Work out the value of x. Show your working clearly.​

Answer:

try your best

Step-by-step explanation:

u can do it!!

The ratio of the number of empty tables to the total number of tables is 13:21

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, 8 of the tables at Joy's Italian Restaurant are full, and the other 13 tables are empty, we are asked to find the ratio of the number of empty tables to the total number of tables,

Number of empty table = 13

Total number of tables = 13 + 8 = 21

Ratio of the number of empty tables to the total number of tables = 13 / 21

Hence, the ratio of the number of empty tables to the total number of tables is 13:21

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Let a = units of A produced

Let b = units of B produced

At least 30 units of product A and 10 units of product B are required daily, and the maximum number of units per day should not exceed 80.

Therefore

a ≥ 30

b ≥ 10

a + b ≤ 80

Product A yields a profit of $15 and product B yields a profit of $8.

Therefore the objectve profit function is

P(a,b) = 15a + 8b

Answer:

The objective function is

P(a,b) = 15a + 8b, subject to

a >= 30;  b>= 10;  a+b <= 80

Create a graph that displays the constraints and calculates maximum profit at the boundary points. The solution region is shaded.

The maximum profit occurs when a=70 and b=10.

Answer:

P= 15a + 8b

Step-by-step explanation:

The difference between the volume of the sphere and an approximation using a left sum with 16 intervals is 17.51 mm.

The term called volume in math is known as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Here we know that the sphere has a radius of 2 mm.

Then the volume of the sphere is calculated by using the formula,

=> V = 4/3πr³

Here we know that the value of r = 2.

Then the volume is calculated as,

=> V = 4/3 x π x 2³

When we simplify this one then we get,

=> V = 10.67π = 33.51

Here we need to find the difference between the volume of the sphere and an approximation using a left sum with 16 intervals is

=> 33.51 - 16

=> 17.51

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Answer:

..........................

The fire station should be located at the midpoint (a/2) of the road to minimize the expected distance from the fire.

The total distance cost will be infinite if we start at one point on a given line at an infinite distance. However, as we move this point toward the given points, the total distance cost begins to decrease. After a while, it then increases once more, reaching infinite at the other infinite end of the line. Therefore, the distance cost curve resembles a U-curve, and its bottom value must be determined.

The fire station should be located at the midpoint (a/2) of the road (0,a) to minimize the expected distance from the fire.

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Answer: 189 degrees

Step-by-step explanation:

Since 17x + 2 = 16x + 9, we can solve for x:

17x + 2 = 16x + 9

Subtract 16x from both sides:

x + 2 = 9

Subtract 2 from both sides:

x = 11

The angle indicated in bold is 17x + 2, so we just substitute 11 into x and get 17 * 11 + 2, = 187 + 2 = 189 degrees :>

The equation in the simplest form that represents the perimeter of the bookend in centimeters is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Part A :

Perimeter of a closed figure is the sum of the lengths of it's boundary.

Given the lengths of the sides of the bookend as,

5m - 14, 2m - 7, 3/2 m + 2 and 3m + 8.

Perimeter is given as 58 centimeters.

(5m - 14) + (2m - 7) + (3/2 m + 2) + (3m + 8) = 58

(5m + 2m + 3/2 m + 3m) + (-14 - 7 + 2 + 8) = 58

23/2 m - 11 = 58

11 [tex]\frac{1}{2}[/tex] m - 11 = 58

Part B :

We have,

11 [tex]\frac{1}{2}[/tex] m - 11 = 58

11 [tex]\frac{1}{2}[/tex] m = 58 + 11

11 [tex]\frac{1}{2}[/tex] m = 69

23/2 m = 69

m = 6

Hence the required equation is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.

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Answer:

answer is no

Step-by-step explanation:

If the triangles ABC and DEF are similar, then the measurement of line segment DE = 108.72 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

It is given that triangle ABC is similar to triangle DEF.

It can be seen in the image that ΔDEF is a dilated version of ΔABC.

In ΔABC the measurement of side AB = 23 units

In ΔABC the measurement of side BC = 11 units

In ΔDEF the measurement of side EF = 52 units

In ΔDEF the measurement of side DE = x units

Apply the formula for indirect measurement to find the measurement of side DE.

AB/DE = BC/EF

Substitute the values in the equation -

23/x = 11/52

23 × 52 = 11x

x = (23 × 52)/11

x = 1196/11

x = 108.72

Therefore, the measurement of DE is 108.72 units.

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The 12th term of the geometric sequence 7, -21, 63 is -1240029, this is determined using the Geometric progression formula.

When one term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence.

