If the data below were represented by a comparative bar chart, the bar
representing which of these would be the tallest?
A. Left-handed girls
B. Right-handed boys
C. Right-handed girls
D. Left-handed boys

The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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side length 2 km and slant height 2 km.

the surface area of the pyramid.

area of 4 triangle= 1/2 × 2 × 2 × 4

= 8km

area of rectangle= 2×2

= 4km

area= 4+8

= 12km

so, the surface area of the pyramid is 12km.

Answer: let me explain!

Step-by-step explanation: So this might seem really confusing at first, but it’s actually suuuuuuper easy :P

So, if you think about it, every five seconds the amount of peanuts…well I don’t know how to explain it but let me show you this with numbers.
(4x2)x2x2x2 and so on. The number multiplies by two every five seconds from there. So figure out how many groups of five second there are in 100 seconds by dividing!

It’s 20!

So since 5 happens 20 times, and every time 5 happens, 2 happens, 2 also happens 20 times! (If that makes any sense)

So that answer would be 8x*twenty twos*

Which is…*drumroll please*

8,388,608
I even double checked!

And for the briefcase skeleton thing

She needs to try it 25 times because there are 5 books and each book can be switched with the other 4 times if the first one doesn’t work, therefore you need to multiply and the equation would be 5^2, or in other words, 25.
Don’t forget ur units!

Hope this helps :P

Given:

f(x) is an exponential function.

\(f(2.5)=26\)

\(f(6.5)=81\)

To find:

The value of f(12), to the nearest hundredth.

Solution:

The general exponential function is

\(f(x)=ab^x\)

For, x=2.5,

\(f(2.5)=ab^{2.5}\)

\(26=ab^{2.5}\)          ...(i)

For, x=6.5,

\(f(6.5)=ab^{6.5}\)

\(81=ab^{6.5}\)          ...(ii)

Divide (ii) by (i).

\(\dfrac{81}{26}=\dfrac{ab^{6.5}}{ab^{2.5}}\)

\(\dfrac{81}{26}=b^4\)

Taking 4th root on both sides, we get

\(\sqrt[4]{\dfrac{81}{26}}=b\)

\(b\approx 1.32855\)

Putting b=1.32855 in (i), we get

\(26=a(1.32855)^{2.5}\)

\(26=a(2.03444)\)

\(\dfrac{26}{2.03444}=a\)

\(a\approx 12.7799\)

Now, the required function is

\(f(x)=12.7799(1.32855)^x\)

Putting x=12, we get

\(f(12)=12.7799(1.32855)^{12}\)

\(f(12)=386.4224\)

\(f(12)\approx 386.422\)

Therefore, the value of f(12) is 386.422.

To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

Answer:

To find the answer, we can use the formula:

number of won games / total number of games played = percentage won

Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:

number of won games / x = 0.65

To solve for x, we can cross-multiply:

number of won games = 0.65x

We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:

If the team played 22 games, then the number of won games is:

number of won games = 0.65 * 22 = 14.3

This is not a whole number value, so we can rule out choice A.

We can repeat this process for each answer choice. When we try choice C, we get:

number of won games = 0.65 * 18 = 11.7

This is also not a whole number value, so we can rule out choice C.

When we try choice D, we get:

number of won games = 0.65 * 14 = 9.1

This is also not a whole number value, so we can rule out choice D.

Therefore, the only remaining answer choice is B, which gives us:

number of won games = 0.65 * 20 = 13

This is a whole number value, so the team could have played 20 games in total last season.

Given

Two quadrilaterals on a plane.

Required

we need to find what transformation can be done on quadrilateral 1 to verify it is similar to quadrilateral 2.

Explanation

Since the two quadrilaterals are aligned in terms of angles and sides.

So the only transformation we need to make is to dilate quadrilateral 1 and we can verify it is similar to quadrilateral 2.

So the required transformation is dilation or scaling it down.

Here's a screenshot of the answer below:

Answer: 7

Step-by-step explanation:

3 x 3 = 9 - 2(3)+4

9-6+4

=7

Answer:

slope- (261)

Step-by-step explanation:

Answer: no

Step-by-step explanation:

no it cannot be simplified

3 cannot be divided into both 5's and the √3 is already simplifed

Insured = 72%.

Uninsured = 28%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Here is a table classifying 116 thousand US households (in thousands) in

2013 by tenure and insurance status:

Insurance status      Owns home   Rents home

Insured                              71                13

Uninsured                         27               5

Total house = 71 + 13 + 5 + 27 = 116

Insured = (71 + 13)/116 = 72%.

Uninsured = (5 + 27)/116 = 28%.

Therefore, 72% = insured and 28% = uninsured.

