a survey of 500 high school students was taken to determine their favorite chocolate candy. of the 500 students surveyed, 118 like snickers, 185 like twix, 179 like reese's peanut butter cups, 60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups, and 17 like all three kinds of chocolate candy. how many students like snickers, but not twix or reese's peanut butter cups? a) 118 b) 101 c) 100 d) 18 e) 83 f) none of the above.

The equations for the functions are f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the two given points for f, we can find the slope:

m = (y2 - y1) / (x2 - x1)

m = (-6 - (-2)) / (-3 - (-9))

m = -4 / 6

m = -2/3

Let's use the point (-9, -2):

y - (-2) = (-2/3)(x - (-9))

y + 2 = (-2/3)(x + 9)

Multiplying both sides by 3 to get rid of the fraction:

3y + 6 = -2x - 18

3y = -2x - 24

y = (-2/3)x - 8

So the equation for f is:

f(x) = (-2/3)x - 8

To find the equation for g, we can use the fact that the y-intercept is 6 greater than the y-intercept of f. So if the y-intercept of f is b, then the y-intercept of g is b + 6.

f(x) = (-2/3)x - 8

0 = (-2/3)x - 8

2/3 x = -8

x = -12

The x-intercept of both f and g is -12.

Now we can use the y-intercept and x-intercept to write the equation for g. The slope of g is the same as the slope of f, which is -2/3.

y - (b + 6) = (-2/3)(x - (-12))

y - b - 6 = (-2/3)(x + 12)

Multiplying both sides by 3 to get rid of the fraction:

3y - 3b - 18 = -2x - 24

3y = -2x + 3b - 6

y = (-2/3)x + (3/3)b - 2

y = (-2/3)x + b - 2

So the equation for g is:

g(x) = (-2/3)x + b - 2

We know that the x-intercept of g is -12, so we can plug that in and solve for b:

0 = (-2/3)(-12) + b - 2

0 = 8 + b - 2

b = -6

So the y-intercept of g is -6 + 6 = 0.

Therefore, the equation for g is:

g(x) = (-2/3)x - 2

Hence , the equations for f and g are: f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2

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Answer:

1. 1

2. 1

Step-by-step explanation:

Step 1

recall the eqn of a line y = mx + c

where m is the slope

step 2

compare you eqn given with the eqn y = mx + c

y = mx + c

y = 1 x + 17

then m = 1 which is slope.

both qns follows the same procedure

Answer:

64822

Step-by-step explanation:

Half-life model:

            [tex]P=P_o* \left(\frac{1}{2}\right)^{\frac{t}{D}}[/tex]

[tex]P_o[/tex] is the initial value, D is the time taken for the quantity to reduce half-life and t is the given time period.

       [tex]\sf P_o = 259,288 \ grams\\\\D = 1 \ hour\\\\t = 2 \ hours[/tex]

            [tex]P = 259,288*(\frac{1}{2})^\frac{2}{1}\\\\P = 259,288*(\frac{1}{2})^2\\\\P = 259,288*\frac{1}{4}\\\\P = 64822[/tex]

a) 90° counterclockwise about the origin

How can a rectangle be rotated?

A shape with rotational symmetry is a rectangle, for instance. When a rectangle is rotated around its center, the shape and placement remain unchanged. The placement of the specified points is the only distinction. Rectangles are of order 2 because they have half-turn symmetry.

When rectangle ABCD is rotated 90° counterclockwise about the origin , the vertex of 'A' in rectangle ABCD is (2,1) becomes (-1,2) in rectangle A'B'C'D'.

Therefore when rectangle ABCD is rotated we get rectangle A'B'C'D'.

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The equations that are  quadratic in form are:

x4 – 6x2 – 27 = 0

6(2x + 4)2 = (2x + 4) + 2

6x4 = -x2 + 5

The concept that is been used here is quadratic functions which can be written in three ways  :

Where  vertical line x = h and a not equal to zero, Hence we can see that the three selected options above followed the concept that is decribed as the quadratic function.

