HELPPPP ASAP PLEASE HURRY 50 POINTS
The interval giving the middle 68% of the lifetime of bulbs in hours is given as follows:
(1350, 1450).
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The middle 68% of scores is within one standard deviation of the mean, hence the bounds of the interval are given as follows:
1400 - 50 = 1350.1400 + 50 = 1450.More can be learned about the Empirical Rule at https://brainly.com/question/10093236
#SPJ1
12. For this problem, consider the permutationsα=(1223344551677886),β=(1123384756657284),γ=(1235)(24568)(a) Write each of the permutations as a product of disjoint cycles. (b) Find the order of each permutation. (c) Write each permutation as a product of 2-cycles and determine which are even and which are odd. (d) Write the inverse of each of the permutations as a product of disjoint cycles. (e) Writeαβandβαas products of disjoint cycles, and find their orders.
(a) The permutations can be written as a product of disjoint cycles as follows:
α = (1 5 4 3 2)(6 7 8)
β = (1)(2 3 8 4 7)(5 6)
γ = (1 2 3 5)(4 5 6 8)
(b) The order of each permutation is the least common multiple of the lengths of the disjoint cycles. Therefore:
Order of α = lcm(5, 3) = 15
Order of β = lcm(1, 5, 2) = 10
Order of γ = lcm(4, 4) = 4
(c) The permutations can be written as a product of 2-cycles as follows:
α = (1 2)(2 3)(3 4)(4 5)(5 1)(6 7)(7 8)(8 6)
β = (1 1)(2 3)(3 8)(8 4)(4 7)(7 1)(5 6)(6 5)
γ = (1 2)(2 3)(3 5)(5 1)(4 5)(5 6)(6 8)(8 4)
Since α and β have an even number of 2-cycles, they are even permutations. γ has an odd number of 2-cycles, so it is an odd permutation.
(d) The inverse of each permutation can be found by reversing the order of the elements in each cycle. The inverses can be written as a product of disjoint cycles as follows:
[tex]α^-1 = (1 2 3 4 5)(6 8 7)β^-1 = (1)(2 7 4 8 3)(5 6)γ^-1 = (1 5 3 2)(4 8 6 5)[/tex]
(e) The products αβ and βα can be found by performing the permutations in the given order. The products can be written as a product of disjoint cycles as follows:
αβ = (1 6 8 4 7 2 3 5)(5 1)
βα = (1 7 4 8 6 5 3 2)(2 1)
The order of αβ is lcm(8, 2) = 8, and the order of βα is lcm(8, 2) = 8.
To know more about permutation refer to-
brainly.com/question/30649574#
#SPJ11
20. Let V be an Euclidean space and letx,y∈V. (a)†If∥x+y∥=∥x−y∥then determine⟨x,y⟩. (b) * Show that2⟨x,y⟩≤∥x∥2+∥y∥2. (c) If(z,y)=0for allz∈Vthen show thaty=0. (d) †If∥x∥=∥y∥for somex,y∈Vthen⟨x+y,x−y⟩=0. (e)†Pythagorean theorem: Show that⟨x,y⟩=0if and only if∥x+y∥2=∥x∥2+∥y∥2.
