If the sum of three consecutive natural numbers is 30 , find the numbers. Let us first form the equation. If y is the smallest among the three consecutive natural numbers, then the second smallest would be y+$ and the largest would be .

The correctness of the student's solution, we need to have the equations of the system.

A system of equations is graphed on the coordinate plane. A student concludes that the solution of the system is (-0.5, 1.5). Is this correct? Justify your response.To conclude that a system of equations has a solution in the coordinate plane, a set of ordered pairs (x, y) should satisfy both equations in the system of equations. That is, the system of equations should have a point (x, y) that is a solution of both equations.Only by testing the solution in the given system of equations can we know if the student's conclusion is correct. If the solution is satisfied by the system of equations, then the answer is true. Otherwise, it is false. However, since no system of equations is provided in the question, we cannot test the student's solution.To justify the correctness of the student's solution, we need to have the equations of the system.

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The researcher should reject the null hypothesis, and he can conclude the alternative hypothesis is probably correct.

The alpha level is set prior to the analysis of the data. To use the tool to identify the z-score boundaries, the user must slide the orange lines until the area in the critical region equals the alpha level. The critical region is between the two z-score boundaries. The z-score boundaries for an alpha level a = .001 are: z = 2.58 and z = -2.58, z = 1.96 and z = -1.96, z = 3.29 and z = -3.29. With an alpha of .001, the calculated z statistic of 2.64 is within the critical region. Therefore, the researcher should reject the null hypothesis, and he can conclude the alternative hypothesis is probably correct.

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Therefore, it will cost $510 to carpet the hallway.

Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width. The concept of area is used in many fields, including mathematics, geometry, engineering, and architecture. It is an important measure for determining the amount of material needed to cover a surface, such as carpet or paint, and is used in a wide variety of real-world applications.

Here,

To find the cost of carpeting the hallway, we need to know the total area of both trapezoids in square feet. Let's assume that the trapezoids have parallel sides of length 16 and 18 feet, and a height of 6 feet.

The area of each trapezoid is given by the formula:

Area = (1/2) x (sum of parallel sides) x height

For the first trapezoid, the sum of parallel sides is 16 + 18 = 34 feet. Therefore, the area of the first trapezoid is:

Area1 = (1/2) x (16 + 18) x 6

Area1 = 102 square feet

For the second trapezoid, the sum of parallel sides is also 16 + 18 = 34 feet. Therefore, the area of the second trapezoid is:

Area2 = (1/2) x (16 + 18) x 6

Area2 = 102 square feet

The total area of both trapezoids is:

Total Area = Area1 + Area2

Total Area = 102 square feet + 102 square feet

Total Area = 204 square feet

Now that we know the area of the hallway, we can calculate the cost of carpeting it. We're told that the carpet costs $2.50 per square foot, so we can multiply the area of the hallway by the cost per square foot to find the total cost:

Total Cost = Area x Cost per square foot

Total Cost = 204 square feet x $2.50 per square foot

Total Cost = $510

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Answer: x = 15

Step-by-step explanation:

Expand 1.4(x+5): 1.4x+7+1.6x = 52

Combine like terms: 3x+7 = 52

Subtract 7 from both sides: 3x = 45

Divide both sides by 3: x = 15

Answer:

The answer is x=15

Please give me Brainliest :)

1. Expand the expression

1.4x+7+1.6x=52

2. Simplify

3x+7=52

3. Separate the constants and variables

3x=52−7

4. Add or subtract numbers

3x=45

5. Divide both sides by 3

6. Simplify

x=15

The cat population in Catonsville in 2007 was 200. The answer is option B.

Population refers to the total number of people, animals, or objects in a particular group or area. It is the entire group or collection of individuals, things, or events that we are interested in studying or describing.

We can use the given equation to find the cat population at any given time in years since the beginning of 2010. However, to find the population in 2007, we need to make a conversion from years since the beginning of 2010 to years since the beginning of 2007.

From the beginning of 2007 to the beginning of 2010, there are 3 years, so if we subtract 3 from the number of years since the beginning of 2010, we will get the number of years since the beginning of 2007. Therefore, we need to substitute t = -3 into the given equation and solve for p:

[tex]p = 1600(2)^t\\p = 1600(2)^(-3)\\p = 1600(1/8)\\p = 200[/tex]

Therefore, the cat population in Catonsville in 2007 was 200. The answer is option B.

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The correct relative frequency for X is:

X: $2 $3 $4 $7

P(X): 0.38 0.15 0.28 0.19

First we need to determine the probability of each value of X occurring based on the given data.

We can use the following formula to calculate the probability of a particular value of X:

P(X = x) = f(x)/n

Where

Let's calculate the probabilities for each value of X:

P(X = $2) = 57/150 = 0.38

P(X = $3) = 23/150 = 0.15

P(X = $4) = 42/150 = 0.28

P(X = $7) = 28/150 = 0.19

Therefore, the correct relative frequency for X is:

X: $2 $3 $4 $7

P(X): 0.38 0.15 0.28 0.19

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The answer to the question is 334 kittens.

Given that a cat gave birth to 333 kittens who each had a different mass between 147 g and 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.

First of all, we will find out the range of the mass of kittens. The range is given as follows;Range = Maximum Value - Minimum Value Range = 159 g - 147 g Range = 12 g

Now, the cat gave birth to a 4th kitten with a mass of 57 g, we can say that the minimum value of kitten's mass is 57 g.So, the maximum value of kitten's mass can be calculated as follows;Maximum Value = 57 g + Range Maximum Value = 57 g + 12 g Maximum Value = 69 g Now, we can say that all kittens with a mass of 69 g or less would be born because the minimum value of kitten's mass is 57 g and the range of mass is 12 g.

Therefore, the answer to the question is 334 kittens.

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Answer:

83.6%

Step-by-step explanation:

Let's say the original price is x

x decreased by 12% means 88% of x is left.

0.88x decreased by 5% means 95% of 0.88x is left.

This means the answer is: 0.88x * 0.95 = 0.836

The percent of the total decrease is 83.6%

Hope this helps :)

Have a great day!

The required perimeter of the trapezoid is22 units.

The given vertices of the trapezoid are (1,3), (4,7), (9,7), and (9,3). To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

We can use the distance formula to find the length of each side of the trapezoid:

[tex]{Side 1: }&(1,3) \text{ to } (4,7) \&d = \sqrt{(4 - 1)^2 + (7 - 3)^2} = \sqrt{9 + 16} = 5 \\\text{Side 2: }&(4,7) \text{ to } (9,7) \&d = \sqrt{(9 - 4)^2 + (7 - 7)^2} = \sqrt{25} = 5 \\\text{Side 3: }&(9,7) \text{ to } (9,3) \&d = \sqrt{(9 - 9)^2 + (3 - 7)^2} = \sqrt{16} = 4 \\\text{Side 4: }&(9,3) \text{ to } (1,3) \&d = \sqrt{(1 - 9)^2 + (3 - 3)^2} = \sqrt{64} = 8\end{align*}[/tex]

Therefore, the perimeter of the trapezoid is:

[tex]$\begin{align*}P &= \text{Side 1} + \text{Side 2} + \text{Side 3} + \text{Side 4} \&= 5 + 5 + 4 + 8 \&= 22\end{align*}[/tex]

Thus, the perimeter of the trapezoid is22 units.

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The three examples of contracts are:

Contracts are legal agreements between two or more parties that involve the exchange of goods, services, or money. They can be classified as unilateral or bilateral, express or implied, executed or executory.

Here are three examples of contracts that a person can be a part of:

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Answer:

To solve the problem, we need to add 23 7/8 and 3 1/2 to find the final price.

First, we need to convert 3 1/2 to an improper fraction:

3 1/2 = (2 x 3) + 1/2 = 7/2

Next, we need to find a common denominator between 8 and 2:

8 = 8/1

2 = 2/1 x 4/4 = 8/4

Now we can add the two fractions:

23 7/8 + 3 1/2

= 23 14/16 + 3 8/16 (using 16 as the common denominator)

= 27 6/16

= 27 3/8

Therefore, the stock was priced at $27 3/8 at the end of trading.

a.

There are 15,504 ways to choose 20 batteries from the given types.

b.

there are 18,564 ways to choose 20 batteries such that at least four of them are 9-volt batteries.

To choose 20 batteries from the given 5 types (aaa, aa, c, d, and 9-volt), we can use the combination formula and is given by:

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

5C20 = 5! / (20! * (5-20)!) = 15,504

there are 15,504 ways to choose 20 batteries from the given types.

b. To choose 20 batteries such that at least four of them are 9-volt batteries, we employ the method:

First, we choose four 9-volt batteries out of the total number of 9-volt batteries, which is 1.

we then need to choose the remaining 16 batteries from the remaining 4 types (aaa, aa, c, and d), while making sure that we don't choose any 9-volt batteries.

Applying the combination formula, with n = 4 and r = 16:

4C16 = 4! / (16! * (4-16)!) = 18,564

Therefore, the total number of ways to choose 20 batteries such that at least four of them are 9-volt batteries is:

1 * 18,564 = 18,564

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The abiotic factor that can prevent the organism from becoming preserved, AFTER it has been buried is groundwater.

An abiotic factor refers to a non-living component of an ecosystem that influences the survival and growth of living organisms.

Groundwater can cause the dissolution of minerals present in the sediment that encases the buried organism.

This process can lead to the destruction of the fossilized remains, as the minerals provide the framework for the preservation of the organism's hard parts (such as bones or shells).

Groundwater can also cause the erosion of the sediment, which can expose the buried remains and make them vulnerable to biotic factors such as scavengers, predators, and decomposers.

Predators and animals that eat bones, scavengers and plants that use the nutrients of fossils, and other animals of the same species as the organism that died are all biotic factors that can affect the preservation of the organism, but they do so before or during the burial process.

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The Length of AB in square ABCD is 30 feet.

Since the squares ABCD and EFGH are similar, their corresponding sides are proportional, so we can set up the following relation:

AB/EF = 1/4

We can also use the fact that the ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides. Therefore,

AB²/EF² = (Area of square ABCD)/(Area of square EFGH)

Substituting the given values:

AB²/EF² = (Area of square ABCD)/(14400)

Since the areas of squares are proportional to the square of their sides, we can write,

Area of square ABCD/Area of square EFGH = (AB/EF)²

Substituting this into the above equation and solving for AB, we get,

AB²/EF² = (AB/EF)²

AB² = (AB/EF)² * EF²

AB² = (1/4)² * 14400

AB² = 900

AB = 30 feet

Therefore, the length of the side AB of square ABCD is 30 feet.

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Daniel's pay for the week was $504.00, which includes his hourly pay and his commission on direct phone sales.

To calculate Daniel's pay for the week, we need to find his total earnings, which include his hourly wage and his commission on direct phone sales.

First, let's calculate his commission on direct phone sales. We know that he received $72.00 in commissions, and we also know that his commission is six percent of his sales. So, we can use the formula:

Commission = Sales x Commission Rate

To find his sales, we can rearrange the formula to:

Sales = Commission / Commission Rate

Plugging in the given values, we get:

Sales = $72.00 / 0.06 = $1200.00

So, Daniel's direct phone sales for the week were $1200.00.

Now, let's calculate his hourly pay. He worked for 48 hours at a rate of $9.00 per hour, so his hourly earnings were:

Hourly Pay = Hours Worked x Hourly Rate

Hourly Pay = 48 x $9.00 = $432.00

Finally, we can add his commission and his hourly pay to find his total earnings for the week:

Total Pay = Hourly Pay + Commission

Total Pay = $432.00 + $72.00

Total Pay = $504.00

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When the minimum volume of a clown is 60,000 cm³ and the volume of a car is 3 million cm³, 55 is an upper bound on the maximum number of clowns that can fit in a car. The correct answer is Option A.

Bounds are the maximum and minimum limits that are permitted, within which something can or must be performed. Bounds are used to refer to an acceptable range of values that provide safe operation or performance. In mathematics, a set of bounds can define the limits of the amount of things or objects.

The minimum volume of a clown is 60,000 cm³, so to fit 55 clowns in a car we need:

55 clowns × 60,000 cm³/clown = 3,300,000 cm³

This is lower than the volume of the car. Therefore, 55 is an upper bound on the maximum number of clowns that can fit in the car.

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Answer:

To find the population in the year 2001, we need to work backwards from the given population of 54,000 in 2003.

Let P be the population in the year 2001. From 2001 to 2003, there are two years, during which the population grows at a rate of 5% per annum. We can calculate the population in 2003 using the formula:

P * (1 + r)^n = 54,000

where r is the annual growth rate (5% or 0.05) and n is the number of years (2). Plugging in the values, we get:

P * (1 + 0.05)^2 = 54,000

Simplifying the equation, we get:

P = 54,000 / (1.05)^2

P = 48,543 (rounded to the nearest whole number)

Therefore, the population in the year 2001 was approximately 48,543.

To find the population in the year 2005, we can use the same formula with n = 2 + 2 = 4 (since we want to find the population four years after 2001):

P * (1 + 0.05)^4 = ?

Plugging in the value of P we just found, we get:

48,543 * (1 + 0.05)^4 = 60,723 (rounded to the nearest whole number)

Therefore, the population in the year 2005 would be approximately 60,723

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Answer:

Length = 53 feet

Width = 22 feet

Step-by-step explanation:

Perimeter = 2(length + width)

Then:

a = 2w + 9            Ec. 1

150 = 2(a + w)       Ec. 2

a = length

w = width

From Eq. 1:

a - 9 = 2w            Eq. 3

From Eq. 2:

150 = 2*a + 2*w

150 = 2a + 2w

150 - 2a = 2w        Eq. 4

Equalizing Eq. 3 and Eq. 4

a - 9 = 150 - 2a

a + 2a = 150 + 9

3a = 159

a = 159/3

a = 53

From Eq. 1:

a = 2w + 9

53 = 2w + 9

53 - 9 = 2w

44 = 2w

44/2 = w

w = 22

Check:

From Eq. 2

150 = 2(a+w)

150 = 2(53+22)

150 = 2*75

As per the given APR, the sum of amount after 18 years is $66,373. 60, and the total deposits made over the time period is  $43,200. (option d).

To calculate this, we can use the formula for future value of an annuity:

FV = PMT x (((1 + r)⁻¹) / r)

where FV is the future value, PMT is the monthly payment, r is the monthly interest rate (which is calculated by dividing the APR by 12), and n is the number of payments (which is 18 x 12 = 216 in this case).

Plugging in the numbers, we get:

FV = $200 x (((1 + 0.045/12)²¹⁶ - 1) / (0.045/12)) = $66,373.60

Therefore, you would have approximately $66,373.60 in your investment plan after 18 years.

Now let's compare this amount to the total deposits made over the time period. In this case, the total deposits would be:

$200 x 12 x 18 = $43,200

Hence the correct option is (d).

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The expression 4 triangles to 16 squares when simplified is 1 triangle to 4 squares

Given that

4 triangles to 16 squares

When expressed as ratio, we have

Triangle : Square = 4 : 16

To simplify the ratio Triangle : Square = 4 : 16, we can divide both the numerator and denominator by their greatest common factor, which is 4.

So, we have

Triangle : Square = 4 : 16

Divide both sides by 4:

Triangle/4 : Square/4 = 1 : 4

So the simplified ratio is 1 : 4, which means for every one triangle, there are four squares.

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The option in the question that is equivalent to 3/8 is 2/5.

We can simplify 3/8 and 2/5 so that they have a common denominator:

3/8 = 3*(5/5)/(85/5) = 15/40

2/5 = 2(8/8)/(5*8/8) = 16/40

Since 15/40 and 16/40 have the same denominator, we can compare their numerators to see which is larger:

15/40 < 16/40

Since 16/40 is larger, we can conclude that 2/5 is greater than 3/8.

Therefore, the option that is equivalent to 3/8 is 2/5.

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Using the property of a kite: the angles formed by two unequal sides of a kite are equal. The value of ∠BCD∠BCD is

∠BCD = ∠BAD ⇒ ∠BCD = 106°  

In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.

According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.

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Answer:

36 × 10^6 m²

Step-by-step explanation:

Given the side length of a square = 6 × 10³m,

To solve for the area of a square, use the following formula:

A = S² where:

S = side of the square

Substitute the given value for the side into the formula:

A = S²

A = (6 × 10³)²

A = 36000000 or 36 × 10^6 m²

NOTE:

6 × 10³ is also the same as 6 × 1000 = 6000,

(6 × 10³)² is essentially 6,000² = 36,000,000

Therefore, its area in square meters is 36 × 10^6

Answer:

7

Step-by-step explanation:

x  + 3 = 10

x + 3 - 3 = 10 - 3

x = 7

The PC is initially worth $3,340.

Given that a computer loses half of its worth after six years, and assuming that value is $835, we must determine the device's original value.

What does the term "starting value" mean?

The starting output value is the initial value.

Let's say that computer's starting value is x.

As a result, after four years,

It is X/2 for the fourth year.

It is X/2 for the fifth year.

It's X/4 in the sixth year.

We stated that the PC will be worth $835 after six years. Hence, we may express it as,

X/4 = $835

X=4( $835)

X= $3,340

Hence, the initial value of the computer is $3,340.

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The vector u2 is (0, √3/3, 2/3). It is a unit vector that is orthogonal to both 8,-8,8 and 0,5,5.

Given two vectors 8,-8,8 and 0,5,5, we need to find another unit vector that is orthogonal to both the given vectors. Let's call this vector u1.The vector u1 can be obtained by taking the cross product of the two given vectors:u1 = (8,-8,8) × (0,5,5)u1 = (-40,-40,40)

To get a unit vector, we need to normalize u1 by dividing it by its magnitude:|u1| = √((-40)² + (-40)² + 40²) = 60u1 = (-40/60, -40/60, 40/60) = (-2/3, -2/3, 1/3)Now we need to find another unit vector that is orthogonal to u1.

One way to do this is to take the cross product of u1 with another vector, and then normalize the result. We can choose any vector that is not parallel to u1. For example, we can choose the vector (1,0,0).u2 = u1 × (1,0,0)u2 = (-2/3, -2/3, 1/3) × (1,0,0)u2 = (0,1/3,2/3)

To get a unit vector, we need to normalize u2 by dividing it by its magnitude:|u2| = √(0² + (1/3)² + (2/3)²) = 1/√3u2 = (0, √3/3, 2/3)

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Refer to pic...........