determine the solution to the equation.

Answer:

The correct option is;

C) 6554

Step-by-step explanation:

The given data are;

Day,   Amount of change in Bacteria

1,            2

2,          -8

3,           32

4,          -128

Given that the data follows a geometric sequence, we have;

The first term of the series = 2, the common ratio = -4, the sum of a geometric progression is given by the following formula;

\(S_n = \dfrac{a \times \left (r^n - 1\right )}{r - 1}\)

Which gives;

\(S_7 = \dfrac{2 \times \left ((-4)^7 - 1\right )}{(-4) - 1} = \dfrac{2 \times \left (-16384- 1\right )}{-4 - 1} = \dfrac{2 \times \left (-16385\right )}{-5} = 6554\)

Therefore, the correct option is C) 6554.

The t-test assuming equal variances means Pooled t-test in which variances of the two sample populations are equal.

The pooled t-test is the statistical procedure that assumes that population variances are equal. Finding a weighted average of the two independent sample variances is referred to as pooling. By combining data from samples from populations 1 and 2, we may estimate the common variance when there is solid evidence that population 1's variance is equal to population 2's variance.

Compare the ratio of the two sample standard deviations as a quick way to verify this. The ratio would be compared as: S1/S2. The ratio would be 1, or, in the event that the two are equal.

However, we cannot anticipate the ratio to be exactly 1, as they are samples and as a result, there will be some errors. Thus, the pooled t-test implies whether the null-hypothesis should be accepted or rejected.

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To determine which events are mutually exclusive, we need to identify the events that cannot occur at the same time.

The options for the events are: Landing on a shaded section Landing on an even number Landing on an odd number Landing on a section that is not shaded Now let's analyze the options Landing on a shaded section (1 or 4) and landing on an even number (2 or 4) are mutually exclusive, as they cannot occur at the same time.

Landing on a shaded section (1 or 4) and landing on an odd number (1 or 3) are not mutually exclusive, as they can occur at the same time if the spinner lands on section 1. The mutually exclusive events in this scenario are:  Landing on a shaded section Landing on an even number

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From the given information, the two mutually exclusive events are:
1. Landing on a shaded section (sections 1 or 4)
2. Landing on an even number (sections 2 or 4)

Therefore, these are the two options that are mutually exclusive based on the spinner's configuration.

The term "mutually exclusive" refers to events that cannot occur at the same time. In this case, we need to determine which events on the spinner are mutually exclusive given the information provided.

To start, let's list the numbers on the spinner: 1, 2, 4, and 3. We are told that sections 1 and 4 are shaded, and the spinner is pointed at number 2.

Event 1: Landing on a shaded section.
This event includes landing on either section 1 or section 4. Since these sections are shaded, they cannot occur simultaneously with any other section on the spinner.

Event 2: Landing on an odd number.
This event includes landing on either section 1 or section 3. These sections are mutually exclusive with the even numbers, which are 2 and 4.

Event 3: Landing on a multiple of 4.
This event includes landing on section 4. Since section 4 is shaded, it cannot occur simultaneously with any other section on the spinner.

Event 4: Landing on an even number.
This event includes landing on either section 2 or section 4. These sections are mutually exclusive with the odd numbers, which are 1 and 3.

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Answer:

one solution

Step-by-step explanation:

they have different slopes and are linear

Answer:

Her monthly rate per month is $12

Step-by-step explanation:

On the 0 month is what she already had in her bank account.

Also the months are going by 2's so it's going by $24 dollars every 2 months, so 24 divided by 2 is 12.

Normal distribution is a continuous, symmetric, bell-shaped distribution of a variable, and the mean, median, and mode are equal and located at the center of the distribution. True A

This is the definition of a normal distribution, which is also known as a Gaussian distribution. The curve of a normal distribution is bell-shaped because it has higher frequency values in the middle than it does at either end, and it is symmetric because it is mirrored around its center.

                                The normal distribution is the most common probability distribution, with many naturally occurring events that can be modeled using it. The normal distribution is used in statistics, engineering, economics, and other fields to model a variety of real-world phenomena.

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Answer:

2.7*10³=2700

note if power positive you add '0s' to the back eg 10³=1000 if the power is negative e.g10^-3 add to the front and a decimal e.g 0.001

\(\\ \sf \longmapsto 2.7\times 10^3\)

\(\\ \sf \longmapsto 27\times 10^{-1}\times 10^3\)

\(\\ \sf \longmapsto 27\times 10^{-1+3}\)

\(\\ \sf \longmapsto 27\times 10^2\)

\(\\ \sf \longmapsto 27\time 100\)

\(\\ \sf \longmapsto 2700\)

Answer:

Between 0 and 3: decreasing

Between 3 and 4: constant (stays the same)

Between 4 and 8: decreasing

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

First bullet is called Perfect Square Trinomial (PST), the first and last is a perfect square and the middle is twice the product of the squared first and last term.  To factor, just copy the middle sign and square the first and last term.

---

2nd bullet is also a PST with a value on a. Likewise you just need to square the first and last term. Then, copy the middle sign.

--

3rd bullet is a trinomial. To get the factor, get the prime factor of the value of a. Then, find the factors of 8 that when add up results to the value of b.

-

4th bullet is a special case. First get the square root of the first and last term, and copy the sign, Then, copy the factors and change it to the opposite sign.

Answer:

G The theoretical probability is less than the experimental probability

\((5x^{4} )^{3} \\=5x^{4*3} \\=5x^{12}\)

I used the law of exponents as indicated below:

\((x^{n} )^{m} \\=x^{n*m} \\=x^{nm}\)

Answer:

Its B and E

Step-by-step explanation:

PLS MAKE ME BRAINLIEST

Answer:

16 = Y

Step-by-step explanation:

Answer:

1539/4 (improper fraction) or 384 3/4 (simplified fraction)

Step-by-step explanation:

To find the improper fraction, write 384.75 as a fraction:

384.75/1

Then, since you have 2 decimal places after the ., multiply the entire fraction by 100:

38475/100

Next, find the GCF, which is 25, and simplify this fraction to find the final improper fraction:

1539/4

To find the simplified fraction, we already have the whole number, 384, so we have to convert 0.75 to a fraction which is 3/4, because 0.75 is 3/4 of 100:

384 3/4

Hope this helps :)

Answer:

hola hi

La verdad no se Inglés y no te podría ayudar

The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²

Missing data from the problem:

radius of the barrel = 0.4 meters

height of the barrel = 1.2 meters

The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:

A = 2. πr² + 2. πr.h

Where:

r = radius

h = height

Plug the parameters into the formula:

A = 2. π(0.4)² + 2. π(0.4).(1.2)

A = 13 m²

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The rate of change of y with respect to x for this linear function is 1/5 or 0.2

A linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.

Mathematically, the average rate of change (slope) of a linear function can be calculated by using this formula;

\(Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Substituting the given points into the formula, we have;

Average rate of change = (3 - 2)/(10 - 5) = (4 - 3)(15 - 10)

Average rate of change = 1/5 or 0.2

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The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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A regression model allows us to examine how the probability distribution of a dependent variable, Y, might be related to one or more independent variables (collectively called X). Therefore, the correct answer is (a) regression model.

A regression model is a statistical tool used to model the relationship between a dependent variable (often denoted as Y) and one or more independent variables (often denoted as X). It can help us understand how changes in the independent variables affect the values of the dependent variable, and can be used to make predictions or estimate values of the dependent variable based on specific values of the independent variables.

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Answer:

The length of the missing side is 18yd

Step-by-step explanation:

Sq30 - Sq 24 = Sq (x)

The expressions are expanded to give;

1. 2x² - 5x

2. 6x² + 8x

3. 6x² - 12xy

Algebraic expressions are defined as expressions consisting of  variables, coefficients, constants, terms and factors.

These expressions are also known to consist of mathematical operations, which includes;

From the information given, we have that;

a. x (2x - 5)

expand the bracket

2x² - 5x

b. 2x (3x+4)

expand the bracket

6x² + 8x

c. 6x(x-2y)

expand the bracket

6x² - 12xy

Hence, the expressions are 2x² - 5x, 6x² + 8x and 6x² - 12xy

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Answer:

1) 2x² - 5x

2) 6x² + 8x

3) 6x² - 12xy

Step-by-step explanation:

1) x ( 2x - 5 )

To expand the above, multiply both terms inside the brackets by x.

2x² - 5x

2) 2x ( 3x + 4 )

To expand the above, multiply both terms inside the brackets by 2x.

6x² + 8x

3) 6x ( x - 2y )

To expand the above, multiply both terms inside the brackets by 6x.

6x² - 12xy

Answer:

Yes it does

Step-by-step explanation:

did it on edge

The solution to the problem shows us that we have that m = 21.

1/3(m - 12) = 3

We would now have to multiply all the terms on the left hand side by 1/3 and by so doing apply the distributive property and we are going to have that;

m/3 - 4 = 3

We would now have to add four to both sides so that we can have the equation balanced and we have that;

m/3 - 4 + 4 = 3 + 4

m/3 = 7

We can now multiply both sides by three as we can see to have the solution to the problem and then we are going to have that;

m/3 * 3 = 7 * 3

m = 21

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We find that the probability of a randomly generated sequence of 24 binary digits having exactly half of the digits as 0s is C(24, 12) / 2^24.

To find the probability that exactly half of the 24 binary digits are 0s in a randomly generated sequence, we can use the following steps:
Determine the total number of possible sequences.
Since there are 24 binary digits and each digit can be either 0 or 1, the total number of possible sequences is 2^24.
Calculate the number of sequences with exactly 12 0s.
In a sequence of 24 binary digits, we want to choose 12 positions for the 0s. This can be done using the combination formula, which is C(n, k) = n! / (k!(n-k)!), where n is the total number of digits and k is the number of 0s. In this case, n = 24 and k = 12. So, C(24, 12) = 24! / (12! * (24-12)!).
Compute the probability.
Divide the number of sequences with exactly 12 0s by the total number of possible sequences. Probability = C(24, 12) / 2^24.
By following these steps, we find that the probability of a randomly generated sequence of 24 binary digits having exactly half of the digits as 0s is C(24, 12) / 2^24.

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Answer: Infinite Solutions.

Step-by-step explanation:

We will transform both equations into slope-intercept form.

       Equation M: 3y = 3x + 6 ➜ y = x + 2

       Equation P: y = x + 2

The two given equations are the same, meaning there are infinite solutions. We can also see this when we graph these two equations, see attached. It's hard to show as they overlap infinitely, but I did my best.

Answer:

B (x+7=19)

Step-by-step explanation:

We don't know Steve's age, so make his age=x. If his parrot is 19 years old and he's 7 years older than Steve, you would be adding 7 years onto Steve's age. So, to do that it would be x+7=19 or B!

By using  Fundamental Theorem of Calculus, we find the derivative of the function g(x) = In { sqrt( t + t^3)dt } limit from x to 0 is  ln(sqrt(x + x^3)).  The derivative of the function g(x) = { In (1+t^2) dt} where limit are from x to 1 is  ln(1 + x^2).

The Fundamental Theorem of Calculus, which states that if a function is defined as the definite integral of another function, then its derivative is equal to the integrand evaluated at the upper limit of integration.

So, applying this theorem, we have:

g'(x) = d/dx [∫x_0 ln(sqrt(t + t^3)) dt]

= ln(sqrt(x + x^3)) * d/dx (x) - ln(sqrt(0 + 0^3)) * d/dx (0)

= ln(sqrt(x + x^3))

Therefore, g'(x) = ln(sqrt(x + x^3)).

Using the Fundamental Theorem of Calculus, we have:

g'(x) = d/dx [∫1_x ln(1 + t^2) dt]

= ln(1 + x^2) * d/dx (x) - ln(1 + 1^2) * d/dx (1)

= ln(1 + x^2)

Therefore, g'(x) = ln(1 + x^2).

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____The given question is incomplete, the complete question is given below:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = In { sqrt( t + t^3)dt } limit from x to 0.  8. g(x) = { In (1+t^2) dt} where limit are from x to 1.