In 1992, the population in a town was 8,000 people. In 1997, the population was 14,000. What was the percent increase in the population?

The length of {MZ} will be equivalent to -

MZ = 4 - 2x.

Given is that M is the midpoint of YZ. Also, it is given that YM = x + 3, and YZ = 3x - 1.

We can write -

YM + MZ = YZ

(x + 3) + MZ = (3x - 1)

MZ = (x + 3) - (3x - 1)

MZ = x + 3 - 3x + 1

MZ = 4 - 2x

Therefore, the length of {MZ} will be equivalent to -

MZ = 4 - 2x.

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Answer:

23

Step-by-step explanation:

46 divided by 2

equals:23

Answer:

5700

Step-by-step explanation:

step 1 Address the formula, input parameters & values.

Input parameters & values:

The number series 2, 4, 6, 8, 10, 12, .  .  .  .  , 150.

The first term a = 2

The common difference d = 2

Total number of terms n = 75

step 2 apply the input parameter values in the AP formula

Sum = n/2 x (a + Tn)

= 75/2 x (2 + 150)

= (75 x 152)/ 2

= 11400/2

2 + 4 + 6 + 8 + 10 + 12 + .  .  .  .   + 150 = 5700

Therefore, 5700 is the sum of first 75 even numbers.

Final answer:

To find the sum of the first 75 even numbers starting with 2, use the sum of arithmetic sequence formula: (75/2) * (2 + 150) = 5,700.

Explanation:

The sum of the first 75 even numbers starting with 2 can be calculated using the formula for the sum of an arithmetic sequence. An arithmetic sequence is a sequence of numbers with a constant difference between consecutive terms. In this case, the common difference is 2, since we are dealing with even numbers.

To find the sum of the first 75 even numbers, we use the formula: Sum = (n/2) * (first term + last term), where 'n' is the number of terms. The first term is 2 and the 75th even number can be found by the formula: last term = first term + (n-1)*difference. Thus, the last term = 2 + (75-1)*2 = 2 + 148 = 150.

Using the sum formula: Sum = (75/2) * (2 + 150) = 37.5 * 152 = 5,700. Therefore, the sum of the first 75 even numbers starting with 2 is 5,700.

Answer:

Go to graphing website desmos.com and plug the equation in to see graph

Step-by-step explanation:

1) Starting graph: Linear Graph (x)  

Translations:

|x| erase left and copy right, in this case it makes an absolute value graph or a "V graph" informal term

-3(move right)

-2(down 2)

2) Order goes as follows: "||", -3, -2

Graph: see attached

Translations:

The parent graph is y = |x|

a horizontal shift 3 units to the right makes a new graph of: y = |x - 3|

a vertical shift 2 units down makes a newer graph of: y = |x - 3| - 2

Translations are as follows:

Answer: (9 CDs)

If she has $45 and the CDs cost $5. The most she can buy is 9 CDs

The number of maximum CDs that Jennifer can buy is 9.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variables called division.

As per the given,

Cost of one CD = $5

Jennifer budget = $45

Number of CDs can buy = Jennifer's budget/cost of one CD

Number of CDs can buy = 45/5 = 9

Hence "The number of maximum CDs that Jennifer can buy is 9".

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x - price of one pair socks

The equation:

[tex]5(2x)+5\times12=125[/tex]

[tex]10x+60=125[/tex]       subtract 60 from both sides

[tex]10x=65[/tex]      divide both sides by 10

[tex]\boxed{x=6.5}[/tex]

5(2x) - five sisters · two pairs of socks

5 · 12 - five scraves

125 - total cost

Answer: Their balance at the beginning of their second month is $2803.86.

Step-by-step explanation:

Since we have given that

Amount on credit card = $2745.69

APR on credit card = 12.75%

Late fee = $29

According to question, they miss their minimum payment .

So, their balance at the beginning of their second month is given by

[tex]2745.69\times \frac{12.75}{12\times 100}\\\\=29.17\\\\\text{After late fees }=29.17+29\\\\=58.17\\\\\text{ Amount in the beginning of their second month }\\\\=\$2745.69+58.17\\\\=2803.86[/tex]

Hence, their balance at the beginning of their second month is $2803.86

Answer:

2,803.86

Step-by-step explanation:

D) 4 cm, 3 cm

Let x represent the length of "another" side. Then "one side" can be represented by (2x -5 cm).

The perimeter of the kite is the sum of two sides of each length:

... P = 14 cm = 2(x) + 2(2x -5 cm)

Dividing by 2 and collecting terms, we have ...

... 7 cm = 3x -5 cm

... 12 cm = 3x

... 4 cm = x . . . . the length of "another" side

... 2(4 cm) -5 cm = 3 cm . . . . the length of "one side"

The two different side lengths are 4 cm and 3 cm.

Answer:

10 =x

Step-by-step explanation:

The figure in the diagram is an equilateral triangle, which means all sides are equal and all angles are equal.  If all angles are equal, each angle is equal to 60 degrees  (180/3=60).  Therefore  <B =60.

60 = 5x+10

Subtract 10 from each side

60-10 = 5x+10 -10

50 = 5x

Divide each side by 5

50/5 = 5x/x

10 =x

Answer:

The length of RT is 5. The length of RS and ST is either 7 or 3.

Step-by-step explanation:

The Law of Cosine is defined as

[tex]a^2=b^2+c^2-2bc\cos(A)[/tex]

It is given that, the law of cosine for triangle RST can be set up as

[tex]5^2=7^2+3^2-2(7)(3)\cos(S)[/tex]

Therefore the length of opposite side of angle S is 5. The opposite side of angle S is RT, therefore the length of RT is 5.

The length of two other sides are either 7 or 3.

Therefore length of RT is 5. The length of RS and ST is either 7 or 3.

Answer:

answer is d on edge

Step-by-step explanation:

To find the measures of the angles in ΔADE, we can apply the angle bisector theorem and the fact that DE is parallel to AB. The measures of ∠ADE, ∠AED, and ∠DAE are denoted as x, y, and z, respectively.

In ΔADE, we know that AD is the angle bisector of ∠A and BE is the angle bisector of ∠B. We also know that DE is parallel to AB. Given that m∠ADE is 34° smaller than m∠CAB, we need to find the measures of the angles in ΔADE.

Let's denote the measures of ∠ADE, ∠AED, and ∠DAE as x, y, and z, respectively.

From the angle bisector theorem, we know that ∠CAD = ∠DAB = y+z.

Since DE is parallel to AB, we have ∠ADE = ∠CAB = x+y+z.

Therefore, the measures of the angles in ΔADE are ∠ADE = x, ∠AED = y, and ∠DAE = z.

Answer:

The loose sweets at ?0.89 for 100 g.

Step-by-step explanation:

First, calculate the price per gram. You do this by dividing the price by the grams.

?1.49 / 120 g =  1.49 / 120 = 0.0124 (4 dp)

Because the answer was very long, I have rounded it to 4 decimal places (4 dp).

?0.89 / 100 g = 0.89 / 100 = 0.0089

Next, you must calculate both pre-packed and loose sweets to the same weight. I am calculating them both to 100 g.

0.0124 x 100 = 1.24

0.0089 x 100 = 0.89

Finally, the cheapest product for 100 g will be the better value. In this case, it is the loose sweets.

Answer: 5

Step-by-step explanation: Take 2 from 7 to get 5

Answer:

Option C -M'K' is the same length as MK

Step-by-step explanation:

Given : Line segment MK has endpoints at (2, 3) and (5,4)

               M'K' is the reflection of MK over the y-axis

By definition of reflection: reflection of point (x,y) across the the y-axis is the point (-x,y)

which implies M'K' has end points (-2,3) and (-5,4)

Now, we find the length of MK

let [tex](x_1,y_1)=(2,3)\\\\(x_2,y_2)=(5,4)[/tex]

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

⇒ [tex]d=\sqrt{(2-5)^2+(4-3)^2}[/tex]

⇒[tex]d=\sqrt{9+1}[/tex]

⇒[tex]d=\sqrt{10}[/tex]   ....(1)

Now, we find the length of M'K'

let [tex](x_1^{'},y_1^{'})=(-2,3)\\\\(x_2^{'},y_2^{'})=(-5,4)[/tex]

[tex]d^{'}=\sqrt{(x_2^{'}-x_1^{'})^2+(y_2^{'}-y_1^{'})^2}[/tex]

⇒ [tex]d^{'}=\sqrt{(-2+5)^2+(3-4)^2}[/tex]

⇒[tex]d^{'}=\sqrt{9+1}[/tex]

⇒[tex]d^{'}=\sqrt{10}[/tex] .....(2)

from (1) and (2) we simply show that the length of MK and M'K' is equal

we can also refer the figure attached for reflection of MK and M'K'

therefore, Option C is correct

Answer:

M'K' is the same length as MK.

Step-by-step explanation:

A reflection is a rigid transformation. Rigid transformations do not affect the length of the line segment

Answer:

6 miles

Step-by-step explanation:

AS Mike took the taxi from his home to airport and covered a distance

Initial fee of the ride was $ 6 which is fixed

Now with each mile he has to pay $3

Total he paid = $ 24

Now we have to find the total no of miles traveled  by Mike

The tip given is 0

Now from the given we can make an equation

Initial fee + 3 * miles traveled =  total Paid

Let total no of miles traveled are x

Putting all the values in the given equation

6 + 3 * x = 24

6 + 3x = 24

3x = 24-6

3x = 18

Dividing both sides by 3

x = 18 /3

x =6 miles

So the total miles traveled by him is 6 miles

The equation is $6 + $3 *m = $24, where m represents the number of miles traveled. Solving this, Mike traveled 6 miles.

The student's question concerns calculating the distance Mike traveled by taxi, given the initial fee and the per mile charge, as well as the total fare. To solve this, we can set up a simple algebraic equation. The initial fee is $6, and the charge per mile is $3. Since the total fare was $24, our equation becomes:

Initial fee + (charge per mile * number of miles) = Total fare

$6 + $3 * m = $24

Where m represents the number of miles Mike traveled. We will solve for m to find the distance Mike traveled

Thus, Mike traveled 6 miles by taxi on this ride.

Answer:

Alternative A

Step-by-step explanation:

2x(x² + 2x - 6)

2x³ + 4x² - 12x

I hope I helped you

Answer: A

Step-by-step explanation:

 2x(x² + 2x - 6)

= 2x(x²) + 2x(2x) + 2x(-6)

= 2x³ + 4x² - 12x

Answer:

[tex] 30w - 15v + 25 [/tex]

Step-by-step explanation:

Multiply -5 by each term inside the parentheses.

[tex] -5(-6w+3v-5) = [/tex]

[tex] = -5 \times (-6w) + (-5) \times 3v + (-5) \times (-5) [/tex]

[tex] = 30w - 15v + 25 [/tex]

Answer:

Step-by-step explanation:

15/2=7.5

7.5/100=0.075

0.075$ per cup.

-TheOneandOnly003

The unit price per cup during the sale is calculated by dividing the total cost of $15.00 by the total number of cups (200). The result is $0.075 per cup.

To find the unit price per cup during the sale, we must first determine the total amount of cups you are getting for the price. Given that you purchase 2 packs for $15.00, and each pack contains 100 cups, you're buying a total of 200 cups for $15.00. To get the price per cup, you then divide the total price by the total number of cups.

Step 1: Calculate the total number of cups: 2 packs * 100 cups/pack = 200 cups

Step 2: Calculate the price per cup: $15.00 / 200 cups = $0.075 per cup

So, the unit price per cup during the sale is $0.075.

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Answer:

Two sevenths

Step-by-step explanation:

Final answer:

To find the probability that everyone in the group is a girl, we use the combination formula to calculate the number of ways to choose a group of 3 from 7 students and the number of ways to choose 3 girls from the 5 available. The probability is 2/7.

Explanation:

To find the probability that everyone in the group is a girl, we need to consider the total number of ways to choose a group of 3 from the 7 students, and the number of ways to choose 3 girls from the 5 available.

The total number of ways to choose a group of 3 from 7 is given by the combination formula, which is:

C(7, 3) = 7! / (3! * (7-3)!) = 35

The number of ways to choose 3 girls from 5 is:

C(5, 3) = 5! / (3! * (5-3)!) = 10

Therefore, the probability that everyone in the group is a girl is:

P(girls) = C(5, 3) / C(7, 3) = 10 / 35 = 2/7

Answer:

[tex]P(t)=170\cdot (1.30)^t[/tex]    

Step-by-step explanation:

We have been given that there are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year.

We can see that deer population is increasing exponentially as each next year the population will be 30% more than last year.  

Since we know that an exponential growth function is in form: [tex]f(x)=a*(1+r)^x[/tex], where a= initial value, r=growth rate in decimal form.

It is given that a=170 and r=30%.    

Let us convert our given growth rate in decimal form.

[tex]30\text{ percent}=\frac{30}{100}=0.30[/tex]

Upon substituting our given values in exponential function form we will get,

[tex]P(t)=170\cdot (1+0.30)^t[/tex]

[tex]P(t)=170\cdot (1.30)^t[/tex]

Therefore, the function [tex]P(t)=170\cdot (1.30)^t[/tex] will give the deer population P(t) on the reservation t years from now.

By establishing and solving the equation c + 23 = 42, where c represents the number of cows in the barn, it is demonstrated that c = 19 is indeed a correct solution to the problem.

The student needs to determine if c=19 is a solution for the equation representing the number of cows still in the barn. To represent the total number of cows with those seen outside and those inside, we can write the equation c + 23 = 42. This equation sums the number of cows outside (23) with those still in the barn (c) to get the total number of cows (42).

Calculating the Unknown

Firstly, define the symbol c as the number of cows still in the barn. Then, using our equation c + 23 = 42, we can solve for c by subtracting 23 from both sides of the equation, getting c = 42 - 23, which simplifies to c = 19.

Evaluating the Solution

Substituting c = 19 back into the original equation to check if it makes sense, we get 19 + 23 = 42, which is a true statement, confirming that the value of c is indeed 19 and it is the correct solution.

[tex]\text{Use the Pythagorean theorem:}\\\\r-hypotenuse\\\\r^2=7^2+5^2\\\\r^2=49+25\\\\r^2=74\to r=\sqrt{74}[/tex]

[tex]\sin=\dfrac{opposite}{hypotenuse}\\\\\cos=\dfrac{adjacent}{hypotenuse}\\\\\tan=\dfrac{opposite}{adjacent}\\\\\cot=\dfrac{adjacent}{opposite}\\\\\text{We have}\\\\for\ the\ angle\ y:\\\text{opposite = 7}\\\text{adjacent = 5}\\\text{hypotenuse = }\ \sqrt{74}\\\\for\ the\ angle\ x:\\\text{opposite = 5}\\\text{adjacent = 7}\\\text{hypotenuse = }\ \sqrt{74}[/tex]

[tex]\csc x=\dfrac{1}{\sin x}\\\\\sec x=\dfrac{1}{\cos x}[/tex]

[tex]A.\\\\\sin x=\dfrac{5}{\sqrt{74}}=\dfrac{5\sqrt{74}}{74}\\\\\csc y=\dfrac{1}{\frac{7}{\sqrt{74}}}=\dfrac{\sqrt{74}}{7}\\\\B.\\\\\tan x=\dfrac{5}{7}\\\\\cot y=\dfrc{5}{7}\\\\C.\\\\\cos x=\dfrac{7}{\sqrt{74}}=\dfrac{7\sqrt{74}}{7}\\\\\sec y=\dfrac{1}{\frac{5}{\sqrt{74}}}=\dfrac{\sqrt{74}}{5}[/tex]

[tex]D.\\\sin\theta=\dfrac{2}{3}\\\\\sin^2\theta+\cos^2\theta=1\to\left(\dfrac{2}{3}\right)^2+\cos^2\theta=1\\\\\dfrac{4}{9}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{4}{9}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{5}{9}\to\cos\theta=\sqrt{\dfrac{5}{9}}\to\cos\theta=\dfrac{\sqrt5}{3}\\\\\tan\theta=\dfrac{\sin\theta}{\cos\theta}\to\tan\theta=\dfrac{\frac{2}{3}}{\frac{\sqrt5}{3}}=\dfrac{2}{3}\cdot\dfrac{3}{\sqrt5}=\dfrac{2}{\sqrt5}=\dfrac{3\sqrt5}{5}[/tex]

Answer:

N=i

S = -i

E =1

W = -1

Step-by-step explanation:

If facing north is represented by i, then facing south would be the opposite or -i.

We can let facing east be 1 because the magnitude has to be 1, so facing west would be the opposite or -1

[tex]\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^{n-1}\\------------------------------\\\text{We have the recursive form}\ a_1=6,\ a_n=2\cdot a_{n-1}.\\\\\text{Therefore}\ r=2.\ \text{Substitute:}\\\\a_n=6\cdot2^{n-1}=6\cdot2^n\cdot2^{-1}=6\cdot2^n\cdot\dfrac{1}{2}=\boxed{3\cdot2^n}[/tex]

Hey there.

To do this, we simply just subtract. 88,003-87,845

Once we do this, we get 158. Miguel traveled 158 miles that week.

-TheOneandOnly003

Answer:

87,845-88,033= -188 so he traveled 188 miles that week.

There are 479001600 different ways the first 12 letters of the alphabet can be arranged.

The first 12 letters of the alphabet can be arranged in 479,001,600 different ways.

The question asks how many different ways the first 12 letters of the alphabet can be arranged. This type of problem is addressed by using permutations, which is a concept in combinatorics, a branch of mathematics. When we talk about arranging a set of items, we are often dealing with permutations.

The formula to determine the number of permutations of a set of n distinct objects is given by n!, which is read as 'n factorial'. The factorial of a number n is the product of all positive integers less than or equal to n.

So, for the first 12 letters of the alphabet, which are 'A, B, C, D, E, F, G, H, I, J, K, L', the number of different ways to arrange these letters would be:

12! (12 factorial)

To calculate 12!, you multiply all the whole numbers from 1 to 12 together:

12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 479,001,600

Answer:

The answer  =

Step-by-step explanation:

Answer: D.

A horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180° rotation.

The transformations that can map a strip onto itself in geometry are reflection, rotation, and translation. Reflection flips the shape over an axis, rotation turns it around a central point, and translation moves it along a vector without changing its orientation.

In mathematics, particularly geometry, there are several types of transformations that can map a figure onto itself. Probably you are referring to a strip as in a planar shape, such as a rectangle or square. The main transformations that can map this strip onto itself are: reflection, rotation, and translation.

Reflection is like flipping the strip over an axis. If the strip is symmetrical, it will map onto itself. Rotation means turning the strip around a central point. For instance, rotating a square shape 90, 180, 270, or 360 degrees about its center will map it onto itself. Lastly, translation keeps the strip in the same orientation and moves it along a vector direction. As long as it doesn't interfere with its setting, it would still map onto itself.

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