Use the line plot to answer the question.
What is the median number of trips taken to the food store in one week?
A. 1
B. 3
C. 1.5
D. 2

We can show that these data can be modeled using a linear function in the following manner:

a) We must compute the differences in the number of high school graduates in each year in order to model the data using a linear function. For instance, the difference between the 1993 and 1994 graduation rates is 5,479 - 5,410, or 69. This pattern of differences suggests that a linear function can be used to model the data.

The annual change in the number of graduates serves as the slope for the linear function. The slope, for instance, is 69 between 1993 and 1994 and 76 between 1994 and 1995. The slope for the linear function is, in general, the difference between the number of graduates in successive years, therefore it is the slope between graduates in consecutive years.

b) Y = mx + b, where y is the number of graduates, x is the year, m is the slope, and b is the y-intercept, is the formula for a linear function that represents the data. We need to know the values of m and b in order to calculate the formula for the linear function that describes the data.

We can use the slope between any two consecutive years to get the value of m. For instance, m = 69 since the slope from 1993 to 1994 is 69. The number of graduates in the first year of the data, which is the y-intercept, can be used to determine the value of b.

For instance, if the first year of the data is 1993 and that year had 5,479 graduates, then b = 5,479. Consequently, y = 69x + 5,479 is the equation for the linear function that models the data.

c) Functional notation can be used to indicate the number of high school graduates in 1994. The formula is y = 69x + 5,479, where x is the year and y is the total number of graduates. Therefore, y = 69(1994) + 5,479 = 137,123 is the total number of graduates in 1994. We may enter the numbers of x and b into the formula from section c to obtain y = 69 (1994) + 5,479 = 137,123.

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The missing reasons are

1. Corresponding Angle

2. Alternate Exterior Angle

We know, if a line intersects two parallel lines, the corresponding interior angles on the same side of the transversal will be congruent (equal).

1. Since CL || EK

Then, by the property of parallel line

<BFJ = <ADF (Corresponding Angle)

2. Since CL || EK

Then, by the property of parallel line

<EBH= <LDM (Alternate Exterior Angle)

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Answer:

A number

Step-by-step explanation:

The limit of h(x) as x approaches infinity is ∞, and as x approaches 0, is undefined due to division by zero.

x h(x)

1 2 + 2

2 1.41 + 1

4 2 + 0.25

8 2.83 + 0.125

16 4 + 0.0625

To find the limit of h(x) as x approaches infinity, we see that h(x) = √(x) + 2/x - 5. As x increases without bounds, the square root of x and 2/x both approach infinity, but the value of -5 is constant. Therefore, the limit of h(x) as x approaches infinity is infinite.

To find the limit of h(x) as x approaches 0, we see that h(x) = √(x) + 2/x - 5. As x approaches 0, the value of the square root of x approaches 0, and the value of 2/x approaches infinity. However, the value of -5 is constant. Therefore, the limit of h(x) as x approaches 0 is -5 + ∞, which is undefined.

The limit of h(x) as x approaches 0 is undefined.

You could also say that the function is not defined at x = 0, meaning that the limit as x approaches 0 does not exist.

It's worth noting that the original function is not defined when x=0 as we are dividing by x, so it's impossible to calculate the limit of this function at that point.

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A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

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The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

below

Step-by-step explanation:

<b = 90-55= 35

he added 90 to 35. that's the mistake

Answer:

So why are quadratic functions important? Quadratic functions hold a unique position in the school curriculum. They are functions whose values can be easily calculated from input values, so they are a slight advance on linear functions and provide a significant move away from attachment to straight lines.

Step-by-step explanation:

The slope of given line is -3 and the y-intercept of the line is -2.

A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity.

Here, we know that slope intercept form of straight line;

            y = mx + c

Given equation;

          y = -3x - 2

compare this equation with general equation, we get

    m = -3 and c = -2

Thus, The slope of given line is -3 and the y-intercept of the line is -2.

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Answer:

Graph the linear function described by the equation

y=-3x-2

Step 1: Identify the slope and y-intercept.

slope =

Step-by-step explanation:

Answer:

The tranformation ocurred in the graph is b.

Step-by-step explanation:

Because it is going inner, meaning the tranformation ocurred in the graph is b.

B is the correct answer. Vertical shrink. This is a very good example of a vertical stretch going inward.

Answer: A good way to get a small standard error is to use a large sample.

Step-by-step explanation:

In order to find the small standard error, there is always need of a complete set which is called the large sample.

If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.

Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!

-From a 5th Grade Honors Student

Answer:

42

Step-by-step explanation:

Heres the signifigance,

"The number 42 is, in The Hitchhiker's Guide to the Galaxy by Douglas Adams, the "Answer to the Ultimate Question of Life, the Universe, and Everything," calculated by an enormous supercomputer named Deep Thought over a period of 7.5 million years."

Hope this Helps

Answer:

42

Step-by-step explanation:

"The number 42 is, in The Hitchhiker's Guide to the Galaxy by Douglas Adams, the "Answer to the Ultimate Question of Life, the Universe, and Everything," calculated by an enormous supercomputer named Deep Thought over a period of 7.5 million years. "

Source: wikipedia

Answer:

16

Step-by-step explanation:

10÷5/8=16

Answer:

7

Step-by-step explanation: Trust me

Answer:

Calculate the average of the five original cards:

2+5+7+8+9=31

31/5 = 6.2

So, if a card was removed, the four remaining cards would have an average of 6, meaning that they would add up to 24.

31-x=24?

Subtract 31 from both sides: -x=-7

Divide by -1 on both sides: x=7

So, we know that 7 was removed.

Let me know if this helps!

Answer:

g^8

Step-by-step explanation:

The "." means multiplication. Therefore take g as common.

But, for the powers its different.  

When constants are being multiplied, the powers will be added together:

g^5 x g^3

=g^ 5+3

=g^8

If the constants were being added then the powers would hv been multiplied: g^5 + g^3

= g^5 x 3

=g^15

Similarly, if the constants were being divided then the powers would hv been substracted: g^5/g^3

=g^5-3

=g^2

And if the constants were being substracted the the powers would hv been divided: g^5 - g^3

=g^5/3

So, therefore ur answer is g^8.

Hope u understood :D

Answer:

B, C, and D

Step-by-step explanation:

A) 5 x 1/8 is 5/1 times 1/8 which is 5/8 (Incorrect)

B) 8 x 1/5 is 8/1 times 1/5 (multiply straight across and you get 8/5 (Correct)

C) 2 x 4/5 (again, it's 2/1 just multiply straight across and you are basically only multiplying the two numerators each time. Because 1 times 5 will always be 5) (Correct)

D) Correct because 4 times 2 is 8 which is over 5, hence, 8/5 (Correct)

E) 2 times 6 is 12 over 5 which is 12/5, not 8/5. (Incorrect)

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Answer:

B. {-5, -4, 2}

Step-by-step explanation:

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Answer:

x = 10

y = 1

DE = 7

AC = 14

Step-by-step explanation:

x + 2 = 24/2

x = 12 - 2

x = 10

y + 6 = x - 3

y = 10 - 3 - 6

y = 1

After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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Answer: 1/5 or 0.2

Step-by-step explanation:

STEP 1⇒1 1/5 = 1 · 5 + 1/5 = 5 + 1/5 = 6/5

STEP 2⇒6/5 - 2/5 = 6 - 2/5 = 4/5

STEP 3⇒4/5(-3/4) = 4 ·(-3)/5 · 4 = -12/20 = -3/4

STEP 4⇒-3/5 · 3 = -3 · 3/5 · 1 = -9/5

STEP 5⇒-9/5 ÷ (-9) = -9 · 1/5 · 9 = 9/45 = 1/5

Answer:

3/320

Step-by-step explanation:

Order of operations rule require that we perform work presented inside parentheses first.  

Working from left to right:  1 1/5 -2/5 = 6/5 - 2/5 = 4/5.  Then:

[(1 1/5−2/5)·(−3/4)3]÷(−9) becomes [(4/5)·(−3/4)3]÷(−9)

Note that the quantity (4/5)·(−3/4)3 is inside the square brackets and is thus next to be done.  Assuming that by (-3/4)3 you actually meant (-3/4)³, we end up with -27/64, and thus (4/5)·(−3/4)3 becomes (4/5)(-27/64), which reduces to -27/320.  

Going back to the result [(4/5)·(−3/4)3]÷(−9) above, we replace (4/5)(-3/4)³ with -27/320:  [-27/320]÷(−9).  Here we're dividing one negative number into another, which results in a positive quotient:  3/320

Answer: x = 1, x = -1

Step-by-step explanation:

\((3x^{2} -2) + (2x^{2} -6x+3)\\3x^2 -2 +2x^2 -6x+3\\5x^2-6x^2 +1\\-x^2 +1=0\\-x^2 = -1\\x^2=1\\\sqrt{x^2}=\sqrt{1} \\x = 1, -1\)

The interest rate is 11.05%.

What is the interest rate?

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

Here, we have

Given:  an investment of $5,000 to grow to $8,000 in 9 years if interest is compounded continuously.

We have to find the interest rate.

Investment = $5,000

Time(x) = 9 years

n = 12

Annual amount = $8,000

A = P(1+r/n)ⁿˣ

r = n(A/P)⁻ⁿˣ - 1

r = 12(8000/5000)⁻¹⁰⁸ - 1

r = 12(1.6)⁻¹⁰⁸ -1

r = 12(1.0043) - 1

r = 11.05%

Hence, the interest rate is 11.05%.

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Step-by-step explanation:

X= {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23}

P= {2,3,5,7,11,13,17,19,23}

Q= {2,4,6,8,10,12,14,16,18,20,22}

a= {2,3,4,5,6,7,8,10,11,12,13,14,16,17,18,19,20,22,23}

b= {2,}

c= we first find p'

p'={1,4,6,8,9,10,12,14,15,16,18,20,21,22}

c={4,6,8,10,12,14,16,18,20,22}

d=we do same here but we already have p' so we find for q'

q'={1,4,6,8,9,10,12,14,15,16,18,20,21,22}

d={1,4,6,8,9,10,12,14,15,16,18,20,21,22}

Answer:

The angle measure that is coterminal with the angle 7π/12 is 285°. So, the correct option is C.

