The graph of the exponential function f(x) is shown below. Which statement about the features of the graph for f(x) is correct?
A. The value of f(x) doubles for every 4 unit increase in x
B. The value of f(x) is increasing for each unit decrease in x
C. The value of f(x) is decreasing for each unit increase in x
D. The y -intercept of f(x) is 40

After solving the given inequality question, we will get  x < -9.

A mathematical sign for comparing two values or expressions is an inequality symbol. Inequality symbols include: (less than), > (greater than), (less than or equal to), and (greater than or equal to). Inequalities can be used to represent connections between two or more variables, for as 5 10 indicating that 5 is less than 10. Inequalities can also be used to define mathematical equations or to describe connections between variables. The equation x + 2 7 can, for example, be used to represent the relationship between x and 7, or to communicate that the value of x must be less than 5 for the equation to be true.

In the given question,

2/3x + 2y < -1/3x + 1

⇒ 2/3x + 2y - (-1/3x + 1) < 0

⇒ 5/3x + 3 < 0

⇒ 5/3x < -3

⇒ x < -9

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Answer:

8/25

Step-by-step explanation:

5+8+12=25
8/25

Answer: 8/25

Step-by-step explanation:

Find probability with item/total.

total is 25

there are 8 chocolate chip cookies

8/25 is your answer

HOPE THIS HELPS _ MM

Answer:

4 more laps to reach the goal of 14.4 km.

Step-by-step explanation:

First, let's find the total distance covered so far: 720 m x 16 laps = 11,520 m.

Next, let's convert the goal distance to meters: 14.4 km x 1000 m/km = 14,400 m.

Finally, let's subtract the total distance covered from the goal distance to find the remaining distance: 14,400 m - 11,520 m = 2,880 m.

Since a lap is 720 m long, the remaining distance can be divided by 720 m to find the number of laps left: 2,880 m ÷ 720 m = 4 laps.

Therefore, the runner needs to run 4 more laps to reach the goal of 14.4 km.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade.  So, there are 299 eighth graders in the school.

We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade. To find the number of eighth graders, we can use the fact that the total number of students is the sum of the number of students in each grade level:

Total number of students = Number of sixth graders + Number of seventh graders + Number of eighth graders

Substituting the given values, we get:

800 = 226 + 275 + Number of eighth graders

Simplifying and solving for the number of eighth graders, we get:

800 = 501 + Number of eighth graders

Number of eighth graders = 800 - 501

Number of eighth graders = 299

Therefore, there are 299 eighth graders in the school.

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Answer:

JGK = 29 degrees

Step-by-step explanation:

i hope this helped :)

Answer:

a. 54 = 2 * 3³

b. 108 = 2² * 3³

c. 360 = 2² * 3² * 5

etc.

Step-by-step explanation:

So, you need to have a list of primes handy:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, ...

Now, take your number and try to divide it by the first prime, 2.

54 = 27 * 2

That worked. Note down the 2 and repeat with the result. You find 27 cannot be divided by 2 again, but it can be divided by 3 (the next prime in the list):

27 = 9 * 3

Note down the 3 and repeat:

9 = 3 * 3

Note down a 3 again.

So you have

54 = 2*3*3*3 = 2 * 3³

You can continue this until the result is a prime number itself. Then you are done.

Answer:

2.0333

Step-by-step explanation:

log 108

Express 108 in terms of 2 & 3.

108 = 2 * 2 * 3 * 3 * 3 = 2² * 3³

log 108 = log 2² * 3³ = log 2² + log 3³ [Using Product Law]

= 2log 2 + 3log 3 [Using Power Law]

Now put the values of log 2 & log 3:

2log 2 + 3log 3

= 2*0.3010 + 3*0.4771

= 0.6020 + 1.4313

= 2.0333

Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.

Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.

Measures of variability include the range, variance, and standard deviation, and they give us a sense of how spread out the scores in a distribution are. These measures help us understand the variability or dispersion of the data and how far the individual scores in a distribution deviate from the mean or other measures of central tendency.

Measures of central tendency, such as the mean, median, and mode, describe the central or typical value of a set of scores. They provide a summary of the data and a single value that represents the center of the distribution.

The decisions regarding graph size, shape, and style are usually based on the type of data being presented and the message being conveyed. A histogram, for example, may be used to visually display the distribution of a set of scores, and the size, shape, and style of the graph can be adjusted to highlight important features of the data.

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A sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.

To determine the required sample size for a 90% confidence interval with a margin of error of at most 0.04, we can use the formula:

[tex]n = \left(\frac{z \cdot \sigma}{E}\right)^2[/tex]

where:

n is the sample size

z is the z-score associated with the desired confidence level (90% confidence level corresponds to z = 1.645)

σ is the standard deviation of the population (unknown, so we use 0.5 as a conservative estimate, since the proportion of students who would patronize the nightclub is unknown and assumed to be 0.5 for maximum variability)

E is the maximum desired margin of error (0.04)

Plugging in the values, we get:

n = (1.645 * 0.5 / 0.04)²

n ≈ 424

Therefore, a sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.

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The probability that the ninth woman to appear is in position 17 is about 5.59%

We can approach this problem by using the binomial probability distribution. Let X be the number of women among the first 16 people in the line. Then X follows a binomial distribution with parameters n = 16 and p, the probability that any given person among the first 16 is a woman. We want to find the probability that X = 8, since this means that the ninth woman to appear is in position 17.

The probability of any given person being a woman is not specified in the problem, but we can assume that it is 0.5 for simplicity. Therefore, p = 0.5, and we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items. In this case, it gives the number of ways to choose k women from the first 16 people in the line.

Using this formula with n = 16 and k = 8, we get:

P(X = 8) = (16 choose 8) * 0.5^8 * 0.5^8

= 12870 * 0.00390625

= 50.27

This means that the probability of exactly 8 women appearing among the first 16 people in the line is about 50.27%.

Given that there are 8 women among the first 16 people, the probability that the ninth woman appears in position 17 is 1/9, since there are 9 possible positions for the ninth woman to appear, and they are all equally likely.

Therefore, the overall probability that the ninth woman to appear is in position 17 is:

P(X = 8) * (1/9) = 50.27% * (1/9) = 5.59%

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Answer: et's call the amount of strawberries Gill uses "x" grams. We know that the ratio of strawberries to bananas is 7:3, so we can set up an equation:

x/144 = 7/3

To solve for x, we'll multiply both sides of the equation by 144:

x = 7/3 * 144

x = 7 * 48

x = 336

So Gill uses 336 grams of strawberries in the smoothie.

Step-by-step explanation:

Melissa earned [tex]$152.84\\[/tex] this week. This means that she earned a total of [tex]$174.49[/tex] over the two week period.

To determine how much Melissa earned last week, we can subtract the [tex]$21.65[/tex] that she earned more this week from the total amount earned over the two week period. Therefore, Melissa earned [tex]$152.84[/tex] this week, and [tex]$21.65[/tex] more than she earned last week. Subtracting [tex]$21.65[/tex]from [tex]$174.49[/tex] gives us [tex]$152.84[/tex], which is the amount Melissa earned last week. This means that Melissa earned [tex]$152.84[/tex] last week .To summarize, Melissa earned $152.84 this week, which was[tex]$21.65[/tex] more than she earned last week. This means that Melissa earned a total of [tex]$174.49[/tex]over the two week period, and by subtracting [tex]$21.65[/tex] from the total amount earned over the two week period, we can determine that Melissa earned[tex]$152.84[/tex] last week.

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The current age of Rita is 17 years and Cheryl is 7 years respectively, according to mentioned data.

Let us assume Rita's present age be x and Cheryl's age be y.

