Since the function is h(t) = −5t² + 15t, the domain of the function h(t) is 0 ≤ t ≤ 3
What is the domain of a function?The domain of a function is the range of input values that make the function have real values.
Now given the function h(t) = −5t² + 15t, it will have real values when
h(t) ≥ 0
So, h(t) ≥ 0
⇒ −5t² + 15t ≥ 0
Factorizing, we have
-5t(t - 3) ≥ 0
5t(t - 3) ≤ 0
t(t - 3) ≤ 0
t ≤ 0 and t - 3 ≤ 0
t ≤ 0 and t ≤ 3
For t ≤ 0, say -1, t(t - 3) = -1(-1 - 3) = -1(-4) = 4 ≥ 0
For 0 ≤ t ≤ 3, say 2, t(t - 3) = 2(2 - 3) = 2(-1) = -2 ≤ 0
For t ≥ 3, say 4, t(t - 3) = 4(4 - 3) = 4(1) = 4 ≥ 0
Since we require t(t - 3) ≤ 0, the domain of t is thus 0 ≤ t ≤ 3
So, the domain of the function h(t) is 0 ≤ t ≤ 3
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In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 35 and 48 minutes on the treadmill.
Using the normal distribution, there is a 0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given, respectively, by:
[tex]\mu = 42.5, \sigma = 4.8[/tex]
The probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill is the p-value of Z when X = 48 subtracted by the p-value of Z when X = 35, hence:
X = 48:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48 - 42.5}{4.8}[/tex]
Z = 1.15
Z = 1.15 has a p-value of 0.8749.
X = 35:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 42.5}{4.8}[/tex]
Z = -1.56
Z = -1.56 has a p-value of 0.0594.
0.8749 - 0.0594 = 0.8155.
0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.
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Suppose f′(6)=5 and g′(6)=7.
Find h′(6) where h(x)=4f(x)+5g(x)+1.
The value of the derivative of functions h'(6) as requested in the task content is; 55.
What is the value of h'(6)?Since it follows from the task content that the function h(x)=4f(x)+5g(x)+1.
Hence, the derivative of h(x) can be evaluated as;
h'(x)=4f'(x)+5g'(x)
On this note, by substitution, it follows that;
h'(6)=4(5)+5(7)
h'(6) = 55.
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Rate:
168 ounces
14 boxes
How much does the spaghetti in each box weigh? Find the unit rate.
Answer:
12 ounces
Step-by-step explanation:
168 divided by 14 = 12
Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with a mean of 35.5 inches and a standard deviation of 2.5 inches. About 2.4% of the years, the annual rainfall will exceed how many inches? (Round your answer to one decimal place.)
The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.
What is the average annual rainfall?Generally, the equation for the probability is mathematically given as
[tex]P( X < x) = p( Z < x - \mu / \sigma)[/tex]
Therefore
[tex]P( X > x) = 0.021[/tex]
[tex]P( X < x ) = 1 - 0.021\\\\\p( X < x) = 0.979[/tex]
[tex]P( Z < x - \mu / \sigma) = 0.979[/tex]
The z score for the probability of 0.979 is 2.034, according to the table of z values.
[tex]x - \mu / \sigma \\\\x= 2.034[/tex]
In the given equation, replace the values of mu and sigma with their respective values, and then solve for x.
[tex]x - 35.5 / 2.5 \\x= 2.034[/tex]
In conclusion, The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.
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Need help with that I don’t understand it
The answer is no. b.
Step-by-step explanation:
The answer is no b. u just take common
evaluate 5(x-1)-2 when x=3 (urgent)
Answer: 8
Step-by-step explanation:
Since x=3, we can plug in 3 for x in the equation:
[tex]5(3-1)-2\\5(2)-2\\10-2\\8[/tex]
⊱________________________________________________________⊰
Answer:
8
Step-by-step explanation:
Plug in 3 for x
[tex]\sf{5(3-1)-2}[/tex]. [tex]\large\textbf{[Perform the operation in parentheses]}[/tex][tex]\sf{5(2)-2} \ \ \ \ \ \large\textbf{[Multiply 5 by 2 next]}[/tex]
[tex]\sf{10-2} \ \ \ \ \large\textbf{[Subtract]}[/tex]
[tex]\sf{8}[/tex]
Done !! Hope this made sense to you !!
⊱________________________________________________________⊰
[tex]\small\pmb{\tt{CALLIGRAPHY}}[/tex]
The graphs of f(x) and g(x) are shown below.
f(x) = -x g(x) =2x
Which of the following is the graph of (g-f)(x)?
[tex](g-f)(x)=g(x)-f(x)=2x-(-x)=3x[/tex]
The graph is shown in the attached image.
Find the missing length indicated. need help
Step-by-step explanation:
the formula for the height in a right-angled triangle is
h = sqrt(p×q)
p and q being the segments of the Hypotenuse left and right from the point, where the height intersects with the Hypotenuse.
so, in our case
12 = sqrt(16×(x-16))
let's square this to eliminate the square root :
144 = 16×(x - 16) = 16x - 256
400 = 16x
x = 25
The probability distribution for a
random variable x is given in the table.
x
-5 -3 -2 0
Probability 17
13 .33 16
2
.11
3
.10
Find the probability that -2 < x < 2
Answer:
0.6 or 60%
Step-by-step explanation:
According to the distribution table, the percent values within the interval of [- 2, 2] are:
0.33, 0.16, 0.11Add them together to get the required answer:
0.33 + 0.16 + 0.11 = 0.6 or 60%The answer is 0.6 or 60%.
The respective probabilities that lie in the interval [-2, 2] are 0.33, 0.16, and 0.11. Therefore, the probability it lies in the interval is equal to the sum of the probabilities.
0.33 + 0.16 + 0.110.49 + 0.110.6 = 60%Find f−1(x) for f(x)=15+12x.
Answer:
[tex]\text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]
Step-by-step explanation:
[tex]\text{f}^{-1}(x)[/tex] is the notation for the inverse of a function.
The inverse of a function is a reflection in the line y = x.
Given function:
[tex]\text{f}(x)=15+12x[/tex]
To find the inverse of the given function:
Step 1
Replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=15+12x[/tex]
Step 2
Rearrange the equation to make x the subject:
[tex]\implies y-15=15+12x-15[/tex]
[tex]\implies y-15=12x[/tex]
[tex]\implies \dfrac{y-15}{12}=\dfrac{12x}{12}[/tex]
[tex]\implies x=\dfrac{y-15}{12}[/tex]
Step 3
Replace x with [tex]\text{f}^{-1}(x)[/tex] and y with x → this is the inverse function:
[tex]\implies \text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]
Step 4 (if necessary)
The domain of the function is the range of the inverse function.
The range of the function is the domain of the inverse function.
Therefore, as the domain and range of the given function are unrestricted, so too are the domain and the range of the inverse function:
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[tex]\\ \rm\leadsto y=15+12x[/tex]
Interchange x and y
[tex]\\ \rm\leadsto x=15+12y[/tex]
Solve for y
[tex]\\ \rm\leadsto 12y=x-15[/tex]
[tex]\\ \rm\leadsto y=\dfrac{x-15}{12}[/tex]
That's the inverse
Marco has joined a bowling league, and is trying to raise his average to 130. On his last four games he scored 128, 127, 123, and 122. How much will he need to score on the next game to raise his mean to 130?
The score Macro needs in his next game to have a mean of 130 is 150.
What should be the next score?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
130 = (128 + 127 + 123 + 122 + x) / 5
Where x represents the fifth score
130 = (500 + x) / 5
130 x 5 = 500 + x
650 = 500 + x
650 - 500 = x
x = 150
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Identify an equation in point-alope form for the line perpendicular to y-x-7 that passes through (-2,-6).
Answer:
[tex]y + 6 = -1(x + 2).[/tex]
Step-by-step explanation:
Let's find the general equation of the given line:
[tex]y - x - 7 = 0\\\\y = x + 7.[/tex]
We can see that [tex]m = 1.[/tex]
Thus, the slope of any perpendicular line to the line [tex]y = x + 7[/tex] is [tex]-1.[/tex]
Given that the perpendicular line passes through (-2, -6), its point-slope form equation is as given:
[tex]y - y_1 = m(x - x_1)\\\\y - (-6) = -1(x - (-2))\\\\y + 6 = -1(x + 2).[/tex]
Two-thirds of a number x is at least 10. Find the smallest possible prime number x.
The smallest possible prime number x is 17.
What is Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
given, Two-thirds of a number x is at least 10.
So,
2/3 x ≥ 10
x ≥ 15
First prime number that is bigger than 15 is 17.
therefore, The smallest possible prime number x is 17.
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Tim Worker is checking his earnings statement. His weekly earnings are $520.00. If he claims two exemptions, how much tax is withheld? 18.73 15.40 17.65 16.48
The tax that will be withheld is D. $16.48.
How to calculate the tax?From the information, it was stated that Tim Worker is checking his earnings statement and that his weekly earnings are $520.00.
The tax that will be withheld will be:
= 3.16% × $520
= $16.48
In conclusion, the correct option is D.
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O. Find the distance between P (10,-7) and Q (7,- 10). Leave your answer in radical
form.
Answer:
[tex]3 \sqrt{2} [/tex]
Step-by-step explanation:
You can the distance between P(10,-7) and Q(7,-10) by using 'PQ=
[tex] \sqrt{(10 - 7) ^{2} } + \sqrt{ ( - 7 + 10) ^{2} } [/tex]
Also, for example the distance between A(a,b) and B(c,d)
is
[tex] \sqrt{(a - c)^{2} } + \sqrt{(b - d) ^{2} } [/tex]
Answer:
[tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.
Step-by-step explanation:
To find the distance between two points, we can use the Distance Formula.
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given:
P (10, -7) ⇒ x₁ = 10, y₁ = -7
Q (7, -10) ⇒ x₂ = 7, y₂ = -10
Substitute the given values into the formula and simplify.
[tex]\\\implies d=\sqrt{\bold{(7-10)}^2+\bold{(-10-(-7))}^2}\\\\\implies d=\sqrt{\bold{(-3)}^2+\bold{(-10+7)}^2}\\\\\implies d=\sqrt{9+\bold{(-3)}^2}\\\\\implies d=\sqrt{\bold{9+9}}\\\\\implies d=\sqrt{\bold{18}}\\\\\implies d=\sqrt{\bold{9}\times2}\\\\\implies d=3\sqrt{2}[/tex]
The distance between points P and Q is [tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.
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where is the center of the circle and the radius is how many units?
Answer:
8,9,5
Step-by-step explanation:
A baseball player had 4 hits in 8 games. At this rate, how many hits will the baseball player have in the next 28 games?
O 14
O24
28
O 56
Answer:
14
Step-by-step explanation:
If a baseball player records 4 hits in 8 games, then the player records 1 hit every 2 games. Therefore, the player will have 14 more hits in the next 28 games.
A group of researchers wants to develop an experiment to determine whether a new drug effectively treats high blood pressure. The researchers want to inject the drug in monkeys first to determine whether there are any potential serious side effects.
Part A: What are some possible ethical issues to this type of testing? (5 points)
Part B: While conducting the experiment, the researchers find that blood pressure levels return to normal, and they declare the drug is the cause of the change. Is this a good assumption? Explain. (5 points)
The ethical issues about testing with animals is it resulting in suffering and they have the right to live without human interference.
What is Experiment?This is defined as a procedure which is carried in order to support or refute a hypothesis.
The blood pressure returning to normal when the drugs were used on the animals is a good assumption as most parts of the animal and human body work similarly.
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Suppose that X-N (2,6) is a normal distribution with mean 2 and standard deviation 6. What value of x has a z-score of three?
The value of x has a z-score of three is 20
How to determine the value of x?The given parameters are:
Mean = 2
Standard deviation = 6
z = 3
The z-score is calculated as:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]3 = \frac{x -2}{6}[/tex]
Multiply through by 6
18 = x - 2
Add 2 to both sides
x = 20
Hence, the value of x has a z-score of three is 20
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Find sec, tan 0, and sin 0, where is the angle shown in the figure.
Give exact values, not decimal approximations.
0
4
5
The exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.
How to determine the trigonometric ratiosFrom the figure, we have the values of the sides to be;
opposite side = 5Adjacent side = 4Let's use Pythagorean theorem to find the hypotenuse(x)
Hypotebuse square = opposite side square + adjacent side square
Substitute the values deduced from the figures given
x² = 5² + 4²
x² = 25 + 16
x² = 41
x = [tex]\sqrt{41}[/tex]
x = 6. 4
sin θ = opposite/hypotenuse
Substitute the values
sin θ = 5/ 6. 4
tan θ = opposite/ adjacent
Substitute the values
tan θ = 5/ 4
sec θ = hypotenuse/ adjacent
substitute the values
sec θ = 6. 4/ 4
Thus, the exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.
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Which of the following equations is an example of inverse variation between
the variables x and y?
Answer:
we need a whole example not just the variables.
Step-by-step explanation:
4
Select the correct answer from each drop-down menu.
AABC is similar to ADEF. The ratio of the perimeter of AABC to the perimeter of ADEF is 1:10. T
The length of the longest side of AABC is
2
4
16
30
units. The ratio of the area of AABC to the are.
