The perimeter of a rectangle is 172 feet. Find the length and width if the length is an integer and the width is 2 times the next consecutive integer.

Step-by-step explanation:

is there something missing in the question ?

or is this meant to be a trick question ?

let me repeat :

pot1 contains 5 black and 7 white beads

pot2 contains 6 white beads (and nothing else, right ?)

then one bead is drawn from each pot.

so, 1 bead from pot1, and 1 bead from pot2.

the bead from pot1 is either white or black.

the bead from pot2 is white for sure.

so, the probability to get at least 1 white bead is 100% or 1, as there will be always the white bead taken from pot2.

quick answer (A)

ALL real numbers less than or equal to 8

The size of the angle subtended at the center of the circle is θ = 80.5397°

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

A = θ/360 x πr²

where;

θ is the central angle of the sector

r is radius

Given data ,

The area of a sector of a circle of radius 8cm is 45cm²

On simplifying , we get

A = θ/360 x πr²

45 = θ/360 ( 22/7 ) ( 8 )²

45 = ( θ/360 ) ( 201.1428 )

Divide by 201.1428 on both sides , we get

( θ/360 ) = 0.22372159

Multiply by 360 on both sides , we get

θ = 80.5397

Hence , the angle is θ = 80.5397°

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Answer:

hi helo bol ke gatu jama gol ke

The difference between the numbers given is 6.882.

Based on the information given, it should be noted that difference means subtraction.

The difference between the numbers given will be:

= 7 - (7 - 6.882)

= 7 - 0.118

= 6.882

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The Fall (drop)  of drainage piping is: A. 5".

In order to determine the fall (drop) of drainage piping we would need to multiply the drainage piping by the inch per feet.

Hence:

Using this formula

Fall (drop) of drainage piping = Drainage piping× inch per feet

Where:

Drainage piping=20

Inch per feet=1/4"

Let plug in the formula

Fall (drop) of drainage piping =20×1/4"

Fall (drop) of drainage piping =5"

Therefore the correct option is A. 5".

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One of the numbers would be 321. Hence option B is true.

Used the concept of the Number system that states,

A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.

Given that,

The ratio of the two numbers is 2/3, and their sum is 535.

Let us assume that,

The two numbers are x and y.

Hence we have;

[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex]  .. (i)

And, [tex]x + y = 535[/tex]   .. (ii)

From equation (i);

[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex]

[tex]x = \dfrac{2y}{3}[/tex]

Substitute the above value of x in (ii);

[tex]x + y = 535[/tex]

[tex]\dfrac{2y}{3} + y = 535[/tex]

[tex]2y + 3y = 535 \times 3[/tex]

[tex]5y = 1605[/tex]

[tex]y = 321[/tex]

From equation (i);

[tex]x = \dfrac{2y}{3}[/tex]

[tex]x = \dfrac{2\times 321}{3}[/tex]

[tex]x = 214[/tex]

Therefore, the number is 321. So option B is true.

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Answer:

Step-by-step explanation:

$1,248.92

Answer:

Step-by-step explanation:

Answer:

the answer is 8

Step-by-step explanation:

thats what i got

(a) The scale used in the analysis is qualitative as the data is not assigned any numeric value.

The daily performance is an ordinal variable, as the values assigned are ranked according to an order of the delivery time.

(b) The frequency table of the given data is:

Variable Frequency

Early  23

On-time  65

Late            9

Lost            3

Total 100.

(c) The relative frequency table for the given data is:

Variable Frequency Relative frequency

Early  23           23/100 = 0.23 = 23%

On-time  65           65/100 = 0.65 = 65%

Late            9             9/100 = 0.09 = 9%

Lost            3             3/100 = 0.03 = 3%

(a) The scale used in the analysis is qualitative as the data is not assigned any numeric value.

The daily performance is an ordinal variable, as the values assigned are ranked according to an order of the delivery time.

(b) The frequency table is a table showing frequency of each variable for the number of times they appear in the data.

The frequency table of the given data is:

Variable Frequency

Early  23

On-time  65

Late            9

Lost            3

Total 100.

(c) The relative frequency for a variable is the ratio of its frequency to the total frequency.

The relative frequency table for the given data is:

Variable Frequency Relative frequency

Early  23           23/100 = 0.23 = 23%

On-time  65           65/100 = 0.65 = 65%

Late            9             9/100 = 0.09 = 9%

Lost            3             3/100 = 0.03 = 3%

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Answer:

C.

Step-by-step explanation:

The center of the circle lies on the x-axis

The radius of the circle is 3 units.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The standard equation of a circle is expressed as:

[tex]x^2 + y^2 + 2gx + 2fy + C = 0[/tex]

Where

Given a circle whose equation is

Let's get the center of the circle

2gx = -2x

2g = -2

We have that;

g = -1

Similarly, 2fy = 0

given that

f = 0

Centre = (-(-1), 0) = (1, 0)

This explains that the center of the circle lies on the x-axis

We move further to the radius

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9

= 3 units

The radius of the circle is 3 units.

