Answer:
The statements A,C,F,G and H are true.
Step-by-step explanation:
It is given that the radius of circle before dilation is [tex]\frac{1}{2}ft[/tex] and the scale factor is 8.
The circumference of original circle is,
[tex]S_1=2\pi r[/tex]
[tex]S_1=2\pi \times \frac{1}{2}=\pi[/tex]
The area of original circle is,
[tex]A_1=\pi r^2[/tex]
[tex]A_1=\pi (\frac{1}{2})^2[/tex]
[tex]A_1=\frac{\pi}{4}[/tex]
The dilation by scale factor 8 means the radius of new circle is 8 times of the original circle.
[tex]r=8\times \frac{1}{2}[/tex]
Therefore the radius of new circle is 4 ft and the statement A is true.
The circumference of original circle is,
[tex]S_2=2\pi r[/tex]
[tex]S_2=2\pi \times 4=8\pi[/tex]
[tex]\frac{S_2}{S_1}=\frac{8\pi}{\pi} =8[/tex]
The new circumference will be 8 times the original circumference. The statement C is true.
The area of original circle is,
[tex]A_2=\pi r^2[/tex]
[tex]A_2=\pi (4)^2[/tex]
[tex]A_2=16\pi[/tex]
[tex]\frac{A_2}{A_1}=\frac{16\pi}{\frac{\pi}{4}}=64[/tex]
The new area will be 64 times the original area. Therefore statement F is true.
The new circumference will [tex]8\pi[/tex],The new area will be [tex]16\pi[/tex] square feet.
A 5-foot ladder is leaning against a 4-foot wall. How far must the bottom of the ladder be from the base of the wall so that the top of the ladder rests on the top of the wall?
PLEASE HELP?? EASY 5 POINTS!!! The two models shown have the same volume. Complete the equation and expression below about the volume of each figure.
making use of Archimedes’s Principle, displacements, and buoyancy, explain why some objects float on water, but others do not.
Answer:
If the weight is equal to the buoyant force, it will float. The same is true for if the weight is less than the buoyant force. However, if the weight is greater than the buoyant force, it will sink.
Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (3x + 1) / (x + 1)^3(x^2 + 8)^2
Armando has a baseball card that is worth $45. The value of the card is increasing at a rate of 1.5% per year. How much will the card be worth in 15 years?
An open rectangular box has volume 32 cm3. find the lengths of the edges giving the minimum surface area
An open rectangular box with a volume of 32 cm³ would have its minimum surface area when it takes the form of a cube. In this case, each side of the box would be approximately 3.174 cm.
Explanation:To minimize the surface area of an open rectangular box given a constant volume, the box should take the shape of a cube. This is because a cube is the three-dimensional shape that has the minimum surface area for a given volume. The volume V of the box is given as 32 cm³. Since for a cube, the volume V = a³ where a is the side length of the cube, we need to find the value of a such that the volume is equal to 32cm³.
To do this, we use the cube root function as follows: a = ∛V = ∛32 = 3.174 cm.
So, for a rectangular box with a volume of 32 cm³, the lengths of the edges that would give the minimum surface area would all be approximately 3.174 cm.
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An open rectangular box with a volume of 32 cm³ would have its minimum surface area when it takes the form of a cube.
In this case, each side of the box would be approximately 3.174 cm.
To minimize the surface area of an open rectangular box given a constant volume, the box should take the shape of a cube.
This is because a cube is the 3-dimensional shape that has the minimum surface area for a given volume.
The volume V of the box is given as 32 cm³.
Since for a cube, the volume V = a³ where a is the side length of the cube, we need to find the value of a such that the volume is equal to 32cm³.
To do this, we use the cube root function as follows:
a = ∛V
= ∛32
= 3.174 cm.
So, for a rectangular box with a volume of 32 cm³, the lengths of the edges that would give the minimum surface area would all be approximately 3.174 cm.
John's goal is to have more than -7 dollars in his bank account by the end of the month. The variable d is the number of dollars in John's bank account at the end of the month. Write an inequality in terms of d that is true only if John meets his monthly goal.
Answer:
d > - 7
Step-by-step explanation:
Here, d represents the number of dollars in John's bank account at the end of the month.
As per statement,
In John's account,
The balance must be more than -7 dollars,
That is, Number of dollars at the end of each month > - 7 ( '>' is used for more than )
⇒ d > - 7
Which is the required inequality.
EASY 5 POINTS!!! You have a new pool and want to know its volume. The pool is 5 feet deep and has a radius of 7 feet. About how much water can the pool hold? Use 3.14 for pi.
Answer:
The volume of water that can be hold by the pool is approximately 770 cubic feet.
Step-by-step explanation:
To calculate it we have to use the volume formula for a cylinder. This is:
[tex]Volume=pi*r^{2}*h\\pi=3.14\\r=radius\\h=deep[/tex]
Solving the equation with the given values:
[tex]Volume=3.14*7^{2} *5\\Volume=769.3 cubic feet \\Aprox.Volume= 770 cubic feet[/tex]
The volume of water that can be hold by the pool is approximately 770 cubic feet.
How many different three digit numbers can be written using digits 1,2,3,4,5 without any repeating digits? Thank you.
We can use the principles of permutation to find out that there are 60 different three-digit numbers that could be formed using the digits 1,2,3,4,5 without repetition.
Explanation:In order to find out how many different three-digit numbers can be formed using the digits 1,2,3,4,5 without repetition, we use the principles of permutation. Firstly, we should determine how many options we have for each digit place in the three-digit number.
There are 5 possible digits for the first place (since none has been used yet).There are 4 remaining digits for the second place.Finally, there are only 3 digits left to fill the third place.We then multiply these options together (5 x 4 x 3) which equals to 60 different three-digit numbers.
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can someone please explain proportions?
How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between x=1 and x=b is equal to 240?
Lori rented a car for one day. The daily rental rate was $12.50 plus 25 cents per mile. The total cost of her rental was $46. How many miles did she drive that day?
The answers 80kg, 88 divided by 110 then times by 100
The student is completing a two-step mathematical operation to find a percentage by dividing 88 by 110 and then multiplying the result by 100. The '80kg' mention seems to be unrelated. Without more context, it's difficult to relate this to the given references, though they involve calculations and conversions in physics.
Explanation:The student seems to be performing a two-step operation where they are first dividing 88 by 110 and then multiplying it by 100. This is a common way of finding percentages. To get the result first, divide 88 by 110 which equals 0.8. Secondly, multiply 0.8 by 100 to get 80%. The '80kg' seems irrelevant to this operation if no further context is provided, it could be a weight measurement in physics.
In terms of any associations with the provided references, it seems that the question might be related to converting some measurements or calculating kinetic energy ('K'). However, without additional information, it's hard to ascertain the exact nature of the task.
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Which expression is the greatest common factor (GCF) of the terms of trinomial 12x^7y^9 + 6x^4y^7 - 10x^3y^5
Answer: 2. [tex]\mathbf{2x^3y^5}[/tex]
Step-by-step explanation:
Greatest common factor of any two or more expression is the largest common expression that divides them.The given expression : [tex]12x^7y^9 + 6x^4y^7 - 10x^3y^5[/tex]
Term 1 : [tex]12x^7y^9[/tex]
Term 2 : [tex]6x^4y^7[/tex]
Term 3: [tex]- 10x^3y^5[/tex]
Lowest power of x = 3
Thus , The highest common power of x = [tex]x^3[/tex] (i)
Lowest power of y = 5
The highest common power of y =[tex]y^5[/tex] (ii)
Greatest common factor of 12, 6 , -10= 2 [Because 2 is the largest number that divides all of them] (iii)
From (i) , (ii) , (iii) , we have
Greatest common expression : [tex]2x^3y^5[/tex]
Hence, the correct answer is 2. [tex]\mathbf{2x^3y^5}[/tex]
The product of (n^2-6n+3)and -4 is
A basketball player makes 39% of her shots from the free throw line. suppose that each of her shots can be considered independent and that she takes 5 shots. let x = the number of shots that she makes. what is the standard deviation for x?
Answer: 1.09
Step-by-step explanation:
Given : A basketball player makes 39% of her shots from the free throw line.
i.e. Proportion of her shots from the free throw line: p= 0.39
We assume that each of her shots can be considered independent .
She takes 5 shots.
i.e. Number of trials : n= 5
Let x = the number of shots that she makes.
Then , the standard deviation for x will be :-
[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{5(0.39)(1-0.39)}\\\\=\sqrt{1.1895}=1.09064201276\approx1.09064201276\approx1.09[/tex]
Hence, the standard deviation for x= 1.09
Final answer:
The standard deviation for the number of shots made by a basketball player who has a 39% success rate and takes 5 shots is approximately 1.09 shots, calculated using the binomial distribution formula.
Explanation:
To find the standard deviation for the number of shots made by a basketball player who makes 39% of her shots, we use the concept of a binomial distribution.
Given that each shot is independent and that she takes 5 shots, with x representing the number of shots made, we can calculate the standard deviation using the formula for a binomial distribution.
The formula for the standard deviation (σ) in a binomial distribution is σ = √[n × p × (1 - p)], where n is the number of trials (in this case, 5 shots), and p is the success probability per trial (in this case, 0.39 for making a shot).
Plugging in the values, we get σ = √[5 × 0.39 × (1 - 0.39)] = √[5 × 0.39 × 0.61] = √[1.1885] ≈ 1.09 shots.
Therefore, the standard deviation for the number of shots made is approximately 1.09 shots.
The data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique. Which of the numbers below is the best measure of the central tendency of the data? {3, 3, 4, 4, 4, 5, 5, 5, 5, 30}
Plastic storage bins are designed so they can be nested. The picture shows how each one fits inside another, leaving only the top part showing. The 4 stacked 10-gallon bins shown here measure 29 inches high. The height of the stack grows at the rate of 4 inches for each added bin. Write an equation in the form y = mx + b to describe the relationship between x, the number of nested bins, and y, the height of the stack.
Which of the following is not one of the three ways to express ratio A 3/4 B 3:4 C 3 of 4 D 3 to 4
The length of a spring is a linear function of the weight of the object compressing it. For a particular spring, the length decreases by 1.5 inches for every 3 pounds pressing down on it. When 4 pounds are on the spring, the length of the spring is 8 inches long. What is the length of the spring if 15 pounds are pressing down on the spring?
You and two friends (Adam and Alana) will only play a game if it is fair for all three of you. The game your friend has proposed is to roll two number cubes (numbered 1-6) and find the sum. If the sum. If the sum is from 1-4 you get the point, 5-8 Adam gets the point, and 9-12 Alana gets the point.
Yes, the game was fair and no one had a better advantage.
Answer:
yes!
Step-by-step explanation:
no one had a better advantage.everyone had the same amount of advantage.
The ratio of the length of an airplane wing to its width is 9 to 1. If the length of a wing is 40.4 meters, how wide must it be?
The table shows how an elevator 500 feet above the ground is descending at a steady rate. Which equation represents the height, h(t), of the elevator in feet, as a function of t, the number of seconds during which it has been descending? h(t) = 5t + 500 h(t) = 5t – 500 h(t) = –5t + 500 h(t) = –5t – 500
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – x = 25
5.52, –4.52
is the correct answer,never forget negatives!
Find the circumference and the area of a circle with diameter
2ft
The circumference of a circle with diameter 2ft is 2π ft and the area is π ft².
Explanation:To find the circumference of a circle, you can use the formula C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 2ft, so the circumference would be C = π(2) = 2π ft. To find the area of a circle, you can use the formula A = πr², where A is the area and r is the radius. Since the radius is half the diameter, the radius would be 2ft/2 = 1ft. Therefore, the area would be A = π(1)² = π ft².
Final answer:
The circumference of a circle with a diameter of 2 feet is approximately 6.28 feet, and the area is approximately 3.14 square feet using the formulas C = πd and A = πr².
Explanation:
To find the circumference and the area of a circle with a diameter of 2 feet, we can use the formulas for circumference and area. The diameter of the circle is given as 2 feet. Therefore, the radius (r) is half of the diameter, which is 1 foot.
The formula for the circumference of a circle is C = πd where C is the circumference, π (pi) is approximately 3.14159, and d is the diameter. Since the diameter (d) is 2 feet, the circumference is:
C = π × 2 feet ≈ 3.14159 × 2 feet ≈ 6.28318 feet
So the circumference is approximately 6.28 feet.
The formula for the area of a circle is A = πr² where A is the area and r is the radius of the circle. Using the radius 1 foot, we find the area as follows:
A = π × (1 foot)² ≈ 3.14159 × 1 foot × 1 foot ≈ 3.14159 square feet
So the area of the circle is approximately 3.14 square feet.
An apartment has 1026 square feet of carpeting. How much is this in square meters? Use the following conversion: 1 square meter is 10.8 square feet.
Evaluate the line integral where f(x,y,z)=3sin(x)i−(cos(y))j−5xzk and c is given by the vector function r(t)=t5i−t4j+t3kr(t)=t5i−t4j+t3k , 0≤t≤10≤t≤1.
Write a function rule for the table. (2, $16.00), (4, $32.00), (6, $48.00), (8, $64.00)
If f(x) = 5x – 6, what is the equation for f–1(x)?
Answer:
5x-2+^3 hole
Step-by-step explanation:
The inverse of f(X) = (x +6 ) /5
What is inverse function?The inverse of a function f is denoted by f^-1 and it exists only when f is both one-one and onto function. Note that f^-1 is NOT the reciprocal of f. The composition of the function f and the reciprocal function f-1 gives the domain value of x.
(f o f^-1) (x) = (f^-1 o f) (x) = x
Steps To Find An Inverse FunctionThe following sequence of steps would help in conveniently finding the inverse of a function. Here we consider a function f(x) = ax + b, and aim at finding the inverse of this function through the following steps.
For the given function f(x) = ax + b, replace f(x) = y, to obtain y = ax + b.Interchange the x with y and the y with x in the function y = ax + b to obtain x = ay + b.Here solve the expression x = ay + b for y. And we obtain y = (x - b/aFinally replace y = f^-1(x), and we have f^-1(x) = (x - b)/a.Given:
f(x) = 5x – 6
let y= f(x) = 5x – 6
Now, Interchange the x with y and the y with x.
x= 5y -6
x+6 = 5y
y = (x +6 ) /5
So, f^-1(x) = (x +6 ) /5
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HELP PLEASE
Evaluate the expression.
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
v ⋅ w
a) -41
b) <-20, -36, 15>
c) <-28, 18, -35>
d) -9
Answer:
v . w = <-20, -36, 15>
Step-by-step explanation:
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
To find the dot product of vectors we multiply the numbers
We need to multiply v and w
vectors is in the form of <x,y,z>
Multiply all the x values
4 times -5= -20
6 times -6 = -36
-5 times -3 = 15
So v . w = <-20, -36, 15>