Therefore, the first, fourth and fifth options are correct.

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Answer:

A, D, E

Step-by-step explanation:

The angle the road makes is 3.43°

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

A 6% downgrade means that for every 100 units of horizontal run.

The vertical height decreases by 6 units.

The grade has a downward angle of

tan⁻1(6/100) = 3.43°

Hence, the angle the road makes is 3.43°

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Answer:

(8, 9 000)

Step-by-step explanation:

The transformation of g(x) = 3(2)⁻ˣ+2   from the parent function f(x) = 2ˣ    will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up,

What is a transformation function?

A function that transforms one function or graph into another, typically a related function or graph, is called a transformation function.

How to convert the parent function into the transformation function?

The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.

Here, we have

Transformation Function - g(x) = 3(2)⁻ˣ+2

Parent Function - f(x) = 2ˣ

To convert the parent function into the transformation function, we will follow some steps:

Hence, the transformation of g(x) = 3(2)⁻ˣ+2   from the parent function f(x) = 2ˣ   will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up.

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The ratio of c and 10 is c:10.

According to the question,

We have the following information:

We have one variable and one number which are c and 10 respectively.

Now, we already know that ratio can be simply understood as division. So, to find the ratio of c and 10 we will divide c by 10. We also know that a variable can not be divided by a number.

(For example, x can not be divided by 20.)

So, we will replace the sign of division by that of the ratio.

c/10

c:10

Hence, the ratio of c and 10 is c:10.

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In the given equation, the value of n is (p - k - m).

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given an equation, p = n + k + m

Solving for n, we get

n = p - k - m

Hence, In the given equation, n = p - k - m

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Answer:

  124.2 miles

  ∠310.1°

Step-by-step explanation:

You want to know the bearing and distance to the airport from a plane that is 95 miles east and 80 miles south of it.

The Pythagorean theorem or the distance formula can be used to find the distance to the airport.

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((95 -0)² +(-80 -0)²) = √(9025 +6400) = √15425

  d ≈ 124.197 . . . . miles

The plane is about 124.2 miles from the airport.

The reference angle with respect to the +y axis can be found using the tangent relation.

  Tan = Opposite/Adjacent

  tan(α) = 95/80 = 19/16

  α = arctan(19/16) ≈ 49.9° . . . . . . CCW from +y axis

The bearing angle is measured clockwise from the +y axis (north), so is ...

  bearing = 360° -49.9° = 310.1°

The bearing to the airport is 310.1°.

__

Additional comment

Some navigators would refer to the bearing as N 49.9° W.

Less commonly, it might be referred to as W 40.1° N. Usually, N and S are the reference directions, with the modification being E or W from there. The less common usage might be chosen if an angle less than 45° is wanted.

The bearing is often reported to the nearest degree, without any degree symbol, as N50W.

The value of the equation y(t) at y(25) is 150

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Equations can be linear, quadratic or polynomials.

if y(t) = -14t + 500

The y(25)  means substitute t = 25 into the equation

y(25) = -14(25) + 500

y(25) = -350 + 500

y(25) = 150

In conclusion, the value of y(25) is 150

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125° is the  angle of CBD

An angle pair that forms a straight line is referred to as a straight angle pair. This pair's sum of any two or more angles is always equal to 180°.

A straight angle has a 180° angle.

The two angles are from a straight line, and they sum to 180 degrees.

A + B + C = 180

8x -41+ 9x+17 = 180

Conjoin similar terms

17x -24 = 180

24 more on each side

17x -24+24 = 180 +24

17x = 204

multiply by 17

17x/17 = 204/17

x =12

We desire CBD angled.

CBD = 9x+17

= 9*12+17=108+17

= 125

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The distance between the two points (5,6) and (10,12) is [tex]\sqrt{61}[/tex]

What is the distance between two points formula?

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a standard formula to calculate the distance between two points. This equation can calculate the separation between any two locations on an x-y plane.

Solution explained:

First, Write the distance formula:

[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]

Now,

Substitute (5,6) and (10,12) into [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex] :

[tex]\sqrt{(10 - 5)^{2} + (12 - 6)^{2}}[/tex]      Calculate

[tex]\sqrt{(5)^{2} + (6)^{2}}[/tex]                      Calculate

[tex]\sqrt{25 + 36}[/tex]                            Calculate

Hence. the distance between points (5,6) and (10,12) is [tex]\sqrt{61}[/tex].

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Yes, he can mow the lawn in 2 hours.

We can define the work done as, a work done in a given period of time.

Given that, Theo mows a lawn. After working for 1 3/5 hours, he has mowed 7/9 of the lawn

In [tex]1\frac{3}{5}[/tex] hours he mows 7/9 part of lawn

Therefore, in 8/5 hours he is mowing 7/9 part of lawn

In 1 hour = 7/9*5/8 = 35/72

In 2 hours = 35/72*2 = 35/36 ≈ 1

Hence, Yes, he can mow the lawn in 2 hours.

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The total number of students at library using part part whole model is 13.

What is part part whole model ?

  The idea that numbers may be divided into parts, often known as the part-whole model or part-part-whole reasoning, is one that can be used to the study of mathematics. The relationship between the entire number and its component components will be clear to children utilising this model, which will aid learners in connecting addition and subtraction.

Here Number of student who leave library = 6

Number of students who stay at library = 7

Here we have to take  Number of student who leave library as one part and Number of students who stay at library as another part . Then

Total number of students at library at start = 6+7 = 13.

The part part whole model like,

=>        Total = 13

Part=6              Part=7

Hence the Total number of students is 13.

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The length of the shortest ladder is 16.64 ft.

In triangle ABC, using Pythagoras theorem

[tex]AC^{2} = AB^{2} + BC^{2}[/tex]  OR

[tex]L^{2} = h^{2} + (x+4)^{2}[/tex]       .....(1)

We also have similar triangles if we consider:

△ABC and △DEC

Which gives us the proportional relationship:

AB:DE = BC:EC

or    h/8 = (4+x) / x

h = 8( 4+x) /x      

Substituting this last expression for h into Eq [1] we get:

[tex]L^{2} = \frac{(8(x+4))^{2} }{x^{2} } + (x+4)^{2}[/tex]

Our aim is to now minimize L wrt x, and this involves looking for critical points of the derivative, so differentiation wrt x we get:

[tex]2L\frac{dL}{dx} = 2( 8 + \frac{32}{x} ) (-\frac{32}{x^{2} } ) + 2(x+4)[/tex]

At a critical point the derivative is zero and so we have the equation:

         =  [tex]2 (x + 4) ( 1 - \frac{256}{x^{3} } ) = 0[/tex]

From here we can find the value x :

x + 4 = 0                                                            1 - [tex]\frac{256}{x^{3} }[/tex]  = 0

x = -4                                                                 x  = [tex]\sqrt[3]{256}[/tex]

We require x > 0 so we neglect the -ve solution and only take +ve solution

therefore the minimum height of the ladder can be given by putting the value of x in eqn 1.

[tex]L^{2} = ( 8 + \frac{32}{\sqrt[3]{256} } )^{2} + ( \sqrt[3]{256} +4) ^{2}[/tex]

L² = 277.14

L = 16.64 ft

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Answer: 31, 33, 35

Step-by-step explanation:

The graph that represents the equation y - 4.5 = 2.5(x - 5) is the third graph

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, y - 4.5 = 2.5(x - 5).

y - 4.5 = 2.5x - 12.5.

y = 2.5x - 8.

Now, to determine the graph we'll choose some random values of x for which we'll have different values of y.

When x = - 1 , y = - 10.5 ⇒ (-1, -10.5 ).

When x = 0 , y = - 8 ⇒ (0, - 8).

When x = 1 , y = -5.5 ⇒ (1, -5.5).

