Plot A shows the number of hours ten girls watched television over a one-week period. Plot B shows the number o
hours ten boys watched television over the same period of time.
Television Viewing Hours for a One-Week Period
Plot A
8 9 10
04
2 3
Plot B
4100
6005
4307
16
27
2 3 4 5
6 7 8 9
Which statement correctly compares the measures of center in the two sets of data?

The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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The 90% confidence interval for the mean is (264.6935,275.5065)

A confidence interval (CI) in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified confidence level; the 95% confidence level is the most frequent, but other levels, such as 90% or 99%, are occasionally used. The confidence level denotes the long-run proportion of related CIs that include the true value of the parameter. For example, 95% of all intervals generated at the 95% level should contain the parameter's true value.

From the given data ,

Sample mean = X = 270.1

Sample standard deviation = s = 9.3268

n = 10

Therefore , the 90% confidence interval for the mean is ,

\(\bar{X}\)±\(t_{n-1,\alpha /2}\)(s/√n)

270.1 ± \(t_{10-1.0.10/2}\)(9.3268/√10)

270.1 ±1.8331 ×2.9494

270.1 ± 5.4065

(264.6935,275.5065)

Therefore, the 90% confidence interval for the mean is (264.6935,275.5065)

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The complete question is:

"The following are airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport. 269 255 267 285 274 275 266 258 271 281

(a) Compute a 90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles. (Round your answers to three decimal places.)"

Answer:

2/15+2/15

Step-by-step explanation:

I hope this is correct and have a great day

The area of the teacher workroom is 64 feet squared

Answer:

Step-by-step explanation:

we know that density is given as

density=mass/volume

the volume of the cylinder

v= πr^2h

v=3.142*1.5^2*14.4

v=3.142*2.25*14.4

v=101.8cm^3

Given that density =0.00123g/cm^3

mass= density*volume

masss= 0.00123*101.8

mass= 0.125214 g

Answer:

168.75

Step-by-step explanation:

135.00 + 25% is 168.75

168.75 - 25% is 135.00

The expression (f/m)(x) - (m/f)(x) is calculated by substituting the given functions into the expression and simplifying, resulting in \((-x^2 + 3x + 2) / (3x - 6)\), while (f/m)(0) - (m/10) is directly computed as -7/6.

(a) To compute the expression (f/m)(x) - (m/f)(x), we need to substitute the given functions f(x) and m(x) into the expression and simplify.

The expression (f/m)(x) represents f(x) divided by m(x), and (m/f)(x) represents m(x) divided by f(x).

\((f/m)(x) = (3x - 6) / (x^2 - 8)\)

\((m/f)(x) = (x^2 - 8) / (3x - 6)\)

Substituting the functions into the expression, we have:

\((f/m)(x) - (m/f)(x) = (3x - 6) / (x^2 - 8) - (x^2 - 8) / (3x - 6)\)

To simplify this expression further, we can find a common denominator and combine the fractions. However, since the denominator (3x - 6) appears in both terms, we can simplify the expression as follows:

\((f/m)(x) - (m/f)(x) = (3x - 6 - (x^2 - 8)) / (3x - 6)\)

Simplifying the numerator, we have:

\((3x - 6 - x^2 + 8) / (3x - 6) = (-x^2 + 3x + 2) / (3x - 6)\)

This is the simplified form of the expression (f/m)(x) - (m/f)(x).

(b) To compute the expression (f/m)(0) - (m/10), we need to substitute x = 0 into (f/m)(x) and x = 10 into (m/f)(x) and then perform the subtraction.

Substituting x = 0 into (f/m)(x), we have:

\((f/m)(0) = (3(0) - 6) / (0^2 - 8) = -6 / (-8) = 3/4\)

Substituting x = 10 into (m/f)(x), we have:

\((m/f)(10) = (10^2 - 8) / (3(10) - 6) = 92 / 24 = 23/6\)

Therefore, (f/m)(0) - (m/10) = (3/4) - (23/6) = (9/12) - (23/6) = (-14/12) = -7/6

In conclusion, the expression (f/m)(x) - (m/f)(x) simplifies to \((-x^2 + 3x + 2) / (3x - 6)\), and (f/m)(0) - (m/10) equals -7/6.

