State the coordinates of the point.

The axis of symmetry of equation f(x) = x² - x³ - 4 is x = 2/3.

The axis of symmetry is a vertical line that passes through the vertex of a parabolic function, which is the highest or lowest point on the graph depending on the direction of the parabola. The equation f(x) = x² - x³ - 4 is a cubic function that can be written in standard form as:

f(x) = -x³ + x² - 4

To find the axis of symmetry, we need to first find the x-coordinate of the vertex. This can be done by taking the derivative of f(x) and setting it equal to zero:

f'(x) = -3x² + 2x = 0

x(2-3x) = 0

x = 0 or x = 2/3

Since the coefficient of the x³ term is negative, the vertex of the cubic function is a maximum. Therefore, the axis of symmetry is the vertical line passing through the x-coordinate of the vertex, which is x = 2/3.

Find out more about the axis of symmetry

brainly.com/question/30483535

#SPJ4

Answer:

The correct answer is OD.

Step-by-step explanation:

To find how many classes each instructor teaches per week, you need to set up and solve a system of equations based on the given information. In other words,

Let x be the number of classes Bo teaches per week and y be the number of classes Erica teaches per week.

The first equation is based on the total number of classes they teach

x + y = 37

The second equation is based on the relationship between their numbers of classes

y = 2x - 14

To solve this system, you can use substitution or elimination methods. For example, using substitution, you can plug in y = 2x - 14 into the first equation and get

x + (2x - 14) = 37

Simplify and solve for x

3x - 14 = 37

So, Bo teaches 17 classes per week and Erica teaches 20 classes per week.

Answer:

A. 19 Bo; 18 Erica

Step-by-step explanation:

im good like that hehe

Answer:

a two-dimension surface formed by two number lines.

The probability that an ugly splice is weak is 2/3.

This can be calculated by multiplying the probability of weak splices (1/1000) with the probability of ugly splices (1/20) and the probability that a weak splice is also ugly (2/3).

In order to calculate the probability that an ugly splice is weak, we need to use the equation: P(A∩B) = P(A) * P(B|A). In this equation, A represents the probability of weak splices (1/1000), and B represents the probability of ugly splices (1/20).

The probability that a weak splice is also ugly (2/3) is then multiplied by A and B, giving us a final answer of 2/3. This means that 2 out of every 3 ugly splices are weak.

To know more about probability click on below link:

https://brainly.com/question/30034780#

#SPJ11

Answer:

bar chart

Step-by-step explanation:

you are right box plot, histogram and a circle graph aren't the right ones

The given chain which has a negligible mass is draped over the sprocket which has a mass of 2 kg and a radius of gyration of k0=50 mm.

If the 4-kg block A is released from rest in the position s=2 m. Using energy methods, determine the angular velocity of the sprocket at the instant s=4 m.First of all, draw a FBD of the system at s=2 m and at s=4 m.At s=2 m Let the velocity of the block A be v2m/s.At s=4 m Let the velocity of the block A be v4m/s.Let the angular velocity of the sprocket be ω rad/s. Draw FBD at both states and clearly label datum.For the block A at s=2 m Velocity of the block A, v=0 (Initial velocity)

Kinetic energy of the block A,KE1=12mv²=12×4×(0)²=0Potential energy of the block A,PE1=mgh=4×9.81×2=78.48JFor the block A at s=4 mLet h be the height by which the [tex],KE1=12mv²=12×4×(0)²=0[/tex]block A falls. Velocity of the block A, [tex]v=√2gh=√2×9.81×h[/tex]Kinetic energy of the block A,KE2=[tex]12mv²=12×4×[√2gh]²=8gh[/tex] Joule (J)Total potential energy of the system at s=2 m,PE1=2×g×k0 Joule (J)When the block falls from s=2 m to s=4 m, the change in the potential energy of the system is,ΔPE=PE2-PE1Where,PE2=2×g×(2k0) Joule (J)Let the change in the potential energy of the system be ΔPE1 Joule (J).

