Find the arc length of the shape

The solution for theta in the equation cos2theta = -1 in the range [0, 2π) is Ф = π/2

Given the equation

cos2theta = -1

Express properly

cos(2Ф) = -1

Take the arc cos of both sides

So, we have

2Ф = π

Divide both sides by 2

Ф = π/2

Hence, the value of theta in the range is π/2

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Answer: I got it :)

The equation that represents the number of haircuts she needs to do is 10.5x = 168.

Step-by-step explanation:

Given, The Hair Care Salon charges a stylist $30 per day to rent a station at the salon, Rhonda, a stylist makes $10.50 on each haircut.

Therefore, She needs to earn $138 + $30 to make a profit of $138 and let

'x' be the number of haircuts.

Therefore, the equation that equation that represents this situation is.

10.50x = 138 + 30.

10.5x = 168.

There are 100 seats in business class and 260 seats in economy class on the plane. As,we know that for every 13 seats in economy class, there are 5 seats in business class. We can write this as a fraction:5/13. This fraction represents the ratio of seats in business class to seats in economy class.

We can use this ratio to find the actual number of seats in each class, let's start by finding the total number of seats in business class. To do this, we need to know what fraction of the total number of seats is in business class. We can write this as: 5/18. This fraction represents the ratio of seats in business class to the total number of seats and  can use this fraction to find the actual number of seats in business class:5/18 * 360 = 100. So there are 100 seats in business class.

Now we can use the ratio of seats in economy class to find the actual number of seats in that class. We know that there are 13 seats in economy class for every 5 seats in business class. So the ratio of seats in economy class to seats in business class is:13/5, We can use this ratio to find the actual number of seats in economy class: 13/5 * 100 = 260, so there are 260 seats in economy class.

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The measurement that is closest to the area of the shaded region is 19 square inches.

So to determine the area of shaded region. we first find by the area of the big rectangle.

Let the dimensions of  rectangle are 10 by 15 inches.

The area would be

[tex]A = 10 *15\\= 150\ inches^{2}[/tex]

Now, we calculate the area of small rectangle.

Let the dimensions of rectangle are 10 by 13 inches.

The area would be

[tex]A = 10 *13\\= 130\ inches^{2}[/tex]

Now we calculate the difference between these two area,

= 150 - 130 inches²

= 20 inches²

19 value is the closest to 20.

So, 19 in² is the closest to the area of the shaded region.

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Complete Question :

Two rectangles were used to form the following figure. Use the ruler provided to measure the dimensions of the figure to the nearest quarter of an inch.

Which measurement is closest to the area of the shaded region of this figure in square inches?

a. 19 in²

b. 11 in²

c. 6 in²

d. 8 in²

The variation model can be used to find the value of f = 42(m/p) for any given values of m and p.

What is the variation model?

The variation model is a mathematical model that describes the relationship between two or more variables. It is used to represent how the value of one variable changes in response to changes in another variable. The variation model can be direct or inverse, depending on whether the two variables change in the same direction or in opposite directions. In a direct variation model, two variables are directly proportional to each other, meaning that when one variable increases, the other variable also increases in the same proportion. This can be represented mathematically as y = kx. In an inverse variation model, two variables are inversely proportional to each other, meaning that when one variable increases, the other variable decreases in the same proportion. This can be represented mathematically as y = k/x.

If f varies directly with m and inversely with p, we can write:

f ∝ m/p

Using the constant of proportionality k, we can write:

f = k(m/p)

To find the value of k, we can use the given information that f=36 when m=6 and p=7:

36 = k(6/7)

Solving for k, we get:

k = 36(7/6) = 42

Now that we have the value of k, we can use the variation model to find the value of f for any given values of m and p:

f = 42(m/p)

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The measure of angle 1 is 50° and the measure of angle 2 is 130°.

Given that the chord intercepted arc RQ is 53° and the chord intercepted arc ST is 47°, we need to find the measures of angles 1 and 2.

According to a geometric property, the measure of the angle formed by two chords that intersect inside the circle is half the sum of the intercepted arcs. Applying this property, we can find the measure of angle 1:

measure of angle 1 = (53° + 47°) / 2

= 100° / 2

= 50°

Next, we can use the fact that the sum of angles 1 and 2 is 180° to find the measure of angle 2:

measure of angle 1 + measure of angle 2 = 180°

50° + measure of angle 2 = 180°

measure of angle 2 = 180° - 50°

measure of angle 2 = 130°

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Answer:

m∠1 =

✔ 50°

m∠2 =

✔ 130°

Step-by-step explanation:

edg2023

Answer:

y = 3x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 3 and c = 5 , then

y = 3x + 5

Note that the linear equation that represents this relationship is y = -3x + 9.

To write a linear equation to represent this relationship, we need to find the slope and y-intercept of the line that passes through the given points.

Using the formula for slope, we have:

slope = (change in y) / (change in x)

= (0 - 9) / (3 - 0)

= -3

Now we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line. Let's use the point (0, 9):

y - 9 = -3(x - 0)

Simplifying, we get:

y - 9 = -3x

Adding 9 to both sides, we get:

y = -3x + 9

Therefore, the linear equation that represents this relationship is y = -3x + 9.

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Answer:

57.7 cubic inches

Step-by-step explanation:

1 ounce = 1.8 cubic inches

32 ounces = 57.7 cubic inches

So, the capacity is 57.7 cubic inches.

Based οn the given οptiοns, the mοst likely cοrrelatiοn value fοr this scatterplοt wοuld be r = -0.383.

Cοrrelatiοn refers tο the statistical relatiοnship between twο οr mοre variables. In οther wοrds, it measures hοw strοngly twο variables are related tο each οther. A cοrrelatiοn value ranges frοm -1 tο +1, with -1 indicating a perfectly negative cοrrelatiοn, 0 indicating nο cοrrelatiοn, and +1 indicating a perfectly pοsitive cοrrelatiοn. A cοrrelatiοn cοefficient οf 0 means there is nο linear relatiοnship between the twο variables.

The cοrrelatiοn cοefficient ranges frοm -1 tο +1, where -1 indicates a perfect negative cοrrelatiοn, 0 indicates nο cοrrelatiοn, and +1 indicates a perfect pοsitive cοrrelatiοn. Based οn the given οptiοns, the mοst likely cοrrelatiοn value fοr this scatterplοt wοuld be r = -0.383. This indicates a mοderate negative cοrrelatiοn between the variables.

The absοlute value οf the cοrrelatiοn cοefficient (0.383) suggests that the relatiοnship is nοt particularly strοng, but there is sοme evidence tο suggest that as οne variable increases, the οther variable tends tο decrease.

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To find the probability that a randomly selected book has fewer than 168 pages, we need to use the empirical rule, which is a guideline for how data is distributed in a normal distribution.

The empirical rule states that (approximately):

In this case, we have:

We can calculate how many standard deviations away from the mean x is by using this formula:

Plugging in our values, we get:

This means that x is one standard deviation below the mean.

So, we are looking for the probability that a randomly selected book has a value less than -1 standard deviations from the mean. Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Therefore, approximately 34% of the data falls between the mean and -1 standard deviation.

To find the area under the normal distribution curve to the left of -1 standard deviation, we can use a standard normal distribution table (z-table) or calculator. The area to the left of -1 standard deviation is approximately 15.87%.

Therefore, the probability that a randomly selected book has fewer than 168 pages is approximately 15.87%.

// I hope this helps! //

Answer:

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Class 10

>>Maths

>>Areas Related to Circles

>>Area of Sector and Length of an Arc

>>Find the length of the arc in terms of p

Question

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Find the length of the arc in terms of π that subtends an angle of 30

∘

at the centre of a circle of radius 4 cm.

Easy

Updated on : 2022-09-05

Solution

verified

Verified by Toppr

⇒ θ=30

o

and r=4cm

⇒ Length of an arc =

360

o

θ

(2πr)

Where, θ is angle subtended at a center.

2πr is circumference of a circle.

⇒ Length of an arc =

360

o

30

o

×2π×4

⇒ Length of an arc =

12

2π×4

∴ Length of an arc =

3

2π

We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392

Given, Random variable Z follows standard normal distribution. To find the value of u such that P(−0.62-0.62)Now, we will find the Z value for -0.62 using standard normal table as follows:-We get the value of P(Z<-0.62) as 0.2676Now, P(Z>-0.62)=1-P(Z<-0.62)=1-0.2676=0.7324Now, P(-Z<0.62)=P(Z<0.62)=0.7324We know, 0.62 lies between u=0 and u', we can find u' using standard normal table as follows:-From the standard normal table, we get that P(Z<0.62)=0.7315P(Z<0)=0.5Now, Z follows standard normal distribution, Z~N(0, 1) => 0.62=(u'-0)/1 => u'=0.62To find the value of u, let's use the formula Z = (X - μ) / σ where X is the observation, μ is the mean and σ is the standard deviation. We know, standard normal distribution is given by Z~N(0, 1) => σ=1Now, P(-0.62 P(Z P(u P(Z P(u) = 0.7392Now, using standard normal table, we get the value of Z when P(Z

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Bill needs to make monthly payments of approximately $206.81 in order to pay off his balance in 18 months.

The effective rate of interest the bank is charging Bill is approximately 10.4%

From the question, we are to calculate how much Bill's monthly payment will be

To find the monthly payment Bill needs to make in order to pay off his balance in 18 months, we can use the formula for the present value of an annuity:

PMT = PV / ((1 - (1 + r)^(-n)) / r)

Where PMT is the monthly payment

PV is the present value of the outstanding balance

r is the monthly interest rate

and n is the number of payments (in this case, 18).

First, we need to calculate the monthly interest rate. Since the annual interest rate is 9.7%, the monthly interest rate is:

r = 0.097 / 12 = 0.0080833

Next, we can plug in the values for PV, r, and n:

PMT = 3400 / ((1 - (1 + 0.0080833)^(-18)) / 0.0080833)

PMT ≈ $206.81

Hence, Bill needs to make monthly payments of $206.81

To find the effective rate of interest the bank is charging Bill, we can use the formula:

(1 + r)^12 - 1

Where r is the monthly interest rate.

Plugging in the value for r, we get:

(1 + 0.0080833)^12 - 1 ≈ 0.104

Hence, the effective rate of interest is approximately 10.4%.

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Alex feeds his cat 1/21 of the bag each day.

The fraction of the bag that Alex feeds his cat each day is 1/21. This can be calculated using the following formula:

Fraction of Bag = 1/3 / 7

Using algebra, we can solve this equation by multiplying both sides of the equation by 7, which results in the following equation:

1/3 = (1/21) * 7

Simplifying the equation, we get

1/3 = 1/21

Therefore, the fraction of the bag that Alex feeds his cat each day is 1/21.

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Answer:

Step-by-step explanation:

QR^2=PQ^2+PR^2

QR^2=(8[tex]\sqrt{3}[/tex])^2+(8)^2=8^2*(3+1)=8^2 * (4)

PR=8*2=16

answer is C

The mean cost per container is 1.13 dollars. A 90% confidence interval estimate for the mean is (0.66, 1.60) dollars. Not all costs per container fall inside the confidence interval. The costs of 1.89 and 0.89 dollars per container do not fall inside the confidence interval.

The coach for a sports team computed the mean cost per container of popular sports drinks, which was found to be $1.13. A 90% confidence interval estimate for the mean was calculated to be between $0.66 and $1.60. However, the costs of $1.89 and $0.89 per container did not fall within the confidence interval, indicating that they are not representative of the mean cost. This information could be used to make an informed decision on which sports drink to use for the team, considering factors such as cost and confidence in the mean cost per container.

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6 teaspοοns οf baking sοda are needed fοr 9 cups οf sugar in Trisha's recipe.

We can set up a prοpοrtiοn using the given ratiο οf sugar tο baking sοda:

3 cups sugar : 2 teaspοοns baking sοda

We want tο find hοw many teaspοοns οf baking sοda are needed fοr 9 cups οf sugar, which we can represent as:

9 cups sugar : x teaspοοns baking sοda

Tο set up a prοpοrtiοn, we can crοss-multiply the ratiοs:

3 cups sugar * x teaspοοns baking sοda = 9 cups sugar * 2 teaspοοns baking sοda

Simplifying, we get:

3x = 18

Dividing bοth sides by 3, we get:

x = 6

Therefοre, 6 teaspοοns οf baking sοda are needed fοr 9 cups οf sugar in Trisha's recipe.

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The approximate length of side XY is 3.16 units, side YZ is 4 units, and side ZX is 4.24 units. The approximate perimeter of triangle XYZ is 10.32 units.

To calculate the approximate perimeter of triangle XYZ, we must first find the approximate length of each side. To do this, we can use the Pythagorean theorem. For side XY, we calculate 3² + 3² = 9 + 9 = 18. We then take the square root of 18, which is approximately 3.16. For side YZ, we calculate 4² + 3² = 16 + 9 = 25. We then take the square root of 25, which is approximately 4. For side ZX, we calculate 4² + 4² = 16 + 16 = 32. We then take the square root of 32, which is approximately 4.24. Finally, we add the lengths of all three sides together to get the approximate perimeter of triangle XYZ, which is 3.16 + 4 + 4.24 = 10.32.

