Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. What is the median weight of the players?

Answer:

The value of 'y' when x = -4 is 2.3

Step-by-step explanation:

Curve of best fit can be found by plotting the points on MS Excel and drawing a curve that goes through the points as shown in the attached graph

The equation that approximate the curve from which the y-value at a x-value of -4 can be estimated is found as follows

The general equation for a quadratic equation is y = a·x² + b·x + c

Therefore, we get;

2 = a·(-3)² + b·(-3) + c

2 = 9·a - 3·b + c

5 = 0·a + 0·b + c

5 = c

7.3 = 1·a + 1·b + c = a + b + 5

7.3 = a + b + 5

2.3 = a + b

2 = 9·a - 3·b + 5

-3 = 9·a - 3·b

Solving gives;

a = 13/40, b = 79/40

The equation of the quadratic curve is therefore;

y = (13/40)·x² + (79/40)·x + 5

When x = -4, we get;

y = (13/40)·(-4)² + (79/40)·(-4) + 5 = 2.3

When x = -4, y = 2.3

Plotting the points on MS Excel we find from the attached graph that the estimated value of 'y' when x = -4 is as calculated (2.3).

Yes , rotating is  a congruence transformation.

What is a congruence transformation?

A transformation that changes the position of the figure while not dynamical its size or form is termed a congruity transformation.

Main body:

A congruity transformation is that the movement or locating of a form specified it produces a form that is congruent to the initial.

Translations, reflections, and rotations are the three types of congruence transformations. That is, the pre-image and the image are always congruent.

Hence ,rotating is  a congruence transformation.

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Answer:

no because it's too expensive

(only my opinion tho)

Answer:

x = -5

Step-by-step explanation:

Dots are data points in scatterplots, hence dots which deviates from the main dot cluster are classed as potential outliers.

Outliers are data points that are significantly different from the rest of the data. They can be caused by a number of factors, such as data entry errors, measurement errors, or simply by the fact that the data is not normally distributed. Outliers can have a significant impact on the results of statistical analyses, so it is important to identify and deal with them appropriately.

Therefore, data points which varies significantly from the main data point cluster would be seen as potential outliers and may be subjected to further evaluation depending on our aim for the analysis.

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Answer:

Esta persona invirtió $ 6000 a la cuenta bancaria que paga 5 % de interés simple anual y $ 19000 a la cuenta bancaria que paga 6 % de interés simple anual.

Step-by-step explanation:

Esta persona invierte \(x\) a la cuenta bancaria que paga 5 % de interés simple anual y \(25000-x\) a la cuenta bancaria que paga 6 % de interés simple anual. Recibe \(1440\) como consecuencia de las ganancias de las dos cuentas, es decir:

\(\frac{5\cdot x}{100} + \frac{6\cdot (25000-x)}{100} = 1440\) (1)  

Ahora procedemos a resolver la ecuación resultante:

\(5\cdot x + 150000-6\cdot x = 144000\)

\(150000-144000 = 6\cdot x - 5\cdot x\)

\(x = 6000\)

En consecuencia, esta persona invirtió $ 6000 a la cuenta bancaria que paga 5 % de interés simple anual y $ 19000 a la cuenta bancaria que paga 6 % de interés simple anual.

The solution of the given inequality 4(x² - 5) - (x² - 5)² > -12 is x ≥ √3 or x ≤ -√3.

The given inequality is 4(x² - 5) - (x² - 5)² > -12. In order to solve the given inequality, first, we will multiply (x² - 5)² by -1 to get rid of the squared term. Next, we will simplify the terms by using the distributive property. Then, we will collect the like terms and solve the inequality.

Multiply (x² - 5)² by -1. => -(x² - 5)² = -x⁴ + 10x² - 25

Now, the given inequality is:

4(x² - 5) - (x² - 5)² > -12

4(x² - 5) + x⁴ - 10x² + 25 > -12

Simplify the terms by using the distributive property:

4x² - 20 + x⁴ - 10x² + 25 > -12

Simplifying further:

x⁴ - 6x² + 13 > 0

Collect like terms and solve the inequality:

(x² - 3)² + 4 > 0

As the square of any number is always greater than or equal to 0, so

(x² - 3)² ≥ 0 ⇒ (x² - 3)² + 4 ≥ 4

Hence, x² - 3 ≥ 0 ⇒ x² ≥ 3 ⇒ x ≥ ±√3

Therefore, the solution of the given inequality is x ≥ √3 or x ≤ -√3.

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Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

5 Inches

Step-by-step explanation:

If one inch is three miles, and the final destination is 15 miles away; 15 miles divided by 3 miles per inch (15/3) is 5 inches.

Answer:

2 bags

Step-by-step explanation:

Let the number of bags be b.

Let the number of candies in each bag be c.

The number of bags was 9 less than the number of candies in each bag. That is:

b = c - 9

She bought 22 candies.

This means that The number of candy in each bag multiplied by the numbe of each bag is 22:

b * c = 22

bc = 22

=> (c - 9) * c = 22

\(c^2 - 9c = 22\\\\c^2 - 9c - 22 = 0\\\\c^2 - 11c + 2c - 22 = 0\\\\c(c - 11) + 2(c - 11) = 0\\\\(c + 2) (c - 11) = 0\\\\=> c = -2, c = 11\)

Since the number of candies can only be a positive number, c = 11.

Therefore:

b = 11 - 9

b = 2

Katy bought 2 bags of candy containing 11 candies each.

Therefore, the probability that a randomly selected battery lasts longer than 48 hours is 0.9452.

To solve this problem, we can use the z-score formula and the standard normal distribution.

First, we calculate the z-score for the value of 48 hours:

z = (x - μ) / σ

where x is the value (48 hours), μ is the population mean (40 hours), and σ is the population standard deviation (5 hours).

z = (48 - 40) / 5

z = 8 / 5

z = 1.6

Next, we need to find the probability corresponding to a z-score of 1.6 using the standard normal distribution table or a calculator. Looking up the z-score of 1.6 in the standard normal distribution table, we find that the corresponding probability is approximately 0.9452.

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The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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Answer:

x = 0     y = 2

Step-by-step explanation:

4x + 2 = -2x + 2

6x + 2 = 2

6x = 0

x = 0

y = 4(0) + 2

y = 2

The exponential distribution may be used to predict the failure rate of certain items over time. An LED light bulb has an expected lifetime of 25000 hours. Assuming that the lifetime of the LED light bulb follows the exponential distribution, the probability that it will last more than 3 years is closest to (C) 53%. Correct answer is option C

This is because the lifetime of an LED light bulb can be estimated using the following equation : P(x > 3 years) = 1 - P(x ≤ 3 years)where x is the lifetime of the LED light bulb.If we convert 3 years to hours, we get 3 * 365 * 24 = 26280 hours. As a result, P(x ≤ 3 years) = P(x ≤ 26280 hours)

Using the formula for exponential distribution, the probability of the LED light bulb failing after 26280 hours is : Probability = 1 - e^{-λx} Where λ is the failure rate per hour and x is the length of time in hours.We can now calculate the value of λ by dividing the expected lifetime of the bulb by the total number of hours.

 λ = 1/25000 hours  This implies that the probability of the LED light bulb failing after 26280 hours is : P (x ≤ 26280 hours)

Therefore, the probability that the LED light bulb will last more than 3 years is approximately 53 percent. The Correct answer is option C

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i attached a pdf, hopefully it helps you understand!

y-axis 6 5 4 3 2 1 x=ax S 4 -3 2  -1 1 2 3 4 5 6 -1 -2.    

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A transformation modifies the parent function's graph.

The graph of a parent function is changed by a transformation. Transformations come in three different flavors: translations, reflections, and dilations.

A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.

Making pictures or replicas of an object is part of transformation geometry. You are introduced to transformation geometry in grade 9 through the use of translation, reflection, dilation, and rotation.