Pythagorean theorem: Show that ⟨x, y⟩ = 0
Let V be an Euclidean space and let x, y ∈ V.(a) If ∥x + y∥ = ∥x − y∥ then determine ⟨x, y⟩.We know that ∥x + y∥² = ⟨x + y, x + y⟩ = ⟨x, x⟩ + ⟨x, y⟩ + ⟨y, x⟩ + ⟨y, y⟩ = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x − y∥² = ⟨x − y, x − y⟩ = ⟨x, x⟩ − ⟨x, y⟩ − ⟨y, x⟩ + ⟨y, y⟩ = ∥x∥² − 2⟨x, y⟩ + ∥y∥²Since ∥x + y∥ = ∥x − y∥, we have ∥x∥² + 2⟨x, y⟩ + ∥y∥² = ∥x∥² − 2⟨x, y⟩ + ∥y∥²⟨x, y⟩ = 0(b) Show that 2⟨x, y⟩ ≤ ∥x∥² + ∥y∥².We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x + y∥² ≥ 0So ∥x∥² + 2⟨x, y⟩ + ∥y∥² ≥ 0⟨x, y⟩ ≤ (∥x∥² + ∥y∥²)/2(c) If (z, y) = 0 for all z ∈ V then show that y = 0.Let z = y, then (y, y) = 0⟨y, y⟩ = ∥y∥² = 0∥y∥ = 0So y = 0(d) If ∥x∥ = ∥y∥ for some x, y ∈ V then ⟨x + y, x − y⟩ = 0.We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x − y∥² = ∥x∥² − 2⟨x, y⟩ + ∥y∥²Since ∥x∥ = ∥y∥, we have ∥x∥² = ∥y∥²So ∥x + y∥² − ∥x − y∥² = 4⟨x, y⟩ = 0⟨x, y⟩ = 0(e) Pythagorean theorem: Show that ⟨x, y⟩ = 0 if and only if ∥x + y∥² = ∥x∥² + ∥y∥².We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²If ⟨x, y⟩ = 0, then ∥x + y∥² = ∥x∥² + ∥y∥²If ∥x + y∥² = ∥x∥² + ∥y∥², then 2⟨x, y⟩ = 0⟨x, y⟩ = 0
Learn more about Pythagorean theorem
brainly.com/question/14930619
#SPJ11
when an integer m is divided by 5 the remainder is 3. When m is divided by 7 the remainder is 1. If m is greater than 40 but less than 80, what is one possible value of m.
One possible value of m is 53.
A possible value of m can be found using the Chinese Remainder Theorem. The Chinese Remainder Theorem states that if two numbers a and b are relatively prime, then there exists an integer x such that:
x ≡ a (mod m)
x ≡ b (mod n)
In this case, we have:
m ≡ 3 (mod 5)
m ≡ 1 (mod 7)
Both 5 and 7 are prime so we can start by finding the smallest positive integer that is congruent to 3 (mod 5) and 1 (mod 7). This integer is 18:
18 ≡ 3 (mod 5)
18 ≡ 1 (mod 7)
Now, we can add multiples of 5*7 = 35 to 18 until we find a value of m that is greater than 40 but less than 80:
18 + 35 = 53
53 is greater than 40 but less than 80, so one possible value of m is 53.
Therefore, one possible value of m is 53.
To learn more about Chinese Remainder Theorem:
https://brainly.com/question/30811240#
#SPJ11
I think it's B but I'm not sure
Use the solid figure to determine whether each statement is true or false. A?
b?
c?
d?
e?
f?
To make the solid figure true using column A and column B are as follow,
1.ice cube → cube
2.tissue roll → cylinder
3.match box →rectangular prism
4.volleyball →sphere
5.can of sardines →cylinder
6.milk box → rectangular prism
7.volcano →cone
8.toblerone →triangular prism
9.bus→rectangular prism
10.roof of a nipa hut→ triangular pyramid
Solid figure represents the following shape,
1. Ice cube represents the cube shape as all the sides are of same length.
2. Tissue roll represents the cylindrical shape.
3. Match box is an perfect example for rectangular prism.
4. Volleyball represents the spherical shape.
5. Can of sardines is one of the perfect example of cylinder.
6. Milk box is also one of the example of rectangular prism
7.volcano represents the cone.
8.toblerone is representing triangular prism.
9.bus is a example of rectangular prism
10.roof of a nipa hut it is an example of triangular pyramid
Learn more about solid figure here
brainly.com/question/29161618
#SPJ4
The above question is incomplete, the complete question is:
Choose the solid figure in Column B to make each statement is true of column A.
Column A.
1.ice cube
2.tissue roll
3.match box
4.volleyball
5.can of sardines
6.milk box
7.volcano
8.toblerone
9.bus
10.roof of a nipa hut
Column B.
A. cone
B. cube
C. cylinder
D. rectangular prism
E. sphere
F. square pyramid
G. triangular prism
H. triangular pyramid
Mark is training for a mini triathlon he rode his bike 3/4 Mille ran 2/4 milks and swam 1/4 mile each day how does the distance he biked in 3 days compare to the distance he swam in 3 days in 5 days in 6 days why
The comparison between the distance he biked and swam is 3 : 1.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information the comparison of the distance he swam to the distance he biked can be represented in the form of ratios.
