Philip ran 438 mile yeterday. Michael ran 158 mile yeterday. How much farther did Philip run than Michael?
Answer:
he ran 280 miles more than Michael
Step-by-step explanation:
438-158=280
what is the mode frequency of the age variable?
The mode frequency can be a useful tool for understanding the distribution of the data and identifying any outliers or anomalies in the data set.
The mode frequency of the age variable refers to the most frequently occurring age in a given set of data. This measure of central tendency is particularly useful when working with categorical data, such as age ranges.
To calculate the mode frequency, one must first organize the data into a frequency distribution table, which lists all the different ages and the number of times each occurs. The age with the highest frequency is then considered the mode frequency.
For example, if there are 100 individuals in a data set and the ages range from 20 to 60, we would organize the data into age ranges, such as 20-29, 30-39, etc. Then we would count how many individuals fall into each age range and record this information in the frequency distribution table.
If the age range with the highest frequency occurs more than once, we have a multi-modal data set. On the other hand, if there is only one mode frequency, the data set is considered unimodal.
To know more about frequency here.
https://brainly.com/question/14926605
#SPJ4
Write an equation to represent the linear function comparing the number of months after the first month (x) to the number of total customers served (y)
Part 1: A small local coffee shop opened in January 2012. In the first month, the coffee shop served 400 customers. After that, the coffee shop served 70 customers each month.
Part 2:How many customers were served after 12 TOTAL months of being in business? HINT: Remember what the variable x represents
An equation to represent the linear function comparing the number of months after the first month (x) to the number of total customers served (y), 400 + 70x
The number of customers served after 12 months, 1240
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
In the first month, the coffee shop served 400 customers
After that, the coffee shop served 70 customers each month
Suppose, coffee shop served x number of months after first month,
Total people served = 400 + 70x
The number of customers served after 12 months,
Total people served = 400 + 70x12
= 400 + 840
= 1240
To know more about Equation check:
https://brainly.com/question/1529522
#SPJ1
The standard deviation of a simple random sample of 15 customer waiting times is found to be 4.8 minutes. Find the test statistic to test the claim that the standard deviation of all customer waiting times is greater than 3.5 minutes. Use a 0.01 significance level.
The test statistic to test the claim that the standard deviation of all customer waiting times is greater than 3.5 minutes, 7.444
What is Standard deviation ?Standard deviation is a measure of the spread or dispersion of a set of data. It quantifies how much the individual data points in a set deviate from the mean (average) value of the set. In other words, it tells you how much the data is scattered around the mean.
The test statistic to test the claim that the standard deviation of all customer waiting times is greater than 3.5 minutes can be calculated using the following formula:
Z = (s / σ) x √n
where s is the sample standard deviation (4.8 minutes), σ is the population standard deviation (3.5 minutes), and n is the sample size (15).
Z = (4.8 / 3.5) x √15
= 7.444
So the test statistic is 7.444.
To know more about Standard deviation check:
https://brainly.com/question/23907081
#SPJ1
A painter can paint 3 small rooms in the same time it takes him to finish 1 large room and 1 small room. It takes him 7 hours to finish a large room. Find the number of hours it takes the painter to finish a small room.
Answer:
It's 3.5 hours. Or 3 hours and 30 minutes.
Step-by-step explanation:
If the painting of 3 small rooms takes as much time as the painting of 1 large and 1 small rooms then it takes the same amout of time to paint 1 large room and 2 small rooms.
7 hours = 1 large room
1 large room = 2 small rooms
1 small room is half the time of a large room
1/2 of 7 = 3.5
3.5 hours is 3 hours 30 minutes.
please help me with my questions
Answer:
m= -3/2
Step-by-step explanation:
To find slope
[tex]m \: = \frac{y2 - y1}{x2 - x1} [/tex]
We have our x1 and y1 of (2,5)
We have our x2 and y2 of (8,-4)
Now we plug in
= (-4-5)/(8-2)
= (-9)/(6)
Simplifying it would be
[tex]m = - \frac{3}{2} [/tex]
Answer: slope 'm' = -3 / 2
Step-by-step explanation: Using the formula m=(y2-y1)/(x2-x1), where 'm' is the slope of the line connecting the two points, we can plug in our x and y values:
x1 = 2
x2 = 8
y1 = 5
y2 = -4
Once we plug in our x and y values, we get the equation
m = (-4 - 5) / (8 - 2)
--> -9 / 6 (We can simplify this fraction to get or answer of -3 / 2)
the surface area of an egg shell scales as the mass of the egg shell raised to what power?
The surface area of an egg shell scales as the mass of the egg shell raised to 1.82694
The term surface area in math is defined as the area occupied by a three-dimensional object by its outer surface
Here we know that the area of a cube with edged is proportional to the second power d² while its volume is proportional to the third power d³.