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Answer:

Step-by-step explanation:

Answer:

95% of confidence intervals are

(197.706 , 198.294)

Step-by-step explanation:

Explanation:-

Given sample size 'n'=100

Mean of the sample  x⁻ = 198

The standard deviation of the Americans =15

95% of confidence intervals are determined by

            \((x^{-} - Z_{\alpha } \frac{S.D}{\sqrt{n} } , x^{-} +Z_{\alpha } \frac{S.D}{\sqrt{n} })\)

Level of significance = 0.05

Z₀.₀₅ = 1.96

        =   \((198 - 1.96 \frac{15}{\sqrt{100} } , 198 +1.96\frac{15}{\sqrt{100} })\)

       =  ( 198 -0.294 ,198 +0.294)

       = (197.706 , 198.294)

95% of confidence intervals are

(197.706 , 198.294)

Answer:

\(m\angle 3=30^\circ,~m\angle 8=150^\circ\)

Step-by-step explanation:

Angles and Lines

We must recall some properties of angles and lines:

Linear pair of angles: Two angles are linear if they are adjacent angles formed by two intersecting lines. They must add up to 180°.

Corresponding angles: They are angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are congruent, i.e., they have the same measure.

The figure shows two parallel lines a and b, crossed by the line m. These conditions make the following relations be true:

Angles 3 and 4 are linear pair

Angles 8 and 4 are corresponding.

The first relation leads to:

\(m\angle 3+m\angle 4 = 180^\circ\)

The second relation leads to:

\(m\angle 4 = m\angle 8\)

Since:

\(m\angle 3=x\)

\(m\angle 8=5x\)

Substituting:

\(x + 5x = 180^\circ\)

Simplifying:

\(6x = 180^\circ\)

Solving for x:

\(x = 180^\circ/6\)

\(x = 30^\circ\)

Now,

\(m\angle 3=x=30^\circ\)

\(m\angle 8=5x=150^\circ\)

\(m\angle 3=30^\circ,~m\angle 8=150^\circ\)

Answer:

4

Step-by-step explanation:

It's going backwards by two

Answer:

\(Average = \$873\)

Step-by-step explanation:

Given

$1000 for 9 days

$750 for 10 days

$850 for 4 days

$900 for other days

Required

Compute the daily average

First, we need to compute the number of days her balance is $900

Assuming the billing cycle is 30 days;

\(Number\ of\ days = 30 - (9 + 10 + 4)\)

\(Number\ of\ days = 30 - 23\)

\(Number\ of\ days = 7\)

The Average is then calculates using:

\(Average = \frac{\sum fx}{x}\)

\(Average = \frac{1000 * 9 + 750 * 10 + 850 * 4 + 900 * 7}{9 + 10 + 4+ 7}\)

\(Average = \frac{26200}{30}\)

\(Average = 873.333333333\)

\(Average = \$873\) --- Approximated

Answer:

9(1000) + 10(750) + 4(850) + 7(900)

                    30

Step-by-step explanation: I got it right

Answer:

0.108

Step-by-step explanation:

Given that:

Number of flights reached early = 65

Number of flights reached on time = 273

Number of flights reached late = 218

Number of flights canceled = 44

To find:

The probability that a flight is early.

Solution:

First of all, let us have a look at the formula for probability of an event E.

Formula for probability of an event E can be observed as:

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}\)

Here, Event E is that the flight is early.

Number of favorable cases is equal to the number of a flights which reached early i.e. 65

Total number of cases is the total number of flights.

i.e. 65 + 273 + 218 + 44 = 600

So, the required probability is:

\(P(E) = \dfrac{65}{600} = \bold{0.108}\)

Answer:

A

Step-by-step explanation:

It has to go down 46 degrees to get to 0 and then 8 more to get to - 8. The total is A -- 54

Step-by-step explanation:

check the pic for workings

ans is 343.35KN

Answer:

714 packets of sweets

Step-by-step explanation:

So if there are 17 boxes with 42 sweets in each of them, we can just multiply 17 and 42 and we get teh amout of sweets in them since multiplication is just repeated addition.

Answer:

E ( 16 , $464 )

$4907

$4395

Step-by-step explanation:

Solution:-

- The supply curve is an upward sloping curve that denotes the relation between the quantity of goods ( oil ) supplied ( q ) and the market price ( p ). Such that the market price ( p ) increases with each additional unit of oil sold.

- The supply function S ( q ) for the commodity ( oil ) is expressed as:

                             \(S ( q ) = q^2 + 13q\)

- The demand curve is a downward sloping curve that is derived from the concept of diminishing marginal utility i.e with each additional unit of oil consumed people are willing to pay less for the additional unit. The demand curve D ( q ) for the commodity ( oil ) is expressed as:

                            \(D ( q ) = 992 - 17q - q^2\\\\\)

- The two graphs are plotted and given in the attachment with quantity of oil ( q ) on the x-axis and market price ( p ) on the y-axis.

- The equilibrium point is the ordered pair of ( quantity of oil , market price ) where the demand curve and supply curve intersect. This is the point where manufacturing sell and the customers buy the commodity.

