The mean of the scores is 8.5. Option B
What is mean?You should recall that mean simply means average. Mean in this case is the sum of the product of scores and their frequency divided by the sum of the frequency.
The table below helps to understand the mean very well
Column 1 frequencies
x f fx
5 1 5
6 2 12
7 5 35
8 5 40
9 7 63
10 10 100
∑f=30 ∑fx= 255
Mean is calculated by the formula
Therefore the Mean = ∑fx/∑f = 255/30 Mean = 8.5
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Correct question
A 2-column table with 6 rows. Column 1 is labeled score with entries 5, 6, 7, 8, 9, 10. Column 2 is labeled Frequency with entries 1, 2, 5, 5, 7, 10.
What was the mean score on the quiz?
7.5
8.5
9
10
1/8 times y = 4 what is y
Answer: 32
Step-By-Step Explanation: 1/8 times 32 = 4
I multiplied 8 by 4 to get 32 then checked my answer by multiplying 1/8 and 32.
4 if the mixing ratio of a sample of air is 2 grams/kilogram, and the temperature of the sample is 25 degrees celsius, yielding a saturation mixing ratio of 20 grams/kilogram, what is the relative humidity of the sample?
Because the temperature is greater, the relative humidity of the atmosphere is higher.
Relative humidity: What is it?Water vapor is also measured by relative humidity (RH), which is stated as a percentage but RELATIVE to the air's temperature. In plenty of other terms, it is a comparison between the quantity of water vapor that is really present in the air and the maximum amount water vapor that is possible for the air at the current temperature.
How can relative humidity be determined from temperature?By deducting the temperature just on wet-bulb thermometer from of the temperature just on dry-bulb thermometers and utilizing a relative humidity chart, one may determine the relative humidity.
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What is the equation of the line that passes through the point (1,-3) and has a slope of -3
Answer:
Step-by-step explanation:
The equation of line passing from point (x1,y1) and having slope m is
y- y1 =m(x- x1)
m=-3, x1=1, y1=-3
y-(-3) = -3(x-1)
y+3=-3(x-1)
y+3=-3x+3
y=-3x
3x+y=0
Answer:
y + 3x = 0
Step-by-step explanation:
The formula for equation of the line is :
y - y1 = m ( x - x1 )
NB: The m is the slope, then use substitution, solve and equate everything to 0
Martina rents a room in her home to guests. She charges a $25 flat fee per night for one person. Additional guests are welcome to stay, but she charges $10 per person. She expects guests to check out by 10 a.m. and charges an extra $5 per hour for late checkouts. Select the linear equation that correctly represents how much Martina collects for one night of stay in her home.
The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z
The linear equation to represent how much Martina collects for one night of stay in her home is:
y = 25 + 10x - 5z
where:
y is the total amount collected in dollars
x is the number of additional guests (besides the first one)
z is the number of hours the guests check out late
This equation represents the flat fee of $25 per night for the first guest, the additional fee of $10 per person per night for additional guests, and the extra fee of $5 per hour for late checkouts.
Therefore, The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z
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Find the equation of the median from vertex A if the coordinates are A(-3,-1), B(3,5) and C(7,-3)
Answer: [tex]y-1=\frac{1}{4}(x-5)[/tex]
Step-by-step explanation:
The median from vertex [tex]A[/tex] passes through [tex]A[/tex] and the midpoint of [tex]\overline{BC}[/tex].
Using the midpoint formula, the midpoint of [tex]\overline{BC}[/tex] has coordinates [tex]\left(\frac{3+7}{2}, \frac{5-3}{2} \right)=(5, 1)[/tex].
Therefore, we need the equation of the line passing through [tex](-3,-1)[/tex] and [tex](5,1)[/tex].
The slope of this line is [tex]\frac{-1-1}{-3-5}=\frac{1}{4}[/tex].
Using point-slope form, the equation is y[tex]y-1=\frac{1}{4}(x-5)[/tex].
Let $a,$ $b,$ $c$ be positive real numbers. Find the minimum value of \[\frac{(a b)(a c)(b c)}{abc}.\]
The minimum value of the expression is [tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex], with a, b, and c be positive real numbers.
What is the positive real number?
In mathematics, the set of positive real numbers is the subset of those real numbers that are greater than zero. The non-negative real numbers, also include zero.
