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The graph of exponential function, is described below.

What is an exponential function?

The mathematical formula f(x) = e^x stands for the exponential function. The term, unless specifically stated otherwise, generally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.

The formula for an exponential growth function is y = ab^x, where a > 0 and b > 1. As can be seen in the example of f(x) = 2x below, the graph will ascend. The numbers get smaller as x gets closer to negative infinity, as you can see.

If b > 1 , then the graph's slope is positive and exponential growth is depicted. The value of y approaches infinity as x rises. The value of y approaches zero as x falls.

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Answer:

The mistake is that you are supposed to do the 15 - 4 first, getting 11, then applying the distributive property and multiplying 11 by 1x and 3.

Hope this helped! Have a nice day, and plz mark as brainliest if correct!!!

-Lil G

Answer:c

Step-by-step explanation:

Answer:

The equation for 3 cups equals 24 cookies is = 24 divided by 3 or 3 times 8, so that makes your awnser 12 times 3= 36 times 8 equals 288, so 288 cookies.

Step-by-step explanation:

Dozen-12

Answer:

you going to need 4 1/2 or 4.5 cups of sugar

Answer:

Look below for the screenshot :)

Answer:

420 m^2

Step-by-step explanation:

Ancho: x

Largo: 2x + 2

2x + 2(2x+2) = 88

2x + 4x + 4 = 88

6x = 88 - 4

x = 84/6

x = 14

Ancho: 14

Largo : 30

Area: 14 * 30 = 420 metros cuadrados

Answer:y=-1/3x+10/3

Step-by-step explanation:

If the line is perpendicular it means the slope is the negative reciprocal of the line. The slope of line r should be -1/3. Now the equation for line r is: y=-1/3x+b. We then can plug in values: 3=-1/3(1)+b=3=-1/3+b, b=10/3. The equation is: y=-1/3x+10/3.

Answer:

Step-by-step explanation:

y = 3x - 2

slope m1 = 3

Slope of line r = -1/m1 = -1/3

Equation of line in slope intercept form:  y= mx +b

\(y=\dfrac{-1}{3}x+b\)

Plugin x = 1 and y= 3 in the above equation.

\(3=\dfrac{-1}{3}*1+b\\\\3= \dfrac{1}{3}+b\\\\\\3+\dfrac{1}{3}=b\\\\\dfrac{9}{3}+\dfrac{1}{3}=b\\\\\\b =\dfrac{10}{3}\)

Equation of line r :

\(y = \dfrac{-1}{3}x + \dfrac{10}{3}\)

The derivative of a function represents the rate of change of the function with respect to its variable. This rate of change is described as the slope of the tangent line to the curve of the function at a specific point. The derivative of the cosine function can be found by applying the limit definition of the derivative to the cosine function.

\(f(x) = cos(x) then f'(x) = -sin(x)\).

Let's proceed with the proof.  Definition of the Derivative: The derivative of a function f(x) at x is defined as the limit as h approaches zero of the difference quotient \(f(x + h) - f(x) / h\) if this limit exists. Using this definition, we can find the derivative of the cosine function as follows:

\(f(x) = cos(x) f(x + h) = cos(x + h)\)

Now, we can substitute these expressions into the difference quotient: \(f'(x) = lim h→0 [cos(x + h) - cos(x)] / h\)

We can then simplify the expression by using the trigonometric identity for the difference of two angles:

\(cos(a - b) = cos(a)cos(b) + sin(a)sin(b)\)

Applying this identity to the numerator of the difference quotient, we obtain:

\(f'(x) = lim h→0 [cos(x)cos(h) - sin(x)sin(h) - cos(x)] / h\)

We can then factor out a cos(x) term from the numerator:

\(f'(x) = lim h→0 [cos(x)(cos(h) - 1) - sin(x)sin(h)] / h\)

We can then apply the limit laws to separate the limit into two limits:

\(f'(x) = lim h→0 cos(x) [lim h→0 (cos(h) - 1) / h] - lim h→0 sin(x) [lim h→0 sin(h) / h]\)

The first limit can be evaluated using L'Hopital's rule:

\(lim h→0 (cos(h) - 1) / h = lim h→0 -sin(h) / 1 = 0\)

Therefore, the first limit becomes zero:

\(f'(x) = lim h→0 - sin(x) [lim h→0 sin(h) / h]\)

Applying L'Hopital's rule to the second limit, we obtain:

\(lim h→0 sin(h) / h = lim h→0 cos(h) / 1 = 1\)

Therefore, the second limit becomes 1:

\(f'(x) = -sin(x)\)

Thus, we have proved that if \(f(x) = cos(x), then f'(x) = -sin(x)\).

