The function below can be used to model the area of a rectangle in square centimeters, a, if the rectangle has a perimeter of 72 centimeters and a width of w what is the domain

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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Answer:

16%

Step-by-step explanation:

50 events and C shows 8

50/8 = 16%

Answer:

The Answer is 0.16 = 16%

Answer:

Range is called a set of possible outputs..in an realtion or function.

Every relation is not function but all function is relation

Actually some specified relations are called function.

Thanks

Here Range= {5}

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7. If a figure measures 7 centimeters high, 3 centimeters wide and 2 centimeters deep, what is the volume of the figure?

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The volume of the figure is 42.

Step-by-step explanation:

= 2 x 7 x 3

= 14 x 3

= 42

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The angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

We shall evaluate for the angle of elevation θ in degree, and then convert the result to radian as follows:

θ = tan⁻¹(4255/2000)

θ = 64.82482°

we multiply by π/180 to convert to radian;

θ' = 64.82482° × π/180

θ' = 1.13186 rounded to five decimal place.

Therefore, the angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.

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The value of the determinant |A| = 1

In the above question, a determinant is given, having k as one of the entry

We need to find the, value of |A|

If A is the matrix, then |A| stands for the matrix's determinant. The first element of the first row is multiplied by a secondary 2x2 matrix made up of the other 3x3 matrix elements that do not belong to the row or column to which your first chosen element belongs in order to get the determinant of the 3x3 matrix.

Calculus, linear algebra, and advanced geometry frequently make use of the determinant of a matrix.

So, |A| = a11(a22.a33 - a23.a32) - a12(a21.a33 - a23.a31) + a13(a21.a32 - a22.a31)

|A| = 1.(1 -0) - 0(0 - 0) + 0(0-k)

|A| = 1

Hence, the value of the determinant |A| = 1

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Answer:

\(y=-\frac{6}{5}x-\frac{41}{5}\)

Step-by-step explanation:

Parallel lines have the same slope.

\(6x+5y=11 \\ \\ 5y=-6x+11 \\ \\ y=-\frac{6}{5}x+\frac{11}{5}\)

So, the slope of the line we need to find is -6/5.

\(y+7=-\frac{6}{5}(x+1) \\ \\ y+7=-\frac{6}{5}x-\frac{6}{5} \\ \\ y=-\frac{6}{5}x-\frac{41}{5}\)

Options :

No, the sample size is too small.

Yes, the x distribution is normal with mean μ x = 66 and σ x = 1.5.

Yes, the x distribution is normal with mean μ x = 66 and σ x = 6.

Yes, the x distribution is normal with mean μ x = 66 and σ x = 0.4.

Answer:

No, the sample size is too small.

Step-by-step explanation:

Given that:

Mean, μ = 74

Standard deviation, σ = 8

Sample size, n = 16

Based on the information given, in other to be able to make inference on the x distribution of sample means, then the size of the sample of utmost importance in statistic. Large sample sizes (usually > 30) gives are always required as sampling distribution conform to the population distribution Inn terms of mean as the sample size grows larger as the distributon becomes approximately normal.

However, the sample size given above is well below 30.hence, making it difficult to say anything about the distribution of sample means

Answer:

24.5%

Step-by-step explanation:

Given

P(Off-Campus) = 0.30

P(Part-Time Job | Off-Campus) = 0.62

P(Part-Time Job | On-Campus) = 0.65

Inferred

P(On-Campus) = 0.70

P(No Part-Time Job | Off-Campus) = 0.38

P(No Part-Time Job | On-Campus) = 0.35

Calculation

P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)

0.35 = P(No Part-Time Job ∩ On-Campus)/0.70

0.245 = P(No Part-Time Job ∩ On-Campus)

Therefore, 24.5% of students that live on campus do not have a part-time job.

Answer:

360

Step-by-step explanation:

5 * 3 * 4 * 6 = 5 * 4 * 3 * 6 = 20 * 18 = 360

Answer:

360

Step-by-step explanation:

5x3=15

15x4=60

60x6=36

To find the unit rate, we need to determine how much distance Margo covers in one unit of time. We can do this by dividing the distance by the time.

Distance = 1/4 mile

Time = 1/12 hour

Unit rate = Distance ÷ Time

Unit rate = (1/4 mile) ÷ (1/12 hour)

We can simplify this division by multiplying both the numerator and denominator by the least common multiple of 4 and 12, which is 12.

Unit rate = (1/4 mile) ÷ (1/12 hour) x (12/12)

Unit rate = (3/4 mile) ÷ 1 hour

Unit rate = 3/4 mile per hour

Therefore, Margo's unit rate is 3/4 mile per hour. This means that she can cover a distance of 3/4 mile in one hour of walking.

Answer:

3mph

Step-by-step explanation:

1/12 of an hour will be 5 min. In 5 min she can walk 1/4 mile then in one hour she can walk 1/4 x 12. This means her rate will be 3 miles per hour.

