Pull out a factor of 1/n from the summand and the result follows.
[tex]\displaystyle \lim_{n\to\infty} \sum_{i=1}^n \frac{i^4}{n^5} = \lim_{n\to\infty} \frac1n \sum_{i=1}^n \left(\frac in\right)^4 = \boxed{\int_0^1 x^4 \, dx}[/tex]
PLEASE HELP ILL MARK BRAINEST!! WHAT IS THE RISE, RUN, AND F(X).
Answer:
First question (on left) f(x) = 5x-3. second question (on right) f)x) = 1/2*x
Step-by-step explanation:
rise(left) 4. run (left) 20.
rise(right) 8. run(right) 4.
What is the height of a cylinder if the diagonal is 13 inches and the radius is 5 inches?
Answer:
12 inches.
Step-by-step explanation:
You have to use the pythagorean formula. The measurements you stated form a right angle. Therefore, a^2 + b^2 = c^2. In this equation, we know c=13, and b=5. So therefore c^2 - b^2 = 144. We have to solve for a, so square root 144 to get 12.
Answer:12 in
Step-by-step explanation:
what is the rate of change of the linear function that has a graph that passes through the points (-5, -2) and (-2, 6)
The rate of change of the linear function whose graph passes through points (-5, -2) and (-2, 6) is: 2.7.
What is the Rate of Change of a Linear Function?The rate of change of a linear function is given as change in y over change in x.
Given the points:
(-5, -2) and (-2, 6)
Change in y = 6 -(-2) = 8 units
Change in x = -2 -(-5) = 3 units
Rate of change = 8/3 = 2.7.
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50 points!!! Which equation is represented on the graph?
Answer:
I think the answer is b ill look into it a Lil more
Write the phrase as an expression.
a number t cubed
Answer:
[tex]t^{3}[/tex]
Step-by-step explanation:
cubed means to the power of 3
Given that sin0 =, 8/17what is cos 0?
Enter your answer, as a simplified fraction, in the boxes.
cos 0=
Answer:
Cos 0 = 15/17
Step-by-step explanation:
.................................................
How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)
Answer:
Make use of the fact that as long as [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex]:
[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex].
[tex]\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}[/tex].
[tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].
Step-by-step explanation:
Assume that [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex].
Make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] and [tex]\csc(\theta) = (1) / (\sin(\theta))[/tex] to rewrite the given expression as a combination of [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex].
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}[/tex].
Since [tex]\cos(\theta) \ne 0[/tex]:
[tex]\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}[/tex].
Substitute this equality into the expression:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].
By the Pythagorean identity, [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex]. Rearrange this identity to obtain:
[tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex].
Substitute this equality into the expression:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].
Again, make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] to obtain the desired result:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}[/tex].
−5 2/3 − 1/6 = i need more letters
Answer:
-5 5/6
Step-by-step explanation:
convert 2/3 into 4/6 and when u subtract a positive from a negative u add it instead
8.
Consider a function which takes certain values, as shown in the table below.
--
x | -2 | 0 | 3 | 8 |
y | 10 | 6 | 0 | -10 |
Find the average rate of change between x = -2 and x = 0
Step-by-step explanation:
i just answered this.
the average change rate is the change of the functional result in a given interval relative (= divided by) to the length of the interval of the input variable.
in short
( f (interval upper limit) - f (interval lower limit) ) /
(interval upper limit) - (interval lower limit)
upper limit = 0
lower limit = -2
the functional values (y) are 6 and 10 at these points.
so, we get
(6 - 10) / (0 - -2) = -4 / 2 = -2
Giving Brainlist Please Help!!! A classmate incorrectly calculated the area of the parallelogram as 48 ft2. What is the correct area?
Answer:
D. 60 ft²
Step-by-step explanation:
Area formula :
base x heightSolving :
10 ft x 6 ft60 ft²Answer:
D. 60 ft2
Step-by-step explanation:
Area of a parrelleogram:
bxh
base x hieght
The base is 10ft, the height is 6 ft
(it cannot be 8ft because that line is slanted)
10x6=60ft2
Solve for d -6 = d/3
21
-21
18
-18
Amina and her mother are buying green coffee beans to make qahwa, an Arabic
coffee recipe. Green coffee beans cost $0.58 for each ounce. Amina and her
mother buy 12.5 ounces of green coffee beans. What is the total cost of the green
coffee beans?
Answer:
$36.3
Step-by-step explanation:
The total cost of the Green coffee beans is $7.25.
What is Total Cost?Total cost (TC) is the minimum cost of producing some quantity of output. This is the total economic cost of production and is made up of variable cost, which varies according to the quantity of a good produced and includes inputs such as labor and raw materials, plus fixed cost.
Here, Green coffee beans cost $0.58 for each ounce.
Amina and her mother buy 12.5 ounces of green coffee beans
Total cost = cost each ounce X Number of ounces
TC = 12.5 X 0.58
TC = $ 7.25
Thus, the total cost of the Green coffee beans is $7.25.
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You decide to buy a tablet for college. The tablet you want is currently on sale for 29% off the original price. If the original price was $899, what is the current price? Round your answer to the nearest cent (2 decimal places).
Answer:
638.29
Step-by-step explanation:
This is the answer because 29 percent of 899 is somewhere around 260.71
Substract that and you get 638.29
Passengers, who are travelling in a car west along a road that runs east-west, see a mountain 9 km away on a bearing of 290°. When they have travelled a further 5 km west along the road, what will be the distance to the mountain?
Please help need done by the next hour! Will mark Brainliest
Answer:
you did not even show the answer
Step-by-step explanation:
you have to post it lol;)
In the rectangular prism shown above, the distance between any two neighboring points on a line segment is the same. For example, the distance between points 1 and 2 is the same as the distance between points 13 and 20, which is the same as the distance between points 15 and 16. Place the cross sections indicated by the tiles in order from least area to greatest area.
A rectangular prism is a shape that has six faces which are rectangular.
What is a rectangular prism?Your information is incomplete as the diagram of the rectangular prism isn't given. Therefore, an overview will be given.
It should be noted that a rectangular prism simply means a three dimensional sold shape that has six faces that are rectangles.
The formula that's used to calculate the volume of a rectangular prism will be:
= Length × Width × Height
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Type the correct answer in the box. use numerals instead of words. a population of beetles increases by 5% every year. if at the start of the year the population is at 10,000 beetles, what will its population be after three years? at the end of the third year the population of beetles will be .
At the end of the third year the population of beetles will be 11,576beetles
Exponential equationsThe standard form of an exponential function is given as:
y = ab^t
Given the following parameters
initial population 'a" = 10,000 beetles
Time = 3 years
rate b = 1.05
Substitute into the formula
y = 10,000(1.05)^3
y = 10,000(1.1576)
y = 11,576 beetles
Hence at the end of the third year the population of beetles will be 11,576beetles
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Drag each expression to its equivalent.
Answer:
x-3+2x+3+2x = 5x
x+8+4x-3x-4 = 2x+4
4x+x-11-5X+25+4x = 4x+14
3x+5-2x-5x+9+8x = 4x+14
5+9x-7-4X-3x+6 = 2x+4
6x-9-5x+4-x+5x+5 = 5x
Step-by-step explanation:
Simplified by adding like terms
(100 points + brainliest)
A box of chocolates contains five milk chocolates, three dark chocolates, and 8 white chocolates. You randomly select and eat three chocolates. The first piece is milk chocolate, the second is dark chocolate, and the third is white chocolate.
What is the probability that this event happens? Show all of your steps used to solve this problem.
Answer:
3.6%
Step-by-step explanation:
This is an example of dependent events. When events are dependent, you have to multiply the probability of each event that happens after each other. Probability is desired outcome over all possible outcomes. For the milk chocolate, there are 5 pieces we can pick out of 16, so it's 5/16. Next, the probability of dark chocolate is 3/15 (There is one less piece of chocolate overall now). For the white chocolate, the possibility is 8/14. So now we have to multiply:
5*3*8 120 1
______ = _____ = ___ = (about) 0.036
16*15*14 3360 28
So, that's 3.6%
Hope this helps!
Travis is cutting strips of paper for a project. He needs strips that are 114 inches wide. He cut his first strip too wide. His percent error was 10%. How wide did Travis cut the strip of paper? Enter your answer as a mixed number in simplest form in the box.
Travis cuts 125 whole 2/5 inches wide strip if the percent of error was 10% the actual length of the strips he needs to cut was 114 inches
What is the percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
We have:
The length Travis needs to cut = 114 inches
Percent of error = 10%
Let's assume he cuts x inches wide strip
So from the percent of error formula:
[tex]\rm \dfrac{x-114}{114} = \dfrac{10}{100}[/tex]
[tex]\rm x = \dfrac{114}{10}+114[/tex]
[tex]\rm x = \dfrac{1254}{10}\Rightarrow \dfrac {627}{5}[/tex] or
[tex]\rm x = 125\dfrac{2}{5} \ inches[/tex]
Thus, Travis cuts 125 whole 2/5 inches wide strip if the percent of error was 10% the actual length of the strips he needs to cut was 114 inches
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Answer:
it’s 1 3/8 I don’t know what dude it’s talking about
Step-by-step explanation:
1. As shown in the diagram below, the radius of a cone is 2.5 cm and its
slant height is 6.5 cm. How many cubic centimeters are in the volume of
the cone?
6.5
The number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³
Calculating the volume of a coneFrom the question, we are to determine the volume of the cone
The volume of a cone can be calculated by using the formula,
[tex]V = \frac{1}{3} \pi r^{2} h[/tex]
Where V is the volume
r is the radius
and h is the height
From the given information,
radius, r = 2.5 cm
slant height, l = 6.5 cm
First, we will determine the height of the cone
By Pythagoras' theorem
[tex]l^{2} = r^{2} + h^{2}[/tex]
Where [tex]l[/tex] is the slant height
r is the radius
and h is the height of the cone
Then, we can write that
[tex]6.5^{2} = 2.5^{2} + h^{2}[/tex]
[tex]42.25 = 6.25 + h^{2}[/tex]
[tex]h^{2}=42.25 - 6.25[/tex]
[tex]h^{2} =36[/tex]
[tex]h = \sqrt{36}[/tex]
∴ h = 6 cm
Now, putting the parameters into the equation for the determining the volume of a cone, we get
[tex]V = \frac{1}{3}\times \pi \times 2.5^{2} \times 6[/tex]
[tex]V = \pi \times 6.25\times 2[/tex]
[tex]V = 12.5 \pi[/tex] cm³ OR 39.27 cm³
Hence, the number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³
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The figure is cut into 15 equal pieces. Shade 2/3 of the figure.
Answer:
Shade 10 of the pieces.
Step-by-step explanation:
What is the remainder of (x3+5x2−32x−7)÷(x−4) ? Enter your answer in the box.
Answer:
x^2+5x-36-7/x
Step-by-step explanation:
assuming x^3 and 5x^2
Iggy is practicing for a marathon by running laps on the
track at school. Each lap covers 0.7 kilometers, and he
has already run 19.6 kilometers. How many laps does he
need to run if he wants to complete 91 kilometers?
Mr. and Mrs. Nozaki are moving from Riverside to Prarieton. The distance from their old house to their new house is 1003 miles. If their car gets 23.6 miles per gallon, how many gallons of gas will they need for the trip?
The total amount of the fuel needed for the trip is 42.5 gallons if the distance from their old house to their new house is 1003 miles.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have total distance between from their old house to their new house:
d = 1003 miles
The car travel 23.6 miles per gallon
So the total amount of the fuel needed = 1003/23.6 = 42.5 gallons
42.5 gallons fuel will be required to travel 1003 miles
For the return trip (considering 23.6 miles per gallon) the same amount of fuel will be needed.
So the total fuel needed including roundtrip = 42.5×2 = 85 gallons
Thus, the total amount of the fuel needed for the trip is 42.5 gallons if the distance from their old house to their new house is 1003 miles.
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Find the volume of the solid (pls help me :// )
=====================================================
Explanation:
The triangular face has area of base*height/2 = 4*10/2 = 40/2 = 20 square cm.
Multiply this prism base area by the depth of the prism to get 20*2 = 40 cubic cm.
It might help to place the triangular prism so the triangular face is along the ground, so you can think of that face as the floor of this triangular room. The volume of this room is equal to the floor area times the height of the room.
volume of the room = (floor area)*(height of the room)
volume of the prism = (base area)*(height of the prism)
For any prism, the base faces are always parallel and congruent to each other.
Please help me with this math problem!! I will give brainliest!! :)
Wrong answer sorry. Hope you find it!
PLEASE HELP ME!!
find the Trinomial!
Answer:
[tex]a^{4}-2a^{2} -24[/tex]
Step-by-step explanation:
We do FOIL to solve this
Which of the following are roots of the polynomial function? Check all that apply. F(x) = x3 - 5x2 - 13x - 7
Answer:
Write properties of function:
x intercept/zero: [tex]x_{1} =-1;x_{2} =7[/tex]
Step-by-step explanation:
x² - 6x - 7 = x² - 7x + x - 7
⇒ x(x - 7) + 1(x - 7)
⇒ (x + 1) (x - 7)
Thus, x³ - 5x² - 13x - 7 = (x + 1)(x + 1)(x - 7)
[tex]~~~~~~~~x^3 -5x^2 -13x -7=0\\\\\implies x^3 +x^2 -6x^2 -6x-7x-7=0\\\\\implies x^2(x+1) -6x(x+1) -7(x+1)=0\\\\\implies (x+1)(x^2 -6x -7) = 0\\\\\implies (x+1)(x^2 +x -7x-7)=0\\\\\implies (x+1) [x(x+1) -7(x+1)]=0\\\\\implies (x+1)(x+1)(x-7) = 0\\\\\implies (x+1)^2 (x-7) = 0\\\\\implies x = -1,~ x = 7\\\\\text{Hence, the roots are}~ -1~ \text{and}~ 7[/tex]
1. Find the least common multiple of x² + x-12 and x² + 2x - 15
Least Common Multiple = (x-3) (x+5) (x+4)
Step-by-step explanation:
First we solve for x² + x-12
Factorise=> x² + 4x - 3x - 12
Taking common=> x ( x+4 ) - 3 (x+4 )
=> (x-3) (x+4)
Now we will solve for x² + 2x - 15
Factorise=> x² + 5x - 3x - 15
Taking common=> (x-3) (x+5)
we see here (x-3) is common in both the equations so We write it only 1 time as we have to find least common multiple .
Ans. Lest common multiples are = (x-3) (x+5) and (x+4)