A town's population has been growing linearly. In 2003 the population was 22,000. The population has been growing by 1700 people each year. Write an equation for the population, P, x years after 2003. P = Preview Use the formula to find the population in 2009: Preview

By using the concept of arithmetic series, it can be calculated that

y - x = 1250

What is arithmetic series?

Arithmetic series are those series whose difference between two consecutive terms are same.

The odd integers forms an arithmetic series

For the sum of first 25 odd integer

First odd integer = 1

25th odd integer = 49

Sum of first 25 odd integers = [tex]\frac{25}{2}(1 + 49)[/tex] = 625

x = 625

For the sum of first 50 odd integers

First odd integer = 1

50th odd integer = 99

Sum of first 50 odd integers = [tex]\frac{50}{2}(1 + 99)[/tex] = 2500

Sum of next 25 odd integers = 2500 - 625 = 1875

y = 1875

y - x = 1875 - 625 = 1250

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30% was the discount recived

At that point, the area of the rhombus is changing at a rate of -1 cm²/min (measured in square centimeters per minute).

A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the form of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen. The graphic below illustrates some examples of rhombuses in everyday objects, like a diamond, a kite, an earring, etc.

Here,

The area of a rhombus is given in terms of its diagonal lengths x and y,

A = (1/2)xy

A' = (1/2)(x'y +xy')

A' = (1/2)((-7 cm/min)(6 cm) +(4 cm)(10 cm/min))

A' = (1/2)(-42 cm²/min +40 cm²/min)

A' = -1 cm²/min

The rate of change of the area of the rhombus at that instant (in square centimeters per minute) is -1 cm²/min.

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In the given triangle MNO, the length of MN is 10

From the question, we are to determine the length of the unknown side in the triangle

The side is MN

From the given information, we have that  

In ΔMNO,

∠M ≅ ∠O

Thus,

ΔMNO is an isosceles triangle

Since angle M is congruent to angle O, the sides facing the two angles will also be congruent.

That is,

NO ≅ MN

From the given information,

NO = 10

Therefore,

MN = 10

Hence, the length of MN is 10

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Answer:

The dots shown in the graph are the answers.

Step-by-step explanation:

Answer: (-0.25, .75)

The first two events are not independent, with a probability P = 0.00603

The second pair of events is independent, and the probability is P = 0.0625

First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.

A) Now, if Lacy first draws a spade card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.

The probability of drawing a 10 card at first is:

P = 4/52 (because there are 4 10's and a total of 52 cards).

The probability of drawing a 4's after is:

Q = (4/51)

The joint probability is the product of the individual probabilities, this will give: p = P*Q = (4/52)*(4/51) = 0.00603

B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).

The probability of drawing a spade is:

P = 13/52

Now we replace the spade card drawn.

The probability of drawing a club will be:

Q = 13/52

The joint probability is:

p = P×Q = (13/52)² = 0.0625

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Answer:

f(g(x)) = 2x + 3

Step-by-step explanation:

f(g(x)) is called a composite function

To compute f(g(x)) simply substitute whatever g(x) definition is wherever there is an x in f(x)

We have [tex]g(x) = 6x + 9[/tex]

[tex]f(x) = \dfrac{x}{ 3}[/tex]

So instead of x just use 6x + 9 to get

[tex]f(g(x)) = \dfrac{6x+9}{3} = 2x + 3[/tex]

There are 358,800 different ways that a 4-letter password might be used.

For the stated question-

For the fourth letter, we might select any letter between A and Z besides the first, second, and third letters.

SO;

Number of possible combinations for 4-letter passwords

= 26 × 25 × 24 × 23

= 358,800

Thus, there are 358,800 different ways that a 4-letter password might be used.

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The complete question is-

To log on to a certain computer account, the user must type in a 4-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 4-letter passwords are possible.

Answer:

Slope is 2/3.

Step-by-step explanation:

I can't help you plot the points, but the slope formula is y2-y1/x2-x1.

2-4/3-6. -2/-3. This simplifies to 2/3.

A reasonable estimation of the total area of the room to be painted is:

Estimation involves the approximation of values with number rounding.

Estimates make it easier to do some mathematical operations involving fractions or decimals.

The area is the space occupied by a two-dimensional object.

The area is always the product of the length and width (height or depth).

Given the dimensions of the room:

Length of one side = 29¹/₂ ft

Height of the four sides = 8 ft

Length of the second side = 38³/₈ ft

Based on estimation, the dimensional values are approximated to:

Length of one side of the rectangular room = 30 ft

Height of the four sides = 8 ft

Length of the second side of the rectangular room = 40 ft

There are four walls for the room, and we can deduct the areas of the door and window, but these are not given, so we ignore them.

The area of the four walls can be computed as follows:

Area of two sides with same dimensions = 480 ft² [2(30 x 8)]

Area of two sides with same dimensions = 640ft² [2(40 x 8)]

Total area = 1,120 ft² (480 ft² + 640 ft²)

Thus, the options that satisfy the estimated area of the four walls of the room are Options A and E.

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The probability that the cost will be between $250 and $470 is 0.7354.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

Automobile repair costs continue to rise with the average cost now at $367 per repair.†

Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88.

We have to find the probability that the cost will be between $250 and $470.

P( 250 < x < 470 ) = P( x <470 ) - P( x < 250 )

P( x < 470 ) = NORMDIST( 470 , 367, 88, 1 ) = 0.8272

P( x < 250 ) = NORMDIST( 250 , 367, 88, 1 ) = 0.09183

P( 250 < x < 470 ) = 0.8272 - 0.09183 = 0.7354

P( 250 < x < 470 ) = 0.7354

Hence, the probability that the cost will be between $250 and $470 is 0.7354.

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Answer:

50

Step-by-step explanation:

1500/30=50

Answer:

50 words per minute

brainliest plss

The length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.

Using cos law:

W = √(41² + 17² - 2×41×17 cos 134)

After solving:

W = 54.20 cm

Thus, the length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.

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Answer:

a. 120 represents the total number of cow legs and chicken legs

b. 48 represents the total number of cow heads and chicken heads

c. System:

        Let x = number of cows

        Let y = number of chickens      

        1. 2x + 4y = 120

        2. x + y = 48

d. I am going to use substitution for this problem

    Step 1: Solve for y in the equation x + y = 48

         1. x + y = 48 → y = -x + 48

    Step 2: Substitute -x + 48 for y in 2x + 4y = 120    

         2. 2x + 4(-x + 48) = 120

    Step 3: Solve for x

         3. 2x - 4x + 184 = 120 → -2x + 184 = 120 → -2x = -64 → x = 32

    Step 4: Sustitute 32 for x in x + y = 48

         4. (32) + y = 48

    Step 5: Solve for y

         5. y = 16

    Number of chickens on the farm (y) = 16

    Number of cows on the farm (x) = 32

Step-by-step explanation:

All of it is above :)

The lowered value will thus be £16265.28.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

Therefore, the decreased sum is: 16265.2777 = 16855.21 - (16855.21 3.5/100) = (16855.21 - 589.93235).

Next, we'll round the number to two decimal places: 16265.2777, 16265.278, and 16265.28

Hence, The lowered value will thus be £16265.28.

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Answer:

Step-by-step explanation:

1/27,20/9

the probability that all 36 problems in the homework will be completed in less than 180 minutes

P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)

given that

there are 36 independent problems

mean(μ) = 6minutes

standard deviation(σ) = 3 minutes

sample standard deviation = σ/[tex]\sqrt{n}[/tex]

 = 3/[tex]\sqrt{36}[/tex]

 =3/6

 =0.5

the sample mean x of 36 questions answering time approximately follows a normal distribution with mean 6 minutes and sample standard deviation is 0.5 minutes

now we need to find the probability that all 36 problems in the homework will be completed in less than 180 minutes

P(∑[tex]\left \{ {{i=36} \atop {i=1}} \right.[/tex] [tex]X_{i}[/tex] < 180) = P(X<5) = P(Z<-1) = ∅(-1)

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The probability that a randomly selected jury of 12 people is all male is 2.01 × 10⁻⁵   .

In the question ,

it is given that ,

total number of people in the jury pool is 30 people ,

the total number of men in the jury pool is = 16 ,

total number of women in the jury pool is = 14 ,

So , 12 members can be selected from 30 people in ³⁰C₁₂ ways ,

So , total number of ways = ³⁰C₁₂ = 86493225 ways

and 12 male can be selected from 16 men in ¹⁶C₁₂ ways

= ¹⁶C₁₂ = 1820.

So , the probability of selecting 12 men is = 1820/86493225

= 0.00002104211

≈ 2.01 × 10⁻⁵

Therefore , the required probability is 2.01 × 10⁻⁵  .

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Answer: Alternate exterior angles --> 1,8 and 2,7

Vertical angles --> 2,3 and 5,8

Corresponding angles --> 1,5 and 2,6

Alternate interior angles --> 3,6 and 4,5

Answer:

8%

Step-by-step explanation:

pls mark brainliest

Answer : The interest rate have been 8 %

Step-by-step explanation :

First we have to calculate the simple interest.

As we know that:

Simple interest = Total amount - Principle

Simple interest = $130,000 - $50,000

Simple interest = $80,000

Now we have to calculate the interest rate.

Using simple interest formula:

where,

S.I = simple interest = $80,000

P = principle = $50,000

R = interest rate = ?

T = time = 20 years

Now put all the given values in the above formula, we get:

Therefore, the interest rate have been 8 %

Found answer from Alleei!

The time at which the pool was full is 4:00 when the water is in the 4 inches tank .

In mathematics, multiplication is one of the four basic arithmetic operations. It represents the basic idea of repeated addition of the same number.

The height of the tank is 4 feet water pouring is turned on at 11:00 at 11:25 the depth of the water in the tank is 4 inches.

which means,

To fill 4 inches it takes = 25 min

To fill 1 inch it takes = 25/4 min 4 feet = 4×2.54 = 48 inches

To fill 48 inches it takes = 48 × 25/4

                     = 300 min

                          = 5 hours

So, 5 hours after 11:00 will be 4:00

Hence, the time at which the pool was full is 4:00

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The number of free throws = 5

The number of two point shots = 8

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of free throws be = x

Let the number of two point shots be = y

The total number of shots made by Madelyn is = 13

So , the equation is

x + y = 13   be equation (1)

The total number of points scored by Madelyn is = 21

So , the equation is

x + 2y =   be equation (2)

On simplifying the equation , we get

Subtracting equation (1) from equation (2) , we get

2y - y = 8

y = 8

Therefore , the value of y is 8

And , The number of two points be = 8

Substituting the value for y in equation (1) , we get

x + y = 13

x + 8 = 13

Subtracting 8 on both sides of the equation , we get

x = 5

Therefore , the value of x is 5

And , the number of free throws is 5

Hence , The number of free throws = 5

The number of two point shots = 8

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No , as we fail to reject the null hypothesis Mr. Goodman claim that his evaluations are significantly different than the history department's.

What is null hypothesis?

Test statistic  X2 =1.9196

p value =0.5893

No , as we fail to reject the null hypothesis Mr.Goodman claim that his evaluations are significantly different than the history department.

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Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.

What do you mean by sampling?

Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.

According to the question,

A true sampling would be a mixed demographic group. A sampling from several like areas:

e.g. infront of the student store, infront of the regular store, infront if a food pantry, infront of ... or even better do a blind survey.

Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.

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The Expected Value to the player for one play of the game is - 7.784.

In probability theory, the weighted average is expanded upon by the expected value. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the anticipated value.

Price of raffle ticket= $10

First price= $5460

Second prize= $496

Remaining 18 prize= $100

$0 for the remaining tickets= 3500-20=3480 tickets

When winning the 1st prize, the winnings = $5460−$10=$5450.

When winning the 2nd prize, the profit= $496−$10=$486.

When winning the other 18 prizes, the profit= $100−$10=$90.

When there is no winning, the loss= $0

The probability is calculated by dividing the number of likely outcomes by the total number of outcomes:

P(X=5450)= 1/3500

P(X= 486)= 1/3500

P(X= 90)= 18/3500

P(X= -10)= 3480/3500

The product of each alternative and its probability equals the expected value, which is added up:

E(X)= ∑ xP(x)

      = 5450 * [tex]\frac{1}{3500}[/tex] + 486 * [tex]\frac{1}{3500}[/tex] + 90 * [tex]\frac{18}{3500}[/tex] + (-10) * [tex]\frac{3480}{3500}[/tex]

      = [tex]\frac{-27224}{3500}[/tex]

      = - 7.784

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Mean and standard deviation for the sample distribution is in the main body.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

sample Mean

Population mean =mu = ∑ xi /N

Mu represents pop mean

∑xi = the sum of all scores in the dataset

sample mean is the average score of a sample on a given variable and is represented by

x bar = ∑ xi /N

SE.M(Sample error of the Mean) is

=σ/√n

standard deviation is

σ = √∑(xi - υ)²/N

hence the formula for each of terms is as follows.

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[tex] \Large{\boxed{\sf Option \ D) \ \ Infinite \ solutions }} [/tex]

[tex] \\ [/tex]

We will solve this equation by isolating x.

[tex] \\ [/tex]

Given equation:

[tex] \sf 2.5(5x + 2) = 12.5x + 5 [/tex]

[tex] \\ [/tex]

Expand the left side of the equation using the following distributive property:

[tex] \blue{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \green { \boxed{ \sf Distributive \: property \text{:}}} \\ \\ \sf A(B + C) = AB + BC \\ \end{array}}\\\end{gathered} \end{gathered}} [/tex]

[tex] \\ [/tex]

[tex] \sf \overbrace{\sf 2.5}^{A} (\underbrace{\sf 5x}_{B} + \overbrace{\sf 2}^{C}) = 12.5x + 5 \\ \\ \sf 2.5 \times 5x + 2.5 \times 2 = 12.5x + 5 \\ \\ \sf 12.5x + 5 = 12.5x + 5 [/tex]

[tex] \\ [/tex]

Now, subtract 5 from both sides of the equation:

[tex] \sf 12.5x +5 - 5 = 12.5x + 5 - 5 \\ \\ \sf 12.5x = 12.5x [/tex]

[tex] \\ [/tex]

Finally, divide both sides of the equation by 12.5:

[tex] \sf \dfrac{12.5x}{12.5} = \dfrac{12.5x}{12.5} \\ \\ \\ \boxed{\boxed{\sf x = x}} [/tex]

[tex] \\ [/tex]

Since any value is equal to itself, the equation has infinite solutions.

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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The equation to find the total number of questions (q) on Tim's math test is 76 = 4x + 0

Number of wrong questions = 10

Points received for right question = 4 points

Points received for wrong question = 0 points

Total of Tim's score = 76%

Let

the number of questions right answered by Tim be x.

Total points gained by Tim for the right answer = number of questions right answered x Points received for a right answer

= x × 4

= 4x

Points gained by Tim for the wrong answer = number of questions wrong answered x Points received for a wrong answer

= 10 × 0

= 0

Total points scored by Tim = Points gained for the right answer + Points gained for the wrong answer

76 = 4x + 0

76 = 4x

divide both sides by 4

x = 76/4

x = 19

Hence, the number of question answered right by Tim are 19.

Total number of questions attempted by Tim

Total number of questions attempted by Tim

= number of questions answered right +number of questions answered Wrong

= 19 + 10

= 29

Hence, the total number of questions attempted by Tim is 29.

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We must first transform matrix A into a triangular or diagonal matrix in order to determine its determinant.

Using the row operations to change the matrix, having three rows and five columns, in a triangular matrix, having three rows and three columns.

combining the first and second rows, then the first and third rows:

(1 0 2 0 3 0 1 2 3 4 1 0 3 0 5         (1 0 0 2 4            (1 0 3 0 8        (3 0 5 2 11

  0 0 0 2 4                                +   0 0 0 2 4)    +     1 0 3 0 8)   =   0 0 0 2 4

   1 0 3 0 8)                                                                                      2 0 6 0 16)

subtracting the second and third rows from the first row

We get a triangular matrix

(3 0 5 2 11           (0 0 0 2 4        (2 0 6 0 16             (1 0 5 0 3

0 0 0 2 4      -     0 0 0 2 4)    -    2 0 6 0 16)     =     0 0 0 2 4

2 0 6 0 16)                                                                 0 0 0 0 0)

Now that the matrix is triangular, we can use the determinant formula for triangular matrices, which states that the determinant of a triangular matrix is equal to the product of the diagonal elements. The diagonal elements of matrix A are 1, 0, and 0, so the determinant of matrix A is 0.

Therefore, the determinant of matrix A is 0, and we can find it by only using the three basic properties in Treil section the determinant formula for triangular and diagonal matrices, and row or column operations.

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