(Projectile Motion) Mary is outside her apartment building. She needs to pass her key to John, who is 6 m above the ground floor of the building. Mary has no time to run upstairs, so she throws the key towards John. Suppose the height, h m, of the key above the ground floor at time t seconds is given by h = -11t² + 20t + 1. Is it possible for John to catch the key? Justify your answer.​

The degree of effect refers to the extent to which any differences in the outcome variables are related to the experimental treatment. It can be quantified using various statistical measures and is an important consideration in experimental design and analysis. However, it is not the only factor to consider, and other factors such as the magnitude of effect and potential confounding variables should also be taken into account.

In experimental design and analysis, the degree to which any differences in the outcome variables are related to the experimental treatment is an important consideration. This is typically referred to as the "degree of effect" or "degree of difference."

The degree of effect refers to the extent to which the experimental treatment produces differences in the outcome variables being measured. This can be quantified using various statistical techniques, such as the analysis of variance (ANOVA) or regression analysis, which compare the variation in the outcome variable between groups or over time. It is typically expressed as a statistical measure, such as a p-value or a confidence interval, which indicates the level of confidence that can be placed in the observed differences. A low p-value or a narrow confidence interval indicates a high degree of effect, indicating that any observed differences are likely to be related to the experimental treatment rather than chance or other factors.

In addition to the degree of effect, it is also important to consider the magnitude or size of the effect. This refers to the extent or strength of the differences between the treatment groups, and can be expressed using various effect size measures, such as Cohen's d or eta-squared. A larger effect size indicates a stronger or more meaningful difference between the groups, and is generally considered to be more important than a smaller effect size.

However, it is important to note that the degree of effect and magnitude of effect are not the only factors to consider when evaluating the results of an experiment. Other factors, such as the study design, sample size, and potential confounding variables, can also affect the interpretation of the results and the conclusions that can be drawn.

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The area of the given figure is 66 square miles.

As we can see in the figure, we have 2 different rectangles attached to one another. So the total area of the figure will be the area of the vertical rectangle plus the area of the horizontal rectangle.

Area of the horizontal rectangle = L₁ × W₁

L₁ = 9 mi

W₁ = 2 mi

∴ Area = 9 mi × 2 mi

= 18 square miles

Area of the vertical rectangle = L₂ × W₂

L₂ = 12 mi

W₂ = 4 mi

∴Area = 12 mi × 4 mi

= 48 square miles

Now, the total area of the figure = the area of the vertical rectangle + the area of the horizontal rectangle.

= 48 square miles + 18 square miles

= 66 square miles.

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Answer:

  x²/9 +y²/64 = 1

Step-by-step explanation:

You want the figure defined by x = 3sin(θ) and y = 8cos(θ) to be described by an equation in rectangular form.

The trig identity sin(x)² +cos(x)² = 1 is helpful here.

  x = 3sin(θ)   ⇒   x/3 = sin(θ)

  y = 8cos(θ)   ⇒   y/8 = cos(θ)

Combining these using the above identity, we have ...

  (x/3)² +(y/8)² = 1 . . . . . . the equation of an ellipse

We can simplify the denominators to ...

  x²/9 +y²/64 = 1

__

Additional comment

The attached graph uses different colors and textures to show the two forms of expressing the graph result in the same figure.

The amount of paper used to create the label was approximately 201.06 cm². This was calculated by multiplying the diameter of 16 cm by the height of 8 cm and then multiplying the result by 3.14 (T).

The amount of paper used to create the label for an 8 cm tall cylinder can with a diameter of 16 cm can be calculated by using the formula for the lateral surface area of a cylinder (T*r*h). T is the constant pi, which is equal to 3.14. r is the radius of the cylinder, which is equal to half of the diameter (16 cm/2 = 8 cm). h is the height of the cylinder, 8 cm. Therefore, the lateral surface area of the cylinder can is calculated by multiplying 3.14 by 8 cm (radius) by 8 cm (height). This results in 201.06 cm² of paper needed to create the label. The label can be wrapped around the cylinder, covering the whole surface area of the can.

