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When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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Answer:

perpendicular

Step-by-step explanation:

7y = -x - 3

y = -1/7 x - 3/7

-1/7 is the reciprocal of the opposite, so the lines are perpendicular

Answer:

(41%, 53%)

Step-by-step explanation:

Given that:

Politician Alec's vote = 47%

Candidate Simeon = 42%

Margin of Error = 6%

Interval which describes Alec's chances of winning

Chances of Alec winning (p) = 47%

Margin of Error = 6%

Interval :

p ± margin of error

47% ± 6%

47% - 6% ; 47% + 6%

(41%, 53%)

To test a hypothesis using the p-value approach, you need to follow these steps:

1. Formulate the null and alternative hypotheses:
  - The null hypothesis, denoted as H0, states that there is no significant difference or relationship between the variables being studied.
  - The alternative hypothesis, denoted as Ha or H1, states that there is a significant difference or relationship between the variables.

2. Verify the requirements of the test:
  - Before performing the hypothesis test, you need to ensure that the assumptions and requirements of the test are met. These requirements may vary depending on the type of test and data you have. Common requirements include independence, random sampling, normality, and equal variances.

3. Choose an appropriate significance level (α):
  - The significance level, denoted as α, is the predetermined threshold below which we reject the null hypothesis. Commonly used significance levels are 0.05 (5%) and 0.01 (1%).

4. Calculate the test statistic:
  - The test statistic is a numerical value that summarizes the evidence against the null hypothesis. The specific test statistic depends on the type of hypothesis test being conducted. For example, if you're testing the difference between two population means, you might use the t-test or z-test.

5. Calculate the p-value:
  - The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming that the null hypothesis is true. It measures the strength of the evidence against the null hypothesis. A small p-value suggests strong evidence against the null hypothesis, while a large p-value suggests weak evidence.

6. Make a decision:
  - Compare the p-value to the significance level (α) you chose in step 3. If the p-value is less than or equal to α, reject the null hypothesis. If the p-value is greater than α, fail to reject the null hypothesis.

Remember that failing to reject the null hypothesis doesn't necessarily prove it to be true. It simply means that there is not enough evidence to support the alternative hypothesis.

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Answer:

\(\{ x: x < 0 \} \cup \{ x: x > 1 \}\)

Step-by-step explanation:

A function is increasing when its gradient is positive (so y-coordinates are increasing).

We have a graph, rather than a function given to us, so we don't need to use any calculus.

Looking at the graph, we can see that before x=0, the graph is going up (gradient is increasing).

Between x=0 and x=1, the function is decreasing.

After x=1, the function is increasing again.

We can use mathematical notation to express this.

\(\{ x: x < 0 \} \cup \{ x: x > 1 \}\)

Or

\(x < 0\ \text{and}\ x > 1\)

A function assigns the values. The interval on which the given function is increasing is (-∞,0)∩(1,∞).

A function assigns the value of each element of one set to the other specific element of another set.

For the given functions graph, the interval on which the given function is increasing is the interval of the function where the slope of the function is positive. Therefore, the interval of the function on which the given function is increasing is (-∞,0) and (1,∞). The interval for the given function can also be written as (-∞,0)∩(1,∞).

Hence, the interval on which the given function is increasing is (-∞,0)∩(1,∞).

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Answer:

88

Step-by-step explanation:

Use the following formula

Average=Sum/Count

89+91+84=264

264/3

88

Given

A rectangular park of length 60 m breadth 50 m encloses with volleyball court of length 18 m and breadth 10 m.

To find:

The area of the park excluding the court at the rate of Rs 110 per square meter.​

Solution:

Area of a rectangle is:

\(Area=length \times breadth\)

Area of whole park is:

\(A_1=60 \times 50\)

\(A_1=3000\)

Area of volleyball court is:

\(A_2=18 \times 10\)

\(A_2=180\)

Now, the area of the park excluding the court is:

\(A=A_1-A_2\)

\(A=3000-180\)

\(A=2820\)

Therefore, the area of the park excluding the court is 2820 square meter.

Answer:

see explanation

Step-by-step explanation:

? and 110° are alternate exterior angles and are congruent , that is

? = 110°

84° and ? are alternate interior angles and are congruent , so

? = 84°

? and 100° are consecutive interior angles and sum to 180° , then

? + 100° = 180° ( subtract 100° from both sides )

? = 80°

Answer:

D. \(a^{2} + b^{2} = c^{2}\)

Step-by-step explanation:

Pythagorean Theorem

Based on the above, the width of the rectangle is 10.

Let's use "w" to represent the width and "l" to represent the length of the rectangle.

From the problem, we know that the area of the rectangle is 40, so we can write:

Area = length × width

40 = l × w

We also know that the width is 2 less than 3 times the length, so we can write:

width = 3l - 2

Now we can substitute this expression for "w" in the equation for the area: 40 = l × (3l - 2)

Expanding the right side gives: 40 = 3l² - 2l

Rearranging and dividing by 2 gives:

3l²- 2l - 40 = 0

(3l + 10)(l - 4) = 0

Therefore, l = 4 (because the length cannot be negative), and we can find the width using the expression we found earlier:

width = 3l - 2

width = 3(4) - 2

width = 10

So the width of the rectangle is 10. Therefore, the answer is  10.

