The length of a rectangle is 5 in longer than its width.

If the perimeter of the rectangle is 58 in, find its length and width.

Answer:

The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.

Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:

y = 40,000(0.93)^3

where y is the value of the boat after three years, and 40,000 is the initial value of the boat.

Simplifying this equation, we get:

y = 40,000(0.7951)

y = 31,804

However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.

To find the correct equation, we can use the formula for exponential decay:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.

In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.

So we can set up an equation:

32,174.28 = 40,000(0.93)^3

Simplifying this equation, we get:

32,174.28 = 31,804.00

This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:

y = 40,000(0.93)^t

where t is the time in years.

Answer:

pls attatch a pic so i can help u out :)

Step-by-step explanation:

The total amount of paper required is 3π(3+√71)unit²

The equation for the surface area of a cone is given as follows:

A = πr²+πrs.

Height of the cone, h = 8 & radius of the cone = 3, the slant height s is given as: s = √(r²+h²)

Substituting the values of r & h to determine s

s = √(8²+3²)

s = √71

Substituting the values to get Area,

A=π*3²+π*3*√71.

A=3π(3+√71)

Hence, the required paper will be A=3π(3+√71)unit²

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Answer:

22.  \((x-1)^2+(y+2)^2=74\)

26.  \(x^2+y^2=81\)

Step-by-step explanation:

The center of a circle is the midpoint of the diameter.

\(\textsf{midpoint}=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

(where \((x_1,y_1)\) and \((x_2,y_2)\) are the endpoints of the diameter)

The radius of the circle is the distance between the center and an endpoint of the diameter.

\(\textsf{radius}=\sqrt{(a-x_1)^2+(b-y_1)^2}\)

(where \((a,b)\) is the center of the circle, and \((x_1,y_1)\) is an endpoint of the diameter)

The center-radius form of a circle: \((x - a)^2+(y-b)^2=r^2\)

(where (a, b) is the center and r is the radius)

Question 22

\(\textsf{Let }(x_1,y_1)=(-4.5)\)

\(\textsf{Let }(x_2,y_2)=(6,-9)\)

\(\textsf{center}=\left(\dfrac{-4+6}{2},\dfrac{5-9}{2}\right)=(1,-2)\)

\(\textsf{radius}=\sqrt{(1+4)^2+(-2-5)^2}=\sqrt{74}\)

⇒ equation of circle: \((x-1)^2+(y+2)^2=74\)

Question 26

\(\textsf{Let }(x_1,y_1)=(0,9)\)

\(\textsf{Let }(x_2,y_2)=(0,-9)\)

\(\textsf{center}=\left(\dfrac{0+0}{2},\dfrac{9-9}{2}\right)=(0,0)\)

\(\textsf{radius}=\sqrt{(0-0)^2+(0-9)^2}=9\)

⇒ equation of circle: \(x^2+y^2=81\)

The given term of the arithmetic sequence is -18. The correct option is (A).

An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.

This difference is known as the common difference of the sequence.

The given arithmetic sequence is as below,

27, 22, 17, 12, 7, 2,...

Since the nth term of an arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

Where d is the common difference.

The common difference for the given sequence is,

d = 22 - 27

  = -5

Substitute d = -5 and n = 10 in the general form of nth term to obtain,

a₁₀ = a₁ + (n - 1)d

     = 27 + -5(10 - 1)

     = 27 - 45

     = -18

Hence, the value of the 10th term of the given sequence is -18.

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The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

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The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:

A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.

A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.

A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.

A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.

B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.

B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.

Finally, performing the remaining operations:

(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.

(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.

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The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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Answer:

B

Makes the most sense for the question and answer

The correct proof of sin(90-theta)=cos theta is given below.

We have given that

Malia tried to prove that cos(theta) = sin (90 - theta)

The formula for sin(a-b) is sin(a)cos(b)-cos(a)sin(b)

\(Sin(90-\theta)=cos\theta\)

\(sin(90-\theta)=sin(90)cos(\theta)-cos(90)sin(\theta)\\We \ know\\ sin(90)=1 and cos(90)=0\\=(1)cos(\theta)-(0)sin(\theta)\\=cos(\theta)\)

Therefore we get sin(90-theta)=cos theta.

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Answer:

$62.50

Step-by-step explanation: 250 divided by 4 equals $62.10

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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Answer:

256π

Step-by-step explanation:

2π(8²) + 2π(8)(8) <== exponents first

2π(64) + 2π(64) <== multiply

128π + 128π <== add

256π <== final answer

Note: 8 * 8 can also be written as 8²

Hope this helps!

Answer:

256π

Step-by-step explanation:

4π(8²) =   4π(64)=  804.2477193

804.2477193/π = 256π

C. H2 1,96

To establish whether there is a significant difference between treatments using the Kruskal-Wallis test, the calculated value of H should be compared to the critical values ​​in the table of H values. The critical value of H to use depends on the significance level chosen for the test (0.05 in this case).

Using a significance level of 0.05, the critical value of H for a sample size of n-8 for each treatment is approximately H2 1.96. That is, if the calculated H value is greater than 1.96, we can conclude that there is a significant difference between the treatments.

Hence, the correct answer in this case is c. H2 1,96

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There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Answer:

For 2 it's 27,247 and for 3 it's 31393.86

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Answer:

The simple answer is 1/2

Step-by-step explanation:

7/14=1/2

79/11 as a mixed number is  \(7\frac{2}{11}\).

A fraction that has the numerator higher than or equal to the denominator is said to be an improper fraction.

We have an improper fraction 79/11.

In order to change into improper fraction:

First, we find the whole number.

79/11 = 7.1818181818

79/11 ≈ 7.

Here, 7 is the whole number.

In order to figure this out, multiply the whole number we calculated 7 by the original denominator (11). After that, the outcome of that multiplication is deducted from the initial numerator:

79 - (11x 7)

= 79 - 77.

= 2.

2 is the numerator.

So, 79/11  = \(7\frac{2}{11}\), which is a mixed fraction.

Therefore, the mixed number is  \(7\frac{2}{11}\).

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Going by current exchange rates, Mitchell has $134.13 dollars remaining.

Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding.

The current exchange rate of Canadian dollars to US dollars is:

CAD $ 1.26 : 1 USD

When Mitchell first exchanged the USD to CAD$, it became:

= 150 x 1.26

= CAD$ 189

He then spends CAD$ 20 which leaves him with:

= 189 - 20

= CAD$ 169

He then exchanges this back to US$:

= 169 / 1.26

= US$ 134.13

Mitchell has US$ 134.13 remaining.

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The side b is approximately 80.02 feet in length. In a right triangle ABC with angle C equal to 90°, if angle B is 37.56° and side a is 49.94 feet, we can solve for side b using the trigonometric function sine.

First, we can label the triangle as follows:

Side a is opposite angle A,

Side b is opposite angle B,

Side c is the hypotenuse.

Let's label the triangle with the given and asked for information. Angle C is the right angle, angle B is 37.56°, side a is 49.94 feet, and side b is the side we are trying to find.

Using the sine function, we have:

sin(B) = opposite/hypotenuse

sin(37.56°) = a/b

Now we can substitute the known values:

sin(37.56°) = 49.94/b

To solve for b, we rearrange the equation:

b = 49.94 / sin(37.56°)

Using a calculator, we find:

b ≈ 80.02 feet.

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The width would be 4 and the length would be 9.

I got this answer based off of trial and error.

The question says..

"The length of the rectangle is one inch more than twice the width."

So we will take the width we guess times in by 2 and add one to get the length

ex.  W × 2 + 1 = length

ex.  4 × 2 + 1 = length   ← What I did    

Checking perimeter

4 + 4 + 9 + 9 = 26cm

Formula:  W + W + L + L = 26 cm

Answer:

The length is 9, the width is 4.

Step-by-step explanation:

Assume that the length is \(a\), the width is \(b\).

The perimeter is 26, so \(2(a+b) = 26\).

The length is one inch more than twice the width, so \(a - 2b = 1\).

By solving the system of equations below we get the answer:

\(\left \{ {{2(a+b)=26} \atop {a-2b=1}} \right. \\\left \{ {{2a + 2b=26} \atop {a-2b=1}} \right. \\\left \{ {{3a=27} \atop {a-2b=1}} \right. \\\left \{ {{a=9} \atop {9-2b=1}} \right. \\\left \{ {{a=9} \atop {b=4}} \right.\)

The area of the circular plate is approximately 43.14 square inches.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

The circumference of a circle can be calculated by the formula:

C = 2πr

where C is the circumference, π (pi) is a constant value approximately equal to 3.14, and r is the radius of the circle.