In trigonometry, coterminal angles are two angles in standard position with the same terminal side. It's not hard to notice that two angles are coterminal if one angle is a multiple of 360° added or subtracted from the other. For example, if an angle is -750°, it is coterminal with an angle of 30°.

To find coterminal angles with a given angle, add or subtract any multiple of 360 degrees (for degrees) or 2π (for radians). In this case, to find the coterminal angle for the angle 7π/12, you need to add or subtract 2π until you get an angle that's between 0 and 2π.7π/12 is equal to (2*π + 3π/12). As a result, it is a full circle with a remainder of 3π/12, or π/4.

The number of radians must be between 0 and 2π (360°) to find the coterminal angle. The number of radians to subtract or add is obtained by evaluating the number of full circles between the two angles.285° is equal to 5π/6 (in radians).

To determine the coterminal angle, add 2π to the angle (which is the equivalent of a full circle) so that the number of radians is between 0 and 2π.285° + 360° = 645°

In radians, 645° is equal to 11π/6, which is equivalent to 285°. Therefore, 285° is the angle measure that is coterminal with the angle 7π/12.

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Answer:

105.6 ft

Step-by-step explanation:

1 acre = 43,560 ft²

2/3(43,560) = 29,040

x = width of the lot

Area = (275 ft)(x) = 29,040 ft²

x = 29040/275 = 105.6 ft

Answer:

It will make 4 90° turns, because each 1/4 turn or 15 minutes is 90°.

1a) One example of an acute triangle in art or architecture could be the triangular roof of a traditional Chinese pagoda. The triangular sails of a sailboat or the triangular shape of a musical instrument like a guitar or violin may also feature acute triangles.

A common example of a right triangle in architecture is the corner of a rectangular building or the shape of a doorframe. In art, right triangles can be found in geometric abstract art or in the perspective lines used to create depth in a painting or drawing.

For an example of an obtuse triangle in art or architecture, one could look at the shape of the great pyramids in Egypt. The triangular shape of the roof of an A-frame house or the shape of a triangle formed by intersecting curved arches in a cathedral could also be examples of obtuse triangles.

1b) i can't print it for you so just print what i said in 1a and find the angles using a protracter. if you dont know how to do that here is how:

1. Place the protractor at the vertex (corner) of the angle where the two lines meet.

2. Line up one of the sides of the angle with the baseline (zero line) of the protractor.

3. Read the degree value where the other side of the angle crosses the number scale on the protractor.

4. If the angle is acute (less than 90 degrees) or obtuse (more than 90 degrees), use the smaller angle formed by the two sides of the angle to measure.

1c) i can't find the angles for you but here is how to verify using exterior angle theorm: To use the exterior angle theorem to verify angle measurements, you need to first identify the exterior angle of the triangle in question. Then, you need to find the measures of the two opposite interior angles. Lastly, you add those interior angle measures together to see if they are equal to the measure of the exterior angle. If they are equal, then the measurement is verified. If not, then there may be an error in the measurements or the theorem may not apply to the particular situation. It's important to note that the exterior angle theorem applies only to triangles and not other polygons.

2a)here is how to: To construct a pair of congruent triangles using straightedge and compass , you need to follow the process of constructing congruent segments and congruent angles . To begin, draw a line segment and label it as the base of your triangle. Then, using the compass, draw arcs of the same radius from both endpoints of the base. These arcs will intersect at two points. From each point of intersection, draw a line segment to the opposite endpoint of the base. These two line segments will form the sides of your triangle. Repeat this process, but this time draw the base at a different angle to create a second congruent triangle.

2b: here is how to prove + example:

To prove that a pair of triangles are congruent, you need to show that they have the same size and shape. This can be done using several shortcuts in geometry, depending on the given information. Here is an example of how to use the SSS (side-side-side) congruence shortcut to prove that two triangles are congruent:

Given: Triangle ABC and triangle DEF, where AB = DE, BC = EF, and AC = DF.

To prove: Triangle ABC is congruent to triangle DEF.

Shortcuts: SSS congruence.

Proof:

Since AB = DE and BC = EF, we know that segment AC corresponds to segment DF, as they are the remaining sides of each triangle.

Therefore, triangle ABC and triangle DEF share three corresponding sides, namely AB, BC, and AC.

According to the SSS shortcut, if two triangles have three corresponding sides that are congruent, then the triangles are congruent.

Hence, triangle ABC is congruent to triangle DEF.

3a) here is how to: To construct an angle bisector using a straightedge and compass , first draw the angle using the straightedge. Then place the compass on the vertex of the angle and draw an arc that intersects both rays of the angle. Without changing the radius of the compass, put it on each of the points where the arc intersects the angle, and draw two more arcs. These two arcs should intersect at a single point on the bisector of the angle, and this is the point where the bisector should be drawn using the straightedge. Make sure to show all construction marks, including the original angle, the arc from the vertex, the two additional arcs, and the final bisector line.

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