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Answer:

C. Ferris wheel

Step-by-step explanation:

Circumference = pi x diameter

Take each of the entries from the diameter column and multiply by 3.14. They are all correct except for the Ferris wheel.

70.5 x 3.14 = 221.37

a. To calculate the probability that the first two people share a birthday, we can consider the scenarios where the second person's birthday matches the first person's birthday.

Assuming there are 365 possible birthdays (ignoring February 29th), the probability that the second person has the same birthday as the first person is 1/365. Therefore, the probability that the first two people share a birthday is 1/365.

b. To calculate the probability that at least two people share a birthday, we can consider the complementary probability, which is the probability that all three people have different birthdays.

For the first person, any birthday is possible. So the probability that the second person has a different birthday is (364/365), and the probability that the third person has a different birthday from the first two is also (364/365).

Therefore, the probability that all three people have different birthdays is (364/365) * (364/365).

To find the probability that at least two people share a birthday, we subtract this complementary probability from 1:

P(at least two people share a birthday) = 1 - [(364/365) * (364/365)]

Using this formula, we can calculate the probability that at least two people share a birthday.

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Answer: 3/10

Step-by-step explanation:

From the question, we are informed that Kieran picks a bead out of a bag without looking and that he records the colour and replaces the bead.

He does this 50 times and he picks out a red bead 15 times. The probability of picking a red bead will be the number of times a red bead was picked divided by the number of title times a bead was picked. This will be:

= 15/50

= 3/10

Answer:

Whats the problem?

Step-by-step explanation:

By using the concept of maxima, it can be calculated that

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

What is maxima of a function?

Maxima of a function gives the maximum value of the function in a given interval or in the whole domain.

Let the length of the rectangle be l m and width of the rectangle be w m

Perimeter (P) = 2(l + w)

By the problem,

2(l + w) = 72

l + w = \(\frac{72}{2}\)

l + w = 36

w = 36 - l

Area (A) = l \(\times\) w

A = l \(\times\) (36 - l) = \(36l - l^2\)

Differentiation with A with respect to l

\(\frac{dA}{dl} = 36 - 2l\)

For maximum area,

\(\frac{dA}{dl} = 0\)

36 - 2l = 0

2l = 36

l = \(\frac{36}{2}\)

l = 18 m

\(\frac{d^2A}{dl^2} = -2 < 0\)

Hence area is maximum

w = 36 - 18 = 18 m

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

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To determine the control limits for the fraction of defective batteries using three sigma limits, we will follow certain steps. A sample of 50 batteries was used to collect data and the data below shows how many batteries out of each sample failed the test. Sample Number of Failed Batteries 1 4 2 2 3 5 4 2 5 4 6 8 7 3 8 2.

First, we need to find the mean of the sample size of the failed batteries and use it to calculate the upper and lower control limits (UCL and LCL). Next, we will calculate the fraction of batteries that failed for each sample, which is value = (number of failed batteries)/50.

Now, let us find the mean and standard deviation of these fractions. First, we will calculate the sum of all the values and divide it by the number of values to get the mean. Mean = (4 + 2 + 5 + 2 + 4 + 8 + 3 + 2)/400 = 0.0375. Then, we will find the standard deviation of these values, which is 0.0172.

The upper and lower control limits will now be calculated. Upper control limit = 0.0375 + 3(0.0172) = 0.0891. Lower control limit = 0.0375 - 3(0.0172) = -0.0141.

However, we can see that the lower control limit is negative, which is not possible since the fraction value cannot be negative. Thus, we will set the lower control limit to zero. The final control limits for the fraction of defective batteries are: Upper control limit = 0.0891 and Lower control limit = 0.0000 (or 0).

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Answer: um i think 300

Step-by-step explanation:

The density of a substance is its ratio of its mass to its volume. This determines the mass of the substance. The appropriate option to the question is:

b. to a higher level than it did in Cylinder 1.

The density of a mass determines the volume of liquid that would be displaced when put in a liquid. This is known as the Archimedes principle. It relates the mass of a material to its volume.

The density of the steel marble is more than that of the glass, thus it is expected that the liquid should rise above that of cylinder 1. Because the steel marble would displace more volume of water than the glass marble.

The given cylinders have equal measures and size, and contains the same volume of water. Thus, the water should rise to a higher point compared to that of cylinder 1.

Therefore the required answer is: b. to a higher level than it did in Cylinder 1.

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The Python script above prompts the user for the values of a, b, c, x, and y, and then tests whether the point (x, y) lies on the parabola described by the equation y=ax^2+bx+c. If the point lies on the parabola, the script prints out a message stating this. Otherwise, the script prints out a message stating that the point does not lie on the parabola.

The function is_on_parabola() takes in the values of a, b, c, x, and y, and then calculates the value of the parabola at the point (x, y). If the calculated value is equal to y, then the point lies on the parabola. Otherwise, the point does not lie on the parabola.

The main function of the script prompts the user for the values of a, b, c, x, and y, and then calls the function is_on_parabola(). If the point lies on the parabola, the script prints out a message stating this. Otherwise, the script prints out a message stating that the point does not lie on the parabola.

To run the script, you can save it as a Python file and then run it from the command line. For example, if you save the script as parabola.py, you can run it by typing the following command into the command line:

python parabola.py

This will prompt you for the values of a, b, c, x, and y, and then print out a message stating whether or not the point lies on the parabola.

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The ratio of cos A in the right triangle is 12 / 13.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the ratio of cos A using trigonometric ratios.

Using cosine ratio,

cos A = adjacent / hypotenuse

Therefore,

adjacent side = 12

hypotenuse side = 13

cos A = 12 / 13

Therefore, the ratio is 12 / 13

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Answer:

The answer is C!

Step-by-step explanation:

Answer:

D

NOTE: the answer "C" is NOT correct... see the image the green is "C" the purple is "D"

Step-by-step explanation:

Step-by-step explanation:

first, for such questions, we sound always sorry the list of data points :

9, 10, 12, 15, 17

the mean is the sum of all data points divided by the number of data points. we have 5 data points.

mean = (9+10+12+15+17)/5 = 63/5 = 12.6

median is the data point for which half of the other data points are smaller, and the other half of other data points are larger.

so, for our 5 days points,

median = 12

the middle element in our sorted list.

mode simple defines the data value that appears the most frequently in the list.

in our case all values appear exactly once.

some people say then that the mode is all numbers in the list.

but most commonly we say that this list has no mode.

Interval notation uses parenthesis and brackets, while inequality notation uses inequality symbols.

a)

Interval notation: [-4, 8)

Inequality notation: \(-4\leq x<8\)

x >= -4, x < 8

---For inequality notation, it can also be written as two separate inequalities. I am not sure what your teacher is looking for, so I will provide both the compound and separate formats.

b)

Interval notation: (-infinity, 7)

Inequality notation: x < 7

c)

Interval notation: (-infinity, -6) U (0, infinity)

Inequality notation: \(-6> x \geq 0\)

x < -6, x >= 0

Hope this helps!

Answer:

30 5/6

Step-by-step explanation:

185 = 30x6 + 5

Answer:

30 5/6

Step-by-step explanation:

Answer:

(-∞, ∞)

Step-by-step explanation:

\(5(1+x)=5x+5\)

\(5+5x=5x+5\)

\(5x=5x\)

\(x=x\)

Answer:

Scale factor = \(\frac{1}{2}\)

Step-by-step explanation:

Perimeter of the actual flag = 22 in.

Perimeter of the scale drawing of the flag = 11 in.

Since, perimeter of a triangle = Sum of all three sides of the given triangle

Therefore, scale factor of the drawing

= \(\frac{\text{Measure of the side of drawing}}{\text{Measure of the side of actual}}\) = \(\frac{\text{Perimeter of drawing}}{\text{Perimeter of actual}}\)

= \(\frac{11}{22}\)

= \(\frac{1}{2}\)

Therefore, scale factor of the drawing will be \(\frac{1}{2}\).                                        

Each side of the scaled triangle will be half of the actual triangle.

The hypothesis test results show that there is sufficient evidence to conclude that the population represented by Sample 1 has a higher mean than the population represented by Sample 2. The p-value is less than 0.05, so we can reject the null hypothesis.

The null hypothesis is that the population mean of matched-pair differences is equal to 0. The alternative hypothesis is that the population mean of matched-pair differences is greater than 0. The test statistic is t = 2.78, which has 9 degrees of freedom. The p-value for this test statistic is 0.008, which is less than 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant difference between the two populations.

The assumptions that need to be made in order to perform this procedure are that the matched pairs are independent and that the differences are normally distributed.

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A statement of inequality that correctly compares two numbers is: D. 6,365.1 < 6,365.999.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

In this scenario, a statement of inequality that correctly compares two numbers is 6,365.1 < 6,365.999.

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The sequence is 5,9,13,17,...

Determine the common difference for the sequance

This equation allows you to calculate the speed of light (c) using the distance (d) between antinodes in the standing wave pattern inside the microwave oven.

What is the determination of the speed of light  in a microwave oven?

The determination of the speed of light (c) in a microwave oven experiment and writing an equation for c in terms of distance (d). The distance between the food medium and the magnetron is not important for determining c because the standing waves created inside the oven have a consistent wavelength regardless of their distance from the magnetron. The wavelength (λ) is determined by the frequency of the microwaves, which is a constant value (2.45 GHz in most microwave ovens).

To calculate the speed of light (c) in terms of distance (d) instead of wavelength (λ), you can use the relationship between the measured distance (d) and the wavelength (λ), where d represents half of the wavelength (d = 1/2 λ). By rearranging this equation, you can find the wavelength in terms of the distance: λ = 2d.

Now, you can use the fundamental relationship c = νλ, where ν is the frequency of the microwaves (2.45 GHz). Substitute λ with 2d to get the equation for c in terms of d:

c = ν(2d)

This equation allows you to calculate the speed of light (c) using the distance (d) between antinodes in the standing wave pattern inside the microwave oven.

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