The calculated age of the sample is 2865 years. Since this is less than 5,000 years, the scientist's hypothesis that the tree bark is over 5,000 years old is incorrect.
To determine if the scientist's hypothesis is correct, we can use the concept of half-life and the given information.
The half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the original amount of carbon-14 in a sample would have decayed.
In this case, the fossilized tree bark is thought to be over 5,000 years old. If the sample contains 75% of the original amount of carbon-14, it means that 25% of the carbon-14 has decayed.
Let's calculate the number of half-lives that have passed:
(100% - 75%) / 50% = 0.25 / 0.5 = 0.5
So, 0.5 half-lives have passed.
Since each half-life is 5730 years, we can calculate the approximate age of the sample:
0.5 half-lives × 5730 years per half-life = 2865 years
The calculated age of the sample is 2865 years. Since this is less than 5,000 years, the scientist's hypothesis that the tree bark is over 5,000 years old is incorrect.
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Instead of multiplying a number by 1/4, I multiplied it by 1/8 and got 2. What was I originally supposed to get as a result?
PLS HELP ME!!
A circular hot spring has a diameter of 110 meters. Over time, the diameter
of the spring decreases by 3 meters. By how many square meters does the
area of the hot spring decrease? PLEASEE IM BEGGING ANSWER ;(
Answer:
Step-by-step explanation:
Hello!
We want to know the area of the original circle - the now circle.
The original circle's diameter is 110 meters.
To figure out the area you use this formula: [tex]r^2*pi[/tex]
The diameter is 107 meters, so the equation is [tex]55^2[/tex][tex]*\pi[/tex].
The area is about 9503.3 meters.
The next area is the "now circle".
The now circle's diameter is 107 meters.
When you use this formula, you end up with [tex]53.5^2*\pi[/tex].
The area is about 8892 meters.
So it's just basic subtraction!
I'll let you figure out the rest.
:)
Michelle was fishing in her canoe at point A in the lake depicted
above. After trying to fish there, she decided to paddle due east
at a steady speed of 10 miles per hour. As she paddled, a wind
blowing due south at 5 miles per hour caused a change in her
direction. To the nearest tenth of a mile, what is the velocity,
represented by vector AC, of her canoe?
A 8.6 miles per hour
B 10 miles per hour
11.2 miles per hour
D 17.2 miles per hour
The velocity represented by vector AC of Michelle's canoe is approximately option C. 11.2 miles per hour.
How did we get the value?To determine the velocity, represented by vector AC, of Michelle's canoe, use the concept of vector addition.
Break down the motion into its components:
1. Paddling due east at 10 miles per hour: This motion can be represented by a vector pointing in the positive x-direction with a magnitude of 10 mph.
2. Wind blowing due south at 5 miles per hour: This motion can be represented by a vector pointing in the negative y-direction with a magnitude of 5 mph.
To find the resultant velocity, add these two vectors. Using the Pythagorean theorem, calculate the magnitude of the resultant velocity:
AC² = AB² + BC²
AB (paddling east) = 10 mph
BC (wind blowing south) = -5 mph (negative sign due to opposite direction)
AC² = (10 mph)² + (-5 mph)²
AC² = 100 mph² + 25 mph²
AC² = 125 mph²
Taking the square root of both sides:
AC ≈ √(125) mph
AC ≈ 11.2 mph (rounded to the nearest tenth)
Therefore, the velocity represented by vector AC of Michelle's canoe is approximately 11.2 miles per hour.
The correct answer is option C: 11.2 miles per hour.
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From the diagram below, given the side lengths marked, and if we know that < C is congruent to < E, we can say that
If we know that <C is congruent to <E, we can say that: (a). the two triangles are similar by SAS.
How to complete the statementfrom the question, we have the following parameters that can be used in our computation:
The triangles (see attachment)
Two triangles are similar when the ratio of their corresponding sides are equal and their corresponding angles are congruent.
So, we have
Ratio = BC/AC = 6/3 = 2.
