karl has $400 in a savings account. the interest rate is 10%, compounded annually. what type of model best fits this situation?

Answer:

h ≤ - 2

Step-by-step explanation:

Given :

Score on each of first 3 holes = +1

Total number of holes = 9

Target score - 9 or better ≤ - 9

Number of holes left = 9-3 = 6

h = average score on each of last 6 holes to meet target score ;

3 * (+1) + (number of holes left * average score) = target score

3 + (6 * h) ≤-9

3 + 6h ≤ - 9

6h ≤ - 9 - 3

6h ≤ - 12

h ≤ - 2

Answer:

z = 4/3 or 1 1/3

Step-by-step explanation:

z−4/9−1/3=5/9

Change 1/3 to have a denominator of 9

1/3 *3/3 = 3/9

z−4/9−3/9=5/9

Combine like terms

z -7/9 = 5/9

Add 7/9 to each side

z-7/9+7/9 = 5/9+7/9

z = 12/9

z=4/3

or as a mixed number

z = 1 1/3

Answer:

8,036 here is the answer

Answer:

8 036 here is answer

Step-by-step explanation:

I just calculated

Answer:

4(9a-4)

Step-by-step explanation:

36a - 16

We can factor 4 from each expression.

4*9a - 4*4

4(9a-4)

Answer:

The value of u is -2.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

6/7=(2-8)/(u-5)

6/7=-6/(u-5)

6/7(u-5)=-6

6/7u-30/7=-6

6/7u=-6+30/7

6/7u=-42/7+30/7

6/7u=-12/7

u=(-12/7)/(6/7)

u=(-12/7)(7/6)

u=-12/6

u=-2

Answer:

\(r\le \:12.5\)

Step-by-step explanation:

Answer:

r<=12.5

Step-by-step explanation:

87.5-150 = -62.5

-62.5/-5 = 12.5

you multiplied by a negative so the symbol switches

<=

Answer:

44-4i

Step-by-step explanation:

It will take approximately 14.6 years to triple and 19.5 years to quadruple.

To solve this problem, we can use the formula for exponential growth, which is:

P(t) = P0 \(e^k^t\)

Where P(t) is the population at time t, P0 is the initial population, k is the constant of proportionality, and e is the mathematical constant approximately equal to 2.71828.

Since the population is doubling in 7 years, we know that:

2P0 = P0 \(e^k^7\)

Simplifying this equation, we can cancel out P0 on both sides and take the natural logarithm of each side:

ln(2) = 7k

Solving for k, we get:

k = ln(2)/7

Now, to find out how long it will take for the population to triple or quadruple, we just need to plug in the appropriate values of P0 and solve for t.

For tripling:

3P0 = P0  \(e^k^t\)

ln(3) = kt

t = ln(3)/k ≈ 14.6 years

For quadrupling:

4P0 = P0  \(e^k^t\)

ln(4) = kt

t = ln(4)/k ≈ 19.5 years

This problem involves exponential growth, which is a type of growth where the rate of growth is proportional to the current amount. In this case, the population is growing at a rate proportional to the number of people present at time t.

To solve this problem, we need to use the formula for exponential growth, which relates the population at time t to the initial population and the constant of proportionality.

Using the fact that the population has doubled in 7 years, we can find the value of the constant of proportionality, which allows us to calculate the time it will take for the population to triple or quadruple.

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Using Euler integration, the next values of x and y can be determined as follows:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Euler integration is a numerical method used to approximate solutions to differential equations. It is based on the concept of dividing the interval into small steps and using the derivative at each step to calculate the next value. In this case, we are given the current values of x=2, y=8, and y'=9, with a step size of delta_X=5.

To determine the next values of x and y, we use the following formulas:

x_next = x_current + delta_X

y_next = y_current + delta_X * y'

Substituting the given values into the formulas, we have:

x_next = 2 + 5 = 7

y_next = 8 + 5 * 9 = 53

Therefore, the updated values of x and y using Euler integration are x=7 and y=53.

It's important to note that Euler integration provides an approximate solution and the accuracy depends on the chosen step size. Smaller step sizes generally lead to more accurate results. Other numerical methods, such as Runge-Kutta methods, may provide more accurate approximations.

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The area under a Normal curve depends on the interval being considered and the parameters of the Normal distribution, such as its mean and standard deviation.

To determine which of the given intervals corresponds to the smallest area under a Normal curve, we need to consider the properties of the Normal distribution. The Normal distribution is a symmetric bell-shaped curve that is completely determined by its mean and standard deviation. The mean, denoted by µ, is the center of the curve, while the standard deviation, denoted by σ, determines the spread of the curve.

Option b) µ to µ + 3σ corresponds to the interval that covers almost all the area under a Normal curve, as about 99.7% of the area lies within three standard deviations of the mean. Therefore, this option cannot correspond to the smallest area under a Normal curve.

Option a) Q1 to Q3 and option d) µ - σ to Q3 both cover more area than option c) Q1 to µ + 2σ. The interval Q1 to Q3 covers the entire middle 50% of the distribution, while the interval µ - σ to Q3 covers at least 50% of the distribution, as almost all the area lies within three standard deviations of the mean. Therefore, option c) Q1 to µ + 2σ corresponds to the smallest area under a Normal curve.

In summary, the interval corresponding to the smallest area under a Normal curve is option c) Q1 to µ + 2σ.

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Answer:

see below

Step-by-step explanation:

cos  = adj/ hypotenuse

Cos A = 30 /34

Simplifying

Cos A = 15/17

Answer:

Kevin completed 3 races

Step-by-step explanation:

So to solve this first you would add up all of the miles Kevin ran.

\(3.5+4+1.8=9.3\)

Then you would take the total amount he ran and divide it by 3.1 to see how many races he would have completed

\(9.3 / 3.1=3\)

The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.

The formula for pooled variance is:

pooled variance = (SS₁+ SS₂) / (df₁ + df₂)

where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.

Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in

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Answer: 135/20=6.75

Step-by-step explanation:

Long division (picture attached below)

Using exponential function it will take approximately 2.6 years for the population to reach 26676

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.

The formula given in this question is

P(t) = 988(3.5)ˣ

The time it will take to reach a population of 26676 is

26676 = 988(3.5)ˣ

x = 2.6 years

It will take approximately 2.6 years

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The two positive angles are 5π/2 and 13π/2, while the two negative angles are -11π/2 and -19π/2.

A quadrantal angle is an angle that lies on the x or y-axis in standard position. In this case, the given quadrantal angle is θ = -7π/2.

To find the co-terminal angles within the range of -6π to 4π, we can add or subtract multiples of 2π from the given angle.

For positive angles, we can add 2π to the given angle. Adding 2π to -7π/2, we get 5π/2 as the first positive co-terminal angle. Adding another 2π, we obtain 13π/2 as the second positive co-terminal angle.

For negative angles, we can subtract 2π from the given angle. Subtracting 2π from -7π/2, we get -11π/2 as the first negative co-terminal angle. Subtracting another 2π, we obtain -19π/2 as the second negative co-terminal angle.

Therefore, the two positive co-terminal angles with θ = -7π/2 within the range of -6π to 4π are 5π/2 and 13π/2. The two negative co-terminal angles are -11π/2 and -19π/2.

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Using the given logarithmic values, we can find \(\( \log_b 75 \)\) by expressing it in terms of \(\( \log_b 3 \)\) and \(\( \log_b 5 \).\) By applying logarithmic properties, we simplify \(\( \log_b 75 \)\) to \(\( 1.7 \).\) Therefore, the correct answer is B. \(\( 1.7 \).\)

The value of \(\( \log_b 75 \)\) can be found using properties of logarithms. From the given information, we have \(\( \log_b 2 = 0.4 \), \( \log_b 3 = 0.5 \),\) and \(\( \log_b 5 = 0.6 \).\) We can use these values to express \(\( \log_b 75 \)\) in terms of these logarithms and apply logarithmic properties to simplify.

The prime factorization of 75 is \(\( 3^1 \cdot 5^2 \).\) Using the property \(\( \log_b (xy) = \log_b x + \log_b y \),\) we can write \(\( \log_b 75 = \log_b (3^1 \cdot 5^2) = \log_b 3^1 + \log_b 5^2 \).\)

Using the given values, we substitute \(\( \log_b 3 = 0.5 \)\) and \(\( \log_b 5 = 0.6 \),\) giving us \(\( \log_b 75 = 0.5 + 2 \cdot 0.6 \).\)

Simplifying further, we have \(\( \log_b 75 = 0.5 + 1.2 = 1.7 \).\)

Therefore, the correct answer is B. \(\( 1.7 \),\) which represents the value of \(\( \log_b 75 \)\) using the given logarithmic values.

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The variance of the total loss due to hurricanes hitting this house in the next ten years is 40,000,000.

To calculate the variance of the total loss due to hurricanes hitting the house in the next ten years, we can use the properties of the Poisson and exponential distributions.

Given:

Mean number of hurricanes in ten years (λ) = 4

Mean loss due to each hurricane (μ) = 1000

The variance of a Poisson distribution is equal to its mean (λ). So, the variance of the number of hurricanes in ten years is also 4.

The variance of an exponential distribution is equal to the square of its mean (μ²). So, the variance of the loss due to each hurricane is 1000² = 1,000,000.

Since the losses are mutually independent and independent of the number of hurricanes, we can use the properties of variance to calculate the variance of the total loss.

The total loss due to hurricanes in ten years is the sum of the losses from each individual hurricane. Since there can be a different number of hurricanes each year, we need to consider the total number of hurricanes as a random variable.

The total loss (X) can be expressed as:

X = L₁ + L₂ + ... + Lₙ

Where L₁, L₂, ..., Lₙ are the losses due to each individual hurricane.

Since the number of hurricanes is Poisson distributed with a mean of 4, the total number of hurricanes (N) in ten years is also Poisson distributed with a mean of 4 multiplied by 10 (mean number per year multiplied by the number of years).

N ~ Poisson(4 * 10) = Poisson(40)

The variance of a Poisson distribution is equal to its mean (λ). So, the variance of N is 40.

Now, we can use the properties of variance to calculate the variance of the total loss.

Var(X) = Var(L₁ + L₂ + ... + Lₙ)

Since the losses are independent, the variance of the sum is equal to the sum of the variances:

Var(X) = Var(L₁) + Var(L₂) + ... + Var(Lₙ)

Since each loss (Lᵢ) is exponentially distributed with a variance of 1,000,000, we can substitute:

Var(X) = 1,000,000 + 1,000,000 + ... + 1,000,000 (40 times)

Var(X) = 40 * 1,000,000

Var(X) = 40,000,000

Therefore, the variance of the total loss due to hurricanes hitting this house in the next ten years is 40,000,000.

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The statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups is independent-sample t test.

Given that,

We have to find the statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups.

We know that,

The independent Samples t take a look at analyzes the manner of two separate organizations to see if there's statistical guide that the populace imply values are statistically extensively distinctive. A parametric take a look at is the unbiased Samples t take a look at.

since, the two agencies are independent and we're checking if difference is good sized is independent-samples t test.

consequently, the statistical test that compares the distribution of imply differences between two companies to the imply difference among  corporations is unbiased-pattern t check.

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Answer:

m = 0

Step-by-step explanation:

AB has a slope of y2 - y1 / x2 - x1 so -8-5/3-3 so -13/0 = undefined so it is a vertical line, so any line that is horizontal will be perpendicular to it, so horizontal lines have a zero slope

Nate’s revenue will exceed his expenses when he has mowed at least 21 lawns and has earned a total of $525 or more.

The answer to this question depends on the total cost of Nate’s lawn mower and gas. If we assume that Nate’s lawn mower costs $500 and that he needs $20 of gas to mow each lawn, then Nate’s total expenses are $520. This means that Nate’s revenue must exceed $520 before his business will be profitable.

Nate’s revenue comes from charging clients $25 per lawn. This means that Nate must mow at least 21 lawns before his revenue exceeds his expenses. If Nate mows more than 21 lawns, then his revenue will exceed his expenses.

To reach this point, Nate must be sure to keep his expenses low and to market his business effectively. With hard work and dedication, Nate will be able to make a profit from his lawn-mowing business.

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The total amount that Jimmy has saved is $420.

Ratio shows the relationship between two or more numbers. It is the  number of times that one value is contained within other value.

Total amount saved = (sum of ratios x total value of R5 saved) / ratio that represents R5 saved

Sum of ratios = 2 + 5 + 7 = 14

Total value of R5 saved = 12 x 5 = R60

= (14 x 60) / 2 = $420

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Answer:

the answer is -1/12

Answer:

b is your answer

Step-by-step explanation:

This is because 1/6 divided by -1/2 = -1/12

The speed the package hits the porch when it is released by the drone is 16.9 m/s (approx)

Given data: Height of drone, h = 14.1 m

           Velocity of drone, v = 22.6 km/h

The speed the package hits the porch when it is released by the drone.

It is given that the drone is flying at a height of 14.1 m above the porch and it releases the package. The package falls freely under gravity.

               We can use the formula for the velocity of a freely falling body to calculate the speed the package hits the porch.                                  

                                                     v² = u² + 2gh

Here, g is the acceleration due to gravity and u = 0 as the package is initially at rest.

Therefore, the above formula becomes,

                                                v² = 2ghv = √(2gh)

We know that the height of the drone above the porch is h = 14.1 m.

We can convert the velocity of the drone,

                                             v = 22.6 km/h, into m/s.

                                             1 km/h = 1000 m/3600 s = 0.27778 m/sv = 22.6 km/h = 22.6 × 0.27778 m/s = 6.27708 m/s

Substituting the given values in the above formula, we get,

                                          v = √(2gh)= √(2 × 9.81 m/s² × 14.1 m)≈ 16.91 m/s

Therefore, the speed the package hits the porch when it is released by the drone is 16.9 m/s (approx)

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(x+1) dοes nοt divide x^4 - x - 1 evenly.

In Mathematics, there are twο different methοds tο divide the pοlynοmials. One is the lοng divisiοn methοd. Anοther οne is the synthetic divisiοn methοd. Amοng these twο methοds, the shοrtcut methοd tο divide pοlynοmials is the synthetic divisiοn methοd.

It is alsο called the pοlynοmial divisiοn methοd οf a special case when it is dividing by the linear factοr.  It replaces the lοng divisiοn methοd.  In certain situatiοns, yοu can find this methοd easier.

Tο use synthetic divisiοn, we write the pοlynοmial as:

\(\rm x^4 - x - 1 = 0x^3 + 1x^2 + 0x - 1x - 1\)

Nοw we will perfοrm synthetic divisiοn using -1 as the rοοt (since we are checking if X+1 is a factοr).

-1 | 0   1   0  -1  -1

|    0  -1   1  -2

|-----------------

0   1  -1   0  -3

The numbers οn the bοttοm rοw οf the synthetic divisiοn table are the cοefficients οf the resulting pοlynοmial after dividing by (x+1). We can see that the last number, -3, is nοnzerο, which means that (x+1) is nοt a factοr οf \(x^4 - x - 1\).

Therefοre, (x+1) dοes nοt divide \(x^4 - x - 1\) evenly.

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1. (4a - 5)+(3a + 6) = 7a + 1.
To solve, you simply combine the like terms (4a and 3a) to get 7a, and then combine the constants (-5 and 6) to get 1.

2. (6x + 9)+ (4x^2 - 7) = 4x^2 + 6x + 2.
To solve, you combine the like terms (6x and 4x^2) to get 4x^2 + 6x, and then combine the constants (9 and -7) to get 2.

3. (6xy + 2y + 6x) + (4xy - x) = 10xy + 2y + 6x - x = 10xy + 2y + 5x.
To solve, you combine the like terms (6xy and 4xy) to get 10xy, then combine the constants (2y and -x) to get 2y - x, and finally combine the like terms (6x and 5x) to get 11x. The final answer is 10xy + 2y + 5x.

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Answer:

The correct answer is y = -6x - 4

Step-by-step explanation:

The given equation of the line : y = -6x + 2

Now, the general equation of the line in the slope-intercept form is given by : y = mx + c

Now, comparing the given equation with the general form, We get slope, m = -6

We need to find the equation of the line which is parallel to the given line and since the slope of two parallel lines are equal so the slope of the required line will also be -6

And it passes through the point (-1, 2)

The required equation will be :

⇒ y - 2 = -6 × (x + 1)

⇒ y - 2 = -6x - 6

⇒ y = -6x - 4

Therefore, The required equation is y = -6x -4

Hence, The correct answer is. y = -6x - 4

Brainlist?????

Answer:

the first option

Step-by-step explanation:

i know there's a rule to all of this but it's been a while since i've done this kind of math.

if you plug in the zeros to the equation, they solve

(-2, 0) --> (-2-2)(-2+1)(-2+2) = 0

(-1, 0) --> (-1-2)(-1+1)(-1+2) = 0

(2, 0) --> (2-2)(2+1)(2+2) = 0

Answer: DE = 17

Step-by-step explanation:

You can solve by similar triangle ratios or by pythagorean theorem:

AB/CD = CD/x

54/76.5 = 12/x

Solve for x:  54x = 12(76.5) = 918

x = 918/54 = 17

Or, because CDE is a right triangle:

\(12^{2} + 12^{2} = x^{2}\)

\(x^{2} = 288\\\)

x = \(\sqrt{288} = 17\)

Answer:

B

Step-by-step explanation:

He was accepted to UCLA's School of Management