1.7.3 Quiz: Linear and Exponential Growth
What is the common ratio in this sequence: 5,15,45,135?
Options:
A.5
B.-3
C.1/3
D.3

To find the union and intersection of the intervals I₁ = (-2, 2] and I₂ = [1, 5), let’s consider the overlapping values and the combined range.

The union of two intervals includes all the values that belong to either interval. Taking the union of I₁ and I₂, we have:

I₁ U I₂ = (-2, 2] U [1, 5)

To find the union, we combine the intervals while considering their overlapping points:

I₁ U I₂ = (-2, 2] U [1, 5)
= (-2, 2] U [1, 5)

So the union of the intervals I₁ and I₂ is (-2, 2] U [1, 5).

Now let’s find the intersection of the intervals I₁ and I₂, which includes the values that are common to both intervals:

I₁ ∩ I₂ = (-2, 2] ∩ [1, 5)

To find the intersection, we consider the overlapping range between the two intervals:

I₁ ∩ I₂ = [1, 2]

Therefore, the intersection of the intervals I₁ and I₂ is [1, 2].


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Answer:

2.5

Step-by-step explanation:

1/6 + 5/8

First find the lcm of 6 and 8

l c m of 6 and 8 =24

convert each fraction to its equivalent with 24 as its denominator

That is;

1/6 = 4/24

5/8 = 15/24

Then add

4/24 + 15/24

= 19/24

The equation that represents how much will be in the account after 7 years is f(x) = 5500 * (1.028)⁷

From the question, we have the following parameters that can be used in our computation:

The equation that represents how much will be in the account after 7 years is represented as

f(x) = P * (1 + r)ˣ

Where

P = 5500

r = 2.8% =

Substitute the known values in the above equation, so, we have the following representation

f(x) = 5500 * (1 + 2.8%)ˣ

Evaluate the sum

f(x) = 5500 * (1.028)ˣ

After 7 years, we have

f(x) = 5500 * (1.028)⁷

Hence, the equation is f(x) = 5500 * (1.028)⁷

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Answer:

D

Step-by-step explanation:

Capital of babylonian

The integral, ∫ [ (9ˣ - eˣ )/3ˣ ] dx evaluate value is 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3). So, the correct answer is option (c).

Integration is defined as the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up all their areas. If d/dx(F(x) = f(x), then ∫ f(x) dx = F(x) + C, where C is integration constant and indefinite integrals. We have an integral, say , I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

and we have to determine its value.

I = ∫ [ (9ˣ - eˣ )/3ˣ ] dx

=> I = ∫ [ (9ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3²ˣ/3ˣ - eˣ/3ˣ ] dx

=> I = ∫ [ (3ˣ - eˣ/3ˣ ] dx

=> I = ∫ 3ˣ dx - ∫ eˣ3⁻ˣ dx

=> I = 3ˣ/ ln(3) - eˣ/3ˣ(1 - ln 3) + C

( since, ∫aˣ dx = aˣ/ln a)

where C --> integration constant

So, the required value is 3ˣ/ln(3)-eˣ/3ˣ(1 - ln 3).

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Complete question:

Find integral ∫ [ (9ˣ - eˣ )/3ˣ ] dx .

a) 3ˣ - eˣ/(1 - ln 3) + C

b) 9ˣ/2ln3 - eˣ/(3ˣ ln 3) + C

c) 3ˣ/ln3 - eˣ/3ˣ(1 - ln 3) + C

d) 3ˣ/ln3 - eˣ/3ˣ + C

To compare the means of three independent sections, three separate independent sample t-tests were conducted. The p-values for each pairwise comparison are as follows: the p-value for comparing sections 1 and 2 is 0.2458, the p-value for comparing sections 1 and 3 is 0.0267, and the p-value for comparing sections 2 and 3 is 0.3667. Based on a significance level of α = 0.05, the pairwise comparison of sections 1 and 3 indicates a statistically significant difference in means.

In the first pairwise comparison between sections 1 and 2, the p-value of 0.2458 is greater than the significance level of α = 0.05. Therefore, we do not have sufficient evidence to conclude that there is a statistically significant difference in means between sections 1 and 2.

In the second pairwise comparison between sections 1 and 3, the p-value of 0.0267 is less than the significance level of α = 0.05. This indicates that there is a statistically significant difference in means between sections 1 and 3.

In the final pairwise comparison between sections 2 and 3, the p-value of 0.3667 is greater than α = 0.05. Hence, we do not have enough evidence to conclude that there is a statistically significant difference in means between sections 2 and 3.

Therefore, based on the conducted t-tests, the only pair of groups that have statistically significantly different means at the 0.05 significance level is sections 1 and 3.

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Hello!

