For the typical glass thickness of 3.12 mm, the 95% two-sided confidence interval will be (3.067,3.173).
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.
Here,
mean x=3.12 mm
Standard deviation s=0.14 mm
number of sample n=21
two-sided confidence interval,
=x±tₐ÷₂(s/√n)
a=1-0.95
a=0.05
t₀.₀₅,₂₀=1.725
=3.12±1.725*(0.14/√21)
=3.12±1.725*(0.14/4.58)
=3.12±1.725*0.0306
=3.12±0.053
=(3.067,3.173)
The 95% two-sided confidence interval for the mean glass thickness of 3.12 mm will be (3.067,3.173).
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Find the area of the shaded region in the figure. Round results to the nearest uni. Use 3.14
The Area of the shaded part is 3.44 cm²
Area of circle:The formula used to find the Area of a circle is given by
Area of circle = 2πrWhere r is the radius of the circle
Area of Square:The formula used to find the Area of a Square is given by
Area of Square = Side²
Here we know
The radius of the circle = 2m
As we know Area of a Circle = 2πr
=> Area of given circle = 2(3.14)2 = 12.56 cm²
Area of circle = 12.56 cm²
As we can see the circle is inscribed in a square
Then the Length of the side square = diameter of the circle
=> Length of side = 2 × Radius of circle = 2 × 2 cm = 4 cm
Length of side = 4 cm
As we know Area of the square = side²
=> Area of given square = 4 × 4 = 16 cm²
Now using the above value we will friend the area of the shaded part
Area of shaded part = Area of the square - Area of the circle
= 16 cm² - 12.56 cm² = 3.44 cm²
Therefore,
The Area of the shaded part is 3.44 cm²
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Could some one please help me with this question.
In the octagon, the measurement of the largest exterior angle is 90°.
What is polygon?In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words, poly, which means numerous and gon, means sides.
The given exterior angles of the octagon are,
x°, 2x°, 3x°, 4x°, 5x°, 7x°, 8x°, and 10x°.
The sum of the exterior angle of the octagon is 360°.
Implies that,
x + 2x + 3x + 4x + 5x + 7x + 8x + 10x = 360
40x = 360
x = 9
The largest exterior angle = 10 x = 10 × 9 = 90°.
The required largest exterior angle is 90°.
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Which of the following is equivalent to 5(x+6)-6(3x+3)=10
Answer:
B
Step-by-step explanation:
5x + 30 - 18x - 18 = 10
-13x + 12 = 10
Could Someone Let me know if I checked off the correct answer? And if not explain what I did wrong.
Answer:
See below ( you have it correct !)
Step-by-step explanation:
See image below....sometimes it is easier to see these things if you extend some lines a bit:
Solve the equation: x^2-13/2 x+15/2=0
Answer:
Step-by-step explanation:
199/4
Find the reciprocals of the following numbers.
a, if a ≠ 0
The Reciprocal of a (if a ≠ 0) is...
Reciprocal of a = [tex]\frac{1}{a}[/tex]
What is Reciprocal ?
In Mathematics , reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n.
What are real numbers ?
In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions .
According to the given information
a ≠ 0
a is a real number
By the definition of reciprocal
Reciprocal of a will be the inverse of a = [tex]\frac{1}{a}[/tex]
Reciprocal of a = [tex]\frac{1}{a}[/tex]
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f(x)=x²-25
Find f(9)
Music Company A charges a $ 15 membership fee and $ 0.75 each to download a song. Music Company B charges $ 0.90 each to download a song with no membership fee.
a. For what number of songs will both companies charge the same amount? Justify your answer using mathematics.
songs
You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money? Justify your answer using mathematics.
(i) At a total of 100 Songs the Charges for Company A and Company B will be Equal.
(ii) I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
What is Linear Equation in One Variable?
A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.
Solution:
Let, Songs Downloaded be x
Total Charges of Company A = 15 + 0.75*x
Total Charges of Company B = 0.9*x
(i) Total Charges by Company A = Total Charges by Company B
15 + 0.75*x = 0.9*x
15 = 0.15*x
x = 100 songs
(ii) Charges by Company A to Download 150 Songs = 15 + 0.75 * 150
= 15 + 112.5 = $127.5
Charges by Company B to Download 150 Somgs = 0.9 * 150 = $135
I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5
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43. What system of inequalities is represented by the graph? (1 point)
-2 -1
2
- C
0
-1
0 1
2
Oy≤3x-2 and y2-4x+2
Oy23x-2 and y≤-4x+2
Oy≤-2x+3 and y 22x-4
Oy2-3x-2 and y ≤4x+2
3 4 question is in the photo. Please help if you can and thank you in advance.
The graph's representation of the inequality system is
y≤3x-2 and y≥-4x+2. So, option a is correct.
What is meant by inequality?One of the basic ideas of social justice theories is the existence of unequal status, rights, and opportunities. In public conversation, it might be confusing because various people often interpret it differently. There are some frequent variants, though. In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. As an illustration, suppose you wish to get a 250 new bicycle. Different types of inequality are indicated by a variety of notations, including:
A less than sign, such as a, denotes that an is greater than b.
Therefore, The system of inequalities that is represented by the graph is
y≤3x-2 and y≥-4x+2. So, option a is correct.
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-8y² - 1 = -8y
Quadratic equation
Answer:
y = (2 + √2)/4 ; y = (2 - √2)/4
Step-by-step explanation:
-8y² + 8y - 1 = 0
8y² - 8y + 1 = 0
discriminant = 64 - 4(8) = 64 - 32 = 32 = 2^4 * 2
y = (8 + [tex]\sqrt{2^4 * 2}[/tex])/16
(8 + 2²√2)/16
(8 + 4 √2) / 16
4(2+√2)/16
(2+√2)/4
y = (8 - [tex]\sqrt{2^4 * 2}[/tex])/16
(8 - 4√2) / 16
4(2-√2)/16
(2-√2)/4
Why do you think taxes have become more complicated since 1913?
Answer:
Before 1913, federal government revenues came mainly from taxes on goods—tariffs on imported products and excise taxes on items like whiskey.
Step-by-step explanation:
What was the tax rate in 1913?
The act levied a tax of one percent on all incomes above the exemption with additional surtax rates imposed for progressively higher incomes. Those surtax rates started at one percent for those making $20,000 or more and topped out at a mere six percent on incomes in excess of $500,000.
what is the average rate of change of the function on the interval from x=1 to x=2? f(x) = 10(5.5)^x
Answer: 246.7
Step-by-step explanation:
Pls help. Writing Linear equations from key information
1. goes through the points (-6,1) and (-3,2)
2. goes through the points (-3.2) and (8,2)
3. y-intercept = -1, goes through the point (3,8)
4. goes through the points (1,11) and (1,-2)
The linear functions in this problem are given as follows:
1. y = 1/3x + 3.
2. y = 2.
3. y = 3x - 1.
4. x = 1.
How to define the linear functions?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope.b is the y-intercept.For item 1, the points are given as follows:
(-6, 1) and (-3,2).
When x increases by 3, increases by 1, hence the slope is given as follows:
m = 1/3.
Then:
y = 1/3x + b.
When x = -3, y = 2, then the intercept b is calculated as follows:
2 = 1/3(-3) + b
b = 3.
Thus the function is:
y = 1/3x + 3.
Then items 2 and 4 are given as follows:
2 -> horizontal line -> y = 2.4 -> vertical line -> x = 1.For item 3, we have an intercept of -1, hence:
y = mx - 1.
When x = 3, y = 8, hence the slope m is calculated as follows:
8 = 3m - 1
3m = 9
m = 3.
Hence the function is:
y = 3x - 1.
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Help Please!!
