An object is traveling at a steady speed of 10 and one tenth km​/h. How long will it take the object to travel 4 and nine tenths km ​? First round to the nearest integer to find the estimated answer. Then find the exact answer.

Answer: [tex]m\angle A=116\°[/tex]

Step-by-step explanation:

The missing figure is attached.

For this exercise it is important to remember that, by definition, the opposite interior angles of an inscribed quadrilateral are supplementary, which means that their sum is 180 degrees.

Based on this, you can identify that the angle D and the angle B are opposite and, therefore, supplementary.

Knowing that, you can write the following equation:

[tex]x+28\°=180\°[/tex]

Now you must solve for "x" in order to find its value. This is:

[tex]x=180\°-28\°\\\\x=152\°[/tex]

Then:

[tex]m\angle D=152\°[/tex]

You know that:

[tex]m\angle A=(x-36)\°[/tex]

Therefore, since you know the value of "x", you can substitute it into   [tex]m\angle A=(x-36)\°[/tex] and then you must evaluate, in order to find the measure of the angle A. This is:

 [tex]m\angle A=152\°-36\°\\\\m\angle A=116\°[/tex]

Answer:

0.00418

Step-by-step explanation:

The probability of the first one being defected is 3/479, as we have 3 defectives containers in a total of 479 containers.

If the first one is defected and removed, now we have 478 containers, with 2 being defective.

So the probability of the second one being picked being defective, given that the first one was defective, is 2/478 = 1/239 = 0.00418

Answer:

C. 160,000

Step-by-step explanation:

Given that the measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300 cm.

Also given that each of the three measurements has an error of at most 1 cm

COnsider the worst case where each dimension is increased by 1 cm

Then we measure the dimensions as 201 , 201 and 301

So volume would be measured as

[tex]201*201*301\\= 12160701[/tex] cubic cm

Actual volume of the box = [tex]200*200*300\\=12000000[/tex] cubic cm

Difference maximum possible = 160701 cubic cm

Out of the five options given option C is nearest to this value

So answer is

C. 160,000

Answer:

The assumption will depend on the argument that C. Any decrease in per capita sales of cigarettes in Coponia will result mainly from an increase in the number of people who quit smoking entirely.

Step-by-step explanation:

Per capita income or average income measures the average income earned per person in a given area in a specified year. It is calculated by dividing the area's total income by its total population. Per capita income is national income divided by population size.

Tax is a compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions.

Answer: U' = (0, 1)

Step-by-step explanation:

U = (3, -5)

rotate 90° counterclockwise means (x, y) = (-y, x)

new U = (5, 3)

down 2 units means subtract 2 from the y-coordinate

newer U = (5, 1)

left 5 units means subtract 5 from the x-coordinate

U' = (0, 1)

Answer:

Step-by-step explanation: they are asking “What is x + 3 + y”. So use Pythagorean’s theorem to get x (it should be 4) and then find y and I think u get square root of 13, then add 4 + 3 + square root 13

Answer: the third option is the correct answer.

Step-by-step explanation:

The given quadratic equation is expressed as

x² - 10x + 24 = 0

We would apply the method of factorization by finding two numbers such that their sum or difference is -10x and their product is 24x^2. The two numbers are - 6x and - 4x. Therefore,

x² - 6x - 4x + 24 = 0

x(x - 6) - 4(x - 6) = 0

(x - 6)(x - 4) = 0

Therefore, the solutions to the equation are

x = 4 or x = 6

Answer:

Therefore the wire should be anchored at 10 ft away from pole which is 10 ft long.

Step-by-step explanation:

Given that , The distance between two poles is 30 ft.

The length of 1st pole is = 20 ft

The length of second pole is = 10 ft.

Let the wire anchored to the ground at a distance x ft from the second pole.

