A contractor is building a new subdivision. A rectangular piece of land for a new house and yard
is 60 feet wide. The length of the land is longer than the width by a distance of n feet. Which
equation represents the area of the land?
OAA = 3,600 + 60m
OB A = 60n
OC A = 3,600+ n
OD. A = 240 + 2n

As the point moves along the helix, it traces out a three-dimensional surface in space.The space curve would look like a helix in graph.

1. First, we need to find the vector-valued function r(t) using the given parameter.

2. We can use the parameter x+z=2 to solve for the y-coordinate in terms of t:

y = √(4 − (1+sin t)2 − (1 − sin t)2).

3. We can now substitute this expression into the vector-valued function to obtain:

r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k

4. The space curve represented by the intersection of the surfaces is a helix in a graph.

The space curve represented by the intersection of the surfaces is a helix. It is a three-dimensional curve that can be described by a vector-valued function r(t) with parameter t. The vector-valued function r(t) is given by:

r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k.

The helix can be visualized as a spiral that wraps around a cylinder and is generated by a point travelling around the circumference of the cylinder at a constant speed. This can be observed by noting that the x- and z-coordinates of the vector-valued function are constant and only the y-coordinate changes over time. As the point moves along the helix, it traces out a three-dimensional surface in space.

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It is false that the probability of an individual from this population will have a weight greater than 72 pounds is 0.31 instead it is 0.70

According to the question,

Weight of population follows normal distribution

Mean of population : u = 75 pounds

Population Standard deviation : σ = 5.9 pounds

We have to Check if the probability an individual from this population will have a weight greater than 72 pounds is 0.31

Probability that weight is greater than 72 = P( x > 72)

Subtracting by 75 both sides and then dividing by 5.9

=> P( x - 75 / 5.9 > 72 - 75 / 5.9)

Using Z-statistics,

=> P( z > -3/5.9)

=> P( z > -0.508)

=> 1 - P(z < -0.50)

Using Probability distribution table for z,

=> 1 -  0.305

=> 0.70

Which is not equal to 0.31

Hence, It is false that Probability that weight is greater than 72 is 0.31

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Answer:

one 2

one 3

two 4's

one 5

one 6

Step-by-step explanation:

We can use the combination formula to derive how many sets of two can be obtained from this set of 4 numbers. We are using the combination formula instead of the permutation formula because, in this situation, order doesn't matter; the mean of 1 and 3 is the same as the mean of 3 and 1.

[tex]_nC_r = \dfrac{n!}{r!(n-r)!}[/tex] where [tex]n[/tex] is the number of things to choose from and [tex]r[/tex] is the number of things we are choosing. Hence the equation for this problem is:

[tex]_4C_2 = \dfrac{4!}{2!(4-2)!}[/tex]

[tex]_4C_2=\dfrac{24}{2(2)}[/tex]

[tex]_4C_2 = 6[/tex]

So, there are 6 ways to pick 2 cards from a total of 4. We can lay out these 6 possibilities from the given numbers on each card:

(1, 3)     (3, 5)     (5, 7)

(1, 5)     (3, 7)

(1, 7)

Then, we can calculate the mean, or average, of each.

2           4           6

3           5

4

Finally, we can conclude that the distribution of the means for each possible set of number pairs is:

one 2

one 3

two 4's

one 5

one 6

Step 3 shows the result of applying the subtraction property of equality

Two or more expressions with an Equal sign is called as Equation.

The given equation is 1/4(12x+8)+4=3.

We need to find which step has the property of substitution.

The Subtraction Property of Equality states that an equal value subtracted or removed from two equal items will result in a new equal amount.

Given step 1 is 3x+2+4=3

Opened the brackets on left side and multiplied with 1/4.

Step 2: 3x + 6 = 3.

Added the numbers on the left.

Step 3: 3x = -3

Equal value subtracted or removed from two equal items will result in a new equal amount. So Subtracted both sides by 6.Step 3 shows the result of applying the subtraction property of equality

Step 4: x = -1

Divided both sides by 3.

Hence, in step 3 we have used the property of subtraction.

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The statement that is the best interpretation of the mean is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

The data of the number of days members visited a certain fitness center varied from 0 to 7.

The mean of the random variable x = 3.12

The mean of the random variable is also known as the long-run average value of a random variable.  

Hence, we conclude that the best interpretation of the mean in the given question is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

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Answer:

g(-2) = -14

Step-by-step explanation:

We just need to substitute -2 for x

g(-2) = -3 * (-2)^2 - 2 = -3 * 4 - 2 = -12 - 2 = -14

Answer:

1st {-6, -3, 0, 3, 6}

Step-by-step explanation:

range is the output that is "y", so the range is a set of {-6, -3, 0, 3, 6}

The volume of the stone if, The volume of the water is 110 cm³, and The volume of the water and the stone is 150 cm³, is 40 cm³.

The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.

Given:

The volume of the water = 110 cm³,

The volume of the water and the stone = 150 cm³,

Calculate the volume of the stone as shown below,

The volume of stone = The volume of the water and the stone - The volume of the water

The volume of stone = 150 - 110

The volume of stone = 40

Thus, the volume of the stone is 40 cm³

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The two linear functions have the same y-intercept. Then the correct option is A.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The function 3x + 2y = 8 and the other function is graphed.

Convert the standard linear function into slope-intercept form. Then we have

3x + 2y = 8

2y = 8 - 3x

y = 4 - (3/2)x

The y-intercept of the linear function is 4 and the y-intercept of the graphed line is also 4.

The two capabilities have a similar y-catch. Then, at that point, the right choice is A.

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The vertex of the graph (3, 0)

What is Vertex of graph?

A vertex or node is the basic building block of a graph in discrete mathematics, and more precisely in graph theory. An undirected graph is made up of a set of vertices and a set of edges, whereas a directed graph is made up of a set of vertices and a set of arcs.

According to question

when f(x) = 0

that's the minimum point, the vertex, or the intersection of two lines,  g(x) = 0.25x − 0.75 and h(x) =  0.75 - 0.25x

Therefore

find the intersection of Two line which are

⇒ y = x/4 - 3/4

⇒ 4y = x - 3 → First line

⇒ y = 3/4 - x/4  

⇒ 4y = 3 - x → Second line

So x - 3 = 3 - x

2x = 6 ,

x = 3

And y = 0

hence the vertex of f(x) = (3, 0)

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The function f(x) is an absolute function and the function g(x) will be twice the function f(x). The table is completed below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = |x| - 2 and g(x) = 2 f(x)

The function g(x) is rewritten as,

g(x) = 2 (|x| - 2)

g(x) = 2|x| - 4

The function f(x) is an absolute function and the function g(x) will be twice the function f(x).

x           f(x) = |x| - 2               g(x) = 2f(x)

-2                0                               0

-1                -1                               -2

0                -2                              -4

 1                -1                               -2

2                0                                0

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From the given Isosceles trapezoid ABCD, the three correct statements are:

∠ADC ≅ ∠BCD

AD ≅ BC

AC ≅ BD

An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths.

Particularly in isosceles trapezoids, there are unique correlations. "Equal legs" is what the term "isosceles" denotes. Non-parallel sides on isosceles trapezoids have the same lengths. The "legs" are another name for these equal sides.

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. A triangle with two congruent sides is referred to as being isosceles, in other words.

Thus, three correct statements are -

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Answer:

Since YA=AX, XB=BZ, ZC=CY, it follows that A, B and C are the midpoints of the sides TX, XZ, ZY. AB, BC, AC are parallel to the sides and equal to their half. In fact, AB = YC=ZC. Therefore BC=AY.)

Good luck;)

Step-by-step explanation:

Answer:

m<P = 31°

Step-by-step explanation:

Use this symbol < for angle, not <.

<P and <Q are complementary.

That means that their measures add to 90°.

m<P + m<Q = 90°

Now we substitute 7x + 3 for m<P and 16x - 5 for m<Q.