- To determine the equilibrium point ( E ) we will equate the two curves S ( q ) and D ( q ) as follows:

                            \(S ( q ) = D ( q )\\\\q^2 + 13q = 992 - 17q - q^2\\\\2q^2 + 30q - 992 = 0\\\\q = -31 , q = 16\)

- We will ignore the negative value of quantity of goods and accept q = 16 units. Plug the value in either of the two equations of curve:

                           \(S ( 16 ) = ( 16 )^2 + 13*( 16 )\\\\S ( 16 ) = 464 . dollars\)

- The ordered pair for the equilibrium point is:

Answer:            E ( 16 , $464 )

- Consumer surplus (CS) is the region bounded by the market equilibrium price ( pe = $464 ) and the demand curve D ( q ). We will employ the use of calculus and evaluate the area of the region using integrals as follows:

                           \(\int\limits^1^6_0 [ {D(q) - p_e} ] \, dq \\\\\)

- Evaluate the quantity ( q ) over to the equilibrium quantity ( qe = 16 ):

                        \(CS = \int [ 992-17q-q^2 - 464} ] \limits^1^6_0 . dq = \int [ 528-17q-q^2 } ].dq \limits^1^6_0\\\\CS = [ 528q - \frac{17}{2}*q^2 - \frac{1}{3}*q^3 ] \limits^1^6_0\\\\CS = [ 528(16) - \frac{17}{2}*(16)^2 - \frac{1}{3}*(16)^3 ]\\\\CS = 4907 . dollars\)

Answer: Their is a consumer surplus of ( $ 4907 ) for this commodity.

- Producer's surplus ( PS ) is the region bounded by the market equilibrium price ( pe = $464 ) and the supply curve S ( q ). We will employ the use of calculus and evaluate the area of the region using integrals as follows:

                           \(\int\limits^1^6_0 [ {p_e - S(q)} ] \, dq \\\\\)

- Evaluate the quantity ( q ) over to the equilibrium quantity ( qe = 16 ):

                        \(PS = \int [ 464 - q^2 - 13q ] \limits^1^6_0 . dq \\\\PS = [ 464q - \frac{13}{2}*q^2 - \frac{1}{3}*q^3 ] \limits^1^6_0\\\\PS = [ 464(16) - \frac{13}{2}*(16)^2 - \frac{1}{3}*(16)^3 ]\\\\PS = 4395 . dollars\)

Answer: Their is a producer's surplus of ( $ 4395 ) for this commodity.

Answer:

x = 8

Step-by-step explanation:

These are corresponding angles, and they are equal to one another.

\(7x+3=3x+35\\4x+3=35\\4x=32\\x=8\)

The dealer's cost of the refrigerator is found to be $123.50.

The concept of percent increase is simply the amount of increase from the original to the final number expressed in terms of 100 parts of the original.

As, per the given question;

Selling price = $617.50

Dealer's cost = 25%

Let 'x' be the marked price/original price of the refrigerator.

Then,

x + 25% of x = 617.50

Solving;

x + (25x)/100 = 617.50

125x = 61750

x = 61750/125

x = 494

The original price of the refrigerator was$494.

Then, the cost of the dealer; 25% of x.

= (25×494)/100

= 123.50

Therefore, the dealer's cost of the refrigerator is $123.50.

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Answer:

The slope means that each year the average professional baseball player's salary increased by $144,750 for every year after 2000.

The y-intercept means that in year 0 (2000) the average professional baseball player's salary was $1,998,000

The predicted average salary in 2007 is $3,011,250

(b)

The initial value represents the average professional baseball player's salary in year 0 (2000), which was $1,998,000.

The growth factor means that the rate of change increases each year by 1.062 times the previous year's increase.

The predicted average salary in 2007 is $3,044,233.94

Explanation:

The problem gives us two pieces of information:

In year 2000, we call t = 0, the average salary was $1,998,000

In year 2006, we call t = 6, the average salary was $2,866,500

If we want to make a function of the average salary variation over the years, we have two points that must lie in the equation of that function:

(0, 1998000) and (6, 2866500)

For (a) we need to assume that is linear growth. The equation of a line is:

Where:

m is the slope

b is the y-intercept. In this case, since we established the year 2000 as t = 0, b = 1998000

Given two points P and Q, we can find the slope by the formula:

Then, if we call:

P = (0, 1998000)

Q = (6, 2866500)

Thus, the equation of the linear growth model is:

Now, we can use this to find a prediction for 2007. 2007 is 7 years since 2000; thus t = 7

In (b) we assume an exponential growth. The formula for the exponential growth is:

Where:

a is the initial value. In this case, the average salary in 2000, $1,998,000

r is the ratio of growth. We need to find this value

t is the time in years

Then, we can use the point (6, 2866500), and the fact that a = 1998000:

And solve:

We call the term "1 + r" growth factor.

Now, we can write the formula:

To find a prediction of the average salary in 2007, we use the function and t = 7:

Answer:

44%

Step-by-step explanation:

60%-16% the answer is up ahead.

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x).

\(lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5\)

from the graphs n f (x) and g( x) are 1 and 5 .

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