The sportsman has a final distance with respect to his home equal to 305 meters.
How to determine the distance of a sportsman with respect to a home
In this problem we must the final distance of the sportsman with respect to his home. This can be determined by the following expression:
X = ∑ xₙ, for n = {1, 2, 3, ..., N}
Where the sportsman goes far away for his home for x > 0, in meters.
Now we proceed to determine the final distance:
X = + 350 m - 125 m + 80 m
X = + 305 m
The final distance of the sportsman with respect to his home is 305 meters.
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The US Department of Energy reported that 45% of homes were heated by natural gas. A random sample of 314 homes in Oregon found that 175 were heated by natural gas. Test the claim that proportion of homes in Oregon that were heated by natural gas is different than what was reported. Use a 5% significance level.
The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.
Hypothesis testingNull hypothesis: The proportion of homes in Oregon heated by natural gas is the same as the reported national average of 45%.
Alternative hypothesis: The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.
We can use a two-tailed z-test to test this hypothesis.
The test statistic is calculated as:
z = (p - P) / √[P(1-P)/n]
where p is the sample proportion, P is the hypothesized population proportion (0.45), and n is the sample size.
Using the values given in the problem, we have:
p = 175/314 = 0.557
P = 0.45
n = 314
Plugging these values into the formula, we get:
z = (0.557 - 0.45) / √[0.45(1-0.45)/314] = 3.039
Using a standard normal distribution table, we find that the probability of getting a z-value of 3.039 or higher (in absolute value) is less than 0.005.
Since the significance level is 0.05, which is greater than the p-value, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.
Therefore, the proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.
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(2a² b c³) (-a² b⁵)
pls help asap!
Answer:
-2a⁴ b⁶ c³
Step-by-step explanation:
2a² b c³ (-a² b⁵)
determine the signs for multiplication or division
-2a²bc³a²b⁵
multiply the monomials
-2a⁴b⁶c³
(then done)
Complete the statement by filling in the blank. Write your answer on a
separate sheet of paper.
A ___________ is a frequency distribution using the means computed from all
possible random samples of a specific size taken from a population. To get the
possible samples use the formula ______, where N is the ________ and n is the ____
size to be taken. The total probability of the sample mean must be equal to ____.
A sampling distribution is a frequency distribution using the means computed from all possible random samples of a specific size taken from a population.
To get the possible samples, use the formula "N choose n", where N is the population size, and n is the sample size to be taken. The total probability of the sample mean must be equal to 1.
Since the mean of all possible samples must be equal to the population mean. The sampling distribution is an important concept in statistics as it allows us to make inferences about the population based on the characteristics of the sample, and helps us estimate parameters and test hypotheses.
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Random sample of 250 students taken with a population of 7500 surveyed about their majors. In the sample, 75 students were Art majors. How many students in total population are are Art majors?
Therefore, we estimate that there are 2250 Art majors in the total population.
What is proportion?In mathematics, a proportion is an equation that states that two ratios are equal. A ratio is a comparison of two quantities expressed as a fraction or a decimal. Since both sides of the equation are equal, the proportion is true. Proportions are used in many mathematical and real-world contexts, such as in geometry, finance, and statistics. They are useful for comparing and scaling quantities, and for solving problems involving unknown quantities or variables.
Here,
We can use proportions to estimate the total number of Art majors in the population based on the proportion of Art majors in the sample.
The proportion of Art majors in the sample is:
75/250 = 0.3
We can assume that this proportion is representative of the proportion of Art majors in the population.
So, if x is the total number of Art majors in the population, then we can set up the following proportion:
0.3 = x/7500
To solve for x, we can cross-multiply and simplify:
0.3 * 7500 = x
x = 2250
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Which of these is an accurate way to measure the volume of a rectangular prism
A. Fill it with water and then weigh the water.
B.Trace each face of the prism on centimeter grid paper, and then count the number of squares it comprises.
C. Measure the length and the width, and then multiply the two values.
D. pack it with unit cubes, leaving no gaps or overlaps, and count the number of unit cubes.
The correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.
What is a rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.
It also goes by the name cuboid.
Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.
It is referred to as a prism because of the length of its cross-section.
There are 6 faces, 8 vertices, and 12 edges on a rectangular prism.
A rectangular prism's volume can be determined by packing unit cubes into it without any gaps or overlaps, then counting the number of unit cubes.
A rectangular prism's surface area is equal to the sum of the areas of each of its faces.
It can be calculated using the formula 2(lw+ wh+ hl).
Therefore, the correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.
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There are two yellow and three green balls in a tub. Ashraf picks a ball without looking. What is his probability that the ball is (i) yellow (ii) green (iii) red
Answer:
Since there are only yellow and green balls in the tub, there is no possibility of picking a red ball. Therefore, the probability of picking a red ball is zero.
(i) The probability of picking a yellow ball can be calculated by dividing the number of yellow balls by the total number of balls. In this case, there are two yellow balls and three green balls, so the total number of balls is 2 + 3 = 5. The probability of picking a yellow ball is 2/5 or 0.4, which is 40%.
(ii) Similarly, the probability of picking a green ball can be calculated by dividing the number of green balls by the total number of balls. In this case, there are three green balls and five total balls. Therefore, the probability of picking a green ball is 3/5 or 0.6, which is 60%.
(iii) As mentioned earlier, there are no red balls in the tub. Hence, the probability of picking a red ball is 0.
how does cot^2(x)-tan^2(x)=csc^2(x)-sec^2(x)
The proof of cot²(x) - tan²(x) = csc²(x) - sec²(x) is the help of trigonometry
identity and Pythagorean identity .
what is trigonometry identity ?A trigonometric identity is an equation that is true for all values of the variables in the equation, where the variables are trigonometric functions such as sine, cosine, tangent, cotangent, secant, or cosecant.
The Pythagorean identity is a fundamental trigonometric identity that relates the three basic trigonometric functions: sine, cosine, and tangent, in terms of the unit circle or right triangle.
Proof of cot²(x) - tan²(x) = csc²(x) - sec²(x)The identity you provided, cot²(x) - tan²(x) = csc²(x) - sec²(x), is a trigonometric identity that can be derived from the Pythagorean identity and the reciprocal identities. Here's one way to prove it:
Start with the Pythagorean identity:
sin²(x) + cos²(x) = 1
Divide both sides by sin²(x):
1 + cos²(x)/sin²(x) = 1/sin²(x)
Recall that cot(x) = cos(x)/sin(x) and tan(x) = sin(x)/cos(x):
1 + cot²(x) = csc²(x)
Subtracting sec²(x) from both sides:
cot²(x) - tan²(x) = csc²(x) - sec²(x)
Therefore, cot²(x) - tan²(x) = csc²(x) - sec²(x) is a valid trigonometric identity.
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Use the expression below to complete the following tasks.
(3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab)
What is the additive inverse of the polynomial being subtracted?After you rewrite subtraction as addition of the additive inverse, how can the like terms be grouped?
With additive inverse and by grouping like terms the simplified form of the expression is 6a²-13ab-b².
The given expression is 3a²-5ab+b²-(-3a²+2b²+8ab).
Here,
3a²-5ab+b²+3a²-2b²-8ab
Group like terms, that is
(3a²+3a²)+(-5ab-8ab)+(b²-2b²)
= 6a²-13ab-b²
Therefore, with additive inverse and by grouping like terms the simplified form of the expression is 6a²-13ab-b².
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Drag each value to the correct location on the equation. Not all values will be used. Convert radians to degrees. 4 /9
4[tex]\pi[/tex]/9 radians equals 80 degrees.
How will you convert radians into degrees?To convert a radian angle to a degree angle, multiply it by 180°/[tex]\pi[/tex]. To convert a degree angle to a radian angle, multiply it by [tex]\pi[/tex]/180°.
We utilize the conversion factor that 1 radian = 180/[tex]\pi[/tex] degrees to convert radians to degrees.
So we multiply 4[tex]\pi[/tex]/9 radians by the conversion factor to get degrees:
[tex]\\\frac{4\pi }{9} * \frac{180}{\pi } \\\frac{720}{9}[/tex]
On simplifying we get,
720 / 9 = 80 degrees
As a result, 4[tex]\pi[/tex]/9 radians equals 80 degrees.
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Complete question:
attach in the image form
Find cos(2π/3) I need help
Answer:
We can use the cosine double angle formula to find cos(2π/3):
cos(2θ) = cos^2(θ) - sin^2(θ)
Letting θ = π/3, we get:
cos(2π/3) = cos^2(π/3) - sin^2(π/3)
Using the values of cosine and sine of π/3 (which are known), we have:
cos(2π/3) = (1/2)^2 - (√3/2)^2
Simplifying, we get:
cos(2π/3) = 1/4 - 3/4
cos(2π/3) = -1/2
Therefore, cos(2π/3) is equal to -1/2.
