The probability that the hotel receives at least one of the defective sets is 0.571 or 57.1%.
The probability of receiving at least one of the defective sets is calculated using the formula for the binomial distribution. The formula has 3 variables: the number of trials (n) being 8, the probability of success (p) being 0.286 (4 defective sets divided by 14 total sets) and the number of successes (k) being 1. We calculate the probability by plugging the variables into the formula and summing the probabilities of all the k values from 1 to 8. This gives us a probability of 0.571 or 57.1%.
P(k≥1) = Σ P(X=k)
= P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8)
= 0.286^1.0 x 0.714^7.0 + 0.286^2.0 x 0.714^6.0 + 0.286^3.0 x 0.714^5.0 + 0.286^4.0 x 0.714^4.0 + 0.286^5.0 x 0.714^3.0 + 0.286^6.0 x 0.714^2.0 + 0.286^7.0 x 0.714^1.0 + 0.286^8.0 x 0.714^0.0
= 0.571 or 57.1%
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Given that is it ever possible to have
Explain.
The answer is yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.
What are square roots?A square root of a number is a value that, when multiplied by itself, gives the number.
Given that, is it possible √a+√b = √a+b
Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.
If either a or b equals zero, then the sums would be the same.
Since the square root of 0 is ±0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.
Hence, it is possible to have the sum of square roots equal the square root of the sum of the radicands.
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jay designed 4 t-shirts. sal designed 5 times as many t-shirts. which equation shows how many more t-shirts sal designed?
The equation which shows that how many more t- shirts sal designed is x^{y} .....
If jay designed 4 t-shirts and sal designed 5 times as many t-shirts. So the equation which shows how more t- shirts sal designed is....
Firstly we make the data to simplify the peoblem:
Suppose:
T-shirts designed by jay = x
T-shirts designed by sal = y
As t-shirts designed by jay are 4 so
x=4
and t-shirts designed by sal are 5 times as many t- shirts so
y= 5times = 4×4×4×4×4 = 1,024
So the equation which shows how many more t-shirts sal designed will be:
Required equation = x^{y}
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Passing through (3, 4) and perpendicular to the line whose equation is y=1/9x+8; slope-intercept form
Answer:
y = -9x + 31
Step-by-step explanation:
We can find the slope of the second line using the formula
[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the second line and m1 is the slope of the first.
Thus, since 1/9 is the slope of the first line, we have
[tex]m_{2}=-\frac{1}{(1/9)} \\m_{2}=-9[/tex]
Since the slope intercept form is y = mx + b, where b is the y-intercept, we need to it in the second line by plugging in (3, 4) for x and y and -9 for m:
[tex]4=-9(3)+b\\4=-27+b\\31=b[/tex]
Q) Moira and Non share some money in the ratio 3 : 7.
Non gets $28 more than Moira.
a) What is the total amount of money that they share?
b) How much money do they each get?
The 3 : 7 ratio into which the amount of money is shared by Moira and Non where Non gets $28 more than Moira, indicates;
a) The total amount of money they share is $70
b) The amount Moira gets is $21, while the amount Non gets is 3 : 7
What is a ratio?A ratio is a quantitative expression that specifies the number of times a value is contained within another value.
The ratio by which Moira and Non share the money = 3 : 7
The amount Non gets = 28 + The amount Moira gets
Let x represent the amount Moira gets, therefore;
The amount Non gets = 28 + x
The specified ratio indicates;
[tex]\dfrac{x}{28 + x} = \dfrac{3}{7}[/tex]
7·x = 3 × (28 + x)
7·x = 84 + 3·x
7·x - 3·x = 84
4·x = 84
x = 84 ÷ 4 = 21
x = 21
The total amount of money = The amount Moira gets + The amount Non gets
Therefore; The total amount of money = x + 28 + x = 2·x + 28
2·x + 28 = 2 × 21 + 28 = 70
The total amount of money = $70
b) The amount of money Moira gets, x = $21
The amount of money Non gets = $28 + $21 = $49
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Write the standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and
foci at (5, 0) and (-5, 0).
Answer:
The answer is the standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and foci at (5, 0) and (-5, 0), which is:
x^2 - \frac{y^2}{5} = 1
This equation describes the shape of the hyperbola and allows you to determine the location and size of the hyperbola on a coordinate plane.
