The gap is approximately 259,854.9 inches wide.
What is the circumference of a circle?
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle.
The Earth's equator has a circumference of about 24,901 miles. The new circular band has a circumference of 25,036 inches.
When the steel band was cut and spliced, it increased the circumference by 36 inches. Since the circumference is directly related to the diameter, the new band is also larger in diameter than the original band.
We can use this increase in circumference to find the increase in diameter:
25,036 inches / 2π = 3957.1 inches
24,901 miles * 12 inches/mile = 298,812 inches
The gap is the difference between the two diameters:
298,812 inches - 3957.1 inches = 259,854.9 inches
Hence, The gap is approximately 259,854.9 inches wide.
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How do you find B when given the slope and a point?
When the slope m and a point (x₁, y₁) is given then the y-intercept (b) is given by an expression y = y₁ - mx₁
We know that the slope-intercept form of equation of line is y = mx + b
where m is the slope of the line and b is the y-intercept of the line.
We need to find the value of b i.e., y-intercept when the slope and a point is given.
We know that the equation of line with slope m and passing through point (x₁, y₁) is given by the formula
(y - y₁) = m(x - x₁)
If we simplify above equation we get,
y - y₁ = mx - mx₁
y = mx - mx₁ + y₁
y = mx + y₁ - mx₁
y = mx + (y₁ - mx₁)
Comparing above equation with slope-intercept form we get the y-intercept ,
b = y₁ - mx₁
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If p and q are rational numbers, which equation is always true?
A. -p+q=p-q
B. p-q=p+(-q)
C. p+(-q)=p+q
D. p-q=0
Solving the provided question, we can say If p and q are rational numbers, which equation p-q=0 is true
what is rational numbers?Any number that can be expressed as a ratio (or fraction) of two integers is said to be rational. A rational number is a fraction that has a nonzero denominator. 1/2, 1/5, and 3/4 are examples of rational numbers. Additionally a rational number, "0" may be expressed in a variety of ways, including 0/1, 0/2, and 0/3. However, 1/0, 2/0, 3/0, etc. The number seven is logical. When two integers are divided, the result is known as a rational number. Divide the whole number 7 by the whole number 1 to obtain the rational number 7. Since two integers may be divided to yield 7, it is known as a rational number.
If p and q are rational numbers, which equation
p-q=0 is true
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what should you do next? what should you do next? come up with a theory to explain why movie preference is related to birth week. perform experiments to test your hypothesis. propose several alternative hypotheses. refine your hypothesis.
To develop a theory on the relationship between birth week and movie preference, the next steps would be to:
Conduct research to gather existing information on the topic and identify any potential gaps in knowledge.Develop a hypothesis that explains the potential relationship between birth week and movie preference.Design and conduct experiments to verify the hypothesis.Analyze the results of the experiments and use them to support or refute the hypothesis.Propose alternative hypotheses and design additional experiments to test them.Refine the original hypothesis based on the results of the experiments and continue to test it through further research.To know more about hypothesis refer to:
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Regroup to express the number in a different way.
71,830 = 6 ten thousands + * thousands + 8 hundreds + 3 tens
what is the * equal to??
In the regrouping to use a different expression for the number in place of * is 11 thousands.
Here we have to write the regroup to express the number as 71,830 = 6 ten thousands + 11 thousands + 8 hundreds + 3 tens
What in elementary math is regrouping?
When doing mathematical operations like addition or subtraction, regrouping is the process of creating groups of ten. When dealing with double digits, this happens most frequently. Technically, though, it happens whenever you get a response that is more than 10.
Where using regrouping, you may frequently solve addition or subtraction problems, and this is when the Place Value Table comes in extremely handy.
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Is there any number that can be expressed as a ratio of two integers?
The numbers that can be expressed as a ratio of two integers are called as Rational Numbers , and one such example is [tex]\frac{2}{3}[/tex] .
What are Rational Numbers ?
The Rational Numbers are defined as the ratio of two integers where the denominator is non zero .
Mathematically , the rational numbers are the numbers that can be expressed in the form of [tex]\frac{p}{q}[/tex] , where [tex]q\neq 0[/tex] .
So , We can say that any fraction that fits under category of rational numbers, where denominator and numerator are integers and denominator is not equal to zero.
Few Examples of that can expressed as ratio of integers are :
(i) [tex]\frac{1}{2}[/tex] , here 1 and 2 both are integers , and [tex]2\neq 0[/tex] .
(ii) [tex]\frac{5}{6}[/tex] , here 5 and 6 both are integers , and [tex]6\neq 0[/tex] .
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What is 9 + 10 i need to know???
Answer:
9 + 10 is 19
Step-by-step explanation
To find this count up from 10 9 times.
Answer:
Step-by-step explanation:
19...
we add on 9 to 10, making 19
How do you graph a negative and positive slope?
When a line has negative slope, it goes down and right OR up and left.
We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.
The slope of the line describes the steepness of a line.
Also, if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ
m = tan θ
In order to graph a negative slope, we must know that a negative number in the ratio to move down along the y-axis or to the left along the x-axis.
Suppose the negative slope is of the form m = -b/a
This means, for every 'a' units change in the horizontal distance there is -b unita change of vertical distance.
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I need help can somebody help please M-4=2m
Answer: I believe the answer is M= -4
Step-by-step explanation:
Worth 20 Points
The angle between 0 and 2\pi in radians that is coterminal with the angle (5)/(2)\pi in radians is
The angle between the angles 0 to 2π is π / 2.
What is the coterminal angle?The coterminal angles are the angles that have the same initial side and the same terminal sides. We determine the coterminal angle of a given angle by adding or subtracting 360° or 2π to it. In trigonometry, the coterminal angles have the same values for the functions of sin, cos, and tan.
The coterminal angle will be calculated by subtracting the angle 2π from the angle 5π / 2.
Coterminal angle = ( 5π / 2 ) - 2π
Coterminal angle = π / 2
Hence, the value of the angle will be π / 2.
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which is the following exterior angles
which is the following exterior angles
Answer:
6,4,3,2
What is it called when two segments have the same length?
When the two segments have the equal lengths then they are called congruent segments.
As given in the question,
Let us consider two different segments named AB and CD.
Length of the segment AB is equal to 5 cm __(1)
Length of the segment CD is equal to ( 6 - 1 ) cm.
⇒Length of CD = 5cm __ (2)
Length of segment AB is equal to the length of segment CD.
⇒ measure of (AB ) = measure of (CD)
This implies that the two segment with the same length are called congruent to each other.
Therefore, the segment having equal length are called congruent segments.
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A car travels 13 miles to the North before turning and drive 10 miles East.
From here, they drive 5 miles South, another 2 miles East, and finally drive miles South. What is their displacement?
Their displacement , that is shortest distance is equals to 13 miles
What is Displacement ?
Displacement can be defined as the shortest path covered from one path to another.
Given,
A car travels 13 miles to the North before turning and drive 10 miles East.
From here,
they drive 5 miles South, another 2 miles East, and finally drive 3 miles South
So, the shortest distance can be called as the displacement
displacement = [tex]\sqrt{a^2+b^2}[/tex]
so,
a = 10+2
b = 13-5-3
b = 5
displacement = √(12^2 + 5^2 )
displacement = √169
displacement = 13
Hence, Their displacement , that is shortest distance is equals to 13 miles.
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14.6/9 rounded to nearest whole number
Answer:
15 x 9 is equal to 14.6/9 nearest whole number
Step-by-step explanation:
Find the perimeter of both figures. Hint: find the missing sides first
Side of first diagram is 6.6 and Perimeter of first diagram is 23.6.
What is perimeter?
Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.
15. to find sides of triangle using pythagoras theorem.
[tex](hypo)^2=(side)^2+(side)^2[/tex]
As, the triangle is right angles triangle so we can use pythagoras theorem,
10/2=5
Putting values,
[tex](12)^2=(10)^2+(side)^2[/tex]
[tex]144 = 100+(side)^2\\144-100=(side)^2\\side=\sqrt{44}[/tex]
side=6.6
Perimeter of triangle P= sum of all sides
=6.6+12+5
=23.6
Perimeter is 23.6
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[tex]4+5 √x =14\\[/tex]
The value of x for 4 + 5√x = 14 is 4.
What is simplification?Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
Given 4 + 5√x = 14
5√x = 14 - 4
5√x = 10
√x = 10/5
√x = 2
square both side
(√x)² = 2²
x = 4
Hence the value of x is 4.
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6-3 practice proving that a quadrilateral is a parallelogram
Answer:FX rtydf
V a s
Step-by-step explanation:gcvgvhjtv
ax
9=7+a
a+b=b+5
find out the value of busing both questions
Answer:
First question :
a = 2
Second question :
a = 5
b = [tex]\frac{-a+5}{0}[/tex]
out of 60 customers at a restaurant in one evening, 41 said they liked the service, 49 said they liked the food, and 37 said they liked both the service and the food. how many said they liked neither the service nor the food?
33 out of 60 customers said they liked neither the service nor the food.
At a restaurant on one evening, 60 customers were surveyed about their experience. Of those customers, 41 said they liked the service, 49 said they liked the food, and 37 said they liked both the service and the food.
To answer the question of how many said they liked neither the service nor the food, we can subtract the numbers of those who liked the service, food, or both from the total number of customers.
60 customers - 41 who liked the service - 49 who liked the food - 37 who liked both = 33 customers who liked neither the service nor the food.
In conclusion, 33 out of 60 customers said they liked neither the service nor the food at the restaurant on the evening in question. This data shows that the majority of customers enjoyed their experience, with over two-thirds of customers liking either the food, the service, or both.
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Draw a box-and-whisker plot for the set of data. 23. 5, 18. 2, 3. 3, 23. 3, 11. 3, 18. 8, 78. 8, 69. 1, 2. 2, 16. 1, 54. 9, 44. 8, 37. 4.
The five number summery of the data set is minimum = 2.2, Q1 = 3.3, median = 23.3, Q4 = 69.1 and maximum = 78.8
What is Boxplot ?A box plot is a visual representation of the localization, dispersion, and skewness of a collection of numerical data through its quartiles.
The center "box" denotes the group's middle 50% of points. The inter-quartile range is the range of scores from the lower to higher quartile. The interquartile range encompasses the middle 50% of the scores. 75 percent of the scores are lower than the highest quartile.
When doing descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.
Arranging the data in ascending order :
2.2, 3.3, 11.3, 16.1, 18.2, 18.8, 23.3, 23.5, 37.4, 44.8, 54.9, 69.1, 78.8
Total number of data = 13
The minimum value = 2.2
The maximum value = 78.8
The median is 7th term = 23.3
The Q1 of 1st quartile = 3.3
The Q4 of 4th quartile = 69.1
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Oliver chooses four of his toy cars and measures their wheel length and then calculates the circumference. If he was to divide the circumference by the diameter for each of his wheel length, what would he find? A) Each time you get 0. 32. B) Each time you get 0. 64. C) Each time you get 3. 14. D) Each time you get 6. 28
If Oliver chooses four of his toy cars and measures their wheel length , and If he divide circumference by diameter for each of his wheel length, then he would find that (c) each time Oliver will get 3.14 .
let radius of circular wheel be = r ;
the diameter of the circular wheel will be = 2r ;
So , the circumference of the wheel is = 2πr ;
on dividing circumference by the diameter for each of his wheel length ,
we get ;
= [tex]\frac{2\pi r}{d}[/tex] ;
Substituting the value of diameter, d = 2r ;
we get ;
= [tex]\frac{2\pi r}{2r}[/tex] ;
After simplification ,
we have ;
= π .
We know that, value of [tex]\pi[/tex] is [tex]3.14[/tex] .
Therefore , On dividing each time we will get 3.14 .
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Can anyone help me solve this question?
e. Use the expansion of (1 + x)^5 to find the exact value of (1 + √5)^5
Answer:
176 +80√5
Step-by-step explanation:
You want the exact value of (1 +√5)^5.
Binomial expansionThe coefficient of the expansion are found in Pascal's triangle (attached). Row 5 is used for the 5th power:
(a +b)^5 = a^5 +5·a^4·b + 10·a^3·b^2 +10·a^2·b^3 +5·a·b^4 +b^5
ApplicationWhen a = 1 and b = √5, this becomes ...
