Pam invested money into a small stock market account. After several years of continued growth, the table below shows how much her investment earned.
Investment Earnings

Years 1 2 3 4 5
Money Earned $31.25 $125 $500 $2,000 $8,000
Which of the following functions would best model the data above?

Answer:

The vertex form of a quadratic equation is:

[tex]f(x) = (x-3)^2+4[/tex]

the minimum value of f(x) is [tex]y=4[/tex]

Step-by-step explanation:

Given a quadratic equation of the form [tex]f (x) = ax ^ 2 + bx + c[/tex] then the x coordinate of the vertex is

[tex]x=-\frac{b}{2a}[/tex]

So for  [tex]f(x)=x^2-6x+13[/tex]

[tex]a=1\\b=-6\\c=13\\[/tex]

Therefore

The x coordinate of the vertex is:

[tex]x=-\frac{(-6)}{2(1)}[/tex]

[tex]x=3[/tex]

The y coordinate of the vertex is:

[tex]f(3)=(3)^2-6(3)+13[/tex]

[tex]y=f(3)=4[/tex]

By definition the minimum value of the quadratic function is the same as the coordinate of y of its vertex

So the minimum value  is [tex]y=4[/tex]

The vertex form of a quadratic equation is:

[tex]f(x) = a(x-h)^2+k[/tex]

Where

a is the main coefficient. [tex]a=1[/tex]

h is the x coordinate of the vertex. [tex]h=3[/tex]

k is the y coordinate of the vertex. [tex]k=4[/tex]

So the vertex form of a quadratic equation is:

[tex]f(x) = (x-3)^2+4[/tex]

Answer:

a.  [tex]f(x)=(x-3)^2+4[/tex]

b. The minimum value is 4

Step-by-step explanation:

The given function is: [tex]f(x)=x^2-6x+13[/tex]

We add and subtract half the square of the coefficient of x.

[tex]f(x)=x^2-6x+3^2-3^2+13[/tex]

This becomes: [tex]f(x)=x^2-6x+9-9+13[/tex]

The first three terms form a perfect square trinomial.

[tex]f(x)=(x-3)^2+4[/tex]

The function is now in the form:  [tex]f(x)=a(x-h)^2+k[/tex], where V(h,k) is the vertex.

Therefore the vertex is (3,4).

The minimum value  is the y-value of the vertex, which is 4.

Answer: Third and fifth option

3) The median is the number in the middle on an ordered set of data.

5) To find the middle of an even data set, find the average of the two middle numbers.

Step-by-step explanation:

Given a set of data ordered from lowest to highest, the median of the data is the number that is in the middle. In other words, it is a number x for which it is true that 50% of the data is greater than x and the other 50% of the data is less than x.

For example, for the following set of 7 data:

2, 3, [5], 8, 13

the median is 5.

If the data number is even, for example 10 data:

3, 5, 9, 12, [19, 21], 33, 35, 40, 69

The median is the average between the two data that are in the middle

[tex]\frac{19 +21}{2} = \frac{40}{2} = 20[/tex]

Note that the median only represents a partition of the ordered data set. Therefore, it is not affected by outlier. For example

2, 4, 4.5, 4.8, 5          Median = 4.5

2, 4, 4.5, 67, 1506     Median = 4.5

The median does not represent the difference between the highest and the lowest data.

Therefore the correct affirmations are:

3) The median is the number in the middle on an ordered set of data.

5) To find the middle of an even data set, find the average of the two middle numbers.

Answer:

[tex]b=\frac{g}{x} + \frac{5}{x^{3} } +\frac{1}{x^{2} }[/tex]

Step-by-step explanation:

[tex]10=\frac{5}{-2}-b(-2)^{2} +1\\\\\\9=\frac{5}{-2} -b(4)\\\\-18=5-b(4)\\\\-23=-b(4)\\\\\frac{-23}{4} =-b\\\\\frac{23}{4}=b\\\\\\b=\frac{23}{4}[/tex]

Answer:

QPR

Step-by-step explanation:

It is triangle QPR because of the order of corresponding angles.

if the perimeter of 1/4 of the circle is 7.14, then the full circle is 4(7.14) = 28.56.

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=28.56 \end{cases}\implies 28.56=2\pi r \\\\\\ \cfrac{28.56}{2\pi }=r\implies 4.55\approx r[/tex]

and the radius is the same on any location of the circle.

A quarter of a circle having a perimeter 7.14 feet has a radius of 4.55 feet.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

If a complete circle has a perimeter of 2πr, the quarter of a circle should have (2πr/4) = (1/2)πr.