Given, He rode his bike 3/4 miles and swam for 1/4 mile.
Therefore, The ratio of biking : swimming = 3/4 : 1/4.
Now, Multiplying by 4 to get rid of the denominator we have,
Biking : Swimming = 3 : 1.
As the days in both comparisons increase in the same manner the ratio will remain the same.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
A student used factor by grouping to factor the expression below. How can you tell that the student made an error when factoring? Explain the error.
Student's work: 6x² – x – 12
6x² – 9x + 8x – 12
3x(2x – 3) – 4(–2x +3)
The error made by the student is instead of taking +4 as common he has taken - 4 as common.
Factoring by grouping terms:To factor an expression by grouping, we need to look for groups of terms that have common factors. Then, we factor out those common factors from each group and see if there is a common factor that can be further factored out.
Here we have
6x² – x – 12
The above expression can be factorized as follows
=> 6x² – x – 12
= 6x² – 9x + 8x – 12 [ Splitting the middle term ]
= 3x(2x – 3) + 4(2x – 3) [ Grouping the terms ]
= (3x + 4)(2x – 3)
Hence, the factors of given expression are (3x + 4) and (2x – 3)
The error made by the student is in step 3 instead of taking +4 as common he has taken - 4 as common which doesn't give the common factors in the next step taken.
Therefore,
The error made by the student is instead of taking +4 as common he has taken - 4 as common.
Learn more about Factoring at
https://brainly.com/question/23717579
#SPJ1
Which comparison is not correct?
-7 < -2
-1 > -5
7 > -9
5 < -8
[tex]5 < - 8[/tex]
__________
What is the surface area for a box with 12 as length, 10 as height and 3 as width.
Answer: 372 units²
Step-by-step explanation:
We can use this formula to solve for the surface area:
Surface Area = 2lw + 2lh + 2hw
We will substitute the known values and solve:
Surface Area = 2lw + 2lh + 2hw
Surface Area = 2(12)(3) + 2(12)(10) + 2(10)(3)
Surface Area = 372 units²
Teresa can paddle her kayak 6 miles per hour in still water. It takes her as long to paddle 9 miles upstream as it takes her to travel 27 miles downstream. Determine the speed of the river's current.
The speed of the river's current is 3 miles per hour.
How To determine the speedTo determine the speed of the river's current, we can use the formula d = rt, where d is the distance, r is the rate, and t is the time.
We can set up two equations, one for upstream and one for downstream, and solve for the speed of the river's current.
For upstream:
9 = (6 - c)t
For downstream: 27 = (6 + c)t
Since it takes her the same amount of time to paddle 9 miles upstream as it does to travel 27 miles downstream, we can set the two equations equal to each other:
9 = (6 - c)t = 27 = (6 + c)t
Simplifying and solving for c:
9(6 + c) = 27(6 - c) 54 + 9c = 162 - 27c 36c = 108 c = 3
Therefore, the speed of the river's current is 3 miles per hour.
Learn more about speed at
https://brainly.com/question/28224010
#SPJ11
Solve the proportion.
$\frac{x}{4}=\frac{2}{5}$
$
The value of x from the proportion is x = 1.6
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion equation be represented as A
Now , the value of A is
( x / 4 ) = ( 2 / 5 )
On simplifying , we get
Multiply by 4 on both sides , we get
x = ( 2 * 4 ) / 5
x = 8/5
On further simplification , we get
x = 1.6
Therefore , the value of x is 1.6
Hence , the proportion is x = 1.6
To learn more about proportion click :
https://brainly.com/question/7096655
#SPJ9
I'm so confused on thins can someone PLEASE help me??? It's Algebra by the way
Answer:
Degree: The degree of the function is 3.
X-Intercepts with multiplicity greater than 1: x = -2 and x = 0
How many distinct x-intercepts?: There are two distinct x-intercepts.
How many zeros are there?: There are three zeros, one at x = -2 and two at x = 0 (with a multiplicity of 2).
population 31,200 now... increase 10% per year... what ws the population 2 years ago?
The population two years ago was 28,080.
To calculate this, we need to use the following formula: Population two years ago = Population now - (Population increase rate x Number of years). Therefore, the population two years ago was 31,200 - (10% x 2) = 28,080.
