The values of the means for the two types of glasses suggest about the shape of glasses used is 22ml on average.
When it comes to pouring drinks, bartenders are expected to pour a specific amount of liquid into each glass. However, there may be some variation in the amount poured depending on the shape of the glass. In this scenario, we have data on the actual amount poured by bartenders into a short, wide glass when asked to pour 44.3 ml. We will use this data to calculate the mean and standard deviation and interpret their values.
The mean is the average amount poured into the short, wide glass. To find the mean, we add up all the amounts poured and divide by the number of samples. Using the data provided, we get a mean of 57.889 ml, rounded to three decimal places.
However, the mean doesn't tell us the whole story. We also need to consider the standard deviation, which tells us how much the amounts poured vary from the mean.
To calculate the standard deviation, we first need to find the variance. We calculate this by subtracting the mean from each amount poured, squaring the differences, adding them up, and dividing by the number of samples minus one. Using the data provided, we get a variance of 479.716 ml², rounded to three decimal places.
To get the standard deviation, we take the square root of the variance. Using the data provided, we get a standard deviation of 21.904 ml, rounded to three decimal places.
Interpreting the values of the mean and standard deviation, we can say that a typical amount poured into a short, wide glass is 57.889 ml, while a typical deviation from the mean amount poured is 21.904 ml. This means that the amounts poured vary by about 22 ml on average, which could be due to differences in pouring technique or the shape of the glass.
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hich statements describe the length of the sides of an isosceles right triangle if one leg is 6√2 feet? Select all that apply.
The length of the other leg is 6 feet.
The length of the hypotenuse is 12 feet.
The length of the hypotenuse is 6 feet.
The length of the other leg is 6√2 feet.
The correct statements are:
The length of the other leg is 6√2 feet.
The length of the hypotenuse is 12 feet.
What is Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given:
One leg of an isosceles triangle is 6√2 feet.
As, we know isosceles triangle two of its sides equal in length then the other side can be 6√2 feet.
Now, using Pythagoras theorem
H² = P² + B²
H² = (6√2)² + (6√2)²
H² = 72 + 72
H² = 144
H= 12 units
The statements that applies here are:
The length of the other leg is 6√2 feet.
The length of the hypotenuse is 12 feet.
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Answer:
The answer is B and D
Step-by-step explanation:
I took the test.
let me know if you would like an explanation down in the comments!
in a sample of 20 men, the mean height was 178 cm. in a sample of 30 women, the mean height was 164 cm. what was the mean height for b oth groups put together?
In a sample of 20 men, the mean height was 178 cm and a sample of 30 women, the mean height was 164 cm, then the mean height for both groups combined is approximately 172.4 cm.
To find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size.
We can begin by finding the total height of all the individuals in both groups combined. The total height for the men's group would be 20 multiplied by the mean height of 178 cm, which is 3560 cm.
Similarly, the total height for the women's group would be 30 multiplied by the mean height of 164 cm, which is 4920 cm. Adding these two values gives a total height of 8480 cm for both groups combined.
Next, we need to find the total sample size, which is the sum of the sample sizes of the two groups. The total sample size is 20 + 30 = 50.
Finally, we can calculate the weighted average of the means of each group using the formula:
Weighted average = (weight of group 1 * mean of group 1 + weight of group 2 * mean of group 2) / (weight of group 1 + weight of group 2)
In this case, the weights of each group are proportional to their sample sizes. Therefore, the weighted average can be calculated as:
Weighted average = (20/50 * 178 cm) + (30/50 * 164 cm) = 172.4 cm
In summary, to find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size. This is done by multiplying the sample size of each group by its mean height, adding the values, and then dividing by the total sample size.
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A TV at £800 plus VAT at 20%
What is the total cost of the TV
Answer:
it will be £960
Step-by-step explanation:
first £800×20/100
simplify £8×20
£160= VAT
Total cost=VAT+ normal cost
£160+£800
=£960
Let f(x)=-5x^(3)-8x^(2)-4x+3 and g(x)=3x^(3)-2x^(2)-8x-4.