Step-by-step explanation:
The standard form equation for a hyperbola with center at the origin, vertices at (1, 0) and (-1, 0), and foci at (5, 0) and (-5, 0) is given by:
$$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$
where $a$ and $b$ are the lengths of the semi-major and semi-minor axes, respectively. In this case, the distance between the vertices is 2, so the semi-major axis is 1 and the semi-minor axis is $\sqrt{5}$. Therefore, the equation of the hyperbola is:
$$\frac{x^2}{1^2} - \frac{y^2}{\sqrt{5}^2} = 1$$
which simplifies to:
x^2 - \frac{y^2}{5} = 1
Write an equation of the line that passes through (4, 8) and is perpendicular to the line y = x-5.
An equation of the perpendicular line is
The slope of a line that is perpendicular to the line y = x - 5 is the negative reciprocal of the slope of y = x - 5. The slope of y = x - 5 is 1, so the slope of the line that passes through (4, 8) and is perpendicular to y = x - 5 is -1.
We can use the point-slope form of a line to write the equation of the line that passes through (4, 8) and has a slope of -1. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, (x1, y1) is (4, 8) and m is -1, so the equation of the line is y - 8 = -1(x - 4). Simplifying this equation, we get y - 8 = -x + 4. Adding 8 to both sides of the equation, we get y = -x + 12. This is the equation of the line that passes through (4, 8) and is perpendicular to y = x - 5.
in a factorial anova, compared to a design with only one independent variable, a major modification of using anova to analyze variability is that the sources of
A t-test cannot cover more than one group. This has to do with the underlying method used to calculate the test value.
Explain about t-test?
The t-test is designed to compare the means of two populations based on the means of the two samples. (any sample from either population).
The most important observation is that the t-test computes the difference between two sample means.
If you have trouble understanding 'variance', you can use the word standard deviation from the previous text to get your points.
In other words, there is more than one difference between the groups, but we want one measure of Total Difference Between Groups. The t-test cannot do that.
So the procedure for groups of three or more is: Run ANOVA first. As a second step, if you have reason to believe that differences exist (based on this test), you can use the t-test to determine where those differences lie.
A t-test cannot cover more than one group. This has to do with the underlying method used to calculate the test value.
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You might need:
Nizhoni adds water at a constant rate to a 2 L reservoir in a water filtering pitcher until it is full.
At the same time, water goes through the filter and out of the reservoir, into the pitcher. It takes
5/11 minutes to fill the reservoir, then another 3 minutes for the reservoir to empty.
3 1/3 minutes for it to empty. at what rate does nizhoni add water to the reservoir?
At the rate of 4 2/5 L of water is added into the reservoir per minute.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
As It takes 5/11 minutes to fill the reservoir.
So, the rate at which Nizhoni adds water to the reservoir.
Rate= Volume/ Time taken
Rate = 2 L/ (5/ 11)
= 2 x 11/5
= 22/5 L/ min
= 4 2/5 L/ min.
Hence, at the rate of 4 2/5 L of water is added into the reservoir in one minute.
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Answer: 5
Step-by-step explanation: I answered this question.
What are the types of triangles based on their sides and angles? How do you classify a triangle as equilateral, isosceles, scalene, acute, right, or obtuse? Give an example of each.
Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles.
A triangle is scalene if all of its three sides and angles are differentScalene-Triangle-1
In the figure, all three symbols that are given on each side are different, which denotes that all three sides are unequal.
If two of its sides are equal, a triangle is called an isosceles.One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.
A triangle with all three equal sides is called equilateral.The sum of all three angles of an equilateral triangle is equal to 180 degrees. 60° + 60° + 60° = 180°
Acute angles measure less than 90 degrees.the examples of acute angles are 25°, 36°, 47°, 64°, 55°, 72°, 80° and so on
Right angles measure 90 degrees.Examples of right angles are all around us. We can see right angles in the corners of a room, book, cube, windows, and at several other places.
Obtuse angles measure more than 90 degreesExamples of obtuse angles include 166°, 121°, 110°, 117°, and 91°.
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PLEASE HURRY! Gianna has 23 feet of leftover wood to use to build a bookshelf. The design calls for two side pieces that are each 4 feet in length, plus a top piece, a bottom piece, and three shelves that are equal in length.
How long is each shelf?
___ feet
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a conical salt spreader is spreading salt at a rate of 3 cubic feet per minute. the diameter of the base of the cone is 4 feet and the height of the cone is 5 feet. how fast is the height of the salt in the spreader decreasing when the height of the salt in the spreader (measured from the vertex of the cone upward) is 3 feet? give your answer in feet per minute.
Answer:
-25/(12π) ft/min ≈ -0.663 ft/min
Step-by-step explanation:
You want the rate of change of height of the salt in a cone with height 5 ft and diameter 4 ft, filled 3 ft up from the vertex, and decreasing in volume at the rate of 3 cubic feet per minute.
