Both expressions are equivalent and represent the same result. So the final answer is that the new position of the submarine in relation to sea level is -1,320 feet.
To find the new position of the submarine in relation to sea level, we need to take into account its initial position and the rate at which it descends.
The submarine starts at a depth of -1,260 feet, so this will be our starting point.
We know that the submarine descends at a rate of 5 feet per minute for 12 minutes. To calculate how far it descends in total, we can multiply the rate by the time:
5 feet/minute x 12 minutes = 60 feet
So the submarine descends 60 feet in total. However, since it is descending, we need to subtract this value from the initial depth of -1,260 feet:
-1,260 feet - 60 feet = -1,320 feet
Therefore, the expression that represents the new position of the submarine in relation to sea level is:
-1,260 - (5 x 12) = -1,320
Alternatively, we could also write this as:
-1,260 + (-5 x 12) = -1,320
Both expressions are equivalent and represent the same result. So the final answer is that the new position of the submarine in relation to sea level is -1,320 feet.
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Answer:
Step-by-step explanation:
the answer is B
suppose 20% of all widgets produced at a factory are defective. a simulation is used to model widgets randomly selected and then recorded as defective or working. which simulation best models the scenario?
The best simulation to model the scenario of randomly selecting widgets and recording them as defective or working is a Bernoulli trial simulation.
A Bernoulli trial simulation is used when there are only two possible outcomes, such as success or failure. In this case, the two outcomes are defective or working widgets. The simulation involves randomly selecting a widget and recording whether it is defective or working. This process is repeated multiple times to generate a sample of widgets. The probability of success, or the proportion of defective widgets, is known and remains constant throughout the simulation. This type of simulation is appropriate for modeling the scenario because it allows for the calculation of the probability of selecting a defective widget and can be used to estimate the proportion of defective widgets in the factory's production.
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how do we find the median if the number of observations in a data set is odd?
To find the median of a data set when the number of observations is odd, you follow these steps:
Arrange the data set in ascending order.
Identify the middle observation in the ordered data set.
The value of the middle observation is the median.
For example, let's say you have the following data set with an odd number of observations:
3, 5, 1, 2, 4
To find the median, you would:
Arrange the data set in ascending order: 1, 2, 3, 4, 5
Identify the middle observation, which is 3.
Therefore, the median of this data set is 3.
In summary, when the number of observations in a data set is odd, the median is the middle value when the data is arranged in ascending order.
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The greyed letters are the question. The blackened letters is the solution. How do I get there?
Answer:
sin²θ
Step-by-step explanation:
* trig identities are sin²θ + cos²θ = 1, sin²θ = 1 - cos²θ.
tan²θ = sin²θ/cos²θ.
sec²θ = 1/cos²θ.
Now we can begin to work it out.
(sec²θ - 1) / (1 + tan²θ)
Simplify sec and tan
((1/cos²θ) - 1) / (1 + (sin²θ/cos²θ))
now multiply every term by cos²θ
((cos²θ/cos²θ) - cos²θ) / ((cos²θ + sin²θ))
= (1 - cos²θ) / 1
= 1 - cos²θ
= sin²θ
3. Brittney randomly selected 30 cars in a parking lot and determined each car's year of manufacture. She
made this stem-and-leaf plot to show the results.
A. There are about 70,000 cars in the city where Brittney lives. According to Brittney's data, about how
many of the cars in her city were manufactured before the year 2000?
( made before 2000 on graph)
(of cars on graph)
(# of cars in her city)
a. Hint: Use a proportion:
B. Find the lower quartile and upper quartile of the data.
C. About how many of the cars in Brittney's city were manufactured between the years you found in part
B7
D. Explain how you found your answer to part C.
A. From the stem and leaf plot below, there are about 28,000 cars manufactured before 2000.
B. lower quartile (Q1) is between the 7th and 8th values (1995+1997)/2 = 1996. Upper quartile is the 23rd and 24th values (2009 + 2010) = 2009.5.
C. The number of cars in the city that were manufactured between 1996 and 2009.5 is 37100.
D. To determine the number of car manufactured in 1996 and 2009.5, first determined the relevant proportions from the sample data. Then, multiply the proportion by the total number of cars in the city to estimate the number of cars manufactured before between 1996 and 2007.5,
How do we calculate the numbers of cars manufactured within a given period of time using the stem-and-leaf plot?A. To find the number of cars manufactured at the given period, we find the number of cars sampled that were created before 2000. From the stem-and-leaf plot, we can see that there are 12 cars manufactured before 2000.