Ratio = FE/DE = 4/2 = 2.
Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.
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7. These triangles are similar. Find the area of the smaller
triangle to the nearest whole number.
105 ft²
16 ft
12 ft
Answer
79 ft²
59 ft²
49 ft²
89 ft²
The area of smaller triangle is 59 square feet.
The area of the larger triangle is 105 square feet.
And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.
Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.
Since, the corresponding edges of similar triangles are proportional.
Therefore, y/x=16/12
y=4/3x
Also, the area of larger triangle is 105 square feet.
1/2×4/3x×16=105
The above equation can be written as
1/2×4/3x×4/3×12=105
1/2×x×12=59
Area of smaller triangle = 59 square feet
Hence, the area of smaller triangle is 59 square feet.
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What is the median of 2,4,6,8 and 10
Answer:
The median is the middle value in the set. Since there are 5 values in this set, the middle value is the third value, which is 6.
Therefore, the median of the set {2, 4, 6, 8, 10} is 6.
Select the correct answer. Which value of x from the set [4, 5, 6, 7), makes this equation true? 4(8-x) = 8 OB. 5 OC. OD. 7 C. 6
Answer:
6
Step-by-step explanation:
The correct answer is C. 6.
If we substitute 6 for x in the equation, we get 4(8-6) = 4(2) = 8.
This is the only value of x that makes the equation true.
Applying the General Multiplication Rule A box contains four red balls and eight black balls. Two balls are randomly chosen from the box, and are not replaced. Let event B be choosing a black ball first and event R be choosing a red ball second. What are the following probabilities? P(B) = P(R | B) = P(B ∩ R) = The probability that the first ball chosen is black and the second ball chosen is red is about percent.
The probability that the first ball chosen is black and the second ball chosen is red is 24.24%
How do i determine the probability?First, we shall obtain the total balls present in the box. Details below:
Red ball (R) = 4Black ball (B) = 8Total ball =?Total ball = 4 + 8
Total ball = 12 balls
Next, we shall obtain the probability of chosen a black ball first. Details below:
Black ball (B) = 8Total ball = 12 ballsProbability of chosen a black ball first, P(B) =?P(B) = n(B) / n(T)
P(B) = 8 / 12
Next, we shall obtain the probability of chosen red as the 2nd ball. Details below:
Red ball (R) = 4Total pen = 11Probability of chosen red as the 2nd ball, P(R | B) =?P(R | B)= n(R) / n(T)
P(R | B) = 4 / 11
Finally, we shall obtain the probability that the first ball chosen is black and the second ball chosen is red. Details below:
Probability of chosen a black ball first, P(B) = 8 / 12Probability of chosen red as the 2nd ball, P(R | B) = 3 / 11Probability that the 1st ball is black and the 2nd is red, P(B ∩ R) =?P(B ∩ R) = [P(B) × P(R | B)] × 100
P(B ∩ R) = [(8 / 12) × (3 / 11)] × 100
P(B ∩ R) = 0.2424 × 100
P(B ∩ R) = 24.24%
Thus, the probability that the first ball chosen is black and the second ball chosen is red is 24.24%
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Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4.4 in. Each of the triangular faces has a base of 4.4 in and a height of 3.8 in. How much paper would it take to cover the entire pyramid?
52.8 square inches of paper to cover the entire Pyramid.
The amount of paper needed to cover the entire pyramid, we need to determine the total surface area of the pyramid.
The pyramid consists of a square base and four triangular faces.