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Answer:

21 hazardous state waste sites in State Y.

Step-by-step explanation:

x=2n-8

x=34

2n-8=34

2n=42

n=21

The answer about  number of defective DVDs in a carton are mean number is 0.15, the variance is 0.1575, and the standard deviation is 0.397.

Let X be the number of defective DVDs in a randomly chosen carton of DVDs. We know that:

P(X=0) = 0.90 (90% contain no defective DVDs)

P(X=1) = 0.05 (5% contain one defective DVD)

P(X=2) = 0.03 (3% contain two defective DVDs)

P(X=3) = 0.02 (2% contain three defective DVDs)

Mean: The mean of X is given by:

μ = E(X) = Σ(xi × P(xi)), where xi is the number of defective DVDs and P(xi) is the probability of having xi defective DVDs.

μ = (00.90) + (10.05) + (20.03) + (30.02)

= 0.15

Therefore, the mean number of defective DVDs in a carton is 0.15.

Variance: The variance of X is given by:

σ² = E((X-μ)²) = Σ((xi-μ)² × P(xi)), where xi is the number of defective DVDs and P(xi) is the probability of having xi defective DVDs.

σ² = ((0-0.15)²⁰.⁹⁰) + ((1-0.15)²⁰.⁰⁵) + ((2-0.15)²⁰.⁰³) + ((3-0.15)²⁰.⁰²)

= 0.1575

Therefore, the variance of the number of defective DVDs in a carton is 0.1575.

Standard deviation: The standard deviation of X is given by:

σ = √(σ²)

σ = √(0.1575)

= 0.397

Therefore, the standard deviation of the number of defective DVDs in a carton is 0.397.

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Since the angle is in quadrant 2, the sine will be pοsitive. Therefοre, the value οf sin 0 is: sin 0 = 0.8

Trigοnοmetry is a branch οf mathematics that deals with the relatiοnships between the sides and angles οf triangles. It is used tο study and sοlve prοblems invοlving triangles, especially right triangles.

Since cοsine is negative and the angle is in quadrant 2, we knοw that the sine will be pοsitive. We can use the Pythagοrean identity tο find the value οf sine:

sin²θ + cοs²θ = 1

Substituting the value οf cοsine, we get:

sin²θ + (-6/10)² = 1

Simplifying, we get:

sin²θ + 36/100 = 1

sin²θ = 1 - 36/100 = 64/100 = 0.64

Taking the square rοοt οf bοth sides, we get:

sin θ = ±0.8

Since the angle is in quadrant 2, the sine will be pοsitive. Therefοre, the value οf sin 0 is:

sin 0 = 0.8

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Therefore , the solution of the given problem of equation comes out to be y = 1/2x - 1 is the equation for the image of the line following a -2 unit translation on the y-axis.

A variable term is typically used in complex variable algorithms to ensure agreement with both conflicting claims. Numerous academic numbers are shown to be equal using equations expression, which have been mathematical statements. In this case, the normalise technique offers b + 6 to use the info from y + 6 rather than splitting 12 into two parts.

Here,

By deducting 2 from each point's y-coordinate, one can acquire the image of the line after it has been translated -2 units on the y-axis.

The initial formula is

=>  y = 1/2x + 1.

=> y = 1/2x + 1 - 2 when 2 is subtracted from it.

When we simplify, we obtain:

=> y - 2 = 1/2x - 1.

Consequently, y = 1/2x - 1 is the equation for the image of the line following a -2 unit translation on the y-axis.

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y = 1/2x - 1 is the equation for the image of the line.

A mathematical statement proving the equality of two expressions is known as an equation. Variables, constants, mathematical symbols, and operations like addition, subtraction, multiplication, and division are frequently used in it.

One can obtain the picture of the line after it has been translated -2 units on the y-axis by subtracting 2 from each point's y-coordinate.

The basic equation is given

y = 1/2x + 1

y - 2 = 1/2x + 1 - 2          [translated -2 units on the y-axis]

Simplify,

y - 2 = 1/2x - 1

Therefore, y = 1/2x - 1 is the equation for the image of the line.

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Travis is practicing his free throws at a basketball practice, and his coach set a goal for him to achieve an 85% or higher free throw percentage before he can go home.

A free throw is a type of shot made in basketball from the free-throw line, usually given to a player after a foul has been committed by the opposing team. To calculate Travis's free throw percentage, the number of successful free throws he makes must be divided by the total number of free throws he attempted, then multiplied by 100 to get a percentage.

