Answer:
7
Step-by-step explanation:
=[(5)×2]+[(30)-5]÷5
=(10)+(25)÷5
=35÷5
=7
Solve the problem. Give the equation using x as the variable, and give the answer.
The product of 9, and a number increased by 6, is 135. What is the number?
The equation is
(Do not simplify.)
Question
what is the domain of the
function y = 3 sqtx
[tex] \displaystyle \rm \sum_{n = 0}^ \infty \frac{(n! {)}^{2} }{(2n + 1)!} [/tex]
Observe that
[tex]\dfrac{(n!)^2}{(2n+1)!} = \dfrac{n!(2n-n)!}{(2n+1)(2n)!} = \dfrac1{(2n+1)\binom{2n}n}[/tex]
Starting with a well-known series
[tex]\displaystyle 2\arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}[/tex]
we take some (anti)derivatives to find a sum that more closely resembles ours.
Let [tex]f(x)=2\arcsin^2(x)[/tex]. Then
[tex]\displaystyle f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{n \binom{2n}n}[/tex]
[tex]\displaystyle x f'(x) = 2 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{n \binom{2n}n}[/tex]
[tex]\displaystyle x f''(x) + f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n-1}}{\binom{2n}n}[/tex]
[tex]\displaystyle x^2 f''(x) + x f'(x) = 4 \sum_{n=1}^\infty \frac{2^{2n} x^{2n}}{\binom{2n}n}[/tex]
Noting that both sides go to zero as [tex]x\to0[/tex], by the fundamental theorem of calculus we have
[tex]\displaystyle \sum_{n=1}^\infty \frac{2^{2n} x^{2n+1}}{(2n+1)\binom{2n}n} = \frac14 \int_0^x (t^2 f''(t) + t{}f'(t)) \, dt[/tex]
so that when [tex]x=\frac12[/tex], and rearranging some factors and introducing a constant, we recover a useful sum.
[tex]\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac12 \int_0^{1/2} (x^2 f''(x) + x f'(x)) \, dt[/tex]
Integrate by parts.
[tex]\displaystyle \int_0^{1/2} x^2 f''(x) \, dx = \frac14 f'\left(\frac12\right) - 2 \int_0^{1/2} x f'(x) \, dx[/tex]
[tex]\displaystyle \int_0^{1/2} x f'(x) \, dx = \frac12 f\left(\frac12\right) - \int_0^{1/2} f(x) \, dx[/tex]
Then our sum is equivalent to
[tex]\displaystyle \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} = 1 + \frac18 f'\left(\frac12\right) - \frac14 f\left(\frac12\right) + \int_0^{1/2} \arcsin^2(x) \, dx[/tex]
The remaining integral is fairly simple. Substitute and integrate by parts.
[tex]\displaystyle \int_0^{1/2} \arcsin^2(x) \, dx = \int_0^{\pi/6} u^2 \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} - 2 \int_0^{\pi/6} u \sin(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 2 \int_0^{\pi/6} \cos(u) \, du \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1[/tex]
Together with
[tex]f\left(\dfrac12\right) = 2 \arcsin^2\left(\dfrac12\right) = \dfrac{\pi^2}{18}[/tex]
[tex]f'\left(\dfrac12\right) = \dfrac{4\arcsin\left(\frac12\right)}{\sqrt{1-\frac1{2^2}}} = \dfrac{4\pi}{3\sqrt3}[/tex]
we conclude that
[tex]\displaystyle \sum_{n=0}^\infty \frac{(n!)^2}{(2n+1)!} = \sum_{n=0}^\infty \frac1{(2n+1)\binom{2n}n} \\\\ ~~~~~~~~~~~~~~~~~~ = 1 + \left(\frac18\cdot\frac{4\pi}{3\sqrt3}\right) - \left(\frac14\cdot\frac{\pi^2}{18}\right) + \left(\frac{\pi^2}{72} + \frac\pi{2\sqrt3} - 1\right) \\\\ ~~~~~~~~~~~~~~~~~~ = \boxed{\frac{2\pi}{3\sqrt3}}[/tex]
The area of circle Z is 64 ft².
