Answer:
[tex] v(t) = 8t +5[/tex]
And that represent the instantaneous velocity at a given time t.
And then we just need to replace t =2 in order to find the instantaneous velocity and we got:
[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]
Step-by-step explanation:
For this case we have the position function s(t) given by:
[tex] s(t) = 4t^2 + 5t+5[/tex]
And we can calculate the instanteneous velocity with the first derivate respect to the time, like this:
[tex] v(t) = s'(t)= \frac{ds}{dt}[/tex]
And if we take the derivate we got:
[tex] v(t) = 8t +5[/tex]
And that represent the instantaneous velocity at a given time t.
And then we just need to replace t =2 in order to find the instantaneous velocity and we got:
[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]
Triangle SRQ undergoes a rigid transformation that results in triangle VUT. 2 right triangles with identical side lengths and angle measures are shown. The second triangle is shifted up and to the right. Which statements are true regarding the transformation? Select two options. SQ corresponds to VU. AngleR corresponds to AngleU. UV corresponds to RS. AngleS corresponds to AngleT. QS 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.
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:
I am confused about the wording on this problem and also when I used the Pythagorean theorem it came out as wrong.
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
Option D is cut off but option d is 6a+16
Please Help
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
Two poles are connected by a wire that is also connected to the ground. The first pole is 20 ft tall and the second pole is 10 ft tall. There is a distance of 30 ft between the two poles. Where should the wire be anchored to the ground to minimize the amount of wire need
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.
Explanation: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:
Relationship 1: a = sqrt((20)^2 + x^2), based on the Pythagorean theorem; Relationship 2: b = sqrt((10)^2 + (30 - x)^2)
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.
Learn more about Minimization in Mathematics here:https://brainly.com/question/29034147
#SPJ11
help me pass this course please somebody, anybody
Using the points (0, 0), (6, 0), and (0, 8) to form a triangle, find the length of the three sides of the triangle.
7, 8, 5
6, 8, 10
8, 6, 3
6, 8, 9
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.
Use the given functions f and g to find f + g, f − g, fg, and f g . State the domain of each. (Enter your answer for the domain in interval notation.) f(x) = 3x + 6, g(x) = x + 2.
Find the domain of each problem.
f + g = Domain=
f-g= Domain=
(f)(g)= Domain=
f/g=Domain=
2.) Find (g ○ f)(x) and (f ○ g)(x) for the given functions f and g.
f(x) = 3/(x+5), g(x) = 3x − 6
(g ○ f)(x) =
(f ○ g)(x) =
3.) Use the method of completing the square to find the standard form of the quadratic function.
f(x) = x2 − 8x + 2
y =
4.) Use the vertex formula to determine the vertex of the graph of the function.
f(x) = x2 − 14x Write the function in standard form.
f(x) =
5.) Use the vertex formula to determine the vertex of the graph of the function.
f(x) = 3x2 − 10x + 1 Write the function in standard form.
f(x) =
Answer: The answers are stated below
Step-by-step explanation: Attached below is the explaination of the solution.
f + g =4x + 8 Domain - (-∞, ∞)
f - g = 2x + 4 Domain - (-∞, ∞)
(f)(g) = 3x² + 12x + 12 Domain - (-∞, ∞)
f/g = [tex]\frac{3x + 6}{x + 2}[/tex] Domain - [tex](-\infty, -2) \cup (-2, \infty)[/tex]
To solve the problems involving the functions f and g, we start by defining the functions:
Given functions:
[tex]f(x) = 3x + 6[/tex]
[tex]g(x) = x + 2[/tex]
1. Finding f + g, f - g, fg, and f/g:
f + g:
[tex]f + g = (3x + 6) + (x + 2) = 4x + 8[/tex]
Domain: All real numbers, [tex](-\infty, \infty)[/tex]
f - g:
[tex]f - g = (3x + 6) - (x + 2) = 2x + 4[/tex]
Domain: All real numbers, [tex](-\infty, \infty)[/tex]
fg:
[tex]fg = (3x + 6)(x + 2) = 3x^2 + 12x + 12[/tex]
Domain: All real numbers, [tex](-\infty, \infty)[/tex]
f/g:
[tex]f/g = \frac{3x + 6}{x + 2}[/tex]
However, g(x) cannot be zero: [tex]g(x) = 0[/tex] for [tex]x = -2[/tex].
Domain: All real numbers except [tex]x = -2[/tex] , which is [tex](-\infty, -2) \cup (-2, \infty)[/tex]
2. Finding (g ◦ f)(x) and (f ◦ g)(x):
(g ◦ f)(x):
[tex]g(f(x)) = g(3x + 6) = (3x + 6) + 2 = 3x + 8[/tex]
(f ◦ g)(x):
[tex]f(g(x)) = f(x + 2) = 3(x + 2) + 6 = 3x + 12[/tex]
3. Completing the square for f(x) = x² - 8x + 2:
First, take the coefficient of [tex]-8[/tex], halve it to get [tex]-4[/tex], and square it to get [tex]16[/tex].
Therefore:
[tex]f(x) = (x^{2} - 8x + 16) - 16 + 2 = (x - 4)^{2} - 14[/tex]
Now in standard form:
[tex]y = (x - 4)² - 14[/tex]
4. Vertex formula for f(x) = x² - 14x:
Vertex formula: [tex]x = -\frac{b}{2a}[/tex] where [tex]a=1, b=-14[/tex].
Therefore:
[tex]x = -\frac{-14}{2(1)} = 7[/tex]
Substituting [tex]x=7[/tex] back to find y:
[tex]f(7) = 7^{2} - 14(7) = 49 - 98 = -49[/tex]
Standard form:
[tex]f(x) = (x - 7)^{2} - 49[/tex]
5. Vertex for f(x) = 3x² - 10x + 1:
Vertex x-coordinate:
[tex]x = -\frac{-10}{2(3)} = \frac{10}{6} = \frac{5}{3}[/tex]
Substitute [tex]x=\frac{5}{3}[/tex] back to find y:
[tex]f(\frac{5}{3}) = 3(\frac{5}{3})^{2} - 10(\frac{5}{3}) + 1[/tex]
Calculate the value:
[tex]3(\frac{25}{9}) - \frac{50}{3} + 1 = \frac{75}{9} - \frac{150}{9} + \frac{9}{9} = -\frac{66}{9} = -\frac{22}{3}[/tex]
The standard form becomes:
[tex]f(x) = 3(x - \frac{5}{3})^{2} - \frac{22}{3}[/tex]
Will mark the Brainliest !!!!! A team of 5 boys and 4 girls will be chosen from a group of 16 boys and 13 girls,
1. If Bob is one of the students, how likely is he to be picked?
2. If Jane is also a student, how likely is it that Jane and Bob will both be picked?
3. How likely is it that at least Jane or Bob will be picked?
4. How many different teams are possible?
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
What is the length of the missing side FP? Round answer to the nearest tenth.
Answer:
Step-by-step explanation:
Considering the given triangle KFP, to determine FP, we would apply the sine rule. It is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes
FP/SinK = FK/SinP = KP/SinF
Therefore
FP/Sin 49 = 66/Sin 85
Cross multiplying, it becomes
FPSin85 = 66Sin49
0.996FP = 45 × 0.7547
0.996FP = 33.9615
FP = 33.9615/0.996
FP = 34.1
The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300 cm. If each of the three measurements has an error of at most 1 cm, which of the following is closest to the maximum possible difference, in cubic cm, between the actual capacity of the box and the capacity computed using these measurements?A. 100,000.B. 120,000.C. 160,000.D. 200,000.E. 320,000.
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
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
Enter your answer in the box.
°
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]
Identify the sample chosen for the study. The number of hours a group of 12 children in Mrs. Smith's kindergarten class sleep in a day. Answer2 Points The 12 children selected in Mrs. Smith's kindergarten class. All children in Mrs. Smith's kindergarten class. The number of hours children sleep.
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.
Explanation: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.
Learn more about Sample in a study here:https://brainly.com/question/37770653
#SPJ3
Which of the following is the solution to the quadratic equation x2 - 10x + 24 = 0?
x = -4, 6
x = 4, -6
x = 4, 6
x= -4, -6
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
A recycling bin is in the shape of a right rectangular prism. The bin is 12 meters long, 5 1/2 meters wide, and 6 1/2 meters tall. What is the volume of the recycling bin? Omg Help me!Please i dont get this?
Answer: The volume is 143
Step-by-step explanation:
Sanjay bought 12 granola bars,which was 4 times as many granola bars as Lena bought.which equation shows the number of granola bars,b,that Lena bought?
Mr. Daniels is building a clubhouse for his children. He has decided that the floor will be square with an area of 64 square feet. Write this number using a power greater than 1 and a lesser base.
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.
Beth is writing out the steps using the "Shortest Route Algorithm". She just finished writing out all the routes for the third step. What route should she circle next?
Group of answer choices
AD; 8
ACE; 6
ACBE; 8
ACBD; 7
Answer:
ACBD; 7Explanation:
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
Read more about algorithms at:
https://brainly.com/question/24793921
A batch of 479 containers for frozen orange juice contains 3 that are defective. Two are selected, at random, without replacement from the batch. a) What is the probability that the second one selected is defective given that the first one was defective? Round your answer to five decimal places (e.g. 98.76543).
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
In the past, every ten-percentage-point increase in cigarette prices in the country of Coponia has decreased per capita sales of cigarettes by four percent. Coponia is about to raise taxes on cigarettes by 9 cents per pack. The average price of cigarettes in Coponia is and has been for more than a year 90 cents per pack. So the tax hike stands an excellent chance of reducing per capita sales of cigarettes by four percent.
Which of the following is an assumption on which the argument depends?
A. Tobacco companies are unlikely to reduce their profit per pack of cigarettes to avoid an increase in the cost per pack to consumers in Coponia.
B. Previous increases in cigarette prices in Coponia have generally been due to increases in taxes on cigarettes.
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.