1. Base Surface Area:
The surface area of the square base can be calculated by finding the area of a square with sides measuring 4.4 inches. The formula for the area of a square is side length squared:
Base Surface Area = (4.4 in)² = 19.36 in²
2. Triangular Faces Surface Area:
Each triangular face of the pyramid has a base of 4.4 inches and a height of 3.8 inches. The formula for the area of a triangle is 1/2 times the base times the height:
Triangular Face Surface Area = 1/2 * (4.4 in) * (3.8 in) = 8.36 in²
Since the pyramid has four triangular faces, the total surface area of the triangular faces is:
Total Triangular Faces Surface Area = 4 * (8.36 in²) = 33.44 in²
3. Total Surface Area:
To calculate the total surface area of the pyramid, we add the base surface area to the total triangular faces surface area:
Total Surface Area = Base Surface Area + Total Triangular Faces Surface Area
= 19.36 in² + 33.44 in²
= 52.8 in²
Therefore, it would take approximately 52.8 square inches of paper to cover the entire pyramid.
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Name two other positive angles of rotation that take A to B. Explain your reasoning
The two other positive angles of rotation that take Point A to Point B on the unit circle is (5π/6) and (5π/6) + 2π .
Given data ,
To find two other positive angles of rotation that take Point A to Point B, we need to consider the angle values that yield the same coordinates as (1, 0) after rotating counterclockwise.
The position of Point A is (1, 0) on the unit circle.
Now, let's find the coordinates of Point B after rotating (7π/6) radians counterclockwise.
To rotate counterclockwise by (7π/6) radians, we can subtract (7π/6) from the angle of Point A. So, the angle for Point B would be:
Angle of Point B = 0 - (7π/6) = - (7π/6)
Now , for positive angles of rotation, we can add multiples of 2π to the angle of Point B while keeping the same coordinates. Adding 2π to the angle gives us:
Angle of Point B = - (7π/6) + 2π = (5π/6)
Hence , two other positive angles of rotation that take Point A to Point B are (5π/6) and (5π/6) + 2π. Both of these angles yield the same coordinates as Point B, which is (1, 0) on the unit circle.
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Which country is directly east of the Atlantic Ocean?
NEED HELP ASAP WILL GIVE BRAINLIEST HELP!
Consecutive Interior Angles.
They are on the same side of a line that cuts through two other lines.
A conveyor belt carries supplies from the first floor to the second floor which is 23 feet higher. The belt makes a 60-degree angle with the ground.
How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot.
PLEASE no spam!!
Answer:
caculations below
Step-by-step explanation:
A conveyor belt carries supplies from the first floor to the second floor which is 23 feet higher. The belt makes a 60-degree angle with the ground.
To calculate the distance traveled by the supplies from one end of the conveyor belt to the other, we can use the trigonometric function of sine.
sin(60) = opposite / hypotenuse
Here, the opposite side is the height difference between the two floors, which is 23 feet.
sin(60) = 23 / hypotenuse
To find the hypotenuse, we can rearrange the above equation:
hypotenuse = 23 / sin(60)
Using a calculator, we get:
hypotenuse = 26.5 feet
Therefore, the supplies travel approximately 26.5 feet from one end of the conveyor belt to the other.
Rounding the answer to the nearest foot, we get:
The supplies travel approximately 27 feet from one end of the conveyor belt to the other.
Let f(x)
(4-x-x²
2x - 1
lim
2+1
Use a graph to determine the following limits. Enter DNE if the limit does not exist.
lim
2-1
f(x) =
f(x)
if x ≤ 1
if x > 1
lim f(x)
z 1
Answer:
See below for answers and explanations
Step-by-step explanation:
[tex]\displaystyle \lim_{x\rightarrow1^{-}}f(x) = 4-(1)-(1)^2=4-1-1=3-1=2\\\\\lim_{x\rightarrow1^{+}}f(x) = 2(1)-1=2-1=1\\\\\lim_{x\rightarrow1}f(x) = DNE[/tex]
Note that [tex]\displaystyle \lim_{x\rightarrow1^-}f(x)[/tex] represents the left-side limit (so the limit of f(x) as x approaches 1 from the left), and [tex]\displaystyle \lim_{x\rightarrow1^+}f(x)[/tex] represents the right-side limit (so the limit of f(x) as x approaches 1 from the right)
Because [tex]\displaystyle \lim_{x\rightarrow1^-}f(x)\neq\displaystyle \lim_{x\rightarrow1^+}f(x)[/tex], then [tex]\displaystyle \lim_{x\rightarrow1}f(x)=DNE[/tex]
I hope this helped!
Match the point in slope, given to the corresponding equation of a line
(3,6) and slope =1/2
(2,1) and slope =1/3
(4,-2) and slope = -2
(-2,8) and slope = 1
(-4,3) and slope = -1/2
Using the slope-intercept form, the equation of the lines are
a. 2y = x + 9
b. 3y = x + 1
c. y = x - 6
d. y = x + 10
e. y = -1/2x + 1
What are the equation of line?In the given question, we have the coordinate of a point and the slope of the line.
To determine the equation of the straight line, we have to use the formula of slope-intercept which is given as; y = mx + c.
Plugging the values into the formula.
a. (3, 6) and slope = 1/2
equation of line = y = mx + c = 6 = 1/2(3) + c
6 = 3/2 + c
c = 9/2
The equation of line is y = 1/2x + 9/2 ; 2y = x + 9
b. The point is (2,1) and slope is 1/3
Equation of line is;
y = mx + c
1 = 1/3(2) + c
c = 1 - 2/3
c = 1/3
Equation of line is y = 1/3x + 1/3; 3y = x + 1
c. The point is (4, -2) and slope is 1
y = mx + c
-2 = 1(4) + c
c = -2 - 4 = -6
y = x - 6
d. The point is (-2, 8) and slope is 1
y = mx + c
8 = 1(-2) + c
c = 10
y = x + 10
e. The point is (-4, 3) and slope is -1/2
y = mx + c
3 = -1/2(-4) + c
3 = 2 + c
c = 1
y = -1/2x + 1
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3 siblings reported how long they worked out at the gym. Write the names of the siblings from shortest to longest time.
The names of the siblings from shortest to longest time are:
Rafael= 75min = 1 hour and 15 minutes.
Leanne= 1 hour and 25 minutes
Ray= 1 3/4 = 1 hour and 45 minutes.
What is the time about?To be able to compare 1 hour and 25 minutes with 1 3/4 (1.75 hours), one need convert the minutes to hours. 1 hour is equal to 60 minutes, so 1 hour and 25 minutes is equivalent to 1.42 hours.
1.42 hours is smaller than 1.75 hours. hence Ray has the longest time.
So according to the given information, note that:
Rafael: Rafael took 75 minutes, and it is equal to 1 hour and 15 minutes.Leanne: Leanne took 1 hour and 25 minutes. This is longer than Rafael's but it is shorter than Ray's time.Ray: Ray took 1 hour and 45 minutes. So, it is the longest time among the three siblings.Hence, the siblings' names listed from shortest to longest time are Rafael, Leanne, and Ray.
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Direction: Read each item carefully. Encircle the best answer from the given
choices.
1. What is A U B; if A = {<, +, =, x) and B = {=, +, /, >}
A. {<, +, =, X}
C. {<, +, =, x, /, >}
B. (=, +, /, >}
D. {<, +, =, x, =, +, /, >}
2. What is An M; if A = {1, 2, 4) and M = {2, 3, 5}?
A. {1}
C. (3)
B. (2)
D. (4)
3. What is Bn C; if B = {C, O, U, G, H) and C = {F, E, V, E, R)
C. (F, E, V, E, R}
A. {}
B. (C,O,U,G,H}
D. (C, O, U, G, H, F, E, V, E, R}
4. What is M - J; if M = {soap, alcohol, sanitizer, mask) and J = {alcohol,
sanitizer, mask, gloves}?
A. {alcohol)
C. {mask}
B. (gloves)
D. (soap}
5. What is complement of set A if U = {Frontliners, sacrifice, their, lives, to,
combat, coronavirus) and B = {Frontliners, sacrifice, their, lives)
A. (Frontliners)
C. (to, combat, coronavirus}
1) The value of A ∪ B is,
A ∪ B = {<, +, =, /, >, x }
2) The value of A ∩ M is,
A ∩ B = {2}
3) The value of B ∩ C is,
B ∩ C = { }
4) The value of M - J is,
M - J = {soap}
5) The complement of set A is,
A' = (to, combat, coronavirus}
Now, WE can simplify as;
1) We have;
A = {<, +, =, x) and B = {=, +, /, >}
Hence, We get;
The value of A ∪ B is,
A ∪ B = {<, +, =, /, >, x }
2) Given that,
A = {1, 2, 4) and M = {2, 3, 5}
Hence, The value of A ∩ M is,
A ∩ B = {2}
3) Given that;
B = {C, O, U, G, H) and C = {F, E, V, E, R)
Hence, The value of B ∩ C is,
B ∩ C = { }
4) Given that;
M = {soap, alcohol, sanitizer, mask) and J = {alcohol, sanitizer, mask, gloves}
Hence, The value of M - J is,
M - J = {soap}
5) Given that;
U = {Frontliners, sacrifice, their, lives, to, combat, coronavirus) and A = {Frontliners, sacrifice, their, lives)
Hence The complement of set A is,
A' = U - A
A' = (to, combat, coronavirus}
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Find the values of x with the answers in simplest radical form
The value of x with the answers in simplest radical form is 18.
We are given that;
The right triangles with dimension
Now,
The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
1. 14^2+14^2=x^2
196+196=x^2
x^2=392
x=19.7
2. x^2+X^2=12^2
2x^2=144
x^2=72
x=8.48
3. 9[tex](\sqrt{2} )^2[/tex]+9[tex]\sqrt{2})^2[/tex]=x^2
162+162=x^2
324=x^2
x=18
Therefore, by pythagoras theorem the answer will be 18.
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write an explicit formula for an the nth term of the sequence 40, 33, 26
Answer:
[tex]a_{n}[/tex] = - 7n + 47
Step-by-step explanation:
there is a common difference between consecutive terms , that is
33 - 40 = 26 - 33 = - 7
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 40 and d = - 7 , then
[tex]a_{n}[/tex] = 40 - 7(n - 1) = 40 - 7n + 7 = - 7n + 47
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rewrite the fractions 2/3 and 4/15 as fraction with least common denominator
Answer: To rewrite the fractions 2/3 and 4/15 with the least common denominator (LCD), we need to find the smallest multiple that both denominators, 3 and 15, divide into evenly.
The prime factorization of 3 is 3, and the prime factorization of 15 is 3 * 5.
To find the LCD, we take the highest power of each prime factor that appears in either denominator. In this case, the highest power of 3 is 3, and the highest power of 5 is 5.
The LCD is the product of these highest powers: LCD = 3 * 5 = 15.
Now, we can rewrite the fractions with the least common denominator:
2/3 = (2/3) * (5/5) = 10/15
4/15 = (4/15) * (1/1) = 4/15
Therefore, the fractions 2/3 and 4/15 can be rewritten with the least common denominator as 10/15 and 4/15, respectively.
Step-by-step explanation:
The three steps below were used to find the value of the expression [(-10 + 2) - 1] + (2 + 3). Step 1: ? Step 2: -9 + 2 + 3 Step 3: -7 + 3 Which expression is missing from Step 1? Question 3 options: [-10 + -1 + 2] + (2 + 3) [-8 - 1] + (2 + 3) [-10 + 1] + (2 + 3) [8 + 1] + (2 + 3)
Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).
In order to find the missing expression in Step 1, let's analyze the given steps and the final expression.
Step 1: ?
Step 2: -9 + 2 + 3
Step 3: -7 + 3
To find the missing expression in Step 1, we need to work backwards from Step 3 to Step 1.
In Step 3, the expression "-7 + 3" gives us a result of -4.
In Step 2, the expression "-9 + 2 + 3" gives us a result of -4.
So, the missing expression in Step 1 should also evaluate to -4 when performed correctly.
