A company dyes two sizes of rugs. A small rug requires 8 hours for dyeing, and a medium-size rug requires 12 hours for dyeing. The dyers have to make at least 22 rugs, and they must do it in less than 240 hours. Let x equal small rugs and y equal medium rugs. Which of the following inequalities can be paired with x + y ≥ 22 to create a system that represents this situation?

8x + 12y > 240
12x + 8y > 240
8x + 12y < 240
12x + 8y < 240

The value of the trigonometry identity is tan(2x) = 4/7[√2]

From the question, we have the following parameters that can be used in our computation:

cos(x) = 2√5/5 and 3π/2 < x < 2π

Start by calculating the sine function sin(x) using

sin(x) = √[1 - cos²(x)]

So, we have

sin(x) = √[1 - (2√5/5)²]

This gives

sin(x) = 1/10[√10]

The tangent is then calculated as

tan(2x) = (2sin(x)cos(x))/(cos²(x) - sin²(x))

This gives

tan(2x) = (2 * 1/10[√10] * (2√5/5))/(((2√5/5))² - (1/10[√10])²)

Evaluate

tan(2x) = 4/7[√2]

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The value of a, A and C are 12.31 cm,44.07° and 34.68° respectively

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find C:

b/sinb = c/sinC

17.23/sin101.25 = 10/sinC

17.23 × sin C = sin101.25 × 10

17.23× sin C = 0.98 ×10

sinC = 9.8/17.23

sinC = 0.569

C = sin^-1(0.569)

C = 34.68°

The sum of angle in a triangle is 180

A = 180-(101.25+34.68)

A= 180-135.93

A = 44.07°

a/sinA = b/sin B

a/sin 44.07 = 17.23/sin101.25

a= sin 17.23 × sin 44.07/sin101.25

a =( 17.24× 0.70)/0.98

a = 12.31 cm

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Answer:

3

Step-by-step explanation:

[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\ \\=\frac{f(1)-f(-1)}{1-(-1)}\\ \\=\frac{3-(-3)}{1+1}\\\\=\frac{3+3}{2}\\ \\=\frac{6}{2}\\ \\=3[/tex]

Answer:

x ≥ 3

Step-by-step explanation:

3x ≥ 9

x ≥ 3

The 95% confidence interval estimate for the true proportion of women in Europe who use the internet is = (34.968%, 35.032%)  can be calculated using the following formula:

p ± z*(√(p(1-p))/n)

where pis the sample proportion (35% in this case), z is the z-score for a 95% confidence level (approximately 1.96), and n is the sample size (750 in this case).

Substituting the values, we get:

35% ± 1.96 * (√(35%(1-35%)/750))

= 35% ± 1.96 * (√(0.35 * 0.65/750))

= 35% ± 1.96 * (√(0.000936))

= 35% ± 0.0312

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The amount that Cameron is paid per hour, given the number of hours he worked, is $ 17 per hour

To find the payment that Cameron got per hour, you first need to find the number of hours that he worked.

This number of hours is:

= 4 pm  - 8 am

= 1500 hours - 0800 hours

= 7 hours

The payment per hour is therefore:

= Amount Cameron paid / Number of hours worked

= 120 / 7

= $ 17 per hour

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The number listed below that are the solution of equation are option A 16 and option C 1.

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, while the square root of a number can be found by looking for a number that, when squared, yields the original value.

The given equation is:

√s² = s

The numbers that satisfy thus equation are 16 and 1.

Negative numbers do not satisfy the equation as the square root of a number is a positive number, and hence the two sides will not be equal.

Hence, the number listed below that are the solution of equation are option A 16 and option C 1.

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Answer:

x = Approximately 4.92. (Tech: 4.923076923076923)

Step-by-step explanation:

To solve for x in the equation,

x - 1/4(12 - x) = x + 3(4 - x) - 2x

Expand the terms on the right side:

x - 1/4(12 - x) = x + 12 - 3x - 2x

Combine like terms:

x - 1/4(12 - x) = -3x + 12

Isolate x on one side of the equation:

1/4(12 - x) + 3x = 12 + x

Combine like terms:

1/4(12 - x) + 3x = 13

Distribute 3x:

1/4(12 - x) + 3x = 13

3x = 13 - 1/4(12 - x)

Multiply both sides by 4:

12x = 52 - (12 - x)

Combine like terms:

13x = 64

Finally, divide both sides by 13:

x = 4.923076923076923

So the value of x is approximately 4.92.

Answer: Depends on the unit. IF INCHES: 6 1/2 = 78 Inches

Step-by-step explanation:

6.5 x 12 = 78

Please reply if not inches, I can try to help you after ^^

Answer:

16

Step-by-step explanation:

Any number to the power of 0 is 1

1/4^-2 -> 4^2 -> 16

Answer: 16

Step-by-step explanation:

-2^0 = 1

y^-2 => 1/y^2 => 1/4^2 = 1/16

1/ (1/16)

1 x 16/1 = 16

Answer: $1486.01

Step-by-step explanation: 200*(1.2^(12-1))

The equation 5 + 4 - 2 = 9 - 2 represents a situation in which the scientist is measuring the mass of an object using a pan balance.

The equation shows that 5 units of mass are added to one pan, 4 units of mass are added to the other pan, and then 2 units of mass are removed from each pan. The equation shows that the total mass in both pans remains unchanged, which indicates that the pans are still in balance. The fact that the equation is balanced, with the same amount of mass on each side, suggests that the pans are in balance because the mass has been distributed evenly between them. The balance operates on the principle of equal weights, where equal weights on opposite sides will cancel each other out, resulting in a balanced state.

Therefore, by removing 2 units of mass from each pan, the scientist is maintaining the balance between the two pans. As long as the pans remain balanced, the scientist can accurately determine the mass of the object being measured. The equation 5 + 4 - 2 = 9 - 2 represents the scientist's assurance that the pans are still in balance and that the measurement of mass can be considered accurate.

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It is unlikely for your height to be 70 inches exact because there are infinite number of possible ways.

Height is considered a continuous variable because it can take on any value within a certain range, including fractional values. Continuous variables are not limited to specific set of values, but can take on any value within a specified range. This is in contrast to discrete variables, which can only take on a specific, limited set of values. The continuous nature of height allows for precise measurement and calculation, as opposed to rounding to the nearest whole number.

When we talk about height, height is measure and hence it is a continuous variable. This means that it is possible for a person's height to be exactly 70 inches, but it is unlikely due to the vast number of possible values.

Hence, it is very unlikely for height to be specific.

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Uniform distribution best describes the given shape of the distribution.

The uniform distribution is a probability distribution that has the same probability of occurrence across a defined interval. It is also sometimes referred to as a rectangular distribution or a flat distribution.

The uniform distribution is defined by two parameters, a and b, which represent the lower and upper bounds of the interval. For example, if a uniform distribution is defined between 0 and 1, the probability of any number between 0 and 1 occurring is equal and the same.

The uniform distribution has several properties, including:

The mean of the distribution is equal to the midpoint of the interval, (a + b) / 2.

The variance of the distribution is equal to (b - a)² / 12.

The distribution is symmetrical, meaning that it is equally likely for any value within the interval to occur.

Applications of the uniform distribution include modelling random processes such as coin flips, die rolls, and random sampling. It is also often used as a prior distribution in Bayesian statistics.

Hence, the correct answer is A.

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--The given question is incorrect; the correct question is

"Which BEST describes the shape of the distribution?

A) uniform

B) skewed right

C) skewed left

D) roughly symmetrical"--

The solution to the figure shown is Option D.

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the figure be represented as A

Now , the front part of the figure is shown

And , on reflection , the position of the figure will be changed

The top part of the figure has 4 cubes

And , the side view of the figure has 2 cubes

From the options , we can see that the Option D satisfies the figure shown in the question

As , the front view will have a cube above the second cube and top view will show 4 cubes and the side view will show 2 cubes respsectively

Hence , the figure is solved

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The minimum size of a cut where size is number of edges in the cut, for a graph that has more than one connected component is 1.

In graph theory, a bridge, also known as a cut-edge, is a fundamental concept that refers to an edge in a graph that has the property of disconnecting the graph when it is removed. This means that when an edge is considered a bridge, the removal of that edge would result in an increase in the number of connected components in the graph. The importance of bridges in graph theory lies in the fact that they provide a way to break down a complex graph into smaller, simpler components that can be analyzed and understood individually. Bridges can be found in many different types of graphs, including undirected graphs, directed graphs, and weighted graphs. It is also important to note that in a graph with more than one connected component, there must exist at least one bridge, meaning that the minimum size of a cut in a graph is 1. This is because a bridge is the edge that separates the graph into two or more separate components.

The minimum size of a cut in a graph is 1. This occurs in the case of a "bridge", where removing a single edge from the graph would result in two separate connected components. In any graph with more than one connected component, there must exist at least one bridge, meaning that the minimum size of a cut is 1.

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The discount is $30 and the rate of discount for the truckload of Kurt's Dirt selling for $120 but bought for $90 is 25%.

The discount rate refers to the percentage of price reduction offered to retail customers.

To compute the discount rate, we first determine the amount of discount.  Then the result is expressed as a percentage of the initial price before the discount.

The selling price of a truckload of Kurt's Dirt = $120

The discounted price = $90

The amount of discount = $30 ($120 - $90)

Discount rate = 25% ($30/$120 x 100).

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Answer:

Probability of an even number product as requested = 7/10 = .7 = 70%

Step-by-step explanation:

Combinations of 2 digits from among 5 = 5!/(3!)(2!) = 10. Those combinations of 2 digits resulting in an even number product are even*even and even*odd. There are 2 even digits, (2,4) and 3 odd digits, (1,3,5).

Combinations of 2 even digits and 3 odd digits = 3*2 = 6. Combinations of 2 exact digits = 1*1 = 1. Thus, 6+1 = 7 different 2-digit products result in even numbers from among 10 possible 2-digit products.

