Which is true about the relationship between 1 inch and 1 foot? A. 1 inch is 12 times as long as 1 foot. B. 1 foot is 12 times as long as 1 inch. C. 1 foot is 6 times as long as 1 inch. D. 1 inch is 6 times as long as 1 foot.

Answer:

If the zeroes of a quadratic function are -1 and 6, then its factored form is:

(x + 1)(x - 6) = 0

Expanding the left side:

x^2 - 5x - 6 = 0

So the quadratic function in standard form is:

f(x) = x^2 - 5x - 6

Answer:

f(x) = x^2 - 5x - 6

Step-by-step explanation:

To create a quadratic function with zeroes -1 and 6, we can start by using the zero product property to write out the factors of the equation:

(x + 1)(x - 6) = 0

Expanding the factors, we get:

x^2 - 5x - 6 = 0

This quadratic equation is in standard form with a leading coefficient of 1. Therefore, the quadratic function with zeroes -1 and 6 is:

f(x) = x^2 - 5x - 6

This function can also be graphed on the coordinate plane as a parabola with a vertex at (2.5, -10.25) and its axis of symmetry at x = 2.5. The graph would intersect the x-axis at -1 and 6, confirming that these are the zeroes of the function.

The ratio of the volume of both spheres is: 1/(24√3)

The formula for the volume of a sphere is expressed as:

V = ⁴/₃πr³

where:

r is radius

V is volume

We are told that the radii of the two spheres have a ratio of 1:2√3. Thus:

Volume of sphere A/Volume of sphere B = (1:2√3)³

= 1/(24√3)

Read more about Volume of sphere at: https://brainly.com/question/10171109

#SPJ1

f(4) = 537. and f(-3) = 363.  To find f(-3), we replace x with -3 in the expression similarly for x=4.

what is expression  ?

In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.

In the given question,

To find f(-3), we replace x with -3 in the expression:

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

= 3(81) - 4(-27) + 3(9) + 15 - 3

= 243 + 108 + 15 - 3

= 363

Therefore, f(-3) = 363.

To find f(4), we replace x with 4 in the expression:

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

= 3(256) - 4(64) + 3(16) - 20 - 3

= 768 - 256 + 48 - 23

= 537

Therefore, f(4) = 537.

To know more about expression , visit:

https://brainly.com/question/14083225

#SPJ1

The expression Negative 3 6/7 times negative 3 1/3 has a value of -12 6/7

We have the following statement as the given parameter

Negative 3 6/7 times negative 3 1/3

Next, we rewrite the above statement using numbers and operators

-3 6/7 * 3 1/3

The above statement is a product expression that multiplies the values of -3 6/7 and 3 1/3

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

-3 6/7 * 3 1/3 = -27/7 * 10/3

Evaluate

-3 6/7 * 3 1/3 = -9/7 * 10

Rewrite as

-3 6/7 * 3 1/3 = -90/7

Simplify

-3 6/7 * 3 1/3 = -12 6/7

This means that the value of the expression is -12 6/7

Read more about expression at

brainly.com/question/15775046

#SPJ1

The value for the trigonometric expression cos(A+B) is (5√7 - 288)/325

Explain trigonometry.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It includes the study of trigonometric functions such as sine, cosine, and tangent, which are used to calculate unknown angles or sides of a triangle. Trigonometry has many practical applications in fields such as engineering, physics, and navigation.

According to the given information

We can use the trigonometric identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) to find cos(A + B).

Since cos(A) = -5/13 and A is in Quadrant II, we can use the Pythagorean identity sin²A + cos²A = 1 to find sin(A). Solving for sin(A), we get sin²A = 1 - cos²A = 1 - (-5/13)² = 144/169. Since A is in Quadrant II, sin(A) is positive, so sin(A) = √(144/169) = 12/13.

Similarly, since sin(B) = 24/25 and B is in Quadrant II, we can use the Pythagorean identity to find cos(B). Solving for cos(B), we get cos²B = 1 - sin²B = 1 - (24/25)² = 7/625. Since B is in Quadrant II, cos(B) is negative, so cos(B) = -√(7/625) = -√7/25.

Substituting these values into the identity for cos(A + B), we get:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

          = (-5/13)(-√7/25) - (12/13)(24/25)

          = (5√7)/(13*25) - (12*24)/(13*25)

          = (5√7 - 288)/(13*25)

          = (5√7 - 288)/325

To know more about trigonometry visit

brainly.com/question/26719838

#SPJ1

Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

What is the Pigeonhole Principle?

The Pigeonhole Principle is a fundamental concept in combinatorics, which is a branch of mathematics that deals with counting and analyzing the properties of sets of objects. The principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

We can solve this problem using the Pigeonhole Principle, which states that if n+1 objects are distributed among n boxes, then there is at least one box that contains two or more objects.

In this case, we want to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to find the minimum number of T-shirts that we must take out of the bag to guarantee this.

Let's consider the worst-case scenario, where we take out all the T-shirts that are of one size or one color.

If we take out all 18 small red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color (since we could still get a small black T-shirt).

Similarly, if we take out all 19 small black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 13 large black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 15 large red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to take out at least 19 T-shirts to be sure that we have at least two T-shirts that differ only by size or only by color. (We add one to the largest number of T-shirts of one color or size.)

Therefore, Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

To learn more about the Pigeonhole Principle visit:

https://brainly.com/question/13982786

#SPJ1

Answer:

Here

Step-by-step explanation:

The volume of a rectangular prism is found by multiplying the length, width, and height.

Volume = Length x Width x Height

Volume = 11 ft x 8 ft x 4 ft

Volume = 352 cubic feet

The surface area of a rectangular prism is found by adding up the areas of all six faces.

Surface area = 2lw + 2lh + 2wh

Surface area = (2 x 11 ft x 8 ft) + (2 x 11 ft x 4 ft) + (2 x 8 ft x 4 ft)

Surface area = 176 + 88 + 64

Surface area = 328 square feet

Therefore, the volume of the rectangular prism is 352 cubic feet and the surface area is 328 square feet.

1. The equation for the function is defined as follows: g(x) = (1/3)^x - 2.

2. The range of the function is given as follows: The set of real numbers less than -5.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

For item 1, the function has an horizontal asymptote at y = -2, hence it is defined as follows:

y = a(1/3)^x - 2.

When x = 0, y = -1, hence the parameter a is obtained as follows:

-1 = a - 2

a = 1.

Thus the function is:

g(x) = (1/3)^x - 2.

For item 2, we have that the function is:

Hence the range of the function is given as follows:

The set of real numbers less than -5.

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Answer: A

Step-by-step explanation: cuz of the

pie chart

Answer: x = -11

Step-by-step explanation:

Sub in y= 3-1/2x into 3x+4y=1 for y, and solve for x.

[tex]3x+4(3-\frac{1}{2}x) =1\\3x + 12 - 2x =1\\\\\ x = -11[/tex]

For pythagorean theorem  the triangle is a 3, 4 ,5 triangle 15 would be the length 5, and 9 would be the lenght 3. So we would multiply each side to getthe answer your lookin for. Which the third side would be, I think im right, i just did this in my head but im only 11 so dont bully me plsssss

ANSWER 12

The equation for the circle graphed in the coordinate axis is:

(x - 5)^2 + (y - 6)^2 = 16

Remember that the equation for a circle whose center is at (a, b) and has a radius R is.

(x - a)^2 + (y - b)^2 = R^2

On the graph, we can see that the center of the circle is at (5, 6), and the radius of the circle is R = 4 units. Then the equation for the circle in the graph is:

(x - 5)^2 + (y - 6)^2 = 4^2

(x - 5)^2 + (y - 6)^2 = 16

That is the equation we wanted to find.

Learn more about circles at:

https://brainly.com/question/1559324

#SPJ1

Answer: So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.

Step-by-step explanation:

Let O be the center of the circle, and let A and B be the points of tangency of the two tangents with the circle. Since OA and OB are radii of the circle, they have the same length of 8 centimeters.

Let C be the vertex of the angle formed by the two tangents. Since the tangents are perpendicular to the radii at the points of tangency, we have that angle AOC = angle BOC = 90 degrees.

Since the measure of the angle formed by the two tangents is 80 degrees, we have that angle AOB = 180 - 80 - 80 = 20 degrees.

Let D be the foot of the perpendicular from C to line AB. Then angle OCD = 90 - 20/2 = 80 degrees, so triangle OCD is an isosceles triangle. Therefore, we have that OD = OC = 8 centimeters.

