Answer:
h = 1
Step-by-step explanation:
5h - 2h + 6 = 9h
3h + 6 = 9h
6 = 6h
1 = h
The perimeter of a rectangular lot of land is 480 {ft} . This includes an easement of x feet of uniform width inside the lot on which no bulding can be done. If the bulldable area is
The perimeter of a rectangular lot of land is 480 ft, which includes an easement of x feet of uniform width inside the lot on which no building can be done. Hence, the area of the entire rectangular lot of land is (240x - 7x² + 2x³)/2 sq.ft.
The Perimeter of the rectangular land = 480 ft
Let the width of the rectangular lot be x and the length be ySo,Perimeter of the rectangular lot = 2(x+y). According to the given question, there is an easement of x feet on which no building can be done. Therefore, the buildable area = (y-2x) × (x) = A sq.ft
Again the perimeter will be equal to the sum of all four sides of the land. Therefore, the perimeter will be equal to (y+2x) + (x+y) = 2x + 2y + x = 480 ft. Or 3x + 2y = 480 ft.
We have two equations here:
2(x + y) + 2x = 480, or 2x + 2y = 240 —-(1)and
(x + y) + x + y = 240 or 2x + 2y = 240 —-(2)
Equating both the equations, we get2x + 2y = 240, or3x + 2y = 480
Thus, y = (480 - 3x)/2So the area of the buildable portion of the land is A = x (y - 2x) = x ((480 - 3x)/2 - 2x)= x (240 - 7x)/2sq.ft
To find the total area, we need to add the area of the easement to the buildable area.
Total area = Buildable area + Easement area
Total area = A + (x × x) sq. ft.
(The easement will be x feet wide on both sides.)
Total area = x (240 - 7x)/2 + x² sq.ft= (240x - 7x² + 2x³)/2 sq.ft
Hence, the area of the entire rectangular lot of land is (240x - 7x² + 2x³)/2 sq.ft.
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pleaseeee, helppp, mee ill give brainiest if correct
Answer: Reflection
Step-by-step explanation: reflection: when a figure flips over a line
bowling team member distribution stronglys kewed right srs taken what is sampling distribution of sample mean hight
To recap, as long as the sampling size is large enough, the distribution of the means will be essentially normal. This discovery is most likely the most important result offered in beginning statistics courses. It is known technically as the Theorem of Central Limits.
When we use sample means to establish inferences about a population mean, we will repeatedly rely on the Central Limit Theorem. We now know that we can do it even if the population distribution is not regular.
How large a sample size do we need to assume that group means will be normally distributed? As we showed in the simulation, it all depends on the population demographics. The general rule
Generally, samples of size 30 or higher will have a fairly normal distribution, regardless of the shape of the variable's distribution in the population.
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half of farihas hockey cards got wet and ruined.fariha bought 5 cards to replace some that were lost
There is approximately 10 cards at the start
On a family camping trip, 5 backpacks can fit in the trailer for every 3 people. if 9 people are going on the trip, how many backpacks can fit? 12 backpacks 14 backpacks 15 backpacks 24 backpacks
15 bags are expected for the journey for 9 people to fit backpacks in the trailer.
The fundamental principle of multiplication
To calculate the sum of two or more numbers, utilize the mathematical operation of multiplication. If an event can happen in m different ways and a second event can happen in n different ways after it, then the two events that happen in succession can happen in m n distinct ways.
Given that 5 backpacks can fit in the trailer for every 3 people.
Then 3 people = 5 backpacks
1 people = \(\frac{5}{3}\) backpacks
therefore If 9 people are going on the trip, then;
9 people = \(\frac{5}{3}*9\) backpacks
= 5 x 3
= 15 backpacks
Hence, the trailer can fit 15 backpacks if 9 people go on the trip.
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At what point/s do the following function and their inverses intersect? A.f(x) =3x-8 B.g(x) = √x+2 C.h (x=x³
f(x) =3x-8 and g(x) = √x+2 are the function and their inverses intersect.
A function is a mathematical representation that maps one set of values to another set of values. The inverse of a function is a reflection of the original function over the line y=x, where the input and output are reversed.
For the function f(x) = 3x - 8, the inverse can be found by switching the input and output values, then solving for x.
In this case, we have
=> y = 3x - 8 and x = (y + 8)/3.
The two functions will intersect when the input value is equal to the output value, or when
=> 3x - 8 = (y + 8)/3.
Solving for x, we find that x = 4. This is the only intersection point between the two functions.