The foundation of the problem transformation approach is the notion that, if we are unable to address the given problem directly, we will move it to a setting where we can do so. The method's fundamental component is how the problem is broken down into smaller tasks.

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Answer:

Step-by-step explanation:

Discussion and Correction

The algrebra  itself is fine. The exclusions are not so good. The difficulty comes in the denominator. It factors into (2x)(x - 3). x cannot take on a value of 0 (that was pointed out and that is correct). The problem comes in the plus/minus 3. Plus 3 is correct. x - 3 will come 0 if x = 3. Nothing bad will happen if x = - 3

Answer: So the exclusions in the denominator should be modified to x = 3.

Answer:

The excluded values are x-values that make the denominator of the original expression zero, since \(\dfrac{a}{0}\) is undefined.

\(x = -3\) is not an excluded value since this x-value does not make the  denominator zero.

\(x = -3\) makes the numerator zero, but as \(\dfrac{0}{a}=0\) it is not an excluded value.

Therefore, step 3 of her work should read:

\(\textsf{Finding excluded values}:x\neq 0\:\textsf{and}\:x\neq 3\)

Answer:

Step-by-step explanation:

The answer is d

Answer: False

Step-by-step explanation:

A cup with a hole in it loses 2 ounces of water in the first minute. This mathematically means

Add -2 (loses ⇒ means getting less)

Then the cup loses 2 ounces of water in the second minute. This mathematically means

Add -2 (loses ⇒ means getting less)

In total,  and means loses 4 ounces in two minutes.

Thus, the statement below does not describe a situation in which opposite quantities combine to make zero, so this statement is false

Company A has a higher risk percentage (55%) compared to Company B (3%).

To compute the Coefficient of Variation (CV) for each company, we need to use the formula:

CV = (Standard Deviation / Mean) * 100

Let's calculate the CV for each company:

For Company A:

Risk Percentage = 55%

Return = 14%

For Company B:

Risk Percentage = 3%

Return = 14%

Since we don't have the standard deviation values for each company, we cannot calculate the exact CV. However, we can still compare the riskiness of the two companies based on the provided information.

The Coefficient of Variation measures the risk relative to the return. A higher CV indicates higher risk relative to the return, while a lower CV indicates lower risk relative to the return.

In this case, Company A has a higher risk percentage (55%) compared to Company B (3%), which suggests that Company A is riskier. However, without the standard deviation values, we cannot make a definitive conclusion about the riskiness based solely on the provided information. The CV would provide a more accurate measure for comparison if we had the standard deviation values for both companies.

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Answer:

-12

Step-by-step explanation:

6G = -72

G = -72 / 6

G = -12

Answer:

b/a

Step-by-step explanation:

Perpendicular lines have slopes that are opposite sign and reciprocals (flipped over).

In the equation

ax + by = c,

the slope of the line is

-a/b

If you haven't memorized this pattern yet, you can calculate it by solving ax+by=c for y.

by = -ax +c

y = -a/b x + c/b

The slope is -a/b

So a perpendicular line would be opposite sign and flipped, b/a

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

201.06

Step-by-step explanation:

The type of standard score that has a mean (m) of 0 and a standard deviation (sd) of 1 is known as the Z-score.

The Z-score, also referred to as the standard score, is a statistical measure that standardizes a given value in a distribution. It indicates how many standard deviations a particular value is away from the mean of the distribution. When the mean (m) is 0 and the standard deviation (sd) is 1, the resulting Z-score is based on this standardization. The formula for calculating the Z-score is (x - m) / sd, where x represents the value being standardized. By using this formula with m = 0 and sd = 1, the Z-score provides a standardized value that allows for comparisons and analysis across different datasets with varying means and standard deviations.

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To solve for d:

1. Remove parenthesis:

2. Leave the terms with d in one side of the equation:

-Add 1.2 in both sides of the equation:

-Substract 0.3d and 0.1d in both sides of the equation:

3. Opperate similar terms:

4. Divide into (-0.2) both sides of the equation: