Perimeter < 18.7 feet
4,1 ft
4.9 ft/
6.4 ft
x ft
Inequality:
Solution:

5777 divided by 160 is 36.10625.

the data is given in the the question is as follows:

5777 divided by 16 , that means,  5777 / 160 = 36.10625

                  36.10625

          160| 5777

                 -  5760

                          170

                      -   160

                             1000

                           - 960

                                 400

                             -    320

                                      800

                                   -   800

                                        000

Division is just opposite of the multiplication . There are four basic operations in mathematics and division is from one the basic operations . the four operation are addition, subtraction , multiplication , division.  Division is used when we split the large groups into the smaller one , so that each group will have equal items. there are different types of method used for division. the above one is the chunking method or in simple word repeated subtraction method.

Thus, 5777 divided by 160 is 36.10625.

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Answer:

The answer is "Option b"

Step-by-step explanation:

Please find the complete question in the attached file.

In 2006:

Top coats= 297

Parkas= 210

Jackets =213

Raincoats=137

Trench coats =103

Total: \(297+210+213+137+103=960\)  

In 2007:

Top coats =223

Parkas = 210

Jackets= 285

Raincoats = 259,

Trench coats =127

Total: \(223+210+285+259+127=1,104\)

Calculating the percentage of the increasing total sales:

\(\to \frac{1,104-960}{960}\times 100=15\%\)

Calculating the percentage of the increasing sales of the trench coats:  \(\to \frac{127-103}{103}\times 100 \approx 23.3\%\)

Because \(23.3\%- 15\%=8.3\%\) sales of the Trench coats increase by 8.3% point is faster than the total coat sales.

Answer:

B

Step-by-step explanation:

An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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Answer:

90°

Step-by-step explanation:

Hi!

I forgot the theorems exact name but it's something like "radius to a line that is tangent to the circle is always perpendicular to the tangent line" and perpendiular means 90°

Answer:

=)

Step-by-step explanation:

You could do 40 x 2 = 80 - 5 = 75 x 3 = 225

So if this is right, The answer would be 225

The valid conclusion that we can have from the given premises are:∃xQ(x) and ∃x¬P(x) → ∃xQ(x).∃xQ(x) can be proved by taking ∃x¬P(x) from the premises and then by applying resolution steps with the premise

∀x(P(x) ∨ Q(x)) we get ∃xQ(x).

Q2. (4300)8 is the octal expansion of the number that succeeds (4277)8. Here's how we can find the solution: In octal, the digits are 0, 1, 2, 3, 4, 5, 6, and 7. To find the next number after (4277)8, we just add 1 to the last digit. So, the next number would be (4278)8.

However, since the last digit is 7, we have to "carry over" to the next digit. We add 1 to the 8's place, but that carries over to the next digit, and so on. So, the next number after (4277)8 is (4300)8. Q3. (E1F)16 is the hexadecimal expansion of the number that precedes (E20)16.

Here's how we can find the solution:In hexadecimal, the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. To find the number that precedes (E20)16, we just subtract 1 from the last digit. Since the last digit is 0, we have to "borrow" from the digit to its left. That digit is E, which is one less than F.

So, we borrow from that digit and add 1 to the last digit. Thus, the number that precedes (E20)16 is (E1F)16.

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The required formula to calculate exterior angle and an interior angle are  360°/n and (n-2) * 180°/n.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides). To create a closed figure, a minimum of three line segments must be connected end to end.

The measure of an exterior angle of a regular polygon with n sides is given by 360°/n. The measure of an interior angle of a regular polygon with n sides is given by (n-2) * 180°/n.

So if you provide the number of sides of the polygon, I can give you the measures of the exterior and interior angles rounded to the nearest tenth if necessary.

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The expression that represents the ratio of the difference of the two means to Sidney’s mean absolute deviation is given by: Option B: 4/3.28

Mean absolute deviation is the average of the absolute deviation of each observation from their mean, for a considered set of observations.

For this case, the table of mean and mean absolute deviation is given as:

\(\begin{array}{ccc}&Mean&M.A.D.\\\text{Sidney}&82&3.28\\\text{Phill}&78&3.96\end{array}\)

(M.A.D refers to Mean Absolute Deviation).

So, difference in their mean is 82 - 78 = 4

Absolute deviation  for Sidney is 3.28

Thier ratio is: 4/3.28

Thus, the expression that represents the ratio of the difference of the two means to Sidney’s mean absolute deviation is given by: Option B: 4/3.28

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Answer:

Option B: 4/3.28

Step-by-step explanation:

Answer:

Yes

12, 35, 37

16, 30, 34

20, 21, 29

No

18, 24, 42

Step-by-step explanation:

Required

Determine which length form a right triangle

To do this, we make use of Pythagoras theorem where the square of the largest length = the sum of the squares of the other lengths

So:

(1) 12, 35, 37 --- Yes

\(37^2 = 35^2 + 12^2\)

\(1369 = 1225 + 144\)

\(1369 = 1369\)

(2) 16, 30, 34 --- Yes

\(34^2 = 16^2 + 30^2\)

\(1156 = 256 + 900\)

\(1156 = 1156\)

(3) 18, 24, 42 --- No

\(42^2 =18^2 + 24^2\)

\(1764 =324 + 576\)

\(1764 =900\)

\(1764 \ne 900\)

(4) 20, 21, 29 -- Yes

\(29^2 = 20^2 + 21^2\)

\(841= 400 + 441\)

\(841= 841\)

Based on the Pythagorean Triple, "12, 35, 37", "16, 30, 34" and "20, 21, 29" will form a right triangle(YES), while "18, 24, 42" will not (NO).