(1 +√5)^5 = 1 + 5·√5 +10·5 + 10·5√5 +5·25 +25√5
= (1 +50 +125) +(5 +50 +25)√5
(1 +√5)^5 = 176 +80√5
just a quick addition to "sqdancefan" superb reply above
[tex]\qquad \qquad \textit{binomial theorem expansion} \\\\ \qquad \qquad (1+\sqrt{5})^{5}~\hspace{4em} \begin{array}{clcl} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^{5 }(\sqrt{5})^0\\ 2&+5&(1)^{4}(\sqrt{5})^1\\ 3&+10&(1)^{3}(\sqrt{5})^2\\ 4&+10&(1)^{2}(\sqrt{5})^3\\ 5&+5&(1)^{1}(\sqrt{5})^4\\ 6&+1&(1)^{0}(\sqrt{5})^5 \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]1(1)+5(1)(\sqrt{5})^1+10(\sqrt{5})^2+10(1)(\sqrt{5})^3+5(\sqrt{5})^4+(\sqrt{5})^5 \\\\\\ 1+5\sqrt{5}+50+50\sqrt{5}+125+25\sqrt{5}\implies {\Large \begin{array}{llll} 176+80\sqrt{5} \end{array}}[/tex]
Select “Rational” or “Irrational” to classify each number
Answer: rational, irrational, irrational
Step-by-step explanation:
An easy way to figure out if a number is rational is by checking to see if it can be written as a fraction. 0.44 can be written as a fraction: 44/100
Any square root that is not a perfect root is an irrational number. An irrational number can be a decimal that is non-terminating (it doesn't end) and a non-repeating decimal (it doesn't repeat).
Is the line shown on the scatter plot a good
line of fit?
Yes, because the line follows the pattern
of the data but excludes the outlier.
Yes, because the line models
a positive association.
No, because the dat& does not have a
linear association.
No, because the line does not pass
through any of the data points.
●
●
●
●
●
The scatter plot's line is a strong line of fit because it Yes, as the line depicts a favorable association.
Is a line of best fit a scatter plot?A scatter plot's maximum number of points and an approximately equal number of points above and below the line are the parameters that define the line of best fit. It is employed to examine the type of relationship between two variables. In general, a graph's "line of best fit" passes through the center of each scatter point.
Stronger correlations occur when points are located along the line of best fit. the sum of squares of errors for each and every conceivable line. The most accurate line is the one with the lowest total of squared errors. The correlation between the two variables is higher when the data points are drawn so that they nearly form a straight line.
Therefore the correct answer is Yes, because the line models a positive association.
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finding interior and exterior angles of polygon worksheet.
How do you solve these problems?
To find the measure of an interior angle of a polygon, you can use the formula: (n-2) * 180 / n, where n is the number of sides in the polygon.
What is angles of polygon worksheet?This formula is derived from the fact that the sum of all interior angles in a polygon is (n-2) * 180 degrees, and by dividing that by the number of sides, we get the measure of one interior angle. For example, if you have a hexagon (6 sides), the measure of an interior angle would be (6-2) * 180 / 6 = 120 degrees.To find the measure of an exterior angle of a polygon, you can use the formula: 360 / n, where n is the number of sides in the polygon. This formula is derived from the fact that the sum of all exterior angles of a polygon is always 360 degrees and by dividing that by the number of sides, we get the measure of one exterior angle. For example, if you have a hexagon (6 sides), the measure of an exterior angle would be 360 / 6 = 60 degrees.To solve a problem, simply substitute the number of sides in the polygon into the appropriate formula and solve for the angle measure.Sum of interior angles of a polygon
=x+(x+75)+2x+33+140
solving for x,
x+x+75+2x+33+140=540
4x+248=540
4x=540-248
4x=292
x=[tex]\frac{292}{4}[/tex]
x=73
Angle x=73
angle x+75
=73+75
=148
Angle 2x=2*73=146
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Is 8:9 and 5:6 equivalent
Answer:
Yes
Step-by-step explanation:
because 8/10 can 4/5 by diving by 2
There are 10 cards placed face down on a table. Four of the cards have stars on them and the other 6 are blank. You win if you draw a card with a star. How can the game be made fair? MULTIPLE CHOICE
The game is already fair.
Add 2 cards with stars.
Add a star to 1 of the blank cards.
Take away 2 blank cards.
If you win if you draw a card with a star, the way the game can be made fair is; C: Add a star to 1 of the blank cards.
How to analyze fair chance?
A basic game of chance is one that considered fair if every player has an equal probability of winning. A choice is deemed to be fair if all possible options have an equal probability of being chosen.
The first one is out of the equation to win because it isn't fair.
We want a 50/50 chance to win. Thus, If we add 2 cards with stars, then the chance of winning increases by a large portion much. However, If we take away 2 blank cards, it would be fair, but we want to still have 10 cards. Thus, the only choice left is to add a star to 1 of the blank cards.
Therefore we can conclude that the way the given game can be made fair is given by the option C to add a star.
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PLS HELPP!!!!!!
Ms. Lea ate ¾ of a bag of skittles, Ms. Peter ate 65% of her bag of skittles and Mr. Thomas ate 0.85 of his bag. Ms. Cassie ate ⅘ of her bag. Who ate the most? Explain how you know.
2. Write in order from least to greatest
30%, 23%, ⅕, 0.18, 2/9, 0.25
Answer:
0.18, 2/9, 23%, 0.25, 30%
Step-by-step explanation:
you have one type of chocolate that sells for $6.80/lb and another type of chocolate that sells for $8.80/lb. you would like to have 8 lbs of a chocolate mixture that sells for $6.90/lb. how much of each chocolate will you need to obtain the desired mixture? you will need lbs of the cheaper chocolate and lbs of the expensive chocolate.
You will need 6.25 lbs of the cheaper chocolate, and 1.75 lbs of the more expensive chocolate to get 8 lbs of a chocolate mix that sells for $6.90/lbs.
To find the specific amounts of each chocolate needed to make 8 lbs of a chocolate mixture that sells for $6.90/lb, we can substitute x + y = 8 into the equation (6.80x + 8.80y) / (x + y) = 6.90 and solve for x.
First, we'll substitute x + y = 8 in the equation:
(6.80x + 8.80y) / 8 = 6.90
6.80x + 8.80y = 55.20
x = (55.20 - 8.80y) / 6.80
We know that x + y = 8, so we can substitute that in for y:
x = (55.20 - 8.80(8 - x)) / 6.80
x = (55.20 - 70.40 + 8.80x) / 6.80
Now we'll solve this equation for x:
8.80x = 125.60 - 70.40
8.80x = 55.20
x = 55.20 / 8.80
x = 6.25
So, you will need 6.25 lbs of the cheaper chocolate, and
8 - 6.25 = 1.75 lbs of the more expensive chocolate.
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(05.03)
Bev has to cut her grandma's grass this weekend and wants to know exactly how much area she will be cutting. Calculate the area of the polygon. Be sure to show all your work and explain your answer. (6 points)
Here is a picture
Answer:
220.5 square feet
Step-by-step explanation:
You want to know the area of an irregular shape.
CompositionThe figure can be decomposed into a triangle and a trapezoid by extending the vertical line through the figure.
TriangleThe triangle has side lengths 15 ft and 15 ft, so its area is ...
A = 1/2bh
A = 1/2(15 f)(15 ft) = 112.5 ft²
TrapezoidThe trapezoid has bases of 25 ft and 29 ft, and a height of 4 ft, so its area is ...
A = 1/2(b1 +b2)h
A = 1/2(25 ft +29 ft)(4 ft) = 108 ft²
LawnThe area of the grass will be the total of these areas:
grass area = triangle area + trapezoid area
grass area = 112.5 ft² +108 ft² = 220.5 ft²
The area of the grass is 220.5 square feet.
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
2+x=5. x+1=4. 5+x= negative 2
Step-by-step explanation:
Solve my getting X by itself to one side. you do this by moving the number on the side of the question. therefore you perform the inverse operation. inverse of addiction is subtraction and inverse of subtraction is addition.
2+x=5.
-2. -2
x=3
x+1=4
-1. -1
x=3
-5+x= -2
+5. +5
x=3