Question 2 [10] Give the following grouped data: Intervals frequency [50-58) 3 [58-66) 7 [66-74) 12 [74-82) 0 [82-90) 2 [90-98) 6 2.1 Use the data above to calculate the mean (3) 2.2 What is the first quartile for the grouped data (4) 2.3 Derive the accumulative frequency table

We see that since they are congruent triangles, their corresponding sides are also equal.

-> 2x + 1 = x + 3.
-> x + y = 3x - 3y

From the first equation, we can solve for x ;

2x + 1 = x + 3

Minus both sides by 1 :

2x = x + 2

Finally, minus both sides by x :

x = 2.

We substitute the value of x = 2 into the second equation :

2 + y = 6 - 3y

Add both sides by 3y :

2 + 4y = 6

Solve for y : 4y = 4 -> y = 1.

The 2nd relationship || u + v || = √ { || u ||² + || v ||² }, and the 4th relationship || u + v || < || u || + || v || holds for the sum of the magnitudes of vectors u and v, which are perpendicular.

In the question, we are asked to identify the relationships that hold for the sum of the magnitudes of vectors u and v, which are perpendicular to each other.

The magnitude of a vector A is shown as || A ||.

Thus, the magnitude of vector u is || u ||, and of vector, v is || v ||.

By vector algebra, we know that,

|| u + v || = √ { || u ||² + || v ||² + 2( || u || )( || v || ) cos θ }, where θ is the angle between vector u and vector v.

Now, we are given that vectors u and v are perpendicular to each other, thus, θ = 90°, which gives cos θ = 0, or,

|| u + v || = √ { || u ||² + || v ||² }, making the 2nd relation true.

Now, we have, || u + v || = √ { || u ||² + || v ||² }.

Squaring both sides, we get:

|| u + v || ² = || u ||² + || v ||² = { || u || + || v || }² - 2(|| u ||)(|| v ||),

or, || u + v || ² < { || u || + || v || }² {Since, 2(|| u ||)(|| v ||) > 0},

or, || u + v || < || u || + || v || {Taking square roots}, making the 4th relation true.

Thus, the 2nd relationship || u + v || = √ { || u ||² + || v ||² }, and the 4th relationship || u + v || < || u || + || v || holds for the sum of the magnitudes of vectors u and v, which are perpendicular.

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For the complete question, refer to the attachment.

Answer:

-x + 5 or -1x + 5

Step-by-step explanation:

Combine like terms:

2x + 3x - 6x = -1x or -x

-3 + 12 - 4 = 5

Simplify:

-x + 5 or -1x + 5

Hope it helps!

Answer:

if i did it right its -13

Step-by-step explanation:

hope you have a good day

Answer: p+(-q)

Step-by-step explanation:

The slope of the line in the given graph is 0.5

From the question, we are to calculate the slope of the line in the given graph

To calculate the slope, we will pick two points on the line shown in the graph

Picking the points (1, 1) and (3, 2).

Using the formula,

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (2 - 1) / (3 - 1)

Simplify the expression on the right side

Slope = 1 / 2

Slope = 0.5

Hence,

The slope of the line is 0.5

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The  distance between the ships is increasing at a rate of approximately 18.71 km/h.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the two sides are the distance traveled by ship A and the distance traveled by ship B.

Let's start by calculating the distance traveled by ship A from noon to 4:00 p.m., which is 4 hours:

distance = rate × time = 40 km/h × 4 h = 160 km

Now let's calculate the distance between the two ships at noon:

distance = √(170² + 0²) = √28900 ≈ 170.13 km

At 4:00 p.m., ship A has traveled 160 km east, and ship B has traveled 25 km/h × 4 h = 100 km north. We can use the Pythagorean theorem to calculate the new distance between the two ships:

distance = √(170² + 160² + 100²) ≈ 244.95 km

Therefore, the distance between the ships at 4:00 p.m. is approximately 244.95 km. To find the rate of change of this distance, we can subtract the initial distance from the final distance and divide by the time interval:

rate of change = (244.95 km - 170.13 km) / 4 h ≈ 18.71 km/h

Therefore, the distance between the ships is increasing at a rate of approximately 18.71 km/h.

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Answer:

x + 1/2

Step-by-step explanation:

1/2 x + 3/4  + 1/2 x - 1/4

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

= 2/2 x + 2/4

= x + 1/2

The type of table relationship that best describes the given narrative is the "One-to-many relationship."

This relationship implies that one entity in a table is associated with multiple entities in another table, but each entity in the second table is associated with only one entity in the first table.

