Solve the following


i} p+ 3 = 205 ii} 2x/7 = 4 iii} 3y - 6 = 9

By AA similarity Triangle PQR and TQS are similar.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given:

As, PR || TS then

<RPQ = <TSQ (Alternate Interior Angle)

< <QTS = <QRP (Alternate Interior Angle)

So, Triangle PQR and TQS are similar by AA similarity criteria.

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Answer:

53.85 %

Step-by-step explanation:

use ratio to solve.

14/26 = x/100

1400/26 = x

x = ~53.85%

Answer:

10+5v=70

Step-by-step explanation:

this is because you need to consider the outright monthly cost of $10 first. then you don't know how many visits you'll need so you have to fill in v and multiply it by the cost per visit. and it must equal 70 so that it is equal to the other membership.

The equation 70 = 10 + 5v is used to determine the number of visits per month needed for two membership types to cost the same. Solving the equation would provide that 12 visits a month will make both memberships cost the same.

The subject of this question is Mathematics, and it is related to the topic of linear equations. Given the problem, we know that there are two types of membership options:

Here, Y represents the total cost of the membership each month and v represents the number of visits to the water park per month. You can set these two equations equal to each other in order to find the number of visits (v) needed for the two membership types to cost the same amount:

70 = 10 + 5v

You solve the equation for v to get: v = (70 - 10) / 5 = 12

Therefore, it would take 12 visits per month for both memberships to cost the same.

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Part A:

Based on the medians, the plants in Group A grew less on average, as compared to the plants in Group B.

Part B:

The range and IQR are greater in Group B as compared to Group A, so there is less variability in the growth of plants in Group B.

A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.

Given:

Caleb is comparing the growth of plants using two different fertilizers.

The box-and-whisker plot is given.

From the diagram, we can clearly see that the median of A is less than the median of B.

Part A:

Based on the medians, the plants in Group A grew less on average, as compared to the plants in Group B.

Part B:

The range and IQR are greater in Group B as compared to Group A, so there is less variability in the growth of plants in Group B.

Therefore, the blanked words are given above.

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The high level of airline ticket sales that travel agencies experience during summer is an example of (option C.)Seasonal component of a time series.

A time series is a set of observations collected over a period of time, and it can be decomposed into various components, including trend, cyclical, seasonal, and random variation.

The trend component represents the overall pattern of the time series, such as an upward or downward trend. The cyclical component represents the repeating patterns that are not related to the regular seasons or calendar years. The seasonal component represents the regular variations that occur at specific times of the year, such as the summer months in this example. The random variation represents the unpredictable fluctuations in the time series.

Since the high level of airline ticket sales during summer is a regular variation that occurs every year at the same time, it is an example of the Seasonal component of a time series.

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Complete question:

The high level of airline ticket sales that travel agencies experience during summer is an example ofwhich component of a time series?

A.Trend.

B.Cyclical.

C.Seasonal.

D.Random variation

Answer: a. To create the graph, we need to find the speed (in km/min) of Lin and Andre. The speed is calculated as distance divided by time.

For Lin: speed = 1.5 km / 5 min = 0.3 km/min

For Andre: speed = 2 km / 8 min = 0.25 km/min

We can plot these speeds as points on a graph with time on the x-axis and speed on the y-axis.

b. The point for Lin is (5, 0.3) and for Andre is (8, 0.25).

c. From the graph, we can see that Lin was biking faster, with a speed of 0.3 km/min compared to Andre's speed of 0.25 km/min.

Step-by-step explanation:

Answer: A = 24

Step-by-step explanation:

Hi, I think you may be looking for the Area of a square, or rectangle.

Step 1. A = bh

Step 2. A = (4 * 6)

Step 3. A = 24

Answer:

24

Step-by-step explanation:

plug in the values of b and h into the equation

Since b=4 we would put:

A=4*h

Now plug in h, which is equal to 6

A = 4*6

So, 4 multiplied by 6 equals 24. This means A is equal to 24

The function f(x) = 500(1 - 0.19)^x² is an exponentially decaying function.

The rate of decay is 0.19 or 19% and an equivalent expression to it is

f(x) = 500(0.9)^x.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = 500(1 - 0.19)^x² for the price of a share of stock.

This would be an exponentially decaying function because (1 - 0.19) is less than 1.

The rate of exponential decay is 0.19 or 19%.

An equivalent expression to the function f(x) = 500(1 - 0.19)^x² is,

f(x) = 500(0.9)^x.

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The simplification of the given rational expression when x is not equal to 2 or negative 3 is determined as (x + 1)/(x + 3).

The simplification of the given expression when x is not equal to 2 or negative 3 is determined as follows;

[tex]$=\frac{(x+1)(x-2)}{(x-2)(x+3)}$[/tex]

cancel "[tex]$\mathrm{x}$-2[/tex]" since it is common to numerator and denominator

[tex]$$=\frac{(x+1)}{(x+3)}$$[/tex]

Thus, the simplification of the given rational expression when [tex]$\mathrm{x}$[/tex]is not equal to 2 or negative 3 is determined as [tex]$(x+1) /(x+3)$[/tex].

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For rectangle ABCD, the value of x is 6.44 inches

Consider the following diagram.

From this figure we can observe that the dimansions of the rectangle: length is given by expression (7x + 1) and width is given by expression 'x'

We know that tha formula for the perimeter of the rectangle,

P = 2 × (length + width)

Here, the perimeter of rectangle ABCD is 105 inches.

Using above formula of perimeter we get an expression,

P = 2 × ((7x + 1)+ x)

105 = 2 × (8x + 1)

We solve above equation for x.

105/2 = 8x + 1

52.5 - 1 = 8x

8x = 51.5

x = (51.5)/8

x = 6.44 inches

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Answer:

Step-by-step explanation:

ok so it is 100 amount budgeted i calculated all of them dont be mad if i did it wrong i am really bad at math and here is a calmng photo to calm you and elp you think

Answer:

16

Step-by-step explanation:

(fog)x=f{g(x)}

=f(x-2)

=(x-2)^2

So,

(fog)(-2)=(-2-2)^2

=-4^2

=16

Answer:

MN ≈ 92.1

Step-by-step explanation:

given the figures are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{MN}{IJ}[/tex] = [tex]\frac{KL}{GH}[/tex] ( substitute values )

[tex]\frac{MN}{21}[/tex] = [tex]\frac{57}{13}[/tex] ( cross- multiply )

13 MN = 21 × 57 = 1197 ( divide both sides by 13 )

MN ≈ 92.1 ( to the nearest tenth )

Answer: To find the highest common factor (HCF) of two polynomials, we can use the Euclidean algorithm for polynomials. The Euclidean algorithm involves dividing the larger polynomial by the smaller polynomial and continuing the division process until the remainder is zero. The last non-zero remainder is the HCF of the two polynomials.

In this case, we have:

2x^3 + x^2 - 3x = (2x^3 - x^3) + x^2 - 3x

= x^3 + x^2 - 3x

Now, we divide x^3 + x^2 - 3x by x^3 - x

x^3 + x^2 - 3x = x^3 - x * (1 + x - 3)

= x^3 - x * (x^2 - 2x + 3)

We cannot simplify this expression further, so the HCF of 2x^3 + x^2 - 3x and x^3 - x is x^3 - x.

Step-by-step explanation:

Answer:

x < -28

Step-by-step explanation:

5x < -28

x < -28/5

The two numbers that can be true for the equations are 5 and 12

From the information given, we have the equations;

x+y=17

x-y=7

From equation (1), make 'x' the subject of formula

x = 17 - y

Now, substitute the value into the formula, we have;

17 - y - y= 7

collect like terms

-y-y = 7 - 17

Subtract the iike terms

-2y = -10

Make 'y' the subject

y = 5

Substitute the value

x = 17 -5

x = 12

Hence, the values are 12 and 5

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By standard deviation, 3.4 defects per million that a six sigma program has. Whereas the remaining ones are not appropriate in this context.

What does standard deviation mean ?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                               Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Describe standard deviation using an example?

The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.

                         The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second is, however, obviously more dispersed.

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The summation notation for the given arithmetic series is  [tex]\sum_1^4(4n)[/tex]

An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms.

Given is an arithmetic series, 4+8+12+16, we need to find the summation notation for the given arithmetic series,

To generate the terms of a series given in sigma notation, successively replace the index of summation with consecutive integers from the first value to the last value of the index.

To generate the terms of the series given in sigma notation above, replace n by 1, 2, 3 and 4

[tex]\sum_1^4(4n)[/tex] = 4(1) + 4(2) + 4(3) + 4(4)

= 4 + 8 + 12 + 16

= 40

Therefore, the sum of the series is 40

Hence, the summation notation for the given arithmetic series is  [tex]\sum_1^4(4n)[/tex]

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The value of "n" is approximately 2.6666667.

Exponent is a mathematical operation that represents repeated multiplication of the same number.

We can start by simplifying the left side of the equation:

(2^(2n))^4 * (2^n)^2 = 2^16 - 1

Using the exponent rules:

a^m * a^n = a^(m + n)

We can simplify the left side of the equation further:

2^(4n + 2n) = 2^16 - 1

Combining the exponents:

2^(6n) = 2^16 - 1

Now we can use the fact that if a^m = a^n, then m = n to solve for "n":

6n = 16

Dividing both sides by 6:

n = 16/6 = 8/3

Therefore, The value of "n" is approximately 2.6666667.

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The measure of the angle ∠PSR will be equal to 25 degrees.

One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

Given that In quadrilateral PQRS, the exterior angle at Q when PQ is extended measures 155 and PS = QR.

The measure of the angle PSR will be calculated as:-

∠Q exterior  = 155

∠PQR = 180 - 155

∠PQR = 25

∠PQR = ∠PSR = 25°

Therefore, the value of the angle ∠PSR is 25°.

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Answer:

36 cm²

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

Rhombus has four equal sides. Since perimeter is 36 cm, each side is:

Area of rhombus is the product of base and altitude:

Answer: 36cm

Step-by-step explanation:

Let's call the number of candles Roma sold for $5 each "x".

What is the unitary method's formula?

What is the unitary method's formula? The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

Since she sold 200 candles in total, we know that x + 3y = 200, where y is the number of sets of three candles she sold for $11.

We also know that the total revenue was $788, so we can set up another equation based on the total revenue:

5x + 11y = 788

Now that we have two equations, we can use substitution to solve for x. First, let's solve for y:

y = (200 - x) / 3

Plugging this expression for y into the second equation:

5x + 11((200 - x) / 3) = 788

Expanding and simplifying the equation:

5x + (2200 - 11x) / 3 = 788

Multiplying both sides by 3 to get rid of the fraction:

15x + 2200 - 11x = 2364

Combining like terms:

4x = 164

Finally, dividing both sides by 4 to solve for x:

x = 41

So Roma sold 41 candles for $5 each at the craft fair.

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Answer:

Step-by-step explanation:

KE = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

We are given the mass of the bumblebee as 0.015 kg and its velocity as 21.0 m/sec. We can plug these values into the formula to calculate its kinetic energy:

KE = (1/2) * m * v^2

= (1/2) * 0.015 kg * (21.0 m/sec)^2

= (1/2) * 0.015 kg * 441.0 m^2/sec^2

= 2.92625 J

Therefore, the bumblebee has 2.92625 Joules of kinetic energy as it hits the windshield.

Answer:

The kinetic energy of the bumblebee as it hits the windshield is given by the equation KE = 0.5 x 0.015 kg x (21.0 m/s) squared. This gives us a total of 945 J of kinetic energy.

Answer:

She should walk at a rate of 16 km/hr

Step-by-step explanation:

At a rate of 12 km/hr, she would have traveled 4 km in 20 minutes. This can be calculated by finding the ratio of 20 minutes to 1 hour which is 1/3. We then multiply this ratio by the rate to find the distance Shalu needs to walk to school.

We then need to find the necessary km/hr in order for Shalu to travel 4 km in 15 minutes. 15 minutes is a quarter of 1 hr. Therefore a rate of 4 km/15 minutes is equal to a rate of 16 km/hr. This means that the average speed Shalu would have to walk is 16 km/hr.

The weight of Trevor's goat will be 51 pounds at age 3.

We can use the following equation to calculate the weight of Trevor's goat at age 3,

Weight at age 3 = 6 3/8 × 8

First, we require to convert 6 3/8 to an improper fraction, so we multiply 6 by 8 to get 48 and then add the numerator 3 to get 51. So, 6 3/8 can be composed as 51/8.

Next, we multiply 51/8 by 8 to calculate the weight at age 3,

51/8 × 8 = 408/8 = 51

Therefore, the weight of Trevor's goat will be 51 pounds at age 3.

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--The given question is incomplete; the complete question is

"Trevor's pet goat weighed 6 3/8 pounds when it was born. By age 3, the goat weighed 8 times as much. Fill each box with a number or symbol from the list to show how to find the weight of Trevor's goat at age 3."--

Maxine paid total amount of $10800 on the loan.

The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

Maxine took loan of $9000

Interest she paid = 20%

Total interest = (20/100) × 9000

                      = $1800

Total amount = $9000 + $1800 = $10800.

Hence, $10800 is total amount Maxine paid at end of the loan.

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The numeric values of the graphed function at x = 1 and x = 3 are given as follows:

Tracing a vertical line through the coordinate x = 1, we have that the line would cross the graph at approximately y = 0.7, hence the numeric value is estimated as follows:

f(1) = 0.7.

Following the same procedure through x = 3, the line would cross the graph at approximately y = 0.4, hence the numeric value is estimated as follows:

f(3) = 0.4.

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Answer:

tsa=6a^2

=6x(6.5x6.5)

=235.3cm sq.

Step-by-step explanation:

i hope it will help u

Answer:The distance cover by Noah in 1 hour to cover distance is 6.5 miles

Step-by-step explanation:

The greatest number of people that they may invite and still stay within their budget is 126 persons.

An equation is a mathematical statement in symbolic form that indicates that two things are exactly the same. Equations are written with an equal sign (=) as follows:

The statements above are similar. Equations can be used to express the similarity of two expressions composed of one or more variables.

For example, for real x members, the following equation is always true:

x(x - 1) = x² − x.

The above equation is an example of identity.

An equation that is always true regardless of the values of the variables in it. 

According to the question:

Oscar and Julie Ashton have a budgeted $4,500 for their reception.

The reception hall charges a $90 cleanup fee plus $35 per person.

Let the total number of persons be = p

Clean up is a one time charge.

So, the inequality forms:

90+ 35p= < $4500

90 + 35p =< $4500

35p =< $4500 - 90

35p=< 4410

p=< 4410 : 35

p =< 126 persons

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