We are given that the circumference of the circular plate is 23.3 inches, so we can use this information to find the radius:

23.3 = 2πr

Dividing both sides by 2π, we get:

r = 23.3 / (2π) ≈ 3.71 inches

Now that we know the radius, we can use the formula for the area of a circle:

A = πr²

Substituting the value we found for r, we get:

A = π(3.71)²

A = 3.14 × 13.76

A ≈ 43.14 square inches

Therefore, the area of the circular plate is approximately 43.14 square inches.

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Answer:

Simplifying

-9 + 4 = 40

Combine like terms: -9 + 4 = -5

-5 = 40

Solving

-5 = 40

Couldn't find a variable to solve for.

This equation is a the left and right sides are not equal, therefore there is no solution.

Hope This Helped

Answer:

Step-by-step explanation:

The GCF of numbers is the greatest common factors between the numbers

The GCF of the years is 1

The intervals are given as: 13 years and 17 years

Factor both intervals (i.e. 13 and 17)

13 = 1 * 13

17 = 1 * 17

The common factor between both products is 1

So, we have:

GCF = 1

Hence, the GCF of the years is 1

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The length of the square in centimetres in algebraic expression is 25m

The perimeter of a square is m meters.

The length of the each side of the square in centimetres can be represented in an algebraic expression as follows:

Therefore,

perimeter of a square = 4l

where

Therefore,

m = 4l

where

l = m / 4 meters.

Therefore, the side length of the square in centimetres is as follows:

1 meters = 100 cm

m / 4 meters  = ?

cross multiply

length of the square in meters = m / 4 × 100

length of the square in meters = 100m / 4

length of the square in meters = 25m

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Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

Answer:

Kelsie's debt is less than 20$

Step-by-step explanation:

The selling price is the cost a customer pays for a good or service.

(1) Profit % = 25% . (2) Profit % = 6% . (3) Profit = Rs.9712 .

(4) Profit = Rs.9712 . (5) Loss % =  7.5% .

The amount a buyer pays for a good or service is known as the selling price.

It may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of other companies in the market.

The cost price of an item is the sum paid for it or the cost at which it was produced. C.P. stands for "cost price." Selling Price: The selling price of a good is the price at which it is sold.

So, the table would be:

(1)

CP = Rs.8000 , SP = Rs.10000

if SP > CP, we have profit.

Profit = SP - CP = 10000 - 8000 = Rs.2000 .

Profit % = (Profit * 100) / CP = (2000 * 100) / 8000 = 25% .

(2)

SP = Rs.6890 , Profit = Rs.390 .

CP = SP - Profit = 6890 - 390 = Rs.6500 .

Profit % = (Profit * 100) / CP = (390 * 100) / 6500 = 6% .

(3)

CP = Rs.25000 , Loss = Rs.1000 .

SP = CP - Loss = 25000 - 1000 = Rs.24000 .

Loss % = (Loss * 100) / CP = (1000 * 100) / 25000 = 4% .

(4)

CP = Rs.48560 , Profit = 20% .

SP = CP * (100 + Profit%) / 100 = (48560 * 120) / 100 = Rs.58272 .

Profit = SP - CP = 58272 - 48560 = Rs.9712 .

(5)

CP = Rs.28320 , SP = Rs.26196 .

CP > SP, we have a Loss.

Loss = CP - SP = 28320 - 26196 = Rs.2124 .

Loss % = (Loss * 100) / CP = (2124 * 100) / 28320 = 7.5% .

Therefore, the selling price is the cost a customer pays for a good or service.

(1) Profit % = 25% . (2) Profit % = 6% . (3) Profit = Rs.9712 .

(4) Profit = Rs.9712 . (5) Loss % =  7.5% .

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Complete question:

Find the profit or loss and complete the table.

Cost Price Selling Price Profit () Loss

Profit Loss

Percentage Percentage

6000

1000

6000

(a) 5000

(b) 6200

(c) 2400

(d) 1900

400

300

1590

190​

The population of US is 330 million approx.

A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." The number "%" is used to symbolize it.

Given

population of new york = 2.727272% population of US

population of new york = 9 million

population of US = 1/2.727272% of new york

population of US =  36.6666 x 90,00,000

population of US = 33,00,00,087.9 = 330 million approx

Hence population of US is approx 330 million.

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Answer:

1330 in.

Step-by-step explanation:

38 x 35 = 1330

Answer:

1330

Step-by-step explanation:

area = b x h

base (38)

height (35)

38 x 35 = 1330