In this case, the "Customer" table represents the one side of the relationship, where each customer can have zero, one, or many sales orders. On the other hand, the "Sales order" table represents the many side of the relationship, where each sales order is associated with only one customer. Therefore, for a given customer, there can be multiple sales orders, but each sales order can be linked to only one customer.

It is important to note that the term "many-to-many relationship" is not applicable in this scenario because it states that multiple entities in one table can be associated with multiple entities in another table. However, the narrative explicitly mentions that each sales order is associated with only one customer, ruling out the possibility of a many-to-many relationship. Therefore, the most appropriate description is a one-to-many relationship.

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Answer:

x = 4

Step-by-step explanation:

x + 6 +2x = 2x + 6 + 4

combine like terms:

3x + 6 = 2x + 6 + 4

add numbers:

3x + 6 = 2x + 10

subtract 6 on both sides:

3x + 6 - 6 = 2x + 10 - 6

3x = 2x + 4

subtract 2x from both sides:

3x - 2x = 2x - 2x + 4

x = 4

short explanation:

if you look at the equation, both sides have 6 and 2x which would cancel each other out. That would leave x = 4

The length of ST in the triangle STU, we can use the sine rule. Given that the measure of angle ZU is 90°, angle ZT is 26°, and US is 13 feet, we can calculate the length of ST to the nearest tenth of a foot. Therefore, the length of ST in the triangle STU is approximately 5.45 feet.

In triangle STU, we have angle ZU as a right angle, which means triangle STU is a right triangle. The sine rule can be used to relate the lengths of the sides and the measures of the angles in a triangle. The sine rule states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant.

Using the sine rule, we can write:

ST / sin ZT = US / sin ZU

Given that sin ZU = 1 (since ZU is a right angle), and US = 13 feet, we can substitute these values into the equation:

ST / sin 26° = 13 / 1

To find the length of ST, we can solve for it:

ST = sin 26° * 13

Evaluating the right-hand side of the equation, we find:

ST ≈ 5.45 feet (rounded to the nearest tenth of a foot)

Therefore, the length of ST in the triangle STU is approximately 5.45 feet.

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The inverse function of g(x) is:

f(x) =  (x - 2)^(2/3) + 3

Two functions are inverses if their composition is equal to the identity, then if f(x) is the inverse of our function, we must have that:

g( f(x) ) = x

Here we know that:

g(x) = (x - 3)^(3/2) + 2

Evaluating this in f(x) we should get:

g( f(x) = (f(x) - 3)^(3/2) + 2  = x

Now we can solve that for f(x).

(f(x) - 3)^(3/2) + 2  = x

( (f(x) - 3)^(3/2) =  x - 2

f(x) - 3 = (x - 2)^(2/3)

f(x) =  (x - 2)^(2/3) + 3

That is the inverse function.

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Answer:

$15.00

Step-by-step explanation:

Multiply the original cost by 1.25 to represent the mark up rate.

Two crucial tasks inherent in the initial stage of group therapy are orientation and establishing group norms.Ambiguity and lack of a structured approach in groups often lead to confusion, inefficiency, and potential challenges.

Orientation involves providing essential information to group members about the purpose, goals, and guidelines of the therapy group.

It helps individuals understand what to expect, builds trust, and creates a sense of safety and predictability within the group. Orientation may include discussing confidentiality, group rules, expectations, and addressing any questions or concerns.

Establishing group norms involves collaboratively developing shared guidelines and expectations that govern the behavior and interactions within the group. This process allows group members to contribute to the creation of a supportive and respectful group climate. Group norms help set boundaries, encourage open communication, and foster a sense of cohesion among members.

Without clear structure and guidance, group members may struggle to understand their roles, goals, or the process of the group therapy. Ambiguity can hinder progress, create frustration, and impede meaningful communication.

Lack of structure may also result in difficulty managing conflicts, decision-making, or time management within the group. It can lead to unequal participation, power struggles, and a lack of accountability.

To address these issues, it is important for group therapy to provide a clear framework, establish ground rules, and facilitate structured activities or interventions that promote clarity, engagement, and progress. A structured approach helps create a supportive environment, enhances group dynamics, and maximizes the therapeutic benefits of the group process.

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Answer:

it more than tripled

Step-by-step explanation:

I'm not sure if you need more but it requires me to type more to send the answer

Answer:

It more than tripled

Step-by-step explanation:

Right on Edge 2021

The probability the sample head proportion is (a) between 0.4 and 0.6 is 0.3146 and the sample head proportion (b) between 0.45 and 0.55 is 0.6385.

The sample proportion of heads is a binomial random variable with n = 150 and p = 0.5.

mean: μ = np = 150(0.5) = 75,

standard deviation is σ = √(np(1-p))

=√(150(0.5)(0.5)) = 5.5.

To use the Normal approximation, we have to use the z-score formula:

z = (x - μ) / σ

where x is the proportion of sample.

We can then use a standard Normal distribution table or calculator to find the probabilities.

a) To find the probability that the sample proportion is between 0.4 and 0.6, we calculate z score :

z1 = (0.4 - 0.5) / 5.5 = -0.18

z2 = (0.6 - 0.5) / 5.5 = 0.18

Using Ztable, the probability that the random variable is between -0.18 and 0.18 is approximately 0.3146.

Therefore, the probability that the sample proportion of heads is between 0.4 and 0.6 is approximately 0.3146.

b) To find the probability that the sample proportion is between 0.45 and 0.55, we find the z score:

z1 = (0.45 - 0.5) / 5.5 = -0.91

z2 = (0.55 - 0.5) / 5.5 = 0.91

Using z table, the probability that a standard Normal random variable is between -0.91 and 0.91 is approximately 0.6385.

Therefore, the probability that the sample proportion of heads is between 0.45 and 0.55 is approximately 0.6385.

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Answer:

The 32 electricians are expected to finish the job in 27 days.

Step-by-step explanation:

In this case we can apply a rule of three to calculate the time it'll take for the 32 electricians to finish the job. This is done below:

24 electricians -> 36 days

32 electricians -> x days

We have to be careful here, since the variables are inversely proportional, since if there are more electricians working on the same job, we expect the job to be finished in fewer days, therefore we need to invert one of the fractions as shown below:

\(\frac{24}{32} = \frac{x}{36}\\32*x = 36*24\\x = \frac{864}{32}\\x = 27\)

The 32 electricians are expected to finish the job in 27 days.

Answer:

27

Step-by-step explanation:

i like mantises! their cute funky bugs. they can turn their heads 180 degrees and are the only insect that can move their head. there are around 2,000 spices of them, most live in tropics, but 18 types are in north America. I have a praying mantis pet, and her name is creature, shes about 6 inches long!

To find the polar coordinates (r, θ) corresponding to the Cartesian coordinates (-6, 6), we can use the following formulas:

r = √(x² + y²)

θ = arctan(y / x)

(a) For the given point (-6, 6):

x = -6

y = 6

First, let's find the value of r:

r = √((-6)² + 6²) = √(36 + 36) = √72 = 6√2

Next, let's find the value of θ:

θ = arctan(6 / -6) = arctan(-1) = -π/4 (since the point lies in the third quadrant)

Therefore, the polar coordinates of the point (-6, 6) are (6√2, -π/4).

(b) For r > 0 and 0 ≤ θ < 2:

In this case, the polar coordinates will remain the same: (6√2, -π/4).

(c) For r < 0 and 0 ≤ θ < 2:

Since r cannot be negative in polar coordinates, there are no valid polar coordinates for r < 0 and 0 ≤ θ < 2.

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Answer:

\(\displaystyle \int_1^6\left|\frac{1}{x}-\frac{1}{x^2}\right|dx=\ln|6|-\frac{5}{6}\)

Step-by-step explanation:

We'll integrate with respect to x.

Recall that the area between some \(f(x)\) and some \(g(x)\) on the interval \([a, b]\) is given by:

\(\displaystyle \int_a^b|f(x)-g(x)|dx\)

The function \(x=6\) will be the upper bounds of our definite integral. The lower bounds will be the intersection of \(\displaystyle y=\frac{1}{x}\) and \(\displaystyle y=\frac{1}{x^2}\). Set the functions equal to each other and solve for x:

\(\displaystyle \frac{1}{x}=\frac{1}{x^2},\\\\x^2=x,\\x=1\)

Therefore, we'll be integrating the area between \(\displaystyle \frac{1}{x}\) and \(\displaystyle \frac{1}{x^2}\) on the interval \([1, 6]\). In integral notation, this is:

\(\displaystyle \int_1^6\left|\frac{1}{x}-\frac{1}{x^2}\right|dx\)

To evaluate this integral, recall that \(\displaystyle \int \frac{1}{x}dx=\ln|x|+C\) and \(\displaystyle \int \frac{1}{x^2}dx=\int x^{-2}dx=-x^{-1}+C=-\frac{1}{x}+C\).

Therefore,

\(\displaystyle \int_1^6\left|\frac{1}{x}-\frac{1}{x^2}\right|dx=\int_1^6\ln|x|-\left(-\frac{1}{x}\right)dx=\int_1^6\ln|x|+\frac{1}{x}dx\)

Solving yields:

\(\displaystyle\left \left(\ln|x|+\frac{1}{x}\right) \right \vert_1^6=\ln|6|+\frac{1}{6}-\left(\ln|1|+\frac{1}{1}\right)=\ln|6|+\frac{1}{6}-0-1=\boxed{\ln|6|-\frac{5}{6}}\)

Answer:

\(\ln 6 - \dfrac{5}{6}\)

Step-by-step explanation:

To find the area enclosed by curves and lines, use definite integration:

\(\displaystyle \int^b_a \text{f}(x)\:\:\text{d}x \quad \textsf{(where a is the lower limit and b is the upper limit)}\)

Definite integrals have limits.  The limits tell you the range of x-values to integrate the function between.

Given functions:

\(\begin{cases}y=\dfrac{1}{x}\\\\y=\dfrac{1}{x^2}\end{cases}\)

The upper limit has been given as x = 6.

The lower limit is the point of intersection of the two curves.

To find the lower limit, equate the functions and solve for x:

\(\implies \dfrac{1}{x}=\dfrac{1}{x^2}\)

\(\implies x=1\)

Therefore, the limits for this integration are x = 1 and x = 6.

To find the area enclosed by the two curves, the point of intersection and the line x=3, integrate the areas under both curves using definite integration and subtract the area under the lower curve from the area under the upper curve.

\(\begin{aligned}\displaystyle \int^6_1 \dfrac{1}{x}\:\:dx-\int^6_1 \dfrac{1}{x^2}\:\:dx & = \int^6_1\left(\dfrac{1}{x}-\dfrac{1}{x^2}\right)\:\:dx \\\\& = \int^6_1\left(\dfrac{1}{x}-x^{-2}\right)\:\:dx\\\\& = \left[\ln |x| + \dfrac{1}{x} \right]^6_1\\\\& = \left(\ln 6 + \dfrac{1}{6} \right) - \left(\ln 1 + \dfrac{1}{1} \right)\\\\& = \left(\ln 6 + \dfrac{1}{6} \right) - \left(0 +1\right)\\\\& = \ln 6 -\dfrac{5}{6}\end{aligned}\)

Integration Rules

\(\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}\)

Increase the power by 1, then divide by the new power.

\(\boxed{\begin{minipage}{3.5 cm}\underline{Integrating $\frac{1}{x}$}\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}\)

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Answer:

2x+8

Step-by-step explanation:

Answer:

\(4x^{2} +2x\)

Step-by-step explanation:

I'm not sure what you want, because it says "which expression", but you didn't provide any answer choices.

So all you have to do for this is combine like terms, and the only ones were 7x and -5x, which equals 2x.

Answer:

$ 1,375

Step-by-step explanation:

20,000 - 14,500 = 5,500

5,500 ÷ 4 = 1,375

Answer:

16/3

Step-by-step explanation:

formula :

p = kq

k = 8/3

so that is k

it will be like this "p = 8/3 x"

p = 8 × 2 / 3

p = 16/3

cant divide 3 with 16.

so, "p = 16/3" is the answer

Answer:

Less than 40

Step-by-step explanation:

because you are dividing 40 so it's being taken apart and shared

Answer:

Each friend gets less than 40 jellybeans

Step-by-step explanation:

Jenn is sharing the jellybeans equally among a group of friends, meaning each friend gets the same amount of jellybeans as everyone else.

Divide 40 by the amount of friends Jenn has. The number cannot exceed 40 because x is not 1 - there is more than one person in this situation. This means that the highest number of jellybeans Jenn can share is 20 - 2*20 = 40.

Therefore each friend gets less than 40 jellybeans.

Answer:

Gabriel spent $12 in just Donuts. If fritters are $2 a piece, he could buy 2 fritters at max. Perhaps he bought an extra donut to equal $17.

Step-by-step explanation:

Answer:

7 donuts and 5 fritters

Step-by-step explanation:

Answer: a

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

obtaining food

Here's is the answer:

- 1/9                                                            

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9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the number of 2-point field goals Rebecca made. Then the number of 3-point field goals can be represented by t, where ...

  x = 2t -68   ⇒   t = (x +68)/2 . . . . . number of 3-point field goals

The number of free throws made was x -38.

Rebecca's total point count was ...

  1(x -38) +2x +3(x +68)/2 = 847

  9/2x +64 = 847

  9/2x = 783

  x = (2/9)(783) = 174

  x -38 = 136

  (x +68)/2 = 121

Rebecca made 136 free throws, 174 2-point field goals, 121 3-point field goals.