Jenny deposits $105 into an account that earns 4% interest compounded annually. What is the balance in her account after 11 years? (Round to the nearest cent)​

A graph of the cube root function g(x) = 1/2x³ is shown in the image below.

In 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.

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

When the parent cube root function f(x) = x³ is vertically shrunk by a scale factor of 1/2, the transformed function g(x) is given by;

g(x) = kf(x)

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

g(x) = 1/2x³.

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Answer:

(x-2)*x

Step-by-step explanation:

\(x^{2}-2x\)

its maximum common divisor is x

\(\frac{x^{2}-2x }{x}\)

\((x-2)*x\)

The probability of a license plate meeting all the given criteria is approximately 0.0000126, or  \(1.26 x 10^{-5\).

Given that: A city issues 3-digit license plates and digits are 0 to 9.

Having all different digits:

To calculate this probability, use the same approach as before:

Number of favourable outcomes = 10 × 9 × 8

Total number of possible outcomes = 10 × 10 × 10

Probability = (Number of favourable outcomes) / (Total number of possible outcomes)

Probability = (10 × 9 × 8) / (10 × 10 × 10)

Probability = 720 / 1000

Probability = 0.72                                        (*)

Having at least one even digit:

So, the license plate must have all odd digits (1, 3, 5, 7, or 9).

Number of favourable outcomes = 5 × 5 × 5

Total number of possible outcomes = 10 × 10 × 10

Probability = (5 × 5 × 5) / (10 × 10 × 10)

Probability = 125 / 1000

Probability = 0.125                                      (1)

Now, the probability of having at least one even digit is the complement of the above probability:

Probability of having at least one even digit = 1 - 0.125

Probability = 0.875                                  (2)

Having the digits in ascending or descending order:

Ascending: 012, 123, 234, 345, 456, 567, 678, 789

Descending: 987, 876, 765, 654, 543, 432, 321, 210

Total favourable outcomes = 8 + 8

Total favourable outcomes = 16

Probability = 16 / 1000

Probability = 0.016                                 (3)

Having a specific digit in a specific position:

Let's say want the digit 7 to be in the first position.

Number of favourable outcomes = 1

Total number of possible outcomes = 10 × 10

Probability = 1 / 100

Probability = 0.01                                              (4)

Now, to find the probability of all criteria being met simultaneously, multiply the individual probabilities:

Probability of meeting all criteria = Probability (1) × Probability (2) × Probability (3) × Probability (4)× Probability (*)

Probability of meeting all criteria = 0.125 × 0.875 × 0.016 × 0.01 × 0.72

Probability ≈ 0.0000126

Hence, the probability of a license plate meeting all the given criteria is approximately 0.0000126.

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Answer:

0.3758 = 37.58% probability that at most one of her first 10 arrows hits the target

Step-by-step explanation:

For each shot, there are only two possible outcomes. Either they hit the target, or they do not. The probability of a shot hitting the target is independent of any other shot, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Each arrow with a probability 0.2

This means that \(p = 0.2\)

First 10 arrows

This means that \(n = 10\)

What is the probability that at most one of her first 10 arrows hits the target?

This is:

\(P(X \leq 1) = P(X = 0) + P(X = 1)\)

So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074\)

\(P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684\)

Then

\(P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1074 + 0.2684 = 0.3758\)

0.3758 = 37.58% probability that at most one of her first 10 arrows hits the target

The following sets of side dimensions could be combined to create a right triangle 6, 8, 13 is √3, √13, 4.

In the triangle, there are three angles: two acute angles and one 90-degree angle. The hypotenuse, perpendicular, and base are the terms used to describe the sides of a right-angled triangle.

The next choice shows the triangle's side length:

The point is,

The hypotenuse square of a right-angled triangle is equal to the sum of its squares on its other two sides, according to Pythagoras' Theorem.

Using Pythagoras' Theorem.

Use the formula:

a² + b² = c²

For 4, 8, 11

4, 8, 11

4² + 8² = 16 + 64 = 80

11² = 121

80 is not equal to 121 it cann ot form a right triangle

For 6, 8, 13

6² + 8² = 36 + 64 = 100

13² = 169

100 is equal to 169 - 69 can form a right triangle

For √3, √5, 8

(√3)² + (√5)² = 3 + 5 = 8

8² = 64

8 is equal to 64 cannot form a right triangle

For √3, √13, 4

(√3)² + (√13)² = 3 + 13 = 16

4² = 16

16 is equal to 16 can form a right triangle

In order to create a right triangle, one may utilise the following set of side measurements √3, √13 and 4 form a triangle.

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Answer:

Hello,
If you want f(x) read this.

Step-by-step explanation:

I am going to use Horner's method.

\(\begin {array}{c|c|c|c}&x^2&x&1\\---&--&--&--\\&4&5&-9\\x=2&&8&26\\---&--&--&--\\&4&13&\boxed{17}\\x=2&&8&42\\---&--&--&--\\&4&\boxed{21}&59\\x=2&&8\\---&--&--&--\\&\boxed{4}&29\\\end {array}\\\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\So\ \boxed{F(x)=4x^2+21x+17}\\\\Proof:\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\\\=4x^2-16x+16+21x-42+17\\\\=4x^2+5x-9\\\)

I hope this is what you want.

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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The number of lionfish after 6 years will be 85,609. The recursive equation for \(f(n)\) will be \(f(n) = 4242.42(1.65)^n - 1300n\).

Consider the function:

\(y = a (1 \pm r)^x\)

Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

lionfish are considered an invasive species, with an annual growth rate of 65%.

Then the equation will be

\(f(n) = P(1.65)^n\)

\(\text{P = initial population}\)

A scientist estimates there are 7,000 lionfish in a certain bay after the first year.

\(7000 = P(1.65)\)

    \(P = 4242.42\)

Then the equation will be

\(f(n) = 4242.42(1.65)^n\)

The number of lionfish after 6 years will be

\(f(n) = 4242.42(1.65)^6\)

\(f(n) = 85608.58\)

\(f(n) \cong 85,609\)

If scientists remove 1,300 fish per year from the bay after the first year.

Then the recursive equation for f(n) will be

\(f(n) = 4242.42(1.65)^n - 1300n\)

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Answer:

f(x) = x^3 - x^2 + 16x - 16

Step-by-step explanation:

If a polynomial has the zeros 1, 4i, and -4i, then it must have the factors (x - 1), (x - 4i), and (x + 4i). This is because a factor of (x - a) produces a root of x = a.

To find the polynomial, we can multiply these factors together:

(x - 1)(x - 4i)(x + 4i)

= (x - 1)(x^2 - (4i)^2)

= (x - 1)(x^2 + 16)

= x^3 + 16x - x^2 - 16

So the polynomial function in standard form with real coefficients whose zeros include 1, 4i, and -4i is:

f(x) = x^3 - x^2 + 16x - 16

The rate of the pump is 14 gallons per minutes, means that pump pumps 14 gallons of water in one minute.

In one hours there are 60 minutes.

Determine the gallons of water pump in 1 hour (60 minutes).

Answer: 840 gallons of water.

Answer:

Step-by-step explanation:

The compound interest formula:

A = P(1+r/n)^rt

P = 3500

n = 1

r = 0.06

t = 1, 2

Let's do 1 year:

3500(1 + 0.06)^0.06

3512.25

2 years:

3500(1 + 0.06)^0.06(2)

3524.55

Hope this helps!

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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The probability that (50) dies within 10 years and dies after (40) is at least 0.02 but less than 0.04. So the answer is B. At least .02 but less than .04.

To calculate the probability that (50) dies within 10 years and dies after (40), we need to find the joint probability of the two events happening together.

Let X and Y be the future lifetimes of (40) and (50), respectively. We want to find P(Y≤10 and X<Y). Using the Law of Total Probability, we can write:

P(Y≤10 and X<Y) = ∫P(Y≤10 and X<Y|X=t) fX(t)dt

where fX(t) is the probability density function of X.

Since the force of mortality for (40) is constant, the probability density function for X is given by:

f X (t)=ue −ut

where u=0.05.

For (50), we have the survival function S(y) = 1 - y/10. So, the probability density function for Y is:

fY(y) = S'(y) = 1/10

Now, we can substitute these expressions into the integral and simplify:

P(Y≤10 and X<Y) = ∫P(Y≤10 and X<Y|X=t) fX(t)dt

= ∫∫P(Y≤10 and X<Y|X=t) fY(y)fX(t)dydt

= ∫∫P(Y≤10 and t<Y) (1/10)(0.05)e^(-0.05t)dydt

= (1/10)∫e^(-0.05t) ∫1≤y≤10 e^(0.1y) dydt

= (1/10)∫e^(-0.05t) (e - e^(-t/10)) dt

Evaluating this integral, we get:

P(Y≤10 and X<Y) ≈ 0.0286

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The simplified expression is  d/ c⁴.

To simplify the expression cd³ c⁻⁵ x d⁻², we can combine the variables with the same base (c and d) by adding their exponents:

Using the property of exponents as

When multiplying two exponential expressions with the same base, you can add the exponents. This can be expressed as follows:

aᵇ x aⁿ= aᵇ⁺ⁿ

When dividing two exponential expressions with the same base, you can subtract the exponents. This can be expressed as follows:

aᵇ / aⁿ= aᵇ⁻ⁿ

So, cd³ c⁻⁵ x d⁻²

= c¹⁻⁵ x d³⁻²

= c⁻⁴ x d¹

= dc⁻⁴

Again from the property of exponents

a⁻ᵇ = 1/aᵇ

So,  dc⁻⁴

= d/ c⁴

Therefore, the simplified expression is  d/ c⁴.

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━━━━━━━☆☆━━━━━━━

▹ Answer

Her dad's swimsuit costs $65.

▹ Step-by-Step Explanation

Since Monica's swimsuit is $35, we will subtract that from the total amount spent, $170.

$170 - $35 = $135

Since Monica's mom's swimsuit costs 2x Monica's we will multiply 35 * 2:

$35* 2 = $70

We will now add Monica's cost and her moms' cost:

$35 + $70 = $105

To find Monica's dads' cost, we will subtract 105 from 170:

$170 - $105 = $65

Her dad's swimsuit costs $65.

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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Answer:

1. y = 3x - 1

2. y = -3x

3. y = 2x + 4

4. y = 2.5x - 4

5. y = 4x

6. y = -3/4x -0.25

7. uhhh two lines  since one definitlye doesn’t work

Step-by-step explanation: I couldn’t add more than 5 pics it’s the limit sadly.

Considering the data we have been provided, we can build a multiple regression model as follows.

a.) In MS Excel, we enter the data set and utilize the "Correlation" option under Data > Data Analysis to create the correlation matrix and answer the question. The correlation matrix may be seen below.

[Fig. 1]

Correlation coefficients for at least one of the independent variables are larger than 0.7.

b.) We must look at the column labeled "Won" in the correlation matrix. The variables are Runs, Hits, Earned Run Average (ERA) and Walks if the criteria are 0.4.

c.) In MS Excel, we enter the data set and utilize the "Regression" option under Data > Data Analysis to create the regression model and answer the question. The result is shown below.

[Fig. 2,3,4]

Runs, ERA, and SO are all significant, with p-values less than 0.05. As a result, we recreate the regression model with these three independent variables.

[Fig. 5,6,7]

The right answer is Won = 80.321 + (0.101) X1 + (-14.276) X3 + (-0.011) X4.

The R2 value of the model is 0.948. This suggests that these factors can predict 94.8% of the number of victories. This model does not make use of the same variables as the previous one (b).

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Complete

Find the integral of  \(f(x) =  16sin^2 (x ) cos(x) dx\)

Answer:

The solution is    \(\frac{16}{3} sin^{3}x + c\)

Step-by-step explanation:

So

   \(Let \  u  =  sin(x)\)

=>  \(\frac{du}{dx}  =  cos (x)\)

=>   \(du  =  cos(x)dx\)

So

   \(\int\limits {16sin^2 (x ) cos(x) dx} \, \equiv \int\limits {16u^2  du}\)

=>  \(\int\limits {16u^2  du} = 16 [\frac{u^3}{3} ] + c\)

Now substituting sin(x) for u  

      \(\frac{16}{3} u^3 + c  =  \frac{16}{3} sin^{3}x + c\)

So the  integral of  \(f(x) =  16sin^2 (x ) cos(x) dx\)  is

      \(\frac{16}{3} sin^{3}x + c\)

We are given the following two equations.

We are asked to find out whether these equations of lines are parallel, perpendicular, or neither​.

First of all, let us re-write these equations into the standard slope-intercept form.

This simply means to separate the y variable.

Similarly, for the other equation

Now recall that the standard slope-intercept form is given by

Where m is the slope and b is the y-intercept.

Comparing the standard form with our two equations we see that

Slope of 1st equation = 7

Slope of 2nd equation = 7

So the two equations have an equal slope.

Whenever two equations have equal slopes then the lines are parallel.

Therefore, the given equations are parallel.

Answer:

-8

Step-by-step explanation:

47 - 55

= 47 + (-55)

= -8

Hope it helps ⚜

\(\huge\text{Hey there!}\)

\(\mathsf{4x^2 - 29 = 0}\\\\\large\textsf{ADD 29 to BOTH SIDES}\\\mathsf{4x^2 - 29 + 29 = 0 + 29}\\\\\textsf{CANCEL out: -29 + 29 because that gives you 0}\\\\\textsf{KEEP: 0 + 29 because that helps you solve for the x-value}\\\\\mathsf{0 + 29 = \bf 29}\\\\\textsf{NEW EQUATION: }\mathsf{4x^2 = 29}\\\\\large\textsf{DIVIDE 4 to BOTH SIDES}\mathsf{\dfrac{4x^2}{4}=\dfrac{29}{4}}\\\\\large\textsf{{CANCEL out:} }\mathsf{\dfrac{4}{4}}\textsf{ because that gives you 0}\)

\(\textsf{KEEP: }\mathsf{\dfrac{29}{9}}\large\textsf{ because that helps solve for the x-value}\)

\(\textsf{NEW EQUATION: }\mathsf{x^2=\dfrac{29}{4}}\)

\(\large\textsf{TAKE the SQUARE ROOT}\)

\(\mathsf{x = \pm \sqrt{\dfrac{29}{4}}}\)

\(\text{Random fact: if you see the symbol }\mathsf{\bf \pm}\text{ it usually means plus-or-minus.}\\\\\text{Okay, now lets answer the last step to your question!}\)

\(\mathsf{\sqrt{\dfrac{29}{4}}= \boxed{\bf 2.692582}}}\\\\\mathsf{OR}\\\mathsf{- \sqrt{\dfrac{29}{4}} =\boxed{ \bf -2.692582}}\)

\(\boxed{\boxed{\huge\textsf{Answer: \bf x = 2.692582 or x = -2.692582 }}}\\\huge\checkmark\)

\(\large\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

(5,0)

(0,-5)

\(\frac{-5-0}{5-0}= -1\)

Answer:

its the thrid one i think i might be wrong srry

Step-by-step explanation:

Answer:

20/53

Answer number 4

Step-by-step explanation:

There are 20 brown, 16 orange, 4 navy, and 13 purple marbles. A marble is drawn at random. What is the probability the marble is brown?

Let's first add the marbles together.

20+16+4+13=53

there are 53 marbles altogether.

20 of the marbles are brown.

So the probability of drawing a brown marble is 20/53

\(\huge\blue{\fbox{\tt{Solution:}}}\)

We can simplify the expression using trigonometric identities.

First, we can use the double angle formula for sine to write sin(2x) = 2sin(x)cos(x).

Next, we can use the double angle formula for cosine to write cos(2x) = cos^2(x) - sin^2(x) = 1 - 2sin^2(x). Rearranging this equation gives 2sin^2(x) - 2cos^2(x) = -cos(2x) + 1.

Substituting these identities into the original expression gives:

tan(x-1) ( sin2x-2cos2x) = tan(x-1) [2sin(x)cos(x) - 2(1 - 2sin^2(x))]

= 2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)

We can use the identity tan(x) = sin(x)/cos(x) to simplify this expression further:

2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)

= 2sin(x)cos(x)/(cos(x-1)) - 2sin(x)/(cos(x-1)) + 4sin^2(x)/(cos(x-1))

Multiplying both sides of the equation by cos(x-1) gives:

2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x-1) = 2(1-2sin(x)cos(x))

Expanding the left-hand side of the equation gives:

2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x) - 4sin^2(x) = 2 - 4sin(x)cos(x)

Simplifying this equation gives:

4sin^2(x) - 2sin(x) - 2 = 0

This is a quadratic equation in sin(x), which can be solved using the quadratic formula.

Answer: sin(0) = 40.804/41

Step-by-step explanation:

Answer:

slope = 5/3

y-intercept = -4

Step-by-step explanation:

First, move the x to the other side of the equation:
-3y=-5x+12
Then, divide BOTH sides by -3, so that there is no coefficient next to y:
y=5/3x-4

Then, just look at the constant and coefficient next to x (m). The slope is 5/3 and the y-intercept is -4.

Hope this helps!

Answer:

\(y = \frac{5}{3}x - 4\)

Step-by-step explanation:

move the 5x to a -5x

-3y= -5x+12

-3/-3= -5x÷ -3 12÷ -3