What is the value of r?
A- r= 4 ft
B- r= 8 ft
C- r = 16 ft
D - r = 32 ft
Answer:
Step-by-step explanation:
[tex]A=64\pi ft^2[/tex]
[tex]r=\sqrt{\frac{A}{\pi } }[/tex]
[tex]r=\sqrt{\frac{64\pi }{\pi } }[/tex]
[tex]r=\sqrt{64}[/tex]
[tex]r=8[/tex]
So the radius is 8 ft.
Hope this helps! Mark as brainliest!
Based on the histogram below, how are data distributed, and where is the mean located in relation to the median?
Answer:
C) Positively skewed, and the mean is to the right of the median.
Step-by-step explanation:
A histogram is a graphical representation of the distribution of numerical data.
A histogram is:
Positively skewed (right-skewed) if the long tail is on the positive side of the peak.Negatively skewed (left-skewed) if the long tail is on the negative side of the peak.Since the long tail of the given histogram is on the positive side of the peak, the histogram is positively skewed (right-skewed).
The mode is the value that occurs most often in a set of data.
In a histogram, the mode is the highest point.
The median and mean fall to the right of the mode in a right-skewed (positively skewed) histogram, and the mean is always to the right of the median: mode < median < mean.
The median and mean fall to the left of the mode in a left-skewed (negatively-skewed) histogram, and the mean is always to the left of the median: mean < median < mode.
So the correct definition of the given histogram is:
C) Positively skewed, and the mean is to the right of the median.A sum of money is to be divided among A B and C in the ratio 2:3:5 the smallest share amounts
to $600 what is the total sum of money to be shared
The correct answer is $3000.
It is quite effective to compare two or more values using the division approach. Therefore, it would be accurate to state that a ratio is a comparison or simplification of two quantities of the same type. This relationship illustrates how many times one quantity is equivalent to the other. The ratio may be defined as the number we use to represent one quantity as a percentage of the others.
As given ratio A:B:C = 2:3:5
let, A=2x, B=3x, C=5x
2x=600
x=600/2
x=$300
Total money = 2x+3x+5x
=x(2+3+5)
=x(10)
=300×10
=$3000
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A light bulb consumes 12600 watt-hours in 3 days and 12 hours. How many watt-hours does it consume per day?
A light bulb will consume 3,600 watts - hours in 1 day if it consumes 12,600 watts in 3 days 12 hours.
We are given that:
Consumption in 3 days 12 hours = 12,600 watts
12 hours = 12 / 24 days = 0.5 days
Days = 3 + 0.5 days = 3.5 days
Now, by using the unitary method, we get that the consumption by a light bulb in 1 day will be equal to:
3.5 days = 12,600 watts
1 day = 12,600 / 3.5 watts
1 day = 3,600 watts
Therefore, a light bulb will consume 3,600 watt - hours in 1 day if it consumes 12,600 watts in 3 days 12 hours.
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I really need the work and answer to these problems, i wish to understand it better
Answer:
asdfasdf
Step-by-step explanation:
asdfasdfasdfasdfasdf
Hello un I need help with my Science if you can help me with it
Answer:
well wheren is the question
I can't remember if I already posted this one....
so here we are *again (possibly*)
also ignore that I picked A it was an accident :')
Answer:
B
Step-by-step explanation:
3/20 15%,20%, 25%, 1/3 33%
All my work and answer is provided in the attached screenshot to my answer! :)
Have a great day!
help asap i will give crowns to the best
Answer: the answer is 42.5
help with this please
Using integrals, the probabilities and desired measures are given as follows:
a) P(0 < X) = 0.5.
b) P(0.6 < X) = 0.392.
c) P(-0.5 ≤ X ≤ 0.5) = 0.125.
d) P(X < -2) = 0.
e) P(X < 0 or X > -0.5) = 1.
f) x = 0.965.
