On an island, frogs are always either green or blue in some initial ratio of blue to green frogs. The number of blue frogs increased by 60% while the number of green frogs decreased by 60%. It turns out that the new ratio of blue frogs to green frogs is the same as the previous ratio in the opposite order (green frogs to blue frogs). By what percentage did the overall number of frogs change?

Answer: $34.25

Step-by-step explanation:

The quantity of additive which Belle put in each can as required is; 1/8 pint.

It follows from the task content that the quantity of additive which Belle put in each can be determined if 1/2 of a pint of special paint additive is shared among 4 cans of paint.

The resulting expression which given the required quantity is;

1/2 ÷ 4

= 1/2 × 1/4

= 1/8.

On this note, the quantity of additive in each can of paint is 1/8 pint of special paint additive.

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The relationship between a young person's height and the recommended wheel diameter is a function, as each input is associated to a single output.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The input and output variables for this problem are given as follows:

As for each height, there is only one recommended wheel diameter, we have that each input is mapped to a single output, and thus the relationship between a young person's height and the recommended wheel diameter is a function.

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Given a set A={1,2,3,4,5,6,7}, a relation induced by the partition of set A is

(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}

Generally, A set comprises elements or members that may be mathematical objects of any sort, including numbers, signs, points in space, lines, other geometric forms, variables, or even other sets. A set is a mathematical formula for a collection of various things.

A relation induced by a partition of a set is a relation that defines a way of grouping elements in the set into subsets, called "blocks" or "cells". In this case, the set

A={1,2,3,4,5,6,7}

can be partitioned into at least 3 subsets. For example, one possible partition is

A={1,2,3}, {4,5}, {6,7}.

The relation induced by this partition is a relation that assigns to each element in one of the 3 subsets, i.e.

(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}

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Using pythagoras theorem formula, c² = a² +b²  We can see that the two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

What is Pythagoras' theorem ?

Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

The two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

Let the sides of the triangles be a, b and c. According to Pythagoras theorem;

c² = a² +b²

where:

a is the hypotenuse (longest side)

For triangle A:

c = 13

b = 12

Get "a"

13² = 12² +b²

b² = 25

=> b = 5 cm

Similarly for triangle B:

c² = 5² +12²  = 169

=> c=13 cm

We can see that the two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

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a) X is a binomial random variable because there is a fixed number of trials, for each trial, the probability of winning is the same, and for each trial there are only two possible outcomes, winning and losing.

b) The mean and the standard deviation of X are given as follows:

This means that out of nine friends, the expected number of those who area expected to win a prize is of 1.125, varying around 0.99.

c) At least 3 friends winning a prize is not unusual, as 3 is less than 2.5 standard deviations above the mean.

The binomial distribution represents the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The change of winning is of one in eight, hence the parameter p is obtained as follows:

p = 1/8 = 0.125.

There are nine friends, hence the parameter n is given as follows:

n = 9.

Then the mean is of:

E(X) = 9 x 0.125 = 1.125.

The standard deviation is of:

[tex]\sqrt{V(X)} = \sqrt{9 \times 0.125 \times 0.875} = 0.99[/tex]

A measure is considered unusual if it is more than 2.5 standard deviations above the mean, hence the upper bound is given as follows:

More than 1.125 + 2.5 x 0.99 = 3.6 friends.

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Answer:

The annual percentage yield (APY) is the effective annual rate of return on an investment, taking into account the effects of compounding. To calculate the APY, we can use the formula:

APY = (1 + (APR / n))^n - 1

Where APR is the annual percentage rate (the stated interest rate), and n is the number of times the interest is compounded per year.

In this case, the APR is 4.86% and the interest is compounded daily, so n = 365 (the number of days in a year).

APY = (1 + (0.0486 / 365))^365 - 1

Plugging in the numbers, we get:

APY = (1 + 0.000132876712328767123)^365 - 1

APY ≈ 4.87%

So, the annual percentage yield is 4.87%

Answer: -4/5

Step-by-step explanation:

(0,2) and (4,-3) are two coordinates here.

Using the slope formula, i.e, m = (y₂ - y₁)/(x₂ - x₁) = 4/-5 = -4/5

The plotted graph is shown below.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

s (h) = √64h

now, when h=0

s(0) = √64h = 0

and, when h= 5

s(5) = √64h

        = √64 x 5

       = 8 x 2.25

       = 17.88

and, when h= 10

s(25) = √64h

        = √64 x 10

       = 8 x 3.162

       = 25.29

and, when h= 15

s(25) = √64h

        = √64 x 15

       = 30.98

and, when h= 20

s(25) = √64h

        = √64 x 20

       = 35.77

and, when h= 25

s(25) = √64h

        = √64 x 25

       = 8 x 5

       = 40

The plotted graph is shown below.

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Answer: find zero on the number line then put a dot on -7/5 (-1 2/5) then do the same on positive 7/5 (1 2/5

Step-by-step explanation:

find zero on the number line then put a dot on -7/5 (-1 2/5) then do the same on positive 7/5 (1 2/5 . I think that is correct sorry if it isnt.

Step-by-step explanation:

The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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Answer:

1,2,3,4,6,12,18

Step-by-step explanation:

uh

Answer:The function is linear because we are dealing with a straight line.

Step-by-step explanation:

The minimum and maximum values, over the interval x ≥ 3, for the function f(x) = -|x - 1| + 1 graphed are -36 and 64 respectively.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Here Relative minimum are the minimum values  in the interval

Looking at the graph, we find the lowest point in the interval

Relative minimum : (-3, -36) and (3,-36)  

y value -36

Looking at the graph, we can find the highest point in the interval

Relative maximum : (0,64)  

y value 64

The minimum and maximum values, over the interval x ≥ 3, are -36 and 64 respectively.

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Using the proportionality relationship equation, y = 3/2x, the complete table is:

x   |  y  

0     0

1      3/2

2      3

The equation of a proportional relationship between x and y can be represented as y = kx, which means that the constant of proportionality, k, is y/x.

For example, if the constant of proportionality between two variables x and y is given as 4, therefore, the equation of the proportional relationship will be stated as y = 4x.

Given the following:

Constant of proportionality, k = 3/2.

The equation of the proportional relationship is: y = 3/2x

Use the equation, y = 3/2x to complete the table by substituting the values of x into the equation:

For x = 1:

y = 3/2(1)

y = 3/2

For x = 2:

y = 3/2(2)

y = 3

Therefore, the complete table is:

x   |  y  

0     0

1      3/2

2      3

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The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

[tex]~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}[/tex]

The following are the values for the length of each rectangles:

(a) L = 37.5 m

(b) L = 26.2 cm

(c) L = 25.5 km

(d) L = 20 m

In calculating for the area of rectangle, the breadth is multiplied by the length of the rectangle.

We shall evaluate for the Lengths of the rectangles as follows:

Length = 375 m²/ 10 m

Length = 37.5 m

Length = 393 cm²/ 15 cm

Length = 26.2 cm

Length = 280.5 km²/ 11 km

Length = 25.5 km

Length = 340 m²/ 17 m

Length = 20 m

Hence, 37.5 m, 26.2 cm, 25.5 km, and 20 m are the respective values for the length of rectangles with area 375 m², 393 cm², 280.5 km², and 340 m².

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Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

Answer:

The correct answer is: parallel

The two equations are in the form of y = mx + b and y = mx + b, which are the standard forms of linear equations.

and the slope of the two equations are different, so they are not coincident and not intersecting. They are parallel lines that never meet, so the system of equations is parallel.

6. The measure of angle BEC is 48°

7. The measure of angle 1 is 41°

8. The value of x is 12

   The measure of angle UST is 36°

6. The angles AEB and BEC form a straight line whose angle measure is 180°.

So that,

∠AEB + ∠BEC = 180°

132° + ∠BEC = 180°

∠BEC = 180° - 132°

∠BEC = 48°

7. The angles 1 and 5 form a right angle whose measure is 90°.

So that,

∠5 + ∠1 = 90°

49° + ∠1 = 90°

∠1 = 90° - 49°

∠1 = 41°

8. The angles RSU and UST form a right angle whose measure is 90°.

∠RSU + ∠UST = 90°

(5x - 6)° + (2x + 12)° = 90°

(7x + 6)° = 90°

7x° = (90 - 6)°

7x° = 84°

x = 12

∠UST =  (2x + 12)°

∠UST =  (2(12) + 12)°

∠UST =  (24 + 12)°

∠UST = 36°

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The domain and range of the function y = 1/2 - 1 lies on  (-∞, ∞)

The collection of all input values (sometimes referred to as independent variables) for which a function is defined and yields a valid output is known as the domain of the function. It is the collection of all possible values that can be entered into a function.

All real numbers, for instance, fall inside the domain of the function        f(x) = x², since any real number may be squared to yield an accurate result.

On the other hand, a function's range is the collection of all feasible output values (also known as the function's dependent variable) that it can generate. It is the collection of all outcomes that the function is capable of producing.

For instance, since squaring real numbers makes the range of the function f(x) = x² all non-negative values.

It's vital to remember that not all functions have the same range or are defined for all conceivable input values. For instance, because the square root function x is not defined for negative numbers, all real numbers that are not negative fall within its domain.

In conclusion, the collection of all input values for which a function is defined and yields a valid output is known as the domain of the function. The collection of all potential output values that a function may produce is known as its range.

In the given function;

y = 1/2x - 1

The domain of this function is (-∞, ∞)

The range of the function f(x) = 1/2x - 1 is (-∞, ∞)

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Answer:

e + 8

Step-by-step explanation:

Answer:

[tex]\boxed{y = 4x + 7}[/tex]

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

where m is the slope and b the y-intercept

To find the slope, take the two points, find the difference in y values and divide by the corresponding difference in x values

Two points are [tex](- 1, 3)[/tex] and [tex](- 2, -1)[/tex]

Difference in y values [tex]= -1 -3 = -4[/tex]

Difference in corresponding x values [tex]= -2 - (-1) = -2 + 1 = -1[/tex]

Slope

 [tex]m = \dfrac{-4}{-1} = 4[/tex]

So the equation of the line is of the form
[tex]y = 4x + b[/tex]

To find b, take the coordinates of any of the two points and plug the x and y values into the above equation and solve for b

Let's take point (-1, 3)

Plug in values:

[tex]3 = -4 + b\\\\3+4 = b\\ \\b = 7[/tex]

Therefore the equation of the line is
[tex]\boxed{y = 4x + 7}[/tex]

Using the decay constant on the exponential function, the mass of the sample that will be left in 2013 is 35g

An exponential function is a function that can be expressed in the form     f(x) = b^x, where b is a positive real number and x is a real number. The graph of an exponential function is a curve that increases or decreases rapidly as x increases or decreases.

In the exponential decay, the decay function can be given as;

y = ae⁻ⁿˣ

The disintegration constant is also know as the rate of decay and we can calculate it as;

260 = 470e⁻ⁿ⁽³⁾

n = 0.197

n = 0.2

The disintegration constant is 0.2

The amount left in 2013 will be;

y = 470e⁻⁽⁰.²⁾⁽¹³⁾

y = 34.90

The mass in 2013 is 35g

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The system of equations can be used to find the number of pounds, x, of dried fruits and the number of pounds y, of nuts is; 6x + 2y = 40

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution the power of the equation must be in one degree.

We are given that the dried fruits cost $6 per pound

The nuts cost $2 per pound. It costs Simon $40 to make 12 pounds of trail mix.

We need to find  the number of pounds, x, of dried fruits and the number of pounds, y, of nuts that Simon used to make 12 pounds of trail mix.

Therefore, the system of equation will be 6x + 2y = 40

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Answer:

2

Step-by-step explanation:

To find the approximate annual growth rate of the stock, we can use the formula for compound annual growth rate (CAGR):

CAGR = (Ending value / Beginning value)^(1/n) - 1

Where n is the number of years.

In this case, the beginning value is $2545.30, the ending value is $4152.57 and the number of years is 6.

So, CAGR = (4152.57 / 2545.30)^(1/6) - 1

The CAGR is approximately 26.8% which is the answer 2.