An elevator has a placard stating that the maximum capacity is 1884 lb-12 passengers. So, 12 adult male passengers can have a mean weight of up to 1884/12=157 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 157 lb. (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.) Does this elevator appear to be safe? BICICIE The probability the elevator is overloaded is (Round to four decimal places as needed) Does this elevator appear to be safe? OA. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity OB. No, 12 randomly selected people will never be under the weight limit. OC. Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity OD. Yes, 12 randomly selected adult male passengers will always be under the weight limit. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275. Round to four decimal places. www OA. 0.4332 OB. 0.9332 OC. 0.5000 OD. 0.0668 Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Cost 9 2 3 5 9 10-> 4 2 68 67 Number 52 55 85 A. 0.235 OB. 0.708 OC. 0.246 OD. -0.071 86 83 73
The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.
Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:
Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.
We can write as below:
Maximum capacity per person=1884/12=157lb.
And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586
Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.
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Of all rectangles with a perimeter of 10 meters, which one has the maximum area? (Give both the dimensions and the area enclosed)
Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters.
Of all rectangles with an edge of 10 meters, the one that has the greatest zone(area) could be a square.
To see why, let's assume that a rectangle with a border of 10 meters has measurements of length L and width W.
At that point, we know that:
2L + 2W = 10
Rearranging this condition, we get:
L + W = 5
Presently, we need to discover the most extreme range encased by the rectangle, which is given by:
Area = L x W
Able to illuminate for one variable in terms of the other utilizing the condition L + W = 5:
L = 5 - W
Substituting this expression for L into the condition for the zone, we get:
Zone = (5 - W) x W
Extending and disentangling this expression, we get:
Area = 5W - W²
To discover the most extreme esteem of this quadratic expression, we will take its subsidiary with regard to W and set it to break even with zero:
dArea/dW = 5 - 2W =
Tackling for W, we get:
W = 2.5
Substituting this esteem back into the condition for the edge, we get:
L = 2.5
Hence, the measurements of the rectangle that has the greatest region are L = 2.5 meters and W = 2.5 meters, which implies it could be a square. The most extreme zone enclosed by the rectangle is:
Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters.
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I went shopping and bought a shirt for $15.60, a skirt for $28.80, and some leggings for $4.50. Tax is 6%. What was the total cost of my purchase?
1. In the figure below, jk is parallel to mn and pq is parallel to rs. Which statement is TRUE?
(photo below)
2. Parallelogram PQRS is a square . The length of side PQ = 2x + 8 and the perimeter of ABCD = 96. What is the length of side PQ?
(picture below)
Answer:
The first one!
Step-by-step explanation:
a° = c°
I took this test, be careful. a°+c°=180° is not correct... I selected that one on accident and I got a 75 % SO BE CAREFUL and don't be an idiot like haha
Answer:
the answer is A=C
Step-by-step explanation:
i took the test and got it right:)
Unit 8: Right Triangles & Trigonometry Homework 2: Special Right Triangles...Please Help!
a family of four goes to a movie theatre and spends $26.50. they buy 2 tickets for adults, and 3 boxes of popcorn at $2.50 per box. what is the cost of one adult ticket
Answer:
$9.5
Step-by-step explanation:
3x2.50= 7.50
26.50-7.5 =19
19/2 = 9.5
9.5 for one adult ticket
Hi!
First, let's add (or multiply) the boxes of popcorn.
2.50 + 2.50 + 2.50 (or 2.50 x 3) is 7.50. so the popcorn all together is $7.50.
Next, we subtract the popcorn cost from the cost altogether.
26.50 - 7.50 = $19
Next, we divide the $19 by two.
19 ÷ 2 = 9.50
To make sure this is true, what we do is multiply 2 x 9.50.
2 x 9.50 = 19.
So 9.50 is your answer.(NOTICE: your problem says a family of 4. you didn't give me the total for the other 2 people who were going to the movie, so this is just my estimate for just those 2 adults. If it's not correct, that is the reason why, otherwise, it is the answer.)
Hope this helps!
~~~PicklePoppers~~~Simplify. Express your answer using positive exponents. w^3 x w^5
\(w^8\) is the expression using positive exponents.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
w³ x \(w^5\)
= \(w^{3 + 5}\)
= \(w^8\)
Thus,
\(w^8\) is the final expression.
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Complete the problem. Check your answer in the back of the book.
3. Joseph Lee's check register balance is $8,754.33. He compares his
statement with his check register. He notes that the bank paid him
$2.86 in interest and deducted a $1.20 service charge for bill payment.
