Answer:
x + 6 = 3
-3 + 6 = 3
Step-by-step explanation:
x + 6 = 3
x + 6 - 6 = 3 - 6
x = -3
A tree is 4 1/2 feet tall. It is expected to grow 1 3/4 feet per year. At this growth rate, how many years will it take for the tree to have a height greater then 40 feet?
Answer:
21 years
Step-by-step explanation:
Given
[tex]Initial\ Height = 4\frac{1}{2}[/tex]
[tex]Final\ Height = 40[/tex]
[tex]Difference = 1\frac{3}{4}[/tex]
Required
Determine the years it'll take to grow to the final height
This question depicts arithmetic progression and will be solved using
[tex]T_n = a + (n - 1)d[/tex]
Where
[tex]T_n = 40[/tex]
[tex]a = 4\frac{1}{2}[/tex]
[tex]d = 1\frac{3}{4}[/tex]
Substitute these values in the given formula;
[tex]40 = 4\frac{1}{2} + (n - 1)1\frac{3}{4}[/tex]
Convert all fractions to decimal
[tex]40 = 4.5 + (n - 1) * 1.75[/tex]
Open Brackets
[tex]40 = 4.5 + 1.75n - 1.75[/tex]
Collect Like Terms
[tex]1.75n = 40 - 4.5 + 1.75[/tex]
[tex]1.75n = 37.25[/tex]
Divide both sides by 1.75
[tex]n = \frac{37.25}{1.75}[/tex]
[tex]n = 21.2857142857[/tex]
[tex]n = 21[/tex] (Approximated)
The number of years it will take for the tree to have a height greater than 40 feet is 23 years
Given:
Height of the tree = 4 1/2 feet
Growth rate per year = 1 3/4 feet
Expected growth rate = 40 feet
Expected Number of years = y
The inequality:
4 1/2 + 1 3/4y > 40
Subtract 4 1/2 from both sides
1 3/4y > 40 - 4 1/2
7/4y > 40 - 9/2
7/4y > (80-9)/ 2
7/4y > 79/2
divide both sides by 7/4
y > 79/2 ÷ 7/4
y > 79/2 × 4/7
y > (79×4) ) (2×7)
y > (316) / 14
y > 22.57142857142857
Approximately,
y > 23 years
Therefore, number of years it will take for the tree to have a height greater than 40 feet is 23 years
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there are five united states athletes, four russian athletes, three french athletes, and one german athlete. How many rankings of the 13 athletes are there
Answer:
There are 6227020800 possible rankings
Step-by-step explanation:
Given
[tex]Athletes= 13[/tex]
Required
Number of Rankings
Let the number of athletes be n;
Since each athlete can only take one position at any given instance, the number of rankings is [tex]n![/tex]
Where [tex]n = 13[/tex]
Substitute 13 for n
[tex]13! = 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 *3 * 2 *1[/tex]
[tex]13! = 6227020800[/tex]
Hence, there are 6227020800 possible rankings
Calculus (2) Master Needed to show steps of evaluating the integral b=0, a= pi/2 :[tex]\int\limits^a_b {(t^2-3t)sint} \, dt[/tex] I get stuck after applying integration by parts and simplified the negative, I get [tex](t^2-3t)*-cost |\frac{\pi /2}{0} + \int\limits^a_b {cost * (t-3)} \, dt[/tex] what am I supposed to do at this stage? Or did I do it wrong? Step by step is needed!
Answer:
[tex]\displaystyle \int\limits^{\pi/2}_ {0} \,(t^2-3t)\sin t\, dt = \pi -5[/tex]
Step-by-step explanation:
We want to evaluate the integral:
[tex]\displaystyle \int\limits^{\pi/2}_ {0} \,(t^2-3t)\sin(t)\, dt[/tex]
Since this is a product of two functions, we can use Integration by Parts. Recall that:
[tex]\displaystyle \int u\, dv = uv - \int v\, du[/tex]
Let u be t² - 3t and let dv be sin(t).
Thus:
[tex]du = 2t - 3\, dt[/tex]
And:
[tex]\displaystyle v = \int \sin t\, dt = - \cos t[/tex]
So:
[tex]\displaystyle =\left(-\cos t\right)\left(t^2-3t\right)\Bigg|_0^{\pi/2}-\int_{0}^{\pi/2} \left(-\cos t\right)\left(2t-3\right)\, dt[/tex]
Simplify:
[tex]\displaystyle = - \left(\cos t\right)(t^2-3t)\Bigg|_{0}^{\pi /2}+\int\limits^{\pi/2}_ {0} \,\cos(t)(2t-3)\, dt[/tex]
We can use IBP once more.
Let u be 2t - 3 and let dv be cos(t). Therefore:
[tex]du = 2\, dt[/tex]
And:
[tex]\displaystyle v = \int \cos t\, dt = \sin t[/tex]
So:
[tex]\displaystyle = - \left(\cos t\right)(t^2-3t)\Bigg|_0^{\pi/2}+\left(\sin(t)(2t-3)\Bigg|_0^{\pi /2}-\int\limits^{\pi/2}_0 \, 2\sin(t)dt \right)[/tex]
Evaluate:
[tex]\displaystyle =-\left(\cos t\right)(t^2-3t)+\sin(t)(2t-3)+2\cos(t)\Bigg|_0^{\pi /2}[/tex]
Evaluate the first section:
[tex]\displaystyle \begin{aligned} &= -\cos\left(\frac{\pi}{2}\right)\left(\left(\frac{\pi}{2}\right)^2-3\left(\frac{\pi}{2}\right)\right)+\sin\left(\frac{\pi}{2}\right)\left(2\left(\frac{\pi}{2}\right)-3\right)+2\cos \left(\frac{\pi}{2}\right)\right) \\ \\ &= (0) + (1)(\pi -3) + (0) \\ \\ &= \pi -3 \end{aligned}[/tex]
And the second:
[tex]\displaystyle \begin{aligned} &= -\cos(0)((0)^2-3(0))+(\sin(0))(2(0)-3)+2\cos(0 ) \\ \\&=(0)+(0)+(2) \\ \\ &= 2\end{aligned}[/tex]
Therefore:
[tex]\displaystyle \int\limits^{\pi/2}_ {0} \,(t^2-3t)\sin(t)\, dt = (\pi -3) -(2) = \pi -5[/tex]
You are riding the bus to school and you realize it is taking longer because of all the stops you are making. The time it takes to get to school, measured in minutes, is modeled
using the function (0) - ** - 3x' . dx - 6, where x is the number of stops the bus makos. If the bus makes 2 stops after you board, how long does it take you to get to
school?
Answer:
7 minutes
Step-by-step explanation:
Ann, Emily, and Bob collect stickers. They have a total of 70 stickers in the ratio 2:3:5, respectively. How many stickers does each child have?
Answer:
The stickers are divided by groups of
2/10, 3/10 and 5/10
2/10 * 70 = 14
3/10 * 70 = 21
5/10 * 70 = 35
14 + 21 + 35 = 70
So, the stickers are allotted to the 3 children in a group of
14 to one child, 21 to another child, and 35 to the third child.
Step-by-step explanation:
A student puts $250 into an account that pays 2% simple interest every year. How much
money in total is in their account after 3 years?
if dm=50 what ia the value of r?
Answer:
r = 15
Step-by-step explanation:
Line segments DG and GM add up to DM:
r + 3 + 4r - 28 = 50
5r - 25 = 50
5r = 75
r = 15
Answer:
15
Step-by-step explanation:
Given:
DG = r + 3GM = 4r - 28DM = 50r = ?Solution:
DM = DG + GMr + 3 + 4r - 28 = 505r - 25 = 505r = 50 + 255r = 75r = 75/5r = 15pls pls help meee Provide the missing reasons for the proof.
