Mr. Doyle needs to mow his rectangular lawn that measures 23 x 25 square feet. Does he need to find the area or the perimeter of the lawn if he wants to mow the entire lawn? What is the total amount of lawn that he will mow?

The graph has y-intercept (0,5) and increases with a constant ratio of 3.

A function in mathematics is a connection between a set of inputs (sometimes referred to as the domain) and a set of outputs (also referred to as the range). Each input value is given a different output value.

The y-intercept lies at (0, 5) because the value of the function at x=0 is 530 = 5. The 'constant ratio' is 3, meaning that any increment of 1 in x causes the function value to grow by a factor of 3. (That serves as the exponential term's foundation.)

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Missing parts;

Which of the following statements is true for a function with equation f(x) = 5(3)*?

The graph has y-intercept (0,5) and increases with a constant ratio of 3.

The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.

The graph has y-intercept (0, 3) and increases with a constant ratio of 5.

The graph has y-intercept (0,5) and decreases with a constant ratio of 3.

Answer:

B= 21

Step-by-step explanation:

A^2 + B^2 = C^2

72^2 + B^2 = 75^2

Solve for B

B = 21

Answer:

≈3.4

Step-by-step explanation:

Answer:

3 and 9/23

you could easily just leave it as 78/23

Answer:

Three-hundred twenty six thousandths

Step-by-step explanation:

3 x 1/10 + 2 x 1/100 + 6 x 1/1000

what is the question???

Step-by-step explanation:

btw

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Answer:

Step-by-step explanation:

You can use the Law of Cosines after you find y or θ. Using the given information, you can apply the Pythagorean theorem, the Law of Sines, or the definition of the cosine trig function.

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides and angles in a right triangle. It tells you ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

The Pythagorean theorem relates the measures of the sides. It tells you ...

  y² +5² = 12²

  y = √(144 -25) = √119

The trig relations above tell you ...

  sin(α) = 5/12   ⇒   α = arcsin(5/12) ≈ 24.624°

 cos(θ) = 5/12   ⇒   θ = arccos(5/12) ≈ 65.376°

Of course, once you find one of the angles, you can find the other. The sum of the two acute angles in a right triangle is 90°.

Using the definitions above for the trig functions, you have ...

  sin(θ) = y/12 = (√119)/12

  cos(θ) = 5/12

  tan(θ) = y/5 = (√119)/5

Using trig identities, you have ...

  csc(θ) = 1/sin(θ) = 12/√119 = (12√119)/119

  sec(θ) = 1/cos(θ) = 12/5 = 2.4

  cot(θ) = 1/tan(θ) = 5/√119 = (5√119)/119

_____

Additional comment

The attached calculator screen shot shows you the angle θ on the first line, and the value of y on the second line. The csc, sec, and cot are shown on the third line. You will notice the angle mode (DEG) is seen in the lower left corner. If the calculator angle mode is set to radians, you will see the angles as relatively small radian values: θ ≈ 1.141, α ≈ 0.4298.

We have shown both exact values and decimal values you can round to the desired precision.

Answer:

the a answer is five

Step-by-step explanation:

divide 42 by 8 and round it it up to the closest whole number

Answer: a= -18/2

Step-by-step explanation:

2a + 2x3 = -12

2a + 6 = -12

2a + 6 - 6 = -12 - 6 ( subtract 6 from both sides)

2a = -18 (Divide 2 by both sides)

a= -18/2

One possible path Melanie can take to walk from school to the post office and then to the library is to first head east on Main Street from the school.

She can continue on Main Street until she reaches the intersection with Elm Street, where she can turn left and head north. After walking for a few blocks, she will reach the post office, which will be on her left.
Once she has finished at the post office, Melanie can continue north on Elm Street until she reaches the intersection with Maple Street. She can turn left on Maple Street and walk for a few blocks until she reaches the library, which will be on her right.
Another possible path Melanie can take is to walk west on Lincoln Street from the school until she reaches the intersection with Oak Street. She can turn right on Oak Street and head north until she reaches the post office, which will be on her left.
After visiting the post office, Melanie can continue north on Oak Street until she reaches the intersection with Birch Street. She can turn left on Birch Street and walk for a few blocks until she reaches the library, which will be on her right.

