For every 3 girls in Mr Hegarty's class there are 5 boys. What is the ratio of boys to girls in the class?
Give your answer in its simplest form.

Answer:To divide -5 by 1,000, we can use a calculator or perform long division.

Using a calculator, we get -0.005 as the result.

To perform long division, we can follow these steps:

1. Write -5 as the dividend and 1,000 as the divisor.

2. Place the divisor outside the long division bracket and the dividend inside the bracket.

3. Divide the first digit of the dividend by the divisor. In this case, 1,000 does not go into -5, so we write 0 as the first digit of the quotient.

4. Bring down the next digit of the dividend (which is 0) and place it next to the 0 in the quotient.

5. Divide 1,000 into 0, which gives 0 as the next digit of the quotient.

6. Continue bringing down digits from the dividend and dividing until you have enough decimal places in the quotient. In this case, we can stop after two decimal places because we know the answer is not 200.

7. The final result is -0.005.

Therefore, -5 divided by 1,000 is equal to -0.005.

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Based on the above, the equivalent equations are 4x = 15 and 4x - 15 = 0.Hence options A and C are correct.

To determine which equations are equivalent to 3x + 5 = 20 - x, we need to simplify and manipulate the original equation until it has the same form as the other equations. Here's how we can do it:

3x + 5 = 20 - x

Add x to both sides:

4x + 5 = 20

Subtract 5 from both sides:

4x = 15

So the equation 4x = 15 is equivalent to 3x + 5 = 20 - x.

Therefore, the other equations are not equivalent:

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Select all of the equations that are equivalent to 3x + 5 = 20 - x.

4x = 15

2x = 25

4x  - 15 = 0

-4x+20 = -5

x - 20 = 5 + 3x

The fractions that are equivalent to 14 are 28 2 over 8 520 5 over 20 416 4 over 16.

To find the fraction = 14, multiply or divide both the numerator and denominator of 14 by the same number.

The fraction 14 can be written as 14/1.

Multiplying the numerator and denominator of 14/1 by 2 gives:

28/2 = 14

Multiplying the numerator and denominator of 14/1 by 3 gives:

42/3 = 14

Multiplying the numerator and denominator of 14/1 by 4 gives:

56/4 = 14

28/2 = 14

70/5 = 14

So the fraction corresponding to 14 is:

28/2

42/3

56/4

70/5

Of the choices given in the question, only 28 equals 2/8, and 56 equals 4/16 14. Any other option is wrong.

So the correct answer is:

28 2/8

56 4/16 . 

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A cylinder with a radius of 3 ft and a height of 4 ft has the same volume as one with a radius of 4 ft and a height of 9 ft.

We can determine how much interior room a cylinder has by measuring its volume. The volume would be the same as how much material would fill the full can if you had one.

Volume of cylinder = π*r²*h

r is the radius and h is the height.

For given cylinder:

r = 4 ft and h = 9 ft

Volume of given cylinder = π*4²*9

Volume of given cylinder = 144π cu. ft.

Now, from the options:

As, its is clear from  formula of cylinder that there is a square of radius.

Thus,

take radius r = 3 ft  such that r² = 9 ft and height h = 4 ft.

These are the same dimensions as the given cylinder.

Thus, a cylinder with a radius of 3 ft and a height of 4 ft has the same volume as one with a radius of 4 ft and a height of 9 ft.

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To solve the equation \begin{equation}-\log{\left(x^2 - 15\right)} = \log{\left(2x\right)}\end{equation}, the following steps can be taken:

Apply the logarithmic identity log(a) = log(b) if and only if a = b to obtain the equation x^2 - 15 = 2x.

Move all the terms to one side of the equation to get x^2 - 2x - 15 = 0.

Factor the quadratic expression to obtain (x - 5)(x + 3) = 0.

Use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero, to get x - 5 = 0 or x + 3 = 0.

Solve for x in each equation to obtain x = 5 or x = -3.

Therefore, the steps to solve the equation log(x^2 - 15) = log(2x) from 1 to 5 are:

Apply the logarithmic identity to get x^2 - 15 = 2x.

Move all the terms to one side of the equation to get x^2 - 2x - 15 = 0.

Factor the quadratic expression to obtain (x - 5)(x + 3) = 0.

Use the zero product property to get x - 5 = 0 or x + 3 = 0.

Solve for x in each equation to obtain x = 5 or x = -3.

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Answer:

18 blinks per min since 126 divided by 7 equals 18.

x = 6 is a valid solution to the equation 3x + 5 = 23.

However, we can give you some general tips on how to approach a math problem when given a specific value of a variable like x = 6:1. Identify the equation or problem that involves x.2.

Replace every instance of x in the equation with the given value, which in this case is 6.3.

Simplify the equation by performing any necessary operations (addition, subtraction, multiplication, division, etc.)4. Solve for the unknown value if possible.

For example, if the equation is 3x + 5 = 23 and x = 6, we would replace every instance of x with 6:

3(6) + 5 = 23

Simplify by multiplying 3 and 6 and adding 5:

18 + 5 = 23

Simplify further by adding 18 and 5: 23 = 23.

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The quantities that are less than 16 cups are: 6 pints (A) and 3 quarts (E).

let's convert each option to cups:

A. 6 pints: There are 2 cups in a pint, so 6 pints × 2 cups/pint = 12 cups.

B. 1 gallon: There are 16 cups in a gallon, so 1 gallon = 16 cups.

C. 5 quarts: There are 4 cups in a quart, so 5 quarts × 4 cups/quart = 20 cups.

D. 8 pints: There are 2 cups in a pint, so 8 pints × 2 cups/pint = 16 cups.

E. 3 quarts: There are 4 cups in a quart, so 3 quarts × 4 cups/quart = 12 cups.

Now, let's see which options are less than 16 cups:

A. 6 pints: 12 cups (less than 16 cups)

B. 1 gallon: 16 cups (not less than 16 cups)

C. 5 quarts: 20 cups (not less than 16 cups)

D. 8 pints: 16 cups (not less than 16 cups)

E. 3 quarts: 12 cups (less than 16 cups)

So, the quantities that are less than 16 cups are: 6 pints (A) and 3 quarts (E).

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Answer:

Option C.

Step-by-step explanation:

Gross pay = (total hours works) * pay rate

                 = (4.7 + 7.3 + 6.4 + 5.8 + 5.4) * 12.1

                 = 29.6 * 12.1

                 = $358.16

This number is closest to 354.53, so C is the correct answer.

Given that √7 is a solution to the equation x² = 7, we can use this equation to find a decimal approximation of √7 that satisfies the given condition.

First, we can estimate that √7 is between 2.5 and 3, since 2² = 4 < 7 and 3² = 9 > 7.

Next, we can try using a decimal approximation of √7, such as 2.6 or 2.7, and square it to see if the result is between 6.9 and 7.1.

If we try 2.6, we get:

(2.6)² = 6.76

Since this is less than 6.9, we can try a larger value, such as 2.7:

(2.7)² = 7.29

Since this is greater than 7.1, we can try a value between 2.6 and 2.7, such as 2.65:

(2.65)² = 7.0225

This result is between 6.9 and 7.1, so a decimal approximation of √7 that satisfies the given condition is approximately 2.65.

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The angles 45 degrees, 30 degrees, and 105 degrees do not form a valid triangle.

In a triangle, the sum of the angles must be 180 degrees. However, in this case, the sum of the three angles is:

45 + 30 + 105 = 180

This tells us that these three angles can be arranged in a straight line, but they cannot form a triangle.

In a valid triangle, the sum of the two smaller angles must be greater than the measure of the largest angle. However, in this case, the sum of the two smaller angles (30 degrees and 45 degrees) is only 75 degrees, which is less than the measure of the largest angle (105 degrees).

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Answer:

48 ft^3

Step-by-step explanation:

Volume = (length x width x height)/3

V = (b times b times h)/3

V = (4 x 4 x 9)/3

V = 144/3

V = 48

(units: cubic feet --> 48 ft^3)

Answer:

0.098

Step-by-step explanation:

The system of equations that represent the question are:

6a + 8p = 6.54

7a + 5p = 5.68

(option D)

A linear equation is an equation that has a single variable that is raised to the power of one. The general form of a linear equation is y = mx + c

Where:

The form of the equations in this question are:

(number of apples bought x price of one apple) + (price of one pear x number of pears bought) = total cost of the apples and pears

6a + 8p = 6.54

7a + 5p = 5.68

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The system of equations that represent the question are: 6a + 8p = 6.54 and 7a + 5p = 5.68. Option D

A linear equation is an equation with one variable raised to the power of one. It can be written in the form y = mx + c, where m represents the slope and c represents the y-intercept.

The given equations are in the form of:

6a + 8p = 6.54

7a + 5p = 5.68

These equations represent the total cost of buying apples and pears based on their respective prices per unit. 'a' represents the number of apples bought, 'p' represents the number of pears bought.

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The range of standard IQR (Interquartile Range) numbers is option b) 0-15. The correct option is B).

The interquartile range (IQR) is a measure of variability used in statistical analysis. The IQR is often used as a measure of spread because it is less sensitive to outliers than the range. Standard IQR numbers are values that have been standardized to fit within a specific range of 0-15.

Standardizing the IQR allows for easier comparison of data across different datasets, as it ensures that the IQR values fall within a consistent range. The range of standard IQR numbers is often used in educational assessments and other standardized tests to report the variability of student performance or other metrics. So, the correct answer is option B).

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Six can be represented using 3 bits, but 2⁴ = 16 unique numbers can be represented using four bits. However, 20 can be represented using 5 bits since 2⁵ = 32 unique numbers can be represented using five bits.

The question "show that the numbers 0 to 7 can be written using 3 binary digits (bits).Binary numbers are constructed by concatenating bits (binary digits).

Each bit can take on one of two values: 0 or 1. Binary notation is frequently utilized in computer engineering to represent data, instructions, and addresses. Three bits can represent 2³ = 8 unique numbers since each bit has two options (0 or 1).

Thus, the numbers 0 to 7 can be represented using 3 bits since 2³ = 8. We can also figure out how many bits are required to represent the numbers 0 to 6 or 0 to 20.

Six can be represented using 3 bits, but 2⁴ = 16 unique numbers can be represented using four bits. However, 20 can be represented using 5 bits since 2⁵ = 32 unique numbers can be represented using five bits.

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The determinant of the given matrix is -51.

A square matrix's related scalar value is known as a determinant. It is calculated based on the matrix's components using a specified formula. The determinant has several uses in linear algebra, including the resolution of systems of linear equations, the discovery of eigenvalues and eigenvectors, and the assessment of invertibility. If and only if a matrix's determinant is nonzero, the matrix is invertible. The determinant is also employed in other branches of mathematics, such as differential geometry and the determination of the volume of parallelepipeds.

The determinant of the matrix is calculated using the formula:

D = a(ei - fh) - b(di - fg) + c(dh - eg)

Substituting the values we have:

3(-20 - 5(-1)) - (-1)(20 - 54) + 4(2*(-1) - (-2)*(-1)) = -51

Hence, the determinant of the given matrix is -51.

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Answer:

81

Step-by-step explanation:

For 1 rod:

V = πr²h

V = 3.14 × (3 cm)² × 20 cm

V = 565.2 cm³

Total volume of steel used: 45,781.2 cm³

45,781.2 cm³ / 565.2 cm³ = 81

Answer: 81

Burger Quick's box plot has a larger IQR than Super Fast Food's, hence Super Fast Food is better able to predict their wait time

A measurement of statistical dispersion, or the spread of the data, is the interquartile range (IQR). It is described as the variation between the data's 75th and 25th percentiles. The fourth spread, middle 50%, midspread, or H-spread1 are further names for the IQR.

The dataset is displayed using a box plot, which is a standardized method based on the five-number summary of the minimum, maximum, sample median, and first and third quartiles

The box plot displays measurements made from data acquired from interviews with 20 people on how long they waited at a drive-through restaurant window.

Burger Quick's box plot has a larger IQR than Super Fast Food's, hence Super Fast Food is better able to predict their wait time.

A data set is divided into quartiles to calculate the IQR (Interquartile Range), which is a measure of variability. The first quartile (Q1) is subtracted from the third quartile (Q3) to determine it.

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The probability that the weight of a randomly selected steer is between 1000 and 1520lbs is approximately 0.9192, or 91.92%.

Standard deviation = sqrt(variance) = sqrt(40,000) = 200

z = (x - μ) / σ

where z is the standardized value, x is the value of interest, μ is the mean, and σ is the standard deviation.

For x = 1000:

z1 = (1000 - 1100) / 200 = -0.5

For x = 1520:

z2 = (1520 - 1100) / 200 = 2.1

Using a calculator, we can use the normal cdf function with the z-scores to find the area between z1 and z2:

P(z1 < z < z2) = normal cdf(-0.5, 2.1) ≈ 0.9192

Rounding to four decimal places, we get:

P(1000 < x < 1520) ≈ 0.9192

Therefore, the probability that the weight of a randomly selected steer is between 1000 and 1520lbs is approximately 0.9192, or 91.92%.

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Step-by-step explanation & Answer

C = 2pir = 2pi(13) = 26pi = 81.68"

Which we can easily find.

But that is for 1 rotation in the question it says 5!

