Answer:
2. 5/4
Step-by-step explanation:
The constant of proportionality in this proportional relationship is the ratio of y to x for any given pair of values. To find it, we can divide the y value by the x value for one of the pairs. For example, using the first pair (x = 2, y = 5/2), we can divide 5/2 by 2 to get the constant of proportionality:
(5/2) / 2 = 5/4
On average, the earth is 93 million miles away from the center of the sun.
A) Assuming that the earth's orbit is circular, estimate the number of miles our planet travels in one complete revolution around the sun.
B) The complete revolution around the sun takes 1 year. How fast is the earth moving in this orbit in feet per second?
step by step please
Step-by-step explanation: A) The number of miles the earth travels in one complete revolution around the sun can be estimated using the circumference of the circular orbit.
Circumference = 2 * π * radius
Since the average distance from the earth to the sun is 93 million miles, this is the radius of the circular orbit:
Circumference = 2 * π * 93 million miles
Simplifying, we get:
Circumference = 186 million * π miles
So the number of miles the earth travels in one complete revolution is approximately 186 million * π miles.
B) To find the speed of the earth in feet per second, we need to divide the total distance by the time it takes to travel that distance.
The complete revolution takes 1 year, or 365.25 days. So the time it takes to travel the distance is 365.25 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 31,536,000 seconds.
Speed = Total distance / Time
Speed = 186 million * π miles / 31,536,000 seconds
We can convert miles to feet:
Speed = 186 million * π * 5280 feet/mile / 31,536,000 seconds
So the speed of the earth in its orbit around the sun is approximately 66,600 feet per second.
Answer:
A) One complete revolution around the sun is equal to the circumference of a circle with radius 93 million miles. The circumference of a circle with radius r is given by 2πr, so the circumference of the earth's orbit is 2π * 93 million = 186 million miles * π.
B) To convert this distance to feet per second, we first need to convert miles to feet (1 mile = 5280 feet). The distance the earth travels in one complete revolution is 186 million miles * 5280 feet/mile = 979,680,000,000 feet. If this distance is travelled in one year, then the speed of the earth in feet per second is 979,680,000,000 feet / (365 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute) = 66,620 feet/second.
what is the average value of the function y=x sinx on the interval [0,3pi/2]
The average value of a function over the interval to be -π/4 + C/3π.
In this case, we need to calculate the average value of y=xsin(x) over the interval [0,3π/2]. To calculate this, we must first calculate the integral of the function over the interval. This is done by finding the antiderivative of the function and then evaluating the antiderivative at the upper and lower limits of the interval. The antiderivative of the function is -cos(x) + sin(x)x + C. Evaluating this at the lower and upper limits of the interval, we get 0-0 + 0 + C = C. To calculate the average value of the function, we divide the integral by the length of the interval. The length of the interval is 3π/2, so the average value of the function over the interval is the integral divided by 3π/2. Evaluating the integral, we get -cos(3π/2) + sin(3π/2)(3π/2) + C. Substituting in the values, we get -(-1) + 1(3π/2) + C = -π/2 + C. Finally, dividing this by 3π/2, we get the average value of the function over the interval to be -π/4 + C/3π.
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92% of what number is 345
Answer:
375
Step-by-step explanation:
Formula+ Number x 100/percent= 345x100/92=375
2 questions to answer. Solve each of the following inequalities, 1. [tex]\frac{10q+9}{2}[/tex] ≤ \frac{3}{8}[/tex] 2. [tex]\frac{5(-5s-1)}{6}[/tex] > - [tex]\frac{9}{5}[/tex] ( negative 9 over 5) representing each solution on a number line.
Answer:
To solve the inequality ≤ \frac{3}{8}, we need to find all the values of x that will make the inequality true. We can start by setting the inequality equal to zero and solving for x.
x ≤ \frac{3}{8}
To graph the solution on a number line, we can use an open circle at \frac{3}{8} to indicate that the value is not included in the solution. So the solution set is: (-∞,3/8)
To solve the inequality > -\frac{9}{5}, we need to find all the values of x that will make the inequality true. We can start by setting the inequality equal to zero and solving for x.
x > -\frac{9}{5}
To graph the solution on a number line, we can use an open circle at -\frac{9}{5} to indicate that the value is not included in the solution. So the solution set is: (-9/5, ∞)
Step-by-step explanation:
The balcony of an apartment is 4 feet wide by 7 feet long. on a scale drawing of the apartment, the balcony is 0.8 inch wide by 1.4 inches long, and the kitchen is 2.4 inches wide by 2.8 inches long. what is the actual width of the kitchen? enter your answer in the box. the actual width of the kitchen is___feet.
Answer:
The actual dimensions of the kitchen are 12 feet by 14 feet
Step-by-step explanation:
The kitchen's real measurements are 12 feet by 14 feet.
Detailed explanation:
4 / 0.8 = 5, 7 / 1.4 = 5. The actual drawing ratio is a 5:1 ratio.
Consequently, 2.4 inches multiplied by 5 is 12 feet and 2.8 inches multiplied by 5 equals 14 feet.
12 ft. x 14 ft.
ORFind the scale of the drawing
[tex]\frac{0.8}{4} \frac{in}{ft.} = \frac{1.4}{7} = 0.2 \frac{in}{ft.}[/tex]
To determine the precise dimensions subtract 0.2 from the measurements on the scale illustration to get 12 feet (2.4/0.2).
2.8/0.2 = 14 ft
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Marisa has just won a contest. She must decide between two prize options:
Option A: Collect a lump-sum payment of $50 000.
Option B: Receive $800 at the end of every quarter for 10 years from an
investment. The investment earns 8%/annum, compounded
quarterly.
How much more money would she have if she chooses the lump sum?
Marissa will earn $ 1678.41 more if she chooses the Lumpsum amount of money.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
Given, Marisa has just won a contest. She must decide between two prize options:
Option A: Collect a lump-sum payment of $50 000.
Option B: Receive $800 at the end of every quarter for 10 years from an investment. The investment earns 8%/annum, compounded quarterly.
We must calculate how much the future value has an 800$ quarterly payment for 10 years at 8%.
R = 800
rate = 0.08
Compounded quarterly
i = 0.08/4 = 0.02
t = 10 years
m = 10 *4
From the formula of the present value of Annuity:
FV = R. ((1 + i)^m - 1)/i
FV = 48321.59
Since the lump sum payment is 50,000$
The difference in payments = 50,000 - 48321.59
The difference in payments = 1678.41
Therefore, Marissa will earn $ 1678.41 more if she chooses the Lumpsum amount of money.
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Which one is it? A B C or D
Answer:B
Step-by-step explanation:If you count the blocks it adds
up to 53
2. Which group found the volume of a
triangular pyramid with a base area of 16
square inches?
The volume of a triangular pyramid can be found using V = 1/3AH where A = area of the triangle base, and H = height of the pyramid or the distance from the pyramid's base to the apex.
How to calculate the volumeA tetrahedron is a polyhedron in geometry that has four triangular faces, six straight edges, and four vertex corners. It is often referred to as a triangle pyramid. The simplest regular convex polyhedron is the tetrahedron. A triangle base, three triangular faces, and a common vertex make up the geometric shape known as a triangular pyramid.
The formula for calculating the volume of a triangular pyramid is Volume= 1/3 × Base area × Height. The dimensions required to find the surface area of a triangular pyramid are the side, height, and slant height.
Note that an overview was given as your information is incomplete.
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Show that A is an eigenvalue of A if and only if λ is an eigenvalue of AT. [Hint: Find out how A-A and AT-AI are related.]In order for x to be an eigenvalue of A and AT, there must exist nonzero x and v such thatandUse matrix algebra and the equations from the first step to write matrix equations involving A-AI and AT-XI.The equations areandMatrix AT-X ismatrix A-21.How can this relationship between AT-1 and A-I be used to determine information about X?A. Since the two matrices are equal, the nonzero vector x must be a constant multiple of the nonzero vector v.B. Since the two matrices are transposes, if either (AT-AI)x=0 or (A-AI)v=0 has at least one nontrivial solution, then all of the statements of the Invertible Matrix Theorem are false for both matrices.C. Since the two matrices are inverses, if either (AT-x=0 or (A-AI)v=0 has at least one nontrivial solution, then all of the statements of the Invertible Matrix Theorem are true for both matrices.
This relationship between AT-1 and A-I be used to determine information about matrix X by option (A) and (C).
(A) Since the two matrices are equal, the nonzero vector x must be a constant multiple of the nonzero vector v and (C) Since the two matrices are inverses, if either (AT-x=0 or (A-AI)v=0 has at least one nontrivial solution, then all of the statements of the Invertible Matrix Theorem are true for both matrices.
