please help i need this to pass the class

Answer:

Answer is C.

Step-by-step explanation:

\( ( {a}^{5} {b}^{2} {c}^{5} )( {ac}^{2} ) \)

form brackets of common terms:

\( = ( {a}^{5} .a)( {b}^{2} )( {c}^{5} . {c}^{2} )\)

from law of indices:

\({ \boxed{ \bf{ {x}^{n} \times {x}^{m} = {x}^{(n + m)} }}}\)

therefore:

\( = \{ {a}^{(5 + 1)} \} \{ {b}^{2} \} \{ {c}^{(5 + 2)} \} \\ = {a}^{6} {b}^{2} {c}^{7} \)

Answer:

============================

\(\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}\)

Bring both fractions into common denominator:

\(\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}\)

Simplify:

\(\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =\)

\(\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =\)

\(\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =\)

\(\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =\)

\(\dfrac{4\sqrt{14} }{7-4} =\)

\(\dfrac{4}{3} \sqrt{14} }\)

Compare the result with given expression to get:

Answer:

156

Step-by-step explanation:

1 foot = 12 inches

hope it helps

Answer:

3x%x+1-5/5

3× 5x

Step-by-step explanation:

3x-5x

35yx 53yx

Answer:

-2

Step-by-step explanation:

y^3=-8.

y=cube root of -8 = -2

Answer: 8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Hope this helped you !!!

Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

Answer:

  d = e

Step-by-step explanation:

An inscribed sphere in a cube will have a diameter equal to the edge length of the cube:

  d = e

__

The distance between the faces of the cube is the same as the edge length.

Step-by-step explanation:

3-2(3x+1)=19

\(3 - 6x - 2 = 19 \\ 1 - 6x = 19 \\ - 6x = 19 - 1 \\ - 6x = 18 \\ x = - 3\)

1. To estimate the probability of catching a bass in a lake using a special type of bait, the forest ranger could employ the following process:  Random Sampling, Bait Experiment, Data Collection,  Probability Calculation.

2. a.  the probability of selecting 'S' at random is P(S) = 2/12 = 1/6.

b. The probability of selecting a vowel at random is P(vowel) = 4/12 = 1/3.

1. To estimate the probability of catching a bass in a lake using a special type of bait, the forest ranger could employ the following process:

a. Random Sampling: The ranger could randomly select a sample of fishermen or anglers who frequently fish in the lake. This would ensure a representative sample of individuals who are likely to have experience with different fishing techniques and bait preferences.

b. Bait Experiment: The ranger could provide each participant in the sample with the special bait and observe the outcomes of their fishing attempts. It would be important to control for other variables such as fishing location, time of day, and weather conditions to isolate the impact of the bait.

c. Data Collection: The ranger would record the number of successful bass catches and the total number of fishing attempts for each participant. This data would be used to calculate the observed probability of catching a bass with the special bait.

d. Probability Calculation: The ranger could calculate the proportion of successful bass catches out of the total fishing attempts for the sample. This proportion would serve as an estimate of the probability of catching a bass in the lake using the special bait.

2. a. P(S): The letter 'S' appears twice in the word "RECKLESSNESS." The probability of selecting 'S' at random is determined by the ratio of the number of occurrences of 'S' to the total number of letters in the word. Since there are two 'S's in the word and a total of 12 letters, the probability of selecting 'S' at random is P(S) = 2/12 = 1/6.

b. P(vowel): To determine the probability of selecting a vowel at random from the word "RECKLESSNESS," we need to identify the vowels in the word. The vowels in the word are E, E, E, and the letter O. Therefore, there are four vowels out of a total of 12 letters. The probability of selecting a vowel at random is P(vowel) = 4/12 = 1/3.

In both cases, the probabilities are calculated by dividing the number of favorable outcomes (occurrences of 'S' or vowels) by the total number of possible outcomes (total letters in the word).

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Answer:

y = 9

Step-by-step explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Divide 7 from both sides of the equation:

(7y)/7 = (63)/7

y = 63/7

y = 9

9 is your answer for y.

~

Answer:

9

Step-by-step explanation:

7×9=63

.

The result of the subtraction of matrices E and F is given as follows:

E - F = [19 -7]

          [2 15]

The matrices in the context of this problem are defined as follows:

E =

[9 2]

[12 8]

F =

[-10 9]

[10 -7]

When we subtract two matrices, we subtract the elements that are in the same position of the two matrices.

