Arthur wants to build an enclosure for his rabbits. The enclosure needs to have an area of at least 10 square feet. The length of the enclosure needs to be 3 feet longer than the width. What are the possible lengths of the enclosure?

For the function f( x) = 3x- 2 and g( x) = x2, the workout fg( x) is 3x2- 2.

What is 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 inclusively appertained to as the function's sphere and codomain, independently. originally, functions represented the idealized relationship between two changing amounts.

A formula, rule, or legislation that specifies how one variable( the independent variable) and another variable are related( the dependent variable).

Four orders of functions live functions with return values and arguments.

This function accepts arguments and gives back a result.

functions that take arguments but have no return values.

functions with return values and no arguments.

functions that have no arguments or return values.

we are given two function f( x) and g( x);

f( x) = 3x- 2 and

g( x) = x2

So, for fg( x), we've to put value of g( x) into f( x);

Hence, the equation will be;

fg( x) = 3x2- 2.

thus, for the function f( x) = 3x- 2 and g( x) = x2, the fg( x) is 3x2- 2.

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The expanded form of the expression is 10 + 9 + 0.3 + 0.00 + 0.005

He runs the 100 meters dash in 19.305 seconds.

Therefore, the seconds he runs the race can be represented in expanded form as follows:

Expanded form is a way to write a number by adding the value of its digits.

We can use a place value chart to think of the value of a number's digits.

Therefore,

19.305 in expanded form is as follows:

19.305 = 10 + 9 + 0.3 + 0.00 + 0.005

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$1800 is the amount invested

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed.

Nico invests some money at 8%;

let M = amount invested

Nico also invests M - 800 at 7%

After 1 year, the total interest is $214.

M (0.08) + (M - 800)0.07 = $214

0.08M + 0.07M - 56 = $214

0.15M - 56 =  $214

0.15M = $160 + $56

0.15M = $270

Divide both sides of the equation by 0.15

M = $1800

Hence, the amount invested is $1800

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Answer:

the answer would be -4

Step-by-step explanation:

its gonna look like this 2/-.5=-4

Answer:

-4

Step-by-step explanation:

because 1/2 equals 0.5 in a calculator you can type 2÷-0.5 which equals -4

Answer:

D

Step-by-step explanation:

3 | 1   5   - 8   6

   ↓   3    24   48

   ----------------------

    1   8   16    54 ← Remainder

Answer:

Step-by-step explanation:

you need to show us what circle x looks like

Answer:

a+75+65= 180(sum of angle of triangle)

a+140=180

a=180-140

a=40

Answer:

1

Step-by-step explanation:

g(2)=5(2)-9     Simplify

g(2)=10-9        Subtract

g(2)=1              Write value for g

g=1

Answer:

∠A= ∠E, ∠H = ∠D

and the last one

Step-by-step explanation:

opposite angles are equal, alternative interior angle are equal.

Answer:

∠A = ∠E and ∠H = ∠D.

∠E = ∠H and ∠F = ∠G

Step-by-step explanation:

Angles A and E are one set of corresponding angles and angles H and D are another set.  Corresponding angles are always congruent to each other and thus equal. Therefore, ∠A = ∠E and ∠H = ∠D.

Angles E and H are one set of vertical angles and angles F and G are another set.  Vertical angles are also always congruent to each other and thus equal.  Therefore ∠E = ∠H and ∠F = ∠G

Each worker would take home a net pay of $586.71.

What is the net pay?

The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.

To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.

To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.

For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:

Gross Pay for 40 hours = $15.90/hour x 40 hours = $636

For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:

Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88

Therefore, their total gross pay would be:

Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88

Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:

Total Deductions = 28% x $814.88 = $228.17

Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:

Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71

Therefore, each worker would take home a net pay of $586.71.

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Answer:

rhombus is not a trapezoid

Step-by-step explanation:

rhombuses dont have one pair of parellel sides

EXPLANATION

The cost for each dount hole is 99cents/4 = 24.75 cents/dount hole

Answer:

please explain with detail

Step-by-step explanation:

One possible solution from the graph(attached at the end of the solution) is selling 9 bags of popcorn and 5 bags of candies.

As per the given data:

The number of popcorn bags is x

The number of candies is y

The cost of each popcorn bag is $7

The cost of each candy is $4

She has $80 to spend on them

Inequality is the nonequal comparison of two or more variables and numbers.

So the first inequality is

7 x + 4 y ≤ 80

Since she must buy no less than 16 bags of popcorn and candies

The second inequality is

x + y ≥ 16

The red area represents the 1st inequality

The blue area represents the 2nd inequality

The solutions lie in the common part of red and blue colors

One possible solution is ordered pair (9,5)

(Graph attached at the end of solution)

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Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

Let's find the mean, median, and mode for each set of numbers:

Set: 40, 38, 29, 34, 37, 22, 15, 38

Mean: To find the mean, we sum up all the numbers and divide by the total count:

Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125

Median: To find the median, we arrange the numbers in ascending order and find the middle value:

Arranged set: 15, 22, 29, 34, 37, 38, 38, 40

Median = (29 + 34) / 2 = 63 / 2 = 31.5

Mode: The mode is the number(s) that appear(s) most frequently in the set:

Mode = 38 (appears twice)

Set: 26, 32, 12, 18, 11, 14, 21, 12, 27

Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222

Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32

Median = 18

Mode: No mode (all numbers appear only once)

Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15

Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611

Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15

Median = 8

Mode: Mode = 8 (appears 4 times)

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

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The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

We have,

To determine the angle created by the bottom of the ramp and the ground, we can use the trigonometric function of sine.

In the given triangle, the height is 6 ft and the base is 16 ft.

The angle we want to find is opposite the height (let's call it θ).

The sine of an angle is defined as the ratio of the opposite side to the hypotenuse.

sin(θ) = opposite/hypotenuse

sin(θ) = 6/16

sin(θ) = 0.375

To find the angle θ, we can take the inverse sine (also known as arcsine) of 0.375:

θ = arcsin(0.375)

θ ≈ 22.62°

To meet safety regulations, the angle should be no more than 18°. Therefore, the contractor needs to lower the ramp by:

22.62° - 18° ≈ 4.62°

Thus,

The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

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Answer:

16

Step-by-step explanation:

Step 1: Write down the function \(f(x)=7x^2+2x+3.\)

Step 2: Write down the limit definition of the derivative:
\(f'(x)= lim_{h0} \frac{f(x+h)=f(x)}{h} .\)

Step 3: Substitute the function \(f(x)\) into the limit definition:
\(f'(x)=lim_{h0} \frac{(7(x+h)^2+2(x+h)+3)-(7x^2+2x+3)}{h}.\)

Step 4: Simplify the expression inside the limit:
\(f'(x)=lim_{h0}\frac{7x^2+14xh+7h^2+2x+2h+3-7x^2-2x-3}{h} .\)

Step 5: Combine like terms:
\(f'(x)=lim_{h0} \frac{14xh+7h^2+2h}{h} .\)

Step 6: Factor out an \(h\) from the numerator:
\(f'(x)=lim_{h0} \frac{h(14x+7h+2h}{h} .\)

Step 7: Cancel out the \(h\) in the numerator and denominator:
\(f'(x)=lim_{h0}(14x+7h+2).\)

Step 8: Evaluate the limit as \(h\) approaches 0:
\(f'(x)=14x+2.\)

Step 9: Substitute \(x=1\) into the derivative:
\(f'(1)=14(1)+2=14+2=16.\)

The Slope of the tangent line to the curve \(f(x)=7x^2+2x+3\) at \(x=1\) would be \(16.\)

a)Perimeter of given right angle triangle is 48.

Perimeter of dilated right angle triangle is 192.

b) Area of given figure is 96cm²

Area of figure after dilation is 1536cm².

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Given,

Triangle given,

Base = 12

hypotenuse = 20

Leg =  16

Dimensions of new triangle after dilatated by scale factor of 4:

Base = 48

hypotenuse = 80

Leg = 64

Area of right angled triangle:

Base × Leg/2

Area of given figure:

12 × 16/2

12 × 8

96

Area of given figure is 96cm²

Area of figure after dilation:

48 × 64/2

24 × 64

1536

Area of figure after dilation is 1536cm².

Perimeter of right angle triangle:

Perimeter of given figure:

12 + 20 + 16

48

Perimeter of given right angle triangle is 48.

Perimeter of dilated figure:

48 + 80 + 64

192

Perimeter of dilated right angle triangle is 192.

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On solving the provided question, we can say that Probability(A and B) = P(A)P(B|A) and P(E or F) = P(E) + P(F) - P(E and F)

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Probability(A and B) = P(A)P(B|A).

P(A and B) = P(B and A), this may also be written as P(A and B) = P(B)P(A|B).

Using the general multiplication rule, we have

P(E and F) = P(E)P(F|E)

.392 = P(E)(.7)

P(E) = .56

   P(E and F) = P(F)P(E|F)

.392 = P(F)(.56), so

P(F) = .7

P(E or F) = P(E) + P(F) - P(E and F)

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The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.

Given, A 6000-seat theater has tickets for sale at $24 and $40.

How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?

first, assign variables:

X = # of $24 tickets,  Y = # or $40 tickets

write equations based on the data presented:

"6000 seat theater..."

   X + Y = 6000 ...equation 1

"total revenue of 168,000"

The revenue from each type of ticket is the cost times the number sold, so:

  24X + 40Y = 168,000 .....equation 2

from equation 1:

   X = 6000 - Y

substitute this into equation 2:   (replace X with 6000-Y)

   24 (6000 - Y) + 40Y = 168,000

expand:

144,000 -24Y + 40Y = 168,000

rearrange and simplify:

    16Y = 168,000 - 144,000

    y = 24000/16

     Y = 1500

from equation 1:

     X = 6000 - 1500

     X = 4500

hence the number of tickets for sale at $24 should be 4500.

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Answer: To calculate the average cost per widget, we need to consider both the fixed costs and the variable costs.

Fixed costs: $34,000

Variable costs per widget: $5.00

Total costs = Fixed costs + (Variable costs per widget × Number of widgets)

Total costs = $34,000 + ($5.00 × 7,000)

Total costs = $34,000 + $35,000

Total costs = $69,000

Average cost per widget = Total costs / Number of widgets

Average cost per widget = $69,000 / 7,000

Average cost per widget ≈ $9.86

Therefore, the average cost per widget of producing 7,000 Wild Widgets is approximately $9.86.

Step-by-step explanation: :)

Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

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Answer: 250

Step-by-step explanation:

This problem is attempting to explain the distributive property to you.

The distributive property states that if you have the numbers a, b, and c:

\((a*c) + (b*c) = c * (a+b)\)

In your specific case, this would look like this:

\((23+37) * 4\frac{1}{6}\)

\(60 * \frac{(4*6)+1}{6}\)

\(60*\frac{25}{6}\)

To simplify, we factor a 6 out of the equation:

\(10*25 = 250\)

Considering the given allowances, it is found that:

a) Tom's allowances are of $66,000, while Solomon's are of $40,000.

b) Tom's net income is of $151,500.

c) Solomon's net income is of $160,000.

An allowance is an exemption in the taxable income of a person, meaning that taxes are not paid over this amount.

Solomon is single, hence he only has the personal allowance of $40,000, and his net income will be of:

Solomon's net income = 0.75 x 160,000 + 40,000 = $160,000. (75% because 25% of the amount not claimed in allowances is paid in taxes).

Tom's allowances are given as follows:

Hence his total allowances are of:

$40,000 + $10,000 + $16,000 = $66,000.

His net income will be of:

Tom's new income = 0.75 x 114,000 + 66,000 = $151,500.

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Required trapizoidal approximation is 174.

What is trapezoidal rule?

The trapezoidal rule is a numerical integration method used to approximate the definite integral of a function over a given interval. It is based on approximating the area under the curve of the function by dividing it into trapezoids and summing up their areas.

To use the trapezoidal rule, you first need to choose an interval [a,b] over which to integrate the function. Then, you divide the interval into a number of subintervals of equal width, typically denoted by h = (b-a)/n, where n is the number of subintervals.

Here,

Using the trapezoidal rule, the approximation of the integral is given by:

\(\int_{-4}^4 f(x),dx \)

\( = \frac{1}{2}[(f(-4)+f(-1))(-1-(-4))+(f(-1)+f(0))(0-(-1)) +(f(0)+f(4))(4-0)] \)

\( = \frac{1}{2}[ (4+18)(-1-(-4)) + (18+36)(0-(-1)) + (36+50)(4-0) ]\)

\(\\ = \frac{1}{2}[22(-3)+54(1)+86(4)] \\ = 174\)

Therefore, the correct answer is 174.

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Answer:It´s asking what the vale of P(4,3) is equal to and it´s P(4, 3) = 24

Step-by-step explanation:

The equivalent expression to the sentence "9 more than the quotient of x and 5" is given as follows:

x/5 + 9.

The sentence in the context of this problem is defined as follows:

"9 more than the quotient of x and 5"

The quotient of x and 5 is given by the division of x by 5, as follows:

x/5.

9 more means that 9 is added to the quotient of x and 5, hence the equivalent expression to the sentence "9 more than the quotient of x and 5" is given as follows:

x/5 + 9.

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Answer:

Use Sin if Opposite Hypotenuse, Use Cosine if Adjacent Hypotenuse, and Use Tangent if Opposite Adjacent