The Pythagorean triple can be described as any three set of integers representing sides of a right triangle that are solutions to the Pythagorean Theorem, which is given as:

c² = a² + b².

c is the longest side of the right triangle or largest of the set of integers of the Pythagorean triple.

Thus, find out which set of lengths will form a right triangle:

12, 35, 37 will form a right triangle, because:

37² = 35² + 12²

1,369 = 1,369

Also, the rest set of lengths will form a right triangle except, "18, 24, 42".

Thus, based on the Pythagorean Triple, "12, 35, 37", "16, 30, 34" and "20, 21, 29" will form a right triangle(YES), while "18, 24, 42" will not (NO).

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The total distance rose traveled by the tenth day's end is 117km

Rose went on a hiking trip, on the 1st day she walked a distance of 18kilometers.

It states that each day she walks 90% of the distance she walked the day before.

Similarly, on the next day she walked 90% of the distance she walked the day before.

We need to find the distance walked by her on an nth day is;

dₙ = d₁* rⁿ⁻¹

From the above formula;

Distance covered on second day = d₂ = 0.90(d1)

                                                               = 0.90(18) = 16.2

Similarly for day three = d₃ = 0.90(d₂)

                                            = 0.90(16.2) = 14.58

Since as d₁ = 18 and r = 90% = 0.90

The final answer on the tenth day makes it n = 10;

The total sum of distance covered by rose;

∑dₙ = d₁ * (1-rⁿ / 1-r)

∑d₁₀ = 18 * (1 - 0.90¹⁰ / 1 -0.90)

∑d₁₀ = 117km

The total distance rose traveled by the tenth day's end is 117km.

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Answer:

I think X is 3. Sorry if it's wrong!

Step-by-step explanation:

5 x 3 = 15 x 10 = 150

The circumference of a tire with a diameter of 16 inches is 50.3 inches (rounded to one decimal place), calculated using the formula C = π * d.

Multiplication is a mathematical operation that involves adding a number to itself a certain number of times, or combining equal groups of objects to find the total quantity. It is represented by the "x" symbol and is used to find the product of two or more numbers. For example, 2 multiplied by 3 is equal to 6 (2 x 3 = 6). Multiplication is one of the fundamental arithmetic operations and is used in various mathematical concepts and applications in everyday life.

The circumference of a tire is the distance around its outer edge. It can be calculated using the formula C = π * d, where d is the diameter of the tire. The diameter is the distance from one edge of the tire to the opposite edge, passing through the center. In this case, given that the diameter of the tire is 16 inches, substituting this value into the formula gives C = π * 16 = 50.3 inches (rounded to one decimal place). Therefore, the correct answer is 50.3 inches, as it represents the circumference of a tire with a diameter of 16 inches. The other options provided are not correct, as they do not accurately calculate the circumference based on the given diameter.

Therefore, The circumference of a tire with a diameter of 16 inches is 50.3 inches (rounded to one decimal place), calculated using the formula C = π * d.

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Answer:

47.10

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

... Cos = Adjacent/Hypotenuse

The value y is the length of the hypotenuse, and the given length 35 is the side adjacent to the given angle. Thus, the cosine relationship will be helpful.

Filling in the given values, we have ...

... cos(42°) = 35/y

Multiplying by y/cos(42°), we can find y to be ...

... y = 35/cos(42°) ≈ 35/0.7431

... y ≈ 47.10

Y will be approximately  47.10 in length

Step-by-step explanation:

we will use this  form that we memorized in our schools ............. SOH CAH TOA

CAH means , Cos ∅= Adjacent/Hypotenuse

Given values

∅ =42°

hypotenuse= y

adjacent side length = 35

now putting in our values  into

Cos ∅= Adjacent/Hypotenuse

OR

cos(42°) = 35/y

by multiplying y on both sides we get

y= 35/cos( 42°)

cos(42°)= 0.743

so  y= 35/0.743    

y = 47.10632

OR

y ≈ 47.10

12 cm, 35 cm, 37 cm measurements could not represent the side lengths of a right triangle. So the option C is correct.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle must equal the square of the longest side.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two legs (the sides that make the right angle) is equal to the square of the hypotenuse (the side opposite the right angle). Mathematically, this can be written as a² + b² = c².

So the sides of option C "12 cm, 35 cm, 37 cm" could not represent the side lengths of a right triangle because 12 cm² + 35 cm² ≠ 37 cm², these side lengths could not represent a right triangle.

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The diameter of the given circle with a circumference of 28.6 centimeters is approximately 9.11 cm.

The circumference of a circle is given by the simple formula: C = πd, where C is the circumference, π is the constant pi and d is the diameter of the circle.

Given that the circumference of the circle is 28.6 cm, we can use the formula to find the diameter:

28.6 = πd

d = 28.6/π

Using 3.14 as an approximation for π, we get:

d ≈ 28.6/3.14 ≈ 9.11

Therefore, the diameter of the circle is approximately 9.11 cm.

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The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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Answer:

answer b

Step-by-step explanation:

A parallelogram that must be a square can be described by the statement: "A parallelogram in which all angles are right angles (90 degrees) is a square."

In a parallelogram, opposite sides are parallel and congruent, and opposite angles are also congruent. However, for a parallelogram to be a square, it must have additional properties:

All angles are right angles: In a square, all four angles are equal and measure 90 degrees. This distinguishes a square from a general parallelogram where the angles can be acute or obtuse.

All sides are congruent: In a square, all four sides are equal in length. This equality of side lengths sets a square apart from a rectangular parallelogram, where only opposite sides are congruent.

Diagonals are congruent and bisect each other at right angles: The diagonals of a square are equal in length and intersect at right angles, dividing the square into four congruent right triangles.

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Complete question:

Which statement describes a parallelogram that must be a square? A parallelogram with opposite sides that are congruent and diagonals that bisect the angles. A parallelogram with a right angle and diagonals that bisect the angles. A parallelogram with a right angle and opposites sides that are congruent. A parallelogram with all sides congruent.

The projected value for the car after 10 years is equal to $10,503.42.

In Mathematics and Statistics, a population or physical asset such as a car that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:

\(P(t) = I(1 - r)^t\)

Where:

By substituting given parameters, we have the following:

\(P(t) = I(1 - r)^t\\\\P(10) = 28500(1 - 0.095)^{10}\\\\P(10) = 28500(0.905)^{10}\)

P(10) = $10,503.42

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Answer:

74 and 79

Step-by-step explanation:

one standard deviation= 5°

range of one standard deviation: (78-5) to (78+5)

                                                        73° to 83°

the completed multiplication table is:  40  45  50  ,72  54  60 and 56  90  70 .by using common factor  logic we can solve this question.

what is  common factor ?

A common factor is a number that divides evenly into two or more other numbers. For example, the common factors of 12 and 18 are 1, 2, 3, and 6, because all of these numbers divide evenly into both 12 and 18.

In the given question,

From the given table, we can see that:

The first row reads 40, 45, 50 (which are multiples of 5).

The second row has an unknown number (let's call it x), 54, and 60.

The third row reads 56, an unknown number (let's call it y), 70 (which are also multiples of 7).

To find the missing numbers, we can use the fact that multiplication is commutative, meaning that the order of the factors does not matter. Therefore, we can fill in the missing numbers by looking for factors that are common to both the row and column headers.

Starting with the second row, we can see that the common factor between x and 54 is 9, since 9 x 6 = 54 and 9 x x = ?. So, the missing number in the second row is 9 x 10 = 90.

Moving on to the first column, we can see that the common factor between 40 and 56 is 8, since 8 x 5 = 40 and 8 x 7 = 56. So, the missing number in the second row, first column is 8 x 9 = 72.

Finally, we can find the missing number in the first row, second column by finding the common factor between 45 and 60, which is 15, since 15 x 3 = 45 and 15 x 4 = 60. So, the missing number in the first row, second column is 15 x 5 = 75.

Therefore, the completed multiplication table is:

40  45  50

72  54  60

56  90  70

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Step-by-step explanation:

(x+1)(x-5)(x-6)

p(x)= 30+(19*x)-(10*x^2)+x^3

The polynomial that can represent the graph can be written as (x+1)(x-5)(x-6).

A polynomial is a variable expression made up of indeterminates and coefficients that uses only the addition, subtraction, multiplication, and non-negative integer exponentiation operations.

As we can see that the graph is intersecting the x-axis at three different points, therefore, the graph is intersecting the x-axis at -1, 5, and 6.

Hence, the polynomial that can represent the graph can be written as (x+1)(x-5)(x-6).

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39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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Answer:

Step-by-step explanation:

Since T is midpoint, ST and TU have equal length:

Substitute the values and solve for x:

T is the midpoint

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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The probability that the tennis player will make exactly 3 first serves out of 8 attempts is 0.278%.

To solve this problem, we can use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes (in this case, first serves) in a fixed number of independent trials (in this case, serves). The formula for the binomial distribution is:

P(X = x) = (n choose x) x pˣ x (1 - p)ⁿ⁻ˣ

where P(X = x) is the probability of getting x successes, n is the number of trials, p is the probability of success in each trial, and (n choose x) is the binomial coefficient, which represents the number of ways to choose x successes out of n trials.

Using this formula, we can plug in the values from our problem:

P(X = 3) = (8 choose 3) x 0.6³ x (1 - 0.6)⁸⁻³

P(X = 3) = (8! / (3! x 5!)) x 0.216 x 0.32768

P(X = 3) = 0.278%

This means that out of 1000 attempts, we can expect the player to make exactly 3 first serves around 2-3 times. It's important to note that this is just an estimation, and the actual number of successful serves may vary.

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