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What are the coordinates of the hole in the graph of the function?

f(x)=x^2−3x−10/x−5
Enter your answer in the boxes.

Answer:

Step-by-step explanation:

Remark

The method of finding the area of the ring is to find the area of the outer ring and subtract the area of the hole in the middle.

Outer ring

r = 10 + 4  = 14 inches

Area = pi * r^2

Outer ring area = pi * 14^2

Outer ring area = 196 pi

Inner hole

Area unshaded part = pi * r^2

r = 10

Area = pi * 10^2

Area = 100 pi

Area of the shaded part

area of the shaded part = outter circle area - inner circle area

outter circle area = 196 * pi

inner circle area = 100 pi

Area of the shaded part = 196 pi - 100 pi

Area of the shaded part = 96 pi

pi = 3.14

Area of the shaded part = 96 * 3.14

Answer area of the shaded part = 301.44

Answer area of the shaded part = 301.4 rounded to the nearest tenth

The second problem is done exactly the same way. Only the numbers have been changed. I will give you the answers to the main part of the problem and you can try and get what I got. If we disagree, be preparred to tell me what you got so I correct mine if it is wrong.

Outter Radius = 18 + 8 = 26

Area of outter circle =  pi * 26^2

Area of outter circle =  676 pi

Inner Circle area hole = pi * 18^2

Inner Circle area hole = 324 pi

Area of the shaded part = outter circle - inner circle

Area of the shaded part = 676 pi - 324 pi

Area of the shaded part = 352 pi

pi = 3.14

Area of the shaded part = 352 * 3.14

Answer: area of shaded part rounded to 1 decimal place = 1105.3

The rectangular equation of the tangent line at θ = (3π/2) for the polar curve r = 5/(3 - cos(θ)) can be determined using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope of the tangent line, we need to differentiate the polar equation with respect to θ and evaluate it at θ = (3π/2). The slope (m) of the tangent line is given by dy/dx.

Let's calculate the slope (m):

r = 5/(3 - cos(θ))

Differentiating both sides with respect to θ:

dr/dθ = [d(5/(3 - cos(θ)))/dθ]

Using the quotient rule and chain rule, we can calculate dr/dθ as follows:

dr/dθ = [(-5sin(θ)(3 - cos(θ)) - 5*(sin(θ))*sin(θ)) / (3 - cos(θ))^2]

Substituting θ = (3π/2):

m = dy/dx = dr/dθ / (dθ/dx)

dθ/dx is the reciprocal of dx/dθ, which is 1/(dr/dθ) in this case.

Now we can find the slope (m) by substituting the values:

m = [-5sin(3π/2)(3 - cos(3π/2)) - 5*(sin(3π/2))*sin(3π/2)] / [(3 - cos(3π/2))^2]

Once you have the slope (m), you can substitute the point (3π/2, r) into the point-slope form of the equation to find the y-intercept (b) and write the equation of the tangent line.

To determine the rectangular equation of the tangent line at θ = (3π/2) for the given polar curve, you need to calculate the slope (m) using the derivatives and substitute the point into the point-slope form of the equation.

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Answer:

r=1.3in

Step-by-step

hope this helps:)

Answer:

18.41

Step-by-step explanation:

31.56/12 = 2.63

2.63 X 7 = 18.41

Have a great day!

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The probability that both batteries pass the test is; 11/20

Total Number of Batteries tested = 16

Number of Batteries that fail the Test = 4

Number of batteries selected at Random = 2

Probability that both batteries fail the test = (4/16) * (3/15)

Probability that both batteries passed the test = 12/16 * 11/15 = 11/20

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\(\displaystyle \dfrac{\dfrac{4c^2-36}{8c^2-24c}}{\dfrac{12c+36}{2c^2 -6c}}\\\\\\=\left(\dfrac{4c^2 -36}{8c^2 -24c}\right) \cdot \left(\dfrac{2c^2 -6c}{12c+36}\right)\\\\\\=\left[\dfrac{4(c^2 -9)}{8(c^2-3)}\right]\cdot\left[\dfrac{2(c^2-3)}{12(c+3)}\right]\\\\\\=\dfrac{8(c^2-3^2)}{8 \cdot 12(c+3)}\\\\\\=\dfrac{(c+3)(c-3)}{12(c+3)}\\\\\\=\dfrac{c-3}{12}\)

\(\text{Hence the answer is d.}\)

Answer:

d

Step-by-step explanation:

separate the 2 divisions and simplify each , that is

\(\frac{4c^2-36}{8c^2-24c}\) ← factor numerator/ denominator

= \(\frac{4(c^2-9)}{8c(c-3)}\) ← factor difference of squares on numerator

= \(\frac{4(c-3)(c+3)}{8c(c-3)}\) ← cancel (c - 3) and 4/8 on numerator/ denominator

= \(\frac{c+3}{2c}\)

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

\(\frac{12c+36}{2c^2-6c}\) ← factor numerator/ denominator

= \(\frac{12(c+3)}{2c(c-3)}\) ← cancel 12 and 2 on numerator/ denominator

= \(\frac{6(c+3)}{c(c-3)}\)

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

to divide the top fraction by the lower fraction

leave top fraction, change division to multiplication, turn lower fraction upside down.

