A toy factory makes toy bunnies.
Each toy bunny holds a carrot. A bunny's height, h(x)
is three times the length of the carrot, x.

2. Write an equation for the function h(x).
h(x) =

[tex]~~~~~~ \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 &\pounds 7900\\ r=rate\to 2.3\%\to \frac{2.3}{100}\dotfill &0.023\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 7900\left(1+\frac{0.023}{1}\right)^{1\cdot 5} \implies A=7900(1.023)^5\implies A \approx 8851.26[/tex]

Answer:

The answer is 685 km hopefully I understood your question and helped you ☻

Step-by-step explanation:

710 km - 25 = 685

Answer:

the slope of the line is -11/7 and the y-intercept is 8.

Step-by-step explanation:

First, we'll add 11x + 7y to both sides:

-11x - 7y + 11x + 7y = -56 + 11x + 7y

0 = -56 + 11x + 7y

Then, we'll add 56 to both sides:

0 + 56 = -56 + 11x + 7y + 56

56 = 11x + 7y

Finally, we'll divide both sides by 7:

56/7 = (11x + 7y)/7

8 = (11x + 7y)/7

Now we have the equation in slope-intercept form:

y = -(11/7)x + 8

So in this case, the slope of the line is -11/7 and the y-intercept is 8.

2 apples is equivalent to 6 bananas.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here; Scale1 as 20 bananas equal to 4 pineapples

Scale 2 as 2 pineapple equals 4 bananas and 2 apple

Let the weights of pineapple, bananas , apple as x,y,z respectively

Thus 20y=4x

      or x=5y

Again 2x=4y+2z

or      10y=4y+2z

          6y=2z

           z=3y

Thus 2 apples or 2z=6y that is 6 bananas

Hence, 2 apples is equivalent to 6 bananas.

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Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation

Given: Taylan sold 7 total frames, with the number of plastic frames being less than twice the number of wooden frames

Let x = number of wooden frames

Since the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation to represent this:

x + (x * 2) < 7

2x < 7

x < 7/2

x = 3

Therefore, Taylan sold 3 wooden frames and 5 plastic frames.

Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation

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Answer:

18 cups but each gallon = 16 cups. so 1.125 gallons

Step-by-step explanation:

ratio = 1/3 salt :1 water = 1 salt : 3 water

so 6 salt :18 water

Answer:

Area of a trapezoid=1/2(a+b)h where a and b are the bases and h is the height.

Step-by-step explanation:

if x=4, the value of  the expression x^2+2x is 24

An algebraic expression can be described as a mathematical expression comprising of variables, terms, coefficients, factors and constants.

Algebraic expressions are also known to comprise of some mathematical or arithmetic operations, such as;

From the information given, we have the expression as;

x² + 2x

For the value of x = 4, substitute the value of x as 4 in the expression, we get;

(4)² + 2(4)

find the square, we have

16 + 2(4)

expand the bracket

16 + 8

add the values

24

Thus, the value is 24

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The polynomial function that has the zeros 3 and 4 - 5i is P(x) = (x - 3)((x - 4)^2 + 25)

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

zeros 3 and 4 - 5i

The polynomial is represented as

P(x) = (x - zeros)

So, we have

P(x) = (x - 3)(x - (4 - 5i))(x - (4 + 5i))

Expand

So, we have

P(x) = (x - 3)((x - 4)^2 + 25)

Hence, the polynomial is P(x) = (x - 3)((x - 4)^2 + 25)

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The equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t is x - 5y - 2z = 30

The plane is passing through point P₀(-1, -7, 2)

And the parametric equation of the line is:

x = -1+t , y= -7-5t , z= -2t

L: (-1, -7, -2) + t(1, -5, -2)

The required plane passes through P₀ and perpendicular to line L.

The direction vector of L is V = <1, -5, -2>.

The equation of a plane with normal vector <1, -5, -2> passing through a given point P(x₁, y₁, z₁) is

1(x - x₁) - 5(y - y₁) - 2(z - z₁) = 0

The equation of plane P passing through point P₀ (-1, -7, 2) is:

1(x - (-1)) - 5(y - (-7)) - 2(z - 2) = 0

(x + 1) - 5(y + 7) - 2(z - 2) = 0

x - 5y-2z + 1 - 35 + 4 = 0

x - 5y - 2z = 30 is the required equation of the plane

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The complete question is:

Find the equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t

The answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.

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The length of side x is √2 units. The solution has been obtained by using the trigonometry formulas.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry." In order to find the unknown or missing angles or sides of a right triangle, one can apply the trigonometric formulas, functions, or identities. Angles can be expressed in radians or degrees in trigonometry. The most frequent trigonometric angles used in calculations are 0, 30, 45, 60, and 90 degrees.

We are given a right-angled triangle with hypotenuse 2units.

We know that sin theta = opposite side/hypotenuse

Also, sin 45° = 1/√2

So,

⇒sin 45° = x/2

⇒1/√2 = x/2

⇒2/√2 = x

⇒√2 = x

Hence, the length of side x is √2 units.

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Answer: There are a few different ways to approach this problem, but one common method is to use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we want to find the probability of at least one psychologist being chosen, which is the same as 1 minus the probability of no psychologists being chosen.

To find the probability of no psychologists being chosen, we first need to calculate the total number of ways to choose 3 people from a group of 54, which is:

54 choose 3 = 54! / (3! * 51!) = 19,958

Then we need to find the number of ways to choose 3 psychiatrists from a group of 24, which is:

24 choose 3 = 24! / (3! * 21!) = 1,344

Now, we can use these values to calculate the probability of no psychologists being chosen:

P(no psychologists) = (24 choose 3) / (54 choose 3) = 1,344 / 19,958 = 0.067 or 6.7%

Finally, we can use the complement rule to find the probability of at least one psychologist being chosen:

P(at least one psychologist) = 1 - P(no psychologists) = 1 - 0.067 = 0.93 or 93%

So the probability that at least one psychologist is chosen from the conference is 93%

Step-by-step explanation:

To compare the two different numbers 12 and 23 using different sentences are :

a. Twelve is less than twenty three or twenty three is greater than twelve.

b. 12 < 23 or 23 > 12.

Choose two numbers:

Let the numbers be 12 and 23.

Two different sentence to compare the considered numbers we have,

First method is using words.

a. twelve is less than twenty three.

Twenty three is greater than twelve.

Second method is symbolic method :

b. 12 < 23

'<' symbol represents less than.

23 > 12

'>' symbol represents the greater than.

Therefore, using two different method to compare two numbers are :

a. Word method : Twelve is less than twenty three or twenty three is greater than twelve .

b. Symbolic method : 12 < 23 or 23 > 12.

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The theoretical yield of Fe₂(SO₄)³ if 20.00 g of FePO₄ reacts with an excess of Na₂SO₄ is 26.52g.

The amount of a product produced by a reaction is expressed in terms of the reaction's yield.

Given the chemical equation:

2FePO₄ + 3Na₂SO₄ → Fe₂(SO₄)₃ + 2Na₃PO₄

Theoretical molar ratios:

2 mol FePO₄  : 3 mol Na₂SO₄ : 1 mol Fe₂(SO₄)₃ : 2 mol Na₃PO₄

Convert 20.00 g of FePO₄  into a number of moles

number of moles = mass in grams / molar mass

molar mass of FePO₄  = 150.82 g/mol

Number of moles = 20.00 g / 150.82 g/mol = 0.1326 mol FePO₄

Proportionality

1 mol Fe₂(SO₄)₃                x

----------------------- =  ------------------------

2 mol FePO₄            0.1326 mol FePO₄

Solve for x:

x = (0.1326 / 2) x 1 mol Fe₂(SO₄)₃ = 0.0663 mol Fe₂(SO₄)₃

Convert 0.0663 mol Fe₂(SO₄)₃ into grams

mass in grams = number of moles x molar mass

molar mass Fe₂(SO₄)₃ = 399.88 g/mol

mass = 0.0663 mol x 399.88 g/mol = 26.51 g

Depending on the number of decimal digits used by one or other you might obtain 26.52 instead 26.51, that difference does not count.

Therefore, the theoretical yield of Fe₂(SO₄)³ is 26.52g.

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The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

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Answer:Answer: $532.50

Step-by-step explanation:

564.45 = 1.06x

564.45/1.06 = x

532.50=x

Check: 532.50 × .06 = 31.95

532.50+31.95 = 564.45 True!

The inequality in standard form that describes this situation is  10x + 57y < 999.

This refers to the relationship between two values that are not of the same value.

Solving the inequality, we have:

Let x be the number of b=racelets that can be made and y be the number of necklaces that can be made. The inequality in standard form that describes the situation is:

x = the number of bracelets

y = the number of necklaces

Number of beads / bracelets =10

Number of necklaces = 57

10x + 57y < 999.

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The row percentage of A is 0% , B is 83.3% and of C is 15.4%.

Percentage describes the relative value of a number. Its shows the 100th part of the number with respect to a number whose value is provided in the problem.

Here various data is given about A, B and C in the format of two tables and this shows the relationship between the two.

Now, the row  percentage of A is

[tex]\frac{0}{5} * 100=0%[/tex]%

Then, the row percentage of B is

[tex]\frac{10}{12}*100 = 83.3%[/tex]%

Now, we have to find the row percentage of C

[tex]\frac{2}{13}*100 = 15.4%[/tex].%

Hence, The row percentage of A is 0, the row percentage of B is 83.3% and the row percentage of C is 15.5%.

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The expression to determine the distance between the lowest and the highest point is -

{x} = 14505 + |- 282|

Given is a diagram that shows several planes, lines, and points.

The correct statement with respect to line {h} is -

Line h has points on planes R, P, and T.

Therefore, line {h} has points on planes {R}, {P} and {T} is the correct alternative.

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The y-intercept of function f is 1.

f(x) = -3x -2 , -∞ < x < -2 = -x + 1, -2 ≤ x < 3  = 2x + 5, 3 ≤ x < ∞

For y-intercept, x =0, f(x) = -x + 1                   [∵ -2 < 0 < 3]

f(0) = -0 + 1 = 1

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet.

This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y. That is, f(x) can not have more than one value for the same x. To use the language of set theory, a function relates an element x to an element f(x) in another set.

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The function's description is accurate if (b) The graph of g(x) will ultimately surpass the graph of f. (x).

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Graphs can be used to represent functions.

The correct statement that describes the function is: (b) The graph of g(x) will eventually exceed the graph of f(x).

From the graphs, we have the following highlights

The graph of g(x) is constantly increasing as the value of x increases

The graph of f(x) is on decreasing (not constantly) as the value of x increases

The above highlights mean that: the value of g(x) would exceed g(x), at some point.

Hence, the correct statement that describes the function is: (b) The graph of g(x) will eventually exceed the graph of f(x).

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Answer: c. (5,2)

Step-by-step explanation:  We have two equations here and need to calculate the value of x and y.

The two equations are:

2x+5y = 20

3x - 4y = 7

Using the Substitution method,

2x=20-5y

x=(20-5y)/2

Now substitute the value of x in equation (2)

3 × [tex]\frac{20-5y}{2} - 4y = 7[/tex]

60-15y-8y = 14

60-23y=14

-23y = -46

y=2

Now put the value of y in any equation.

x = (20-10)/2

x=5          

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The value of x and y is -10 and 5 respectively in the given equations.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The first linear equation is - x + 3y = 5

The second linear equation is - -3x - 2y = 20

On evaluating individually the equation obtained is -

-3x - 2y + x + 3y = 20 + 5

-2x + y = 25

Multiply equation (1) with 3 -

3(x + 3y) = 5 × 3

3x + 9y = 15.....(3)

Adding equation (3) and (2) -

-3x - 2y + (3x + 9y) = 20 + 15

-3x - 2y + 3x + 9y = 35

-2y + 9y = 35

7y = 35

y = 35/7

y = 5

Substituting the value of y in equation (1) -

x + 3y = 5

x + 3(5) = 5

x + 15 = 5

x = 5 - 15

x = -10

Therefore, the value of x and y is -10 and 5 respectively.

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Answer:

6 and 4

Step-by-step explanation:

the first number is x and the second is y , then triple x is 3x , so

3x + y = 22 → (1)

the second number y is equal to twice x , less 8 , that is 2x - 8 , so

y = 2x - 8 → (2)

solving the 2 equations simultaneously.

substitute y = 2x - 8 into (1)

3x + 2x - 8 = 22

5x - 8 = 22 ( add 8 to both sides )

5x = 30 ( divide both sides by 5 )

x = 6

substitute x = 6 into (2) for y

y = 2(6) - 8 = 12 - 8 = 4

first number is 6 and second number is 4

No, 35/24 will never be on the board because the arithmetic and harmonic means can only generate positive integers.

No, 35/24 will never be on the board because the arithmetic and harmonic means can only generate positive integers. To calculate the arithmetic mean of two numbers, one adds the two numbers and divides the sum by two. The harmonic mean of two numbers is calculated by taking the reciprocals of the two numbers and dividing their sum by two. In the case of 1 and 2, the arithmetic mean is 1.5 and the harmonic mean is 2/3. So, the numbers on the board will be changed to 1.5 and 2/3 every day. 35/24 is a fraction and cannot be generated from the arithmetic and harmonic means of 1 and 2. Therefore, it will never be on the board.

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The solution is Option B.

The rotation of the line JK around the point P by 180° will be J'K'

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the rotation angle be represented as A

Now , the value of A is 180°

Let the points be represented as J and K

Let the rotated point be represented as J'K'

And , when a point is rotated by and angle 180° , the x and y coordinates of the point will become their additive inverse

For a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

And , the figure which represents the coordinates of the point J' and K' is when K' is below and J' is above

Hence , the solution is Option B.

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The proportion of the individuals that spend more than $400 is 0.35 and  the percent of calls answered in less than 5 minutes is 5.3%

Probability 1

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

Mean = 384

Standard deviation = 48

x = 400

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (400 - 384)/40

z = 0.4

The required probability is

P = P(z > 0.4)

So, we have

P = 0.345

Probability 2

Here, we have

Mean = 12.4

Standard deviation = 4.3

x = 5

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (12.4 - 4.3)/5

z = 1.62

The required probability is

P = P(z > 1.62)

So, we have

P = 5.3%

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The end behavior of the radical function represented by this graph is option C. As x decreases in value, f ⁡ ( x ) increases in value. As x increases in value, f ⁡ ( x ) decreases in value.

A radical function is a type of mathematical function that includes a radical symbol, such as a square root sign (√) or cube root sign (3√), in its equation.

The graph of a radical function is a curve that may open upward or downward, depending on the specific function. For example, the graph of the square root function, y = √x, starts at the point (0,0) and extends upward and to the right, creating a "V" shape. As the input (x) increases, the output (y) also increases, but at a decreasing rate.

Therefore, the correct answer is as given above

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Answer:

30/20 = 6/4 = 2/3 (I hope this makes sense)

Step-by-step explanation:

U are dividing by LCM