He finds these outstanding checks and deposits:
Check 845: $751.75 Check 847: $2,455.89 Deposit: $805.14.
PLEASE HELP ASAP!!!!!!!
The sum of all the angles in a triangle is equal to 180 degrees
x = 180-(65+30) = 85 degrees
pls answer this i need help
Answer:
Step-by-step explanation:
a) Number = x
Multiply it by 3 = 3*x = 3x
Now add 4 to it: 3x + 4
Equation:
3x +4 = 22
b)
3x + 4 = 22
Subtract 4 from both sides
3x + 4 -4 = 22 - 4
3x = 18
Divide both sides by 3
3x/3 = 18/3
x = 6
Answer:
Below in bold.
Step-by-step explanation:
The equation is
3x + 4 = 22
3x = 22 - 4 = 18
x = 18/3
x = 6.
Tickets to the zoo cost $12 for adults and $8 for children. The school has a budget of $240 for the field trip. An equation representing the budget for the trip is 240=12x+8y. Here is a graph of this equation:
Answer:
18 children
Step-by-step explanation:
Given
\(240 = 12x +8y\)
Required (missing part of the question):
Number of children that will be able to go to the zoo if 8 adult tickets are purchased
The graph is missing. However, the question can be solved without the graph.
From the question and equation, we can deduce the following:
x represents adultsy represents childrenSo, when 8 adult tickets were sold.
This means
\(x = 8\)
Substitute 8 for x in \(240 = 12x +8y\)
\(240= 12 * 8 + 8y\)
\(240= 96+ 8y\)
Subtract 96 from both sides
\(240 - 96 = 96 - 96 + 8y\)
\(144 = 8y\)
\(8y = 144\)
Solve for y
\(y= \frac{144}{8}\)
\(y= 18\)
This means that 18 children will be able to go
What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%?
a. z = 0.52
b. z = 0.84
c. z = -0.84
d. z = -0.52
Using the normal distribution, the value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is:
z = -0.52.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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 value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is is the 30th percentile, which is Z with a p-value of -0.3, hence z = -0.52.
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Which of the expressions below can be factored using the difference of squares method?
A. 9x^2 - 16y2
B. 9x-16y
C. 9x^2 + 1672
D. 9x + 16y
Answer: A. \(9x^2 - 16y^2\) .
Step-by-step explanation:
A difference of squares problem is factored as :\(a^2 - b^2 = (a + b)(a - b)\)For this both terms in the form of squares and a minus sign between them.From all the options only option A has both terms square and they minus sign between them.
Also, \(9x^2 - 16y^2= (3x)^2-(4y)^2=(3x+4y)(3x-4y)\)
Here a= 3x and b= 4
Hence, the correct answer is A. \(9x^2 - 16y^2\) .
Answer:
A
Step-by-step explanation:
how do you multiply a square root by a square root and a whole number?
for example, the square root of 5 times (4 times the square root of 5) is 20, but i don’t understand how rob solve for this thanks!
To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication
Given data ,
Let the numbers be represented by the expression A
Now , the value of A is
A = √2 × 3√5
First, you can simplify each square root:
√2 = 1.4142 (rounded to 4 decimal places)
3√5 = 5.1962 (rounded to 4 decimal places)
Next, you can multiply the two simplified square roots and the whole number:
√2 × 3√5 = 1.4142 × 5.1962 × 3
= 22.3607 × 3
= 67.0821
Hence , the expression is A = √2 × 3√5 = 67.0821
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Which mean (average), arithmetic or geometric, is best as a measure of central tendency and why?
How do you calculate the population and sample standard deviation and variance assuming equal weights? Historical data?
Describe and explain the standard deviation and variance and how are they used.
The arithmetic mean is commonly used as a measure of central tendency because it is intuitive, easy to calculate, and suitable for most data types.
The arithmetic mean, or simply the mean, is the sum of all data values divided by the number of values. It is commonly used as a measure of central tendency because it is intuitive and easy to calculate. However, the mean can be influenced by extreme values, known as outliers, which may distort its interpretation. In contrast, the geometric mean is useful for dealing with multiplicative quantities, such as growth rates or ratios, but it is less commonly used as a measure of central tendency.
To calculate the population standard deviation and variance, assuming equal weights, you first find the mean of the data set. Then, for each data point, subtract the mean and square the result. Sum up all the squared differences, divide by the total number of data points, and take the square root to obtain the standard deviation. Variance is obtained by taking the average of the squared differences from the mean, without taking the square root.
