Here is a map of a town.
It has a scale of 2 cm to 7 km.
A centimetre ruler is shown on the map.
What is the real-life distance between the ice rink and the theatre?

Answer:

8.09017

calculations

We can use the Pythagorean theorem to find the diagonal distance across the rug. According to the theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side (the hypotenuse).

In this case, the length and width of the rug form the two shorter sides of a right triangle, and the diagonal distance is the hypotenuse. So we can use the formula:

diagonal^2 = length^2 + width^2

Plugging in the values given in the problem, we get:

diagonal^2 = 8^2 + 5^2

diagonal^2 = 64 + 25

diagonal^2 = 89

To solve for the diagonal, we take the square root of both sides:

diagonal = sqrt(89)

Using a calculator, we get:

diagonal ≈ 9.43 feet

Therefore, the diagonal distance across the rug is approximately 9.43 feet.

The volume of the stone is 1032 cm³.

The volume of the stone can be calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 2.7 cm. Therefore, the volume of the stone is V = 10 x 24 x 2.7 = 648 cm³.

The volume of the water in the container is calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 7 cm. Therefore, the volume of the water in the container is V = 10 x 24 x 7 = 1680 cm³.

The difference between the volume of the water and the volume of the stone is the volume of the water displaced by the stone, which is V = 1680 - 648 = 1032 cm³. Therefore, the volume of the stone is 1032 cm³.

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Answer:

B linear

Step-by-step explanation:

If the rate of change stayed the same then it has to be a straight line so no C or D, and it cant be A be cause there is a rate of change.

Answer:

115.50

Step-by-step explanation:

Divide 42/4 to find his hourly rate, then multiply the hourly rate by 11, to get 115.50

Answer:

$115.05

Step-by-step explanation:

If he earns $42 in 4 hours than he earns $10.05 in 1 hour

42 / 4 = 10.5

10.5 x 11 = 115.5

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. This statement is not correct.

When a pyramid and a prism have the same base and height, the volume of the pyramid is one-third ([tex]\frac{1}{3}[/tex]) the volume of the prism.

This can be seen from the formula for the volume of a rectangular prism, which is:

[tex]The volume of the prism = base area x height[/tex]

And the formula for the volume of a rectangular pyramid is:

The volume of the pyramid = [tex]\frac{1}{3}[/tex] x base area x height

Since the base area and height of the pyramid and prism are the same, we can compare their volumes by dividing the volume of the pyramid by the volume of the prism:

[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex] x base area x height/base area x height

Simplifying this expression, we get:

[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex]

Therefore, the volume of a pyramid with the same base and height as a prism is one-third [tex](\frac{1}{3})[/tex] the volume of the prism.

The complete question is:-

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. True/False.

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Answer: Answers below

Step-by-step explanation:

1. $15.64

2. 5370.28 Yen

3. 13425.70 Yen

4. $100

5. 67128.51 Yen

6.$782.08

Answer: 1: 15 2: 5370 3:13400 4: 160 5: 67100 6: 780

Step-by-step explanation: These are rounded to the nearest 100th

Answer:

I hope this explains it!

Step-by-step explanation:

1. Select which conversion approach you wish to use:

a. Convert from actual (real) size to scale.

b. Convert from scale to actual (real) size.

2. Enter the scale factor; for example, if you wish to work with a 1/6th scale, input 6.

3. Enter the dimensions of the actual object (or measurements of the scaled object if you are planning on converting a scale to an actual size)

4. Select the unit of measurement from the drop-down list

5. Click on the "Convert" button to generate the results.

Answer:

I guess the value be 26x

hope it helps u

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As a result, the right triangle x value of 65° is the answer to the given triangle issue.

Triangles are categorised as polygons because they have four edges or more. Its shape is simple and symmetrical. The characters ABC make a square angle that is a triangle. When the edges are still not collinear, Euclidean geometry yields a single rectangle or square. Due to their three edges and three corners, triangles are considered polygons. The corners of a triangle are where its three edges meet. Angles in a trapezoid add up to 360 °.