Here we know that for any bounded solid object, here we have which encloses a region with some volume V and its enclosing surface has area A, where as the same kind of proportions can be derived in terms of a linear dimension d of the object, here for example the diameter of the object.
AS we all know that the surface area is directly proportional to the 3rd power of the mass of the egg, here we have A = km³ where A is the surface area, k a constant of proportionality, and m the mass.
For a chicken egg we have 28 = k(60)⁰°⁶⁷
Here by solving for k we get:
=> k = 28/60⁰°⁶⁷ ≈ 1.82694
To know more about surface area here.
https://brainly.com/question/29298005
#SPJ4
y = (x - 2)^2 - 7
Solve for x
find the distance between the planes 5x−4y−z=65x−4y−z=6 and 4y−5x z=−484y−5x z=−48.
The distance between the two planes 5x−4y−z=65x−4y−z=6 and 4y−5x z=−484y−5x z=−48 is sqrt(7/10).
What is vector ?
A vector is a mathematical object that has both magnitude (or length) and direction. Vectors can be used to represent physical quantities such as velocity, force, or displacement, where the magnitude represents the size of the quantity and the direction represents its orientation in space.
Let n1 and n2 be the normal vectors of the two planes, respectively.
The normal vectors are:
n1 = <5, -4, -1> and n2 = <5, -4, 1>.
The projection of n1 onto n2 is:
projn1 onto n2 = (n1 . n2 / ||n2||^2) * n2 = (n1 . n2 / ||n2||^2) * (n2 / ||n2||) = (n1 . n2 / ||n2||) * n2 / ||n2|| = (n1 . n2) * n2 / ||n2||^2.
The dot product of n1 and n2 is:
n1 . n2 = 5 * 5 + (-4) * (-4) + (-1) * 1 = 25 + 16 + 1 = 42.
The magnitude of n2 is:
||n2|| = sqrt(5^2 + (-4)^2 + 1^2) = sqrt(30).
Therefore, the projection of n1 onto n2 is:
(n1 . n2) * n2 / ||n2||^2 = 42 * <5, -4, 1> / 30 = <7/3, -4/3, 7/30>.
So , The distance between the two planes 5x−4y−z=65x−4y−z=6 and 4y−5x z=−484y−5x z=−48 is sqrt(7/10).
To learn more about vector visit : brainly.com/question/29740341
#SPJ4
Solve the system of equations by the substitution method. 1/3x-y=2 x - 3y = 6
Answer:
No solution
Step-by-step explanation:
1/3x-y=2
x - 3y = 6
Times the first equation by -3
-x + 3y = -6
x - 3y = 6
0 = 0
So, there is no solution.
HELP ASAP PLSSSS
Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
(graph and chart is attatched)
The slope of f(x) is greater than the slope of g(x).
The slope of f(x) is less than the slope of g(x).
The slope of f(x) is equal to the slope of g(x).
The slope of g(x) is undefined.
is area = ∫ β α f ( x ) d x as positive, negative or zero? note two vertical lines indicate α and β . select a for positive area, b for negative area and c for zero area.
Depending on the value of the definite integral of f(x) calculated between two limits, α and β, the area between two vertical lines can be positive, negative or zero.
The area between two vertical lines is given by the definite integral of a function f(x) calculated between two limits, α and β. In order to determine whether the area is positive, negative or zero, the values of the definite integral of f(x) calculated between two limits, α and β, must be known.
If the value of the definite integral of f(x) calculated between two limits, α and β, is greater than zero, then the area between the two vertical lines is positive. Mathematically, this can be expressed as:
Area = ∫βαf(x)dx > 0
Similarly, if the value of the definite integral of f(x) calculated between two limits, α and β, is less than zero, then the area between the two vertical lines is negative. Mathematically, this can be expressed as:
Area = ∫βαf(x)dx < 0
Lastly, if the value of the definite integral of f(x) calculated between two limits, α and β, is equal to zero, then the area between the two vertical lines is zero. Mathematically, this can be expressed as:
Area = ∫βαf(x)dx = 0
Therefore, depending on the value of the definite integral of f(x) calculated between two limits, α and β, the area between two vertical lines can be positive, negative or zero.
Learn more about definite integral here:
https://brainly.com/question/29974649
#SPJ4
throwing the ball deep to the receivers _____ the wisest thing to do when it is third and long.
When it is third and long, the best move is typically to make a long pass to a wide receiver because it has the probability to gain the greatest yardage.
Throwing the ball far downfield is frequently the best move when the team has to gain a lot of yardage to continue the drive on third and long. The most yards may be gained by a deep pass to a wide receiver since it might extend the action past the original line of scrimmage. The prospect of a huge play, in which the receiver catches the ball and runs for a bigger gain, is also made possible. A deep pass might also throw the defense off because they might not be anticipating the offense to go for a long gain. But a deep pass can also be dangerous because it might result in a turnover if the receiver doesn't pay attention.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
if v × w = 6 i − 7 j 9k, and v · w = 9, find tan where is the angle between v and w.