Rate of change of heightThe rate of change of height is the rate of change of volume, divided by the surface area.
Surface areaThe given cone dimensions tell you the radius is 2/5 of the height of the cone, so the radius of the surface when it is filled to a depth of 3 ft is ...
r = (2/5)(3 ft) = 1.2 ft
The area of the surface is the area of a circle with this radius:
A = πr² = π(1.2 ft)² = 1.44π ft²
ApplicationThen the rate of change of height is ...
h' = V'/A
h' = (-3 ft³/min)/(1.44π ft²) = -25/(12π) ft/min ≈ -0.663 ft/min
A certain amount of money wa divided between Jaya and jyoti in the ratio 3:4. If jaya recieved R 2700,then how much wa the total
Using the ratio provided and the value divided for Jaya and with simple arithmetic, The answer is 6300.
What do you mean by ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
What do you mean by proportion?Comparing two integers that each stand for a component of a whole results in a proportion. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10.
ratio = 3:4
for Jaya,
3x=2700
x=2700/3
x=900
total = 3x+4x
=3*900 + 4*900
=6300
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What are the first two steps when finding the value of the expression below?
65 (30-24 divided 6× 2)
Use the drop-down menus to explain the first two steps.
The first step us to find the value of ____
The second step is to find the value of ___
Answer:
The first step is 24 divided by 6 ..... (4)
The second step is 4 x 2 ...... (8)
Step-by-step explanation:
65(30-24 divided by 6 x 2)
65(30- 4 x 2)
65(30 - 8)
65(22)
1,430
what is the difference between 6x2 and 6²
Answer:
6x2 is multiplying 6 by 2 while 6² is said as '6 squared' meaning 6x6.
Step-by-step explanation:
6x2 is basic multiplication of 6x2 while 6² means we should completed 6x6.
if x,10,2x-4, and 12 are in proportion find the value of x
Answer:
x=5
Step-by-step explanation:
To find the value of x, we need to first set up the proportion using the given information. Since the given values are in proportion, we can set up the proportion as follows:
x / 10 = (2x - 4) / 12
Next, we can cross-multiply to solve for the value of x:
12x = 10(2x - 4)
12x = 20x - 40
-8x = -40
x = 5
Thus, the value of x is 5. This means that the other values in the proportion are also 5, 10, 10, and 12, respectively.
Mio bought x grams of flour. Sol bought 3 8 more than that. Select ALL of the equations that represent the relationship between the amount of flour that Mio bought, x, and the amount of flour that Sol bought, y.
1) y= 3/8x
2) y= 5/8x
3) y= x+3/8x
4) y= x-3/8x
5) y= 11/8x
The equation that correctly represents the problem is 3) y = x+ 3/8x
What is a linear equation with two variables?An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
Given here, mio brought x grams and sol bought 3/8 times more than x hence, sol bought y = x + 3/8x
Hence, the correct option is 3) y=x+3/8x
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Ethan buy a video game on ale. If the video game ueully cot $39. 99 and it wa on ale for 20% off how much did ethan pay?
Answer:
$31.99
Step-by-step explanation:
I have no idea what to put here
Need Help!!!!!!!!! Solve for side similar triangle
Answer:
UT=11
Step-by-step explanation:
UV is twice the length of RS. Since UV=11 then RS=22. UT is also twice the length of RS. So if RS=22, then UT=[tex]\frac{1}{2} * 22[/tex]. UT=11
A certain arcade game gives players tickets. The table below shows the number of tickets a player gets for the number of points.
Answer: Each point appears to give the same number of tickets
9 points give 54 tickets
Step-by-step explanation:
Each point appears to give the same number of tickets
To find the number of tickets, a point gives
divide the number of tickets by the number of points.
18/3 = 6
you get six tickets per point
find the number of points that give 54 tickets by dividing 54 by 6
54/6=9
9 points give 54 tickets
Simplify 5r + 4p - 8r + 6
Answer: -3r+4p+6 or 4p-3r+6
Step-by-step explanation:
Combine like terms
5r-8r=-3r
4p
6
-3r+4p+6
Answer:
–3r + 4p + 6
Step-by-step explanation:
5r + 4p – 8r + 6
= 5r – 8r + 4p + 6
= –3r + 4p + 6
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A manufacturing company is producing dinner plates with a radius of 6 inches. They plan to put a gold edge on each plate.
a. Determine how much gold edging they will need for each plate.
b. How much gold edging will they need for a box of 24 plates?
