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Question 4: You are creating an obstacle for a community event. The area of the rectangular space is represented by the expression 8x^2 - 12x. The width of the rectangular space is represented by the expression 4x.
Part A: Write an expression to represent the length of the rectangular space. (1pts)

SHOW ALL WORK TO FIND ALL LENGTHS (3pts) (MANDATORY!)

Answer: Length of Rectangular Space
______________________________
Part B: Prove your answer from Part A is corrected by multiplying the length and width of the rectangle. SHOW ALL WORK!!

Answer Write the expression in standard form:
___________________________________

Answer:C

Step-by-step explanation:

[tex](x-3)^2=5\\we \ should \ find \ square \ root \ of \ each \ side,\\\sqrt{(x-3)^2}=\sqrt{5}\\1)x-3=\sqrt{5}x=\sqrt{5}+3\\2)3-x=\sqrt{5}\\x=3-\sqrt{5}\\\\so,x=3\± \sqrt{5}[/tex]

The value οf a = 3, b=-10, c-8

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm. A nοn-zerο term (a 0) fοr the cοefficient οf x² is a prerequisite fοr an equatiοn tο be a quadratic equatiοn.

The x² term is written first, then the x term, and finally the cοnstant term is written when cοnstructing a quadratic equatiοn in standard fοrm. In mοst cases, the numerical values οf letters a, b, and c are expressed as integral values rather than fractiοns οr decimals.

The equatiοn given 5x²-2=2x²+10x+6

3x²-10x-8=0

values οf a = 3, b=-10, c-8

Hence the value οf a = 3, b=-10, c=8

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(a) P(green or red) = 0.3946

(b) P(blue, red, or yellow) = 0.7606

(c) P(not brown) = 0.7807

(d) P(not green) = 0.6559

What is probability?

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.

The total number of M&M's is 2552.

(a) P(green or red) = P(green) + P(red)

= 364/2552 + 507/2552

= 0.2692

(b) P(blue, red, or yellow) = P(blue) + P(red) + P(yellow)

= 399/2552 + 507/2552 + 351/2552

= 0.4917

(c) P(not brown) = 1 - P(brown)

= 1 - 538/2552

= 0.7891

(d) P(not green) = 1 - P(green)

= 1 - 364/2552

= 0.8575

Hence,

(a) P(green or red) = 0.3946

(b) P(blue, red, or yellow) = 0.7606

(c) P(not brown) = 0.7807

(d) P(not green) = 0.6559

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Answer:

Horizontal distance between the wall and the bottom of ramp = 25.4 inches.

Step-by-step explanation:

Pythagorean theorem:

          AB  -> wall ;  AB =  14 inches    

         AC -> Wooden plank ; AC = 29 inches

        BC -> horizontal distance between the wall and the bottom of ramp(pank).

           Pythagorean theorem,

                       [tex]\boxed{\bf base^2 + altitude^2 = hypotenuse^2}[/tex]

                         BC² + AB² = AC²

                           BC² + 14² = 29²

                          BC² + 196 =  841

                                     BC² = 841 - 196

                                             = 645

                                       BC = √645

                                       BC = 25.4 inches

Horizontal distance between the wall and the bottom of ramp = 25.4 inches.

Given,

Length = 29 inches

Height = 14inches

Here,

Pythagorean theorem:

AB  -> wall ;  AB =  14 inches    

AC -> Wooden plank ; AC = 29 inches

BC -> horizontal distance between the wall and the bottom of ramp (plank).

Pythagorean theorem,

Base²  + Perpendicular² = Hypotenuse²

BC² + AB² = AC²

BC² + 14² = 29²

BC² + 196 =  841

BC² = 841 - 196

= 645

BC = √645

BC = 25.4 inches

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The probability of randomly selecting a temperature between 70 and 75 is approximately 0.8291.

To find the probability that a randomly chosen temperature is between 70 and 75, we need to use the z-score formula as shown below:

z = (x - μ) / σ

Where:x = 70 and 75μ = 79σ = 4z1 = (70 - 79) / 4 = -2.25z2 = (75 - 79) / 4 = -1P(70 < x < 75) = P(-2.25 < z < -1)

To find the probability for the above inequality, we need to use a calculator. We know that the probability of the standard normal distribution is equal to 1.

Hence, P(-2.25 < z < -1) = Φ(-1) - Φ(-2.25) = 0.8413 - 0.0122 ≈ 0.8291. Therefore, the probability is about 0.8291.

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On solving the question we have that We can see that RS + ST = RT, equation  confirming that S is on segment RT: RT = RS + ST = 5 + 10 = 15

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

Because S is on the section RT, we know that RS + ST = RT. As a result, we may construct the following equation:

RS + ST = 3x + 1 + (x + 2) = 15

To simplify this equation, we can combine similar terms:

4x + 3 = 15

Subtraction of 3 from both sides yields:

4x = 12

When we divide both sides by 4, we get:

x = 3

RS = x + 2 = 5 and ST = 3x + 1 = 10 as a result.

We can see that RS + ST = RT, confirming that S is on segment RT:

RT = RS + ST = 5 + 10 = 15

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Answer:

the number 228

Step-by-step explanation:

Let's call the smallest number in the consecutive sequence "x". Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.

If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) or 9x + 36.

We know that the sum of the remaining 9 numbers is 2023, so we can set up the equation:

9x + 36 = 2023

Solving for x, we get:

9x = 1987

x = 221

Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.

If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.

Answer:

12 × 3 = 36

the top of the diagram will also equal 36

138-72=66

66 ÷2= 33

33÷3 =11

therefore x=11

Answer:

perimeter = 138

p=2(138+12)

p=2×150

p=300

x=300

For the equilateral triangles we have:

1) x = 5, y =  √50

2) a = 2, b = √8

3)y = 8, x = √128

4) a = b = 7/√2

We can see some triangles, remember that for a right triangle whose angles are 45°, we have an equilateral triangle.

So the two legs have the same measure.

1) Here we can see that x = 5, and the hypotenuse is given by:

y^2 = 5^2 + 5^2

y^2 = 50

y = √50

2) Here we have a = 2, then the hypotenuse is:

b^2 = 2^2 + 2^2

b^2 = 8

b = √8

3) Here we have y = 8, then the hypotenuse is:

x^2  = 8^2 + 8^2

x^2 = 128

x = √128

On the last triangle we can see that the hypotenuse is 7, and we know that a = b

then:

7^2 = a^2 + b^2

7^2 = a^2 + a^2

49 = 2*a^2

(49/2) = a^2

√(49/2) = a

7/√2 = a = b

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Answer: I THINK 4.

Step-by-step explanation:

Sorry if it is wrong!! :'D

If Bill starts work at 8:15, works until 4:45, and has 90 minutes of breaks. Bill works for 36.25 hours in 5 days.

Work per day typically refers to the amount of time or effort expended by an individual during a typical working day.

First, let's find out how many hours Bill works in one day.

        8 hours and 45 minutes - 90 minutes of breaks

           = 7 hours and 15 minutes

           = 7.25 hours of work per day.

       7.25 hours per day x 5 days = 36.25 hours.

Therefore, Bill works for 36.25 hours in 5 days.

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Using the equation y = 7x , we can compute that when x = 2, y = 14 and when x = 4 , y = 28. So, correct option is B.

The equation y = 7x relates the variables y and x, where y is a function of x. To compute the value of y for a given value of x, we simply substitute that value of x into the equation and solve for y.

When x = 2, we can substitute this value into the equation:

y = 7(2) = 14

Therefore, when x = 2, y = 14.

Similarly, when x = 4, we can substitute this value into the equation:

y = 7(4) = 28

Therefore, when x = 4, y = 28.

So, the correct option is B: When x = 2, y = 14 and when x = 4, y = 28.

In summary, to compute the value of y for a given value of x using an equation, we substitute that value of x into the equation and solve for y. In this case, when x = 2, y = 14, and when x = 4, y = 28, according to the given equation y = 7x.

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The value of q in the question is q>-12/15

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions

The given inequality is 5(p−3q)<12

Opening the bracket we have

5p - 15q < 12

The solution can only be gotten if we assume p = 0

the substitute p=0 in the inequality to have

-15q < 12

dividing both sides by -15 to have

-15q/-15 < 12/-15

therefore q > 12/-15

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The cοrrect answer tο the given questiοn is d. the central limit theοrem.

The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.

The basis fοr using a nοrmal prοbability distributiοn tο apprοximate the sampling distributiοn οf the sample means and pοpulatiοn mean is the central limit theοrem.

The central limit theοrem states that fοr a sufficiently large sample size, the sampling distributiοn οf the sample means will be apprοximately nοrmal, regardless οf the shape οf the pοpulatiοn distributiοn. This theοrem allοws us tο make statistical inferences abοut the pοpulatiοn mean based οn the sample mean using the prοperties οf the nοrmal distributiοn, such as the mean and standard deviatiοn.

Therefοre, the cοrrect answer tο the given questiοn is d. the central limit theοrem.

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From the graphs in the given coordinate plane, the functions that have complex roots are function b, function d and function f.

From the question, we are to determine the functions that have complex roots in the given coordinate plane.

In a quadratic graph, if the vertex of the quadratic function lies above the x-axis, and the parabola opens upward, there will be NO x-intercepts. The graph will have complex roots.

Also, if the vertex of the quadratic function lies below the x-axis, and the parabola opens downward , there will be NO x-intercepts.

The graph will have complex roots.

In the given coordinate plane, the functions that have complex roots are function b, function d and function f.

Hence, the functions b, d, and f have complex roots.

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Answer:

3x+5x=8x

-3t+-t=-4t

3p+3p=6p

2n+n=3n

5g+-g=4g

7y+y=8y

4+12=16

Step-by-step explanation:

e [0.1}

We know that P(X < 2.24) = 0.7257. Also, the mean is 2.Let us calculate the variance of the given normal distribution random variable. Given that P(X < 2.24) = 0.7257, we have to find variance. Let us solve this question as follows:We know that mean of normally distributed random variable is μ and standard deviation is σ. As the mean is 2, μ = 2.We have the z-score: z = (2.24 - 2) / σFrom the normal distribution table, we can find out that P(Z < 0.80) = 0.7881Now, we have the following equation:0.7881 = (2.24 - 2) / σσ = 0.3158Finally, we can find the variance (σ^2) = 0.3158^2 = 0.0995 ≈ 0.1Therefore, the correct answer is option e. 0.1.

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Value of Q3 is approximately 114.1 given mean and standard deviation.

We must identify the IQ score that separates the bottom 9% from the top 91% in order to determine P9. The normal distribution of IQ scores has a mean of 100 and a standard deviation of 15, as is well known. The z-score for the 9th percentile can be calculated using a calculator or a typical normal distribution table.

[tex]z = invNorm(0.09) = -1.34[/tex]

The formula for converting a z-score to an IQ score is as follows:

IQ equals z * standard deviation + mean, or -1.34 * 15 + 100, or 79.1.

P9 is therefore roughly 79.1.

We must identify the IQ score that distinguishes the top 25% from the rest in order to determine Q3. Assuming a normal distribution, IQ values have a mean of 105 and a standard deviation of 15. Since the top 25% and the 75th percentile are the same, we can use a calculator or a conventional normal distribution table to determine the z-score that represents the 75th percentile:

[tex]z = invNorm(0.75) = 0.67[/tex]

We can then use the formula for transforming a z-score to an IQ score:

IQ = z * standard deviation + mean = 0.67 * 15 + 105 = 114.05

Therefore, Q3 is approximately 114.1.

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The surface area οf the cοntainer is 314 ft².

A rectangle is a geοmetric shape that has fοur sides and fοur right angles (90 degrees) with οppοsite sides being parallel and equal in length. It is a type οf quadrilateral, a pοlygοn with fοur sides.

Tο find the surface area οf a rectangular prism, we need tο add the areas οf all six faces. The fοrmula fοr the surface area οf a rectangular prism is:

Surface area = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height οf the rectangular prism.

Substituting the given values, we get:

Surface area = 2(5)(9) + 2(5)(8) + 2(9)(8)

Surface area = 90 + 80 + 144

Surface area = 314 square feet

Therefοre, the surface area οf the cοntainer is 314 ft².

Answer: 314 ft².

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Answer:

28

x 76

----

168 (units digit of 76 multiplied by 28)

1408 (tens digit of 76 multiplied by 28)

----

2128

Therefore, 28x76 is equal to 2128.

Step-by-step explanation:

The weight of the smaller dog is 5.6 pounds.

Let the weight of the smaller dog be x, then,

The weight of the larger dog = 1.4 pounds.

The combined weight of the dogs =  12.6 pounds.

Therefore,

The sum of the weight of the larger dog and smaller dog = the combined weight of the dogs.

That is,

1.4 + x + x = 12.6

1.4 + 2x =  12.6

2x = 12.6 - 1.4

2x = 11.2

x = 11.2 ÷ 2

x = 5.6.

Hence, the weight of the smaller dog is 5.6 pounds.

?

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Your question is incomplete, and the complete question would be:

Karen has two dogs. the larger dog weighs 1.4 pounds more than the smaller dog. the combined weight of the two dogs is 12.6 pounds. what is the weight of the smaller dog?

Answer:

9 hope u get it right budddyyyy

a) The populations in 1980, 1990, 2000, and 2010 are 157,000, 218,000, 269,000, and 308,000 respectively.

b) the population will reach 390,000 in 270 years

c) No, as t increases, the population increases rapidly

(a) To find the population in 1980, 1990, 2000, and 2010, we substitute the corresponding values of t into the given model and round the answers to the nearest whole number.

Population in 1980: P = 75.9e^(0.0316*10) = 156,604

Population in 1990: P = 75.9e^(0.0316*20) = 217,643

Population in 2000: P = 75.9e^(0.0316*30) = 269,099

Population in 2010: P = 75.9e^(0.0316*40) = 308,227

(b) To find when the population of Horry County will reach 390,000, we need to solve the equation 390 000 = 75.9e^(0.0316t) for t.

Taking the natural logarithm of both sides, we get:

ln(390,000/75.9) = 0.0316t

Simplifying, we get:

t = ln(390,000/75.9)/0.0316 ≈ 270.395

Rounding down to the nearest whole year, we get that the population will reach 390,000 in 270 years

(c) The model assumes that the population growth rate will remain constant over time. However, in reality, population growth rates can be affected by a variety of factors, such as changes in birth and death rates, immigration, emigration, and natural disasters.

Therefore, it is unlikely that the model will be valid for long-term predictions of the population. The model can provide a good estimate of the population for the short-term, but it is not reliable for predictions far into the future.

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For no solution 7x+10

For one solution8x+0

For infinite solution 7x+5

An infinite solution is a solution to a system of equations that has an infinite number of possible solutions. In other words, any value for the variables in the system will satisfy all the equations.

2x+5+2x+3x

On adding the values with variables, x=7

On adding constant values=5

2x+5+2x+3x=7x+5

For no solution

7x+5=7x+10

For one solution

7x+5=8x

x=5

For infinite solution

7x+5=7x+5

Hence, For no solution 7x+10

For one solution 8x+0

For infinite solution 7x+5.

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The grouping of data  or sample points is a component of the machine learning process known as clustering.

The task of arranging a set of objects into an identical group in a way that makes them more similar to one another than those found in different groups is known as cluster analysis or clustering.

A scatter plot is an unique type of plot or mathematical diagram that displays data for usually 2 parameters for a collection of data. It uses Cartesian coordinates.

Coordinates, it is a set or group of values that show an exact or accurate position.

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For given quadratic equation, the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.

What exactly are quadratic equations?

A quadratic equation is a second-degree polynomial equation of the form:

ax²+ bx + c = 0

where x is the variable and a, b, and c are constants, with a ≠ 0. The term "quadratic" comes from the Latin word "quadratus", which means "square". In other words, a quadratic equation is an equation that involves the square of the variable x.

Now,

We are given that the profit of the company (in millions of dollars) can be represented by the equation y = x² - 16x + 67, where x is the number of years since the company started.

We want to find when the company had a profit of 7 million dollars.

So, we can set y = 7 in the equation:

7 = x² - 16x + 67

Rearranging and simplifying:

x² - 16x + 60 = 0

Now, we can solve for x using the quadratic formula:

x = (-(-16) ± √((-16)^2 - 4(1)(60))) / 2(1)

x = (16 ± √(16)) / 2

x = 8 ± 2

Therefore, the solutions are x = 10 or x = 6.

This means that the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.

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The sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]

What is sum?

In mathematics, the term "sum" refers to the result obtained by adding two or more numbers or quantities together. It also be used to refer to the total amount of something, such as the sum of money you have in your bank account, or the sum of the lengths of all the sides of a polygon.

To find the sum or difference of [tex]-2x^2+x+6 + (5x^2-4x-2)[/tex] we need to combine like terms.

[tex]-2x^2+x+6 + (5x^2-4x-2) &\\\\= (-2x^2 + 5x^2) + (x - 4x) + (6 - 2)[/tex]

[tex]&= 3x^2 - 3x + 4[/tex]

Therefore, the sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]

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Step-by-step explanation:

Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?

Answer:

a. When x > k, the cost of running the ad for a week can be expressed as:

C = p + e(x - k)

where C is the cost in dollars, p is the cost per k lines, e is the cost per extra line, and (x - k) is the number of extra lines over k.

b. When x ≤ k, the cost of running the ad for a week can be expressed as:

C = p

where C is the cost in dollars and p is the cost per k lines. Since the number of lines x is less than or equal to k, there are no extra lines and the cost is simply the base cost of p dollars for k lines.

Hope this helped! I'm sorry if it's wrong. If you need more help, ask me! :]

The equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex] and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex]

A mathematical equation, such as 6 x 4 Equals 12 x 2, states that two quantities or units are similar. A noun that ranks. When two or more components must be taken into account together in to fully understand or describe the whole scenario, this is known as an equation.

a) To find the equation of the straight line shown, we need to determine its slope (or gradient) and [tex]y-[/tex]intercept. We can do this by choosing two points on the line and using the point-slope formula:

slope [tex]=[/tex] (change in y) / (change in x)

Let's choose the points [tex](1, 3)[/tex] and [tex](4, 7)[/tex] from the line.

slope [tex]= (7 - 3) / (4 - 1) = 4 / 3[/tex]

Now we can use the point-slope formula with one of the points to find the equation:

[tex]y - y1 = m(x - x1)[/tex]

where m is the slope and (x1, y1) is one of the points on the line.

Let's use the point (1, 3):

[tex]y - 3 = (4/3)(x - 1)[/tex]

Simplifying:

[tex]y = (4/3)x + 1[/tex]

So, the equation of the straight line shown is [tex]y = (4/3)x + 1[/tex].

b) To complete the statement "[tex]y = 3x + 5[/tex] passes through [tex](0, -5)[/tex]", we need to substitute [tex]x = 0[/tex] and [tex]y = -5[/tex] into the equation and verify that it is true:

[tex]y = 3x + 5[/tex]

[tex]-5 = 3(0) + 5[/tex]

[tex]-5 = 5 - 5[/tex]

[tex]-5 = -5[/tex]

Since the equation is true, we can say that the point [tex](0, -5)[/tex] is on the line [tex]y = 3x + 5[/tex].

c) We know that the gradient of the line we want to find is the same as [tex]y = 3x + 5[/tex], which is [tex]3[/tex]. We also know that it passes through the point [tex](0, 12)[/tex].

Using the point-slope formula with [tex]m = 3[/tex] and [tex](x1, y1) = (0, 12)[/tex]:

[tex]y - 12 = 3(x - 0)[/tex]

Simplifying:

[tex]y = 3x + 12[/tex]

So, the equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex]and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex].

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