Explain whether the given equation defines an exponential function. give the base
for each function.
y=x^6

Answer:

3(10m - 2)+(3+6m-3)

30m-6+3+6m-3

30n+6m-6+3-3

36m-6

6(6m-1)

Answer:

36m - 6

Step-by-step explanation:

3 ( 10m - 2 ) + ( 3 + 6m - 3 )

→ Expand the brackets

30m - 6 + 3 + 6m - 3

→ Simplify

36m - 6

Answer:

C

Step-by-step explanation:

Answer:

it b or c

Step-by-step explanation:

Answer:

2/5 of 15 is 6

Step-by-step explanation:

Multiply 2 and 15

2 × 15 = 30

Divide 30 by 5

30 ÷ 5 = 6

No, the F-test statistic cannot be less than 1 when it represents the larger of two sample variances.

The F-distribution is always a positive distribution with a range of values greater than zero. The F-test value is always greater than or equal to 0, but it is not always less than or equal to 1.

The numerator, representing the bigger sample variance, is always greater than or equal to the denominator, representing the smaller sample variance. Consequently, the F-ratio, which is the ratio of the larger to the smaller variance, is always greater than or equal to 1. Thus, an F-test statistic that is less than 1 is mathematically incorrect.

Therefore, an F-test statistic is always a positive number that is greater than or equal to zero and greater than or equal to 1. This is because the numerator of an F-distribution is always greater than or equal to the denominator.

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Answer:

Seriously, It is just 400, or C

Step-by-step explanation:

Answer:

69r 420s

Step-by-step explanation:

you gotta do that and do this to that and after that you get that

Answer:

81 eggs

Step-by-step explanation:

already had 9 eggs

6 crates x 12 eggs in each crate

= 72 eggs

72+9=81

The two consecutive integers are -8 and -7, or 7 and 8.

To solve this problem, we can use the concept of consecutive integers. Let's call the first integer x. The next consecutive integer would be x + 1.

According to the problem, the product of these two consecutive integers is 56. So we can set up the equation:

x * (x + 1) = 56

Expanding the equation, we get:

x^2 + x = 56

Rearranging the equation to standard quadratic form:

x^2 + x - 56 = 0

Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Factoring is the simplest method in this case. We can factor the equation as:

(x + 8)(x - 7) = 0

Setting each factor equal to zero, we get two possible solutions:

x + 8 = 0  or  x - 7 = 0

Solving these equations gives us:

x = -8  or  x = 7

So the two consecutive integers are -8 and -7, or 7 and 8.

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Answer:

Welp, good luck the answer is c

Step-by-step explanation:

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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Answer:

3 pi 9

Step-by-step explanation:

The given statement "The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line" is true because it provides the best fit line.

The simple linear regression equation estimates the relationship between two variables - a dependent variable (y) and an independent variable (x) - by fitting a straight line through the data points.

The line is chosen so that the sum of the squared deviations (also known as the sum of squared errors or SSE) between the observed values of y and the predicted values of y on the line is minimized.

In other words, the simple linear regression equation finds the line that is closest to all the data points in terms of the vertical distance between the points and the line.

This line is chosen to minimize the sum of squared deviations because it provides the best estimate of the relationship between x and y, and it allows for the prediction of y values for a given x value.

Thus, minimizing the sum of squared deviations is a crucial aspect of the simple linear regression equation because it ensures that the line of best fit provides the most accurate estimate of the relationship between the variables.

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Let the length of the side of the square being cut out equal x

The length of the box would be 4.5 - 2x

The width of the box would be 3 -2x

Volume = (4.5 -2x) * (3-2x) * x

Simplify to:

V = 4x^3 - 15x^2 + 13.5x

B See picture: The greatest volume would be the point of the highest curve.

x = 0.589 y = 3.565, Rounded to the nearest tenth x = 0.6

Process: entered the equation from A into Desmos. The Y value would be the volume, so found where the volume was the highest and then found the related x value.

C) X is the side length of the corner squares being cut out, which would also be the height of the box. The Y value is the volume of the box.

The given limit is: lim (x->0) (sin(9x) / x)

To estimate this limit, we can apply L'Hôpital's Rule since we have an indeterminate form (0/0 as x approaches 0). L'Hôpital's Rule states that if the limit of the ratio of the derivatives of the numerator and the denominator exists, then the limit of the original function exists and is equal to that value.

Taking the derivative of the numerator and the denominator with respect to x:

Numerator: d(sin(9x))/dx = 9cos(9x)
Denominator: d(x)/dx = 1

Now, we find the limit of the ratio of the derivatives:

lim (x->0) (9cos(9x) / 1)

As x approaches 0, cos(9x) approaches cos(0), which is 1. Therefore, the limit is:

lim (x->0) (9cos(9x) / 1) = 9(1) = 9

So, the limit exists and is equal to 9.

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The answer is 32 pounds. using division operation

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

Elena estimates 8 pounds of meat will feed about 36 people.

So we can tell that 36 people will have 8 pounds of meat.