For the circle x² + y² = 9, the radius is expressed as:

r² = 9

r = 3 units

Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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The probability of selecting five students from the class, where there will be two freshmen girls and three freshmen boys is 0.23 approximately.

Probability is the game of chance. Probability of an event is the ratio of the required outcome to the total possible outcome.

Given that In a math class of 30 students, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. In Probability, the word "and" means multiplication

The probability that in a randomly selected group of five students from the class, there will be two freshmen girls and three freshmen boys can be expressed as follow

12/15 x 11/14 x 11/15 x 10/14 x 9/13

132/210 x 990/2730

130680/573300

0.2279

Therefore, the probability that in a randomly selected group of five students from the class, there will be two freshmen girls and three freshmen boys is 0.23 approximately.

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Answer:

4 and 1

Step-by-step explanation:

Answer:

[tex]2x^2+1-\dfrac{x}{2x^2-3}[/tex]

Step-by-step explanation:

Use the long division method to divide polynomials:

[tex]\large \begin{array}{r}2x^2\phantom{)))))}+1\phantom{)}\\2x^2-3{\overline{\smash{\big)}\,4x^4-4x^2-x-3\phantom{)}}}\\\underline{-~\phantom{(}(4x^4-6x^2)\phantom{-b))))))}}\\0+2x^2-x-3\phantom{)}\\\underline{-~\phantom{()}(2x^2\phantom{))))}-3)}\\-x\phantom{))))))}\end{array}[/tex]

Therefore:

[tex]\dfrac{4x^4-4x^2-x-3}{2x^2-3}=2x^2+1-\dfrac{x}{2x^2-3}[/tex]

Answer:

2√10

Step-by-step explanation:

We can use the Pythagorean theorem to solve this because it is a right triangle. a^2+b^2 = c^2

7^2-3^2 = x^2

49-9 = x^2

40 = x^2

√4*√10 = 2√10

Answer: B

Step-by-step explanation:

A) False. Rotations do not preserve parallelism.

B) True. Rotations are rigid motions and thus preserve angle measure.

C) False. A rotation that changes the location of every point except for the center of rotation.

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}[/tex]

False, because the number 40 is a composite number, those that cannot be broken down are called Prime Numbers.

Prime numbers are numbers that are used to decompose any number, but prime numbers cannot be decomposed, since they only have two Divisors, which are 1 and itself.

[tex]~\sf{Atte: Murdock:)}[/tex]

Answer: False

Step-by-step explanation:

All whole numbers can be decomposed into prime factors. For the number 40, the prime factorization would be [tex]2 * 2 * 2*5[/tex]. Since all 4 of those numbers are prime numbers, the answer is false.

Probability is 17.5% that 3 of them entered a profession closely related to their college

According to the statement

we have given that survey of 300 college graduates, 46% reported that they entered a profession closely and

We know that  For each college graduate, there are only two possible outcomes. Either they have entered a profession closely related to their college major, or they have not. The probability of a college graduate having entered a profession closely related to their college major is independent of other college graduates, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

This is P(X = 3) when n = 8. and the value of p is 0.46 put the value in the binomial formula then the outcome of answer will 17.5%

So, Probability is 17.5% that 3 of them entered a profession closely related to their college

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Answer:

  the graph of f has 3 turning points

Step-by-step explanation:

The graph of a function has a turning point (local extreme) where the derivative is zero and changes sign.

The derivative of a function tells you the slope of that function's graph. When the derivative is positive, the function is increasing. When the derivative is negative, the function is decreasing.

Where the derivative changes sign from positive to negative, the graph of the function changes direction from increasing to decreasing. At the point where the derivative is zero (between positive and negative), the graph is neither increasing nor decreasing. A tangent to the function at that point is a horizontal line, and the function itself is at a local maximum, a turning point.

The reverse is also true. When the derivative changes sign from negative to positive, the function changes from decreasing to increasing. The turning point where that occurs is a local minimum.

If the derivative crosses the x-axis (changes sign) 3 times, then there are three local extremes in the graph of f. The graph of f has 3 turning points.

__

Additional comment

In the attached graph, we have constructed a derivative function (red) that crosses the x-axis 3 times. It is the derivative of f(x), which is shown in blue. The purpose is to show the local extremes of f(x) match the zero crossings of the derivative.

Answer:  C) Sometimes positive; sometimes negative

============================================================

Explanation:

Pick a value between x = -1 and x = 0. Let's say we go for x = -0.5

Plug this into f(x)

f(x) = x(x+3)(x+1)(x-4)

f(-0.5) = -0.5(-0.5+3)(-0.5+1)(-0.5-4)

f(-0.5) = -0.5(2.5)(0.5)(-4.5)

f(-0.5) = 2.8125

We get a positive value.

This shows that f(x) is positive on the region of -1 < x < 0

----------------

Now pick a value between x = 0 and x = 4. I'll use x = 1

f(x) = x(x+3)(x+1)(x-4)

f(1) = 1(1+3)(1+1)(1-4)

f(1) = 1(4)(2)(-3)

f(1) = -24

Therefore, f(x) is negative on the interval 0 < x < 4

----------------

In short, f(x) is both positive and negative on the interval -1 < x < 4

It's positive when -1 < x < 0

And it's negative when 0 < x < 4

Answer:

sometimes positive sometimes negative

Step-by-step explanation:

I did it on Khan Academy

If a semicircle is rotated about the x axis of the graph then the resulting three dimensional shape will be a sphere.

