Find a rule for the following table of value

Since quadratic function f has vertex (4, 15) and passes through the point (1, 20), an equation that represents f is: B. f(x) = 5/9(x - 4)² + 15.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided above, we can determine the value of a as follows:

f(x) = a(x - h)² + k

20 = a(1 - 4)² + 15

20 = 9a + 15

a = 5/9

Therefore, the required quadratic function is given by:

f(x) = a(x - h)² + k

f(x) = y = 5/9(x - 4)² + 15

Read more on vertex here: brainly.com/question/14946018

#SPJ1

No, the values in the table do not represent a proportional relationship because the y-values are not a constant multiple of the corresponding x-values.

Based on the given table:

x | 0 | 1 | 2 | 3
y | 0 | 3 | 5 | 6

The values in the table do not represent a proportional relationship. To be proportional, all of the y-values should be a constant multiple of the corresponding x-values. However, in this case, the ratio of y/x is not constant (3/1, 5/2, 6/3). Therefore, the relationship is not proportional.

More on proportions: https://brainly.com/question/29963982

#SPJ11

The radius of the line of latitude through X is approximately 5729 km, and the latitude of Y is approximately 43°.

Let X be the starting town with coordinates (28°N, 66°E), and let Y be the destination town which is 3900 km due South of X. We want to find the radius of the line of latitude through X, and the latitude of Y.

First, we can find the distance between X and Y using the Pythagorean theorem. The distance due South is 3900 km, and the distance due East is 28° × R, where R is the radius of the Earth. Using t=2 and R=6406 km, we have:

distance due East = 28° × 6406 km × cos(66°) ≈ 2055.6 km

distance between X and Y = sqrt((3900 km)^2 + (2055.6 km)^2) ≈ 4498.6 km

Next, we can find the latitude of Y using the formula:

latitude of Y = 90° - arctan(distance due South / radius of the Earth)

Using t=2 and R=6406 km, we have:

latitude of Y = 90° - arctan(3900 km / 6406 km) ≈ 43°

Finally, we can find the radius of the line of latitude through X using the formula:

radius of line of latitude = radius of the Earth * cos(latitude of X)

Using the coordinates of X, we have:

latitude of X = 28°N

radius of line of latitude = 6406 km * cos(28°) ≈ 5729 km

For more about radius:

https://brainly.com/question/30106091

#SPJ4

The total area of the figure is 215π square feet

From the question, we have the following parameters that can be used in our computation:

Radius, r = 5 cm

Height, h = 14 cm

So, we have

A1 = πr²

A1 = π * 5² = 25π

A2 = 2πrh

A2 = 2 * π * 5 * 14 = 140π

A3 = 1/2(4πr²)

A3 = 1/2(4π * 5²) = 50π

So, we have

Total area = 25π + 140π + 50π

Evaluate

Total area = 215π

Hence, the total area is 215π

Read more about area at

https://brainly.com/question/24487155

#SPJ1

The given value of 19 is not a unit of measurement, so it cannot be converted to an equivalent measure.

4 in. - 10.2 cm

7 kg - 15.4 lb

6 gal - 22.7 L

5 ft - 1.5 m

Note: The given value of 19 is not a unit of measurement, so it cannot be converted to an equivalent measure.

Learn more about measurement

brainly.com/question/4725561

#SPJ11

Answer:

The answer is 5.8cm to 1 d.p

Step-by-step explanation:

volume of cube=L³

200=L³

cube root both sides

³√200=³√L³

L=5.8cm to 1 d.p

To find the cost of each folder, we need to first set up a system of equations based on the given information. Let x be the cost of a spiral notebook and y be the cost of a folder. We can create the following equations:

1)  2x + y = $6.70 (Rylan's purchase)

2)  3x + 5y = $12.85 (Olivia's purchase)

First, we can solve equation 1 for y:

y = $6.70 - 2x

Next, substitute this expression for y into equation 2:

3x + 5($6.70 - 2x) = $12.85

Now, solve for x:

3x + $33.50 - 10x = $12.85

Combine like terms:

-7x = -$20.65

Now, divide by -7:

x = $2.95

Now that we know the cost of a spiral notebook, we can plug this value back into the expression we found for y:

y = $6.70 - 2($2.95)

y = $6.70 - $5.90

y = $0.80

So, the cost of each folder is $0.80.

To Know more about cost refer here

https://brainly.com/question/15135554#

#SPJ11

Answer:To find the value of x, bring the all the variable to the left side and bring all of the remaining values to the right side. You then simplify the values to find the answer.

Step-by-step explanation:

Answer:

im not sure bud because i don't know  what is the full question?

Step-by-step explanation:

o, the correct sequence of transformations that would result in figure M' is: A) Reflection over the y-axis, then translation down 5 units.

In mathematics, a transformation is a process that changes the position, size, or shape of a geometric figure. Transformations are often used to study the properties of geometric objects and to solve problems in various areas of mathematics, such as geometry, algebra, and calculus.

Here,

Looking at the coordinates of the vertices of M and M', we can see that M' is obtained from M by reflecting it over the y-axis and then translating it down 5 units. So, the correct sequence of transformations that would result in figure M' is:

A) Reflection over the y-axis, then translation down 5 units.

This means that we first reflect M over the y-axis to obtain a new rectangle, which we can call M''. Then, we translate M'' down 5 units to obtain M'. Therefore, the sequence of transformations is:

Reflection over the y-axis

Translation down 5 units

This sequence of transformations will map M onto M'.

To know more about transformation,

https://brainly.com/question/29641135

#SPJ1

Answer: 9 x 10^4

Step-by-step explanation:

9 ten thousands in standard form is written like this: 90,000

To convert this into scientific notation, we simply count how many spaces we want to move the decimal point.

So far, our number looks like this with a decimal point: 90000.0

To make this number equal to 9, we have to move the decimal point 4 spaces to the left.

The 4 then becomes our exponent.

So now we have 9 by itself, and all we do is multiply it by 10 with an exponent of 4, to show you are multiplying 10 four times.

Therefore, 9 ten thousands written in scientific notation is 9 x 10^4

Let's denote the cost of one apple as 'a' and the cost of one banana as 'b'. We can set up a system of two equations to represent the given information:

4a + 9b = 12.70   (equation 1)

8a + b = 17.70    (equation 2)

We can use either substitution or elimination method to solve for 'a' or 'b'. Let's use the elimination method by multiplying equation 2 by 9 and subtracting it from equation 1:

4a + 9b = 12.70

-(72a + 9b = 159.30)   (multiplying equation 2 by 9)

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

-68a = -146.60

Dividing both sides by -68, we get:

a ≈ 2.16

Therefore, the cost of one apple is approximately $2.16.

To know more about costs , refer here :

https://brainly.com/question/14725550#

#SPJ11

Using Pythagorean theorem the distance between the school and the fire station is approximately 4.7 miles, while the distance between the school and the hospital is approximately 7.8 miles.

To solve this problem, we can use the Pythagorean theorem to find the distances and then add them up to get the total distance between the school and the fire station, and then between the school and the hospital.

Part A:

Let's call the middle school point A, Town Hall point B, and the fire station point C. We can draw a right triangle with AB as the base, BC as the height, and AC as the hypotenuse. Using the Pythagorean theorem, we have:

AC^2 = AB^2 + BC^2

AC^2 = 4.3^2 + 1.7^2

AC^2 = 18.98 + 2.89

AC^2 = 21.87

AC ≈ 4.7 miles (rounded to the nearest tenth)

Therefore, the length of the straight line between the school and the fire station is approximately 4.7 miles.

Part B:

Let's call the hospital point D. We can draw another right triangle with CD as the base, BC as the height, and BD as the hypotenuse. Using the Pythagorean theorem, we have:

BD^2 = BC^2 + CD^2

BD^2 = 1.7^2 + 3.1^2

BD^2 = 2.89 + 9.61

BD^2 = 12.5

BD ≈ 3.5 miles (rounded to the nearest tenth)

Now, we can add the distance between A and B (4.3 miles) to the distance between B and D (3.5 miles) to get the total distance between A and D:

AD ≈ 7.8 miles (rounded to the nearest tenth)

Therefore, the length of the straight line between the school and the hospital is approximately 7.8 miles.

To know more about Pythagorean theorem refer here:

https://brainly.com/question/343682?#

#SPJ11

The inequalities represented are:

In mathematics, an inequality is a statement that two values or expressions are not equal. It is used to compare two values and determine the relationship between them. Inequalities use symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Inequalities can be solved and graphed on a number line to show all possible solutions that satisfy the inequality. They are commonly used in algebra and calculus to express a range of values for a variable.

Read more on inequality here:https://brainly.com/question/24372553

#SPJ1

The height of the given trapezoid-shaped tabletop is 75.5 centimeters.

The height of the trapezoid-shaped tabletop. To calculate the height, we can use the formula for the area of a trapezoid: A = (1/2)(b1 + b2)h, where A is the area, b1 and b2 are the lengths of the bases, and h is the height.

Given the area (A) is 7,701 square centimeters, the longer base (b1) measures 119 centimeters, and the shorter base (b2) is 85 centimeters, we can solve for the height (h) using the following steps:

1. Plug in the given values into the formula: 7,701 = (1/2)(119 + 85)h
2. Simplify the expression inside the parentheses: 7,701 = (1/2)(204)h
3. Multiply the two numbers inside the parentheses: 7,701 = 102h
4. Divide both sides of the equation by 102 to solve for h: h = 7,701 / 102
5. Calculate the value of h: h ≈ 75.5 centimeters

So, the height of the trapezoid-shaped tabletop is approximately 75.5 centimeters.

To learn more about Trapezoid

https://brainly.com/question/17078769

#SPJ11

The volume of the solid is A. [tex]\pi/3[/tex]

The volume of a solid in geometry signifies the space it occupies inside a three-dimensional area. It denotes how much content can fill up its inner region, and as usual, measured in units like cubic feet, meters, or centimeters.

Finding the measurement formula varies from shape to shape but commonly involves multiplying width, height, and length. Given that many sectors rely on this term, such as engineering, architecture, and physics, understanding the concept of the volume of a solid weighs significantly.

If we take a cross-section of (x,y)perpendicular to the x-axis, with width dx, now the cross-section is a quarter circle with radius y.

Thus, the volume of the cross-section, since y = 2x becomes: [tex]\pi x^2 dx[/tex]

Now, the volume of the solid when integrated becomes: [tex]\frac{\pi }{3}[/tex]

Option A is correct.

Read more about volume of a solid here:

https://brainly.com/question/20284914

#SPJ1

Option D is the correct answer as it groups the numbers into sets of five, assigns them as either a "make" or a "miss", and preserves the order of the original set.

The set of random numbers provided represents the binary outcome of a basketball player making or missing a free throw. To simulate the event of making five free throws in a row, we need to group the numbers into sets of five and assign each set as either a "make" or a "miss".

Option A simply groups the numbers into sets of five, but does not indicate whether they are a "make" or a "miss". Option B groups the numbers into sets of five and assigns them as either a "make" or a "miss", but the order of the numbers has been changed.

Option C groups the numbers into sets of five, assigns them as either a "make" or a "miss", and preserves the order of the original set.

This allows for an accurate simulation of the event of making five free throws in a row using the provided set of random numbers.

So, correct option is D.

To learn more about numbers click on,

https://brainly.com/question/20592845

#SPJ4

Complete question is:

Suppose the following set of random numbers is being used to simulate the event of a basketball player making five free throws in a row. How should the numbers be rearranged?

860583 785814 010122 337198 621549 034076 796495 978078 433330

333153

A. 860 583 785 814 010 122 337 198 621 549 034 076 796 495 978

078 433 330 333 153

B. 8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597

8078 4333 3033 3153

C. 86058 37858 14010 12233 71986 21549 03407 67964 95978

07843 33303 33153

D. 860583 785814 010122 337198 621549 034076 796495 978078

433330 333153

For a normal distribution with a mean of 68 and a standard deviation of 9, the percentage of scores less than 50 is 2.28%.

It is given that scores on a psychology exam have a normal distribution with a mean of 68 and a standard deviation of 9. The percentage of scores less than 50 can be determined as follows.

1. Calculate the z-score for 50 using the formula:

z = (X - μ) / σ

where

X = 50 (the value we're comparing to)

μ = 68 (mean)

σ = 9 (standard deviation)

2. Plug in the values:

z = (50 - 68) / 9 = -18 / 9 = -2

3. Use a z-table or calculator to find the area to the left of z = -2. This represents the percentage of scores less than 50.

4. Based on the z-table or calculator, the area to the left of z = -2 is approximately 0.0228, which means that around 2.28% of scores were less than 50.

So, about 2.28% of scores on the psychology exam were less than 50.

Learn more about Normal distribution:

https://brainly.com/question/4079902

#SPJ11

The calculated value of sin of the angle is 1/96

From the question, we have the following parameters that can be used in our computation:

cos(θ) = 1/3

tan(θ) = 1/32

The value of sin of the angle is calculated as

sin(θ) = cos(θ) * tan(θ)

substitute the known values in the above equation, so, we have the following representation

sin(θ) = 1/3 * 1/32

Evaluate the products

so, we have the following representation

sin(θ) = 1/96

Hence, the value of sin of the angle is 1/96

Read more about trigonometry function at

https://brainly.com/question/24349828

#SPJ1

p + q + 36 = 0 is the equation that is true. From this equation, we can say that p + q = -36.

If we substitute x = 1 in the given function, we get:

f(1) = [tex](1)^4 + 5(1)^3 + p(1)^2 + q(1) + 30[/tex]

= 1 + 5 + p + q + 30

= p + q + 36

We are given that f(1) = 0. Therefore, we have:

p + q + 36 = 0

This is the equation that is true. From this equation, we can say that p + q = -36.

Now, let's see why this is the case. When we substitute x = 1 in the given function and get f(1) = 0, it means that (1, 0) is a point on the graph of the function. This point lies on the x-axis, which means that the function intersects the x-axis at x = 1. Since the x-axis is the line y = 0, this means that f(x) = 0 when x = 1.

Using this information, we can write an equation in terms of p and q. If we substitute x = 1 in the given function and get f(1) = 0, it means that:

f(x) = [tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q))[/tex]

Therefore, we have:

[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = 0[/tex]

Since (1,0) is a point on the graph of the function, we know that x = 1 is a root of this equation. Therefore, we have:

[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = (x - 1)(x^2 + (7+p)x + (36-p-q))[/tex]

We know that (x - 1) is a factor of this equation, so we can use polynomial long division to divide the expression [tex](x^2 + (7+p)x + (36-p-q))[/tex] by (x - 1). The quotient will give us the other two roots of the equation. However, we do not need to find these roots to answer the question. All we need to know is that p + q = -36.

To know more about function, refer to the link below:

https://brainly.com/question/25394520#

#SPJ11

The value of x is 16.

Given,

The m line is parallel with the n line.

We need to find the value of x.

If two lines are parallel the corresponding angles are congruent.

Example:                              

                         [tex]\sf D[/tex] /

                          /

[tex]\sf A[/tex]<----------------[tex]\sf F[/tex]/----------------------->[tex]\sf B[/tex]

                      /

[tex]\sf C[/tex] <-----------[tex]\sf M[/tex]/------------------------------>[tex]\sf D[/tex]                    

                  /

            [tex]\sf E[/tex]  /

[tex]\sf AFD = CMF[/tex]

[tex]\sf AFM = CME[/tex]

From the figure, we see that

[tex]\sf 8x + 5 + 4x - 17 = 180[/tex]

[tex]\sf 12x - 12 = 180[/tex]

[tex]\sf 12x = 180 + 12[/tex]

[tex]\sf 12x = 192[/tex]

[tex]\sf x = \dfrac{192}{12}[/tex]

[tex]\sf x = 16[/tex]

Thus the value of x is 16.

Learn more about parallel lines and corresponding angles here:

brainly.com/question/12274210

The p-value for this hypothesis test is approximately 0.1317.

To calculate the p-value for the hypothesis test, we need to perform a one-sample proportion test using the sample data provided.

Let's define the null and alternative hypotheses:

Null hypothesis (H₀): The proportion of Marriott customers carrying two Wi-Fi devices is equal to or less than 0.60.

Alternative hypothesis (H₁): The proportion of Marriott customers carrying two Wi-Fi devices exceeds 0.60.

Sample size (n) = 120

Number of customers with two Wi-Fi devices (x) = 78

To test the hypothesis, we can use the normal approximation to the binomial distribution since the sample size is reasonably large.

First, calculate the sample proportion:

[tex]\hat{p}[/tex] = x / n = 78 / 120 = 0.65

Next, calculate the test statistic (z-score):

z = [tex]\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }[/tex]

= (0.65 - 0.60) / √((0.60 * (1 - 0.60)) / 120)

= 0.05 / √(0.24 / 120)

= 1.1180

Now, we can find the p-value corresponding to the calculated test statistic using a standard normal distribution table or a statistical calculator.

In this case, the p-value for a one-sided test (since we are testing if the proportion exceeds 0.60) is approximately 0.1317.

Therefore, the p-value for this hypothesis test is approximately 0.1317.

Learn more about p-value here

https://brainly.com/question/31418383

#SPJ4

To construct a confidence interval for the average bonus that all employees working for financial companies in New York City received last year, we need to know the sample size and the level of confidence. Without this information, we cannot calculate the confidence interval. Please provide the sample size and the level of confidence to proceed with the solution.

To know more about sample size refer here:

https://brainly.com/question/31734526

#SPJ11

Let's assume that the length of the rectangle is x and the width is y.

The perimeter of the rectangle is given by:

P = 2x + 2y

Substituting P = 62, we get:

62 = 2x + 2y

Simplifying the above equation, we get:

x + y = 31

The area of the rectangle is given by:

A = xy

To find the area, we need to solve for one of the variables, either x or y. We can use the equation x + y = 31 to solve for y in terms of x:

y = 31 - x

Substituting this expression for y in the equation for the area, we get:

A = x(31 - x)

Expanding the above expression, we get:

A = 31x - x^2

To find the maximum area, we need to find the value of x that maximizes A. We can do this by completing the square:

A = - (x^2 - 31x)

A = - [(x - 15.5)^2 - 240.25]

A = 240.25 - (x - 15.5)^2

The maximum area occurs when x = 15.5, so the dimensions of the rectangle are:

x = 15.5 mm

y = 31 - x = 15.5 mm

The area of the rectangle is:

A = xy = 15.5 mm × 15.5 mm = 240.25 mm^2

Therefore, the area of the rectangle is 240.25 square millimeters.

To know more about area of rectangle , refer here :

https://brainly.com/question/8663941#

#SPJ11

Answer:

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5The slope represents the rate of change of the monthly rate with respect to the fee to join. For every increase of $1 in the fee to join, the monthly rate increases by $10.

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5The slope represents the rate of change of the monthly rate with respect to the fee to join. For every increase of $1 in the fee to join, the monthly rate increases by $10.The y-intercept represents the initial cost of joining the gym. It is the amount that the gym charges even if the fee to join is $0. In this case, the gym charges $5 to join.

The incorrect statement about the intersecting triangles is A. CG ≅ FG.

With intersecting triangles, it is not always guaranteed that segments like CG and FG will be congruent. The lengths of CG and FG will depend on the specific configuration of the chords and their intersection point G.

However, CE/EG = FD/DG statement is TRUE. This is a consequence of the Intersecting Chords Theorem. When two chords intersect inside a circle, the products of their segments are equal.

Since ∠CEG ≅ ∠FDG intersect inside a circle, the corresponding intercepted arcs create equal angles at the intersection point. Therefore the statement is true.

ΔCEG ~ ΔFDG is also true because we know that the triangles share an angle and have proportional sides.

The answer above is in response to the full question below;

In the diagram of circle A shown below , chords CD and EF intersect at G, and chords CE and FD and drawn

Which statements is not always true?

a. CG ≅ FG    

b. CE/EG = FD/ DG

c. ∠CEG ≅ FDG  

d. ΔCEG ~ ΔFDG

Find more exercises on intersecting triangles;

https://brainly.com/question/28008595

#SPJ1

The freezer chest has 20 cubic feet of space inside to hold frozen foods.

To find the amount of space inside the freezer chest, we need to calculate its volume. The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.

Using the measurements given, we can plug them into the formula and calculate:

V = 4 ft x 2.5 ft x 2 ft
V = 20 cubic feet

Therefore, there is 20 cubic feet of space inside the freezer chest to hold frozen foods.

More on freezer: https://brainly.com/question/27234071

#SPJ11

If buying three movie tickets and a popcorn, which costs $5.50, is the same price as buying two tickets snacks worth a total of 16.50, one movie ticket costs $2.20.

Let the cost of one movie ticket be represented by x.

According to the problem, buying three movie tickets and a popcorn costs $5.50, so we can set up the equation:

3x + $5.50 = 2y

where y is the cost of snacks.

Similarly, buying two tickets and snacks worth a total of $16.50 can be represented by the equation:

2x + y = $16.50

We can solve this system of equations by substituting the first equation into the second equation for y:

2x + (3x + $5.50) = $16.50

5x + $5.50 = $16.50

5x = $11

x = $2.20

To learn more about costs click on,

https://brainly.com/question/21948868

#SPJ1

"The probability that the first freshman to arrive will be seated at a round table is (5/13)."

To calculate the probability, we need to determine the total number of seats and the number of seats at round tables.

There are 8 rectangular tables with 6 chairs each, so the total number of seats at rectangular tables is 8 * 6 = 48.

There are 5 round tables with 4 chairs each, so the total number of seats at round tables is 5 * 4 = 20.

The total number of seats in the community center is 48 + 20 = 68.

The probability of the first freshman being seated at a round table is the number of seats at round tables (20) divided by the total number of seats (68), which gives us 20/68 = 5/17.

Therefore, the correct answer is option C: 5/17.

In conclusion, the probability that the first freshman to arrive will be seated at a round table is 5/17. This is obtained by dividing the number of seats at round tables by the total number of seats in the community center.

To know more about probability refer here:

https://brainly.com/question/31828911

#SPJ11

The correct options are: A and D

Streets 2 and 3 are parallel and Street 1 is intersecting it

Parallel lines are two or more straight lines that continue indefinitely without ever crossing each other, despite their extended lengths. They have an equal inclination and remain the same distance apart at all times. Consequently, intersections will never occur between them.  

On the contrary, if non-parallel lines exist, they intersect to create one point, famously known as the 'point of intersection'. This specific point supplies the solution to the system of equations formed by the two lines.

Hence, we can see from the given image that Streets 2 and 3 are parallel and Street 1 is intersecting it

Read more about parallel lines here:

https://brainly.com/question/16742265

#SPJ1