Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.
Explain about the Exponential equation:Calculating the exponential growth as well as decay of a given collection of data is done using an exponential function, which is a mathematical function.
Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread. An exponential function has the following form at its most fundamental level.
f(x) = [tex]a^{x}[/tex]
Exponential equation for the amount of Caffeine
C = 80[tex](2)^{-t/6}[/tex]
Amount of caffeine C = 60 mg.
60 = 80[tex](2)^{-t/6}[/tex]
3/4 = [tex](2)^{-t/6}[/tex]
Taking log on both sise:
[tex]log_{2}(3/4) = -t/6[/tex]
Solve the log function using the log calculator:
-t/6 = (-0.41)
t = 0.41 * 6
t = 2.46 hours
Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.
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Correct question:
The biological half-life of caffeine is about 6hr. If one cup of coffee has 80 mg of caffeine, then the amount of caffeine C (in mg) remaining after t hours is given by C = 80[tex](2)^{-t/6}[/tex]
How long will it take for the amount of caffeine to drop below 60 mg?
The table summarizes results from 982 pedestrian deaths that were caused by automobile accidents.
What is the length of the unknown leg of the right triangle?
The length of the unknown leg of the right triangle is 6.2 ft rounded to one decimal place, using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
we shall represent the unknown leg of the right triangle with the letter "x" so that by Pythagoras rule we can evaluate for x as follows:
8² = 5² + x²
x = √(8² - 5²) {make TV the subject}
x = √(64 - 25)
x = √39
x = 6.2450
Therefore, the length of the unknown leg of the right triangle is 6.2 ft rounded to one decimal place, using the Pythagoras rule.
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i need help finding x
Answer:
Step-by-step explanation:
Formula for the sum of interior angle of an n-gon is S = (n-2)x180°.
So for our 5 sided polygon we get:
S = (5-2)x180° = 540°
Now we can solve:
[tex]100+4x+(3x+3)+(5x-2)+103=540[/tex]
[tex]12x+204=540[/tex]
[tex]12x=336[/tex]
[tex]x=28[/tex]°
Solution: [tex]x=28[/tex]°
Answer: x=43
Step-by-step explanation:
We know The interior angles in a hexagon sum to 720°.
so we can add all the angles and equal them to 720
100 + 4x + (3x + 3) + (5x-2) + 103 = 720
Simplify by combining like terms
(100 + 3 -2 + 103) and (4x + 3x +5x)
204 + 12x = 720
Subtract 204 from both sides to isolate x
204 - 204 + 12x = 720 - 204
12x = 516
Divide both sides by 12 to solve for x
12/12 x = 516/12
Simplify
x = 43
to check your work, substitute the value of x into your equation and solve
100 + 4x + 3x + 3 + 5x-2 + 103 = 720
100 + 4(43) + (3)(43) + 3 + (5)(43) -2 + 103 = 720
100 + 172 + 129 + 3 + 215 -2 + 103 = 720
720 = 720
They equal so your solution is correct
Each time Caroline goes shopping she decides whether or not to buy fruit. The probability that she does buy fruit is 0.4. Independently, she then decides whether or not to buy a CD, with a probability of 0.6 that she does buy a CD. Work out the probability that she buys fruit or buys a CD or both.
Answer:
To work out the probability that Caroline buys fruit or buys a CD or both, you can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are events.
In this case, A is the event that Caroline buys fruit and B is the event that Caroline buys a CD.
The probability that Caroline buys fruit is 0.4 and the probability that Caroline buys a CD is 0.6.
To find the probability that Caroline buys fruit and a CD, you can multiply the probabilities of the two events:
P(A and B) = P(A) x P(B) = 0.4 x 0.6 = 0.24
Therefore, the probability that Caroline buys fruit or buys a CD or both is:
P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.6 - 0.24 = 0.76
So, the probability that Caroline buys fruit or buys a CD or both is 0.76 .
100 POINTS + BRAINLIEST!!
a is 15 days
b is 20%
hope this helps you
Answer:
a is 15 daysb is 20%
Step-by-step explanation:
A family has two cars. During one particular week, the first car consumed 25 gallons of gas and the second consumed 20 gallons of gas. The two cars drove a
combined total of 1075 miles, and the sum of their fuel efficiencies was 50 miles per gallon. What were the fuel efficiencies of each of the cars that week?
First car: miles per gallon
Second car: miles per gallon
We can conclude after answering the presented question that As a equation result, the first car's fuel efficiency was 15 miles per gallon, whereas the second car's fuel economy was 35 miles per gallon.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Let's name the first car's fuel efficiency (miles per gallon) x and the second car's fuel efficiency y. We are aware of the following:
The first automobile used 25 gallons of gas and covered 25 miles.