Therefore, if A is an eigenvalue of A, then λ must be an eigenvalue of AT, and vice versa. This can be seen by comparing the equation (A-λI)x=0 with the equation (AT-λI)v=0. If x is an eigenvector of A with eigenvalue λ, then it follows that v=x is an eigenvector of AT with eigenvalue λ. And if v is an eigenvector of AT with eigenvalue λ, then it follows that x=v is an eigenvector of A with eigenvalue λ.
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what is the unsigned octal equivalent of the following unsigned hexadecimal value?
The process of converting a hexadecimal value to octal involves two steps: first converting the hexadecimal value to binary, and then converting the binary value to octal.
Hexadecimal is a number system that uses 16 digits, from 0 to 9 and A to F, to represent values. It is commonly used in computer science, as it provides a concise representation of binary data.
To convert a hexadecimal value to an octal value, the hexadecimal number must first be converted to binary, and then the binary number must be converted to octal.
The octal number system uses 8 digits, 0 to 7, to represent values. To convert a binary number to octal, the binary number is split into groups of 3 bits each, starting from the rightmost bit.
The value of each group is then found by adding up the values of the bits that are turned on.
In this case, the unsigned hexadecimal value is given, and we need to find its unsigned octal equivalent.
To do this, we first convert the hexadecimal value to binary. We then group the binary digits into groups of 3 bits each and find the octal equivalent of each group.
The final answer is the concatenation of the octal values of each group, from left to right.
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A square has vertices P(2,4), Q(6,8), R(10,4) and S(6,0)
Which set of steps should a student follow to prove that the diagonals of the square are perpendicular to each other?
A) Step 1: Find the slope of diagonal PR and slope of diagonal QS Step 2: Show that m1 x m2=-1
B) Step 1: Find the slope of diagonal and slope of diagonal Step 2: Show that
C) Step 1: Find the slope of diagonal and slope of diagonal Step 2: Show that
D) Step 1: Find the slope of diagonal and slope of diagonal Step 2: Show that .
A set of steps which a student should follow to prove that the diagonals of the square are perpendicular to each other include the following: A) Step 1: Find the slope of diagonal PR and slope of diagonal QS Step 2: Show that m₁ × m₂ = -1.
How to determine whether the quadrilateral is a square by using slope?In order for a quadrilateral to be a square, the two (2) pairs of its sides must be equal (congruent) and perpendicular to each other. Therefore, we would have to calculate the slope of each side by using this mathematical expression:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Where:
x and y represents the data points or side lengths of a quadrilateral.
For side PQ, the slope is given by:
Slope (m) = (8 - 4)/(6 - 2)
Slope (m) = (4)/(4)
Slope (m) = 1.
In Mathematics, a condition that must be met for two (2) lines or side lengths to be perpendicular is given by:
m₁ × m₂ = -1
1 × m₂ = -1
m₂ = -1
Slope (m₂) = -1
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I don’t know how to explain how do I do it
The fraction value 3/8 of the total students 24 will be (students who rides the bus) 9.
What is a fraction?
In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.
For example, 5/10 is a fraction.
Here, 5 is a numerator and 10 is a denominator.
There are four different types of fractions. They are:
Unit Fraction – In a fraction, the numerator with 1 is called a unit fraction. For example, ½, ¼
Proper Fraction – If a numerator value is less than the denominator value, it is called a proper fraction. Example: 7/9, 8/10
Improper Fraction – If a numerator value is greater than the denominator value, then it is called an improper fraction. Example: 6/5, 11/10
Mixed Fraction – If a fraction consists of a whole number with a proper fraction, it is called a mixed fraction. Example 5 ¾, 10 ½
Now,
Given
Total students=24
Fraction of students who rides the bus=3/8
So, no. of students who rides the bus=3/8*24
=3*3
=9
Hence,
The no. of students who rides the bus is 9.
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Write an algorithm to find the substring from the given string that is the same when read forwards and backwards. Input The input consists of a stringinputStr, representing the given string for the puzzle. Output From the given string, print a substring which is the same when read forwards and backwards.
An algorithm to find the substring from the given string that is the same when read forwards and backwards in python language.
Here's a basic algorithm in Python to find the longest palindromic substring:
def longest_palindromic_substring(input_str):
n = len(input_str)
if n == 0:
return ""
dp = [[False for _ in range(n)] for _ in range(n)]
longest_len = 1
longest_start = 0
for i in range(n):
dp[i][i] = True
for start_idx in range(n - 1, -1, -1):
for end_idx in range(start_idx + 1, n):
if input_str[start_idx] == input_str[end_idx]:
if end_idx - start_idx == 1 or dp[start_idx + 1][end_idx - 1]:
dp[start_idx][end_idx] = True
if end_idx - start_idx + 1 > longest_len:
longest_len = end_idx - start_idx + 1
longest_start = start_idx
return input_str[longest_start : longest_start + longest_len]
The above algorithm uses dynamic programming to solve the problem in O(n^2) time complexity, where n is the length of the input string.
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In which of the following drawings is DE parallel to AC?
According to the triangle proportionality theorem, the drawings where DE is parallel to AC is: C.
What is the Triangle Proportionality Theorem?The Triangle Proportionality Theorem states that in any triangle, the ratio of the length of a side to the length of the segment from its endpoint to the line containing the opposite side is constant, and equal to the ratio of the lengths of the other two sides. If the ratios are equal, then the segment that joins two sides is parallel to the third side.
In figure C, we have the following:
AD/DB = CE/EB
Substitute
22.5/15 = 24/16 = 1.5
Therefore, the correct drawing is: C.
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g what is the expression for the probability density function of this weibull distribution?
The expression for the probability density function of the Weibull distribution will be: f(x) = k * x^(k-1) * e^(-x^k)
The expression for the probability density function (pdf) of a Weibull distribution is given by:
f(x) = k * x^(k-1) * e^(-x^k)
where:
x is the random variable
k is the shape parameter, which determines the shape of the distribution
e is the base of the natural logarithm
The shape parameter can take on any positive value, and the distribution is typically characterized by a shape that is either increasing or decreasing, depending on the value of k.
If the value of the k is less than 1, the distribution has a decreasing hazard rate, indicating that the failure rate decreases over time.
If the value of the k is greater than 1, the distribution has an increasing hazard rate, indicating that the failure rate increases over time.
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All lines parallel to the line 3x – 8y = 4 are given by equations of the form (a) 3x – 8y = 0 (b) 3x – 8y = c for a constant c (c) 8x – 3y = c for a constant c (d) none of these
The slopes of perpendicular lines are opposite reciprocals and hence option D is correct
The slope of the given line is 3/8, so its opposite reciprocal is -8/3. From the options we have to find a line with this slope.
In the given line, it was easy to find the slope because the equation is in slope-intercept form, but in the options the equations are in standard form,
If we solve this for y we get the slope-intercept form,
Thus the slope of a line whose equation is in standard form is,
• Option A: a = 3, b = 8. The slope is -3/8 → ,not perpendicular
• Option B: a = 3, b = -8. The slope is 3/8 → ,not perpendicular
• Option C: a = -8, b = 3. The slope is 8/3 → ,not perpendicular
• Option D,: a = 8, b = 3. The slope is -8/3 → ,this line is perpendicular, to the given line
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Melody is saving her money for a new MP3 player that costs $72. She has already saved $52. She just received a gift of B dollars from her brother, but she still does not have enough money to buy the MP3 player. Which number sentence below represents this situation?
Answer:
b+52<72
Step-by-step explanation:
in one year, three awards (research, teaching, and service) will be given to a class of 25 graduate students in a math department. if each student can receive at most one award, how many possible selections are there?
The number of possible selections is 13,800.
A permutation is the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination is the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]C_{n,r} = \frac{n!}{(n-r)! r !}[/tex] , [tex]P_{n,r} = \frac{n!}{(n - r) !}[/tex]
where,
n is the number of choices available,
and r is the choices to be made.
According to the question,
The number of possibilities in which the students can be selected and the awards can be given is,
[tex]= \frac{25!}{(25 - 3) !}[/tex]
[tex]= \frac{25 !}{22 !}[/tex]
= [tex]\frac{25 * 24 * 23 * 22 !}{22!}[/tex] = 1380
Hence, there are 13,800 possible selections.
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An ancient artifact is four times as old as an antique book. In 200 years, the artifact will be 3 times as old as the book. How old is the artifact now?
The current age of the artifact is 1600 years
How old is the artifact now?Let's call the current age of the artifact "a" and the current age of the book "b".
The artifact is four times as old as the book, so we have:
a = 4b
In 200 years, the artifact will be a + 200 and the book will be b + 200.
From the problem, we know that in 200 years:
a + 200 = 3 (b + 200)
Expanding the right side:
a + 200 = 3b + 600
Substituting a = 4b:
4b + 200 = 3b + 600
Solving for b:
b = 400
So the current age of the book is 400 years old.
Recall that
a = 4b
So, we have
a = 400 * 4 = 1600
And the current age of the artifact is 4 times that, or 1600 years old.
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Pls help me with solving the problem below.
The value of a+ b + c + d + e + f is 2.
What is Factored Form?It is referred to as being in factored form when a quadratic expression is represented as the sum of two linear factors plus a constant.
We have to factor x² – y² – z² + 2yz.
Using the general rule that p² – 2pq + q² = (p – q)² .
So we want to rearrange the last three terms.
= x² + (–y² – z² + 2yz)
Now, If we were to factor out a –1 from the last three terms, we have
= x² – (y² + z² – 2yz)
Now put y² + z² – 2yz = (y – z)².
= x² – (y – z)²
This expression is actually a differences of squares.
We know p² – q² as (p – q)(p + q).
=x² – (y – z)²
= (x – (y – z))(x + (y – z))
Now, let's distribute the negative one in the trinomial x – (y – z)
= (x – (y – z))(x + (y – z))
= (x – y + z)(x + y – z)
Now, comparing (x – y + z)(x + y – z) and (ax + by + cz)(dx + ey + fz)
we get a = 1, b = –1, c = 1, d = 1, e = 1, and f = –1.
So, a+ b + c + d + e + f
= 1 - 1 + 1+ 1 +1 - 1
= 2
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PLEASE HURRY WILL GIVE BRAINLYIST
A sign says that the price marked on all music equipment is 30% off the original price. You buy an electric guitar for the sale price of $315. Some answers will not be used. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. How much money did you save off the original price of the guitar? What is the original price? What percent of the original price is the sale price?
Answer:220.5
Step-by-step explanation:
Do 315 - 30%
You saved $135 off the original price of the guitar. The original price is $450. The sale price is 30% off the original price.
if the sample coefficient of determination (r2) is 0.80, this means that:select one:20 percent of the variation in the dependent variable is explained by the regression20 percent of the variation in the independent variable is explained by the regression.80 percent of the variation in the dependent variable is explained by the regression.80 percent of the variation in the independent variable is explained by the regression.
The interpretation is that 18% of the variation in the dependent variable can be explained by the variation in the independent variable.
Coefficient of determination R²
The percentage of variance in the dependent variable that is explained by the independent variable is shown by the coefficient of determination. R² value is always in the range between 0 and 1. As opposed to 1, which shows that the independent variable fully explains the variation in the dependent variable, 0 means that the independent variable is utterly ineffective at predicting the variance in the dependent variable. It is stated as a percentage.
Interpretation of
R²=0.18
Since
R² is expressed in percentage terms,
R²=0.18
=18/100
=18%
Accordingly, the variation in the independent variable can account for 18% of the variation in the dependent variable. 82% of the variance is unaccounted for and cannot be attributed to the independent variable.
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The full question would be
How do you interpret a coefficient of determination, r 2, equal to 0.18 A? The interpretation is
Start with y divide by 7 then add 2
The condition "y divide by 7 then add 2" can be represented as expression, [tex]\frac{y}{7} +2[/tex]
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
A condition,
y divide by 7 then add 2
Here, we have to apply two operation to complete this expression,
1. Division
2. Addition
First, doing division operation,
y divide by 7
⇒ y/7
Now, second operation which is addition of 2
⇒ [tex]\frac{y}{7} + 2[/tex]
Hence, the expression is [tex]\frac{y}{7} + 2[/tex]
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Ryan needs to solve the equation x2−8x−9=0 by completing the square. Which pair of steps is the most efficient way to begin?
The required Solutions of the given quadratic equation are 9 or -1.
What is quadratic equation?x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.
According to question:x²−8x−9=0
To solve it by completing the square.
x² − 8x + 16 − 16 −9=0
(x - 4)² = 25
x - 4 = ± 5
So,
x - 4 = 5 or x - 4 = -5
x = 9 or x = -1
Thus required Solution of equation are 9 or -1.
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At the beach, Ayana and her sister both built sandcastles and then measured their heights. Ayana's sandcastle was 1/2 of a foot tall and her sister's was 3/8 of a foot tall. How much taller was Ayana's sandcastle than her sister's?
Write your answer as a fraction or as a whole or mixed number.
Ayana's sandcastle is 1/8 foot taller than her sister's.
What is fraction?Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, specific value, or a thing.
Given,
Ayana's sandcastle was 1/2 of a foot tall
Her sister's was 3/8 of a foot tall.
Difference between the height of the both sandcastle
= 1/2 - 3/8
= (4 - 3)/8
= 1/8
Hence, Ayana's sandcastle is taller than her sister's by 1/8 foot.
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Can someone help pls
Answer: 264
Step-by-step explanation:
calculated each area, shown in the picture above
Member of a club bought on book for $3. 50 and each member need a pair of knitting needle for $3. 20 and yarn for $5. 40. They pent $63. 70 in total how amny memebr are there?
The price per book is $3.50, the knitting needle is $3.20, the yarn is $3.20 and the total spent is $63.70. Then, the number of members present there are 7 members.
An equation is a formula that connects two expressions with an equal sign and expresses their equivalence.
Given the price of the book is $3.50. The price of a knitting needle is $3.20. And, the price of the yarn is $5.40. The total amount spent by the member is $63.70.
Let us consider the number of members as x. The given situation is written in an equation as,
[tex]\begin{aligned} 3.50 + 3.20x + 5.40x &= 63.70\\8.60x& = 63.70 - 3.50\\8.60x& = 60.20\\x &= \frac{60.20}{8.60}\\x &= 7\end{aligned}[/tex]
The required answer is 7.
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The stem & leaf diagram shows the times it takes all the people in an office to finish a crossword
The number of people took more than 25 minutes to finish a crossword is 9.
What is stem and leaf plot?A stem and leaf plot also called a stem and leaf diagram is a way of organizing data into a form that makes it easy to observe the frequency of different types of values. It is a graph that shows numerical data arranged in order. Each data value is broken into a stem and a leaf.
A stem and leaf plot is represented in form of a special table where each first digit or digit of data value is split into a stem and the last digit of data in a leaf.
From the given stem and leaf plot, we have
10, 11, 14, 24, 25, 26, 27, 28, 34, 34, 40, 42, 45 and 47
So, the number of people took more than 25 minutes is 9.
Therefore, the number of people took more than 25 minutes to finish a crossword is 9.
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Use dimensional analysis to perform the following conversions, show all your work and report the answer in the correct number of significant figures. a. 261 g ---> kg b. 3 days ---> seconds c. 9,474 mm ---> cm d. 0.73 KL ---> L
The conversions are 0.261 kg, 300000 seconds, 947.4 cm and 730 L.
a. 261 g to kg
For converting grams to kg, we divide by 1000.
(261 / 1000)= 0.261 kg
The number of significant figures in 261 g is 3 and the number of significant figures in the answer 0.261 kg is also 3.
b. 3 days to seconds
1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds
1 day = 24 x 60 x 60 seconds
Therefore, 3 days = 3 x 24 x 60 x 60 seconds = 2, 59, 200 seconds
Since, the number of significant figures in 3 days is 1, hence we write 2, 59, 200 as 300000 seconds, such that it has 1 significant figure.
c. 9, 474 mm to cm
For converting mm to cm, we divide by 10
(9474 / 10) = 947.4 cm
The number of significant figures in 9, 474 mm is 4 and the number of significant figures in the answer 947.4 cm is also 4.
d. 0.73 KL to L
1 KL = 1000 L
0.73 KL = 0.73 X 1000 L = 730 L
The number of significant figures in 0.73 KL is 2 and the number of significant figures in the answer 730 L is also 2.
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Part A
Mike made 56 of his free throw attempts, and Lisa made 79 of her free throw attempts. Which of the following shows 56 and 79 written with a common denominator? Select all that apply.
1018 and 1018
1518 and 1418
3036 and 2736
3018 and 2718
3036 and 2836
Part B
Use the given numbers to create the fraction for the total number of Mike’s and Lisa’s made free throw attempts? Use Part A for help.
1 2 3 9 11 18 29
Mike made 15/18 of his free throw attempts.
Lisa made 14/18 of her free throw attempts.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
We have to given that;
Mike made 5/6 of his free throw attempts.
And, Lisa made 7/9 of her free throw attempts.
Now, We can solve as;
To bring the denominator, we need to take the LCM of the denominator, therefore,
⇒ 5/6, 7/9
We know that the LCM of 6 and 9 is 18.
⇒ 5×3/6×3, 7×2/9×2
⇒ 15/18, 14/18
Thus, Mike made 15/18 of his free throw attempts.
And, Lisa made 14/18 of her free throw attempts.
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