Here,

Given:

Triangle is 90 degrees because of its right orientation.

The total of the triangle's angles is 180 degrees.

Thus,

=> x + 25° + 90° = 180°

=> x + 115° = 180°

=> x = 180° -115°

=> x = 65°

Thus, the value of x is 65°.

As a result, the answer to the provided triangle problem is

Right triangle's x number is 65 degrees.

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The type of sampling used to conduct a study on depression among the elderly is convenience sampling, which is a type of non-probability sampling technique where samples are selected because they are conveniently available and accessible, and the sample size for this study was calculated to be 30.

The type of sampling used to conduct a study on depression among the elderly is convenience sampling. Convenience sampling is a type of non-probability non-probability  where samples are selected because they are conveniently available and accessible .

In this study, a sample of 30 patients in one nursing home was used for the convenience sampling. The formula for calculating the sample size for convenience sampling is [tex]N = (N1*N2)/(N1+N2[/tex]), where N is the sample size, N1 is the population size, and N2 is the desired sample size. In this case, N1 is the total number of elderly patients in the nursing home, and N2 is 30. Therefore, the sample size for this study is calculated as follows: [tex]N = (N1*30)/(N1+30) = 30[/tex].

Convenience sampling is a quick and easy way of obtaining a sample, but it can be biased due to the presence of sampling errors and selection bias. Sampling errors occur when the sample is not representative of the overall population, while selection bias occurs when certain groups of people are more likely to be included in the sample than others. Therefore, it is important to consider the potential sources of bias when conducting a study using convenience sampling.

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Liam saved $192.05 from his summer jobs.

It is based on the probability that something will happen. The fundamental underpinning of theoretical probability is the justification for probability. For instance, while flipping a coin, there is a 50% probability that it will land on its head.

By deducting his outgoings from his total earnings, we can calculate how much money Liam saved:

m = 328.65 - 136.60

Condensing the phrase:

m = 192.05

Liam was able to save $192.05 as a result of his summer jobs.

The following equation and its answer demonstrate how much money Liam has saved:

m = 328.65 - 136.60

m = 192.05

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a) The basic formula is [tex]y=v_0t-gt^2/2[/tex]

[tex]9.81m/sec^2 x \ t^2 - (14 m/sec x t) - 60m = 0[/tex]

quadratic equation t= -b+/- √b^2-4ac /2a

t= 14+- √(-14)^2 -4(4.905)(-60)/ 2(4.905) = 5.20 sec

b) [tex]y=v_0t-gt^2/2[/tex]

At max height H, [tex]V_y = 0[/tex]

[tex]Vy^2 = V^2_{0y} - 2g(y-y_0)[/tex]

[tex]0=(14)^2 -2(9.81)(H-60)[/tex]

[tex]H=70m[/tex]

The ball would fall 10m from max height of 70m. set y=0 and H=10m

[tex]y=gt^2/2+H, t = 1.42 \ sec[/tex].

[tex]\bold{Therefore, 5.2 - 1.42 = 3.77 \ sec}[/tex]

Answer:   8x + 6y = $56.50

Step-by-step explanation:

I think this is right!

We may infer that the constant of proportionality (unit rate) between the amount spent and the quantity of ice cream cones purchased is $5.50 per cone because the unit rate is the same for both weeks.

The unit rate, or constant of proportionality, between the amount spent and the quantity of ice cream cones purchased is $5.50 per cone.

We divide the total sum by the quantity of cones purchased to determine the unit rate.

The unit rate for last week is: $22 x 4 cones = $5.50 per cone.

The unit price for this week is: $33 divided by six cones, or $5.50 each cone.

We may infer that the constant of proportionality (unit rate) between the amount spent and the quantity of ice cream cones purchased is $5.50 per cone because the unit rate is the same for both weeks.

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The value of the ratio t:m:w in its simplest form is 3:8:28.