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The value of P(greater than 4 or less than 5) is 66.7%

From the question, we have the following parameters that can be used in our computation:

Spinner = 3 4 5

Using the above as a guide, we have the following:

4 or 5 = 2

Total = 3

So, we have

P(greater than 4 or less than 5) = 2/3

Evaluate

P(greater than 4 or less than 5) = 66.7%

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The solution is 5/4.

A square root of a number is a value that, when multiplied by itself, gives the number. In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.

For example, 4 and −4 are square roots of 16, because 4² = ² = 16.

here, we have,

√150/√96

=√6√25/√6√16

=5√6/4√6

=5/4

Hence, The solution is 5/4.

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Examining the driving information between Roger and Rita we can say that

Since the Roger and Rita drive at constant speed we check their speed at 1 hour

Roger = in 1 hour covers a distance of 65 miles

Rita = in 1 hour covers a distance of 93 miles

Hence we can say that Rita has a head start,

solving for the head start

= 93 miles - 65 miles

= 22 miles

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The correct way to write the ratio using fractional notation is [tex]\frac{2}{9}[/tex]  (two-ninths).

In math, a fraction is a mathematical expression that shows pars in a whole. Due to this, fractions include a numerator (number placed above) and a denominator (number placed below).

Ratios and fractions are equivalent, which means you just need to make sure the first number is the numerator and the second number is the denominator. Moreover, the fraction should be simplified if possible. Based on this, the fraction is:

[tex]\frac{2}{9}[/tex]

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For f(1) = 0 the statement is true that (x - 1) is the factor of the function.

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given a function,

f(x) = x⁶ - x⁴ + 2x² - 2

and f(1) = 0

substitute the values,

f(x) = x⁶ - x⁴ + 2x² - 2

f(1) = 1⁶ - 1⁴ + 2(1)² - 2

f(1) = 0

so when x = 1 function is zero,

so x - 1 = 0 and (x - 1) is one of the factor of function f(x).

Hence the statement is true.

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Step-by-step explanation:

above is the explanation of the question

The probability of choosing a fisher from Clearwater who had a license is 54/(54+36) = 0.6, and the probability of choosing a fisher from Mountain View who did not have a license is 10/(10+90) = 0.1.

Assuming that the choices are independent, the probability of both events happening together is the product of their probabilities:

P(Clearwater had a license and Mountain View did not have a license) = P(Clearwater had a license) x P(Mountain View did not have a license)

= 0.6 x 0.1

= 0.06

Therefore, the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license is 0.06.

Answer:

The probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license is 0.06

Step-by-step explanation:

To solve this problem, we can use the multiplication rule of probability, which states that the probability of two independent events both occurring is equal to the product of their individual probabilities.Let event A be the event that a fisher chosen from Clearwater Park had a license, and let event B be the event that a fisher chosen from Mountain View Park did not have a license. Then, we need to find the probability of A and B occurring together, which we can write as P(A and B).

Using the given information, we can calculate the probabilities of events A and B as follows:

P(A) = 54/(54+36) = 0.6 (the proportion of fishers at Clearwater Park with a license)

P(B) = 10/(90+10) = 0.1 (the proportion of fishers at Mountain View Park without a license)

Since the events are independent (since no one fished at both parks), we can use the multiplication rule to find the probability of A and B occurring together:

P(A and B) = P(A) * P(B) = 0.6 * 0.1 = 0.06

There are no such pairs. The sum of the reciprocals of any two positive integers is always greater than[tex]$\frac14$[/tex].

The sum of the reciprocals of any two positive integers is [tex]$\frac{1}{m} + \frac{1}{n}$[/tex], which is always greater than [tex]$\frac14$[/tex]. Therefore, there are no distinct ordered pairs of positive integers [tex]$(m,n)$[/tex] so that the sum of the reciprocals of m and n is [tex]$\frac14$[/tex]

For any two positive integers m and n, the sum of their reciprocals is [tex]$\frac{1}{m} + \frac{1}{n}$[/tex] which is always greater than [tex]$\frac14$[/tex] This is because [tex]\frac{1}{m}$ ,$\frac{1}{n}[/tex] are both positive numbers, and so their sum must be greater than [tex]$\frac14$[/tex]Therefore, there are no distinct ordered pairs of positive integers [tex]$(m,n)$[/tex] so that the sum of the reciprocals of m and n is [tex]$\frac14$[/tex].

