Mila bought stock in a company two years ago that was worth
x
x dollars. During the first year that she owned the stock, it decreased by 35%. During the second year the value of the stock decreased by 32%. Write an expression in terms of
x
x that represents the value of the stock after the two years have passed.

However, if the decisions drawn from both methods differ (e.g., one rejects the null hypothesis while the other does not), then the conclusions are not the same.

In order to compare the conclusions obtained using the p-value method with your initial conclusion, it is essential to first understand the p-value's role in hypothesis testing. The p-value is a probability that helps in determining the statistical significance of your test results. A smaller p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, leading to its rejection in favour of the alternative hypothesis. Conversely, a larger p-value (typically > 0.05) suggests weak evidence against the null hypothesis, and therefore, it cannot be rejected.
When comparing the conclusions, assess if both methods lead to the same decision regarding the null hypothesis. If your initial conclusion rejects the null hypothesis and the p-value method yields a p-value ≤ 0.05, then the conclusions are the same. Alternatively, if your initial conclusion does not reject the null hypothesis and the p-value method results in a p-value > 0.05, the conclusions also align.
However, if the decisions drawn from both methods differ (e.g., one rejects the null hypothesis while the other does not), then the conclusions are not the same. In such cases, it is crucial to revisit the methodology and ensure the correctness of the approach taken, as it is vital to have consistent and accurate results in any statistical analysis.

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Answer:

see proof below

Step-by-step explanation:

Let

p1,p2 = half lengths of chord p

q1,q2 = half length of chord q

By the intersecting chord theorem,

p1*p2 = q1*q2,    substituting p1=p2, q1=q2

p1^2 = q1*2

Take square-roots and reject negative roots

p1 = q1

therefore

p1=p2 = q1=q2, or

two parts of one chord are equal to the two parts of the other.

Answer:

Below

Step-by-step explanation:

The area is just the two side lengths multiplied together

area = (4x+13)(5x-2) = 20x^2 +57x -26   units^2

In general form, the equation is 8x² + 30x - 2x = 0.

In factored form, the equation is 4x(2x + 7) = 0.

To solve the equation 8x² + 30x = 2x, we can rearrange it to bring all the terms to one side:

8x² + 30x - 2x = 0

Combining like terms:

8x² + 28x = 0

Now, let's factor out the common factor of 4x:

4x(2x + 7) = 0

To find the solution set, we set each factor equal to zero and solve for x:

4x = 0 -> x = 0

2x + 7 = 0

2x = -7

x = -7/2

Therefore, the solution set for the equation is {0, -7/2}.

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Answer:

200

Step-by-step explanation:

It is given that the same player is going to play a game one after another continuously about 200 times. During the game the player is going to pick up  black color balls.

If the player picks at least one black color ball at one time of the game, therefore, the probability of the number of black balls that the player is going to pick is 200 balls.

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Answer:

2x-y-1=0

Step-by-step explanation:

.

The roots of the equation z² + z + 1 = 0 are:-

1/2 + i(sqrt(3))/2-1/2 - i(sqrt(3))/2

The given equation is:

z² + z + 1 = 0

We can solve this equation by using the formula of quadratic equation:

z = [-b ± sqrt(b² - 4ac)] / 2a

On comparing with the general form ax² + bx + c = 0, we can find that

a = 1, b = 1 and c = 1

Now substituting these values in the formula, we get:

z = [-1 ± sqrt(1 - 4(1)(1))] / 2(1)

On simplifying, we get:

z = [-1 ± sqrt(-3)] / 2

Therefore the roots of the equation z² + z + 1 = 0 are:-

1/2 + i(sqrt(3))/2-1/2 - i(sqrt(3))/2

The roots of the given equation are given above.

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Answer:

(2A /h) - b1 = b2

Step-by-step explanation:

A = 1/2 h ( b1 + b2)

Multiply each side by 2

2A = 2*1/2 h ( b1 + b2)

2A =  h ( b1 + b2)

Divide each side by h

2A/h= h/h ( b1 + b2)

2A/h=  b1 + b2

Subtract b1 from each side

2A /h - b1 = b2

Answer:

Solution given:

a.

p=2/3

q=-1/3

r=1/6

now

p-q+r=2/3-(-1/3)+1/6

=\(\frac{2*2+1*2+1}{6}=\frac{7}{6}\)

c.

p=-1/5

q=-3/10

r=2/5

now

p-q+r=-1/5-(-3/10)+2/5

=\(\frac{-1*2+3+2*2}{10}=\frac{5}{10}=½\)

Answer:

Step-by-step explanation:

The expression given:

Evaluate for each case:

a)

p = 2/3, 1 = -1/3, r = 1/6

c)

p = 1/-5, q = -3/10, r = 2/5

The spread of the data in the histogram is uneven or skewed to the right.

A histogram is a graphical representation of data used to display the distribution of values in a dataset, showing data in bins or intervals along the horizontal axis.

The data distribution in the histogram is uneven or tilted to the right. This suggests that there are fewer students who have gone water skiing less frequently (1 to 5 trips) and more students who have gone water skiing more frequently (11 to 15 trips). The frequency is greatest between 11 and 15 visits, which is reflected by the largest bar in the histogram.

In given problem, the skewed distribution of the given data shows that there are more no. of the students doing water-skiing regularly than those who are doing it less frequently.

This might imply that there is a group of students who are more experienced or enthusiastic about water skiing, and they have gone on more excursions than other students who have gone on less trips. It also implies that the majority of students fall within the 11 to 15 trip period, which might imply a common pattern or trend in the data.

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The best description of the spread of the data is that it is skewed or unevenly distributed.

A histogram is a graphical representation of data used to display the distribution of values in a dataset, showing data in bins or intervals along the horizontal axis.

Based on the given histogram, the data is not evenly distributed across the five intervals. The majority of students have been water-skiing between 11 and 15 times, with a frequency of 5. There are fewer students who have been water-skiing between 16 and 20 times, with a frequency of 4, and even fewer students who have been water-skiing between 21 and 25 times, with a frequency of 3.

The spread of the data refers to how far apart the values in the dataset are from each other. In this case, the data is not evenly spread across the different intervals. The values in the dataset are more concentrated in the interval of 11 to 15, and less concentrated in the intervals of 1 to 5 and 21 to 25. This indicates that the majority of students have been water-skiing a similar number of times, while fewer students have been water-skiing either a lot or a little.

Therefore, the best description of the spread of the data is that it is skewed or unevenly distributed.

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The complete question is:

A group of students was asked about the number of times they had been water-skiing. The data is shown in the histogram.

A histogram titled Water Skiing Trips. The x-axis is labeled Number of Times Water Skiing and has intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 6. There is a shaded bar for 1 to 5 that stops at 1, for 6 to 10 that stops at 2, for 11 to 15 that stops at 5, for 16 to 20 that stops at 4, and for 21 to 25 that stops at 3.

Which of the following best describes the spread of the data? Explain its meaning in this situation?

Based on the temperature at 6:00 am and the temperature at 6:00pm, the change in temperature can be shown by the formula D. |–5 – 7| = |–12| = 12°F.

To find the change in temperature, you need to subtract the temperature at 6: 00 pm from the temperature at 6: 00 am.

The change in temperature is therefore:

= | temperature at 6 am - temperature at 6pm |

= | -5 - 7 |

= | - 12 °F|

The absolute value of - 12 °F is 12 °F which was therefore the change in temperature.

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Answer:

134.94128...

Step-by-step explanation:

Volume of a cone = 1/3 x height x pi x radius^2

1/3 x 8 x pi x 4^2 = 134.04128...

There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

According to the given question.

Total number of items, n = 12

Total numbers of items to be selected, r = 5

Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.

\(^{n} P_{r} = \frac{n!}{(n-r)!}\)

Where,

\(^{n} P_{r}\) is the total number of permutations.

n is the total number of objects.

r is teh total number of objects to be selected.

Therefore,

The number of different groups or permutaions of 5 items that can be selected from 12 distinct group

\(^{12} P_{5}\)

\(= \frac{12!}{(12-5)!}\)

\(= \frac{12!}{7!}\)

\(= \frac{12\times11\times10\times9\times8\times7!}{7!}\)

= 12 × 11 × 10 × 9 × 8

= 95040

Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

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Answer: 2nd diagram, explanation below

Step-by-step explanation:

Since it is 8 magnet students for 3 magic students, the second diagram is correct.

The second part, you would need to set up a system of equations:

Let m = magnet students and t = magic students

t + 25 = m

(8/3)t = m. Since m = m, substitute: t + 25 = (8/3)(t). Now solve for t: t = 8t/3 - 25,

t = (8t - 75)/3, in this step I turned 25 into 75/3 and place it with 8t so it doesn't change the value of the equation.

3t = 8t - 75, in this step I multiplied every term by 3 to eliminate the demoninator. Now I solve the final steps:

-5t = -75, 5t = 75

t = 15

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Answer:

It's the bottom one

Step-by-step explanation:

Well, It says that 8 magnets to every 3 magic tricks so it is obviously the bottom one because the bottom has 3 magic tricks and 8 magnets. And there would be 15 students.

TRUNCATED to one decimal place, it's 50.2

ROUNDED to one decimal place, it's 50.3

The round-off of 50.272 to 1 decimal place using rules of rounding

numbers are 50.3.

Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.

Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.

So, 50.272 becomes 50.3 when rounded to one decimal place.

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The expected value of buying one ticket in this charity raffle is $0.42. This means that, on average, a person can expect to win approximately $0.42 if they purchase a single ticket.

To calculate the expected value, we need to consider the probability of winning each prize multiplied by the value of the prize. Let's break it down:

- There is a 1/5000 chance of winning the $600 prize, so the expected value contribution from this prize is (1/5000) * $600 = $0.12.

