solve for x 0°<x<360
3cos2x +sinx=1​

The length of the ladder that is leaning on the building would be = 24ft. That is option B.

To determine the length of the ladder, the sine rule needs to be obeyed. That is

= a/sinA = b/sinB

Where;

a = 8.2 ft

A = 180-( 70+90

= 180- 160

= 20°

b = X

B = 90°

That is;

8.2/sin20° = b/sin90°

Make b the subject of formula;

b = 8.2×1/0.342020

= 23.9

= 24 ft

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The diagram represents the trajectory of an airplane at take off the angle representing the airplane's trajectory is approximately 147.83 degrees.

To solve this problem, let's denote the angle of the airplane's trajectory as x degrees. According to the given information, the angle representing the trajectory of the jet is 15% greater than the airplane's trajectory.

The angle representing the trajectory of the jet can be calculated as:

x + 0.15x = 1.15x

Therefore, the angle representing the trajectory of the jet is 1.15x degrees.

Given that the airplane's trajectory is at 170 degrees, we can set up the following equation:

1.15x = 170

To solve for x, divide both sides of the equation by 1.15:

x = 170 / 1.15 ≈ 147.83

Thus, the angle representing the airplane's trajectory is approximately 147.83 degrees, and the angle representing the jet's trajectory is approximately 1.15 * 147.83 ≈ 170 degrees.

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In mathematics, notation is used to simplify and make our understanding of equations and problem statements easier.

Mathematical notation makes use of various symbols in order to represent operations, unspecified numbers, relations, and any other mathematical objects or entities, and proceeds to assemble them into understandable expressions and formulas.

A notational convention is a set of representatives consisting of symbols that are used to express mathematical equations, in this case, the notational convention adopted is that all the free variables of a formula are among u1, u2, u3 . . . un. as shown in the image provided.

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The figures paired are given as follows:

| -3| = 3

|-2| >  1

0 < |-1|

The left over is 2. This is based on the principle of absolute values.

The absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.

A number's absolute value can be conceived of as its distance from zero along the real number line.

As a result, the absolute value of -3 is 3, which suggests that |-3| = 3.

-2 in absolute terms equals 2. That is |-2| greater than 1.

the inverse value of -1 equals 1. This equals 0 |-1|.

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Answer: 9 fish

Step-by-step explanation:

To find the answer all you have to do is multiply the amount of fish per gallon (0.12) to the total amount to gallons (75).

75 x 0.12 = 9

A 75-gallon aquarium will hold about 8 fish.

Stocking guidelines are 1 inch of adult fish per gallon of tank water. When applying this rule of thumb, we have to keep in mind that a 75 gallons water tank only holds about 70 gallons of water.

Then the number of fish in the tank would be:

Number of fish = density of fish * volume of water in the tank

Number of fish = 0.12 * 70

Number of fish = 8.4

So there are about 8 fish in the tank.

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The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20

The simple interest formula is J = C ∙ i ∙ t, where J is interest, C is principal, i is interest rate, and t is time. To calculate the simple interest, just substitute the values ​​in the formula and perform the calculation.

Calculate the deposit:

[tex]D=R4.80 + 1.20% of R5,000\\=R4.80 + (1.20/100) * R5,000\\= R4.80 + R60\\= R64.80[/tex]

Now, the deposit amount for the branch:

[tex]DB=R8.00 + 1.50% of R5,000\\= R8.00 + (1.50/100) * R5,000\\= R8.00 + R75\\= R83.00[/tex]

The difference will be:

[tex]Difference = R64.80 - R83.00\\Difference = -R18.20[/tex]

The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20. Therefore, John's statement is incorrect.

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5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².

Firstly, we will calculate the area of the square of paper in which the holes are punched.

Side of square = 12 cm

Area of square = side²

= (12) ²

= 144 cm²

Now, we will calculate the area of the bigger punch holes

Radius of big punch hole = 3 cm

Area of 1 big punch = π (radius) ²

= 22/7 × (3)²

22 / 7 × 9

= 198 / 7 cm²

Area of 4 punches = 4 × 198/7

= 792/7 cm²

Now, we will calculate the area of smaller punch whose radius is 1cm

Area = 22/7 × 1²

= 22/7 cm²

Now, we will calculate the total area covered by circles

Total area covered by circles = area of small punch + area of 4 big punch

= 22/7 + 792/7

= 814 /7 cm²

Remaining area = area of square - area of circles

= 144 - 814/7

= (1008 - 814) / 7

= 194 / 7

= 27.714 cm²

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The total population of alligators will be 375.