Find (F-G)(X) Find(f-g)(-1)
The value of (f - g)(-1) is 5.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = -5x³ - 8x² - 4x + 3
g(x) = 3x³ - 2x² - 8x - 4
Now,
(f - g)(x)
= f(x) - g(x)
= -5x³ - 8x² - 4x + 3 - (3x³ - 2x² - 8x - 4)
= -5x³ - 8x² - 4x + 3 - 3x³ + 2x² + 8x + 4
= -8x³ - 6x² + 4x + 7
Now,
(f - g) (-1)
Substitute x = -1.
= -8(-1)³ - 6(-1)² + 4(-1) + 7
= -8 x -1 - 6 - 4 + 7
= 8 - 6 - 4 + 7
= 8 - 10 + 7
= 15 - 10
= 5
Thus,
(f - g)(-1) = 5
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1.
f(x) = x² - 8x + 17
The roots of the quadratic equation are -
{x} = 4 ± i(√2/2)
What is the general form of a quadratic equation?The general form of a quadratic equation is -
y = f(x) = ax² + bx + c
Given is the quadratic equation as -
f(x) = x² - 8x + 17
We can write the roots of the equation as -
x = {- b ± √(b² - 4ac)}/2a
x = {8 ± √(64 - 68)}/2
x = {8 ± i√2}/2
x = 4 ± i(√2/2)
Therefore, the roots of the quadratic equation are -
{x} = 4 ± i(√2/2).
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NEED THIS ASAP……………
……………..
The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.
Solving a function:We can solve the given function by adding or subtracting the same integer on both sides. Here adding or subtracting the same number on both sides doesn't change the condition of the function. In end-use trial and error mothed to find the value of the variable 'x'
Here we have
f(x) = - 6x + 14 and g(x) = - 2ˣ + 6
The solution of - 6x + 14 = - 2ˣ + 6 can be calculated as follows
=> - 6x + 14 = - 2ˣ + 6
=> - 6x + 8 = - 2ˣ
=> - 6x + 8 = - 2ˣ
=> - 6x + 2ˣ = - 8
By using the trial and error method
At x = 2
=> - 6(2) + 2² = -8
=> - 12 + 4 = -8
Therefore,
The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.
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a student committee has 6 membersâ4 undergraduate and 2 graduate students. a subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. what is the probability that there will be no graduate students on the subcommittee?
The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in (4 choose 3) = 4 ways.
The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in (6 choose 3) = 20 ways.
Therefore, the probability that there will be no graduate students on the subcommittee is:
Number of subcommittees with only undergraduate students / Total number of possible subcommittees
= 4 / 20
= 1/5
= 0.2
So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
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What number would correctly replace the G?
An office is planning to divide a common area into a social area and a quiet area. The quiet area takes up one-third of the space. The architect draws this plan at a scale of 1 ft.: 4 cm. What is the area of the social area on the plan?
Answer:
Let's call the total area of the common space "A". Since the quiet area takes up one-third of the space, its area is A/3.
The scale of the plan is 1 ft.: 4 cm, which means that one foot on the plan represents 4 cm in real life. So, the area of the social area on the plan is 4 times smaller than the actual area of the social space.
Therefore, the actual area of the social space is (A - A/3) = 2A/3. And the area of the social area on the plan is (2A/3) / 4.
Area of the social area on the plan is (2A/3) / 4.
Here,
Let the total area of the common space "A".
Since the quiet area takes up one-third of the space, its area is A/3.
The scale of the plan is 1 ft.: 4 cm
So,
One foot on the plan represents 4 cm in real life.
So, the area of the social area on the plan is 4 times smaller than the actual area of the social space.
Therefore, the actual area of the social space is (A - A/3) = 2A/3.
Thus the area of the social area on the plan is (2A/3) / 4.
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Select all factors of the expression 7x³ - 28xy²
Answer:
7 and 7x
Step-by-step explanation:
We distributing these factors are the only that can make sense
Unit 4: congruent triangles
Homework 7: Proofs review.
please help, i don’t know the answers to 1 or 4.