The ratio of the area of ∆ABC to the area of ∆DEF is; 1:100.
What is the ratio of the area of ∆ABC to the area of ∆DEF?Since, a major criterion for similarity and congruence of triangles is that the ratio of corresponding sides are equal.
On this note, since the task content suggest that the ratio of the perimeters is; 1:10, it follows from conventional mathematics that the ratio of their areas is given as; 1²:10²; 1:100.
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where are the two variables is part A? Tiya earns $7 an hour mowing her neighbor's lawn.
Part A: Create two variables and determine which is dependent and which is independent for this situation. (4 points)
The two variables are; earnings, y and hours, x in which case, the former is the dependent variable while the latter is the independent variable.
Which is the dependent and which is the independent variable?It follows from the task content that Tiya earns $7 an hour mowing her neighbor's lawn.
On this note, it follows that the amount of money earned by Tiya is a dependent variable which solely depends on the number of hours spent on the job, which is the independent variable.
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`H_0: p = 0.63`
`H_1: p > 0.63`
Your sample consists of 150 subjects, with 96 successes. Calculate the test statistic, rounded to 2 decimal places
`z=`
The test statistic, rounded to 2 decimal places is equal to
How to calculate value of the test statistic?For this sample, the hypothesis is given by:
H₀: μ₁ ≤ μ₂
H₁: μ₁ > μ₂
Assuming this sample has a normal distribution, we would use a pooled z-test to determine the value of the test statistic:
Substituting the given parameters into the formula, we have;
[tex]z = \frac{\frac{96}{150} \;-\;0.63}{\sqrt{0.63\; +\; \frac{1\;-\;0.63}{150}} }\\\\z = \frac{0.64 \;-\;0.63}{\sqrt{0.63\; +\; \frac{0.37}{150}}}\\\\z = \frac{0.01}{\sqrt{0.63\; +\; 0.0025}}\\\\z = \frac{0.01}{\sqrt{0.6325}}\\\\[/tex]
z = 0.01/0.7953
z = 0.013.
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Q19. When a resistor is placed across 230M supply (de) the
current is 12A. What is the value of resistor that must
De connected in parallel to increase the load current
to 16a
The value of the resistor that must be connected in parallel is 57.47 ohms
How to determine the resistor connected across the 230 V supplyVoltage (V) = 230 VCurrent (I) = 12 AResistor 1 (R₁) =?V = IR
230 = 12 × R₁
Divide both sides by 12
R₁ = 230 / 12
R₁ = 19.17 ohms
How to determine the total resistanceVoltage (V) = 230 VCurrent (I) = 16 ATotal resistance (Rₜ) =?V = IR
230 = 16 × Rₜ
Divide both sides by 12
Rₜ = 230 / 16
Rₜ = 14.375 ohms
How to determine the resistor connected in paralleResistor 1 (R₁) = 19.17 ohms Total resistance (Rₜ) = 14.375 ohmsResistor 2 (R₂) = ?1/Rₜ = 1/R₁ + 1/R₂
Collect like terms
1/R₂ = 1/Rₜ - 1/R₁
R₂ = (Rₜ × R₁) / (R₁ - Rₜ)
R₂ = (14.375 × 19.17) / (19.17 - 14.375)
R₂ = 57.47 ohms
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The isosceles trapezoid is part of an isosceles triangle with a 34° vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not drawn to scale.
Suppose a set of scores in College Mathematics are 5, 15, 25, 30, 3. Which of the following is true?
a.
the mean is equal to the median
b.
the mean is less than the median
c.
the mean is greater than the median
d.
the mode is 15
Answer: c. the mean is greater than the median
Explanation:
To find out the correct answer, we first must know the true meanings and the method of calculation of the terms, "mean", "mode" and "median".
Mean: The mean is a type of average. It is the sum of all the values in a set of data, such as numbers of measurements, divided by the numbers of values on the list.
Formula for finding mean-[tex]\bar{x} = \dfrac{\sum x}{n}[/tex] where, [tex]\bar{x}=[/tex] sample mean
[tex]\sum x =[/tex] sum of each value in sample
[tex]n =[/tex] number of values in the sample
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the mean is 5.875 (6+3+9+6+6+5+9+3/8).
Mode: The mode is the number which appears most often in a set of numbers.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6.
Median: The median is the "middle" of a sorted list of numbers in ascending order (small to big). To find the Median, place the numbers in value order and find the middle.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the median is 6. (in 3,3,5,6,6,9,9, the middle number is 6 )
with an even amount of numbers things are slightly different.
In that case we find the middle pair of numbers, and then find the value that is half way between them. This is easily done by adding them together and dividing by two. (basically averaging the middle two numbers incase there is an even set of numbers)
Example: 3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29
When we put those numbers in order we have:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers.
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
In this example the middle numbers are 21 and 23.
To find the value halfway between them, add them together and divide by 2: 21 + 23 = 44, then 44 ÷ 2 = 22
So the Median in this example is 22.
(Note that 22 was not in the list of numbers ... but that is OK because half the numbers in the list are less, and half the numbers are greater.)
Now that you understand the terms clearly, let's find out the mean, mode and median from your given set of numbers.
5, 15, 25, 30, 3
Mean: (5+15+25+30+3)/5 is, 15.6
Mode: None since none of the numbers repeated more than once.
Median: 3,5,15,25,30 , so the middle number is 15 .
Since there is no mode, option d. can never be the answer. And clearly, 15.6 is greater than 15 so the answer should be c. the mean is greater than the median.
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Find the point on the line y = 5x + 2 that is closest to the origin.
Answer: [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]
Step-by-step explanation:
The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to [tex]y=5x+2[/tex] and crosses the origin.
We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.
Opposite Reciprocal of 5: [tex]-\frac{1}{5}[/tex]
Now that we have the slope and the point, we can use the point-slope form to get the equation of the perpendicular.
Point-Slope Form: [tex]y-y_1=m(x-x_1)[/tex] (m is slope, [tex]x_1[/tex] and [tex]y_1[/tex] are the point's coordinates)
[tex]y-0=-\frac{1}{5}(x-0)\\y=-\frac{1}{5}x[/tex]
Since we need to find a point on the original line that's closest to the origin, we need to find the intersection of the line and its perpendicular. We can do this by setting both lines equal to each other and solving for x and y.
[tex]5x+2=-\frac{1}{5}x\\25x+10=-x\\26x=-10\\x=-\frac{10}{26}\\x=-\frac{5}{13}[/tex]
Substituting x in any of the equations will give us y. Here, I will put it in the equation [tex]y=-\frac{1}{5}x[/tex]
[tex]y=-\frac{1}{5}*-\frac{5}{13}\\y=\frac{5}{65}\\y=\frac{1}{13}[/tex]
The closest point to the origin on the line [tex]y=5x+2[/tex] is [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]
The point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).
What is the point slope form?The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
The given equation of a line is y=5x+2 ------(I)
The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to y=5x+2 and crosses the origin.
We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.
So, slope of perpendicular line is -1/5
The equation of the point slope form is: (y - y1) = m(x - x1)
Now, substitute m=-1/5 and (x, y)=(0, 0), we get
y-0=-1/5 (x-0)
y=-1/5 x -----(II)
Equate equation (I) and (II), we get
5x+2=-1/5 x
⇒ -x=25x+10
⇒ -26x=10
⇒ x= -5/13
So, y=-1/5 x =1/13
Therefore, the point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).
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The lengths of the sides of a pentagons are 2'', 6'', 10'' , 14'', and 24''. calculate the lengths of the sides of a similar pentagon if the shortest side is 5'' .
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"How to get the lengths of the sides of a similar pentagon?
All the measures must be multiplied by the same scale factor to get a similar pentagon.
If in the original pentagon the shortest side measures 2", and in the similar pentagon the shortest side measures 5", then we have:
5" = k*2"
5"/2" = k = 2.5
Then the scale factor is 2.5
To get the other sides of the pentagon, we just need to multiply the other sides of the original pentagon by 2.5
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"If you want to learn more about similar figures:
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A candy company designs a package to hold chocolates. The height of the container is 13 inches and the diameter of its bottom is 9 inches. Diagram shows a shape with circular base and curved surface meeting at a point. The diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches. Which shape best models the package, and what is the approximate surface area of the package? The best model for the package is a . The approximate surface area is square inches.
The best model for the package is a cone and the approximate surface area is 258 square inches.
How to illustrate the information?From the information given, it was stated that the diagram shows a shape with circular base and curved surface meeting at a point. The diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches.
In this case, the information given about the diagram shows that it's a cone.
Also, given the information, the total surface area of the cone that has a slant height and diameter is given as:
= π(d/2)(d/2 + l)
In such a situation, it should be noted that d represents the diameter in the question. The surface area is the total area that's covered by its surface.
Therefore, the best model for the package is a cone and the approximate surface area is 258 square inches.
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