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Answer:

x = \(-\frac{2}{3}\)

Step-by-step explanation:

I used the FOIL method

[(2x + 3) (3x + 2)] − [(3x + 2) (2x− 3)] = 0

\((6x^{2} +4x+9x+6) - (6x^{2} -9x+4x-6)=0\)

\((6x^{2} +13x+6) - (6x^{2} -5x-6)=0\)

\((6x^{2} +13x+6) - 6x^{2} +5x+6=0\)

combine like terms

\(6x^{2} -6x^{2} = 0\)

\(13x+5x=18x\)

\(6+6=12\)

so, \(18x +12 = 0\)

subtract 12 on both sides

\(18x=-12\)

divide by 18 to isolate x

\(x=-\frac{12}{18}\)

and simplifies to

\(x=-\frac{2}{3}\)

Answer:

Step-by-step explanation:

Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.

He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.

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9514 1404 393

Answer:

  (-2, -3), (1, 6), (2, 9) are plotted in the attached graph

Step-by-step explanation:

For x = -2, y = 3(-2) +3 = -3. The ordered pair is (-2, -3).

For x = 1, y = 3(1) +3 = 6. The ordered pair is (1, 6).

For x = 2, y = 3(2) +3 = 9. The ordered pair is (2, 9).

The graph is attached.

Answer:

yes

Step-by-step explanation:

When one outcome is favored over another, we call this favoritism or preference.

When one outcome is favored or chosen over another, it is referred to as favoritism or preference. Favoritism implies a bias towards a particular outcome or individual, while preference suggests a personal inclination or choice.

This concept is commonly encountered in various contexts. For example, in decision-making, individuals may show favoritism towards a specific option based on personal preferences or biases. In voting, people may have a preference for a particular candidate or party. In sports, teams or players may be favored over others due to their past performance or popularity. Similarly, in competitions, judges or audiences may exhibit favoritism towards certain participants.

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When one outcome is favored over another, it signifies a subjective inclination or bias towards a specific result based on personal factors, and this preference can influence decision-making and actions.

When one outcome is preferred or desired over another, we commonly refer to this as a preference or favoritism toward a particular result. It implies that there is a subjective inclination or bias towards a specific outcome due to various factors such as personal beliefs, values, or goals. This preference can arise from a range of contexts, including decision-making, competitions, or evaluations.

The concept of favoring one outcome over another is deeply rooted in human nature and can shape our choices and actions. It is important to recognize that preferences can vary among individuals and may change depending on the circumstances. Furthermore, the criteria for determining which outcome is favored can differ from person to person or situation to situation.

In summary, when one outcome is favored over another, it signifies a subjective inclination or bias towards a specific result based on personal factors, and this preference can influence decision-making and actions.

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Answer:

-2/5

Step-by-step explanation:

Answer:

-2/5

Step-by-step explanation:

get a calculator and click those numbers you will find out the answer

(A) The estimated volume of the elliptic paraboloid using the lower left corners as sample points are V ≈ 97.

(B) The estimated volume using the upper right corners as sample points is V ≈ 92.

(C) The average of the two estimates is V ≈ 94.5.

(D) The exact value of the volume using iterated integrals is V = 2.5.

(A) To estimate the volume by dividing R into 4 equal squares and choosing the sample points to lie in the lower left-hand corners:

Divide the x-axis into 2 equal intervals: [0, 1] and [1, 2].

Divide the y-axis into 2 equal intervals: [0, 1] and [1, 2].

Choose the sample points to be the lower left corners of each square: (0, 0), (1, 0), (0, 1), (1, 1).

Calculate the height of each square by substituting the sample points into the equation of the elliptic paraboloid: z = 100 - x² - 4y².

For the sample points, we get the heights: z1 = 100, z2 = 96, z3 = 96, z4 = 92.

Calculate the area of each square: ΔA = (2/4)² = 1/4.

Estimate the volume by multiplying the area of each square by its corresponding height and summing them up: V ≈ (1/4)(100 + 96 + 96 + 92) = 97.

(B) To estimate the volume by dividing R into 4 equal squares and choosing the sample points to lie in the upper right-hand corners, we follow the same steps as in (A), but this time we choose the sample points to be the upper right corners of each square: (1, 1), (2, 1), (1, 2), (2, 2).

Calculating the heights and estimating the volume, we get V ≈ (1/4)(96 + 92 + 92 + 88) = 92.

(C) The average of the two estimates from (A) and (B) is (97 + 92)/2 = 94.5.

(D) To compute the exact value of the volume using iterated integrals, we integrate the function f(x, y) = 100 - x² - 4y² over the region R=[0,2]×[0,2]:

∬R f(x, y) dA = ∫[0,2] ∫[0,2] (100 - x² - 4y²) dy dx

To evaluate the double integral ∬R f(x, y) dA, where f(x, y) = x and R = [3, 4] × [2, 3], we integrate the function over the given region as follows:

∬R f(x, y) dA = ∫[2,3] ∫[3,4] x dy dx

Integrating with respect to y first:

∫[2,3] ∫[3,4] x dy dx = ∫[2,3] (xy) [3,4] dx

= ∫[2,3] (4x - 3x) dx

= ∫[2,3] (x) dx

= (1/2)x² | [2,3]

= (1/2)(3)² - (1/2)(2)²

= (1/2)(9) - (1/2)(4)

= 4.5 - 2

= 2.5

Therefore, the result of the double integral ∬R f(x, y) dA is 2.5.