Rita's age two years ago = 3 × Cheryl's age two years ago

x - 2 = 3 (y - 2) - equation 1

Rita's age after three years = 3 × Cheryl's age after three years

x + 3 = 2 (y + 3) - equation 2

Solving equation 1

x - 2 = 3y - 6

x = 3y - 6 + 2

x = 3y - 4

Solving equation 2

x + 3 = 2y + 6

x = 2y + 6 - 3

x = 2y + 3

Keep the value of x from equation 2 in equation 1

2y + 3 = 3y - 4

Rearranging the equation

3y - 2y = 3 + 4

y = 7

Keep the value of y in equation x = 2y + 3

x = 2×7 + 3

x = 14 + 3

x = 17

So, Cheryl's and Rita's age is 7 and 17 years respectively.

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Answer:

Step-by-step explanation:

200 rimwjh hdwqheywgygwuivug

Answer:

  about 2.43 seconds

Step-by-step explanation:

You want the time when the height described by h = -16t² +36t +7 is equal to zero.

The quadratic equation ...

  -16t² +36t +7 = 0

can be solved using the quadratic formula. It tells you the solution to ...

  ax² +bx +c = 0 is ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Then the solutions to the given quadratic are ...

  [tex]x = \dfrac{-36\pm\sqrt{36^2-4(-16)(7)}}{2(-16)}=\dfrac{9\pm\sqrt{109}}{8}\approx\{-0.180,2.430\}[/tex]

The ball will hit the ground after about 2.43 seconds.

Answer:

Step-by-step explanation:

I probalby am not reading the question correctly, but it seems be be asking the distance between Myrna's fingertip (18 feet above the ground!) and the top of the 27' foot flagploe.  We are not told where Myrna is standing, nor how she got her fingertip 18 feet high.  Since we are asked for a diagram, I did the best I could, not knowing much about Myrna other than she must be tall.  On her behalf, I assumed Myrna was directly under the flagpoe.  As shown in the attached diagram, her fingertip is 9 feet below the top of the flagpole.  

If the 24 foot wire is stretched all the way (i.e., it takes 24 feet to reach Myrna's fingertip), then she is not standing directly below the flagpole.   But this isn't clear in the problem.  In any event, if the question is how far she is from the very top of the flagpole from where she is standing, it would be the 24 foot lenght of the wire connecting her to the top of the flagpole.  If the question just wants the vertical distance, then it is 9 feet.

If she is standing away from the flagpole, then a diagram would appear roughly as follows:

 x

 x      s

 x 27'        s   24'

 x                       s

 x  ----------z--------------   y

 x                                   y

 x                                   y 18'

 x   ----------z--------------  y                  

flagpole                       Myrna

The distance z is calculated using the Pythagorean Theorem in the top triangle.  The left side is (27'-18') or 9'.  The hypotenuse is 24'.

  z^2 + 9^2 = 24^2

z = 22.2 feet.

Answer:

OD 52020 cubic inches

Step-by-step explanation:

15.0×24.0=360

=360×8.5=3060

3060 inches×17 boxes=52020 inches

Therefore;52020 cubic inches storage space is needed for the crayons

Answer:

linear

Step-by-step explanation:

when you graph x/2 it is a straight line, therefore it is linear

The angle m∠B of the quadrilateral has a measure of 72°

The complete question is added as an attachment

For any quadrilateral, the sum of its four interior angles is equal to 360°,

Using the above as a guide, we have the following:

17x + 5 + 13x + 7 + 118° + 80° = 360°

Evaluate the like terms

So, we have

30x + 210° = 360°

Subtract 210° from both sides

30x = 150°

So, we have

x = 5

Given that

B = 13x + 7

We have

B = 13 * 5 + 7

Evaluate

B = 72

Therefore, the measure for the angle m∠B is 72°

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If the difference between the water temperature and the room temperature is halved every 5 minutes, then the water temperature in degrees fahrenheit, after 15 minutes 86 f        

If a cup is boiling water (212 f) is placed to cool in a room whose temperature remains constant at 68 f. suppose the difference between the water temperature and the room temperature is halved every 5 minutes .

Temperature can be measured in degree celsius, degree fahrenheit and kelvin. so here the temperature measured in degree fahrenheit

Initially the difference between water and room temperature is,

212 - 68 = 144f                

For every 5 minutes the difference of water and room temperature is halved,

After 5 minutes the difference is, 144/2 = 72 f

After 10 minutes the difference is, 72/2 = 36 f

After 15 minutes the difference is, 36/2 = 18 f

So the water temperature in degrees fahrenheit, after 15 minutes will be the sum of room temperature and difference between the temperatures of water and room after 15 minutes and it is given as, 18 f + 68 f = 86 f

Therefore, the water temperature in degrees fahrenheit, after 15 minutes is 86 f.

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The graplh shows that it will take 3.33 weeks to pay up the money borrowed

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function as as follows

c = money borrowed from your parents =  $50.00

m = you are paid $15 per week to walk the dog for 20 minutes each weekday = $15

x = number of weeks

y = amount remaining

The equation is

y = 15x - 50

From the graph the pay will be completed at x = 3.33 (3.33, 0)

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Answer:

213 ft^2

Step-by-step explanation:

In this problem, we can create a larger rectangle that engulfs this image with a few missing pieces on the corners. The area of that rectangle would be 18ft * 17 ft = 306 ft^2. The sum of the missing pieces is 2ft * 7ft + 5ft * 6 ft + 7ft * 7ft  = (14 + 30 + 49)ft^2 = 93 ft^2. So, the area of this figure is 306 - 93 = 213 ft^2

ANSWER: S=173ft^2

_._._._._._._._._._._._.

In the context of John's baking, the vertex with the maximum profit represents the point where John can maximize his profit. The vertex of a parabola represents the point at which the function reaches its maximum or minimum value.

The profit function is often modeled as a quadratic equation, where the vertex represents the maximum point of the parabola. In this case, the profit function may be a function of the number of cakes or pastries sold, the price at which they are sold, and the cost of producing them. When the profit is maximized at the vertex, it means that John is producing and selling the optimal number of cakes and pastries at the optimal price to maximize his profit. The vertex represents the sweet spot for John's baking business, where he can earn the most profit with the least amount of costs. Therefore, understanding the meaning of the vertex with the maximum profit is important for John to make informed decisions about his business, including the optimal number of cakes and pastries to produce, the price to sell them, and how to allocate his resources to maximize his profits.

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On solving the provided question, we can say that in a day, the expression will be  16*24 of 10.9% = 384 od 10.9% = 41.856

In mathematics, it is pοssible to multiply, divide, add, or remove. The construction of an expression is as follows: Expressiοn, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expressiοn (such as addition, subtraction, multiplicatiοn or division etc.) Expressions and phrases can be cοntrasted.

Any mathematical statement with variables, numbers, and an arithmetic οperation between them is called an expression or an algebraic expression. Fοr instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expressiοn, all of which are separated by the arithmetic sign +.

Dr. Drew cοnsumes 16 ounces of a caffeinated beverage first thing in the mοrning

Caffeine wears off at a rate of apprοximately 10.9% an hour.

in a day, the expression will be  16*24 of 10.9% = 384 od 10.9% = 41.856

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The value of x is given as follows:

x = 131º.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Considering the above text, the measure of the top angle of the bottom triangle is given as follows:

a = 180 - 98

a = 82.

The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence:

2b + 82 = 180

2b = 98

b = 49.

(the sum of the measures of the internal angles of a triangle is of 180º).

Considering the vertical angles, the base angles of the top triangle are given as follows:

b = 49.

Hence the value of x is given as follows:

x = 180 - 49

x = 131º.

(as the top triangle is also isosceles, and the angle measure x is the exterior angle of an interior angle with measure of 49º).

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The ways the system of equations 9x - 2y = 43x+8y=12can be solved are:

A) Multiply the first equation by 4, then add the equations.

D) Multiply the second equation by 3, then subtract the equations.

From the given equations,9x - 2y = 43x+8y=12we need to use wyas of solving simultaneous equation to solve it.

Then if we Multiply the first equation by 4,  thge we can then perform addition to the second equation like

9x - 2y = 4

36x - 8y = 4

3x+8y=12

then if we add to equation 2 we have

39x =12

then we can solve x = 12/39

The same can be done with equation D .

Therefore, option A and D are correct.

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Answer:

Step-by-step explanation:

To solve the system of equations:

9x - 2y = 4 ...(1)

3x + 8y = 12 ...(2)

We can use elimination method by adding or subtracting the equations in a way that one variable is eliminated.

Here are the possible ways to solve the system:

A) Multiply the first equation by 4, then add the equations.

Multiplying the first equation by 4 gives:

36x - 8y = 16

Adding the resulting equation to the second equation gives:

36x - 8y + 3x + 8y = 16 + 12

Simplifying the equation:

39x = 28

x = 28/39

Substituting x in equation (1) gives:

9(28/39) - 2y = 4

Solving for y gives:

y = -155/78

Therefore, the solution is (x,y) = (28/39, -155/78).

B) Multiply the second equation by 3, then add the equations.

Multiplying the second equation by 3 gives:

9x + 24y = 36

Adding the resulting equation to the first equation gives:

9x - 2y + 9x + 24y = 4 + 36

Simplifying the equation:

18x + 22y = 40

Dividing the equation by 2 gives:

9x + 11y = 20

Substituting 9x from equation (2) gives:

3x + 8y = 12

Solving for x gives:

x = (12 - 8y)/3

Substituting x in equation (3) gives:

9[(12-8y)/3] + 11y = 20

Solving for y gives:

y = 16/39

Substituting y in equation (2) gives:

3x + 8(16/39) = 12

Solving for x gives:

x = 28/39

Therefore, the solution is (x,y) = (28/39, 16/39).

C) Multiply the first equation by 3, then add the equations.

Multiplying the first equation by 3 gives:

27x - 6y = 12

Adding the resulting equation to the second equation gives:

27x - 6y + 3x + 8y = 12 + 12

Simplifying the equation:

30x = 24

x = 4/5

Substituting x in equation (1) gives:

9(4/5) - 2y = 4

Solving for y gives:

y = -23/10

Therefore, the solution is (x,y) = (4/5, -23/10).

D) Multiply the second equation by 3, then subtract the equations.

Multiplying the second equation by 3 gives:

9x + 24y = 36

Subtracting the second equation from the first equation gives:

6x - 26y = -8

Solving for x gives:

x = (26y - 8)/6

Substituting x in equation (2) gives:

3[(26y-8)/6] + 8y = 12

Solving for y gives:

y = 16/39

Substituting y in equation (1) gives:

9x - 2(16/39) = 4

Solving for x gives:

x = 28/39

Therefore, the solution is (x,y) = (28/39, 16/39).

Answer:

-47

Step-by-step explanation:

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b^2−4 (ac)

Substitute in the values of a, b, and c.

1^2 − 4 (4 x 3)

Evaluate the result to find the discriminant.

Simplify each term.

One to any power is one.

1 − 4 (4 x 3)

Multiply

−4 (4 x 3)

Subtract 48 from 1.

-47

The statement that correctly compares the two functions is

They have the same x-intercept and the same end behavior as x approaches ∞.

A function's final behaviour is represented by the value of f(x) as x approaches infinity. Both functions in this scenario have the same final behaviour because they both have unbounded growth, or they both go to positive infinity.

To find y-intercept of a function we have to put x= 0

So, The y-intercept of f(x) is y = -3.

and, The y-intercept of g(x) is y = -4.

To  find x -intercept of a function put y = 0

So, The x-intercept of f(x) is x = 1.

and, The x-intercept of g(x) is x = 1.

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