Answers
Answer:
1.) 9
2.) 15
3.) 7
Step-by-step explanation:
1.) There are no repeat letters, so the cardinality is the number of letters, here 9
2.) There's half the numbers from 1 to 30 in the set, so 30/2 = 15
3.) There are 7 distinct days of the week, so the answer is 7
Related Questions
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
Answers
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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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.
Answers
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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Differential Equations Dilemma
Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the
following functions that vanishes identically.
f(x) = 4x, g(x) = 2x², h(x) = 8x-12x²
Enter the non-trivial linearcombination.
(16)4x + (__)2x²+ (__)(8x-12x²) = 0
Answers
The equation with nontrivial linear combination is (16)4x + ( -48 )2x²+ (-8 )(8x-12x²) = 0
We can solve this problem following some steps.
Let's assume the value is A for blank one and it is B for blank two.
Now we can rewrite the equation as,
(16)4x + (A) 2x²+ (B)(8x-12x²) = 0
Or, 64x + 2Ax² + 8Bx - 12Bx² = 0
After rearrangement, we can write this equation as,
x ( 64 + 8B) + x²( 2A - 12B) = 0
We can consider the whole equation as zero, only when the coefficient of both x and x² is zero, To complete a nontrivial combination, we have to write,
∴ ( 64 + 8B) = 0 [ Coefficient of x ]
Or , 8B = -64
Or, B = -64/8 = -8
Again following the previous concept we can also write, ( 2A - 12B ) = 0
[ Coefficient of x² ]
Now, we should put the value of B = -8
∵ ( 2A - 12B ) = 0
Or, 2A + 96 = 0
Or, 2A = - 96
Or, A = - 48
So, the value of A is -48, and the value of B is -8
Now we can conclude,
(16)4x + ( -48 )2x²+ ( -8 )(8x-12x²) = 0
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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?
Answers
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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The digit 3 in 5,630, is 10 times the value of the digit 3 in 342.
Answers
The digit 3 in 5,630, is not 10 times the value of the digit 3 in 342. It's false.
How to calculate the value?It should be noted the question has to do with place value. In this case, the digit 3 in 5,630 gives a value of 30.
On the other hand, the digit 3 in 342 is 300.
Therefore, we can see that the digit 3 in 5,630, is not 10 times the value of the digit 3 in 342.
Therefore, the correct option is false.
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The digit 3 in 5,630, is 10 times the value of the digit 3 in 342. True or. false?
What does x=
How to figure this out?
Answers
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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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 :')
Answers
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!
A light bulb consumes 12600 watt-hours in 3 days and 12 hours. How many watt-hours does it consume per day?
Answers
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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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
Answers
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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Round 3,532 to the nearest thousand
Answers
Answer:
4,000
Step-by-step explanation:
8 - (6 - 8x) = 4x + 5
Answers
The value of the x in the linear equation is a 3/4.
According to the statement
We have to find that the value of the x.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
8 - (6 - 8x) = 4x + 5
Now we have to solve this
Then
8 - (6 - 8x) = 4x + 5
8 - 6 + 8x = 4x + 5
Now, rearrange the above written terms for the value of the x
2 + 8x = 4x + 5
4x = 3
x =3/4.
So, The value of the x in the linear equation is a 3/4.
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PLEASE HELIP ITS DUE TODAY
Answers
Answer:
x = 6
Step-by-step explanation:
As stated, the scale factor from two figures is 1/4
To find the value of x we can simply use the following equation
[tex] \frac{(1.5)}{x} = \frac{1}{4} [/tex]
cross multiply expressions
x = 6
What are the slope and the y-intercept of the linear function that is represented by the equation y=9x-2
Answers
Answer:
Gradient: 9
Y-intercept: -2
Step-by-step explanation:
The equation of a line is expressed in this format:
y = mx + c
Where m is the gradient (slope) of the line, and c is the y intercept.
The equation in the question is already in this format, meaning the values can be read directly from it without needing any rearranging.
m = 9, c = -2.
Based on the histogram below, how are data distributed, and where is the mean located in relation to the median?
Answers
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.If Jessie can answer multiplication problems at a rate of 6 problems every 20 seconds. If she has a 10 minute test with 175 questions on it, will she finish in time?
Answers
Answer:
yes
Step-by-step explanation:
to solve this you must first find her rate
6 / 20 is her rate
you want to know how many she can do in ten minutes so we must find how many seconds are in 10 minutes
10 * 60 = 600
175 / 600 is the rate needed fro the test
now make them have the same denominator
6 / 20 is also 180 / 600
175/600 is less than 180/600 so yes she will finish the test in time
Given that A, O & B lie on a straight line segment, evaluate the size of the smallest angle.
Answers
The smallest angle on the line will be 36°
What do you understand by straight line segment?A line segment seems to be a straight line that connects two places. A line segment does indeed have a predetermined length. A ruler can be used to determine the shortest distance between the two points.
What is another name for a straight angle?A straight angle in geometry is an angle with a vertex point of 180 degrees. It basically generates a straight line with sides that point in opposite directions first from the vertex. It is also known as "flat angles."
