=
Graph the solution to the inequality on the number line.
|y8|≤2

The data shown in the dot plots above doesn't support Merrell's claim that he randomly assigned rats to treatment groups. It doesn't support it because the dot plots are not similarly distributed.

There are a few discrepancies in the data that are not possible if rats were randomly assigned to treatment groups.

Difference between the two dot plots:

There is a noticeable difference between the two dot plots.

The dot plot on the left shows that most rats in Group 1 weigh between 200 and 240 grams.

On the other hand, in Group 2, most rats weigh between 240 and 280 grams.

The two groups' data are not similarly distributed, and there is an overlap in the weight of rats in the two groups. Furthermore, the data suggests that heavier rats were placed in Group 2 while lighter rats were placed in Group 1.

This difference implies that rats were not randomly assigned to treatment groups.

Other information should be considered:

The information shown in the dot plots alone is not enough to conclude that the rats were not randomly assigned to treatment groups.

We must investigate further and gather more information to confirm our assumptions about the rats' treatment groups. Randomization guarantees that each rat has an equal probability of being assigned to a treatment group.

The two groups must be equivalent in every aspect except for the treatment they get.

Therefore, it's essential to confirm that there was no selection bias in the rat selection process.

This means that rats were picked randomly from a large population, and no specific rat characteristics influenced the selection process.

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Answer:

9 plus 11 plus 12 =

Step-by-step explanation:

x is 22

Area models are used to visually represent multiplication problems by partitioning the given dimensions into smaller units. Each area model consists of a collection of polygons that fill the entire area. To determine the polygon group to which Jessalyn's area models belong, we need to identify the common polygons used in all three models. Answer : the area models of 3 x 3, 4 x 6, and 7 x 2 all belong to the polygon group of rectangles.

1. Examine the three given multiplication problems: 3 x 3, 4 x 6, and 7 x 2.

2. Draw area models for each of the multiplication problems. For example, for 3 x 3, Jessalyn would draw a 3x3 grid divided into squares.

3. Analyze the polygons used in the area models. In each model, the polygons used will be rectangles.

4. Since rectangles are common to all three area models, the polygon group to which Jessalyn's area models belong is the group of rectangles.

5. Rectangles are quadrilaterals with four right angles, and all sides opposite to each other are congruent.

6. Therefore, the area models of 3 x 3, 4 x 6, and 7 x 2 all belong to the polygon group of rectangles.

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Profit per kilogram = R1.90

The profit per kilogram is the difference between the selling price and the cost price per kilogram.

a) To find the profit per kilogram, we can use the following formula:

Profit per kilogram = Selling price per kilogram - Cost price per kilogram

Therefore,

Profit per kilogram = R2.80 - R0.90

Profit per kilogram = R1.90

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Answer:

Positive

Step-by-step explanation:

hope it helps :)

Answer: positive

Step-by-step explanation:

Answer:

The first derivative of \(r(t) = 5\cdot t^{-2}\) (r(t)=5*t^{-2}) with respect to t is \(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3}).

Step-by-step explanation:

Let be \(r(t) = \frac{5}{t^{2}}\), which can be rewritten as \(r(t) = 5\cdot t^{-2}\). The rule of differentiation for a potential function multiplied by a constant is:

\(\frac{d}{dt}(c \cdot t^{n}) = n\cdot c \cdot t^{n-1}\), \(\forall \,n\neq 0\)

Then,

\(r'(t) = (-2)\cdot 5\cdot t^{-3}\)

\(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3})

The first derivative of \(r(t) = 5\cdot t^{-2}\) (r(t)=5*t^{-2}) with respect to t is \(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3}).

Let μ be the mean of the distribution and let σ be its standard deviation.

We know that 54 falls two standard deviations above the mean, this can be express as:

We also know that 42 falls one standard deviation below the mean, this can be express as:

Hence, we have the system of equations:

To find the mean we solve the second equation for the standard deviation:

Now we plug this value in the first equation:

Therefore, the mean of the distribution is 46

The equation representing the relationship between the number of students, the number of adults, and the dollar amount received at the game is 2.75s + 5.25a = 281.25.

Let's denote the number of students as 's' and the number of adults as 'a'.

The cost of each student entry is $2.75, so the total amount collected from student entry fees would be 2.75s.

Similarly, the cost of each adult entry is $5.25, so the total amount collected from adult entry fees would be 5.25a.

The total amount collected at the game is given as $281.25.

Therefore, the equation representing the relationship between the number of students, the number of adults, and the dollar amount received at the game is:

2.75s + 5.25a = 281.25

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Since the function F(x) is continuous, we have that; P(X > 4) = 0. The distribution function F(x) for a random variable X that has the following distribution function given by; F(x) = {0 when x ≤ -2}(x² + 5)/(9) when -2 < x ≤ 3{1 when x > 3}.

The value of the probability of the events that P(-2 ≤ X ≤ 1), P(1 < X ≤ 4), and P(X > 4) are needed to be found.

(i) When -2 ≤ X ≤ 1. Since the function F(x) is continuous, we have that;

P(-2 ≤ X ≤ 1) = F(1) - F(-2)

= (1² + 5)/9 - 0

= 6/9

= 2/3

(ii) When 1 < X ≤ 4.

The probability that P(1 < X ≤ 4) = F(4) - F(1)

= 1 - (1² + 5)/9

= (9 - 6)/9

= 1/3

(iii) When X > 4.

Since the function F(x) is continuous, we have that;

P(X > 4) = 1 - F(4)

= 1 - 1

= 0.

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Answer:

please what is equaling to

Answer:

12

Step-by-step explanation:

\(\sqrt{8} * \sqrt{18} =12\)

Step-by-step explanation:

Look, you're taking these kinds of questions too serious and that's why you believe they're hard, now pay close attention:

the areas are defined in cm² but the radius is defined in cm, so you need find the positive root of cm².

\( \sqrt{ \frac{5500 {cm}^{2} }{220 {cm}^{2} } } = \frac{r}{5cm} = = > \\ 5 = \frac{r}{5} = = = > r = 25\)

and the question wants the base area:

\(s = \pi {r}^{2} = = = > s = 3.14 \times {(25cm)}^{2} = = > 1963.5 {cm}^{2} \)

Answer:

Option A is correct.

Step-by-step explanation:

Given

To determine

What is the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4.

Using the point-slope form of the line equation

\(y-y_1=m\left(x-x_1\right)\)

where

substituting the values m = 1/4 and the point (4, -8)

\(y-y_1=m\left(x-x_1\right)\)

\(y-\left(-8\right)=\frac{1}{4}\left(x-4\right)\)

\(y+8=\frac{1}{4}\left(x-4\right)\)

Subtract 8 from both sides

\(y+8-8=\frac{1}{4}\left(x-4\right)-8\)

\(y=\frac{1}{4}x-1-8\)

\(y=\frac{1}{4}x-9\)

Writing the equation in the standard form

As we know that the equation in the standard form is

Ax+By=C

where x and y are variables and A, B and C are constants

so

\(y=\frac{1}{4}x-9\)

\(x=4y+36\)

\(x - 4y = 36\)

Therefore, the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4 will be:

\(x - 4y = 36\)

Hence, option A is correct.

Answer:

140 degrees

Step-by-step explanation:

first start by making the given angles equal each other because they are congruent.

2x+28=6x+4

Subtract 4 on both sides

2x+24=6x

subtract 2x on both sides

24=4x

divide both sides by 4 to get x

24/4=4x/4

6=x

next to find the actual number of the angle, plug 6 back into either one of the equations. Im gonna use the first one.

2x + 28

2(6) + 28

12+28= 40

Now that we have the number, we already know that a full circle is 360 degrees so half a circle is 180.

Take 40 and subtract from 180

180-40= 140

Well, m∠1 and m∠3 are congruent by the Vertical Angle Congruent Theorem (VACT). This means that because the angles are opposite of each other, their angles are the same because they are formed by the same two intersecting lines.

Because of this, we can set m∠1 and m∠3 equal to each other:

m∠1 = m∠3

(2x + 28) = (6x + 4)

2x + 28 = 6x + 4

-4x + 28 = 4

-4x = -24

-x = -6

x = 6

Knowing that x equals 6, we can use this to find m∠2. By the Supplementary Angles Theorem (SAT), angles that are on the same line add up to equal 180°. To use the SAT, we need to plug x in to find m∠1 or m∠3, because they are both the same:

x = 6

m∠1 = (2x + 28)

m∠1 = 2(6) + 28

m∠1 = 12 + 28

m∠1 = 40°

m∠3 also equals 40°.

Now that we have the value for ∠1 (or ∠3), we can use the SAT:

m∠2 + m∠3 = 180 ← You could also use m∠1, because they both equal the same!

m∠2 + 40 = 180

m∠2 = 140°

So, the measure of ∠2 is 140°.

If you have any questions, feel free to ask! :)

The helicopter is about  \(2928.6\) feet high.

We can use trigonometry to find the height of the helicopter. Let's draw a diagram to better visualize the problem:

        |

        |

        | h

        |

        |     65°

        |-----------

 Helicopter   1000 ft   Landing pad

The angle of depression from the helicopter to the landing pad is 65 degrees, which means that the angle between the horizontal line and the line of sight from the helicopter to the landing pad is also 65 degrees. Let's call the height of the helicopter "h".

Using trigonometry, we can write:

tan(65°) = h / 1000

Solving for h, we get:

\(h = 1000 \times tan(65^\circ)\)

Using a calculator, we find:

\(h \approx 2928.6\)feet

Therefore, the helicopter is about   \(2928.6\) feet high.

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The line cross the Y axis in y=-2

The equation of a line is Y=ax+b where a is the slope and b the y intercept of the line

we know that for x=3 => y=4 then we plug the values we know in the equation of the line:

now we use the point we know:

then solve for b

The the y intercept of the line is y=-2

The maximum height of the projectile is 56.53 meters.

The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.

This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.

To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).

The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.

To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.

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To solve this question we will use the following expression to compute the theoretical probability:

Now, recall that the possible outcomes of rolling a die are 1, 2, 3, 4, 5, and 6. Therefore the probability of obtaining no 6 in each rolling is:

Then, the probability of obtaining no 6's in four rollings is:

Simplifying the above product we get:

Answer:

The expected value for the number of subjects who are vaccinated and are diseased is  56.7

Since we are given the information that a new vaccination is being used in a laboratory experiment to investigate whether it is effective. there are 273 subjects in the study.  We can calculate this by taking the total number of subjects who are vaccinated (119) and multiplying it by the proportion of subjects who are diseased

(47/273).  119 x (47/273) = 56.7

which is  the expected value for the number of subjects who are vaccinated and are diseased

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The answer is in the image (it ends up being -935)

Step-by-step explanation:

2 equations with 2 variables can be solved in 2 relatively different ways :

1. by elimination (we multiply if needed the equations by certain factors, so that when adding both equations one variable is eliminated).

2. by substitution : we use one equation to express one variable by the other, which we then used in the second equation.

in both cases we then solve for the one remaining variable. and then we use one of the other equations to solve for the second variable.

since the equations are so similar already, we use the first approach. we don't need to multiply anything by a factor, the terms in x are the same with different signs, so we just add both equations :

-x + 6y = 9

+ x + 6y = -3

-------------------

0 12y = 6

y = 6/12 = 1/2 = 0.5

x + 6×1/2 = -3

x + 3 = -3

x = -6

FYI - how would substitution work ?

e.g.

x + 6y = -3

x = -3 - 6y

that we use now in the other equation

-(-3 - 6y) + 6y = 9

3 + 6y + 6y = 9

3 + 12y = 9

12y = 6

y = 6/12 = 1/2 = 0.5

and then

-x + 6×1/2 = 9

-x + 3 = 9

-x = 6

x = -6

The function f takes a binary string of length 2, and returns the first bit of that string, which is either 0 or 1.

Therefore, the range of f is {0, 1}.

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Answer:

Option C 20

GOOD LUCK FOR THE FUTURE! :)

Answer:

18.0625 ft²

Step-by-step explanation:

4.25 × 4.25

18.0625 ft²

The expression for the amount of money, in dollars, Teri has is x-2.

Since Jennie has x dollars while Teri has $6 less than does Jennie, this means that Teri will have: x - 6

Since Teri does not spend any money and earns $4, the the total amount that Teri has will be:

= x - 6 + 4

= x - 2

Therefore, Teri has x-2.

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All of the following are measures of central tendency except the range.

The range is a measure of dispersion, representing the difference between the largest and smallest values in a dataset. It provides information about the spread or variability of the data but does not provide information about the central tendency.

On the other hand, measures of central tendency are statistical measures that aim to summarize the center or typical value of a dataset. They include the mode, median, and mean.

The mode represents the most frequently occurring value(s) in the dataset.

The median is the middle value when the data is arranged in ascending or descending order. It divides the dataset into two equal halves.

The mean is the arithmetic average of all the values in the dataset. It is calculated by summing all the values and dividing by the total number of values.

Therefore, option C, range, is not a measure of central tendency as it focuses on the spread or dispersion of the data rather than summarizing the central or typical value.

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Answer:

Yes, your total savings on gas is proportional to the number of beverages you purchase.

Step-by-step explanation:

What is a proportional relationship?

A proportional relationship, also known as direct relation, between two variables exists when the ratio between every pair of data is constant.

In this case the variables are:

number of beverage purchased

savings

Thus, as per every beverage purchase you save $ 0.20 the ratio of total savings to the number of beverage purchases is:

savings / beverages purchase = $ 0.20 / beverage

That means that you can determine the savings by multipliying the number of beverages times $ 0.20.

For proportional relationships it is easy to build a table that shows the behavior of the variables. This shows you that:

Number of beverages   savings    ratio

        1                              $ 0.20      $0.20 / 1 beverage = 0.20

        2                             $ 0.40      $0.40 / 2 beverages = 0.20

        3                             $ 0.60       $0.60 / 3 beverages = 0.20

        4                             $ 0.80       $0.80 / 4 beverages = 0.20

The correct answer is b. On average, LinkedIn users would send between 5.48 and 8.72 total messages per year with the new algorithm.

The 95% confidence interval provided by Yue Bing suggests that the true difference in the average number of messages sent per year between the two groups of users (those using the new algorithm and those using the old algorithm) is likely to be between 5.48 and 8.72. This means that we can be 95% confident that the true difference in the average number of messages sent per year falls within this range. It does not necessarily mean that all LinkedIn users will send more or fewer messages with the new algorithm, but rather that the average number of messages sent by users using the new algorithm is likely to be within this range.
Your answer: d. On average, all LinkedIn users would send more messages with the new algorithm than with the old algorithm.

Explanation: Yue Bing computed a 95% confidence interval for the difference between the two parameters, which is (5.48, 8.72) messages per year. Since the entire interval is positive, this indicates that the new recommendation algorithm likely leads to an increase in the average number of messages sent by LinkedIn users compared to the old algorithm.

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Answer:

Find the are

Step-by-step explanation:

pi method