So,ΔPE1=PE2-PE1=2gk0 Joule (J)The total energy of the system is conserved.

So,ΔPE1=KE2ω²+Iω²Where,ΔPE1 is the change in the potential energy of the systemKE2 is the kinetic energy of the block A when it is at s=4 mI is the moment of inertia of the sprocket about its axisω is the angular velocity of the sprocket at s=4 mSo,ω²=ΔPE1KE2+Iω²Substitute the values of ΔPE1, KE2 and I in the above equation.

[tex]ω²=(2gk0)8gh+mr²ω²=(2×9.81×50×10⁻³)8×h×h+2×1×(50×10⁻³)²ω²=0.7848h²+2.5×10⁻³[/tex]

Therefore,ω=√(0.7848h²+2.5×10⁻³) rad/s.

Substitute the value of h=2 m in the above equation.ω=2.808 rad/s.So, the angular velocity of the sprocket at the instant s=4 m is 2.808 rad/s.

for such more questions on angular velocity

https://brainly.com/question/6860269

#SPJ11

8760 hours in a​ year, one television was on for 438 hours. 5% is the percentage of 8760 hours television was on.

The percentage is the a ratio in which the value of the whole (denominator) is always 100. For example, if Ram scored 40% marks in his math test, it means that he scored 40 marks out of 100. It is written as 40/100 in the fraction form and 40:100 in terms of ratio. Here "%" signifies the symbol of percentage and is read as "percent" or "percentage".

Total number of hours in a year=8760hrs

Television was on for=438hrs

percentage=438/8760 x 100 = 5

Therefore, 438hr is 5 percent of 8760hr.

to know more about ratio, visit:

https://brainly.com/question/13419413

#SPJ1

We may conclude after answering the presented question that rectangle Therefore, the expression for the width of the porch is x + 2 feet.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

area of a rectangle

Area = length x width

To do this, we can factor the expression for the area, which gives us:

x² + 9x + 14 = (x + 2)(x + 7)

Area = length x width

(x + 2)(x + 7) = (x + 7) x width

x + 2 = width

Therefore, the expression for the width of the porch is x + 2 feet.

To know more about rectangle visit:

https://brainly.com/question/29123947

#SPJ1

According to the exponential growth formula , there will be 38400 bacteria present after 3 days.

The given formula for the bacteria population, f(x) = 75 - 8², seems to be incorrect. Since the bacteria reproduce by dividing in half every 8 hours, we should use an exponential growth formula.

Let's denote the number of bacteria present after z days as f(z). Since there are 24 hours in a day, there are 3 reproduction cycles in a day (24 hours / 8 hours per cycle = 3 cycles). Therefore, the total number of reproduction cycles after z days is 3z.

The formula for the bacteria population after z days is: f(z) = 75 * 2^(3z)

Now, let's find the total number present after 1, 2, and 3 days.

1 day: f(1) = 75 * 2^(3 * 1) = 75 * 2^3 = 75 * 8 = 600
There will be 600 bacteria present after 1 day.

2 days: f(2) = 75 * 2^(3 * 2) = 75 * 2^6 = 75 * 64 = 4800
There will be 4800 bacteria present after 2 days.

3 days: f(3) = 75 * 2^(3 * 3) = 75 * 2^9 = 75 * 512 = 38400
There will be 38400 bacteria present after 3 days.

To know more about exponential growth formula, visit:

https://brainly.com/question/31251941#

#SPJ11

The sample size required is 182 families should be interviewed.

To calculate the number of families that should be interviewed to obtain the desired precision and degree of confidence, one must first determine the minimum sample size required to achieve the desired degree of confidence. As the standard deviation of the sample was computed to be $400 with the mean of $60,000.

Sample size formula: n = (Z² * s²) / E²

The formula for the degree of confidence: Z = 2.576

Sample size formula: n = (Z² * s²) / E²

Substituting the values, we get n = (2.576² * $400²) / $90²= 181.49 = 182 families. The sample size required is 182 should be interviewed families.

To learn more about "Standard deviation": brainly.com/question/23907081

#SPJ11

In a direct proof of the theorem "if r and s are rational numbers, then the product of r and s is a rational number," the following assumptions or facts are typically used:

Using these facts, a direct proof of the theorem can be constructed by assuming that r and s are rational numbers and then showing that their product is also a rational number. Specifically, we can express r and s as fractions with integer numerators and denominators, multiply their numerators together to obtain the numerator of the product.

Since the numerator and denominator of the product are both integers, and the denominator is nonzero, the product is a rational number.

For more details about theorem click here:

https://brainly.com/question/30066983#

#SPJ11

The vertical distance between (2, 11/3) and (2, -4/3) is -5 units.

The distance formula is a mathematical equation used to find the distance between two points in a plane. It is derived from the Pythagorean theorem and is expressed as:

d = √((x₂- x₁)²+ (y₂ - y₁)²)

The distance formula can also be extended to three-dimensional space by adding an additional term to the equation.

The two points (2, 11/3) and (2, -4/3) have the same x-coordinate, which means they lie on a vertical line. To find the vertical distance between these two points, we simply subtract their y-coordinates:

Vertical distance = (y-coordinate of second point) - (y-coordinate of first point)

= (-4/3) - (11/3)

= -15/3

= -5

Therefore, the vertical distance between (2, 11/3) and (2, -4/3) is -5 units. Since this is a negative value, it means that the second point is located 5 units below the first point.

To know more about coordinate, visit:

https://brainly.com/question/16634867

#SPJ9

The height of the arch at a distance of 1.5 meters from the center is approximately D. 1.73 meters

The shape of a semi-elliptical arch can be described by the equation:

y = c * sqrt(1 - (x/a)^2)

where "a" is half the span of the arch, "c" is the central height of the arch, and (x,y) are the coordinates of a point on the arch, measured relative to the center of the arch.

In this case, we have a span of 6 meters, so a = 3 meters. The central height of the arch is 2 meters, so c = 2 meters. We want to find the height of the arch at a distance of 1.5 meters from the center, so x = 1.5 meters.

Substituting these values into the equation, we get:

y = 2 * sqrt(1 - (1.5/3)^2)

y = 2 * sqrt(1 - 0.25)

y = 2 * sqrt(0.75)

y = 2 * 0.866

y = 1.732

Therefore, the height of the arch at a distance of 1.5 meters from the center is approximately 1.73 meters. Answer D

Learn more about  the geometry of curves:https://brainly.com/question/28199103

#SPJ11

Your question is incomplete, but probably the complete question is :

A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.

A.   1.41 m C.   1.56 m

B.   1.63 m D.   1.73 m

Answer:

Step-by-step explanation:

Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails.

To the nearest percent, what is the experimental probability of Project B?

The experimental probability of Project A is 0.53.

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

As per the given data:

We are given that there are two projects, Project A and Project B.

A student has to choose one out of the two projects and, the student's choice is represented by the flip of a coin where heads representing Project A and tails representing Project B.

Head's = Project A

Tail's = Project B

Total number of trials = 110

Number of heads in the trials = 58 heads

Number of tails in the trials = 52 tails

For finding out the experimental probability of Project A:

= Number of favorable outcomes / Total number of trials

Number of favorable outcomes = Number of heads

= Number of heads / Total number of trials

= 58 / 110

= 0.53 (approx)

The experimental probability of Project A is 0.53.

Hence, The experimental probability of Project A is 0.53.

To learn more on Probability, click:

brainly.com/question/30034780

#SPJ2

Answer:

To find the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures, we first need to convert both temperatures to Celsius or Fahrenheit. Since Oklahoma's temperature is given in Fahrenheit and New Jersey's temperature is given in Celsius, we'll convert Oklahoma's temperature to Celsius.

Using the formula F = 1.8C + 32, we can solve for C:

-31°F = -35°C

(To see how we arrived at this conversion: first, we use the formula to convert Fahrenheit to Celsius: F = 1.8C + 32. Rearranging the equation, we can solve for C: (F - 32) / 1.8 = C. Plugging in -31°F for F, we get (-31 - 32) / 1.8 = -35°C)

Now we can find the difference in Celsius between the two temperatures:

|-35°C| - |-37°C| = |-2| = 2°C

So the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures is 2°C.

The width of the bookshelf will be 6 inches when the area and length are 216 in and  36 inches.

What is the width?

Width is a dimension of a geometrical figure that tells about the structure of the figure. In general, width is used to measure the object.

What is formulae of width?

Width is obtained by dividing area and length.

                               W=A/L

substitute values, 216/36= 6inches.

The width is gonna be 6 because all you have to do is divide 216 and 36

To know more about Area visit:

https://brainly.com/question/11952845

#SPJ1

The total number of t-shirts principal ordered in $1520 for the school store is given 214.

Let us consider the number of t-shirts the principal ordered be equal to 'x'.

The cost of each t-shirt is equal to $7.

⇒ The total cost of 'x' t-shirts =  7x dollars.

Shipping cost is a flat rate for any order, regardless of the number of t-shirts =  $22

Total cost of the order (including shipping) =  $1520.

Required equation is equal to,

7x + 22 = 1520

Subtract 22 from both sides of the equation we get,

⇒ 7x = 1498

Divide both sides of the equation by 7 we get,

⇒ x = 214

Therefore, the number of t-shirts ordered by  principal for the school store is equal to  214.

Learn more about ordered here

brainly.com/question/29025841

#SPJ4

The study described in the question is a randomized crossover trial, where each participant serves as their own control by receiving both treatments  in a randomized order

In a matched pairs experiment, each subject is paired with another subject who is similar in some relevant characteristic, and one subject receives the treatment while the other serves as a control. The two subjects in each pair are matched on this characteristic to reduce the effect of confounding variables.

In contrast, a randomized crossover trial is a type of experiment in which each participant receives both treatments (in this case, canned soup and fresh soup) in a randomized order, with a washout period between the treatments to minimize carryover effects. In this study, the participants were randomly assigned to either start with canned soup or fresh soup and then switched to the other treatment after a two-day break. Each participant thus serves as their own control, and the difference in outcome between the two treatments is compared within each individual.

Learn more about matched pair here

brainly.com/question/23413412

#SPJ4

The given question is incomplete, the complete question is:

Bisphenol A in Your Soup Cans Bisphenol A (BPA) is in the lining of most canned goods, and recent studies have shown a positive association between BPA exposure and behavior and health problems. How much does canned soup consumption increase urinary BPA concentration? That was the question addressed in a recent study1 in which consumption of canned soup over five days was associated with a more than 1000 % increase in urinary BPA. In the study, 75 participants ate either canned soup or fresh soup for lunch for five days. On the fifth day, urinary BPA levels were measured. After a two-day break, the participants switched groups and repeated the process. The difference in BPA levels between the two treatments was measured for each participant. The study reports that a 95 % confidence interval for the difference in means (canned minus fresh) is 19.6 to 25.5 ?g/L. 1Carwile, J., Ye, X., Zhou, X., Calafat, A., and Michels, K., ‘‘Canned Soup Consumption and Urinary Bisphenol A: A Randomized Crossover Trial,” Journal of the American Medical Association, 2011; 306(20): 2218–2220.Is this a randomized comparative experiment or a matched pairs experiment?

The equation in slope- intercept form is y = x - 1/5

It is important to note that the expression representing the equation of a line in slope- intercept form is written as;

y = mx + c

Such that the parameters are;

collect the variables and constants, we have;

- y = 1/5 - x

reconstruct the expression

- y = -x + 1/5

Divide both sides by the coefficient of y , we have;

y = x - 1/5

Learn about slope-intercept form at: https://brainly.com/question/1884491

#SPJ1

Answer:

11.52 feet

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius.