D. At present, the price of a pack of cigarettes in Coponia includes taxes that amount to less than ten percent of the total selling price.
E. The number of people in Coponia who smoke cigarettes has remained relatively constant for the past several years.
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.
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(X>1800)P(X>1800)P, (, X, is greater than, 1800, ).
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.
Explanation: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%.
Heron wants to buy a video game. The price is regularly priced at 55 dollars. The store has a discount of 20% off and a sales tax of 6%. How much will Heron pay for the video game
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.
Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A’s speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?
[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]
student enrollment at a local school is concerning the community because the number of students has dropped to 504 which is a 20% decrease from the previous year. what was the student enrollment the previous year?
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]
Of the two production methods, a company wants to identify the method with the smaller population mean completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on
a.
matched samples.
b.
worker samples.
c.
pooled samples.
d.
independent samples.
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
sampling the blood pressures of the same people before and after they receive a dosethe same people being measured when the group is given two different tests at different timesThe completion time data collection method used by the company, which involves each worker using both production methods, is based on matched samples.
Explanation: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.
The population of a city is expected to increase by 7.5% next year. If p represents the current popultion, which expression represents the expected populations next year?
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)
Evan has $0.45 worth of pennies and nickels. He has a total of 21 pennies and nickels altogether. Determine the number of pennies and the number of nickels that Evan has.
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.
Learn more about equation:
https://brainly.com/question/13136492
A jar contains six blue marbles and five red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble. Find the probability of the following event. Both of the selected marbles are red.
The jar has 6+5=11 marbles.
We have to find the probability of the following event:
1.We pick a marble from a jar that has 11 marbles in total, 5 of them are red
2.We pick a marble from a jar that has now 10 marbles in total, 4 of them are red (because in the previous step we picked a red marble and did not put it back in the jar)
The probability of the first event is:
[tex]P_1=\frac{5}{11}[/tex]
The probability of the second event is:
[tex]P_2=\frac{4}{10}=\frac{2}{5}[/tex]
The probability of the both events to happen is:
[tex]P=P_1\cdot P_2=\frac{5}{11}\cdot \frac{2}{5}=\frac{2}{11}=0.1818[/tex]
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.
Final answer:
To find the time it will take for an object to travel a certain distance at a given speed, divide the distance by the speed. The estimated time to travel 4.9 km at a speed of 10 km/h is approximately 0.5 hours. The exact time, considering the speed as 10.1 km/h, is also approximately 0.5 hours.
Explanation:
To find the time it will take for an object to travel a certain distance at a given speed, we can use the formula:
Time (in hours) = Distance (in kilometers) / Speed (in kilometers per hour)
First, let's round the speed to the nearest integer, which is 10 km/h. To estimate the time it will take to travel 4.9 km, we can divide the distance by the estimated speed:
Estimated Time = 4.9 km / 10 km/h ≈ 0.49 hours ≈ 0.5 hours
To find the exact time, we will use the given speed of 10 and one-tenth km/h. We can convert this speed to decimal form, which is 10.1 km/h. Now, we can calculate the exact time:
Exact Time = 4.9 km / 10.1 km/h ≈ 0.485 hours ≈ 0.5 hours
Therefore, it will take approximately 0.5 hours or 30 minutes for the object to travel 4.9 km.
Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses but cannot work more than 30 hours per week in order to attend classes. Write a system of inequalities that models this situation where p represents the hours he works at the pizzeria and b represents the hours he works at the bookstore.
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)
Lauren coordinates a construction projects for a cement company. A government project requires constructing two rectangular concrete slabs of dimensions 24× 24× 1 feet. Additionally, the company sends a 20% surplus of concrete to ensure the job can be completed. If a cement truck can carry a maximum of 8 cubic yards of cement, what's the fewest number of trucks that Lauren should send? A)1 B)2 C)3 D)4 E)5lar
The fewest number of trucks Lauren should send is D) 4 trucks.
Step-by-step explanation:
Step 1:
The rectangular slab's dimensions are [tex]24 \times 24 \times 1[/tex] feet. Each truck can carry 8 cubic yards of cement.
First, we need to determine the volume of the slabs in yards. 1 foot = 0.333 yards. So 24 feet = [tex]24\times 0.3333[/tex] = 8 yards.
The volume of the slab = [tex]8 \times 8 \times 0.3333[/tex] = 21.3312 cubic yards.
Step 2:
The company sends a surplus of 20% to make sure the job can be completed. So the total cement sent is the required volume and an extra 20%.
The total cement sent = The required cement + 20%.
= 21.3312 + 20% = 25.597 cubic yards.
Step 3:
So to find the number of trucks needed, we divide the cement sent by the load each truck can carry. Each truck can carry 8 cubic yards of cement. So
The number of trucks needed = [tex]\frac{therequiredload}{load per truck} = \frac{25.597}{8} = 3.199625.[/tex]
If 3.199 trucks are needed, it means 4 trucks are needed which is option D.
A researcher asks a sample of brothers and sisters to rate how positive their family environment was during childhood. In this study, the differences in ratings between each brother and sister pair were compared. The type of design described here is called a
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.