The least number of consecutive positive integer that is required to make the sum of the reciprocals greater than three is 7.
What is an integer?An integer is simply a number that is not a fraction.
The first four consecutive positive integers are:
1, 2, 3 , 4.
Their reciprocals are:
1/1, 1/2, 1/3, 1/4; and
The sum of them are greater than 2; that is
1/1 + 1/2 + 1/3 + 1/4 = 2.08333333333 > 2
to make the expression >3
We would require the following integers
1/1 + 1/2 + 1/3 + 1/4+ (1/5) + (1/6) + (1/7) + (1/8)+ (1/9) + (1/10) + (1/11) = 3.01987734488
Thus, the additional consecutive reciprocal integers that is required to make the sum of the reciprocal of the fist four greater than 3 is 7.
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Suppose a household’s income increases from $2500 to $3000 and quantity demanded changes from 190 to 150. What is the income elasticity?
a.
0.6
b.
$500
c.
-1.05
d.
2.5
The income elasticity for the household is -1.05.
What is the income elasticity?Income elasticity measures how quantity demanded changes when there is a change in the income of a person / household
Income elasticity = percentage change in quantity demanded / percentage change in income
percentage change in income = (3000 / 2500) - 1 = 0.2 = 20% percentage change in quantity demanded =( 150 /190) - 1 = -0.21 = -21%Income elasticity = -21% / 20 = -1.05
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What is the probabily of the 90th percentile given mean of 262 and a standard deviation of 45
The probability of the 90th percentile given a mean of 262 and a standard deviation of 45 is 319.672
Here,
The formula for the percentile probability is
[tex]P=\mu+z\sigma[/tex]
P=262 + 1.2816(45)
P = 319.672
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what is the inverse of f(x)=(-2x+2)/(x+7)?
By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).
How to find the inverse of a function
In this question we have a rational function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:
[tex]x \to y[/tex]
[tex]f(x) \to x[/tex]
[tex]x = \frac{-2\cdot y + 2}{y+7}[/tex]
x · (y + 7) = - 2 · y + 2
x · y + 7 · x = - 2 · y + 2
2 · y + x · y = - 7 · x + 2
y · (2 + x) = - 7 · x + 2
[tex]g(x) = \frac{- 7\cdot x + 2}{x + 2}[/tex]
By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).
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the function f(x)=-3 cos(2x+pi/4) has ___
The domain will be ( 0, ∞) and the range of the function F(x) = -3Cos[2x+[tex]\dfrac{\pi}{4}[/tex]] will be [[tex]\dfrac{-\pi}{8}[/tex] , -3 ] and [ [tex]\dfrac{3\pi}{8}[/tex],3].
What are domain and range?Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
The range of the function we can see from the graph of the function will be from [[tex]\dfrac{-\pi}{8}[/tex] , -3 ] and [ [tex]\dfrac{3\pi}{8}[/tex],3]
The domain of the function will be all the values of the real numbers for the function ranges from ( 0, ∞ ).
Therefore the domain will be ( 0, ∞) and the range of the function F(x) = -3Cos[2x+[tex]\dfrac{\pi}{4}[/tex]] will be [[tex]\dfrac{-\pi}{8}[/tex] , -3 ] and [ [tex]\dfrac{3\pi}{8}[/tex],3].
The complete question is given below:-
what is the domain and range of the function
F(x) = -3Cos[2x+[tex]\dfrac{\pi}{4}[/tex]] .
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What is the value of y?
Enter your answer in the box
Y=_
Answer:
the angles of a triangle always equal 180 so
34+x-5+4y=180
simplify
29+x+4y=180
-29
x+4y=151
-4y
x=-4y+151
then put this into the original equation
29-4y+151+4y=180
simplify
29+151=180
so this proves that this works
-1/4x-151=y
Hope This Helps!!!
On Tuesday, a city’s parking meter income is up $311 from Monday’s income, m. So, Tuesday’s income is m + 311
If m is 894, what is m + 311
I'm kinda lost in this problem. Can you teach me how to solve these
53) Vertical angles are congruent, so [tex]m\angle IDA=121^{\circ}[/tex]
54) [tex]\angle YDA[/tex] and [tex]\angle YDF[/tex] are supplementary, so [tex]m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}[/tex]
55) Because vertical angles are congruent, [tex]m\angle FDI=59^{\circ}[/tex]. Now, because DR bisects [tex]\angle FDI[/tex], this means [tex]m\angle RDI=\frac{59}{2}=29.5^{\circ}[/tex]
56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32
Let the numbers below represent the lengths of the sides of a triangle. Which of the triangles is a right triangle?
I. 4, 5, 6
II. 6, 8, 10
III. 5, 13, 14
IV. 7, 11, 13
A
I
B
II
C
III
D
IV
Answer:
B. II (6, 8, 10)
Step-by-step explanation:
A set of triangle side lengths will form a right triangle if they satisfy the Pythagorean theorem. The sum of squares of the shortest two sides must equal the square of the longest side.
__
Pythagorean triplesSets of integers that satisfy the Pythagorean theorem are called "Pythagorean triples." Some of these for smaller integers are ...
(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17)
If small integer side lengths are not one of these triples, or a multiple of one of these triples, they will not form a right triangle.
I. not a match to any triple
II. matches (3, 4, 5) multiplied by 2 -- a right triangle
III. not a match to any triple
IV. not a match to any triple
_____
Pythagorean equationOf course, you can actually compute the squares to see if they satisfy the Pythagorean theorem:
I. 4² +5² = 41 ≠ 6² (acute triangle)
II. 6² +8² = 100 = 10² -- right triangle
III. 5² +13² = 194 ≠ 14² (obtuse triangle)
IV. 7² +11² = 170 ≠ 13² (acute triangle)
__
form factorThe sum f = a² +b² -c² (where c is the longest side) can be considered to be a "form factor" for the triangle. For ...
f>0, the sides form an acute triangle f=0, the sides form a right trianglef<0, the sides form an obtuse triangleThis "form factor" is related to the largest angle (C) by ...
cos(C) = f/(2ab)
Which equation can be used to solve for x in the following diagram?
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
Which describes the spread of the data in the two box plots?
The range of shelter A is 22. The range of shelter B is 18.
What are the measures of spread?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number. The range is the difference between the two numbers.
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62 divided by 8,694
Answer:
50.007131355
Step-by-step explanation:
A calculator lol?
Which algebraic expression is a trinomial?
Answer:
?
Step-by-step explanation:
because there is no picture or option
Find the missing term or terms in each arithmetic sequence.
4) ..., 27,__,__,__, 43, ...
I need help again please!!!!!!
Answer:
I believe the terms would be 31, 35, 39.
Step-by-step explanation:
We know this because 43-27 is 16. since there are 3 terms missing, we divide the answer by 4, and you get 4. The number you get there is how many you add to each term to get the missing ones. For example, 27+4=31. The pattern is adding 4 to each term. Hope I helped!
A cell phone plan charges $38 a month, and an additional $12 a month for each gb of data used. write an equation for the monthly cost (y) of the cell phone plan in terms of the number of gb of data used (x).
Answer:
y = 38 + 12x
Step-by-step explanation:
38is fixed cost per month and since the charge is $12 per GB, the variable cost is 12x where x is the GB used
Which of the following is equivalent to 5√12 - 2√27?
Answer:
A. 4 root 3
Step-by-step explanation:
Please can someone help me on this I’m trying to revise for my test and I don’t understand this question
Answer:
∠ EAB = 85°
Step-by-step explanation:
∠ EBC and ∠ BCD are same- side interior angles and sum to 180° , so
∠ BCD = 180° - ∠ EBC = 180° - 148° = 32°
the sum of the 3 angles in Δ ADC = 180° , that is
∠ EDC + ∠ BCD + ∠ EAB = 180°
63° + 32° + ∠ EAB = 180°
95° + ∠ EAB = 180° ( subtract 95° from both sides )
∠ EAB = 85°
Answer:
first of all the line EAB is a triangle and all the angles in a triangle equate to 180° therefore;
[tex]angle \: ebc = 148 \\ angle \: edc = 63 \\ 148 + 63 = 180[/tex]
next I subtract 148 from 63 which gives 85⁰ therefore eab is equals 85⁰
Please help!!!
Consider the segment UV.
Type the correct answer in each box. Use numerals instead of words.
What is
-8/15of21/12
Determine the measure of each indicated angle.
The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
Given that:-
∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²
The angles will be calculated as follows:-
13x² + 12x² + 20x² = 180
45x² = 180
x² = 4
x = ±2
The angles will be:-
∠ABC = 13x² = 13 x ( 2² ) = 52
∠ACB = 12x² = 12 ( 2² ) = 48
∠CAB = 20x² = 20 ( 2² ) = 80
Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.
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What is the answer for the question down below
Answer:
This is the ray BAStep-by-step explanation:
Ray can be defined as a part of a line that has a fixed starting point but no end point.
The starting point is B and on its way to infinity, it passes through point A.
Correct sign is
[tex]\huge\boxed{\overrightarrow{BA}}[/tex]
if you are examining a triangle with given measurements for one leg and the hypotnuse,how will you determine the measure of the unknown leg?
We will apply the Pythagoras theorem to find the measure of the unknown leg in a triangle when one leg and the hypotenuse are provided dimensions.
What is the definition of a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.
According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.
[tex]\rm h^2 = p^2+ b^2[/tex]
Where,
h is the hypotenuse
p is the perpendicular
b is the base
If any of the two is given the third side will be obtained using the Pythagoras theorem.
In a triangle with given measurements for one leg and the hypotenuse, we will determine the measure of the unknown leg by the Pythagoras theorem.
Hence we willl apply the pythogorous theorem for finding the unknown side.
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Question 3 of 21
Which of the following are the domain and range that represent the inverse of
the function f(x), given the mapping diagram of f(x) below?
Answer: C
Step-by-step explanation:
The inverse of a function maps the domain onto the range.
Kate used 555 grams of wool to knit a sweater, hat, and scarf. She used 5 times less grams for the hat than for the sweater. She used 5 more grams for the hat than for the scarf. How many grams of wool did she use to knit for each?
(Give explanation)
Answer:
Sweater: 392 [tex]\frac{6}{7}[/tex]
Hat: 78[tex]\frac{4}{7}[/tex]
Scarf: 83[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
Set the sweater = x
The hat = [tex]\frac{1}{5}[/tex] x
The scarf = [tex]\frac{1}{5}[/tex] x + 5
x + [tex]\frac{1}{5}[/tex] x + [tex]\frac{1}{5}[/tex] x + 5 = 555
Combine like terms
1[tex]\frac{2}{5}[/tex] x + 5 = 555
Subtract 5 from both sides
1[tex]\frac{2}{5}[/tex] x = 550
Divide by 1[tex]\frac{2}{5}[/tex]
x = 392 [tex]\frac{6}{7}[/tex] This is how much wool was used for the sweater.
Divide by 5 to get the hat = 78 [tex]\frac{4}{7}[/tex]
Add 5 to that to get the scarf: 83[tex]\frac{4}{7}[/tex]
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle . Triangle ABC with right angle marked at vertex B. Side AC, opposite vertex B, is labeled 14. Dashed segment is drawn from vertex B to point D on side AC. Angle BDA is marked right angle. Angles A and C both marked 45 degrees. Segment AD is labeled 7. (dragged tiles) 7(squareroot)3 7(square root) 7. 14. 14(squareroot)3. 14(square root)2
The segment length is 14 (square root)2
Given that Triangle ABC is right angle triangle
The vertex marked is B where side AC is the hypotenuse
The side of AC is at Vertex B is 14
The dash segment from vertex B to point D on side AC
Angle BDA is marked right angle .
Angles A and C both marked 45 degrees.
As shown in diagram
Triangle ABC is drawn according to the statement where B is vertex
The side lengths are 14
Now to find Another side length that is x
So , the equation formed is
x*cos45 = 14
x/√2 = 14
x = 14√2
Hence the length of the segment is 14√2
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Answer:
Step-by-step explanation:
The segment length is 14 (square root)2
Given that Triangle ABC is right angle triangle
The vertex marked is B where side AC is the hypotenuse
The side of AC is at Vertex B is 14
The dash segment from vertex B to point D on side AC
Angle BDA is marked right angle .
