The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
Option B is the correct answer.
We have,
To find the probability that the mean of the sample will be between 94.7 inches and 95.3 inches, we can use the Central Limit Theorem.
According to the Central Limit Theorem, the distribution of sample means approaches a normal distribution as the sample size increases.
In this case, the mean of the population (μ) is 95 inches and the standard deviation of the population (σ) is 0.52 inches.
Since the sample size is sufficiently large (n = 30), we can assume that the distribution of sample means will be approximately normal.
To calculate the probability, we need to standardize the sample mean using the z-score formula:
z = (x - μ) / (σ / √n)
where:
x = sample mean
μ = population mean
σ = population standard deviation
n = sample size
Let's calculate the z-scores for the lower and upper limits:
z1 = (94.7 - 95) / (0.52 / √30)
z2 = (95.3 - 95) / (0.52 / √30)
Now, we can use a standard normal distribution table or a calculator to find the probability associated with these z-scores.
Using a standard normal distribution table or a calculator, we find:
P(z1 < Z < z2) ≈ 0.436
Therefore,
The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
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The track below has two straight lengths and two curved ends. What is the distance around the track to the nearest tenth of a meter?
The Distance around the track is 400.4 meters
In order to determine the distance around a track with two straight sections and two curved ends,
we must first determine the lengths of each section.
Let us consider the given diagram.The distance of the straight section can be determined by adding the length of two opposite sides together. Let us assume that each side of the straight section measures 50 meters. Thus, the total length of the straight section is:50m + 50m = 100mTo calculate the length of the curved sections, we must first determine the radius of each section.
This can be done by dividing the diameter by 2, since the diameter is not given,
we can divide the total length of each curved section by pi (3.14) and then divide the answer by 2 to get the radius of each section.
Let's say the total length of each curved section is 150 meters, therefore, the radius is:150m / 3.14 / 2 = 23.89m (rounded to the nearest hundredth)
Therefore, the circumference of each curved section is:2πr = 2 x 3.14 x 23.89 = 150.18m (rounded to the nearest hundredth)
So, the total distance around the track is:100m + 150.18m + 150.18m = 400.36 meters (rounded to the nearest tenth).
Therefore, the distance around the track is 400.4 meters (rounded to the nearest tenth).
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Triangles DEF and D'E'F' are shown on the coordinate plane below: H F D D' 2 -8-7--5-4-3-2-1 1 2 3 4 5 6 7 8 T 20 F CO What rotation was applied to triangle DEF to create triangle D'E'F'?
please help me it's due tomorrow
The value of sin θ is equal to 3/5.
We have,
Given that θ is the angle for which [tex]cos^{-1}(4/5)[/tex] is equal to, we can determine the value of sin θ using the trigonometric identity:
sin²θ + cos²θ = 1
To find sin θ, we can rearrange the identity as:
sin θ = √(1 - cos²θ)
Since θ satisfies the condition 0 < θ < π/2, we know that cos θ is positive, and thus we can directly substitute [tex]cos^{-1}(4/5)[/tex] into the equation:
sin θ = √(1 - (4/5)²)
sin θ = √(1 - 16/25)
sin θ = √(9/25)
Since 0 < θ < π/2, sin θ is positive.
Therefore:
sin θ = 3/5
Hence,
The value of sin θ is equal to 3/5.
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Label each of the following scale factors based on whether they would cause an expansion or a contraction.
0.75
4/5
-7
11/9
-4.3
NO LINKS!
Answer:
0.75 = contraction
4/5 = contraction
-7 = expansion
11/9 = expansion
-4.3 = expansion
Step-by-step explanation:
The scale factor is a numerical value that expresses the proportional change in size between an original object or figure and a scaled version of it.
ExpansionIf the magnitude of the scale factor is greater than 1, it indicates an expansion, meaning the new size is larger than the original size.
ContractionIf the magnitude of the scale factor is between 0 and 1, it indicates a contraction, meaning the new size is smaller than the original size.
ReflectionIf the scale factor is negative, it indicates a reflection in addition to the expansion or contraction.
[tex]\hrulefill[/tex]
As 0.75 is between 0 and 1, the scale factor of 0.75 would cause a contraction.
As 4/5 is between 0 and 1, the scale factor of 4/5 would cause a contraction.
As the magnitude of -7 is 7, and 7 is greater than 1, the scale factor of -7 would cause an expansion.
As 11/9 is greater than 1, the scale factor of 11/9 would cause an expansion.
As the magnitude of -4.3 is 4.3, and 4.3 is greater than 1, the scale factor of -4.3 would cause an expansion.
Answer:
0.75: Contraction
4/5: Contraction
-7: Expansion
11/9: Expansion
-4.3: Expansion
Step-by-step explanation:
0.75: This scale factor is less than 1, indicating a decrease in size. It would cause a contraction.4/5: This scale factor is less than 1, indicating a decrease in size. It would cause a contraction.-7: This scale factor is negative, indicating a change in direction. It would cause an expansion.11/9: This scale factor is greater than 1, indicating an increase in size. It would cause an expansion.-4.3: This scale factor is negative, indicating a change in direction. It would cause an expansion.find the equation of the line. the line passes through the points (5, 2) and (- 4, - 4)
to get the equation of any straight line, we simply need two points off of it.
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-4}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-4}-\underset{x_1}{5}}} \implies \cfrac{ -6 }{ -9 } \implies \cfrac{2}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{5}) \\\\\\ y-2=\cfrac{2}{3}x-\cfrac{10}{3}\implies y=\cfrac{2}{3}x-\cfrac{10}{3}+2\implies {\Large \begin{array}{llll} y=\cfrac{2}{3}x-\cfrac{4}{3} \end{array}}[/tex]
I need someone’s Help on this question
[tex]\begin{array}{llll} \text{\LARGE -3}(4x-7y&=&2)\\ ~~ \text{\LARGE 4}(3x-3y&=&6) \end{array}\implies \stackrel{ \textit{\LARGE eliminating "x"} }{\begin{array}{llll} -12x+21y&=&-6\\ ~~ 12x-12y&=&24\\\cline{1-3}\\ \qquad 0+9y&=&18 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \text{\LARGE -3}(4x-7y&=&2)\\ ~~ \text{\LARGE 7}(3x-3y&=&6) \end{array}\implies \stackrel{ \textit{\LARGE eliminating "y"}}{\begin{array}{llll} -12x+21y&=&-6\\ ~~ 21x-21y&=&42\\\cline{1-3}\\ \quad 9x+0&=&36 \end{array}}[/tex]
now to get them hmmm we can use either equation, say hmmm let's use the 2nd one
[tex]9x+0=36\implies x=\cfrac{36}{9}\implies \boxed{x=4} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{4(4)-7y=2}\implies 16-7y=2\implies 16=7y+2 \\\\\\ 14=7y\implies \cfrac{14}{7}=y\implies \boxed{2=y} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill~(4~~,~~2)~\hfill~[/tex]
quick clarification for a misleading material in the question
what's the second pair? well, is a system of equations of two lines, they only meet at one point, so there's only one pair, or we can say the second pair is the same as the first pair, redundant and unnecessary, but hmmm so it's.
Answer:
Question 1:
In order to eliminate the x variables in this systems of equations problem using the elimination method, the value of x in the top and bottom equations must cancel each other out.
In order to get this to happen, we can multiply the top equation by 3 and the bottom equation by -4. This way the x value of the top equation becomes 12x and the x value of the bottom equation becomes -12x. These values would cancel each other out, letting you solve for y.
So, question 1 answer: (3, -4) OR (-3, 4)
(both will result in getting a 12x and -12x in the top or bottom that will cancel)
Question 2:
The idea from question 1 can be applied here too:
To eliminate the y variables, we must make the y values in the top and bottom equations cancel each other out.
We can multiply the top equation by 3 and the bottom equation by -7, resulting in -21y in the top equation, and 21y in the bottom equation.
So, question 2 answer: (3, -7) OR (-3, 7)
(both will result in getting a 21y and -21y in the top or bottom that will cancel)
Show your work please it’s due Tuesday please
let's convert all mixed fractions to improper fractions, then add them up.
[tex]\stackrel{mixed}{2\frac{1}{10}}\implies \cfrac{2\cdot 10+1}{10}\implies \stackrel{improper}{\cfrac{21}{10}}~\hfill \stackrel{mixed}{1\frac{2}{7}} \implies \cfrac{1\cdot 7+2}{7} \implies \stackrel{improper}{\cfrac{9}{7}} \\\\\\ \stackrel{mixed}{4\frac{9}{10}}\implies \cfrac{4\cdot 10+9}{10}\implies \stackrel{improper}{\cfrac{49}{10}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{21}{10}+\left(\cfrac{9}{7}+\cfrac{49}{10} \right)\implies \cfrac{21}{10}+\left(\cfrac{(10)9~~ + ~~(7)49}{\underset{\textit{using this LCD}}{70}} \right)\implies \cfrac{21}{10}+\left(\cfrac{90+343}{70} \right) \\\\\\ \cfrac{21}{10}+\left(\cfrac{433}{70} \right)\implies \cfrac{21}{10}+\cfrac{433}{70}\implies \cfrac{(7)21~~ + ~~(1)433}{\underset{\textit{using this LCD}}{70}}\implies \cfrac{147+433}{70} \\\\\\ \cfrac{580}{70}\implies \cfrac{58}{7}\implies 8\frac{2}{7}[/tex]
Step-by-step explanation:
[tex]2 \frac{1}{10} + (1 \frac{2}{7} + 4 \frac{9}{10} )[/tex]
[tex]2 \frac{1}{10} = \frac{21}{10} [/tex]
[tex]1 \frac{2}{7} = \frac{9}{7} [/tex]
[tex]4 \frac{9}{10} = \frac{49}{10} [/tex]
[tex] \frac{21}{10} + ( \frac{9}{7} + \frac{49}{10} )[/tex]
[tex]( \frac{9}{7} + \frac{49}{10} ) = \frac{90 + 343}{70} = \frac{433}{70} [/tex]
[tex] \frac{21}{10} + \frac{433}{70} = \frac{147 + 433}{70} = \frac{580}{70} = 8 \frac{2}{7} [/tex]
A line passes through the point(-7,-4) and has a slope of 3
Answer:
[tex]y=3x+17[/tex]
Step-by-step explanation:
Use point-slope form
[tex]y-y_1=m(x-x_1)\\y-(-4)=3(x-(-7))\\y+4=3(x+7)\\y+4=3x+21\\y=3x+17[/tex]
Melanie invested $2,500 at 5% for 15 years. Josiah invested $1,000 at 10% for five years. Who will earn the most money over time?
Answer:
Melaine
Step-by-step explanation:
[tex]\text{Melaine's Total Earnings}=\$2500(1.05)^{15}=\$5197.32\\\text{Josiah's Total Earnings}=\$1000(1.10)^{10}=\$2593.74[/tex]
Therefore, Melaine will earn the most money over time
Given the following definitions: U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 5} B = {1, 3, 5, 7} How many elements are in A' ∩ B' ? Your Answer:
[tex]A'=\{3,6,7\}\\B'=\{2,4,6\}\\A'\cap B'=\{6\}[/tex]
Therefore, [tex]n(A'\cap B')=1[/tex].
Answer:
1 element
Step-by-step explanation:
A' means not A and B' means not B
∩ means both
so now we have how many elements are not in A and not in B
A has 1,2,4,5 so not A will be 3,6,7
B has 1,3,5,7 so not B will be 2,4,6
now we look at what not A and not B have together and that is 1 element {6}
The Peel Trading Company received an invoice dated September 20 for $ less 25%, 20%, terms 5/10, 2/30, n/60. Peel made a payment on September 30 to reduce the debt to $5000 and a payment on October 20 to reduce the debt by $3000.
(a)
What amount must Peel remit to pay the balance of the debt at the end of the credit period?
(b)
What is the total amount paid by Peel?
The Total amount paid by Peel is $8000. Peel must remit $13,333.33 to pay the balance of the debt at the end of the credit period.
(a) To determine the amount Peel must remit to pay the balance of the debt at the end of the credit period, we need to calculate the remaining balance after the two payments.
The original invoice amount is not given in the question, so we'll calculate it using the given discounts. Let's assume the original invoice amount is X dollars.
First, let's calculate the amount after a 25% discount:
Amount after 25% discount = X - 0.25X = 0.75X
Next, let's calculate the amount after a 20% discount:
Amount after 20% discount = 0.75X - 0.20(0.75X) = 0.75X - 0.15X = 0.60X
Now, let's consider the payment on September 30 to reduce the debt to $5000:
Remaining balance after September 30 payment = 0.60X - $5000
Finally, let's consider the payment on October 20 to reduce the debt by $3000:
Remaining balance after October 20 payment = (0.60X - $5000) - $3000
To find the amount Peel must remit to pay the balance, we set the remaining balance equal to zero and solve for X:
(0.60X - $5000) - $3000 = 0
Simplifying the equation:
0.60X - $8000 = 0
0.60X = $8000
X = $8000 / 0.60
X = $13,333.33
Therefore, Peel must remit $13,333.33 to pay the balance of the debt at the end of the credit period.
(b) To find the total amount paid by Peel, we sum the two payments made by Peel:
Total amount paid = $5000 + $3000
Total amount paid = $8000
Therefore, the total amount paid by Peel is $8000.
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.................................................................
Second option is the answer to this questions
Answer:
Rosa can make one one unique insosceles triangle
Step-by-step explanation:
cause What is the full meaning of equilateral?
having all sides equal
: having all sides equal. an equilateral triangle. an equilateral polygon. see triangle illustration. : having all the faces equal.
magiging tall triangle lang naman yung triangle ni rosa hindi naman yan equal so insosceles at hindi naman equal side yung 7cm(2x) na stick with 5cm 100 percent sure ako na insosceles yarn
LEO is rotated -270 about the point (1,1) Draw the image of this rotation using the interactive graph
Please find attached the drawing of the image of the triangle ΔLEO following a rotation transformation of -270° about the point (1, 1), created with MS Excel
What is a rotation transformation?A rotation transformation is one in which the points on a geometric figure are rotated or turned about a specified point by a specified amount and direction.
The coordinates of the vertices of the triangle ΔLEO are;
L(-3, 4), E(-5, -3), O(-6, 1)
The relative coordinates of the vertices of the triangle ΔLEO to the (1, 1) are;
Relative coordinates of L ⇒ '(-3 - 1, 4 - 1) = '(-4, 3)
Relative coordinates of E ⇒ '(-5 - 1, -3 - 1), = '(-6, -4)
Relative coordinates of O ⇒ '(-6 - 1, 1 - 1) = '(-7, 0)
The coordinates of a point (x, y), following a rotation of -270° (270° clockwise) is (-y, x)
Therefore, the coordinates of the vertices of the triangle following a rotation of -270° about the point (1, 1), are;
'(-4, 3) → Rotation → ''(-3, -4)
'(-6, -4) → Rotation → ''(4, -6)
'(-7, 0) → Rotation → ''(0, -7)
The coordinates of the vertices relative to the origin are therefore;
''(-3 + 1, -4 + 1) ⇒ L'(-2, -3)
''(4 + 1, -6 + 1) ⇒ E'(5, -5)
''(0 + 1, -7 + 1) ⇒ O'(1, -6)
The coordinates of the vertices of the image of the triangle ΔLEO can be used draw the image using MS Excel, as shown in the attached diagram of the triangle ΔLEO and the image ΔL'E'O'
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there are 2 containers of beads. container a has 400 black beads and 250 white beads. container b has 200 black beads and 670 white beads. how many black and white beads must be transferred from b to a so that 50% of the beads in a are white and 25% of the beads in b are black?
Step-by-step explanation:
First box contains 8 black and 12 white beads Second box contains 9 black and 6 white beads.
(a) One black bead from each box is taken.
Number of such cases = 8×9=72
Total number of possibilities = 20×15=300
Probablity of getting both black beads =
300
72
=
25
6
(b) One black and one white bead is taken.
So if one black bead is taken from first box then one white bead is taken from second box and if one white bead is taken from first box then one black bead is taken from second box.
Number of such cases = 8×6+12×9=48+108=156
Total number of possibilities = 20×15=300
Probablity of getting one black and one white bead =
300
156
=
25
13
1. Illustrate an exterior angles
of a triangle and Name all the
exterior angles.
PLS NEED ANSWER ASAPPP
Step-by-step explanation:
An exterior angle of a triangle is formed when one side of a triangle is extended. The nonstraight angle (the one that is not just the extension of the side) outside the triangle, but adjacent to an interior angle, is an exterior angle of the triangle (Figure 1 ).
Exterior angle of a triangle.
In Figure 1, ∠ BCD is an exterior angle of Δ ABC.
Because m ∠1 + m ∠2 + m ∠3 = 180°, and m ∠3 + m ∠4 = 180°, you can prove that m ∠4 = m ∠1 + m ∠2. This is stated as a theorem.
Theorem 26: An exterior angle of a triangle is equal to the sum of the two remote (nonadjacent) interior angles.
I need some help if anyone sees this and knows how please lmk!!
The true statement are:
Both printers will print the same number of poster for $25.Poster Perfect cost less if you want to print more than 5 posters.Poster Perfect: Since Poster Perfect charges a setup fee of $10 plus $3 per poster, the total cost will increase linearly with the number of posters printed.
We can set up equation as
y= 10 + 3x where x is number of pieces
The graph will show a constant slope for PrintPro:
Since PrintPro charges a flat rate of $5 per poster with no setup fee, the total cost will increase at a constant rate as the number of posters printed increases.
We can set up equation as
y= 5x where x is number of pieces
For x = 5
Poster Perfect: y= 10+ 15 = $25
PrintPro: y = 25
and, for x= 6
Poster Perfect: y= 10 + 18 = $28
PrintPro: y = 30
So, the true statement are:
Both printers will print the same number of poster for $25.
Poster Perfect cost less if you want to print more than 5 posters.
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the population of a small town, P, as a function of time, t, in years past 1940 is given below.
P= 1304 + 300t
The population grew to 5650 in 13.48 years .
Given,
Population of town in 1940 is a function given by:
P= 1304 + 300t
Now,
Let total number of population after certain years be 5650.
Let t1 be the year in which the population reached a count of 5650. Solve for t1:
5650= 1304 + 300t1
t1 = 13.48 years
The population grew to the number 5650 in 13.48 years past 1940, approximately 1954 .
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Solve the following system of equations with the substitution method:
y=3/5x-15
y=-3/4x+12
Answer:
x = 20, y = -3
Step-by-step explanation:
Set both equations equal to each other
[tex]\displaystyle y=\frac{3}{5}x-15\\\\y=-\frac{3}{4}x+12\\\\\\\\\frac{3}{5}x-15=-\frac{3}{4}x+12\\\\\frac{12}{20}x-15=-\frac{15}{20}x+12\\\\\frac{27}{20}x-15=12\\\\\frac{27}{20}x=27\\\\x=20\\\\y=\frac{3}{5}x-15\\\\y=\frac{3}{5}(20)-15\\\\y=\frac{60}{5}-15\\\\y=12-15\\\\y=-3[/tex]
Que número estoy pensando si al multiplicarlo por 4 y luego de sumarle 16 obtengo 8?
Para encontrar el número que estás pensando, podemos plantear una ecuación. Denotemos al número desconocido como "x". Según la información proporcionada, podemos escribir la ecuación:
4x + 16 = 8
Ahora resolvamos la ecuación para encontrar el valor de "x":
4x = 8 - 16
4x = -8
x = -8/4
x = -2
Entonces, el número que estás pensando es -2.
If Sherry Smith received 820 votes, how many total votes were cast? Round your answer to the nearest whole number.
Sherry Smith received 820 votes, the total Number of votes cast was 1000.
The total number of votes cast if Sherry Smith received 820 votes, you need to be provided with information on the percentage of votes Sherry Smith won. This is because knowing the percentage of votes Sherry Smith won would enable you to calculate the total number of votes cast, as follows:
If Sherry Smith won x percent of the total votes cast, then the total number of votes cast would be:
A total number of votes cast = (820 ÷ x) × 100We can use the formula above to calculate the total number of votes cast as follows:
If Sherry Smith won 82 percent of the total votes cast, then the total number of votes cast would be: Total number of votes cast = (820 ÷ 82) × 100Total number of votes cast = 1000 votes
Therefore, Sherry Smith received 820 votes, and the total number of votes cast was 1000.
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To win the jackpot, 4 different numbers are randomly selected from 1 to 45 and one number from 1 to 30. The order of the first 4 numbers does not matter. What is the probability of winning the jackpot on one try? type your answer as a fraction or in scientific notation
The probability of winning is given as P(winning) = 1 / 4,469,850
How to solve for the probabilityC(45, 4) = 45! / [4!(45-4)!]
= 45*44*43*42 / (4*3*2*1)
= 148995
So, the total number of possible outcomes is 148995 * 30 = 4,469,850.
Now, we have to figure out the number of winning outcomes. In a lottery, there's typically only one winning combination (the numbers drawn), so the number of winning outcomes is 1.
This is an incredibly small probability, indicating that the chances of winning this kind of lottery on a single ticket are extremely low.
P(winning) = 1 / 4,469,850
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What percent of the 8th graders prefer comedies? Round your answer to the nearest whole number percent.
Answer:
Step-by-step explanation:
Thee percentage of 8th graders that prefer comedies is 44%
Probability of an eventpercentage is the ratio of required to the total number of samples in an experiment.
Here,
8th graders that prefer comedies = 18
Total number of 8th graders = (10+18+13) = 41
P(8th that prefer comedies) = (18/41) × 100% = 43.90
Therefore, the percentage of 8th graders that prefer comedies is 44%.
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A bus is scheduled to leave the terminal at 10:15 in the morning and travel for 5 3/4 hours to Bally city. If the bus leaves the terminal 35 minutes late, when will it arrive in Bally city?
Answer:
Step-by-step explanation:
3/4 hours=3/4×60=45 minutes
10:15+5.45 hrs=16:00+0:35=16:35=4.35 pm
so C
A steep mountain is inclined 74 degrees to the horizontal and rises to a height of 3,400 feet above the surrounding plain. A cable car is to be installed running to the top of the mountain from a point 940 feet out in the plain from the base of the mountain. Find the shortest length of cable needed. Round to two decimal places.
Answer:
Step-by-step explanation:
To find the shortest length of cable needed, we can use trigonometry to calculate the length of the hypotenuse of a right triangle formed by the mountain, the cable car, and the ground.
Let's denote the height of the mountain as H = 3,400 feet and the horizontal distance from the base of the mountain to the point where the cable car will be installed as D = 940 feet.
In the right triangle, the vertical leg represents the height of the mountain, the horizontal leg represents the distance from the base to the point where the cable car is installed, and the hypotenuse represents the length of the cable.
We can use the sine function to relate the angle of inclination, the height, and the hypotenuse of the triangle:
sin(angle) = opposite/hypotenuse
In this case, the angle of inclination is 74 degrees, and the opposite side is the height of the mountain (H).
Therefore, we can write the equation as:
sin(74 degrees) = H/hypotenuse
Rearranging the equation, we have:
hypotenuse = H / sin(74 degrees)
Let's calculate the value of sin(74 degrees) and substitute the values to find the length of the hypotenuse:
sin(74 degrees) ≈ 0.9613
hypotenuse = 3,400 / 0.9613 ≈ 3,535.89 feet
Therefore, the shortest length of cable needed is approximately 3,535.89 feet when rounded to two decimal places.
The point A (p, -2) is mirrored in the point B (6,-q). The image is A'(4, -8). What is p and q?
Answer:
p =4
q = -2
Step-by-step explanation:
To mirror is to reflect. See the picture
An open box is constructed from a sheet of A4-size paper by cutting equal-size squares from the four corners and then folding the resulting tabs upwards. If A4-size is 210 mm by 300 mm, what is the maximum possible volume that the box can have?
The maximum possible volume that the box is 446,514.56 cubic millimeters.
Let's assume that we cut squares with side length "x" from each corner of the A4-size paper.
When we fold the resulting tabs upwards, the dimensions of the base of the box will be reduced by 2x on each side.
Therefore, the length of the base of the box will be (300 - 2x) mm, and the width will be (210 - 2x) mm.
The height of the box will be equal to the side length of the squares we cut, which is "x" mm.
The volume of the box is given by the product of its length, width, and height:
Volume = (300 - 2x) (210 - 2x) x
To find the maximum possible volume, we can take the derivative of the volume function with respect to "x" and set it equal to zero:
dV/dx = 0
dV/dx = (300 - 2x)(210 - 2x) + x(-2)(210 - 2x) = 0
(300 - 2x)(210 - 2x) - 2x(210 - 2x) = 0
(300 - 2x)(210 - 2x) - 420x + 4x² = 0
63000 - 840x + 4x² - 420x + 4x² - 420x + 4x³ = 0
8x³ - 1680x + 63000 = 0
x³ - 210x + 7875 = 0
On solving we get x= 46.4 mm
Now, Volume = (300 - 246.4)(210 - 246.4 46.4
= 446,514.56 cubic millimeters.