So multiply it by 5

81.68 x 5 = 408.4

Thus the answer to your problem is, 408.4

Answer:408.4

Step-by-step explanation:

The calculated area of the wall art is 474 square inches

from the question, we have the following parameters that can be used in our computation:

The composite figure

The area of the figure is the sum of the individual areas

So, we have

Area = 21 * 9 + 9 * 19 + 6 * 19

So, we have

Area = 474

Hence, the area is 474 square inches

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The length, breadth, and height of the rectangular block are 256 cm, 192 cm, and 320 cm respectively.

To calculate the length, breadth, and height of a rectangular block whose ratio is 4:3:5 and its volume is 3840 cm3,

follow the steps below:

The ratio of length, breadth, and height is 4:3:5 respectively.

Therefore, assume the length to be 4x, the breadth to be 3x, and the height to be 5x, where x is the common factor.

Then, the volume of the block is calculated as:

Volume = length × breadth × height= 4x × 3x × 5x= 60x³

Since the volume of the block is 3840 cm³, we can equate the equation above to 3840 and solve for x, then find the

length, breadth, and height.

60x³ = 3840 x³ = 3840/60 x³ = 64

Length = 4x = 4 × 64 = 256 cm

Breadth = 3x = 3 × 64 = 192 cm

Height = 5x = 5 × 64 = 320 cm

Therefore, the length, breadth, and height of the rectangular block are 256 cm, 192 cm, and 320 cm respectively.

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With given coordinates of the endpoints of line, the length is 17.75 units.

What are coordinates ?

Coordinates are a set of numbers that describe the position or location of a point in space. In a two-dimensional plane, coordinates are typically represented by two values, an x-coordinate and a y-coordinate, which describe the horizontal and vertical position of a point, respectively.

Now,

The length of a line segment in a two-dimensional plane can be calculated using the distance formula:

d=√[(x₂ - x₁)² + (y₂ - y₁)²]

where (x₁, y₁) and (x₂, y₂) = coordinates of the endpoints of the line segment

In this case, the coordinates of the endpoints are (4.25, 6.25) and (22, 6.25)

d = √[(22 - 4.25)² + (6.25 - 6.25)²]

= √[(17.75)² + (0)²]

= √(315.0625)

= 17.75

Therefore,

             the length will be  17.75 units.

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Multiple regression is a technique which allows researchers to explain a criterion variable through an accurate

combination of two or more predictor variables.

Regression is a statistical measure used in finance, investing and other disciplines that attempts to determine the

strength of the relationship between one dependent variable (usually denoted by Y) and a series of other changing

variables (known as independent variables).

Multiple regression is a statistical method used to analyze the relationship between a dependent variable and multiple

independent variables.

It is often used to estimate the effect of a single independent variable on a dependent variable while controlling for

other independent variables.

Multiple regression is a technique that allows researchers to explain a criterion variable through an accurate

combination of two or more predictor variables.

In summary, multiple regression is a technique that allows researchers to explain a criterion variable through an

accurate combination of two or more predictor variables.

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Accοrding tο the given infοrmatiοn, the equatiοn y = -3x - 2 represents the same line as the equatiοn 3y+3x=2y-2.

An equatiοn is a mathematical assertiοn that prοves the equality οf twο expressiοns. The equals sign (=) separates the twο sides, which make up the οbject. The expressiοns in the equatiοn's twο sides may include numerical values, variables, and mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Tο turn the equatiοn 3y+3x=2y-2 intο the y=mx+b fοrm, yοu need tο isοlate y οn οne side οf the equatiοn.

First, simplify the left-hand side οf the equatiοn by cοmbining the like terms οf 3y and 3x:

3y + 3x = 2y - 2

3y - 2y = -3x - 2

y = -3x/1 - 2/1

Nοw, the equatiοn is in the y=mx+b fοrm, where m is the slοpe and b is the y-intercept. In this case, the slοpe m is -3 and the y-intercept b is -2.

Therefοre, the equatiοn y = -3x - 2 represents the same line as the equatiοn 3y+3x=2y-2.

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The total price Briana will pay for the sweater after discount is $34.2.

What is discount?

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.

Here the Sale price of sweater on sale = $45

Discount = 30%

Sale tax rate = 6%

If cost is 100% , after 30% discount and 6% sale tax rate then ,

cost price = 100%- 30%+6% = 70%+6%=76%

Now cost price = 76% of 45

=> 76%×45

=> 76/100 ×45

=>$34.2

Hence the  total price Briana will pay for the sweater is $34.2.

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