When we can compare the simplified equation to the standard forms of the four main types of conic sections, we get that it has the form of an ellipse with its center at (3,6), a horizontal axis of length 2a = 4, and a vertical axis of length 2b = √(5/4)*4 = 2√5.
What are the standard forms of the four main types of conic sections?Circle: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is its radius.
Ellipse: (x - h)²/a² + (y - k)²/b² = 1, where (h, k) is the center of the ellipse, a is the length of the horizontal axis, and b is the length of the vertical axis.
Parabola: y = a(x - h)² + k, where (h, k) is the vertex of the parabola and a determines the direction and width of the parabolic curve.
Hyperbola: (x - h)²/a² - (y - k)²/b² = 1, where (h, k) is the center of the hyperbola. The distances between the center and each vertex on the horizontal axis and the vertical axis are denoted by the letters a and b, respectively.
The given equation is in the standard form of a conic section:
5(x − 3)² = 20 − 4(y − 6)²
To identify the type of conic section, we can simplify the equation by dividing both sides by 5:
(x − 3)² = 4 − (4/5)(y − 6)².
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A farmer wants to buy between 90 and 100 acres of land. He is interested in a rectangular piece of land that is 1,500 yards long and 300 yards wide. > The piece of land is being sold as one complete unit for $87,000. If the farmer does not want to spend more than $900 an acre, does the land meet all of his requirements?
According to the given scenario the rectangular piece of land, it doesn't meet all of his requirements, the amount of the land satisfied what needs, but the price is too large.
What about rectangular?
The term "rectangular" is used to describe something that has a shape or form that resembles a rectangle, which is a four-sided flat shape with four right angles, where opposite sides are equal in length. In other words, a rectangular object has two pairs of parallel sides that are perpendicular to each other, and all four of its angles measure 90 degrees. Some common examples of rectangular objects include sheets of paper, computer screens, windows, and many types of furniture such as tables and bookshelves.
According to the given information:
He is interested in a rectangular piece of land that is 1500 yards long and 300 yards wide, that means, 1500 x 3=4500ft and 300 x 3=900ft
Area= 4500*900=[tex]4050000ft^2[/tex] = 4050000/43560 = 92.97 acre =93 acre
The piece of land is being sold as one complete unit for $87,000
∴ So, 87000/93= $935.48 per acre.
∴ No, the amount of the land satisfied what ne needs, but the price is too large
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The U.S. forest service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal. Of these, 89 say Yes. We want to construct a 95% confidence interval to estimate the proportion of all visitors to Yellowstone who favor the proposal, with a margin of error of +/-3%. How many visitors must we sample?
a. 150 visitors
b. 1,030 visitors
c. 525 visitors
d. 268 visitors
e. 4,120 visitors
The number of visitors that we must sample to construct a 95% confidence interval is (b) 1,030 visitors.
In order to construct the 95% confidence interval with a margin of error of ±3%, we need to find the sample size that will give us a margin of error of 0.03 or less.
The formula used to find desired sample-size is :
⇒ n = (Z² × p × (1-p)) / (E²)
Where, n = required sample size
Z = Z-score for required level of confidence (1.96 for 95% confidence)
p = proportion of visitors who favor proposal;
E = margin of error = (0.03);
We don't know the value of p, So, we use the sample proportion as an estimate:
⇒ p' = 89/150 = 0.5933;
Substituting the values,
we get,
⇒ n = (1.96² × 0.5933 × (1-0.5933)) / (0.03²)
⇒ 1029.67 ≈ 1030.
Therefore, the number of visitors to sample is (b) 1,030 visitors.
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when performing bedside spirometry on a 35-year-old woman who is 5 feet 7 inches tall, you obtain a peak flow measurement of 2.3 l/sec. the best interpretation of this test result is?
The interpretation of a peak flow measurement obtained from bedside spirometry on a 35-year-old woman who is 5 feet 7 inches tall would suggest that her lung function is lower than what is predicted for her age and height, indicating some degree of airway obstruction or restriction.
To interpret the results of the spirometry test, we need to compare the obtained peak flow measurement to the predicted values based on the individual's age, height, gender, and race. This is because the normal lung function varies depending on these factors.
For instance, the predicted peak flow measurement for a 35-year-old woman who is 5 feet 7 inches tall is approximately 4.25 l/sec.
Therefore, an interpretation of the obtained peak flow measurement of 2.3 l/sec is that it is lower than the predicted value, indicating that the woman may have some degree of airway obstruction or restriction.
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What is the positive solution to the equation y=6x^2-54?
What is the negative solution to y=½x^2+x-12?
Since we are lοοking fοr a negative sοlutiοn, the answer is x = -6.
What is Equatiοn ?In mathematics, an equatiοn is a statement that twο expressiοns are equal. An equatiοn usually cοntains οne οr mοre variables, which are placehοlders fοr unknοwn values. The variables can be represented by letters, such as x, y, z, and sο οn.
Tο find the pοsitive sοlutiοn tο the equatiοn [tex]y=6x^2-54[/tex], we can set y tο 0 and sοlve fοr x as fοllοws:
[tex]0 = 6x^2 - 54[/tex]
Adding 54 tο bοth sides:
[tex]54 = 6x^2[/tex]
Dividing bοth sides by 6:
[tex]9 = x^2[/tex]
Taking the square rοοt οf bοth sides:
x = ±3
Since we are lοοking fοr a pοsitive sοlutiοn, the answer is x = 3.
Tο find the negative sοlutiοn tο the equatiοn [tex]y =\frac{1}{2}x^2+x-12[/tex], we can set y tο 0 and sοlve fοr x as fοllοws:
[tex]0 = \frac{1}{2}x^2 + x - 12[/tex]
Multiplying bοth sides by 2 tο get rid οf the fractiοn:
[tex]0 = x^2 + 2x - 24[/tex]
Factοring the left side:
0 = (x + 6)(x - 4)
Setting each factοr equal tο zerο and sοlving fοr x, we get:
x + 6 = 0 οr x - 4 = 0
x = -6 οr x = 4
Therefοre, Since we are lοοking fοr a negative sοlutiοn, the answer is x = -6.
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Jasper had a $10 bill. He spent $5.50 with tax on plants for his fish tank. He spent some more money on a pretty rock for his tank. After he paid, he had $2.21 in change. Write an expression that shows what Jasper spent and had left. Use x to stand for the money he spent on the rock.
Answer:
$10 -$5.50 -x = $2.21
if you want to solve for x do 10-5.50-2.21=x
:D
Two cakes and three-quarters of another cake were eaten at a party.
how do you write this amount as a fraction?
Answer:
[tex]2\frac{3}{4}[/tex]
Step-by-step explanation:
because 2 is whole
then 3/4 is just there
so we put them together
brainliest please
Answer:
Step-by-step explanation:
Why is it not possible to make a right triangle using lengths of 4 feet, 8 feet, and 10 feet?
A 7-pack of raffle tickets costs $6.58. What is the unit price?
Answer: 1.06 rounded
Step-by-step explanation:
7/6.58 = 1.06 rounded
Hope it helps I'm running out of time!!
Have a nice day!!!!
Pls help me with dis
Answer:
The Answers
Step-by-step explanation:
Flag = 46
Clover = 46
Hat = 27
Acorridan thing = 198
Final answer = 317
you made an impulsive life decision to apply as a food critic for and managed to get hired. the employer offers to pay you 0.00776 centi-dollars every 4 milli-seconds with all trips paid for as long as you give an honest review of all the food you try. how many dollars per hour are you making?
Therefore, you are making approximately 0.00003 dollars per hour as a food critic.
To calculate how many dollars per hour you will be making, you need to follow these steps: Convert the pay rate from centi-dollars per millisecond to dollars per hour and multiply the pay rate by the number of milliseconds in one hour (3,600,000) Round the answer to two decimal places
The formula to calculate the pay rate in dollars per hour is given as: Pay rate (dollars per hour) = (Pay rate (centi-dollars per millisecond) x 100 x 60 x 60 x 1000) / (1,000 x 1,000)As given, your pay rate is 0.00776 cent-dollars per 4 milliseconds. Pay rate (dollars per hour) = (0.00776 x 100 x 60 x 60 x 1000) / (1,000 x 1,000)
Pay rate (dollars per hour) = 0.000027936Pay rate (dollars per hour) ≈ 0.00003 (rounded to two decimal places)
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larry can make one batch of 3 cookies every 8 minutes. mary can make one batch of 5 cookies every 12 minutes. how long will it take them to make a combined total of 60 cookies?
The total time taken to make combined 60 cookies by Larry and Mary is equal to 75.79 minutes.
Rate at which each person can make cookies
Time to make one batch of 3 cookies made by Larry = 8 minutes
⇒Number of cookies per minute = 3/8 cookies
Time to make one batch of 5 cookies made by Mary = 12 minutes
⇒Number of cookies per minute = 5/12 cookies
Combined rate at which they make cookies,
= 3/8 + 5/12
= 9/24 + 10/24
= 19/24 cookies per minute
Together they can make 19/24 cookies per minute.
To make a total of 60 cookies,
Let 't' be the time in minutes required to make 60 cookies.
⇒ (19/24) t = 60
⇒ t = (60)/(19/24)
⇒ t = 75.79 minutes (rounded to two decimal places)
Therefore, total time taken by Larry and Mary approximately 75.79 minutes to make a combined total of 60 cookies.
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divide x^4+x^3+7x^2-6x+8 by x^2+2x+8 A) What is the remainder from this division?
By answering the presented question, we may conclude that Therefore, the remainder from this division is -12x - 48.
what is divide?Division is one of the four fundamental operations in mathematics, and it is the act of combining two numbers to create a new number. Other operations include addition, subtraction, and multiplication. Division is the inverse of multiplication. When you divide twelve into three equal parts, you get four in each group when you multiply three groups of four by twelve. The fundamental purpose of sharing is to identify how many equal groups exist when equitably sharing, or how many individuals belong to each group. To divide is to divide anything into two or more equal parts, such as classes, categories, groups, or subdivisions.
We can use long division to divide [tex]x^4 + x^3 + 7x^2 - 6x + 8 by x^2 + 2x + 8[/tex] as shown below:
[tex]x^2 + ( -2x + 3 )[/tex]
_____________________
[tex]x^2 + 2x + 8 | x^4 + x^3 + 7x^2 - 6x + 8[/tex]
[tex]- (x^4 + 2x^3 + 8x^2)[/tex]
-----------------------
[tex]-x^3 - x^2 - 6x[/tex]
[tex]+ ( -x^3 - 2x^2 - 8x)[/tex]
-----------------------
[tex]7x^2 + 2x + 8[/tex]
-[tex](7x^2 + 14x + 56)[/tex]
-----------------
[tex]-12x - 48[/tex]
Therefore, the remainder from this division is [tex]-12x - 48.[/tex]
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A rectangular prism measures 3 ft by 6ft by 5 ft. if the dimensions of the box were quadrupled, how would the surface area of the box change.
Answer:
The surface area would increase by a factor of 16.
Or you could also say:
Quadrupling the dimensions makes the surface area 16 times the original surface area.
Step-by-step explanation:
The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
In this case, the surface area of the original rectangular prism with dimensions 3 ft by 6 ft by 5 ft would be: 2(3)(6) + 2(3)(5) + 2(6)(5) = 36 + 30 + 60 = 126 square feet.
If the dimensions of the box were quadrupled, the new dimensions would be 12 ft by 24 ft by 20 ft. The new surface area would be: 2(12)(24) + 2(12)(20) + 2(24)(20) = 576 + 480 + 960 = 2016 square feet.
So, if the dimensions of the box were quadrupled, the surface area would increase from 126 square feet to 2016 square feet. This represents an increase in surface area by a factor of 16.
2. One of Kara's birthday balloons has a leak. The amount of air in the balloon can be modeled by the
function A(t) = 1.48 (0.87), where A(t) is the number of cubic feet of air in the balloon t seconds
after the leak begins.
a. According to the model, by what percentage is the balloon losing air each second?
Therefore, according to the model, the balloon is losing air at a rate of 13% per second.
What is function?In mathematics, a function is a rule that maps each element in one set, called the domain, to a unique element in another set, called the range. A function can be represented by an equation, a graph, or a table. Functions are commonly used to describe relationships between variables, such as how the area of a square changes as its side length increases. They are a fundamental concept in calculus, linear algebra, and many other branches of mathematics.