The geometric progression is given by the formula:

aₙ = arⁿ⁻¹

a = first term = 7

r = common ratio = - 21 / 7 = - 3

n = number of terms = 12

Therefore, substituting the values in the GP:

a₁₂ = 7 × -3¹²⁻¹

a₁₂ = 7 × -3¹¹

a₁₂ = 7 × -177147

a₁₂ = -1240029

Therefore, the 12th term of the geometric progression is -1240029.

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The change represents growth and percentage rate of increase is 95.8%.

The exponential function y = 880(1.958)^x is a function that models growth.

The base of the exponential function, 1.958, is greater than 1. This means that the function is increasing with respect to x, which is the independent variable.

For every unit increase in x, the function increases by a factor of 1.958. This is evident from the fact that 1.958 is raised to the power of x.

The percentage rate of increase is calculated by taking the difference between the base of the exponential function and 1, and then multiplying that difference by 100%.

In this case, the base of the exponential function is 1.958, so the percentage rate of increase is

(1.958- 1)*100 = 95.8%.

This means that for every unit increase in x, the value of y increases by 95.8% of its previous value.

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Answer:

-1

Step-by-step explanation:

top: -20/(-4) = 5

bottom: -49+44 = -5

5/(-5) =-1

Answer:

Category A 0.75

Category B 0.25

Hope it helps !!

Xavier is not getting better mileage with his new car.

it is given that

distance traveled by Xavier's new car in 20.28 gallons = 472miles

the mileage can be calculated using the formula = (distance traveled)/( gallons of fuel used).

So, the mileage of the new car = 472/20 = 23.06 miles per gallon, and the mileage of Xavier's former car = 20.28 miles per gallon.

From the above data, we can see that the mileage of the former car is greater than the new car.

Therefore, Xavier is not getting better mileage with his new car.

The given question is incomplete, the complete question is

Xavier's new car uses 25 gallons for 472  miles, His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?

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The percent of error is 17.65% .

The percent of error is a way to measure the difference between the expected value and the actual value. In this case, Peter expected to earn $425 in a week but he actually earned $500.

So, the difference between the expected value and the actual value is $75. The percent of error is calculated by taking the difference between the actual value and the expected value, dividing that by the expected value, and multiplying the result by 100%.

In this case, (500-425)/425*100% = 17.65%, which means that Peter's actual earnings were 17.65% higher than what he expected to earn.

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If the engine with 12 gallon fuel tank uses fuel at a constant rate of 0.6 gallons per hour , then the equation to find number hours the engine has been running is "12 - 0.6x = 9.3"  .

the total capacity of the tank is = 12 gallon ;

the constant use rate of engine is = 0.6 gallons per hour ;

the amount of fuel left in the tank is = 9.3 gallons ;

let the number of hours the engine is running is = x hours  ;

the above situation can be represented as ⇒ 12 - 0.6x = 9.3 ;

⇒ 12 - 0.6x = 9.3  ;

⇒ 12 - 9.3 = 0.6x  ;

⇒ 0.6x = 2.7  ;

⇒  x = 2.7/0.6  ;

⇒ x = 4.5 hours

Therefore , the engine has been running for 4.5 hours .

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A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.

You can utilize methods based on the dot-product and cross-product of vectors to create a vector that is perpendicular to another supplied vector. The total of the products of the relevant components is the dot-product of the vectors A = (a1, a2, a3) and B = (b1, b2, b3):

AB = a1 b2 + a2 b2 + a3 b3. The dot product of two vectors that are perpendicular is equal to zero.

The formula for calculating the cross-product of two vectors is AB = (a2 b3 - a3 b2, a3 b1 - a1 b3, a1 b2 - a2*b1).

A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.

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Answer:

18 miles

Step-by-step explanation:

m = # of miles

$4.60 + ($0.50/mi)m = $13.60

($0.50/mi)m = $13.60 - $4.60 = $9.00

m = ($9.00) / ($0.50/mi) = 18 miles

The inequalities that are equivalent are 3x+6≤8+ 2x and 12-3x ≤18

Inequalities are simply defined as relations that makes a non-equal comparison between two mathematical expressions, equations or numbers.

It is mostly used to compare two numbers or expressions based on the magnitude on the number line.

Inequality signs in mathematic include;

Given the inequalities;

3x + 6 ≤ 8 + 2x

collect like terms

3x - 2x≤ 8 - 6

subtract like terms

x ≤ 2

12-3x ≤18

collect like terms

3x≤ 18 - 12

3x ≤ 6

Divide both sides by 3

x ≤ 2

Hence, the inequalities are 3x+6≤8+ 2x and 12-3x ≤18

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The diagonal is equal to the sum of the square roots of the width and height.[tex]\sqrt{}[/tex]14[tex]n^{2}[/tex]

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In the given image the triangle POR and triangle FGH are not equal or similar to each other.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In ΔPQR, the line segment PQ measures 35 units.

In ΔPQR, the line segment PR measures 49 units.

In ΔPQR, the line segment QR measures 63 units.

In ΔFGH, the line segment FG measures 69 units.

In ΔFGH, the line segment GH measures 38 units.

In ΔFGH, the line segment HF measures 67 units.

These two triangles are not similar to each other.

Both these triangles have different measurements of line segments.

Both these triangles have no data available for their angles.

The only way the two triangles are similar is that they both are scalene triangles as they both have different measuring sides.

Therefore, the two triangles are not similar.

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The value is a parameter because the class of 28 students is a population.

A statistic is a measure calculated from a sample of the population, whereas a parameter is a measure that is calculated from the entire population. It is generally a numeric value that is used to characterise a population trait. A probability distribution is defined or described by a fixed value that is typically unknown.

The population's mean, variance, and standard deviation are just a few parameters. By employing statistical techniques like maximum likelihood estimation, these parameters are often calculated from a sample of data. In the given question, since from a class of 28, the average score was 72% of the population which is the total, this value is a parameter.

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The area of rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.

So, from the definition of the area of the rectangle.

Area = length x width

Given:

Thus,

Area = (5x + 4)(x^2+3x+2)

Simplifying,

Area = 5x(x^2+3x+2) + 4(x^2+3x+2)

Area = 5x³ + 19x² + 22x + 18

Thus, the area of the rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.

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The complete question  is-

A rectangle has a height of x+4x+4 and a width of x^2+3x+2. Express the area of the entire rectangle.

The distance between the two points R and S is √2.

The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places.

The distance between the two points R and S can be calculated using the Pythagorean theorem. Given the coordinates (x, y) for point R and (x + 1, y + 1) for point S, the distance d between R and S is given by:

d = √((x + 1 - x)^2 + (y + 1 - y)^2) = √(1^2 + 1^2) = √2.

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Answer:

To solve the equation 7cos(9x)−1=1, we first need to move the 1 to the left side of the equation:

7cos(9x) = 2

To find the solutions of the equation, we can divide both sides by 7:

cos(9x) = 2/7

Now we will use the inverse cosine function, denoted as arccos, to find the angle that has a cosine value of 2/7. Since the function cos is periodic with period 2Pi, it's range is [-1,1], we will look for the solutions between 0 and 2Pi.

x = (1/9)arccos(2/7) + (2kPi)/9 for k =0,1,2,....

we can also express the solution in degrees by multiplying the radian measure with 180/Pi.

x = (20/63)arccos(2/7) + (160*k) for k =0,1,2,....

or

x = (20/63) * arccos(2/7) * (180/pi) + (160*k) for k =0,1,2,....

where k is an integer.

So, x = (20/63) * arccos(2/7) * (180/pi) + (160*k) where k =0,1,2,.... is an expression that represents all solutions to the equation in degrees.

The estimated cost of tuition in 2018 using this linear function model is $726,430

What is the linear function?

A linear function is a mathematical function that describes a straight line. The general form of a linear function is:

y = f(x) = mx + b

To estimate the cost of tuition in 2018 using a linear function model, we can use the two given data points to find the slope and y-intercept of the line.

First, we can find the slope of the line by using the formula:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) is the data point for 2002 and (x2, y2) is the data point for 2012.

Substituting the values, we get:

m = (8,240 - 4,790) / (2012 - 2002) = 3,450 / 10 = 345

Next, we can use one of the data points and the slope to find the y-intercept of the line. Let's use the data point for 2002:

y = mx + b

4,790 = 345 * 2002 + b

b = 4,790 - 345 * 2002 = -1,015,290

So, the equation of the line is y = 345x - 1,015,290

To estimate the cost of tuition in 2018, we can substitute x = 2018 into the equation:

y = 345(2018) - 1,015,290 = 726,430

Hence, the estimated cost of tuition in 2018 using this linear function model is $726,430

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Answer:

-7

Step-by-step explanation:

angles in a triangle add up to 180⁰

90⁰+30⁰+(x+67)=180⁰

187+x=180⁰

x=180⁰-187⁰

x=-7

Answer:

yes

Step-by-step explanation:

A proportional relation has an equation of the form

y = kx,

where k is a real number.

y = 2.2x is an equation of the form y = kx with k = 2.2, so y = 2.2x is proportional.

Answer: yes