A particle of mass mm moves in the plane with coordinates ( x ( t ) , y ( t ) )(x(t),y(t)) under the influence of a force that is directed toward the origin and has magnitude k / \left( x ^ { 2 } + y ^ { 2 } \right)k/(x 2 +y 2 )—an inverse-square central force field.

Answer: The domain is : (-∞,5)∪(5,∞)

there is no x intercepts

y-intercept= (0,-29/5)

asymptotes= x=5, no horizantal, oblique y=x-5

there is no holes

range= (-∞,-4]∪[4,∞)

Step-by-step explanation:

One pipe takes 6 hours to fill the pool and the other takes 12 hours.

Pipe A fills 1/x of the pool per hour, and Pipe B fills 1/y of the pool per hour. In other words, A takes x hours to fill the pool and B takes y hours to fill the pool.

Together, they fill 1/x + 1/y of the pool per hour. So, 4 hours times that rate should equal 1 full pool, since together they take 4 hours to fill the pool. That gives you your first equation:

4(1/x + 1/y) = 1

You're also told that if one pipe fills half the pool and the other takes over to fill the rest, it will take 9 hours. We don't know how long Pipe A works, so call that number of hours t. Pipe B must work for 9 - t hours.

So, Pipe A, working for t hours, fills half the pool:

t(1/x) = 1/2

And Pipe B, working for 9 - t hours, fills half the pool:

(9-t)(1/y) = 1/2

You now have a system of three equations (because this is an exceptionally complicated pipe-filling-pool problem):

4(1/x + 1/y) = 1

t(1/x) = 1/2

(9-t)(1/y) = 1/2

Solve for t in that second equation, then plug it into the third equation:

t(1/x) = 1/2

t = x(1/2)

t = x/2

(9 - x/2)(1/y) = 1/2

Now you've got a system of two equations:

4(1/x + 1/y) = 1

(9 - x/2)(1/y) = 1/2

Solve for y in the second equation, then plug that into the first equation:

(9 - x/2)(1/y) = 1/2

(9 - x/2) = y(1/2)

2(9 - x/2) = y

18 - x = y   (this is a really nice-looking form of that equation; we'll use it again later)

4(1/x + 1/y) = 1

4(1/x + 1/(18-x)) = 1

4/x + 4/(18-x) = 1

(4(18-x))/(x(18-x)) + (4x)/(x(18-x)) = 1

(4(18-x) + 4x)/(x(18-x)) = 1

4(18-x) + 4x = x(18-x)

72 - 4x + 4x = 18x - x2

72 = 18x - x2

x2 - 18x + 72 = 0

(x - 6)(x - 12) = 0

x - 6 = 0    OR    x - 12 = 0

x = 6  OR    x = 12

So, Pipe A takes either x = 6 or x = 12 hours to fill the pool alone.

When Pipe A takes 6 hours to fill the pool, Pipe B takes 12. When Pipe A takes 12 hours to fill the pool, Pipe B takes 6.

These cases are equivalent, since the original problem makes no distinction between the pipes.

Hence, one pipe takes 6 hours to fill the pool and the other takes 12 hours.

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The confidence interval is (0.309, 0.389).

Calculate a 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.

Sample size, n = 782

Sample proportion, p = x/n = 0.349105

Confidence level, 1 - α = 98% = 0.98 Implies

Level of significance, α = 0.02

At α = 0.02, the two-tailed critical value from the z-table, Zα/2 = 2.33

Then, the 98% confidence interval is,

It gives, 0.309≤ p ≤0.389

Lower endpoint = 0.309

Upper endpoint = 0.389

We are 98% confident that the proportion of all suspected criminals who were captured is within the confidence interval. If we were to take a large number of random samples of size 782, 98% of the resulting confidence intervals would contain the true proportion of all suspected criminals who were captured.

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Answer:

A) -20

Step-by-step explanation:

[tex]4y(4y-4)-4(-4y+5+4y^2)\\\\16y^2-16y + 16y-20-16y^2\\\\-20\\[/tex]

The confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

On Subtracting 1 from your sample size, we get

150 – 1 = 149.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 149 and α = 0.025

from the table at df = 149 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(150) = 2.28

Now, 2.262 × 2.28 = 5.17

So, the confidence interval be,

(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)

Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

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The amount of the tip that Jack gave to the waiter will be $9.42.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Jack took Diane out to supper to praise her birthday. The all out bill for the supper was $62.80. Jack needs to tip the server precisely 15%.

The amount of the tip will be given as,

⇒ 15% of $62.8

⇒ 0.15 x $62.8

⇒ $9.42

The amount of the tip that Jack gave to the waiter will be $9.42.

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Answer:

give the guy under me a brainlist lol

Step-by-step explanation:

Answer:

1/8(3x+4y+3)

Step-by-step explanation:

The expression that represents the orders is 12 * (5 + 3.5)

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

The above parameters mean that:

Expression for Sean's purchase = Number of cupcakes in a box * (Number of boxes ordered for his sister’s graduation party + Number of boxes ordered for the Variety Show party)

Substitute the known values in the above equation, so, we have the following representation

Expression for Sean's purchase = 12 * (5 + 3.5)

Hence, the expression is 12 * (5 + 3.5)

In (a), we have

Expression = 12 * (5 + 3.5)

Evaluate the sum

Expression = 12 * 8.5

Evaluate

Expression = 102

This means that the total number of box is 102

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Complete question

A baker packages 12 cupcakes to a box. Sean orders 5 boxes for his sister’s graduation party and 3.5 boxes for the Variety Show party. Write an expression that shows the calculations you could use to find the number of cupcakes Sean orders.

Write a different expression to model sean's order.eveluate not expressions to check that they are equivlent .How many cupcakes does sean have

If he deleted 10 songs to every 3 he kept, then he originally had 26 songs

The solution of compound inequalities is -6 < x < 24.

A compound inequality is a sentence that contains two inequality statements connected by the words "or" or "and." The conjunction "and" denotes that both statements of the compound sentence are true at the same time. It is the intersection or overlap of the solution sets for the individual statements. "Or" indicates that the entire compound sentence is true if either statement is true. It is the union or combination of the solution sets for each individual statement. A conjunction is a compound inequality that contains the word "and."

Inequalities are expressions that do not have an equal sign between them.

Given,

X - 7<17or-6x>36

First,

x - 7 < 17

x < 17 + 7

x < 24

Similarly,

-6x >36

x < [tex]\frac{-36}{6}[/tex]

x < -6

Thus,  compound inequality's solution is -6 < x < 24

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EVENT 1 has a probability value of 0.5.

EVENT 2 has a probability value of 0.5.

There is an equal chance of getting a HEAD or a TAIL when flipping a fair coin.

A coin has two faces: Head and Tail, and the total probability is always 1

1/2 = 0.5 is the likelihood of getting a head.

1/2 = 0.5 is the probability of receiving a tail.

When the coin is tossed for the first time, E1 is the event when TAIL comes up.

When the coin is tossed a second time, E2 represents the circumstance in which HEAD appears.

EVENT 1 has a probability value of 0.5.

EVENT 2 has a probability value of 0.5.

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The times that buses arrive at bus stops in various cities and in various climates are noted by a researcher in a notebook. This study is an observational one. Here option D is the correct answer.

It is an observation because it involves systematically noting people's actions, things, and occurrences without engaging in conversation or other interactions. In observational studies, the impact of a risk factor, diagnostic test, therapy, or other intervention is observed without an attempt to alter who is or is not exposed to it.

Two categories of observational studies are cohort studies and case-control studies. It cannot be a single-blind experiment, nor can it be a double-blind experiment since it is not an experiment.

Single-blind refers to a subject or an assessor. When a study is double-blind, neither the patient nor the outcome evaluator is aware of who received the prescription. It is not a survey because it relies on interviews with a representative sample of people as the main way of gathering data.

Complete question:

A researcher writes down in a notebook the arrival times of different city buses at a bus stop during different weather conditions. Which kind of study is this?

A - observational

B - survey

C - single-blind experiment

D - double-blind experiment

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Cost to order as per the economic order quantity model is equal to 10units.

As given in the question,

Demand of units per month = 20 units

Ordering cost  =  $10 unit

Carrying cost = 40% of 10

                       = (40 /100) × 10

                       = $4

Economic order quantity model ( EOQ)

= √[ 2 × ( Demand rate ) × ordering cost ]/ carrying cost

Substitute the value we get,

= √ ( 2 × 20 × 10 )/ 4

= √400 / 4

= √100

= 10 units.

Therefore , as per the economic order quantity (EOQ) model cost to order is for 10 units.

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Answer:

30

Step-by-step explanation:

Triangles add up to 180.

Your known sides are: 15x, 31x-2, and 90 (the square on the corner of the angle tells you that it's a right angle or 90 degrees.)

First make an equation to find X

this looks like: 15x+31x-2+90=180

I just added the sides we know and set them to equal 180. Because triangles add up to 180.

Now solve this by first combining like terms

15x+31x-2+90=180 (do the numbers with x's) so 15x+31x

46x-2+90=180 (now combine the numbers without X's) so -2+90

46x+88=180 (now since 88 is positive, do the opposite and subtract it from 180. This is because 180 is on the other side of the = sign.)

46x=92 (now since 46x means 46 times x, you do the opposite of multiplication and divide 92 by 46.

This gives you x=2

Now the last thing you need to do is solve for angle A

Angle A says "15x" so you can substitute our x value (2) for the x

This looks like 15(2)    15 times 2 is 30

so 30 should be your answer

The expression (5/3)x + (5/9)y is equivalent to the given expression. which is the correct answer would be an option (A).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question as:

(2/3)x - (4/9)y + x + y

Rearrange the terms in the above expression,

(2/3)x + x - (4/9)y + y

Combine the likewise terms,

(5/3)x + (5/9)y

Therefore, the expression (5/3)x + (5/9)y is equivalent to the given expression.

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Using the compound interest formula, we know that $7,672 is the interest on investments earned.

The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors.

The resulting value is subsequently deducted from the loan's entire original amount.

So, interest earned on investment:

A = 9,875 (1 + 0.048/12)^ 12(12)

A = $ 15,547

Interest on investments is the money received:

= $ 15,547 - $ 9,875

= $ 7,672

Therefore, using the compound interest formula, we know that $7,672 is the interest on investments earned.

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Complete question:

An investment of $9,875 earns 4.8% interest compounded monthly over 12 years. approximately how much interest is earned on the investment?

a. $4,740

b. $7,458

c. $7,672

d. $17,567

Answer: Both the National Institute of Standards and Technology (NIST)

Step-by-step explanation:

Electrical potential  at any point along the x-axis is V = Q/2πε0(1/R1 − 1/R3) and V at x is Vx = 0.55Q/πε0a

Given info,

A square in the x-y plane in free space has a point charge of q at comer (a/2,a/2) and the comer (a/2,-a/2) and a point charge of -q at (-a/2, a/2) and (-a/2, -a/2).

Let,

V = Q/4πε0R1 + Q/4πε0R2 + −Q/4πε0R3 + −Q/4πε0R4

  = Q/2πε0(1/R1 − 1/R3)

With,

R1 = √[(x - a/2)² + (a/2)²]

R3 = √[(x + a/2)² + (a/2)²]

At x = a/2,

R1 = a/2

R3 = a√5/2

Vx = 0.55Q/πε0a.

Therefore, Electrical potential is V = Q/2πε0(1/R1 − 1/R3) and V at x is Vx = 0.55Q/πε0a

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Answer:

Step-by-step explanation:

Percentages are a powerful way to compare samples with different numbers of observations. By standardising measures using a scale of 0 to 100, samples can be compared quickly and easily. Any graph of the data, however, must include the full range of 0 to 100 to ensure that false impressions are not created.

Answer:

I Think its b

Step-by-step explanation:

(show that the ratio UV_XY and WV_ZY are equivalent.)

*3rd thing*

if it is wrong (which i dont think it is) then show me a study guide or some way to learn more about it, hope this helps

The change in her investment, due to the lost money is $112

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

Rate of loss = $4 per day

Duration = 4 weeks

From the above parameter, we can calculate the amount of money lost to the investment using:

Amount lost = Duration * Rate of loss

Substitute the known values in the above equation

So, we have the following equation

Amount = 4 weeks * $4

Convert weeks to days

Amount = 28 * $4

Evaluate the quotient

Amount = $112

Hence, the amount is $112

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Given that each individual has a  [tex]\frac{1}{n}[/tex] chance of receiving their own name, we may indicate whether or not person I received their own name by using a sequence of n identically distributed Bernoulli random variables with

[tex]P=\frac{1}{n}[/tex] .

The total number of people who received their own name is the sum of these Bernoullis. The linearity of expectation causes the expected value of the sum to equal the sum of their respective expected values.

Since each summand has expected value  [tex]\frac{1}{n}[/tex]  and there are n of them, the expected value is one.

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Kennedy needs purchase at least 42 sets of spoons.

The minimum set of spoons needed in the restaurant = 512 spoons.

Available spoons = 264.

Each set on the sale has 6 spoons.

Let the minimum number of spoon set required be 'x'.

Then,

6x + 264 ≥ 512

Solving the in equality.

6x ≥ 512 - 264

6x ≥ 248

x ≥ 248/6

x ≥ 41.33

Thus, Kennedy needs purchase at least 42 sets of spoons.

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The hypotenuse - leg congruency can be applied in both right triangles.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.

In other words, if the hypotenuse and a leg of a right triangle are each congruent with the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.

Hence, the legs of the right triangle are congruent and one of the legs are congruent.

Therefore, the hypotenuse - leg congruency can be applied.

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Answer:

$28/hour

Step-by-step explanation:

224 ÷ 8 = 28