Answer:
1. SAS
2. Not congruent
Step-by-step explanation:
1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.
If you rotate the first triangle, you'll see that it is the same as the second.
4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.
The solution is,
1. SAS
2. AAS
3. SAS
4. Not congruent.
What is congruent triangle?Two triangles are congruent if all three pairs of corresponding sides are equal. Two pairs of corresponding sides and the corresponding angles between them are equal.
here, we have,
we know that,
To identify which triangles are congruent measure the angles and sides of each of the triangles and compare them.
Meaning of congruent:
In mathematics, the word congruent is used if two figures have the same size and shape, although their orientation can be different.
Two triangles are congruent:
In the case of triangles two factors should be considered:
1) Lengths of each side are equal.
2) Angles are equal.
This means that to determine if the triangles are congruent, we must measure each side and angle and make sure these are the same in each triangle.
now, we have,
1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.
If you rotate the first triangle, you'll see that it is the same as the second and, similar for 2 & 3 by AAS & SAS.
4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.
Hence, 1. SAS
2. AAS
3. SAS
4. Not congruent.
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Please help with triangles
The value of x is given as follows:
x = 131º.
How to obtain the value of x?An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.
Considering the above text, the measure of the top angle of the bottom triangle is given as follows:
a = 180 - 98
a = 82.
The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence:
2b + 82 = 180
2b = 98
b = 49.
(the sum of the measures of the internal angles of a triangle is of 180º).
Considering the vertical angles, the base angles of the top triangle are given as follows:
b = 49.
Hence the value of x is given as follows:
x = 180 - 49
x = 131º.
(as the top triangle is also isosceles, and the angle measure x is the exterior angle of an interior angle with measure of 49º).
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Pls solve 3,4,5!!! Tyyy (I will mark brainliest!)
Answer:
Step-by-step explanation:
4 = d
5=1/5
3 the first one is 4x1/12 and 2x3/12
1004.8 into 3 significant figures
Rounding off the 1004.8 into 3 significant figures will give 1000.
Significant Figures:Since significant figures are established as digits, they are also known as significant digits. By counting all of the values beginning with the first non-zero digit on the left, it is possible to determine the number of significant digits.
For example, the number of significant figures in 567 is 3.
The number of significant figures in 2.671 is 4.
Here we have a number
1004.8 need to be rounded off for 3 significant figures
Since 4 is less than 5 then the resultant number = 1000
[ 4 and 8 neglected since 4 < 5]
Therefore,
Rounding off the 1004.8 into 3 significant figures will give 1000.
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HELP ME!
A passenger train leaves a train depot 2 h after a freight train leaves the same depot. The freight train is traveling 28 mph slower than the passenger train. Find the rate of each train if the passenger train overtakes the freight train in 3 h.
A. Passenger train ___ mph
B. freight train ___ mph
Answer: A. Passenger train: 52 mph B. Freight train: 24 mph
Step-by-step explanation:
On a coordinate plane, how are the locations of the points (2 , -1) and (2 , 1) related?
On a coordinate plane, locations of the points (2 , -1) and (2 , 1) related by reflection across the x-axis.
It is given that the locations of the two points are (2 , -1) and (2 , 1).
We have to find the relation between two points.
From the given points (2 , -1) and (2 , 1), it is clear that the y-coordinates are same but the sign of x-coordinates are opposite.
If a figure is reflected across the y-axis, then we change the sign of y-coordinate and the x-coordinates remain same,
So, it is reflection across the x-axis.
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Please help, I’ll give brainliest!!!!!!!!!!!!
The ordered pairs from the graph of quadratic and linear equations are (-2, 7) and (2, -1)
what is graph of a quadratic and linear equationA graph of a quadratic equation is a parabolic curve that opens up or down, depending on the sign of the coefficient of the squared term. A general form of a quadratic equation is given by:
y = ax^2 + bx + c,
where a, b, and c are constants. The graph of this equation can be plotted by choosing a range of values for x and calculating the corresponding values of y.
