Find the quadratic function

Answer:

  (a)  5024 ft³

Step-by-step explanation:

You want the difference in volumes of two cones with height 16 ft, where the larger has diameter 40 ft and the smaller has diameter 20 ft.

The volume of a cone is given in terms of its radius as ...

  V = π/3(r²h) . . . . . . r=radius; h=height

The radius is half the diameter, so the formula with diameter is ...

  V = π/3(d/2)²h = π/12d²h

The two given cones have the same height, but different diameters. The difference in volumes will be ...

  V2 -V1 = (π/12)((d2)²h) -(π/12)((d1)²h) = (πh/12)((d2)² -(d1)²)

  V2 -V1 = 3.14(16 ft)/12 × ((40 ft)² -(20 ft)²) = 3.14·16/12·1200 ft³

  = 3.14·1600 ft³ = 5024 ft³

The difference in volumes of the two cones is 5025 cubic feet.

There are 12 different combinations of transportation and weather conditions for the family trip to Washington D.C.

To find the total number of different combinations of transportation and weather conditions for the family trip to Washington D.C, we can use the multiplication rule of counting, which states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.

There are three different transportation options: plane, car, and train, and four different weather conditions: sunny, windy, rainy, and cloudy. To find the total number of different combinations, we simply need to multiply the number of transportation options by the number of weather conditions:

Total number of combinations = number of transportation options x number of weather conditions

Total number of combinations = 3 x 4

Total number of combinations = 12

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To cover the length of all four walls in a room that measures 15' x 10', minus 3' for the door opening, it would require 50 feet of rubber wall base.

A rubber wall base is a type of molding that is installed at the base of walls to protect the wall and add aesthetic appeal to the room. To calculate the amount of rubber wall base required for a room, we need to determine the perimeter of the room, which is the sum of the length of all four walls.

In this case, the room measures 15' x 10', which means that the length of the four walls would be (2 x 15) + (2 x 10) = 30 + 20 = 50 feet.

However, we need to subtract 3 feet for the door opening because the rubber wall base does not need to cover the area where the door is located. Therefore, the total amount of rubber wall base required for the room would be 50 - 3 = 47 feet.

But, we need to add some extra footage for corner pieces and cuts. Typically, it is recommended to add an extra 5% to 10% of the total length of the wall base to account for these additional pieces. So, adding 5% of 47 feet, we get an additional 2.35 feet, which we can round up to 3 feet.

Therefore, the final answer is 47 + 3 = 50 feet.

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Answer:

18.84

Step-by-step explanation:

:)

Brad needs to score between 72 and 79 on the fourth test in order to get a C for the semester.

To explain why this is so, we need to first understand how the grade for the semester is calculated.Since the final course grade depends entirely on the average of four equally weighted 100-point tests, this means that each test will count for 25% of Brad’s final grade. Therefore, Brad needs to get an average score of 70-79 (inclusive) on the four tests combined in order to get a C for the semester.

In order to calculate what range of scores Brad needs to get on the fourth test in order to get a C for the semester, we need to look at the scores he has already obtained on the first three tests. Brad has scored 87, 89 and 78 on the first three tests. This gives him a total score of 254 (87+89+78=254). This means that Brad needs to get a score of between 70 and 79 on the fourth test in order to reach a total score of between 280-309 (inclusive), which will result in an average score of between 70-79 (inclusive), and give Brad a C for the semester.

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Therefore , the solution of the given problem of percentage comes out to be Donica spends $735 in rent.

A statistic or measure that is stated as a percent of 100 is referred to as "a%" in statistics. The terms "pct," "pct," and "pc" are also uncommon. However, it is commonly denoted by the symbol "%". There are no measurements; the proportion of the total sum is flat. Because the numerator of percentages almost always equals 100, they are genuinely integers. Either the percent sign (%) or the word "fraction" must come before a number to indicate that it represents a percent.

Here,

Sales royalty for Donica is calculated as follows:

=>  $12,475 * commission of 4%

=>  $499 commission

Donica's overall earnings for the previous month after deducting the commission were:

Total income equals monthly salary plus commission.

=>  Total income=  $1950 + $499.

=>  $2449 in total profits

We need to multiply Donica's total income by 30% to determine how much she spends in rent:

=>  Rent is 30% of total income.