Given a semicircle on a graph.

A semicircle is a half circle .A sphere is a geometrical object that is a three dimensional  shape , It is the set of points that are all at the same distance r from given point in three dimensional shape.

Rotation is basically an action of rotating around an object or an axis.

If a semicircle is rotated about x axis then the resulting figure will be a sphere. This is because of the fact that when the semi circle is rotated about the x axis then all the points will be at equal distance in all directions from the center.

Hence if a semicircle is rotated about x axis then the resulting figure will be a sphere.

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Answer: [tex]\frac{12}{x}[/tex] is an asymptote

Step-by-step explanation:

Apply a table, and plug in values of x into the equation.  For example f(2)=[tex]\frac{12}{2} =6[/tex]. That's one of the points on the graph that we just found (2,6)

The percentage of dogs who didn't try to bite the groomer is; 65%.

If follows from the task content that the number of dogs is 300 of which, 0.35 faction of the whole tried to bite the groomer.

Hence, the faction that did not try to bite the groomer is; 0.65 which corresponds to 65% when expressed as a percentage.

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Answer:

946

Step-by-step explanation:

Let's make an equation :

34% of x = 321.8

Covert 34% into decimal by dividing by 100 :

34 ÷ 100 = 0.34

Rewrite equation with decimal form :

0.34x = 321.8

Divide both sides by x to make x the subject :

x = 321.8 ÷0.34

x = 946.470588235

To the nearest whole number will be 946 as 4 rounds it down

So our final answer will be 946

Hope this helped and have a good day

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{34}{100} \sdot x = 321.8[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \cfrac{(321.8) \sdot(100)}{34} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 946.47[/tex]

Round off to nearest whole number :

[tex]\qquad \sf  \dashrightarrow \: x = 946[/tex]

Answer:

sin(x - y) = 0.21

Step-by-step explanation:

we have the sin values which we need to get cos values

sin (A-B) = sin A cos B - sin B cos A

sin² A + cos² A = 1

sin x = 4/9

cos² x = 1 - sin² x = 1 - 16/81 = 65/81

cos² x = 65/81

cos x = √65/9

sin y = 1/4

cos² y = 1 - sin² y = 1 - 1/16 = 15/16

cos² y = 15/16

cos y = √15/4

sin(x − y) = sin x cos y - sin y cos x

sin(x - y) = 4/9 √15/4 - 1/4 √65/9

sin(x - y) = (4√15-√65)/36

sin(x - y) = 0.21

socratic Narad T

Answer: C

Step-by-step explanation:

on edg

The individuals in this data set that can be gotten is B) Compression bandage styles and this data set contains A) 3 variables, 1 of which is categorical.

A categorical variables serve as the variable type that posses two or more categories.

This categories could be nominal variable, however considering the data , we can see that the first two are quantitative data and the data are:

THE COMPLETE QUESTION IS:

Alek is taking an inventory of styles of compression bandages for work. Here is the data he has collected.

The individuals in this data set are:Choose 1 answer:

A) Blood Centers

B) Compression bandage styles

C) Nurses

This data set contains:Choose 1 Answer:

A) 3 variables, 1 of which is categorical

B) 3 variables, 3 of which are categorical

C) 6 variables, 1 of which categorical

D) 6 variables, 3 of which are categorical

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The equivalent expression of [tex]\frac{3x^{-6}y^{-3}}{15x^2y^{10}}[/tex] is [tex]\frac{1}{5x^{8}y^{13}}[/tex]

The expression is given as:

[tex]\frac{3x^{-6}y^{-3}}{15x^2y^{10}}[/tex]

Divide 3 and 15 by 3

[tex]\frac{x^{-6}y^{-3}}{5x^2y^{10}}[/tex]

Apply the law of indices

[tex]\frac{1}{5x^{2+6}y^{10+3}}[/tex]

Evaluate the sum

[tex]\frac{1}{5x^{8}y^{13}}[/tex]

Hence, the equivalent expression of [tex]\frac{3x^{-6}y^{-3}}{15x^2y^{10}}[/tex] is [tex]\frac{1}{5x^{8}y^{13}}[/tex]

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Answer:

21x^2 + 33x + 16

Step-by-step explanation:

(14x^2 + 13x + 12) + (7x^2 + 20x + 4)

Combine like terms:

14x^2 + 7x^2 = 21x^2

13x + 20x = 33x

12 + 4 = 16

Thus:

21x^2 + 33x + 16

Answer:

21x^2 + 33x + 16.

Step-by-step explanation:

(14x2 + 13x + 12) + (7x2 + 20x + 4)   Remove the parentheses:

= 14x2 + 13x + 12 + 7x2 + 20x + 4    Bring like terms togethher:

= 14x^2 + 7x^2 + 13x + 20x + 12 + 4

= 21x^2 + 33x + 16.