Using the relation between velocity, distance and time, it is found that it took the knight 20 hours to traveled from one kingdom to another.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
v = d/t
On the first day, he traveled at a speed of 10 mph, a distance of d, hence:
10 = d/t
t = d/10
On the second day, he traveled at a speed of 8 mph, a distance of 180 - d, hence:
8 = (180 - d)/t
t = (180 - d)/8
Equaling both equations for t, we find the distance on the first day, hence:
d/10 = (180 - d)/8
8d = 1800 - 10d
18d = 1800
d = 100 miles.
The time on the first day was:
t = 0.1d = 0.1 x 100 = 10 hours.
On the second day he traveled the same amount of time, hence, in total, he traveled 20 hours.
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I bet you can't solve this...
The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account. Solve for r.
r = 0.04
r = 0.14
r = 0.26
r = 0.40
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Lets solve for r ~[tex]\qquad \sf \dashrightarrow \: 816 = 600( 1 + 9r)[/tex]
[tex]\qquad \sf \dashrightarrow \: 816 = 600 + 5400r[/tex]
[tex]\qquad \sf \dashrightarrow \: 5400r = 816 - 600[/tex]
[tex]\qquad \sf \dashrightarrow \: 5400r = 216[/tex]
[tex]\qquad \sf \dashrightarrow \: r = \dfrac{216}{5400} [/tex]
[tex]\qquad \sf \dashrightarrow \: r= \dfrac{4}{100} [/tex]
[tex]\qquad \sf \dashrightarrow \: r = 0.04[/tex]
The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account. On solving the linear equation for r, we get r = 0.04 (a).
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Given in the question,
[tex]816 = 600(1 + 9r)\\\\\frac{816}{600} = 1+9r\\ \\\frac{816}{600} -1 = 9r\\\\\frac{216}{600} = 9r\\\\r = \frac{216}{600* 9 } = 0.04[/tex]
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Matt bought 4 packages of cookies. Each package had 24 cookies. He ate 9 cookies. Write an expression to show how many cookies are left.
Answer:
4 * 24 - 9 = 87 cookies left.
Step-by-step explanation:
5/8 of the sixth grades plan to take athletics in seventh grade. What represents the part of the students do not plan to take athletics in seventh grade
Answer: 3/8
Step-by-step explanation:
5/8 of them want to, so you subtract 5/8 from 1
1-(5/8)
(8/8)-(5/8)
((8-5)/8)
3/8
One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table.
A 2-column table with 9 rows. Column 1 is labeled number of free throws made with entries 0, 1, 2, 3, 4, 5, 6, 7, 8. Column 2 is labeled Probability with entries 0.002, 0.008, 0.04, 0.12, 0.23, 0.28, 0.21, 0.09, 0.02.
What is the probability that the basketball player will make at least six free throws out of the eight attempts?
0.11
0.21
0.30
0.32
The likelihood that the basketball player will convert at least six of his or her eight free throw tries is 0.32.
What is meant by probability ?The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics refers to the study of events subject to probability.
The ratio of all potential cases to the number of cases that are favorable to an event determines its likelihood when there is no reason for us to believe that any one of these circumstances will happen more frequently than any other, making them all equally likely.
The likelihood that an event will occur is quantified by probability. The probability of an event is the relative frequency throughout time of that event. Probabilities are all numbers between 0 and 1, inclusive—that is, any numbers between 0 and 1.
Therefore, the correct answer is option d) 0.32.
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Let f be a function defined on all of that satisfies the additive condition f(x+y)=f(x)+f(y) for all a.) Show that f(0)=0 and that f(-x)=-f(x) for all x in .
b.) Show that is f is continuous at x=0, then f is continuous at every point in c.) Let k=f(1). Show that f(n)=kn for all n in the natural numbers, and then prove that f(z)=kz for all z in . Now, prove that f(r)=kr for any rational number r.
d.) Use (b) and (c) to conclude that f(x)=kx for all x in . Thus, any additive function that is continuous at x=0 must necessarily be a linear function through the origin.
Let f be a function defined on all of that satisfies the additive condition is,
f(x) = [tex]kx[/tex] for every x∈ R.
