one side of a square is (-3n+7). what is its perimeter?

The solution to the inequality expression x + 1 ≥ 3 and 4/3x < -8 in interval notation is (-6, 2]

The inequality expression is given as

x+1 >_ 3 or 4/3x < -8

Rewrite the given expression properly

So, we have the following representation

x + 1 ≥ 3 or 4/3x < -8

Evaluate the like terms in the above expression

This gives

x ≥ 2 or 4/3x < -8

Make the coefficient of x 1

So, we have

x ≥ 2 or x < -6

Rewrite as

2 ≤ x or x < -6

Combine the inequalities

2 ≤ x < -6

Express as interval

(-6, 2]

Hence, the solution is (-6, 2]

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Answer:

c

Step-by-step explanation:

the maximum value for f(x) is only 8.

Answer:

it's the maximum value is the same for both functions

The domain of a function is defined as the set of input values a function can take.

In the case of our function, the domain is all the values contained in the ellipse on the left.

These values are

which is our domain. The answer we got matches choice B; therefore, choice B is the correct answer.

The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. \(2^3\) {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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Answer:

Inequality: y <= 15x

Step-by-step explanation:

y <= 15x

This means the profit per items is no more than 15 per item

The area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

To find the area of the surface obtained by rotating the circle

\(x^2 + y^2 = r^2\) about the line y = r, we can use the method of cylindrical shells.

The circle \(x^2 + y^2 = r^2\) is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.

When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.

Consider a small strip on the circle at a distance y from the line y = r.

This small strip is at a distance r - y from the y-axis.

The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).

The width of this strip is the change in x, which we can denote as dx.

The area of this small strip is then given by the product of its length and width, which is 2πy dx.

Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):

Total Surface Area = ∫[from -r to r] 2πy dx

Now, we need to express y in terms of x using the equation of the circle \(x^2 + y^2 = r^2:\\y^2 = r^2 - x^2\)

y = ±√(r² - x²)

Since we are considering the upper half of the circle, we take the positive square root:

y = √(r² - x²)

Now, we can rewrite the integral with respect to x:

Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx

To solve this integral, we can make a trigonometric substitution:

Let x = r sin(θ), then dx = r cos(θ) dθ.

When x = -r, θ = -π/2, and when x = r, θ = π/2.

Now the integral becomes:

Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ

Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ

Now, we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

√(1 - sin²(θ)) = cos(θ)

Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ

Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2

Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ

Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]

Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]

Since sin(π) = 0 and sin(-π) = 0:

Total Surface Area = 2πr² [(π/2 - (-π/2))/4]

Total Surface Area = 2πr² (π/2)

Total Surface Area = π²r²

So, the area of the surface obtained by rotating the circle \(x^2 + y^2 = r^2\) about the line y = r is π²r² square units.

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Answer:

d  138

Step-by-step explanation:

<5 is vertical to <2, so they are congruent.

<2 is corresponding to the 138° angle, so they are congruent.

m<5 = m<2 = 138°

Answer: d  138

Answer:

and independent variable It is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable. and a Just like an independent variable, a dependent variable is exactly what it sounds like. It is something that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it.

Step-by-step explanation:

The kinetic energy = 1/2 mv^2      starts at zero

  the work required is the kinetic energy the ball attains

    6.3 ounce = 6.3 /16 = .39375 lb

KE = 1/2 ( .39375 lb)/ ( 32.2 ft/s^2)  *  ( 85 ft /s)^2 = 44.17 ft-lbs

Answer:

\(W=59.7408J\)

Step-by-step explanation:

From the question we are told that:

Force \(f=4N\)

Force Direction \(\arrow (4,-2)\)

Distance traveled \(d_t=7ft \aprrox\ 2.1336m\)

Distance traveled Direction point (0,4) to point (5,-1)

Generally the equation for work done is mathematically given by

 \(W=force*distance\)

 \(W=f*d_t\\W=4*7*2.1336\)

 \(W=59.7408J\)

The length of each piece of fabric is, 3/4 yards.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

There are 3 pieces of fabric.

And, The total length of the pieces of fabric is 2 1/4 yards.

Here,  Each piece of fabric is the same length.

Hence, The length of each piece of fabric is,

⇒ 2 1/4 ÷ 3

⇒ 9/4 × 1/3

⇒ 3/4 yards

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Answer:

12

Step-by-step explanation:

The whole pizza comprises 360°

If each piece comprises 30°  of the circle, there will be ;

360 / 30   = 12 pieces

the volume of the solid that lies between the paraboloid 2 2 zx y and the sphere 2 22 xyz 2 is (4/15)π.

To find the volume of the solid between the paraboloid and the sphere, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the paraboloid is 2z = r^2 and the equation of the sphere is x^2 + y^2 + z^2 = 2r^2.

We can rewrite the sphere equation as z = (2-r^2)/2 and set it equal to the equation of the paraboloid, giving us:

2r^2 = r^2 + y^2

Simplifying this expression, we get:

y^2 = r^2

This means that the solid lies within the cylinder y^2 + z^2 = 2r^2.

To find the limits of integration, we need to determine the range of r, theta, and z that define the solid. The sphere has a radius of √2, so we know that r must be less than or equal to √2. For theta, we can integrate from 0 to 2π.

To find the limits of integration for z, we need to determine the range of z values for a given r and theta. Substituting r^2/2 for z in the equation of the sphere, we get:

x^2 + y^2 + (r^2/2)^2 = 2r^2

Simplifying this expression, we get:

x^2 + y^2 = (3/4)r^2

This means that for a given r and theta, z can vary from r^2/2 to √(2 - (3/4)r^2).

To find the volume of the solid, we can integrate the function r from 0 to √2, theta from 0 to 2π, and z from r^2/2 to √(2 - (3/4)r^2), using the formula for volume in cylindrical coordinates:

V = ∫∫∫ r dz dr dθ

Evaluating this integral, we get the volume of the solid as (4/15)π.

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Answer:

the shorter leg = 9mm

the longer leg = 12mm

the hypotenuse is 15mm

Step-by-step explanation:

x^2 +(x+3)^2 =(x+6)^2

x^2 + x^2 + 6x +9=x^2 + 12x +36

x^2-6x-27=0

(x+3)(3-9)=0

x=-3 (impossible) ... or x=9

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

                             ( -∞ , ∞ )

Set-Builder Notation:

                                  { x | x ∈ R }

The range is the set of all valid  y  values. Use the graph to find the range.

Interval Notation:

                               ( -∞ , ∞ )

Set-Builder Notation:

                                 { y | y ∈ R }

Determine the domain and range.

Domain:  ( −∞ , ∞ ), { x | x ∈ R }

Range:  ( −∞ , ∞ ), { y | y ∈ R }

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Answer:

48

Step-by-step explanation:

can be divided into two 4x6 rectangles. Therefore, the area is 4x6 + 4x6 = 48

Answer:

$1529

Step-by-step explanation:

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the final amount (balance) in the account

P = the initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = the annual interest rate (as a decimal)

t = the time period (in years)

Plugging in the given values, we get:

A = 1000e^(0.0855)

A = 1000*e^0.425

A = 1000*1.529

A = 1529

Therefore, the balance after 5 years with continuous compounding at 8.5% interest rate is $1529.

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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Answer:

\( {x}^{2} + {(y - 139)}^{2} = {125}^{2} \)

Answer:1 =5

             2 = 55/3

             3= 11

Step-by-step explanation:

hope i could help lol

Answer:The answer is 7 pancakes, I think.

Step-by-step explanation:

28:20

?:5

Divide 28 by 20.

You get 1.4 because every person eats 1.4 .

Multiply 1.4 by 5. You give all of the five people 1.4 pancakes each.

The total will be 7 pancakes.

Step-by-step explanation:

elimination means that we multiply one or both equations by certain numbers, so that the sum of terms of the same variable across both equations is 0.

then the sum of both equations is one equation in one variable.

with the solution of that we go into any of the original equations to solve for the second variable.

I suggest in our case to multiply the first equation by -4. and then x add both equations.

-4x - 16y = -88

4x + y = 13

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

0 - 15y = -75

y = -75/-15 = 5

with this y = 5 we go e.g. into the second original equation.

4x + 5 = 13

4x = 8

x = 8/4 = 2

The effect on the trial balance if the purchase of marketable securities of $1,000 had been recorded to the equipment account in error is that the trial balance would not be in balance anymore.

A trial balance is a financial statement that summarizes all the accounts of a company's general ledger with its debit balances and credit balances to check if they are equal. When the purchase of marketable securities of $1,000 is recorded to the equipment account in error, this means that the entry was recorded in the wrong account. The equipment account would be overstated by $1,000 and there would be no change in the marketable securities account, thus leading to a mismatch between the total debit and credit amounts recorded. As a result, the trial balance would not be in balance anymore.

Explanation:A trial balance is a summary of all the accounts of a company's general ledger. It's a statement that lists all the debit balances in one column and all the credit balances in another column, which is used to confirm the accuracy of the accounts before preparing the financial statements of a company. The totals of both columns should match if the trial balance is correct. If not, it indicates an error that needs to be corrected.

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The probability that Z lies between 0.7 and 1.98 is 0.2181.

To find the probability that Z lies between 0.7 and 1.98, we need to calculate the area under the standard normal distribution curve between those two values.

Using a standard normal distribution table or calculator, we can find the area to the left of 0.7 (or the probability that Z is less than 0.7) to be 0.7580. Similarly, the area to the left of 1.98 is 0.9767.

To find the area between the two values, we can subtract the smaller area from the larger area:

0.9767 - 0.7580 = 0.2187

Since we want the probability that Z lies between the two values, we can round this to 0.2181, which is closest to answer choice D.

Therefore, the answer is D. 0.2181.

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Answer:

38

Step-by-step explanation:

(5)^2+2(8)/2(2)+3(3)=25+16/4+9=25+4+9=38

Answer:

In Princeton's wig shop, the total number of wigs is the sum of the number of blonde wigs and the number of brunette wigs. Since 1/4 of the wigs are blonde and 2/3 of the wigs are brunette, the fraction of wigs that are either blonde or brunette is 7/12.

Answer:

\(\frac{11}{12}\)

Step-by-step explanation:

\(\frac{1}{4}\) + \(\frac{2}{3}\)  The common denominator is 12  make equivalent fractions with 12 as the denominator

\(\frac{1}{4}\) x \(\frac{3}{3}\) = \(\frac{3}{12}\)

\(\frac{2}{3}\) x \(\frac{4}{4}\) = \(\frac{8}{12}\)

\(\frac{3}{12}\) + \(\frac{8}{12}\) = \(\frac{11}{12}\)

The factorization of the given elements in Z[i] is:

(a) 3 (irreducible)

(b) 7 (irreducible)

(c) 4 + 3i = (2 + i)(2 + i)

(d) 11 + 7i (irreducible)

To factor the elements in the ring of Gaussian integers Z[i], we can use the norm function to find the factors with norms dividing the norm of the given element. The norm of a Gaussian integer a + bi is defined as N(a + bi) = a² + b².

Let's factor each element:

(a) To factor 3, we calculate its norm N(3) = 3² = 9. Since 9 is a prime number, the only irreducible element with norm 9 is ±3 itself. Therefore, 3 is already irreducible in Z[i].

(b) For 7, the norm N(7) = 7² = 49. The factors of 49 are ±1, ±7, and ±49. Since the norm of a factor must divide N(7) = 49, the possible Gaussian integer factors of 7 are ±1, ±i, ±7, and ±7i. However, none of these elements have a norm of 7, so 7 is irreducible in Z[i].

(c) Let's calculate the norm of 4 + 3i:

N(4 + 3i) = (4²) + (3²) = 16 + 9 = 25.

The factors of 25 are ±1, ±5, and ±25. Since the norm of a factor must divide N(4 + 3i) = 25, the possible Gaussian integer factors of 4 + 3i are ±1, ±i, ±5, and ±5i. We need to find which of these factors actually divide 4 + 3i.

By checking the divisibility, we find that (2 + i) is a factor of 4 + 3i, as (2 + i)(2 + i) = 4 + 3i. So the factorization of 4 + 3i is 4 + 3i = (2 + i)(2 + i).

(d) Let's calculate the norm of 11 + 7i:

N(11 + 7i) = (11²) + (7²) = 121 + 49 = 170.

The factors of 170 are ±1, ±2, ±5, ±10, ±17, ±34, ±85, and ±170. Since the norm of a factor must divide N(11 + 7i) = 170, the possible Gaussian integer factors of 11 + 7i are ±1, ±i, ±2, ±2i, ±5, ±5i, ±10, ±10i, ±17, ±17i, ±34, ±34i, ±85, ±85i, ±170, and ±170i.

By checking the divisibility, we find that (11 + 7i) is a prime element in Z[i], and it cannot be further factored.

Therefore, the factorization of the given elements in Z[i] is:

(a) 3 (irreducible)

(b) 7 (irreducible)

(c) 4 + 3i = (2 + i)(2 + i)

(d) 11 + 7i (irreducible)

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The value of dy when x=5 and dx=-0.2 is -15

Given, y=8x2−5x−1

Thus, we need to find dy/dx. Using the power rule of differentiation, we have:

dy/dx = d/dx (8x^2) - d/dx (5x) - d/dx (1)

dy/dx = 16x - 5 - 0 = 16x - 5

Now, we need to evaluate the value of dy when x=5 and dx=-0.2.

Therefore,

dy/dx = 16x - 5When x=5,dy/dx = 16 × 5 - 5 = 75

Hence, the value of dy when x=5 and dx=-0.2 is -15. Therefore, we can find the dy/dx of a function by using the power rule of differentiation. In this problem, we first used the power rule of differentiation to get the derivative of y. We then evaluated the value of dy by substituting x=5 and dx=-0.2.

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The height is 7.04 feet at the rafter's peak that makes an angle of 28° and 15 feet long.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Length of rafter = 15 feet,

Angle made by rafter with the horizontal = 28°

Apply sin formula to determine the length x of the rafter,

sinθ = x / 15

sin28°  = x / 15

0.469 = x / 15

x = 7.04

The height of the rafter is 7.04.

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Answer:

\(-6 < k < 2\)

Step-by-step explanation:

Given

\(y = x^2 - 2x\)

\(y =kx -4\)

Required

Possible values of k

The general quadratic equation is:

\(ax^2 + bx + c = 0\)

Subtract \(y = x^2 - 2x\) and \(y =kx -4\)

\(y - y = x^2 - 2x - kx +4\)

\(0 = x^2 - 2x - kx +4\)

Factorize:

\(0 = x^2 +x(-2 - k) +4\)

Rewrite as:

\(x^2 +x(-2 - k) +4=0\)

Compare the above equation to: \(ax^2 + bx + c = 0\)

\(a = 1\)

\(b= -2-k\)

\(c =4\)

For the equation to have two distinct solution, the following must be true:

\(b^2 - 4ac > 0\)

So, we have:

\((-2-k)^2 -4*1*4>0\)

\((-2-k)^2 -16>0\)

Expand

\(4 +4k+k^2-16>0\)

Rewrite as:

\(k^2 + 4k - 16 + 4 >0\)

\(k^2 + 4k - 12 >0\)

Expand

\(k^2 + 6k-2k - 12 >0\)

Factorize

\(k(k + 6)-2(k + 6) >0\)

Factor out k + 6

\((k -2)(k + 6) >0\)

Split:

\(k -2 > 0\) or \(k + 6> 0\)

So:

\(k > 2\) or k \(> -6\)

To make the above inequality true, we set:

\(k < 2\) or \(k >-6\)

So, the set of values of k is:

\(-6 < k < 2\)