A graph of a linear equation is a straight line. A general form of a linear equation is given by:
y = mx + b,
where m is the slope of the line and b is the y-intercept.
In this problem, the ordered-pairs will be the point in which they intersect with each other.
Looking carefully at the graph, the ordered pair will be at points
A = (-2, 7)
B = (2, -1)
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Which graph represents a linear function
Answer:
Any line except a vertical line represents a linear function.
Step-by-step explanation:
Any "diagonal" line is a linear function. Even a horizontal line represents a linear function. Only a vertical line does NOT represent a linear function.
A triangle has a perimeter of 9x 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle? x 13 x − 1 8x − 7 17x − 1
The length of the third side of a triangle with perimeter 9x + 6 and measures of other two sides of the triangle is equal to option a. x + 13.
Perimeter of the triangle is equal to
= 9x + 6
First side of the triangle = 5x
Second side of the triangle = 3x - 7
Let 'n' be the third side of the triangle
perimeter of the triangle = 9x + 6
⇒ 5x + 3x - 7 + n = 9x + 6
⇒ n + 8x - 7 = 9x + 6
⇒ n = 9x -8x + 6 + 7
⇒ n = x + 13
Therefore, the third side of the triangle with given perimeter of the triangle is equal to option a. x + 13.
The above question is incomplete , the complete question is :
A triangle has a perimeter of 9x + 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle?
a. x + 13 b. x − 1 c. 8x − 7 d. 17x − 1
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3-83. Challenge Problem! Find the dimensions of the generic rectangle below. Then write an equivalency
statement (length width = area) of the area as a product and as a sum.
x²
3x
-5x
-15
The dimensions are 5 units each
The area of the rectangle is 25 units
How to determine the dimensions
It is important to note that algebraic expressions are defined as expressions that are composed of variables, terms, cofficients, constants and factors.
They are also described as expressions with mathematical operations.
From the information given, we have that;
x² - 5x + 3x - 15
To solve the quadratic equation, let us use the factorization method
Group the values in pairs
(x² - 5x) + (3x - 15)
factor the terms
x(x -5) +3(x - 5)
Then, x + 3 = 0
x = -3
And x - 5 = 0
x =5
But area of a rectangle is;
= Length× width
= 5 × 5
= 25 square units
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how many modes are there in the following data set, which represents the number of days worked in october for 10 programmers of a software company? data set: 7,20,22,17,19,15,27,30,14,7
To mode of given data set of number of days worked in october for 10 programmers of a software company is 7 and 14.
The mode of a data set is the value that appears most frequently. In this case, we can see that both 7 and 14 appear twice, while all other values appear only once. Therefore, there are two modes in this data set: 7 and 14.
To solve mathematically, we can use the mode formula:
mode = value with the highest frequency
In this case, we have two values with the highest frequency, which are 7 and 14. Therefore, the mode of given data set is 7 and 14.
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The formula for the area of any triangle is a equals 1/2. The carpenter is actually using the following expression to represent the area of a triangle eight A= (1/2) (B)(B +5) which statement best matches the carpenters triangle
Answer:
The statement "A = (1/2) (B)(B + 5)" represents the area of a triangle, where B is the base of the triangle and (B + 5) is the height. This formula is used by the carpenter to calculate the area of a triangle with a given base and height.
Step-by-step explanation:
the town's population has increased for 80,000 to 90,000 in the past 10 years. what was the present increase.
The percentage increase in the population of the town is 12%.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Increase in population = 90,000 - 80,000 = 10,000
Percentage increase = 10,000/80,000 * 100 = 100/8 = 12.5%
Hence the percentage increase in the population of the town is 12%.
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ted has a part time job, he is paid £7.90 per hour,
last week he worked for 15 1/2 hours
what is ted total pay for last week
Answer: £122.45
Step-by-step explanation: 7.90*15.5
Answer: 109?
Step-by-step explanation:
2[73-(4x5)]
I think the answer is 106 but can someone double check? Thanks
Answer:
yes its 106
Step-by-step explanation:
brainly removed my answer
Simplify (6x-15)/(4x^2-25)
How do you do this problem? can you show me how to do it? I am struggling on this
The values and graph of the equation 3x - 2y = 6 is attached below while the slope is 3/2
What is equation of lineThe equation of a straight line can be represented in various forms. One of the most commonly used forms is the point-slope form, which is represented as:
y - y1 = m (x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line, which is the rate of change of y with respect to x.
Another common form of the equation of a line is the slope-intercept form, which is represented as:
y = mx + b
where m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.
In this problem, we need to write the table of values and the find the slope of the line.
3x - 2y = 6
rewriting this equation;
2y = 3x - 6
y = 3x/2 - 3
when y = 0
0 = 3x/2 - 3
3x/2 = 3
3x = 2 * 3
3x = 6
x = 2
when x = 0
y = 3(0)/2 - 3
y = 0 - 3
y = -3
The slope of the line can be calculated using the two points from above.
slope (m) = y₂ - y₁ / x₂ - x₁
m = -3 - 0 / 0 - 2
m = 3/2
The slope is 3/2
The graph of the equation is attached below
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8. If a || b, m/2 = 63°, and m29 = 105°, find the measure of each angle please!! help neeeded need angles A through L pls answer correctly
The measure of each angle is given below:
a. m<1 = 105° - 63° m<1 = 42°b. m<3 + m<2 + m<1 = 180° m<3 = 75°c. m<4 = m<1 m<4 = 42°d. m<5 = m<2 m<5 = 63°e. m<6 = m<3 m<6 = 75°What is an Angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The measure of angles {contd.} is:
f. m<7 = m<9 m<7 = 105°g. m<8 = m<6 m<8 = 75°h. m<10 = m<8 m<8 = 75°i. m<11 = m<4 m<11 = 42°j. m<12 = 180° - m<11 m<12 = 138°k. m<13 = m<11 m<13 = 42°l. m<14 = m<12 m<14 = 138°Read more about angles here:
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The price of a gallon of unleaded gas was $2.81 yesterday. Today, the price rose to $2.88. Find the percentage increase. Round your answer to the nearest tenth of a percent.
The percentage increase of the gas would be 2.5%.
How to calculate a percentage increase?We can calculate the value of the percentage increase by the following formula,
percentage increase = (final value - initial value) / initial value × 100%
As per the given question, we have
initial value = $2.81 , and final value = $2.88
Substitute the values in the above formula, and we get
percentage increase= (2.88 - 2.81 ) / 2.81 × 100%
percentage increase = (0.07) / 2.81× 100%
percentage increase = 0.0249 × 100%
Apply the multiplication operation, and we get
percentage increase = 2.49%
Thus, the percentage increase of an item would be 2.5%.
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please help ASAP !!!!
First, use the equation for a hemisphere. Since a sphere's equation is [tex]\frac{4}{3}\pi r^{3}[/tex], and a hemisphere is half a sphere, we can use the equation [tex]\frac{2}{3}\pi r^{3}[/tex]. We know the radius is 6 inches, and we can approximate pi as 3.14, so now let's plug in our values:
[tex]\frac{2}{3}\ (3.14) 6^{3}=\frac{2}{3} \ (3.14)(216)= \frac{2}{3}(678.16)= 452.16[/tex]
The volume of the hemisphere is about [tex]452.16 in^{3}[/tex].
The formula for the volume of a cone is [tex]\pi r^{2}\frac{h}{3}[/tex]. Again, let's plug in our values:
[tex](3.14)(36)\frac{6}{3} =(3.14)(36)(2)=(3.14)(72)=226.08[/tex]
The volume of the cone is about [tex]226.08 in^{3}[/tex].
Subtract 226.08 from 452.16 and you get 226.08.
The volume of the remaining solid will be [tex]226.08 in^{3}[/tex].