Line q has an equation of y+7=9(x+4). Line r is perpendicular to line q and passes through (9,–10). What is the equation of line r?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer:
Y= -1/9x-9 that's the answer, you're welcome
The equation of line which is perpendicular to the line q is given by
y = ( -1/9 )x - 9
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
The point is P ( 9 , -10 )
Let the equation of line q be y + 7 = 9 ( x + 4 )
Now , on simplifying the equation , we get
y + 7 = 9x + 36
Subtracting 7 on both sides of the equation , we get
y = 9x + 29
Now , the slope of the equation q is m₁ = 9
Now , since the line r is perpendicular to line q
The product of the slope is -1
So , m₁ x m₂ = -1
Substituting the values in the equation , we get
9 x m₂ = -1
Divide by 9 on both sides of the equation , we get
m₂ = -1/9
So , the slope of the line r m₂ = -1/9
The equation of line is given by y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - ( -10 ) = -1/9 ( x - 9 )
On simplifying the equation , we get
y + 10 = -1/9 ( x - 9 )
y + 10 = ( -1/9 )x + 1
Subtracting 10 on both sides of the equation , we get
y = ( -1/9 )x - 9
Therefore , the value of A is y = ( -1/9 )x - 9
Hence , the equation of line r is y = ( -1/9 )x - 9
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A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey.
Invent four new versions of this lemonade recipe:
1: One that would make more lemonade but tastes the same as the original recipe.
2: One that would make less lemonade but taste the same as the original recipe.
3: One that would have a stronger lemon taste than the original recipe
4: One that would have a weaker lemon taste than the original recipe.
Since the lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey we can use mathematical operations to make different lemonades with the following recipes:
1) To make more lemonade taste the same as the original, we can use the multiplication operation on the above recipe as follows:
Lemons = 10
Cups of water = 4
Tablespoons of honey = 4
2) To make less lemonade taste the same as the original recipe, we can use the division operation as follows:
Lemons = 2.5
Cups of water = 1
Tablespoons of honey = 1
3) To make lemonade that has a stronger lemon taste than the original recipe, we can use the subtraction operation as follows:
Lemons = 4
Cups of water 1
Tablespoons of honey
4) To make lemonade that has a weaker lemon taste than the original recipe, we can use the addition operation as follows:
Lemons = 6
Cups of water 3
Tablespoons of honey = 3
Original Lemonade Recipe:Lemons = 5
Cups of water = 2
Tablespoons of honey = 2
1) Using the multiplication operation to make more lemonade taste the same as the original:
Lemons = 10 (5 x 2)
Cups of water = 4 (2 x 2)
Tablespoons of honey = 4 (2 x 2)
2) Using the division operation to make less lemonade taste the same as the original recipe:
Lemons = 2.5 (5 ÷ 2)
Cups of water = 1 (2 ÷ 2)
Tablespoons of honey = 1 (2 ÷ 2)
3) Using the subtraction operation to make lemonade that has a stronger lemon taste than the original recipe:
Lemons = 4 (5 - 1)
Cups of water 1 (2 - 1)
Tablespoons of honey = 1 (2 - 1)
4) Using the addition operation to make lemonade that has a weaker lemon taste than the original recipe:
Lemons = 6 (5 + 1)
Cups of water 3 (2 + 1)
Tablespoons of honey = 3 (2 + 1)
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Picture is the question
The months when the temperature will be 0 °C are May and August.
What is a trigonometric function?A trigonometric function is a function that has the trigonometric ratios.
What is temperature?Temperature is the degree of hotness or coldess of a body.
How to find the months in which the temperature is zero degrees?Since the average monthly temperature of a particular city is T(m) = 10cos(πm/6) + 5 where m = number of months of year and January begins at m = 0.
To find the number of months in which the temperature would be 0°C. This means T(m) = 0.
So, T(m) = 10cos(πm/6) + 5
0 = 10cos(πm/6) + 5
-10cos(πm/6) = 5
cos(πm/6) = 5/10
cos(πm/6) = -0.5
cos⁻¹cos(πm/6) = cos⁻¹(-0.5)
(πm/6) = π - π/6 or (πm/6) = 3π/2 - π/6 (since cos is negative int he second and third quadrant respectively)
πm/6 = 5π/6 or πm/6 = 8π/6
⇒ m = 5π/6 × 6/π or m = 8π/6 × 6/π
⇒ m = 5 or m = 8
Since m = 5 is May and m = 8 is August,
The months when the temperature will be 0 °C are May and August.
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10 points and brainliest.
two people need to answer or i won't be able to give brainliest
Fifteen students completed 80 puzzles. How many puzzles would 1 student complete? Round the answer to the nearest tenth.
1.6
0.2
5.3
15.0
5.3
80/15=5.3
which means each person completed 5.3 puzzles
Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below.
Negative 5 x minus 3.5 greater-than 6.5. Negative 5 x greater-than 10. x greater-than negative 50.
A number line going from negative 110 to positive 10. A closed circle is at negative 50. Everything to the right of the circle is shaded.
She should divide both sides by -5 while multiplying the other side by -5. She also did not replace the > symbol with a symbol.
What is an inequality ?An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
From given question :
-5x-3.5>6.5
-5x > 10
X > -50
Since, we have to solve for x
so, we will isolate x on anyone side
step-1:
Add both sides by 3.5
- 5x - 3.5 + 3.5 > 6.5 + 3.5
- 5x > 10
step-2:
Divide both sides by -5
we know that whenever we divide both sides by negative sign , it's inequality gets revered
so, we get
- 5x / -5 < - 50 / -5
we get
x < 10
so,
She should divide both sides by -5 while she multiplied by -5 on other side
and she also did not change the > symbol to a < symbol
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A wood state casket labeled 6/6XX would measure in length 6 feet 6 inches and in width
Answer: 28 inches
Hope this helps!!! :)
There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. How many are left in
the box?
The number of sweets left in the box after giving 35% is 325.
How to find the sweet left in the box?There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. The number of sweets left in the box can be calculated as follows:
Therefore, the number of sweet left in the box = 500 - 35% of 500
number of sweet left in the box = 500 - 35 / 100 × 500
number of sweet left in the box = 500 - 17500 / 100
number of sweets left in the box = 500 - 175
= 325
Therefore, the number of sweets left in the box will be 325
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HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!HELP MEEEEEEEEEEEEEEEEEEEEE PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]x=-2 \implies y=(1/3)^{-2}=3^{2}=9\\\\x=-1 \implies y=(1/3)^{-1}=3\\\\x=0 \implies y=(1/3)^0=1\\ \\ x=1 \implies y=1/3\\\\x=2 \implies y=(1/3)^2 =1/9[/tex]
Using these points, the correct graph is shown in option C.
Can a triangle be formed with side lengths 15, 7, and 6? Explain
Answer:no
Step-by-step explanation:
There is a property with triangles that the sum of two sides of a triangle should always be greater than the 3rd side.
Here if we take the two smaller sides their sum is 7 + 8 = 15 which is equal to the third side.
So it is not possible to construct a triangle with sides 7, 8, and 15 respectively.
The area of the Sea of Japan is 1.007 × 106 km2. The area of the Southern Ocean is 2.0327 × 107 km2. Find the total area. Write the final answer in scientific notation with the correct number of significant digits.
2.1334 × 107 km2
3.0397 × 1013 km2
2.133 × 107 km2
3.040 × 1013 km2
The total area of the Sea of Japan and the Southern Ocean is 2.1334 × 10⁷ km². The correct option is the first option 2.1334 × 10⁷ km²
Calculating the total area of the Sea and OceanFrom the question, we are to calculate the total area of the sea and ocean
From the given information,
"The area of the Sea of Japan is 1.007 × 106 km²"
and
"The area of the Southern Ocean is 2.0327 × 107 km²"
Thus,
The total area of the sea and ocean = 1.007 × 10⁶ km² + 2.0327 × 10⁷ km²
The total area of the sea and ocean = 0.1007 × 10⁷ km² + 2.0327 × 10⁷ km²
The total area of the sea and ocean = 2.1334 × 10⁷ km²
Hence, the total area is 2.1334 × 10⁷ km²
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Look at photo for problem
Just need chart filled out
6. y=(x-2)(x-4)
On solving the given equation y=(x-2)(x-4) the point on the graph are as follows:
(4,0), (2,0), (5,3), (3,-1) &(0,8)
What is a graph?