Standard deviation measures the average distance between each data point and the mean. A larger standard deviation indicates a greater spread or variability in the data. Variance is similar to standard deviation but lacks the square root, so it represents the average of the squared differences. These measures are commonly used in statistical analysis to describe the dispersion of data points, assess the uncertainty or variability in a sample or population, and make comparisons between different data sets. They play a crucial role in hypothesis testing, confidence intervals, and inferential statistics.
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Question
The table shows the balance of an account each year. Years Balance
0 $40
1 $42
2 $44
3 $46
What is the interest rate of the account? What is the balance after 10 years?
Interest rate:
%
Balance after 10 years: $
Skip to navigation
The balance after 10 years based on an interest rate of 5.25% will be $461.25.
The interest rate of the account can be calculated by using the formula I = P × R × T, where I is the interest amount, P is the original principal amount, R is the annual interest rate, and T is the time in years.
Using this formula, we can calculate the interest rate as follows:
I = 422 - 401 = 21
P = 401
T = 1
R = I / (P × T) = 21 / (401 × 1) = 0.0525
Therefore, the interest rate of the account is 5.25%.
To calculate the balance after 10 years, we can use the formula A = P(1 + rt), where A is the final amount (balance after 10 years), P is the original principal amount, r is the interest rate, and t is the number of years.
Using this formula, we can calculate the balance after 10 years as follows: A = 401(1 + 0.0525 × 10) = 461.25
Therefore, the balance after 10 years will be $461.25.
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Will give brainliest to first person
Answer:
\(x^{2} +6x+5\)
Step-by-step explanation:
A=lw
A=(x+5)(x+1)
A= \(x^{2} +6x+5\)
6th grade math help me pleaseeee...
Answer:
-3.8
Step-by-step explanation:
u = 3.8
u × -1 = 3.8 × -1
-u = -3.8
find the value of w and x. Round the answers to the nearest tenth.
Answer:
Step-by-step explanation:
sin50=w/10
w=10sin50
w=7.66
sinx=w/11
x=arcsin(w/11)
x=arcsin(10sin50/11)
x=44.14 degrees
A jewelry store has 212.75 ounces of 14-carat gold in stock. (a) how many custom necklaces can be manufactured if each requires 2 7/8 ounces of gold? (b) if gold is currently selling for $1,050 per ounce, how much is the gold in each necklace worth (in $)?
Answer:
a. The number of custom necklaces that can be manufactured if each requires 2 7/8 ounces of gold is 74 necklaces.
b. The value of the gold in each necklace is $1761
Step-by-step explanation:
(a) Number of necklaces
2\(7/8\) ounces of gold=2.875
No of necklaces=212.75oz x 1 necklaces/2.875oz
=74 necklaces
(b)Value of gold in each necklace
There are 2.875 oz of 14K gold in each necklace. Pure gold is 24K.
Mass of pure gold=2.875oz x 14k/24k
=1.677083oz
Pure 24K gold is worth $1050/oz.
Value of pure gold=1.677oz x 1050/1oz
= 1760.9 dollars
The value of the gold in each necklace is $1761
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The number of custom necklaces that can be manufactured if each requires 2 7/8 ounces of gold is 74 necklaces and the value of the gold in each necklace is $ 1761.
2 ounces of gold = 2.875 oz.
Number of necklaces = 212.75 oz. x 1 necklaces / 2.875 oz.
= 74 necklaces
Value of gold in each necklace
There are 2.875 oz. of 14K gold in each necklace.
Mass of pure gold=2.875 oz. x 14 k / 24 k
= 1.677083 oz.
Pure 24K gold is worth $ 1050 / oz.
Value of pure gold= 1.677oz x 1050 / 1oz
= 1760.9 dollars
The value of the gold in each necklace is $1761
Therefore, the number of custom necklaces that can be manufactured if each requires 2 7/8 ounces of gold is 74 necklaces and the value of the gold in each necklace is $ 1761.
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MULTIPLE CHOICE Given the lengths of the three sides of a triangle determine which triangle is not a right triangle . A
B
C
D
Answer:
D. is not right triangle
Step-by-step explanation:
10²+ 49² = 2501 ≠ 50²
A city grid of Anytown, USA is shown on the grid below. The fire department is represented by quadrilateral RSTU. Another fire department is opening in a different part of the city to maximize fire protection. The size of the new department's property must be congruent to the older department. Vertices A and B are plotted on the grid below to represent two vertices of the new fire department quadrilateral ABCD:
Map of Anytown. The line y equals 6 is Main Road. The line y equals 3 is Rose Lane. The line y equals negative 5 is Crystal Ave
What could be the ordered pairs representing vertices C and D of quadrilateral ABCD so that the new fire department is congruent to the old fire department? (4 points)
C(−7, 3), D(−7, 5)
C(2, 3), D(2, 5)
C(−2, 3), D(−2, 5)
C(0, 3), D(0, 5)
Answer:
C(0, 3), D(0, 5)Step-by-step explanation:
Points we are interested in given:
A(-4, 5), B(-4, 3)Points C and D have 2 possible places
1. To the left from A and B on the grid. They will have coordinates:
(-8, 3) and (-8, 5) (red points on the grid)2. To the right from A and B on the grid. They will have coordinates:
(0, 3) and (0, 5)Correct answer choice reflecting these coordinates is the last one which reflects the second option
Also see attached
Answer:
The answer is C!
Explanation:
I just took the test! :)
These cones are similar. find the surface
area of the smaller cone. round to the
nearest tenth.
2 cm
3 cm
surface area = [? ] cm2
surface area = 75 cm?
Answer:
33.3 is your answer
Step-by-step explanation:
The surface area of the smaller cone A₁ is approximately 33.3 cm² when rounded to the nearest tenth.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
Two cones A₁ and A₂ are similar.
The radius of A₁ = 2 cm
radius of A₂ = 3 cm
The surface area of A₁ = ? cm²
surface area of A₂ = 75 cm²
Since the cones A₁ and A₂ are similar, their corresponding sides are proportional.
Specifically, the ratio of their radii is the same as the ratio of their surface areas. That is,
(radius of A₁) / (radius of A₂) = (surface area of A₁) / (surface area of A₂)
We can use this relationship to solve for the surface area of A₁:
(surface area of A₁) = (radius of A₁ / radius of A₂)^2 × (surface area of A₂)
Substituting the given values, we get:
(surface area of A₁) = (2/3)² × 75
(surface area of A₁) = 4/9 × 75
(surface area of A₁) ≈ 33.3 cm²
Therefore, (surface area of A₁) ≈ 33.3 cm²
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xavier is a teacher and takes home 90 papers to grade over the weekend. he can grade at a rate of 6 papers per hour. how many papers would xavier have remaining to grade after working for 12 hours?
The number of papers xavier have remaining after working for 12 hours is 18
How many papers would xavier have remainingXavier can grade 6 papers per hour, so in 12 hours he can grade:
6 papers/hour x 12 hours = 72 papers
Therefore, after working for 12 hours, Xavier would have
90 - 72 = 18 papers remaining to grade.
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if the least-squares regression line for predicting y from x is y = 50 – 15x, what is the predicted value of y when x = 3?
The predicted value of y when x = 3, based on the least-squares regression line equation y = 50 - 15x, is y = 50 - 15(3) = 5.
The given least-squares regression line equation y = 50 - 15x represents a linear relationship between the variables x and y. In this equation, the coefficient of x (-15) represents the slope of the line, and the constant term (50) represents the y-intercept.
To find the predicted value of y when x = 3, we substitute x = 3 into the equation and solve for y. Plugging in x = 3, we have y = 50 - 15(3). Simplifying this expression, we get y = 50 - 45 = 5.
Therefore, when x = 3, the predicted value of y based on the least-squares regression line is 5. This means that according to the regression line, when x is 3, the expected or estimated value of y is 5.
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Which of the following is NOT a monomial?
O
x
O -
2x-3
O
155
Answer:
2x -3
Step-by-step explanation:
Answer:
2x-3 isn't monomial. hope u like it
Write the equations of the following ellipes in their colonical forms and hence determine the
a] Their Co-Ordinates of their ellispes
b] Their area of the ellipses
c] Their perimeter of the ellipse
d] Their vertices
e] Their foci
f ] Length of major and minor axis
The equation of ellipse are 4x² + 5y ² - 24x² - 20y + 36= 0 2x² ‐ 5y² + 8x + 10y + 13= 0
a) The coordinates of the ellipse are centered at (3, 2).
b) The area of the ellipse is a = √5 and b = √20.
c) Perimeter ≈ π * (3(a + b) - √((3a + b)(a + 3b))).
d) The vertices of the ellipse are located at (3 ± √5, 2) and (3, 2 ± √20).
e) The foci of the ellipse cannot be determined in this case because the equation does not contain information about the foci.
f) The length of the major axis is 2a, The length of the minor axis is 2b.
Let's analyze each given equation of the ellipse and determine the requested information.
a) Equation: 4x² + 5y² - 24x - 20y + 36 = 0
To write the equation in standard form, we need to complete the squares for both x and y terms.
Rearranging the terms:
4x² - 24x + 5y² - 20y + 36 = 0
Completing the squares for x:
4(x² - 6x) + 5y² - 20y + 36 = 0
4(x² - 6x + 9) + 5y² - 20y + 36 = 4(9)
4(x - 3)² + 5y² - 20y + 36 = 36
4(x - 3)² + 5(y² - 4y) = 0
Completing the squares for y:
4(x - 3)² + 5(y² - 4y + 4) = 0 + 5(4)
4(x - 3)² + 5(y - 2)² = 20
Comparing this with the standard form of the ellipse equation:
[(x - h)²/a²] + [(y - k)²/b²] = 1
We can see that a² = 5, b² = 20, h = 3, and k = 2.
b) Area of the ellipse:
The area of the ellipse can be calculated using the formula: Area = π * a * b, where a and b are the semi-major and semi-minor axes, respectively.
In this case, a = √5 and b = √20.
So, the area of the ellipse is Area = π * √5 * √20 = π * 2 * √5.
c) Perimeter of the ellipse:
There is no simple formula to calculate the exact perimeter of an ellipse. However, an approximation formula can be used: Perimeter ≈ π * (3(a + b) - √((3a + b)(a + 3b))).
In this case, a = √5 and b = √20.
Plugging in the values, we can calculate the approximate perimeter of the ellipse.
d) Vertices:
The vertices of the ellipse can be determined using the formula:
Vertex on the x-axis: (h ± a, k)
Vertex on the y-axis: (h, k ± b)
In this case, the vertices will be (3 ± √5, 2) and (3, 2 ± √20).
e) Foci:
The foci of the ellipse can be determined using the formula:
Foci on the x-axis: (h ± c, k)
Foci on the y-axis: (h, k ± c)
where c = √(a² - b²) for a > b.
In this case, c = √(5 - 20) = √(-15) = imaginary value (since it is negative).
f) Length of major and minor axes:
The length of the major axis is 2a, where a = √5.
The length of the minor axis is 2b, where b = √20.
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Over the past 4 years, a customer's fixed income portfolio value has dropped by 5%. During the same period, the Consumer Price Index has dropped by 2%. Based on these facts, which statement is TRUE?
The statement that is TRUE based on the given facts is that the customer's fixed income portfolio has experienced a greater decline in value than the decrease in the Consumer Price Index (CPI).
To elaborate, the customer's fixed income portfolio has dropped by 5% over the past 4 years. This means that the value of their portfolio has decreased by 5% compared to its initial value. On the other hand, the Consumer Price Index (CPI) has dropped by 2% during the same period. The CPI is a measure of inflation and represents the average change in prices of goods and services.
Since the customer's portfolio has experienced a decline of 5%, which is larger than the 2% drop in the CPI, it indicates that the value of their portfolio has decreased at a higher rate than the general decrease in prices. In other words, the purchasing power of their portfolio has been eroded to a greater extent than the overall decrease in the cost of goods and services measured by the CPI.
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How many department stores have fewer than 60 pairs of boots?
Answer:
The answer is below
Step-by-step explanation:
The question is not correct, the correct question is:
The regional manager of a chain of department stores created the following stem-and-leaf plot showing the number of pairs of boots at each of the stores:
I 0 I
I 1 I 7 8
I 2 I 0 5 8
I 3 I 4 4 7 8
I 4 I 0
I 5 I
I 6 I
How many department stores have more than 60 pairs of boots
Answer:
The stem and leaf plot is a table which is used to represent a value with the first and other digit as the stem while the last digit is the leaf.
From the table attached, the first column is the stem and the remaining column are the leafs. Therefore from the table, below are the pairs of boots in different stores:
17, 18, 20, 25, 28, 34, 34, 37, 38 and 40.
All the store have fewer than 60 boots. This means that the number of stores with more than 60 pairs of boots is 0
Help me with ixl please
A straight line = 180°. You have: 58° , 40°, and q so:
q = 180° - (58° + 40°)
q = 82°
Answer:
82
Step-by-step explanation:
180 i s the line length so
180-40=140
140-58=82