For an activity in class, student used pieces of string to measure road on a map. They used a map scale to determine the distance between two cities. One group measured the distance between Fort Myers and Miami on a Florida state map. The string distance was 7.75 inches, which represents a real-life distance of about 155 miles. Another group measured the distance between Tampa and Orlando on the same map and found that distance to be 4.25 inches. What is the real-life distance to the nearest mile between Tampa and Orlando

An effective sampling method is not cast doubt on the usefulness of the sample

The effective sample is a calculation of the approximate sample size needed to obtain the same degree of accuracy as a simple random sample. It is denoted mathematically by the formula n/D, where n represents the sample size and D denotes the design effect. It is employed as a means of condensing the volume of data.

Effective sample size calculations are mostly used for qualitative analyses of the sample size. The sample size calculates the total number of measurements or observations made during an experiment or survey. The effective sample size—rather than the actual sample size—is utilized in this assessment since it is thought that a sample size of 30 is necessary for an analysis to be valid.

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The series can be written as:

∑(n=1 to ∞) (2/3)^(n-1) * 2 = 6

The given series is: 2, 4/3, 8/9, 16/27, ...

To write this series in sigma notation, we need to find a pattern. We can see that each term is twice the previous term divided by 3. So, we can write:

a(n) = (2/3) * a(n-1), with a(1) = 2

We can use this recursive formula to write the series in sigma notation:

∑(n=1 to ∞) (2/3)^(n-1) * 2

The first term is when n=1, and it equals 2. The common ratio is (2/3), so we can use the formula for an infinite geometric series to find the sum:

S = a(1)/(1-r) = 2/(1-2/3) = 6

Therefore, the series can be written as:

∑(n=1 to ∞) (2/3)^(n-1) * 2 = 6

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Answer:

22.5 feet

Step-by-step explanation:

volume of a retangular shape: l*w*h

4.5*2.5*2=22.5

On solving the provided question, we can say that - Area enclosed by the square and the circle= 400 - 314 = 86 ft sq

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Side of the square =20feet

Therefore,

Radius of the inscribed circle= 20/2 = 10 feet

Area of square=20 X 20 = 400 feet sq.

Area of circle=\(\pi * r^{2} \\\pi * 10*10\\3.14*100\\314 ft sq\)

Area enclosed by the square and the circle= 400 - 314

                                                                           = 86 ft sq

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Step by step solution is above

Answer:

Option A is correct

Step-by-step explanation:

Bobby = 1/8

Danny = 1/5

Let's add up both fractions:

1/8 + 1/5 =

1*5/8*5 + 1*8/5*8 =                   (multiplying both the numerator and                              

5/40 + 8/40 = 13/40                 denominator by the opposite denominator)

Together, they both cut 13/40 of the entire lawn.

Let's check each option:

A) Together the boys didn't even cut half the yard.

True, half of the yard is 20/40, and 13/40 < 20/40

B) The boys were able to cut more than half the yard.

False, half of the yard is 20/40, and 13/40 is not greater than 20/40

C) The boys cut almost three-fourths of the yard.

False, three-fourths of the yard is 30/40, and 13/40 is not close.

D) Together the boys cut almost the entire yard.

False, the entire yard is 40/40 and 13/40 is not close.

-Chetan K

Answer:

True

Step-by-step explanation:

So the radius would be 5 (as you times it by 2 to get 10)

Therefore

2a=10 is the same as what the circle with diameter d=2r=10

the value of side z is 52.5

What is an isosceles triangle ??

An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.

in this figure, it is an isosceles triangle as two sides of the triangle are equal.

In the given ΔABC,

given ΔDFE ≅ ΔCFB

x= 45*2.5 = 112.5

z = 112.5-60= 52.5

Hence the value of side z is 52.5

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Answer:

Hey there!

20^2+25^2=c^2

400+625=c^2

1025=c^2

Square root 1025 is the correct answer, so option C.

Let me know if this helps :)

Answer: B

Step-by-step explanation:

Answer:2734375

Step-by-step explanation:

q=35/7=5

b9=b1*q^8=7*5^8=2734375

Answer: 34°

Step-by-step explanation:

1. 4x+3x-8=90, add 8 to both sides, so -8 cancels on the left side and 90 becomes 98. Then combine 4x and 3x, you get 7x=98, finally divide both sides by 7, the 7 on the left side cancels and 98 becomes 14. So X=14.

2. Now input 14 into 3x-8. So 3(14)-8=34°, check your work by input 14 in 4x and then adding them both together, they should equal 90. So 4(14)=56 and 34+56=90 so 34° is correct.

Answer:

the measurement of x is 30 degrees

Answer:

Its c

Step-by-step explanation:

Answer:

yes it is C

Step-by-step explanation:

For the answer of factors of expression (12 + 54), in the form of a(b + c), where a is the GCF of 12 and 54 is equals to 6( 2 + 9).

In math, to factor a number means to express it as a product of (other) whole numbers, called its factors. For example, if 7x5 = 35, 7 and 5 are both factors. The divisors that give the remainder to be 0 are the factors of the number. We have an expression of numbers, 12 + 54. We have to write this expression in form of a( b + c), where a is GCF of 12 and 54. Now, we can write the factors of 12 and 54 are 12 = 2×2×3

54 = 2×3 ×3×3

The greatest common factor, GCF of 12 and 54 is 2×3 = 6. So, 12 + 54 = 6× 2 + 6×9

Taking out the common factor 6 from above expression, 6( 2 + 9) which is required form a( b + c). Hence, required expression is 6( 2 + 9).

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Answer:

Step-by-step explanation:

Let's assume the initial number of men at the exhibition is 10x, and the initial number of women is 3x.

After 110 men left, the number of men remaining is 10x - 110.

The total number of people remaining is (10x - 110) + (3x) = 13x - 110.

According to the given information, the number of men remaining (10x - 110) is 5/12 of the total number of people remaining (13x - 110). We can write this as an equation:

10x - 110 = (5/12)(13x - 110)

To solve this equation, we can start by simplifying both sides:

10x - 110 = (65/12)x - (55/6)

To get rid of the fractions, we can multiply both sides of the equation by 12:

12(10x - 110) = 65x - 110(2)

120x - 1320 = 65x - 220

Next, we can bring the x terms to one side and the constant terms to the other side:

120x - 65x = 1320 - 220

55x = 1100

Dividing both sides by 55, we find:

x = 20

Now, we can substitute the value of x back into the initial expressions to find the number of men and women:

Number of men = 10x = 10(20) = 200

Number of women = 3x = 3(20) = 60

Therefore, there were 60 women at the exhibition

Hope this answer your question

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Answer:

\( slope (m) = -\frac{3}{4} \)

Step-by-step explanation:

Slope of the line using two pairs of values from the table, (-2, 5) and (2, 2):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 5}{2 - (-2)} = \frac{-3}{4} \)

\( slope (m) = -\frac{3}{4} \)

Answer:

-2x-y=3

-2x=3+y

-2x=4

y=2

Kirk will drive 15 kilometer east  to get back to his home

The problem will be solved using basic addition operator and subtraction

Let the given information be represented as follows

he drives 15 kilometers west = 15 W

45 kilometers east = 45 E

75 kilometers west = 75 W

Kirk will drive East to get home = ?

since the distances are all in the horizontal direction we add up the west directions and subtract the east direction

15 W + 75 W = 45 E + ?

90 W = 45 E + ?

? = 90 - 45

? = 45 E

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The work done by the gas during the isothermal expansion is 331.32 J.

Isothermal Expansion refers to a process in which the temperature of a system stays constant while the volume increases. In this process, an ideal gas expands from 1.1 m³ to 1.8 m³, and the gas constant is R = 8.314 J/(mol K).

The work done by the gas during the isothermal expansion can be calculated as follows:Answer:During an isothermal process, the change in internal energy of the system is zero since the temperature remains constant.

Therefore,ΔU = 0The first law of thermodynamics is given by:ΔU = q + w

where q is the heat absorbed by the system, and w is the work done on the system.Since ΔU = 0 for an isothermal process, the above equation reduces to:w = -q

During an isothermal process, the heat absorbed by the system is given by the equation:q = nRTln(V₂/V₁)Where, n is the number of moles, R is the gas constant, T is the temperature, V₁ is the initial volume, and V₂ is the final volume.

Substituting the given values, we have:q = (1 mol) × (8.314 J/(mol K)) × (293 K) × ln(1.8 m³ / 1.1 m³)q = 331.32 J

Therefore, the work done by the gas during the isothermal expansion is given by:w = -qw = -(-331.32 J)w = 331.32 J

Thus, the work done by the gas during the isothermal expansion is 331.32 J.

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-1-2= -3

3-7 = -4

\( \sqrt{ { - 3}^{2} + { - 4}^{2} } = 5\)

Answer:

$ 12 × 40/hr = $ 480

$ 588- $ 480 = $ 108 left over

12 × 1.5 = $ 18 OT rate

108 ÷ 18 = 6 hrs of OT

By engaging in these exercises, students can develop a deeper understanding of conditional statements and logical reasoning, which are essential skills for further studies in mathematics and logic.

In Unit 2 of a logic and proof course, homework 3 focuses on conditional statements.

Conditional statements are fundamental concepts in logic and mathematics, representing logical implications between two statements.

They are typically expressed in "if-then" format, where the "if" part is the hypothesis and the "then" part is the conclusion.

The homework may involve tasks such as:

Identifying conditional statements: Students are given a set of statements and asked to identify which ones are conditional statements.

They need to recognize the "if-then" structure and correctly identify the hypothesis and conclusion.

Analyzing the truth value of conditional statements:

Students may be given conditional statements and asked to determine whether they are true or false.

They need to evaluate the hypothesis and conclusion to determine if the implication holds in each case.

Writing converse, inverse, and contrapositive statements:

Students may be required to manipulate given conditional statements to form their converse, inverse, and contrapositive statements.

This involves switching the positions of the hypothesis and conclusion or negating both parts.