Answer:
b. common sides
c. from statement a and b
d. from statement c
f. from statement e
g. by SAS axiom
h. from statement g
Point M is the midpoint of FG. Can the value of variable a be determined? Explain F(b+1, a+2). M(3,5). G(2a, 3b+3)
Answer:
YES, the value of a is 2Step-by-step explanation:
Given the coordinates F(b+1, a+2, M(3,5) and G(2a, 3b+3), if M is the midpoint of F and G then, to get the value of a and b we will use the formula for calculating the midpoint a shown;
M(X, Y) = (x₁+x₂/2, y₁+y₂/2)
X = x₁+x₂/2 and Y = y₁+y₂/2
From the given coordinates x₁ = b+1, y₁ = a+2, x₂ = 2a, y₂ = 3b+3, X = 3 and Y = 5
Substituting the given parameters into the formula, we can get the value of a and b as shown;
3 = b+1+2a/2
6 = 2a+b+1
2a+b = 5 ............... 1
Similarly, for the Y coordinate;
5 = a+2+3b+3/2
10 = a+2+3b+3
a+3b = 10-2-3
a+3b = 5 ........ 2
Solving equation 1 and 2 simulatneously using elimination method
2a+b = 5 ............... 1 * 1
a+3b = 5 ........ 2 * 2
---------------------------------------------------------
2a+b = 5 ...........3
2a +6b = 10.......... 4
subtract 3 from 4
b - 6b = 5-10
-5b = -5
b = -5/-5
b = 1
substitute b =1 into equation 2 to get a;
a + 3b = 5
a + 3(1) = 5
a = 5-3
a = 2
From the calculation above it is seen that the value of variable a can be determined and it is equivalent to 2
Answer:
To determine the value of a, set up and solve a system of equations in two variables. The value of a is 2
Step-by-step explanation:
what is equivalent to 48+12.
Answer:
60
Step-by-step explanation:
x=48+12 Find what x is
x=60 X is 60
2 5 7 Which algebraic expression represents the phrase "two times the quantity of a number minus 12"? 0 2y - 12 0 207-12) O 200 + 12) 0 2y + 12
Answer:
2y - 12
Step-by-step explanation:
1. Two times of a number n is 2n2. Minus 12 is - 123. Together it is 2n - 12Correct answer choice is:
2y - 12A scale drawing of a house shows 9cm
x10cm. If 6cm=12 ft, what are the actual
dimensions?
Answer:
what the answer is b
Step-by-step explanation:
hope this helped
Including a 5% sales tax, an inn charges $160.65 per night. Find the inn's nightly cost before tax is added
Answer:
$80.12
Step-by-step explanation:
Step 1:
$160.65 × 0.5
Answer:
$80.12
Hope This Helps :)
Answer:
160.65*0.05-8.0325
160.65-8.0325=152.6175 so $152.62
Step-by-step explanation:
9. Margie and Glenn are trying to solve the following system of equations.
5x - 4y= 23
7x + 8y = 5
Glenn thinks that the elimination method will not work. Margie is not so sure about that.
With your team, decide whether Glenn is correct and write a few sentences justifying
your conclusion. If the elimination method will work, show how. If not, use another
method to solve the system.
select the decimal that is equivalent to 29/37
Answer:
I googled it and it said that 29/37 as a decimal was 0.783783784
The required equivalent recurring decimal expression to 28/37 is given as [tex]0.\bar7\bar8\bar3[/tex].
An equivalent expression, equivalent to 29/37 is to determine.
Recurring Decimal is defined as also named repeating decimal, is a decimal number that only consists of repeating digits after a certain interval after the decimal. For example, 94.642642642..., 213.569569... etc.
Given fraction,
= 28/37
when dividing 28 by 37 the outcome is
= 0.783783783783.......
The above expression is a recurring decimal it can be transformed as [tex]0.\bar7\bar8\bar3[/tex] where the bars over the number show the repeating digits.
Thus, the required equivalent recurring decimal expression to 28/37 is given as [tex]0.\bar7\bar8\bar3[/tex].
More information about recurring decimal check it out here:
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Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p: n = 195, x = 162; 95% confidence.a. 0.788 < p < 0.873.
b. 0.789 < p < 0.873.
c. 0.778 < p < 0.883.
d. 0.777 < p < 0.884.
Answer:
c. 0.778 < p < 0.883.
Step-by-step explanation:
The formula for confidence interval for proportion =
p ± z score × √p(1 - p)/n
p = x/n
n = 195, x = 162
z score for 95% confidence Interval = 1.96
p = 162/195
p = 0.8307692308
p ≈ approximately equal to = 0.8308
0.8308 ± 1.96 × √0.8308 × (1 - 0.8308)/195
0.8308 ± 1.96 ×√0.8308 × 0.1692/195
0.8308 ± 1.96 × √0.0007208788
0.8308 ± 1.96 × 0.0268491862
0.8308 ± 0.052624405
Confidence Interval
= 0.8308 - 0.052624405
= 0.778175595
Approximately = 0.778
= 0.8308 + 0.052624405
= 0.883424405
Approximately = p
0.883
Therefore, the confidence interval for this proportion = (0.778, 0.883) or option c. 0.778 < p < 0.883
I NEED HELP FAST
Hawaiian monk seals dives to a dept of -4.13 meters. By how many meters does it need to change his position to get back to sea level?
Answer:
45
Step-by-step explanation:
What numbers is 90 divisble by
90 tiene 12 divisores:
1; 2; 3; 5; 6; 9; 10; 15; 18; 30; 45; 90
[tex]\framebox{\parbox[t][1.0cm]{4.50cm}{\addvspace{0.2cm} \centering $ \;\; 10\, \;\ \\ $ } }\\[/tex]
Step-by-step explanation:
What numbers are divisible by 90?
For this question, there are more than 1 answer. I am doing the number 10 because it is easier.
I have attached an image. You will have to turn the image because it was taken from mobile.
Hope this helps!
a number is multiplied by 8 and that product is added to 2. The sum is equal to the product of 2 and 25 . Find the number
Answer:
6
Step-by-step explanation:
So we have a number (let's call it x) and it was multiplied by 8 and added by 2. Therefore:
[tex]8x+2[/tex]
And we are told that the sum is equal to the product of 2 and 25 (or 50). Thus:
[tex]8x+2=50[/tex]
To find the number, we just need to find x. Thus, subtract 2 from both sides:
[tex]8x=48[/tex]
Divide both sides by 8:
[tex]x=6[/tex]
And we're done!
So, our original number was 6.
answer the following please answer! i'll mark brainliest!
Answer:
0.2x+1???
Step-by-step explanation:
2x/3x+1=-3
-3=2x/3x+1
-3 x 3x + 1
-9x + 1
2x/-9x+1
0.2x+1
henry begins to drain a water tank by opening a valve. Then he opens another valve. Then he closes the first valve. He leaves the 2nd valve open until the tank is empty. Discrete or Continuous?
Answer:
Continuous
Step-by-step explanation:
There is never a period of time when the water's flowing halts because the opening and closing of the first and second pipe are overlapping. Hope this helps (:
what decimal or fraction goes in the box
Answer:
Your answer would be 7.
Step-by-step explanation:
Hope I helped!!!
help me, i will give a lot of points for this
solve the question x/-4 = 3/4 so 'x' is equal to?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 3 }}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ \frac{x}{ - 4} = \frac{3}{4} }[/tex]
Do cross multiplication
[tex] \dashrightarrow{ \sf{x \times 4 = 3 \times ( - 4)}}[/tex]
[tex] \dashrightarrow{ \sf{4x = - 12}}[/tex] ( Multiplying a positive integer and negative integer gives a negative integer )
Divide both sides of the equation by 4
[tex] \dashrightarrow{ \sf{ \frac{4x}{4} = \frac{ - 12}{4} }}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{x = - 3}}[/tex]
Hope I helped!
Best regards! :D
12,333 to the nearest hundred
Answer: 12,300
Step-by-step explanation: So you first locate the hinders a place. Then you look at the numbers behind it. If it is less than under 49 then you keep it at the hundred unit that it is at. In this case 300. That’s how you get it! Sorry I’m bad at explaining.
y=x ^2+3 A) translate 3 units right B) translate 3 units right C) translate 3 units up D) translate 3 units down
Answer:
translate 3 units up
In Yakuna it was -13 degrees in the morning. The highest tempature was 29. Was was the total number the temp. increased
Answer:
42 degrees
Step-by-step explanation:
Use a number line.
-13 - 13 = 0.
Now, we are at the base, 0. Then, add 29.
13 + 29 + 42.
The answer is 42. Hope it helps!
2) Paul has two and two-thirds pounds of peanuts and a quarter of a pound of cashews . How many more pounds of cashews does he have
Answer:
Step-by-step explanation:
2 2/3
Combine these radicals.
– бу 100 +36
оооо
о – бу 136
0 – 616
What the answer!
Answer:
Answer. 5.0/5. 6.
Step-by-step explanation:
I am not doing step by step you should know this
Robert came in first for threefourths_large of his races. Express this fraction as a decimal. (1 point) 0.75 0.7 7.5 1.33
Answer:0.75 just divide us top number by bottom ez
Step-by-step explanation: