Write the ratio. Explain what the ratio means.

butterflies : caterpillars


For every _

butterfly/butterflies, there is/are _

caterpillar(s).

The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.

It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Hence, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Consequently, it follows that the greatest possible quotient as required is; 25.

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The equation given as -y = 3x is a direct variation. The constant of variation is - 1/3

It shows the relationship between two variables that can be described mathematically by an equation where one variable equals a constant multiplied by the other.

A straightforward correlation between two variables is referred to as direct variation. In this case, the constant of variation will be k.

This will be Illustrated as:

y = kx

-1 = 3k

Divide

k = -1/3

The constant is - 1/3.

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Equivalent function has the same domain and range. Equivalent and equal terms are not the same both have different meanings in mathematics.

A function is said to be equal if its Domain and Range are identical. Complete solution, step by step: A and B should be two sets. Now, by function, we mean a rule that guarantees that f(a)=b exists for all a. As a result, set A is referred to as the Domain of File and set B as the Range Off.

Despite being comparable to 1 + 1, 2 is believed to be equal to 2. When two items or amounts are exactly the same, as when 12 is equal to 12, yet 12 is equivalent to 2/4 since they reflect the same value, we can say that they are equal.

In mathematics, an equivalent can be defined in one of two ways. This is thus because there are various definitions for the concept of equivalent in mathematical theory. Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.

Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects.

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Kiran would choose scale of 1 to 50.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilised. It is employed to change the size of an object. If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scale factor can be determined.

Given:

As, The scale “1 inch to 6 feet” is equivalent to the scale “1 to 72,” because there are 72 inches in 6 feet.

The scale “1 to 100” would make a scale drawing that is smaller than the scale “1 to 72,” because each inch on the new drawing would represent more actual length.

The scale “1 to 50” would make a scale drawing that is larger than the scale “1 to 72,” because Kiran would need more inches on the drawing to represent the same actual length.

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The options are as follow:

1 to 50

1 to 72

1 to 100

Answer:

Step-by-step explanation:

the answer is 152

The equation of line passes through the point (2, 3) will be;

⇒ y = 1/2x + 2

And, Graph of this equation of line is shown in figure.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (2, 3).

And, The perpendicular line is,

⇒ y - 4 = - 2 (x + 3)

⇒ y -  4 = - 2x - 6

⇒ y = - 2x - 2

Now,

Since, The equation of line passes through the point (2, 3).

So, We need to find the slope of the line.

Since, The product of slope of the perpendicular line is - 1.

Hence, Slope of the given perpendicular line is,

⇒ y = - 2x - 2

m = dy/dx = - 2

m = - 2

So, The slope of line is,

⇒ m₂ = - 1/m

         = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - 3 = 1/2 (x - 2)

⇒ y - 3 = 1/2 (x - 2)

⇒ y - 3 = 1/2x - 1

⇒ y = 1/2x - 1 + 3

⇒ y = 1/2x + 2

Therefore, The equation of line passes through the point (2, 3) will be;

⇒ y = 1/2x + 2

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Jeremiah average velocity during the drive was 80 km/h while the instantaneous velocity at one point was 105 km/h

An equation is used to show the relationship between numbers and variables.

Average velocity is the ratio of total distance travelled to total time taken. Instantaneous velocity is the velocity at a particular point in time.

Jeremiah completed a straight, 120 km drive in 1.5 hours, hence:

Average velocity = total distance / total time

Average velocity = 120 km / 1.5 hours = 80 km/h

At one point during the drive, he saw that his speedometer read 105 km/h, hence:

Instantaneous velocity = 105 km/h

The average velocity is 80 km/h while the instantaneous velocity is 105 km/h

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There is no sufficient evidence that we can use in order to substantiate the claim of the publisher,

The null hypothesis H0: p = 0.47

The alternative hypothesis is H1: p > 0.47

The question requires us to test the fact that more than 47 percent of the readers have their own personal computer. This is therefore the claim that is to be tested here.

There is no sufficient evidence to substantiate the claim because of the lack of certain details that would have been used to carry out the hypothesis test.

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Answer:

Step-by-step explanation:

12/3=24/6

then, 24/6+17/6=41/6

So Cheng must purchase 32 cubic feet of sculpting material.

Each pyramid has a square base with edge length of 2 feet and a height of 6 feet. The area of the square base is (2 feet)^2 = 4 square feet. The volume of each pyramid is 1/3 * base area * height = 1/3 * 4 square feet * 6 feet = 8 cubic feet.

Since there are four identical pyramids in the sculpture, the total volume of material needed to create the sculpture is 4 * 8 cubic feet = 32 cubic feet. So Cheng must purchase 32 cubic feet of sculpting material.

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Answer:

D

Step-by-step explanation:

The distance of the ball thrown is 67 ft. approx.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here θ=63 and length of the field as 60 and let d be the distance

∴ Cos (180-63-90)=60/d

                  d        = 60/cos(27)

                   d       = 67 (approx)

Hence, The distance of the ball thrown is 67 ft. approx.

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Answer: 1/2 is the slope.

Step-by-step explanation: (-2-6)/(2-6) = -8/-4

-8/-4 Simplified is 1/2

Therefore 1/2 is your slope

Hope this helps!

The rate of change for the graph, when x=0 and x=1 is 2 units.

What is average rate of change?

This expression represents the average rate of change of the function f(x) over the range a<=x<=b, is less than or equal to x, and is less than or equal to b -

[f(b)-f(a)]/b-a

​

The rate of change of graph is determined by the formula -

[f(b)-f(a)]/b-a

[f(1)-f(0)]/1-0

Here, in the graph it can be clearly seen that f(0)=-1 and f(1)=1.

Plugging in the values -

[1-(-1)]/1

(1+1)/1

2

Therefore, the rate of change is 2 units.

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The 3 different polynomial equations are linear polynomial equations, quadratic polynomial equations, and cubic polynomial equations.

A polynomial equation is one where a polynomial is set equal to zero. i.e., it is an equation created with variables, non-negative integer exponents, and coefficients together with operations and an equal sign.

A polynomial equation is always like "polynomial = 0". Algebraically, it is of the form p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₁ x¹ + a₀x⁰ = 0, where

aₙ, aₙ₋₁, ...., a₁, a₀ are coefficients and all these numbers are real numbers.

'x' is the variable.

p(x) means "polynomial in terms of variable x"

'n' is a non-negative integer, it is the degree of p(x).

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Answer: D

Step-by-step explanation:

The statement says that the angles GIH and QRS must be the same measurement. To show that on diagrams, we use markings : if angles have the same markings, then it means they have the same measurement.

That way, we just need to see which diagram has the right measurements.

First, the angles GIH and QRS are the angles we see named by the letter in the center : then GIH and QRS.

So it must be the angles with letters of I and R that have the same markings.

A : doesn't work for I and R

B : doesn't work for I and R

C : doesn't work for I and R

D : works for I and R

it should be the D, of course if I didn't see well don't hesitate to make sure it's correct with what I said before :)

Answer:

the answer would be D

Step-by-step explanation:

the answer is D because of the person above me

The value of x is 8.

Angles are formed whenever two or more straight lines intersect. These angles produced thus have individual and some common properties of which some can add up to form complementary angles, or supplementary angles.

Two angles are said to be supplementary if the value of their sum add up to 180^o.

From the given question, we can deduce that;

m<1 + m<2 = 180^o              (definition of complementary angles)

(17x - 30) + (7x + 18) = 180^o

17x - 30 + 7x + 18 = 180^o

24x - 12 = 180

24x = 180 + 12

24x = 192

x = 192/ 24

  = 8

x = 8

The value of x is 8.

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Answer:

Irrational

Step-by-step explanation:

it equals 6.7 which is not a perfect square

Answer:

10 mm

Step-by-step explanation:

Draw an equilateral triangle. Label each side 12 mm.

Draw one altitude from one vertex perpendicular to the opposite side. Label the length of the altitude h.

The altitude divided the opposite side into two congruent segments, each one measuring 6 mm.

Now use the Pythagorean Theorem.

a² + b² = c²

(6 mm)² + h² = (12 mm)²

36 mm² + h² = 144 mm²

h² = 144 mm² - 36 mm²

h² = 108 mm²

h = 6√3 mm

h ≈ 10 mm

Answer: 3.5 cm or 35 mm

Step-by-step explanation:

12/3 =4 for each side of triangle

cutting the triangle in half, bottom side(a) 4 becomes 2

2^2 + b^2 = 4^2

4 + b^2 = 16

subtract 4 from both sides

b^2 = 12

b = 3.464 cm or 3.5 cm

convert 3.5 cm to 35 mm

The solution to the equation is g = 4π² ( L / T² )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The formula to determine the time period of a simple pendulum is given by

T = 2π √ ( L / g )   be equation (1)

where L = length of string

g = acceleration due to gravity

On simplifying the equation , we get

Divide by 2π on both sides of the equation , we get

√ ( L / g ) = T / 2π

Squaring both sides of the equation , we get

( L / g ) = T² / ( 2π )²

( L / g ) = T² / 4π²

Now , taking reciprocals on both sides of the equation , we get

g / L = 4π² / T²

Multiply by L on both sides of the equation , we get

g = 4π² ( L ) / T²

On simplifying the equation , we get

g = 4π² ( L / T² )

Therefore , the value of A is 4π² ( L / T² )

Hence , the equation is g = 4π² ( L / T² )

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Angles are classified into three. They are acute angles, obtuse angle and right angle.

Therefore the three names of angles are - acute angles, obtuse angle and right angle.

Acute angles are angles that measure less than 90 degrees. They are smaller than a right angle and are often described as "sharp."

Right angles are angles that measure exactly 90 degrees. They are often represented by a square corner or the letter "L" shape.

Obtuse angles are angles that measure greater than 90 degrees but less than 180 degrees. They are larger than a right angle and are often described as "blunt."

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Answer:
y = 1/9 + 2/9x

Step-by-step explanation:

9y - 2x = 1

9y = 1 + 2x             (get rid of x)

y = 1/9 + 2/9x        (divide 9 on both sides)

In answering the question, we discovered that a sample size of 20 was required in order to reach this conclusion.

The sample size is the number of observations used to estimate a certain population. The population was used to determine the sample size.

The act of promoting a product to increase sales is known as advertising. Based on the scenario given, the advertisement is misleading for the following reasons:

For this finding to be reliable, a sample size of 20 samples is rather small. Although the company was aware that the fertilizer treatment might get rid of weeds in approximately 2 weeks, customers said it would take 4 weeks for all of the weeds to die.

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Answer:

==================================

a1 = 85 = first term

d = -4 = common difference

an = a1 + d(n-1)

an = 85 - 4(n-1)

an = 85 - 4n + 4

an = -4n+89

a10 = -4*10+89

a10 = 49 is the tenth term

The 95% confidence interval for the true mean number of reproductions per hour for the bacteria is given as follows:

(3.78, 4.22)

The bounds of the confidence interval are calculated according to the equation presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters are given as follows:

[tex]\overline{x} = 4, \sigma = 1.9, n = 283[/tex]

Hence the lower bound of the confidence interval is of:

[tex]4 - 1.96\frac{1.9}{\sqrt{283}} = 3.78[/tex]

The upper bound of the confidence interval is of:

[tex]4 + 1.96\frac{1.9}{\sqrt{283}} = 4.22[/tex]

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The first row of the SHORT BINGO card contains 5 numbers, one from each of the sets $1-10$, $11-20$, $21-30$, $31-40$, and $41-50$. Since the WILD square is in the middle of the card, it does not affect the possibilities for the first row.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

For the first column, there are 10 possibilities, as it can contain any number from the set $1-10$.

For the second column, there are 10 possibilities, as it can contain any number from the set $11-20$.

For the third column, there are 9 possibilities, as it can contain any number from the set $21-30$ except the one already used.

For the fourth column, there are 10 possibilities, as it can contain any number from the set $31-40$.

For the fifth column, there are 10 possibilities, as it can contain any number from the set $41-50$.

The total number of distinct possibilities for the values in the first row of a SHORT BINGO card is the product of the possibilities for each column, which is:

10 * 10 * 9 * 10 * 10 = 90000.

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P(even) is  50%

It is simple to calculate the likelihood of one die roll.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

First, keep in mind that a prime number is an integer that has exactly two factors: 1 and the number itself (which is why 1 does not qualify: it has only one factor). The appropriate numbers from 6 onward are 2,3,5. Your response, given that there are six sides, is: P(prime) = 3/6 = 1/2 = 50%

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Answer:

Lauren will finish the race faster 7 seconds faster, and 14 meters ahead.

Step-by-step explanation:

To answer this question, I will use the strategy of finding the slope of each of the proportional relationships (y = 8x for Lauren's run and y = ?x for Amani's run). The slope represents the rate at which the distance changes for each unit of time, so the person with the greater slope will finish the race faster.

To find the slope of Amani's run, I will use the tool of point-slope form, which is y - y1 = m(x - x1). I will plug in the coordinates for the second point listed in the table for Amani's run (5 seconds and 30 meters) to get y - 30 = m(5 - x1). Since I don't know the value of x1, I will solve for it in terms of m. I get x1 = 5 - (30/m).

Next, I will plug in the coordinates for the first point listed in the table for Amani's run (3 seconds and 18 meters) into the equation y - 30 = m(5 - (30/m)). I get 18 - 30 = m(5 - (30/m)). Solving for m, I find that Amani's run has a slope of m = -6.

Since Lauren's run has a slope of 8 and Amani's run has a slope of -6, Lauren will finish the race faster. To find out by how much, I will use the tool of proportional reasoning. Since the slope represents the rate at which the distance changes for each unit of time, the difference in the slopes (8 - (-6)) represents the difference in the rate at which the distance changes for each unit of time between the two runs. The difference is 14, so Lauren will finish the race 14 meters ahead of Amani for each second that they run. Since the race is 100 meters long, Lauren will finish the race approximately 7 seconds faster than Amani.

Answer:

yes

Step-by-step explanation:

After solving the equation: the nearest cent, the interest earned is $467.

Interest is a mathematical concept used to describe the cost or gain associated with the use of money over a period of time. It is usually expressed as a percentage rate of the principal (the amount borrowed or invested). Interest can be earned or paid, depending on the situation.

Using the formula B=p(1+r)t, John's final balance after 1 year is B = 4069(1+0.12)1 = $4,536.28.
The interest earned in 1 year is the difference between the final balance and the starting amount, which is $4,536.28 - $4,069 = $467.28. To the nearest cent, the interest earned is $467.

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