f(x) = e^-x . Find the equation of the tangent to f(x) at x=-1​

Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.

Part 1 of 2:

The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.

To calculate the new cost after 11 years, we can use the formula:

New Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

New Cost = $0.60 * (1 + 3%)^11

        ≈ $0.60 * (1 + 0.03)^11

        ≈ $0.60 * (1.03)^11

        ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.

Part 2 of 2:

If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.

Using the formula:

Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years

Plugging in the values:

Final Cost = $0.60 * (1 + 3%)^11

          ≈ $0.60 * (1 + 0.03)^11

          ≈ $0.60 * (1.03)^11

          ≈ $0.60 * 1.432364654

Rounding to the nearest cent, the final cost would also be $0.86.

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Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?

When two sample means are significantly different, "the difference is too great to attribute to chance".

The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).

Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.

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Answer:

q=8

Step-by-step explanation:

The ratio of sides from bigger to smaller is 1/2.

q=1/2(16)

q=8

Hope it helps!

Answer:

10cm x 20cm = 78.7402 inches

Step-by-step explanation:

10 x 20 is 200

200 cm is 78.7402 inches

Answer:

Step-by-step explanation:

Answer:

 \(\int\limits {\frac{V-1}{1+2V+V^{2} } } \, dv\)    \(= log V + (\frac{2 }{1+v} )+C\)

Step-by-step explanation:

Step(i):-

Given  

                \(\int\limits {\frac{V-1}{1+2V+V^{2} } } \, dv\)

           =   \(\int\limits {\frac{V-2+1}{1+2V+V^{2} } } \, dv\)

         \(= \int\limits {\frac{V+1}{(1+V)^{2} } } \, dv+\int\limits {\frac{-2}{(1+V)^{2} } } \, dv\)

       = \(= \int\limits {\frac{1}{(1+V) } } \, dv+\int\limits {\frac{-2}{(1+V)^{2} } } \, dv\)

Step(ii):-

By using integration formula

\(\int\limits {\frac{1}{x} } \, dx =logx +C\)

\(\int\limits {x^{n} } \, dx = \frac{x^{n+1} }{n+1} +C\)

      \(= \int\limits {\frac{1}{(1+V) } } \, dv+\int\limits {\frac{-2}{(1+V)^{2} } } \, dv\\= log V + (\frac{-2(1+v)^{-2+1} }{-2+1} )+C\)

   \(= log V + (\frac{-2(1+v)^{-1} }{-1} )+C\)

  \(= log V + (\frac{2 }{1+v} )+C\)

Answer:

Following are the solution to the given point:

Step-by-step explanation:

Grade of students:

Grade of student:

In point a:

Grade of \(9^{th}\) students:

\(\to n= 6\\\\\to Mean = \frac{ \sum x_i}{n} \\\\\)

               \(= \frac{ 5+1+2+5+2+8}{6}\\\\ = \frac{24}{6}\\\\ = 4\)

\(\to Variance\\\\\sigma^2 = \frac{\sum(x_i -\bar{x})^2}{n-1}\)

    \(=\frac{1}{5}(10)\\\\=2\)

\(\to Standard \ deviation ( \sigma) :\\\\= \sqrt{\sigma^2}\\\\= \sqrt{2}\\\\= 1.141\)

Since the Grade of \(9^{th}\) student's variance is higher than \(12^{th}\)grade,  

In point b:

Please find the attached file.

The plot above shows that the student of the ninth grade is spread more widely, as the student from 0-8 to 12 is from 0-4.

Answer:

x = \(\frac{17}{14}\)

Step-by-step explanation:

simplify both sides of the equation

-9x + 10 - 5x = - 7

-9x + 10 + - 5x = -7

(-9x + -5x) + (10) = -7 (combine like terms)

-14x + 10 = -7

subtract 10 from both sides

-14x + 10 - 10 = -7 - 10

-14x = -17

divide both sides by -14

\(\frac{-14x}{-14}\) = \(\frac{-17}{-14}\)

x = \(\frac{17}{14}\)

Answer:

Step-by-step explanation:

1. Get mileage per gallon by dividing miles traveled by gallons used

\(\frac{125}{5} = 25 mpg\\\)

2. Divide miles you want to travel by the mileage per gallon you got on the first step

\(\frac{400}{25} = 16 gallons\)

Answer:

This is the answer I understood and got.

B. Yes. There is a constant of proportionality of $4.50.

Step-by-step explanation:

When you divided 9/2, you get 4.5

When you divide 22.5/5, you get 4.5

When you divide 31.5/7, you get 4.5

* REMEMBER IT'S ASKING DO THE NUMER OF GAMES AND PRICE FOR A PROPORTIONAL RELATIONSHIP *

So, y= 4.5x

Answer:

  A: f(x)=2x^2 +12x +10

  B: f(0) = 10

Step-by-step explanation:

Part A:

f(0) is a constant in the equation if the form is such that for x=0, all terms are zero except one of them. Standard form is one such form. This is the equation in standard form:

  f(x) = 2x^2 +12x +10

__

Part B:

  f(0) = 0 + 0 + 10

  f(0) = 10

Answer:

Bryan had 400$ in his bank account before he withdraw

Step-by-step explanation:

60$ ---- 15%(set what you have)

x$ ------100%(set what you need)

(x$ x 15%) 15x =(60$ x 100%)6000( cris cross the sides)(the signs dont matter )

x=400

Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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The y-intercept of the linear model is 211,400, which represents the estimated number of automobiles in the town in the year 2015 (when the independent variable is zero).

To find the y-intercept of the linear model, we need to determine the value of the dependent variable (the number of automobiles) when the independent variable (the number of years since 2015) is equal to zero.

Let's first find the slope of the line, which represents the rate of change of the number of automobiles per year:

slope = (change in number of automobiles) / (change in number of years)

slope = (2420 - 1890) / (2020 - 2015) = 106 automobiles per year

Now we can use the point-slope form of a linear equation to find the y-intercept:

y - y1 = m(x - x1)

where y1 is the value of the dependent variable when the independent variable is x1. In this case, x1 = 2015, y1 = 1890, and m = 106 (the slope we just calculated).

y - 1890 = 106(x - 2015)

To find the y-intercept, we can set x = 0:

y - 1890 = 106(0 - 2015)

y - 1890 = -213,290

y = 211,400

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Answer:

bananas: 2480

plantains: 20

Step-by-step explanation:

equations:

b+p=2500

b=124p

just plug then in and solve

Answer:

20 plantains and 2480 bananas

Step-by-step explanation (b is bananas + p is plantains):

2500 = b+p

b=124*p

2500=(124*p)+p

2500=125p (divide by 125)

20=p

b=124(20)

b=2480.

20

Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Answer: Length (in feet) x width (in feet) = area in sq. ft. 

Step-by-step explanation:

Answer:

Step-by-step explanation:

If order matters (much like forming... a 4 digit number-maybe for a safe?), you will be computing "permutations".  The  formula for "r" items chosen from  "n" items, where order matters is   Npermutations = nPr  =  n!/ (n-r)!

Npermutations = 10P6 =  10!/(10-6)= 10*9*8*7*6*5 = 151200

When order doesn't matter (such as in dealing a poker hand, its the cards you end up with that matter not the order in which they are dealt into your hand) you will be computing combinations.   The formula for the number of combinations of  "r "items from "n" choices is  Ncombinations =  nCr = n!/((n-r)!r!)

Ncombinations = 10C6 =  10!/((10-6)!6!) =  (10*9*8*7)/(4*3*2*1) = 210

Notice how there are far fewer combinations than permutations.  This makes sense because if you think about how 6 colors  {red, blue, green, white, black, yellow} can be arranged, there are 6!=720 ways to arrange these 6 colors if order matters.  If order doesn't matter, this set of 6 colors counts only once.
Same thing with numbers :)

Hope this helped, brainliest is always appreciated! :)

Have a nice day CX
~Mitsuna

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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Answer:

3.5 *10-⁷

3.5*10-⁶

4.8*10-⁷

4.8*10⁷

Answer:

X. f(x)

0 -10

3 -4

5 0

6 2

then now polt the following points on

graph

(0,-10),(3,-4),(5,0),(6,2)

Step-by-step explanation:

hi by hi by hi bye hi by hi bye bye

Answer: Number 1 answer: I agree with Andre. Number 2 answer: The diagram could represent 14.

Step-by-step explanation:

1. I agree with Andre because the squares are all tenths. so the first rectangle has 10 tenths which is 100. The four small squares equal 40 since 4 tenths is 40. If you add them both you get 140.

2. The diagram could represent 14 because you can think of the squares as ones. so ten ones is 10, and four ones is 4. So 10 plus 4 is 14.

Hope this helped keep on asking questions. Plz mark me brainliest

ANSWER:

1st option: f(x) = -f(-x)

STEP-BY-STEP EXPLANATION:

The polynomial function is symmetric about the origin in the odds functions, where the following is true:

Then it would be:

If f(x) = -f(-x), then the graph of the polynomial function is symmetric about the origin.

The correct answer is the 1st option: f(x) = -f(-x)

Answer:

3.3, 3.3031, 3.403, 3.43

Step-by-step explanation:

When you start you start at the very far left and go over from each number until you reach the end to see which one has a higher value then the other itself.

Answer: 80 cowls

Step-by-step explanation:

5/(1/16)

The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.

Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.

The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.

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Answer:

  1

Step-by-step explanation:

You want the value of the sum a+b if the line ax+by=6 graphs the same as the line -2x +4y = 12.

The equations describe the same line, so have infinite solutions, if the coefficients and constants are the same.

Here, we notice that the constant in the second equation (12) is double that in the first equation (6). We can make them the same by dividing the second equation by 2:

  (-2x +4y)/2 = 12/2

  -x +2y = 6

Since we want this to be the same line as ...

  ax +by = 6

we must choose ...

Then the sum of the coefficients is ...

  a + b = (-1) + (2) = 1

The value of a+b is 1.

Answer:

Step-by-step explanation:

Temperature is a function of the time of day. There can be only one temperature at any particular time.

In contrast, a particular temperature can occur more than one time in a day, so time is not a function of temperature.

Answer:

Step-by-step explanation: