A student ran the Turkey Trot 5K (5 kilometers) race on Thanksgiving Day. Using the ratio 1 mile : 1.61 kilometers, which set-up would correctly convert 5 kilometers to miles

Answer: The correct answer is the Law of Large Numbers

Step-by-step explanation:

Imagine flipping a coin. There is a 50% likelihood that you would get tails. However, it doesn't happen all the time. If you flipped it just a few times, you could get all tails and have 100% tails.

However, if you experimented a lot of times (a large number), you almost certainly wouldn't get all tails. You would get close to 50%. That is the main point of the law.

The more trials you do, the more likely you will get close to the theoretical value.

The best description of the value of the expression 2x - 7, when x = 5 is B. The result is a prime number.

A prime number cannot be divided by another number except by itself or 1.

Common prime numbers include 2, 3, 5, 7, 11, 13, 17, and 19.

The value of 2x – 7, when x = 5 is 3.

3 is a prime number as well as a whole number, but it is not a composite number.

Thus, we can conclude that the result of solving the expression is the prime number 3.

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Answer:

ray:

Part of a line, containing one endpoint and extending to infinity in one direction.

line segment

Two points on a line, and all the points between those two points.

Step-by-step explanation:

The number of bars of the same color could be used to show the number of hours that Dan studies hence he studied for 2/3 hours in four days.

The term multiplication refers to the number of times that a number is added to itself. For instance, if I add four three times, I could shorten the expression as four multiplied by three.

If we look at the diagram, we can see that in each tile, there are always two bars of the same color out the whole three bars. The bars that are of the same color shows the number of hours that Dan studied.

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In this mathematical expression, the original number is 4.

We can use a mathematical equation to work out the original number.

A mathematical equation uses variables, numbers, and constants to show that two values are equal.

Mathematical equations connect two mathematical expressions using the equal sign (=).

Let the original number = x

According to the statement:

2x + 28 = {4}{9}

This implies that:

2x + 28 = 36

Subtracting 28 from both sides gives:

2x = 8

x = 4

Thus, the original number is 4.

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Answer:

40

Step-by-step explanation:

140 + x  = 3*(100-x)

140 + x = 300 - 3x

x + 3x = 300 - 140

4x = 160.

x = 40.

In mathematics, a line's slope, also known as its gradient, is numerical representation of line's steepness and direction. The equation will be [tex]y= \frac{-1}{3}x +5[/tex].

In mathematics, a line's slope, also known as its gradient, is numerical representation of  line's steepness and direction. The letter m is the frequently used to represent slope; the reason for this usage is unclear, although it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for the straight line as "[tex]y = mx + b[/tex]" and "[tex]y = mx + c[/tex]," respectively.

The ratio of "vertical change" to "horizontal change" between the (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or design.

Let, x= -3, x1= -2, y= 5, y1= 2

Then,

slope= [tex]\frac{x-x1}{y-y1} = \frac{-3-(-2)}{5-2} =\frac{-1}{3}[/tex]

now,

y= mx+c

y= [tex]\frac{-1}{3}[/tex]x+ 5

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Integers are 3, 4 and 5.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.

Given Data

Let the three consecutive integers are :

x, x+1 and x+2

According to question
3(x+1) = 4 - 2(x+x+2)

3x + 3 = 4 - 2(2x + 2)

3x + 3 = 4 - 4x - 4

3 = 4x-3x

x= 3

Integers are 3, 4 and 5.

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Yes if there is a positive correlation existing between the paving of streets and the number of registered cars then paving more streets would result in the increase in the registered cars.

This is the term that is used to tell us that there is the presence of a correlation that would make the two variables that we are talking about to move in the same direction. That is when one increases, the other would have to increase as well.

Such that we would have the increase in the number of paved street to cause an increase in the number of registered cars in the place.

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Answer:

b

Step-by-step explanation:

The graph was reflected over the y-axis.

The discriminant of the quadratic equation is 11.1.

The discriminant is the expression that we could use to deduce the kind of roots that a quadratic equation would have. Note that when we say the roots of the equation, we are talking about the solutions of the quadratic equation. We shall now try to obtain the discriminant of this equation as we can see below.