For the function g(x) = √x + 2, the inverse can be found by switching the input and output values, then solving for x.
In this case, we have
=> y = √x + 2 and x = y² - 2.
The two functions will intersect when the input value is equal to the output value, or when
=> √x + 2 = y² - 2.
Solving for x, we find that x = 4. This is the only intersection point between the two functions.
Therefore option (a) and (b) is correct.
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The force that a car exerts on the road is 13,600n.
Each of the car's 4 tyres has an area of 0.02m2 in contact with the road.
Work out the pressure that th car exerts on the road, in n/m2
the pressure that the car exerts on the road is 170,000 N/m².
what is force?A physics concept called force defines how two items interact and affect how an object moves. The usual definition of it is the sum of the acceleration and mass of an object. In other terms, force is the quantity of energy needed to alter an object's state of motion. As force is a vector quantity with both magnitude and direction, it is measured in the SI system of units called Newtons (N). The forces of gravity, friction, tension, and electromagnetic fields are a few examples.
To calculate the pressure that the car exerts on the road, we can use the formula:
pressure = force / area
where force is the force that the car exerts on the road, and area is the total area of the contact between the tires and the road.
In this case, the force that the car exerts on the road is 13,600 N, and each tire has an area of 0.02 m². Since there are four tires, the total area of the contact between the tires and the road is:
total area = 4 * 0.02 m² = 0.08 m²
Using the formula, we can now calculate the pressure that the car exerts on the road:
pressure = force / area = 13,600 N / 0.08 m² = 170,000 N/m²
Therefore, the pressure that the car exerts on the road is 170,000 N/m².
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If 1400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is: (a) 4.6% compounded annually: $ 2195.05 correct (b) 4.6% compounded semiannually: $ (a) 4.6% compounded quarterly: $ 2211.88 correct (b) 4.6% compounded monthly: $ 2215.75 correct (a) 4.6% compounded daily (ignore leap years): $ 2217.63 correct
The compound interest calculated for 10 years annually, semi-annually, quarterly, monthly, and daily are (a) $2195.05, (b) $2206.18 (c) $2211.88 (d) $2215.75, and, (e) $2217.63
The formula for Compound Interest is
Amount = Principal X (1 + r/n100)ⁿˣ
where,
Principal = original mount
n = no. of times the interest is applied
t = time period
Here,
Principal = $1400
x = 10
r = 4.6
a)
Since it is compounded annually, the interest will be given 10 times in 10 years. therefore, once a year
Hence,
n = 1
Amount = 1400 X (1 + 4.6/100)¹⁰
= 1400 X (104.6/100)¹⁰
= 1400 X (1.046)¹⁰
= $2195.05
b)
Since the interest is compounded semi-annually here, it will be calculated twice a year.
Hence, n = 2
Therefore we get
Amount = 1400 X (1 + 4.6/200)²⁰
= 1400 X (204.6/200)²⁰
= 1400 X (1.023)²⁰
= $2206.18
c)
Since it is compounded 4 times a year now,
n = 4
Hence we get
Amount = 1400 X (1 + 4.6/400)⁴⁰
= 1400 X (1.0115)⁴⁰
= $2211.88
d)
Here, the interest is calculated 12 times a year
Hence we get
Amount = 1400 X (1 + 4.6/1200)¹²⁰
= 1400 X (10038)¹²⁰
= $2215.75
e)
Here we are told to ignore leap years, hence we are only going to consider a year to have 365 days.
Hence,
n = 365
Therefore, we get
Amount = 1400 X (1 + 4.6/36500)³⁶⁵⁰
= 1400 X (1 + 4.6/36500)³⁶⁵⁰
= 1400 X (1.00012)³⁶⁵⁰
= $2217.63
Correct Question
If 1400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is:
(a) 4.6% compounded annually
(b) 4.6% compounded semiannually
(c) 4.6% compounded quarterly
(d) 4.6% compounded monthly
(e) 4.6% compounded daily (ignore leap years)
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Construct a grammar over {a, b} whose language is {a mb n : 0 ≤ n ≤ m ≤ 3n}
To construct a grammar over {a, b} whose language is {a mb n : 0 ≤ n ≤ m ≤ 3n}, the following rules can be used: S → AB | BABA → aAb | aSb | bA | bB | AAB → aAb | aSb | bAS → In the above grammar rules, S is the starting symbol. Now, let's check if this grammar is fulfilling the given requirements or not. Let's start with the base condition i.e., n = 0If n = 0, then the language is {ε} and S → ε is a valid rule.
