The numbers 8, 1, −7, −12 are listed from greatest to least.
True or False

Answer:

Protects reputable debt collectors from unfair competition——- FAIR DEBT COLLECTION ACT

allows consumers to exercise their rights regarding disputes —— FAIR CREDIT BILLING ACT

restricts creditors from issuing credit —— CREDIT CARD ACCOUNTABILITY RESPO…

specifies the purpose of a credit report and how it —— FAIR CREDIT REPORTING ACT

Step-by-step explanation:

Answer:

Protects reputable debt collectors from unfair competition——- FAIR DEBT COLLECTION ACT

allows consumers to exercise their rights regarding disputes —— FAIR CREDIT BILLING ACT

restricts creditors from issuing credit —— CREDIT CARD ACCOUNTABILITY RESPO…

specifies the purpose of a credit report and how it —— FAIR CREDIT REPORTING ACT

Step-by-step explanation:

4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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Answer: 0.0622009569378

Step-by-step explanation:

Change the third line only .

Amd at 4th line

\(\\ \tt\Rrightarrow ∆TFS\cong∆PFQ(ASA)\)

Answer:

Step-by-step explanation:

3(x + 2) = 3x - 6

3x - 6 = 3x - 6

Subtract 6 from both sides of the equation. Then you will get 3x = 3x - 12. Now subtract 3x from both sides of the equation. Leaving you with 0 = -12. So I guess it’s correct?

Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Answer: P(x)=  x³ - 3 x² - 46 x +168

Step-by-step explanation:

(4,6, -7)

hence the polynomial will be equal to

P(x) = (x-4) (x-6) (x+7)

P(x) = (x-4) (x²+7 x -6 x -42)

P(x) = (x-4) (x²+x -42)

P(x) = x³ + x²-42 x -4 x² -4 x +168

P(x) =  x³ - 3 x² - 46 x +168

hence, the required polynomial is P(x) =  x³ - 3 x² - 46 x +168

The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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Option A is correct. The value of function (f/g)(x) is found to be  \(\sqrt[3]{3x}\)/(3x+2) where the condition is that  x ≠  -2/3.

In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

The new function obtained by performing f first and then g is the combination of two functions g and f.

Given:

f(x) = \(\sqrt[3]{3x}\)

g(x) = 3x + 2

(f/g)(x) =  \(\sqrt[3]{3x}\)/(3x+2)

Also, the denominator should not be equal to 0.

So, 3x + 2 ≠ 0

     x ≠  -2/3

Therefore, the value of function  is found to be  \(\sqrt[3]{3x}\)/(3x+2) where the condition is that  x ≠  -2/3. So, Option A is correct

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Answer:

C. (5,7)

Step-by-step explanation:

One endpoint at 1,3 and the midpoint at 3,5Your answer would be to as two to each the x and y of the midpoint. So the answer would be 5,7.

Answer:

A) - Value that corresponds to surviving the year would be: $-197

- Value Corresponding to not surviving = $98803

B) $-88.1

C) Yes, because the insurance company expects to make an average profit of $88.1 on every 29 year-old male that it insures for 1 year.

Step-by-step explanation:

A) We are told that the life insurance company charges $197 for insuring that the male will live through the year.

Thus, the value that corresponds to surviving the year would be: $-197 since amount that's paid out is $-197

We are told that the policy pays out $100,000 as a death benefit.

Therefore, the value that corresponds to not surviving the year is:

$100000 - 197 = $98803

B) From complement rule in probability;

P(not surviving) = 1 - P(surviving) = 1 - 0.9989 = 0.0011

Expected value would be;

μ = Σx•P(x) = (98803 × 0.0011) + (-197 × 0.9989) = $-88.1

C) Yes, because the insurance company expects to make an average profit of $88.1 on every 29 year-old male that it insures for 1 year.

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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The logarithmic function is y = 5.11 + 0.88 ln(x+1), the estimated manufacturing sales in 2015 is 6.94 trillion dollars, the quadratic model for the function y = 0.6518x^2 + 5.9024x + 1.3225

1.

a. To find a logarithmic model for the data, we will use the form y = a + b ln(x), where y represents Manufacturing Sales in trillions of dollars and x represents the number of years after 2008. We can use the six data points to solve for the constants a and b:

At x = 1 (i.e., in 2009), y = 5.11, so:

5.11 = a + b ln(1)

a = 5.11

At x = 2 (i.e., in 2010), y = 5.75, so:

5.75 = 5.11 + b ln(2)

b = (5.75 - 5.11) / ln(2) = 0.88

Using these values, the logarithmic model for the data is:

y = 5.11 + 0.88 ln(x+1)

b. To estimate Manufacturing Sales in 2015 using the logarithmic model, we need to evaluate the model at x = 7 (i.e., seven years after 2008):

y = 5.11 + 0.88ln(8) ≈ 6.94 trillion dollars

2.

a. To find a quadratic model for the data, we will use the form y = ax^2 + bx + c, where y represents Manufacturing Sales in trillions of dollars and x represents the number of years after 2008. We can use the six data points to solve for the constants a, b, and c:

Using a calculator, we can obtain:

a ≈ 0.6518

b ≈ 5.9024

c ≈ 1.3225

Using these values, the quadratic model for the data is:

y = 0.6518x^2 + 5.9024x + 1.3225

b. To estimate Manufacturing Sales in 2015 using the quadratic model, we need to evaluate the model at x = 7 (i.e., seven years after 2008):

y = 0.6518(7^2) + 5.9024(7) + 1.3225 ≈ 8.000 trillion dollars

c. It appears that the quadratic model gives a more reliable result for 2015, as it predicts a higher sales amount than the logarithmic model, which may be more realistic given the overall trend of increasing sales over time. However, this conclusion should be taken with a grain of salt, as both models are based on relatively few data points and are therefore subject to some degree of uncertainty.

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Answer:

  see attached for a sketch

  area = 5 1/3 square units

Step-by-step explanation:

You want the area under the square root curve, above y=0, from x=0 to x=4.

The area is found by integrating a differential of area over appropriate limits. A vertical slice will have hight √x and width dx, so we have ...

  dA = (√x)dx

  A = ∫(√x)dx

The power rule can be used for the integration:

  \(\displaystyle A=\int_0^4{x^{\frac{1}{2}}}\,dx=\left[\dfrac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]^4_0=\dfrac{2}{3}(4^\frac{3}{2})=\dfrac{16}{3}=\boxed{5\dfrac{1}{3}}\)

The area of the region is 5 1/3 square units.

__

Additional comment

You will notice that the area is bounded by a rectangle 4 units wide and 2 units high, for an area of 4·2 = 8. The area under the parabolic curve is 2/3 of that: 2/3·8 = 16/3 = 5 1/3 square units.

This fraction will be true for any area bounded by a parabola where the vertex is one of the corners of the rectangle.

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Answer:

standard form=ax+by+c=0

Step-by-step explanation:

0.25x-0.2y-0.1=0

If Carson wants to use a sheet of fiberboard 29 inches long to create a skateboard ramp with a 19∘angle of elevation from the ground. The height that the ramp will rise from the ground at its highest end is 9 inches.

Given data:

Length of the ramp = 29 inches

Angle of elevation  = 19 degrees

Now let determine the height of the ramp by making use of the SOH CAH TOA identity:

SOH = Sine is opposite over hypotenuse

CAH =  Cosine is adjacent over hypotenuse

TOA =Tangent is opposite over adjacent

Let h represent the height

sin 19  = opp/hyp

sin 19 = H/29

H = 29 × sin 19

H = 9.4 inches

H= 9 inches (Approximately)

Therefore we can conclude that 9 inches is the height of the ramp.

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Answer: 9.4

Step-by-step explanation:

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Answer: He does have enough crates to ship out the avocados.

Step-by-step explanation: 205 avocados fit inside a shipping container. At a big grove, 7000 avocados were picked. 36 cargo containers belong to the owner. As a result, he can fit a total of = avocados. And since he has 7000 avocados, he does indeed have enough crates to carry the fruit.

Answer:

Step-by-step explanation:

2 steps

     3.7 = x +(-5) , add 5 to both sides

3.7+ 5 = x + (-5) +5

    8.7 = x , combine like terms

or 1 step

  3.7 = x +(-5), add 5 to both sides and combine like terms

  8.7 = x

More scores were in the interval 75-79 than any other interval

a. Class Interval Frequency

70-74    8

75-79    16

80-84    12

85-89     4

b. The % more than 84 = 4/40 x 100

=10%/

c. The % less than 75 = 8/40 x 100

= 20%

d. More scores were in the interval 75-79 than any other interval

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Answer:

B. 500

Hope this helps!! :D

Answer:

The answer is B

explanation:

78.8 is nearly 80 and 6.8 is nearly 7

so an estimate would be 80 × 7

= 560

The area between the solid line (y=x+4) and the dotted line (y=-2x-2) represents the system of inequalities solution set.

Two linear inequalities system on a coordinate plane. The first has a solid line graphed with a negative slope of one, a negative y-intercept, and a shaded origin area. The area encompassing the origin is shaded, and the second is a dashed vertical line 3 units to the left of the origin.

x ≥ –3; y ≥ x – 2

x > –3; 5y ≥ –4x – 10

x > –3; y ≥ –x + 1

x > –2; y ≥ –x – 1

The solution set for the system of inequalities is represented by the region between the solid line (y=x+4) and the dotted line (y=-2x-2).

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(7 × 10⁻¹) × (23 × 10⁻²)

Step-by-step explanation:

0.7 × 0.23

= (7 × 10⁻¹) × (23 × 10⁻²)

Therefore , the solution of the given problem of circle comes out to be arc length 3.93 feet.

Every area of the plane that is separated by a specific amount from this additional point makes a circle (center). As a result, it is a curve made up of spots that are separated from one another on the surface. Additionally, it rotates similarly about the centre at every angle. Every collection of endpoints in the confined, two-dimensional sphere of a circle is uniformly spaced apart from the "centre."

Here,

A circle with a radius of 3 feet is equal to its diameter as follows:

=> C = 2πr = 2π(3) = 6π feet

Since there are 360° of angles in a circle's centre, the angle for a 75° curve is:

5/24 of a complete circle is 75/360.

Therefore, the 75° arc's extent is

5/24 × 6π = 5π/4 ≈ 3.93 feet

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Recall the well-known series

\(\displaystyle 2 \arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}\)

Replace x with √x :

\(\displaystyle 2 \arcsin^2(\sqrt x) = \sum_{n=1}^\infty \frac{(4x)^n}{n^2 \binom{2n}n}\)

Differentiate both sides:

\(\displaystyle -\frac{\arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^n}{n \binom{2n}n}\)

Multiply by 4x :

\(\displaystyle -\frac{4x \arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^{n+1}}{n \binom{2n}n}\)

All the series I've mentioned converge for |x| < 1, so we can take x = -1/4 to find the value of the sum we want.

\(\displaystyle \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n \binom{2n}n} = -\frac{4 \times \left(-\frac14\right) \arcsin\left(\sqrt{-\frac14}\right)}{2\sqrt{-\frac14-\left(-\frac14\right)^2}} = -\frac{\arcsin\left(\frac i2\right)}{\frac{\sqrt5\,i}2}} = \boxed{\frac2{\sqrt5} \mathrm{arsinh}\left(\frac12\right)}\)

where

\(\arcsin\left(\frac i2\right) = z \iff 2\sin(z) = -2i\sinh(iz) = i \implies z = i \, \mathrm{arsinh}\left(\frac12\right)\)

Answer:

Step-by-step explanation:

If we are looking for the time(s) that the ball is at a height of 15, we simply sub in a 15 for the height in the position equation and solve for t:

\(15=-16t^2+23t+7\) and

\(0=-16t^2+23t-8\)

Factor this however you factor a quadratic in class to get

t = .59 seconds and t = .85 seconds.

This means that .59 seconds after the ball was thrown into the air it was 15 feet off the ground. Then the ball reached its max height, gravity took over, and began pulling it back down to earth. The ball passes the height of 15 feet again on its way down after .85 seconds.

Answer:

Step-by-step explanation:

The required expression represents the number of the small marbles, medium marbles, and large marbles are m = 4s  and l = 3 + 5m.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the number of small marbles be s, medium marbles are m and large marble is l.
According to the question,
He has four times as many small marbles as medium marbles. The number of large marbles is three more than five times the number of medium marbles.
m = 4s
and
l = 3 + 5m

Thus, the required expression represents the number of the small marbles, medium marbles, and large marbles are m = 4s  and l = 3 + 5m.

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