suppose a population of 200 crickets double in size every 4 months. How many crickets will there be after 2 years?

PLEASE HELP <br> Match each expression to the scenario it represents

joja [24]

Answer:

i)

0.79m

ii)

1.21m

iii)

7/5m

iv)

3/5m

Step-by-step explanation:

i)

The price of a USB memory stick selling at a 21% discount off its marked price (m)

The marked price m represents 100% of the value of the USB memory stick. Offering a 21% discount off the marked price will mean that the USB will be selling at;

(100 - 21)% of the marked price m

=79% of m

= (79/100)*m

= 0.79m

ii)

The price of a CD that sells for 21% more than the amount (m) needed to manufacture the CD.

The amount (m) needed to manufacture the CD would represent 100% of the value of the CD. Selling the CD for 21% more than the amount (m) needed to manufacture the CD will imply that the selling price is;

(100+21)% of m

= 121% of m

= (121/100)*m

= 1.21m

iii)

The final value of a painting after its initial value, m, increases by 2/5.

The initial value of the painting is given as m. The value of the painting is said to increase by 2/5 which means that the increase in its value would be;

2/5 of m

=2/5 * m

=2/5m

The final value of the painting will thus be;

initial value + increase in value

=m + 2/5m

= m(1+2/5)

=7/5m

iv)

The total number of markers that Nancy has if she gives away 2/5 of her m markers to Amy.

Initially, Nancy had a total of m markers. By giving away 2/5 of her markers to Amy, her markers reduced by;

2/5 of m

=2/5*m

=2/5m

The new number of her markers will be given by;

initial numbers - total given to Amy

= m - (2/5m)

= m(1 - 2/5)

=m(3/5)

=3/5m

5 0

3 years ago

Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collect

mars1129 [50]

Answer:

If the controller uses the high-low method to estimate costs, the cost equation for electricity costs is "Total cost = $5,010 + ($6.45 * Machine hours)".

Step-by-step explanation:

Note: The data needed to estimate costs using the high-low method is merged together. It is therefore sorted before answering the question as follows:

Month Machine Hours Electricity Costs

January 2,000 $18,950

February 2,400 $22,100

March 1,400 $14,050

April 2,600 $24,100

May 3,300 $28,800

June 2,800 $23,100

July 3,600 $25,300

August 3,000 $23,300

September 1,500 $16,600

October 3,200 $27,100

November 4,200 $32,100

December 3,700 $28,300

The explanation of the answer is now provided as follows:

Step 1: Calculation of variable cost per hour

From the data above, the highest Machine Hours and Electricity Costs occur in November, while the lowest occur in March. Therefore, we have:

Variable cost per hour = (Highest Electricity Costs - Lowest Electricity Costs) / (Highest Machine Hours - Lowest Machine Hours = ($32,100 - $14,050) / (4,200 – 1,400) = $18,050 / $2,800 = 6.44642857142857

Rounding to 2 decimal places as required, we have:

Variable cost per hour = $6.45

Therefore, the variable-cost components using the high-low method is $6.45.

Step 2: Calculation of total fixed cost

The formula for calculating the total cost is given as follows:

Total cost = Total Fixed Cost + Total Variable Cost ................. (1)

Where;

Total Variable Cost = Variable cost per hour * Machine hours at a particular Electricity Costs

Using highest levels of activity and substitute into equation (1), we have:

$32,100 = Total Fixed Cost + ($6.45 * 4,200)

Total Fixed Cost = $32,100 - ($6.45 * 4,200) = $32,100 - $27,090 = $5,010

Therefore, the fixed-cost components using the high-low method is $5,010.

Step 3: Derivation of the cost equation for electricity costs

The cost equation for electricity costs can be obtained based on the total cost function given in equation (1) above, where:

Total Fixed Cost = $5,010

Total Variable Cost = Variable cost per hour * Machine hours = $6.45 * Machine hours

Substituting the values into equation (1), we have:

Total cost = $5,010 + ($6.45 * Machine hours)

Therefore, if the controller uses the high-low method to estimate costs, the cost equation for electricity costs is "Total cost = $5,010 + ($6.45 * Machine hours)".

8 0

3 years ago

Solve the following using Substitution method<br> 2x – 5y = -13<br><br> 3x + 4y = 15

Digiron [165]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$2x-5y=-13, \: 3x+4y=15$

Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

$2x-5y=-13$

Add 5y to both sides of the equation.

$2x=5y-13$

Divide both sides by 2.

$x=\frac{1}{2}\left(5y-13\right) \\$

Multiply $\frac{1}{2}\\$ times 5y - 13.

$x=\frac{5}{2}y-\frac{13}{2} \\$

Substitute $\frac{5y-13}{2}\\$ for x in the other equation, 3x + 4y = 15.

$3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15 \\$

Multiply 3 times $\frac{5y-13}{2}\\$ .

$\frac{15}{2}y-\frac{39}{2}+4y=15 \\$

Add $\frac{15y}{2} \\$ to 4y.

$\frac{23}{2}y-\frac{39}{2}=15 \\$

Add $\frac{39}{2}\\$ to both sides of the equation.

$\frac{23}{2}y=\frac{69}{2} \\$

Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

$\large \underline{ \underline{ \sf \: y=3 }}$

Substitute 3 for y in $x=\frac{5}{2}y-\frac{13}{2}\\$ . Because the resulting equation contains only one variable, you can solve for x directly.

$x=\frac{5}{2}\times 3-\frac{13}{2} \\$

Multiply 5/2 times 3.

$x=\frac{15-13}{2} \\$

Add $-\frac{13}{2}\\$ to $\frac{15}{2}\\$ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

$\large\underline{ \underline{ \sf \: x=1 }}$

The system is now solved. The value of x & y will be 1 & 3 respectively.

$\huge\boxed{ \boxed{\bf \: x=1, \: y=3 }}$

8 0

2 years ago

Which equation can pair with x-y=-2 to create a consistent and dependent system?

MrRissso [65]

See the explanation

<h2>Explanation:</h2>

A system that has one or infinitely many solutions is called <em>consistent. </em>If an equation in a system tells us no new information then the equations of the system are <em>dependent. </em>In other words, to find an equation that creates a consistent and dependent system with the given equation we have to get the same line:

The given line is:

$x-y=-2$

If we multiply both sides of the equation by a constant we will have the same line when plotting, therefore let's multiply by 3:

$3(x-y)=3(-2) \\ \\ 3x-3y=-6$

So a system of two linear equation that is consistent and dependent is:

$\left \{ {{x-y=-2} \atop {3x-3y=-6}} \right.$

<h2>Learn more:</h2>

Graph of lines: brainly.com/question/14434483#

#LearnWithBrainly

3 0

3 years ago

There are approximately 7.5x10^18 grains of sand on earth.There are approximately 7x10 ^27 atoms in an average human body.Are th

Likurg_2 [28]

They are more atoms in a body, only 75,000,000,000,000,000,000 grains of sand
and
7,000,000,000,000,000,000,000,000,000
atoms in a body, at the end , the number of atoms seem longer and larger.

5 0

3 years ago