Resolve ax/a+x into an infinite series. Write the first 5 terms. Consider x as the variable. Then, use summation notation to create a formula for the infinite series

Since the angles in DBC and BDA are equal, we have:

DBC ≅ BDA

What is the Angle-Angle Similarity Theorem?

The Angle-Angle Similarity Theorem, also known as the AA Similarity Theorem, states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Given: AD // BC, AB // CD

To prove: DBC =~ BDA

From the given, we have AD // BC and AB // CD.

This means that AD is parallel to BC and AB is parallel to CD.

Since AB is parallel to CD, corresponding angles are equal.

Let the angle BCD = x.

Then, angle BAD = x.

Since AD // BC, corresponding angles are equal.

Let the angle DCB = y.

Then, angle DAC = y.

Now, we can see that angle BDA + angle DAC = y + x.

And angle DBC + angle DCB = y + x.

Since the sum of the angles in a triangle is 180 degrees,

angle BDA + angle DAC + angle DBC = 180.

So, y + x + y + x = 180.

Therefore, 2y + 2x = 180.

And, y + x = 90.

Since the angles in DBC and BDA are equal, we have:

DBC =~ BDA

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The value of p such that the matrix M does not have an inverse is given as follows:

p = -5.

The matrix M for this problem is given as follows:

M = [7 2

       p -1].

As it is a 2 x 2 matrix, the determinant is obtained with the multiplication of principal diagonal subtracted by the multiplication of the secondary diagonal, hence:

|M| = -7 - 2p.

The matrix does not have an inverse if the determinant assumes a value of zero, hence the value of p is obtained as follows:

-7 - 2p = 0

2p = -7

p = -7/2

p = -5.

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Note that 11 > S or S < 11 is given in the in the Line Graph attached. The above simply means that 11 as a quantity is greater that the factore represented by "s".

A line graph is a graphical depiction of changing information over time. It is a diagram created by connecting points with line segments.

Line graphs may be used to demonstrate how something evolves over time.

Line graphs are useful for displaying data that has peaks (ups) and troughs (downs) or was gathered in a short period of time. The pages that follow discuss the various components of a line graph.

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Answer:

C. 6/48

Step-by-step explanation:

mutliply both numerator and denominator

Answer:

The answer is 3.2 x 10-21.

Step-by-step explanation:

To solve this problem, we need to use the rules of exponents. The first step is to calculate the exponents for each number.

For 9 × 104, the exponent is 3 (9 × 104 = 90000).

For 3,000,000, the exponent is 2 (3,000,000 = 3000000).

For 0.00243, the exponent is -3 (0.00243 = 0.00000243).

Now, we can calculate the answer by multiplying the exponents:

3 × 2 × (-3) = -6

Then, we need to multiply the numbers together to get the final answer:

(9 × 104)² × (3,000,000)² × (0.00243) = 9 x 10-6 x 9 x 10-12 x 0.00243 = 3.2 x 10-21.

The required value of angle x for a given hexagon is 20°.

What is a hexagon?

In terms of geometry, a hexagon is a closed, six-sided polygon in two dimensions. Six vertices and six angles make up a hexagon. The words "hexa" and "gonio" both refer to six.

A hexagon's internal angles add up to 720°. All of the sides and interior angles of a regular hexagon are the same lengths.

Given, the interior angles of a hexagon are 7x°, 7x°, 4x°, 7x°, 7x°, and 4x° respectively.

So, the sum of interior angles = 720°

or, 7x° + 7x° + 4x° + 7x° + 7x° + 4x° = 720°

or, 36x° = 720°

or, x = 720/36

or, x =20°

Hence, the required value of x is 20°.

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There were 75 total number of persons present at the party

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The amount of people who ate lasagna was 12 less than 3/5 of the total number of people.

Let x represent the total number of people at the party.

The number of people that ate lasagna = (3/5)x - 12

The number of people who ate lasagna were 33. Hence:

The number of people that ate lasagna = 33

Therefore the equation is:

33 = (3/5)x - 12

(3/5)x = 45

x = 75

The total number of people is 75

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Yes, it would be unusual to get a score of 0 on a binomial distribution with a mean of 2.5 and a standard deviation of 1.4. This is because the expected value of such a distribution is much higher than 0.

Yes, it would be unusual to get a score of 0 on a binomial distribution with a mean of 2.5 and a standard deviation of 1.4. This is because the expected value of such a distribution is much higher than 0. The binomial distribution is a type of probability distribution which is used to describe the probability of a discrete event occurring a certain number of times in a given number of trials. The mean of the binomial distribution is the expected value of the events, while the standard deviation is a measure of how much the values of the events vary from the expected value. In this case, the expected value is 2.5, and the standard deviation is 1.4. This means that the probability of getting a score of 0 is quite low, since the expected value is so much higher than 0. Therefore, it would be considered unusual to get a score of 0 on this binomial distribution.

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The coordinates of triangle ABC after dilation are; (-6, -3), (0, 9) and (3, 3)

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given that, a triangle ABC with coordinates, A (-2, -1) B (0, 3) C (1, 1)

This triangle is dilated by a scale factor of 3,

SInce, the scale factor is greater than 3, therefore, dilation shows an enlargement.

The rule of dilation is given by;

(x, y) → (kx, ky), where k is dilation factor.

Let triangle ABC is dilated to form triangle A'B'C'

Therefore, the coordinates of triangle A'B'C' are;

A' = 3(-2, -1) = (-6, -3)

B' = 3(0, 3) = (0, 9)

C' = 3(1, 1) = (3, 3)

The graph is attached.

Hence, the coordinates of triangle ABC after dilation are; (-6, -3), (0, 9) and (3, 3)

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This can be modeled as a Poisson distribution. The mean number of patients admitted per day is 2.5, so the Poisson parameter λ = 2.5. The probability that the hospital will not have enough beds on any given day is the probability that more than 1 patients will be admitted, which is given by:

P(X > 1) = 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - (e^-2.5 * 0 + e^-2.5 / 1!)

= 1 - e^-2.5 * (1 + 2.5)

This is the probability that the hospital will not have enough beds to accommodate its newly admitted patients on any given day.

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The equation of line m passing through the points (0, 0) and (1, 6) is y = 6x

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Line M goes through the points (0, 0) and (1, 6). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-0=\frac{6-0}{1-0} (x-0)\\\\y=6x[/tex]

The equation of line m is y = 6x

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The value of a is given as follows:

a = 12.

We have two parallel lines that are cut by a transversal, and the two angles are between the parallel lines and on the same side of the transversal, meaning that they are consecutive interior angles.

Consecutive interior angles are supplementary, meaning that the sum of their measures is of 180º, hence the value of a can be found as follows:

10a + 2 + 5a - 2 = 180

15a = 180

a = 180/15

a = 12.

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Answer: a = 12.

Step-by-step explanation: did the same question got it right

Answer:

25% increase

Step-by-step explanation:

Percentage increase = [tex]\frac{100-80}{80} * 100=\frac{20}{80} * 100 = 25%[/tex]

Yes she is correct, because 810 km is approximately 500 miles

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

The distance between Cale and Johannesburg is 810 km.

1 mile is converted as 1.609km

There 1km = 1/1.609 miles

810 km = 1/1.609 × 810

= 503.4 miles

If this value is approximated to the nearest hundred,then it will be

500 miles

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Answer:

If x-y=9 is a true equation, we can substitute this equation into 5+x−y to find its value.

5 + x - y

= 5 + x - (x - 9) (since x - y = 9)

= 5 + x - x + 9

= 5 + 9

= 14

So, the value of 5 + x - y would be 14 if x-y=9 is a true equation.

The written description of the given expression would be 14 less a number. That is option A.

Less than which is represented by the symbol such as < is used in arithmetics to show that a given value is less than the value of which it is being compared to.

The given expression = X - 14. Where X is the unknown number which is compared with 14.

Therefore, according to the expression, 14 less than a number is the same as X - 14.

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Based on the information provided, Derek will have made $480 more in buttered popcorn than in caramel popcorn.

To calculate his earnings with popcorn, let's use the expression given for each type of popcorn:

Buttered popcorn:

8w+9

8 x 12 + 9

96 + 9 =105

105 x 11 = $1155 (Total earnings for buttered popcorn)

Caramel popcorn:

6w-11

6 x 12 - 11

72 - 11 = 61

61 x 11 = $671 (Total earnings for caramel popcorn)

Now, let's calculate the difference:

$1155 - $671 =$480

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Answer: 4a = D; 4b = B

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Let x be the distance between 1st Street and 2nd Street along Pike Avenue.

As 1st Street and 2nd Street are parallel we can use the Side Splitter Theorem to calculate x:

[tex]\implies \sf x:300=40:40+160[/tex]

[tex]\implies \sf x:300=40:200[/tex]

[tex]\implies \sf \dfrac{x}{300}=\dfrac{40}{200}[/tex]

[tex]\implies \sf x=\dfrac{40}{200} \cdot 300[/tex]

[tex]\implies \sf x=60\; ft[/tex]

To calculate the distance between 2nd Street and the landmark along Pike Avenue, subtract the found distance between 1st Street and 2nd Street along Pike Avenue from the length of Pike Avenue:

[tex]\implies \sf 300-60=240\; ft[/tex]

The code from solving the expressions is MGWMGWW

1. 7b

2. 6y - 1

3. -m + 0.5

4. 9x - 2y

5. 4j

6. -12x + 22

7. 6m - 8

Algebraic expressions are expressions that are composed of coefficients, variables, terms, factors and constants.

They also consist of mathematical operations, such as;

Given the expression;

b + b + b + b + 3b

collect the like terms

7b

2(4y-  3) - 2x + 5

collect like terms

6y - 1

Hence, the code is MGWMGWW

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The equation we need is[tex]P(3 < =x < =5) = (x^3 - 3x^2 + 5x - 3)/24[/tex]. We can solve this in R by using the dbinom() function. The code is: dbinom(3:5, size=4, prob=0.25) which yields an answer of 0.3125. This means that the probability of 3 to 5 bicycle accidents occurring in the next four months is 0.3125.

The equation for the probability of a certain number of bicycle accidents occurring in the next four months is [tex]P(x) = (x^3 - 3x^2 + 5x - 3)/24[/tex], where x is the number of accidents. To solve this equation with R, we can use the dbinom() function which is used to calculate the binomial cumulative distribution function. We set the size parameter to 4 (the number of months) and the probability parameter to 0.25 (the probability of a bicycle accident occurring at the intersection in a single month). The code is dbinom(3:5, size=4, prob=0.25). This yields an answer of 0.3125, meaning that the probability of 3 to 5 bicycle accidents occurring in the next four months is 0.3125. This calculation is useful for understanding the likelihood of certain numbers of bicycle accidents occurring in a given time period, and can be used to inform decisions about safety at intersections.

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Answer:

Step-by-step explanation:

B. 64^(1/2) is greater than 64^(1/3).

The length of ED is,  3√10

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

In a figure,

⇒ PB = BC = 6

Now, By the figure,

⇒ ΔFPD and ΔEMD are congruent.

Hence, We can formulate;

⇒ FP / EM = PD / MD

Let the length of MD = x

⇒ FP / EM = PD / MD

⇒ 6 / 3 = (9 + x) / x

⇒ 2x = 9 + x

⇒ 2x - x = 9

⇒ x = 9

Hence, The length of MD = 9

Now, In  ΔEMD;

⇒ ED² = EM² + MD²

⇒ ED² = 3² + 9²

⇒ ED² = 9 + 81

⇒ ED² = 90

⇒ ED = √90

⇒ ED = 3√10

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The financial planner invested $4,737.50 in the mini-mall development plan and $1,012.50 in the savings account.

The amount invested in the savings account is equal to the total amount invested minus the amount invested in the mini-mall development plan. We can express this as an equation:

Total Investment - Investment in Mini-Mall Development Plan = Investment in Savings Account

Substituting the values given in the problem, we get:

$5,750 - Investment in Mini-Mall Development Plan = Investment in Savings Account

To solve for the Investment in Mini-Mall Development Plan, we need to use the combined interest earned for the first year. We can express this as an equation:

Interest Earned = (Investment in Savings Account x Interest Rate) + (Investment in Mini-Mall Development Plan x Interest Rate)

Substituting the values given in the problem, we get:

$475 = (Investment in Savings Account x 0.02) + (Investment in Mini-Mall Development Plan x 0.12)

Solving for Investment in Mini-Mall Development Plan, we get:

Investment in Mini-Mall Development Plan = ($475 - (Investment in Savings Account x 0.02))/0.12

Substituting the values given in the problem, we get:

Investment in Mini-Mall Development Plan = ($475 - ($5,750 - Investment in Mini-Mall Development Plan x 0.02))/0.12

Solving for Investment in Mini-Mall Development Plan, we get:

Investment in Mini-Mall Development Plan = $4,737.50

Therefore, the financial planner invested $4,737.50 in the mini-mall development plan and $1,012.50 in the savings account.

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From the given data points representing the number of new homes that built in each neighborhood. The median number of houses is 26.

The median is the middle value of a set of numerical data when the data is arranged in ascending or descending order. In a set of odd number of data points, the median is the middle value. In a set of even number of data points, the median is the average of the two middle values.

To find the median, you arrange the numbers in order from least to greatest and then pick the middle number(s).

5, 12, 13, 20, 26, 29, 30, 31

In this case, there are 8 numbers, so the median is the middle number, which is 26.

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The inches of snow that fall at this rate is 8 inches

From the question, we have the following parameters that can be used in our computation:

10 inches of snow fall for 1 1/4 hour

Ths means that the unit rate is

Unit rate = 10 inches/1 1/4 hour

Evaluate the quotint

Unit rate = 8 inches per hour

For one hour, we have

Snow = 8 * 1

Evaluate

Snow = 8

Hence, the amount is 8 inches

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