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no of students in each van = 6

no. of students in each bus = 42

This can be solved by equation solving.

An equation is a formula in mathematics that uses the equals sign (=) to represent the equality of two expressions.

Given that,

Let, x = no. of students in van

y = no. of students in bus

According to the question:

5x + 4y = 198 .............. (1)

4x + 3y = 150 ............. (2)

Multiply equation (1) by 4 and equation (2) by 5 we get:

20x + 16y = 792

20x + 15y = 750

now after subtractions:

or, y = 42

putting the value of y in equation (1) we get:

5x + 4(42) = 198

or, 5x + 168 = 198

or, 5x = 30

or, x = 6

Thus, no of students in each van = 6

no. of students in each bus = 42

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The equation y = -5x - 1 is steeper than the equation y = -2x - 7.

In mathematics, the relative slope or rate of change of two lines or curves is referred to as "steeper." If one line or curve's slope or rate of change is larger than another, it is said to be steeper than the other.

To compare the steepness of two linear equations, we can look at their slopes, which represent the rate of change of the dependent variable (y) with respect to the independent variable (x). The slope of a line is given by the coefficient of x in the equation y = mx + b, where m is the slope.

Let's compare the slopes of the two equations:

y = -5x - 1: The coefficient of x is -5, so the slope is -5.

y = -2x - 7: The coefficient of x is -2, so the slope is -2.

Since the slope of the first equation (-5) is greater in magnitude than the slope of the second equation (-2), we can conclude that the first equation is steeper than the second equation.

Alternatively, we can look at the absolute values of the slopes. The absolute value of the slope of the first equation is 5, which is greater than the absolute value of the slope of the second equation, which is 2. This confirms that the first equation is steeper than the second equation.

Therefore, the equation y = -5x - 1 is steeper than the equation y = -2x - 7.

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The area of the segment is 28.92 unit square

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

Angle, θ = 50 degrees

Radius, r = 15 units

Using the above as a guide, we have the following:

Area of a segment =  (½) × r² × [(π/180)(θ – sin(θ)]

Substitute the known values in the above equation, so, we have the following representation

Area of a segment =  (½) × 15² × [(π/180)(15 – sin(15 degrees)]

Evaluate

Area of a segment =  28.92

Hence, the area is 28.92

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The length of each side of the octagon with area of 392 square centimeters and an apothem of 14 centimeters is  7  centimeters .

Compared to lower sided shapes, an octagon's area is a little more complicated. A normal octagon's area is equal to 4 as. Where "s" stands for the octagonal side and "a" for the apothem, which runs straight from the pentagon's center to one of its sides.

The formula for the area of a regular octagon is:

A = 4 × apothem × side

Using this formula and the given values, we can solve for the length of each side of the octagon:

392 = 4 × 14 × side

Dividing both sides by 4 × 14, we get:

side = 392 ÷ (4 × 14)

Simplifying the right-hand side, we get:

side = 392 ÷ 56 = 7 cm.

Therefore, the length of each side of the octagon is  7 cm .

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The scale factor of the drawing is 5:36.The scale factor is the amount by which a shape is increased or shrunk.

Scale factor is the proportion of an original object's scale to a new one that is an representation of it that is a different size (bigger or smaller). For instance, by increasing each side by, say, 2, we can expand overall size of the a rectangle having lengths of 4 cm and 8 cm. The scale discrepancy between two things is contrasted by a scale factor, which is a ratio. You can figure out the scale factor by selecting two comparable or related components on the two items you are comparing. By comparing every one of these two elements, you may determine a ratio.

When we find the scale factor , we obtain:

5 inches = 1 yard

1 inches=[tex]\frac{1}{5}[/tex] yard.

actual , 1 inche = [tex]\frac{1}{36}[/tex] yard

Scale factor= [tex]\frac{\frac{1}{36} }{\frac{1}{5} }[/tex]= [tex]\frac{5}{36}[/tex].

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Answer:

[tex] \frac{23}{10} [/tex]

The two longest ribbons that were cut from the spool measure a combined 132 inches in length.

