A scientist used a microscope to count the number of bacterial cells in a petri dish every hour.
Which function most accurately represents this data, where n is the number of bacteria and 1 is the time elapsed, in hours?
a. n=2t
b. n=2^t
c n=t^2
d. n=√t​

Answer:

Step-by-step explanation:

Cos(x)=18/44=0.41

x=65.85

Step-by-step explanation:

5. 4b = b + b + b + b (A)

4b = 2b + 2b (C)

6. 111 = 14a

a = 111/14

a = 7.92

Answer:

Ethan will use 49

fl oz of orange juice, and he will have a total of 77

fl oz of punch.

Step-by-step explanation:

He uses a ratio of 7 to 4 of orange juice to sparkling water.

7/4 = ?/28

4 * ? = 7 * 28

Divide both sides by 4.

? = 7 * 7

? = 49

He will use 49 fl oz of orange juice.

The total amount made is: 49 fl oz + 28 fl oz = 77 fl oz

Answer:

Ethan will use 49

fl oz of orange juice, and he will have a total of 77

fl oz of punch.

Options:

a) If corresponding pairs of sides and corresponding pairs of angles of two triangles are congruent, then the triangles can be matched up exactly using rigid motions.

b) If two triangles can be matched up exactly using rigid motions, then the corresponding pairs of sides and corresponding pairs of angles of the triangles are congruent.

c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

d) If corresponding pairs of sides and corresponding pairs of angles of two triangles are not congruent, then the triangles are not congruent.

Answer:

c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Step-by-step explanation:

For both pairs of triangles, what you proved is how to use rigid motions (i.e. rigid transformations) to make congruent shapes.

When rigid transformation is applied to a shape, the image (i.e. result) of the  transformation produces an exact shape (i.e. equal corresponding angles and corresponding sides), meaning that the side lengths and the angles of the preimage (before transformation) and the image (after transformation) is unaltered.

Option (c) is true

Answer:

i dont know

Step-by-step explanation:

a) chi-square = (30-1) * 7.338 / 5 = 42.456 b) The probability of having a sample variance between 2.766 and 7.883 is the difference between the cumulative probabilities of chi-square2 and chi-square1.

To find the probability in both cases, we need to use the chi-square distribution with n-1 degrees of freedom, where n is the sample size.

a) To find the probability that the sample variance is greater than 7.338, we need to find the upper tail probability of the chi-square distribution.

The chi-square statistic is calculated as:

chi-square = (n-1) * s^2 / sigma^2

In this case, n = 30, s^2 = 7.338, and sigma^2 = 5.

chi-square = (30-1) * 7.338 / 5 = 42.456

b) To find the probability that the sample variance is between 2.766 and 7.883, we need to find the cumulative probability within that range.

First, we calculate the chi-square statistics for both values:

chi-square1 = (30-1) * 2.766 / 5 = 15.359

chi-square2 = (30-1) * 7.883 / 5 = 43.179

The probability of having a sample variance between 2.766 and 7.883 is the difference between the cumulative probabilities of chi-square2 and chi-square1.

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Answer: pull the upper right hand corner (of the smaller box) all the way to the upper right hand corner of the bigger box, then pull the upper left hand corner of the smaller box all the way over to the other side but leave two squares on the end, this gives you 18 boxes across the top which works since 2cm is three boxes. make sure each side of the square has 18 boxes and you’ll be good

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

[tex]\frac{1}{4} - \frac{1}{6}[/tex]

[tex]\frac{6 - 4}{24}[/tex]

[tex]\frac{2}{24}[/tex]

Converting to its simplest form, divide numerator and denominator by 2 = 1/12

Answer:

-4y - 7

Step-by-step explanation:

−4y−4+(−3)

-4y - 4 - 3

-4y - 7

Answer:

-7x - 5

Step-by-step explanation:

Combine like terms.

Table one represents a linear function for the given data.

A linear function is a mathematical function that can be written in the form:

y = mx + b

where "m" and "b" are constants, and "x" and "y" are variables.

