Aarav has budgeted $300 to spend on hanging planters and raised garden beds. Each hanging planter costs $16, and a raised bed costs 1. 5 times as much as a hanging planter

Applying the two-tangent theorem, the perimeter of the polygon = 70 cm.

To find the perimeter of a polygon, sum all the side lengths of the polygon all together.

If two tangent segment of a circle are drawn to meet at a point outside the circle, the two-tangent theorem says they are congruent together, that is, they have equal length.

Applying the two-tangent theorem, the following side lengths that are missing as labelled in the diagram attached below are:

a = 13 cm

b = 9 cm

c = 5 cm

d = 8 cm

Therefore:

Perimeter of the polygon = 13 + a + b + 9 + 5 + c + d + 8

Plug in the values

Perimeter of the polygon = 13 + 13 + 9 + 9 + 5 + 5 + 8 + 8 = 70 cm.

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Answer:30

Step-by-step explanation:

30 is the smallest number that has three different prime factors.

The equivalent of (h+h)(2) of the function h(x) = 5x - 6 is 5[5(2) - 6] -6 which is option B

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

This means that if the object x is in the set of inputs (called the domain) then a function f will map the object x to exactly one object f(x) in the set of possible outputs (called the codomain).

h(x) = 5x - 6

(h + h)(x) = h(x) in x. This means put the function in h(x)

so x = 5x - 6

so (h + h)(x) = 5(5x-6) -6

if x = 2,

we have (h + h)(2) = 5[5(2) -6] -6

In conclusion the expression  5[5(2) -6] -6 is equivalent to (h+h)(2)

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Option (c) 75% of Country A women weigh between 110 and 240 pounds.

What is the five-number summary?

When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

Given, the five-number summary of Country A:

92, 110, 120, 160, 240

Then, we get

Minimum value = 92, First quartile = 110, Median = 120, Third quartile=160,

Maximum value = 240

Between 110 and 240 pounds, data lies from the First quartile to Maximum value which represents 75% of the data.

Hence, Option (c) 75% of Country A women weigh between 110 and 240 pounds.

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Answer:

x=1/4k

Step-by-step explanation:

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Answer:

y = 10, x = 18

Step-by-step explanation:

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The graph of the function f(x) = x² + 7x + 10 is attached.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix. The general equation of a parabola is -

y = a(x - h)² + k

We have the following equation of a quadratic equation representing parabola as -

f(x) = x² + 7x + 10

Refer to the graph of the function f(x) attached. It can be seen that it is a parabola opening upwards.

Therefore, the graph of the function f(x) attached.

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The rectangle that has side lengths of 5 units and 6 units is (b) the rectangle that has a perimeter of 22 units

The complete question is added at the end of this solution

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

Side lengths = 5 units and 6 units

These side lengths can be represented as

Length = 5 units

Width = 6 units

The area of a rectangle is calculated as

Area = Length * Width

Substitute the known values in the above equation, so, we have the following representation

Area = 5 units * 6 units

Area = 30 square units

The perimeter of a rectangle is calculated as

Perimeter = 2 * (Length + Width)

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (5 units + 6 units)

Perimeter = 22 units

Comparing the above to the options, we have

(b) The rectangle with a perimeter of 22 units

Hence, the true statement is (b)

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Possible question

Which rectangle has side lengths of 5 units and 6 units?

(a) The rectangle with an area of 22 square units

(b) The rectangle with a perimeter of 22 units

(c) The rectangle with a perimeter of 22 square units

(d) The rectangle with an area of 30 units

Answer:

k = -3

Step-by-step explanation:

Lines in the form y=k are horizontal. The lowest point on the parabola has a y-value of -3. That is the value where y=-3 will intersect the parabola at exactly one point. Every k value above this will have 2 points of intersection.

The translation applied to the triangle is:

T(x, y) → (x +4, y - 5)

Sp the correct option is the first one.

To analyze the translation we only need to compare the coordinates of one of the vertices.

Let's see the vertex H.

The coordinates of H are (-4, 1)

The coordinates of H'' are (0, -4)

Then the translation is defined by the difference between these coordinates:

(0, -4) - (-4, -1) = (4, -5)

Then the translation here is:

T(x, y) → (x +4, y - 5)

So the correct option is the first one.

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Answer:

F(x) = m1/5

Step-by-step explanation:

Answer: yes, 1/3, 1/3x

Step-by-step explanation:

Does x vary directly with y?

This basically means is this a linear function and the answer is yes it is.

What is the constant of variation?

The constant of variation is 1/3 because you have to multiply each x value by 1/3 to get the y value

What is the function rule?

y = 1/3x

Answer:

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

Answer:48

Step-by-step explanation:

Wherever you see an x on the right, you put a 16. That's what f(16) means.

f(16) = 1/3 (4 - 16)^2

f(16) = 1/3 (- 12)^2

f(16) = 1/3 (144)

f(16) = 48

Answer:

[tex]h=\frac{V}{\pi r^{2} }[/tex], 20 meters

Step-by-step explanation:

The formula for the volume of the silo is: [tex]V=\pi r^{2} h[/tex]

You are given:

Volume= 6,280 cubic meters

Radius= 10 meters

Therefore, you can solve for the height by getting h on it's own side.

The formula for the height of the silo is given by:  [tex]h=\frac{V}{\pi r^{2} }[/tex]

Now solve using the given values:   [tex]h=\frac{6,280}{\pi (10)^{2} }[/tex]

The height of the silo = 20 meters

The equation that represents the graph will be y = - (2)ˣ + 3.

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 equation is given below.

y = A · (2)ˣ + k

At x = 0, the value of y is 2.

2 = A + k          ...1

At x = 1, the value of y is 1.

1 = 2A + k         ...2

Subtract equation 1 from equation 2, then we have

A = -1

Then the value of k is given as,

2 = -1 + k

k = 2 + 1

k = 3

The equation that represents the graph will be y = - (2)ˣ + 3.

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The fog(x) of the function will be 6x² -2x - 5 and gof(x) of the function will be 12x² + 62x - 80.

The collection of values that can be plugged into a function's domain is called its parameters. The x values for a function like f(x) are contained in this collection (x). The collection of numbers that the operator assumes is known as its range.

As per the given information in the question,

f(x) = 2x - 5 and,

g(x) = 3x² - x

fog(x) = 2x - 5 and,

gof(x) =  2x - 5

fog(x) = f(g(x))

= f (3x² - x) = 2(3x² - x) -5

= 6x² -2x - 5

gof(x) = g(f(x))

= g (2x - 5) = 3(2x - 5)² + 2x - 5

= 12x² - 75 + 60x + 2x -5

12x² + 62x - 80.

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120/15=f/18 is the equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

Margie hands out 100 flyers in 2 hours.

Jaxon hands out 18 flyers in 15 minutes.

We need to find the equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours.

Let us convert hours to minutes

2 hours=120 minutes.

Let f be the number of flyers Jaxon handed out in 2 hour.

18/15=f/120

Apply cross multiplication

120/f=15/18

120/15=f/18

Hence, 120/15=f/18 is the equation can be used to determine f, the number of flyers Jaxon handed out in 2 hours

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Answer: -$155

Step-by-step explanation:

Using this formula

New status=(-Account status-Cheque amount)-Bank charges

Let plug in the formula

New status= (-$112-$22)-$21-

New status=-$134-$21

New status=-$155

Inconclusion The new status of John's account at this point is -$155

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Answer:

Linda starts the month with $15 in debt. Each hour, she makes 2.5 dollars. How many hours will it take for Linda to get out of debt?

A situation that can be represented by the expression 2.5x - 15 is given below.

Let's consider a situation where you are tracking the amount of money you earn from selling handmade crafts. In this scenario, the expression 2.5x - 15 can represent your net earnings after deducting the initial investment and expenses.

Suppose you invest a certain amount of money in materials and supplies to create your crafts. The variable x represents the number of crafts you sell. Each craft generates a profit of $2.50. Therefore, the term 2.5x represents the total profit you earn from selling x crafts.

However, running a business incurs expenses. In this case, the expression -15 represents $15, which is the total expense or cost associated with producing and selling your crafts.