When x = 2 , y = -3 ⇒ (2, -3).

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Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

As given in the question,

Given equation is :

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x

Simplify the original equation to get the equivalent equation

Least common multiple is 2 and 2x is equal to 2x

Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is Equivalent to the proportion is given by:

( x + 1) / 2x = (x² -7x +10)/4x

Therefore, original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.

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Answer:

23%

Step-by-step explanation:

We can create two equations:

\[m = \frac{1}{5}(A - s)\]\[s  = \frac{1}{20}(A - m)\]

Substituting we get:

\[m = \frac{1}{5}(A - \frac{1}{20}(A - m))\]which yields:

\[m = \frac{19}{99}A\]

Now we can find s and we get:

\[s = \frac{4}{99}A\]

Since we want to find what fraction of $A$ did Roger pay for his movie ticket and soda, we add $m$ and $s$ to get:

\[\frac{19}{99}A + \frac{4}{99}A \implies \boxed{\text{(D)}\ 23\%}\]

Ana and Bonita were born nn year apart and its value of nn is 12.

Here we have to find nn which difference in the year in which Ana and Bonita were born.

Let x be the age of Ana and y be the age of Bonita.

It is given that last year Ana was 5 times as old as Bonita so from this statement we get the first equation:

x - 1 = 5(y -1)

x -1 = 5y - 5

5y -x = 4--------(1)

The second statement is Ana is square of Bonita's age. From this we get another equation:

x = y²-----------(2)

Putting equation 2 in equation 1 we get:

5y - y² = 4

y² - 5y +4 = 0

y² - 4y - y + 4 = 0

y(y-4) -1(y -4) = 0

(y - 4)(y -1) = 0

y = 4,1

As x = y²

x = 4² = 16 or x = 1² =1

We cannot take 1 as there is a difference in their age

So we get x = 16 and y =4

So the difference in their age = 16-4= 12

Therefore we get the value of nn as 12.

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Answer: D

Step-by-step explanation:

It can take 3 years that a physics major to spend doing post-graduate research

Given that,

A physics professor is curious about the proportion of physics majors who will pursue post-graduate study during the coming years. He has the probability distribution shown below. x P(x) x*P (x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05

To find P(X<=3)

P(X<=3)=P(X=0,1,2,3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

            = 0.35+0.20+0.15

            = 0.7

P(X<=3)=0.7

Hence, A physics major may need to spend three years conducting post-graduate research. and the probability that a physics major will spend no more than three years conducting post-graduate research is 70% or 0.7

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If a country's public debt in 2009 was $11,982,000,000,000 and its budget for 2010 was $101,347,000,000 in deficit, the public debt in 2010 is $12083347000000.

As given

if the public debt of a country in 2009 was $11,982,000,000,000 and the budget for 2010 was in deficit by $101,347,000,000 .

Total public debt in 2010 = Public debt in 2009 + Amount by which 2010 budget deficit .

= $ 11982000000000 + 101347000000

= $ 12083347000000

Therefore the public debt in 2010 is $12083347000000.

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The percentage increase in the area of the building from its initial space is 35% of the increase. Hence, option A is correct.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the data provided in the question,

The initial area of the building = 12,500

Increase in area of building = 16875

The percentage increase in the area will be,

% increase = (16875 - 12500)/12500 ×100

⇒  4375/12500 × 100

% increase = 35%

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In 286 ways are there to distribute seven identical apples and six identical pears to three distinct people.

There are 7 identical apples and 6 identical pears.

So total number of fruits here = 7+6 = 13 identical fruits

The number of ways to distribute 13 fruits in three distinct people is given by [tex]=^{13}C_3=286[/tex] ways.

Hence the number of ways is 286.

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Answer:

1. 10

Step-by-step explanation:

1. 20% of 50

[tex] \frac{20}{100} \: \: \: \times \: \: \: 50 \\[/tex]

=

[tex] \frac{1000}{100} [/tex]

= 10