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What is the volume, in cubic in, of a rectangular prism with a height of 8in, a width of 13in, and a length of 18in?
Answer:
Step-by-step explanation:
V = width x length x height
= 13 x 18 x 8
= 1,872 in³
Answer:
A rectangular prism is a three-dimensional shape that has six rectangular faces. The volume of a rectangular prism is the amount of space inside it. To find the volume of a rectangular prism, we can use the formula: V = lwh, where l is the length, w is the width, and h is the height of the prism. In this case, we are given that the height is 8 in, the width is 13 in, and the length is 18 in. Plugging these values into the formula, we get:
V = lwh
V = (18)(13)(8)
V = 1872
Therefore, the volume of the rectangular prism is 1872 cubic inches.
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According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this increased by approximately 0.6% per year. If this trend continues, in which year will 46% of babies be born out of wedlock?
The ages of members in a family are: 70, 42, 29, 64, 38, 35, 42, 34 What is the mean? What is de Median? What is de mode? What is de Range? What is the standard deviation?
The mean is 46.75, the median is 40, the mode is 42, the range is 41, and the standard deviation is approximately 13.12.
To find the mean, median, mode, range, and standard deviation of the given ages, let's organize the data in ascending order:
29, 34, 35, 38, 42, 42, 64, 70
Mean:
To find the mean, we sum up all the values and divide by the total number of values:
Mean = (29 + 34 + 35 + 38 + 42 + 42 + 64 + 70) / 8
= 374 / 8
= 46.75
Median:
The median is the middle value in a sorted dataset. In this case, we have an even number of values, so we take the average of the two middle values:
Median = (38 + 42) / 2
= 40
Mode:
The mode is the most frequently occurring value. In this case, the mode is 42 since it appears twice, more than any other value.
Range:
The range is the difference between the highest and lowest values:
Range = 70 - 29
= 41
Standard Deviation:
To find the standard deviation, we need to calculate the deviations from the mean, square them, take the average, and then find the square root:
Deviation from the mean: (29-46.75), (34-46.75), (35-46.75), (38-46.75), (42-46.75), (42-46.75), (64-46.75), (70-46.75)
Squared deviations: 339.2656, 167.5625, 122.0625, 71.0625, 21.0625, 21.0625, 340.5625, 527.0625
Average squared deviation: (339.2656 + 167.5625 + 122.0625 + 71.0625 + 21.0625 + 21.0625 + 340.5625 + 527.0625) / 8
= 172.6719
Standard Deviation: √172.6719 ≈ 13.12
Therefore, the mean is 46.75, the median is 40, the mode is 42, the range is 41, and the standard deviation is approximately 13.12.
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If annual interest rate is 8.25% on 90,900.00 What is my interest for 1/2 a month. It's for 8 years.
To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:
Total number of months = 8 years x 12 months/year = 96 months
Next, we can calculate the interest for half a month:
Interest = Principal x Rate x Time
Where:
- Principal = $90,900.00
- Rate = 8.25% (annual interest rate)
- Time = 0.5/12 years (half a month, expressed in years)
Rate needs to be converted to a monthly rate, so we divide it by 12:
Rate = 8.25% / 12 = 0.6875% (monthly interest rate)
Time needs to be expressed in years, so we divide it by 12:
Time = 0.5/12 years
Now we can calculate the interest:
Interest = $90,900.00 x 0.006875 x 0.0416667
Interest = $25.08 (rounded to the nearest cent)
Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.
Answer:
The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64
Step-by-step explanation:
Make a plan:
Monthly Interest Rate: 8.25% / 12 = 0.006875Interest for 1/2 month is 90900 * 0.006875 * 0.5 = 312.46875Total Interest for 8 years is 312.46875 * 8 * 12 = 30032.64Solve the problem:The monthly Interest Rate is 8.25% / 12 = 0.006875 (Ground Truth)Interest for 1/2 month is 90900 * 0.006875 * 0.5 = 312.46875 (ground truth).Total Interest for 8 years is 312.46875 * 8 * 12 = 30032.64 (ground truth).Draw the conclusion:
The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64Hope this helps!