\(\large\boxed{x = 5}\)

11 - (3x + 1) = 7(x - 6) + 2

Distribute the coefficients outside of the parenthesis:

11 - (3x) - (1) = 7(x) + 7(-6) + 2

Simplify:

11 - 3x - 1 = 7x - 42 + 2

Combine like terms:

10 - 3x = 7x - 40

Add 3x to both sides to isolate x:

10 = 10x - 40

Add 40 to both sides:

50 = 10x

Divide both sides by 10:

x = 5

Answer:

11-3x-1=7x-42+2

Put all like terms together

10+40=10x

x=50

Answer:

25.2%

Step-by-step explanation:

Step one:

given data

The glove was priced $ 62.00 on Monday

and $ 46.36 on Saturday

We can see that there was a price reduction

Required

The percentage reduction in price

Step two:

Percent reduction = change in price/old price *100

Percent reduction = 62-46.36/62 *100

Percent reduction = 15.64/62 *100

Percent reduction = 0.252 *100

Percent reduction = 25.2%

Answer:

18

Step-by-step explanation:

\(distance=\sqrt{(1+2)^2+(2+1)^2}=\sqrt{18}.\)

Answer:

60%

Step-by-step explanation:

15/25=60%

you ate 15 out of 25 so that means you ate 3 out of 5 if you divide both 15 and 25 by 5. And 3 out of 5 is 60%.

The minimum percentage of recent graduates who have salaries between $22,800 and $27,000 is 75%

What is chebyshev's theorem ?

The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.

Given that

μ=24900,σ = 1050

From above we have

μ-2σ = 24900 -2. 1050 = 22800

μ+2σ = 24900 + 2. 1050 = 27000

That is k =2 and

1- 1/k^2 = 1 - 1/4 = 3/4 = 75%

So according to Chebyshev's Theorem, at least  75.0% of recent graduates who have salaries between $22,800 and $27,000.

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Answer:

tanD =4/7

Step-by-step explanation:

tanD = P/B

Where P=4 and B=7

So;

tanD=4/7

To find the coordinates of the endpoints of the image A'B' (A9B9) after dilation of AB by a scale factor of 2 centered at (3,5), follow these steps:

Step 1: Use the given scale factor (2) and center of dilation (3,5).

Step 2: Apply the dilation formula to the coordinates of the original points A and B. The formula for dilation with scale factor k centered at (h,k) is:

A'(x', y') = (h + k(x - h), k + k(y - k))

Step 3: Substitute the given options for A9 and B9 into the dilation formula and check which pair of coordinates satisfy the formula.

After applying the formula, it is determined that the coordinates of the endpoints of the image A9B9 after dilation with a scale factor of 2 centered at (3,5) are:

A9(21, 6) and B9(7, 4).

Option (2) is correct.

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Answer:

C.) the quantitnes are equal

Step-by-step explanation:

An equation of the plane with the given characteristics is:

15x - 8y - 14z = 37.

We can use the cross product to find a vector that is perpendicular to both the plane we're given (8x+7y+4z=17) and the plane we're trying to find.

First, we find the direction vector of the line that passes through the two given points:

<5, 1, -7> - <5, 3, 1> = <0, -2, -8>

Now, let's find the normal vector of the plane we're given, which is the coefficients of x, y, and z in the equation 8x+7y+4z=17:

<8, 7, 4>

To find a vector perpendicular to both of these, we take the cross product:

<0, -2, -8> x <8, 7, 4> = <-60, 32, 56>

This vector is perpendicular to both lines, so it is a normal vector to the plane we're looking for.

Now, we need to find the constant term in the equation of the plane. We can use either of the two given points to do this. Let's use (5, 3, 1):

-60(x - 5) + 32(y - 3) + 56(z - 1) = 0

Simplifying, we get:

-60x + 300 + 32y - 96 + 56z - 56 = 0

-60x + 32y + 56z = -148

Dividing through by -4, we get:

15x - 8y - 14z = 37

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There are no specific numbers to provide, and the minimum product is undefined in this case.

The minimum product of two numbers whose difference is 48 is obtained when the two numbers are consecutive integers. Let's represent the smaller number as x.

The next consecutive integer would be x + 1. The difference between these two numbers is (x + 1) - x = 1.

According to the given information, the difference between the two numbers is 48. So we have the equation:

x + 1 - x = 48

Simplifying the equation, we find:

1 = 48

This equation is not solvable, as it leads to an inconsistency. It means that there are no two numbers whose difference is exactly 48. Therefore, there are no specific numbers to provide, and the minimum product is undefined in this case.

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Answer:

D: they all type equally fast

Step-by-step explanation:

Answer:

Answer below!

Step-by-step explanation:

You would start at (0, -4) which is the y-intercept according to the equation.

Other points:

y(1) = 3x - 4

     = 3(1) - 4

     = 3 - 4

     = -1

(1, -1)

y(2) = 3(2) - 4

      = 6 - 4

      = 2

(2, 2)

It takes 10 hours to reach a population of 200,000 at the growth rate of 7% per hour.

We can use the formula for compound interest to calculate the time it takes for the population of bacteria to reach 200,000.

The formula is:
A = P(1+r)^t

Where:
A = final amount (200,000)
P = initial amount (50,000)
r = growth rate (7% per hour expressed as decimal)
t = time (in hours)

We can rearrange the formula to solve for t:
t = log(A/P) / log(1+r)

By plugging in the given values:
t = log(200000/50000) / log(1+ 0.07)

The answer will be in hours, so we need to use a calculator or a log function in a programming language to get the answer.

Alternatively, you can use the rule of 70, which says that the number of years required to double a population at a given growth rate is approximately 70/growth rate. So in this case it is 70/7 = 10 hrs.

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To find the maximum likelihood estimator (MLE) for λ, we need to maximize the likelihood function L(λ) with respect to λ of the Poisson distribution

First, let's write the probability density function (PDF) of the Poisson distribution:
P(X = k) = (e^(-λ) * λ^k) / k!

The likelihood function can be defined as the product of the probabilities for each observation in the random sample. Since the sample is independent and identically distributed, we can write the likelihood function as:
L(λ) = P(x1, x2, ..., xn | λ) = P(x1 | λ) * P(x2 | λ) * ... * P(xn | λ)

Taking the logarithm of the likelihood function (log-likelihood) will simplify the calculations. The log-likelihood function is:
log(L(λ)) = log(P(x1 | λ)) + log(P(x2 | λ)) + ... + log(P(xn | λ))

Now, let's calculate the derivative of the log-likelihood function with respect to λ:
d/dλ log(L(λ)) = d/dλ (log(P(x1 | λ)) + log(P(x2 | λ)) + ... + log(P(xn | λ)))
= d/dλ (log(P(x1 | λ))) + d/dλ (log(P(x2 | λ))) + ... + d/dλ (log(P(xn | λ)))

To find the MLE, we set the derivative equal to zero and solve for λ:
d/dλ log(L(λ)) = 0

The derivative of log(P(x | λ)) with respect to λ can be calculated using the logarithmic differentiation technique. After taking the derivative, we equate it to zero and solve for λ.

By solving the equation, we will obtain the MLE for λ.

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Answer:

30 miles.

Step-by-step explanation:

To calculate distance traveled, you multiply the miles per hour by the number of miles. In this problem, it is 20 times 1.5 or 20 times 1 1/2. This equals 30 miles per hour.

The number that was left out is 70.

Average is the sum of a set of numbers divided by the total numbers in the data set.

Average = sum of numbers / total numbers

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Answer:

Marcus will pay $44 for that game

Explanation:

The coupon will allow him a wavier of 20% on the price of the game. Thus, the money Marcus needs to pay is: $(55-0.20*55) = $(55-11) = $44

To maintain a familywise significance level of 0.1 across all ten hypothesis tests use a significance level of 0.01.

To maintain a familywise significance level of 0.1 for ten hypothesis tests, you need to adjust the significance level for each individual test to account for multiple testing.

One commonly used method is the Bonferroni correction.

The Bonferroni correction involves dividing the desired overall significance level (0.1) by the number of tests (10) to obtain the adjusted significance level for each individual test.

Adjusted significance level = Overall significance level / Number of tests

Adjusted significance level = 0.1 / 10 = 0.01

Therefore, for each individual test, you should use a significance level of 0.01 to maintain a familywise significance level of 0.1 across all ten hypothesis tests.

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The formula for the final velocity,\(v_{f}\) , in terms of initial velocity, vi, acceleration, a, and time, t is given by \(V_{f}=at+V_{i}\)

A =\((V_{f}-V_{i} )/t\)  You can put \(1\) under A and then cross multiply.

\(at =V_{f} -V_{i}\)

Get \(V_{f}\)  by adding  \(V_{i}\) in both sides of the equation.

\(at+V_{i} =V_{f}\)

                                                OR

The final speed \(V_{f}\) in terms of other parameters is given by the relation \(V_{f}\)\(=at+V_{i}\)

How to calculate the acceleration of an object?

Mathematically, acceleration is calculated using this formula:

\(a=(V_{f}-V_{i} )/t\)

Where:

Making \(V_{f}\) the subject of the formula, we have:

\(at =V_{f} -V_{i}\)

\(V_{f} =V_{i} +at\)

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Given the following:

Then:

In this case, we are given:

a = (9x + 26)

b = 251

To find c, we rest a whole circle (360) and rest angle b:

And now, we use the formula from above:

And solve for x:

The answer is the last option, x = 5

The weakest correlation is represented by the value of c. 0.11.

The weakest correlation is represented by the value that is closest to zero, as it indicates a weaker relationship between the variables. In this case, the answer is: c. 0.11

A correlation coefficient of 0.11 is closer to zero than the other options provided, indicating a weaker correlation compared to the rest. The negative values (-0.75 and -0.27) represent negative correlations, but their magnitudes are larger than 0.11, making them stronger correlations (although still considered weak in general). The positive value of 0.54 represents a moderate positive correlation.

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