A machinist must cut 12 strips of metal that are each 2 ft 6 7/8 in. long. What is the total length needed in​ inches?

The equation for a parabola with a focus at (9, 0) and a directrix at y = -4 is y = (x - 9)^2 - 4.

Parabola is a type of curve that is symmetrical around a line called the directrix. It is an important conic section and is described by a quadratic equation.

This equation is derived from the equation for a parabola in standard form, which is y = a(x - h)^2 + k.
To find the equation for the parabola, we need to determine the values of a, h, and k. The focus of the parabola is (9, 0), so h = 9. The directrix of the parabola is y = -4, so k = -4. The value of a can be determined by the distance between the focus and the directrix, which is 4. So a = 1/4.
Putting these values together, we get y = (x - 9)^2 - 4.

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Answer:

288

Solution

(8x5)x4=160

(8x8)x2=64

160+64=288

The correct justification to each box. The answer is 2(y − 5) + 4 = 4 given.

What is meant by box ?

To the complete questions is;

Drag the correct justification to each box.

2(y−5)+4=4

2y−10+4=4 []

2y−6=4 []

2y=10 []

y=5 []

2y − 10 + 4 = 4 Distributive Property

2y − 6 = 4 Addition

2y = 10 Addition Property of Equality

y = 5 Division Property of Equality

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Answer: Cost = $70 + ($13)(n)

Step-by-step explanation: As we can see that the cost of the banquet is 70$ and for each person attending there will be a 13$ extra so as to model this problem, let's from an expression. The expression that models the problem can be written as -

Cost = $70 + ($13)(n)

In this expression 'n' will be the number of people attending the banquet at that time.

In this expression the 'x' will be the number of people attending the banquet. 'y' will be the cost of the banquet. y-intercept will be 70$, which is actually the cost of the banquet and the slope will be 13$ which is the cost for each person that will be attending.

Answer:

y=-140x I think so

Step-by-step explanation:

Answer: 90

Step-by-step explanation:

f(x) = 3x^2-2x+5

f(-5) = 3 x (-5)^2 - 2(-5) + 5

f(-5) = 3 x (-5)^2 - 2(-5) + 5

f(-5) = (3x25) +10 + 5

f(-5) = 75 + 15

f(-5) = 90

To find the value of f(-5) for the given function , we just need to put the value of x ( which is -5) in the given function. Let's do it!

[tex] \purple{\frak{\implies f(x) = 3x^2-2x+5}} \\ [/tex]

[tex] \sf \implies f(-5) = 3 \times (-5)^2 - 2(-5) + 5 \\ [/tex]

[tex] \sf \implies f(-5) = 3 \times (-5)^2 - 2(-5) + 5 \\ [/tex]

[tex] \sf \implies f(-5) = (3\times 25) +10 + 5 \\ [/tex]

[tex] \sf \implies f(-5) = 75 + 10+5\\ [/tex]

[tex] \purple{\frak{ \implies f(-5) = 90} }\\ [/tex]

The equation for an exponential function is f(x) = [tex](ab)^{x}[/tex], where a and b are constants, and the value of f(12) is 1144.14.

An exponential function is one that raises the independent variable to a power. It is typically stated as f(x) = [tex]b^{x}[/tex], where b is the base and x is the exponent. Several real-world phenomena, such as population expansion, radioactive decay, and compound interest, are modelled using exponential functions.

The equation for an exponential function is f(x) = [tex](ab)^{x}[/tex], where a and b are constants.

Since we know that f(3.5) = 10 and f(9.5) = 30, we can solve for a and b.

We first need to solve for b. We can use the equation: b = f(x) / f(x-1)

So, b = 30 / 10 = 3

Now, we can solve for a. We can use the equation: a = f(x) / [tex]b^{x}[/tex]

So, a = 10 / [tex](3)^{3.5}[/tex] = 0.093

Now, we can plug in the values for a and b and x = 12 into our equation to find f(12).

f(12) = 0.093 * [tex]3^{12}[/tex] = 1144.14

Therefore, the value of f(12), to the nearest hundredth, is 1144.14.

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The most appropriate graph to visualize the information is a PIE CHART. The frequency bar graph makes an independent bar of each fruit each, while it is ideal, it is not easy to identify the total or percentage of each.