The total meat will require for 1 person will be 8/36 pounds

she is expecting 144 people

So total meat required will be = 8/36 * 144 = 32 pounds

Hence she will have to make meat of 32 pounds in order to feed 144 people.

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Answer:

Having trouble using logarithmic differentiation!

Answer:

Step-by-step explanation:

The discriminant is what's under the square root sign in the quadratic equation.  The equation for the discriminant is \(b^{2}-4ac\), where b is the coefficient of x, a is the coefficient of \(x^{2}\), and c is the number with no variable attatched to it.  If we plug in the numbers (\(17^{2} -4*4*3\)) it gives you 241, which is the discriminant.  Since 241 is more than zero, it has 2 zeros.  If the discriminant was 0, there'd be 1 zero, and less then zero there would be zero zeros.

Step-by-step explanation:

The sum of consecutive squares is

\(1^2+2^2+\dots+n^2=\frac16n(n+1)(2n+1)\)

Therefore

\(1^2+2^2+\dots+30^2=\frac16(30)(31+1)(2\cdot30+1) = 9455\)

The value of mean is 5.5 and the value of standard deviation is 1.44.

Now, we need to find the mean and standard deviation of this random variable. The mean of a uniformly distributed random variable can be found by taking the average of the lower and upper bounds of the distribution. In this case, the lower bound is 3 and the upper bound is 8, so the mean would be:

Mean = (3+8)/2 = 5.5

So, the expected number of tickets purchased by an individual is 5.5.

Next, we need to find the standard deviation. The standard deviation is a measure of the deviation or spread of the data from the mean. For a uniform distribution, the formula for standard deviation is:

Standard Deviation = (Upper Bound - Lower Bound) / √12

Plugging in the values, we get:

Standard Deviation = (8-3) / √(12) = 1.44

This means that on average, the number of tickets purchased by an individual is expected to deviate from the mean by about 1.44 tickets.

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The range of x will be -5 to 9 so -5° < x < 9°.

The three-sided shape known as a triangle is sometimes used to allude to it. Every triangle has three sides and three angles, some of which might be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

The minimum possible value of angle  3x + 15 is 0°

So,

3x + 15 = 0

x = -5

The maximum possible value of angle 3x + 15 is 42°

So,

3x + 15 = 42

x = 9

Hence the range of x will be -5° < x < 9°.

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Answer:

96cm

Step-by-step explanation:

4cm x 4cm x 6cm = 96scm

Answer:

D

Step-by-step explanation:

that's where they cross

Answer: It would be E

Step-by-step explanation:

Answer:

4 US liquid gallons = 16 US liquid quarts

( Multiply the volume value by 4 )

Have a wonderful day! :-)

Answer:

16 quarts in 4 gallons

Step-by-step explanation:

1 gallon equals 4 quarts

Peter's gross semi-monthly earnings are P7,717.5 and each of his men's gross semi-monthly earnings are P6,150.

To calculate Peter's gross earnings,

We need to find the commission he earns on his own sales and the override commission he earns on his men's sales.

Peter's Commission on his own sales:

2.5% of P5,500 = P137.5

Peter's Override Commission on his men's sales:

0.5% of (number of men * P4,000) = 0.5% of (number of men * 4000)

Let's assume he has 4 men.

Then the total override commission would be:

0.5% * 4 * 4000 = P80

So Peter's gross semi-monthly earnings would be:

P5,500 + P137.5 + P80 + P2,000 = P7,717.5

To calculate the gross earnings of each of Peter's men, we need to find their basic semi-monthly salary, their commission on their own sales, and their transportation allowance.

Each man's basic semi-monthly salary: P4,000

Each man's Commission on their own sales will be:

3.75% * P4,000 = P150

So each man's gross semi-monthly earnings would be:

P4,000 + P150 + P2,000 = P6,150

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One of the primary goals of creating a frequency distribution for quantitative data is to properly represent the data as a whole. As a result, it is correct, as it accurately depicts the data as a whole.

Frequencies are organized into frequency distributions, which are visual displays, to make the information easier to understand. A frequency distribution can display absolute or relative frequencies, such as ratios or percentages. A frequency distribution can be represented by a graph or a frequency table. A frequency distribution can show both the exact number of observations and the proportion of observations that fall within each range. In the latter case, the distribution is referred to as a relative frequency distribution. The frequency of observation is the number of times it appears in the data. For example, the frequency of the number 9 in the following list of numbers is 5. (Because it happens five times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9

One of the primary goals of creating a frequency distribution for quantitative data is to properly represent the data as a whole.

As a result, it is correct, as it accurately depicts the data as a whole.

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Answer: (2,7) & (6,5)

Step-by-step explanation:

Answer:

\(\boxed{(-4,~1)}\)

.

Step-by-step explanation:

Just input the point to test the truth

Let's try (-4, 1) → x = -4 and y = 1

\(y > |x| - 5\)

\(1 > |-4| - 5\)

\(1 > -(-4) - 5\)

\(1 > 4 - 5\)

\(1 > -1 \to \bold{true}\)

So, (-4, 1) is its solution

Answer:

(-4, 1)

Step-by-step explanation:

you can solve this quicly