Then, the distance of anchored from the first pole is = (30-x)

The total length of the wire is L = m+n

We know the pythagorean theorem,

Height²+base² = hypotenuse²

To find the value of m and n we use  pythagorean theorem

From the left side triangle in the picture we get,

10²+x²= m²

⇒m²=100+x²

[tex]\Rightarrow m= \sqrt {100+x^2[/tex]

and right side  triangle in the picture we get,

20²+(30-x)² = n²

⇒n²= x²-60x+1300

[tex]\Rightarrow n= \sqrt {x^2 -60x+1300}[/tex]

Then ,

[tex]L= \sqrt{(100+x^2)}+\sqrt{(x^2-60x+1300) }[/tex]

Differentiating with respect to x

[tex]L'= \frac {2x}{2\sqrt{100+x^2}}+ \frac{2x-60}{2\sqrt {x^2-60x+1300}}[/tex]

For minimize, L' =0

[tex]\frac {2x}{2\sqrt{100+x^2}}+ \frac{2x-60}{2\sqrt {x^2-60x+1300}}=0[/tex]

[tex]\Rightarrow \frac {x}{\sqrt{100+x^2}}=- \frac{x-30}{\sqrt {x^2-60x+1300}}[/tex]

Squaring both sides

[tex]\Rightarrow( \frac {x}{\sqrt{100+x^2}})^2=(- \frac{x-30}{\sqrt {x^2-60x+1300}})^2[/tex]

[tex]\Rightarrow x^2(x^2-60x+1300)= (x^2-60x+900)(100+x^2)[/tex]

[tex]\Rightarrow x^4 -60x^3+1300x^2= 100x^2-6000x+90000+x^4-60x^3+900x^2[/tex]

[tex]\Rightarrow 300x^2+6000x-90000=0[/tex]

[tex]\Rightarrow x^2+20x-300=0[/tex]

[tex]\Rightarrow x=10,-30[/tex]

Therefore x = 10. [x=-30 negligible, since distance can not negative]

Therefore the wire should be anchored at 10 ft away from pole which is 10 ft long.

The problem can be solved geometrically through the principles of trigonometry. By setting up two right triangles formed by the telephone poles and the anchoring point, we can create two equations by Pythagorean Theorem. By taking the derivative of the total wire length and setting it to zero, we can find the optimal value for 'x' (location of the anchoring point) which results in the minimal amount of wire used.

To solve for the minimal amount of wire needed, we can use the principles of mathematics. More specifically, we will use the concept of trigonometry and geometry to create two right triangles. The taller pole (20ft), the shorter pole (10ft) and the point on the ground where the wire is anchored form the two right triangles, one with 20ft height and another with 10ft height.

Let's denote the length of wire between the taller pole and ground as 'a', between the shorter pole and the ground as 'b', and the distance between the point on the ground where the wire is anchored and the base of the first pole as 'x'. We have:

The total length of wire used (which we want to minimize) is a + b.

To find the minimal length, we can take the derivative of 'a+b' with respect to 'x' and set the derivative equation to 0 then solve for 'x'. This will give you where to place the anchor on the ground (minimal amount of wire used) between the two poles. You may find out an optimal 'x' value that is less than 30ft, ensuring that the anchoring point is between the two poles.

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Answer:

The true statements are 2 and 3.

Step-by-step explanation:

Triangle SRQ undergoes a rigid transformation that results in triangle VUT

So, ΔSRQ ≅ ΔVUT

So, point S will map to point V, point R will map to point U and point Q will map to point T.

According to the previous, We will check the statements:

1) SQ corresponds to VU. Wrong because SQ corresponds to VT

2) ∠R corresponds to ∠U. True

3) UV corresponds to RS. True

4) ∠S corresponds to ∠T.  Wrong because ∠S corresponds to ∠V

5) QS corresponds to RS. Wrong because QS corresponds to TV

So, The true statements are 2 and 3.

2) ∠R corresponds to ∠U

3) UV corresponds to RS.

Answer:

The true statements are 2 and 3.

Step-by-step explanation:

Triangle SRQ undergoes a rigid transformation that results in triangle VUT

So, ΔSRQ ≅ ΔVUT

So, point S will map to point V, point R will map to point U and point Q will map to point T.

According to the previous, We will check the statements:

1) SQ corresponds to VU. Wrong because SQ corresponds to VT

2) ∠R corresponds to ∠U. True

3) UV corresponds to RS. True

4) ∠S corresponds to ∠T.  Wrong because ∠S corresponds to ∠V

5) QS corresponds to RS. Wrong because QS corresponds to TV

So, The true statements are 2 and 3.

2) ∠R corresponds to ∠U

3) UV corresponds to RS.Step-by-step explanation:

Answer:

The answer is 630 students

Step-by-step explanation:

For this case, we have 504 students and the student enrollment has decrease 20%, which mean 504 is the 80% of the total student enrollment of the previous year.

[tex]100 - 20 = 80[/tex]%

This is a direct proportion problem. As shown bellow:

504 -> 80%

x      -> 100%  

For solving this we use the Mathematical Rule of Three, a method of having three numbers to help calculate the unknown.

b  ->  c

x   ->  a

The algorithm for rule of three is the following:

[tex]x = \frac{a * b}{c} \\\\x= \frac{504*100}{80} =\frac{50400}{80}=630\\ \\x=630[/tex]

Answer:

P ( X > 1800) = 0.1734

Step-by-step explanation:

Given:-

- The mean, u = 1497

- The standard deviation, s.d = 322

Find:-

P(X>1800)

Solution:-

- We will denote a random variable X that follows a normal distribution for the SAT scores in 2014 with parameters mean (u) and standard deviation (s.d) as follows:

                                  X ~ N ( 1497 , 322 )

- The following probability can be calculated by first computing the Z-score value:

                                 P ( X < x ) = P ( X < Z )

Where,

                                 Z = ( x - u ) / s.d

- P(X > 1800) have the corresponding Z-score value:

                                Z = ( 1800 - 1497 ) / 322

                                Z =  0.941

- Hence, using Z-table:

                               P ( X > 1800) = 1 - P ( Z < 0.9471 )

                               P ( X > 1800) = 1 - 0.8266

                               P ( X > 1800) = 0.1734

The probability that a randomly selected person scored above 1800 on the SAT is approximately 17.36%, after calculating the corresponding z-score and looking up the probability in the Standard Normal Distribution table.

To find P(X>1800), we first need to calculate the z-score for an SAT score of 1800. The z-score is computed as:

z = (X - μ) / σ

Where X is the SAT score, μ is the mean, and σ is the standard deviation. Given μ = 1497 and σ = 322, we have:

z = (1800 - 1497) / 322 = 303 / 322 ≈ 0.941

Once we have the z-score, we can use the Standard Normal Distribution table to find P(Z > 0.941). We find that P(Z > 0.941) ≈ 0.1736. Thus, the probability that a randomly selected college-bound senior has an SAT score above 1800 is approximately 0.1736 or 17.36%.

Final answer:

The antique purchased by Juan increases in value by 10% each year. The value of the antique after 2 years can be found by calculating the expression $200a, where a is a constant. The value of [tex]\( a \) is \( 1.21 \).[/tex]

Explanation:

To find the value of a, we need to represent the annual increase of 10% in terms of multiplication.

After the first year, the value of the antique increases by [tex]\( 10\% \) of its previous value, which is \( 0.10 \times 200 \) dollars.[/tex]

After the second year, the value of the antique increases by [tex]\( 10\% \) of its value at the end of the first year, which is \( 0.10 \times (200 + 0.10 \times 200) \) dollars.[/tex]

Generally, after \( n \) years, the value of the antique will be [tex]\( 200 \times (1 + 0.10)^n \) dollars.[/tex]

The expression given for the value of the antique 2  years after purchase is 200a , where a is a constant. This represents the value of the antique after 2  years.

Equating the expression to the value of the antique after 2 years, we have:

[tex]\[ 200a = 200 \times (1 + 0.10)^2 \][/tex]

Now, let's solve for \( a \):

[tex]\[ 200a = 200 \times (1.10)^2 \][/tex]

200a = 200 \times 1.21

200a = 242

Dividing both sides by 200:

[tex]\[ a = \frac{242}{200} \][/tex]

[tex]\[ a = 1.21 \][/tex]

Therefore, the value of [tex]\( a \) is \( 1.21 \).[/tex]

Answer:

The distance is 6.3 units

Answer:

Explanation:

The "Shortest Route Algorigtm" aims to determine the most efficient or short route, when a several alternative pahtways can connect or be used to implement a solution.

A graph is drawn with the different nodes and paths that connect them. The distance between every pair of consecutive nodes is written.

The picture shows that for the step #1, there are, in principle, three routes: AB, AC, and AD.

AB must be discarded because it is not viable (a negative distance is not possible).

AC is more efficient than AD because the distance of AC is 3 and the distance of AD is 8. Thus AC is selected and circled.

To continue from AC, the possible routes are shown in step #2. They are ACB; 3 and ACE; 6.

ACB i s shorter, thus ACB is circled.

In step #3, the possible routes are ACBE; 8 and ACBD; 7. Thus, route ACBD is shorter, and it shall be circled.

The conclusion of the algorithm is that the route ACBD is the shoretes (most efficient).

The route to circle next is route ACBD; 7

From the question, we understand that she wants to determine the shortest route.

This means that, she has to circle the node with the smallest value in each step.

From the diagram, the smallest node in step 3 is ACBD; 7

Hence, the route to circle next is route ACBD; 7

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Answer: P = Po ( 1 + 0.075)

Step-by-step explanation: let Po = initial population

P = final population.

The increase in population is by 7.5%, which implies that if the initial population Increases by 7.5%, we would have a new (current) population.

Final population = initial population + increament of initial population.

Where increment of initial population = 7.5% of Po = 0.075 Po

P = Po + 0.075Po

P = Po ( 1 + 0.075)

The amount paid by Heron for the video game  is $46.64.

Step-by-step explanation:

Here, the marked price of the video game  = $55

The discount percentage on the video game  = 20%

Calculating 20% of the $55, we get:

[tex]\frac{20}{100} \times 55 = 11[/tex]

So, the discount offered on the video game  = $11

Selling Price  = Marked Price  - Discount

                        =$55 - $11 = $44

Now,  the tax percentage on the video game  = 6%

Calculating 6% of the $44, we get:

[tex]\frac{6}{100} \times 44 =2.64[/tex]

So, the tax  on the video game  = $2.64

New Selling Price  = Selling Price  +  Tax

                        =$44 + $2.64  = $46.64

So, the amount paid by Heron for the video game  is $46.64.

The number of pennies and nickels that has a worth of $0.45 is 15 and 6 respectively

Given:

total worth = $0.45

Total coins = 21

let

number of pennies = x

number of nickels = y

x + y = 21 (1)

0.01x + 0.05y = 0.45 (2)

multiply (1) by 0.01

0.01x + 0.01y = 0.21 (3)

0.01x + 0.05y = 0.45 (2)

subtract (2) from (1)

0.05y - 0.01y = 0.45 - 0.21

0.04y = 0.24

y = 0.24 / 0.04

y = 6

substitute y = 6 into (1)

x + y = 21 (1)

x + 6 = 21

x = 21 - 6

x = 15

Therefore, the number of pennies and nickels that has a worth of $0.45 is 15 and 6 respectively.

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Answer:

6, 8, 10,

Step-by-step explanation:

you start at zero and go 6 units to the right, then from zero, you go 8 units up; this forms a right triangle with the smaller sides being 6 and 8. Then u can use the Pythagorean theorem to find the bigger side.

The sample in the study refers to the 12 children in Mrs. Smith's kindergarten class. A sample is a subset of people selected from a larger group for study purposes. In this research, the data being analyzed only pertains to these selected individuals.

In this study, the sample chosen is the group of 12 children in Mrs. Smith's kindergarten class. This is because the data being collected and scrutinized is related to these particular individuals. In this context, 'sample' refers to the subset of people chosen from a larger group (the population) for research or study purposes. It is the set of individuals on which the study or experiment is conducted. In this case, the larger population could be considered all children in kindergarten, but the sample for the study is specifically the 12 children in Mrs. Smith's class, as the study only includes their sleep patterns.

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Answer:

Step-by-step explanation:

The total number of permutations of boys and girls on the team are:

¹⁶P₅*¹³P₄

1.

Bob will be one of the fixed boys to be picked. Hence, actually 4 boys are to be picked from 15. The permutations of girls being picked remains the same.

Probability = Permutations with Bob as one of the boys / Total permutations

Probability = (¹⁵P₄*¹³P₄) / (¹⁶P₅*¹³P₄) = ¹⁵P₄ / ¹⁶P₅

Probability = [tex]\frac{15!}{(15-4)!}/\frac{16!}{(16-5)!}[/tex] = 15! / 16! = 1/16

2.

Now, Bob is one of the fixed boys and Jane is one of the fixed girls. Hence, actually 4 boys are to be picked from 15 and 3 girls are to be picked from 12.

Probability = Permutations with bob as one of the boys and jane as one of the girls / Total permutations

Probability = (¹⁵P₄*¹²P₃) / (¹⁶P₅*¹³P₄) = (1/16)*(1/13) = 1/208

3.

Now, the probability that at least Jane or Bob will be picked has been asked. This probability is a combination of three probabilities:

Probability = (Probability that only Bob will be picked) + (Probability that only Jane will be picked) + (Probability that both will be picked)

Probability = 1/16 + 1/13 + 1/208 = 0.123

4.

Total teams possible = ¹⁶P₅*¹³P₄ = 8994585600 teams are possible

Answer:

(a) V(0) = 50 gal, V(20) = 0 gal

(b)At t= 0 the tank is full.

At t=0 the tank is empty

(c)

Time       volume

 0               50 gal

 5                37.5 gal

 10              25 gal

 15             12.5 gal

20                0 gal

(d)

Net change of volume = 50 gal

Step-by-step explanation:

Given that the capacity of the tank is 50 gal.

Torricelli's Law gives the volume of water remaining in the tank after t minutes as

[tex]V(t)=50(1-\frac{t}{20})^2[/tex]

(a)

To find V(0), we put t = 0 in the above equation

[tex]V(0)=50(1-\frac{0}{20})^2[/tex]

        [tex]=50(1-0)^2[/tex]

        = 50 gal

To find V(20), we put t =2 0 in the above equation

[tex]V(20)=50(1-\frac{20}{20})^2[/tex]

        [tex]=50(1-1)^2[/tex]

        = 0 gal

(b)

At t= 0 the tank is full.

At t=0 the tank is empty.

(c)

Time                                          V(t)

  0                                  [tex]50(1-\frac{0}{20})^2=50 \ gal[/tex]

  5                                  [tex]50(1-\frac{5}{20})^2=37.5 \ gal[/tex]

 10                                  [tex]50(1-\frac{10}{20})^2=25 \ gal[/tex]

 15                                 [tex]50(1-\frac{15}{20})^2=12.5 \ gal[/tex]

 20                                [tex]50(1-\frac{20}{20})^2=0[/tex]

(d)

Net change of volume = V(0) -V(20)

                                     =(50-0) gal

                                    = 50 gal

The volume V(t) of water remaining in the tank after t minutes is given by V(t) = 50(1−t/20). V(0) represents the initial volume of water in the tank, which is 50 gallons. V(20) represents the volume of water remaining in the tank after 20 minutes, which is 0 gallons.

(a) To find V(0), substitute t = 0 into the equation V(t) = 50(1−t/20).

V(0) = 50(1−0/20) = 50(1−0) = 50(1) = 50

Similarly, to find V(20), substitute t = 20 into the equation V(t) = 50(1−t/20).

V(20) = 50(1−20/20) = 50(1−1) = 50(0) = 0

(b) V(0) represents the initial volume of water in the tank, which is 50 gallons. V(20) represents the volume of water remaining in the tank after 20 minutes, which is 0 gallons.

(c) Creating a table of values of V(t) for t = 0, 5, 10, 15, 20:

t | V(t)

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

0 | 50

5 | 37.5

10 | 25

15 | 12.5

20 | 0

(d) The net change in volume V as t changes from 0 min to 20 min is V(20) - V(0).

V(20) - V(0) = 0 - 50 = -50 gallons

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Answer:

p+b[tex]\leq[/tex]30 .......(i)

12.50p+9.50b[tex]\geq[/tex]300 .......(ii)

Step-by-step explanation:

Marcus Hourly Rate at the local pizzeria = $12.50 per hour

Marcus Hourly Rate at the university bookstore = $9.50 per hour

Let the number of hours worked at the local pizzeria=p

Let the number of hours worked at the university bookstore=b

Since he cannot work more than 30 hours per week in order to attend classes, the total of the hours:

p+b[tex]\leq[/tex]30 .......(i)

If he earns $12.50 for p hours at the local pizzeria,

Income from local pizzeria=12.50p

If he earns $9.50 for b hours at the university bookstore,

Income from university bookstore=9.50b

He must make at least $300 per week, therefore his total income must not be less than $300