Given, The perimeter of a quarter circle is 7.14 feet.

Therefore,

(1/2)πr = 7.14.

πr = 14.28.

r = 14.28/3.14.

r = 4.55 feet.

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Answer: x=14

Step-by-step explanation:

1. Simplify 1/5(x−4) to (x−4)/5​​.

(−x−4)/5=−2

2. Multiply both sides by 5.

−x+4=−2×5

3. Simplify 2×5 to 10.

−x+4=−10

4. Regroup terms.

4−x=−10

5. Subtract 4 from both sides.

−x=−10−4

6. Simplify −10−4 to −14.

−x=−14

7. Multiply both sides by −1.

x=14

[tex]\frac{4z^2-16z+15}{2z^2-11z+15}[/tex]   Factor the numerator and the denominator

[ax² + bx + c]

4z² - 16z + 15     Since a > 1, multiply a and c together, then find the factors of (a·c), that adds or subtracts to = b.

(a·c) --> (4 · 15) = 60

Factors of 60:

1 · 60, 2 · 30, 3 · 30, 4 · 15, 5 · 12, 6 · 10  

[The only factor is 6 and 10, (-6) + (-10) = -16] So you substitute -6z - 10z for -16z

4z² - 6z - 10z + 15   Factor out 2z from 4z² - 6z, and factor out -5 from -10z + 15

2z(2z - 3) - 5(2z - 3) Factor out (2z - 3) and your left with:

(2z - 3)(2z - 5)

Do the same for the denominator, and you should get (z - 3)(2z - 5)

Now you have:

[tex]\frac{(2z - 3)(2z-5)}{(z-3)(2z - 5)}[/tex]   You can cancel out (2z - 5)

[tex]\frac{2z - 3}{z-3}[/tex]

ANSWER

[tex]\frac{(2z-3)}{(z-3)} [/tex]

EXPLANATION

The given expression is:

[tex] \frac{4z^2-16z+15}{2z^2-11z+15} [/tex]

Let us split the middle terms to get,

[tex]\frac{4z^2-6z - 10z+15}{2z^2-6z - 5z+15} [/tex]

Factor by grouping:

[tex]\frac{2z(2z-3) - 5(2z - 3)}{2z(z-3) - 5(z - 3)} [/tex]

Factor further:

[tex]\frac{(2z - 5)(2z-3)}{(2z - 5)(z-3)} [/tex]

We cancel the common factors,

[tex]\frac{(2z-3)}{(z-3)} [/tex]

where

[tex]z \ne \frac{5}{2} \: or \: z \ne3[/tex]

Answer:

25

Step-by-step explanation:

You can get that the common difference for all of the terms if four by finding the difference between -3 and 5, which gives us four. Using this, we can calculate the last term by doing 5+4*5 which is 25.

Answer:

6

Step-by-step explanation:

Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:

120/(n+24) = (120/n) -16

Multiplying by n(n+24) gives ...

120n = 120(n+24) -16(n)(n+24)

0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms

n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller

(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic

The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.

The woman bought 6 items.

_____

Check

When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.

Answer:

20%

Step-by-step explanation:

So, 40 is the dependent and 8 is the independent

40% divided by 8% equals 5%

100% divided by 20% equals 5%

Answer:

The product of [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{3}[/tex] is [tex]\frac{5}{9}[/tex] .

Step-by-step explanation:

Multiply both numerators and denominators.

[tex]\frac{5*2}{6*3}[/tex]

[tex]\frac{10}{18}[/tex]

Simplify this by dividing both the numerator and denominator by 2.

[tex]\frac{10/2}{18/2}[/tex]

[tex]\frac{5}{9}[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{The word product means multiply}[/tex]

[tex]\dfrac{5}{6}\times\dfrac{2}{3}=\ ?\\\\\\\dfrac{5(2)}{6(3)}=\dfrac{5\times2}{6\times3}\\\\\bf{5\times2=10}\\\\\bf{6\times3=18}\\\\\\=\dfrac{10}{18}\\\\\\\text{Both numbers foes into two so we can DIIVIDE it by two}\\\\\\\dfrac{10\div2}{18\div2}=?[/tex]

[tex]10\div2=5\\\\\18\div2= 9\\\\\\\boxed{\boxed{\bf{Answer:\dfrac{5}{9}}}}\checkmark[/tex]

[tex]\text{Good luck on your asignment and enjoy your day!}\\\\\\\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]7.5m^2[/tex]

Step-by-step explanation:

Divide the composite shape into two shapes, a rectangle and a triangle.