Probability of an even number product as requested = 7/10 = .7 = 70%

Answer:

6x-6y=0

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The proof that the angles are similar have been done below

To prove that two triangles are similar, we need to show that they have congruent angles.

We can use the Angle-Angle (AA) Similarity theorem, which states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

In triangle ABC, angles A and B are equal to angles A and D in triangle ADE. So, according to the AA Similarity Theorem, triangles ABC and ADE are similar.

Thus, we can write:

ABC ~ ADE

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By  simple interest , 2108 is the balance after 6 years.

What does compound and simple interest mean?

Simple interest and compound interest are the two methods that can be used to compute interest. The principal, or initial amount of a loan, is used to compute simple interest.

                                Compound interest is often referred to as "interest on interest" since it is computed using the main amount and the interest that has accrued over the course of previous periods.

annual simple interest = 4%

principal = $1700

 Time = 6 years

  interest = PRT/100

            = 1700 * 6 * 4/100

            =   408

 the balance after 6 years  = 1700 + 408

                                               =    2108

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The two quadrilaterals TUVW and EFGH are similar.

Those polygons look the same but are different in size.

And in similar polygons,

the corresponding sides are in constant proportion to each other and the corresponding angles are equal to each other.

Given:

TUVW and EFGH are the two quadrilaterals.

The sides of the polygon TUVW are equal.

And the sides of the polygon EFGH are equal.

That means the corresponding sides will have a constant ratio.

And corresponding angles are congruent.

So, the polygons are similar.

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The equation for the rate of change of concentration is Δc/Δt, and this is equal to the rate of change of concentration over a given interval, -0.0680 m/s.

To calculate the final concentration, we must use the equation Δc = rate × time, where Δc is the change in concentration, and rate and time are the rate of change of concentration and the interval, respectively. Plugging in our values, Δc = -0.0680 m/s × 3.0 s = -0.204 m. This means that the final concentration of c is 2.700 m - 0.204 m, which is equal to 2.496 m.

To summarize, the rate of change of concentration equation is Δc/Δt = rate of change, and the equation to calculate the final concentration is Δc = rate × time. Plugging in the rate of change and interval, we get Δc = -0.0680 m/s × 3.0 s = -0.204 m, which gives us the final concentration of c at the end of the same interval as 2.496 m.

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Answer:

D(t) = 20 * sin(B * t - B * 3 + k * 2π) + 45 = 20 * sin(B * (t - 3) + k * 2π) + 45

Step-by-step explanation:

The temperature over a day can be modeled by a sinusoidal function of the form:

D(t) = A * sin(Bt + C) + D

Where A is the amplitude (half the difference between the high and low temperatures), B is the angular frequency, C is the phase shift, and D is the vertical shift.

From the given information, we know:

The high temperature is 85 degrees.

The low temperature of 45 degrees occurs at 3 AM, or 3 hours after midnight.

So, the amplitude is (85 - 45)/2 = 20

The temperature at 3 AM can be found by setting t = 3:

D(3) = 20 * sin(B * 3 + C) + 45

So, the vertical shift is 45.

Finally, we can find the phase shift by using the fact that the low temperature occurs at 3 AM:

C = -B * 3 + k * 2π

Where k is an integer.

Putting it all together, we get:

D(t) = 20 * sin(B * t - B * 3 + k * 2π) + 45 = 20 * sin(B * (t - 3) + k * 2π) + 45

This is the equation for the temperature, D, in terms of t.

Answer:

The solution to the system of two linear equations is p = -6.

Step-by-step explanation:

First, we can isolate the variable p on one side of the equation. Subtract 8 from both sides to get 1/6p = -1/3p + 6.

Next, we can subtract -1/3p from both sides to get 4/6p = 6.

Finally, we can divide both sides by 4/6 to get p = -6.

Answer:

64.4 meters

Step-by-step explanation:

divide 7000 cm (7 metre) by 5 cm

you get 1400

multiply that by the smaller wingspan

Answer:

65.71

Step-by-step explanation:

According to the model's scale, which is 5 cm to 7 m, there are 7 m on the actual plane for every 5 cm on the model. By dividing the wingspan of the model by the scale factor and multiplying the result by the equivalent size in metres, we may determine the real plane's wingspan.

 With a model's wingspan of 46 cm, this means: (46 cm) * (7 m/5 cm) = 65.71 m (46 cm) / (5 cm/7 m) 

The actual airplane's wingspan is therefore roughly 65.71 metres.

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24

24x3.14

75.36

75.36/3.14

= 24 its b

Answer: 36pi(cm)^2 Answer B

Step-by-step explanation:

The number of the one-point shot is 17 and the number of the 2 point shot is 36.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that at a basketball​ game, a team made 53 successful shots. They were a combination of​ 1- and​ 2-point shots.

Let the one-point shot is x and the 2 point shot is y. The equations can be written as below:-

x + y = 53

-x - 2y = -89

_________

y = 36

The value of x will be calculated as:-

x + y = 53

x + 36 = 53

x = 53 - 36

x = 17

Hence, the one-point shot number is 17, and the two-point shot number is 36.

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