So the area of the larger square is 900% of the area of the smaller square.
What is area?Area is a measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters (m²) or square feet (ft²). To find the area of a shape, you need to measure the length and width of the surface or region and then multiply those measurements together.
Here,
If the sides of a square are increased by a scale factor of 3, then the new square will have sides that are 3 times as long as the original square. The area of a square is proportional to the square of its sides, so the area of the new square will be 3² = 9 times as large as the area of the original square. Therefore, the area of the larger square is 900% of the area of the smaller square.
Alternatively, we can use the formula for the area of a square, A = s², where A is the area and s is the side length. If the side length is increased by a scale factor of 3, then the new side length is 3s. Therefore, the area of the new square is:
A' = (3s)²
= 9s²
The ratio of the area of the new square to the area of the original square is:
A' / A = (9s²) / (s²)
= 9
Multiplying by 100% to convert to a percentage, we get:
A' / A = 900%
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If the terminal point of 0 is (0, -1), what is tan 0?
A. Undefined
B. 1
C. -1
D. 0
The tangent function for the given terminal point is undefined.
The given terminal point of Θ is (0,-1). The tangent of an angle is defined as the quotient between the y-component and the x- component of the terminal point.
So, according to the question, tan Θ = -1/0. Hence, tan Θ is undefined as -1/0 is not defined.
Hence, tan Θ for the given function is not defined.
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7.003x10^-5 in standard form
Answer:
0.00007003 is the standard form of 7.003x10^-5. In scientific notation, the number is expressed as 7.003 multiplied by 10 raised to the power of negative five. To convert it to standard form, the decimal point has to move to the left by five places since the exponent is negative. The resulting number is a decimal with four zeros before the first nonzero digit. Standard form is a way of representing numbers that does not use exponents and is useful in comparing and performing operations on numbers.
use the standard normal distribution table to determine the percent of data less than
z= 1.67
The percent of the data less than Z = 1.67 is ?
Step-by-step explanation:
Look at the table for z = 1.67
You have the wrong table.......the table you posted is for negative z-scores
for z -score = + 1.67 , the value is .9535 = 95.35 %
PLEASE HELP!!
A cone has a radius of 3 inches and a slant height of 12 inches.
What is the exact surface area of a similar cone whose radius is 6 inches?
Enter your answer in the box.
Surface area of similar cone =
___in²
Surface area of similar cone is 44π square inches
What does a cone in maths ?
A cone is referred to as a "right cone" when its vertex is higher than the base's centre (i.e., when the angle formed by the vertex, base center, and any base radius is a right angle); otherwise, the word "oblique" is used. A cone is referred to as an elliptic cone when the base is assumed to be an ellipse rather than a circle.
The surface area of a cone is given by:
surface area = πr(r + l)
where r is the radius and l is the slant height.
surface area of original cone = π(3)(3 + 12) = 45π
slant height of similar cone = (6/3)(12) = 24 inches
surface area of similar cone = π(6)(6 + 18) = 144π
ratio of surface areas = surface area of similar cone / surface area of original cone
= (144π) / (45π)
= 3.2
Therefore, The exact surface area of the similar cone is 6 times the surface area of the original cone,
6 × 45π = 144π square inches
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A state's labor department conducted a study regarding the mean yearly earnings per household in the state. The department randomly selected 533 households in the state to be the sample. The population mean is $49,829.00. The department also found the standard deviation to be $933.00. What is the approximate standard error of the mean, assuming a 99.7% confidence level? 1.75 40.41 17.45 23.09
The approximate standard error of the mean, assuming a 99.7% confidence level is 40.41.
Given population mean (µ) = $49,829
population standard deviation (σ) = $933
the randomly selected households (n) = 533 households
the confidence level = 99.7%
To find the standard error of the mean at a 99.7% of confidence level, we will substitute the above values in the below equation,
Standard error of the mean = σ/√n = 933/√533 ≅ 40.41
From the above analysis, we can conclude that the standard error of the mean at a 99.7% confidence level is 40.41.
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Answer:
40.41
Step-by-step explanation:
Plato/Edmentum
Claude has a 10-pound package of hamburger meat and an
11.5-pound package of hamburger meat. Can he make the number of
hamburger patties shown? Choose Yes or No.
A. 87 1/4-pound hamburger patties
B. 45 1/2-pound hamburger patties
C. 30 1/2 -pound and 274-pound hamburger patties
D. 29 3/4 -pound hamburger patties
Answer: We can solve this problem by finding the total weight of the meat and then dividing by the weight of each patty to see if we can make the desired number of patties.
Let's add the weights of the two packages of meat:
10 + 11.5 = 21.5
For option A, we need 87 1/4-pound patties.
Each pound of meat will yield 4 patties of this size, so 21.5 pounds of meat will yield:
21.5 x 4 = 86 patties
Since we need 87 patties, Claude does not have enough meat for option A.
For option B, we need 45 1/2-pound patties.
Each pound of meat will yield 2 patties of this size, so 21.5 pounds of meat will yield:
21.5 x 2 = 43 patties
Since we need 45 patties, Claude does not have enough meat for option B.
For option C, we need 30 1/2-pound patties and 2 74-pound patties.
Each pound of meat will yield 2 patties of the smaller size and 1 patty of the larger size, so 21.5 pounds of meat will yield:
(21.5 x 2) + (2 x 1) = 43 + 2 = 45 patties
Since Claude only has 21.5 pounds of meat, he does not have enough for option C.
For option D, we need 29 3/4-pound patties.
Each pound of meat will yield 1.5 patties of this size, so 21.5 pounds of meat will yield:
21.5 x 1.5 = 32.25 patties
Since we only need 29.75 patties, Claude has enough meat for option D.
Therefore, the answer is Yes, Claude can make 29 3/4-pound hamburger patties.
A soccer ball is kicked in the air off a 27.0-meter high hill. The equation h(t) = -2t^2 + 4t + 27 gives the approximate height h, in meters, of the ball t in seconds after it is kicked. Does the ball reach a height of 40 m?
The ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.
To determine if the ball reaches a height of 40 meters, we can substitute h(t) = 40 into the equation and solve for t.
40 = -2t² + 4t + 27
Rearranging the terms, we get:
2t² - 4t - 13 = 0
We can solve for t using the quadratic formula:
t = [4 ± √(4² - 4(2)(-13))]/(2(2))
t = [4 ± √(176)]/4
t ≈ 3.38 or t ≈ -0.88
Since time cannot be negative, we can discard the negative solution. Therefore, the ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.
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a student score 80 on a test last week and 90 on thesame test this week. what is the percent increase in score
Answer:
12.5%
Step-by-step explanation:
We Know
A student scored 80 on a test last week and 90 on the same test this week.
What is the percent increase in the score?
We Tale
(90 ÷ 80) x 100 = 112.5%
Then we take
112.5 - 100 = 12.5%
So, the percent increase in score is 12.5%
Me González designed a ramp for his caras shown in the picture below
what is the volume of the ramp in cubic feet
The ramp has a volume capacity of around 37.5 cubic feet.
How to solveCalculating the volume of a triangular prism shaped ramp follows a specific formula. First, identify the shape and refer to the equation:
Volume = (1/2) * Base Area * Height
To begin, the base is always in a right-angled triangle form, where its area depends on its width denoted as W, and height noted specifically as H.
Based on these computations, knowing that its triangular base measures 5 feet at its length while taking its height equates 3 feet therefore assessing how much it covers can be found using:
Triangle Area = (1/2) * Base * Height
Substituting values into solving areas leads us to have an answer of over 7 square feet.
Next is computing the volume of the said triangular prism. Placing all given data results in the same formula:
Volume = (1/2) * Base Area * Height
With one-half of the product of both areas which resulted in 7.5 square feet and then multiplying the figure by 10 ft, this yields us an approximate volume of 37.5 cubic feet.
In conclusion, we have determined that the ramp has a volume capacity of around 37.5 cubic feet.
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Length (L) = 10 feet
Width (W) = 5 feet
Height (H) = 3 feet
Mr. González designed a ramp for his car with a length of 10 feet, a width of 5 feet, and a height of 3 feet. What is the volume of the ramp in cubic feet?
HELPPPPPPPPP GNG IM STURGGLING 100 POINTS
some the following equation
x^4+4x^3+3x^2=0
Answer:
x = 0, -1, -3
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor to equal zero.
a cylinder candle has a diameter of 9 cm and a height of 12 CM. It is placed in a cylindrical box. there's a space of 0.5 CM between the candle and the box to allow for packaging material. what is the height of the cylindrical box?
If a candle having diameter as 9 cm, height as 12 cm is placed in a cylindrical box, then the height of the cylindrical box will be 13cm.
The "cylindrical-candle" diameter is given as = 9 cm;
The "cylindrical-candle" height is given as = 12 cm;
The candle is placed in a box which has a space of 0.5 cm between the candle and the box for packaging material;
which means that, there will an additional 0.5 cm in the top and bottom of the candle,
So, the height of the "cylindrical-box" is written as : 0.5 + 12 + 0.5;
Therefore, the "cylindrical-box" has a height of 13 cm.
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find the inverse of f(x)=2^x+2
us the function odd, even, or neither?
Find the areas of the trapezoids.
Answer:
Area = ½* height(a+b)
Where;
a=4units
b=8units
h=6units
Therefore Area= ½*6(4+8)
= ½*6*12
=36sq.un
Answer:
24sq²
Step-by-step explanation:
Area = ( b1 + b2) x h
---------------------
2
Area = (8 + 4) x 6
---------------------
2
Area = (12) x 6
---------------------
2
A = 72/2
A = 36
A = 1/2 * b * h
A = (1/2) * 4 * 6
A = (1/2) * 24
A = 12
36 - 12 = 24sq²
I hope this helps!
The square on the right is a scaled copy of the square on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
The scale factor between a square of dimensions 7 by 7 and a scaled copy of dimensions 21/2 by 21/2 is 3/2 or 1.5.
We know that the dimensions of the square on the left are 7 by 7, and the dimensions of the square on the right are 21/2 by 21/2.
To find the scale factor, we can divide the dimensions of the square on the right by the dimensions of the square on the left
scale factor = (21/2) / 7
We can simplify this fraction by dividing both the numerator and the denominator by the greatest common factor, which is 7
scale factor = (21/2) / 7 = (21/2) * (1/7) = 3/2
Therefore, the scale factor is 3/2, or 1.5.
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. The students in a furniture-making class make a tabletop shaped like the figure shown. The tabletop has squares cut out of the corners. a. What is the area of the tabletop?
The area of the tabletop made by the students in the furniture - making class would be 26 ft ²
How to find the area ?We can see that this tabletop made by students in the furniture - making class takes the form of a composite shape with two smaller rectangles and one large rectangle.
The area of the large rectangle is:
= 4 ft x ( 1 + 3 + 1 )
= 4 ft x 5 ft
= 20 ft ²
The area of the two smaller rectangles is:
= 2 x ( 3 ft x 1 ft )
= 2 x 3
= 6 ft ²
The total area of the tabletop is:
= 20 + 6
= 26 ft ²
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helpppppp pleaseeeee
When -3 (row 1) is added to row 2, the result would be [ 1 - 4 | 8 ]
[ 0 10 | 10 ].
How to add the matrix ?The first thing to do is to multiply each element in row 1 by - 3 :
- 3 x 1 = - 3
- 3 x - 4 = 12
- 3 x 8 = - 24
Then, we need to add the result to the elements in row 2:
3 + ( - 3 ) = 0
- 2 + 12 = 10
10 + ( - 24 ) = - 14
The resulting matrix would therefore be:
[ 1 - 4 | 8 ]
[ 0 10 | - 14 ]
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Rectangle ABCD and A’B’C’D’ are similar.
a. What is the scale factor from ABCD to
A’B’C’D’?
b. What is the scale factor from A’B’C’D’ to
ABCD?
Where Rectangle ABCD and A’B’C’D’ are similar.
a. the scale factor from ABCD to A’B’C’D’ is 1/2
b. What is the scale factor from A’B’C’D’ to ABCD is 2
What is scale factor?In mathematics, a scale factor is the ratio of matching measurements of an item to a representation of that thing. The copy will be bigger if the scaling factor is a full number. The duplicate will be smaller if the scaling factor is a fraction.
When the scale factor is less than one, you are going from big to small. You are dilating negatively.
When you are going from small to big, you scale factor is reversed. In this case, we had 1/2 in a, in b it became 2/1 which = 2.
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Full Question:
Rectangle ABCD and A’B’C’D’ are similar.
a. What is the scale factor from ABCD to A’B’C’D’?
b. What is the scale factor from A’B’C’D’ to ABCD?
See attached image.
Are low elevation, high precipitation areas close or far from the ocean.
Answer:
low lying areas
James deposited $10,000 into an account that earns 5.5% compound interest, compounded semiannually. How much interest will James earn after 10 years?
Answer:
$17,204.28
Step-by-step explanation:
So first of all you want to start by finding what P, r and t would be.
P = Principal amount ($$)r = interest rate (%)t = time (years)Once I found all of those I put them into the equation (l = Prt) and solved (by putting it into a calculator obviously). That is how I came up with my answer. Check the screenshot provided to see what P, r and t would be and to see all my work! :)
Hope this helps! :)
Have a great day!
Pls help i rlly need help
Answer:
C. Luisa is incorrect, it's not 0. It's only zero when you get "x=0" as an answer but the variable x got canceled here. And as 3=3, it is a true statement so it includes all real numbers. If you had gotten 3=8 for example, it would be a fake statement, so then no solution.
And for the second part,
1. No solution
5x+24=5x+25
24=25
It's false
2. One solution
12p-7=-3p+8
15p=15
P=1
3. One solution.
3x+20=5x
20 = 2x
X = 10
where should the linear inequality y ≤ 1/4 x- 3 be shaded?
The required direction of the inequality is below the line.
How to find the direction of inequality in graph?If you're not graphing a vertical line, the inequality's sign will tell you which half-plane to shade. Shade above the line when using the or > sign. Shade below the line if the symbol or is used. Larger solutions are to the right and smaller solutions are to the left, respectively, for a vertical line.
According to question:To check the direction, we will take points from the graph and put in the given inequality.
At point (2, 0)
y ≤ x/4 - 3
0 ≤ 2/4 - 3
0 ≤ -25
It is false
Again
At (2, -4)
y ≤ x/4 - 3
-4 ≤ 2/4 - 3
-4 ≤ -2.5
It is true,
Thus, we can say the direction of the inequality is below the line.
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A music app has a shuffle play function.
This function allows songs to be played in a random order without repeat.
Gabriella puts songs A, B and C on shuffle play.
List all the possible orders of songs A, B and C.
One has been done for you.
ABC,
Answer:ABC(Done for you)
ACB
BAC
BCA
CAB
CBA
Step-by-step explanation:
Can someone please help with this question and break it down so I can learn a better way to do it.
Using trigonometry and the Pythagorean theorem, the length of the hypotenuse AC is found to be 3.5 cm, and using the Pythagorean theorem again, the length of BC is found to be approximately 1.75 cm.
Using trigonometry and the given angle and side length information, we can solve for the length of side BC (x).
We know that
sin(A) = opposite/hypotenuse
sin(30) = AC/7
AC = 7 × sin(30)
AC = 3.5 cm
Using the Pythagorean theorem, we have
BC² = AC² - AB²
BC² = (3.5)² - (7)² sin²(30)
BC² = 3.0625
BC = √3.0625
BC = 1.75 cm (rounded to two decimal places)
Therefore, the value of x is approximately 1.75 cm.
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Today's clients are ages 15, 72, 8, 89, 14, 16, 24, and 38. What is the range of the clients' ages?
Answer:
81
Step-by-step explanation:
The difference between the maximum and minimum values in a collection of data is known as the range. We must first determine the lowest and maximum values before we can determine the age range of the clients.
the minimum age is 8, and the maximum age is 89.
Therefore, the range of the clients' ages is:
Max age - Min age = 89 - 8 = 81
So the range of the clients' ages is 81.
What is the solution of x=9y and 3y - 3x =24
Answer:
Step-by-step explanation:
The solution to the system of equations `x=9y` and `3y - 3x =24` can be found by substituting the value of `x` from the first equation into the second equation. This gives us `3y - 3(9y) = 24`, which simplifies to `-24y = 24`. Solving for `y`, we get `y = -1`. Substituting this value of `y` into the first equation, we get `x = 9(-1) = -9`. So the solution to the system of equations is `(x,y) = (-9,-1)`.
Is there anything else you would like to know?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
[tex]f(0) = 6.2 \sqrt{4.5} + 18 = 31.2[/tex]
my bike tire has a radius of 12 inches how much distance will i cover after 50 rotations
Therefore , the solution of the given problem of unitary method comes out to be 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).
What is a unitary method?The well-known simple approach, real variables, and any crucial elements from the very initial And specialised inquiry can all be used to finish the work. Customers may then be given another chance to try the product in response. If not, significant impacts on our understanding of algorithms will vanish.
Here,
The circumference of the circle the bike tyre forms is equal to the distance travelled in one rotation of the tyre. The following formula determines a circle's circumference:
=> C = 2πr
where the mathematical constant is roughly equivalent to 3.14159 and r is the circle's radius.
Your bicycle tyre's radius in this instance is 12 inches. The tyre's circumference is as follows:
=> C = 2π(12) = 24π inches
You may easily calculate how far you will travel after 50 spins by multiplying the tyre's circumference by the number of turns:
=> Covered distance: 50 × 24π ≈ 376.99 inches
As a result, after 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).
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What rate of interest, to the nearest tenth of a percent, compounded quarterly is needed for an investment of $1600 to grow to $2400 in 11 years
Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by
[tex]A=P(1+r/n)^{nt}[/tex]
where P = Principal, r = annual rate of interest, n = the number of times interest is compounded per year & t = time in years.
The given principal is $1600 for 11 years & amount is $2400 compounded quarterly.
To find the rate of interest compounded quarterly for 11 years substitute the given values in the above formula i.e
[tex]2400=1600(1+r/4)^{11*4}[/tex]
r=3.70%.
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The ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1, 60), (2, 240), (3, 960), (4, 3840)}
What is the function equation in sequence notation?
ANSWER: 60(4)t−1
just took the test
Answer: w(t) = 60 * 4^(t-1).
Step-by-step explanation:
The given ordered pairs model an exponential function of the form w(t) = ab^t, where w is the function name, t is the input variable, a is the initial value, and b is the growth factor.
From the first ordered pair (1, 60), we can see that the initial value a is 60. From the second and third ordered pairs (2, 240) and (3, 960), we can see that the output value is multiplied by 4 when the input value increases by 1. This means that the growth factor b is 4.
So, the function equation in sequence notation is w(t) = 60 * 4^(t-1).