We can see that the rectangle has dimensions of 3 x 2.

We can use the area formula.

[tex]A=b*h[/tex]

[tex]A=3*2[/tex]

[tex]A=6[/tex]

We can also see that the triangle has a height of 3 and a base of 1 (3 - 2).

We can use the area formula.

[tex]A=\frac{1}{2}(b*h)[/tex]

[tex]A=\frac{1}{2}(3)[/tex]

[tex]A=1.5[/tex]

Now we can add these areas together.

[tex]1.5 +6=7.5[/tex]

ANSWER

Y-intercept: 3000

Slope:-275

Linear equation:y=-275x+3000

EXPLANATION

The straight line touches the y-axis at

(0,3000).

The y-intercept is b=3000

The line also passes through (2,2450).

The slope is calculated using the formula,

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

[tex] = \frac{3000 - 2450}{0 - 2} [/tex]

[tex] = \frac{550}{ - 2} = - 275[/tex]

The slope is -275.

The linear equation is given by:

[tex]y = mx + b[/tex]

[tex]y = - 275x + 3000[/tex]

Answer:

y = 1/2x -8

Step-by-step explanation:

The two marked points are 1 unit apart vertically and 2 units apart horizontally. The vertical rise is positive for a positive horizontal run, so the slope is ...

rise/run = 1/2

The y-intercept is the leftmost marked point, at y=-8. Then the slope-intercept form of the equation of the line is ...

y = slope·x + y-intercept

y = 1/2x -8

Answer:

B. (-2, 0) and (1, 0)

Step-by-step explanation:

The equation can be factored as ...

y = 2(x^2 +x -2) = 2(x +2)(x -1)

The x-intercepts are the values of x where y=0, so will be the values of x that make one or the other of the binomial factors zero:

x = -2

x = 1

Then the intercept points are (-2, 0) and (1, 0). . . . . . . . . matches choice B

Answer:

2.5 inches in height

Step-by-step explanation:

Givens

water flowing = 7500 in^3 / minute

water flowing = 75000 in^3 / minute * 10 minutes

Tank diameter = 196 inches

Tank radius = 196 inches /2

Tank radius = 98 inches

h_10 minutes = ??

Formula

V = pi r^2 h

Solution

75000 = 3.14 * 98^2 * h

75000 = 3.14 * 9604 * h

75000 = 30156.56 * h

h = 75000 / 30156.56

h = 2.487 which rounded to the nearest 1/10 is

h = 2.5 inches. Seems awfully small doesn't it, considering the volume flowing in.

Answer: upon itself

Step-by-step explanation: apex

there are 4,500 of 4 digit multiples of 2

Answer:

4500

Step-by-step explanation:

So you would do 1/3 times 4 so that is 1 and 1/3

The total distance that was run by Runners who each ran for 1/3 of a mile​ will be 4/3.

The distance is defined as the length of the space between the two points separated from each other.

From the graph, the distance of 1/3 miles is covered by 4 runners so the total distance will be calculated as:-

Distance = 1/3  x  4

Distance = 4/3  miles

Hence the total distance that was run by Runners who each ran for 1/3 of a mile​ will be 4/3.

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Answer:

(2,1) is the only solution to the linear equation

Step-by-step explanation:

to solve, just plug in the values given into the orignal expression. remember, the answer on the left has to be equal to the answer on the right.

(2,1)

4(2) + 3(1) = 11 --> 8 + 3 = 11 --> 11 = 11 (2,1) is a solution to the linear equation

(6,0)

4(6) + 3(0) = 11 --> 24 + 0 = 11 --> 24 ≠ 11 (6,0) is not a solution to the linear equation

(0,1)

4(0) + 3(1) = 11 --> 0 + 3 = 11 --> 3 ≠ 11 (0,1) is not a solution to the linear equation

Answer:

The volume of the pyramid is [tex]6.125\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base of the pyramid

h is the height of the pyramid

Find the area of the base B

[tex]B=3.5^{2}= 12.25\ cm^{2}[/tex]

we have

[tex]h=1.5\ cm[/tex]

substitute

[tex]V=\frac{1}{3}(12.25)(1.5)[/tex]

[tex]V=6.125\ cm^{3}[/tex]

Answer:

93.6 inch^2

Step-by-step explanation:

sides=6 side-length=6 inches Apothem= 5.2 inches Area= 6*(1/2)(6)(5.2)

The area of the regular hexagon is 93.6 square centimeter.

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write area as -

V = ∫∫F(x, y) dx dy

Given is a regular hexagon with a side length of 6 cm and an apothem of approximately 5.2.

We can write the area of the regular hexagon as -

A = {3√3}/2 x a²

A = {3√3}/2 x 6 x 6

A = 93.6 square centimeter

Therefore, the area of the regular hexagon is 93.6 square centimeter.

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Answer:

50,000

Step-by-step explanation:

Set up a proportion:

6/1500 = 200/x

Cross multiply and solve for x:

200x1500 = 6x

300000 = 6x

50000 = x

Answer:

50000

Step-by-step explanation:

Find the "unit rate" for occupancy:  

1500 ft²

------------- = 250 ft²/person

6 people

Now multiply this unit rate by 200 people.  "people" drops out, and you are left with

250 ft²

--------------- * 200 people = 50,000 ft²

1 person

Enter 50000.  200 people will need 50000 ft² of housing.

Answer: OPTION A

Step-by-step explanation:

You can convert  30 kilograms to grams ([tex]1\ kilogram= 1,000\ grams[/tex]), then:

[tex](30\ kilograms)(\frac{1,000\ grams}{1\ kilogram})=30,000\ grams[/tex]

Then, if a book in the bookcase has a mass of 400 grams and you need to find the number of books of the same mass that would take to equal the mass of the bookcase, you can divide the weight of the bookcase (in grams) by the weigth of one of these books.

Therefore:

[tex]books=\frac{30,000\ grams}{400\ grams}\\\\books=75[/tex]

Answer:

Step-by-step Answer:

6 reindeer, from which we fly 5, in N1 ways.

Each of the five must be arranged in N2 ways.

The total number of arrangements is therefore N1*N2 arranglements.

Note: C(n,r) = n!/((r!(n-r)!)

N1 = 6 choose 5 = C(6,5) = 6!/(5!/1!) =  6 ways

(same as number of ways to choose 1 reindeer to be left out).

N2 = 5! ways (5 choices for the first, 4 choices for the second, 3 for the third, and 2 for the fourth, and 1 for the last) = 5*4*3*2*1 = 120 ways.

So total number of arrangements

= N1 * N2 = 6 * 120 = 720 ways.

Alternatively, you can line up the 5 vacant spaces and choose the first among 6 reindeer, second among 5, third among 4, fourth among 3, and the last one among 2 for a total of

6*5*4*3*2 = 720 arrangements.

Answer:

B(5,2)

Explanation:

AC=8 units

AB must equal 2 units.

If line AC is y=x-3, and x values are -1<x<7 in AC, then B is located in x= 5. Plug x in equation.

y=5-3

y=2

B(5,2)

Answer:

Step-by-step explanation:

55 LRD = 1 USD

100 LRD = 1 CHD

[tex]1 LRD = \frac{1}{55} USD\\\\100 LRD = \frac{100}{55} USD = 1\frac{45}{55} USD=1\frac{9}{11} USD\\1 CHD = \frac{100}{55} USD\\1 USD = \frac{55}{100} CHD = 0.55CHD[/tex]

the answer is C. move the decimal place to the left 4 times since it is positive to the 4th power

Answer:

26 terms

Step-by-step explanation:

The n-th term of this sequence with a common difference of 5 and a first term of -2 is ...

an = -2 +5(n -1)

The sum of the first n terms is ...

(a1 +an)/2·n = (-2 -2 +5(n -1))/2 ·n = 1573

n(5n -9) = 3146

5n^2 -9n -3146 = 0 . . . . . quadratic in standard form

Using the quadratic formula, we can find the positive solution for n to be ...

n = (9+√((-9)^2-4(5)(-3146)))/(2·5) = (9+√63001)/10 = 260/10 = 26

26 terms must be added to give the desired sum.

_____

Relevant formulas are ...

Sn = n(2a1 +d(n-1))/2 . . . . sum of n terms of arithmetic sequence with first term a1 and common difference d

x = (-b±√(b^2 -4ac))/(2a) . . . . . solutions to ax^2 +bx +c = 0

Answer:

  square inch — is a unit of area, not volume

Step-by-step explanation:

Some volume measures have their own unit, like liters, cups, pints, quarts, gallons, bushels, or barrels.

Other volume units are the cube of a linear measure, such as cubic centimeters, cubic inches, cubic feet, or cubic meters.

Still other volume units are a hybrid of an area measure and a linear measure, such as acre-feet.

A measure that is the square of a linear unit is an area measure, not a volume measure.

Answer:

Step-by-step explanation:

"square inch" is a unit of area, not of volume.