What is 5.75% of $6,000? (Express answer as dollars as cents.)

perimeter = 2L+2W

L=2+w

40 = 2L+2W

40= 2(2+w)+2W

40=4+2w+2w

36=4w

w=9

L=9+2=11

2(9) = 18, 2(11) = 22, 22+18 = 40

L=11

W=9

 Area = L x w

area = 11x9= 99 square yards

The product of the functions[tex]\( f(x) = x^2 + 4x - 1 \) and \( g(x) = 5x - 7 \) is \( 5x^3 + 13x^2 - 33x + 7 \).[/tex]

The correct answer is indeed [tex]{C} \),[/tex] which matches [tex]\( 5x^3 + 13x^2 - 33x + 7 \).[/tex]

To find the product[tex]\( (f \cdot g)(x) \)[/tex], where [tex]\( f(x) = x^2 + 4x - 1 \)[/tex] and [tex]\( g(x) = 5x - 7 \),[/tex]we need to perform the multiplication of these two functions.

Start by expanding [tex]\( f(x) \cdot g(x) \):[/tex]

1. Write down ( f(x) ):

[tex]\[ f(x) = x^2 + 4x - 1 \][/tex]

2. Write down ( g(x) ):

[tex]\[ g(x) = 5x - 7 \][/tex]

3. Perform the multiplication [tex]\( f(x) \cdot g(x) \)[/tex]:

 [tex]\[ f(x) \cdot g(x) = (x^2 + 4x - 1)(5x - 7) \][/tex]

4. Distribute [tex]\( x^2 + 4x - 1 \)[/tex] across ( 5x - 7 ):

 [tex]\[ f(x) \cdot g(x) = x^2 \cdot (5x - 7) + 4x \cdot (5x - 7) - 1 \cdot (5x - 7) \][/tex]

5. Perform the multiplications:

[tex]\[ x^2 \cdot (5x - 7) = 5x^3 - 7x^2 \][/tex]

  [tex]\[ 4x \cdot (5x - 7) = 20x^2 - 28x \][/tex]

 [tex]\[ -1 \cdot (5x - 7) = -5x + 7 \][/tex]

6. Combine all the terms:

[tex]\[ f(x) \cdot g(x) = 5x^3 - 7x^2 + 20x^2 - 28x - 5x + 7 \][/tex]

7. Simplify by combining like terms:

[tex]\[ f(x) \cdot g(x) = 5x^3 + (20x^2 - 7x^2) + (-28x - 5x) + 7 \][/tex]

 [tex]\[ f(x) \cdot g(x) = 5x^3 + 13x^2 - 33x + 7 \][/tex]

Therefore, the product [tex]\( (f \cdot g)(x) \) is \( 5x^3 + 13x^2 - 33x + 7 \).[/tex]

The correct answer is indeed [tex]{C} \),[/tex] which matches [tex]\( 5x^3 + 13x^2 - 33x + 7 \).[/tex]

Answer: Second option : (5, −2)

Step-by-step explanation: Given system of inequalities

y ≤ x − 5

y ≥ −x − 4

Plugging x=5 and y=-2 in first inequality

-2  ≤ 5 − 5

-2 ≤  0 : True.

Plugging x=5 and y=-2 in second inequality

-2 ≥ −5 − 4

-2 ≥ -9 : Also true.

Point  (5, −2) satisfied both of the given inequalities in the system.

Therefore, (5,-2) is correct option.

The base of parallelogram is 15 inches.

A parallelogram is a two-pair quadrilateral with parallel sides. A parallelogram has opposite sides that are the same length and have opposite angles that are the same size. Additionally, the interior angles on the same transversal side are supplemental. 360 degrees is the sum of all the interior angles.

Given area  of a parallelogram is 60  square inches

area of parallelogram is given by product of base and height,

Area = b × h

where b = base and  h = height

height = 4 inches

Area = b × h

60 = b × 4

b = 60/4 = 15 inches

Hence the base is 15 inches.

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Answer:

[tex]x=2+-i \sqrt{6}[/tex]

Step-by-step explanation:

[tex]x^2 + 4x + 10[/tex]

To find out the solution we set the expression =0 and solve for x

[tex]x^2 + 4x + 10=0[/tex]

Apply quadratic formula to solve for x

[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

a=1, b=4, c=10 plug in the values in the formula

[tex]x=\frac{-4+-\sqrt{4^2-4(1)(10)}}{2a}[/tex]

[tex]x=\frac{-4+-\sqrt{-24}}{2(1)}[/tex]

The value of square root (-1) is 'i'

[tex]x=\frac{-4+-2i\sqrt{6}}{2}[/tex]

Divide each term by 2

[tex]x=2+-i\sqrt{6}[/tex]

Final answer:

Calculating the overall percentage of defective products from the given data, we find that 150 out of 1000 products are defective, leading to an overall defect rate of 15%.

Explanation:

The question asks us to calculate the overall percentage of defective products based on the given scenarios. Firstly, it's mentioned that 75% of 1000 products are shipped on time, which means 750 are shipped on time and 250 are initially defective.

Since clients complain that 10% of the products are defective and 5% of the products are shipped late or are defective, we need to consider these percentages in our calculations.

To find the number of defective products, we can assume the 10% complaint rate on the entire batch of products which would lead to 100 out of 1000 products being defective. This is the initial estimated number of defective products.

To address the 5% of the products that are both shipped late and are defective, we consider this as an additional defect rate on top of the existing one, which would be another 50 products.

Total defects would then be the sum of defects from the complaints about defects and the defects because of shipping delay, which amounts to 100 + 50 = 150 defective products. To find the overall percentage, we divide 150 by 1000 and multiply by 100, giving us an overall defect rate of 15%.

Answer:

Plan B is correct answer.

Step-by-step explanation:

Raise the price by 10 percent each week until the price reaches $8.00.

Week 1. Starting price $5

[tex]0.1\times5=0.5[/tex]

price becomes = [tex]5+0.5=5.5[/tex]

Week 2.

[tex]0.1\times5.5=0.55[/tex]

Price becomes = [tex]5.5+0.55=6.05[/tex]

Week 3.

[tex]0.1\times6.05=0.605[/tex]

Price become = [tex]6.05+0.605=6.655[/tex]

Week 4.

[tex]0.1\times6.655=0.6655[/tex]

Price becomes = [tex]6.655+0.6655=7.320[/tex]

Week 5.

[tex]0.1\times7.320=0.732[/tex]

Price becomes = [tex]7.320+0.732=8.052[/tex]

So, we can see that in 5 weeks the price becomes $8 from $5. Therefore, plan B is the best plan.

A drawer contains five pairs of socks that are brown, black, white, red, and blue. Claude takes the red socks out of the drawer. What is the probability of Claude choosing the red socks on his first pick?

Answer: 1/25

Answer:

The answer would be 1/25 Hopefully this any T4L students!

Answer:

Term

Step-by-step explanation:

hope this helps

The angles of triangle PQR are ordered from largest to smallest as <>R,

The question involves applying the principles of geometry to compare lengths of sides in a triangle, and thereby determine the relative magnitude of angles in triangle PQR. According to the triangle inequality theorem, the largest angle in a triangle is opposite the longest side, and the smallest angle is opposite the shortest side. Given that the side lengths are represented as PQ = 3x + 2, QR = x, and RP = x + 2, we can compare the expressions to conclude which side is longest and which is shortest, assuming all values of x are positive since they represent lengths.

Firstly, it is obvious that QR (x) is the shortest side since it is just x without any additional positive value. Secondly, between RP (x + 2) and PQ (3x + 2), PQ will always be longer than RP for all positive x because it has a larger coefficient in front of x. Hence, the angle opposite PQ (angle R) will be the largest angle, and the angle opposite QR (angle P) will be the smallest. The angle at Q will be between the other two angles in terms of their measurements since PQ is longer than RP but both are longer than QR.

To summarize, the angles of Triangle PQR ordered from largest to smallest are: ∠R, ∠Q, and ∠P.

(x^2)/a^2+(y^2)/b^2=1

a>b

a=6, a^2=36

foci=(a^2-b^2)^(1/2)

4=(36-b^2)^(1/2)

16=36-b^2

b^2=36-16

b^2=20

b=2(5)^(1/2) or (20)^(1/2)

1=(x^2/36)+(y^2/20)

Answer:

y=-2x+5

Step-by-step explanation:

The equation of velocity of sound in air is v = 20 √(273 + t). In this problem, we need to find the temperature when the velocity is 329 meters/s. You need to measure the time it takes a sound to travel a measured distance in order to measure its speed in air.

Given:

Velocity of sound in air equation = v = 20 √(273 + t)

Velocity = 329 m/s

To solve:

V = 20 √(273 + t)

329 = 20 * sqrt(273 + t)

16.45 = sqrt(273 + t)

273 + t = 16.45^2

t- 16.45^2-273

t = -2.4 degrees Celsius

So, the temperature when the velocity is 329 meters per second is -2.4 degrees Celsius.

Answer:  The correct option is (A) 2 + 0.2 + 0.02 + 0.002 +  .  .  .

Step-by-step explanation:  We are given to select the correct geometric series that converges.

We know that

a geometric series converges if the modulus of its common ratio is less than 1.

Option (A) : 2 + 0.2 + 0.02 + 0.002 +  .  .  .

Here, first term, a= 2  and the common ratio is given by

[tex]r=\dfrac{0.2}{2}=\dfrac{0.02}{0.2}=\dfrac{0.002}{0.02}=~.~.~.~=0.1\\\\\Rightarrow |r|=|0.1|=0.1<1[/tex]

So, this geometric series will converge.

Option (A) is correct.

Option (B) : 2 + 4 + 8 + 16 +  .  .  .

Here, first term, a= 2  and the common ratio is given by

[tex]r=\dfrac{4}{2}=\dfrac{8}{4}=\dfrac{16}{8}=~.~.~.~=2\\\\\Rightarrow |r|=|2|=2>1.[/tex]

So, this geometric series will not converge.

Option (B) is incorrect.

Option (C) : 2 - 20 + 200 - 2000 +  .  .  .

Here, first term, a= 2  and the common ratio is given by

[tex]r=\dfrac{-20}{2}=\dfrac{200}{-20}=\dfrac{-2000}{200}=~.~.~.~=-10\\\\\Rightarrow |r|=|-10|=10>1.[/tex]

So, this geometric series will not converge.

Option (C) is incorrect.

Option (D) : 2 +2 + 2 + 2 +  .  .  .

Here, first term, a= 2  and the common ratio is given by

[tex]r=\dfrac{2}{2}=\dfrac{2}{2}=\dfrac{2}{2}=~.~.~.~=1\\\\\Rightarrow |r|=|1|=1.[/tex]

So, this geometric series will not converge.

Option (D) is incorrect.

Thus, the correct option is (A).

The geometric series that converges is 2+0.2+0.02+0.002+ ...:

Thus, option (A) is correct.

In a geometric series, the terms are multiplied by a constant ratio to obtain the next term.

If the absolute value of the common ratio is less than 1, the series converges.

A. 2 + 0.2 + 0.02 + 0.002 + ...:

In this series, the common ratio is 0.1 (each term is divided by 10).

Since the absolute value of the common ratio is less than 1, this series converges.

B. 2 + 4 + 8 + 16 + ...:

In this series, the common ratio is 2 (each term is multiplied by 2).

Since the common ratio is greater than 1, this series diverges.

C. 2 - 20 + 200 - 2000 + ...:

In this series, the terms alternate in sign, but the absolute value of the common ratio is 10.

Since the absolute value of the common ratio is greater than 1, this series diverges.

D. 2 + 2 + 2 + 2 + ...:

In this series, the common ratio is 1 (each term is the same).

Since the common ratio is equal to 1, this series neither converges nor diverges. It is a divergent series.

Therefore, the geometric series that converges is 2 + 0.2 + 0.02 + 0.002 + ...

Thus, option (A) is correct.

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