We can simplify the expression as follows:
a^2 b^2 c = (ab)^2 c.
Now, we can use the AM-GM inequality to find the minimum value of the expression:
[tex][(ab)^2 c \ge \left(\frac{(ab)^2 + c}{2}\right)^2 = \left(\frac{(ab + c)^2 - 2abc}{4}\right)^2.][/tex]
As the minimum value is achieved when equality holds, we can set the equation to the original expression and simplify it.
[tex][(ab)^2 c \ge \left(\frac{(ab)^2 + c}{2}\right)^2 = \left(\frac{(ab + c)^2 - 2abc}{4}\right)^2.][/tex]
[tex]$a^2b^2c = \frac{(a^2b^2+ 2ab^2c+c^2b^2) - 2abc}{4}$[/tex]
[tex]$4a^2b^2c = (a^2b^2+ 2ab^2c+c^2b^2) - 2abc$[/tex]
4abc = (ab + c)(ab + c) - 2abc
4abc = (ab + c)^2 - 2abc
6abc = (ab + c)^2
so the minimum value is: [tex]$(\frac {(ab+c)^2}{6})^{\frac{1}{2}}$[/tex]
[tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex]
Hence, the minimum value of the expression is [tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex], with a, b, and c be positive real numbers.
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Which best describes the range of the function fx 2 3 x?
On solving the provided question, we can say that the range of the function f(x) = 2(3)x is best described by y > 0.
What is range?The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.
The range of the function f(x) = 2(3)x is best described by y > 0.
Especially when the constant is e, a function whose value is a constant increased to the power of the argument.
An exponential function is a function with the form, where b is referred to as the base and x can be any real number, if b is any number such that and.
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What is the value of |−13| − |21|
Answer:
- 8
Step-by-step explanation:
the absolute value function always gives a positive value, that is
| - a | = | a | = a
then
| - 13 | - | 21 |
= | 13 | - | 21 |
= 13 - 21
= - 8
Each week, Alfonso earns $85 for every shift he works at the theater and $15 for every dog-walking job. He uses the expression 85x 15y to keep track of his earnings. Part A: Identify the coefficients and variables in the expression. (3 points) Part B: How many terms are in the expression, what are they, and how do you know
Part A:Coefficients in are 85 and 15.
X represents theatrical shifts, Y represents dog-walking gigs.
Part B: Two phrases, the first of which indicates the amount of money he makes from his work in the theater and the second, from dog-walking. A sum or a deduct sign is used to demarcate each phrase.
Part A: The information we don't know is contained in an expression's variable. In this instance, we don't know how many dog-walking jobs he has in addition to his theater duties. We have 2 variables—x and y—because of this. The variable is multiplied by the coefficient, which is a number. Since there are two variables in this situation, there are two coefficients: 85 and 15.
Part B: A sum or a subtract sign is used to denote the separation of each term in an equation. The terms are the numbers and variables that occur before and after the sum sign because there is only one sum in this situation. 85x and 15y are involved. He initially discloses how much money he makes for each shift at his total annual salary at the theater is determined by multiplying his hourly wage by the number of shifts he works. The second one is the sum of the money he makes from each dog-walking work multiplied by the number of jobs he completes; this is the total amount he makes from the dog-walking jobs.
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What is ratio grade 7?
Ratio grade 7 is a mathematical concept that involves comparing two or more quantities using a ratio. It is a common part of mathematics curriculums for middle and high school students.
1. A ratio is a comparison of two or more numbers.
2. Ratios can be expressed as a fraction, a decimal, or a percentage.
3. Ratios are used to compare quantities of different kinds and are used to find relationships between them.
4. In grade 7, students will learn about ratios and how to use them to solve various problems. They will also learn about proportionality, rates, and unit rates.
5. Ratios can also be used to compare measurements, such as lengths, weights, and areas.
6. Students will also use ratios to calculate proportions, which can be used to solve problems involving proportional relationships.
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What is the equation of this graphed line?
y=2x+2
y=-2x-2
y=6x+6
y=-6x-6
By calculating the given equations with points none of the equation represents equation of this graphed line.
What is the equation of the line?
The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y-intercept.
We have given the,
y = 2x+2
y=-2x-2
y=6x+6
y=-6x-6
And, the graph.
