100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!

The population of Westville increased by approximately 99.95 people from 2015 to 2016.

To find the increase in population from 2015 to 2016 in Westville, we need to use the formula:

Increase in population = (Population density in 2016 - Population density in 2015) x Land area

First, we need to find the population density in 2016. To do that, we can divide the population of 2,000 people by the land area of 84.4 square miles:

Population density in 2016 = 2,000/84.4 ≈ 23.69 people per square mile

Next, we can plug in the values into the formula:

Increase in population = (23.69 - 22.5) x 84.4 ≈ 99.95 people

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The logarithmic form of the equation (1/7)³ = 1/343 is given as follows:

[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]

A logarithm is a mathematical function that represents the power to which a given base must be raised in order to obtain a given number. Logarithms are often used to simplify calculations involving very large or very small numbers.

In this problem, we raise 1/7 to the third power to obtain the number 1/343, hence the logarithm of base 3 of the number 1/343 is of 1/7, and then the expression is given as follows:

[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]

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Answer:

D. 1,0 & -3,0

Step-by-step explanation:

because the two lines pass through points 1,0 and -3,0 at the x-axis

Answer:

your answer is D. 1,0 & -3,0

Step-by-step explanation:

The given information describes a pair of congruent triangles. The corresponding vertices, angles, and sides of the triangles are congruent. The congruent angles are ∠REM ≅ ∠MOC, ∠ERM ≅ ∠MCO, and ∠CMO ≅ EMR. The congruent sides are ER ≅ CO, MO ≅ EM, and CM ≅ RM. The congruent triangles are ΔMER ≅ ΔMOC.

1) the corresponding vertices are

R ~ C and

E ~ 0

2) The corresponding angle are

∠E ~∠O  and

∠ R ~ ∠C

3)

The corresponding sides are;

ER ~ CO;

MO ~ EM

CM ~ RM

4)  the congruent angles are:

∠REM ≅ ∠MOC

∠ERM ≅ ∠MCO

∠CMO ≅ EMR

5) the congruent sides are:

ER ≅ CO;

MO ≅ EM

CM ≅ RM

6) the congruent triangles are;

ΔMER ≅ ΔMOC

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The expression of 1 picoseconds as a decimal would be = 0.000000000001 picoseconds.

The scientific notation of representation of figures is a systematic way of representation of too large or too small figures encountered in everyday arithmetics.

From the table above, the larger figures are represented with 10 ^ X without a negative sign.

But the smallest figures are represented with 10 ^ -X with a negative sign.

The scientific notation for 1 picoseconds = 10^-12

When converted to decimal

= 0.000000000001 picoseconds.

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No, any court case should not be based solely on probabilities as probability does not imply certainty.

Compute the probability of another couple being in that area with the same characteristics

CHARACTERISTIC ASSUMED PROBABILITY

Drives a yellow car 1 out of 12

Man over 6 feet tall 1 /10

Man wearing tennis shoes 1/4

Man with beard 1/11

Woman with blond hair 1/3

Woman with hair in a ponytail 1 /13

Women over 6 feet tall 1/100

We will use the multiplication rule as all the characteristics should be present in the couple.

The probability of another couple being in that area with the same characteristics is given as

P(Drives a yellow car) x P(Man with beard) x P(Woman with blond hair) x P(Woman with hair in a ponytail) x P(Woman over 6 feet tall) = 1/12 x 1/11 x 1/3 x 1/13 x 1/100 = 1/514800

The characteristics dependent on the sum of the probabilities is not equal to 1.

The assumption of independence would lead to use of the addition rule instead of the multiplication rule, and hence the probability would change (the probability would increase).

No, any court case should not be based solely on probabilities as probability does not imply certainty.

No, the couple who was arrested should not be convicted if there were no eyewitnesses as probability does not imply certainty.

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The line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).

A function is a mathematical concept that relates an input value (or values) to an output value (or values) according to a specific rule or set of rules. It can be thought of as a machine that takes in one or more inputs and produces a corresponding output. Functions are often represented using function notation, such as f(x) or g(t), where the variable in the parentheses (x or t) represents the input and the value of the function (f(x) or g(t)) represents the output.

To identify the line of symmetry and vertex of the parabola given by the function [tex]f(t) = -16t^2 + 60t + 16[/tex], we need to use the formula:

t = -b/2a

where "a" is the coefficient of the [tex]t^2[/tex] term (-16 in this case) and "b" is the coefficient of the t term (60 in this case).

Part A: Identify the line of symmetry of the parabola.

Using the formula above, we get:

t = -60 / 2(-16) = 1.875

So the line of symmetry of the parabola is t = 1.875.

Part B: Identify the vertex of the parabola.

To find the vertex, we need to substitute the value we found for t into the original function:

[tex]f(1.875) = -16(1.875)^2 + 60(1.875) + 16 = 77[/tex]

So the vertex of the parabola is (1.875, 77).

Therefore, the line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).

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There are 1820 different orders possible for selecting any 4 toppings out of a list of 16 toppings.

To calculate the number of different orders possible for selecting any 4 toppings out of a list of 16 toppings,

we can use the combination formula:

nCr = n! / r!(n-r)!

where n is the total number of items, r is the number of items to be selected, and ! represents the factorial operation.

Substituting the given values, we get:

16C4 = 16! / 4!(16-4)!

16C4 = (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1)

16C4 = 1820

Therefore, there are 1820 different orders possible.

Option D. 1,820 is the correct option.

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Answer:

To calculate how much is deducted from Scott’s paycheck, we need to first find out how much his employer pays for his health insurance premium.

55% of the annual premium is covered by the employer, so we can calculate this as:

0.55 x $20,969 = $11,532.95

Therefore, Scott’s employer pays $11,532.95 towards his health insurance premium.

To find out how much is deducted from Scott’s paycheck, we need to divide the remaining 45% of the premium by the number of pay periods in a year. Since Scott is paid biweekly, he receives 26 paychecks in a year.

45% of the annual premium is not covered by the employer, so we can calculate this as:

0.45 x $20,969 = $9,437.55

To find out how much is deducted from each biweekly paycheck, we can divide $9,437.55 by 26:

$9,437.55 ÷ 26 = $363.75 (rounded to the nearest cent)

Therefore, Scott’s employer pays $11,532.95 towards his health insurance premium and $363.75 is deducted from each of his biweekly paychecks for health insurance.

Step-by-step explanation:

lets call the line (d)

amd the given eq of the line is (d')

so (d) is perpendicular to (d')

slope(d)×slope(d')=-1

-2(1/2)=-1

so (d): y=1/2x + b

point A (4, -3) belongs to (d) so,

Ya=1/2Xa+b

-3=1/2(4)+b

b=-5

(d):y=1/2x-5

The probability of selecting an elm or oak tree is 0.38.

The probability of selecting an elm or oak tree is the sum of the probabilities of selecting an elm and selecting an oak:

P(elm or oak) = P(elm) + P(oak)

P(elm) = 0.04

P(Oak) =0.34

Plug in these values

= 0.04 + 0.34

= 0.38

Therefore, the probability of selecting an elm or oak tree is 0.38.

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The cost of an individual ticket is contingent upon the overall expenditure of the performance and the quantity of tickets purchased.

Ticket sales refer to the purchase of one or multiple admission passes to an occasion, which may be facilitated either through the Event Management System, online, mobile app, third-party voucher providers (such as Groupon), or physically, among other options.

Based on the fact that there is no much details on the ticket sales, it present ]an obstacle in knowing the number cost of individual tickets. To determine the cost of each ticket, we need to have the total expenditure or the quantity of tickets sold.

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Answer: C

Step-by-step explanation:

1/2 pound of almonds = 5/6 cup of almond butter

To find out how much almond butter 1 pound of almonds will make, we need to multiply both sides of the equation by 2:

1 pound of almonds = (2 × 1/2) pounds of almonds = 2 × 5/6 cups of almond butter

Simplifying, we get:

1 pound of almonds = 5/3 cups of almond butter

So, a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds is more than 2 cups of almond butter. Therefore, the answer is (c) more than 2 cups of almond butter.

Answer: b) between 1 1/2 and 2 cups of almond butter

Step-by-step explanation:

We can create a proportion to help us solve this question.

         [tex]\displaystyle \frac{\frac{1}{2} lbs\;almonds}{\frac{5}{6}lbs\;butter } =\frac{1lbs\;almonds}{xlbs\;butter}[/tex]

Now we can cross multiply.

         [tex]\displaystyle \frac{1}{2} *x=\frac{5}{6} *1[/tex]

         [tex]\displaystyle \frac{1}{2}x =\frac{5}{6}[/tex]

Next, we will divide both sides of the equation by one-half.

         [tex]\displaystyle x =\frac{5}{6}\div \frac{1}{2}[/tex]

         [tex]\displaystyle x =\frac{5}{6}* \frac{2}{1}[/tex]

         [tex]\displaystyle x =\frac{10}{6}[/tex]

Lastly, we will find which answer option this falls under by creating an improper fraction. This leads us to answer optoin b, b) between 1 1/2 and 2 cups of almond butter.

         [tex]\displaystyle 10-6=4\text{, so } 1\frac{4}{6} =1\frac{2}{3}[/tex]

City Bank paid more interest than First National Bank over the 5-year period.

What is compound interest?

Compound interest is the interest earned on both the principal amount and the accumulated interest from previous periods.

We can use the formula for compound interest to calculate the amounts of interest earned by the two banks over 5 years:

Amount of interest with First National Bank = [tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]

where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.

Amount of interest with First National Bank

=[tex]$500\left(1 + \frac{0.085}{1}\right)^{1\times 5} - 500$[/tex]

= $235.15 (rounded to two decimal places)

Amount of interest with City Bank =[tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]

where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year (365 in this case, since interest is compounded daily), and t is the number of years.

Amount of interest with City Bank

=[tex]$500\left(1 + \frac{0.0825}{365}\right)^{365\times 5} - 500$[/tex]

= $240.45 (rounded to two decimal places)

The difference in the amounts of interest paid by the two banks is:

$240.45 - $235.15 = $5.30

Therefore, City Bank paid more interest than First National Bank over the 5-year period.

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It is true. The trigonometric identity  [tex]\frac{cscx+secx}{sinx + cosx}[/tex] = cotx + tanx

To verify that (cscx+secx)/(sinx + cosx) = cotx + tanx

csc = [tex]\frac{1}{sin}[/tex]  and Sec = [tex]\frac{1}{cos}[/tex]

If we insert the values, it would be

[tex]\frac{ 1/sinx + 1/cosx}{sinx + cosx}[/tex]

= [tex]\frac{cosx + sinx}{sinx * cosx}[/tex] ÷  ([tex]\frac{1}{sinx + cosx}[/tex])

= [tex]\frac{1}{sinx * cosx}[/tex]

[tex]\frac{Sin^2 x + Cos^2x}{Sin x Cos x}[/tex]  =  [tex]\frac{Sin^2x}{SinxCosx}[/tex]  +  [tex]\frac{Cos^2x}{SinxCosx}[/tex]

= cotx + Tanx

Mind you

cotx = [tex]\frac{1}{tanx}[/tex] = [tex]\frac{cosx}{sinx}[/tex]

tanx = [tex]\frac{sinx}{cosx}[/tex]

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Answer:

the other two sides of the rectangle is 147

Step-by-step explanation:

because since u told us that there is a side with a length of 6 cm and u also gave us the preimeter which can help us do this so what I did is 6 x 2 why because if one side is 6cm then the other side will also be 6cm and then 6 x 2 = 12 and this is what I did 306 - 12 = which equalls 294 and then divide that by 2 = 147 please mark as brainliest bye have a great day :D

The two lines are parallel because they have thesame slope and different y intercept

If two non-vertical lines that are in the same plane has the same slope. However the lines will have different y intercept.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Therefore putting the equations 15x−6y=−5 and 5x−2y=5 into that form.

15x-6y = -5

-6y = -15x-5

y = 5x/2 +5/6

for the second equation,

5x-2y =5

-2y = -5x-5

y = 5x/2 +5/2

therefore , the two lines are parallel because they have the same slope( 5/2) and different y intercept.

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The interest he earns in 10 years =  $395.42.

What is compound interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest.

Here the Principal P = $500

Rate of interest= 6% = 6/100 = 0.06

Number of years t= 10 years.

Now using  compound interest formula then,

=> Amount = [tex]P(1+r)^t[/tex]

=> Amount = 500[tex](1+0.06)^{10[/tex] = [tex]500\times1.06^{10[/tex]

=> Amount = $895.42.

Now interest = $895.42 - $500 = $395.42

Hence the interest he earns in 10 years =  $395.42.

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Based on the given data, the age of Mr. Wright currently is 30 years

If Micah is 3 years old, then Lilly is twice as old, which means that

Lilly is 2 * 3 = 6 years old.

Now we know that Mr. Wright is five times as old as his daughter, Lilly, so Mr. Wright's age is:

5 * 6 = 30 years old.

Therefore, Mr. Wright is 30 years old.

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The inequality |x + 7| ≥ 2 has the solution set x ≤ –9 or x ≥ –5, as required.

We can write an absolute value inequality with the given solution set as follows:

|x + 7| ≥ 2

Here's how we arrived at this inequality:

First, we find the midpoint of the given solution set:

midpoint = (-9 + (-5)) / 2 = -7

Next, we find the distance from the midpoint to each endpoint of the solution set:

distance to -9 = |-7 - (-9)| = 2

distance to -5 = |-7 - (-5)| = 2

The maximum distance is 2, so we use c = 2 in the inequality.

Since the midpoint is to the left of both endpoints, we use the form |x - b| ≥ c.

Plugging in b = -7 and c = 2, we get:

|x + 7| ≥ 2

This inequality has the solution set x ≤ –9 or x ≥ –5, as required.

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Answer:

inflationary expenditure gap of $500

Step-by-step explanation:

At AE2 there is an inflationary expenditure gap of $500 (assuming full-employment output is $2000). The fiscal authority could increase taxes or decrease expenditures, which will shift the aggregate expenditures schedule down to AE0.

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The perimeter of the rhombus is approximately 7.6 units.

XZ is perpendicular to WY and XE is 4,

Since WXYZ is a rhombus because only the diagonal of the rhombus and square bisect each other at 90°

By the Pythagorean theorem, we have:

XE² = XY² + EY²

4² = XY² + (7/2)²

XY = 1.9

So the perimeter of WXYZ is 4(XY), rounded to the nearest tenth:

4(1.9) ≈ 7.6 units.

Therefore, the perimeter of the rhombus is approximately 7.6 units.

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Answer: 5,8,6,1

Step-by-step explanation:

math

The solutions to the dividing fractions prompts are as follows:

6. 4/3

7. 2/13

8. 33/2

9. 24/35

10. 63/20

To solve the divisions, note that the second divisor is inversed and multiplied. For the following problems, the divisions can be gotten as follows:

6. 8/9 ÷ 2/3

= 8/9 × 3/2

=24/18

=4/3

7. 12/13 ÷ 6

= 12/13 × 1/6

= 12/78

=6/39

= 2/13

8.  11/5 ÷ 2/15

= 11/5 × 15/2

165/10

= 33/2

9. 6/7 ÷ 5/4

6/7 × 4/5

= 24/35

10. 7/2 ÷ 10/9

7/2 × 9/10

63/20

So, the above are ways to determine the step-by-step answers.

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On sοlving the prοvided questiοn we can say that equatiοn Miles already ran -target distance = Miles still tο run 60 - 24 = 36 miles left tο run

A mathematical equatiοn is a fοrmula that links twο statements and uses the equals sign (=) tο indicate equality. In algebra, an equatiοn is a statement that demοnstrates the equality οf twο mathematical expressiοns.

We may begin by subtracting the miles Mοna has already ran frοm her οbjective distance tο get the number οf miles she must run each day tο accοmplish her gοal:

Miles already ran - target distance = Miles still tο run

60 - 24 = 36 miles left tο run

Since there are three days left in the week, Mοna must run:

36 miles ÷ 3 days = 12 miles per day

On a number line, we may begin with 24 and add 12 fοr each remaining day:

24 ------ 36 ------ 48 ------ 60

Tο represent this οn a number line, we can start at 24 and add 12 fοr each remaining day:

|---|---|---|---|---|---|---|

0 5 10 15 20 25 30 35 40

^ ^ ^

Day 5 6 7

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Answer: a

Step-by-step explanation:

24  boxes were used this week

12 boxes of recycled paper were used last week
For this week double of this amount was used

When calculating double the amount that was used, this means we have to multiply the initial amount by 2

In this case, we have to multiply 12 by 2

= 12 × 2

= 24

Hence 24 boxes of recycled paper was used this week

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