According to the given data:We know the the sum of the straight angle is = 180°
So,
(5a + 18) + (48 - a) + (8a -30 ) = 180°
5a - a + 8a + 18 +48 - 30 = 180°
12a + 36 = 180°
12a = 180 - 36
a = 12°
So putting the value of a in the equation:
(5a + 18) = 5 *12 + 18 = 78°
(48 - a) = 48 - 12 = 36°
(8a -30 ) = 96 - 30 = 66°
36° < 66° <78°
So the smallest angle on the line will be 36°
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Find the z-intercepts and the coordinates of the vertex for the parabola y=x2+6x+5 if there is more than one x intercept awpweate them with commas
Answers
The x-intercepts of the parabola are (-1,0) and (-5,0) and the coordinates of the vertex are ( -3 , - 4 ).
A parabola is a graphical representation of a function of the form y=g(x) where g(x) is a quadratic polynomial of x.
The locus of a point which is equidistant point also known as focus and equidistant from a given line known as directrix forms a parabola.The general equation of a parabola is given by y =4a(x-h)²+k(h, k) is the vertex of the parabola.The given equation of the parabola is y = x² + 6x + 5
to find the x-intercepts we have to take the value of y at zero.
∴ x² + 6x + 5 = 0
or, x² + 5x + x + 5 = 0
or, x (x + 5) + 1 ( x + 5 ) = 0
or, (x+5)(x+1)=0
either x=-5 or x=-1
Therefore the x-intercepts of the graph is (-1,0) and (-5,0)
Now to find the vertex of the parabola:
y = x² + 6x + 5
or, y = x² + 2·x·3 + 3² - 4
or, y = (x + 3)² - 4
Therefore from the above equation we can say that the vertex of the parabola is at ( -3 , - 4 ).
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Write an equation that can be used to solve the problem. Find the solution to the problem. Angles A and B are complementary angles. Determine the measures of angles A and B if angle A is 8 times the size of angle B.
Answers
Answer:
A = 80
B = 10
Step-by-step explanation:
a + b = 90
a = 8b
above are the two equations that we will used to find A and B.
substitute in 8b for a in the first equation.
a + b = 90
8b + b = 90 Combine like terms
9b = 90 Divide both sides by 9
b = 10
If b is 10, than a must be 80.
T is the midpoint of SU if ST is 3x and TU is x+8 what is TU
Answers
The value of the line segment TU is 12 units.
What basically is a line segment?A line segment is a fixed-length section of the a line to two ends.
It is distinct from a line in that it has no origins or ending points and can be expanded in both directions.a line segment AB, the span of which is proportional to the distance between its endpoints A and BAccording to the question;
TU = x + 8 and ST = 3x are the lengths.
SU is the total length of the line segment.
Now, it is clear that SU is divided into parts such that;
SU = ST + TU
As, T is the mid point of the line SU;
The,
ST = TU
Equating the values;
3x = x + 8
Solving the equation;
3x -x = 8
x = 4
Put the value of x in TU;
TU = x + 8
TU = 4 + 8
TU = 12
Therefore, the value of the line segment TU is found as 12 units.
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Jay sells his smartphone to Louise and makes a 20% profit. Louise then sells the
smartphone after a year to Angel, and makes a 10% loss. Louise sold the smartphone
to Angel for £652. How much did Louise pay for the smartphone, and how much did
Jay pay for the smartphone originally?
Answers
Answer:
Jay paid £573.76 for the smart phone originally.
Rectangular paintings hang on the wall of an art gallery. One painting has a area of 24 square feet and another has an area of 32 square feet the paintings have whole number side lengths and have one pair of side lengths in common. What could the common side lengths be?
Answers
The common side length of the paintings is 8 feet
What are areas?The area of a shape is the amount of space on the shape
How to determine what common side lengths could be?The given parameters are
Area of painting 1 = 24 square feet
Area of painting 2 = 32 square feet
Express the areas as the product of their factors
So, we have
24 = 2 * 2 * 2 * 3
32 = 2 * 2 * 2 * 4
Multiply the common factors
Common factors =2 * 2 * 2
Evaluate the product
Common factors = 8
This represents the common side length
Hence, the common side length of the paintings is 8 feet
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How many tens are in the number 345
Answers
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
if you take 3/10 of a number and add 2 , you get 17
Answers
Step-by-step explanation:
Are you asking for the number?
Which expression best estimates-18-
-181-232
O 18+3
O-18+3
O-18+(-3)
O 18+(-3)
Answers
Answer:O 18+3
O-18+3
O-18+(-3)
Step-by-step explanation:O 18+3
O-18+3
O-18+(-3)
Question
what is the domain of the
function y = 3 sqtx
Answers
Consider oo as infinity sign
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.
Answers
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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What is the sum of 15 and a number plus 12
Answers
Answer:
15 + (n + 12)
Step-by-step explanation:
the nth term of 1,3,5,7, … is
Answers
Answer: an=2(n-1)+1
Step-by-step explanation:
1,3,5,7, …
As the terms progress in the sequence, each term get increased by 2 to get to the next term. Hence, the change is linear and can be modeled with the function y=2(x-1)+1 where y=term value, x=term number and 1 is the first term in the sequence.
y=2(x-1)+1
an=2(n-1)+1 ==> n=term number while an=term value. an=nth term
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?
Answers
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
[tex] \displaystyle \rm \sum_{n = 0}^ \infty \frac{(n! {)}^{2} }{(2n + 1)!} [/tex]
Answers
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]