- There are 3/5000 chances of winning the $300 prize, so the expected value contribution from these prizes is (3/5000) * $300 = $0.18.

- There are 5/5000 chances of winning the $40 prize, so the expected value contribution from these prizes is (5/5000) * $40 = $0.04.

- Finally, there are 20/5000 chances of winning the $5 prize, so the expected value contribution from these prizes is (20/5000) * $5 = $0.08.

Summing up all the expected value contributions, we get $0.12 + $0.18 + $0.04 + $0.08 = $0.42.

Therefore, if you buy one ticket in this raffle, the expected value of your winnings is $0.42.

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The simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

To simplify the given expression, let's evaluate the square roots individually and then perform the addition.

√900 = 30, since the square root of 900 is 30.

√0.09 = 0.3, as the square root of 0.09 is 0.3.

√0.000009 = 0.003, since the square root of 0.000009 is 0.003.

Now, we can add these simplified values together

√900 + √0.09 + √0.000009 = 30 + 0.3 + 0.003 = 30.303

Therefore, the simplified value of the expression √900 + √0.09 + √0.000009 is 30.303.

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Answer:

118/125

Step-by-step explanation:

We can find first the probability that there isn’t suitable weather:

60/100 * 60/100 * 60/100 = 3/5 * 3/5 * 3/5 = 27/125

now we have just to do this operation

125/125 - 27/125 = 118/125

Answer: 1/30

Step-by-step explanation:

Here's the correct question:

A dump truck brought 1⁄3 of a ton of rock on the first trip, 1⁄2 of a ton on the second trip, but on the third trip, had to take back 4⁄5 of a ton. What was the total weight of the rock left at the construction site?

To calculate the the total weight of the rock left at the construction site goes thus:

= 1/3 + 1/2 - 4/5

The lowest common multiple of 3,2 and 5 is 30. Therefore, we'll make the fractions have a common denominator.

= 1/3 + 1/2 - 4/5

= 10/30 + 15/30 - 24/30.

= 1/30

The correct expression for the estimated model is: In (odds ratio) = -7.8562 +0.0304 Income + 1.2804 Lawnsize. This model was created using binary logistic regression analysis to study the characteristics that differentiate home owners who have a lawn service (code 1) and those who do not (code 0).

The additional information available for these 30 home owners includes family income (Income, in thousands of dollars) and lawn size (Lawn Size, in thousands of square feet). The estimated model shows that for every one unit increase in income,

the odds of having a lawn service increase by 0.0304, and for every one unit increase in lawn size, the odds of having a lawn service increase by 1.2804. This information can be useful for the marketing manager to target potential customers based on their family income and lawn size.
The correct expression for the estimated model in this case is:

ln(odds ratio) = -7.8562 + 0.0304 Income + 1.2804 Lawn Size

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Answer:

It is 8.1 × 10^-7

Step-by-step explanation:

\( {(9 \times {10}^{ - 4} )}^{2} \\ = \{{9}^{2} \times {10}^{( - 4 \times 2)} \} \\ = 81 \times {10}^{ - 8} \\ = 8.1 \times {10}^{ - 7} \)

☆Concept:-

The Question is based on the law of exponents .

The law to be used in this question is

\(\boxed{\sf a^m\times a^n=a^{m+n}}\)

Solution:-

\(\\ \tt\longmapsto (9\times 10^{-4})^2\)

\(\\ \tt\longmapsto 9^2\times 10^{-4(2)}\)

\(\\ \tt\longmapsto 81\times 10^{-8}\)

\(\\ \tt\longmapsto 8.1\times 10^{-7}\)

The true average amount of warpage in all such pieces of laminate lies between 0.0609 and 0.0653 inches with 99% confidence.

a) To construct a 99% confidence interval for the average amount of warpage in all such pieces of laminate, we can use the formula:

CI = X ± Z × (s / √n)

where X is the sample mean warpage, Z is the Z-value from the table below, s is the sample standard deviation and n is the number of observations.

The Z-value for a 99% confidence interval is 2.576. (refer the image)

Plugging in the values we get:

0.0631 ± 2.576 × (0.0072 / √45)

= [0.0609, 0.0653]

b) To construct a 90% confidence interval for the average amount of warpage in all such pieces of laminate, we can use the same formula as above but with a different Z-value.

The Z-value for a 90% confidence interval is 1.645.

Plugging in the values we get:

0.0631 ± 1.645 × (0.0072 / √45)

= [0.0618, 0.0644].

c) Because we need to be more positive that our interval contains the genuine population mean as our confidence level rises, the interval for a 99% confidence level is greater than that for a 90% confidence level. This suggests that in order to account for all possible values of the population mean, we must widen our interval.

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Answer:

54

Step-by-step explanation:

126+54=180

Answer:

-3 + 8 = 5

Step-by-step explanation:

When we have a "minus a negative", it's a positive. So the - -8 is the same as + 8.

LMK if you have questions.

-3 + -8 = -11

is that a nice one or something