In this form, "m" represents the slope of the line, and "b" represents the y-intercept, the point where the line crosses the y-axis. The slope of the line is the rate of change of the function, representing how much the value of "y" changes for every unit change in "x".

The given table is,

x         y

1         5

2       10

3       15

4       20

5       25

The slope of the given data is,

m = ( 10 - 5 ) / ( 2 - 1 ) = 5

m = ( 15 - 10 ) / ( 3 - 2 ) = 5

m = ( 20 - 15 ) / ( 4 - 3 ) = 5

Here the slope is constant, so the function is linear.

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The test statistic is 1.09. The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. The range of the p-value is 0.1 to 1.

If the p-value is less than 0.05, we reject the null hypothesis and conclude that the new brand of cookies has more than 10 chocolate chips per cookie.

If the p-value is greater than 0.05, we fail to reject the null hypothesis and cannot conclude that the new brand of cookies has more than 10 chocolate chips per cookie.

In this case, the p-value is between 0.1 and 1. Therefore, we cannot conclude that the new brand of cookies has more than 10 chocolate chips per cookie.

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may not know the answer that well but try this called symbolab. Hope that could help you

Answer:

3(x+y)=45

x+y=15

y=-1x +15

so

slope(m) = -1

Answer: WY = 27

Step-by-step explanation:

Due to WX being a Perpendicular Bisector WY = WZ

4x - 5 = 2x + 11

Add 5 to both sides

4x = 2x + 16

Subtract 2x from both sides

2x = 16

Divide by 2

x = 8

So 4x - 5 of x = 8

4*8 = 32 - 5 =27

Answer:

27

Step-by-step explanation:

WY = WZ because XZ = XY

[tex]2x + 11 = 4x - 5\\(2x + 11) - 11 = (4x - 5) -11\\2x = 4x - 16\\-2x = -16\\x = 8\\\\WY = 4x - 5\\WY = 4(8) -5\\WY = 32 - 5\\WY = 27[/tex]

Using synthetic division and the remainder theorem, we can determine if [x−(3−2i)] is a factor of f(x)=x^2−6x+13.

To determine if [x−(3−2i)] is a factor of f(x)=x^2−6x+13, we can use synthetic division. First, we need to rewrite the given factor in the form x - c, where c is the conjugate of 3 - 2i, which is 3 + 2i.

Performing synthetic division with 3 + 2i as the divisor: f(x)=x^2−6x+13, we can use synthetic division. First, we need to rewrite the given factor in the form x - c, where c is the conjugate of 3 - 2i, which is 3 + 2i.

Performing synthetic division with 3 + 2i as the divisor:

 3 - 2i  |  1   -6   13

           __________________

           (remainder)

If the remainder is zero, then [x−(3−2i)] is a factor of f(x). However, if the remainder is nonzero, then [x−(3−2i)] is not a factor of f(x). Therefore, based on the result of the synthetic division, we can determine if [x−(3−2i)] is a factor of f(x).

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The slope of the graph of the function g(x) is 1, indicating that for every unit increase in x, the corresponding value of g(x) increases by 1.

To find the slope of the graph of the function g(x), we can use the power rule of differentiation. Let's differentiate g(x) step by step:

Step 1: Express g(x) in a simplified form.

g(x) = 4(1/4[tex]x^1[/tex])

Step 2: Simplify the expression.

g(x) = x

Step 3: Differentiate g(x) to find the slope.

The derivative of g(x) with respect to x is simply 1, as the derivative of x with respect to itself is 1.

Therefore, the slope of the graph of g(x) is 1.

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The sample size required to ensure a margin of error of at most 0.065 for a 92.5% confidence interval is 523.

To estimate the proportion of shoppers using credit cards with a desired margin of error and confidence level, determining the appropriate sample size is crucial.

In this scenario, we aim to achieve a margin of error of no more than 0.065 for a 92.5% confidence interval. The sample size required to fulfill these criteria is 523.

To comprehend the significance of these calculations, it's essential to understand the concepts of margin of error and confidence level. The margin of error represents the maximum amount of uncertainty we can tolerate in our estimate.

In this case, we want our estimate of the proportion of shoppers using credit cards to be accurate within ±0.065. A smaller margin of error indicates greater precision in our estimate.

The confidence level, on the other hand, reflects the level of certainty we have in the accuracy of our estimate.

A confidence level of 92.5% implies that if we were to repeat the sampling process numerous times, we would expect approximately 92.5% of the resulting confidence intervals to contain the true proportion of credit card-using shoppers.

The formula to calculate the sample size required for a proportion estimation is based on the desired margin of error, confidence level, and an assumed proportion (usually 0.5 for maximum variability).

This formula incorporates a z-value, which corresponds to the desired confidence level. For a 92.5% confidence level, the z-value is approximately 1.81.

By plugging the values into the formula and solving for the sample size, we find that a sample size of 523 is necessary to estimate the proportion of shoppers using credit cards with a margin of error no greater than 0.065 and a confidence level of 92.5%.

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Answer:

Area of the given fan is 763.4 cm²

Step-by-step explanation:

Area of a sector in a circle = [tex]\frac{\theta}{360}(\pi r^2)[/tex]

Here, angle θ = Central angle subtended by the arc

r = Radius of the circle

Since, fan is in the form of a sector of a circle with radius = 27 cm

Measure of the central angle subtended by the arc FN = ∠FAN = 120°

Area of the fan = [tex]\frac{120}{360}(\pi )(27)^2[/tex]

                         = [tex]\frac{729\pi }{3}[/tex]

                         = 243π

                         = 763.407

                         ≈ 763.4 cm²

Therefore, area of the given fan is 763.4 cm²

Answer:

Lower (or First) Quartile = 15

Step-by-step explanation:

Answer:

15 I think

Step-by-step explanation:

been a while since I did that but I think 15

The advantage of nonparametric statistical procedures is that they require fewer requirements to be met. This means that nonparametric statistical procedures are more flexible than parametric ones.

Statistical procedures refer to a collection of mathematical techniques that allow researchers to conduct statistical analyses. Statistical procedures are usually classified as either parametric or nonparametric.

A statistical procedure is considered parametric if it assumes that the population follows a specific distribution.

A statistical procedure is considered nonparametric if it does not assume that the population follows a particular distribution.

One of the advantages of nonparametric statistical procedures is that they require fewer assumptions than parametric statistical procedures. This means that they are more flexible and can be used in situations where the assumptions of parametric statistical procedures are not met.

Additionally, nonparametric statistical procedures are more robust to outliers and can be used when the data are skewed or have a non-normal distribution.

Another advantage of nonparametric statistical procedures is that they are easy to compute.

Unlike parametric statistical procedures, which require complex computations, nonparametric statistical procedures can be calculated using simple methods that are easy to understand.

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Using Euler's Method with a step size of 0.3 and the given initial data and differential equation, the approximate value of y(1.3) is 0.3 × 2[tex]e^{0.3[/tex].

To approximate the value of y(1.3) using Euler's Method, we need to take one step with a step size of h and update the y-value accordingly. Here's how to do it step by step:

Determine the step size, h. In this case, we want to approximate y(1.3) using the initial data at y(1). Since we know that x increases from 1 to 1.3, the step size is h = 1.3 - 1 = 0.3.

Calculate the slope at the initial point (x0, y0). The slope can be found using the given differential equation y'(x) = 2x[tex]e^a[/tex] - y. Plugging in the values x0 = 1 and y0 = 0, we get:

y'(1) = 2(1)[tex]e^{0.3[/tex] - 0 = 2[tex]e^{0.3[/tex].

Compute the approximate value of y at the next step. Using Euler's Method, we can update the y-value as follows:

y1 = y0 + h × y'(x0, y0)

= 0 + 0.3 × 2[tex]e^{0.3[/tex].

Evaluating the expression:

y1 = 0.3 × 2[tex]e^{0.3[/tex].

This gives us the approximate value of y(1.3) using Euler's Method with the given initial data and differential equation.

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Answer: 134

(Hope this helped with whatever you needed it for <3)

The general solution to the differential equation (D^2 + 4)y = 6sin(2x) + 3x^2 is y = A sin(2x) + B cos(2x) + (3/4)x^2.

To solve the given differential equation (D^2 + 4)y = 6sin(2x) + 3x^2, where D represents the derivative operator, we can use the method of undetermined coefficients.

The homogeneous solution to the equation is y_h = A sin(2x) + B cos(2x), where A and B are arbitrary constants.

Therefore, the general solution to the differential equation is y = A sin(2x) + B cos(2x) + (3/4)x^2, where A and B are arbitrary constants. This solution accounts for both homogeneous and particular solutions.

The specific values of A and B can be determined by applying initial or boundary conditions if given.

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Answer: 4/5

Step-by-step explanation: It is 8/10, but if you simplify it, it is 4/5.

The value of sin(u+v) is -16/13. The value of sin(u+v) can be determined using trigonometric identities and the given information. We are given that sin(u) = 5/13 for 0 ≤ u ≤ π and tan(v) = -3/4 for π/2 ≤ v ≤ π.

To find sin(u+v), we need to use the sum of angles formula for sine. According to this formula, sin(u+v) = sin(u)cos(v) + cos(u)sin(v).

From the given information, we know the value of sin(u) = 5/13. To find cos(u), we can use the Pythagorean identity [tex]sin^2(u) + cos^2(u) = 1[/tex]. Plugging in the value of sin(u), we have [tex](5/13)^2 + cos^2(u) = 1[/tex]. Solving for cos(u), we find cos(u) = 12/13.

Similarly, we know that tan(v) = -3/4. Using the identity tan(v) = sin(v)/cos(v), we can solve for sin(v) and cos(v). We have sin(v)/cos(v) = -3/4, which implies sin(v) = -3 and cos(v) = 4.

Now we have all the values needed to calculate sin(u+v). Substituting the known values into the sum of angles formula, we get sin(u+v) = (5/13)(4) + (12/13)(-3) = 20/13 - 36/13 = -16/13.

Therefore, the value of sin(u+v) is -16/13.

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Answer:

85

Step-by-step explanation:

Answer:

(2b-a)x(2b-3)x(2b+3)

Step-by-step explanation:

Step-by-step explanation:

the formula for the area of a sector is

(x°(r^2)π)/360

with x being the angle

r bring the radius of the circle

(255(13.4)^2π)/360

399.6

Hope that helps :)

Answer:

The answer is 399.6 not 399.4. I put 399.6 as my answer on acellus and I got it right.

Answer:

92.75 miles

Step-by-step explanation:

3.71 / 2 = 1.855

1.855 * 50 miles = 92.75 miles

In solving simple probability questions, the calculations involved are usually straightforward. The key lies in identifying the applicable concepts and selecting the appropriate tools or formulas. Equally important is recognizing when these tools do not apply, enabling proper interpretation of data.

Understand the problem: Carefully read and comprehend the question to determine what information is given and what needs to be calculated. Identify the relevant concepts and tools that can be utilized.

Select the appropriate formula: Based on the problem statement and the involved concepts, choose the relevant formula or method to calculate the probability or confidence interval. Examples include the addition rule, multiplication rule, or Bayes' theorem.

Apply the given information: Substitute the known values into the formula, ensuring proper assignment and consistency of units.

Perform the calculations: Use mathematical operations to compute the desired probability or confidence interval. Take note of any special conditions or considerations mentioned in the problem.

Provide a clear answer: Express the result in a well-formatted manner. For probability questions, the answer may be a single value or a range, depending on the problem. Confidence interval questions require a properly formatted statement that includes the estimated parameter, range, and confidence level.

Validate and interpret the answer: Review the calculations for accuracy, and round the answer if necessary. Additionally, interpret the result within the context of the problem, providing explanations or conclusions as needed.

By practising with a variety of probability problems and confidence interval questions, you can improve your ability to identify relevant concepts and select the appropriate tools to solve them accurately. Furthermore, this practice will enhance your skills in recognizing when others may be misusing or misinterpreting data in real-world scenarios.

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