A combination of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division make up an algebraic expression in mathematics. Mathematical, scientific, engineering, and engineering problems are represented and solved using algebraic expressions.

One or more variables, which represent unknowable or varying quantities, and one or more constants, which represent fixed values, can both be present in an algebraic expression. Typically, the variables are represented by letters like x, y, or z. The symbols +, -, x, and y, respectively, stand in for addition, subtraction, multiplication, and division. Additionally, terms are grouped and the order of operations are indicated by using parentheses.

For instance, the mathematical formula 3x + 2y - 5 combines the two variables x and y with the three constants 3, 2, and 5. While -5 is a constant term, the terms 3x and 2y are the variables multiplied by their coefficients.

By combining like terms, or terms with the same variable raised to the same power, algebraic expressions can be made simpler. For instance, the terms 3x and 4x, as well as 2y and -3y, are like terms in the expression 3x + 2y - 5 + 4x - 3y. These terms combined result in the abbreviated expression 7x - y - 5.

Mathematical operations like solving equations, graphing functions, and evaluating formulas all use algebraic expressions. Additionally, they are used in practical applications like figuring out interest rates, resolving optimization issues, and simulating natural phenomena.

The two longest ribbons cut from the spool are those with lengths of 63 and 69, according to the provided stem-and-leaf plot. Their total is therefore:

63 + 69 = 132

So, the total length of the 2 longest ribbons cut from the spool is 132 inches.

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Note that:

The vertical angles are given as follows:

∠CFB vs ∠AFD

∠CFA vs ∠DFB

The complimentary pair of angles is :

∠CFE vs ∠EFA.

Complementary angles are a pair of two angles whose sum equals 90 degrees. In other words, when two angles are complementary, one angle is said to be the complement of the other.

For example, if angle A and angle B are complementary, then A + B = 90 degrees.

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Full Question:

See the attached

Answer:

x = 12

x = 9

Step-by-step explanation:

See picture below :)

The only statement that is true about the translation is; ∠I ≅ ∠K.

Translation in transformation is defined as the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

Now, from the given triangle, mapping ∠H onto ∠J means they are to be equal and by default it also means if that is the case, then we can equally say that ∠I ≅ ∠K.

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The side of the small square is equal to the length of the rectangles, which is 16cm.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.


We can calculate the area of the small square by using the formula A = side² where A is the area and side is the length of the side of the square. Thus, A = 16² = 256 cm².

Now, the area of the large square is equal to the area of the small square plus the area of the four rectangles. The area of each rectangle is equal to 16 x 4 = 64 cm² Thus, the total area of the large square is 256 + 4(64) = 512 cm²

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Answer: x=24

Step-by-step explanation:

Ok, this one is a bit tricky, you just have to keep in mind that directions specifically state that this is a rectangle.

A rectangle's opposite sides will always be the same, so the side opposite to 7 (the bottom of the rectangle) is also 7.

Now we should only be concerned with the triangle that includes the side-length that is x. So now we can use the Pythagorean theorem:

(leg length)^2+(other leg length)^2=(hypotenuse)^2

So if we plug in the values we have:

7^2+x^2=25^2

Solve for x:

49+x^2=625

x^2=625-49

x^2=576

x=[tex]\sqrt{576}[/tex] (square root is the inverse of square)

x=24

Hope this helps :)

The value of the original price is $185

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

Sales price = $222.00

Percent of markup = 20%​

The original price is calculated as

Original=  Sales Price/(1 + Markup)

Substitute the known values in the above equation, so, we have the following representation

Original = 222/(1 + 20%)

Evaluate

Original = 185

Hence, the original price is $185

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Complete question

Diane wants to buy a leather chair at 20% markup. The sale price is $222. What was the original price?

Answer:

28.346

Step-by-step explanation:

divide the length value by 2.54

Answer:

-1/10

Step-by-step explanation:

     [tex]\sf (-3 , \frac{-7}{2}) \ ; \ x_1 = -3 ; \ ; y_1=\frac{-7}{2}[/tex]

     [tex]\sf (2 , -4) ; \ x_2 = 2 \ ; \ y_2 = -4[/tex]

             [tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                       [tex]= \dfrac{-4-[-\frac{7}{2}]}{2-[-3]}\\\\\\= \dfrac{-4+ \frac{7}{2}}{2+3}\\\\[/tex]

                        [tex]\sf = \dfrac{ \frac{-4*2}{1*2}+ \frac{7}{2}}{5}\\\\\\= \dfrac{ \frac{-8+7}{2}}{5}\\\\\\= \dfrac{ \dfrac{-1}{2}}{5}\\\\= \dfrac{-1}{2*5}\\\\\\= \dfrac{-1}{10}[/tex]

Measure of MP is 10 units.

Angle bisector theorem states that if a line segment is drawn from a vertex of a triangle to the opposite side such that it bisects the angle, then the two parts of the opposite side which are divided by the line segment is proportional to the other two sides of the triangle.

Given is a triangle MNO.

Line segment NP bisects the angle MNO.

MO is divided into two segments MP and PO.

By the Angle Bisector Theorem,

MP / PO = MN / ON

Substituting,

MP / 8 = 15 / 12

MP = (15 / 12) × 8

MP = 10

Hence the measure of MP is 10.

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Answer:

Below

Step-by-step explanation:

Look for the letter that is between 1 and 2 ...very close to 2

=  1.85    <===== very close to '2'

The cube root of 36 is a number between 3 and 3.5, and can be represented mathematically as ∛36.

Square roots are simply the opposite operation of squaring a number. For example, the square root of 9 is 3 because 3 x 3 = 9.

Similarly, the cube root is the opposite operation of cubing a number. The cube root of a number is the value that, when cubed, gives the original number. For instance, the cube root of 27 is 3 because 3 x 3 x 3 = 27.

Now, to answer your question, "What is 36 cube root?" - this can be written as ∛36 or as the cube root of 36. To find the cube root of 36, we need to find a number that, when cubed, gives 36.

We can start by using trial and error. We know that 2 x 2 x 2 = 8, which is less than 36. We also know that

=> 3 x 3 x 3 = 27, which is less than 36.

So, we can try a number between 3 and 4. Let's try 3.5.

If we cube 3.5, we get 42.875, which is greater than 36.

If we try a number lower than 3.5, we will get an even greater value. Therefore, the cube root of 36 is between 3 and 3.5.

We can use more precise methods to find the cube root of 36, such as using a calculator or estimating with decimal approximations. However, using trial and error is a simple and effective way to find an approximate answer.

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The Whole numbers in mathematics are represented in the form of {0 , 1 , 2 , 3 , 4 , ... } .

The Whole Numbers are defined as a set of positive integers, including zero, which do not have a fractional or decimal component.  

The set of whole numbers is denoted by the symbol "W", and it can be expressed as : W = {0, 1, 2, 3, 4, 5, 6, ...}

In other words, the set of whole numbers is the set that starts with 0 and includes all the positive integers which can be obtained by repeatedly adding 1 to the previous number .

The Whole numbers are used to represent the quantities that cannot be divided into smaller parts.

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Answer:

f(x) = (x + 3)(x - 4) / (x + 3)

Step-by-step explanation:

In order for a rational function to have a hole at x = 4 and a vertical asymptote at x = -3, the denominator must be equal to zero at x = 4 and the numerator must be equal to zero at x = -3. This can be accomplished with the following expression:

f(x) = (x + 3)(x - 4) / (x + 3)

Answer:

Domain: {-3, 5, 0, -1, -2, 1}

Range: {-6, -4, -2, 1, 3}

The relation is a function.

Step-by-step explanation:

The domain of this relation is the set of all x-values from the ordered pairs, which are:

Domain: {-3, 5, 0, -1, -2, 1}

The range of the relation is the set of all y-values from the ordered pairs, which are:

Range: {-6, -4, -2, 1, 3}

To determine if the relation is a function, we need to check if there are any repeated x-values with different y-values. If there are no such cases, then the relation is a function.

Looking at the domain and range, we can see that each x-value has only one corresponding y-value, so there are no repeated x-values with different y-values. Therefore, the relation is a function...

Answer:

there are 3 feet in one meter.

Step-by-step explanation:

12 inches = 1 foot.

39.3701 inches = 1 meter.

39.3701 ÷ 12 = 3.281.

3.281 is simplified to 3.

There are about 3 feet in 1 meter.

Hope this helped! Have a Good Day!

Answer:

Step-by-step explanation:

Applying the distance formula, we get that the distance is sqrt(14^2+(-3)^2)=sqrt(205), which is approximately 14.3178211. Rounding to the nearest tenth, we get that the distance is 14.3 units long.

Answer:

AC=9CM

Step-by-step explanation:

Since ABCD is a kite, we know that the two diagonals, AC and BD, intersect at right angles and that the two pairs of adjacent sides are congruent. Therefore, we have:

AC = BD and AB = BC = CD = DA

We also know that DE = EB, which means that triangle ADE is congruent to triangle BEC (by the side-side-side congruence rule), so we have:

AD = BC and AE = EC

AD=5cm and DC=4cm

Combining these equations, we have:

AC = AD + DC

AC=5cm+4cm=9cm

In the model above, the 8 that the arrow points to is 1/10 times the 8 to the left of the arrow and 10 times the 8 to the right of the arrow.

In Mathematics, a place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

Generally speaking, the place value of the 8 that the arrow points to is tens and as such, we have the following:

8 = 80 × 1/10

8 = 0.8 × 10

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According to the Empirical Rule, approximately 68% of the data in a normal distribution will fall within ±1 standard deviation of the mean. The correct option is (d) 68%

The Empirical Rule is a statistical rule of thumb that describes the approximate proportions of data that fall within a certain number of standard deviations from the mean in a normal distribution.

The Empirical Rule states that for a normal distribution:

About 68% of the data will fall within 1 standard deviation of the mean

About 95% of the data will fall within 2 standard deviations of the mean

About 99.7% of the data will fall within 3 standard deviations of the mean

Therefore, option (b) 68 is the correct answer.

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The area of the circle is more than 18 square units of the smaller square inside it and less than 36 square units of the bigger square which the circle is enclosed in. The circumference of the circle is question 2 is equal to 47 to the nearest whole number.

The circumference of a circle is the distance around its edge or perimeter. It can be calculated using the formula:

Circumference = 2 x π x radius

where π (pi) is a mathematical constant approximately equal to 3.14.

Alternatively, the formula can be expressed using the diameter of the circle, which is the distance across the circle passing through its center:

Circumference = π x diameter

The second question have its diameter as 15cm hence its circumference is evaluated as:

Circumference = 3.14 × 15cm

Circumference = 47.1cm.

The first question have the area of the bigger square equal to 36 square units and that of the smaller square equal to 18 square units, since the smaller square is enclosed by the circle and the circle is enclosed by the bigger square, then the area of the circle is more than 18 square units and less than 36 square units.

In conclusion, the area of the circle is more than 18 square units and less than 36 square units for the first question. And the circumference of the circle for the second question is equal to 47 to the nearest whole number.

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Answer:

6,16

Step-by-step explanation:

The correct way to measure the zone of inhibition is to place a known amount of an antimicrobial agent on a solid medium.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The zone of inhibition is then measured as the area surrounding the antimicrobial agent where microbial growth has been inhibited. This area is typically measured in millimeters. To accurately measure the zone of inhibition, it is important to ensure that the size of the inoculum and the amount of antimicrobial agent used remain constant. Additionally, it is important to consider the type of organism being studied, as different organisms can have different levels of susceptibility to the antimicrobial agent. Finally, the medium used should be appropriate for the organism being studied, as different media can produce different results.

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The equation of the points is y + 4 = -7(x = 24)

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

(-4,24) and (7,-53)

The slope is calculated as

m = (-53 - 24)/(7 + 4)

m = -7

The equation is then calculated as

y - y1 = m(x - x1)

Substitute the known values in the above equation, so, we have the following representation

y + 4 = -7(x = 24)

Hence, the equation is y + 4 = -7(x = 24)

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