A relation is a specific instance of a function graph. A function is truly equivalent to its graph in set theory and the current mathematical underpinnings.
It is frequently more helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. For instance, the codomain should be considered while determining if a function is onto (surjective) or not. The codomain of a function is not determined by the graph alone.
It is typical to use the phrases function and graph of a function interchangeably since, although referring to the same thing, they suggest distinct ways of looking at it.
1)
let y=0
0=(x-2)(x-4)
i.e. x = 4 and 2
2)
Let x =0
y=(0-2)(0-4)
y=8
3)
Let x = 3
y=(3-2)(3-4)
y=-1
4)
Let x = 5
y=(5-2)(5-4)
y=3
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How is a system of two linear inequalities in two variables different from a system of two linear equations in two variables?
Answer:
A system of two linear inequalities in two variables is a set of two linear inequalities that involve two variables, such as x and y. A system of two linear equations in two variables is a set of two linear equations that involve two variables, also typically x and y.
There are several key differences between a system of two linear inequalities in two variables and a system of two linear equations in two variables:
Inequalities use symbols such as "less than" or "greater than" to indicate the relationship between the variables, whereas equations use the equal sign (=).
The solution to a system of linear inequalities is a region in the coordinate plane, whereas the solution to a system of linear equations is a single point.
The solution to a system of linear inequalities is found by graphing the inequalities on the coordinate plane and finding the region where they intersect, whereas the solution to a system of linear equations is found by solving the equations for the values of the variables.
The solution to a system of linear inequalities may include an infinite number of points, whereas the solution to a system of linear equations is always a finite number of points.
Overall, the main difference between a system of two linear inequalities in two variables and a system of two linear equations in two variables is the way in which the solutions are represented and found.
Write the statement "the sum of a number and 10.7 is at most −3.2" as an inequality.
The given statement:
"the sum of a number and 10.7 is at most −3.2"
Is equivalent to the following inequality:
x + 10.7 ≤ -3.2
How to write the inequality?Here we have the following statement:
"the sum of a number and 10.7 is at most −3.2"
So let's define the variable "x" as "the number", we know that the sum between x and 10.7 is at most -3.2, we can say that the sum is equal to or smaller than -3.2
In that case, the symbol we need to use is: ≤
Then the inequality is:
sum ≤ -3.2
x + 10.7 ≤ -3.2
That is the statement written as an inequality.
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What is the domain of the inverse of the function graphed below?
Write your answer as a compound inequality.
The domain of the inverse function is {5,6}. And as a compound inequality the domain is 5<x<6.
What is compound inequality?A mathematical statement that expresses the inequality between two inequalities combinedly.
from the graph, we have two inequalities, x>5 and x<6
it can be written as 5<x<6
What is inverse of a function?A function that can be obtained by reversing the primary function is termed as inverse of function. it is denoted by f⁻¹.
The graph shown is got from an inverse function whose domain is {5,6} and ranges are {-2, -4}
The graph also refers the inequalities of x>5 And x<6
compound inequalities of domain 5<x<6
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What is the quotient of 14 divided by 3/4
Answer:
18.6
Step-by-step explanation:
Liam spent $5.76 on 12 pounds of potatoes. How much did he spend per pound?
Answer:
$0.48/pound
Step-by-step explanation:
$5.76 divided by 12
The force “F” (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length “L” (in inches) of the handle. A force of 35 pounds is needed when the handle is 6 inches long. If a person needs 25 pounds of force to loosen the bolt, estimate the length of the wrench handle. Round answer to two decimal places if necessary.
______ inches.
The length of the wrench handle 8.4 inches.
What is length?
Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.
f = k/l
35 = k/6
k = 210
f = 210/l
25 =210/l
l = 8.4 inches
The length "L" (in inches) of a wrench handle has an inverse relationship with the force "F" (in pounds) required to remove a certain bolt. In the case of a handle that is 6 inches long, 35 pounds of power is required. The length of the wrench handle if the bolt needs to be loosened with 25 pounds of force is 8.4 .
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