We can rearrange the formula to solve for the radius:

r = (3V/4π)^(1/3)

Substituting the given volume V = 7,234.56 ft³, we get:

r = (3(7,234.56)/(4π))^(1/3) ≈ 11.52 ft

Therefore, the radius of the sphere is approximately 11.52 feet.

The width of the rectangle is 5 meters.

To find the width of the rectangle, let's use the formula for the area of a rectangle, which is:

Area = length x width

We know that the area of the rectangle is 65 square meters. We also know that the length of the rectangle is 8 meters more than the width. Let's call the width "w". Then, the length can be expressed as:

length = w + 8

Substituting this expression for length into the formula for the area, we get:

65 = (w + 8) x w

Simplifying and solving for w, we get:

w² + 8w - 65 = 0

Using the quadratic formula, we get:

w = (-8 ± √(8² + 4(1)(65))) / (2(1))

w = (-8 ± √(324)) / 2

w = (-8 ± 18) / 2

We take the positive value for w since the width cannot be negative:

w = (-8 + 18) / 2

w = 5

Find out more about the width of the rectangle

at brainly.com/question/27555801

#SPJ4

The garden would require 84 plants, which is the same number of plants as the garden's surface area.

The area of the garden can be determined using the formulas below if it is shaped like a right triangle and has sides that are 7 and 24 yards long.

Area of the garden = (1/2) x Base x Height

Area of the garden = (1/2) x 7 x 24

Area of the garden = 84 square yards

Since there is one square yard of area for each plant, the number of plants needed for the garden would be equal to the area of the garden, which is 84 plants.

To learn more about surface area visit;

https://brainly.com/question/29101132

#SPJ4

This shows that they read less frequently than 95.7% of their classmates in the same grade level.

In statistics, a percentile is a metric that is used to express where one observation stands in relation to a larger group of data. It displays the proportion of data points that fall under a given value. For instance, if a student achieves a score in the 90th percentile on a standardised test, it signifies that they outperformed 90% of their peers who also took the test. As an alternative, if a child is taller than 25% of children their age and shorter than 75%, their height is in the 25th percentile for their age.

given

We must first compute the z-score using the following formula to determine the percentile of the child's reading proficiency.

z = (x - μ) / σ

where x represents the child's reading rate, represents the grade-level mean reading rate, and represents the standard deviation.

Inputting the values provided yields:

z = (46.2 - 85) / 22

z = -1.727

We can calculate or use a conventional normal distribution table to obtain the value of 0.0428 for the region to the left of z = -1.727. The child's reading rate is at the 4.28th percentile according to this statistic.

As a result, the child's reading proficiency is 4.3 percentile (rounded to one decimal place).

This shows that they read less frequently than 95.7% of their classmates in the same grade level.

To know more about percentile visit:

https://brainly.com/question/28269290

#SPJ1

There would be a problem with taking readings from the right side of a sphere if the diameters of the spheres were different because the right side of a sphere is not a fixed point, but rather a relative term.

If the diameters of two spheres were different, the right side of one sphere would not be the same as the right side of the other sphere. This means that taking readings from the right side of each sphere would not be a fair comparison, as the points being measured are not equivalent.

For example, imagine two spheres with diameters of 5cm and 10cm, respectively. If we were to take readings from the right side of each sphere, we would be measuring points at different distances from the center of each sphere. This would result in inaccurate measurements and an unfair comparison.

To avoid this problem, it is important to define a consistent point of measurement on each sphere that is equivalent, regardless of the diameter. For example, measuring from the center of each sphere would provide a consistent and fair comparison.

To learn more about sphere click on,

https://brainly.com/question/31066551

#SPJ4

Theoretical probability of drawing the letter "o" is 1/4, or 0.25 as a decimal.

The probability of drawing the letter "o" from the bag of tiles depends on the number of tiles with the letter "o" and the total number of tiles in the bag.

Since the word "Colorado" has two "o's", there are two "o" tiles in the bag. The total number of tiles in the bag is the number of letters in the word "Colorado", which is 8.

Therefore, the theoretical probability of drawing the letter "o" is:

P("o") = number of "o" tiles / total number of tiles

= 2/8

= 1/4

So the theoretical probability of drawing the letter "o" is 1/4, or 0.25 as a decimal.

Learn more about probability

https://brainly.com/question/30034780

#SPJ4

Johnny has 1258 more pineapples than Bobby.

Bobby has 37 pineapples, Johnny has 35 times more pineapples than Bobby. To find how many more pineapples does Johnny have than Bobby, we can use the below formula,

More pineapples = Johnny's pineapples - Bobby's pineapples

Let x be the number of pineapples that Bobby has. Therefore, the number of pineapples owned by Johnny is 35x.

It is given that Bobby originally has 37 pineapples, thus x = 37. The number of pineapples Johnny has = 35*37 = 1295

Thus, difference in number of pineapples between Johnny and Bobby:

=1295-37 = 1258

Therefore, Johnny has 1258 more pineapples than Bobby.

To learn more about how much more of an object someone has refer :

https://brainly.com/question/11756704

#SPJ11

the total cost of 4 nonmember tickets and 2 member tickets would be $116.

Why it is and what is financial literacy?

The expression to find the total cost of 4 nonmember tickets and 2 member tickets would be:

4($24) + 2($10)

This expression represents the cost of 4 nonmember tickets at $24 each, and 2 member tickets at $10 each.

To find the total cost, we simply need to evaluate this expression using basic arithmetic:

4($24) + 2($10) = $96 + $20 = $116

Therefore, the total cost of 4 nonmember tickets and 2 member tickets would be $116.

Financial literacy is the knowledge and skills required to manage one's personal finances effectively. It encompasses a range of topics, including budgeting, saving, investing, managing debt, understanding financial products such as credit cards and loans, and planning for retirement. Financial literacy also involves an understanding of financial concepts such as interest rates, inflation, and risk management.

To know more about financial literacy visit:

https://brainly.com/question/13102912

#SPJ1

Hence, the correct match of probabilities with their corresponding situations is given by option 4.

To match the probabilities with their corresponding situations, we can utilize the formulas given below:

[tex]P(A ∩ B) = P(A) x P(B|A)P[/tex](2 aces) =[tex](4/52) x (3/51) = 1/221[/tex]

P(heart and club) =[tex](13/52) x (13/51) = 169/2652[/tex]P(spade and ace of hearts) = 0P(2 of the same card) = (1/52) + (3/51) + (2/50) + (1/49) + (4/48) + (3/47) + (2/46) + (1/45) = 20/663P(red card and four of spades) = (16/52) x (1/51) = 4/663

Therefore, the probabilities with their corresponding situations are:3: P(spade and ace of hearts) = 0 (Not possible as Ace of hearts is not spade)

4: P(2 aces) = 1/2211: P(heart and club) = 169/26521: P(heart and club) = 169/26522: P(red card and four of spades) = 4/663

for such more questions on probabilities

https://brainly.com/question/13604758

#SPJ11

Answer:

x= 2

Step-by-step explanation:

² means times the number itself 2 times.

2×2=4

The total area of the composite figure is 114.25 square feet.

The area of a circle of diameter D is:

A = 3.14*(D/2)²

And the area of a triangle of base B and height H is:

A = B*H/2

We can decompose the figure into two simpler ones, a triangle of base of 10ft and height of 15 ft, whose area is:

A = 10ft*15ft/2 = 75ft²

And half of a circle of diameter of 10ft, whose area is:

A = 0.5*3.14*(10ft/2)² = 39.25 ft²

Then the total area of the figure is:

area =  75ft² + 39.25 ft² = 114.25 ft²

Learn more about area at:

https://brainly.com/question/24487155

#SPJ1