Proportion of cars = 12/30 = 0.4.
Using the proportion, we find the number of cars manufactured before 2000.
70,000 × 0.4.
=28,000
B The lower quartile (Q1) is the 25th percentile, and the upper quartile (Q3) is the 75th percentile.
= 0.25×(n+1)
= 0.25×(30+1)
= 7.75 Therefore the lower quartile is between 7th and 8th values.
Q1 = (1995+1997)/2 = 1996.
0.75×(n+1)
= 0.75×(30+1)
= 23.25 Therefore the upper quartile is between 23rd and 24th values.
(2009+2010)/2 = 2009.5
C. There are 16 cars manufactured between 1996 and 2009.5
16/30 = 0.53
= 70,000×0.53
= 37100
The answer provided is based on the stem and leaf plot below
3. Brittney randomly selected 30 cars in a parking lot and determined each car's year of manufacture. She made this stem- and-leaf plot to show the results.
CARS IN PARKING LOT-YEAR OF MANUFACTURE
197 | 1
198 | 26
199 | 345577899
200 | 12455677899
201 | 0011222
Key: 197 |1 = 1971
A There are about 70,000 cars in the city where Brittney lives. According to Brittney's data, about how many of the cars in her city were manufactured before the year 2000?
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A parcel of land has the shape of a parallelogram. The land is 240m by 160m. The distance between the 240m side is 40m. Find the distance between the 160m sides
Let's visualize the parallelogram-shaped land with sides of 240m and 160m. We know that the distance between the 240m sides is 40m. Let's denote this distance as "d".
To find the distance between the 160m sides, we can use the concept of similar triangles. The triangles formed by the sides of the parallelogram are similar. In the smaller triangle, the base is 160m, and the corresponding side in the larger triangle is 240m. Similarly, the height of the smaller triangle is "d", and the corresponding side in the larger triangle is 40m. Using the property of similar triangles, we can set up the following proportion:
160m / 240m = d / 40m
Simplifying the proportion, we get:
2/3 = d / 40m
Cross-multiplying, we have:
d = (2/3) * 40m
Calculating the value, we find:
d = 26.67m
Therefore, the distance between the 160m sides of the parallelogram-shaped land is approximately 26.67m.
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C
2 mm
9 mm
What is the length of the hypotenuse? If
necessary, round to the nearest tenth.
C =
millimeters
The value of the length of the hypotenuse is,
⇒ c = √85
Since, Three vertices and three angles totaling 180 degrees make up a triangle, a three-sided polygon with three sides.
And, Two rays (half-lines) that share a terminal make up an angle. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.
We have to given that;
In triangle ,
Perpendicular side = 9 mm
Base = 2 mm
Since, We know that;
The Pythagorean theorem states that the square of the hypotenuse of a right triangle equals the sum of the squares of its two opposite sides.
Hence, By Pythagoras theorem we get;
⇒ Hypotenuse² = Perpendicular² + Base²
⇒ c² = 9² + 2²
⇒ c² = 81 + 4
⇒ c = √85
Thus, The length of the hypotenuse is,
⇒ c = √85
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Which describes the shape of the distribution of total points in Mr. Price's science class? Please help
The shape of the Distribution of total points in Mr. Price's science class, more information about the data is needed, such as the number of observations, the range of values, and the presence of any outliers.
If the data is roughly symmetrical with a peak at the center and tails on either end, then the distribution is said to be normally distributed or bell-shaped. This is the most common shape observed in natural phenomena and social sciences.
If the data has a single peak, but the tails are longer on one side than the other, then the distribution is said to be skewed. If the tail is longer on the left side, the distribution is said to be left-skewed or negatively skewed. If the tail is longer on the right side, the distribution is said to be right-skewed or positively skewed.
If the data has multiple peaks, it is said to be bimodal or multimodal. This can occur when there are two or more distinct groups within the data that have different characteristics.
If the data has no discernible pattern, it is said to be uniform or rectangular. This can occur when there is no underlying pattern in the data or when the data has been artificially manipulated to be evenly distributed.
In order to determine the shape of the distribution of total points in Mr. Price's science class, more information about the data is needed, such as the number of observations, the range of values, and the presence of any outliers.