What is the probability distribution?
The distribution is given by:
f(x) = 1.5x², -1 < x < 1.
The integral of this function will be used to find the probabilities.
In item a, the probability is given by:
[tex]P(0 < X) = \int_{0}^{1} f(x) dx[/tex]
[tex]P(0 < X) = \int_{0}^{1} 1.5x^2 dx[/tex]
[tex]P(0 < X) = 0.5x^3|_{x = 0}^{x = 1}[/tex]
Applying the Fundamental Theorem of Calculus:
P(0 < X) = 0.5(1)³ - 0.5(0)³ = 0.5 - 0 = 0.5.
Item b is similar as item a, just with lower limit 0.6, hence:
P(0.6 < X) = 0.5(1)³ - 0.5(0.6)³ = 0.5 - 0.108 = 0.392.
For item c, the lower limit is -0.5 and the upper limit is of 0.5, hence:
P(-0.5 ≤ X ≤ 0.5) = 0.5(0.5)³ - 0.5(-0.5)³ = 0.125.
For item d, values of -2 and less are not on the range of the distribution, which is between -1 and 1, hence the probability is of 0.
For item e, the intersection of the intervals is the entire range of the function, hence the probability is of 1.
For item f, we have that:
0.5(1)³ - 0.5(x)³ = 0.05
0.5x³ = 0.45
x³ = 0.9.
x = (0.9)^(1/3) -> cubic root
x = 0.965.
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dave has built a storage box and needs to decorate it. It is cuboid 32cm long, 20cm wide and 30 cm tall. what is the volume of daves storage box and what is the surface area?
The volume of Daves storage box is 19200 and the surface area is 4400
What is the volume of daves storage box and what is the surface area?The given parameters are
Length = 32 cm
Width = 20 cm
Height = 30 cm
The volume is
Volume = Length * width * height
So, we have
Volume = 32 * 20 * 30
Evaluate
Volume = 19200
The surface area is
A =2 *(LW + LH + WHW)
So, we have
A = 2 * (32 * 20 + 20 * 30 + 32 * 30)
Evaluate
A = 4400
Hence, the volume of Daves storage box is 19200 and the surface area is 4400
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Lines a & m are parallel. Using the diagram below, what is the degree measure of angle 3? Enter the numerical answer only. Example, if the answer is 12 degrees, only enter 12.
Based on the fact that Lines a and m are parallel, the degree measure of angle 3 is 127
What is the degree measure?Based on the fact that a and m are parallel lines, then this means that the angle 127 degrees is corresponding to angle 1.
This means that the measure of angle 1 is 127 degrees as well because corresponding angles are congruent.
Angle 1 and Angle 3 are vertical angles. Vertical angles are also congruent. This means that if Angle 1 is 127 degrees then angle 3 will be 127 degrees as well.
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How do you solve
9
x
−
4
=
81
?
[tex]9x = 81+4[/tex]
[tex]9x = 85[/tex]
[tex]x = 85/9[/tex](divide using calculator)
The product of s and t, plus r
The expression for the product of s and t, plus r will be (s × t) + r which is st + r.
How to calculate the product?This can be illustrated as an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Therefore, the expression for the product of s and t, plus r will be:
= (s × t) + r.
= st + r.
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There are 6 circles and 3 squares. What is the simplest ratio of squares to circles?
The ratio of squares to circles is 1/ 2
What is ratio?A ratio is defined as the comparison of two or more numbers or elements indicating their sizes in relation to each other.
From the information given, we have that;
There are 6 circleThere are also 3 squaresTo determine the ratio of the squares to circles, we take the quotient of squares to circles, we have;
= 3/ 6
Reduce to simpler form
= 1/ 2
Thus, the ratio of squares to circles is 1/ 2
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suppose that the length of a certain rectangle is 7 meters less than four times its width. The perimeter of the rectangle is 46 meters. find the length and width of the rectangle.
The answer to the given question is length is 17m and width is 6m
Given that a rectangle's length is 7 meters less than its width.
And also given the perimeter of the rectangle is 46 meters.
We know that the rectangle's perimeter is twice the sum of its length and width.
l - length of the rectangle
w - width of the rectangle
P - perimeter of the rectangle
Then we have P = 2 × (l + w)
Given that a rectangle's length is 7 meters less than its width.
⇒ l = 4 × w - 7
Given the perimeter of the rectangle is 46 centimeters.
⇒ 2 × ( l + w) = 46
⇒ 2 × (4w - 7 + w) = 46 (using the value of length given in terms of width)
⇒ 4w - 7 + w = 23 (dividing by 2 on both the sides)
⇒ 5w - 7 = 23
⇒ 5w = 23 + 7
⇒ 5w = 30
⇒ w = 6 (dividing both sides by 5)
Using the width value in the length equation, we get
l = 4 × 6 - 7
⇒ l = 24 - 7
⇒ l = 17
Therefore, The rectangle is 17 meters in length and 6 meters in width.
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What is the sum of 15 and a number plus 12
Answer:
15 + (n + 12)
Step-by-step explanation:
A bottle of ant killer holds 1,5 L of concentrate.
To make up a solution, 5 capfuls are added to 1
L of water. Each capful is 20 mL. How many
litres of solutions can be made if you use the
entire bottle of concentrate? [2]
82,5 L
16,5 L
15 L
Using multiplication, Correct option is B. The amount of solution that can be made from 15 L of concentrate is 16.5L.
What is meant by multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.
Given,
Total ant killers added in the water is 5 × 20mL = 100mL = 0.1L (using 1L = 1000mL)
Total quantity of solution is 0.1L + 1L = 1.1L
It takes 0.1 mL of ant killer to make 1.1L of solution.
⇒ Total solution that can be made from 15L of concentrate is -
⇒ 15L × 0.1L = 16.5L
∴ The solution that can be made from 15L of concentrate is 16.5L
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glider begins its flight 3/4
mile above the ground. After 45 minutes, it is 3/10
mile above the ground. Find the change in height of the glider. If it continues to descend at this rate, how long does the entire descent last?
Answer:
1hour 15
Step-by-step explanation:
The glider begins its flight a mile above the ground.
Distance above the ground after 45 minutes =
Change in height of the glider
Next, we determine how long the entire descent last.
Expressing the distance moved as a ratio of time taken
Therefore: Total Time taken =45+30=75 Minutes
=1 hour 15 Minutes
Round 3,532 to the nearest thousand
Answer:
4,000
Step-by-step explanation:
Which expression best estimates-18-
-181-232
O 18+3
O-18+3
O-18+(-3)
O 18+(-3)
Answer:O 18+3
O-18+3
O-18+(-3)
Step-by-step explanation:O 18+3
O-18+3
O-18+(-3)
The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 60 feet. If w is the width of the rectangle, which expression represents the length?
w+5
w−5
5w
1/5w
Answer:
5
Step-by-step explanation:
What does x=
How to figure this out?
The length of the side x of the triangle ADE is 16.5 units.
What are similar triangles?If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be similar (corresponding sides). When compared individually, similar triangles may have different side lengths, but they must all have the same ratio of their side lengths and equal angles.
From figure, it is given that:
AB = 3 units
BC = 2 units
AD = x units
DE = 11 units
We know that the triangle ABC ~ ADE.
Therefore, the ratio of corresponding sides of the triangles will be same.
Now,
AB/ AD = BC/ DE
3/x = 2/11
Cross multiply to get:
2x = 3(11)
2x = 33
x = 33/2
x = 16.5 units
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Question 11 of 18
What is the length of the diagonal of the square shown below?