It is given that:
f: R → R is a continuous function such that:
[tex]f(x+y)[/tex] = [tex]f(x) + f(y)[/tex] ∀ x , y ∈ R (Equation-1)
Now, let us assume f(1)=k
Also,
f(0) = 0( Since, f(0)=f(0+0)
That is,
f(0)=f(0)+f(0)
By using property (1)
Also,
f(0)=2f(0)
That is,
2f(0)-f(0)=0
That is,
f(0)=0 )
Also,
f(2)=f(1+1)
That is,
f(2)=f(1)+f(1) ( By using property (1) )
i.e.
f(2)=2f(1)
That is,
f(2)=2k
Similarly for any m ∈ N
f(m)=f(1+1+1+...+1)
That is,
f(m)=f(1)+f(1)+f(1)+ ....... +f(1) (m times)
That is,
f(m)=mf(1)
That is,
f(m) = [tex]mk[/tex]
Now,
f(1) = [tex]f(\frac{1}{n} +\frac{1}{n} +......\frac{1}{n} )[/tex]
f(1) = [tex]f(\frac{1}{n} )+f(\frac{1}{n} )+......f(\frac{1}{n} )[/tex]
f(1) = n [tex]f(\frac{1}{n} )[/tex]
f(1) = k
[tex]f(\frac{1}{n} )[/tex] = k * [tex]\frac{1}{n}[/tex]
Also,
when x∈ Q
[tex]x = \frac{p}{q}[/tex]
Then,
[tex]f(\frac{p}{q})[/tex] = [tex]f(\frac{1}{q} )+ f(\frac{1}{q} )+ .....f(\frac{1}{q} )[/tex]
[tex]f(\frac{p}{q})[/tex] = p * [tex]f(\frac{1}{q} )[/tex]
[tex]f(\frac{p}{q})[/tex] = [tex]p\frac{k}{q}[/tex]
[tex]f(\frac{p}{q})[/tex] = [tex]k\frac{p}{q}[/tex]
So,
[tex]f(x) = kx[/tex] for all x belongs to Q
Now, as we know that:
Q is dense in R.
So Э x∈ Q' such that Э a seq < [tex]x_{n}[/tex] > belonging to Q such that:
< [tex]x_{n}[/tex] > ⇒[tex]x[/tex]
Now, we know that: Q'=R
This means that:
Э α ∈ R
such that Э sequence [tex]a_{n}[/tex] such that:
[tex]a_{n}[/tex] belongs to Q,
[tex]a_{n}[/tex] ⇒ [tex]\alpha[/tex]
[tex]f(a_{n} )= ka_{n}[/tex]
( since [tex]a_{n}[/tex] belongs to Q )
Let f is continuous at x=α
This means that:
[tex]f(a_{n} )[/tex] ⇒ [tex]f(\alpha )[/tex]
k [tex]a_{n}[/tex] ⇒ [tex]f(\alpha )[/tex]
k [tex]a_{n}[/tex] ⇒ k [tex]\alpha[/tex]
This means that:
[tex]f(\alpha )[/tex] = k [tex]\alpha[/tex]
This means that:
f(x) = [tex]kx[/tex] for every x∈ R
Therefore,
Let f be a function defined on all of that satisfies the additive condition is, f(x) = [tex]kx[/tex] for every x∈ R.
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Makayla invested $130. She earned a simple interest of 4% per year on the initial investment.
If no money was added or removed from the investment, what was the amount of interest Makayla received at the end of two years? Formula I=PRT
The answer is $10.4
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: Makayla invested $130. She earned a simple interest of 4% per year on the initial investment.
Then SI = 130×4×2 /100
=$10.4
Hence, Simple Interest recieved is $10.4
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1.24) George rides his bike to his friend's house that is 5 kilometers from his house. If he rides
his bike at an average speed of 15 km/h, how long will it take him to get to his
friend's house?
t=d
Answer:
5 km / 15 km/h = 0.3333 hours
Step-by-step explanation:
This is calculated by dividing the distance he has to travel (5 km) by his average speed (15 km/h) and then converting the result to minutes.
0.3333 hours x 60 minutes/hour = 20 minutes
The company Sea Esta has 12 members on its board of directors. In how many different ways can it elect a president, vice-president, secretary and treasurer?
The company Sea Esta can elect a president, vice-president, secretary and treasurer in 495 different ways.
What is Combination in Mathematics?
In mathematics, a combination is a way of selecting a certain number of items from a larger set of items, without regard to the order in which the items are selected. It is a way to count the number of distinct subsets of a given size from a larger set.
The formula for combination is:
(n!) / (r! * (n-r)!)
The company Sea Esta has 12 members on its board of directors, and they need to elect a president, vice-president, secretary, and treasurer. The number of ways to elect these four positions is determined by using the formula of combination, which is:
Where n is the total number of options (in this case, the number of board members) and r is the number of positions to be filled (in this case, 4).
So, the number of ways to elect a president, vice-president, secretary, and treasurer is:
(12!) / (4! * (12-4)!) = (1211109) / (4321) = 495
Therefore, the company Sea Esta can elect a president, vice-president, secretary and treasurer in 495 different ways.
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the bumper is at -1.6 units.
It is programmed to move -2.3units.
Where should the ball be placed?
If the bumper is at -1.6 units and It is programmed to move -2.3units. The bumper should be placed at -3.9 units
How to find the location of the bumperThe location of the bumper is calculated by the concept of addition that takes place when the two values has negative signs values.
The negative numbers are located by the left of zero on the number line. The two points are both negative and have the value of -1.6 units and -2.3 units
Summing the two units together will result to
= -1.6 units + (-2.3 units)
= -1.6 - 2.3
= -3.9 units
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PLS PLS PLS I NEED THIS
Tory and Emilio's motorboats travel at the same speed. Tory pilots her boat 30km before docking. Emilio continues for another 3 hr, traveling a total of 80 km before docking. How long did it take Tory to navigate the 30 km?
120 + 1814x = 180 –134x
Answer:
15/487 or 0.0308008= 0.03
Step-by-step explanation:
You must solve to isolate the x variable.
Examine the triangle below, solve for x and y, rounded to two decimal places.
X=
y=
X
30° 16
y
The value of x and y in right angle triangle is 16√2 and 16
What is a Right Angle Triangle ?
A right triangle is a triangle having one right angle or two perpendicular sides. It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle. The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.
The Pythagorean theorem, often known as Pythagoras' theorem, in Euclidean geometry relates the three sides of a right triangle. This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
In the triangle 2 angles are 90° and 45° respectively.
The third angle is = 180°+90°-45°=45°
The triangle is issosceles triangle
So the side which is not x is 16.
Now by using Pythagoras Theorem
x = √16^2+16^2 = 16√2
The value of x is 16√2
The value of y is y^2 + 16^2 = 16√2^2
y^2 = 512 - 256
y^2 = 256
y = 16
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Tyson is hiking. At the start of his hike, his altitude is $-120$ feet. Halfway through his hike, Tyson measured that his altitude had dropped $70$ feet. Part A Tyson determines that his altitude at the halfway point of his hike is $-50$ feet because $-120\ +\ 70\ =\ -50$ . Did Tyson correctly determine his altitude at the halfway point of his hike? Explain why or why not. If not, calculate Tyson's altitude at the halfway point of his hike.
His altitude at the halfway point is -50 feet
Step-by-step explanation:
At the start of his hike, his altitude is -120 feet.
His altitude had dropped 70 feet.
His altitude at the halfway point of his hike is
= -120 + 70 = -50
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Please help!!! I really need it
Answer:
[tex] \displaystyle{ {f}^{ - 1} (x) = {(x - 4)}^{3} + 1}[/tex]
Step-by-step explanation:
Let y = f(x)
[tex] \displaystyle{y = \sqrt[3]{x - 1} + 4}[/tex]
Finding an inverse, swap x and y
[tex] \displaystyle{x = \sqrt[3]{y- 1} + 4}[/tex]
Then solve for y, first subtract 4 both sides
[tex] \displaystyle{ x - 4= \sqrt[3]{y- 1} + 4 - 4} \\ \\ \displaystyle{ x - 4= \sqrt[3]{y- 1} }[/tex]
Cube both sides
[tex] \displaystyle{ {(x - 4)}^{3} = \left(\sqrt[3]{y- 1} \right)^{3} } \\ \\ \displaystyle{ {(x - 4)}^{3} = y - 1}[/tex]
Add both sides by 1
[tex] \displaystyle{ {(x - 4)}^{3} + 1 = y - 1 + 1} \\ \\ \displaystyle{ {(x - 4)}^{3} + 1 = y}[/tex]
The final y is the inverse. Hence:
[tex] \displaystyle{ {f}^{ - 1} (x) = {(x - 4)}^{3} + 1}[/tex]
If the world were a village of 100 people, there would be
31 Christians
21 Muslims
16 non-religious people
14 Hindus
6 Buddhists
12 with other religions.
What percentage are Muslim?
What fraction are Christian?
What fraction are non-religious?
What percentage have a religion?
Tyy
Step-by-step explanation:
a. 21/100
b.31/100
c. 4/25
d. 3/25
What is the common difference?? Please help me
The common difference of the sequence is -1/2
How to determine the common difference?From the question, we have the following parameters that can be used in our computation:
3/8, -1/8, -5/8, -9/8
The common difference is the difference between successive terms
So, we have
Difference = -1/8 - 3/8
Evaluate the difference
Difference = -1/2
Hence, the common difference is -1/2
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Which graph shows the solution to the system of linear equations? y = 2x − 2 4x − 2y = 4 Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0. Coordinate plane with one line that passes through the points 0 comma negative 1 and 1 comma 1 and another line that passes through the points 0 comma negative 2 and 1 comma 0.
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
What is inequalities?A connection in mathematics that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance.Given the inequalities :
y ≥ 2x + 1
y ≤ 2x - 2
From y ≥ 2x + 1 ;
Since the inequality sign is ≥, a solid line is used to draw the straight line graph of y ≥ 2x + 1
From :
y = mx + c
Where, m = slope ; c = intercept
Hence, a straight line graph with ;
Intercept, c = 1 (where the line crosses the y-intercept)
Slope, m = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality :
0 ≥ 2(0) + 1
0 ≥ 0 + 1
0 ≥ 1
Since this is untrue, the area of the graph that does not contain (0, 0) is shaded.
From : y ≤ 2x - 2
Since the inequality sign is ≤, a solid line is used to draw the straight line graph of y ≤ 2x - 2
Graph the line y ≤ 2x - 2, with ;
Intercept, c = - 2
Slope = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality y ≤ 2x - 2:
0 ≤ 2(0) - 2
0 ≤ 0 - 2
0 ≤ - 2
This is untrue, hence the area of the graph that doesn't include (0, 0) is shaded.
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In the equation below, n is the number of words in some code in t years.
n = 2450t + 500
a) In how many years will the code have 12750 words?
b) How many words will the code have in 10 years?
Answer:
a). t = 5 years.
b). n = 25000 words.
Step-by-step explanation:
From the question it have been given a formula
which is n = 2450t + 500
a) The year
n = 12750 words
n = 2450t + 500
= 12750 = 2450t + 500
= 12750 - 500 = 2450t
= 12250 = 2450t
= 12250/2450 = 2450t/2450.
5 years = t
Or
t = 5 years.
b). The words
t = 10 years
= n = 2450t + 500
= n = 2450(10) + 500
= n = 24500 + 500
n = 25000 words.
did all the major work just need the value:D
Answer:
Expressions B and C
Step-by-step explanation:
A: 20^2 - 18^2 = 400 - 324 = 76 (not A)
B: 8(4^2) + 2^4 = 128 + 16 = 144 (which is equivalent to 12^2)
C: 15^2 - 3^4 = 225 - 81 = 144 (which is equivalent to 12^2)
Hope this helps!
If the probability of s1 = .6 and the probability of F = .40 what is the value at node 4.
Group of answer choices
320
280
310
260
200
We decide on 320 as the best-predicted value. EV(node 4) = 320. The answer is option (a).
What is Probability?
Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.
Probability of S1 = 0.6
Probability of F = 0.40
Value of node y =?
As per the given value if probability of S1 = 0.6
Then the probability of S2 = 0.4
Using payoff values in table equation from except value.
[tex]EV(d_{i})=[/tex] ∑ [tex]V_{ij} S_{J}[/tex]
where [tex]V_{ij}[/tex] = value of payoff
We compute the expected value for each of decisions
EV(Node 8) = 0.6*100+0.4*300
= 180
EV(Node 9) = 0.6*400+0.4*200
= 320
For Node 4, We select the best value from node 8 and node9
The best decision attractive is the line complex branch that EV(node 8) = 180, For node 9,
Therefore, We select the best-predicted value i.e 320.
EV(node 4) = 320
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Please help I will give you brainliest!!!
Answer:
(a) D y = 6x + 7
(b) A 6
Step-by-step explanation:
6x -6 = -7 Subtract 6x from both sides
6x - 6x - y = -6x - 7
-y = -6x - 7 Divide all the way through by -1
y = 6x + 7
The slope is the number before the variable x. (6)
Find the standard parametrization for the line segment joining the points below. Draw coordinate axes and sketch the segment, indicating the direction of increasing t for the
parametrization.
(5.0,5) and (0,4,0)
Find a parametrization for the line segment joining the two points so that the parametrization moves from (5,0.5) to (0,4,0) as t increases from 0 to 1.
You need to know the direction of the line and at least one point on it in order to parametrize a line. x is 5 + 4.0t ,y is 0 + 4.0t
How is a line segment with two points parametrized?You need to know the direction of the line and at least one point on it in order to parametrize a line. You can determine the direction of the line if you know two of its points. Point-slope form → y - y₁ = m (x - x₁)Slope-intercept form → y = mx+bStandard form → ax + by = cWe must locate two vectors parallel to the plane, as well as a point on the plane, in order to discover a parametrization. Finding a location aboard the aircraft is simple. Any number for x and y may be used to compute z using the plane equation. If x and y are set (5,0.5) to (0,4.0) equation (1)means that .x = 5 + 4.0t
y = 0 + 4.0t
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Using any method(s), solve Angle K H P when h = 16.1, p = 24.9 and k = 12.8 (trigonometry)
The angles of the triangle KHP are P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°, respectively.
How to determine the measures of missing angles in a triangleHere we have the case of a triangle where the lengths of three sides are known and measures of angles must be determined. The missing angles can be found by means of law of cosine, whose equations related to the triangle are introduced below;
p² = h² + k² - 2 · h · k · cos P
h² = p² + k² - 2 · p · k · cos H
k² = h² + p² - 2 · h · p · cos K
Given;
h, k, p - Sides
H, K, P - Angles
If we know that h = 16.1, p = 24.9 and k = 12.8, then the measures of the angles are;
cos P = (p² - h² - k²) / (- 2 · h · k)
cos P = (24.9² - 16.1² - 12.8²) / (- 2 · 16.1 · 12.8)
cos P = - 0.478
P ≈ 118.555°
cos H = (h² - p² - k²) / (- 2 · p · k)
cos H = (16.1² - 24.9² - 12.8²) / (- 2 · 24.9 · 12.8)
cos H = 0.823
H ≈ 34.614°
cos K = (k² - h² - p²) / (- 2 · h · p)
cos K = (12.8² - 16.1² - 24.9²) / (- 2 · 16.1 · 24.9)
cos K = 0.892
K ≈ 26.844°
Triangle KHP has the following missing angles: P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°;
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A dilation maps (6, 10) to (3, 5) and the center of dilation is the origin. Given A(12, 4), determine
under the same dilation.
Analyzing the coordinates being provided, the scale factor is found to be 0.5, hence the image of point A(12,4) under the same dilation and the center of dilation as origin is A'(6,2).
What is dilation?A dilation is a transformation in Euclidean space that enlarges or reduces all the points in a figure by a scale factor. In the example given, the dilation maps (6, 10) to (3, 5) with a scale factor of 0.5, and the center of dilation is the origin (0,0). The image of a point A(x,y) under this dilation would be A'(x*0.5, y*0.5). It means the point is scaled down by 0.5 in both x and y coordinate.
How can the dilation described above be used in real-world applications?The dilation described above can be used in real-world applications such as image processing, where it can be used to reduce the size of an image without losing important details, or to enlarge an image without introducing distortion. It can also be used in architectural design to create smaller or larger versions of floor plans and blueprints. Additionally, it can be used in cartography to change the scale of maps without altering the shape of the features on the map.
Analyzing the given dilation map , mapped from (6,10) to (3,5) ,the center of the dilation being origin. We can see that the scaling factor is 0.5.
So , using the same dilation for point A(12,4), The image of A will be,
A'(12*0.5,4*0.5) = A'(6,2)
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If the dimensions of the gym were 24 ft. by 45 ft., how much distance did he save on one lap?
Answer:
18
Step-by-step explanation:
One trip around the gym would be 138 ft.
If we cut the diagonal, we use the Pythagorean theorem to find the distance of the hypotenuse, which is 51 ft.
One trip with the shortcut is 119 ft. (24 + 45 + 51 = 119).