\(\frac{c+3}{2c}\) × \(\frac{c(c-3)}{6(c+3)}\) ← cancel (c + 3) and c on numerator/ denominator

= \(\frac{c-3}{2(6)}\)

= \(\frac{c-3}{12}\) → d

It is well known that utilizing a zip file is an effective method for reducing the size of the document in order to boost storage and sharing possibilities. A zipped folder may be smoothly moved from one place (the transmitter) to another without any issues (the receiver).

One or more files can be compressed and stored together in one location using the ubiquitous ZIP file format. As a result, the file size is less and is simpler to transport and store. After transmission, the receiver can use the files in their original form by unzipping (or extracting) her ZIP file.

In order to increase storage and sharing capabilities by lowering the size of the document, it is known that using a zip file is an efficient technique. A zipped folder may be effortlessly transferred without any hiccups from one location (the transmitter) to another (the receiver). Using Zip files has the primary benefit of reducing the time required to send large files over email. The document's quality is unaffected and is identical to the original file when it is compressed using a zip file.

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In 90 minutes, she would have created 36 drawings.

The first step is to establish a pattern between time and the number of drawing that Frankita creates.

When the question is studied, it can be deduced that every 15 minutes the rate of increase in drawing is (previous drawing + (1 + rate of increase of previous drawing.

Drawing created in 30 minutes = 15 + 2 = 17

Drawing created in 45 minutes = 17 + ( 1 + 2) = 20

Drawing created in 60 minutes = 20 + (3 + 1 ) = 24

Drawing created in 75 minutes = 24 + (4 + 1) = 30

Drawing created in 90 minutes = 30 + (5 + 1) = 36

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Using a system of equations, the diameter of the largest pizza is 30 inches, and the diameter of the smallest pizza is 13 inches.

Let's denote the diameter of the largest pizza as "L" and the diameter of the smallest pizza as "S." According to the problem, the sum of their diameters is 43 inches, which can be represented by the equation L + S = 43. Additionally, the difference in their diameters is 17 inches, leading to the equation L - S = 17.

To solve this system of equations, we can use the method of substitution or elimination. By adding the two equations together, we eliminate the variable "S" and solve for "L": (L + S) + (L - S) = 43 + 17. Simplifying the equation, we get 2L = 60, which yields L = 30.

Substituting the value of L into either equation, we find S: 30 - S = 17. Solving for S, we get S = 13.

Hence, the diameter of the largest pizza is 30 inches, and the diameter of the smallest pizza is 13 inches.

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Answer:

1. No

2. No

3. Yes

4. No

5. Yes

6. No

Step-by-step explanation:

If you want to check if a graph is a function, do a vertical line test. For every vertical line, there should be only 1 point on the line if the graph is a function.

Answer:

where r the graphs i can not help if u don't put the graphs

Step-by-step explanation:

Answer:

diameter = 7 feet

Step-by-step explanation:

Circumference of the circle = pi x d

21.98 = 3.14 x d

d = 21.98/3.14

d = 7 feet

Answer:

4.5

Step-by-step explanation:

High-def television sets would probably be distributed using an intensive strategy. Therefore, option B. is correct.

Intensive distribution refers to a strategy where a product is made widely available through as many outlets as possible. This strategy is typically employed for products that have high demand, are low-cost, and require extensive market coverage. In the case of high-definition television sets, they are popular consumer electronics with a significant market demand.

To determine whether intensive distribution is suitable for high-def television sets, we consider the characteristics of the product. High-definition television sets are relatively low-cost compared to other options in the market, and they are in demand by a broad range of consumers. These factors suggest that an intensive distribution strategy would be appropriate for this product.

Based on the analysis, high-def television sets would most likely be distributed using an intensive strategy. This approach would ensure broad availability and accessibility for consumers, leveraging the product's popularity and fulfilling market demand. By making these television sets widely accessible through multiple outlets, manufacturers can reach a larger customer base, maximize sales potential, and effectively compete in the consumer electronics market.

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Answer:

16 months or a year and 4 months

The percentage error of Bob’s measurement to the nearest tenth of a percent is 3.87%

The percentage error is The difference between the estimated value and the actual value in relation to the actual value is given as a percentage. Analyst use this formula to determine how big is the error in a relation to true value.

Here, given that

The experimental volume of liquid is 18.8 ml, and the actual volume of liquid is 18.1 ml

i.e. exprimental volume=18.8 mL

and, actual volume=18.1 mL

Now, we will calculate the percentage error

So,

percentage error=((Exprimental value-Actual value)/(Actual value))∙100

percntage error=((18.8-18.1))/18.1∙100

percentage error=0.7/18.1∙100

percentage error=0.0387∙100

percentage error=3.87%

Thus,

       We got percentage error of 3.87% in measurement

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Answer:

theres two -169 and 104 but ill say -169

Step-by-step explanation:

Answer:

x = \(\frac{5}{2}\) , y = \(\frac{27}{4}\)

Step-by-step explanation:

Equate the first 2 parts of the ratios on both sides of the equation and solve for x.