5
45
90°
5
5
S
OA. 5,2
B. 5
OC. √5
OD. 5√5
OE. √10
OF. 25
SUBMIT
The square's diagonal length is (E) d = 5√2.
What is a diagonal?A diagonal is a line segment that connects two vertices (or corners) of a polygon. A diagonal is a line segment that connects two non-adjacent vertices of a polygon. It connects the vertices of a polygon, excluding the figure's edges. A diagonal is defined as something with slanted lines or a line connecting one corner to the corner farthest away.A diagonal is a line that connects the bottom left corner of a square to the top right corner.So, we must determine the length of the square's diagonal.
The formula for the diagonal of a square is d = a2; where 'd' is the diagonal and 'a' is the side of the square.Now, d = 5√2. (Refer to the diagram of the square given below)Therefore, the square's diagonal length is (E) d = 5√2.
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The correct question is given below:
What is the length of the diagonal of the square shown below? 5 45° 5 5 90° 5 O A. 5
B. 10
C. 5
D. 5/5
E. 5√2
F. 25
The function y=56.35x can be used to determine the
cost of taking a group of students to a water park. If at
least 15 but no more than 25 students go to the water
park, what is the domain of the function?
the domain of the function y = 56.35 x is 0.27 ≤ x ≤ 0.44.
We are given a function:
y = 56.35 x
We are also given that at least 15 but no more than 25 students go to the water park.
This means that the range of y is:
Range = 15 ≤ y ≤ 25.
Now, we need to find the domain of the function.
Put y = 15 in the equation:
15 = 56.35 x
x = 15 / 56.35
x = 0.27
Put y = 25 in the equation:
25 = 56.35 x
x = 25 / 56.35
x = 0.44
So, the domain becomes:
Domain = 0.27 ≤ x ≤ 0.44.
Therefore, we get that, the domain of the function y = 56.35 x is 0.27 ≤ x ≤ 0.44.
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Gwen volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen worked and the total number of tickets she sold.
Based on the table, write an equation for the relation between the number hours Gwen worked and the number of tickets she sold.
t = h/23
h = 23t
ht = 23
t = 23h
The equation that shows the relation between the number of hours worked and tickets sold is t = 23h (fourth option)
What is the equation?Examining the table, it can be seen that the number of tickets sold increases by 23 for every hour that Gwen works.
Tickets sold when Gwen works for 2 hours = 23 x 2 = 46
Tickets sold when Gwen works for 2 hours = 23 x 3 = 69
Because the tickets sold increase by a constant number, the equation would be modelled as a linear function.
Linear equations have the form : a + bx
Ticket sold = (number of hours x ticket sold in the first hour)
t = 23h
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How many tens are in the number 345
Answer:
Step-by-step explanation:
34 with a remainder of 5. so basically you can say 34 1/2
Answer:
350
Step-by-step explanation:
Rounding 345=350
345 to the nearest thousands is 0
345 to the nearest hundreds is 300
345 to the nearest tens is 350
345 to the nearest whole number is 345
345 to the nearest tenths is 345.0
Given the following values, find the perimeter of the figure shown below:
AB = 7 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm.
Do not include "cm" with your response.
By using the definition of perimeter and addition and subtraction of sides, the perimeter of the composite figure is 22 centimeters.
How to calculate the perimeter of a composite figure
According to the image attached aside, we find a composite figure created by adding three quadrilaterals. The perimeter is the sum of the lengths of all sides of the composite figure, that is, we need to add the lengths of the eight sides of the figure.
p = AB + BC + CD + DE + EF + FG + GH + AH
GH = AB - EF - CD
GH = 7 cm - 3 cm - 1 cm
GH = 3 cm
AH = BC - DE + FG
AH = 3 cm - 2 cm + 1 cm
AH = 2 cm
p = 7 cm + 3 cm + 1 cm + 2 cm + 3 cm + 1 cm + 3 cm + 2 cm
p = 22 cm
The perimeter of the composite figure is 22 centimeters.
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