Next, let's check for n = 1If n = 1, the language is {a, ab} and A → a, B → b or A → aSb are valid rules for generating these strings. Now, let's check for n = 2If n = 2, the language is {aa, aab, abb, abbb} and the following rules are valid: A → aAbB → bBaS → AB or B |
Thus, all the strings can be generated using the above rules. Lastly, let's check for n = 3If n = 3, the language is {aaa, aaab, aabb, aabbb, abbb, abbbb, bbb, bbbb} and the following rules are valid:A → aAbB → bBaS → AB or B | Thus, all the strings can be generated using the above rules. Hence, the grammar over {a, b} whose language is {a mb n : 0 ≤ n ≤ m ≤ 3n} is S → AB | BABA → aAb | aSb | bA | bB | AAB → aAb | aSb | bAS.
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how will the volume of the pyramid change if each side is multiplied by a factor of one-half?
Answer:
I think it will be one eighth times the volume
Step-by-step explanation:
I can find the perimeter and area of the rectangle
Answer:
A = 72, P = 38
Step-by-step explanation:
Area can be found by getting the area of the overall figure, and then subtracting the blank space in the corner
12 * 7 = 84
3 * 4 = 12(invisible rectangle in top right)
84 - 12 = 72
Perimeter can be found by adding all of the sides
12 + 7 + (12-4) + 3 + 4 + (7-4)
The numbers in brackets are the unlabeled sides on the top and left.
Answer:
\(P=38\\ A=72\)
Step-by-step explanation:
To find the perimeter (P), add up all of the side lengths of the figure:
(numbers in parenthesis are the unlabeled values in the figure).
\(12+7+(8)+3+4+(4)=38\)
To find the area of the figure (A), multiply the length and width of the original rectangle \((12*7=84)\). Then, subtract this amount (84) minus the area of the missing rectangle in the top left corner \((4*3=12)\).
Subtract the required values: \(84-12=72\).
Therefore, the perimeter of the figure is 38 units, and the area of the figure is 72 units.
Which of the following describes the transformation from Figure 1 to Figure 2?
A statement which best describe the transformation from Figure 1 to Figure 2 is: C. reflection over the y-axis.
What is a reflection?In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.
In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the y-axis to the coordinates of figure 1, the coordinates of figure 2 include the following:
(x, y) → (-x, y)
Coordinate A = (-6, 5) → Coordinate A' = (-(-6), 5) = (6, 5).
Coordinate B = (-4, 5) → Coordinate B' = (-(-4), 5) = (4, 5).
Coordinate C = (-3, 5) → Coordinate C' = (-(-3), 5) = (3, 5).
Coordinate D = (-5, 4) → Coordinate D' = (-(-5), 4) = (5, 4).
Coordinate E = (-5, 3) → Coordinate E' = (-(-5), 3) = (5, 3).
Coordinate F = (-7, 3) → Coordinate F' = (-(-7), 3) = (7, 3).
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what are the numbers for h?
Answer:
0,1
2,2
4,3
6,4
Step-by-step explanation:
Some Examples
4 = 1/2 (6) + 1
4 = 3 + 1
4=4
----------
2 = 1/2 (2) + 1
2 = 1 + 1
2 = 2
h
0
2
4
6
...................
Use the graph of the parabola to fill in the table .
Using the given graph we can answer the questions:
a. The parabola opens upward.
b. The coordinates of the vertex, which is the point at the bottom of the parabola, are (2,1).
c. The equation of the axis of symmetry is x=2.
d. The y intercept is 5.
The graph has no x intercepts.
In Mrs. Nathan's class, there are 16 boys and 20 girls. What is the ratio of girls to boys in Mrs. Nathan's class?
Answer:
5:4
Step-by-step explanation:
In Mrs. Nathan's class, the ratio of girls to boys is 5:4.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, In Mrs. Nathan's class, there are 16 boys and 20 girls.
the ratio of girls to boys = 20/16
the ratio of girls to boys = 5/4
Therefore, the ratio of girls to boys in Mrs. Nathan's class is 5: 4.
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Liam invests $3,670 in a savings account at his local bank which gives 1.9% simple annual interest. He also invests $2,040 in an online savings account which gives 5.5% simple annual interest. After five years, which one will have earned more interest, and how much more interest will it have earned, to the nearest dollar?
Step-by-step explanation:
Given:
Investment P₁ = $3670Investment P₂ = $2040Rate of interest r₁ = 1.9% SIRate of interest r₂ = 5.5% SITime t = 5 yearsFind amount of interest in both investments:
I₁ = P₁r₁t = $3670*(1.9/100)*5 = $348.65I₂ = P₂r₂t = $2040*(5.5/100)*5 = $561.00As we see the online savings account earns more interest and the difference is:
$561.00 - $348.65 = $212.35 ≈ $2125. Mary ‘s hair was 8 inches long. In three months, it grew another inch at a steady rate. Assume that her hair growth continues at the same rate.
A. Make a table that shows Mary’s hair length for each of the three months and for the next three months.
B. Draw a graph showing the relationship between Mary’s hair length and time in months
Answer:
Here's the answer:
www.slader.com/discussion/question/mays-hair-was-8-inches-long-in-three-months-it-grew-another-inch-at-a-steady-rate-assume-that-her-ha/
Please help, my computer is about to die and this is due in a few minutes. Will mark brainlist if correct.
Answer:
x = 1.5
Step-by-step explanation:
Here, we want to solve for the value of x
By using the tangent from the same point theorem, we have it that;
lh^2 = lj * lk
1^2 = (0.5) * (0.5 + x)
1 = 0.5x + 0.25
1-0.25 = 0.5x
0.5x = 0.75
x = 0.75/0.5
x = 1.5
PLEASE HELP, SOLVE THIS PROBLEM AND GIVE ME THE ANSWER!!!
Answer:
B
Step-by-step explanation:
Recall that \((g \circ f)(x)=g(f(x))\). In other words, we need to find \(f(x)\) first and then put that value into \(g(x)\).
We need to find \((g \circ f)(4) =g(f(4))\)
\(f(x)=4x-2\\\)
\(f(4)=4(4)-2=14\)
\((g \circ f)(4) =g(f(4))=g(14)\)
\(g(x)=-6x^2-8x-8\)
\(g(14)=-6(14)^2-8(14)-8\)
\(g(14) = (g \circ f) (4) =-1296\)
Please help...Will give brainiest
Answer:
19.45
Step-by-step explanation:
The median is the middle number. Put the data in order from smallest to largest
16.3, 17.8,17.8 ,18.0, 18.7,19.3, 19.6,20.1,20.5, 21.9, 25.2 ,25.4
There are 12 pieces of data,
16.3, 17.8,17.8 ,18.0, 18.7,19.3, 19.6,20.1,20.5, 21.9, 25.2 ,25.4
The median lies between the 6th and 7th piece
Add the 6th and 7th together and divide by 2
(19.3+19.6)/2 =19.45
Answer:
\(\large \boxed{\mathrm{19.45}}\)
Step-by-step explanation:
Median of a data set is the middle value.
The data is to be arranged from smallest to largest.
16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4
Find the middle value.
16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4
Average the two middle numbers.
(19.3+19.6)/2 = 19.45
The median of the data set is 19.45.
Eliminate the parameter, t, in the parametric equations, x = 2cos(t) and y = 2sin(t).
A) 4 x2 + 4 y2 = 4
B) x2 + y2 = 2
C) 2 x2 + 2 y2 = 4
D) x2 + y2 = 4
Answer:
D: \(x^2+y^2 = 4\)
Step-by-step explanation:
Square each one, and add them together. Then collect 4 from both.
\(x^2 = 4 cos^2t; y^2 = 4sin^2 t \\x^2 + y^2 = 4( cos^2t+sin^2t) \rightarrow x^2+y^2=4\)
30) AB is tangent to OC. Find the value of d.
(a) 5
(b) 8
(c) 119
(d) 169
5
A
d
12
B
The value of d is 8 units.
Given is a setup of a circular wheel with radius AC of 5 units and a tangent AB of 12 units, we need to find the value of d,
We know that the tangents are perpendicular to the circle,
So, ΔCAB is a right triangle, using the Pythagoras theorem,
BC² = AB² + AC²
BC² = 5² + 12²
BC² = 169
BC = 13
d = 13-5
d = 8
Hence the value of d is 8 units.
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An article is marked to sell at Rs.1300;if 10% discount is allowed,find the discount amount and selling price.
Answer:
discount amount=Rs. 130
selling price=Rs. 1170
Step-by-step explanation:
discount amount=10%of Rs.1300
=10/100*1300
=1300/10
=Rs. 130
selling price=MRP-discount amount
=1300-130
=Rs. 1170
Write the ratio of the first measurement to the second measurement. Compare in millimeters Diameter of ball A: 33mm Diameter of ball B: 5.4 cm
Answer:
The ratio of first measurement to second measurement in millimeters is 11:18
Step-by-step explanation:
Given that:
Diameter of ball A = 33 mm
Diameter of ball B = 5.4 cm
1 cm = 10 mm
5.4 cm = 10*5.4 mm
5.4 cm = 54 mm
Ratio of diameter of ball A to diameter of ball B.
33 : 54
Simplifying the ratio
11 : 18
Hence,
The ratio of first measurement to second measurement in millimeters is 11:18
explain how you can find 3/8 of $800
Answer:
by adding 2 zeros after the 3 and 8 in 3/8
Answer:
turn the problem into 3/8 divided by 800/1. then reciprocal. which leave it at 3/8 x 1/800. cross cancel. 3/1 x 1/100 answer is 3/100 .
Natalie wants to use a sheet of fiberboard 30 inches long to create a skateboard ramp with a 28 angle of elevation from the ground
Answer:
You should raise one side 14 inches
Step-by-step explanation:
I used a right angle triangle calculater at this sight
https://www.calculator.net/right-triangle-calculator.html
An angle measures 33.4° more than the measure of its complementary angle. What is the measure of each angle?
Hey there!
Please remember that complementary angles add up to 90 degrees.
Let's set up an equation in order to find the 2 angles.Let the unknown angle be w.w+33.4=90
That's only half of our equation, because we have two angles.
So the right equation is
w+w+33.4=90
Add the w's:2w+33.4=90
Subtract 33.4 from both sides:2w=90-33.4
2w=56.6
Divide both sides by 2:w=28.3
Add 33.4:28.3+33.4=61.7
Add the angles together:61.7+28.3=90
It works! :-)
Hope everything is clear.
Let me know if you have any questions!
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Question 6 (4 points) Three people use the following procedure to divide a (perfectly divisible and homogenous) cake. Player 1 first divides the cake into two pieces. Next, player 2 selects one of the two pieces. Player 1 gets the other share, while player 2 must now divide the piece he or she picked. Finally, player 3 chooses one of the two pieces that player 2 just created, and player 2 consumes what remains. Suppose that each player cares only about the size of the piece of cake he or she ultimately obtains. Compute the subgame perfect Nash equilibrium (please provide complete strategies, not just the equilibrium payoffs).
The subgame perfect Nash equilibrium involves Player 1 receiving a piece that is no less than 1/4 of the original cake, Player 2 receiving a piece that is no less than 1/2 of the cake, and Player 3 receiving a piece that is no less than 1/4 of the cake. Player 2 obtains the largest piece at 1/2 of the cake, while Player 1 gets a share that is no less than 1/4 of the cake, which is larger than Player 3's share of the remaining cake.
The subgame perfect Nash equilibrium and complete strategies are as follows:
First subgame: Player 1 splits the cake into two pieces. Player 1 takes the smaller of the two pieces, while Player 2 takes the larger. Next, Player 2 divides the larger piece into two. Player 2 chooses the piece that is equal in size to the smaller piece of the initial division. Player 2 gives the other piece to Player 3, who must now select one of the two pieces. If Player 3 selects the smaller piece, Player 2 will obtain the larger of the two pieces that Player 2 divided, which is greater than or equal in size to the piece Player 2 gave to Player 3. As a result, Player 3 chooses the larger of the two pieces. Therefore, the subgame perfect Nash equilibrium involves Player 1 receiving a piece that is no less than 1/4 of the original cake, Player 2 receiving a piece that is no less than 1/2 of the cake, and Player 3 receiving a piece that is no less than 1/4 of the cake. Player 2 obtains the largest piece at 1/2 of the cake, while Player 1 gets a share that is no less than 1/4 of the cake, which is larger than Player 3's share of the remaining cake.Learn more about Nash equilibrium:
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what is the constent
2x^2 +4x + 5
A. 2x^2 B. 4x C. 5 D.2
Answer:
I couldn't fuigure out the answer but here is a link that may help
Link:
https://brazosport.edu/Assets/faculty/agut-ioana/intermediate-algebra/33.%20Solving%20Quadratic%20Equations.pdf
help plz help plz help
Answer:
What grade is this?
Step-by-step explanation:
Answer:
122-180=68
90+68+X=98
180-98=82
X=82
Step-by-step explanation:
hope this helps