=>  Rent = 0.3 * $2449 =  $734.70.

When this is rounded to the closest whole integer, we obtain:

=> Rent = $735

Donica thus spends $735 in rent.

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16.70Therefore, the point estimate that should be used in constructing the confidence interval is -$16.70.

To find the point estimate that should be used in constructing the confidence interval, the formula for the point estimate can be used. The formula is as follows: Point Estimate = Sample Mean of Mail-Order Sales - Sample Mean of Internet Sales = $70.60 - $87.30 = -$16.70.How to find the point estimate?The point estimate is the best estimate of the unknown population parameter based on a given sample of data. In this case, the unknown population parameter is the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases.

To find the point estimate, we need to calculate the difference between the sample mean of mail-order sales and the sample mean of internet sales .The formula for the point estimate is given by :Point Estimate = Sample Mean of Mail-Order Sales - Sample Mean of Internet Sales= $70.60 - $87.30= -$

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The coefficient of determination measures goodness of fit.

The coefficient of determination, often referred to as R-squared, measures the goodness of fit in a regression analysis. It does not measure the independence of variables, economic plausibility, or independence of residuals.

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The sum of the first 50 terms is 3775. Let a be the first term and d be the common difference of the arithmetic sequence.

Then, the tenth term is a + 9d = 28, and the sum of the fifth and seventh terms is 2a + 12d = 32.

Solving these equations simultaneously, we get a = 2 and d = 3.

To find the sum of the first 50 terms, we use the formula for the sum of an arithmetic sequence:

S50 = (50/2)(2a + (50-1)d) = 25(2 + 49(3)) = 3775.

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The probability of John waiting is

0.333.

The probability that it takes John between 9 and 12 minutes to wait in line at the bank is 0.333.

This is because the continuous and uniformly distributed time between 7 and 17 minutes is divided into 10 minutes, meaning each unit is equal to 0.1. Therefore,

the probability of John waiting between 9 and 12 minutes is 3 units of 0.1 which is 0.333.

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The equation of the line of reflection that reflects shape P into shape Q is y = −2x + 12.

To find the equation of the line of reflection that reflects shape P into shape Q, we need to follow some steps:

Step 1: Draw the mirror line. To reflect a point or shape, we must have a mirror line. The mirror line is the line that passes through the reflection and is perpendicular to the reflecting surface. It serves as a reference for reflecting points or shapes.

Step 2: Find the midpoint of PQ. The midpoint of PQ is the point that lies exactly halfway between P and Q.

Step 3: Find the slope of PQ. The slope of PQ is the rise over run or the difference of the y-coordinates over the difference of the x-coordinates.

The slope formula is given by m = (y2 − y1) / (x2 − x1).

Step 4: Find the perpendicular slope of PQ. The perpendicular slope of PQ is the negative reciprocal of the slope of PQ. It is given by m⊥ = −1/m.

Step 5: Write the equation of the line of reflection. The equation of the line of reflection is given by y − y1 = m⊥(x − x1) or y = m⊥x + b, where m⊥ is the perpendicular slope of PQ and b is the y-intercept of the line. To find b, we substitute the coordinates of the midpoint of PQ into the equation and solve for b. Then we substitute m⊥ and b into the equation to get the final answer.

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Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm.

1. Simple Interest Fοrmula: This fοrmula is used tο calculate the interest earned οr paid οn a lοan οr investment. It is calculated as:

[tex]\rm I = P \times r \times t[/tex]

Where I is the interest earned οr paid, P is the principal amοunt, r is the interest rate, and t is the time periοd.

2. Pythagοrean Theοrem: This fοrmula is used tο calculate the length οf οne side οf a right triangle given the lengths οf the οther twο sides. It is calculated as:

[tex]\rm a^2 + b^2 = c^2[/tex]

Where a and b are the lengths οf the twο legs οf the right triangle, and c is the length οf the hypοtenuse.

3. Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]

Where a, b, and c are cοefficients οf the quadratic equatiοn ax² + bx + c = 0, and x is the sοlutiοn.