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The ball will be 864 feet above the ground after 7 seconds. The equation for calculating the height of an object after a certain amount of time given a certain initial velocity is: h = v_0 * t - 0.5 * g * t^2

The equation for calculating the height of an object after a certain amount of time given a certain initial velocity is:

h = v_0 * t - 0.5 * g * t^2

where h is the height, v_0 is the initial velocity, t is the time, and g is the acceleration due to gravity (9.81 m/s^2).

In this case, h = 112 feet/sec * 7 sec - 0.5 * 9.81 m/s^2 * (7 sec)^2

h = 864 feet

The ball will be 864 feet above the ground after 7 seconds.

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The required number would be -23 for the given statement.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

Let the required number would be x.

As per the question, we can write the algebraic form would be as:

-7(x + 7) = 16

Using the distributive property,

-7x - 49 = 16

-7x = 16 + 49

-7x = 65

x = -65/7

x = -23

Thus, the required number would be -23.

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The question seems incomplete, the complete question would be as:

The product of a number and -7 increased by 9, is at most 16. Find the number.

Answer:

100 dimes.

Step-by-step explanation:

Two equations.

First modeling the total money with x as nickels and y as dimes.

0.05x + 0.1y = 12.50

Second, modeling the amount of coins.

x + y = 150

Which you can alter to substitute for in the first equation.

x = 150 - y

Subsitute.

0.05(150 - y) + 0.1y = 12.50

7.5 - 0.05y + 0.1y = 12.50

0.05y = 5

y = 100

Paul has 100 dimes and 50 nickels.

Answer: 4

Step-by-step explanation:

The median is the value in the middle of a data set. When rearranging the data, it should be:

2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 10

4 is directly in the middle since there is 10 numbers exactly to the left and right of it

Hope this helps!

The median of the histogram is M = 5

A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable. Histograms frequently divide data into different "bins" or "range groups" and count how many points are in each bin.

A histogram displays the frequency distribution of a set of continuous data. It is useful for visualizing the shape of the data distribution, such as whether it is symmetrical or skewed, and identifying any outliers or gaps in the data.

One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data.

Given data ,

Let the histogram be represented as A

Now , the value of A is

The frequency of 1 = 0

The frequency of 2 = 1

The frequency of 3 = 5

The frequency of 4 = 5

The frequency of 5 = 4

The frequency of 6 = 2

The frequency of 7 = 1

The frequency of 8 = 1

The frequency of 9 = 1

The frequency of 10 = 1

So , the midpoint of the distribution is M = 10/2 = 5

Hence , the median of the histogram is M = 5

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These polygons have the following areas:

Case 9: 67

Case 10: 72

Case 11: 84

Case 12: 87.5

Case 13: 90

The walkway seal has a cost of $ 774.

In this question we need to determine the areas of irregular polygons and polygonal sections, these areas can be obtained in terms of sums and triangles and rectangles, whose formulas are introduced below:

Triangles

A = 0.5 · w · l

Rectangles

A = w · l

Where:

Now we proceed to determine the areas of each polygon:

Case 9

A = 0.5 · 3 · 4 + 0.5 · 6 · 4 + 0.5 · 2 · 7 + 0.5 · 2 · 7 + 5 · 7

A = 6 + 12 + 7 + 7 + 35

A = 67

Case 10

A = 4 · 0.5 · 3² + 9 · 6

A = 18 + 54

A = 72

Case 11

A = 0.5 · 3 · 12 + 3 · 12 + 0.5 · 3 · 12 + 0.5 · 1 · 4 + 0.5 · 5 · 4

A = 18 + 36 + 18 + 2 + 10

A = 84

Case 12

A = 0.5 · 7 · 3 + 7² + 0.5 · 3 · 4 + 0.5 · 3 · 4 + 4²

A = 10.5 + 49 + 6 + 6 + 16

A = 87.5

Case 13

A = 0.5 · 5 · 3 + 0.5 · 1 · 5 + 10 · 8

A = 7.5 + 2.5 + 80

A = 90

Case 14

A = 4 · 0.5 · (12 ft) · (10 ft) + 2 · (18 ft) · (12 ft) + 2 · (10 ft) · (18 ft)

