In a circle of radius 49 cm, an arc subtends an angle of 72° at the centre. Find the length of the arc and the area of the sector.

It would take 370 days to build the wall with the given conditions.

If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:

60 men x 40 days = 2400 man-days

However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.

The number of man-days required for the first 10 days is:

60 men x 10 days = 600 man-days

The number of man-days required for the second 10 days is:

5 men x 10 days = 50 man-days

The total number of man-days required for the first 20 days is:

600 man-days + 50 man-days = 650 man-days

The remaining work can be completed by the 5 men in:

2400 man-days - 650 man-days = 1750 man-days

Therefore, the total time needed to build the wall is:

20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days

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The statement means that the set X/== is a partition of X, where X is a set and == is an equivalence relation on X.

Intuitively, this means that every element of X belongs to exactly one equivalence class, and the union of all equivalence classes is X.

More formally, a partition of a set X is a set of subsets of X such that:

The union of all subsets is X.

No two subsets have any elements in common.

In this case, the set X/== is a partition of X because it satisfies both of these conditions. First, the union of all equivalence classes is X because every element of X belongs to exactly one equivalence class.

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The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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Answer:

No

Step-by-step explanation:

To determine whether the given set of ordered pairs {(49,13),(61,36),(10,27),(76,52),(23,52)} represents a function, check if each x-value is associated with a unique y-value.

Check the x-values in the set: 49, 61, 10, 76, and 23. There are no repeated x-values.  Still need to check if each x-value has a unique corresponding y-value.

Check the y-values: 13, 36, 27, 52, and 52. There is one repeated y-value, 52, for the pairs (76, 52) and (23, 52).

Conclusion: the y-value 52 is associated with 2 different x-values, therefore the given set of ordered pairs does not represent a function.

Answer:

Step-by-step explanation:

The equation has one real solution when n = 43/9.

To find the values of n for which the equation has one real solution, we need to analyze the discriminant of the quadratic equation. The discriminant is the expression inside the square root of the quadratic formula and determines the nature of the solutions.

In this case, the equation is:

8s = -(n-3)s^2 - 9

To analyze the discriminant, we consider the quadratic equation in the form of as^2 + bs + c = 0. Comparing it with our equation, we have a = -(n-3), b = 8, and c = -9.

The discriminant (D) can be calculated using the formula D = b^2 - 4ac. Substituting the values, we get:

D = 8^2 - 4*(-(n-3))*(-9)

D = 64 - 36(n-3)

D = 64 + 36(3 - n)

D = 64 + 108 - 36n

D = 172 - 36n

For the equation to have one real solution, the discriminant must be equal to zero, D = 0. So, we have:

172 - 36n = 0

36n = 172

n = 172/36

n = 43/9

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Answer:

about 0.52 of the field

30=30 -75=80 = 50 near 52

Step-by-step explanation:

about 0.52 of the field

about 0.64 of the field

about 0.71 of the field

about 0.87 of the field

Answer: To find the total distance Reena covers in 6 days of a week, we need to consider the distance between her school and house for a single round trip and then multiply it by 6.

Given that the distance between the school and Reena's house is 1 km 480 m, we can add the distance for a one-way trip to get the total round trip distance.

Total round trip distance = 1 km 480 m + 1 km 480 m = 2 km 960 m

Now, to find the distance covered by Reena in 6 days, we multiply the round trip distance by 6:

Total distance covered in 6 days = 2 km 960 m * 6

Converting the distance to meters for easier calculation:

2 km 960 m = 2960 m

Total distance covered in 6 days = 2960 m * 6

Calculating the total distance covered:

Total distance covered in 6 days = 17760 m

Therefore, Reena covers a total distance of 17,760 meters (or 17.76 kilometers) in 6 days of a week.

The expression for the area of the trapezoid in this problem is given as follows:

A = 27a³b² square units.

The area of a trapezoid is given by half the multiplication of the height by the sum of the bases, hence:

A = 0.5 x h x (b1 + b2).

The parameters for this problem are given as follows:

h = 3ab, b1 = 7a²b, b2 = 11a²b.

Hence the area is given as follows:

A = 0.5 x 3ab x 18a²b.

A = 27a³b² square units.

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Hello!

you just want the result then:

it's the first answer.

The quotient equation from the synthetic division table is (3x⁴ + 19x³ + 22x² - 6x + 4)/(x + 2) = 3x³ + 13x² - 4x + 2

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

The synthetic division table

The synthetic division table has already been completed,

However, we have the following labels

Divisor  |   Dividend

             |  Some numbers

              |  Quotient  Remainder

using the above as a guide, we have the following:

Divisor = x + 2

Quotient = 3x³ + 13x² - 4x + 2

DIvidend = 3x⁴ + 19x³ + 22x² - 6x + 4

Remainder = 0

So, the quotient equation is

(3x⁴ + 19x³ + 22x² - 6x + 4)/(x + 2) = 3x³ + 13x² - 4x + 2

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a)The number 120 represents the initial height of the firework, in feet.

b)The firework will hit the ground after 3.75 seconds or 12.25 seconds.

c)The firework is 200 feet high when it is at its highest point.

d)The graph of the equation would be a parabola.

e)The firework will reach a height of 200 feet after 3 seconds or 10 seconds.

a. The equation provides the height the firework is above the ground at any time between when it is launched and when it hits the ground.

b. The equation that models when the firework will hit the ground is given by:

[tex]t = (90 ± √(90² - 4 * -16 * 120)) / (-32)[/tex]

Solving for t, we get:

t = 3.75 or 12.25

c. The firework is at its highest point when t = 7.5 seconds. At this point, the height of the firework is given by:

[tex]h₁ = -16(7.5)² + 90(7.5) + 120[/tex]

h₁ = 200

d.The parabola would open downwards, because the coefficient of t² is negative. The parabola would have a maximum point at t = 7.5 seconds, where the height of the firework is 200 feet.

e. The equation for the times at which the firework reaches a height of 200 feet is given by:

[tex]-16t² + 90t + 120 = 200[/tex]

Solving for t, we get:

t = 3 or 10

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11.) The missing length of the triangle = 16.8ft.

12.) Solved

13.) The missing height of the triangle would be = 6.5cm.

14.) The length of the base would be =21.4in

15.) The height of the trapezoid = 15km

16.) The length of the other side of the trapezium = 17ft

17.) The diameter of the circle = 22m.

18.) The perimeter of the square = 76ft.

To calculate the value of the missing part of the triangle, the formula that should be used is the Pythagorean formula and this is given as follows:

For 11.)

C² = a²+b²

where

c = 18.2ft

a = 7ft

b= ?

That is;

b² = 18.2²-7²

= 331.24-49

= 282.24

b =√282.24

= 16.8

For 13.)

The area of the triangle = 45.5cm²

The base = 14cm

The height = x

But the formula for area of triangle= 1/2 base×height

That is;

45.5=1/2×14×h

h = 45.5/7

= 6.5

For 14.)

To calculate the value of the base length, the area of parallelogram should be used. The formula for the area of parallelogram = base×height.

where:

area = 160.5in²

height = 7.5in

base = ?

base = 160.5/7.5

= 21.4in

For 15.)

The area of a trapezium = ½(a+b)h

where:

a = 23

b = 29

h = ?

Area = 390

That is:

390 = 1/2×(23+29)×h

h = 390/26

= 15km

For 16.)

The area of trapezium = 1/2(a+b)h

a = 12ft

b = ?

h = 4ft

area = 58ft²

58 = 1/2(12+b)×4

b = 58-34/2

= 17ft

For 17.)

The area of the circle = πr²

area = 380.13m²

π= 3.14

380.13= 3.14× r²

r² = 380.13/3.14

= 121.0605095

r. =√121.0605095

= 11m

diameter = 2r = 2×11 = 22m

For 18.)

The area of square= a²

area= 361

a= ?= side length

a= √361

= 19

perimeter = 4×19 = 76ft

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Answer:

[tex]x=15[/tex]

Step-by-step explanation:

[tex]\frac{2}{5}=\frac{6}{x}\\\\\mathrm{Multiplying\ }x\mathrm{\ on\ both\ sides,}\\\\\frac{2}{5}(x)=\frac{6}{x}(x)\\\\\mathrm{or,\ }\frac{2x}{5}=6\\\\\mathrm{Multiplying\ '5'\ on\ both\ sides,}\\\\\frac{2x}{5}(5)=6(5)=30\\\\\mathrm{or,\ }2x=30\\\therefore x=15[/tex]

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer:

5x+7 > 17 matches with 3.

1+3x > -5 matches with 2.

2x+1 < 3 matches with 1.

5-3x > 11 matches with 4.

Step-by-step explanation:

The cos x = adjacent side / hypotenuse = -4/5.Hence, the value of cos x is -4/5.

Given that sin x = 3/5 and x is in the second quadrant. We need to find the value of cos x.

To solve this problem, we will use the trigonometric identity.Sin²x + Cos²x = 1.We know sin x, which is in the second quadrant. Let's construct a right-angled triangle to find the value of cos x.

In the second quadrant, the value of sin x is positive, while the value of cos x is negative. This means that the adjacent side of the triangle is negative. In this case, we can label the adjacent side as -4 and the hypotenuse as 5.

Using the Pythagorean theorem, we can solve for the opposite side.

Opposite side = √(hypotenuse² - adjacent side²)

Opposite side = √(5² - (-4)²)

Opposite side = √(25 - 16)

Opposite side = √9

Opposite side = 3

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The number of bananas is 90.

Let's assume the number of bananas is represented by 'B', the number of lychees is represented by 'L', and the number of mangos is represented by 'M'.

From the given information, we have the following equations:

B + L = 384  (equation 1)

B + M = 258  (equation 2)

M = (4/7) * L  (equation 3)

To solve for the number of bananas, we need to eliminate the variables 'L' and 'M' from the equations. We can do this by substituting equation 3 into equation 2:

B + (4/7) * L = 258

To simplify this equation, we can multiply through by 7:

7B + 4L = 1806  (equation 4)

Now we can solve equations 1 and 4 simultaneously. We can multiply equation 1 by 4 and equation 4 by -1 to eliminate 'L':

4B + 4L = 1536  (equation 5)

-7B - 4L = -1806  (equation 6)

Adding equations 5 and 6, we get:

-3B = -270

B = 90

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The equations are written as follows

For Bert's Cab Company:: y = 1 + 3a

For Madeline's Cab Company: y = 3 + 2a

i. To represent the cost in dollars (y) for a cab ride of a miles for each cab driver, we can write the following system of linear equations:

For Bert's Cab Company:

y = 1 + 3a

For Madeline's Cab Company:

y = 3 + 2a

Here, 'a' represents the distance in miles.

ii. To find the distance at which the cost will be the same for both companies, we can set the two equations equal to each other and solve for 'a':

1 + 3a = 3 + 2a

a = 2

Therefore, the cost will be the same for both companies at a distance of 2 miles.

iii. To determine which cab driver's charge will be less for a ride that is 10 miles in distance, we can substitute 'a = 10' into the equations and compare the resulting costs:

For Bert's Cab Company:

y = 1 + 3(10) = 1 + 30 = 31 dollars

For Madeline's Cab Company:

y = 3 + 2(10) = 3 + 20 = 23 dollars

From the calculations, we can see that Madeline's cab company will charge less for a 10-mile ride, with a cost of $23 compared to Bert's cab company, which charges $31.

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The missing step a is the addition of the 4x variable from one side and the subtraction of the 6 to the other side of the equation to isolate x.

The missing steps to complete the equation when solving for x in the equation 2x - 6 = 4(x + 2) are as follows:

a. The addition of the 4x variable from one side to move the x to one side and the subtraction of the 6 to the other side of the equation so x is on one side and the other variable is on the other side of the equal sign.

The correct choice is a. This step involves distributing the 4 to both terms inside the parentheses, resulting in 2x - 6 = 4x + 8. To isolate the x variable, we need to move all the x terms to one side and the constant terms to the other side. Subtracting 4x from both sides gives -6 = 2x + 8. Finally, subtracting 8 from both sides yields -14 = 2x. Dividing both sides by 2 gives x = -7.

Choice b is incorrect because multiplying the 4x variable is not necessary or involved in this particular equation.

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To determine how many more raffle tickets Paul needs to sell, we can subtract the amount he has already sold from the minimum amount required to earn the team jacket.