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Note the full question is :
Which describes the shape of the distribution of total points in Mr. Price's science class? Please help
Write the equation of a circle, in standard form, that has a diameter with endpoints at (-1,-4) and
(11,-4)
The equation of the circle in standard form is (x - 5)² + (y + 4)² = 36
The center of the circle is the midpoint of the diameter.
Using the midpoint formula, we can find the center as follows:
x-coordinate of center = (x-coordinate of endpoint 1 + x-coordinate of endpoint 2)/2
= (-1 + 11)/2
= 5
y-coordinate of center = (y-coordinate of endpoint 1 + y-coordinate of endpoint 2)/2
= (-4 - 4)/2
= -4
So the center of the circle is (5, -4) and the radius is half the length of the diameter:
radius = distance between endpoints of diameter/2
= √(11 - (-1))² + (-4 - (-4))²]/2
= 6
Therefore, the equation of the circle in standard form is (x - 5)² + (y + 4)² = 36
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can you help me with this math
Answer:
B. (1, -2)
Step-by-step explanation:
In order to for it to be a function, the inputs need to have only one output.
The table shows:
(-1, 2), (0, -4), (1, -2), (1, 5), (2, 0), (3, 2), (4, 9)
If a x-value is repeating it is not a function.
the researcher is interested in determining whether there is evidence that the two processes yield different average errors. assume that process a is the first population. the population standard deviations are unknown but are assumed equal. what are the degrees of freedom?
The degrees of freedom for a two-sample t-test with equal variances depend on the sample sizes of the two populations being compared.
The degrees of freedom for this scenario, we need to first understand the statistical test that would be used to compare the average errors of the two processes.
In this case, the appropriate test would be a two-sample t-test, assuming equal variances.
The formula for calculating the degrees of freedom for a two-sample t-test with equal variances is as follows:
df = n1 + n2 - 2
where n1 and n2 are the sample sizes of the two populations being compared. In this case, since process A is the first population, we can assume that n1 represents the sample size for process A.
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a lot is 275 feet deep and sits on 2/3 of an acre. what is the width of the lot?
Answer:
105.6 ft
Step-by-step explanation:
1 acre = 43,560 ft²
2/3(43,560) = 29,040
x = width of the lot
Area = (275 ft)(x) = 29,040 ft²
x = 29040/275 = 105.6 ft
Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark (/) as the fraction bar if necessary.
(-8,0)
-10
10+
-10+
Answer here
(7,3)
10
SUBMIT
The slope of the line above include the following: 1/5.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (3 - 0)/(7 + 8)
Slope (m) = (3)/(15)
Slope (m) = 1/5.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 1/5.
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If a point is chosen inside the regular polygon, what is the probability that the point
chosen is inside the right triangle outlined? Round to the nearest hundredth. Area:
Reg. Polygon=aP/2
The probability that the point chosen is inside the right triangle outlined is approximately 0.3, or 8.33%, rounded to 2 decimal places.
To find the chance that a factor chosen in the ordinary polygon is likewise in the proper triangle mentioned, we need to examine the areas of the two shapes. The location of the everyday polygon may be determined using the formulation:
Area of everyday polygon = (variety of facets × period of 1 side × apothem)/2
The region of the right triangle can be found using the system:
Area of proper triangle = (base × top)/2
The probability is then given by way of the ratio of the 2 areas:
Probability = Area of proper triangle / Area of normal polygon
However, to apply this formulation, we need to recognize some values that aren't given within the query, inclusive of the range of facets, the duration of one facet, the apothem, and the base and peak of the triangle. Without those values, we can't calculate the exact opportunity. We can most effectively estimate it by looking at the discernment and making a few assumptions.
One possible way to estimate the chance is to anticipate that the everyday polygon is a hexagon (has six aspects) and that the right triangle is 1/2 of one among its facets. Then we will approximate the length of one facet as 1 unit and the apothem as 0.866 units (the use of trigonometry). The base and height of the triangle would then be zero. 5 units and 0.866 units respectively.
Using those values, we are able to estimate the areas as follows:
Area of regular polygon ≈ (6 × 1 × 0.866)/2 ≈ 2.598 devices² Area of right triangle ≈ (0.5 × 0.866)/2 ≈ 0.2165 devices²
Probability ≈ 0.2165 / 2.598 ≈ 0.0.33
Therefore, the opportunity is approximately 0.3, or 8.33%, rounded to 2 decimal places.
Note: This is best an estimate primarily based on a few assumptions and approximations. The actual possibility might also vary depending on the actual values of the parameters worried.
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For a car moving at a constant speed, the distance traveled varies directly with the time spent driving. If such a car travels 330 miles in 6 hours, how long does it take to travel 385 miles?
It takes 7 hours to travel 385 miles at a constant speed.
To solve this problem, we need to use the direct variation formula, which states that distance traveled is directly proportional to time spent driving. This means that if we double the time spent driving, the distance traveled will also double.
Using this formula, we can set up a proportion to find the answer. We know that the car travels 330 miles in 6 hours, so we can write:
330/6 = 385/x
Where x is the time it takes to travel 385 miles.
To solve for x, we can cross-multiply and simplify:
330x = 2310
x = 7
It's important to note that this problem assumes that the car maintains a constant speed throughout the entire trip. If the car speeds up or slows down at any point, the distance traveled and time spent driving will not follow a direct variation relationship.
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
Answer: 1/7 as a decimal is 0.143
1-7-as-a-decimal
Let us understand the division method to write 1/7 as a decimal.
Explanation:
To convert any fraction to its decimal form, we just need to divide the numerator by the denominator.
Here, the fraction is 1/7 which means we need to divide 1 by 7 (1 ÷ 7)
This gives the answer as 0.14285714... which can be rounded off and written as 0.143. So, 1/7 as a decimal is 0.143
Irrespective of the methods used, the answer to 1/7 as a decimal will always remain the same.
The diameter of a circle is 5 ft. Find its circumference in terms of
π
Answer:
[tex]\pi 5[/tex]
Step-by-step explanation:
Use the formula [tex]C=\pi d[/tex].
[tex]C=\pi 5[/tex]
So your answer is [tex]\pi 5[/tex].
Mindy makes boots for Belleville Boot Factory. She is paid on the following differential pay scale:
1-50=$1.65
51-150=$3.30
151-200=$4.95
Over 200=$6.00
What is Mindy's pay if she produced 192 boots for the week?
A. $602.30
B. $702.90
C. $1,152.00
D. $620.30
E. None of these
Mindy's pay depends on the number of boots she produced. According to the given pay scale, we can break down her pay as follows:
For the first 50 boots, Mindy earns $1.65 per boot. So, for the first 50 boots, her pay is 50 * $1.65 = $82.50.
For the next 100 boots (51-150), Mindy earns $3.30 per boot. So, for these 100 boots, her pay is 100 * $3.30 = $330.
For the next 50 boots (151-200), Mindy earns $4.95 per boot. So, for these 50 boots, her pay is 50 * $4.95 = $247.50.
In total, Mindy has produced 200 boots so far, and her pay for these boots is $82.50 + $330 + $247.50 = $660.
Now, for the remaining 192 - 200 = -8 boots (less than 200), Mindy earns $6.00 per boot. Since she hasn't produced any additional boots beyond 200, we don't need to consider this part.
Therefore, Mindy's pay for producing 192 boots is $660 (according to the breakdown above).
So, the correct answer is E. None of these.
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Multi-Step: For what values of the variables △QPR congruent to △SPR? In this case, what is m ∠Q?
Answer:
x = 17y = 8∠Q = 85°Step-by-step explanation:
You want the values of the variables x and y, and the measure of angle Q in the given figure when ∆QPR ≅ ∆SPR.
CongruenceThe triangles are congruent by the ASA postulate when the angles at P are congruent and the angles at R are congruent.
Angles at P(2x +1)° = (x +18)°
x = 17 . . . . . . . . . . . divide by °, subtract x+1
(x +18)° = (17 +18)° = 35° . . . . the measures of the angles at P
Angles at R(8y -4)° = (4y +28)°
4y = 32 . . . . . . . . . . . divide by °, add 4-4y
y = 8 . . . . . . . . . divide by 4
(4y +28)° = (32 +28)° = 60° . . . . . . the measures of the angles at R
Angle QThe sum of angles in ∆QPR is 180°, so ...
Q +35° +60° = 180°
Q = 85° . . . . . . . . . . . subtract 95°
For x = 17 and y = 8, the triangles are congruent. m∠Q = 85°.
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The bar chart shows the amount of rubbish found on some beaches.
a) Work out the range of the number of cans found.
b) Work out the range of the number of bottles found.
a) The range of the number of cans found is: 8
b) The range of the number of bottles found is: 5
How to calculate the range of a set of data?The range of a dataset is basically the simplest measurement of the difference between values in a data set. To find the range, we will simply subtract the lowest value from the greatest value while ignoring the others.
a) The range of the number of cans found is simply the difference between the highest number of cans found and the lowest number of cans found.
Thus:
Range of number of cans = 10 - 2
Range of number of cans = 8
b) The range of the number of bottles found is simply the difference between the highest number of bottles found and the lowest number of bottles found.
Thus:
Range of number of bottles = 6 - 1
Range of number of bottles = 5
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Lan's parents asked him to create a budget for his 1,000 monthly income. he determines that he would like to save the remaining amount. What percent of his budget will go towards savings
The percent of Lan's budget that will go towards savings is 35%
The correct option is; 35%
What is a percentage?A percentage is a representation of a ratio as a fraction with a denominator of a hundred, 100.
The amount Lan's income is = $1,000
Lan's budget obtained from a similar question on the internet can be presented as follows;
Expense [tex]{}[/tex] Amount ($)
Car Payment [tex]{}[/tex] $350
Car Insurance [tex]{}[/tex] $100
Fuel [tex]{}[/tex] $120
Cell Phone [tex]{}[/tex] $80
Therefore, Lan's total budget is; $350 + $100 + $120 + $80 = $650
The amount Lan's has to save is; $1,000 - $650 = $350
The percentage of his budget he saves is therefore;
Percent savings = $350/($1,000) × 100 = 35%
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according to the manufacturer, about 26% of sour candy in a package of sandy's sours are grape. what is the probability that the first grape candy chosen from the bag will be, at least, the third candy chosen overall? 0.4524 0.5476 0.1424 0.8576 0.4052
The probability that the first grape candy chosen from the bag will be, at least, the third candy chosen overall is 0.5608.
To solve this problem, we need to use the probability formula:
P(at least third grape candy) = P(first candy is not grape) x P(second candy is not grape) x P(third candy is grape) + P(first candy is not grape) x P(second candy is grape) x P(third candy is grape) + P(first candy is grape) x P(second candy is not grape) x P(third candy is grape) + P(first candy is grape) x P(second candy is grape) x P(third candy is grape)
From the given information, we know that the probability of choosing a grape candy from the bag is 26%. Therefore, the probability of choosing a non-grape candy is 74%.
Using this information, we can substitute the values into the formula:
P(at least third grape candy) = 0.74 x 0.74 x 0.26 + 0.74 x 0.26 x 0.26 + 0.26 x 0.74 x 0.26 + 0.26 x 0.26 x 0.26
Simplifying this expression, we get:
P(at least third grape candy) = 0.4524 + 0.0508 + 0.0508 + 0.0068
P(at least third grape candy) = 0.5608
Therefore, the probability that the first grape candy chosen from the bag will be, at least, the third candy chosen overall is 0.5608.
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Y’all please help I need an explanation and an answer
8 cups = 64cm
From the catalog, we know that a stack of 2 cups is 16 cm tall, and a stack of 4 cups is 20 cm tall.
To find the height of a stack of 8 cups, we can use proportionality.
Let x be the height, in cm, of a stack of 8 cups. Then, we can set up the following proportion:
2 cups / 16 cm = 8 cups / x cm
Cross-multiplying, we get:
2 cups * x cm = 16 cm * 8 cups
Simplifying, we get:
2x = 128
x = 64 cm
Therefore, the height of a stack of 8 cups is 64 cm.
Exponential Functions
Answer:
C(t) = 10,500(1 + 0.07)^t
Step-by-step explanation:
Vector AB has an initial point of (-9,8), an x component of 4, and a y component of -11. find the coordinates of terminal B.
The coordinates of the point B of vector is B ( -5 , -3 )
Given data ,
To find the coordinates of the terminal point B, we can start with the initial point of vector AB and add its components.
Initial point of AB: (-9, 8)
x-component of AB: 4
y-component of AB: -11
To find the coordinates of the terminal point B, we add the x-component and y-component to the corresponding coordinates of the initial point.
x-coordinate of B = x-coordinate of initial point + x-component of AB
x = -9 + 4
x = -5
y-coordinate of B = y-coordinate of initial point + y-component of AB
y = 8 + (-11)
y = -3
Hence , the coordinates of the terminal point B are (-5, -3)
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X
145° 110°
70°
x = [?]°
Enter the number that goes in the green box.
The value of x is 35 degree.
We know,
The angle sum property of a quadrilateral states that the sum of the interior angles of any quadrilateral is always equal to 360 degrees.