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The length of a football field, including the end zones, is 120 yards, which is equal to 4320 inches.

To calculate this, we can use the conversion rate of 1 yard equal to 3 feet and 1 foot equal to 12 inches. This means that 1 yard is equal to 36 inches. To convert 120 yards to inches, we can multiply 120 by 36, resulting in 4320 inches.

To explain this mathematically, we can use the formula:

where Inches/Foot = 12 and Feet/Yard = 3.

Plugging in the appropriate variables, we can calculate the number of inches in a football field as:

Inches = 120 x 3 x 12 = 4320 inches.

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Answer:

The function f(x) = cos^2x + sin^2x is not a straight line, but rather a constant function that always evaluates to 1 for any value of x.To see why this is the case, recall the trigonometric identity that states that the square of the cosine of an angle added to the square of the sine of the same angle equals 1:cos^2x + sin^2x = 1Since this identity holds for all values of x, it follows that f(x) = 1 for all x. Therefore, the graph of this function is a horizontal line at y = 1, not a straight line.

Step-by-step explanation:

Answer:

Step-by-step explanation:

a=graph

b= x=2

Calculating the cost of 4.25 kilogram(kg) is £2.38, by multiplying it by 4.25 kg by 1 kg.

Costs are the expenses incurred in the manufacture, marketing, or preparation of a good or asset for regular use. In other terms, it's the cost incurred to produce a good, buy inventories, sell goods, or prepare equipment for use in a commercial activity.

Given,

2.5 kg cost  £1.40 i.e,

2.5 kg = £1.40

For 1 kg= \(\frac{1.40}{2.5}\)

= £0.56

To find the cost of 4.25 kg:

Then,

1 kg = £0.56

4.25 kg = 0.56 x 4.25

= £2.38

£2.38 is the cost of 4.25kg after calculating it.

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Answer: i think 8

Step-by-step explanation:

Answer:

12.048 kg

Step-by-step explanation:

48 grams = .048 kg

12 kg + .048 kg = 12.048 kg

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The surface area of a cube is decreasing at a rate of 54 cm²/sec when each edge is 13 cm and the edges are shrinking at a rate of 3 cm/sec.

Let's denote the edge length of the cube as x, and the surface area as S. The surface area of a cube is given by the formula S = 6x². To find how fast the surface area is decreasing, we need to find the derivative of S with respect to time, which is dS/dt. Given that dx/dt = -3 cm/sec (since the edges are shrinking at a rate of 3 cm/sec), and x = 13 cm (when each edge is 13 cm), we can substitute these values into the derivative formula: dS/dt = 12x * dx/dt = 12(13)(-3) = -468 cm²/sec. Therefore, the surface area is decreasing at a rate of 468 cm²/sec.

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The bulbs should be replaced every 1636.4 hours to ensure that only 1% burn out between replacement periods.

For a large manufacturing plant, the light bulbs have a lifetime that is normally distributed. It is distributed with a mean of 1800 hours and a standard deviation of 50 hours.

Let the time interval between replacements of the bulb be T. Then the number of bulbs that burn out during a time interval T follows a normal distribution with mean as T/1800 and a standard deviation of T/50.

The probability of the number of bulbs that burn out during a time interval T is less than or equal to 1% is:
P(x < 1% )= P((x- T/1800)/(T/50) < (0.01 - T/1800)/(T/50))

where x is the number of bulbs that burn out during a time interval T. For the standard normal distribution, the cumulative distribution function (CDF) of Z score is denoted by Φ(z).

Then,
P(z < (0.01 - T/1800)/(T/50)) = 0.01
Let z = (0.01 - T/1800)/(T/50)
Then, Φ(z) = Φ((0.01 - T/1800)/(T/50)) = 0.01

We can find the value of z from the standard normal distribution table.
Substituting the value of z in the equation, we get: (0.01 - T/1800)/(T/50) = -2.33
Solving for T, we get: T ≈ 1636.4 hours

Therefore, the bulbs should be replaced every 1636.4 hours to ensure that only 1% burn out between replacement periods.

Therefore, to guarantee that only 1% of bulbs burn out during the replacement periods, it is necessary to replace the bulbs every 1636.4 hours.

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