Let's check the available options:
[-10 + -1 + 2] + (2 + 3) = -11 + 2 + 5 = -4
[-8 - 1] + (2 + 3) = -9 + 5 = -4
[-10 + 1] + (2 + 3) = -9 + 5 = -4
[8 + 1] + (2 + 3) = 9 + 5 = 14
Out of the given options, only option 2, [-8 - 1] + (2 + 3), correctly evaluates to -4. Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).
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two rectangles have the same base lengths. one rectangle has a height that is twice the height of the other rectangle. are the heights and areas proportional
Although the rectangles have the same base lengths, the heights and areas are not directly proportional in this case.
Are the heights and areas of the rectangles proportional?Let's denote the base length of both rectangles as 'b'. If one rectangle has a height that is twice the height of the other rectangle, we can denote the heights as 'h' and '2h', respectively.
The area of a rectangle is calculated by multiplying the base length by the height. Therefore, the area of the first rectangle with height 'h' would be A₁ = b * h, and the area of the second rectangle with height '2h' would be A₂ = b * (2h) = 2b * h.
Comparing the two areas, we have A₁ = b * h and A₂ = 2b * h. It is evident that the areas are not proportional because the area of the second rectangle is twice the area of the first rectangle.
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Determine the voltage dropped on R3, given:
ET = 1325 V, R1 = 76 Ω, R2 = 61 Ω, R3 = 30 Ω, and R4 = 30 Ω
The voltage drop across resistor R₃ is determined as 237.9 V.
What is the total current flowing in the circuit?
The total current flowing in the circuit is calculated by applying Ohm's law as shown below.
V = IR
I = V / R
where;
V is the total voltage in the circuitR is the total resistance of the circuitSince the circuit is in series connection, the total resistance is calculated as follows;
R = R₁ + R₂ + R₃
R = 76 ohms + 61 ohms + 30 ohms
R = 167 ohms
The current flowing in each circuit component is calculated as;
I = V/R
I = 1325 V / 167Ω
I = 7.93 A
The voltage drop across R₃ is calculated as follows;
V₃ = IR₃
V₃ = 7.93 x 30
V₃ = 237.9 V
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The complete question is below:
This cirucit is in series. Determine the voltage dropped on R3, given:
ET = 1325 V, R1 = 76 Ω, R2 = 61 Ω, R3 = 30 Ω, and R4 = 30 Ω
Need help asap
Robin's teacher asked her to find a box that would hold some small
1 inch cubes that the kindergartners used for counting. Robin
found three boxes with the following dimensions: Box A: 4" x 6" x
8" Box B: 6" x 3" x 12" Box C: 6" x 6" x 4" Which box would be
able to hold all the cubes if Robin's teacher had 200 cubes? Box
Volume of Box A =
cu.in.
Volume of Box C =
cu.in. Volume of Box B =
30 pts
cu.in.
The box that would be able to hold all the cubes if Robin's teacher had 200 cubes is given as follows:
Box B.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:
Volume = length x width x height.
Hence the volumes for each box in this problem are given as follows:
Box A: 4 x 6 x 8 = 192 cubic inches.Box B: 6 x 3 x 12 = 216 cubic inches.Box C: 6 x 6 x 4 = 144 cubic inches.As 216 > 144, Box B is the box that could hold all of the 200 cubes.
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In the figure below, S is the center of the circle. Suppose that JK = 20, LM = 3x + 2, SN = 12, and SP = 12. Find the
following.
Length of JN = 10
x = 6
Given ,
S is the center of the circle.
JK = 20
LM = 3x + 2
SN = 12
SP = 12
Now ,
SN and SP are perpendicular to the chords JK and LM respectively .
Perpendiculars drawn from the center of circle to the chords bisect chords into two equal halves .
Thus,
JN = JK/2
JN = 10
Now join SJ,
In ΔSJN ,
Apply pythagoras theorem,
SN² + NJ² = SJ²
12² + 10² = SJ²
SJ = 14.52
SJ =Radius of the circle .
Now,
LP = LM/2
LP = 1.5x + 1
Now join SL,
In ΔSLP
SP² + PL² = SL²
SL = SJ (radius of circle)
So,
12² + (1.5x + 1)² = 244
x = 6
Hence the value of x is 6 and JN is 10 .
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Brian cut of 25% of a stick which was 1.6 meters long what percent of the stick is remaining
Answer:
The remaining is 75%, the length of the stick would be 1.2
Step-by-step explanation:
According to the information given,
We know that Brian cut off 25% of a stick which was 1.6 meters long
and 1.6 is the 100% of the stick:
It is fairly easy to calculate this, subtract 25 from 100 ( 100 - 25 ), which is equal to 75.
Hence, the answer is 75% and 1.2 for the remaining length of the stick
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The frequency table shows the results of a survey about favorite exhibits. Find the relative frequency that a randomly selected student's favourite exhibit was either dinosaurs, or planets, express your answer as a decimal.
Butterfly: 12
Dinosaurs: 25
Planets: 17
Trains: 6
The relative frequency that a randomly selected student's favorite exhibit was either dinosaurs, or planets is 0.7.
How do we find the relative frequency?To find the relative frequency, we will divide the number of students who chose dinosaurs or planets by the total number of students surveyed.
The total number of students surveyed is 12 + 25 + 17 + 6 = 60.
The number of students who chose dinosaurs or planets is 25 + 17 = 42.
Therefore, the relative frequency will then be 42 / 60 = 0.7.
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you have two rocks made of the same material the same temperature. The first rock has twice the mass of the second rock. How does the thermal energy of the two rocks comare
The thermal energy of the first rock is twice the Thermal energy of the second rock.
The thermal energy of an object is directly proportional to its mass. Therefore, if the first rock has twice the mass of the second rock, it will also have twice the thermal energy.
Thermal energy is a measure of the internal energy of an object, which includes the kinetic energy of its particles. In this case, since both rocks are made of the same material and are at the same temperature, we can assume that their particles have the same average kinetic energy per particle.
The thermal energy of an object can be calculated using the formula:
Thermal energy = Mass * Specific heat capacity * Change in temperature
Since the specific heat capacity and the change in temperature are the same for both rocks (as they are made of the same material and are at the same temperature), we can simplify the comparison of their thermal energies based on mass alone.
Let's denote the mass of the second rock as "m" (arbitrary unit). Since the first rock has twice the mass, its mass can be represented as "2m".
Therefore, the thermal energy of the first rock is:
Thermal energy of the first rock = (2m) * Specific heat capacity * Change in temperature
And the thermal energy of the second rock is:
Thermal energy of the second rock = m * Specific heat capacity * Change in temperature
Comparing the thermal energies:
Thermal energy of the first rock / Thermal energy of the second rock = (2m) * Specific heat capacity * Change in temperature / (m) * Specific heat capacity * Change in temperature
The specific heat capacity and the change in temperature cancel out, leaving us with:
Thermal energy of the first rock / Thermal energy of the second rock = 2m / m = 2
Therefore, the thermal energy of the first rock is twice the thermal energy of the second rock.
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Helpppolll ILL GIVE BRSINLYIST ANYTHIBG.
17 in.
8 in.
7
17 in.
30 in.
What is the volume of this figure?
15 in.
The volume of the given figure is 750 in.
Given
Base =30in
Height = 8in
Side = 15
Side = 17
Required to calculate the volume of the given figure
Volume = Base x Height + 2 side x side (there are two rectangle)
= 30 x 8 + 2 x 15 x 17
= 750
The region that a 2D shape covers in an area versus the space a 3D shape occupies is the main distinction between area and volume. Geometry is filled with a wide variety of shapes and sizes.
A mass is a solid body or an assortment of distinguishable visual components that together make a solid form, such as lines, colors, textures, etc. Length, width, and depth make up the three dimensions of volume.
Thus, the volume of the given figure is 750.
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