 5.
Thus, rounded to two significant figures, 646.42 becomes 650.
Learn more about Rounding Numbers here:https://brainly.com/question/19166897
#SPJ3
round to the nears ten 9.42?
Answer:
9
Step-by-step explanation:
In order to round to the nearest ten you must think: what is the nearest multiple of 10. For example, to round 68 to the nearest 10, the nearest whole number is 70, so the answer would be 70. However if you were to round 63 to the nearest 10, to would be 50 since that is the nearest multiple of 10
Answer:9
Step-by-step explanation:
Since the next number is below five you don’t round up it just stays the same
Choose the linear function below that does not have the same y-intercept as the other functions.
Answer:
The answer is a
Step-by-step explanation:
On a coordinate plane, a line goes through points (negative 1, negative 2) and (0, 1).
The linear function that does not have the same y-intercept as the other functions is: Option A
How to find the y-intercept?
The general form of the equation of a Line in slope intercept form is expressed as:
y = mx + c
where:
m is slope
c is y-intercept
1) In this graph, the y-intercept which is where the line crosses the y-axis is: y = 1
2) The y-intercept in the equation y = -8x + 3 is:
y = 3
3) The y-intercept here will be:
y = 3
4) The y-intercept in the equation y = 2x + 3 is:
y = 3
what is 3y takeaway y
Answer:
y = 1/3
Step-by-step explanation:
Nicole shines a light from a window of a lighthouse on a cliff 250 feet above the water level. Nick 10 feet above the water level in a ship off shore, finds that the angle of elevation of the light is 3°. Find the length of the line of sight (light beam) from the ship to Nicole.
We want to find the length of the light beam from the ship to Nicole.
We will see that the solution is 4,585.76 ft.
We can think of this situation as in a right triangle. The adjacent cathetus is the distance between the lighthouse and the ship. The opposite cathetus is the difference in height between Nicole's position and Nick´s position, it is equal to:
250ft - 10ft = 240ft
And the elevation angle is equal to 3°. So we know the angle and the opposite cathetus to this angle, and we want to find the hypotenuse, which is the length of the light beam.
Then we can use the relation:
Sin(θ) = (opposite cathetus)/(hypotenuse)
Solving it for the hypotenuse we get:
hypotenuse = (opposite cathetus)/sin(θ)
Replacing by the values that we know, we get:
hypotenuse = 240ft/sin(3°) = 4,585.76 ft
The length of the line of sight is 4,585.76 ft
If you want to learn more, you can read:
https://brainly.com/question/15345177
To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We are given the angle of elevation of the light, the height of the cliff, and need to calculate the length of the line of sight.
Explanation:To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We have a right triangle formed by the line of sight, the height of the cliff, and the distance from the ship to Nicole. We are given the angle of elevation of the light as 3° and the height of the cliff as 250 feet. Let's denote the length of the line of sight as x and the distance from the ship to Nicole as d. Using the tangent function, we can write:
tan(3°) = 250 / d
Simplifying this equation, we have:
d = 250 / tan(3°)
Now we can substitute the value of tangent of 3° and solve for d. Using a calculator, we find that:
d ~ 8424.78 feet
So, the length of the line of sight from the ship to Nicole is approximately 8424.78 feet.
Learn more about Trigonometry here:https://brainly.com/question/11016599
#SPJ3
Circle A and circle B are similar. A. What is the similarity ratio of circle A to circle B? B. What is the circumference of each circle? Leave answers in terms of . C. What is the ratio of the Circumference of circle B to the Circumference of circle A? Simplify your ratio.
Answer: A) 5/2
B) 10pi for A and 4pi for B
C) 5/2
Step-by-step explanation:
Please find the attached file for the solution
Which correctly uses bar notation to represent the repeating decimal for StartFraction 6 Over 11 EndFraction 0.5ModifyingAbove 4 with bar 0.54ModifyingAbove 54 with bar 0.ModifyingAbove 54 with bar 0.ModifyingAbove 545 with bar
Answer:
Option C is your Correct AnswerStep-by-step explanation:
Answer:
c .54 w/ bar
Step-by-step explanation:
You measure 50 textbooks' weights, and find they have a mean weight of 52 ounces. Assume the population standard deviation is 14.6 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
The 90% confidence interval = 48.603 < μ < 55.397
Explanation:
Given:
Mean = 52
Standard deviation = 14.6
Sample size, n = 50
Confidence Interval, c = 90%
c = 0.9
Significance level, α = 1 - c
= 1 - 0.9
= 0.1
Critical value, z(α/2) = z(0.05) = 1.645
Critical value = ± 1.645
Margin of error, E = [tex]z(\alpha /2) X \frac{SD}{\sqrt{n} }[/tex]
[tex]=1.645 X\frac{14.6}{\sqrt{50} } \\\\= 3.3965[/tex]
Limits of 90% confidence interval are given by:
Lower limit = μ - E
= 52 - 3.397
= 48.603
Upper limit = μ + E
= 52 + 3.397
= 55.397
Thus, 90% confidence interval = 48.603 < μ < 55.397
From an upstairs window, I can see my neighbor’s fence. The angle of depression is 7 degrees. If my window is 15 ft off the ground, how far is my neighbor’s fence from my house?
Answer:
1.84ft
Step-by-step explanation:
From the figure attached,
AB = Height of the window = 15ft
Let the distance between the base of the housr and the fence 'C' = xft
If the angle of depression = 7°
Then angle of elevation of the top of the fence from the house = 7°
Now from right triangle ABC,
tan7° = x/15
x = tan7°×15
x = 0.1227×15
x = 1.84ft
Therefore, distance of the house from the fence is 1.84ft
PLEASE hurry !!!!!! y = 24x^2-14x+5
Answer:
(0.3,3)
Step-by-step explanation:
That is the vertex.
Witch expression has a product of 32.76?
Answer:
20.00+12.76 would give you that sum
Step-by-step explanation:
Answer:
0.00+12.76 would give you that sum
Step-by-step explanation:
Pls BRAINLIEST
if 3n is an odd number, which of the following is an even number?
(a) 3n-1
(b) 3n+2
(c) 3n-2
(d) 3n +2n
Answer:
Option (a).
Step-by-step explanation:
It is given that 3n is an odd number.
We need to find an even number from the given options.
Even numbers: Which are divisible by 2.
Odd numbers: Which are not divisible by 2.
We need know that the numbers are alternatively even and odd.
If we add or subtract 1 from an odd number, we always get an even number.
If we add or subtract 2 from an odd number, we always get an odd number.
3n is an odd number. So,
3n-1 is an odd number.
3n+2 is an even number.
3n+2 is an even number.
3n+2n is an even number because 2n is an even number and sum of two even numbers in always an even number.
Therefore, the correct option is (a).
18
Which transformation shows a reflection of ADEF?
Answer: B
Step-by-step explanation:
The reflection transformation in the second figure shows the correct reflection.
What are the types of translations?There are three types of translations -
reflectionrotationdilationGiven is a triangle ΔDEF.
It is asked to find the possible reflection of the triangle ΔDEF. After the reflection, the lines D'E' will be parallel and will be in the same orientation. So, we can see that the correct orientation is maintained only in the second transformation. So, the reflection transformation in the second figure shows the correct reflection.Therefore, the reflection transformation in the second figure shows the correct reflection.
To solve more questions on graph rotation, visit the link below-
https://brainly.com/question/19527326
#SPJ7
For what values of theta (0 less than or equal to theta less than or equal to 2pi) do maximum r values occur on the graph the polar equation r=4+3 sin3theta? Note that the maximum r-value occurs at a point that is the maximum distance from the pole.
Answer:
Step-by-step explanation:
To find the values of the angle which makes maximum r you use the derivative of r
[tex]\frac{dr}{d\theta}=\frac{1}{3}sin(3\theta)[/tex]
If you equals this derivative to zero you obtain the value of the angle:
[tex]\frac{dr}{d\theta}=0\\\\cos3\theta=0\\\\3\theta=\frac{\pi}{2}\\\\\theta=\frac{\pi}{6}[/tex]
However, the values of 5π/6 and 9π/6 are also available, because makes the sinusoidal function equal to 1.
hence, the answer is:
[tex]\theta_1=\frac{\pi}{6} \\\\\theta_2=\frac{5\pi}{6}\\\\\theta_3=\frac{9\pi}{6}=\frac{3\pi}{2}[/tex]
answer b
The maximum values of r for the polar equation r=4+3 sin 3θ occur at the angles where sin 3θ = 1, within the range of 0 to 2π. Solving the equation 3θ = nπ/2 for odd integers n gives the values of θ where r is maximum, which must be checked against the range [0, 2π].
Explanation:We can find the maximum values of r for the polar equation r=4+3 sin 3θ by looking for the values of θ that give the maximum value for the sinusoidal function sin 3θ.
Since we know that the sine function reaches its maximum value of 1, we can find the values of θ that satisfy the condition sin 3θ = 1 within the given range of θ from 0 to 2π.
Thus, the equation becomes r = 4 + 3(1), which simplifies to r = 7.
Now, we seek to solve 3θ = nπ/2 where n is an odd integer since the sine function is maximum at π/2, 3π/2, 5π/2, and so on. Therefore, we obtain θ values of π/6, π/2, 5π/6, etc., until we reach the limit of 2π.
We must also consider the range of the function which brings us to the fact that θ must lie within [0, 2π].
Thus, we have to evaluate this for values such as θ = π/6, 5π/6, 3π/2, and so on, checking which of these are within the specified range and hence can be considered valid solutions where maximum r values occur.
PLEASEEEEEW ANSWERRRRRRRRR QUICKKKKKMM
Answer:
multiply all the numbers
Step-by-step explanation:
6g=48 g=? Please hell
Answer:
g = 8
Step-by-step explanation:
We're going to isolate g to find out what it equals, so we have to divide both sides by 6.
6g=48
__ __
6 6
g = 8
The solution to the equation 6g = 48 is g = 8.
How to evaluate and solve the given equation?In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical equation:
6g = 48
By dividing both sides of the equation by 6, we have:
g = 48/6
g = 8
Read more on expression here: brainly.com/question/16729936
#SPJ6
What is the simplified form of 3.1 - 5.8n - 4n + 8?
Answer:
-9.8n + 11.1
Step-by-step explanation:
1. Combine like terms
-5.8n - 4n = -9.8n
3.1 + 8 = 11.1
2. -9.8n +11.1
Answer:
-9.8n+11.1
Step-by-step explanation:
You have to add all like terms. That means that -5.8n and -4n have to be added together along with 3.1 and 8. That gets you -9.8n+11.1.
3. There are 350 people in an office building. A local deli randomly surveyed people in the building to determine the average amount spent on lunch each week. Two samples are shown.
Sample 1: {$30, $25, $10, $25, $10} and Sample 2: {$5, $60, $10, $30, $50}
(a) Calculate the mean and the median of each sample.
(b) Which sample has the least spread among its data values? Which sample has the least deviations from the mean among its values?
(c) A third sample was obtained: {$30, $25, $20, $20, $25}. Which data set in Part (a) has measures of center that align more closely with the mean and the median of the new sample? Based on the three samples, which sample is least representative of the population?
Answer:
(a)Sample 1
The Mean = 20
The median = 25
Sample 2
The Mean = 31
The median = 60
(b) Sample 1 has the least spread
Sample 1 has the least deviations from the mean
(c) Sample 1 align with the third sample
The least representative of the population is sample 1
Step-by-step explanation:
The mean is ∑fx/∑f
∑fx = 30 + 25 + 10 + 25 + 10 = 100
∑f = 5
Mean = 100/5 = 20
For the median, we arrange the data in increasing order;
10, 10, 25, 25, 30
The median = the middle number = 25
Sample 2
The mean is ∑fx/∑f
∑fx = 5 + 60 + 10 + 30 + 50 = 155
∑f = 5
Mean = 155/5 = 31
For the median, we arrange the data in increasing order;
5, 10, 30, 50, 60
The median = the middle number = 30
(b) Sample 1 range =$30 -$10 = $20
Sample 2 range =$65 -$5 = $60
Sample 1 has the least spread
Sample 1 standard deviation = 9.354
Sample 2 standard deviation =24.083
Sample 1 has the least deviations from the mean
(c) $30, $25, $20, $20, $25
Mean = 24
$20, $20, $25, $25, $30
Median = $25
∑fx = 120
Therefore sample 1 align with the third sample
The least representative of the population is sample 1 with ∑fx = 100.
If 32 units represent $2,080, find the value of 6 units.
To find the value of 6 units when 32 units are worth $2,080, calculate the per unit value by dividing $2,080 by 32 to get $65 per unit, then multiply by 6 to obtain the value of 6 units, which is $390.
Explanation:The question asks to find the value of 6 units given that 32 units represent $2,080. To solve this, we first find the value of one unit by dividing the total amount of money by the number of units. So, $2,080 divided by 32 units gives us the value per unit.
Next, we multiply the value of one unit by the number of units we want to find the value for, which is 6 units. This will give us the value for 6 units. Let's go through the steps:
Calculate the value of one unit: $2,080 ÷ 32 units = $65 per unit.Find the value of 6 units: $65 per unit × 6 units = $390.Therefore, the value of 6 units is $390.