Finally, since triangle OCD is a right triangle, we can use the Pythagorean theorem to find the length of CD. We have:

CD^2 = OD^2 - OC^2 = 8^2 - 8^2 = 0

Therefore, CD = 0 centimeters.

So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.

Answer:

To determine the number of students who voted for Candidate C, we need to first find what percent of the total votes they received. Looking at the graph, it appears that Candidate C received approximately 40% of the votes.

To find out how many students this represents, we can set up a proportion:

40% = C/150

Where C is the number of votes received by Candidate C.

To solve for C, we can cross-multiply:

0.4 x 150 = C

C = 60

Therefore, 60 students voted for Candidate C.

Charlotte's mistake was assuming that the percentage of votes for Candidate C directly corresponded to the number of students who voted for them. It's possible that more than one student voted for each candidate, and the percentage of votes represents the proportion of all votes each candidate received.

To graph the solution set to the given system of inequalities, we first need to graph the functions f(x) = x^2 - 2 and g(x) = -x^2 + 5.

The graph of f(x) is a parabola that opens upward and has its vertex at (0, -2). The graph of g(x) is also a parabola, but it opens downward and has its vertex at (0, 5). We can plot these two graphs on the same coordinate plane as follows:

[Insert image of two parabolas on a coordinate plane]

Next, we need to shade the regions of the graph that satisfy the given inequalities. The first inequality y > x^2 - 2 represents the region above the parabola f(x) but below the line y = infinity. The second inequality y ≥ -x^2 + 5 represents the region at or above the parabola g(x). The solution set is the intersection of these two regions.  

The shaded region represents all the points (x, y) that satisfy both inequalities, and therefore, the solution set to the system of inequalities.

Answer:

45% = 0.45

(you do this by bringing the decimal over 2 places)

multiply $55 and 0.45 to get $24.75

final answer = $24.75

The equation to calculate the cost of her shoes without shipping included is: x = 55.25

Let x be the cost of Carly's shoes.

The problem states that the total cost of her purchase (including shoes and shipping) is $60.75, so we can set up the equation:

x + 5.50 = 60.75

To find the cost of her shoes without shipping, we need to isolate x. We can do this by subtracting 5.50 from both sides:

x + 5.50 - 5.50 = 60.75 - 5.50

Simplifying:

x = 55.25

Therefore, the equation to calculate the cost of her shoes without shipping included is: x = 55.25

Read more about equation at

https://brainly.com/question/18831322

#SPJ1

The area of the rectangle is 27/70 square feet.

The area of a rectangle is given by the formula:

Area = base x height

Plugging in the given values, we get:

Area = (3/7) x (9/10)

Simplifying, we get:

Area = (27/70) square feet

Therefore, the area of the rectangle is 27/70 square feet.

More on the area of rectangles can be found here: https://brainly.com/question/20693059

#SPJ1

The 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.

(a) The point estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 0.09, which is equal to 27/300.

(b) The sampling error at 98% confidence level for the estimate of the population proportion can be calculated using the following formula:

Sampling error = z*(standard deviation/square root of sample size)

Where z is the critical value at 98% confidence level, which can be found using a standard normal distribution table or calculator. For a 98% confidence level, the z value is 2.33.

Substituting the values, we get:

Sampling error = 2.33*(sqrt(0.09*0.91/300)) = 0.049 or 4.9%

Therefore, the sampling error at 98% confidence level for the estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 4.9%.

(c) The 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 can be calculated using the following formula:

Confidence interval = point estimate ± (z*standard error)

Where point estimate is 0.09, z is the critical value at 98% confidence level which is 2.33, and standard error is the standard deviation divided by the square root of sample size.

Substituting the values, we get:

Confidence interval = 0.09 ± (2.33*sqrt(0.09*0.91/300)) = 0.09 ± 0.114 or (0.026, 0.154)

Therefore, the 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is between 0.026 and 0.154.

(d) After the menu update, the sample mean of the calories of the above sample can be calculated as follows:

New sample mean = 0.96 * 550 = 528

The sample standard deviation after the change is still 40, assuming the variability of calories is not affected by the menu update.

To construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change, we can use the following formula:

Confidence interval = sample mean ± (t*standard error)

Where t is the critical value at 90% confidence level with degrees of freedom (df) = sample size - 1. Using a t-distribution table or calculator with df = 299, we find that t = 1.645.

The standard error can be calculated as follows:

Standard error = standard deviation/sqrt(sample size) = 40/sqrt(300) = 2.31

Substituting the values, we get:

Confidence interval = 528 ± (1.645*2.31) = 528 ± 3.8 or (524.2, 531.8)

Therefore, the 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.

Learn more about confidence interval at https://brainly.com/question/15712887

#SPJ1

The probability that 3 boys are selected for the relay team given that the first election was a girl is approximately 0.122, or 12.2%.

Let B represent the decision to select three boys for the relay team whereas A represents the scenario when a girl was chosen first.

P(B|A) is the conditional probability of B given A.

The Bayes theorem gives us:

P(B|A) is equal to P(A|B)*P(B)/P(A).

Given that the relay team consists of 3 boys, the probability that a girl would be chosen as the first team member is P(A|B). Therefore:

P(A|B) = 7/13 * 6/12 * 5/11 * 7/10 = 0.0871

P(B) represents the likelihood of choosing three males for the relay team in an arbitrary manner.

P(B) = (7C3 * 7C1) / (14C4) = 35/143

P(A) represents the likelihood that a girl will be chosen as the first team member without any restrictions.

P(A) = 7/14 = 1/2

Combining everything, we get the following: P(B|A) = P(A|B) * P(B) / P(A) = 0.0871 * 35/143 / (1/2) = 0.1220.122, or 12.2%.

To learn more about, probability click here:

brainly.com/question/30034780

#SPJ1

The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.

Linear function: y = 3x + 1

x y

3 10

5 16

7 22

9 28

The linear function is positive, which means that the airplane's altitude is increasing as it moves towards the right on the graph. In context, this means that the airplane is ascending as it moves away from the observer towards the rainbow.

The system of equations created by the two functions is:

y = -x^2 + 19

y = 3x + 1

By substituting y in the second equation with the first equation, we get:

-x^2 + 19 = 3x + 1

Solving for x, we get:

x = -2 or x = 5

Substituting these values of x back into either of the equations, we get the corresponding values of y:

(-2, 7) and (5, 16)

These two solutions represent the points of intersection between the rainbow and the airplane's trajectory.

The domain of the rainbow is all real numbers, while the range is y ≤ 19. In context, this means that the rainbow can appear at any point in the observer's field of view, but its highest point is at y = 19.

All of the values in the domain and range make sense in this situation since they are within the physical limits of the observer's perception.

The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.

Learn more on linear functions here https://brainly.com/question/15602982

#SPJ1

Step-by-step explanation:

yes .. when you put x=2 y will be 3 .. you get it?

Francine can type 38 words per minute at this rate.

To find out how many words Francine can type per minute, we need to convert the time she took to type the words into minutes. Since there are 60 minutes in 1 hour, 1 hour and 30 minutes is equivalent to 1 × 60 + 30 = 90 minutes.

Next, we can use the formula:

words per minute = total words / total minutes

where "total words" is the number of words Francine typed (3,420) and "total minutes" is the time she took in minutes (90).

Substituting these values into the formula, we get:

words per minute = 3,420 / 90 = 38

To learn more about rate here:

https://brainly.com/question/23634231

#SPJ1

Thus, Riley's maximum distance from the starting position is 55 inches.

When an input value has a defined output value in reality, functions can be applied. For instance, how long a car has been driving affects how far it has travelled (the output) (the input).

Riley is swaying on a playground swing. As stated in the table, let t denote the passing of time in seconds and let f(t) denote Riley's horizontal displacement from her starting location in inches.

t:   0 ,0.75, 1.5, 2.25, 3,  3.75, 4.5,  5.25,   6,  6.75

f(t): 0 ,38.9, 55, 38.9, 0, -28.9, -55, -38.9, 0, 38.9

Recall that f(t) is positive when Riley swings closest to the starting position and negative when Riley swings in behind starting position.

So,

started from 0 and travelled distance of 55 inches in 1.5 seconds.

She is advancing by up to 1.5 seconds.

Then she begins to move backward, returning to her starting location after 3 seconds, and continuing to do so for an additional 4.5 seconds at a distance of -55.

Then begin to advance and return to the starting position after six seconds

Know more about the function:

https://brainly.com/question/11624077

#SPJ1