The second automobile used 20 gallons of petrol and drove 20 miles.
The two automobiles went a total of 1075 miles, thus 25x + 20y = 1075.
Their combined fuel economy was 50 miles per gallon, thus x + y = 50/1 = 50.
[tex]25x + 20y = 1075\\x + y = 50\\25x + 20y = 1075\\-20x - 20y = -1000\\5x = 75x = 15\\x + y = 50\\15 + y = 50\\y = 35\\[/tex]
As a result, the first car's fuel efficiency was 15 miles per gallon, whereas the second car's fuel economy was 35 miles per gallon.
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Please I’d love some help with a simple explanation on how you got the answers and the answers (obviously)
Given the above circles,
1) x = 42°
2) x = 29°
3) x = 101°
4) x = 37°
5) x = 31°
6) x = 120°
What is the explanation for the above results?1) x = 42° because the Angles at the circumference of a circle
subtended by the same arc are equal. Since 35° and 103° are two of the three angles in a triangle whose third angle subtends the circumference of the circle along with ∠x, and the third angle = 180 - 35 - 103 = 42° therefore, x = 42°
2) x = 29° because according to the central angle theorem, the angle at the circumference is double the one at the center. Since the angle at the circumference is 61°, the one at the center is 122°. Since the line from the center that couches on both sides of the circumference is the radius, they are equal. Hence, the angles formed at their bases are equal.
Thus, x = (180-122)/2
x = 29°
3) 3) x = 101° because the opposite angles of a cyclic quadrilateral are supplementary.
4) x = 37° based on the angle in the alternate segment theorem.
5) x= 31° is based on the "inscribed angle theorem" or the "theorem of the intercepted arc".
This theorem states that if an angle is inscribed in a semicircle, then the angle is a right angle (i.e., it measures 90 degrees). In other words, if you draw any two chords from the ends of the diameter to any point on the arc of the semicircle, then the angle formed by these two chords at the point on the arc will always be 90 degrees.
6) x = 120° on the basis of the "Tangent-Secant Angle Theorem" or "Tangent-Chord Angle Theorem".
In the problem given above, the angle x is formed by two tangents intersecting at the vertex outside the circle, and the Tangent-Secant (or Tangent-Chord) Angle Theorem is used to find its measure.
The arc formed at the points where the two tangents meet is twice the angle formed inside the circle which is = 30°
Thus, where the rest of the arc traced from the upper point of tangency is traced back to the lower point of tangency is called A,
The measure of arc A is 360° - 60° = 300°.
The measure of angle x is half the difference between the measures of the intercepted arcs, which is (300° - 60°)/2 = 120°.
Therefore, the measure of angle x would be 120°.
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PLEASE HELP!!! i am failing and im going to be held back if i dont get my grade up!!!!
Emma spent $45.20 on 5 dozen bagels and a gallon of iced tea. The price of the gallon of iced tea was $5.25. The following equation can be used to find d, the price of each dozen of bagels.
5d + 5.25 = 45.2
What was the price of each dozen of bagels?
A.
$6.99
B.
$7.99
C.
$9.04
D.
$3.79
Answer:
the answer to the question is B
Step-by-step explanation:
no need for explanation just trust the source
A parabola opening up or down has vertex
(-4, -6) and passes through (-14, 13/2)
Write its equation in vertex form.
Answer:
To write the equation of the parabola in vertex form, we use the standard form:
y = a(x - h)^2 + k, where (h, k) is the vertex.
Given that the vertex is (-4, -6), we have:
h = -4 and k = -6
Now, we need to find the value of "a" using the point (-14, 13/2) which lies on the parabola.
Substituting the values in the standard form, we get:
13/2 = a(-14 - (-4))^2 - 6
Simplifying, we get:
13/2 = 100a - 6
100a = 13/2 + 6
a = 19/200
Therefore, the equation of the parabola in vertex form is:
y = (19/200)(x + 4)^2 - 6
Step-by-step explanation:
Find the volume of the figure.
Answer:
165inch^3
Step-by-step explanation:
4×7×3=84inch^3
9×3×3=81inch^3
84+81=165inch^3
The diameter of a cone's circular base is 6 inches. The height of the cone is 12 inches.
What is the exact volume of the cone?
Enter your answer in the box.
Answer:
The correct answer is 36π
Step-by-step explanation:
what month comes under the 250th day of the year?
Answer:september
Step-by-step explanation:
A die is rolled 2 times. What is the probability of getting a 1 on the first roll and a 2 on the second roll.
The probability of getting a '1' on the first roll and '2' on the second roll for the given expression is [tex]\frac{1}{18}[/tex] .
What about probability?
In mathematics and statistics, probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
The probability of an event A is denoted by P(A) and is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In other words, it is the number of ways that event A can occur divided by the total number of possible outcomes.
For example, if you roll a fair six-sided die, the probability of rolling a 4 is 1/6, since there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).
Probability is used in many different fields, such as gambling, statistics, and science, to make predictions about the likelihood of different outcomes. It is also used to model complex systems and to test hypotheses in scientific experiments.
According to the given information:
When a die is rolled 2 times, the output we get
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
Total no of getting '1' on first roll and '2' on second roll = 2
Total outcomes = 36
⇒ [tex]\frac{2}{36}[/tex]
⇒ [tex]\frac{1}{18}[/tex]
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A company performs $3,200 of services during the month and bills customers. The customers are expected to pay next month.
Record the customer billing using (a) accrual-basis accounting and (b) cash-basis accounting.
Recording the customer billing using (a) accrual-basis accounting and (b) cash-basis accounting is as follows:
a) Accrual Method:Customer Billing:
Debit Accounts Receivable $3,200
Credit Service Revenue $3,200
(To record the performance of services for customers during the month.)
b) Cash Method:Customer Billing:
No Record during the current month.
What differentiates cash-basis accounting from accrual-basis accounting?Cash-basis accounting recognizes expenses and revenues when cash exchange takes place.
Accrual-basis accounting matches expenses and revenues to the month or period when the transaction occurs, whether there is a cash exchange or not.
For instance, the accrual-basis will recognize the receipt of cash as follows:
Next Month:
Debit Cash $3,200
Credit Accounts Receivable $3,200
On the other hand, the cash-basis will recognize revenue with the receipt of cash as follows:
Next Month:
Debit Cash $3,200
Credit Service Revenue $3,200
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The first used 20 gal of fuel and the second used 25 gal. The 2 drove 1450 miles and the sum of their fuel efficiencies was 65 miles per gal. What we’re each car fuel efficiency?
Answer: there you go :)
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Step-by-step explanation:
Let x = gallons consumed by car 1
Let y = gallons consumed by car 2
We set up our equations:
35x+40y = 1850 eq1
x+y = 50 eq2
Substituting eq 2 into eq 1,
35x+40(50-x) = 1850
35x+2000-40x = 1850
-5x+2000 = 1850
-5x = -150
x = 30
Substitute value of x into eq 2.
x+y = 50
30+y = 50
y = 20
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Please help asap. i am very confused
Statement (A) is true, Statement (B) is false, Statement (C) is true, Statement (D) is true and Statement (E) is false.
The given information is that P(odd) = 1/3
where odd numbers are 3 and 5, and there are two odd-numbered sections out of six equal sections.
(A) The probability of landing on an odd-numbered section is not exactly 33.33%, but approximately equal to 33.33% or 1/3.
So, statement (A) is true.
(B) The probability of landing on an even-numbered section is not exactly 66.67%, but approximately equal to 66.67% or 2/3.
So, statement (B) is false.
(C) The probability of landing on an odd-numbered section is given as 1/3, which is less than the probability of landing on an even-numbered section, which is 2/3. Therefore, statement (C) is true.
(D) It is given that one of the sections is numbered 6. So, it is not impossible to land on 6. Therefore, statement (D) is false.
(E) To determine if the spinner is fair, we need to know the probability of each outcome, which is not provided in the given information. Therefore, we cannot determine if the spinner is fair or not based on the information given. So, statement (E) is uncertain.
Therefore, the true statements about this game are (A), (C), and (D).
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Find thenonpermissible replacment for x in this expression b^2/-7b+7
We can conclude by answering the provided question that expression As a result, b = 1 is not a valid substitute for b in the equation because it would set the denominator to zero and render the expression undefined.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical association or routine. A real integer, a mutable, or a mix of the two can be used as an equation. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and geometry. They are used in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
The expression is as follows:
[tex]b^2 / (-7b + 7)\\-7b + 7 = 0\\b = 1\\[/tex]
As a result, b = 1 is not a valid substitute for b in the equation because it would set the denominator to zero and render the expression undefined.
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Zacharias wants to download some songs
through an app on his phone. Each song
costs $2 to download and he has $12
remaining in his account. The inequality
2s < 12 represents the number of songs s
he could download. What is the greatest
number of songs Zacharias can download?
Answer: 6 songs.
Step-by-step explanation:
Each song is $2 dollars. $12 divided by $2 equals 6.
So he can download 6 songs.
Plot 1 7/8 abd 2 1/2 on the number line
Charlie's net worth is $-35,354. Which of the following is true?
Responses
He has a negative net worth which means his liabilities are greater than his assets.
He has a negative net worth which means his liabilities are greater than his assets., EndFragment,
He has a negative net worth which means his assets are greater than his liabilities
He has a negative net worth which means his assets are greater than his liabilities , EndFragment,
He has a positive net worth which means his assets are greater than his liabilities.
He has a positive net worth which means his assets are greater than his liabilities. , EndFragment,
He has a positive net worth which means his liabilities are greater than his assets
Answer:
if the mass of 16cm3 of a metal is 20g what is the mass of 30cm3
Trigonometry: Sum and difference Identities
MUST GIVE EXPLANATION:
Will give BRAINLIEST.
Using the sum-to-product formula we get the value as √2 cos(2α)
What is the sum-to-product formula?
The sum-to-product formula is a trigonometric identity that expresses the sum or difference of two trigonometric functions as a product of two trigonometric functions. There are several versions of this formula, depending on the specific functions involved.
We can use the sum-to-product formula to simplify the expression:
cos(2α - π/16) + cos(9π/16 - 2α)
= cos(2α)cos(π/16) - sin(2α)sin(π/16) + cos(9π/16)cos(2α) + sin(9π/16)sin(2α)
= cos(2α)(cos(π/16) + cos(9π/16)) + sin(2α)(-sin(π/16) + sin(9π/16))
= cos(2α)(2cos(5π/16)cos(3π/16)) - sin(2α)(2cos(7π/16)sin(π/16)) (using the sum-to-product formula again)
= 2cos(2α)cos(5π/16)cos(3π/16) - 2sin(2α)cos(7π/16)sin(π/16)
= 2cos(2α)(cos(5π/16)cos(3π/16) - sin(5π/16)sin(3π/16)) (using the product-to-sum formula)
= 2cos(2α)cos(π/4)
= 2cos(2α)/√2
= √2 cos(2α)
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Trey has plastic cubes stored in box that measures 4 ft long, 2 1/2 ft wide, and 2 ft tall.
The edge length of each plastic cube is 1/2 ft.
How many plastic cubes can fit into the box?
Based on the given information, Trey can fit 160 plastic cubes inside the box.
What is volume of cube?
The volume of a cube is calculated by cubing the length of any one side of the cube. In other words, if a cube has sides of length "s", then its volume "V" is V = s³
To calculate the number of plastic cubes that can fit inside the box, we need to first calculate the volume of the box and the volume of each plastic cube. Then, we can divide the volume of the box by the volume of each plastic cube to get the total number of cubes that can fit inside.
The volume of the box is:
4 ft x 2.5 ft x 2 ft = 20 cubic feet
The volume of each plastic cube is:
(1/2 ft) x (1/2 ft) x (1/2 ft) = 1/8 cubic feet
To find out how many plastic cubes can fit inside the box, we can divide the volume of the box by the volume of each plastic cube:
20 cubic feet ÷ (1/8 cubic feet) = 160
Therefore, Trey can fit 160 plastic cubes inside the box.
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Ethan sold 2/3 gallons of lemonade.Kayla sold some lemonade too.Together,they sold 1 1/4 gallons.
Who sold more lemonade,Ethan or Kayla? How much more
Answer: Kayla sold 1/12 gallons more than Ethan.
Step-by-step explanation:
Let's start by finding out how much lemonade Kayla sold. We know that together, Ethan and Kayla sold 1 1/4 gallons, which is the same as 5/4 gallons. We also know that Ethan sold 2/3 gallons. Therefore, we can find how much Kayla sold by subtracting Ethan's sales from the total sales:
Kayla's sales = Total sales - Ethan's sales
Kayla's sales = 5/4 - 2/3
To subtract these fractions, we need to find a common denominator. The smallest common multiple of 4 and 3 is 12, so we can rewrite the fractions with 12 as the denominator:
Kayla's sales = (5/4)(3/3) - (2/3)(4/4)
Kayla's sales = 15/12 - 8/12
Kayla's sales = 7/12
Therefore, Kayla sold 7/12 gallons of lemonade. Now, we need to compare this to Ethan's sales. We can convert Ethan's sales to twelfths to make it easier to compare:
Ethan's sales = (2/3)(4/4) = 8/12
Now we can see that Kayla sold more lemonade than Ethan. The difference in sales is:
Kayla's sales - Ethan's sales = 7/12 - 8/12
Kayla's sales - Ethan's sales = -1/12
The result is negative, which means that Ethan sold 1/12 gallons less than Kayla. Therefore, Kayla sold 1/12 gallons more than Ethan.
As an experiment, a charity decides to use SMART to determine a shortlist from the seven applicants who have
applied for the post of Regional Officer for the Western Region. The main criteria which will be used to
compare candidates are: salary they would expect (SALARY), their experience of charity work (CHARITY EXP),
their managerial experience (MANAGEMENT EXP), their educational qualifications (EDUCATION), their
apparent commitment to the charity's work (COMMITMENT) and the quality of the ideas they put forward on
the form (IDEAS).
(a) Discuss if the weights of the attributes are appropriate. If so, why do you think so? If not, why do you
think the weights are not appropriate? (You don't need to discuss whether the attributes are
appropriate. Only focus on the "weights". This is your own opinion and subjective. You don't need
references for this.)
The personnel manager ranked all the criteria, except salary, in order of importance and then assigned weights
as follows:
COMMITMENT
MANAGEMENT EXP
IDEAS
CHARITY EXP
EDUCATION
Candidate A's aggregated score is 50.
(You don't need to worry about how 50 was calculated.)
The other candidates' aggregated scores are found below.
100
70
65
55
10
b) Scatter plot chart would indicate a positive correlation
c) Candidate D would be the most cost-effective choice, as their expected salary would increase the most. Candidate F would also be a good choice, as their expected salary would increase by £1,000.
What is a Scatter plot chart?A scatter plot chart can be used to plot the data of the two variables on a two-dimensional graph, and the data points can be connected with a line or a curve.
a) The weights of the attributes in this case seem to be appropriate for the purpose of selecting a Regional Officer for the Western Region.
This data shows that the charity is placing a greater emphasis on the candidate's commitment, managerial experience and ideas, as these are likely to be the most important factors in selecting a successful Regional Officer.
Additionally, Education has the lowest weight at 10, indicating that this is not a major factor in consideration.
Overall, the weight of each criteria reflects the importance of the criteria to the charity and is appropriate for this case.
b) The scatter plot chart would indicate a positive correlation between the two variables, with the higher aggregate score corresponding to the higher expected salary.
Based on this chart, candidates A, D and F would be the best 2-3 candidates, with the highest aggregate scores of 50, 90 and 62 respectively.
c) If the charity is prepared to pay £1,000 for each additional aggregate score, then candidate D would be the most cost-effective choice, as their expected salary would increase the most (from £60,000 to £61,000). Candidate F would also be a good choice, as their expected salary would increase by £1,000 (from £52,000 to £53,000).
Candidate A would not be recommended, as their expected salary would increase by only £500 (from £46,000 to £46,500).
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A survey of all beings on planet Boondin found that 60% preferred hopt
juice to all other juices. If 50 beings were surveyed altogether, how
many of them preferred hopt juice?
label optional
Answer:
If 60% of the beings surveyed preferred hopt juice and 50 beings were surveyed altogether, then we can calculate the number of beings who preferred hopt juice by multiplying the total number of beings surveyed by the percentage that preferred hopt juice: `50 x 0.60 = 30`. So, **30** beings preferred hopt juice.
The measures of the angles of a triangle are shown in the figure below. Solve for x.
44°+107°+x°=180
151°+x°=180°
x°=180°-151°
x°=29°
How to solve “What is m
Answer: 120
Step-by-step explanation:
The angle measures should add up to 360
110+130+x=360
240+x=360
x=120
HELLLPPP
Use addition to rewrite the subtraction expression below without changing the
digits. Do not solve.
6-(-20)
Answer:
6+20
Step-by-step explanation:
the table shows the heights and masses of a male gorrila and a female gorilla at zoo.Based on the table, wich statement is true?
Using mensuration, we can find that the mass of male is greater than that of the female's by 63.507kg.
Define mensuration?Mensuration can be defined as a measurement action. Our world is three dimensional. Both elementary school mathematics and secondary school mathematics heavily rely on the idea of measurement. Also, measuring is directly related to our daily life. When we learn to measure items, we practise measuring both 2D and 3D shapes. Both conventional and nonconventional units of measurement can be used to determine the size of objects or quantities.
In the given table,
Height of male = 1.68m.
Mass of male = 158.757kg.
Height of female = 1.448m.
Mass of female = 95.25kg.
Difference between mass of male and female,
= 158.757 - 95.25
= 63.507kg.
The mass of male is greater than that of the female's by 63.507kg.
So, 2nd statement is true.
Rest of the statements are not true.
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11.) Mr. Moran is packing orders for his candle business. One customer ordered 14
vanilla-scented candles. If each candle weighs 12 ounces, how many pounds does
this order weigh?
Answer : 10.5
Explanation: Divide 168/16