Here,
The function A(t) = 1.48(0.87)ⁿ represents the amount of air in the balloon t seconds after the leak begins.
To find the percentage at which the balloon is losing air each second, we need to find the percentage decrease in the amount of air for every one second of time passing.
To do this, we can calculate the ratio of the amount of air at time t=1 second to the amount of air at t=0 seconds, and then find the percentage decrease:
A(1) / A(0) = [1.48(0.87)¹] / [1.48(0.87)⁰] = 0.87
The ratio is 0.87, which means that the balloon is losing 13% of its air each second (since 1 - 0.87 = 0.13, which is 13% expressed as a decimal).
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1. What is the area of ABCD?
2.What is the length of diagonal BD?
Answer:
1. 28.88
2. 7.6
Step-by-step explanation: Not sure if these answers are correct, but this is what I got.
Step-by-step explanation:
so, I understand this is a rhombus, yes ?
I will base my answer on that assumption.
the area of a rhombus is
p×q/2
p, q being the diagonals.
so, all 4 sides are equally long (5 cm).
the angle(s) between the diagonals is (are) 90°.
opposing angles are equally sized (B = D, A = C), and they are split in half by the diagonals.
and always remember : the sum of all angles in a triangle is always 180°.
so,
b1 = b2 = d1 = 50°.
a1 = a2 = c1 = c2 = 180 - 90 - 50 = 40°.
law of cosine :
c² = a² + b² - 2ab×cos(C)
with c being the side opposite of angle C. a, b are the kthe 2 sides.
that applies to all 3 sides and angles.
BD² = 5² + 5² - 2×5×5×cos(c1 + c2) =
= 25 + 25 - 50×cos(80) = 50 - 50×cos(80) =
= 41.31759112....
BD = 6.427876097... cm ≈ 6.43 cm
AC² = 5² + 5² - 2×5×5×cos(b1 + b2) =
= 25 + 25 - 50×cos(100) = 50 - 50×cos(100) =
= 58.68240888...
AC = 7.660444431... cm ≈ 7.66 cm
the area of ABCD is a described
AC × BD / 2 = 24.62019383... cm² ≈ 24.62 cm²
An astronomer knows the distances from herself to stars AAA and BBB, as well as the distance between them. The distances are 450450450, 400400400, and 909090 light years (\text{l. Y. }l. Y. Start text, l, point, y, point, end text) respectively.
If the astronomer's telescope is currently pointed at star AAA, how many degrees must she rotate her telescope to see star BBB?
Do not round during your calculations. Round your final answer to the nearest degree
The astronomer must rotate her telescope 86.829° to see star BBB. Rounding to the nearest degree, the astronomer must rotate her telescope 87°.
We can use the law of cosines to solve this problem. The law of cosines states that for a triangle with sides A, B, and C, A2 = B2 + C2 - 2BCcos(θ), where θ is the angle opposite side C.
In our case, A = 450450450, B = 400400400, and C = 909090. We know that angle θ is the angle we need to find, so we can rearrange the equation to solve for θ.
θ = cos-1(A2 - B2 - C2)/(-2BC)
θ = cos-1((450450450)2 - (400400400)2 - (909090)2)/(-2(400400400)(909090))
θ = cos-1(-9.65 × 10-12)/(-2.8 × 1012)
θ = cos-1(-3.4 × 10-13)
θ = 86.829°
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six boys stood equally spaced on a circle of radius $40$ feet. each boy walked to all of the other non-adjacent persons on the circle, shook their hands and then returned to his original spot on the circle before the next boy started his trip to shake hands with all of the other non-adjacent boys on the circle. after all six boys had done this, what is the least distance in feet that could have been traveled? express your answer in simplest radical form.
The least distance traveled is [tex]$240\sqrt{3}$[/tex] feet.
Each boy shakes hands with the two boys who are not adjacent to him on the circle. Since there are six boys in total, each boy shakes hands with four other boys. We can represent these handshakes on a graph, where the six vertices represent the six boys and the edges represent the handshakes. Each vertex has degree 4, meaning that there are 12 edges in total.
To minimize the distance traveled, each boy should simply walk directly across the circle to shake hands with the two boys on the opposite side. This way, each boy walks a distance equal to the diameter of the circle, which is [tex]2 \times 40 = 80$ feet.[/tex]
Since there are six boys, the total distance traveled is [tex]6 \times 80 = 480$ feet[/tex]. However, we have counted each handshake twice, so we need to divide by 2 to get the total distance traveled. This gives us [tex]240$ feet.[/tex]
To express this answer in the simplest radical form, we can use the fact that an equilateral triangle with side length [tex]s$[/tex] has height [tex]s\sqrt{3}/2$[/tex]. The six handshakes form an equilateral triangle with side length 80, so its height is [tex]80\sqrt{3}/2 = 40\sqrt{3}$ feet[/tex]. Therefore, the total distance traveled is [tex]240\sqrt{3}$[/tex] feet.
Therefore, the correct answer is [tex]240\sqrt{3}$[/tex]feet.
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find the missing parts using trigonometry functions . round to the nearest tenth
The value of the leg x is 18. 36
What are trigonometric functions?Trigonometric functions are defined as those equalities that holds true for all the functions in a given equation.
The various types of trigonometric functions are;
sinecosinetangentcotangentsecantcosecantFor the identities, we have;
cos θ = opposite/adjacent
sin θ = opposite/hypotenuse
tan θ = opposite/adjacent
From the information given, we have;
Using the cosine identity, we get;
cos 57 = 10. 8/x
cross multiply the values
x = 10. 8/0. 5446
divide the values
x = 18. 36
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suppose that a highway is governed by a use fee charged to motorists that is based on congestion, operation and maintenance. the total traffic t is used to determine the cost of 5t2. what is the average cost per motorist?
The average cost per motorist on a highway governed by a use fee based on congestion, operation and maintenance is determined by dividing the total cost ([tex]5t^2[/tex]) by the total traffic (t). So, the average cost per motorist is 5t.
The average cost per motorist for a highway governed by a use fee based on congestion, operation and maintenance can be determined by dividing the total cost ([tex]5t^2[/tex]) by the total traffic (t).
So, the average cost per motorist is 5t.
To better understand how this works, let's look at an example.
Suppose the total traffic is 20.
In this case,
the total cost is 5 × 202 = 2000.
Therefore, the average cost per motorist is 2000/20 = 100.
The cost per motorist is determined by the total traffic because the more cars there are on the highway, the more congested the highway will be.
Consequently, the more congested the highway, the more operation and maintenance is required, and thus the higher the use fee will be.
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LET'S FIND THE QUOTIENTS!:
(4m² + 5m - 6 ) ( m + 2)
HELPPPPP!!!
Answer:
4[tex]m^{3}[/tex] +13m² + 4m - 12
Step-by-step explanation:
Use FOIL type method:
(4m^2 +5m - 6)(m+2)
= (4m^2)(m) + (5m)(m) - (6)(m) + (4m^2)(2) + (5m)(2) - (6)(2)
= 4m^3 +5m^2 +8m^2 -6m +10m -12
combine like terms:
= 4m^3 +13m^2 + 4m -12
A number, x, rounded to the nearest 10 is 630. Another number, y, rounded to the nearest 10 is 420. What are the lower and upper bounds of x + y?
The lower and upper bounds of x + y are 1040 and 1058, respectively.
What are lower bounds and upper bounds?
Lower bounds and upper bounds are used to define the range of possible values for a given quantity or measurement.
A lower bound represents the smallest possible value that a quantity could have, based on the available information or constraints. This means that the actual value of the quantity must be greater than or equal to the lower bound. For example, if we know that a person's height is between 150cm and 170cm, then the lower bound of their height is 150cm.
An upper bound represents the largest possible value that a quantity could have, based on the available information or constraints. This means that the actual value of the quantity must be less than or equal to the upper bound. For example, if we know that a person's weight is between 50kg and 80kg, then the upper bound of their weight is 80kg.
In some cases, we may be able to determine a range of possible values for a quantity using both a lower bound and an upper bound. This range of possible values is sometimes referred to as an interval or a confidence interval.