We can also look at this another way. To calculate the 10% increase per year, we can use the following formula: Population increase rate = (Population now - Population two years ago) / Number of years. Therefore, 10% = (31,200 - 28,080) / 2 = 3,120.
We can use this same formula to calculate the population three years ago. Using the same formula, the population three years ago was 25,960.
To summarize, the population two years ago was 28,080 and the population three years ago was 25,960. The population has been increasing by 10% each year.
To learn more about percentage from given link
https://brainly.com/question/29306119
#SPJ11
I am needing some help with this
The volume of the cone is 1004.8 cm³.
How to find the volume of a cone?Let's calculate the volume of the cone with radius 8 cm and the slant height is 17 cm. Therefore, let's find the volume of the cone as follows:
volume of a cone = 1 / 3 πr²h
where
r = radiush = height of the coneTherefore,
h² = 17² - 8²
h = √289 - 64
h = √225
h = 15 cm
Therefore,
volume of a cone = 1 / 3 × 3.14 × 8² × 15
volume of a cone = 1 / 3 × 3.14 × 64 × 15
volume of a cone = 3014.4 / 3
volume of a cone = 1004.8 cm³
learn more on cone here: https://brainly.com/question/29267007
#SPJ1
what value of x makes the equation 3x(x-6) -8x=-(2x+1)
The value of x is (12 ± √141) / 3. The solution has been obtained by solving the algebraic equation.
What is an algebraic equation?A mathematical expression is said to be "algebraic" if it includes variables, constants, and algebraic operations (addition, subtraction, etc.). The equals sign is a requirement for the expression to satisfy the algebraic equation.
We are given an equation as 3x (x - 6) - 8x = -(2x + 1)
On solving the given equation, we get
⇒3x (x - 6) - 8x = -(2x + 1)
⇒3x² - 18x - 8x = -2x - 1
⇒3x² - 26x = -2x - 1
⇒3x² - 24x = - 1
⇒3x² - 24x + 1 = 0
Using quadratic formula, we get
x = (12 ± √141) / 3
Hence, the value of x is (12 ± √141) / 3.
Learn more about algebraic equation from the given link
https://brainly.com/question/24875240
#SPJ1
One Monday in December, it was `-8`ºC in Harbin, China and `-2`ºC in Beijing, China. Which city was colder on that day?
Harbin was colder than Beijing on that particular day in December because the temperature difference between the two cities was -6ºC.
To figure out which city was colder, we need to compare the difference between the temperatures of the two cities. The temperature difference is the numerical value we get when we subtract one temperature from the other.
In this case, the temperature in Harbin was -8ºC and the temperature in Beijing was -2ºC. To find out which city was colder, we need to calculate the temperature difference between the two cities.
To do this, we subtract the temperature in Beijing from the temperature in Harbin:
-8ºC - -2ºC = -6ºC
So the temperature difference between the two cities is -6ºC. This means that Harbin was colder than Beijing on that day.
We can see that the temperature difference is negative, which tells us that the temperature in Harbin was lower than the temperature in Beijing.
To know more about difference here
https://brainly.com/question/30241588
#SPJ4
Help pls !!!!!!!!!!!!!!!!!!!!!!
Answer:
I think 2nd option..........
a company is building square-bottomed boxes with no tops. the material for the bottom costs $2 per cm2 and the material for the sides costs $1 per cm2. the company has budgeted $96 to build one box. what is the box of largest volume the company can build for $96
The box of largest volume the company can build for $96 is the box that costs exactly $96.
The company can build a box of the largest volume for $96 by calculating the area of the bottom and sides of the box. To calculate the area of the bottom, use the formula A=l x w, where l is the length of one side and w is the width of one side. Since the bottom is square, l=w. Thus, A=l^2. The area of the bottom is then multiplied by the cost of the material for the bottom, which is $2 per cm2, to calculate the total cost of the bottom.
Similarly, to calculate the cost of the sides, use the formula A=2lh + 2wh, where h is the height of the box. The area of the sides is then multiplied by the cost of the material for the sides, which is $1 per cm2, to calculate the total cost of the sides.
The total cost of the box is the cost of the bottom plus the cost of the sides. Since the company has budgeted $96 to build one box, the total cost of the box must not exceed $96. Therefore, the box of largest volume the company can build for $96 is the box that costs exactly $96.
Learn more about largest volume
brainly.com/question/23423861
#SPJ11
The points F(8,-1), G(2,1), H(1, -2), and I(7,-4) form a quadrilateral. Find the desired slopes and lengths, then fill in the words that BEST identifies the type of quadrilateral.
The points F(8,-1), G(2,1), H(1, -2), and I(7,-4) form a quadrilateral. The desired slopes and lengths are follows:
Slopes:The type of quadrilateral that BEST identifies the given points is a parallelogram.
To find the slopes and lengths of the quadrilateral, we will use the slope formula and the distance formula.
Slope formula: m = (y2 - y1)/(x2 - x1)
Distance formula: d = √((x2 - x1)² + (y2 - y1)²)
Slopes:
FG: m = (1 - (-1))/(2 - 8) = -1/3
GH: m = (-2 - 1)/(1 - 2) = 3
HI: m = (-4 - (-2))/(7 - 1) = -1/3
IF: m = (-1 - (-4))/(8 - 7) = 3
Lengths:
FG: d = √((2 - 8)² + (1 - (-1))²) = √(40) = 2√(10)
GH: d = √((1 - 2)²+ (-2 - 1)²) = √(10)
HI: d = √((7 - 1)^2 + (-4 - (-2))²) = √(40) = 2√(10)
IF: d = √((8 - 7)² + (-1 - (-4))^2) = √(10)
From the above calculations, we can see that the slopes of FG and HI are equal, and the slopes of GH and IF are equal. This means that the opposite sides of the quadrilateral are parallel. Additionally, the lengths of FG and HI are equal, and the lengths of GH and IF are equal. This means that the opposite sides of the quadrilateral are also congruent.
Therefore, the type of quadrilateral that BEST identifies the given points is a parallelogram.
Learn more about quadrilateral at https://brainly.com/question/29265709
#SPJ11
In 2011, there were approximately 2.8 million nurses in a large country, with demand for nurses expected to increase by 0.044 million each year. a. Assuming the number of nurses in 2011 represents the demand for that year, express the demand for nurses in the country, D, in millions, as a function of the number of years after 2011,x. b. If the demand increases as expected, during which year will demand for nurses in the country reach 3.5 million? a. D(x)=
The demand for nurses in the country can be expressed as the function D(x) = 2.8 + 0.044x. The year in which the demand for nurses in the country will reach 3.5 million is in 2027.
a. The demand for nurses in the country can be expressed as a function of the number of years after 2011, x, by using the equation D(x) = 2.8 + 0.044x. This equation represents the initial demand in 2011 (2.8 million) plus the expected increase in demand each year (0.044 million) multiplied by the number of years after 2011 (x).
b. To find the year in which the demand for nurses will reach 3.5 million, we can set D(x) equal to 3.5 and solve for x:
3.5 = 2.8 + 0.044x
0.7 = 0.044x
x = 0.7 / 0.044
x = 15.9
Since x represents the number of years after 2011, we can add 15.9 to 2011 to find the year in which the demand will reach 3.5 million:
2011 + 15.9 = 2026.9
Therefore, the demand for nurses in the country will reach 3.5 million during the year 2027.
Learn more about function here: https://brainly.com/question/25638609.
#SPJ11
If 2x-1 is a factor of 24x^4 - 2x^2 +2x +f find f
If 2x-1 is a factor of 24x⁴ - 2x² +2x +f , the value of f is 1 - 2x.
Describe Long division?Synthetic division is a method of polynomial division used to divide a polynomial by a linear expression of the form x - a, where a is a constant. It is a shorthand way of performing long division for polynomials and is particularly useful when the divisor is of the form x - a, as it eliminates the need for writing out the full divisor in each step of the division process.
Since 2x-1 is a factor of the given polynomial, we know that it will divide exactly into the polynomial, leaving no remainder. Therefore, we can use polynomial long division to find the quotient when 24x⁴ - 2x² + 2x + f is divided by 2x-1:
12x³ + 5x² - 3x - f/2 + 1/4
____________________________________
2x - 1 | 24x⁴ + 0x³ - 2x² + 2x + f
- (24x⁴- 12x³)
----------------------
12x^3
- (12x³ - 6x^2)
----------------------
5x^2
- (5x² - 2.5x)
----------------------
2.5x
- (2.5x - f/4)
-----------------------
f/4 + 2x/4 - 1/4
Since there is no remainder, the last term in the quotient must be zero. Therefore:
f/4 + 2x/4 - 1/4 = 0
Simplifying and solving for f, we get:
f/4 = 1/4 - 2x/4
f = 1 - 2x
Therefore, f = 1 - 2x.
To know more about quotient visit:
https://brainly.com/question/29139017
#SPJ1
Jian made some designs using equilateral triangles, as shown below. He noticed that as he added new triangles, there was a
relationship between n, the number of triangles, and p, the outer perimeter of the design. The table below lists the outer
perimeters for the designs shown.
Number of 1 2 3 4
triangles
Outer
Perimeter
3 4 5 6
n
A
Р
Write a rule for finding p, the outer perimeter for a design that uses n triangles.
The perimeter is the tοtal length οf a shape's bοundary, and the rule fοr finding the οuter perimeter οf Jian's equilateral triangle designs is p = n + 1.
What is a perimeter?The perimeter οf a twο-dimensiοnal shape is the tοtal length οf its bοundary, which is the sum οf the lengths οf all its sides. It is typically measured in units such as centimeters, inches, οr meters.
Fοr example, the perimeter οf a square with side length s is 4s, since it has fοur sides οf equal length. The perimeter οf a rectangle with length l and width w is 2l + 2w, since it has twο pairs οf sides οf different lengths.
Nοw, let's cοnsider the relatiοnship between the number οf triangles and the οuter perimeter οf Jian's design. Frοm the table, we can see that the οuter perimeter increases by 1 as the number οf triangles increases by 1. Specifically, the οuter perimeter is always 1 mοre than the number οf triangles used in the design.
Therefοre, we can write the rule fοr finding the οuter perimeter p in terms οf the number οf triangles n as:
p = n + 1
This rule tells us that if we knοw the number οf triangles used in a design, we can find the οuter perimeter by adding 1 tο that number.
Hence, The perimeter is the tοtal length οf a shape's bοundary, and the rule fοr finding the οuter perimeter οf Jian's equilateral triangle designs is p = n + 1.
To learn more about the perimeter, visit:
https://brainly.com/question/397857
#SPJ1
PLS HELP OML IM STRUGGLINGGG !!!!!! best answer = brainliest !!!
Answer:
Area = 15.6
Perimeter = 20.6
Step-by-step explanation:
Both smaller triangles are right triangles
The left triangle is isosceles right triangle since 2 angles are 45o so AB is hypotenuse and the other 2 sides are equal
so c^2 = a^2 + b^2
c^2 = 2a^2
(3√2)^2 = 2a^2
2a^2 = 18
a^2 = 9
a = 3
For the right triangle the angle at B is 60o, hypotenuse is BC
so cos(60) = adjacent/hypotenuse
1/2 = 3/BC
=> BC = 6
sin(60) = opposite/hypotenuse
√3/2 = opp/6
opp = 3√3
so AC = 3 + 3√3 = 6√3
Area of triangle = A = 1/2bh = 1/2(6√3)(3) = 9√3 = 15.6
Perimeter = 3√2 + 6√3 + 6 = 20.6
Write an equation of a circle with center at (4,-1) and a point at (2,-4)
Explain please
Answer:
y=3/2x-7
Step-by-step explanation:
A third grade class is making paper cups and snowman crafts of popsicle sticks. It takes 271 popsicle sticks to make eight pencil cups and 15 snowmen. It takes 373 popsicle sticks to make 14 pencil cups and 15 snowmen. How many popsicle sticks are needed for one snowman?
The total number of popsicle sticks needed to make one snowman using the given conditions for system of equations is equal to 9.
Let us consider 'x' is the number of popsicle sticks required to make one pencil cup.
And 'y' represents the number of popsicle sticks required to make one snowman.
The required set up two equations are,
8x + 15y = 271 ___(1)
14x + 15y = 373 ___(2)
Multiplying both sides of equation (1) by 14 and both sides of equation (2) by -8 we get,
112x + 210y = 3794
-112x - 120y = -2984
Add both the above equations to eliminate the x variable we get,
⇒ 112x + (-112x) + 210y + (-120y) = 3794 + (-2984)
Simplifying the equation we get,
⇒90y = 810
Dividing both sides by 90 we get,
⇒ y = 9
Therefore, number of popsicle sticks required to make one snowman is equal to 9.
learn more about popsicle sticks here
brainly.com/question/20312588
#SPJ4
A European company is selling a new brand of headphones. For h headphones sold, in thousands, a profit of E(h) = -4h^(4) + 7h^(3) - 7h + 20, in ten thousands of Euros, will be earned. How much will be earned in profit for selling 1,500 headphones?
The European company will earn 128,750 Euros in profit for selling 1,500 headphones.
How to find sale profitTo find the profit for selling 1,500 headphones, we need to plug in the value of h into the profit function E(h) and simplify.
Since h is measured in thousands of headphones, we need to divide 1,500 by 1,000 to get h = 1.5.
Now we can plug in h = 1.5 into the profit function and simplify:
E(1.5) = -4(1.5)^(4) + 7(1.5)^(3) - 7(1.5) + 20
E(1.5) = -4(5.0625) + 7(3.375) - 10.5 + 20
E(1.5) = -20.25 + 23.625 - 10.5 + 20
E(1.5) = 12.875
So the profit for selling 1,500 headphones is 12.875 ten thousands of Euros, or 128,750 Euros.
Therefore, the European company will earn 128,750 Euros in profit for selling 1,500 headphones.
Learn more about equation at
https://brainly.com/question/15707224
#SPJ11
PLEASE HELP ASAP
how much percent is 2882.45 of 3374.60?
( include working out and show answer as percentage )
Answer:
97271.1577
Step-by-step explanation:
multiply 3374.60 by 2882.45%
Kim went to the store she bought fewer than 20 pieces of fruit she bought three more apples then oranges how many of each kind of fruit Kim could gave him bought? how many how many pieces of fruit in all?
The number of fruits that Kim bought in all, given the apples and oranges was ;
8 oranges 11 apples How to find the number of fruits ?Let's call the number of oranges that Kim bought "O" and the number of apples that Kim bought "A".
From the problem, we know that Kim bought fewer than 20 pieces of fruit, so we can write:
A + O < 20
A = O + 3
Simplifying:
2O + 3 < 20
2O < 17
O < 8.5
Since O represents the number of oranges, we know that Kim bought fewer than 8.5 oranges. Since she can't buy a fraction of an orange, this means that she must have bought either 8 oranges or fewer.
Now we can use the equation A = O + 3 to find the number of apples she bought:
A = 8 + 3 = 11
So Kim bought 8 oranges and 11 apples.
Find out more on fruits at https://brainly.com/question/27936661
#SPJ1
Julian makes and sells wallets. He estimates that his income can be modeled by y = 18x - 140, where x is the number of wallets he sells. He estimates that his costs to make the wallets can be modeled by y = 7x+160. How many wallets does Julian need to make in order to break even?
Therefore , the solution of the given problem of equation comes out to be julian must sell at least 28 wallets in order to make even.
How do equations operate?Mathematical formulas frequently use the same variable letter to try to impose unity between two assertions. Many academic numbers are shown to be equal using mathematical fraction equations, also known as assertions. Using y + 6 as an illustration, the normalise does not divide 12 into two parts, but instead b + 6. It is possible to determine the connection between each sign part and the number of lines. The significance of a symbol usually contradicts itself.
Here,
For Julian to break even, his revenue must match his expenses. Therefore, we can equalise the two equations and find x:
=> 18x - 140 = 7x + 160
7x is subtracted from both lines to yield:
=> 11x - 140 = 160
140 added to both ends results in:
=> 11x = 300
When we multiply both parts by 11, we get:
=> x = 27.27 (rounded to two integer places) (rounded to two decimal places)
We can round up to the nearest whole amount because Julian cannot sell a fraction of a wallet. Julian must therefore sell at least 28 wallets in order to make even.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1