When the sectors of the circle are rearranged, they are close to forming a (. )
with a length of (. )
units and a width of r units.

The area of the rearranged figure is (. )
to that of the circle. So, the area of the circular base is (. )
square units.

The solution of the given equation is x = 12. The solution is the value, that satisfies the given equation.

Given equation is 5(x - 1) + 3x = 7(x + 1)

On simplifying the equation, we get

5(x - 1) + 3x = 7(x + 1) ⇒ 5x - 5 + 3x = 7x + 7

⇒ 8x - 5 = 7x + 7

⇒ 8x - 7x = 7 + 5

⇒ x = 12

Therefore, the solution for the given equation is x = 12.

Here, the power or the degree of the variable x is 1 in the given equation. Thus, it has only one solution.

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The amount of water that the container can hold will be equal to 972pi in³ that is option D is correct.

A sphere may be defined as the 3-D hollow figure. It has a diameter, surface area and a fixed volume. The formula for the volume of the sphere is equal to

Volume of Sphere = 4/3(πr³)

where r is the radius of the sphere.

According to the figure the diameter of the spherical container is 18 in. Now the radius of the spherical container will be half of the diameter that is

Radius = Diameter/2

Radius = 18 in/2

Radius = 9 in

Now the amount of water that the container can hold will be equal to the volume of the spherical container that is

Volume = 4/3(πr³)

Volume = 4/3(π)(9in³)

Volume = 972π in³  which is the required answer.

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Answer:

True.

False.

True.

Answer:

Domain { 4,8,12,16,20}

Range { 1,2,3,4}

This is not a function because two of the inputs have more than one output

Step-by-step explanation:

The domain is the x values ( input)

Domain { 4,8,12,16,20}

The range is the y values (output)

Range { 1,2,3,4}

This is not a function because two of the inputs have more than one output

Therefore, the estimated average length of the line is 3 customers.

We can approach this problem by using the M/M/1 queueing model, which assumes a Poisson arrival process, an exponential service time distribution, and a single server.

In this case, the arrival rate (lambda) is 10 customers per hour, the service rate (mu) is 5 customers per hour (since the average servicem time is 14 minutes or 0.2333 hours), and there is one server.

The utilization factor (rho) is given by rho = lambda / mu = 10 / 5 = 2, which is greater than 1. This means that the system is not stable, and the queue will grow indefinitely.

To find the average length of the line, we can use Little's Law, which states that the long-term average number of customers in a stable system is equal to the long-term average arrival rate multiplied by the long-term average time spent in the system:

L = lambda * W

where L is the average number of customers in the system, lambda is the arrival rate, and W is the average time spent in the system.

In this case, since the system is not stable, we cannot use Little's Law directly. However, we can still estimate the average length of the line as follows:

Let's assume that the queue is at its steady-state when there are N customers in the system (i.e., being served plus waiting in the line). Then, the average length of the line (Lq) is:

Lq = N - 1

since one customer is being served and the remaining N-1 customers are waiting in the line.

The steady-state condition requires that the arrival rate equals the departure rate, which is the service rate in this case. Therefore, we can use the following formula to estimate N:

N = lambda / (mu - lambda)

Plugging in the values, we get:

N = 10 / (5 - 10) = -2

This negative value indicates that the system is not stable, and there are more customers arriving than the system can handle. However, we can still estimate the average length of the line as:

Lq = |N - 1| = |-2 - 1| = 3

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Answer: 12-pound bag of cat food

Step-by-step explanation:

12 pounds bag of cat food = $18

15 pounds bag of cat food = $24

Let's find the cost per pound of the 12-pound bag first

Take 18 divided by 12 = $1.50 per pound

Now find the cost per pound of the 15-pound bag

Take 24 divided by 15 = $1.60 per pound

So, buying a 12-pound bag of cat food is better because it is cheaper per pound.

the mean and standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population is  18.9.

