Which function family is represented by the table?
x -5 0 5 10 15 20 y 3 4 5 6 7 8

Answer:

The normal price of mixer is $150.

Step-by-step explanation:

Given that:

Normal prices are reduced by 15% in sale.

The normal price of mixer is reduced by $22.50

It means that it is the amount of discount.

Let,

x be the normal price of the mixer.

15% of x = 22.50

\(\frac{15}{100}x=22.50\\0.15x=22.50\)

Dividing both sides by 0.15

\(\frac{0.15x}{0.15}=\frac{22.50}{0.15}\\x=150\)

Hence,

The normal price of mixer is $150.

The normal price of the mixer is $150.

Given that,

Based on the above information, the calculation is as follows;

Let us assume the normal price be x

15%x = 22.50

0.15x = 22.50

x = $150

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Step-by-step explanation:

in such a case, where we have all the sides and need angles, the best tool is the extended Pythagoras (for general triangles and not just for right-angled ones) :

c² = a² + b² - 2ab×cos(C)

c is the side opposite of angle C.

the side opposite of B is CA.

so, we have

220² = 100² + 160² - 2×100×160×cos(B)

48,400 = 10,000 + 25,600 - 32,000×cos(B)

12,800 = -32,000×cos(B)

cos(B) = -12,800/32,000 = -0.4

B = 113.5781785...° ≈ 114°

\(f(g(2))=f(2)=3 \\ \\ g(f(1))=g(2)=2 \\ \\ f(f(4))=f(2)=3\)

Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

Answer:

(4(f(2)

Step-by-step explanation:

If f(x(=3x-1 then f(3)f(2)

The standard deviation by the given  probability distribution is 3.3412.

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We are given that;

x P(x)

−5 0.17

−3 0.21

−1 0.09

3 0.23

5 0.23

7 0.07

Now,

To find the standard deviation, we need to use the formula:

standard deviation = sqrt[∑(x - μ)²P(x)]

where μ is the expected payout.

We have already calculated μ to be 0.76. Using this value and the given probabilities, we can calculate the standard deviation as:

standard deviation = sqrt[( (-5 - 0.76)² * 0.17) + ((-3 - 0.76)² * 0.21) + ((-1 - 0.76)² * 0.09) + ((3 - 0.76)² * 0.23) + ((5 - 0.76)² * 0.23) + ((7 - 0.76)² * 0.07)]

=3.3412

Therefore, by the given data the standard deviation will be 3.3412.

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Answer:

27x^2−9y^2=81

Answer:

Calculate the loss which is 24 cupcakes:

Find the total price of the 24 cupcakes:

24 x 1.59 = 38.16

They incurred $38.16 in losses.

Answer:

Step-by-step explanation: The gradient(slope) y-axis intercept form of a straight line is = mx +b, where m is the gradient(slope), b is the y-axis intercept we are given a gradient of -3, Therefore = -3x +buse the given point (-3, 5) to solve for b5 = -3(-3) + b5 = 9 +bb = -4 Therefore,y = -3x -4or3x +y +4 = 0

Answer:

Let the fraction be qp

So q=p+7

q−6p+17=2

⇒p+7−6p+17=2

⇒p+1p+17=2

⇒p+17=2p+2

⇒p=15

q=15+7=22

So qp=2215.

Step-by-step explanation:

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Answer:

15/22.

Step-by-step explanation:

Let the denominator of original number be x.

Then the fraction is written as  x/(x+7).

From the given info:-

(x+17)/ (x + 7 - 6) = 2

(x+17)/(x+1) = 2

2(x+1) = x+ 17

2x + 2 = x + 17

x = 17-2 = 15.

So the original number = x/x+7

= 15/22.

Answer:

200

Step-by-step explanation:

The sum is 182.5, which is 200 to 1 significant figure.

The second-degree polynomial passing through these three points,

⇒ \(-0.02x^{2} + 3x + 282\)

According to the data given in the question,

Year            Population

1990            250

2000           282

2010            310

According to the question let the year 2000,

⇒ x = 0

If 2000 = x,

Then,

1990 could be  = -10

2010 could be  = 10

As a coordinate, we could write them as:

(-10,250) (0,282) (10,310)

According to the equation,

y = \(ax^{2} + bx + c\)

Taking the coordinate with x = 0,

282 = \(a(0)^{2} + b(0) + c\)

282 = c

Taking the coordinate with x = +10

310 = \(a(10)^{2} + b(10) + c\)

310 = 100a + 10b + 282

100a + 10b = 28 ------- equation 1

Taking the coordinate with x = -10

250 = \(a(-10)^{2} + b(-10) + c\)

250 = 100a - 10b + 282

100a - 10b = -32 ------- equation 2

Solving the equations 1 and 2 for values of a and b,

Consider equation 1,

100a = 28 - 10b

a = \(\frac{28 - 10b}{100}\) -------- equation 3

Putting the value of an in equation 2,

10b = 100a + 32

10b = 100 ( \(\frac{28 - 10b}{100}\) ) + 32

10b = 28 - 10b + 32

b = \(\frac{28 + 32}{20}\)

b = 3

Putting the value of b in equation 3,

a = \(\frac{28 - (10 * 3)}{100}\)

a = -0.02

Quadratic equation = \(-0.02x^{2} + 3x + 282\)

Therefore, the second-degree polynomial passing through these three points,

⇒ \(-0.02x^{2} + 3x + 282\)

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Answer:

386.75

Step-by-step explanation:

added in the picture

The cost of joining the gym for 6 months is 386.75.

Given,

The function G(m) = 49.5m + 89.75 represents the cost of joining the gym in addition to the one-time membership fee.

The cost, G, is measured in dollars for m months.

We need to find the value of G(6).​

Here,

The one-time membership = 89.75.

Now,

Putting m = 6 months in:

G(m) = 49.5m + 89.75

G(6) = 49.5 x 6 + 89.75

       = 297 + 89.75

       = 386.75

Thus the cost of joining the gym for 6 months is G(6) = 386.75.

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Answer:

29.8%

Step-by-step explanation:

\(\frac{3+19+46+23+52+6+11+47+51+32+1+15+82}{13} \approx 29.8\%\)

Answer:

The slope-intercept form of the equation is;

Explanation:

Given that the equation passes through;

And is parallel to the equation;

We can derive the slope from the equation parallel to it;

Using the point-slope formula;

Substituting the point and the slope;

Therefore, the slope-intercept form of the equation is;

The location's volume has been most negatively impacted is Location 63: option D

The volume of returns display low extreme correlation, meaning that a stock market crash or a stock market boom can be associated with both large and small volumes.

The given table shows

                                          Volume over time

Locations                     May                  April                May

                                  last year          This year         this year

location 21                 296                278                   248

location 34                 376                324                   336

location57                  354                328                   314

location 63                  226               186                     198

Totals                        1252               1116                     1096

Based on this table, the volume of returns from last year may to this year April, the location that has least volume is location 63 option D

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Answer:

0.5

Step-by-step explanation:

you have 1/2+1/3 so you take the numerator of the first fraction and multiply it, and do the same for the numerator of the second fraction. you should be left with 2 & 3. you add those two together and there is your answer. if i am wrong please tell me so i can find the mistake.

"After first" will be the one comma that is lacking in this sentence. Imani and Jack, the two best runners, came in first and second, so that is the perfect phrase.

In order to create equilibrium, add a comma after a conjunction. We drove to the beach but turned around since there was no more space in the parking lot. The placement of a comma after a conjunction as opposed to before is one of the most frequent mistakes with commas: Nancy always found time despite having a busy schedule to visit the gym.

explanation :

If any of these seven coordinating conjunctions—and, but, for, or, nor, so, yet—are used to unite independent sentences, you should use commas to separate them.

Place commas after the preceding opening (a) sentences, (b) phrases, or (c) words.

"After first" will be the one comma that is lacking in this sentence. Imani and Jack, the two best runners, came in first and second, so that is the perfect phrase.

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Answer:

-11°C or 1°C

Step-by-step explanation:

The question said that, by the noon, the temperature changes by 6°C, but it doesn't tell you if it changes for a hotter or colder temperature, so its possible the temperature at the noon to be:

-5 -6 = -11°C

or

-5 +6 = 1°C

To graph the possible temperatures, you have to draw a dot at the numbers -11 and 1

The general formula for quadractic expression is given as,

The expression given is,

Comparing the two expressions.

where,

To solve for c, which is the value that will be added to the expression to make it a perfect trinomial. We will apply discriminant formula.

The trinomial expression will now be,

Let us now factorize the expression inorder to write it as a binomial squared,

Hence, the result as a binomial squared is,

Answer:

25

Step-by-step explanation:

3+6×4-2

6×4=24

3+24-2

3+24=27

27-2=25

Step-by-step explanation:

Frequency of a mass-spring system is:

f = √(k/m) / (2π)

Given f = 2/π Hz and m = 20 kg:

2/π Hz = √(k / 20 kg) / (2π)

4 Hz = √(k / 20 kg)

16 s⁻² = k / 20 kg

k = 320 kg/s²

k = 320 N/m

If the 20 kg mass is replaced with an 80 kg mass, the frequency is:

f = √(320 kg/s² / 80 kg) / (2π)

f = √(4 s⁻²) / (2π)

f = 2 Hz / (2π)

f = 1/π Hz

The sprint constant is 320 N/m

And, the frequency is \(1\div \pi Hz\)

Since A 20-kilogram mass is attached to a spring. And, the frequency of simple harmonic motion is 2/p cycles/s.

Now we know that

\(f = \sqrt (k\div m) \div (2\pi)\)

Here

\(f = 2\div \pi Hz\)

and m = 20 kg:

So,

\(2\div \pi Hz = \sqrt (k \div 20 kg) / (2\pi)\\\\4 Hz = \sqrt(k \div 20 kg)\\\\16 s^{-2} = k \div 20 kg\)

k = 320 kg/s²

k = 320 N/m

Now the frequency is:

\(f = \sqrt(320 kg/s^2 \div 80 kg) \div (2\pi)\\\\f = √(4 s^{-2}) \div (2\pi )\\\\f = 2 Hz \div (2\pi)\)

\(f = 1\div \pi Hz\)

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The exponential function that models the population of tiger gar in the lake is given as follows:

\(y = 322.63(1.25)^x\)

An exponential function has the definition presented as follows:

\(y = ab^x\)

In which the parameters are given as follows:

Considering x as the number of years since 2016, the points are given as follows:

(0, 322), (1, 399), (2, 507), (3, 618), (4, 785), (5, 957).

Inserting these points into an exponential regression calculator, the equation is given as follows:

\(y = 322.63(1.25)^x\)

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In relation to the angle L of the right triangle the sides are as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named according to the position of the angles in the right angle triangle.

The sides of a right triangle can also be solved by using Pythagoras's theorem or trigonometric ratios.

Let's identify the sides  j,  k, and I in relation to angle L in terms of opposite, adjacent, and hypotenuse.

Therefore,

The hypotenuse side is the longest side of a right triangle.

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Answer:

44

Step-by-step explanation:

2 + 3 * 9 + 3 * 5

=> 2 + 27 + 15

=> 29 +15

=> 44

Answer:

\(2 + 3 \times 9 + 3 \times 5 \\ = 2 + 27 + 15 \\ = 44 \\ thank \: you\)