A = 240 ft² + 432 ft² + 360 ft²

A = 1032 ft²

And the seal cost is:

C = (0.75 $ / ft²) · (1032 ft²)

C = $ 774

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Ans: 55°

Let's draw two parallel line intersecting angle x° and 45° as shown in the photo.

i) a=25° [Being Alternative Angle]

ii) d=15° [Being Alternative Angle]

iii) c= 45°-d[45°=c+d]

=45°-15°

=30°

iv)b=c[Being Alternative Angle]

v)x=a+b[Combining Angle a & b]

=25°+30°

=55°

Let assume the probability of the three events as P(A), P(B), and P(C), respectively. Then:

(a) The probability that at least one of the three events occurs is given by:

P (A or B or C) = 1 - P (not A and not B and not C) = 1 - P (not A) * P (not B) * P (not C)

where P (not A) is the complement of P (A), and similarly for P (not B) and P (not C).

(b) The probability that exactly one of the three events occurs can be calculated by adding the probabilities of each event occurring individually and then subtracting the probability that two events occur simultaneously.

P (exactly one) = P(A) + P(B) + P(C) - 2 * P (A and B) - 2 * P (A and C) - 2 * P(B and C) + 3 * P (A and B and C)

Note that the above formulas assume that the events are mutually exclusive and exhaustive, meaning that one and only one of the events must occur and the sum of the probabilities of the individual events is equal to 1.

If this is not the case, the probabilities need to be adjusted accordingly.

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a. the probability of finding exactly 6 defects in a carpet roll is approximately 0.0403.

b. the probability of finding 3 or fewer defects in a carpet roll is approximately 0.135.

A) The probability of finding exactly 6 defects in a carpet roll can be calculated using the Poisson probability formula:

P(X = 6) = (e^-λ) * (λ^6) / 6!

where λ = 2.0 (the average number of defects per roll), and e is the mathematical constant approximately equal to 2.71828.

Plugging in the values, we get:

P(X = 6) = (e^-2) * (2^6) / 6! = 0.0403

So the probability of finding exactly 6 defects in a carpet roll is approximately 0.0403.

B) To find the probability of finding 3 or fewer defects in a carpet roll, we need to calculate the cumulative probability:

P(X ≤ 3) = Σ_{i=0}^3 P(X = i) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

where P(X = i) is the probability of finding exactly i defects, which can be calculated using the Poisson probability formula.

Plugging in the values and adding the probabilities, we get:

P(X ≤ 3) = (e^-2) + (e^-2) * (2^1) / 1! + (e^-2) * (2^2) / 2! + (e^-2) * (2^3) / 3!

P(X ≤ 3) = 0.135

So the probability of finding 3 or fewer defects in a carpet roll is approximately 0.135.

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Complete question:

The World Carpet and Rug Company buys medium grade carpet in 100-foot rolls. The average number of defects per roll is 2.0. Assuming that these data follow a Poisson distribution,

A) What is the probability of finding exactly 6 defects in a carpet roll chosen at random?

b) What is the probability of finding 3 or fewer defects in a carpet roll?

Nevaeh would have $54 more in her account than Jonathan, to the nearest dollar.

Let's denote the amount of money Nevaeh has in her account after t years as A, and the amount of money Jonathan has in his account after t years as B.

We can use the formula for continuously compounded interest:

Compound interest finds its usage in most of the transactions in the banking and finance sectors and other areas.

And for monthly compounded interest:

We can plug in t = 14 to get the amounts for each person after 14 years:

The difference between these amounts is the amount by which Nevaeh would have more money in her account than Jonathan, to the nearest dollar:

difference = A - B

difference = round(difference)

Using a calculator, we find that:

difference = 977.78 - 923.61 = 54.17

So, Nevaeh would have $54 more in her account than Jonathan, to the nearest dollar.