The population is the set of word counts of the five essays: {506, 628, 554, 600, 584}. To find the mean and standard deviation of the population, we use the formulas:

Mean = (sum of values) / (number of values)

Standard deviation = sqrt[(sum of squared deviations) / (number of values)]

Using these formulas, we get:

Mean = (506 + 628 + 554 + 600 + 584) / 5 = 574.4

Standard deviation = sqrt[((506-574.4)^2 + (628-574.4)^2 + (554-574.4)^2 + (600-574.4)^2 + (584-574.4)^2) / 5] ≈ 36.5

To list all samples of size 2 with replacement from the population, we can simply list all pairs of elements from the population, allowing for repetition. We get:

{506, 506}, {506, 628}, {506, 554}, {506, 600}, {506, 584}

{628, 506}, {628, 628}, {628, 554}, {628, 600}, {628, 584}

{554, 506}, {554, 628}, {554, 554}, {554, 600}, {554, 584}

{600, 506}, {600, 628}, {600, 554}, {600, 600}, {600, 584}

{584, 506}, {584, 628}, {584, 554}, {584, 600}, {584, 584}

To find the mean of each sample, we simply take the average of the two elements in each sample. For example, for the sample {506, 628}, the mean is (506 + 628) / 2 = 567.

We can list all 25 sample means and calculate their mean and standard deviation. We get:

Sample means: 506, 567, 555, 553, 545, 567, 628, 591, 553, 570, 555, 591, 554, 553, 554, 600, 575, 567, 570, 554, 584, 570, 591, 575, 584

Mean of sample means = (sum of sample means) / (number of samples) ≈ 565.4

Standard deviation of sample means = sqrt[((506-565.4)^2 + (567-565.4)^2 + ... + (575-565.4)^2) / 25] ≈ 18.9

The mean of the sampling distribution is close to the mean of the population, which is expected since the sample means are unbiased estimators of the population mean. The standard deviation of the sampling distribution is smaller than the standard deviation of the population, which is expected since the standard deviation of the sampling distribution decreases as the sample size increases.

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Answer:

I believe the answer is 121.

Step-by-step explanation:

Formula: (a)n = a + (n - 1)d

(a)n = nth Term of the Sequence

a = First Term in the Sequence

d = Common Difference

112th = 15 + (112 - 1)-5

112th = 15 + 111 - 5

112th = 121

Answer:

Step-by-step explanation:

{ 15, 5, -5, -15...}

the rule is

\(a_{1} = 15, a_{n} = a_{n-1} -10\)

the 112th term

\(a_{112} = a_{1} + (n-1) *d\\\\a_{112} = 15 + (112 -1) * (-10)\\\\a_{112} = 15 - 1110\\\\a_{112} = -1095\)

Step-by-step explanation:

then let's change that. you don't want to stay a dumdum, right ?

midpoint. what does that mean ? it is the point exactly in the middle between 2 other points.

what does that mean to be in the middle between 2 other things ?

well, it means that the distance is the same to both other things. otherwise it would not be the middle.

therefore,

4.

QS = 56 ft

exactly the same distance as PQ.

PS = PQ + QS

because Q is the point in the middle between P and S.

it is really that simple.

5.

the line segment PQ is bisected (cut in half) by the line segment MN at point R.

so, we know what the intersection of PQ and MN did to PQ (cut PQ in half). but this does not tell us what it did to MN. it could be also one of the ends of MN that cut PQ in half. we simply don't know.

therefore, we cannot say anything about the midpoint of MN.

and therefore the first 2 answer options are not generally correct. they COULD be correct, but they could be also wrong. therefore they are mathematically and logically not a true statement per se. for that the statement needs to be true unconditionally = in all possible cases.

R is the midpoint of PQ. yes, correct. that's what is meant by being bisected or cut in half at that point.

since the 3rd answer option is correct, the 4th answer option (none of these) is incorrect.

Answer:

Step-by-step explanation:

Look at the 3rd decimal digit (the digit after the hundredths).

For example,4.749 rounds up to 4.75 because the 3rd decimal digit is a 9.

I hope this helps ^^

Answer/Step-by-step explanation:

A. Tens means groups the units into groups of 10. On the other hand,  tenth means one part in ten equal parts written as 1/10. Therefore:

30 tens = 30 x 10 = 300

3 tens = 3 x 10 = 30

3 tenths = 3/10 = 0.3

Thus:

30 tens - 3 tens 3 tenths = 300 - 30.3 = 269.7

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B. 3.4

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C. To find 24 tenths - 1 and 3 tenths, you need to convert the mixed number 1 and 3 tenths into a fraction. 1 and 3 tenths = 1/1 + 3/10. To add these fractions, find a common denominator by multiplying both the numerator and denominator of 1/1 by 10. Thus, 1 and 3 tenths = 10/10 + 3/10 = 13/10. Now you can subtract 24/10 - 13/10 by subtracting the numerators to find the correct answer: 24/10 - 13/10 = 11/10, or 1 and 1 tenth

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D. 6 ones 7 hundredths -2.3

We make a place chart for 6 ones 7 hundredths. We write 0 in the remaining place value.

Hundred     tens    Ones   point     tenths     hundredths       thousandths

 0                0          6            .             0             7                             0

6 one 7 hundredths is 6.07

Now subtract 2.3 from 6.07

6.07 - 2.3 = 3.77

Answer : 3.77

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E. 8.246 - 5 hundredths is equal to 8.196

5 hundredths in number form is 0.050

     8.246

   - 0.050

----------------

     8.196

In subtracting decimals, line up the decimal points to avoid confusion.

Use 0 as padding so that the decimals will contain the same number of digits after the decimal.

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F. In order to determine the result, we have to know about the notation numbers. In a rational number, every position number has a notation.

So, according to the image, we have to change "5 ones 3 tenths":

5 ones 3 tenths= 5*1+3*0.1=5+0.3=5.3

Then:

=5.3-0.53

=4.77

Answer:

Gross pay when she works 46 hours a week = 532 dollars per week

Step-by-step explanation:

Complete question

Find gross pay when she works 46 hours a week

Solution

For working hours less than or equal to 40 hours, kim earns 10.90  per hour

For working hours higher than the basic 40 hours of working, the per hour rate increases by 1.5 time = 1.5 *10.90 = 16 dollars per hour

Gross pay for 46 working hours = 40 *10.90 + 6*16 =  532 dollars per week

Considering that y is between x and z, we have that:

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

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Answer:

b. y=-3x+5

Step-by-step explanation:

If you find the slope(y-y/x-x) I found that the slope is -3. from using the slope and graphing this out, the y-intercept is +5 giving me the answer of y=-3x+5.

I hope this helps have a great day:)

Answer:

y = -3x + 5

Step-by-step explanation:

The answer is correct because I just took the test and I got a 100%.

Answer: 12 hours and 24 Minutes

Step-by-step explanation:

7*60 = 420

810/420 = 1.9285

93- 100 = 53-60

subtract 40 from 93.

1.53*8 = 12.24

Answer: 12 hours and 24 Minutes

The quantity of bread that Debbie uses each week on the average is = 54 loaves of bread

The number of days the restaurant opens per week = 6 days.

The number of bread she uses everyday is = 9 loaves.

Therefore, the quantity of bread that Debbie uses each week on the average is = 6×9 = 54 loaves of bread.

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To answer the question, no, the n-tuple (x,x,x,....x) does not necessarily have to consist of non-negative values.

An n-tuple is a sequence of n elements, and in mathematics, it can refer to a sequence of real numbers, complex numbers, or other types of mathematical objects. In the case of the given set of n-tuples, it specifies that the n-tuple consists of real numbers and that all the elements in the tuple have the same value, which is denoted by x.

The definition of the set only specifies that the elements are real numbers and that they are all equal to each other. Therefore, the elements in the tuple can be positive, negative, or zero.

However, if the context of the problem or application requires the elements to be non-negative, then this restriction should be explicitly stated.

For example, if the n-tuple represents a set of quantities that cannot be negative, such as lengths, areas, or volumes, then it is appropriate to specify that the elements are non-negative real numbers.

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Answer:

Step-by-step explanation:

The theory that views the group as a gestalt, or an evolving entity of opposing forces that act to hold members of the group and to move the group along in its quest for goal achievement, is known as the Group Development Theory. This theory recognizes that a group is more than just the sum of its individual members but rather a dynamic system that undergoes stages of development and experiences internal tensions and conflicts.

According to the Group Development Theory, groups progress through various stages, such as forming, storming, norming, and performing. During the forming stage, group members come together and begin to establish their roles and relationships. In the storming stage, conflicts and power struggles may arise as members express their differing opinions and perspectives. The norming stage involves the establishment of norms and shared values that guide the group's behavior. Finally, in the performing stage, the group functions effectively and works towards achieving its goals.

The Group Development Theory emphasizes the interplay between opposing forces within the group, such as individual needs versus group cohesion, or task-oriented goals versus social-emotional dynamics. These opposing forces create a dynamic tension that drives the group's development and influences its effectiveness in achieving its objectives. By understanding and managing these forces, group leaders and members can foster a positive group environment and enhance the group's overall performance.

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The sampling method used is systematic sampling.

This is because each 49th student is chosen from the population of 496 students.

In systematic sampling, a starting point is selected randomly, and then each nth item in the populace is selected.

In this case, the start line might also have been randomly chosen, however we do not have information approximately that.

However, when you consider that every 49th pupil is selected, this is a clear indication that methodical sampling has been employed.

This sampling technique is often used in conditions in which the population is huge and it isn't viable to select each single item from the population.

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Using the formula of the area of the circle, we know that the base area of the barrel is 3.14 ft² respectively.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

In the center of a circle, equal chords subtend equal angles.

The chord is divided in half by the radius drawn perpendicular to it.

Different-sized circles are comparable.

Rectangles, trapezoids, triangles, squares, and kites can all be encircled by circles.

So, the area of the base of the barrel would be taken out by the formula of the circle:

Radius = 2/2

Radius = 1ft

Now, area:
= πr²

= π1²

= π1

= 3.14*1

= 3.14 ft²

Therefore, using the formula of the area of the circle, we know that the base area of the barrel is 3.14 ft² respectively.

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The formula for calculation of circumference of the circle = d π or 2πr where d is diameter of circle and r is the radius of circle

As given in the question the circumference of the circle whose diameter is 2 cm is 6.28cm and we come to know that value of π used here is 3.14 and not 22/7

So, the circumference of the circle whose diameter is 1cm = d π

              = 1 π

            = 1 3.14

                                                                                          = 3.14 cm

Hence the circumference of the circle whose diameter is 1cm using the value of pi as 3.14 comes out to be pi that is 3.14 cm

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Answer:

Your answer would be c! Have a WONDERFUL DAY!! <3

Step-by-step explanation:

Answer:IT'S C LISTEN TO HER/HIM FOR CHRIST SAKES

Step-by-step explanation:Pls mark me brainliest

The rate of change of the mass of salt in the tank is described by the option Odm/dt = 15-(m/100). The following is a detailed solution to the problem:

a. A tank holds 1000 liters of water, in which 15 kg of salt is dissolved.

Pure water enters the tank at the rate of 10 liters per minute.

The solution is kept thoroughly mixed and is drained from the tank at the same rate. If m is the mass of salt in the tank at time t, then we have to determine the rate of change of the mass of salt in the tank.

The concentration of salt initially in the tank = 15 kg/ 1000 L = 0.015 kg/L.

Concentration of salt at any time t = m/(1000+10t) kg/L (since we are adding pure water at a rate of 10L per minute).

Let the rate of change of the mass of salt be given by Odm/dt.

Now we apply the mass balance equation to salt to find the rate of change of mass of salt in the tank.

From mass balance: Rate of accumulation = Rate of input - Rate of output

Rate of accumulation of salt in the tank = d(m)/dt

Rate of input of salt = 0

Rate of output of salt = (Concentration of salt in the tank) x Rate of output= (m/(1000+10t)) x 10

We now have:

Odm/dt = 0 - [(m/(1000+10t)) x 10]= - (m/ (100 + t)) kg/min

Odm/dt = - m/ (100 + t) kg/min

We can conclude that the option Odm/dt = 15-(m/100) describes the rate of change of the mass of salt in the tank. As the salt dissolves in the tank, the rate of accumulation of salt in the tank decreases and becomes zero when the solution becomes saturated. When this happens, the rate of input of salt will be equal to the rate of output of salt, and there will be no net accumulation of salt.

The rate of change of the mass of salt will be negative when the mass of salt is decreasing and will be positive when the mass of salt is increasing.

This occurs when salt is being added to the tank or when the solution is not yet saturated with salt.

The rate of change of the mass of salt in the tank will be zero at equilibrium.

In conclusion, the rate of change of the mass of salt in the tank is given by the option Odm/dt = 15-(m/100).

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Answer:

Mrs. Taylor bought 200 oranges ;) .

Answer:

200

Step-by-step explanation:

If 30% of the oranges were bad, then that means 0.3 * total number of oranges, were bad. so if 0.3 * total = 60, then 60/0.3 = total number of oranges.

Answer:

x = 3/2            x = -5/2

Step-by-step explanation:

(2x+3) ^2 - 4(2x+3) - 12 = 0

Let m = 2x+3

m^2 - 4m - 12 = 0

Factor

(m-6) (m+2) = 0

Using the zero product property

m-6 = 0    m+2 =0

m = 6    m = -2

Substitute m = 2x+3 back into the equation

2x+3 = 6        2x+3 = -2

2x = 3            2x = -5

x = 3/2            x = -5/2

Answer:

yes; only one range value exists for each domain value.

Step-by-step explanation:

The x value don't repeat. Which is: -3, -1, 1, 5.

Answer:

Answer:

yes, the given relation is a function.

Step-by-step explanation:

The given relation is

{(–3, –2), (–1, 0), (1, 0), (5, –2)}

A relation is called function if each element of the domain is paired with exactly one element of the range.

It means for each value of x there exist a unique value of y.

In the given relation for each value of x there exist a unique value of y.

Therefore the required solution is yes and this relation is a function.

Step-by-step explanation:

letter d

because there is no repeating x's

We are asked to write each of the following vectors in the polar form ⟨r,θ⟩

Where r is the vector's magnitude (in miles) and θ is the vector's angle (in degrees) swept .

1) 12 miles in the direction 45° north of east:

Let us draw a figure to better understand the problem

As you can see, the magnitude is 12 and the angle is 45° measured counter-clockwise from the due east direction.

2) 1.59 miles in the direction 10° west of south:

Let us draw a figure to better understand the problem

As you can see, the magnitude is 1.59 and the angle is 190° measured counter-clockwise from the due east direction.

3) 5.7 miles in the direction opposite of 35° south of east:

Let us draw a figure to better understand the problem

Please note that opposite of 35° south of east is west of north.

As you can see, the magnitude is 5.7 and the angle is 145° measured counter-clockwise from the due east direction.

Answer:

Greater:

\(\sqrt{1/9} > 1/4\)

Step-by-step explanation:

\(\sqrt{\frac{1}{9} } =\frac{\sqrt{1} }{\sqrt{3} } =\frac{1}{3}\)

1/3 is greater than 1/4

Hope this helps