The discriminant is given as;

√b^2 - 4ac

Given;

3x^2 - 10x + 2 = 0

a = 3

b = -10

c = 2

We have;

√(-10)^2 - 4(-3) (2)

√100 + 24

11.1

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Answer: y=12

Step-by-step explanation:

Distribute

Add 10 to both sides

Simplify.

Answer: y = 12

Step-by-step explanation:

2 ( [tex]y\\[/tex] - 5 ) = 14

2[tex]y\\[/tex] - 2 · 5 = 14

2[tex]y\\[/tex] - 10 = 14

(2[tex]y\\[/tex] - 10) + 10 = 14 + 10

2[tex]y\\[/tex] = 24

[tex]\frac{2y}{2} = \frac{24}{2}[/tex]

The value of x if R is the midpoint of QS is 31 units.

The midpoint is the middle point of a line segment.

It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

The midpoint is halfway between the two end points.

Therefore, R is the midpoint of QS

Hence,

QS = QR + RS

QR = 5x - 15

QS = 100

Therefore, QR and RS are congruent because R is the midpoint of QS

QR = RS

Hence,

100 = 5x - 15 + 5x - 15

100 = 10x - 30

100 + 30 = 10x

130 = 10x

divide both sides by 10

x = 130 / 10

x = 13

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The correct answer to task 804 × 79 is 63,516.

When we multiply a number and another together, or a number and a variable, or even a variable with another variable, we mean the product of the two factors. The multiplication sign is " × " .

The step by step explanation of the task above is given below:

804 × 79 = 63,516.

Another example of Multiplication is

40 × 2 = 80.

The product of a and b also means Multiplication.

a and b means a × b = ab.

The product or the multiplication of g and 5 means g × 5 = 5g.

In conclusion, from the detailed information and explanation given above, the product of 804 × 79 is 63,516.

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If the range of the data set is 19. Then the maximum value of the set will be 28.

Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.

The range of the data is the difference between the maximum number to the minimum number. Then the formula is written as,

Range = Maximum value - Minimum value

The range of a set of numbers is 19. And the minimum value is 9.

Then the maximum value of the set is calculated as,

Range = Maximum value - Minimum value

19 = Maximum value - 9

Maximum value = 19 + 9

Maximum value 28

If the range of the data set is 19. Then the maximum value of the set will be 28.

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No, i don't think she is correct as she didn't rounded-off correctly while measuring the diameter of bacteria.

Rounding off is a type of estimation. Estimation is used in everyday life and also in subjects like Mathematics and Physics. Many physical quantities like the amount of money, distance covered, length measured, etc are estimated by rounding off the actual number to the nearest possible whole number.
According to the picture it shows the diameter of the bacteria is 0.00000025691m

So , [tex]2.5691 * 10^-^7m[/tex]  is rounded off and will be equal to [tex]3*10^-^7m\\[/tex]

As, The digit right to 2 is 5 and which already passed halfway up

So, the number 2 will be rounded off to 3 as it being the nearest digit.

Therefore, Bonnie is wrong as she did mistake while rounding - off measurments.

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Answer:

a) 225 meters

b) -162°C

Step-by-step explanation:

a) 5 meters per second for 45 seconds. 5*45 = 225 meters

b) cooled by 18°C per hour over a 9 hour period. -18*9 = -162°C

Answer:

a) 225 meters.

B) -2 °

Step-by-step explanation:

a If it is moving 5 meters per second, then in one second it moves 5 meters, in 2 seconds it move 10 meters, in 3 seconds it move 15 minters.

So to find how much it moved in 454 seconds we would multiply 45 x 5 = 225

B)  In 9 hours it cooled 18 degrees 18/9 = 2.  This means that is cooled 2 degrees per hour.

Answer: 5 and the power is 2

the power used is 2

Step-by-step explanation:

The required solution in scientific notation is 2 × 10¹ .

Scientific notation can be used to indicate values that are either too large or too little to be conveniently written in decimal form (typically would result in a long string of digits).

The given expression is (6.4 × 10³) ÷ (3.2 × 10²)

Simplifying we get :

(6.4 × 10³) ÷ (3.2 × 10²) = 20

This can be written in the scientific notation as : 2 × 10¹

Therefore the required solution is 2 × 10¹

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In linear equations, x = 9.5 Paula use the division property of equality.

What is a formula for linear equations?

The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.

That is, if a, b, and c are real numbers such that a = b and c ≠0, then  

a/b = c/d

The equation was -6x = 57

To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below

    -6x = 57      ( Divide both sides by -6)

-6x/6  = 57/-6

x = 9.5

Hence, we can conclude that the division property of equality.

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The complete question is -

Paula used these steps to solve an equation:

Step 1: -4(7 + 8) - 21 = 25

Step 2: -4r – 32 - 2x = 25

Step 3: -61 – 32 = 25

Step 4: -6x = 57

Step 5: x = -95

Between which two steps did Paula use the division property of equality?

Hence the probability that the spinner will land on something less than 0.75 is 37/50

As we know in between 0 and 1 the decimal numbers are ( 0.1, 0.2, 0.3, 0.4 _ _ _ _ _ 0.95, 0.96, 0.97, 0.98, 0.99, 1.00)

So,

To find the probability = favorable outcomes/ total numbers of outcomes

Favorable outcomes =  0.74 / 1.00

solve the decimal numbers in the simplified form

The probability that the spinner will land on something less than the decimal number 0.75 is 37/50.

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The perimeter and area of each of the composite figure is:

a. Area: 138.6 mm²; Perimeter = 50.27 mm.

b. Area: 120.5 cm²; Perimeter = 42.7 cm

c. Area: 521.1 mm²; Perimeter: 95.8 mm

Area of a circle = πr²

Area of a triangle = 1/2(base)(height).

Area of a rectangle = (length)(width).

The perimeter of a composite figure = the sum of all lengths of the sides surrounding the composite figure.

a. The area of the composite figure = area of rectangle + area of two semicircles

Two semicircles = 1 circle

Area of the rectangle = (15)(5) = 75 mm²

Area of the two semicircles = πr² = π(4.5²) = 63.6 mm²

The area of the composite figure = 75 + 63.6 = 138.6 mm².

Perimeter = 5(2) + 4(3) + (perimeter of 1 circle)

Perimeter = 5(2) + 4(3) + (2πr)

Perimeter = 5(2) + 4(3) + (2π(4.5))

Perimeter = 50.27 mm.

b. Area = area of triangle + area of square + area of half circle

Area = 1/2(base)(height) + s² + 1/2(πr²)

Base = 5 cm

Height = 7 cm

s = √(7² + 5²) = 8.6 cm [Pythagorean theorem]

r = 8.6/2 = 4.3 cm

Area = 1/2(5)(7) + 8.6² + 1/2(π(4.3²))

Area = 120.5 cm²

Perimeter = 5 + 7 + 8.6 + 8.6 + (perimeter of half circle)

Perimeter = 5 + 7 + 8.6 + 8.6 + 1/2(2πr)

Perimeter = 5 + 7 + 8.6 + 8.6 + (2π(4.3))

Perimeter = 42.7 cm

c. Area = area of triangle + area of rectangle + area of half circle

Area = 1/2(base)(height) + (length)(width) + 1/2(πr²)

Base = 32 - 20 = 12 mm

Height = 14 mm

Length = 20 mm

Width = 14 mm

r = 1/2(20) = 10 mm

Area = 1/2(12)(14) + (20)(14) + 1/2(π(10²))

Area = 521.1 mm²

Perimeter = 14 + 32 + hypotenuse of the triangle + (perimeter of half circle)

Hypotenuse = √(12² + 14²) = 18.4 mm

Perimeter of half circle = 1/2(2πr) = 1/2(2π(10)) = 31.4

Perimeter of the composite figure = 14 + 32 + 18.4 + 31.4

Perimeter of the composite figure = 95.8 mm

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The values for the parabola are found as-

For the given question.

The total horizontal distance covered by water is 10 feet.

The maximum height attained by nozzle of water is 8 feet.

Thus, the vertex of parabola (h, k) = (5, 8)

The nozzle was 4 foot above the ground, a = 4.

The equation of parabola becomes;

y = a(x - h)² + k

y = 4(x - 5)² + 8

Thus, the equation of parabola becomes; y = 4(x - 5)² + 8.

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The range thumb rule The minimum and maximum values for the usual value, which is two, are 812.14 and 885.85, respectively.

An efficient way to calculate the range from the standard deviation is to use the range rule of thumb. The range is normally around four times the standard deviation, according to this information. Inferring that your range is around eight if your standard deviation is 2, for example.

As an illustration of a binomial distribution, we'll utilize seeds.

According to given data;

Let "X" represent the number of tomato seeds that actually germinate based on the data provided.

With the knowledge provided above, we can now determine the:

The median number of seeds that we may anticipate to germinate

standard deviation (σ): sqrt of n*p*(1-p)

Once you calculate the mean and standard deviation, you can calculate the minimum usual value and the max usual value.

Now, in your problem:

n = 1415

p = 3/5

so,

the mean would be: (1415)(3/5) = 849

the standard deviation would be:  sqrt (mean)(1-3/5) = 18.4282

Next, we find the minimum and maximum usual values according to the equations you gave:

minimum:  mean - 2(standard deviation)

                = 849 - 2(18.4282)

                = 812.1436

maximum: mean + 2(standard deviation)

                = 849 + 2(18.4282)

                = 885.8564

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The probability is a + b + c = -382

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

Every cube's side is [tex]\sqrt[3]{1000}[/tex] = 10

Since there are 512 unpainted cubes within, the likelihood is 1⁵¹² = 1

There are 8 corners, and each one has a chance of 3 / 6 = 1 / 2 = 2⁻¹ so the probability is 1⁸ / 2 = 1 / 2⁸

There are 8 * 12 = 96 edge pieces (12 edges total, with 8 on each edge; each cube has a probability of 4 / 6 = 2 / 3, so the probability is 2⁹⁶ / 3 = 2⁹⁶ / 3⁹⁶

There are 8 * 8 * 6 = 384 center cubes, each having a chance of 5 / 6, so the probability is 5³⁸⁴ / 6 = 5³⁸⁴ / 6³⁸⁴ = 5³⁸⁴ / (2³⁸⁴ * 3³⁸⁴)

So, the probability is:

(1 / 2⁸) * (2⁹⁶ / 3⁹⁶) * [5³⁸⁴ / (2³⁸⁴ * 3³⁸⁴)]

= (5³⁸⁴ * 2⁹⁶) / (2³⁹² * 3⁴⁷⁰)

= 5³⁹⁴ * 2⁹⁶ * 2⁻³⁹² * 3⁻⁴⁷⁰

= 5³⁸⁴ * 2⁻²⁹⁶ * 3⁻⁴⁷⁰

Thus, a + b + c = -382

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If water is leaking from the bottom of a conical cup that is 20 inches across and 20 inches deep.  The rate that the water level changes when the water is 8 inches deep is: 3 /32π.

dv/dt = rate of cup  loss water per minutes=0.5

r = radius when the water is 8 inches deep

Hence,

20/10  = 8/r

r = 4

Volume of conical cup

v= 1/3πr²h

dv/dt=1/3πr² dh/dt

0.5 = 1/3π × (4)² dh/dt

dh/dt =3 /32π

Therefore the rate is 3 /32π.

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The Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.

As per the question we need to create a division problem where both the divisor and the dividend are decimals and the quotient must be a whole number greater than 1.

So, Let us suppose divisor as 1.5 . Now the dividend must be a decimal number which is greater than 1.5, let's say 5.5.

Now on dividing 5.5 by 1.5,

Divisor = 1.5

Dividend = 4.5

(Dividend/Divisor) = ( 4.5 / 1.5 ) = 3

Quotient = 3

On dividing dividend by divisor the quotient is 3 which is a whole number greater than 1.

So, we can conclude that the Divisor is 1.5 , the Dividend is 4.5 and the quotient is 3.

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Answer:

-0.5 or -1/2

Step-by-step explanation:

(5x) + (3x+4) = 8x+4

8x+4 = 0

8x = -4

x = -0.5

Hope that helps

We are asked to find the values needed for the length CB

The coordinates of points C and B are given as

C(-a, -5b)

Recall that the distance formula is given by

For the given case,

Let us substitute these coordinates into the above distance formula

Therefore, the required values are