Answer:
cos(2π/3) = cos(π/3 + π/3)
= cos²(π/3) - sin²(π/3)
= (1/2)² - (√3/2)²
= 1/4 - 3/4
= -2/4
= -1/2
Step-by-step explanation:
here are the steps:
Convert 2π/3 to degrees: 2π/3 * (180/π) = 120°Use the double angle formula for cosine: cos(2θ) = cos²(θ) - sin²(θ)Substitute π/3 for θ: cos(2π/3) = cos²(π/3) - sin²(π/3)Use the values of cosine and sine of π/3 from the unit circle: cos(π/3) = 1/2 and sin(π/3) = √3/2Substitute these values into the formula: cos(2π/3) = (1/2)² - (√3/2)²Simplify the expression inside the parentheses: cos(2π/3) = 1/4 - 3/4Combine like terms: cos(2π/3) = -2/4Simplify the fraction: cos(2π/3) = -1/2Therefore, cos(2π/3) = -1/2
g(x) is a linear function that makes a line when you graph it. Some of its points are listed in the table below. If this line was graphed completely, would it ever intersect with the circle pictured ? Describe how you know.
x g(x)
-4 -4
-2 -2
2 2
PLEASE HELP! 30 POINTS!
What is Bd?
A. 7.5
B. 8.5
C. 9.4
D. 15
Thus, the length of chord BD of the given circle is found to be 8.5 units.
Explain about the chord of circle:A chord is indeed a straight line that connects two points on a circle's circumference. Because it connects to points on the circle's perimeter, the diameter is thought to be the chord with the longest length.
The lengthiest chord in a circle is called the diameter, and the chord's perpendicular distance to the circle's centre is zero.
Given that: From diagram.
CA = AD = 4.5 + 4 = 9.5 (radius of circle)AM = 4Now, in right triangle, MAD, using the Pythagorean theorem:
(AD)² = (AM)² + (MD)²
(9.5)² = (4)² + (MD)²
(MD)² = 9.5² - 4²
(MD)² = 90.25 - 16
(MD)² = 74.25
MD = 8.5
Thus, the length of chord BD of the given circle is found to be 8.5 units.
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Please help!!!!! Help please!! what is the value of x? is this right???
Answer:
x = 68
Step-by-step explanation:
X + 22 = 90 degrees
90 - 22 = 68 degrees
What is the equation of the following line (0,0) (4,2)
4. Tanya Jackson bought a house and during the first year, was able to rent it for only 7 months at $620 a month. Though the house was vacant for 5 months, Tanya had to pay average expenses of $175 a month for the whole year. She also paid $3,600 in mortgage interest. a. For the first year, what was Tanya's gross income? b. What was her net income or net loss?
A- Tanya's gross income for the first year was $7,940, and b- her net income was $5,840 after subtracting her total expenses.
a. To calculate Tanya's gross income for the first year, we need to multiply the rent per month by the number of months the house was rented:
Gross income from rent = $620/month x 7 months = $4,340
Tanya also paid $175/month in average expenses for the whole year, so her total expenses were:
Total expenses = $175/month x 12 months = $2,100
Adding the mortgage interest paid, Tanya's gross income for the first year was:
Gross income = $4,340 + $3,600 = $7,940
b. To calculate Tanya's net income or net loss, we need to subtract her total expenses from her gross income:
Net income = Gross income - Total expenses
Net income = $7,940 - $2,100
Net income = $5,840
Therefore, Tanya's net income for the first year was $5,840.
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Choose the ordered pair that is a solution for this equation.
3x = 8 - y
A. (3, 1)
B. (2, 2)
C. (8, 0)
Answer:
B. (2, 2)
Step-by-step explanation:
(x, y)
3x = 8 - y
a) 3(3) = 8 - 1
9 = 8 - 1
9 = 7 False
b) 3(2) = 8 - 2
6 = 6 True
c) 3(8) = 8 - 0
24 = 8 False
1) Calculate the area of this triangle. (if h = 4m; b = 7m)
A.
B.
C.
n
28cm
14cm2
28cm2
b
Answer:
B
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 7 and h = 4 , then
A = [tex]\frac{1}{2}[/tex] × 7 × 4 = [tex]\frac{1}{2}[/tex] × 28 = 14 cm²
A slow pitch softball diamond is actually a square 60' on side how far is it from home to 2nd base
Answer:
The distance from home to second base is approximately 84.85 feet in a slow pitch softball diamond that is 60 feet on each side.
Step-by-step explanation:
In a softball diamond that is 60 feet on each side, the distance from home to second base is approximately 84.85 feet. This is based on the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the distance from home to second base forms the hypotenuse of a right triangle with legs that are each 60 / sqrt(2) feet long. Using the Pythagorean theorem, we can calculate that the distance from home to second base is approximately 84.85 feet.