So, 2.5x - 15 calculates your net earnings after subtracting the expenses from the profit. It provides you with a measure of how much money you've made after covering the costs.

By plugging in different values for x, you can evaluate the expression to determine your earnings for various levels of craft sales, allowing you to analyze your profitability and make informed decisions regarding your business.

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Answer:

Step-by-step explanation:

(4,8)..Its the only one in which x doesnt repeat

The average weight of a male Florida panther rounded to the nearest whole number is 53 kg

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Average weight = 52.6 kg

52.6

The number after decimal point is 6 which is more than 5.

So add  1 to the 52, we get 53

Thus, the average weight of a male Florida panther rounded to the nearest whole number is 53 kg

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a) The population of the confidence interval is given as follows: The temperature all days for that summer.

b) The point estimate of the interval is of: 80 degrees Fahrenheit.

c) The margin of error of the interval is of: 8 degrees Fahrenheit.

A confidence interval for a population parameter is built taking a sample of this population.

Then, the interval for the population mean is given as the sample mean plus/minus the margin of error.

The sample in this problem is given as follows:

The temperature for 10 days of summer.

Hence the population is of:

The temperature all days for that summer.

The interval in this problem is given as follows:

(72, 88).

The point estimate is the mean of the bounds, hence:

Point estimate = (72 + 88)/2 = 80.

The margin of error is half the difference of the two bounds, hence:

Margin of error = (88 - 72)/2 = 8.

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Answer:

Triangle PQR is a right triangle. First we have to find the length of each side of the triangle. This can be done using the points provided, along with the Pythagorean theorem, which is a^2+b^2=c^2. PR^2 = (7- -2)^2+(3-5)^2 = 85 => PR = sqrt(85) QR^2 = (7- -1)^2+(3-1)^2 = 68 => QR = sqrt(68) QP^2 = (1-5)^2+(-1 - -2)^2 =17 => QP = sqrt(17) Now that we have the sides of the triangle, we can put them into the Pythagorean theorem again to see that it works out: (Sqrt(17))^2 + (sqrt(68))^2 = (sqrt(85))^2 17 + 68 = 85 85 = 85 Since the Pythagorean theorem works for right triangles, the triangle is indeed a right triangle.

Step-by-step explanation:

The total number of sandwiches they have in all on Sunday is 375 sandwiches.

The amount earned by the cafe if each sandwich cost $4.50 is $1,687.5

Total percentage of ham and turkey sandwiches = 35% + 25%

= 60%

So,

225 = 60% of x

225 = 0.60 × x

225 = 0.60x

divide both sides by 0.60

x = 225/0.60

x = 375

Hence,

Total number of sandwiches = 375

If the cafe sells all the sandwiches at $4.50 each

The total money earned by the cafe = cost of each sandwich × total number of sandwiches

= $4.50 × 375

= $1,687.5

Therefore, the total sandwiches sold in the cafe on Sunday is 375 sandwiches.

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The probability of getting at least one multiple of 3 when a six-sided number cube is rolled 5 times is 1/7776 or 0.01%.

Probability shows the likelihood of an event happening.  it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1.

Probability of getting at least one multiple of 3 = 1/6.

Probability of getting at least one multiple of 3 five times = probability of getting at least one multiple of 3 first time×probability of getting at least one multiple of 3-second time×probability of getting at least one multiple of 3 third time ×probability of getting at least one multiple of 3 fourth time ×probability of getting at least one multiple of 3 fifths time.

Probability of getting at least one multiple of 3 five times

= (1/6) × (1/6) × (1/6) × (1/6) × (1/6)

= 1/7776.

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Answer:100/10000000000

Step-by-step explanation:qazwsxeedcrfvtgbyhn

The probability of picking a purple and green marbles is 0.05.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

Number of purple marble = 50

Number of green marbles = 10

Total number of marbles = 100

The probability of picking a purple and green marbles will be:

= 50/100 × 10/99

= 0.05

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Complete question

A urn contains 100 marbles. Fifty are purple, ten are green, fifteen are red, and twenty-five are orange. Two marbles are drawn at random one after another without replacement. Calculate the probability of picking a purple and green marbles