C. In total, how much would it cost the company to put the gold edging around the plates if it costs $3.25 per 100 inches of gold edging?
a) The amount of gold edging that they will need for each plate is of: 37.7 inches.
b) The amount of gold edging for a box of 24 plates is of: 904.8 inches.
c) The total cost for the box of 24 plates is given as follows: $29.41.
How to obtain the amount of gold edging?The gold edging is placed around the circumference of the circular plate, hence the circumference needs to be obtained.
The circumference of a circle of radius r is given by the multiplication of 2π and r, as follows:
C = 2πr.
The radius of the plate in this problem is given as follows:
r = 6 inches.
Hence the circumference of the plate in this problem is given as follows:
C = 2π x 6 = 12π inches = 37.7 inches.
For the box of 24 plates, the amount needed is given as follows:
24 x 37.7 = 904.8 inches.
It costs $3.25 per 100 inches of gold edging, hence the total cost for the 24 plates is obtained as follows:
904.8/100 x 3.25 = $29.41.
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the perimeter of a triangle is 49 feet. one side of the triangle is 7 feet shorter than the second side. the third side is 4 feet shorter than the second side. find the length of each side
the perimeter of a triangle is 49 feet. The triangle's one side is seven feet shorter than its other. the length of each side , Second side: 16 feet, First side: 9 feet,Third side: 12 feet
To find the length of each side of the triangle, we need to start by looking at the perimeter, which is 49 feet.
Perimeter = 49 feet
Second side = 49 - 4 = 45 feet
First side = 45 - 7 = 38 feet
Third side = 45 + 4 = 49 feet
We know that the third side is 4 feet shorter than the second side, so we can subtract 4 feet from the perimeter to find the length of the second side, which is 16 feet. Then, we know that the first side is 7 feet shorter than the second side, so if we subtract 7 feet from the second side we can find the length of the first side, which is 9 feet. Finally, to find the length of the third side, we add 4 feet to the second side, which gives us 12 feet. Therefore, the length of each side of the triangle is 9 feet, 16 feet, and 12 feet.
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If Hugo has 4 times as many quarters as nickels and they have a combined value of 840 cents, how many of each coin does he have?
Let Q be the number of quarters and N be the number of nickels that Hugo has. We are given that Hugo has 4 * N quarters and that the total number of quarters and nickels is worth 840 cents. Since each quarter is worth 25 cents and each nickel is worth 5 cents, the total number of quarters is worth 25 * Q cents and the total number of nickels is worth 5 * N cents. Therefore, the total number of quarters and nickels is worth 25 * Q + 5 * N cents. Since the total number of quarters and nickels is worth 840 cents, we can set up the following equation to represent this information:
25 * Q + 5 * N = 840
We are also given that Hugo has 4 * N quarters, so we can set up the following equation to represent this information:
Q = 4 * N
We can solve this system of equations to find the number of quarters and nickels that Hugo has. Substituting the value of Q in the second equation into the first equation, we get the following:
25 * (4 * N) + 5 * N = 840
Distributing the 25 on the left side of the equation, we get the following:
100 * N + 5 * N = 840
Combining like terms, we get the following:
105 * N = 840
Dividing both sides of the equation by 105, we get the following:
N = 8
Substituting the value of N into the second equation, we get the following:
Q = 4 * 8
Solving for Q, we get the following:
Q = 32
Therefore, Hugo has 8 nickels and 32 quarters.
Answer:
32 quarters
8 nickels
Step-by-step explanation:
Information:
1 quarter = 25 cents1 nickel = 5 centsDefine the variables:
Let x be the number of quarters.Let y be the number of nickels.If Hugo has 4 times as many quarters as nickels:
[tex]\implies x=4y[/tex]
If the combined value of quarters and nickels is 840 cents:
[tex]\implies 25x+5y=840[/tex]
Substitute the first equation into the second equation and solve for y:
[tex]\implies 25(4y)+5y=840[/tex]
[tex]\implies100y+5y=840[/tex]
[tex]\implies 105y=840[/tex]
[tex]\implies y=8[/tex]
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x=4(8)[/tex]
[tex]\implies x=32[/tex]
Therefore, Hugo has:
32 quarters8 nickelsSergio poured 4/5 of the soda from a 2 liter bottle for his guests. How much soda in liters is still left in the bottle
The soda still left in the bottle is given as 4 liters in 2-liter bottle.