Can anybody help me on the question.
ASAP
The hanger in the illustration will have the value x = 6, and it will remain balanced.
Define equations?Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It demonstrates the equality of the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in each mathematical equation. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.
Here's the query,
Considering the graph,
The hanger's equation is as follows:
4x= 24
There are 4 numbers here that represent the value of the hanger.
So, x+x+x+x will be 24.
The equation is thus:
4x = 24.
Now, by resolving the equation, we can determine the value of x that balances the hanger:
4x = 24.
When you divide 4 on both sides:
x = 24/4
x = 6.
As a result, the hanger will remain in equilibrium for x = 6.
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Is (2, 6) a solution to this system of equations?
y = 3/2x + 3
y = -9x + 1
yes
no
To determine if (2, 6) is a solution to the system of equations:
y = 3/2x + 3 ... (equation 1)
y = -9x + 1 ... (equation 2)
We need to substitute x = 2 and y = 6 into both equations and check if they are true.
Substituting x = 2 and y = 6 into equation 1, we get:
6 = 3/2(2) + 3
6 = 3 + 3
6 = 6
This equation is true.
Substituting x = 2 and y = 6 into equation 2, we get:
6 = -9(2) + 1
6 = -18 + 1
6 = -17
This equation is false.
Since (2, 6) does not satisfy equation 2, it is not a solution to the system of equations. Therefore, the answer is: no.
Solve for b and c. Select BOTH correct answers. Responses c = 8 c = 8 b = 4√3 b = 4√3 b = 8 b = 8 c = 4√3 c = 4√3
The values of b and c include the following:
c = 8
b = 4√3
How to determine the length of b?In order to determine the length of b, we would apply the law of tangent because the given side lengths represent the adjacent side and opposite side of a right-angled triangle.
Tan(θ) = Opp/Adj
Where:
Adj represents the adjacent side of a right-angled triangle.Opp represents the opposite side of a right-angled triangle.θ represents the angle.Therefore, we have the following tangent trigonometric function:
Tan(θ) = Opp/Adj
Tan(30°) = 4/b
√3/3 = 4/b.
b = 4√3
From Pythagorean Theorem, the length of c is given by;
c² = (4√3)² + 4²
c² = 48 + 16
c = √64
c = 8
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Show that the angle bisector of an equilateral triangle is perpendicular to the base
To show that the angle bisector of an equilateral triangle is perpendicular to the base, we can assume an equilateral triangle with sides ABC. Next, we can get an angle bisector in the middle represented by BD which becomes perpendicular to the base BC.
How to prove that the angle bisector is perpendicular to baseAfter getting the angle bisector, we would see that the line segment BD, divides angle BAC into two equal angles, each measuring 30 degrees. Now, we can draw a perpendicular line from point D to the base BC.
We could also draw a line E, which is the perpendicular line that intersects the base BC. We want to show that BD is perpendicular to BC, which means we need to show that angle BDE is a right angle.
Since the sum of angles BDA and ADE is 90 degrees (they form a right angle), and the sum of angles BAD, ABD, and BDA is 180 degrees, it follows that angle BDE must be a right angle.
Therefore, we have shown that the angle bisector of an equilateral triangle is perpendicular to the base.
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A rectangle is shown on the coordinate plane.
The coordinates of the vertices of rectangle are (-3,3),(6,3),(6,-3), (-3,-2). the rectangle is 9 units long and 5 units wide.
Describe Graph?In mathematics and computer science, a graph is a collection of vertices (also called nodes) and edges that connect pairs of vertices. Graphs are used to represent various types of relationships between objects, such as social networks, road networks, electrical circuits, and many others.
Vertices in a graph are typically represented by circles or points, while edges are represented by lines or arcs that connect pairs of vertices. A graph can be directed, where each edge has a direction, or undirected, where edges have no direction.
The coordinates of the vertices of rectangle are (-3,3),(6,3),(6,-3), (-3,-2).
To find the length and width of the rectangle, we need to determine the distance between the points on the x and y axes.
The length of the rectangle is the distance between points (-3,3) and (6,3) on the x-axis:
Length = 6 - (-3) = 9 units
The width of the rectangle is the distance between points (-3,3) and (-3,-2) on the y-axis:
Width = 3 - (-2) = 5 units
Therefore, the rectangle is 9 units long and 5 units wide.
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1. The relationship between distance
measured on a map and the actual
distance on the ground
A. A sketch
B. A statement
C. Layout
D. Scale
What if the correct answer
Answer: A Map Scale.