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Answer:

assuming 13 is supposed to be -13, the equation will be y=-5x+2

Step-by-step explanation:

common difference = -5

y=-5x+b

-3=-5(1)+b - plug in the first term of the sequence

b=2

Answer:

-8

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

If a function f is differentiable at a point a and f(a) is not equal to zero, then the absolute value function |f| is also differentiable at that point.

The proof involves considering two cases based on the sign of f(a) and showing that the limit of the difference quotient exists for |f| at point a in both cases. However, it is important to note that |f| is not differentiable at the point where f(a) equals zero.

To prove that if f is differentiable at a, then |f| is also differentiable at a, provided that f(a) ≠ 0, we need to show that the limit of the difference quotient exists for |f| at point a.

Let's consider the function g(x) = |x|. The absolute value function is defined as follows:

g(x) = {

x if x ≥ 0,

-x if x < 0.

Since f(a) ≠ 0, we can conclude that f(a) is either positive or negative. Let's consider two cases:

Case 1: f(a) > 0

In this case, we have g(f(a)) = f(a). Since f is differentiable at a, the limit of the difference quotient exists for f at point a:

lim (x→a) [(f(x) - f(a)) / (x - a)] = f'(a).

Taking the absolute value of both sides, we have:

lim (x→a) |(f(x) - f(a)) / (x - a)| = |f'(a)|.

Since |g(f(x)) - g(f(a))| / |x - a| = |(f(x) - f(a)) / (x - a)| for f(a) > 0, the limit on the left-hand side is equal to the limit on the right-hand side, which means |f| is differentiable at a when f(a) > 0.

Case 2: f(a) < 0

In this case, we have g(f(a)) = -f(a). Similarly, we can use the same reasoning as in Case 1 and conclude that |f| is differentiable at a when f(a) < 0.

Since we have covered both cases, we can conclude that if f is differentiable at a and f(a) ≠ 0, then |f| is also differentiable at a.

Note: It's worth mentioning that at the point where f(a) = 0, |f| is not differentiable. The proof above is valid when f(a) ≠ 0.

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The unit rate is $9.50 per hour

As the rate for 6 hrs. is $57,

the rate is 57/6=(3×19) / (3×2)

=19/2

=9.50

The unit rate is $9.50 per hour

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Answer:

Since the line has no curve (aka slope) it has an undefined slope. The slope is non existent.

Step-by-step explanation:

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{17\% of 54}}{\left( \cfrac{17}{100} \right)54}~~\approx~~ \text{\LARGE 9.2}\)

According to the information, the price change of $ 6 to $ 2 would generate an elasticity in the demand of 0.33

The price elasticity of demand is an economic term that refers to the measure used to show the amount demanded of a good or service to changes in the price of said good or service.

To find the demand elasticity we must perform the following mathematical procedure:

Price elasticity = (P1 + P2)/(Q1 + Q2) x (Q2 - Q1)/(P2 - P1)

Q1 = 5, p1 = 6

Q2 = 7, p2 = 2

PE = 8/12 x 2/-4 = - 0.33

According to the above, we can establish that the elasticity in demand with a price change of $ 6 to $ 2 would be 0.33.

Note: This Question is incomplete. Here is the complete information:

Attached Image

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Answer:

80%

Step-by-step explanation:

no. of insects=4

total no. of species=5

percentage of the insects

=4/5*100

=4*20

=80%

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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The question is incomplete. The complete question is :

A survey was done to determine the relationship between gender and subject preference. A total of  56 students were surveyed to determine if they liked math, English, social studies, or science as their  favorite subject. The results were then broken down based on whether the respondent was male or  female.

Which of the following is the closest to the joint relative frequency of being a male who likes social studies ?

Solution :

A two way table used in statistics and mathematics is used to show the frequencies or the relative frequencies for any two categorical variables.  One of the category is represented by the rows while the other categories by a column.

Here, in this table it is given that the total surveyed = 56 students

From the table, we know that number of males who likes social studies = 8

Therefore, the closest to the joint relative frequency for being a male who likes the subject social studies is given by :

\($=\frac{8}{56}$\)

\($=\frac{1}{7}$\)

=0.14

Answer:

Oh I want the ponts give me the branlest to!

Step-by-step explanation:

The claim of the production manager is not true because more than 4000 insulating washers are defective per day.

The total amount of insulating washer for the electrical devices produced per day = 225,000.

The amount chosen at random for sampling = 200 washers.

The amount shown to be defective in the chosen sample = 4

If every 200 = 4 defective

225,000 = X

Make c the subject of formula;

X = 225000×4/200

X = 900000/200

X = 4,500.

This shows that the claim is wrong because more than 4000 insulating washers are defective per day.

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The required probability that the total number of spots showing is less than 7 is 9.26%

The probability of an event is found by considering all possibilities that follow the given condition. The probability value cannot exceed the interval [0,1].

Three six-sided dice are rolled at the same time.

It is asked to calculate the probability that the total number of spots showing is less than 7.

If the die is rolled, possible outcomes are as given below.

S: {1, 2, 3, 4, 5, 6}

Number of elements in sample space, n(S) = 6.

Probability of any specific outcome from S = 1/6

If the three dice are rolled together, the total number of elements in the sample space will be \((6^3)\)

Then, the probability of getting any of any specific outcome from this sample will be given by: \(\frac{1}{6^3} =\frac{1}{216}\)

Find the total possibilities for which the total of outcomes of all three dice is less than 7. It is possible when we get the following outcomes.

The minimum total that we get is 3 with outcomes (1,1,1) on three dice.

For a total of 3:

Possible outcomes: [1, 1, 1]

The number of possibilities \(A_1=1\)

For total 4:

Possible outcomes: [1,1,2], [1,2,1], [2, 1, 1]

Number of possibilities \(A_2=3\)

For a total of 5:

Possible outcomes:  [1,1,3], [1,3,1], [3, 1, 1],  [1,2,2], [2,2,1], [2, 1, 2]

The number of possibilities \(A_3=6\)

For a total of 6:

Possible outcomes :  [1,1,4], [1,4,1], [4, 1, 1],[1, 2, 3] ,[1,3,2],[2, 3, 1], [3,2,1], [3, 1, 2],[2,1,3], [2, ,2 ,2]

The number of possibilities : \(A_4=10\)

The number of possibilities for which the total number of spots showing is less than 7 is given by,

\(A_1+A_2+A_3+A_4\)

=> 1+ 3+ 6+ 10

=> 20

The probability that the total number of spots showing are less than 7 is calculated below.

P = 20/216

P = 0.0926

P = 9.26%

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The given question is incomplete, complete question is:

Explain how to solve this problem:

You have three six-sided dice. When all three dice are rolled at the same time, calculate the probability of the following outcomes:

a. The total number of spots showing is less than 7

Answer:

-2 < x<4

Step-by-step explanation:

We have open circles and -2 and 4 so we don't include those numbers

The line is in between so the x is in between

-2 < x<4

Answer: Associative property of multiplication as it is showing that the value does not change although you move the parentheses.

Step-by-step explanation:

Answer: 1 and 3/4 hours were spent rehearsing act 2.

Step-by-step explanation:

5 1/2 total hours spent rehearsing.

take the 3 3/4 hours from act 1.

Subtract 3 3/4 from 5 1/2 to get time spent for act 2.

5 1/2 - 3 3/4 = 7/4

7/4 = 1 3/4

Hope this helps

Answer:

1 3/4 hours

Step-by-step explanation:

Given the time taken to rehearse for act 1 and 2 of a school play to be 5 1/2 hours, if 3 3/4 were spent rehearsing act 1, the amount of time that will be spent in rehearsing act 2 can simply be gotten by taken the difference between the total time taken for both and time spent on act 1.

Mathematically, act1 + act 2 = 5 1/2 hours

If act 1 = 3 3/4 hours

act 2 =  5 1/2 hours - act 1

act 2 =  5 1/2 hours - 3 3/4 hours

Taking the difference between the two values;

= 5 1/2 - 3 3/4

= 11/2 - 15/4

= (22-15)/4

= 7/4 hours

The time taken for practising act 2 will be 1 3/4 hours

Answer:

2.8 miles

Step-by-step explanation:

in 60 minutes = 7 miles

in 1 minute = 7/60 miles

In 24 minutes = 7/60 × 24

Hope this helps.

Answer: She would run 2.8 miles in 24 minutes.

Step-by-step explanation:

\(\frac{x}{24minues} =\frac{7miles}{60minues}\). we cross multiply it, then we got:

      60x = 7(24)

      60x = 168

           x = 2.8 miles

The Hardware Shop in Subang Jaya is considering in-house production of brackets instead of buying them. The setup cost for in-house production is RM25.00, and the shop plans to produce 50 brackets.

In-house production of brackets involves setting up the necessary equipment and processes to manufacture the brackets within The Hardware Shop.

The shop is currently evaluating this option as an alternative to buying the brackets from an external supplier.

To initiate in-house production, there is a one-time setup cost of RM25.00.

This cost covers expenses related to acquiring the required machinery, tools, and materials, as well as setting up the production area.

In terms of production volume, the shop plans to produce 50 brackets. This quantity represents the number of brackets that the shop aims to manufacture within a given time period.

Producing brackets in-house gives the shop control over the quantity and timing of production.

By considering in-house production, The Hardware Shop can potentially reduce dependency on external suppliers, have more control over the production process, and potentially achieve cost savings in the long run. However, it is important for the shop to carefully evaluate the total costs, including setup costs, production costs, and any associated overhead costs, to make an informed decision about whether in-house production is the most viable option for the business.

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