To simplify the ratio t:m:w, we need to find the common factor between t, m, and w.

Using the given ratios, we can write t:m:w as (3x):(8x):(28y), where x is the common factor between t and m and y is the common factor between m and w.

From the given ratio t : m = 3:8, we can say that t is equal to 3 and m is equal to 8.

Similarly, from the given ratio m:w = 4:7, we can say that m is equal to 4 and w is equal to 7.

So, we have

t : m = 3:8 and m:w = 4:7

Multuiply second by 2

t : m = 3:8 and m:w = 8:14

So, we have

t : m : w = 3 : 8 : 14

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Answer:

Step-by-step explanation:

[tex]a)\quad AB[/tex]

[tex]b)\quad AB[/tex]

[tex]c)\quad AC[/tex]

[tex]d)\quad BC[/tex]

[tex]e)\quad BC[/tex]

[tex]f)\quad AC[/tex]

The correct statement is a=b implies that ac=bc.

If the real numbers a and b are such that a=b, then their values are equal.

The result of adding c to both sides of the formula a=b is:

a+c = b+c

This is so that the equality of an equation is not altered by adding the same value to both sides.

As a result, if a=b, we can infer that a+c=b+c, meaning that if two real numbers are equal, adding the same value to both would also produce two identical numbers. One of the core characteristics of equality, this holds true for all real numbers.

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By answering the above question, we may state that Multiplying these equation prime factorizations together, we get:

[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]

A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.

then multiply the prime factors together using the laws of exponents.

[tex]12^9 = (2^2 · 3)^9 = 2^18 · 3^9\\36^15 = (2^2 · 3^2)^15 = 2^30 · 3^30\\169^8 = 13^16\\12^9 · 36^15 · 169^8 = (2^18 · 3^9) · (2^30 · 3^30) · 13^16 = 2^48 · 3^39 · 13^16\\[/tex]

(b)

[tex]16^13 = 2^52\\10^7 = 2^7 · 5^7\\81^18 = (3^4)^18 = 3^72\\[/tex]

Multiplying these prime factorizations together, we get:

[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]

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Answer:

(3h+4)(2h+3)

Step-by-step explanation:

6h^2 + 8h + 9h + 12h

(6h^2+8h) + (9h+12h)

2h(3h+4) + 3(3h+4)

(3h+4)(2h+3)

Answer:

(3h+4) (2h+3)

Step-by-step explanation:

i hope this helps

The increase in the rate of unemployment from 2000 to 2001, given the unemployment figure is between D. 0. 46 % and 0. 49 %.

First, find the rate of unemployment in 2000 to be :

= Unemployment number / Total labor force x 100 %

= 3, 503, 917 / 25, 554, 417  x 100 %

= 13.71  %

The rate of unemployment in 2001 was :

= 3, 745, 300 / 26, 416, 800 x 100 %

= 14. 18 %

The increase in the rate of unemployment is:

= 14. 18 - 13. 71

= 0. 47 %

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Answer:

Therefore, ackrabbits can reach speeds of approximately 59 feet per second.

Step-by-step explanation:

First, we need to convert miles to feet:

40 miles/hour * 5,280 feet/mile = 211,200 feet/hour

Then, we need to convert hours to seconds:

1 hour = 60 minutes/hour * 60 seconds/minute = 3,600 seconds/hour

211,200 feet/hour / 3,600 seconds/hour = 58.67 feet/second

Rounding to the nearest whole number, we get:

59 feet/second

Therefore, ackrabbits can reach speeds of approximately 59 feet per second.

After answering the provided question, we can conclude that C. The expression interquartile range (IQR) of team B's scores exceeds that of team A's scores.

