Multiply the following 2 polynomials

(9 + 2x)(9 - 2x)

The value x of the trapezoid is 3 units.

A trapezoid is a quadrilateral with at least one pair of parallel sides .

The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides.

The midsegment of a trapezoid is parallel to each base, and its measure is half the sum of the lengths of the bases.

Therefore,

29 = 1 / 2 × (23 + 11x + 2)

29 = 1 / 2 × (25 + 11x)

cross multiply

29 × 2 = 25 + 11x

58 = 25 + 11x

58 - 25 = 11x

33 = 11x

divide both sides by 11

x = 33 / 11

x = 3

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The pValue is 0.15625 > 0.05 when  brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.

Let A represent the new pesticide and B be the Ant Killer. Then, you are given that

Brand1 kills ants in 65 of 100 containers:

Xa = 65/100 = 0.65

Brand2 kills ants in 58 of 100 containers:

Xb = 58/100 = 0.58

You know need to find sample variance for both,

s²A =∑(Xi - Xa)²

= 65(1-0.65)² + 35(0 - 0.65)²

= 22.75

s²B =∑(Xi - Xb)²

= 59(1-0.59)² + 41(0 - 0.59)²

= 24.19

You can know do a test for significance

t = (Xa - Xb) / √(sA /nA) +(sB/nB)

and derive the conclusion from there.

Here, Null and alternative hypothesis are generally,

Alternative hypothesis

Here, there are three samples are assumed. They are:

i) Samples are taken independently

ii) Samples must be selected randomly

iii) n₁p₁ ≥ 5 , n₁q₁ ≥ 5, n₂p₂ ≥ 5, n₂q₂ ≥ 5

i.e., p₁ = 0.65 ; p₂ = 0.58 , n₁ = 100

q₁ = 0.35 ; q₂ = 0.42 , n₂=100

Corresponding p-value at Z = 1.01722

p-value = 0.15625 > 0.05

Hence, the pValue is 0.15625 > 0.05 when  brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.

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Answer:

-2n+4

-2×54+4

-108+4

-104

The probability that the married couple will have adjacent desks is 0.22.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Thus, by Fundamental Principle of Counting, the number of possible arrangements where the married coupe has adjacent desks is 80640.

= 8 x 7! x 2

= 80640

Ans the total number of possible arrangements is 362880.

= 9!

= 362880

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

probability = 80640/362880

probability = 0.22

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Maximum area to enclose a rectangular pasture with one side up against a river is equal to 500,000 square feet.

As given in the question,

Let 'l' be the length of the rectangular pasture

And 'w' be the width of the rectangular pasture

Condition:

One side of the pasture is up against a river

Perimeter of the rectangular pasture with one side up against river = l + 2w

⇒ 2000 = l + 2w

⇒ l = 2000 - 2w

Area of the rectangular pasture

=( 2000 - 2w )( w )

= - 2 ( w² - 1000w )

= -2( w² - 1000w + 250000 - 250000 )

= -2 ( w - 500 )² + 500, 000

Maximum area is at w = 500

Maximum area is 500,000

Therefore, the maximum area of the given rectangular pasture is 500,000 square pasture.

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The number of days that the second voyage last's is 480 days.

Given,

The discrepancy in the length of the two excursions, we are asked to determine how many days the second voyage lasted.

We initially assign variables in order to overcome this issue. Let the duration of the first cruise be f days and the duration of the second expedition be s days.

We are aware that the first journey lasted 43 days longer than the second.

In mathematics, f = 43 plus s. (I)

The cumulative duration of the two journeys was 1003 days. Mathematically:

f + s = 1003........(ii) (ii)

We transform I into ii

43 + s + s = 1003

43 +2s = 1003

2s = 1003 - 43

2s = 960

s = 960/2 = 480 days

That is,

The second voyage lasted about 480 days

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Answer:

eighty-four thousand fifty-two

Step-by-step explanation:

the way i think about it is writing it as the sum of the digits together.  

80000+4000+50+2

eighty-four thousand fifty-two

[tex]\begin{array}{ccll} miles&hours\\ \cline{1-2} 5985&4\frac{3}{4}\\[1em] 8505&h \end{array}\implies \cfrac{5985}{8505}~~ = ~~\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{h}[/tex]

[tex]\cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{\frac{h}{1}}\implies \cfrac{19}{27}=\cfrac{19}{4}\cdot \cfrac{1}{h}\implies \cfrac{19}{27}=\cfrac{19}{4h}\implies 76h=513 \\\\\\ h=\cfrac{513}{76}\implies h=\cfrac{27}{4}\implies {\Large \begin{array}{llll} h=6\frac{3}{4} \end{array}}[/tex]

Answer:

The change in temperature is -6.64

The average hourly rate of change is

6 hours or -3.32

The probabilities when choosing a card of the respective color are

1/26, 1/8, 3/169, 1/676

The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

Multiply the total number of possible outcomes by the total number of occurrences. Divide the entire number of ways the event can occur by the total number of potential outcomes after determining the probability event and its related consequences.

The probabilities are:-

p= (1/13)*(1/2)=1/26

p=(1/2)*(1/4)=1/8

p=(1/13)*(3/13)=3/169

p=(1/52)*(1/13)=1/676

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Using the numbers to indicate their locations as pairs of x and y values. Euclidean distance is used to measure all distances.

a. Using the k-means algorithm, we can group the points into three clusters based on their initial cluster centers. The first cluster consists of the points (18, 10), (21, 11), (22, 22), (24, 15), (26, 12), and (26, 13), the second cluster consists of the points (27, 14), (40, 27), (41, 29), (42, 20), and (44, 28), and the third cluster consists of the points (30, 33), (31, 39), (35, 37), (39, 44), (46, 21), (47, 30), (48, 31), and (49, 23).

The silhouette approach, which compares how similar each point is to the points in its own cluster to the points in other clusters, can be used to assess the quality of the clusters. A high silhouette value denotes a well-clustered point, while a low silhouette value denotes a possible incorrect cluster assignment.

b. In hierarchical agglomerative clustering, we first create individual clusters for each point, which are then combined to create a single cluster that contains all of the points. Depending on how they calculate the separation between clusters, the three distinct link approaches will result in a variety of clustering outcomes.

The minimal distance between any two points in each of the two clusters is used by single link to calculate the separation between the clusters. Because it only takes into account the closest pair of points, this can lead to long, thin clusters.

The distance between the clusters is calculated using the maximum distance between any two points in the two clusters. Due to the fact that it only takes into account the farthest pair of points, this can lead to compact, spherical clusters.

The average link calculates the separation between the two clusters by averaging out all of the distances between the points in the two clusters. This takes into account all possible pairs of points and may lead to clusters with more symmetrical shapes.

In general, a single link will create clusters that are the most compact, a complete link will create clusters that are the most spherical, and an average link will create clusters that are more evenly shaped.

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The best way is to pick the one you think has a higher chance

The function representing the points relation is f(x) = 32(3x - 1)

A function is defined as a relation between a set of inputs having one output each.

Given a table, represents some points on the graph of linear function f.

x = -2, 1, 5, 10

f(x) = -224, 64, 448, 928

From option A)

f(x) = 32(3x - 1)

Put x = -2

= 32(-2x3-1)

= 32x(-7) = -224

Hence, The function representing the points relation is f(x) = 32(3x - 1)

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By evaluating the function we will see that the difference is:

f(1) - f(-7)  = 3

Here we have a piecewise function, this is a function that behaves differently on different intervals of its domain.

On the image you can see the different pieces of the function, and on the right the domain of each of the pieces.

The first part works for all the values smaller than -4 and x = -4.

So if we want to evaluate the function in x = -7, we need to use that piece:

f(-7) = |-7 + 5| - 9 = -7

And the second piece works on the interval (-4, 1], so to evaluate in x = 1 we need to use that piece.

f(1) = -1³ - 3*1 = -4

Then the difference is:

f(1) - f(-7) = -4 + 7 = 3

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Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

The values of each measure:

m∠WYZ = 43

m∠WXY = 33

m∠YWX = 61

m∠ZWX = 30.5

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Z is the incenter of WXY.

m∠WYX = 86

This means,

m∠WYZ = m∠XYZ = x

m∠WYZ + m∠XYZ = m∠WYX

2x = 86

x = 43

m∠WXZ = 33.

m∠WXZ = m∠WXY

Now,

The triangle WXY.

m∠YWX + m∠WXY + m∠WYX = 180

m∠YWX + 33 + 86 = 180

m∠YWX = 180 - 119

m∠YWX = 61

m∠ZWX = 61/2 = 30.5

Thus,

The values of each measure:

m∠WYZ = 43

m∠WXY = 33

m∠YWX = 61

m∠ZWX = 30.5

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Answer: B

Step-by-step explanation: One is a triangle and one is not. The bigger one has four sides therefore it is not a triangle

Answer:

  B. Not similar

Step-by-step explanation:

You want an appropriate choice of similarity reason for the triangles shown in the figure.

The side ratios in the smaller triangle are ...

  0.5 : 1 : 1 = 1 : 2 : 2

The side ratios in the larger triangle are ...

  2.25 : 3 : 3.5 = 9 : 12 : 14

The side ratios are not the same, so the triangles are not similar.

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The volume of a pyramid is 60 inches.

Given that,

A pyramid's volume varies in tandem with both its base area and height. When a pyramid's base is square inches and its height is inches, its volume is cubic inches.

V1 = 35 cubic inches

A1 = 15 square inches

h1 = 7 inches

A2 = 36 inches

h2 = 5 inches

To find  : What is V2

The following formula is used to determine a pyramid's volume:

V = (Base Area × Height)/3

V2 = (36 square inches multiplied by 5)/3

V2 = 60 cubic inches

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The probability of obtaining between 70 and 82 tails is 0.2137, that is, option A.

Here, we are given that a fair coin is tossed 130 times.

Thus,

number of trials ⇒ n = 130

p = P(getting tails in a single toss) = 0.5

mean of a binomial distribution = np

= 130*0.5

= 65

variance = np(1-p)

= 65*0.5

= 32.5

standard deviation = sqrt(variance)

= sqrt(32.5)

= 5.7

Now, x = number of tails

X follows a normal distribution with mean 65 and variance 5.7

P(70 < x < 82)

= P( 69.5 < X < 82.5)  [applying continuity correction]

= P[(69.5-65)/5.7 < Z < (82.5-65)/5.7)]

= P(0.79 < Z < 3.07)

= P(Z < 3.07) - P(Z < 0.79)

= 0.9989- 0.7852

= 0.2137

Thus, the probability of obtaining between 70 and 82 tails is 0.2137, hence, option A. .

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The  correct one is Your cousin. If the line is vertical, it will not have a slope.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

So, from the Discussion we came to know about Vertical Line.

But the slope of vertical line is undefined.

Then, the slope intercept form is not possible in vertical line.

Hence, the correct one is Your cousin. If the line is vertical, it will not have a slope.

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Assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.

The magnitude or size of a mathematical object determines whether it is larger or smaller than other objects of the same kind in mathematics.

Formally speaking, the magnitude of an object is the visible outcome of an ordering—of the class of objects to which it belongs.

So, the weight of the person will be:

The scale measures the passenger's normal upward force as it is applied by the floor.

When moving upward, the most force is generated (when starting an upward trip or ending a downward trip).

When there is a downhill acceleration, the normal force is at its lowest.

For any such circumstance:

∑F y​ =ma y  becomes for starting  +591N−mg=+ma and for stopping      +391N−mg=−ma.

Where a stands for the acceleration's magnitude.

To get rid of a and find mg, add these two simultaneous equations:

+591N−mg+391N−mg=0

OR

982N–2mg=0

Fg​ = mg = 982N/2​ = 491N

Therefore, assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.

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Complete question:
A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator later stops, the scale reading is 391N. Assuming the magnitude of the acceleration is the same during starting and stopping, determine the weight of the person.

answer:

20-5y+2x=52

step-by-step explanation:

plug in the values of x & y into the expression and calculate using the order of operations to get the answer. hope that helps!

Answer: 52

Step-by-step explanation:

1. plug in x and y into the expression : 20 - 5(-4) +2(6)

2. multiply the numbers in the parenthesis:  20 + 20 + 12
3. add all the numbers together (simplify): 52

Answer:

29/5 or 5.8

Step-by-step explanation

First, we put the 1 on the other side which turns it positive 5y=29

Then, we divide 29 by 5 which gives us 29/5 which is equal to 5.8

After solving the equation in terms of y will be y = (2/3)x - 4/3.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

The given equation is,

6x - 9y = 12

Then, the equation in terms of y will be,

9y = 6x - 12

Divide the above equation by 3,

3y = 2x - 4

y = (2/3)x - 4/3

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Answer: 24 26 37 60

Step-by-step explanation: im sure

Joni is mistaken because she applied the compounding rate formula rather than just the simple interest rate equation, which is incorrect. $231.53 will belong to her.

The $200 was deposited by Joni into an account that earned interest at a 5% annual compound rate.

Joni calculated and she'll have a final balance of $230 after three years.

The steps are as following,

Because Joni employed the simple interest rate method instead of the compound interest rates formula, she is mistaken $231.53 will belong to her.

The yearly compound interest rate if 5% is stated above.

As a result, she ought to have used the compound interest calculation when calculating.

A = P(1 + r/n)∧(nt)

Amount then becomes:

A = 200(1 + 0.05)³

A = $231.53.

Thus, final amount will be obtained as  $231.53.

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The complete question is-

Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230. Her work is shown below. Step 1: P = 200, r = 5, t = 3 Step 2: I = 200 ∙ 0.05 ∙ 3 Step 3: I = 30 Step 4: 30 + 200 = 230 Is Joni correct? Explain. Joni is not correct, because $230 is just the interest she will earn; she will have $430 total. Joni is not correct; $230 will be her balance after 1 year. After 3 years, she will have $290. Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53. Joni is correct. She correctly applied the I = P · r · t formula, and will have $230.

The value of 'b' will be;

⇒ b = 7 / 11

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 40 - 11b + 7 = 40

Now,

Solve the expression for b as;

The expression is,

⇒ 40 - 11b + 7 = 40

⇒ - 11b + 7 = 0

⇒ 11b = 7

⇒ b = 7 / 11

Thus, The value of 'b' will be;

⇒ b = 7 / 11

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you're ordered to attempt to memorize a series of images. there are 15 images in the series. when you are asked to state the order of the images you remember the first 3 and then it starts to get fuzzy. This is an example of memory retrieval.

What do you mean by series?

The total of a particular sequence of terms is known as a series in mathematics. These phrases often refer to real or complex numbers, though considerably more generality is possible.

In calculus and its generalization, mathematical analysis, the study of series plays a significant role. Most mathematical disciplines employ series, including combinatorics, where generating functions are employed to explore finite structures.

Along with being widely utilized in mathematics, infinite series are also frequently employed in other quantitative fields like physics, computer science, statistics, and finance.

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Answer:1

Step-by-step explanation:

There is a lot more

Answer: n >= -18

Step-by-step explanation:

n/-3 >= 6

(-3)      (-3)

n >= -18