Subtract 119 ft. from 138 feet and you have 18 ft. shorter route than walking the entire perimeter.
I need help question 3 and 4
Answer: k*6 and then you find the reciprocal of k*6 which is 1 over k*6
Step-by-step explanation:
7. The PTA needs to raise $15,000 from its membership. Each membership brings in $25. If they begin with $2500, how many memberships will be needed? Let m represent the number of memberships.
Answer:
m=5000 members
Step-by-step explanation:
15000-2500=12500
12500/25=500
WILL GET 100 PTS!
Juan builds this pedestal for a trophy.
What is the volume of the pedestal?
Answer:
112 in³------------------------------------
The pedestal is the combination of two rectangular prisms.
One of them has dimensions:
9 in by 2 in by 4 inIts volume is:
V = 9*2*4 = 72 in³The other one has dimensions:
(9 - 2 - 2) = 5 in by 2 in by 4 inIts volume is:
V = 5*2*4 = 40 in³Total volume is:
72 + 40 = 112 in³Answer:
112 in³
Step-by-step explanation:
The pedestal is made up of two rectangular prisms.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Volume of a rectangular prism}\\\\$V=w\cdot l\cdot h$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width of the base. \\ \phantom{ww}$\bullet$ $l$ is the length of the base.\\\phantom{ww}$\bullet$ $h$ is the height of the prism.\\\end{minipage}}[/tex]
The dimensions of the largest rectangular prism are:
w = 2 inl = 9 inh = 4 inTherefore, the volume of the largest rectangular prism is:
[tex]\begin{aligned}\implies V&=2 \cdot 9 \cdot 4\\&=18 \cdot 4\\&=72\;\rm in^3\end{aligned}[/tex]
The dimensions of the smaller rectangular prism are:
w = 2 inl = 9 - 2 - 2 = 5 inh = 4 inTherefore, the volume of the smaller rectangular prism is:
[tex]\begin{aligned}\implies V&=2 \cdot 5 \cdot 4\\&=10\cdot 4\\&=40\;\rm in^3\end{aligned}[/tex]
The volume of the pedestal is the sum of the volumes of the largest and smaller rectangular prisms:
[tex]\implies V=72+40=112\; \rm in^3[/tex]
Therefore, the volume of the pedestal is 112 in³.
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given triangle abc prove m∠a=66 2/3
Any triangle's three interior angles add up to 180 degrees, according to the Triangle Sum Theorem.
How do you calculate the triangular sum theorem?Any triangle's three interior angles add up to 180 degrees, according to the Triangle Sum Theorem. m∠1+m∠2+m∠3=180∘.
Here,
According to the triangle sum theorem, a triangle's total angles equal 180°. Therefore, using the Substitution property
=> (3x)° + 90° + (x+10)° = 180°,
=> m(A,B,C) = 180.
To find x, combine similar terms to get
=> 4x + 100 = 180. Then, using the subtraction condition of equality, convert => 13 1/2 to 80.
=> Finally, divide 80 by 5 ( 13 1/2) to find x.
The substitution property may be used to get the measure of the angle A, yielding mA = 5 ( 13 1/2) °.
When the expression is finally simplified, m < A = 66 2/3.
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hello i need help with my math money management math homeowrk but no one wants to help me please help me with my math homework!!
a) The total cost of purchasing the car that is worth $32,000 with the harmonized sales tax (HST) of 13% is $36,160.
b) By leasing the car instead of purchasing it outright, the customer will save $14,760.
c) The lease options for the lessee after returning the car include:
Lease buyoutExtending the leaseSigning a new lease agreementBuying out the car and then reselling it.What is a lease?A lease is a financing option for the use of capital assets.
With a lease, the lessee uses the asset for a specific period and the lessor receives periodic payments.
There are operating and finance (capital) leases. Though, under new accounting standards, all leases are to be classified as finance leases.
Value of the car = $32,000
Harmonized Sales Tax (HST) = 13%
Cost of the car with HST = $36,160 ($32,000 x 1.13)
Lease Arrangement:Down payment = $1,000
Financing part = $35,160 ($36,160 - $1,000)
Installment payments = 48
Periodic payments = $425
Total lease cost = $21,400 ($1,000 + 48 x $425)
Savings (advantages) from leasing = $14,760 ($36,160 - $21,400)
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