If his free throw percentage is 85% or higher, he can go home from the basketball practice.

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The explicit formula is given by the equation a(n) = 50n² + 25n + 25 and the recursive formula is given by a(n) = a(n-1) + 200, with a(1) = 100.

A approach for identifying patterns in numerical sequences is the method of finite differences. It entails first identifying the differences between each word in the sequence, then repeating the procedure with the sequence of differences that results. If a pattern forms where the gaps between the gaps are always the same, the initial sequence exhibits a polynomial pattern. Both the recursive formula, which enables us to compute any term by utilising the previous term in the series, and the explicit formula for the sequence, which allows us to calculate any term in the sequence directly, can be found using the procedure.

Given the views on different days we have:

First finite difference: 300-100 = 200

Second finite difference: 1200-300 = 900

We observe that second finite difference is constant and hence follows a quadratic pattern.

Using the explicit formula we have:

a(n) = 50n² + 25n + 25

where, a(n) is the views on day n.

Using recursive formula:

a(n) = a(n-1) + 200, with a(1) = 100

Hence, the explicit formula is given by the equation a(n) = 50n² + 25n + 25 and the recursive formula is given by a(n) = a(n-1) + 200, with a(1) = 100.

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Philip is not in the top 5% of weights.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur. Probability can also be expressed as a percentage, ranging from 0% to 100%.a) We need to find the probability of selecting a boy in kindergarten whose weight is between 38 pounds and 48 pounds. This can be done by calculating the z-scores and using the z-table.

The z-score for a weight of 38 pounds is:

z = (38 - 44) / 3.2 = -1.875

The z-score for a weight of 48 pounds is:

z = (48 - 44) / 3.2 = 1.25

Using the z-table, the probability of selecting a boy whose weight is between -1.875 and 1.25 is approximately 0.8365.

(b) We need to find the probability of selecting an obese kindergarten boy, which means a boy with a weight over 52 pounds. We can calculate the z-score for a weight of 52 pounds as:

z = (52 - 44) / 3.2 = 2.5

Using the z-table, the probability of selecting a boy whose weight is over 52 pounds is approximately 0.0062.

(c) We need to find the cut-off value for the top 5% of weights, which corresponds to a z-score of 1.645. We can use the z-score formula to solve for the weight value:

z = (x - 44) / 3.2

1.645 = (x - 44) / 3.2

x - 44 = 1.645 * 3.2

x = 49.276

So the cut-off weight value for the top 5% of weights is approximately 49.276 pounds.

Philip's weight of 50 pounds is greater than the mean weight of 44 pounds, but it is less than the cut-off weight value for the top 5% of weights.

Therefore, Philip is not in the top 5% of weights.

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given G(t) = 2 − 3t, G(-3 + h) - G(-3) simplifies to 3h.

To evaluate G(-3 + h) - G(-3), we need to substitute -3 + h and -3 for t in the expression for G(t) and then simplify:

G(-3 + h) - G(-3) = (2 - 3(-3 + h)) - (2 - 3(-3))

= (2 + 3h + 9) - (2 + 9)

= 3h

So, G(-3 + h) - G(-3) simplifies to 3h.

In mathematics, the term "simplest form" refers to the expression of a mathematical term or equation in its most basic or minimal form, typically by simplifying or reducing it as much as possible using mathematical operations or techniques.

if we have an algebraic expression with multiple terms, we can simplify it by combining like terms, expanding brackets, or using other algebraic techniques to reduce the expression to its most basic or minimal form.

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The original fraction is 5/8. The numerator of the original fraction is then n = √6, and the denominator is (√6 + 6). If we add 3 to both the numerator and denominator, we get (√6 + 3)/(√6 + 9). This fraction simplifies to 5/8.

Let the numerator be 'n'. The denominator is 6 more than the numerator, so the denominator is (n + 6).

We can represent this as an equation:

n/(n + 6) = 1

We can solve for the value of n by multiplying both sides by the denominator, (n + 6):

n*(n + 6) = 1*(n + 6)

Simplifying, we get:

n^2 + 6n = n + 6

Subtracting 6n from both sides gives us:

n^2 = 6

Taking the square root of both sides yields:

n = √6

The numerator of the original fraction is then n = √6, and the denominator is (√6 + 6). If we add 3 to both the numerator and denominator, we get (√6 + 3)/(√6 + 9). This fraction simplifies to 5/8.

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Answer:

x=15

Step-by-step explanation:

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