To find the lower and upper bounds of x + y, we need to consider the possible values of x and y that would result in the maximum and minimum values of their sum when added together.
Let's start by considering the possible values of x and y that would round to 630 and 420, respectively, when rounded to the nearest 10:
x: Any number between 625 and 634 would round to 630 when rounded to the nearest 10.
y: Any number between 415 and 424 would round to 420 when rounded to the nearest 10.
To find the lower bound of x + y, we need to add the smallest possible values of x and y:
Lower bound = 625 + 415 = 1040
To find the upper bound of x + y, we need to add the largest possible values of x and y:
Upper bound = 634 + 424 = 1058
Therefore, the lower and upper bounds of x + y are 1040 and 1058, respectively.
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what happens to the function y=3^x when x increases by 1
When x increases by 1 in the function y=3^x, the value of the function will be multiplied by 3.
How to determine what happens when x is increased by 1Given the function
y = 3^x
An increment in the value of x would make the expression be multiplied by 3
To see why this happens, we can compare the value of the function at x and x+1:
y(x+1) = 3^(x+1)
y(x+1) = 3^x * 3 (by the laws of exponents)
y(x+1) = 3 * 3^x
Therefore, we can see that when x increases by 1, the value of the function is multiplied by 3.
This means that the function grows very quickly as x increases.
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How do you do this?
A restaurant has 48 possible meals
that you can choose. A meal has a
I main course, a salad, and a dessert.
The menu lists 6 main courses and 2
salads. How many desserts are
available?
The answer is in the attached image below:
question 8 options: you want to develop a three-sigma -chart. you know the mean of the means is 30 and the average range is 5 based on several samples of size 10. what is the lcl of the -chart? round your answer to two decimal places.
As per the given average, the value of LCL is 20.49.
The average range is the average of the differences between consecutive samples. In your case, you have several samples of size 10, and the average range is 5. This means that on average, the range (maximum value minus minimum value) of each sample is 5.
The mean of the means is simply the average of all the sample means. In your case, the mean of the means is 30.
To calculate the LCL, you use the formula: LCL = mean of the means - 3 x average range / d2, where d2 is a constant that depends on the sample size. For a sample size of 10, d2 is 2.704.
Substituting the values, we get: LCL = 30 - 3 x 5 / 2.704 = 20.49
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Evaluate the expression for x = 5:
2 (x-2)² +5
Therefore, the value of the expression for x = 5 is 23 when the expression is 2*(x-2)² +5.
What is expression?An expression is a mathematical phrase that combines numbers, variables, and operations. Expressions can be simple or complex, and they can represent quantities or relationships between quantities. Expressions can be evaluated by substituting values for the variables, simplifying the operations, and obtaining a numerical result. Some expressions can be simplified or factorized using algebraic rules and techniques.
Here,
To evaluate the expression for x=5, we substitute 5 for x and simplify:
=2(x - 2)² + 5
= 2(5 - 2)² + 5 (substitute x = 5)
= 2(3)² + 5 (simplify inside the parentheses)
= 2(9) + 5 (square 3)
= 18 + 5 (multiply 2 by 9 and add 5)
= 23 (add 18 and 5)
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the side length of a cube is 2y. express the volume of the cube in y.
Answer:
The cube's volume can be represented as 8y^3 when expressed in terms of y.
Step-by-step explanation:
The side length of a cube is given as 2y. To express the volume of the cube in y, we can use the formula for the volume of a cube which is given as V = s^3, where s is the length of one side of the cube.
Substituting 2y as the length of the side of the cube, we get:
V = (2y)^3
Simplifying, we get:
V = 8y^3
Therefore, the volume of the cube expressed in terms of y is 8y^3.
What is the area of the carpet shown below?
Answer:
54.28 ft²
Step-by-step explanation:
A = LW + (1/2)πr²
r = d/2 = 4 ft / 2 = 2 ft
A = (12 ft)(4 ft) + (1/2)(3.14)(2 ft)²
A = 54.28 ft²
Answer:
54.28 ft²
Step-by-step explanation:
That is the answer
A rectangle has an area of 60 square feet. What are all the possible whole number dimensions of the rectangle
Answer:
The possible whole number dimensions of the rectangle are: 1 ft by 60 ft, 2 ft by 30 ft, 3 ft by 20 ft, 4 ft by 15 ft, 5 ft by 12 ft, and 6 ft by 10 ft.
Step-by-step explanation:
If a rectangle has an area of 60 square feet, we can find its possible dimensions by listing all pairs of factors of 60. A factor of a number is a positive integer that divides the number evenly without leaving a remainder.
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
To find all possible whole number dimensions, we need to pair up these factors. For example, the dimensions could be 1 ft by 60 ft, or 2 ft by 30 ft. We can continue pairing up the factors until we have listed all possible combinations:
1 ft by 60 ft
2 ft by 30 ft
3 ft by 20 ft
4 ft by 15 ft
5 ft by 12 ft
6 ft by 10 ft
Therefore, the possible whole number dimensions of the rectangle are: 1 ft by 60 ft, 2 ft by 30 ft, 3 ft by 20 ft, 4 ft by 15 ft, 5 ft by 12 ft, and 6 ft by 10 ft.
Step-by-step explanation:
Factors of 60
1 X 60 ft
2 30
3 20
4 15
5 12
6 X 10
all of these are dimensions of a possible rectangle of 60 ft^2
PLEASE HELP ASAP THANKS
First, you need to find the slope.
m= [tex]\frac{rise}{run}[/tex] = [tex]\frac{y2 -y1}{x2-x1}[/tex]
slope: m= 1/2x
Next, find the y-intercept.
Y-Intercept: 1/2
y=mx+b
Equation: y= 1/2x+1/2
The y-intercept is the point on the y-axis. When you're graphing, you need to graph the y-intercept first. Then graph the slope.
Hope this helps!
Please help me! A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability? Explain please.
The letter (D) O, is the experimental probability closest to the theoretical probability.
What is experimental probability?A probability that has been established by a series of tests is called an experimental probability.
To ascertain their possibility, a random experiment is conducted and iterated over a number of times; each iteration is referred to as a trial.
The goal of the experiment is to determine the likelihood that an event will occur or not.
The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
So, if there are 15 of each letter, the likelihood of each letter occurring should be equal.
Each letter has a probability of getting drawn of 15/75 or 1/5 because there are a total of 75 balls and 5 letters that can be drawn.
This indicates that a theoretical frequency of 1250/5 = 250 would be expected, i.e., each letter should be drawn 250 times, indicating that the solution is D.
Therefore, the letter (D) O, is the experimental probability closest to the theoretical probability.
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Complete question:
A game has 15 balls for each of the letters B, I, N, G, and O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I . 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability?
A. I
B. N
C. G
D. O
Mixed in a drawer are 8 blue socks, 8 white socks, and 2 gray socks. You pull out two socks, one at a time, without looking. Find the probability of getting 2 socks of the same color The probability of getting 2 socks of the same color is
The probability of getting 2 socks of the same color isP(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks)= 28/153 + 28/153 + 1/153= 57/153 = 19/51. Hence, the required probability is 19/51.
The probability of getting 2 socks of the same color is given by P(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks).Given, There are 8 blue socks. There are 8 white socks. There are 2 gray socks. Now, we will find the probability of getting 2 blue socks: Probability of selecting one blue sock from 8 blue socks is 8/18.
Probability of selecting another blue sock from 7 blue socks is 7/17.Probability of getting 2 blue socks is P(2 blue socks) = 8/18 * 7/17 = 28/153. Now, we will find the probability of getting 2 white socks: Probability of selecting one white sock from 8 white socks is 8/18.Probability of selecting another white sock from 7 white socks is 7/17.Probability of getting 2 white socks is P(2 white socks) = 8/18 * 7/17 = 28/153.
Now, we will find the probability of getting 2 gray socks: Probability of selecting one gray sock from 2 gray socks is 2/18.Probability of selecting another gray sock from 1 gray sock is 1/17.Probability of getting 2 gray socks is P(2 gray socks) = 2/18 * 1/17 = 1/153.
Therefore,The probability of getting 2 socks of the same color isP(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks)= 28/153 + 28/153 + 1/153= 57/153 = 19/51. Hence, the required probability is 19/51.
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