In other words, if you add up the measures of all the interior angles of a quadrilateral, the total will always be 360 degrees.
So, applying angle sum property in Trapezium
145 + 110 + 70 + x = 360
325 + x = 360
x = 360 - 325
x = 35 degree
Thus, the value of x is 35 degree.
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Given the following triangle,
If Sin F = 3/5
, then find the Cos D:
Responses
4/3
3/4
3/5
4/5
Answer:
Cos D = 3/5
Step-by-step explanation:
We know that the sine ratio is sin (angle) = opposite/hypotenuse. Thus, sin F = 3/5 indicates that
the side opposite angle F is 3 units (side MD),and the hypotenuse is 5 units (side DF)The cosine ratio is cos (angle) = adjacent/hypotenuse.
When D is the reference angle, side MD is the adjacent side and DF is the hypotenuse.
Because MD = 3 units and DF = 5 units, Cos D = 3/5
Can someone help on this please ? Thank you:)
Answer:
[tex] {2}^{ \frac{2}{7} } \times {2}^{ \frac{2}{7} } = {2}^{ \frac{2}{7} + \frac{2}{7} } [/tex]
[tex] {2}^{ \frac{2}{7} } \times {2}^{ \frac{2}{7} } = {2}^{ \frac{4}{7} } [/tex]
!!! 100 POINTS HELP NOW
A sample of 275 students at a particular college is taken. The students are classified according to their gender and major. The results are given in the contingency table below.
The top line of the table is labeled Major, there are 4 columns labeled Chemistry, Biology, Graphic Design and Electrical Engineering. The left side of the table is labeled Gender and then has two rows labeled Male and Female. Chemistry Major has 35 Males and 31 Females, Biology Major has 34 Males and 36 Females; Graphic Design Major has 38 Males and 29 Females and Electrical Engineering major has 42 males and 30 Females.
Among the students in the sample who are male, what is the relative frequency of chemistry majors? Round your answer to two decimal places.
Group of answer choices
0.53
0.13
0.23
0.24
Rounding to two decimal places, the relative frequency of male students who are chemistry majors is approximately 0.23.Therefore, the answer is 0.23.
To find the relative frequency of male students who are chemistry majors, we need to divide the number of male chemistry majors by the total number of male students in the sample.
According to the contingency table, there are 35 male chemistry majors.
To calculate the relative frequency, we divide the number of male chemistry majors by the total number of male students:
Relative Frequency = Number of Male Chemistry Majors / Total Number of Male Students
Relative Frequency = 35 / (35 + 34 + 38 + 42)
Relative Frequency ≈ 35 / 149
Relative Frequency ≈ 0.2349.
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the point (-12,5) lies on the circle whose center is at the origin. what is the radius of this circle?
The radius of the circle is 13.
To find the radius of the circle with the center at the origin and passing through the point (-12, 5), we can use the distance formula.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
Distance = √[(x2 - x1)² + (y2 - y1)²]
In this case, the center of the circle is at the origin (0, 0), and the given point is (-12, 5). Plugging these values into the distance formula, we get:
Distance = √[(-12 - 0)² + (5 - 0)²]
= √[(-12)² + 5²]
= √[144 + 25]
= √169
= 13
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a flag pole that is 15 feet tall casts a shadow that is 22 feet long. at the same time of day, the shadow of a nearby tree is 52.3 feet long. how tall is the tree?
If a flag pole that is 15 feet tall casts a shadow that is 22 feet long. at the same time of day, the shadow of a nearby tree is 52.3 feet long then the tree is 35.5 feet tall
To determine the height of the tree, we need to use ratios and proportions. We know that the flagpole is 15 feet tall and casts a shadow of 22 feet. Using these values, we can create a proportion:
15/22 = x/52.3
To solve for x, we can cross-multiply:
15 x 52.3 = 22 x
x = (15 x 52.3)/22
x = 35.5
Therefore, the tree is 35.5 feet tall.
In mathematics, proportions are often used to compare two quantities. In this case, we used the ratio of the height of the flagpole to the length of its shadow to create a proportion and find the height of the nearby tree. It's important to note that this calculation assumes that both the flagpole and tree are standing vertically and that the angle of the sun's rays is constant. Understanding and using proportions is a valuable skill in many areas of math and science, including geometry, physics, and engineering. By using ratios and proportions, we can compare different quantities and make calculations that help us better understand the world around us.
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