Expressing the ratios in fractional form, then

\(\frac{x}{3}\) = \(\frac{\frac{15}{4} }{\frac{9}{2} }\) = \(\frac{15}{4}\) × \(\frac{2}{9}\) = \(\frac{5}{6}\) ( cross- multiply )

6x = 15 ( divide both sides by 6 )

x = \(\frac{15}{6}\) = \(\frac{5}{2}\)

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

Equate the last 2 parts of the ratios on both sides and solve for y

\(\frac{\frac{9}{2} }{y}\) = \(\frac{3}{\frac{9}{2} }\) = 3 × \(\frac{2}{9}\) = \(\frac{2}{3}\) ( cross- multiply )

2y = \(\frac{9}{2}\) × 3 = \(\frac{27}{2}\) ( divide both sides by 2 )

y = \(\frac{27}{4}\)

The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D with three variables.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The functions of a point (or vector) in R2 or R3 that have real values will now be looked at. These functions will typically be defined on sets of points in R2, but there will be occasions when we utilise points in R3 and when it is more convenient to think of the points as vectors (or terminal points of vectors).

Each point f(x,y) in D is given a real number f(x,y) according to a real-valued function f defined on a subset D of R2. The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D, and the range of f is the greatest set D in R2 on which f is defined.

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Answer:

4) (3,0)

Step-by-step explanation:

For this question, all you have to do is find the coordinates that are inside the shaded area of both graphs. Only (3,0) is inside the shaded area so that is your answer.

The total amount that Mrs. Figueroa spent on the beef for the spaghetti is D. $18.95.

The total cost of an item is the quantity (units) multiplied by the unit cost price.

For Mrs. Figueroa to determine the total amount she spent on the beef, she has to multiply the unit cost ($3.99) by the units (4.75 pounds).

The number of pounds of beef purchased = 4³/₄ or 4.75 pounds

Cost of beef per pound = $3.99

Total cost of beef = $19.95 ($3.99 x 4.75)

Thus, the total amount that Mrs. Figueroa spent on the beef for the spaghetti is D. $18.95.

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Answer:

18.95

Step-by-step explanation:

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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When a distribution is shown as a symmetrical bell-shaped curve then the mean, median, and mode are equal i.e., option (a) is correct.

A symmetrical bell-shaped curve, also known as a normal distribution or Gaussian distribution, is characterized by its symmetry around the mean.

In this type of distribution, the mean, median, and mode all coincide at the center of the curve.

This means that the central tendency measures, such as the mean (average), median (middle value), and mode (most frequent value), are all equal.

Option (a) states that the mean, median, and mode are equal, which aligns with the properties of a symmetrical bell-shaped curve. This equality occurs because the data is evenly distributed on both sides of the mean, resulting in a balanced distribution.

Options (b) and (d) suggest that the mean is either less than or greater than the median and mode, which does not hold true for a symmetrical distribution.

In a symmetrical distribution, the mean is located at the center of the data, and the median and mode share the same value as the mean.

Option (c) mentions moderate uniformity, but a symmetrical bell-shaped curve does not specifically indicate uniformity. Uniformity refers to a distribution where all data points have equal probability, resulting in a flat line.

In contrast, a symmetrical bell-shaped curve indicates a normal distribution with the majority of data concentrated around the mean, gradually decreasing towards the tails.

Therefore, based on the given options, option (a) is the correct conclusion when the distribution is shown as a symmetrical bell-shaped curve.

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The cost of 100 donuts is $ 1 if a dozen of donuts cost 12 cents.

This question is solved using the unitary method. The unitary method is a method in which you find the value of a unit and then the value of the required number of units.

1 dozen refers to a group of 12.

Cost of 1 dozen donuts or 12 donuts = 12 cents

Cost of 1 donut = \(\frac{12}{12}\) = 1 cent

Cost of 100 donuts = 1 * 100 = 100 cents

100 cents = 1 dollar.

Thus, the cost of 100 donuts is 100 cents or 1 dollar.

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To answer this problem we have to remember that the break even point occur where the revenue function and the cost function have the same value.

Then, this happens when

Pluggin the expressions of our functions and solving for x we have:

Therefore the break even point occurs when x=74000. In this points both functions have value

Answer:

There is a 15% chance a student chosen at random would have brown sandals.

Step-by-step explanation:

The required probability will be 0.15 that a student chosen at random would have brown sandals.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

the probability = number of favorable outcomes /  total number of outcomes.

We have been given that out of 200 students in a school, 30 have brown sandals.

To determine the probability that a student chosen at random would have brown sandals.

The probability = number of favorable outcomes /  total number of outcomes.

The probability = 30 / 200

The probability = 0.15

Thus, the required probability will be 0.15 that a student chosen at random would have brown sandals.

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