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Answer:

x = 1

y = 1

Step-by-step explanation:

Given:

Add up the two equations side-by-side, this will cancel y/b and 1/b:

Subtract the  two equations side-by-side, this will cancel x/a and 1/a:

Answer:

x = 1, y = 1

Step-by-step explanation:

\( \frac{x}{a} + \frac{y}{b} = \frac{1}{a} + \frac{1}{b} .....(1) \\ \frac{x}{a} - \frac{y}{b} = \frac{1}{a} - \frac{1}{b} .....(2) \\ \\ let \: \: \frac{1}{a} = m, \:\:\&\: \: \frac{1}{b} = n \\ so \: equatin \: (1) \: reduces \: to: \: \\ \\ so \: equatin \: (1) \: reduces \: to: \: \\ mx + ny = m + n....(3)\\ and \: equatin \: (2) \: reduces \: to: \: \\ mx - ny = m - n....(4) \\ adding \: equations \: (3) \: (4) \\ mx + ny = m + n \\ mx - ny = m - n \\ - - - - - - - - - - \\ 2mx = 2m \\ x = \frac{2m}{2m} \\ \huge \red{ \boxed{x = 1}} \\ substituting \: x = 1 \: in \: equatin \: (3) \\ m \times 1 + ny \: = m + n \\ m + ny \: = m + n \\ ny = m + n - m \\ ny = n \\ y = \frac{n}{n} \\ \huge \purple{ \boxed{y = 1}}\)

Answer:

Step-by-step explanation:

The length is 25x and 7/25th of the length is 23:

The length is:

ATQ

\(\\ \sf\longmapsto \dfrac{7}{25}\:of\:25x=23\)

\(\\ \sf\longmapsto \dfrac{7}{25}\times 25x=23\)

\(\\ \sf\longmapsto 7x=23\)

\(\\ \sf\longmapsto x=\dfrac{23}{7}\)

Now

\(\\ \sf\longmapsto 25x\)

\(\\ \sf\longmapsto \dfrac{25(23)}{7}\)

\(\\ \sf\longmapsto \dfrac{575}{7}\)

The difference between what consumers are willing to pay for units of the good and the price consumers actually pay for units of the good is called consumer surplus.

Thus, option (C) is correct.

Consumer surplus refers to the difference between the maximum price a consumer is willing to pay for a product or service and the actual price they pay.

Consumer surplus is derived from the concept of the demand curve in economics. The demand curve represents the relationship between the price of a good and the quantity consumers are willing to purchase at that price.

Therefore, the difference between what consumers are willing to pay and actually pay for units is called consumer surplus.

Thus, option (C) is correct.

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Answer:

w= 9

Step-by-step explanation:

\( \sqrt{ - 4w + 61} = w - 4\)

Square both sides:

-4w +61= (w -4)²

\(\boxed{(a - b)^{2} = a^2 -2ab + b^2 }\)

Expand:

-4w +61= w² -2(w)(4) +4²

-4w +61= w² -8w +16

Simplify:

w² -8w +16 +4w -61= 0

w² -4w -45= 0

Factorize:

(w -9)(w +5)= 0

w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

Note:

-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

Why do we use negative square root?

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

Answer: w=9.

Step-by-step explanation:

\(\sqrt{-4w+61}=w-4\)

Tolerance range:

\(\left \{ {{-4w+61\geq 0} \atop {w-4\geq 0}} \right. \ \ \ \ \left \{ {{4w\leq 61\ |:4} \atop {w\geq 4}} \right. \ \ \ \ \left \{ {{w\leq 15,25} \atop {w\geq 4}} \right. \ \ \ \ \Rightarrow\ \ \ \ \\w\in[4;15,25].\)

Solution:

\((\sqrt{-4w+61})^2=(w-4)^2\\-4w+61=w^2-2*w*4+4^2\\-4w+61=w^2-8w+16\\w^2-4w-45=0\\D=(-4)^2-4*1*(-45)\\D=16+4*45\\D=16+180\\D=196.\\\sqrt{D}=\sqrt{196}\\\sqrt{D}=14 \\w_{1,2}=\frac{-(-4)б14}{2} \\w_1=\frac{4-14}{2} \\w_1=\frac{-10}{2} \\w_1=-5\ \notin tolerance\ range.\\w_2=\frac{4+14}{2}\\ w_2=\frac{18}{2} \\w_2=9\ \in tolerance \ range.\)

It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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To find the direction and magnitude of the resultant of these three forces, we can use the law of cosines and the law of sines.

First, we need to resolve each force into its x and y components using trigonometry.

F1x = 80 * cos(30) = 69.28

F1y = 80 * sin(30) = 40

F2x = 95 * cos(45) = 67.08

F2y = 95 * sin(45) = 67.08

F3x = 125 * cos(120) = -62.5

F3y = 125 * sin(120) = -106.6

Then we can find the x and y components of the resultant force by adding the x and y components of each force respectively.

Rx = F1x + F2x + F3x = 69.28 + 67.08 - 62.5 = 74.86

Ry = F1y + F2y + F3y = 40 + 67.08 - 106.6 = 0.48

Finally, using these values we can use the law of cosines to find the magnitude of the resultant force:

R = sqrt(Rx^2 + Ry^2) = sqrt(74.86^2 + 0.48^2) = sqrt(5633.79) = 75.24

And we can use the law of sines to find the direction of the resultant force:

theta = atan2(Ry, Rx) = atan2(0.48, 74.86) = 0.01

Therefore, the magnitude of the resultant force is 75.24 pounds and the direction of the resultant force is 0.01 degrees.

Subtract the monthly fee:

10.58 -5 = 5.58

Divide the remaining amount by cost per minute:

5.58/ 0.09 = 62

He was billed for 62 minutes.

Answer:

Its A

explanation:

The greater than or equal to is usually coloured and normal is not coloured

To solve the equation sinθ(cosθ + 1) = 0 for θ with 0 ≤ θ < 2π, we can apply the zero-product property and set each factor equal to zero.

1. Set sinθ = 0:

This occurs when θ = 0 or θ = π. However, since 0 ≤ θ < 2π, the solution θ = π is not within the given range.

2. Set cosθ + 1 = 0:

Subtracting 1 from both sides, we have:

 cosθ = -1

This occurs when θ = π.

Therefore, the solutions to the equation sinθ(cosθ + 1) = 0 with 0 ≤ θ < 2π are θ = 0 and θ = π.

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i dont know my friend so try asking someone better than cause i have no brain for this type of math

The force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N

A tangible body's mass is the amount of matter it possesses. It's also a metric of inertial or the resistance to velocity when a net force is exerted.

We have:

The mass of the body m = 0.8 kg

As we know,

F = mg

F is the force acting on the body and g is the acceleration due to gravity.

g = 9.8 m-s⁻²

F = (0.8)(9.8)

F = 7.84 kg-m-s⁻²

or

F = 7.84 N

Thus, the force acting on a body of mass 0.8 kg is F = 7.84 kg-m-s⁻² or F = 7.84 N

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Answer:

x=9 and y=1

name the first eqn as eqn one

and the second as eqn two

then subtract both eqns

(eqn is equation)

Answer:

If you were to use the sine formula you would have to use the cosine formula to get one of the opposite sides and then use the sine formula.

For the area why not use 1/2 * 20 to get the base.

Then the height would be 24 * sin 63 = 21.38

That would give an area of 213.8

The value of x that is a counterexample to the student's conjecture is of:

x = 0.

A counter example to a conjecture is a statement that makes the conjecture false.

In the context of this problem, the conjecture is presented as follows:

x + 5 < x².

The conjecture is only true for non-negative numbers, hence the counter example also has to be a non-negative number, meaning that these following options are removed, as they are negative numbers:

For x = 0, the conjecture is given as follows:

0 + 5 < 0²

5 < 0

Which is a false statement, hence x = 0 is the counterexample to the student's conjecture.

At x = 5, the conjecture is given as follows:

5 + 5 < 5².

10 < 25.

Which is true, however, the conjecture has already been shown to be false at x = 0.

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Answer:

give picture

Step-by-step explanation:

Solving inequalities with addition is similar to solving equations with addition in the initial steps, but it differs in the final answer due to the inequality sign. In both cases, you use addition to isolate the variable. However, with inequalities, you must consider the direction of the sign throughout the process.

When solving inequalities with addition, like equations, the goal is to isolate the variable on one side. You use addition to simplify the expression. Begin by treating the inequality like an equation, adding or subtracting the same value to both sides to eliminate constants and isolate the variable.

For example, if you have \(\(2x + 5 > 10\)\), subtract 5 from both sides to get \(\(2x > 5\)\).

Here's where it diverges: since inequalities involve the relationship between two quantities, you need to be mindful of the inequality sign. When you multiply or divide both sides by a negative number, the inequality direction flips.

For example, if you multiply \(\(x < 3\)\) by -2, the sign changes to \(\(x > -6\)\).

Remember, you're looking for a range of values that satisfy the inequality. So, when representing your final answer, use the appropriate inequality sign. For instance, if \(\(3x + 2 \leq 8\)\), after simplifying, you'll have \(\(x \leq 2\)\), indicating that any value of \(\(x\)\) less than or equal to 2 satisfies the inequality.

In summary, while solving inequalities with addition is akin to solving equations with addition in the initial steps, the crucial distinction lies in managing the inequality sign throughout the process and representing the solution as a range of values that satisfy the inequality.

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Complete Question:

How is solving inequalities with addition is similar to or different from solving equations with addition ?

the thickness in scientific notation is:

4.3* 10⁻³ inches

Here we know that the thickness of a dollar bill is 0.0043 inches.

Now, scientific notation refers to the notation where we have a single digit at the left of the decimal point, and the order of the number is defined by a factor of a power of 10.

To write our number in scientific notation we need to count the number of zeros that we have before the first non-zero decimal, and we can see that it is equal to 3.

Then we can move all the digits 3 units to the left, and add a factor 10⁻³ to correct that, then we will get:

0.0043 = 4.3* 10⁻³

From this, we conclude that the thickness in scientific notation is:

4.3* 10⁻³ inches

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Minimum value is 103, lower quartile (Q1): median of first 15 values s 137, median (Q2): median of all 30 values is 153.5, upper quartile (Q3): median of last 15 values is 174 and maximum value is 216

To construct a boxplot from the given data, follow these steps:

1. Arrange the data in ascending order.
2. Find the minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value.

Arranged data:
103, 105, 114, 121, 128, 133, 134, 137, 140, 142, 143, 144, 150, 153, 160, 161, 163, 166, 169, 171, 173, 174, 175, 177, 179, 181, 189, 206, 212, 216

Minimum value: 103
Lower quartile (Q1): Median of first 15 values = 137
Median (Q2): Median of all 30 values = 153.5
Upper quartile (Q3): Median of last 15 values = 174
Maximum value: 216

Based on the calculated values, the important characteristics of the boxplot are as follows:

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Answer:

1.44

Step-by-step explanation:

To find the critical value Zα/2 for a 88% confidence level, we need to first find α/2.

α/2 = (1-0.88)/2 = 0.06/2 = 0.03

Using a Z-table or calculator, we can find the Z-score that corresponds to a cumulative probability of 0.03 from the left tail, which is -1.44.

Therefore, the critical value Zα/2 for a 88% confidence level is 1.44 (positive or negative depending on the direction of the test).

Therefore, probability solution is estimating this likelihood without additional data or analysis is inappropriate correct response is option a.

The main goal of the mathematical branch known as statistical inference is to estimate the likelihood that a statement is accurate or that a particular event will take place. Any number among 0 and 1, where 1 typically denotes confidence and 0 typically denotes possibility, can be used to symbolise chance. A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

Because of the skewed demographic distribution, the right response is (a).

We could use the normally distributed to compute probabilities because the length of adult American ladybirds is distributed normally with a known standard deviation. The normal distribution may not, however, correctly depict the distribution of ladybird lengths in the population due to the skewed population distribution.

Furthermore, even if the difference between the actual community mean and the assumed mean of 1 cm is tiny, the given size of the population of 440000 could result in a statistically significant outcome.

However, because the assumption of normality may not hold true, this does not imply that we can accurately determine the likelihood of a random ladybird in Raleigh being larger than 1.5 centimetres.

Therefore, estimating this likelihood without additional data or analysis is inappropriate.

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The answer is 33degree.

Answer:

b. ll only

Explanation:

Remember, service fees often refer to an amount deducted to pay for the cost of providing particular services, such as ATM service charges, etc.

We can this conclusion because if one decides to deposit money in large batches rather than in small amounts; they will be directly subjecting themselves to excessive charges. Consider, most financial institutions often charge higher fees for larger deposits.

Also, if one decides to avoid using your debit card online they will tend to spend more using traditional cash methods which require increasing the number of one's ATM withdrawal.

However, by trying to limit the number of withdrawals you make from out-of-network ATMs, one saves him or herself of excessive service fees.