Need help with Algebra I

 [tex]3(x+1)(x+7)-(2x+5)^2[/tex] is never positive for any value of x, since it is equal to  [tex]-x^2+4x-4.[/tex]

To prove that  [tex]3(x+1)(x+7)-(2x+5)^2[/tex] is never positive, we can use algebraic manipulation and some basic concepts of quadratic equations.

First, let's expand the expression and simplify:

[tex]3(x+1)(x+7)-(2x+5)^2 = 3(x^2+8x+7)-(4x^2+20x+25)[/tex]

[tex]= 3x^2+24x+21-4x^2-20x-25[/tex]

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

Now we want to show that this expression is never positive for any value of x.

We can start by considering the discriminant of the quadratic expression -x²+4x-4, which is b²-4ac, where a = -1, b = 4, and c = -4. The discriminant is:

[tex]b^2-4ac = 4^2-4(-1)(-4) = 16-16 = 0[/tex]

Since the discriminant is zero, the quadratic equation [tex]-x^2+4x-4[/tex]  has a double root, which means that it touches the x-axis at exactly one point.

Since the coefficient of x² is negative, this means that the parabola opens downward, which implies that the function has a maximum value at the vertex. The x-coordinate of the vertex is given by -b/2a, which in this case is x [tex]= -4/-2 = 2[/tex] .

So, we can conclude that the expression   [tex]-x^2+4x-4[/tex]  is never positive for any value of x, since it has a maximum value of -4 at  [tex]x = 2[/tex] .

Therefore,  [tex]3(x+1)(x+7)-(2x+5)^2[/tex] is never positive for any value of x, since it is equal to [tex]-x^2+4x-4[/tex] .

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Hence [tex]3(x+1)(x+7)-(2x +5)^{2}[/tex] = -1 ([tex]x^{2} + 4x -4[/tex]) as the leading coefficient is -1, therefore is never positive.

Expanding the first and second term and then simplifying it we get,

To solve this equation first we need to simplify the equation and then we need to subtract the simplified term.

[tex](x+1)(x+7) = x^{2} +8x+7\\3(x^{2} +8x+7)=3x^{2} +24x+21\\(2x+5)^{2} =(2x+5)(2x+5)= 4x^{2} +20x+25\\(3x^{2} +24x+21) - (4x^{2} +20x+25)= -x^{2} + 4x - 4 =-1(x^{2} -4x+4)= -1((x+2)(x+2))[/tex]

Because it is always multiplied with -1

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The statement cannot be determined from the graph, the reason is that the graph shows only the chances of survivals of Albertosaurus and it does not define the life span of the Albertosaurus.

When we carefully asses the graph, according to the information provided, the mortality rate of Albertosaurus dinosaurs between 25% and 50% of their maximum life span was significantly higher than the mortality rate of dinosaurs who lived to 75% of their maximum life span. This conclusion cannot be inferred from the graph because it only depicts the possibilities of survival for Albertosaurus and does not specify how long they lived.

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8 people in Malik's apartment building like to eat macaroni and cheese or cookies or both

Of the people in Malik's apartment building, 4 like to eat macaroni and cheese, and 7 like to eat cookies.

Three people like to eat both macaroni and cheese and cookies.

To determine how many people like to eat macaroni and cheese or cookies or both, we will employ the principle of inclusion-exclusion.

In Malik's apartment building, to find out how many people like to eat macaroni and cheese, or cookies, or both, we can follow these steps:
Identify the number of people who like macaroni and cheese (4 people) and cookies (7 people).
Determine the number of people who like both macaroni and cheese and cookies (3 people).
Calculate the total number of people who like either macaroni and cheese or cookies by adding the number of people who like macaroni and cheese (4 people) and the number of people who like cookies (7 people).
4 people + 7 people = 11 people
Subtract the number of people who like both macaroni and cheese and cookies (3 people) from the total calculated in Step 3 to avoid double-counting those who like both.
11 people - 3 people = 8 people

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The Perimeter of the rectangle shaped field is 16x+32 unit.

What exactly is a rectangle?

A rectangle is a four-sided, two-dimensional geometric object with four right angles (90-degree angles) and opposing parallel and equal-length sides. Rectangles are classified as a type of quadrilateral, which is any four-sided polygon.

The opposite sides of a rectangle are also congruent, meaning that they have the same length, and all four angles are congruent, meaning that they have the same measure of 90 degrees. The area of a rectangle can be calculated by multiplying the length and width of the rectangle, while the perimeter can be calculated by adding the lengths of all four sides.

Now,

Given rectangular field has

length = 5x+10

Breadth = 3x+6

As we know Perimeter of a rectangle = 2(L+B)

P=2*(5x+10+3x+6)

P=2(8x+16)

P=16x+32

Hence,

          The Perimeter of the field is 16x+32.

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E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .

To calculate the variance of y, follow these steps:

Recall that for a Poisson distribution, the mean (first moment) is equal to the variance. So, if the first moment of x is less

than the first moment of y by 8, we can write: E(x) = E(y) - 8.

We are also given that the second moment of x is 60% of the second moment of y:

[tex]E(x^2) = 0.6 × E(y^2).[/tex]

Recall that for a Poisson distribution, the second moment is given by [tex]E(X^2) = E(X)² + E(X)[/tex]. Thus, we can write equations

for x and y using this relationship: [tex]E(x^2) = E(x)² + E(x) and E(y^2) = E(y)² + E(y).[/tex]

Plug the expressions from step 1 into the equation from  [tex]E(x^2) = (E(y) - 8)² + (E(y) - 8).[/tex]

Plug the expressions from step 2 into the equation from[tex]0.6 × E(y^2) = (E(y) - 8)² + (E(y) - 8).[/tex]

Solve for [tex]E(y^2)[/tex] from the equation in  [tex]E(y^2) = (10/6) × ((E(y) - 8)² + (E(y) - 8)).[/tex]

Substitute [tex]E(y^2)[/tex] back into the equation for the second moment of y from [tex]E(y^2) = E(y)² + E(y).[/tex]

Solve for E(y) from the equation in

Since E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .

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The radius of each circle is approximately 3.46 units.

Since the two circles are congruent and tangent to each other, their centers are located on the same line perpendicular to the side of the square.

Let the center of each circle be O and the point where the circles are tangent be T. Then, the radius of each circle is equal to the distance from O to T.

Drawing a line from O to T, we can see that it forms a right triangle with one leg equal to the radius of the circle and the other leg equal to half the side length of the square. Using the Pythagorean theorem, we can solve for the radius:

[tex]r^2 + (2)^2 = (4)^2r^2 = 12\\[/tex]

r ≈ 3.46

Therefore, the radius of each circle is approximately 3.46 units, rounded to the nearest hundredth.

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In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding up all the values in the data set and dividing by the total number of values. The mean is also known as the arithmetic mean or average.

The formula for the mean is:

mean = (sum of all values) / (total number of values)

1.To find the mean of these scores, we add them up and divide by the total number of scores:

Mean = (83 + 97 + 85 + 84 + 96 + 80 + 80 + 87 + 91) / 9 = 86

2.To find the median, we first need to put the scores in order from lowest to highest:

80, 80, 83, 84, 85, 87, 91, 96, 97

The median is the middle score, which in this case is 85.

3.To find the mode, we look for the score that occur most frequently. In this case, there are two modes: 80 and 85, each occurring twice.

4.To find the range, we subtract the lowest score from the highest score:

Range = 97 - 80 = 17

Therefore, the mean is 86, the median is 85, the mode(s) are 80 and 85, and the range is 17.

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Answer: Number 10 is you are a rectangle

Step-by-step explanation:

The parameter of interest is the difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer.

The difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer.

This parameter represents the average difference in reaction times between the two groups - those who did not drink beer and those who drank two cans of beer. It is a measure of the effect that drinking two cans of beer has on reaction times, and it is the focus of the hypothesis test being conducted.

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Answer:

x = 122

Step-by-step explanation:

the measure of the chord- chord angle 125° is half the sum of the arcs intercepted by the angle and its vertical angle, that is

125 = [tex]\frac{1}{2}[/tex] (x + 6 + x) ← multiply both sides by 2 to clear the fraction

250 = 2x + 6 ( subtract 6 from both sides )

244 = 2x ( divide both sides by 2 )

122 = x

The measure of central tendency is the most appropriate for this data is median.

There are a few different measures of central tendency to choose from, but the most common ones are the mean, median, and mode.

The mean is the arithmetic average of the data. To find the mean, you would add up all the values and divide by the total number of values. However, the mean can be sensitive to outliers or extreme values, which could skew the results. In this case, there are no extreme values, but the data is not evenly distributed across the three groups, so the mean may not be the best measure of central tendency to use.

The median is the middle value of the data when it is arranged in order from smallest to largest.

This can be a better measure of central tendency when the data is not evenly distributed. In this case, we can find the median by arranging the data in order: 25, 125, 250. The middle value is 125, which means that half of the pet owners surveyed own fewer than 125 pets, and half own more than 125 pets.

So, the median might be a good choice of measure of central tendency in this case.

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Step-by-step explanation:

Area of the TWO ends are each 1/2 b*h = 1/2 * 16 * 6 =48 in^2

    TWO of them would be   2 * 48 = 96 in^2

Then there are 3 sides

   two are  10 * 12  = 120

       two would be    120 x 2 = 240 in^2

     and ONE side 16 * 12 = 192 in^2

Total area is then   96 + 240 + 192 = 528 in^2

The surface area of the triangular prism is 168 square feet.

Surface area is the total area that the surface of a three-dimensional object occupies in space. It is a measure of the amount of material that would be needed to cover the entire surface of the object.

To find the surface area of the triangular prism, we need to find the area of each of its faces and add them together.

The triangular faces have an area of [tex]\frac{1}{2}bh[/tex], where b is the base and h is the height. In this case, the triangular faces have a base of 6 feet and a height of 4 feet, so their area is:

=>[tex]\frac{1}{2}\times6\times4=12ft^2[/tex]

There are two triangular faces, so their total area is [tex]2\times12=24ft^2[/tex]

The rectangular faces have an area of lw, where l is the length and w is the width. In this case, the rectangular faces have dimensions of 9 feet by 5 feet, so their area is:

=> [tex]9\times5=45ft^2[/tex]

There are two rectangular faces, so their total area is

=> [tex]2\times45=90ft^2[/tex]

Finally, the base of the triangular prism is a rectangle with dimensions of 6 feet by 9 feet, so its area is:

=> [tex]6\times9 = 54 ft^2[/tex]

Adding up the areas of all the faces, we get:

=>[tex]24 ft^2 + 90 ft^2 + 54 ft^2 = 168 ft^2[/tex]

Therefore, the surface area of the triangular prism is 168 square feet.

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Answer:

I'm sorry, it is unclear what you are asking. Can you please provide more context or clarify your question?

Step-by-step explanation:

Answer:

2.2 Cm

Step-by-step explanation:

Answer:

the answer is 1.9

Step-by-step explanation:

10 minus 8.1 equals 1.9 because the smallest crocus is 8.1 and the largest is 10 so you subtract those two to find the difference, thank me later!

The sum of the squares of JE and EN is approximately 32. Therefore, we can conclude that the triangle formed by J, E, and N is indeed an isosceles right triangle.

An isosceles right triangle is a triangle that has two sides of equal length and one right angle. In this case, we are given the coordinates of three points J(-4,1), E(-2,-3), and N(2,-1) and we need to determine if the triangle formed by these points is an isosceles right triangle.

Firstly, we need to calculate the length of each side of the triangle. We can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2-x1)^2 + (y2-y1)^2).

Using this formula, we can find that the length of JE is approximately 4.472, the length of EN is approximately 4.472, and the length of JN is approximately 5.657.

Since two sides of the triangle (JE and EN) have the same length, the triangle is indeed isosceles. To determine if it is also a right triangle, we need to check if one of the angles is a right angle.

We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can see that JN is the longest side and its length squared is approximately 32. Therefore, we need to check if the sum of the squares of JE and EN is also approximately 32.

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Answer:

[tex] < 2 \: and \: <7[/tex]

Therefore, the prism's base can be either 9 x 9 inches, 6 x 6 inches, or

4 x 4 inches in size.

.

The amount of space that an object's surface takes up in total is measured by its surface area. It is usually expressed in square units, such as square inches or square metres.The surface area of a three-dimensional object can be determined by adding up the areas of all of its faces.

For instance, the surface area of a rectangular prism can be calculated using the formula below:

A = lw + lh + lw

The formula SA = 2lw + 2lh + 2wh, where l is the prism's length, w is its width, and h is its height, determines the surface area of a rectangular prism. Inputting the values provided yields:

306 is equal to 2l + 2(24) + 2(24) + 48

306 - 48l = 2w(l+24) 153 - 24

l = wl + 48w 153 - 48w = l(w+24) 153 - 24l - 48w = wl

We can identify all potential values of l and w that meet this equation because they are both whole numbers. Since it is a rectangular prism with a square base, we know that l > w. Given that the surface area cannot be more than 306, we also know that l(w+24) 153. We may therefore begin by identifying all variables of (153-48w) bigger than w.and equal to or less than 12 (since w cannot be greater than 12). We get:

W=1, L=9, L=2, L=6, and L=3

Therefore, the prism's base can be either 9 x 9 inches, 6 x 6 inches, or 4 x 4 inches in size.

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The probability that the grocer arranges the fruits in alternating order is 5/16.

It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

There are only two ways that the fruits can be arranged in alternating order: apple-orange-apple-orange-apple-orange-apple-orange or orange-apple-orange-apple-orange-apple-orange-apple.

Let's consider the first case where the first fruit is an apple. The probability of this happening is 1/2 since there are 10 total fruits and 5 of them are apples. Once the first fruit is chosen, there are 4 apples and 5 oranges left. The next fruit must be an orange, which has probability 5/9 of occurring since there are now 9 fruits left and 5 of them are oranges. The third fruit must be an apple, which has probability 4/8 (or 1/2) of occurring since there are 8 fruits left and 4 of them are apples. Continuing in this way, we get the following probability:

(1/2) * (5/9) * (4/8) * (4/7) * (3/6) * (3/5) * (2/4) * (2/3) * (1/2) * 1

The second case where the first fruit is an orange is the same as the first case but with the roles of apples and oranges reversed. So the probability of arranging the fruits in alternating order is:

(1/2) * (4/9) * (5/8) * (3/7) * (4/6) * (2/5) * (3/4) * (1/3) * (2/2) * 1

Simplifying both expressions, we get:

(5!/(4!1!)) * (4!/(2!2!)) * 1/(2^5) + (5!/(4!1!)) * (4!/(2!2!)) * 1/(2^5)

= 10/32 + 10/32

= 5/16

Therefore, the probability that the grocer arranges the fruits in alternating order is 5/16.

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If buses arrive at stop at "15-minute" intervals, then the probability that he waits more than 10 minutes for a bus is "1/3".

Let us denote the arrival-time of the passenger by X, where X is uniformly distributed between 7am and 7:30am. hence, the probability-density-function (pdf) of "X" is written as :

f(x) = 1/30, for 7am ≤ x ≤ 7:30am

f(x) = 0, otherwise

We observe that, the passenger will wait for more than 10 minutes for a bus only if he arrives between 7:00 a.m. and 7:05 a.m. , or between 7:15 a.m. and 7:20 a.m.

So, the probability for waiting time can be written as ;

⇒ [tex]\int\limits^5_0 {\frac{1}{30} } \, dx[/tex] + [tex]\int\limits^{20}_{15} {\frac{1}{30} } \, dx[/tex],

⇒ (1/30)(5 - 0) + (1/30)(20 - 15);

⇒ 1/3.

Therefore, the required probability is 1/3.

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The given question is incomplete, the complete question is

Buses arrive at a specified stop at 15-minute intervals starting at 7am. If a passenger arrives at the stop at a time that is uniformly distributed between 7am and 7:30am, find the probability that he waits more than 10 minutes.

Answer:

Step-by-step explanation:

-16-5x=-16. please help

-16 - 5x = -16

5x = -16 + 16

5x = 0

x = 0 : 5

x = 0

------------------

check

-16 - 5  × 0 = -16           (remember PEMDAS)

-16 = -16

the answer is good

Answer:

x = 0

Step-by-step explanation:

- 16- 5x = - 16

+ 16        + 16

   - 5x = 0

x = 0

Step-by-step explanation: I hope this helps.

Answer:

A histogram is a basic statistical tool that graphically shows the frequency or number of observations of a particular value or within a specified group.

A histogram is a chart that displays data by dividing it into intervals, or "bins," and then counting how many data points fall into each bin. The x-axis of a histogram represents the range of values being analyzed, while the y-axis represents the frequency or count of values that fall within each bin.

Histograms are commonly used to illustrate the distribution of data. They provide a visual representation of the central tendency, variability, and shape of the data. In particular, histograms can reveal patterns in the data such as skewness, outliers, or gaps.

Histograms are frequently used in data analysis across many fields, including finance, biology, psychology, and engineering. They can be created using software programs such as Microsoft Excel, R, Python, or MATLAB.

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The given question is incomplete, the complete question is:

A(n)______ is a basic statistical tool that graphically shows the frequency or number of observations of a particular value or within a specified group

To find the third side length, we can use the fact that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. So we can write: (z + 13) + (2z + 6) > third side Simplifying the left side, we get: 3z + 19 > third side Now we also know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can write: (z + 13) + (2z + 6) + third side = 8z + 11 Simplifying this equation, we get: 3z + 19 + third side = 8z + 11 Subtracting 3z + 19 from both sides, we get: third side = 5z - 8 Therefore, the

Answer:

827.0 cm³

Step-by-step explanation:

The question we are told is to find the volume of water that can fill the paper cup. This means that we have to find the volume of a cylinder (the cup).

1) understand the equation for volume of a cylinder

The formula for the volume of a cylinder is πr²h

The radius would be half the diameter, which is 4.5, and h would be the height which is 13.

2) Solve

This means our working out would be...

3) Round

We have to round this to the nearest tenth which would be 827.0 or 827!

Hope this helps, have a lovely day! :)

Answer:

Step-by-step explanation:

You want the mass of cashews and pecans in a box that sells for $136 if there are 3 fewer kg of cashews at $11.25 per kg than of pecans at $13 per kg.

Let c represent the mass of cashews in kg. Then (c+3) is the mass of pecans. The total value of the mix is ...

  11.25c +13(c +3) = 136

Simplifying the equation gives ...

  24.25c +39 = 136

  24.25c = 97

  c = 4

The mix should contain 4 kg of cashews and 7 kg of pecans.

The area of the given figure is 44 units.

Answer:

Step-by-step explanation:

The side TU of the right triangle is 156.15 metres and the area of the triangle is  6168.07 metres squared.

The side GH of the right triangle is 182.33 metres and the area of the triangle is  8934.27 metres².

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The missing side of the right triangle can be found using Pythagoras's theorem.

Therefore,

a² + b² = c²

where

The area of the right triangle can be found using the formula as follows:

area of a triangle = 1 / 2 bh

where

Hence,

1.

TU² = 175² - 79²

TU² = 30625 - 6241

TU² = 24384

TU = √24384

TU = 156.153770368

TU = 156.15 metres

Area = 1 / 2 × 156.15 × 79

area = 6168.07392952

area = 6168.07 metres squared

2.

GH² = 207² - 98²

GH² = 42849 - 9604

GH = √33245

GH = 182.33211456

GH = 182.33 metres

Area of the triangle  = 1 / 2 × 98 × 182.33

Area of the triangle  = 8934.27361345

Area of the triangle  = 8934.27 metres²

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It would be very surprising to observe a random sample of 30-time intervals between eruptions with a mean of 97 minutes, given the population mean and standard deviation.

Based on the information provided, we know that the mean time between eruptions of Old Faithful is 85 minutes and the standard deviation is 21 minutes. We are also given a sample of 30-time intervals between eruptions, and we want to determine whether it would be surprising to observe a sample mean of 97 minutes.

To answer this question, we need to calculate the standard error of the mean (SEM), which is given by the formula:

SEM = σ / sqrt(n)

where σ is the population standard deviation (21 minutes), and n is the sample size (30). Plugging in the values, we get:

SEM = 21 / sqrt(30) ≈ 3.84

Next, we calculate the z-score for a sample mean of 97 minutes, using the formula:

z = (x - μ) / SEM

where x is the sample mean (97 minutes), μ is the population mean (85 minutes), and SEM is the standard error of the mean (3.84 minutes). Plugging in the values, we get:

z = (97 - 85) / 3.84 ≈ 3.13

Finally, we can look up the probability of observing a z-score of 3.13 or more extreme in a standard normal distribution table (or using a calculator or software). The probability turns out to be very small, less than 0.01.

Therefore, Given the population mean and standard deviation, it would be very unexpected to find a random selection of 30-minute gaps between eruptions with a mean of 97 minutes. This suggests that the sample may not be representative of the population, or there may be some other factors affecting the intervals between eruptions.

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