The amount of soy milk that the grocery store should plan to donate is: 158.

To calculate the total population of alligators in the area, we will assign the following variables:

30 Tagged alligators = m

12 Counted alligators = k

150 alligators seen = n

The total population size (N bar) of alligators is calculated with the formula:

N bar = mn/k

= 30 * 150/12

= 4500/12

375

For the amount of soy milk, we can say that if 25 out of 150 students preferred soy milk, then the number that would prefer soy milk out of 950 will be: 950 * 25/150 = 158.

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Answer: $383.33 per month for the next 4 years

Step-by-step explanation:

The correct answer is save $383.33 per month for the next 4 years. Tuition for one year at a state university is about $12,500, and Greg would like to attend this university. His parents will give him $4,600 for his first year of tuition, so he must save the remaining $7,900. To have enough money to pay for his first year of tuition, Greg must save $383.33 per month for the next 4 years. This is the minimum amount of money he must save, as the other plans require him to save more money than necessary.

Sorry if this is wrong btw fr fr.

Answer:164.58 (D)

Step-by-step explanation:

12,500-4600= 7900

12 months x 4 years makes 48 months, so 7900/48 = 164.58 per month

The area of the sector with an angle of 285 degrees and a radius of 6 units is 28.5π square units.

To find the area of a sector, we can use the formula:

Area of Sector = (Central Angle / 360 degrees) × π ×  (Radius²)

Given that the central angle is 285 degrees and the radius is 6, we can substitute these values into the formula:

Area of Sector = (285 degrees / 360 degrees) ×  π ×  (6²)

Area of Sector = (19/24) ×  π × 36

Area of Sector = (19/24) ×  36π

Area of Sector = (19 × 36π) / 24

Area of Sector = 684π / 24

Area of Sector = 28.5π

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Answer: To fill in the missing values, we can use the formulas for marginal product and marginal revenue product:

Marginal Product = Change in Total Product / Change in Labor

Marginal Revenue Product = Price x Marginal Product

Using the given information, we can fill in the missing values as follows:

Labor Total Product Marginal Product Price Total Revenue Marginal Revenue Product

0 0 - $12 $0 -

2 48 24 $12 $288 $288

4 66 9 $12 $792 $108

6 82 7 $12 $984 $84

8 96 5 $12 $1,152 $60

10 114 9 $12 $1,368 $108

12 132 9 $12 $1,584 $108

14 150 9 $12 $1,800 $108

So the missing values are:

Total Product for labor = 0 and 14: 0 and 150, respectively.

Marginal Product for labor = 0, 8, and 14: -, 5, and 9, respectively.

Total Revenue for labor = 4, 6, and 8: $792, $984, and $1,152, respectively.

Marginal Revenue Product for labor = 0, 4, and 6: -, $84, and $60, respectively.

Step-by-step explanation: :)

The classroom coin box required less than 11.11 Square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient

The 100 square feet of cardboard is enough to build the new coin box with a scale factor of 3 times the classroom coin box, we need to consider the relationship between the areas of the two boxes.

The area of the original classroom coin box is unknown, as it is not given in the problem. However, since we know that the new coin box has a scale factor of 3 times the original, we can infer that its area will be 3^2 = 9 times greater than the original.

Let's assume that the area of the classroom coin box is A square feet. In that case, the area of the new coin box would be 9A square feet.

Now, we are given that 100 square feet of cardboard is available. To determine if it's sufficient, we need to compare this value to the area of the new coin box, which is 9A.

If 100 square feet is greater than or equal to 9A, then it would be enough to build the new coin box. Conversely, if 100 square feet is less than 9A, it would not be enough.

Since we do not have a specific value for A, we cannot determine the exact answer. However, we can provide the argument to defend our solution.the classroom coin box required less than 11.11 square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient.

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Note the question be like :

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn from the bag without replacement, what is the probability that both marbles are red?

The value of inequality :  x≤-9

Given,

Inequality 4(x-3) + 4 ≤ 10+ 6x

Firstly,

The distributive property: 4x-12 + 4 ≤ 10+ 6x

Then,

Combine like terms: 4x -8 ≤ 10+ 6x

Then,

The addition property of inequality: 4x ≤ 18 + 6x

Then,

The subtraction property of inequality: -2x ≤ 18

Then,

The division property of inequality:

Divide both sides of inequality by 2,

So,

x≤-9

Hence after last step the value of x is less than or equal to -9 .

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The solution is: the value of the angles a, b and c are : a = 60, b = 90, c = 100.

Here,

We have that in line CHF, it has two given and one unknown angle.

The total angle of one straight line is 180.

Given that:

a = 180 - 50 -70 = 60

The angle intersecting the CHFD line can be computed by the the total angle inside the triangle.

Angle on EFH would give 180-40-60 = 80 and on EFD the angle would be 100 from 180-80.

Since angle C is congruent to the angle EFD.

c = 100

Take note that in a 4 sided polygon (GEFH), the total exterior angle is 360 degrees.

The different angle would be

angle GHF = 50 + a = 50+60 = 110

angle EFH = 80

angle FEG = 180- c = 180-100 = 80

ANGLE EGH = 360 - GHF -EFH -FEG = 360 - 110-80-80 = 90

since angle AG is congruent to EGH, we can calculate for the angle b which is congruent to its opposite. This would give us formula of

360 = (90+90) + (b) +(b)

360 = 180 +2b

b = 90

Hence, The solution is: the value of the angles a, b and c are : a = 60, b = 90, c = 100.

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Answer:

b=2

Step-by-step explanation:

You are given:

[tex]b^{3} =8[/tex]

What does [tex]b^3[/tex] mean?

It is simply, b·b·b

Therefore:
b·b·b=8

What number could be multiplied by itself three times and equal 8?

...

2

Yay! That's great!

physical sciences 2023

a) The triangles are congruent by the AAA criterion.

b) The triangles are congruent by the SAS criterion.

a) In the first triangle the interior angles are 40 degrees and 30 degrees.

The other interior angle would be 180 - (40 + 30) = 110 degrees.

As per the diagram, the triangles have equal proportionate-sized side lengths.

Therefore, the triangles are congruent by the AAA criterion.

b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.

Therefore, the triangles are congruent by the SAS criterion.

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The sum of the number 199 + 61 by vertical table will be 260.

Since, Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Use the table to add 199 + 61 vertically. Then we have

                                Hundreds          Tens          Ones

Regrouping                    1                       1            

First addend                  1                      9               9

Second addend            0                      6               1

Sum                              2                      6               0

Thus, The sum of the number 199 + 61 by the vertical table will be 260.

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The table to add 199+61 vertically is shown below.

To add 199 and 61 vertically, we'll set up the addition table as follows:

 1  9  9

+   6  1

_________

Let's start by adding the digits in the rightmost column, which is the ones place:

9 + 1 = 10

We write down 0 in the bottom row and carry over the 1 to the top row:    1  9  9

+   6  1

_________

   0

Now, let's add the digits in the next column (the tens place), including the carry-over:

1 + 9 + 1 = 11

We write down 1 in the bottom row and carry over the 1 to the top row:

   1  9  9

+   6  1

_________

  1  1

Finally, let's add the digits in the leftmost column (the hundreds place), including the carry-over:

1 + 1 = 2

We write down 2 in the bottom row:

   1  9  9

+   6  1

_________

  2  1

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Answer:

7, 14

Step-by-step explanation:

Look at the first column of numbers: 2.8 m in 2 min.

We can get a unit rate from those numbers:

2.8 m / 2 min = 1.4 m/min

He walks at a rate of 1.4 m/min

Now multiply the unit rate by each number of minutes to find the number of meter.

Let's do the second column as a check: time = 3 min

1.4 m/min × 3 min = 4.2 m

4.2 m is the number on the table, so our unti rate is correct.

5 min:

1/4 m/min × 5 min = 7 m

10 min:

1.4 m/min × 10 min = 14 m

The numerical value of side length x in the right triangle is 8.

The figures in the image are two similar right triagles.

Since the two right triangles are similar, we equate the ratio of the sides of the two triangles.

x/6 = (x + 4)/9

Cross multiply and solve for x:

6( x + 4 ) = x × 9

Apply distributive property:

6 × x + 6 × 4 = x × 9

Simplifying, we get:

6x + 24 = 9x

Subtract 6x from both sides:

6x - 6x + 24 = 9x - 6x

24 = 9x - 6x

24 = 3x

3x = 24

Divide both sides by 3:

x = 24/3

x = 8

Therefore, the value of 8.

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Option A shows the Venn diagram representing the union of these two events.

A Venn Diagram divides a data-set into separate regions, which are correspond to each activity in the context of the problem.

The intersection region is the region that corresponds to the people sharing both features, with are M and B.

The union region is the region showing at least one of the two features, M and B, hence it is the region in which all the circles are painted.

Hence option a is the correct option in the context of this problem.

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Answer:

B

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer:

Exponential Growth

Step-by-step explanation:

The base of 1.88 is greater than 1, so there will be exponential growth

Answer:

55.0ml is answer = 22.05

Step-by-step explanation:

The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

Using the Central Limit Theorem.

The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. In this case, we have a sample size of 30, which is considered large enough for the Central Limit Theorem to apply.

Calculate the standard error of the mean (SEM):

SEM = σ / √n

SEM = 0.52 / √30

SEM ≈ 0.095

Calculate the z-scores for the lower and upper limits:

z1 = (94.7 - μ) / SEM

z2 = (95.3 - μ) / SEM

z1 = (94.7 - 95) / 0.095 ≈ -0.526

z2 = (95.3 - 95) / 0.095 ≈ 0.316

Find the area under the normal distribution curve between the z-scores using a standard normal distribution table or a calculator. The area represents the probability.

Using a standard normal distribution table or a calculator, the area between -0.526 and 0.316 is approximately 0.436.

Therefore, the probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

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Answer:

19.24 ft

Step-by-step explanation:

x = length of ramp

sin12 = 4/x

x = 4/sin12 = 19.24 ft

The solution of the inequality is -1 ≤ x ≤ 3.

To solve the inequality |2x(x-1)+12| ≤ 18, we can break it down into two separate inequalities:

2x(x-1) + 12 ≤ 18

-(2x(x-1) + 12) ≤ 18

Solving the first inequality:

2x(x-1) + 12 ≤ 18

2x² - 2x + 12 ≤ 18

2x² - 2x - 6 ≤ 0

Solving the second inequality:

-(2x(x-1) + 12) ≤ 18

-2x(x-1) - 12 ≤ 18

-2x² + 2x - 12 ≤ 18

2x² - 2x + 30 ≤ 0

Now, let's solve each inequality separately.

For the first inequality, 2x² - 2x - 6 ≤ 0:

We can factor this quadratic equation:

(2x + 2)(x - 3) ≤ 0

To determine the sign of the inequality, we need to consider the intervals where the expression is positive or negative. We set each factor equal to zero to find the critical values:

2x + 2 = 0 => x = -1

x - 3 = 0 => x = 3

Plotting these critical values on a number line and testing intervals, we find that the solution is -1 ≤ x ≤ 3.

For the second inequality, 2x² - 2x + 30 ≤ 0:

This quadratic equation does not have real solutions, so there are no solutions to this inequality.

Combining the solutions from both inequalities, we have -1 ≤ x ≤ 3.

To graph the solution, we plot the interval -1 ≤ x ≤ 3 on the number line. The shaded region on the number line represents the solution set.

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Given that in circle S, a sector is shaded and ZTSU measures 40°. We are to find out what fraction of the interior of the circle is shaded and simplify the answer.The correct answer is 16π/9 cm².

To find out the fraction of the interior of the circle that is shaded, we need to determine the measure of the central angle that intercepts the entire circle.The total measure of a circle is 360 degrees.

To find the fraction of a circle shaded, divide the number of degrees in the sector by

360.4x = (40/360) × πr² = (1/9) × πr².

We simplify the answer: 4x = πr²/9 Fraction of the interior of the circle that is shaded = 40/360 = 1/9.Expression for the area of the shaded sector in square centimeters is:

A = (40/360) × πr² = πr²/9 =  π(4²)/9 = 16π/9 cm²

Therefore, the correct answer is 16π/9 cm².

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