Ejercicio 2.- La temperatura ambiente a las 8 am era de 61 grados Farenheit. Fue aumentando de forma lineal hasta la 1 pm en que el termómetro marcó 81 grados. a) Escriba una ecuación lineal que muestre la temperatura en función de la hora en ese intervalo. b) Calcule con esa ecuación la temperatura a las 11:15 am. Aproxime a la décima de grado Farenheit si fuera necesario. oprondamos a hacer ecuaciones y resolver​

The area of the path is 80 square meters.

Given: A rectangular flower bed measures 10m by 6m. It has a path  2m wide around it.

To Find: The area of the path.

Solution: We need to subtract the area of the inner rectangle from the area of the outer rectangle.

So,

The outer rectangle has dimensions 14m by 10m (adding 2m to each side of the flower bed), so its area is:

A outer = 14m x 10m = 140 m²

Now,

The inner rectangle has dimensions 10m by 6m (the original dimensions of the flower bed), so its area is.

A inner = 10m x 6m = 60 m²

Now,

The area of the path.

A path = A outer - A inner

           = 140 m² - 60 m²

           = 80 m²

Thus, The area of the path is 80 square meters.

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Answer:

Step-by-step explanation:

Answer:

You can make 12 possible sundaes with these toppings.

Step-by-step explanation:

Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:

1. Fudge & Chocolate Sprinkles

2. Fudge & Rainbow Sprinkles

3. Marshmallow & Chocolate Sprinkles

4. Marshmallow & Rainbow Sprinkles

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

4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.

Thus, the height of flagpole from the ground is found as 23.34 feet.

The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.

The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.

Given data:

Using the trigonometric ratios in the right triangle ABE.

tan 35 = h / 30

h = 30* tan(35)

h = 18.34

Height of flagpole = 18.34 + 5 = 23.34 feet

Thus, the height of the flagpole from the ground is found as 23.34 feet.

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Answer:

Hm

Step-by-step explanation:

The formula to find the circumference of a circle is:

Circumference = 2πr

Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given value of radius, we get:

Circumference = 2 x π x 6

Circumference = 12π

Circumference ≈ 37.7 cm (rounded to one decimal place)

Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.

Answer: Let's say that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is 6 meters longer than the width, which means that the length is (x + 6) meters.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the total area of the rectangle is 16m². Substituting the expressions for length and width, we get:

(x + 6) x = 16

Expanding the product and rearranging, we get a quadratic equation:

x² + 6x - 16 = 0

We can solve this equation by factoring or by using the quadratic formula. Factoring, we get:

(x + 8) (x - 2) = 0

This equation is satisfied when either x + 8 = 0 or x - 2 = 0. Therefore, the possible values for the width are x = -8 or x = 2. However, since the width of a rectangle cannot be negative, we reject the solution x = -8.

Therefore, the width of the rectangle is x = 2 meters. The length is 6 meters longer than the width, so the length is (2 + 6) = 8 meters.

Therefore, the dimensions of the rectangle are 2 meters by 8 meters.

Step-by-step explanation:

The answer of the given question based on the graph is ,  The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.

To dilate line f by scale factor of one half with center of dilation at origin, we  multiply coordinates of each point on line f by 1/2.

The equation of line f can be found by using the points A and B:

slope of line f = (0 - 2)/(2 - 0) = -1

y-intercept of line f = 2

Therefore, the equation of line f is y = -x + 2.

To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:

A' = (0, 2)*1/2 =(0, 1)

B' = (2, 0)*1/2 =(1, 0)

So A' is located at (0, 1) and B' is located at (1, 0) after dilation.

Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.

If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.

To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':

slope of f' = (0 - 1)/(1 - 0) = -1

y-intercept of f' = 0

Therefore, the equation of f' is y = -x.

Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

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The percent of the box that will remain unwrapped by the 60 square feet of paper is about 20.70%

A percentage is a proportion of a number expressed as fraction of a 100

The dimensions in mixed fractions can be expressed as follows;

Height of the box = 1 2/3 feet = 5/3 feet

Width of the box = 4 feet

Length of the box = 5 1/2 feet = 11/2 feet

Surface area of the box, A = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches

The percent of the box that will remain unwrapped is therefore;

Percentage = 60/(227/3) × 100 ≈ 79.3%

The percentage of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%

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The probabilities are as follows:

(a) P(A')= 0.7

(b) P(A∪B) =  0.3

(c) P(A'∩B) =  0

(d) P(A∩B') =  0.1

(e) P[(A∪B)'] =  0.7

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7

(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3

(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0

(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1

(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7

Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.

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The per square meter cost of steel will be $32. The solution has been obtained by using the cylinder.

What is a cylinder?

The cylinder, one of the most basic curvilinear geometric shapes, has long been considered to be a three-dimensional solid. It is regarded as a prism with a circle as its basis in elementary geometry.

We are given that the height of cylinder is 8 m and diameter is 10 m.

So, the radius is 5 m.

Now, using the surface area formula, we get

⇒ S = 2πrh + 2π[tex]r^{2}[/tex]

⇒ S = 2π * 5 * 8 + 2π * [tex]5^{2}[/tex]

⇒ S = 2 * 3.14 * 5 * 8 + 2 * 3.14 * 25

⇒ S = 251.2 + 157

⇒ S = 408.2 square meter

Now, it is given that the total cost of the steel will be $13,062.40.

So, per square meter cost will be:

⇒ Cost = [tex]\frac{13,062.40}{408.2\\}[/tex]

⇒ Cost = $32

Hence, the per square meter cost of steel for the cylinder will be $32.

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Answer:1111

Step-by-step explanation:

The statements are classified as Exponential decay and Linear growth.

a. Exponential decay: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

b. Linear growth: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.

c. Exponential decay: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

d. Linear growth: Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.

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Answer:

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

Use the formula for permutations:

The number of objects is n = 7 books.

Calculate the factorial:

Answer:

Option A: The solution is incorrect because the student did not correctly identify the intersection.

Step-by-step explanation:

Solve by elimination method.

5x + 2y = 10; -10x + 2y = 1

Multiply the second equation by -1, then add the equations together.

(5x + 2y = 10)

-1 (-10x + 2y = 1)

Forms:

5x + 2y = 10

10x - 2y = -1

Add these equations to eliminate y.

15x = 9

Then solve 15x = 9 for x:

15x = 9

15/15 = 9/15 (Divide both sides by 15)

x = 3/5

Now that we've found x let's plug it back in to solve for y.

Write down the original equation:

5x + 2y = 10

Substitute 3/5 for x in:

5x + 2y = 10:

5(3/4)+2y=10

2y+3=10

2y+3-3=10+-3

2y=7

2y/2 = 7/2

y = 7/2

x = 3/5 and y = 7/2.

Comparing the identified answers to the one found by the students, it can be concluded that Option A: The solution is incorrect because the student did not correctly identify the intersection.

Answer:

We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:

x^2 + 12^2 = 16^2

Simplifying:

x^2 + 144 = 256

x^2 = 112

Taking the square root of both sides:

x ≈ 10.6 feet

Therefore, Brenda is approximately 10.6 feet away from the fish.

The surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that consists of two congruent parallel bases in the shape of circles or ellipses, and a curved surface that connects the bases. The height of a cylinder is the perpendicular distance between the bases. A cylinder is a type of prism, and it can be classified as either a right cylinder or an oblique cylinder depending on whether or not its axis is perpendicular to its bases. Right cylinders have circular bases and their axis is perpendicular to the bases, while oblique cylinders have elliptical bases and their axis is not perpendicular to the bases.

Now,

Let the radius of cylinder M be r and its height be h. Then, the radius and height of cylinder N are both 2r, since the radius is equal to the height.

Since the cylinders are similar, their dimensions are proportional, which means:

(height of N) / (height of M) = 5/3

(radius of N) / (radius of M) = (2r) / r = 2

Using the formula for the surface area of a cylinder, we can write:

Surface area of cylinder M: 2πr² + 2πrh

Surface area of cylinder N: 2π(2r)² + 2π(2r)(5/3)h

We are told that the surface area of cylinder N is 256 square feet greater than the surface area of cylinder M. So we can set up the equation:

2π(2r)² + 2π(2r)(5/3)h = 2πr² + 2πrh + 256

Simplifying and solving for h, we get:

4r² + 20rh/3 = r² + rh + 128

3r² - rh - 128 = 0

(3r + 32)(r - 4) = 0

Since the height of the cylinder cannot be negative, we take the positive solution r = 4. Then, the height of cylinder M is (3/5)(4) = 12/5, and the height of cylinder N is 2(4) = 8.

Using the formulas for surface area, we can find the surface areas of both cylinders:

Surface area of cylinder M: 2π(4)² + 2π(4)(12/5) = 131.95 square feet

Surface area of cylinder N: 2π(2(4))² + 2π(2(4))(8) = 319.77 square feet

Therefore, the surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.

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4) Dane read an average of 400 minutes per week. 5)  Diane will have read 2000 minutes after 5 weeks.