As mentioned, Sergio poured 4/5 of the soda from a 2-liter bottle for his guests.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
The soda left in the bottle will be the difference of the total quantity and the quality of the soda poured. So,
= 20 - 4/5 × 20
= 20 - 16
= 4
Thus, the soda still left in the bottle is given as 4 liters of a 2-liter bottle.
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Which interval contains 11 states? Check all that apply. 0 to 3 3 to 6 6 to 9 9 to 12 12 to 15 15 to 18 18 to 21
The intervals that contain 11 states, are given as follows:
3 to 6.6 to 9.What is shown by the bar graph?The bar graph presented by the image shown at the end of the answer shows the number of states present in each interval.
The features of the graph are given as follows:
Horizontal axis: interval.Vertical axis: number of states in each interval.Then the number of states for each interval are given as follows:
0 to 3: 16 states.3 to 6: 11 states.6 to 9: 11 states.9 to 12: 3 states.12 to 15: 3 states.15 to 18: 3 states.18 to 21: 4 states.Hence the intervals 3 to 6 and 6 to 9 are the intervals that contain 11 states, being the correct answers to this problem.
Missing InformationThe bar graph is given by the image shown at the end of the answer.
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10. Solve the following by substitution or elimination.
3x + 2y = 6
- x + 2y = - 2
Answer:
x=___y=_
OR: no solution/ infinite solutions
Please help me it’s for algebra !
Answer:
x=2
y=0
Step-by-step explanation:
-x+2y= -2
-2y. -2y
-x= -2-2y
/-1. /-1 /-1
x=2+2y
3(2+2y)+2y=6
6+6y+2y=6
6+8y=6
-6. -6
8y=0
/8 /8
y=0
3x+2(0)=6
3x=6
/3. /3
x=2
hopes this helps
Using the "split" string method from the preceding lesson, complete the get_word function to return the {n}th word from a passed sentence. For example, get_word("this is a lesson about lists", 4) should return "lesson", which is the 4th word in this sentence. Hint: remember that list indexes start at 0, not 1.
The function to return the nth word of the sentence will be given as -
def get_word(sentence, n):
# Only proceed if n is positive
if n > 0 :
words = sentence.split()
# Only proceed if n is not more than the number of words
if n <= len(words) :
return words[n-1]
return("")
According to the data given in the question we can see that the method to obtain the string will be the split string method,
According to the split string method, we separate distinct parts of the strings based on the delimiter using signs such as comma(,), hyphen(-), whitespace), etc.
To extract the 4th word in the sentence, we will assume position 3 for the 4th word.
#The function to print lesson counting from 0,
print(get_word("This is a lesson about lists", 4))
print(get_word("This is a lesson about lists", -4))
#No printing as the first condition is not met
print(get_word("Now we are cooking!", 5))
#No printing occurs as it also does not meet the condition of the second statement.
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Work out the circumference of this circle. Give your answer in terms of pi.
Answer:
[tex]12\pi[/tex]
Step-by-step explanation:
Circumference Formula: [tex]2\pi r[/tex]
Our radius is 6, plug that in.
[tex]2\pi 6[/tex]
12[tex]\pi[/tex]
Leave in terms of pi, so do not simplify further.
The sum of two numbers is 46. The larger number is 16 more than the smaller number.
Answer:
Smaller number: 15 Larger number: 31
Step-by-step explanation:
Let's call the smaller number x
So, the larger number will be x+16 (it's 16 more)
Then, write an equation:
x (smaller number) + (x+16) (larger number) = 46 (sum)
x+x+16=46
2x+16=46
2x=30
x=15
So, the smaller number is 15
The larger number is x+16, so plug in x:
x+16 = 15+16 = 31
The smaller number is 15, and the larger number is 31
[tex]y = 15 \\ x = 31[/tex]
Step-by-step explanation:
[tex]y + 16 + y = 46 \\ 2y = 30 \\ y = 15 \\ \\ x = 15 + 16 \\ x = 31[/tex]
-5 feet from the urface of the water and plan to explore a hipwreck that i at -75 feet from the urface. If he move at a rate of -8 feet per minute, how many minute doe it take the diver to reach the hipwreck? The diver will take
Using the provided values for the depth and moving rate of the driver , We can use simple unitary method and the answer is 8.75 minute.
What do you mean by unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
What do you mean by arithmetic operators?The arithmetic operator is used to carry out mathematical operations on the provided operands, including addition, subtraction, multiplication, division, and modulus.
initial depth = 5 feet
shipwreck at 75 feet
depth to travel = 75-5 = 70 feet
rate = 8 feet/minute
time = 70/8
=8.75 minute.
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