Both charts could be used to make a display of the information given.

The frequency bar graph makes an independent bar of each fruit each, while it is ideal, it is not easy to identify the total or percentage of each.

The pie chart could be used to represent a whole of the 100 fruits as a single circle and divides the circle into parts based on the number of fruit belonging to each type including their respective percentages.

Also, since the number of fruits/types are just 5, using a pie chart gives a more accurate and readable visual representation of the information.

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Surface area overall of a cone is A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

Volume of a cone:

V = (1/3)πr2h

Cone's slant height:

s = √(r2 + h2)

Lateral surface area of a cone:

L = πrs = πr√(r2 + h2)

Cone (circle) base surface area:

B = πr2

Total surface area of a cone:

A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

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The recursive formula for the sequence is -1, -6, -36, -216

is -1[tex](-6)^{n-1}[/tex].

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16 is a geometric sequence.

We have,

-1, -6, -36, -216 is a geometric sequence.

The first term is -1,

The common ratio.

= -6/-1

= 6

Now,

The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].

So,

= -1[tex](-6)^{n-1}[/tex]

Thus,

The recursive formula is -1[tex](-6)^{n-1}[/tex].

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The gestation period of horses is 417% longer than the gestation period of cats.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

We have been asked to find percentage change of the gestation period of horses and cats.

First of all we will find difference between our two numbers.

Difference= 336-65

                 =271

Now we will find percentage of our difference with respect to gestation period of cats.

Percentage change = 271/65*100

                                 =416.92

Therefore, gestation period of horses is 417% longer than the gestation period of cats.    

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In the given situation the best way for the viewer to comprehend this information is through the graph's histogram.

The distribution of numerical data is roughly depicted by a histogram.

Karl Pearson was the person who first coined the phrase.

The first stage in creating a histogram is to "bin" (or "bucket") the range of values, divide it into a series of intervals, and then count the number of values that fall into each interval.

The bins are often defined as a series of discrete intervals that don't overlap.

The bins (intervals) must be close together and frequently, though not always, have the same size.

The graph's histogram would help the viewer understand this information the best.

Therefore, in the given situation the best way for the viewer to comprehend this information is through the graph's histogram.

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Correct question:

Suppose you want to make a visualization that shows how many students bought certain quantities of candy from the vending machine during the month of September. What chart would best convey this information to the person looking at the graph?

All circles are similar because their shape is same but sizes vary.

Similar figures are those figures which have the same shape, but sizes are different.

To prove the given statement, consider two circles C and C' with radius r and r' respectively.

r can be greater than or less than r'.

Circle C can be dilated to a certain value to get the circle C'.

The shape of both the circles remain same.

But the size is different.

This is the case for any arbitrary circles.

Hence all circles are similar.

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Based on the graph, the average number of feet per day is 0.25 per day.

To calculate the average using the information of the graph, let's identify the highest and lowest number:

Highest number:  200

Lowest number: 75

Now let's find the average: 200 +75 /2 = 125

This means that on average there was a change of 125 feet during the 400 days

Now using this number, let's find the average daily change:

Average = average change/number of days

125/ 400 = 2.5 feet per day

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Answer:

g(x)=x-2/x^2-9

If there is more than one value, separate them with commas.

Step-by-step explanation:

The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of pi radians

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Answer:

Your answer is 42x^2+27x-22

Step-by-step explanation:

Hope this helps :)

variables is a nominal, ordinal, discrete, or continuous variable.Nominal: Labels/categories. Ordinal: Order/ranking. Discrete: Whole numbers. Continuous: Any value in range

Nominal variable: A nominal variable is a type of variable that is used to name, label, or categorize particular attributes that are being measured. It is often used in survey research to represent different categories or groups.

Ordinal variable: An ordinal variable is a type of variable that is used to represent a specific order or ranking of values. It is frequently used when measuring psychological or social characteristics, such as job satisfaction or political opinions.

Discrete variable: A discrete variable is a type of variable that can only take on certain values, such as whole numbers. It is often used to count the number of specific events or occurrences within a given time period.

Continuous variable: A continuous variable is a type of variable that can take on any value within a given range. It is typically used to measure quantity or amount, such as the height or weight of an individual.

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1) There were 1.26 times as many assaults in Year 5 compared to Year 1

2) Graph B best represents the data.

What is Graph?

A graph is a structure that resembles a set of items in discrete mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Given that;

The data is most accurately depicted in bar graph B.

It allows for the following data observations:

In year 1, there were 235 assaults.

Year 1 saw 265 assaults, Year 2 saw 250 attacks, Year 1 saw 280 assaults, Year 1 saw 295 assaults, and Year 2 saw 260 assaults.

1)In the first year, there were 235 assaults, and by the fifth year, there were 295 assaults.

ratio = year5/year1 = 295/235 =1.26

Hence , there were 1.26 times as many assaults in Year 5 compared to Year 1

2) The total number of data points falls between 200 and 300.

Therefore, graph A, whose output value ranges from 0 to 300, is not truly necessary.

Graph B, on the other hand, uses the right range and has a step size of 10, which is also fairly accurate.

Therefore, Graph B best depicts the data.

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Answer:

x = 1/3 and x = -2

Step-by-step explanation:

3x² - 5 = -5x - 3

turn this into a quadratic equation by adding -5x and -3 to the other side

3x² + 5x - 2 = 0

factor:

(3x-1)(x+2) = 0

3x-1 = 0

x = 1/3   AND

x+2 = 0

x = -2

The solutions of the quadratic equation:

3x² - 5 = -5x - 3

are:

x = 1/3

x  = -2

Here we want to solve this quadratic equation:

3x² - 5 = -5x - 3

We can move all the terms to the left side to get:

3x² - 5 + 5x + 3 = 0

3x² +5x - 2  = 0

The solutions are given by the quadratic formula:

[tex]x = \frac{-5 \pm \sqrt{5^2 - 4*3*(-2)} }{2*3} \\\\x = \frac{-5 \pm7 }{6}[/tex]

Then the two solutions are:

x = (-5 + 7)/6 = 1/3

x = (-5 - 7)/6 = -2

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Answer:

10.58

Step-by-step explanation:

here we need to find out the value of x by Pythagoras theorem. By Pythagoras theorem in q right angled triangle the sum of squares of base and perpendicular is equal to the square of hypotenuse. so ,

h² = p² + b²

Now here ,

on using Pythagoras theorem,

h² = p² + b²

16² = 12² + x²

256 = 144 + x²

x² = 256 -144

x² = 112

x = √112

x ≈ 10.58 [ required answer]

and we are done!

-Rishabh

This is an experimental study.

This study demonstrates an experimental design, as the intervention (tutoring and study skills advice) was used to examine the impact it had on the test scores.

An experimental study is used to examine the effects of an intervention or treatment on a group of participants. In this case, the study involved two groups of algebra students, one of which was given additional help in the form of tutoring and study skills advice while the other was not. After a few weeks, the students took a test and the results of the two groups were compared. This study demonstrates an experimental design, as the intervention (tutoring and study skills advice) was used to examine the impact it had on the test scores.

This study demonstrates an experimental design, as the intervention (tutoring and study skills advice) was used to examine the impact it had on the test scores.

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Answer:

The answer would be [tex]x[/tex]=17 because the food cost 85% of Andy's bill, that is, $17.

Step-by-step explanation:

Since 15% of the $20 bill Andy paid was for drink, it means that (100−15)% of the same amount will be for food. Hence, the food came to 85% of the bill.The amount (x) Andy paid for food therefore is:

[tex]x[/tex]= 20 x 85/100

[tex]x[/tex]= 1 x 85/5

[tex]x[/tex] = 85/5

[tex]x[/tex] = 17

So, the answer would be 17$.

The probability of each combination occurring is 1/15.

Let G be the set of grandchildren, G={Connor, Declan, Lucas, Piper, Sedona, Zayne}.

We can use the formula of nP2 to calculate the possible outcomes of the two grandkids being selected, where n is the number of elements in the set G or 6:

6P2 = 6!/(4!2!) = (6 x 5)/2 = 15

Therefore, there are 15 possible combinations in which the two tickets to the holiday show could go to. These 15 combinations are:

Combination 1: Connor and Declan

Combination 2: Connor and Lucas

Combination 3: Connor and Piper

Combination 4: Connor and Sedona

Combination 5: Connor and Zayne

Combination 6: Declan and Lucas

Combination 7: Declan and Piper

Combination 8: Declan and Sedona

Combination 9: Declan and Zayne

Combination 10: Lucas and Piper

Combination 11: Lucas and Sedona

Combination 12: Lucas and Zayne

Combination 13: Piper and Sedona

Combination 14: Piper and Zayne

Combination 15: Sedona and Zayne

The probability of each combination occurring is 1/15.

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Answer: x= (5+√17)/(4) AND x=(5-√17)/(4)

Step-by-step explanation:

You subtract 5x to put it on the other side, so it's 2x^2-5x+1 and then use the quadratic formula. Hope this helps.

Answer:

1 inch = 9 yards

Step-by-step explanation:

Answer:desta's plum

Step-by-step explanation:

Desta's plum weighs 0.198 ounces more than Eddy’s plum.

Given that, Eddy’s plum weighs 3.042 ounces Desta's plum weighs 3.24 ounces.

We need to find whose plum weighs more.

How to subtract decimal numbers?

Subtracting decimals is similar to the usual subtraction of whole numbers. We just need to place the decimal numbers, one below the other, according to their place values along with the decimal point. In some cases the two given numbers are different. If needed, we change the given decimal fractions to like decimal fractions to make the subtraction easier. Two decimals are called decimal fractions if they have an equal number of decimal places.

Now, the weight of Desta's plum-the weight of Eddy’s plum=3.24-3.042

=0.198 ounce

Hence, Desta's plum weighs 0.198 ounces more than Eddy’s plum.

The relationship between the cup size and the cost is proportional and the constant of proportionality is 0.3.

At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $3.60 and a 16-ounce cup costs $4.80.

Let's find if the relationships of the variables are proportional.

proportional relationship are relationships between two variables where their ratios are equivalent.

Therefore, proportional relationship is rep[resented as follows:

y = kx

where

Hence,

3.6 = 12k

k = 3.6 / 12

k = 0.3

4.80 = 16k

k = 4.8 / 16

k = 0.3

Therefore, the constant of proportionality is 0.3

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Answer:

The relationship between the cup size and the cost is proportional and the constant of proportionality is 0.3.

Step-by-step explanation:

The Ferris wheel is 16.63 feet tall.

Angle of depression is the angle which is between a horizontal line and the line of sight which is pointed downwards.

We have a triangle formed here by the information given.

Angle of depression between the Ferris wheel and the friend on the ground = 61°

Distance of friend from the foot of the Ferris wheel = 30 feet

We have to calculate the height of Ferris wheel.

Let x be the required height.

tan 61 = 30 / x

x = 30 / tan 61

x = 30 / 1.804

x = 16.63 feet

Hence the height of the Ferris wheel is 16.63 feet.

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The 9.75 ft wide wall and the 5.75 feet window in the center, through the use of unit conversion

1. The space to fill 4 feet

2. 4 feet = 48 inches

3. 8 pictures

4. Tne new number of pictures with 10 inches width is 4 pictures

Unit conversion is the expression of the same quantity, using different a different unit of measurement

Part of the question obtained from a similar question includes;

The width of the wall Mr. Hamilton decorates with pictures = 9.75 ft

The width of the window at the center of the wall = 5 3/4 feet = 5.75 ft

Location of the window = The center of the wall

Location Mr. Hamilton will fill with the pictures = Left and right sides of the window

The width of each pictiure of a president = 6 inches

1. The length of the space Mr. Hamilton wants to fill with pictures = 9.75 ft - 5.75 ft = 4 ft.

2. The unit convertion factor from feet to cm is;1 ft = 12 inches

Therefore, 4 feet = 4 ft × 12 inches/ft = 48 inches

3. The number of pictures Mr. Hamilton will use, n, is therefore;

n = 48 inches/(6 inches/picture) = 8 pictures

The number of pictures Mr. Hamilton can use for decorating by placing pictures of presidents on the wall is 8 pictures

4. The responses to the questions if the dimensions of the picture are 10 inches are;

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