4) The number "0200100300" represents the number of minutes Diane read each week for 3 weeks. To find out how many minutes she read after the first week, we simply look at the first digit, which is "0." This means that Diane did not read any minutes during the first week.

To find out how many minutes she read after the second week, we add the digits in the first two positions, which are "02." This gives us a total of 2 x 60 = 120 minutes.

To find out how many minutes she read after the third week, we add the digits in the first three positions, which are "020." This gives us a total of 20 x 60 = 1200 minutes.

To find out how many minutes she read each week, we simply divide the total number of minutes by the number of weeks, which is 3. So Diane read a total of 1200 minutes in 3 weeks, which means she read an average of 400 minutes per week.

5) If Diane reads the same number of minutes each week, then she will read that same number of minutes after 4 weeks and after 5 weeks. To find out how many minutes she reads after 4 weeks, we can skip count by the same number repeatedly: 400, 800, 1200, 1600. So Diane will have read 1600 minutes after 4 weeks.

Similarly, to find out how many minutes she reads after 5 weeks, we can skip count again by the same number repeatedly: 400, 800, 1200, 1600, 2000. So Diane will have read 2000 minutes after 5 weeks.

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Answer:

Step-by-step explanation:

We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.

Step-by-step explanation:

data given

men 330 ,days30

men? ,days11

from

men(m) are inversely proportional todays (d)

m=k/d

330×30=k

k=9900

now,

m=9900/11m

m=900

data given

friends 20, time 2hours

friends 30, time?

from

friends (f) are inversely proportional to time (t)

f=k/t

k=20×2

k=40

now,

t=40/30

t=1.3(1:18)

Answer:

Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time

Answer:

2.5cm

Step-by-step explanation:

you half the diameter to get the radius

The correct answer is c: Two terms are even, then two terms are odd. This pattern follows the rule of adding 2, so each successive term is an even number followed by an odd number.

Number is a mathematical object used to count, measure and represent a quantity. It is used to symbolize a numerical quantity or value, and is used in various ways in mathematics, science, engineering, finance and other fields. Numbers are also used to represent relationships between objects, such as the number of sides in a triangle or the number of students in a classroom.

This alternating pattern of even and odd terms is a feature of the pattern, with two terms being even followed by two terms being odd. This pattern continues as the terms increase, with the even terms adding 2 and the odd terms adding 2 as well. This pattern is a good way to remember a sequence of numbers and can be used to help understand patterns in mathematics.

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The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.

The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.

The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:

P(vowel and consonant) = P(vowel) x P(consonant)

= 0.25 x 0.75

= 0.1875

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The correct answer is: A. Y intercept will be less and X will be less.

A linear function's slope is a gauge of how steep the line is. Between any two points on the line, it is the ratio of the change in the y-coordinate to the change in the x-coordinate. The formula is used to compute it:

slope equals (y2 - y1)/. (x2 - x1)

where any two points on the line (x1, y1) and (x2, y2) are.

The company's expenses will rise once it begins paying a driver at a rate of 0.25 cents per mile, which means its profit will decline. The profit curve on the y-axis will go vertically downward as a result of this. But, because the cost of paying the driver is fixed per mile and has no impact on the profit per mile, the slope of the line—which reflects the profit per mile—will stay the same.

Hence, A. Y intercept will be less and X will be less is correct.

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Answer: x=14

Step-by-step explanation:

cb=10.

ac=14

The value of X will be 14.

This is a simple mathematics problem that can be solved by using ratios.

Given, AC : BC : AB = 7 : 5 : 8

AC = X ; BC = 10 ; AB = X + 2

AC/ BC = X/ 10 = 7/5  (Ratios can also be represented as fractions)

X/10 = 7/5

On Transposing,

5X = 70

X = 70/5

X = 14

Alternatively,

BC/AB = 5/8 = 10/ (X + 2)

5/8 = 10/ (X + 2)

On Transposing,

80 = 5X + 10

5X = 70

X = 14

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Answer:

Phn10x12

Step-by-step explanation:

PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]​

Answer:

FV ≈ $5,673.56

Step-by-step explanation:

To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:

FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))

where:

FV is the future value of the annuity

P is the periodic payment (in this case, $225 per month)

r is the interest rate per year (in this case, 5%)

n is the number of years (in this case, 2)

Substituting the given values, we get:

FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))

Using a calculator, we get:

FV ≈ $5,673.56

Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.

Answer:

x = -3 and x = 1 are the two zeroes of this function. Choose one of them for your answer.