Mark went to 8-12 store to by one some soda. he puts money, punches a specific button, then the soda drops from the slot machine. what is the function rule?​

\(\\ \rm\Rrightarrow \dfrac{x^2+3x+2}{x^2-4x-5}\)

\(\\ \rm\Rrightarrow \dfrac{x^2+2x+x+2}{x^2-5x+x-5}\)

\(\\ \rm\Rrightarrow {(x+2)(x+1)}{(x-5)(x+1)}\)

\(\\ \rm\Rrightarrow \dfrac{x+2}{x-5}\)

And

\(\\ \rm\Rrightarrow \dfrac{x^2+7x+12}{x^2-3x-28}\)

\(\\ \rm\Rrightarrow \dfrac{x^2+4x+3x+12}{x^2-7x+4x-28}\)

\(\\ \rm\Rrightarrow \dfrac{(x+4)(x+3)}{(x-7)(x+4)}\)

\(\\ \rm\Rrightarrow \dfrac{x+3}{x-7}\)

The result of 626362737287387287373 times 77474747743874837847348734463763786837 represented in scientific notation is 4.80498727057566113882339366151788673587 × 10⁹⁵.

The number you provided in your question can be represented in scientific notation. Scientific notation is a way of expressing numbers in a compact form that is especially useful for very large or very small numbers. The number you provided in your question can be represented in scientific notation as:

7.7474747743874837847348734463763786837 × 10⁷⁷

And 626362737287387287373 can be represented as:

6.26362737287387287373 × 10¹⁸

The product of these two numbers can be calculated as follows:

(7.7474747743874837847348734463763786837 × 10⁷⁷) × (6.26362737287387287373 × 10¹⁸) =

= (7.7474747743874837847348734463763786837 × 6.26362737287387287373) × (10⁷⁷ × 10¹⁸) =

= 48.0498727057566113882339366151788673587 x 10⁹⁵

So, the result of 626362737287387287373 times 77474747743874837847348734463763786837 in scientific notation is:

4.80498727057566113882339366151788673587 × 10⁹⁵

To know more about scientific notation visit :

https://brainly.com/question/13351372

#SPJ1

Answer:

Step-by-step explanation:

inorder to solve the area of the shaded area;°/360ñRsquared

arc length you use ;°/360ñD

for her last grade for math is b

Step-by-step explanation:

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

3 log (z) -  1/2log (x) - 1/2 log (5) -1/2 log y

Step-by-step explanation:

log(z3)/√x5y)

= log (z3)   - log (√x5y)   [division being subtracted]

= 3 log (z) - {log (√x) + log (√5y)}    [ multiplication being added in the denominator]

= 3 log (z) - {log (x)^1/2 + log (5)^1/2+ log (y)^1/2}  

= 3 log (z) -  1/2{log (x) + log (5)+ log y }

 We can solve inside the curly bracket and then multiply with 1/2 or we can solve it separately

= 3 log (z) -  1/2log (x) - 1/2 log (5) -1/2 log y

How does this work?

1) any two terms being multiplied in logarithms are added with the log of each.

2) the exponent becomes the co- efficient.

3)  any two terms being divided in logarithms are subtracted with the log of each

Answer:

A

Step-by-step explanation:

43987-32650= 11337

And it’s more

A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

Learn more about Probability here:

brainly.com/question/32117953

#SPJ1

From the given question

There are given that the 72.5 cubic centimeters

Now,

The cubic inches of 72.5 cubic centimeters is:

Hence, the answer is 4.424221.

In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.

Congruency Requirements:

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side) 

To learn more about congruency of the triangle, visit:

brainly.com/question/6108628

#SPJ4

Given the following five-number summary: 2.9, 5.7, 10.0, 13.2, 21.1, so Q₁ = 5.7. This can be solved using the concept of quartile.

A kind of percentile is a quartile. The first quartile (Q₁, or the lowest quartile), which corresponds to the 25th percentile of the data, is below which 25% of the data are found. The second quartile (Q₂, or the median), which represents the 50th percentile, indicates that 50% of the data are below this quartile.

There are 5 data points, and the middle value of the lower half of the data set will represent the first quartile. So the second data value is the first quartile. So, Q₁ = 5.7

There are 5 data points, and the middle value of the upper half of the data set will represent the third quartile. The fourth data value is the third quartile. So,

Q₃ = 13.2

SO IQR will be:

= Q₃ - Q₁

= 13.7 - 5.1

= 7.5

Thus, Q₁ = 5.7

To know more about quartile refer to:

https://brainly.com/question/28169373

#SPJ1

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

Learn more about Confidence interval here:

https://brainly.com/question/15712887

#SPJ8

The correct interpretation of the slope and y-intercept of the equation

y = 50 is:

A. The slope predicts a temperature increase of about 50° for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x = 0), the temperature is 0°.

In the given equation y = 50, the slope of 50 indicates that for every increase of 1 chirp per minute (x), the temperature (y) increases by approximately 50° Fahrenheit.

The positive slope suggests a positive correlation between the number of chirps per minute and temperature.

The y-intercept of 0 in this equation represents the temperature when the crickets are not chirping (x = 0). It implies that when there are no chirps per minute, the temperature is at 0° Fahrenheit.

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ1

Answer:

answer is b

Step-by-step explanation:

because all you need to do is flip the signs.

Answer:

Step-by-step Solution:

Simplification: (Distributive Property)

Further Simplification: (Addition/Subtraction)

Hence, the simplified answer is -2w + 16.

Answer:

Step-by-step explanation:

Plug in 6 for x for g(x) and f(x)

f(6) = 2(6)⁵ = 15,552

g(6) = 10 x 4⁶ = 40,960

15,552 < 40,960

f(6) < g(6)

Answer:

x = - 3/2

Step-by-step explanation:

4x^2 + 12x + 9 = 0

(2x + 3)^2 = 0

2x + 3 =0

2x = -3

= - 3/2

The solution is, x = - 3/2

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, given that,

4x^2 + 12x + 9 = 0

(2x + 3)^2 = 0

2x + 3 =0

2x = -3

x= - 3/2

Hence, The solution is, x = - 3/2.

To learn more on equation click:

brainly.com/question/24169758

#SPJ2

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

Read more on dilation and scale factor here: brainly.com/question/4421026

#SPJ1

Answer:

the answer is 2100

Step-by-step explanation:

Answer:

Here's What you do:

There's a picture attached on how a perpendicular lines should look like.

Step-by-step explanation:

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Step-by-step explanation:

The value of expression 50% of 36 is,

⇒ 50% of 36 = 18

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The expression is,

⇒ 50% of 36

Now, We can simplified as;

The expression is,

⇒ 50% of 36

By definition of percent we get;

⇒ 50/100 × 36

⇒ 1/2 × 36

⇒ 36/2

⇒ 18

Thus, The value of 50% of 36 is,

⇒  50% of 36 = 18

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ9

The probability of a defect is 5.7330 x \(10^{-5}\) and the number of defects is 5.73.

To calculate the probability of a defect, we need to find the area under the standard normal curve that lies outside of the process control limits of 9.75 ounces and 10.25 ounces. We can use the standard normal distribution table to find this area.

First, we need to standardize the weight limits as follows -

\(Z_{lower}\) = (9.75 - 10) / 0.25 = -4

\(Z_{upper}\) = (10.25 - 10) / 0.25 = 4

Next, we will find the area under the standard normal curve that lies outside of these limits as follows -

P(Defect) = P(Z < -4) + P(Z > 4)

Using a standard normal distribution table, we can find that P(Z < -4) = 2.8665 x   \(10^{-5}\)  and P(Z > 4) = 2.8665 x  \(10^{-5}\) .

So, the total probability of a defect is -

P(Defect) = 2.8665 x  \(10^{-5}\)  + 2.8665 x  \(10^{-5}\)  = 5.7330 x  \(10^{-5}\)

Finally, we will find the number of defects for a 1,000-unit production run as follows -

The number of defects = 1000 * 5.7330 x  \(10^{-5}\)  = 5.73 (rounded to the nearest whole number).

Read more about Probability:

brainly.com/question/24756209

#SPJ4

Answer:

Option 1

Step-by-step explanation:

From the conclusion drawn by the computer manufacturer, we can assume that there is no correlation between the age and purchase price. The customer would not necessarily purchase a lower or higher priced computer.

Here we can assume that purchasing the computer all depends on the amount of money present on the customer.

Answer:

a³b < 0

Step-by-step explanation:

If a > 0 then a³ > 0

and b < 0

then

a³b → + × - → -

that is a³b < 0

Commitment to goals can be promoted in through:

Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain outcomes, are significant. Commitment helps you stick to your goals in both good and bad times, when obstacles arise. Commitment is influenced by two factors: importance and

Goal commitment is generally defined as an individual's determination to devote time and effort to achieving a goal.

Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain.

Learn more about goal on:

https://brainly.com/question/24693533

#SPJ1

Answer:

Step-by-step explanatory:

x | y

1 | 2.5

2 | 6.25

3 | 15.625

4 | 39.0625

5 | 97.65625

This is true if we are using x as an exponent for y.

If x is not being used as an exponent then this is not true.

Answer:

12 + x --> 18

3x + y --> 23

4y - 10 --> 10

(1)/(2)xy --> (1)/(60)

Step-by-step explanation:

Let's evaluate each expression with the given values of x=6 and y=5:

Expression: 12 + x

Substituting x=6 into the expression, we get: 12 + 6 = 18

Expression: 3x + y

Substituting x=6 and y=5 into the expression, we get: 3(6) + 5 = 18 + 5 = 23

Expression: 4y - 10

Substituting y=5 into the expression, we get: 4(5) - 10 = 20 - 10 = 10

Expression: (1)/(2)xy

Substituting x=6 and y=5 into the expression, we get: (1)/(2)(6)(5) = (1)/(2)(30) = (1)/(60)