An expression in mathematics is a collection of representations, digits, and huge corporations that represent a statistical correlation or fitness regime. A square root, a mutable, or a combo of the two can be used as an expression. Mathematical operators include addition, basic arithmetic, rapid spread, polarisation, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

We can see from the box plots in the image that the box plot for team B is wider than the box plot for team A, indicating that team B has a wider range of scores. As a result, the correct statement comparing the distribution spreads is:

C. The interquartile range (IQR) of team B's scores exceeds that of team A's scores.

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Therefore , the solution of the given problem of triangle comes out to be  x = 15 .

A triangular is a polygon because it has two or maybe more additional sections. It has a straightforward rectangular form. A, B, and C are the only three sides that set a triangle apart from a simple triangle. When the boundaries are not exactly collinear, Euclidean geometry results in a singular area instead of a cube. If a shape has three edges and three angles, it is said to be triangular.

Here,

Triangle ABC ,

=> x /5 = x-6/3

=> 3x = 5x - 30

=> 2x = 30

=> x = 30/2

=> x = 15

Therefore , the solution of the given problem of triangle comes out to be   x = 15 .

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Answer: The distance from the ball to the goal is 11.86 ft.

Step-by-step explanation:

Answer:

≈ 11.9 feet

Step-by-step explanation:

The probability of all the defendants being found guilty is 1/16. Answer: 1/16.

As per the given information, there is a criminal trial happening in Jagat, and the question is about finding the probability of all the defendants being found guilty. Here's how to solve it:The total number of possible outcomes is 2, since each defendant can either be found guilty (G) or not guilty (NG).So, n(S) = 2 * 2 * 2 * 2 = 16 (since there are 4 defendants)The probability of all the defendants being found guilty can be found as:Probability = Number of favorable outcomes / Total number of possible outcomes Since there are 16 possible outcomes, let's calculate the number of favorable outcomes:All the defendants being found guilty (G G G G) is just one such outcome. Hence, the number of favorable outcomes is 1.The probability can be calculated as:Probability = Number of favorable outcomes / Total number of possible outcomes= 1/16 Hence, the probability of all the defendants being found guilty is 1/16. Answer: 1/16.

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Answer:

    m∠4 = 133°

Step-by-step explanation:

Given m∠7 = 37°

Since m∠7 ≅ m∠6 [Vertically opposite angles]

and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]

Therefore, 47°+ m∠4 = 180°

m∠4 = 180 - 47

       = 133°

The solution to the differential equation is:

$$v(t)=\frac{V_0+kCe^{-Ct}}{1+kCe^{-Ct}}$$
Where $V_0$ is the initial velocity and $C$ is the proportionality constant. The limiting velocity of the falling body as $t \to \infty$ is: $$v_{\infty}=\frac{V_0}{1+kC}$$

The instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of x with respect to t: v ( t ) = d d t x ( t ) . v ( t ) = d d t x ( t ) . Like average velocity, instantaneous velocity is a vector with dimension of length per time.

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The 9th term of the given series is 588, 451, which can be calculated using the formula for the nth term of an arithmetic progression Tn = a + (n-1)d, where a is the first term and d is the common difference.

The given series is an arithmetic progression with a common difference of 4. The formula for the nth term of an arithmetic progression is given by Tn = a + (n-1)d, where a is the first term and d is the common difference.

Therefore, for the given series, a = 1 and d = 4.

Substituting these values in the above formula, we get

T9 = 1 + (9-1)4

 = 1 + 32

 = 33

Now, adding 33 to each of the terms of the given series, we get

1 + 33 = 34

5 + 33 = 38

25 + 33 = 58

125 + 33 = 158

Therefore, the required 9th term of the series is 588, 451.

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The volume of the coffee can rounded to the nearest 10th of a decimal place is 226. 08 cubic inches

It is important to note that the coffee can takes the shape of a cylinder.

The formula for calculating the volume of a cylinder is expressed with the equation;

V = πr²h

This is so as the parameters are enumerated thus;

Also, r = diameter/2 = 6/2 = 3 inches

From the information given, we have that;

Volume = 3.14 × (3)² × 8

Multiply the values

Volume = 226. 08 cubic inches

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