Total Income=Income from Pizzeria + Income from University bookstore

12.50p+9.50b[tex]\geq[/tex]300 .......(ii)

Therefore the system of inequalities that models this situation is given as:

p+b[tex]\leq[/tex]30 .......(i)

12.50p+9.50b[tex]\geq[/tex]300 .......(ii)

Answer:

A

Step-by-step explanation:

8(2) = 16

17 (2) = 34

34^2 = 16^2 + x^2

1156 = 256 + x^2

1156- 256 = x^2

900 = x^2

square root of 900 = x

x = 30

15(2) = 30

Answer:

A 15a

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 +b^2 = c^2  where a and b are the legs and c is the hypotenuse

Letting the unknown side be x

(8a)^2 + x^2 = (17a)^2

64a^2 + x^2= 289a^2

Subtracting 64a^2 from each side

64a^2 -64a^2 + x^2= 289a^2-64a^2

x^2 =225a^2

Taking the square root of each side

sqrt(x^2) =sqrt(225a^2)

x = 15a

Answer:

a) matched samples.

Step-by-step explanation:

Matched samples (also known as matched pairs, paired samples or dependent samples) are those samples which can be matched in pairs for one set of item and the sample data are not independent of each other. The pairs don’t have to be different people, it could be the same individuals at different time or tested on different activities for example

The completion time data collection method used by the company, which involves each worker using both production methods, is based on matched samples.

The current method used to collect completion time data involves each worker being required to use both production methods. This method is known as matched samples. It involves using the same subjects in two different conditions to measure the difference in outcomes. In this case, the matched samples design is being used to compare the completion times of the workers using both production methods. The design is a test of dependent means, classified as a matched pairs design. This design is useful in situations where the same subject is being tested in two different conditions. The matched pairs design allows for a more accurate comparison of the two conditions, as it eliminates the variability between different subjects.

Answer:

Matched sample design

Step-by-step explanation:

- A matched subject design uses separate experimental groups for each particular treatment, ( A sample of brothers and sisters - genders ).

- But relies upon matching every subject in one group with an equivalent in another. (The differences in ratings between each brother and sister pair were compared. )

- The idea behind this is that it reduces the chances of an influential variable skewing the results by negating it.

Answer:

Step-by-step explanation:

The relationship is negative, negative correlation

Step-by-step explanation:

Here, given:

The area of the square floor  = 64 sq. ft

Now, as given the floor is in the shape of a square.

Let us assume the side length of the floor = k ft

Area of a square  = (Side) x (Side)

                              = k x k   = 64 sq ft

⇒ k ²  =  64  = (8) ²

⇒ k   = 8 ft

Hence, 64 sq ft   = ( 8 ft) ²

Here, base  = 8 and power = 2, which is greater than 1.

[tex]\boldsymbol{\mathbf{Answer}}[/tex]

[tex]\boldsymbol{\mathbf{Machine \, A \,will\, take \,6 \,hours\, to \,produce\, 1 \,widget \,on\, its\, own.}}[/tex]

[tex]\boldsymbol{\mathbf{Step-by-step \,explanation:}}[/tex]

Let,

performance rate of machine A is x widget per hour.

performance rate of machine A is y widget per hour.

As given, Machine A and Machine B can produce 1 widget in 3 hours working together.

I.e mathemetically,

[tex]\boldsymbol{x + y=\frac{1}{3}......(1)}[/tex]

lly for second statement, Machine A’s speed were doubled, the two machines could produce 1 widget in 2 hours working together.

i.e mathematically,

[tex]\boldsymbol{2x + y=\frac{1}{2}......(2)}[/tex]

Substact equation (1) in (2)

  [tex]x + y=\frac{1}{3}[/tex]

[tex]-2x + y=\frac{1}{2}[/tex]

Resultant equation will be,

[tex]-x=\frac{-1}{6}[/tex]

[tex]\boldsymbol{x = \frac{1}{6}}[/tex]

Performance rate of machine A is \frac{1}{6} widget per hour.

what is time Machine A will take to produce 1 widget on its own.

i.e = [tex]\frac{1}{\frac{1}{6}}[/tex]

[tex]\boldsymbol\mathbf{{=\, 6 \,hours.}}[/tex]

Answer: The volume is 143

Step-by-step explanation: