Brianna found an orange caterpillar and a green caterpillar in her backyard. The green caterpillar was 4 inches long and the orange caterpillar was 1 1/12 inches long. How much longer was the green caterpillar than the orange caterpillar?

Simplify your answer and write it as a fraction or as a whole or mixed number.

Answer:

so the total charge for the job was $50,

so all we need is the finding of x (# of square feet):

10 + 0.20x = 50

Step-by-step explanation:

Solving for x:

0.20x = 50 - 10

0.20x = 40

x = 40/0.20

x = 200 square feet

hope it helps!

1)1000

2) 4.4%

3) 4.4

4) 9%

5)4.4%

6) 0.6%

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Answer:

0.64

Step-by-step explanation:

9/14 is 0.642

rounding that decimal to the nearest hundredth would get you 0.64 because the 2 next to the 4 is below 5 so it would keep it the same.

The image of  y = −2x^2 − 20x + 2 after a translation right 4 units and up 2 units is written in:

The graph will be a vertical parabola opening downwards

when the function y = −2x^2 − 20x + 2 translates right 4 units it gives  

y = -2(x - 4)^2 − 20(x - 4) + 2

going up two units

y = -2(x - 4)^2 − 20(x - 4) + 2 + 2

simplifying the equation further gives

y = -2(x - 4)(x - 4) − 20(x - 4) + 4

y = -2(x^2 - 8x + 16) - 20x - 80 + 4

y = -2x^2 + 16x - 20x - 32 - 80 + 4

y = -2x^2 - 4x - 108

completing the square

-2x^2 - 4x - 108 = 0

-2x^2 - 4x = 108

-2x^2 - 4x + (4/4)^2 = 108 -(4/4)^2

-2x^2 - 4x + (1)^2 = 108 - 1

-2(x + 1)^2 - 107

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Answer:

f(3) = 1728

f(-2) = 1/144

f(1/2) = 2sqrt(3)

Step-by-step explanation: all you is replace x with what ever is in the parenthesis

The explicit function of the packages is f(x) = a +(n-1)d.

What is explicit function?

An explicit function is a function in algebra in which the output variable (dependent variable) can be explicitly written only in terms of the input variable (independent variable). An explicit function usually involves two variables - dependent and independent variables.

the given numbers are 110,88,66,44,22.

This is an AP (arithmetic progression)

f(x) = a +(n-1)d

were,

a is the first term, n is the number of terms, d is the difference.

n= 5, d = 22, a =110

f(x) = 110 +(5-1)22

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Two angles A and B are supplementary when the value of x is 36°.

Two angles are said to be supplementary if their sum is 180°.

Two angles are said to be complementary if their sum is 90°.

Given, m∠A = (2x − 27)° and m∠B = (3x + 27)° are supplimentary to each other.

∴ (2x - 27)° + (3x + 27) = 180°.

2x + 3x - 27 + 27 = 180°.

5x = 180°.

x = 36°.

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Answer: 77 km

Step-by-step explanation:

There are 7 days a week. If Jason runs 11 km each day, the equation for how far he'll run in a week is 7 x 11 km.

7 x 11 km = 77 km.

Answer:

-2x + 11

Step-by-step explanation:

13 - 2 = 11

6x - 8x = -2x

Answer:

Step-by-step explanation:

No solution. This is because they do not cross.

Answer:

part A=329.99=25.72+23.50x

part B=12.95=13 weeks

Step-by-step explanation:

need=329.99

have=25.72

save=23.50 per week

329.99=25.72+23.50x

23.50x=(329.99-25.72)

23.50x=304.24

x=12.95

=x =13

Answer:

[tex]x^{2} +12x+35[/tex]

Step-by-step explanation:

Distribute

(X+7)(X+5)

x^2+5x+7x+35

X^2+12x+35

Hopes this helps please mark brainliest

Answer:

x^2 + 12x + 35

Step-by-step explanation:

Hi! I solved this using the FOIL, or firsts, outsides, insides, and lasts, to simplify:

The firsts, or F, would be: x*x which equals x squared (x^2)

The outsides, or O, would be: x*5 which equals 5x

The insides, or I, would be 7*x which equals 7x

The lasts, or L, would be 7*5 which equals 35

Then, the FOIL method says to add up all the answers you got together:

x^2+5x+7x+35

and then you simplify and get:

x^2+12x+35

I hope this made sense! :)

The required value of function f(g(2)) = 1.

What is a composite function?

When the result of one function is utilized as the input for another, this is known as a composite function.

Typically, a composite function is a function that is embedded within another function. The process of creating a function involves replacing one function for another.

Given, to find the value of the given function f(g(2))

First, we need to find the value of g(2) from the given graph

i.e. g(2) = 4  (i.e. x = 2)

Then, the above value is an input for function f.

So, f(4) = 1 (from the graph at x = 4)

Hence, the value of function f(g(2)) = 1.

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Answer:

2.25 cups of sugar per dozen cookies

Step-by-step explanation:

8 - 1.25 = 6.75

6.75 ÷ 3 = 2.25

The best represents the statement C(5) = 15 is the cost of renting a bicycle for 5 hours is 15 dollars.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Here, we have

Given the function C(x) represents the cost, in dollars, of renting a bicycle for x hours.

So, the best statement that represents the given statement C(5) = 15 is the cost of renting a bicycle for 5 hours is 15 dollars.

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The value of cos x°  is 8 divided by f

We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent or tan = sin/cos

The opposite is the side the angle of consideration is facing

The hypotenuse is the side the right angle  is facing

The adjacent is the side left after determining the opposite and hypotenuse

Given: tan x° = e/8 and sin x° = e/f

Since tan = opposite/adjacent, that means in tan x° = e/8, opposite = e and adjacent = 8. Also, sin = opposite/hypotenuse, so in sin x°= e/f, hypotenuse = f

And cos = adjacent/hypotenuse. Thus,  cos x° = 8/f.

Therefore, the value is cos x° = 8 divided by f is the answer. Pick the first option

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Answer: 20 hrs

Step-by-step explanation:

Answer:

29/400

Step-by-step explanation:

The value of -6,602 - (-4,899) is -1703.

What is simplification?

Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner. Making something simpler is making it less complex.

simplify mathematical expressions by grouping and combining similar terms. This makes the expression easily understandable and solvable.

Given,

-6,602 - (-4,899)

And to simplify it,

we know -(-) = +

we get, after simplification

-6,602 + 4,899 = -1703.

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Answer: D

Step-by-step explanation:

The square root of 50 is less than 8.34, the square root of 15 is less than the absolute value of 4.32, 2.3x10^1 is greater than 2 2/5.

The absolute value of 5.43 is less than 2.1x10^1.

The total amount that Ms. Henderson must pay, given the penalty and the amount of taxes is $1, 478.75

First, find the total penalty on the taxes, to Ms. Henderson.

= Tax amount x Penalty percentage

= 1, 400 x 11 ¹ / ₄%

= $157.50

Because she paid in 6 months, but the penalty is for a year, Ms. Henderson's tax penalty is:

= 157.50 / 2

= $78.75

The total amount to be paid is:

= Taxes owed + Penalty

= 1, 400 + 78. 75

= $1, 478.75

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Answer:

d=3

Step-by-step explanation:

because

8-5=3

5-2=3

2--1=3

-1--4=3

The differentiation of the function  f(x) = sin⁻¹(3x⁵) is  [tex]15x^4/\sqrt{1-9x^{10}}[/tex].

Function is a combination of different types of variable and constants.

A function is denoted by f(x).

The given function is,

f(x) = sin⁻¹(3x⁵)

Differentiate the given function with respect to x

f'(x) = d/dx(sin⁻¹(3x⁵))

The differentiation of sin⁻¹x is  [tex]1/\sqrt{1-x^2}[/tex],

f'(x) =[tex]1/\sqrt{1-(3x^5)^2}\cdot d/dx(3x^5)[/tex]

     = [tex]1/\sqrt{1-9x^{10}}\cdot 15x^4[/tex]

     = [tex]15x^4/\sqrt{1-9x^{10}}[/tex]

The differentiation of f(x) = sin⁻¹(3x⁵) is  [tex]15x^4/\sqrt{1-9x^{10}}[/tex].

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Answer:

1. 11 married females because out of the 19 married, only 8 had more than 15 years of service and 19 - 8 = 11.

2. 10 married males because of out the 18 married with more than 15 years of service, 8 were females and 18 - 8 = 10.

3. 9 single females because out of the 17 with more than 15 years of service, 8 were married and 17 - 8 = 9.

4. 8 married females because it literally says, "8 married female with more than 15 years of service".

gotta go hope this helps sry

The values of the composite functions f(g(x)) and g(f(x)) are (x/4) and (4x - 9),respectively.

We are given two functions, f(x) and g(x). The function f(x) is defined as 1/(x - 3). The function g(x) is defined as (4/x) + 3. A function connects an input to an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. We need to find the composition of the functions.

The first composition is f(g(x)). The composite function is solved below.

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

f(g(x)) = 1/([(4/x) + 3] - 3)

f(g(x)) = 1/(4/x)

f(g(x)) = x/4

The second composition is g(f(x)). The composite function is solved below.

g(f(x)) = g(1/(x - 3))

g(f(x)) = (4/[1/(x - 3)]) + 3

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

g(f(x)) = 4x - 12 + 3

g(f(x)) = 4x - 9

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Given that the HCF of two numbers is 16 and their product is 6,400 then LCM​ is 400.

What is the relation between product of numbers, LCM and HCF?

The relation between LCM, HCF and product of two numbers is as follows:

LCM x HCF = Product of two numbers

According to the given question:

Let the numbers be x and y

Product of the numbers, x*y = 6400

HCF of the numbers is 16

Now according to the relation between numbers, LCM and HCF

LCM x 16 = 6400

LCM = 6400/16

LCM = 400

Hence LCM of the numbers is 400

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The completion of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:

                           Ratio      Amount

Department A     0.25       $15,000

Department B     0.75      $45,000

The ratio is the proportion of the whole shared by two or more numbers.

Ratios are fractional values like proportions.

Ratios, depicted in fractions, decimals, and percentages, show how much a value or variable is contained in another.

Total distributable overhead = $60,000

Ratios = 10,000:30,000

= 1:3

Sum of Ratios = 4

OR

= 0.25:0.75

Sum of Ratios = 1

Department   Square Feet  Ratio    Amount of Overhead Allocated

Dept. A            10,000         A = 1      B = $15,000 ($60,000 x 0.25)

Dept. B            30,000        C = 3     D = $45,000 ($60,000 x 0.75)

Thus, based on the cost driver ratios, Department A bears $15,000, while Department B will be allocated $45,000 of the distributable overheads.

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The graph that shows data in intervals is the: B. histogram.

An histogram is a graph which is used to visualize data in intervals, as rectangular bars. The image attached below is a typical example of an histogram. The graph shows the data in intervals.

A frequency table can also show a set of data that are given in intervals, however, it is not a graph. It can rather be used to create graphs that have intervals, such as a histogram.

Line plot and stem-and-leaf plot are both graphs that show individual data points rather than show the data in intervals.

The answer is therefore: B. histogram.

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The value of  L4 and R4 over [0,7] for the function f(x) = 6x² will be 2[2√0 + 2√2 + 2√4 + 2√6] and  2[2√2 + 2√4 + 2√6 + 2√8] respectively.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that the function is,

I'm assuming that you mean the left and right Riemann sums with four equal subintervals when you refer to L4 and R4.

If so, then Δx = (8-0)/4 = 2, and f(x) = 2√x.

L4 = f(0)Δx + f(2)Δx + f(4)Δx + f(6)Δx

L4 =2[2√0 + 2√2 + 2√4 + 2√6]

R4 = 2[2√2 + 2√4 + 2√6 + 2√8]

Thus, the value of  L4 and R4 over [0,7] for the function f(x) = 6x² will be 2[2√0 + 2√2 + 2√4 + 2√6] and  2[2√2 + 2√4 + 2√6 + 2√8] respectively.

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The ratio in their lowest terms is 4:1

What is a ratio?

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The proportion of lemons to oranges is also 6:8.

We are given two values 1km and 250m

We known that 1km = 1000m

Hence we have to find the ratio of the value 1000m to 250m

To find the ratio just Divide the two numbers we get

1000/250

=4/1

=4:1

Hence the smallest ratio for the term is 4:1

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