7x + 3 + 16x - 5 = 90

Solve for x.

23x - 2 = 90

23x = 92

x = 4

m<P = 7x + 3 = 7 × 4 + 3 = 31

Answer: 31°

Answer: t is the dependent variable  and x the independent variable

Step-by-step explanation: t is the dependent variable it depends upon the values of x that we put in.

x is the independent variable as we can use whatever values we want for x it is not affected by t

Coefficient Cn is determined by Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

To find the coefficients Cn of the eigenfunction expansion of a function f(x), f(x) must be expanded with the eigenfunction yn(x). The expansion of f(x) with respect to the eigenfunction yn(x) is given by

f(x) = Σ[∞], n=1 cnyn(x)

To find the coefficient cn, we need to compute the dot product of f(x) and yn(x).

cn = (f,yn) = ∫[0,4]f(x)yn(x)dx

Since the eigenfunctions yn(x) are orthonormal, the scalar product is given by

cn = ∫[0,4]f(x)yn(x)dx = ∫[0,2]f(x)yn(x)dx + ∫[2,4]f(x)yn(x)dx

Since f(x) = 2/2 x for x in [0,2] and f(x) = 2 for x in [2,4], compute the coefficient cn as I can do it.

cn = ∫[0,2](2/2x)yn(x)dx + ∫[2,4](2)yn(x)dx

= ∫[0,2]xyn(x)dx + ∫[2,4]2yn(x)dx

= 1/2 ∫[0,2] (xyn(x) + 2yn(x)) dx

= 1/2 ∫[0,2] (x+2)yn(x) dx

Therefore, the coefficient Cn is given by

Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

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The second term of the series will be 27.

Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.

Sum to infinity = a/1-r

where s = 300

r = 0.1

a = 300 (1 - 0.1)

a = 300 (0.9)

a = 270

The second term of the progression will be = ar

Second term = 270 x 0.1

Second term = 27

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A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is; 300a + 450b = 6000 and a + 5 = b.

The variables x and y respectively represents  cans of soup and frozen dinners and a and b represents number of cans of soup and frozen dinners.

Let cans of soup be denoted by x

Let each frozen dinner be denoted by y

Now, we are told that each can of soup has 300 mg of sodium and each frozen dinner has 450 mg. Thus;

x = 300

y = 450

It is said that Samuel purchased 5 more frozen dinners than cans of soup  and they all collectively contain 6000 mg of sodium.

Let the no. of cans of soup be 'a' and no. of frozen dinner be 'b'. Thus, we will have the equation as;

ax + by = 6000

a(300) + b(450) = 6000  

300a + 450b = 6000      ------(1)

We are told that Samuel purchased 5 more frozen dinners than cans of soup. This can be represented by the equation;

a + 5 = b    ------(2)

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The general anti derivative or indefinite integral of the function

cos2x - sec²x is 1/2 sin2x + tan x + C .

The given function is of the form : cos2x - sec²x

Now we will use the indefinite integral on the above expression:

∫cos2x - sec²x

This can be broken into :

∫cos2x -  ∫sec²x

Now we will integrate them separately:

∫cos2x, we will use u-substitution.

Let 2x = u

Differentiation both sides we get:

2 dx = du

or, dx = 1/2 du

Hence we will use this value:

∫cos2x

= ∫cos u · 1/2du

= 1/2 ∫ cos u du

=1/2 sin u + C , where C is a constant.

Again we will do the second part of the integral:

∫sec²x

= tan x + C

Hence the required integral will be:

1/2 sin2x + tan x + C .

Now we will use differentiation to check the integral

d/dx (1/2 sin2x + tan x + C )

= d/dx (1/2 sin2x) + d/dx (tan x) + d/dx (C)

= cos 2x + sec² x

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The 6th term of the geometric sequence 27/16, -9/8, 3/4..... is - 2/9

The correct answer option is option B

Given: 27/16, -9/8, 3/4.....

nth term = ar^(n-1)

Where,

First term, a = 27/16

Common ratio, r = -9/8 ÷ 27/16

= -9/8 × 16/27

= -2/3

6th term = ar^(n-1)

= 27/16 × -2/3^(6-1)

= 27/16 × -2/3^5

= 27/16 × -32/243

= - 2/9

In conclusion, negative two ninths is the 6th term of the geometric sequence.

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The result of the expression 11C9 / 11P4 is 1 / 144

The given expression is

11C9 / 11P4

The permutation is defined as the method of arranging the numbers or object in order

The combination is defined as the method of selecting the numbers or object from a collection without any order

The given expression is

11C9 / 11P4

Find the value of each term

11C9 = 11! / (11-9)! × 9!

= 55

11P4 = 11! / (11-4)!

= 7920

Substitute the value of each term in the expression

The expression will be

11C9 / 11P4 = 55/7920

= 1/144

Therefore, the result is 1/144

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The perimeter of the checker board  118.4 cm

Area of each square = 14 sq. cm.

What is the length?

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The meter serves as the foundational unit of length in the International System of Units.

The square root of area is the length of one side

[tex]\text { lengthofeachsquare }=\sqrt{14}=3.7 \mathrm{~cm}[/tex]

[tex]\text { lengthofoneside }=8 * 3.7=29.6 \mathrm{~cm}[/tex]

[tex]P=4 a[/tex]

[tex]=4 * 29.6=118.4 \mathrm{~cm}[/tex]

[tex]\text { Perimeterofthecheckerboard }[/tex]

Therefor we get the perimeter of the checker board  118.4 cm

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The equation which can be used to determine n, the number of calories in each chicken nugget would be 193.5+12 n=288.5+8n

And n = 24.1

Option (C) is correct.

What is a linear equation?

A linear equation is an equation that describes a straight line. Linear equations have the form y = mx + b, where x and y are variables and m and b are constants. The constant m is the slope of the line, and the constant b is the y-intercept, which is the point where the line crosses the y-axis.

To derive this equation, we can start with the fact that the two meals have the same number of total calories. This means that the number of calories in the first meal is equal to the number of calories in the second meal. We can represent this relationship with the equation:

8 nuggets * calories/nugget + 193.5 calories = 12 nuggets * calories/nugget + 288.5 calories

We can then rearrange the terms on the left and right sides of the equation to get the equation in the form given in option C:

193.5 + 12 n = 288.5 + 8 n

Finally, we can solve this equation for n by subtracting 8n from both sides and then dividing both sides by 4:

n = (193.5 - 288.5) / 4 = (-95) / 4 = -23.75

Therefore, the number of calories in each chicken nugget is 24.1 calories.

Hence, option (C) is correct.

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Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient

Let f:R⇒S be a surjective homomorphism of rings with identity.

We have to find if R is a PID, prove that every ideal in S is principal.

We know that,

Let I be the ideal of S

Since f is sufficient homomorphism.

So, f⁻¹(I) is an ideal of R.

Since R is PID so ∈ r ∈ R such that

f⁻¹(I) = <r>

I = <f(r)>

Therefore,

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

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Answer:

Below

Step-by-step explanation:

Only the middle three are tri -nomials  ( three terms)

the third one reduces to  (x+ 2)^2

Answer:

3

Step-by-step explanation:

(x+2)^2

A (3 + 1/2) inches line represents a real distance of 5.985 miles.

First, we know that a (5 + 1/4) inch line on a map represents a 9 mile road, then the conversion from miles to inches is given by the quotient between these two, we will get:

9mi/(5 + 1/4) in = 9mi/(5.25) in = 1.71 mi/in

So, any distance in inches can be multiplied by the above number to get the corresponding measure in miles.

Then for (3 + 1/2) inches we will get:

(3 + 1/2) in*1.71 mi/in = 5.985 mi

So a line of (3 + 1/2) inches has represents a distance of 5.985 miles.

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Step-by-step explanation:

boy come ladies yer wait for you

hvb-amor-jon