Applying the laws of logic:

Students may need to apply logical laws, such as the Law of Detachment or the Law of Modus Tollens, to deduce conclusions based on conditional statements.

Constructing counterexamples:

Students may be asked to provide counterexamples to disprove statements that are falsely claimed to be universally true based on a given conditional statement.

They also help students develop critical thinking and problem-solving abilities, as they have to analyze and manipulate logical structures.

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Equal sides are the paragraph's omission.

Common Side BA is the Missing Piece of the Proof.

The reasons given in the evidence are sufficient to demonstrate that BCA and BFA are similar.

ΔBFA≅ ΔBCA, but not sufficiently to demonstrate that BCA is compatible with BFA.

To demonstrate congruent triangles, we must demonstrate that the corresponding sides are likewise equal, so we must demonstrate that BA = BA (common side) before the Proof is complete.

Hence, Equal sides are the paragraph's omission.

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Answer:

in picture

Step-by-step explanation:

Answer:

i dont understand the question

Step-by-step explanation:

i wnt points so i used this to do it!

If each is a 4-digit number beginning with 1 that has exactly two identical digits , then there are 432 such numbers .

In the question ,

Suppose  that the two identical digits are both 1.

and since the thousands digit must be 1, only one of the other three digits can be 1. This means that the  possible forms for the required numbers are

11xy , 1x1y , 1xy1  ,

Because the number must have exactly two identical digits, x ≠ y, x ≠ 1, and y ≠ 1.

Hence, Of this form there are 3 × 9 × 8 = 216 numbers .

Now suppose that two identical digits are not 1 , we will have the following possibilities:

1xxy , 1xyx , 1yxx

Again, x ≠ y , x ≠ 1 , and y ≠ 1 .

Of this form there are 3 × 9 × 8 = 216 numbers .

So , the total numbers are 216 + 216 = 432 .

Therefore , the total  numbers are 432 .

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$QS$ and $PR$ are parallel sides of the square, they have the same length, which is $10$. Therefore, we can conclude that $XM = NY = 10$.

Given the square $PQRS$ with side length $10$, the points $X$ and $Y$ are located outside the square such that $XQ < XS$ and $YR < YS$. We need to determine the relationship between the lengths of the segments $XY$, $QS$, and $PR$.

Since $XQ < XS$, we can conclude that $X$ lies between $Q$ and $S$. Similarly, since $YR < YS$, we can conclude that $Y$ lies between $R$ and $S$. Therefore, the segment $XY$ intersects the segments $QS$ and $PR$.

Let $M$ be the point of intersection between $XY$ and $QS$, and let $N$ be the point of intersection between $XY$ and $PR$. We can observe that $QS$ and $PR$ divide $XY$ into three segments: $XM$, $MN$, and $NY$.

Since $QS$ and $PR$ are parallel sides of the square, they have the same length, which is $10$. Therefore, we can conclude that $XM = NY = 10$.

In summary, we have $XM = 10$, $MN$, and $NY = 10$.

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The total mass of the paperclips in the box is 6. 144 × 10^1 mg. Option C

1 mass of a paperclip = 8.0 × 10−4 mg

But there are 7.68 × 104 paperclips = x mg

cross multiply

x = 7.68 × 104 × 8.0 × 10−4 mg

Multiply through

x = 61. 44 × 10^ 4 -4

x = 61. 44 × 1

x = 6. 144 × 10^1 mg

Thus, the total mass of the paperclips in the box is 6. 144 × 10^1 mg. Option C

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The value for $\frac{0.\overline{72}}{0.\overline{27}}$ as a common fraction in lowest terms is 2.666

To convert repeating decimals to fractions, we can use the following method:

Let's call the repeating decimal 0.72... = x, and the repeating decimal 0.27... = y.

Then 10x = 7.2... and 10y = 2.7...

Subtracting the original expressions from the above:

10x - x = 7.2... - 0.72...

=> 9x = 7

=> x = 7/9

And similarly,

10y - y = 2.7... - 0.27...

=> 9y = 2

=> y = 2/9

Therefore,

0.72... / 0.27... = x / y = (7/9) / (2/9) = 7/2 = 3.5

A repeating decimal is a decimal that has a repeating pattern of digits after the decimal point. To convert a repeating decimal to a fraction, we need to identify the repeating pattern and convert it to a fraction. This is done by multiplying both the numerator and denominator by a power of 10 that makes the repeating part an integer.

Then, the resulting fraction can be simplified to its lowest terms. In this case, the repeating decimals 0.72... and 0.27... can be converted to the fractions 7/9 and 2/9 respectively, and dividing the two results in a fraction of 7/2 can be simplified to 3.5.

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Answer: 21

Step-by-step explanation:

Mode is the value that appears most often in a set of data values.

        21, 21, 21, 24, 24, 25, 26, 27, 27, 28, 29

Answer:

The mode for the data set is 21

Step-by-step explanation:

The more type of numbers that you see in a data set is the mode... like for example- the data set 1, 1, 1, 5, 6, 7, 5

1 is the mode because there are more 1's than any number in the data set.

Your welcome! ;D