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If a cell phone tower is 24 meters tall and casts a shadow 45 meters long, then 15 m long of a shadow will be cast by a nearby marble column that is 8 meters tall.

A Cell phone tower is 24 meters tall.

Casts of a shadow is 45 meters long.

A nearby marble column that is 8 meters tall.

We have to determine the how long of a shadow will be cast by a nearby marble column.

Since, the triangle △PQR∼△MNO

So from the diagram

MN/PQ = ON/RQ

8/24 = x/45

Multiply by 45 on both side, we get

x = 8/24 × 45

x = 360/24

x = 15

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Since LMNO is a parallelogram, opposite angles are congruent, which means that angle L is congruent to angle N and angle M is congruent to angle O.

Since angles L and M are adjacent angles in a parallelogram, they are supplementary, which means that their sum is 180 degrees. Therefore, the sum of the measures of angles L and M is:

L + M = 180 degrees.

Answer: 180 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

So and L and M add up to 180 degrees.

Answer: Unclear

Step-by-step explanation: I can't see your image/sentence, so I can't help u

Answer:

30/100

Step-by-step explanation:

25%= 25/100

50%= 50/100

3/100 is in the middle of the two fractions. So one of the possible answer can be 30/100 or 30%

Answer:

[tex]\sf \dfrac{2}{5}[/tex]

Step-by-step explanation:

"per cent" means "per hundred".  Therefore, to change a percent to a fraction, remove the % sign and place the number as the numerator of a fraction with 100 as the denominator.

[tex]\sf 25\%=\dfrac{25}{100}[/tex]

[tex]\sf 50\%=\dfrac{50}{100}[/tex]

Any percent between 25% and 50% can be written as a fraction in the same way.  

Choose a number between 25 and 50, place it as the numerator of a fraction with 100 as the denominator:

[tex]\sf \dfrac{40}{100}[/tex]

Now reduce the fraction to its simplest term by dividing the numerator and denominator by the greatest common factor (GCF):

[tex]\sf \dfrac{40 \div 20}{100\div 20}=\dfrac{2}{5}[/tex]

Therefore, the fraction ²/₅ is between 25% and 50% as it is equivalent to 40%.

Answer:

.99

Step-by-step explanation:

345/353 =0.98

cube root =0 .99

so each edge is 0.99 m

The volume of the wood sample is calculated using the given density and mass. Given that this sample is a cube, the volume is also equal to the cube of the edge length. Therefore, finding the cube root of the volume gives us the edge length, which is about 0.99 meters.

The density of a material is defined by the ratio of its mass to its volume, expressed by the formula density = mass/volume. Given that the mass of the sample is 345 kg and the density is 353 kg/m³, you can calculate the volume by rearranging the formula to volume = mass/density. So, the volume comes out to be approximately 0.977 cubic meters. Now, since the sample is a cube, all sides are equal. The volume of a cube is given by the formula volume = edge ^ 3 (edge length cubed). You are hence looking to find the cube root of the volume, which is approximately 0.99 meters. Therefore, the length of one edge of the wood sample is approximately 0.99 meters to the nearest hundredth of a meter.

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The image below (see attachment) illustrates how the rectangle with a vertex of C and a side on line CD is built.

A rectangle can be thought of as a four-sided polygon with two opposite pairs of equal sides and four interior angles that are each 90 degrees. At each corner or vertex, the two sides come together at an angle. Rectangles differ from squares in that their opposite sides are of equal length. Additionally, it is known as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. As a result, the rectangle with the stated lengths and a vertex of C is built as shown in the image attached below (see attachment).

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The probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer is 5/45, or approximately 0.11.

To calculate the probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer, we need to consider the number of possible combinations of socks that result in a match and divide that by the total number of possible combinations of two socks.

The man has a total of 5 pairs of socks, or 10 socks, so there are 10 choose 2, or 45, possible combinations of two socks. Out of these, 5 of them result in a match, because there are 5 pairs of matching socks in the drawer.

Therefore, the probability of getting a matched pair of socks is 5/45, or approximately 0.11. This means that there is an 11% chance that the man will select a matched pair of socks if he randomly selects two socks from the drawer.

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