4. Bοdy Mass Index (BMI) Fοrmula: This fοrmula is used tο calculate a persοn's bοdy mass index, which is a measure οf bοdy fat based οn height and weight. It is calculated as:

BMI = (weight in kilοgrams) / (height in meters)²

A BMI οf 18.5 tο 24.9 is cοnsidered healthy, while a BMI οf 25 tο 29.9 is cοnsidered οverweight, and a BMI οf 30 οr higher is cοnsidered οbese.

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Complete question:

Describe some common or unique mathematical formulas that you use in your life.

Answer:

B. 15

Step-by-step explanation:

its right on edge

Optiοn 2: 40, 80, and 120 square units, is the οnly set οf regiοns fοr the prism's faces that are viable.

A triangular prism is indeed a prism that has three rectangular sides and twο triangular bases. A pentahedrοn, that is. The rectangular base οf the supplied right triangular prism measures b and h and has an area οf bh = 98 square units. Let l stand in fοr the prism's height. The prism's entire surface area is calculated as fοllοws:

2bh + bl + lh

By simplifying and replacing the values οf bh, we οbtain:

2(98) + bl + lh = 466

bl + lh = 135

The areas οf the twο nοn-base sides οf a prism are each (1/2)bl since they are equivalent right triangle with legs b and l. Let's examine each οf the available respοnses tο see if it cοmplies with the requirements:

Optiοn 1: 30, 110, and 190 square units

If the area οf οne οf the nοn-base faces is 110 square units, then (1/2)bl = 110, sο bl = 220. But bl + lh = 135, sο this is nοt pοssible. This grοup οf lοcatiοns is therefοre nοt feasible.

Optiοn 2: 40, 80, and 120 square units

If the area οf οne οf the nοn-base faces is 80 square units, then (1/2)bl = 80, sο bl = 160. This means that lh = 135 - bl = 135 - 160 = -25, which is nοt pοssible. Sο this set οf areas is nοt pοssible.

Therefοre, this set οf areas is nοt pοssible. This grοup οf areas cannοt thus be achieved. If the area οf οne οf the nοn-base faces is 100 square units, then (1/2)bl = 100, sο bl = 200. But bl + lh = 135, sο this is nοt pοssible. Hence, it is impοssible tο cοver this grοup οf areas.

Optiοn 4: 60, 90, and 120 square units

If the area οf οne οf the nοn-base faces is 90 square units, then (1/2)bl = 90, sο bl = 180. This means that lh = 135 - bl = 135 - 180 = -45, which is nοt pοssible. Sο, this set οf areas is nοt pοssible.

Optiοn 2's range οf 40, 80, and 120 square units is the οnly set οf areas fοr the prism's faces that can be cοnsidered.

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The total students who are going on the field trip are 320 students out of 400 students which has been obtained by using the concept of fractions.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

If 4 out of 5 students are going on the field trip, then the fraction of students going on the field trip is 4/5.

To find out how many students are going on the field trip, we can multiply this fraction by the total number of students:

Number of students going on the field trip = (4/5) x 400

Number of students going on the field trip = 320

Therefore, 320 students are going on the field trip.

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Answer:

See below!

Step-by-step explanation:

a) 1, 2, 3, 4, 5

The possible outcomes are all the options that there are on the spinner

b) 2

There are only 2 even numbers!

c) [tex]\frac{2}{5}[/tex] or 0.4

There are 2 out of 5 numbers are even on the spinner so that must be the solution!

d) 1

The spinner has only one multiple of 3, so the possible outcome should also be 1.

e) [tex]\frac{1}{5}[/tex] or 0.2

There are only 1 out of 5 options which are multiples of 3, so that would be our solution

f) 4

There are 4 prime numbers in the spinner (1, 2, 3, 5), so that would be a possible outcome.

g) [tex]\frac{4}{5}[/tex] or 0.8

The spinner has 4 out of 5 prime numbers, so our answer would be that!

Hope this helps, have a lovely day! :)

Using the formula for compound interest we find that the annual rate of increase in the cost of firewood is approximately 7.8%.

We can use the formula for compound interest to calculate the annual rate of increase:

A = P(1 + r)^n

where A is the final price, P is the initial price, r is the annual rate of increase, and n is the number of years.

We know that P = $140, A = $182, and n = 4, so we can solve for r:

182 = 140(1 + r)^4

(1 + r)^4 = 1.3

1 + r = 1.3^(1/4)

r ≈ 0.0777

The annual rate of increase is approximately 0.0777 or 7.8% to the nearest tenth of a percent.

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Fred's Annual pension will be $603.

Average salary = (82000 + 96000 + 105000 + 109000) / 4 = $100,500

Fred's employer will credit him 1.8% of that average for each year he worked, so we can calculate his annual pension as follows:

Annual pension = 0.018 * 4 * 100500 = $7,236

Therefore, Fred's annual pension will be $7,236.

We can simply divide his annual pension by 12:

Annual pension = 7236 / 12 = $603

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Answer: 7.62

Step-by-step explanation:

Answer:

350 centimeters

Step-by-step explanation:

1.5 meters x 3 = 3.5 meters

There are 100 centimeters in one meter

So, 3.5 x 100 = 350

The rate of change of the base of the triangle is (20 - 1/12 × base × b) cm/min when the altitude is h cm and the area is a sq cm. And this is solved by the concept of Differentiation.

The problem asks to find the rate of change of the base of a triangle when the altitude and area of the triangle are given.

Let's use the formula for the area of a triangle, which is A = 1/2 × base × altitude. Taking the derivative with respect to time, we get dA/dt = 1/2 × (d/dt)(base) × altitude + 1/2 × base × (d/dt)(altitude).

Now, we are given that dA/dt = the rate of change of the area = a constant value. Also, we know that (d/dt)(altitude) = the rate of change of the altitude = b cm/min.

Therefore, we can substitute these values into the formula above to get:

a = 1/2 × (d/dt)(base) × h + 1/2 × base × b

We want to find (d/dt)(base) when h and a are given. Since h is given, we can solve for (d/dt)(base) by isolating it in the equation above:

(d/dt)(base) = (2/a) × (a - 1/2 × base × b)/h

Substituting the given values of h and a, we get:

(d/dt)(base) = (2/60) × (120 - 1/2 × base × b)/6

where b is given in cm/min. Simplifying this expression, we get:

(d/dt)(base) = (20 - 1/12 × base × b) cm/min

Therefore, the rate of change of the base of the triangle is (20 - 1/12 × base × b) cm/min when the altitude is h cm and the area is a sq cm

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the area of a square is always the square of its side length, and if the area cannot be expressed as the square of an integer, then we can say that it is not the power of 2.

A square is a quadrilateral that has four equal sides and four right angles. The area of a square is the product of its length and width, which are equal in the case of a square. So, the formula for the area of a square is:

Area = side × side

or

Area = side²

In other words, the area of a square is the square of its side length.

Now, when we say that the area of a square is "not the power of 2," it means that the area cannot be expressed as a perfect square of an integer. For example, if the area of a square is 25, then it is the square of 5, which is an integer, and so the area is the power of 2.

However, if the area of a square is, say, 12, then it cannot be expressed as the square of an integer, since the square of any integer is always a whole number. Therefore, we can say that the area of the given square is not the power of 2.

In summary, the area of a square is always the square of its side length, and if the area cannot be expressed as the square of an integer, then we can say that it is not the power of 2.

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The modular inverse of 11, modulo 1000 is 901. Expressing the answer in integer form.

To find the modular inverse of 11  modulo 1000, we need to find an integer x such that [tex]$11x\equiv1\pmod{1000}$[/tex].

One way to find the modular inverse is to use the extended Euclidean algorithm. Using this algorithm, we can find the greatest common divisor of 11 and 1000 and express it as a linear combination of 11 and 1000.

We can then use the coefficients of this linear combination to express 1 as a linear combination of 11 and 1000.

Applying the extended Euclidean algorithm, we have:

1000= 11 *90 + 10

11 = 10 *1 + 1

Working backward, we can express 1 as a linear combination of 11 and 1000:

1 =11 - 10* 1

= 11 - (1000 - 11*90)

= 901 * 11 - 1 *1000

Therefore, the modular inverse of 11 modulo 1000 is 901, since

11*901=1 mod{1000}.

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The exponential function for the Greenville's population so that the yearly growth rate is visible is given as follows:

G(t) = 24000(1.00124)^t.

An increasing exponential function is modeled according to the rule presented as follows:

y = a(1 + r)^t.

In which:

The function for Greenville's population is given as follows:

G(t) = 24000(1.00496)^4t.

Which means that the population grows at a rate of 0.00496 = 0.496% every four years, hence the yearly growth rate is given as follows:

r = 0.00496/4

r = 0.00124.

Then the function is given as follows:

G(t) = 24000(1.00124)^t.

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Answer:

1.75a + 8b

Step-by-step explanation:

0.75a + 10b + a - 2b ← collect like terms

= (0.75 + 1a) + (10b - 2b)

= 1.75a + 8b

Answer:

1.75a+8b

Step-by-step explanation:

Given here, 0.75a + 10b + a – 2b = 0.75a+a+10b-2b

                                                     =1.75a+8b

Hence, The required equivalent expression is 1.75a+8b

The probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.

To determine the probability of an out-of-control signal occurring on the first sample following the shift, we need to calculate the probability of observing a sample mean or range value that falls outside the control limits.

For the X-bar chart:

New process mean (after the shift) = 702.00

Standard deviation (constant) = 1.738

Sample size (n) = 6

We can calculate the standard error (SE) for the X-bar chart using the formula:

SE = Standard deviation / √(sample size)

SE = 1.738 / √(6) ≈ 0.709

Next, we calculate the control limits for the X-bar chart based on the new process mean:

New UCL = New process mean + 3 × SE

= 702.00 + 3 × 0.709

= 704.127

New LCL = New process mean - 3 × SE

= 702.00 - 3 × 0.709

= 699.873

Now, we need to determine the probability of observing a sample mean outside the control limits, given that the process mean has shifted to 702.00. We can assume a normal distribution for the sample means.

To calculate the probability, we need to determine the z-scores for the new UCL and LCL using the formula:

z = (X - μ) / SE

where X is the value of interest (UCL or LCL), μ is the process mean, and SE is the standard error.

For the UCL:

z = (New UCL - μ) / SE

= (704.127 - 702.00) / 0.709

= 2.999

For the LCL:

z = (New LCL - μ) / SE

= (699.873 - 702.00) / 0.709

= -2.999

We can use a standard normal distribution table or a statistical calculator to find the probabilities associated with these z-scores.

Using a standard normal distribution table, the probability of observing a sample mean greater than the new UCL (2.999 z-score) is approximately 0.0013 (or 0.13%), and the probability of observing a sample mean lower than the new LCL (-2.999 z-score) is also approximately 0.0013 (or 0.13%). Since we are interested in either of these cases (an out-of-control signal), we add the probabilities:

Probability of an out-of-control signal = 0.0013 + 0.0013 ≈ 0.0026 (or 0.26%)

Therefore, the probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.

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Complete question =

Control charts for x-bar and s have been maintained on a proces and have exhibited statistical control. The sample size is n=6. The control chart parameters are as follows:

X-bar: UCL = 708.20, Center line = 706.00, LCL = 703.80

R chart: UCL = 3.420, Center line = 1.738, LCL = 0.052

natural tolerance limits for the process are ±5.214.

the estimated standard deviation is 1.738.

d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occuring on the first sample following the shift?

Answer:

61.27

Step-by-step explanation:

Circle perimeter formula: C=2πr

Quarter circle=2πr/4. Given r=11cm

                     2x3.14x11/4=17.27

Rectangle perimeter: C=2(a+b)

                                    =2（2+20）=44

so, total: 17.27+44=61.27

The answer is x=6x +2

Answer: The coordinates of the reflected point are (0.5, -4)

Step-by-step explanation: When a point is reflected across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. So the point (-0.5, 4) reflected across the y-axis will be (0.5, 4).When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. So the point (0.5, 4) reflected across the x-axis will be (0.5, -4).

Answer:

(5,-4) because if the quadrant one is positive positive quadrant two is negative positive quadrant three is negative negative Quadrant four is positive negative

Step-by-step explanation: Hope this helps!! Mark me brainliest! :))

The identity used to simplify from step 4 to step 5 is the definition of the cosecant function cosecant x = 1/sine x.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's structure is as follows: Expression is (Number/Variable, Arithmetic Operator, Number/Variable).

                                For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

 =  the expression 1/sine x

 = 1/sine x + cosine x/sine x

 =  cosecant x + cosine x/sine x

  = cosecant x + cotangent x.

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