Angles A and C both marked 45 degrees.
As shown in diagram
Triangle ABC is drawn according to the statement where B is vertex
The side lengths are 14
Now to find Another side length that is x
So , the equation formed is
x*cos45 = 14
x/√2 = 14
x = 14√2
Hence the length of the segment is 14√2
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!!!HELP!!!
A plane intersects one cone of a double-napped cone such that the plane is parallel to the generating line.
What conic section is formed?
A. hyperbola
B. circle
C. parabola
D. ellipse
Answer: C. Parabola
Definition: a parabola is a conic section in which it is mostly characterised of having a U-shape wherein it is symmetrical and an open plane curve.
PLEASE HELP
How many integers are there on the number line between $2\sqrt{10}$ and $10\sqrt{2}$?
Answer:
8
Step-by-step explanation:
To one decimal place:
[tex]2 \sqrt{10} = 6.3[/tex]
[tex]10 \sqrt{2} = 14.1[/tex]
So there are eight integers between 2√10 and 10√2: 7, 8, 9, 10, 11, 12, 13, and 14.
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equation to solve is 2a + b = 15.7.
Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2 l plus 2 w equals 62 to find the width of the run.
Which statements are true of the solution? Check all that apply.
The value of w is 10 feet.
The value of w can be zero.
The value of w cannot be a negative number.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.
Answer:
[c] The value of w cannot be a negative number.
[d] Substitution is used to replace the variable l with a value of 20.
[e] The subtraction property of equality is used to isolate the term with the variable w.
Step-by-step explanation:
To figure out which steps of the solution are true, let us solve.
2 l plus 2 w equals 62 -> 2l + 2w = 62
----
2l + 2w = 62
2(20) + 2w = 62 <- Substitution is used to replace the variable l with a value of 20.
40 + 2w = 62
2w = 22 <- The subtraction property of equality is used to isolate the term with the variable w.
w = 11
This means that the value of w is not 10 feet so the first option is incorrect. This shape is a rectangle, so the value of w cannot be 0. Since we cannot have a negative measurement, option three is incorrect. This leaves us with the last three options as our answer, shown by the work above.
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Help ASAP, really stuck
The total length of the wire needed to make this shape is 162cm
Perimeter of a triangleThe perimeter of a triangle is the sum of the external side of the triangle.
Given the following parameters
Length of one side of the outside shape = 24cm
The side length of the smaller triangle = 24/4 = 6cm
The perimeter of the smallest triangle 3(6) = 18cm
The perimeter of the smaller triangle (at the middle) = 12(3) = 36cm
Total length of wire needed. = 3(24) + 3(18) + 36
Total length of wire needed = 72 + 54 + 36
Total length of wire needed = 162cm
Hence the total length of the wire needed to make this shape is 162cm
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You are working in a lab and you need a solution of 22% acid. In the cupboard, you find a 10% and a 30% solution, but not a 22% solution. You will have to make your own 22% solution. You will need liters of the 10% and liters of the 30% to make 15 liters of a 22% solution?
The volume of 10% solution will be 6 l and 9 litre of the 30 % solution will be taken.
What is Volume ?Volume is the space occupied by a three dimensional object .
The concentration of solution required is 22% acid
The concentration of solution available is 10% and 30%
The total volume required is 15 liters
The formula for making a mixture is
Concentration = ( m₁x₁ +m₂x₂) / (x₁+x₂)
22 = (10 * x + 30 *(15 -x))/( 15)
10 x + 450 - 30x =330
-20x = -120
x = 6
The volume of 10% solution will be 6 l
and 9 litre of the 30 % solution will be taken.
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What is the vertex of the quadratic function below y=-x^-2x-5
Answer:
(-1, -4)
Step-by-step explanation:
y = -x² - 2x - 5
y = -1(x² + 2x + 5)
y = -1(x² + 2x + 1 - 1 + 5)
y = -1(x² + 2x + 1) - 4
y = -(x + 1)² - 4