Step-by-step explanation:
A Map Scale is the relationship with the ground.
1. Which set of ordered pairs DOES NOT represent a function?
a. (0, 1), (2,3), (3,4), (5,6)
b. (1, 1), (2, 2), (3,3), (4,4)
c. (1,4), (1, 5), (1,6), (1,8)
d. (0,7), (2, 4), (4,7), (5,7)
Answer:
C.
Step-by-step explanation:
because x value cannot be repeated in an ordered pair
Utilizando los siguientes datos: 9, 9, 14, 7, 12, 8, 11, 19, 15, 11, se pueden calcular las siguientes medidas estadísticas:
Media: 11
Mediana: 11
Rango: 12
Moda: 11 (aparece dos veces, junto con el número 9)
Rango intercuartil (IQR): 6
Mínimo y máximo: 7 y 19, respectivamente.
using the same data as above, make the following data displays.
Box plot:
Line plot:
Answer: Box plot: | o
19 |
18 |
17 |
16 |
15 | o
14 | o
13 |
12 | o o
11 | o o o
10 |
9 | o o
8 | o
7 | o
|___________
Line plot: 19|
18|
17|
16|
15| o
14| o
13|
12| o o
11|o o o
10|
9|o o
8| o
7|o
|___________
1 2 3 4 5 6 7 8 9 10 (data index)
Step-by-step explanation:
Helpppppppp pleaseeeeee
The result of adding -3 (row 1) to row 2 is determined as (0 10) |-14.
What is the result of the row multiplication?The result of the row multiplication in the matrix is calculated by applying the following method;
row 1 in the given matrix = [1 -4] | 8
To multiply row1 by -3, we will multiply each entity by -3 as shown below;
= -3(1 -4) | 8
= (-3 12) | -24
To add the result to 3;
(-3 12) | -24 + (3 -2)|10
= (0 10) |-14
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.
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Music streaming services are the most popular way to listen to music. Data gathered over the last 12 months show Apple Music was used by an average of 1.81 million households with a sample standard deviation of 0.47 million family units. Over the same 12 months Spotify was used by an average of 2.21 million families with a sample standard deviation of 0.32 million. Assume the population standard deviations are not the same. Using a significance level of 0.02, test the hypothesis of no difference in the mean number of households picking either service.
a. Compute the test statistic.
b. Compute the p-value.
Chanasia buys a plastic bucket. The bucket weighs 460 g. The label on the bucket says made with 20% recycled plastic. How many grams of recycled plastic are used to make Chanasia’s bucket?
please help and please show work
92 grams of recycled plastic were used to make Chanasia's bucket
How to calculate the amount of recycled plastic that was used to make Chanasia's bucket?Chanasia buys a plastic bucket
The bucket weighs 460 grams
The label on the bucket says it was made with 20% recycled plastic
The number of grams of recycled plastic that was used to make the bucket can be calculated as follows
= 460/100
= 4.6
= 4.6 × 20
= 92
Hence 92 grams of recycled plastic was used to make the bucket
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A carpenter has two different-sized circular saws. The smaller saw has the radius shown. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.
How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π
.
If the radius of smaller-saw is 1.25 in, and radius of larger-saw is 2 inches, then larger-saw is 4.71 inches greater the smaller-saw.
The "Circumference" of a circle is defined as the distance around the boundary of a circle, it is also called perimeter of circle;
The diameter of the smaller saw can be calculated as:
⇒ diameter = 2 × radius = 2 × 1.25 inches = 2.5 inches;
The diameter of the larger saw is 1.5 inches greater than the diameter of the smaller saw, which means,
⇒ diameter of larger saw = diameter of smaller saw + 1.5 inches,
⇒ diameter of larger saw = 2.5 inches + 1.5 inches = 4 inches;
So, Circumference of circle is = 2 × π × radius;
The Circumference of "smaller-saw" = 2 × 3.14 × 1.25 inches,
⇒ circumference of smaller saw = 7.85 inches;
circumference of "larger-saw" = 2 × 3.14 × 2 inches
⇒ circumference of larger saw = 12.56 inches;
The difference in circumference between the two saws is:
⇒ circumference of larger saw - circumference of smaller saw
⇒ 12.56 inches - 7.85 inches = 4.71 inches;
Therefore, the circumference of the larger saw is 4.71 inches greater than the circumference of the smaller saw.
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The given question is incomplete, the complete question is
A carpenter has two different-sized circular saws. The smaller saw has the radius as 1.25 inch. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.
How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π