a) Express √√√3+ √12 in the form a√3 where a is an integer. √3 b) (i) Express 1 (5) in the form b√3 where b is an integer. 1 (ii) Express (5) 3 in the form 3 C where c is an integer. √√3 √3 ​

Answer:

47.1239 inches

Step-by-step explanation:

The ground covered in one rotation of a circular wheel is the same as the circumference of the wheel

Circumference C = π · d
where d is the diameter

Given d = 15 inches

C = π · 15

   = 47.1239 inches

the answer is 18 hours. if you solve 18.25 *18 + 266 it = 594.5

if you solve 22.75 * 18 + 185 it = 594.5

Answer:

18 hours

Step-by-step explanation:

fist we start with the fees and hours (basic info to help get us started)

company 1

company 2

18 hour with fee factored in

we do this by adding the fee and hours like this

[tex]226 + 18.25(18)[/tex]

and get 594.50

and we do this for company 2 like this

[tex]185 + 22.75(18)[/tex]

and also get 594.50

Mass is a scalar quantity, while weight is a vector quantity. The two are related by the following equation: Weight = Mass × Gravity

Here's a step-by-step explanation:

1. Mass (scalar) is the amount of matter present in an object and is measured in kilograms (kg). It remains constant regardless of location.

2. Weight (vector) is the force exerted by gravity on an object's mass and is measured in newtons (N). It has both magnitude and direction (downward) and varies based on the strength of gravity at a particular location.

3. Gravity is the acceleration due to gravity and is approximately 9.81 m/s² on Earth's surface.

4. To find the weight of an object, you multiply its mass by the acceleration due to gravity:

Weight (N) = Mass (kg) × Gravity (m/s²)

By using this equation, you can determine an object's weight given its mass and the strength of gravity at its location.

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The probability that the first winner lives in Gaston and the second lives in Pike is (1/36).

What is Probability?

A number that reflects the chance or likelihood that a particular event will occur is called probability.

There are 9 customers in total, so there are 9 choices for the first winner.

According to question 2 of these customers live in Gaston

So, there are 2 choices for the first winner to live in Gaston.

After the first winner is chosen, there are only 8 customers remaining.

Now there are 8 choices for the second winner and one of the winners has already been chosen from Gaston, there are only 2 customers left in Gaston, and one of them is from Pike. Therefore, there is only 1 choice for the second winner to live in Pike.

So the probability that the first winner lives in Gaston and the second lives in Pike is (2/9) × (1/8) = 1/36

Therefore, the probability is 1/36, which is the final answer in its simplest form.

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The correct conclusion that can be drawn from the circle graph is given as follows:

Together, Walk and Streetcar are the preferred transportation for 165 residents.

A circle graph, also known as a pie chart, is used to represent data as a circle divided into sectors, where each sector represents a portion of the whole. The size of each sector is proportional to the percentage of the whole that it represents.

Out of 300 residents, the percentages and amounts are given as follows:

Hence the last option gives the correct option in the context of the problem.

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Requried, it takes 6.15 years for the number of insects in the population to double.

We know that the number of insects at the start of the year (n+1) is P+1, where [tex]P_n+1 = kP_n[/tex]

So, we can write:

[tex]P1 = kP_0\\P_2 = kP_1 = k(kP_0) = k^2 P_0\\P_3 = kP_2 = k(k^2 P_0) = k^3 P_0\\P_4 = kP_3 = k(k^3 P_0) = k^4 P_0\\[/tex]

[tex]Pn = k^n P_0[/tex]

To find out how many years it takes for the number of insects in the population to double, we need to find the value of n such that Pn = 2P0.

So, we have:

[tex]2P_0 = k^n P_0[/tex]

Dividing both sides by P_0, we get:

[tex]2 = k^n[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln 2 = n ln k\\n = ln 2 / ln k[/tex]

Substituting the value of k as 1.13, we get:

n = ln 2 / ln 1.13

n ≈ 6.15

Therefore, it takes 6.15 years for the number of insects in the population to double.

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Answer:

P(3,6) Q(3,0) R(6,6)

Step-by-step explanation:

multiply the coordinate of each vertice with the scale factor to obtain their images

Answer:

Step-by-step explanation:

1.  When do you eat dinner?

2.  When do you get ready for school?

3.  When do you brush your teeth?

4. When do you go to school?

5. When do you say your prayers?

6. When do you go to bed?

7. When do you eat lunch?

8. When do you see your dad?

9. When do you drive home from work?

10. When do you eat breakfast?

1. What time does school start?

2. What time is lunch at schoo?

3. What time does school end?

4. What time does your dad come home from work?

5. What time does your favorite show start

6. What time is it now?

7. What time is your bedtime?

8. What time does your plane leave?

9. What time do you wake up?

10. What time does your soccer game start?

Answer:

x  = 2y + 5    (1)

x^2 + y^2  = 5  (2)

Step-by-step explanation:

Sub (1) into (2) to find the y intersection of these functions

(2y + 5)^2  + y^2  =  5      simplify

4y^2 + 20 y + 25 + y^2  = 5

5y^2 + 20y +20  = 0      divide through by 5

y^2 + 4y + 4  =  0      factor

(y + 2)^2  = 0        take the square root of both sides

y + 2   = 0

y  = -2

And x  =    2(-2) + 5   =  1

So....(1, -2)  is the tangent point  because it  is the only point that makes both equations true

1 = 2(-2) + 5   is true      and

(1)^2  + (-2)^2  = 5     is also true

Hope this helps :)

Answer:

Step-by-step explanation:

2x - 5 = 2

2x = 5 + 2

2x = 7

x = [tex]\frac{7}{2}[/tex]

x = 3.5

Answer:

A. 1/3

Step-by-step explanation:

The probability of drawing a blue marble on the first draw is 2/4, or 1/2, since there are two blue marbles out of four total marbles. After one blue marble has been drawn and not replaced, there are now three marbles left in the bag, one blue and two green. Therefore, the probability of drawing a green marble on the second draw is 2/3.

To find the probability of both events happening, we multiply the probabilities:

P(blue, then green) = P(blue) * P(green after blue)

P(blue, then green) = 1/2 * 2/3

P(blue, then green) = 1/3

Therefore, the probability of drawing a blue marble followed by a green marble, without replacing the first marble before drawing the second marble, is 1/3. Answer: 1/3.

Answer: A

Step-by-step explanation: The rate of change is constant, increasing by 10/3 each time, so the function is linear.

Answer:

To solve the equation 85w^2=160 for w, we need to isolate w on one side of the equation.

First, divide both sides by 85:

85w^2/85 = 160/85

Simplifying, we get:

w^2 = 1.88235294118

To solve for w, we need to take the square root of both sides:

sqrt(w^2) = sqrt(1.88235294118)

Since w is a positive length, we can drop the negative square root, so we have:

w = 1.3725...

Rounding to the nearest hundredth, we get:

w ≈ 1.37 ft

Therefore, the width of the backdrop is approximately 1.37 feet.

Answer:90

Step-by-step explanation:80*6=480= All Subjects

78*5=390

480-390=90

Answer: well, since we can assume that the first 5 are 78, he would have to get a 90% in order to get a 80% average

The length of the base, x is b) 2.90.

Let's call the length of the hypotenuse "h" and the length of the base "x". We can use trigonometry to set up an equation relating these three lengths.

Since we know that the triangle is right-angled, we can use the trigonometric function "sine" to relate the angle between the perpendicular and the hypotenuse to the sides of the triangle:

sin(71) = 4/h

Multiplying both sides by h, we get:

h * sin(71) = 4

Next, we can use the Pythagorean theorem to relate the length of the hypotenuse to the length of the base:

[tex]h^{2}[/tex] = [tex]x^{2}[/tex] + [tex]4^{2}[/tex]

Substituting the first equation into the second equation, we get:

[tex](hsin(71))^{2}[/tex] = [tex]x^{2}[/tex] + [tex]4^{2}[/tex]

Simplifying and solving for x, we get:

x = [tex]\sqrt{(hsin(71))^{2}-4^{2} }[/tex]

Using a calculator, we can evaluate this expression and find that x is approximately equal to 2.90.

Therefore, the answer is (b) 2.90.

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Answer:

Step-by-step explanation:

To solve for the angles, you can use the fact that the sum of the angles in a triangle is 180 degrees.

So, you can set up an equation:

43 + 3x + (5x-5) = 180

Simplifying, you get:

8x + 38 = 180

Subtracting 38 from both sides:

8x = 142

Dividing both sides by 8:

x = 17.75

Now that you know x, you can plug it into the expressions for the other two angles to find their measures:

First angle = 3x = 3(17.75) = 53.25

Third angle = 5x - 5 = 5(17.75) - 5 = 83.75

Therefore, the three angles are 43 degrees, 53.25 degrees, and 83.75 degrees.

The approximate amount of paint needed =  438.03 cm²

The correct answer is an option (D)

We know that the formula for the surface area of the cylinder is :

A = (2 × π × r × h) + (2 × π × r²)

Here, the diameter of the can is 9 sm

So, the radius of the can would be,

r = d/2

r = 9/2

r = 4.5 cm

And the height of the can is h = 11 cm

Since the can is cylindrical, we use above formula of surface area of the cylinder to find the amount of paint needed.

Using above formula,

A = (2 × π × r × h) + (2 × π × r²)

A = (2 × π × (4.5) × (11)) + (2 × π × (4.5)²)

A = 311.02 + 127.01

A = 438.03 cm²

Therefore, the correct answer is an option (D)

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The area of sector GPH in square yards is equal to 157 yd².

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

Area of sector = 80(3.14/360) × (15)²

Area of sector = 0.6978 × 225

Area of sector = 157 yd²

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The price of the apple and the pears at the shop in pence would be = 0.5 and 0.73 pence respectively.

Let's represent the apple as = X

Let's represent the pear as = y

That is ;

4x + 3 y = 4.10. ---> equation 1

5x +8y = 6.40 ----> equation 2

Make X the subject of formula in equation 1

4x = 4.1-3y

X = (4.1-3y)/4

substitute X = (4.1-3y)/4 into equation 2.

5[(4.1-3y)/4] + 8y = 6.40

20.5-15y+8y = 6.40×4

20.5 - 7y = 25.6

-7y = 5.1

y = 5.1/7

y = 0.73

Substitute y = 0.73 into equation 1;

4x + 3(0.73) = 4.10.

4x + 2.19 = 4.10

4x = 4.20-2.19

4x = 2.01

X = 2.01/4

X = 0.5

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The length of segment a will is

D. 6

Applying the Law of Cosines with the formula given below

a² = b² + a² - 2bc cos(A)

where

a, b, and c are sides of the triangle and

A, b, ad C are the angles of the triangle

a² = 8² + 10² - 2 x 8 x10  cos (37°).

a² = 64 + 100 - 160 kos(37°).

a² = 164 - 123.2

taking the square root of both sides

a = √40.8

a ≈ 6.39

Therefore, the length of segment a will be 6.39 units.

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The correct option is D, Smoothing time series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the random variation component.

Random variation refers to the natural variability or chance fluctuation of a certain phenomenon or event. It is the deviation from a predictable pattern, caused by random or unpredictable factors. Random variation is a common occurrence in scientific studies and statistical analysis, and it can affect the results of experiments, making it important to consider when drawing conclusions from data.

For example, in a study on the effects of a drug on blood pressure, random variation could be caused by factors such as age, weight, or genetics of the participants. These factors may cause the blood pressure to fluctuate, independent of the drug's effects. Understanding and accounting for random variation is essential in order to obtain reliable and accurate data. Statistical methods such as randomization, replication, and blinding can help to reduce the impact of random variation in studies. In short, random variation is an important consideration in scientific research, and it must be taken into account to ensure the validity and accuracy of the results.

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Complete Question:-

Smoothing time series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:

a. trend component

b. cyclical component

c. seasonal component

d. random variation component

Answer:

247° and 067°

Step-by-step explanation:

the bearing of one point to another is the measure of the angle from the north point N at one point in a clockwise direction to the other point.

(a)

bearing of B from A = 247° ( from N at B clockwise to A )

(b)

bearing of B from A = 067° ( from N at A clockwise to B )

The exact values of the trigonometric sin 2Θ, cos 2Θ, and tan 2Θ are:

sin 2Θ = 720/1681

cos 2Θ = 1521/1681

tan 2Θ = 720/1521

We have,

Since sin Θ = -9/41 and Θ lies in quadrant III, we can use the Pythagorean identity to find the value of cos Θ:

cos²Θ = 1 - sin²Θ

cos²Θ = 1 - (-9/41)²

cos²Θ = 1 - 81/1681

cos²Θ = 1600/1681

cosΘ = -40/41

Using the information we have, we can find the values of sin 2Θ, cos 2Θ, and tan 2Θ:

a.

sin 2Θ = 2sinΘcosΘ

sin 2Θ = 2(-9/41)(-40/41) = 720/1681

b.

cos 2Θ = cos²Θ - sin²Θ

cos 2Θ = (-40/41)² - (-9/41)² = 1521/1681

c.

tan 2Θ = sin 2Θ / cos 2Θ

tan 2Θ = (720/1681) / (1521/1681) = 720/1521

Therefore,

The exact values of sin 2Θ, cos 2Θ, and tan 2Θ are:

sin 2Θ = 720/1681

cos 2Θ = 1521/1681

tan 2Θ = 720/1521

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The total inches Derek has grown in the past three years is 3 inches.

None of the given options is correct.

Given information:

For the previous three years, Derek has become an inch taller every year.

This means that we can add up those three inches to find his total growth over the three-year period.

Thus, 1 + 1 + 1 equals 3 inches.

Derek has therefore gained 3 inches in total over the last three years.

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Answer:

Step-by-step explanation:

the answers is Ax + By + C = 0 y = mx + c y − y1= m(x − x1) m = Δy/Δx = (y2 − y1)/(x2 − x1)

The surface area of the prism is 184 cm², So the correct answer is 184 square centimeters.

A triangular prism is a three-dimensional geometric shape that consists of two congruent parallel triangles as its bases and three rectangular faces connecting the corresponding sides of the two triangles.

The triangular prism has a total of six faces, to find the surface area of the prism we need to find the sum of the area of the six faces.

Here we have

The prism has a rectangular base with dimensions of 10 cm × 6 cm  

The height of the prism is 4 cm and the sides of the triangular faces are 5 cm

Here,

The surface area of the prism

= Area of base + Area of 2 rectangular faces + Area of 2 triangular faces

= 10 cm × 6 cm + 2 [ 10 cm × 5 cm ] + 1/2 2 [ 4 cm × 6 cm ]

= 60 cm² + 100 cm² + 24 cm²

= 184 cm²  

Therefore

The surface area of the prism is 184 cm², So the correct answer is 184 square centimeters.

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Complete Question:

What is the surface area of the triangular prism shown?

32 square centimeters

120 square centimeters

184 square centimeters

1,560 square centimeters

In each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference between two population means conditions not met for Scenario 1, and conditions met for Scenarios 2 and 3.

a. Conditions not met; do not proceed with the hypothesis test. Since the distribution is strongly skewed to the right, the sample size should be much larger (i.e., n > 100) for the t-model to be valid.

b. Conditions not met; do not proceed with the hypothesis test. Since the distribution is strongly skewed for females, the sample size of 37 is too small for the t-model to be valid.

c. Conditions met; proceed with the hypothesis test. Since both distributions are fairly normal and the sample sizes for males and females are each 100, the t-model can be used.

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The question is -

In each of the following scenarios, researchers plan to conduct either a hypothesis test for a population mean or for the difference between two population means. Are the conditions for use of a T-model met?

1. In a random sample of 100 university students, the distribution of time spent at university recreational facilities is strongly skewed to the right.

2. In a random sample of 50 university students (37 females and 13 males), the distribution of time spent at university recreational facilities is strongly skewed to the right for females but not strongly skewed for males.

3. In a study of 100 brother-sister sibling pairs at the university, the distribution of time spent at university recreational facilities for the 100 males is compared to the 100 females; both distributions are fairly normal.

The likelihood of selecting a cut of pepperoni pizza moment given merely have as of now chosen a cut of cheese pizza to begin with is 4/7 or roughly 0.57.

There are a add up to of 8 cuts of pizza, and in the event that you haphazardly select a cut of cheese pizza to begin with, there are presently as it were 3 cuts of cheese pizza cleared out out of 7 add up to cuts cleared out. Since you need to discover the likelihood of selecting a cut of pepperoni pizza moment given that a cut of cheese pizza has as of now been chosen, you would like to calculate the likelihood of selecting a cut of pepperoni pizza from the remaining 4 cuts of pepperoni pizza and 3 cuts of cheese pizza.

The likelihood of selecting a slice of pepperoni pizza moment given that you simply have as of now chosen a cut of cheese pizza to begin with can be calculated utilizing the conditional likelihood equation:

P(Pepperoni moment | Cheese to begin with) = P(Pepperoni moment and Cheese to begin with) / P(Cheese to begin with)

The likelihood of selecting a cut of pepperoni pizza moment and a cut of cheese pizza to begin with is [tex]4/8 x 4/7 = 16/56[/tex]. The likelihood of selecting a cut of cheese pizza to begin with is 4/8, which disentangles to 1/2. Subsequently: P(Pepperoni moment | Cheese to begin with) = (16/56) / (1/2) = 4/7

The complete question is:

You and some friends ordered pizza and have four slices of pepperoni pizza and four slices of cheese pizza remaining. Find the probability that you select a slice of pepperoni pizza second given that you randomly selected a slice of cheese pizza first.

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The system of equations when solved by calculator is (x, y) = (3.304, -0.478)

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

2x - 5y = 9

3x + 4y = 8

Rewrite them in intercept form

So, we have

5y = 2x - 9

4y = -3x + 8

This gives

y = 2/5x - 9/5

y = -3/4x + 2

Solving the system of equations by calculator, we have the following solutions

(x, y) = (3.304, -0.478)

Hence, the solution is (x, y) = (3.304, -0.478)

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Answer:

B) it will take him 11h to mow 12 lawns