Solve the following for θ, in radians, where 0≤θ<2π.
3cos2(θ)+6cos(θ)−4=0

The original sample box had a volume of 343 cubic cm, which is half the volume of the new sample box.

Since the height of the new sample box is twice as long as the original box, its height will be 2×7=14 cm.

The length and width remain the same at 7 cm.

The volume of the new sample box is given by the formula:

V = lwh

Substituting the values, we get:

V = (7)(7)(14) = 686 cubic cm

Therefore, the volume of the new sample box is 686 cubic cm.

Comparing the volumes of the two boxes, we see that the new sample box has a larger volume than the original sample box.

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The area of the composite figure is equal to 12.28 square kilometers

The composite figure can be observed to be made up of a triangle and a semicircle, so we shall calculate for the area of both shape and sum the results to get the total area of the composite figure as follows:

area of triangle = 1/2 × 3 km × 4 km = 6 km²

area of complete circle = 3.14 × 2 km × 2 km = 12.56 km²

area of semicircle = (12.56 km²)/2 = 6.28 km²

total area of the composite figure = 6 km² + 6.28 km²

total area of the composite figure = 12.28 km²

Therefore, the area of the composite figure is equal to 12.28 square kilometers

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Answer:

Step-by-step explanation:The six sample minimums are 15, 15, 15, 18, 18, and 20.

To find the mean of all six sample minimums, we add them up and divide by 6:

(15 + 15 + 15 + 18 + 18 + 20) / 6 = 16.1667

So the mean of all six sample minimums is $16,166.67.

The population minimum is the smallest cost among the four cars, which is $15,000.

The sample minimum is a biased estimator of the population minimum. Since the samples are of size 2, the probability of obtaining the population minimum as the sample minimum is only 1/3 (when the minimum of the two cars selected is the population minimum). Therefore, the sample minimum tends to underestimate the population minimum.

Answer:correct answers 0.42

2.73

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

-6u^2 - 5u + 3 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -6, b = -5, and c = 3. Substituting these values, we get:

u = (5 ± sqrt(5^2 - 4(-6)(3))) / 2(-6)

u = (5 ± sqrt(109)) / (-12)

Therefore, either:

sin(θ) = (5 + sqrt(109)) / (-12)

or:

sin(θ) = (5 - sqrt(109)) / (-12)

The following statements are always true regarding the given diagram having angles: m<3+m<4+m<5=180, m<5+m<6=180, m<2+m<3=m<6.

Statement 2 is always true because the sum of the three angles in a triangle is always 180 degrees.

Statement 3 is always true because the sum of the angles on a straight line is 180 degrees.

Statement 4 is always true because angles 2, 3, and 6 are opposite angles, which means they are congruent.

Thus, statements 1 and 5 are not always true. The sum of angles 3, 4, and 5 could be greater or less than the measure of angle 5. The sum of angles 2, 3, and 5 could be greater or less than the measure of angle 3.

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Since John cannot buy a fraction of a can, he needs to round up to the nearest whole number. So, John needs at least 5 cans of paint to cover the entire wall as per the height and length.

To calculate the area of the wall, we need to multiply the height and the length of the wall.

From the diagram, we can see that the height of the wall is 2 meters and the length is 5 meters.

So the total area of the wall is:

Area = height x length

Area = 2 meters x 5 meters

Area = 10 square meters

To convert this to square feet, we can use the conversion factor:

1 square meter = 10.764 square feet

So:

Area = 10 square meters x 10.764 square feet/square meter

Area = 107.64 square feet

Since 1 can of paint covers 24 square feet, John needs:

Number of cans = Area ÷ Coverage per can

Number of cans = 107.64 square feet ÷ 24 square feet/can

Number of cans = 4.485 cans

Thus, John needs at least 5 cans of paint to cover the entire wall.

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Your question seems incomplete, the probable complete question is:

John needs to paint one wall in his school. He knows that 1 can of paint covers an area of 24 square feet.

John uses a meter stick to measure the dimensions of the wall as shown.

[1 meter = approximately 39 inches]

What is the fewest number of cans of paint John can use to paint the wall?

x² + 5x + 3 = 0, the quadratic equation has two distinct real roots

2x² - 2x + 1 = 0, no real roots. Instead, it has two complex conjugate roots.

x² + 5x + 3 = 0

To determine the nature of the roots of this quadratic equation, we need to calculate the discriminant using the formula:

Discriminant = b² - 4ac

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, a = 1, b = 5, and c = 3.

Discriminant = (5)² - 4(1)(3)

= 25 - 12

= 13

Since the discriminant is positive and not a perfect square, the quadratic equation has two distinct real roots

Now 2x² - 2x + 1 = 0

a = 2, b = -2, and c = 1

Plugging these values into the discriminant formula, we get:

b²  - 4ac = (-2)²  - 4(2)(1) = 4 - 8 = -4

Since the discriminant is negative, the quadratic equation 2x² -2x+1=0 has no real roots.

Instead, it has two complex conjugate roots.

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Answer: the visitor would save $8 with the coupon.

Step-by-step explanation: 10% of $80 = 0.1 x $80 = $8

Answer:

meaning that you're answer would be $7.34 please make brainliest

Step-by-step explanation:

Answer:

none

Step-by-step explanation:

None, 106 is from the numbers being added and it is a right angle

Let's call the cost of each video game "x". We can set up two equations based on the information given:

4x + 2(0.01) = 20.92 (the 0.01 represents the commission fee for each phone)

4x = 20.92 - 0.02

4x = 20.90

x = 5.225

So each video game costs $5.225.

We can double-check our answer using the information about the friend's sales:

4(5.225) + 3(0.01) = 23.44

20.90 + 0.03 = 23.44

23.44 = 23.44

So our answer is correct.

Answer:-30c

Step-by-step explanation:

you subtract 8 from 3c which is -5c than multiply by 6 which is -30c

When distributed directly proportionally among the people, using age, the result would be b) 3 years = 6,000, 7 years = 14,000, 10 years = 20,000.

First, find the total age of the people give :

= 10 + 7 + 3

= 20

To amount that would go to 10 as a directly proportional measure is:

= 10 / 20 x 40, 000

= 20, 000

The amount to 7 as a directly proportional value would be:

= 7 / 20 x 40, 000

= 14, 000

The amount to 3 would follow the same pattern :

= 3 / 20 x 40, 000

= 6, 000

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Answer:

cmon man

Step-by-step explanation:

We want to show that sinθ cosθ = cotθ is not true for all values of θ. To do this, we just need to find one counterexample, i.e., one value of θ for which the equation is not true.

Recall that cotθ = cosθ/sinθ. So, the equation sinθ cosθ = cotθ can be rewritten as sinθ cosθ = cosθ/sinθ.

Multiplying both sides by sinθ, we get:

sin^2θ cosθ = cosθ

Dividing both sides by cosθ, we get:

sin^2θ = 1

Taking the square root of both sides, we get:

sinθ = ±1

So, we need to find a value of θ such that sinθ is equal to ±1. This occurs when θ = π/2 + kπ, where k is an integer.

Now, let's check whether sinθ cosθ = cotθ is true for this value of θ. We have:

sin(π/2 + kπ) = ±1

cos(π/2 + kπ) = 0

cot(π/2 + kπ) = undefined (since cos(π/2 + kπ) = 0)

Therefore, sinθ cosθ = cotθ is not true for θ = π/2 + kπ, and we have found a counterexample. This shows that sinθ cosθ = cotθ is not a trigonometric identity.

Based on the information, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.

standard error will be:

= 0.71 / ✓(195) = 0.051 kilograms

Substituting these values into the formula, we will then get:

Confidence interval = 3.04 ± (1.645) × (0.051)

Confidence interval = 3.04 ± 0.084

Confidence interval = (2.956, 3.124)

Therefore, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.

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The unknown angle in the cyclic quadrilateral is as follows:

m∠DGF = 75 degrees

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's the angle m∠DGF as follows:

The opposite angles of a cyclic quadrilateral have a total of 180°.

4x + 7 + 8x - 31 = 180

12x  - 24 = 180

12x = 180 + 24

12x = 204

divide both sides by 12

x = 204 / 12

x = 17

Hence,

m∠DGF = 4x + 7 = 4(17) + 7 = 68 + 7 = 75 degrees

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The surface area of each square pyramid, we used the formula Surface Area = Base Area + 4 x (1/2 x Base x Height of Face) is 1049.2mm², 1285.8mm² and 2100mm². The cost to cover each pyramid was $1.05, $1.29 and $2.10.

To calculate the surface area of each pyramid, we need to use the formula

Surface Area = Base x Height of face + 2 x ((Base/2) x Slant Height)

For the small pyramid, we have

Surface Area = 20 x 25 + 2 x ((20/2) x 26.46)

Surface Area = 500 + 2 x 10 x 26.46

Surface Area = 1049.2 mm²

Cost to cover the small pyramid

Cost = Surface Area x 0.001

Cost = 1049.2 x 0.001

Cost = $1.05

For the medium pyramid, we have

Surface Area = 20 x 40 + 2 x ((20/2) x 42.43)

Surface Area = 800 + 2 x 10 x 42.43

Surface Area = 1285.8 mm²

Cost to cover the medium pyramid

Cost = Surface Area x 0.001

Cost = 1285.8 x 0.001

Cost = $1.29

For the large pyramid, we have

Surface Area = 30 x 40 + 2 x ((30/2) x 50)

Surface Area = 1200 + 2 x 15 x 50

Surface Area = 2100 mm²

Cost to cover the large pyramid

Cost = Surface Area x 0.001

Cost = 2100 x 0.001

Cost = $2.10

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The value of x and y are,

x = 8 and y = 4

We have to given that;

Tim has $20 to buy snacks for 12 people in an office.

And., Tim is buying bags of pretzels that cost $1.50 per bag and bags of crackers that cost $2.00 per bag.

Let x represent bags of pretzels.

And, y represent bags of crackers.

Hence, We can formulate;

x + y = 12  .., (i)

And, 1.5x + 2y = 20  .. (ii)

From (i);

x = 12 - y

Plug in (ii):

1.5 (12 - y) + 2y = 20

18 - 1.5y + 2y = 20

18 + 0.5y = 20

0.5y = 2

y = 2/0.5

y = 4

And, x = 12 - 4

x = 8

Thus, The value of x and y are,

x = 8 and y = 4

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Using the statistical tool, the following were arrived at:

It should be noted that when arranged from lowest to highest, the IQR represents the central 50% of values.

Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).

These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.

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A linear equation to find the cost for a new customer to rent a bay is y = 2x + 10.

The cost for a new customer to rent a bay for 6 hours is equal to $22.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about the amount of money top golf charges a new customer, the cost can be modeled by this linear equation:

y = mx + c

y = 2x + 10

When x = 6 hours, the cost can be calculated as follows;

y = 2x + 10

y = 2(6) + 10

y = $22.

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The total time taken to walk the museum is t = 3/4 of an hour

Given data ,

Let the time spent at the first 3 exhibits = 3/4 + 3/4 + 3/4 = 9/4 hours

Let the time spent at the museum after the first 3 exhibits = 1 1/2 = 3/2 hours

Total time spent at the museum = 9/4 + 3/2 = (9/4 + 6/4) = 15/4 hours

Since the museum closes after you spend a total of 4 1/2 hours at the museum, we can subtract the total time spent at the museum from the closing time to find the time it took you to walk to the museum:

Closing time - Total time spent at the museum = 4 1/2 - 15/4

On simplifying the equation , we get

A = 9/2 - 15/4

On subtracting the fractions , we get

9/2 - 15/4 = (18/4) - (15/4) = 3/4

Hence , it took you 3/4 hour, or 45 minutes, to walk to the museum

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The total number of employees in the company is 297 if  ratio of union members to nonunion members working for a company is 4 to 7

The given ratio of union members to nonunion members, which is 4 to 7. This means that for every 4 union members, there are 7 nonunion members.

We are also given that there are 108 union members working for the company.

The total number of employees in the company be "x".

Let us from a proportional equation

4/11 = 108/x

To solve for x, we can cross-multiply and simplify:

4x = 1188

x = 297

Therefore, the total number of employees in the company is 297.

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1.) [tex]6p=30[/tex]

2.) Sebastian bought a pack of 30 mechanical pencils and plans to give the same number of pencils each to 6 friends.

Let a varible such as p be the number of pencils given by him to each students.

Now we need to find p we need to divide 30 by 6, we get

[tex]p = \frac{30}{6}[/tex]    

 [tex]to[/tex]

[tex]6p = 30[/tex]

Thus, the equation can he use to find p, the number of pencils each friend will receive is: [tex]6p = 30[/tex]

Answer:

[tex]6p = 30[/tex]

Step-by-step explanation:

3dxnn have's the explanation.

The required statements that are true for the given function are mentioned below.

There are many possible statements that could be true for the function h, given the information provided. Here are a few examples:

is a linear function that passes through the points (-2, 2) and (8, 19).

h is a quadratic function that has a maximum value of 25 at x = 11.

h is a piecewise function that equals 1 for -3 ≤ x ≤ 0, 2x + 3 for 0 < x ≤ 4, and 19 - x for 4 < x ≤ 11.

h is a logarithmic function that equals 1 at x = -3 and approaches 25 as x approaches 11.

Each of these statements is consistent with the given domain, range, and function values at x = -2 and x = 8. There are many other possible statements that could be true for h as well.

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Answer:

To calculate the average annual percentage gain, we need to use the formula:

Average annual percentage gain = ((Ending value / Beginning value)^(1/n) - 1) x 100%

where:

- Ending value = the value of the investment at the end of the period

- Beginning value = the value of the investment at the beginning of the period

- n = the number of years

In this case, the beginning value of the stocks is not given, so we cannot calculate the exact average annual percentage gain. We only know the profit and the ending value. However, we can make an estimate assuming that the profit is equal to the gain, i.e., there were no transaction costs or other fees.

If the profit was $3,250 and the ending value was $10,500, then the beginning value was:

Beginning value = Ending value - Profit

Beginning value = $10,500 - $3,250

Beginning value = $7,250

The number of years is given as 4.

Using the formula above, we can estimate the average annual percentage gain as:

((10,500 / 7,250)^(1/4) - 1) x 100%

= (1.1267^(0.25) - 1) x 100%

= (1.0266 - 1) x 100%

= 0.0266 x 100%

= 2.66%

Therefore, the estimated average annual percentage gain is 2.66%.

Step-by-step explanation:

The area of the shaded region of a circle with a 100 degree angle and a radius of 3cm, using pi=3.14, is approximately 25.64 square centimeters.

To find the area of the shaded region of a circle, we need to subtract the area of the sector formed by the shaded region from the area of the whole circle.

The area of the whole circle is given by

A = πr²

where A is the area of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14 (as given in the question).

Substituting the given values, we get

A = π(3cm)²

A = 28.26 cm² (rounded to two decimal places)

Now, let's find the area of the sector formed by the shaded region.

The angle of the sector is given as 100 degrees. To find the area of the sector, we need to use the formula:

A = (θ/360)πr²

where θ is the angle in degrees, r is the radius of the circle, and π is again approximately equal to 3.14.

Substituting the given values, we get

A = (100/360)π(3cm)²

A = 2.62 cm² (rounded to two decimal places)

Finally, we can find the area of the shaded region by subtracting the area of the sector from the area of the whole circle

Shaded area = Area of circle - Area of sector

Shaded area = 28.26 cm² - 2.62 cm²

Shaded area = 25.64 cm² (rounded to two decimal places)

Therefore, the area of the shaded region of the circle is approximately 25.64 square centimeters.

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--The given question is incomplete, the complete question is given

" Find the area of a shaded region of circle and use 3.14 for pi "--

The data presented shows the growth of the Javanese gibbon population on three different islands over time.

Data trends must be analyzed to determine the type of function that is modeling population growth. A common way to do this is to plot the data points and observe the shape of the curve. However, since the table only contains data, you can analyze trends by looking at the differences between consecutive terms.

To do this, we can calculate the first difference and the second difference in the population data.

The first difference:

- Swing: 40 - 30 = 10, 50 - 40 = 10, 60 - 50 = 10

Example: 60 - 50 = 10, 75 - 60 = 15, 90 - 75 = 15

- Salavati: 80 - 60 = 20, 100 - 80 = 20, 120 - 100 = 20

The second difference:

- Batanta: 10 - 10 = 0, 10 - 10 = 0

- Example: 15 - 10 = 5, 15 - 15 = 0

- Salavati: 20 - 20 = 0, 20 - 20 = 0

The first difference is constant for each island and shows a linear relationship between time and population growth. Also, the second difference is zero, indicating a constant rate of change.

Therefore, we can conclude that the population growth modeling function is a linear function that can be written as

M(x) = mx + b

where x is the time in years, m is the slope (population growth rate), and b is the y-intercept (initial population).

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