From the line in the graph we can take the cordinate points which represents the equation of line.
point (1, 2)
By putting this point we can decide the given equation of line:
y=2(1)+2 = 4
y=-2(1)-2 = 0
y=6(1)+6 =12
y=-6(1) - 6 =-12
Hence, by calculating the given equations with points none of the equation represents equation of this graphed line.
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What defines a 1 to 1 function?
A function is considered a one-to-one function, also called an injective function, if it assigns a unique output value to each input value. In other words, a function is one-to-one if no two different input values have the same output value.
A function f(x) is one-to-one if and only if for any two distinct inputs x1 and x2, it holds that f(x1) ≠ f(x2).
One way to determine if a function is one-to-one is to use the horizontal line test:
if any horizontal line intersects the graph of the function at most once, then the function is one-to-one.
A one-to-one function has an inverse function. The inverse function, f^-1(x), is also a function, it assigns to each output value of f(x), an input value such that f^-1(f(x)) = x.
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Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form. -2, 1, 3
Answer:
Step-by-step explanation:
A polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 1, 3 is (x- -2)(x-1)(x-3) = x^3 - 6x^2 + 11x - 6
A 6-sided die is rolled. Find P(3 or 5).
A.1 / 36
B.1 / 3
C.2
D.1 / 6
When a 6-sided die is rolled, P(3 or 5) is equal to B. 1/3.
A 6-sided die has six possible outcomes: 1, 2, 3, 4, 5, and 6. To find P(3 or 5) or the probability of rolling a 3 or a 5, we need to add the probabilities of rolling each of those numbers separately and then subtract the probability of rolling both numbers (3 and 5) at the same time to avoid overcounting.
The probability of rolling a specific number on a fair die is 1/6, since there are 6 possible outcomes.
So, P(rolling a 3) = 1/6 and P(rolling a 5) = 1/6
P(3 or 5) = P(rolling a 3) + P(rolling a 5) - P(rolling 3 and 5) = 1/6 + 1/6 - 0 (since rolling 3 and 5 is not possible)
= 2/6 = 1/3
Therefore, the probability of rolling 3 or 5 on a fair 6 sided die is 1/3.
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Compute the perimeter. (No it's not 18, not really sure how to solve this problem)
Answer:
23.8
Step-by-step explanation:
Solve for the missing side, x, by using the pythagorean theorem:
5² + 3² = x² **(8-5=3)
x² = 25+9 = 34
x = √34 = 5.831
P = sum of all sides = 5 + 5 + 8 + 5.831 = 23.8
Stephen is making a map of his neighborhood. He knows the following information: His home, the bus stop, and the grocery store are all on the same street. His home, the park, and his friend's house are on the same street. A street map is shown. The streets form a triangle comprised of the locations of home, friends house, and the grocery store. The triangle is intersected by a line formed by the park and the bus stop. Stephen wants to use the Triangle Proportionality Theorem to determine the relationships on his map. He knows the angle between the park, the bus stop, and his home. Which other angle does he need to know
On solving the provided question we can say that in this triangle 6 blocks separate the bus stop from his house.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon.
The graph of the provided data is included below. 10 blocks separate his residence from the park.
His friend's home is 15 blocks away from his home. 9 blocks separate the grocery shop from his home.
The sides are in proportions according to Side-Angle-Side Similarity. Consequently, we calculate a ratio using the corresponding triangles.
= distance from home to friend's home / distance from home to park
= distance from home to grocery / distance from to bus stop
= 15/10 = 9/x
x = 6
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Answer:
His friend's house, grocery store, and his home
Step-by-step explanation:
Had this question on a test and got it right.
rebecca puts her backpack on a fan cart and turns the fan on. she then measures the speed each second afterward. at 10 seconds the cart has a speed of 20 cm per second. how fast will the cart be moving at 12 seconds?
At 12 seconds, the cart will be moving at 24 cm per second.Rebecca is using a fan cart and measuring the rate of the cart at different times.
Rebecca is using a fan cart and measuring the rate of the cart at different times. At 10 seconds, the cart has a speed of 20 cm per second. To calculate the speed at 12 seconds, you can use the formula rate x time = distance. The rate is the speed of the cart at 10 seconds, which is 20 cm per second. The time is the difference between 10 seconds and 12 seconds, which is 2 seconds. Thus, the equation becomes 20 cm/s x 2s = 40 cm. Therefore, the speed at 12 seconds is 24 cm per second.
At 12 seconds, the cart will be moving at 24 cm per second.
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What is the value of x?
x = ____
Enter the number only!
The value of 'x' for the given co exterior angles for the parallel lines PQ ans SR is found as: x = 30.
Explain the term co exterior angles?Co-exterior angles are external angles that are on the same transverse side. Co-exterior angles add up to 180 degrees.The two angles which it are on the same side of such transversal are known as co-interior angles as well as consecutive interior angles. The inside angles total 180 degrees and are known as co-interior angles. It indicates that two internal angles that reside on the identical side of the transversal have a sum that is additional.For the stated question:
(x + 12) + (3x + 48) = 180 (co exterior angles are supplementary)
4x + 60 = 180
4x = 180 - 60
4x = 120
x = 30
Thus, the value of 'x' for the given co exterior angles for the parallel lines PQ ans SR is found as: x = 30.
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Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer: 14.7
Step-by-step explanation:
The remaining interior angle is [tex]135^{\circ}[/tex].
[tex]\frac{x}{\sin 19^{\circ}}=\frac{32}{\sin 135^{\circ}}\\ \\ x=\frac{32 \sin 19^{\circ}}{\sin 135^{\circ}} \\ \\ x \approx 14.7[/tex]
mr. earl e. bird leaves his house for work at exactly 8:00 a.m. every morning. when he averages 40 miles per hour, he arrives at his workplace three minutes late. when he averages 60 miles per hour, he arrives three minutes early. at what average speed, in miles per hour, should mr. bird drive to arrive at his workplace precisely on time?
if 40 makes him 30 mins late and 60 makes him 30 mins early then it only would make since that in between both 40 and 60 is 50 and that would make him go on time
mr. earl e. bird leaves his house for work at exactly 8:00 a.m. every morning
when he averages 40 miles per hour, he arrives at his workplace thirty minutes late.
when he averages 60 miles per hour, he arrives thirty minutes early.
at what average speed, in miles per hour, should mr. bird drive to arrive at his workplace precisely on time?
if 40 makes him 30 mins late and 60 makes him 30 mins early then it only would make since that in between both 40 and 60 is 50 and that would make him go on time
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HELP PLS!!! WILL MARK THE MOST BRAINLIEST
a group of 24 people equally shared 14 pounds of ground beef. how many pounds of ground beef did each person get?
On solving the provide question, we can say that by unitary method each person get = 24/14 = 1.7142857143 pounds of beef
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
a group of = 24 people
equally shared = 14 pounds of ground beef.
each person get = 24/14 = 1.7142857143 pounds of beef
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the number of tornadoes in a given year follows a poisson distribution with mean 3. calculate the variance of the number of tornadoes in a year given that at least one tornado occurs.
So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.
The Poisson distribution is a discrete probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average number of events per interval.
For a Poisson distribution with mean λ, the variance is equal to λ.
Given that at least one tornado occurs in a year, the mean number of tornadoes is 3. Therefore, the variance is also equal to 3.
So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.
It's worth noting that this result is based on the assumption that the number of tornadoes follows a Poisson distribution with mean 3, which may not always be the case in real-world scenarios. The actual number of tornadoes in a given year can be influenced by various factors such as climate, weather patterns, and geography.
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Please help asap!! I need help, how do you solve this??
Answer:
FIRST ONE IS 7
Step-by-step explanation:
SECOUND ONE IS 12THIRD ONME IS 2
sin 0 + cos 0 = 1is a foundational trigonometric identity. %3! If you divide through by ISelect) , then 1+ cot² 0 = csc² 0 will be created. If you divide through by ISelect] . then tan? 0+1 = sec² ) will be created.
These identities are not true and cannot be derived from the first identity.
What is trignomentry ?
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of angles and circles, and to solve problems involving geometric shapes and measurements. Trigonometry is used in many fields such as physics, engineering, and navigation.
The statement "sin 0 + cos 0 = 1" is a correct foundational trigonometric identity. However, it is not possible to derive the identities "1+cot^2(0) = csc^2(0)" or "tan^2(0)+1 = sec^2(0)" by dividing through by cot^2(0) or by tan^2(0) respectively. These identities are not true, and are not a direct consequence of the first identity.
These identities are not true and cannot be derived from the first identity.
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the perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm. the length of side p is 4 cm and the lengths of q and r are equal
PART 2.!!
determine the measure of
The lengths of q and r are 2.5 , 2.5 respectively if the perimeter of an isosceles triangle pqr is 9 cm.
What is a triangle ?A triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.
here, Given that,
The perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm.
the length of side p is 4 cm
Let the lengths of q and r are x and y respectively.
The perimeter of an isosceles triangle = (p+2q)
So,
p+2q = 9
4+2q = 9
2q = 9-4
2q = 5
q = 5/2
q = 2.5 cm
Hence , the lengths of q and r are 2.5 , 2.5 cm respectively .
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a bag contains:5 red marbles 6 blue marbles 3 green marbles 4 black marbles2 yellow marble a marble will be drawn from the bag and replaced 180 times. what is a reasonable prediction for the number of times a red or yellow marble will be drawn?
A reasonable prediction for the number of times a Red or Yellow Marble Draws = (7/20) x 180 = 126.
The total number of marbles in the bag is 20 (5 red, 6 blue, 3 green, 4 black, and 2 yellow). Therefore, the probability of drawing a red or yellow marble is 7/20. Applying this probability to the 180 times a marble is drawn and replaced, we can calculate that the number of times a red or yellow marble is likely to be drawn is 126 (7/20 x 180). This can be expressed as a formula as follows: Red or Yellow Marble Draws = (Number of Red and Yellow Marbles / Total Number of Marbles) x Number of Draws. In this case, Red or Yellow Marble Draws = (7/20) x 180 = 126.
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Sketch the graph of a function f for which f(0)=0, f'(0)=3, f'(1)=0, f'(2)=-1
A function f for f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3.
An easy definition of a function?
As a set of inputs with one output for each, a function is defined as a relationship between them.
A function, expressed simply, is an association between inputs where each input is connected to one and only one output.
when it says something like f(1) = 0 it means that when x = 1, y = 0
so we know one point on the graph is (0,0)
when it says something like f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3
here is a picture of the tangent lines, then what a sketch of the function would be.
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in response to the increasing weight of airline passengers, the federal aviation administration (faa) told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. but passengers vary, and the faa did not specify a standard deviation. a reasonable standard deviation is 35 pounds. a commuter plane carries 30 passengers. find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds. (hint: to calculate this probability, restate the problem in terms of the mean weight.)
The probability of 30 random people having weight more than 6000 pounds is 0.3134 or 31.34%.
To find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds, we can use the Central Limit Theorem (CLT) which states that the sum of a large number of independent and identically distributed random variables will tend to be normally distributed, regardless of the underlying distribution of the individual variables.
Since we know the average weight of a passenger (190 pounds) and a reasonable standard deviation (35 pounds), we can use this information to calculate the mean and standard deviation of the total weight of 30 passengers.
The mean weight of 30 passengers is:
30*190 = 5700 pounds
The standard deviation of the weight of 30 passengers is:
sqrt(30)*35 = 59.8076211353316
Now we can use the standard normal distribution table, or z-score formula to find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.
z = (6000-5700)/59.8076211353316
z = 0.50251572
The probability of a z-score being greater than 0.50251572 is 0.3134, this means that there is a 31.34% chance that the total weight of 30 randomly selected passengers will exceed 6000 pounds.
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I need help with this equation:
A line passes through the points (2,-1) and (4,-1).
I already know the slope is 0, what is the equation of the line? (In slope-intercept form)
The line which passes through the points (2,-1) and (4,-1) has the slope-intercept equation as y = -1.
What is the slope-intercept form?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
The line passes through point (x1,y1) = (2,-1) and (x2,y2) = (4,-1)
The formula to find slope is -
m = (y2-y1)/(x2-x1)
m = (-1+1)/(4-2)
m = 0/2
m = 0
Now use the slope and point (2,-1) to find the y-intercept.
y = mx + b
-1 = 0(2) + b
-1 = 0 + b
b = -1
Write the equation in slope-intercept form as -
y = mx + b
y = 0x + (-1)
y = -1
Therefore, the equation is obtained as y = -1.
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