Amount Paul needs to sell = Minimum amount required - Amount already sold

Amount Paul needs to sell = $230 - $50

Amount Paul needs to sell = $180

Since each raffle ticket costs $2, we can divide the amount Paul needs to sell by the price of each ticket to find the number of tickets he needs to sell.

Number of tickets Paul needs to sell = Amount Paul needs to sell / Price per ticket

Number of tickets Paul needs to sell = $180 / $2

Number of tickets Paul needs to sell = 90

Therefore, Paul needs to sell 90 more raffle tickets to earn a team jacket.

Answer:

The nature of the image formed by a concave mirror depends on the magnification produced by the mirror.

(a) If the magnification produced by the mirror is +3, it indicates that the image formed is magnified and upright. The positive sign of the magnification indicates that the image is virtual. The size of the image will be larger than the size of the object.

(b) If the magnification produced by the mirror is -1, it indicates that the image formed is of the same size as the object but inverted. The negative sign of the magnification indicates that the image is real and formed on the opposite side of the object. The size of the image will be the same as the size of the object, but it will be inverted.

In both cases, the concave mirror is acting as a converging mirror, meaning it brings light rays together to form an image. The specific size of the image cannot be determined without additional information, such as the distance of the object from the mirror and the focal length of the mirror.

Answer: The nature of the image formed by a concave mirror can be determined based on the sign of the magnification produced.

(a) If the magnification is positive (+3), it indicates that the image is magnified and upright. In this case, the image is virtual and located on the same side as the object. The size of the image will be three times larger than the size of the object.

(b) If the magnification is negative (-1), it indicates that the image is diminished and inverted. In this case, the image is real and located on the opposite side of the object. The size of the image will be the same as the size of the object, but it will be inverted.

It's important to note that the actual size of the image cannot be determined solely based on the magnification. The magnification only gives information about the relative size of the image compared to the object. To determine the actual size, additional information, such as the size and distance of the object, is required.

The given equation are linear equations.

To determine whether the given system of equations is linear or nonlinear, we need to examine the power of the variables in each equation.

98317y=1010+2965x

-71389y=5692x-1001

The variable y appears to the power of 1 (no exponent).

The variable x appears to the power of 1 (no exponent).

Since both variables have a power of 1 in both equations, the system is a linear system of equations.

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An equation for the transformed logarithm shown below, that passes through points (-1, 0) and (4, -2) is f(x) = -2log₆(x + 2).

By critically observing the logarithmic graph that models the logarithm function, we can logically deduce that it was reflected across the y-axis.

In Mathematics, the general form of a logarithm function is represented by the following mathematical equation:

f(x) = -alog(x) + k

Where:

Note: The vertical asymptote is at x = -2. Therefore, the logarithm function is given by:

f(x) = -alog(x + 2) + k

Next, we would determine the values of k and a by using the points (-1, 0) and and (4, -2):

0 = -alog(-1 + 2) + k

0 = -a(0) + k

k = 0.

For the value of a, we have:

-2 = -alog(4 + 2) + 0

-2 = -alog(6)

a = 2/log(6)

In conclusion, the required logarithm function in compact form is given by:

f(x) = -alog(x + 2) + 0

f(x) = -2/log(6) × log(x + 2)

[tex]f(x)=\frac{-2log(x+2)}{log6}[/tex]

f(x) = -2log₆(x + 2)

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There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

quadrant IV

Step-by-step explanation:

quadrant I - (+,+)

quadrant II - (-,+)

quadrant III - (+,-)

quadrant IV - (-,-)

The leg Adjacent the angle denoted as A using the principle of trigonometry is b.

The longest leg of a right angle triangle is the hypotenus. The leg which is directly opposite any given angle is the opposite leg while the leg parallel to any given angle is the Adjacent leg.

From the triangle given, the leg parallel to AC is the adjacent leg. Which is the leg b. So, leg b is the Adjacent.

Therefore, the adjacent leg is the one denoted as b.

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The absolute value function for this problem is given as follows:

y = |x - 4| - 6.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The coordinates of the vertex of the function are given as follows:

(4, -6).

The slope of 1 determines the leading coefficient a as follows:

a = 1.

Hence the function is given as follows:

y = |x - 4| - 6.

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Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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