60/12 = 5

12 x 1/4 = 12/4 = 3

Answer:

255.3 people

If you mean 11%, then:

25.3 people

Step-by-step explanation:

\(\frac{y}{230} :\frac{111}{100}\)

y × 100 = 230 × 111

100y = 25530

100y ÷ 100 = 25530 ÷ 100

y = 255.3

If you mean 11%, then:

\(\frac{y}{230} :\frac{11}{100}\)

y × 100 = 230 × 11

100y = 2530

100y ÷ 100 = 2530 ÷ 100

y = 25.3

Answer:

1. min, 2. max, 3. min, 4.max 5.max

Step-by-step explanation:

a. The expected score for Josephine and Crystal is 17.3 and 17.1 respectively.

b. The total probability of these combinations is 0.045 + 0.120 + 0.030 = 0.195.

c. 0.195 the probability that the difference (Josephine minus Crystal) in their scores is -1.

d. 0.008 is the probability that Josephine will score a 9 for the first time the 4th time that Josephine and Crystal play the game.

d.  0.3267. is the probability that Crystal's score will be 17 exactly 3 times.

a. To calculate the expected score for each player, we use the formula:

Expected Score = Σ(\(x_i \times P_i\))

where \(x_i\) is the score and \(P_i\)is the probability of that score.

For Josephine:

Expected Score = 16(0.10) + 17(0.30) + 18(0.40) + 19(0.20) = 17.3

For Crystal:

Expected Score = 17(0.45) + 18(0.40) + 19(0.15) = 17.1

b. To find all combinations of possible scores for Josephine and Crystal that will produce a difference (Josephine minus Crystal) of -1, we need to subtract 1 from Josephine's score and compare it to Crystal's score.

The possible combinations are:

Josephine Crystal Probability

15 17 0.100.45 = 0.045

16 18 0.300.40 = 0.120

17 19 0.20 x 0.15 = 0.030

c. The probability that the difference (Josephine minus Crystal) in their scores is -1 is the sum of the probabilities of the combinations listed in part (b), which is 0.195.

d. The probability that Josephine will score a 9 for the first time on the 4th play is the probability of scoring less than 9 on the first three plays and then scoring exactly 9 on the fourth play.

Assuming that Josephine's scores are independent, we can use the multiplication rule of probability:

Probability = \(P(score < 9)^3\) x P(score = 9)

Probability = \((0.10 + 0.30 + 0.40)^3\) x 0.20

Probability = 0.008.

e. The probability that Crystal's score will be 17 exactly 3 times out of 5 plays is given by the binomial distribution formula:

Probability = \(C(5,3) \times (0.45)^3 \times (0.55)^2\) = 0.3267

where C(5,3) is the number of ways to choose 3 plays out of 5.

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Answer:

*The Museum and the Coffee Shop lie on the opposite sides of the transversal and form a pair of alternate exterior angles

*The Day Care and the Community Center are supplementary angles and on opposite sides of the transversal.

*The Fire Station and the Community Center are consecutive interior angles lying on the same side of the transversal

Step-by-step explanation:

The transversal is the major road that crosses the other two roads shown in the diagram above.

Applying the knowledge of properties of lines, let's consider each statement given, to ascertain which is true and which is untrue:

Statement 1: 'The Fire Station and the Worship Center lie on the same side of the transversal and form a linear pair."

The fire station and the Worship center are on the same side of the transversal, however, they do not form a linear pair. They are corresponding angles.

Statement is NOT TRUE.

Statement 2: "The Museum and the Coffee Shop lie on the opposite sides of the transversal and form a pair of alternate exterior angles."

This statement is TRUE.

The Museum and the Coffee shop form alternate exterior angles pair.

Statement 3: "The Bank, the Museum, the Coffee Shop, the Worship Center are interior angles."

This is NOT TRUE.

They are all EXTERIOR angles.

Statement 4: "The Day Care and the Park are on the same side of the transversal and form a linear pair."

This is NOT TRUE.

They are consecutive interior angles.

Statement 5: "The Day Care and the Community Center are supplementary angles and on opposite sides of the transversal."

This is TRUE.

Statement 6: "The Bank and the Community Center are on opposite sides of the transversal and form a pair of alternate interior angles"

This is NOT TRUE.

They are on opposite side of the transversal but one the bank is an exterior angle while the community center is an interior angle.

Statement 7: "The Park and the Museum are adjacent angles and form a vertical pair of angles."

This is NOT TRUE.

They do not share the same side, so they can't be adjacent angles. They only share the same vertex, which makes them vertical angles.

Statement 8: "The Fire Station and the Community Center are consecutive interior angles lying on the same side of the transversal."

This is TRUE.

Answer:

Shopkeepers gain just by weighing is 22.22%

Step-by-step explanation:

Explanation:

Assume that the shopkeeper bought x units of goods i.e. actual weight of goods.

As the balance used to buy goods weighs 10% more, he actually bought x×110100=1.1x weight units i.e. although the shopkeeper paid for x units, he actually bought 1.1x units by weight.

Now he has 1.1x units of goods, but for selling he uses another balance, which actually measures 10% less i.e. 1−0.10=0.9 units for each unit weight of goods sold.

So while selling 1.1x becomes 1.1x0.90=1.2222... units.

Hence, shopkeepers gain just by weighing is 22.22%

The product of the two numbers as indicated by approximation is; 1,440,000.

It follows from the task content that the product of the two numbers is to be determined.

On this note, upon approximation to the nearest hundred; we have;

1,249 ==> 1,200

1,194 ==> 1,200

Hence, the approximated product is; 1200 × 1200 = 1,440,000.

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Answer:

Step-by-step explanation:

To linearize the function cos^5(x), we can use the following identity:

cos^5(x) = (cos^2(x))^2 * cos(x) = (1 - sin^2(x))^2 * cos(x)

Now, we can use the identity e^(ix) = cos(x) + i sin(x) to rewrite the expression as follows:

(1 - sin^2(x))^2 * cos(x) = ((1 - e^(ix) * e^(-ix))/2)^2 * (e^(ix) + e^(-ix))/2

= (1/16) * (e^(4ix) - 4e^(2ix) + 6 - 4e^(-2ix) + e^(-4ix))

This expression is now linear in terms of e^(ix) and e^(-ix). Therefore, we have linearized the function cos^5(x) as:

(1/16) * (e^(4ix) - 4e^(2ix) + 6 - 4e^(-2ix) + e^(-4ix))

Answer:

1.23

Step-by-step explanation:

Original price = $1.00

Discount = 12% = .12

Tax = 4% = .04

1.00 x .12 = 0.12

1.00-0.12=0.88

0.88 x .04= 0.0352 Round = 0.35

0.88 + 0.35=1.23

The line's equation in point-slope form is shown here. Point (2, 5) is the given point on the line, and slope 2 is the given slope of the line. The slope of this line is -1/2, which is the negative reciprocal of the slope.

A line's point slope form equation is \(y - y_1 = m(x - x_1)\). Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

We require a point on the line and the slope of the line in order to create a line equation in point-slope form. In point-slope form,

\(y - y1 = m(x - x1)\)

As an illustration, suppose we want to formulate the equation of the line passing through the coordinates (2, 5) and having a slope of 2. The values can be entered into the point-slope form as follows:

y - 5 = 2(x - 2)Let's say the given line has the equation \(y - y1 = m(x - x1)\), where (x1, y1) is a point on the line and m is the slope of the line.

we can use the given point (2, 5). Then we can plug in the values into the point-slope form:

\(y - 5 = (-1/2)(x - 2).\)

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Answer:

your answer is going to be y=3x-1

Based on the information we can infer that 5/8 between 6 people is equal to 15/24.

To calculate the part that corresponds to each person, divide the fraction 5/8 by the number of people, which in this case is 6. To simplify the fraction, you can reduce the numerator and denominator by dividing both by their maximum common factor, which is 3.

5 ÷ 3 = 1 and 2 remainder8 ÷ 3 = 2 and 2 remainder

So the fraction can be simplified to 1 2/8, which can also be expressed as 1 1/4 or 5/4 in its most simplified form. This means that each person would receive 5/4 of the original share, and since there are 6 people in total, you can multiply 5/4 by 6 to get the total share that corresponds to all 6 people:

(5/4) x 6 = 30/4 = 15/2 = 15/24

So each person would receive 15/24 of the original amount.

Note: Here is the question in English:

5/8 divided in 6 people

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Answer:

The answer is 100

Step-by-step explanation:

.

Answer:

c) is the correct answer

Step-by-step explanation:

Answer: 16, 64, and 49

Step-by-step explanation: Perfect squares are products made by squaring or multiplying a whole number by itself twice.

11 is not a perfect square since nothing can

be multiplied by itself to give us 11.

The same is true for 62 and 15.

16 is a perfect square since it's possible to find a whole number that can be multiplied by itself to give us 16.

That number is 4 since 4 × 4 = 16.

64 is also one since 8 can be multiplied by itself twice to give us 64.

49 is also one since 7² or 7 × 7 is 49.

Answer:D,E and F

Step-by-step explanation:

Perfect squares are numbers in which their square roots are whole numbers.

From the options

√16 =4

√64 =8

√49 =7

Answer:

Greatest 4 digit no. is -----> 9999................ Its Prime Factors are ----------> 3×3×11×101............... Factorization is as follows -----> 9999= 3×3333,,,,, 3333= 3×1111,,,,, 1111= 11×101,,,,,,,,,, 101= 101×1......

Step-by-step explanation:

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smallest 1000

largest 9999