Hence the result of the subtraction of matrices E and F is given as follows:

E - F = [19 -7]

          [2 15]

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Using Pythagorean theorem, the distance between the two object is and the distance between the two objects is changing at a rate of 3 cm/s.

To solve this problem, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the distance between the two objects. The other two sides are the distances to the magnetic force from object A and object B.

We can set up the equation as follows

(distance between objects)² = (distance to magnetic force from object A)² + (distance to magnetic force from object B)²

Plugging in the values, we get:

(distance between objects)² = (8 cm)² + (10 cm)²

(distance between objects)² = 64 cm² + 100 cm²

(distance between objects)² = 164 cm²

Taking the square root of both sides, we get:

distance between objects = 12.8 cm

The distance between the two objects is changing at a rate of 3 cm/s. This is because the distance to the magnetic force from object A is increasing at a rate of 4 cm/s, and the distance to the magnetic force from object B is increasing at a rate of 5 cm/s. The total change in distance is therefore 9 cm/s, and since the distance between the two objects is 12.8 cm, the rate of change of the distance between them is 3 cm/s.

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SOLUTION

Write out the expression

step1: Multiply the coefficient of the first and last term

Step2: Obtain the factors of the term above that can conveniently replace the second term n the expression

Step3: Replace the second term with the two terms obtained

Step4: Group the term and obtain the common factors

Hence the factors of the expression are (4x-3)(x-6)

The X- intercept is the point where the expression to zero

Hence the X-intercept is (3/4,0) and (6,0)

It is not possible to find two numbers with two decimal places that round to 312 when rounded to one decimal place and have a total of 62.4.

To solve this problem systematically, we can break it down into smaller steps:

Let's assume the two numbers are x and y, both with two decimal places.

We can represent them as x = a.b and y = c.d, where a, b, c, and d are digits.

Rounding x and y to one decimal place gives us the following equations:

Round(x) = a.b ≈ 312

Round(y) = c.d ≈ 312

Since the total of the numbers is 62.4, we have the equation:

x + y = a.b + c.d

= 62.4

From Step 2, we know that both a.b and c.d are approximately equal to 312.

So, we can write:

a.b ≈ 312

c.d ≈ 312

Since a.b and c.d are rounded to one decimal place, we can rewrite them as:

a.b = 312 + p

c.d = 312 + q

p and q are the decimal parts that were rounded.

Substituting the new representations of a.b and c.d into the equation from Step 3, we get:

(312 + p) + (312 + q) = 62.4

Simplifying the equation gives us:

624 + (p + q) = 62.4

Solving for (p + q), we have:

p + q = 62.4 - 624

= -561.6

Since p and q are decimal parts, they must be between 0 and 1. -561.6 is outside this range, which means there are no values for p and q that satisfy the given conditions.

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Step-by-step explanation:

sum of 2 angles on a straight line = 180°

therefore,

y + 120 = 180

y = 180 - 120 = 60

y = 60°

now apply angle sum property of triangle

now,

50 + x + y = 180

50 + x + 60 = 180

110 + x = 180

x = 180 - 110

x = 70

therefore, x = 70 & y = 60

hope this answer helps you dear! take care

Answer:

x = 70°

y = 60°

Step-by-step explanation:

hope it helps u

plzz plzz pLZZ MARK AS BRAINLIEST

Answer:

1: 1

2: 1

3:2/5

4:1/4

Answer:

65

Step-by-step explanation:

180-115 = 65

We can rewrite the right side of the equation as a power of 2 since 8 = 2^3:

(1/32)^x = (2^3)^3-x

Simplifying the right side:

(1/32)^x = 2^(9-3x)

We can write both sides using a common base, say 2:

2^(-5x) = 2^(9-3x)

Now we equate the exponents and solve for x:

-5x = 9 - 3x

-2x = 9

x = -4.5

Therefore, the solution to the equation is x = -4.5.

A function of the form y = Asin (kx) + C or y = Acos(kx) + C is y = 5cos (πx/7 - 3.5) + 3.

What are sine function and cosine function?

Sine and cosine are trigonometric functions of angles in mathematics. In the context of a right triangle, the sine and cosine of an acute angle are described.

The general equation of a sine graph is y = Asin (B (x - D) + C

The general equation of a cosine graph is y = Acos (B (x - D) + C

Where, A = Amplitude and 2π/B = Period.

As per data given,

But the form given in the Question is y = Asin (kx) + C or y = Acos(kx) + C

Here, A = +5 and Vertical Shift C = 3 B or K = π/7.

There seems no vertical shift for sine function.

y = 5sin (πx/7) + 3

Now for cosine function phase shift can be the nearest maximum point of graph from Y -axis on X-axis i.e. +3.5

y = 5cos (πx/7 - 3.5) + 3

Hence, A function of the form y = Asin (kx) + C or y = Acos(kx) + C is y = 5cos (πx/7 - 3.5) + 3.

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3(x + 2) + 35 + 52 = 180

3x + 6 + 87 = 180

3x + 93 = 180

3x = 180 - 93

3x = 87

x = 29

\( \: \)

3(x + 2) = ...

= 3(29 + 2)

= 3(31) = 93°

The total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

To find the total area of the solid figure, we need to determine the areas of each face and then add them together.

The solid figure consists of a rectangular prism with dimensions 3" x 3" x 6" and a pyramid on top with an equilateral triangle base.

First, let's find the area of the rectangular prism. The rectangular prism has two identical square faces with side length 3" and four rectangular faces with dimensions 3" x 6". The total area of the rectangular prism can be calculated as:

Area of the square faces: 2 * (3" * 3") = 2 * 9 square inches

Area of the rectangular faces: 4 * (3" * 6") = 4 * 18 square inches

Total area of the rectangular prism: 2 * 9 + 4 * 18 = 18 + 72 = 90 square inches.

Next, let's find the area of the triangular pyramid. The base of the pyramid is an equilateral triangle with side length 3". The height of the pyramid is 3". The formula to find the area of an equilateral triangle is (sqrt(3) / 4) * (side length)^2. Plugging in the values, we have:

Area of the triangular pyramid: (sqrt(3) / 4) * (3" * 3") * 3" = (sqrt(3) / 4) * 9 * 3 = (sqrt(3) / 4) * 27 = 27sqrt(3) / 4 square inches.

Now, we can find the total area of the solid figure by adding the area of the rectangular prism and the area of the triangular pyramid:

Total area = Area of rectangular prism + Area of triangular pyramid

Total area = 90 square inches + 27sqrt(3) / 4 square inches.

Thus, the total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

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If a function is given that h(t) = 2t^2 - t; t = 4, t = 8, then the net change between the given values of the variable is 92 and the average rate of change between the given values of the variable is 23.

Explanation:

Given that: Based on the provided function h(t) = 2t^2 - t and the given values of t = 4 and t = 8.

To determine the net change and average rate of change, follow these steps:

(a) The difference between the two h(x) values is the net change.

To find the net change, we need to evaluate the function at both values of t and then subtract the results:

Net change = h(8) - h(4)
Net change = (2(8)^2 - 8) - (2(4)^2 - 4)
Net change = (128 - 8) - (32 - 4)
Net change = 120 - 28
Net change = 92

(b) The ratio between the net change and the change between the two input values is used to calculate average net change or average rate of change. The average rate of change can be calculated using the same two points and the formula: f(b)-f(a) / b-a .

To determine the average rate of change, we need to divide the net change by the difference in the t values:

Average rate of change = Net change / (t2 - t1)
Average rate of change = 92 / (8 - 4)
Average rate of change = 92 / 4
Average rate of change = 23

So, the net change is 92 and the average rate of change is 23 between the given values of the variable.

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Step-by-step explanation:

number of hours = more than 12

above 80= 16

total sat = 33

percentage above 80 = 16 / 33 * 100

= 48.48%

to the nearest whole number = 48%

The function which relates the distance traveled d to the time t as the train travels at a constant speed is,

\(f(t)=210t,\\d=210t\)

The speed of a body is the rate at which it covers the total distance is in the time taken. The speed of the body is given as,

\(s=\dfrac{d}{t}\)

Here, (d) is the distance travelled by the body and (t) is time taken by the body to cover that distance.

A train leaves the station at time t=0. Traveling at a constant speed, the train travels 420 kilometers in 2 hours.

If the train travels 420 kilometers in 2 hours. Then by the above relation, the distance it travel in one hour will be,

\(d=\dfrac{420}{2}\\d=210\rm\; km\)

As the train with constant speed travels 210 km per hour. Thus the linear function for this condition can be modeled as,

\(s=\dfrac{d}{t}\\210=\dfrac{d}{t}\\d=210t\)

In the function of time,

\(f(t)=210t\)

Thus, the function which relates the distance traveled d to the time t as the train travels at a constant speed is,

\(f(t)=210t,\\d=210t\)

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The number of women who like watching at least two of the given genres 1640 women.

Let's call the number of women who liked watching comedies C, the number who liked watching fantasy movies F, and the number who liked watching romantic movies R.

From the information given, we know:

C = 1000 * 52% = 520 women liked watching comedies

F = 1000 * 45% = 450 women liked watching fantasy movies

R = 1000 * 60% = 600 women liked watching romantic movies

We also know that:

25% of women liked watching both comedies and fantasy, so 0.25 * 1000 = 250 women.

28% of women liked watching both romantic and fantasy, so 0.28 * 1000 = 280 women.

30% of women liked watching both comedies and romantic, so 0.30 * 1000 = 300 women.

However, these numbers overlap because some women like all three genres, so we have to subtract the number of women who like all three genres from our total. We don't know the number of women who like all three genres, but we can calculate it by adding up the number of women who liked two genres and subtracting from the total number of women:

Number of women who liked all three genres = (C + F + R - (C & F) - (C & R) - (F & R) + (C & F & R)) = (520 + 450 + 600 - 250 - 300 - 280 + (C & F & R))

Since 6% of women liked watching none of these movie genres, we can subtract this from our total:

C & F & R = 1000 - 6% * 1000 = 940 women

So the number of women who like watching at least two of the given genres = (520 + 450 + 600 - 250 - 300 - 280 + 940) = 1640 women.

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Each model should be produced on a weekly basis to maximize net profit is $75,900.

What is Net profit?

In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.

As given,

Number of products sold:

T ≥ 1.5G

Maximize Profit Z = 150T + 130G

Labor Constraint:

Labor hours Available:

Production Department:

Number of labor hours available per day = 58 × 7 = 406

Number of days in a week = 5

Number of lobor ours available per week = 406 × 5 = 2030

Assembly Department:

Number of labor hours available per day = 25 × 7 = 175

Number of days in a week = 5

Number of labor hours available per week = 175 × 5 = 875.

Labor hours Required:

Labor hours required for G1 model:

Labor hours required at Production department = 3.5G

Labor hours required at assembly department = 2G

Labor hours required for T1 model:

Labor hours required at Production department = 4T

Labor hours required at Assembly department = 1.5T

Total labor hours required at Production department = 3.5G + 4T

Total labor hours required at Assembly department = 2G + 1.5T.

Constraint:

Labor hours required ≤ Labor hours Available.

Production department Labor constraint

3.5G + 4T ≤ 2030

Assembly department Labor constraint:

2G + 1.5T ≤ 875

The function:

Maximum Profit Z = 150T +130G

Constraint:

3.5G +4T ≤ 2030

2G + 1.5T ≤ 875

T ≥ 1.5G

Suppose that for example:

10.5G +12T = 6090

 16G + 12T = 7000

Solve both equations simultaneously,

5.5G = 7000 - 6090

5.5G = 910

    G = 910/5.5

    G = 363

Since, T > G

Hence,

T = 363,

G = 165

Calculate Profit:

150T + 130G = 150 × 363 + 130 × 165

                     = 54450 + 21450

                     = 75900

Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.

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Answer:

A. -4

Step-by-step explanation:

f(x) = 2x - 5x + 2

if x = 2

f(2) = 2(2) - 5(2) + 2

     = 4 - 10 + 2

     = -6 + 2

     = -4

The answer is A, -4

Understanding that angle As segment AB is a diameter of circle C, AOB is a straight angle. Moreover, we can infer that angle BON is a right angle, as segment AB and chord MN cross at point O at a right angle.

The smallest side and angle in every triangle are on opposing sides. The middle side and middle angle are always in opposition to one another in triangles.

We may get the length of ON using the Pythagorean theorem:

\(BN2 = ON2 = BO2\)

Given that BO is half of AB's length and AB's diameter is circle C, we have:

\(BO = AB/2 = r\)   (where r is the radius of circle C)

Additionally, since ON is a segment on chord MN, we can apply the following method to determine the length of a chord with two segments separated by a point:

\(MO * NO = MN2\)

Using the specified values in place of MO and NO,

\(MN^2 = (5x + 3) \times (6x)\)

\(MN^2 = 30x^2 + 18x\)

To find MN, we can take the square root of both sides:

\(MN = sqrt(30x^2 + 18x)\)

Therefore, the length of MN is \(sqrt(30x^2 + 18x)\)

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