Which value of x solves the equation cos x° = sin (20° + x°), where 0 < x < 90?

The unit rate or miles per gallon for Blue car is 35.6 miles and for Red car is 36 miles. Red car could travel the greater distance on 1 gallon of gasoline.

44 1/2 = 44 + 1/2

         = (88+1)/2

         = 89/2

1 1/4 = 1 + 1/4

       = (4+1)/5

       = 5/4

28 4/5 = 28 + 4/5

           = (140+4)/5

           = 144/5

Distance blue car covers in 5/4 gallons of fuel = 89/2

     Distance blue car covers in 1 gallon of fuel = (89/2) / (5/4)

                                                                             = (89*4)/(2*5)

                                                                             = 178/5  

                                                                             = 35.6

Distance red car covers in 4/5 gallons of fuel = 144/5

     Distance red car covers in 1 gallon of fuel = (144/5) / (4/5)

                                                                             = (144*5)/(4*5)

                                                                             = 144/5  

                                                                             = 36

Hence, Red car could travel the greater distance on 1 gallon of gasoline by 0.4 miles.

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Answer:

below

Step-by-step explanation:

x = (3+x) / y      divide both sides by x and multiply by y

y = (3+x) / x

y = 3/x  + 1        

y - 1 = 3/x

x = 3 / ( y-1)

The number of containers that are needed to hold all the gravel in one truck is 3.

The first step is to convert the capacity of the truck from cubic yards to tons. In order to do this multiply the unit of conversion by the capacity of the truck in cubic yards.

Multiplication is the mathematical process used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.

1 cubic yards = 1.48 tons

1.48 x 22.5 = 33.3 tons

The next step is to determine the number of containers that can be on the truck. To do this, divide the converted capacity of the truck by the capacity of each container.

Division is the mathematical operation that is used to determine the quotient of two or more numbers. The sign that is used to represent division is ÷.

Number of containers = total capacity of the truck in tons / capacity of one container

Number of containers = 33.3 / 11.1 = 3 containers

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To find the constant of proportionality of a given relationship, divide the given ratios:

8​ grams of yeast for every 500​ grams of flour

⇒ 8/500

⇒ 0.016

We can find the constant that is greater than 1 by reversing the values:

500​ grams of flour for every 8​ grams of yeast

⇒ 500/8

⇒ 62.5

Greater than 1: 62.5

Less than 1: 0.016

Answer:

18

Step-by-step explanation:

to make the 11 denominator turn into 22 they had to multiply by 2

So we multiply the numerator by 2 too

9x2=18

Hopes this helps please mark brainliest

Answer:

If you would like to solve the equation 9/11 = x/22, you can calculate this using the following steps:

Steps to find ?

9/11 = x/22    /*22

x = 9/11 * 22

x = 18

The correct answer should be 18 through my calculations

The missing number in the bracket is 19. The correct option is d. 19

From the question, we are to determine the missing number in the bracket.

The given sequence is

(1,2) (2,5) (3,10) (?,362)

Now, to determine the missing number, we will study the given sequence.

Let the missing number be x

From the sequence, we can observe that

1² + 1 = 2

2² + 1 = 5

3² + 1 = 10

and

x² + 1 = 362

Now, we will solve the equation for x

x² + 1 = 362

Subtract 1 from both sides of the equation

x² + 1 - 1 = 362 - 1

x² = 361

Therefore,

x = √361

x = 19

Hence, the missing number is 19

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The system of inequalities has been solved graphically and one possible solution is buying 4 apples and 12 peaches.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of apples purchased and number of peaches purchased by Alang and his children, and then translate the word problem into algebraic equation as follows:

Since apples for $2 each and peaches for $0.50 each, the cost of fruits is given by:

2x + 0.5y ≤ 20

Also, they must buy a minimum of 16 apples and peaches altogether:

x + y ≥ 16

Therefore, a possible solution when x = 4 is given by:

x + y ≥ 16

4 + y ≥ 16

y ≥ 16 - 4

y ≥ 12

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According to the given triangle, ΔBCE ≅ ΔCBD is proved.

Triangle:

The three-sided polygon that consists of three edges and three vertices is know  as triangle.

Given,

Here we have the triangle and we need to prove the ΔBCE ≅ ΔCBD.

Let us consider ABC be the triangle with sides BC, AC, AB add the opposite angles A, B, C being in length equal to a, b, c respectively.

Here they draw a perpendiculars AD, BE and CF from A, B, C to opposite sides meeting sides BC, AC and AB at D, E, F respectively.

So, here we take the ΔCBD and ΔBCE,

Then the

∠D = ∠E = 90°

So, the Side BC = Side BC and the Side BD = Side CE.

From this relation, and based one the concept of RHS Congruence Criterion

We have identify that, the Corresponding Angle Congruence Test

∠DCB = ∠EBC

Therefore, the  ΔBCE ≅ ΔCBD is proved

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By taking a common denominator, we can find out that the simplified expression of the given expression is [tex]\frac{6c+4}{c^{2} }[/tex] .

The given expression is -

[tex]\frac{6}{c}+\frac{4}{c^{2} }[/tex] ---- (1)

We have to simplify the expression.

From equation (1), we have the given expression as -

[tex]\frac{6}{c}+\frac{4}{c^{2} }[/tex]

Establishing common denominator [tex]c^{2}[/tex], we have

[tex]\frac{6c}{c^{2} }+\frac{4}{c^{2}}[/tex]

Combining the numerator and common denominator, we have

[tex]\frac{6c+4}{c^{2} }[/tex]

Thus, the simplified expression of the given expression is [tex]\frac{6c+4}{c^{2} }[/tex] which is obtained by taking a common denominator.

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Answer:

  150 miles

Step-by-step explanation:

Jina wants to know the number of miles driven that would make the cost of two rental plans the same. One costs $0.15 per mile plus $49.98; the other costs $0.19 per mile plus $43.98.

The difference in cost between the to plans for m miles driven is zero when ...

  (0.15m +49.98) -(0.19m +43.98) = 0

  -0.04m +6.00 = 0 . . . . . . . . simplify

  m -150 = 0 . . . . . . . . . . . . divide by -0.04

  m = 150 . . . . . . . . . . . . . add 150

Jina would need to drive 150 miles for the two plans to cost the same.

The equivalent expression for the expression given; (( 5/7 )² × (1/3)-³)-¹ is; (7/5)² • (1/3)³.

It follows from the task content that the expression which is equivalent to that which is given is to be determined.

Hence, since the given expression is; (( 5/7 )² × (1/3)-³)-¹;

It follows from the power of powers law of indices that we have;

( 5/7 )-² • (1/3)³

Also, according to the negative exponent law of indices; we have;

(7/5)² • (1/3)³.

On this note, the required equivalent expression is; (7/5)² • (1/3)³.

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At a profit of $30 per bike and $1950 operating cost per month the store needs to sell 65 bikes to break even.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The store pays an average of ​$60 per bike. The average selling price of each bicycle is ​$90.

∴ The profit per bike the bicycle store make is $(90 - 60) = $30.

Also, the bicycle store costs ​$1950 per month to operate,

Assuming no. of bikes the store needs to sell to break even is x.

∴ 30x = 1950.

x = 195/3.

x = 65.

The store needs to sell 65 bikes to break even the cost.

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The value of Indices 10x^2y÷ 5xy is 2x^(2y-1)×y^-1

An index is a small number that tells us how many times a term has been multiplied by itself. The plural of index is indices. Below is an example of a term written in index form: 4^3. 4 is the base and 3 is the index.

10x^2y = 10x^2(y)

dividing 5xy with 10x^2y

the coefficient 5 will divide 10 to give 2

therefore the value is

2x^2y÷ xy

using law of INDICIES

the value will be 2x^(2y-1)×y^-1

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Answer:

No, Beth is not correct. One of the x-values, 2, corresponds to two y-values.

The mean height of the team  rounded  to 1 decimal place is 200.0.

The height of this new player is 206.

What is mean Average?

The mean average, of a data set is the sum of all  the numbers divided by the total number of values.

Formular for calculating mean Average:

Mean Average = {Sum of all the values} ÷ {Total numbers of values}

From the question the height of the  players are as follows:

(height) 198,199,200,201,202)

a) Mean Average =(198 +199 +200 +201 +202)

                                             5

                          =1000

                                5

                           =200.0

b) The new player joins the  team to make the Mean Average 201. hence the height of the new player will be calculated using:

Mean Average = {Sum of all the values} ÷ {Total numbers of values}

201 =(198 +199 +200 +201 +202 + x )

                                             6

201  = 1000+ x

               6

crossmultiply to solve for X:

201 *6 =1000+ x

1,206 = 1000+ x

making x subject of the formular we have:

x = 1,206 - 1000

x = 206

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In the situation,  60 births per every 1,000 women ages 15 to 44 years, the statistics used is descriptive statistics.

What is descriptive statistics?

Suppose there is a population and suppose there is a sample of the population. If the inference is made on the sample alone and not on the whole population, the statistics used is called descriptive statistics.

Here, the sample is 60 births per every 1,000 women ages 15 to 44 years.

And the inference is made only about those 60 births per every 1,000 women ages 15 to 44 years, and not on the whole population of women aged between 15 to 44 years. So the statistics used in this case is descriptive statistics.

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By using the formula for the gradient, we can solve a simple equation to find that the value of x is 9.

For a segment whose endpoints are:

P = (x₁, y₁) and Q = (x₂, y₂)

The gradient of the line PQ is:

G = (y₂ - y₁)/(x₂ - x₁)

So it is like the slope of a linear equation.

In this case, the endpoints are:

P = (5, 7)

Q = (x, 15)

And the gradient is equal to 2, so we have G = 2, then we can write the equation:

2 = (15 - 7)/(x - 5)

We can solve this to get:

2*(x - 5) = (15 - 7)

2x - 10 = 8

2x = 10 + 8

2x = 18

x = 18/2 = 9

The value of x is 9.

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Answer:

Answer option C

Step-by-step explanation:

it is a line that ends so it’s C

Answer:

64

Step-by-step explanation:

16 ÷ 12 = 1.33 (rounded to 2 decimal places)

1.33 = scale factor

1.33² = area scale factor

1.33² × 36 = 64 (rounded to a whole number)

J and K have values of 0.38 and 0.50, respectively with sampling distribution for the sample variance.

Given data;

The sampling distribution for the sample variance using the distribution;

(I) To find the value of J,

(II) To find the value of K,

We know;

⇒ ∑P(s²) = 1

⇒ J + K + 0.12 = 1

   J + K = 0.88

   K = 0.88 - K

Now K = 0.5;

J = 0.88 - 0.5

  = 0.38

Therefore, the values of J and K are 0.38 and 0.50 respectively.

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The domain choice that is a possibility is A. A. Real numbers greater than 0.

A continuous function in mathematics is one in which a continuous variation of the argument causes a continuous variation of the function's value. This means that there are no abrupt changes in value, which are referred to as discontinuities.

Option A: Real numbers greater than zero:

Because real numbers are continuous functions, the greater than zero part of them can be used to represent the balance sheet.

Option B: Use only whole numbers: It is not possible.

Whole numbers are discrete, not continuous, and thus cannot represent decimal points.

Option C: Integers: Invalid

Because integers are discrete rather than continuous, they cannot represent decimal points.

Natural numbers are not an option.

Natural numbers, like whole numbers, are discrete rather than continuous and cannot represent decimal points.

In conclusion, the correct option is A.

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The graph of the linear function y - 6 = 4(x - 4) is the bottom right graph.

The point-slope representation of a linear function is given as follows:

y - y* = m(x - x*).

In which the coefficients of the equation are defined as follows:

In this problem, the equation is:

y - 6 = 4(x - 4).

From this equation, the slope is of:

m = 4.

This means that the linear function is increasing, and thus, both the left graphs are not correct.

The coordinates of the point that the function passes through are given as follows:

(4, 6).

The only function that passes through this point is the bottom right function, hence it is the correct graph of y - 6 = 4(x - 4).

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The ratio of the density of cube A to the density of cube B as required in the task content is; 81 : 128.

It follows from the task content that the ratio of the density of cube A to cube B is to be determined.

Recall that the density of an object is given as its mass to volume ratio.

Therefore, given that the volumes are equal; it can be inferred that the density and mass are directly proportional.

Ultimately, the required density ratio can be estimated from the given masses as;

Density of A : Density of B = 81 : 128.

Consequently, the required ratio is; 81 : 128.

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Answer:

$2,700

Step-by-step explanation:

15% of $18,000 = 0.15 × $18,000 = $2,700

Answer:

60

Step-by-step explanation:

5 x8 = 40 40 + 20 = 60

The height of the pyramid is 99.1875 meters when the Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.

Given that,

The Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.

We have to find what would the height be if you gave the base sides of 280m using the same material.

We know that,

Volume of Great Pyramid of Cheops = Volume of the  pyramid  with the base sides of 280m

Volume of Great Pyramid of Cheops is 1/3×(side of the base)²×(height of the pyramid)

Side of the base is 230 meters.

Height of the pyramid is 147 meters.

Volume of the  pyramid  with the base sides of 280m is 1/3×(side of the base)²×(height of the pyramid)

Side of the base is 280 meters.

Height of the pyramid is h meters.

Volume of Great Pyramid of Cheops = Volume of the  pyramid  with the base sides of 280m

1/3×(230)²×(147)=1/3×(280)²×h

h = 99.1875 meters.

Therefore, the height of the pyramid is 99.1875 meters while the Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.

The complete question is:

The Great Pyramid of Cheops is a square-based pyramid, the base has sides of 230m, and the height is 147m.

Using the same material, what would the height be if you give the base sides of 280m.

Please give the answer to the nearest meter.

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14.375 grams of the radioactive isotope will be left after 3 half-lives.

The initial mass of the isotope = 115 gm

after each half-life, the amount of the isotope is reduced to half

therefore,

after the first half-life, the mass of the isotope will become = 115/2

                                                                                          = 57.5 gram

now after the second half live, the mass will again be reduced to half of the previous mass = 57.5/2

                              = 28.75 gram

similarly, after the third half-life, the mass will be half of the previous mass  = 28.75/ 2

           = 14.375 gram

OR

simply we can write that

weight after 3 half-lives will be = 115/ 2³        

                                                = 115 / 8

                                                = 14.375 grams.

So the mass after 3 half-lives is 14.375 grams.

A risky form of a chemical element that releases radiation as it breaks down and will become extra stable. Radioisotopes may additionally arise in nature or be made in a laboratory. In medication, they may be used in imaging exams and in treatment. additionally known as a radionuclide.

Atoms of equal detail with extraordinary numbers of neutrons are known as isotopes. Many elements have one or extra isotopes which might be radioactive. Their nuclei are risky, so they destroy down, decay, and emit radiation.

whilst utilized in cautiously controlled clinical programs, radioactive isotopes are safe and no longer almost as frightening as we first imagined. The radiation from those isotopes has a quick half of lifestyles and handiest give off low stages of radiation. Radioactive isotopes are not constantly risky, though. a few most effective ones supply tiny amounts of radiation. There are radioactive isotopes in nature all around us. maximum of them cause us very little damage.

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Answer:

  x = 9

Step-by-step explanation:

Apparently, you want the solution to (10x -27) = 7x.

Subtract 7x from both sides to get ...

  3x -27 = 0

Divide by 3, and you have ...

  x -9 = 0

Add 9 to show the value of x:

  x = 9

The solution to the given equation is x=9.

__

Additional comment

There is no information here that relates the given equation to b, so we cannot help you find b.

Answer:
a - 67
b - 58
c -  125
d - 23
e - 90

Step-by-step explanation:

Solve for b first

90 - 32 = 58

Then you can solve for a

180 - 58 - 55 = 67

Now solve for c

180 - 55 = 125

Now you can solve for d

180 - 125 - 32 = 23

e is equal to 32 + b, so it is 90.

No, because although two probabilities should be multiplied, it should not be these two probabilities. This is because the two events are likely not independent .

What is Probability ?

Probability is the study of likeliness of an event to happen. The range of probability is 0 to 1.

Now, According to the question:

It is given that

In a certain city, 60% of the heads of household own the house in which they reside,

and 80% of the heads of the household have full-time employment.

percentage of heads of household both own their home and have a full-time job =?

As the probability of a person having both their own home and having

full time employment are not independent.

Hence, No, because although two probabilities should be multiplied, it should not be these two probabilities. This is because the two events are likely not independent.

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