The tangent of the angle between vectors v and w is 2√(21) / 9
We can use the dot product and cross-product formulas to find the angle between two vectors.
The dot product of two vectors v and w is given by:
v · w = ||v|| ||w|| cos(θ)
where ||v|| and ||w|| are the magnitudes of the vectors v and w, and θ is the angle between them.
The cross product of two vectors v and w is given by:
v × w = ||v|| ||w|| sin(θ) k
where k is a unit vector in the direction of the cross product.
Since v × w = 6i - 7j + 9k and v · w = 9, we can find the angle between v and w as follows:
[tex]\theta = sin^{-1}\frac{||v \times w||}{||v|| \ ||w||} = sin^{-1}\frac{||6i - 7j + 9k||}{||v|| \ ||w||}[/tex]
We can find the magnitude of v × w by using the formula for the magnitude of a cross-product:
[tex]||v \times w|| = ||6i - 7j + 9k|| \\\\= \sqrt{6^2 + (-7)^2 + 9^2} = \sqrt{6^2 + 49 + 9^2}\\\\=\sqrt{84} = \sqrt(2^2 \times 3 \times 7) = 2\sqrt{(3 \times 7)[/tex]
We can find the magnitude of v and w using the given dot product formula:
v · w = ||v|| ||w|| cos(θ) = 9
||v|| ||w|| = 9 / cos(θ)
Since we know that ||v|| and ||w|| are positive, we can square both sides to obtain:
[tex](||v|| \ ||w||)^2 = \frac{9 }{cos(\theta))^2} \\\\||v||^2 \ ||w||^2 = \frac{81}{cos^2(\theta)}[/tex]
Finally, using the tangent formula, we can find tanθ:
tan(θ) = sin(θ) / cos(θ) = ||v × w|| / ||v·w|| = 2√(3 × 7) / 9 = 2√(21) / 9.
To learn more about the vectors, visit:
brainly.com/question/24256726
#SPJ4
Adult tickets cost $17.95 and children’s tickets cost $12.95. Disney made $7355 from ticket sales from a total of 500 people. How many adults and children bought tickets?
Answer:
To figure out how many adults and children bought tickets, we can set up a system of equations using the information provided. Let x be the number of adults and y be the number of children. We know that:
x + y = 500 (because a total of 500 people bought tickets)
17.95x + 12.95y = 7355 (because the total revenue from ticket sales is $7355)
We can use the first equation to solve for one of the variables in terms of the other variable. For example, we can substitute y = 500 - x into the second equation:
17.95x + 12.95(500 - x) = 7355
This simplifies to:
17.95x + 6475 - 12.95x = 7355
5x = 1880
x = 376
so there are 376 adults bought tickets and 500-376=124 children bought tickets.
Step-by-step explanation:
Given the function y = √√x - 5 Type in the ordered pair to show the x-intercept of
the function. Type it in using the (x,y) format. Hint: Replace y with 0
Need #15
The x-intercept of the function as an ordered pair is equal to (5, 0).
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
In this context, we would replace the y-value with zero (0) by substituting it into the given equation y = ∛x - 5 as follows;
y = ∛x - 5
0 = ∛x - 5
Taking the cube root of both sides of the function, we have the following:
0 = x - 5
x = 5
Read more on x-intercept here: brainly.com/question/18649322
#SPJ1
suppose the data on quiz scores will be grouped into five classes. the width of the classes for a frequency distribution or histogram is the closest to .
Answer is Taking data:
28 78 74 89 72
50 55 66 26 84
59 64 88 23 27
70 63 42 37 29
How to defined it?The answer is width of class =13
As the data is not given in the question I'm guessing the data from the question I solved before
28 78 74 89 72
50 55 66 26 84
59 64 88 23 27
70 63 42 37 29
as taking the above data,
maximum value=89
minimum value=23
no : of classes scores are divided into=5 classes
As we know for finding the width of class:
width of class = (maximum value-minimum value)/ no ; of classes
width = (89-23)/5=66/5
width=13.2=13
Note : By using the above given formula you can calculate the width of any data just by taking the maximum and minimum values of data and the number of classes the data is divided into.
To learn more about frequency distribution refers to;
https://brainly.com/question/14971730
#SPJ1
refer to the market for good x. p0=$15, pa=$21, p*=$31, pb=$44, p1=$57, q0=10, q*=30, q1=50, and q2=70. what is the quantity demanded when the price is $44?
At a price of $44, the quantity demanded is equal to q*, which is 30 units.
The market for good X is given with a price of $15 at q0 (10 units), a price of $21 at pa, a price of $31 at p* (30 units), a price of $44 at pb, a price of $57 at p1 (50 units), and a price of $70 at q2 (70 units). To calculate the quantity demanded when the price is $44, we first need to identify the price points on either side of $44. In this case, $31 and $57 are the two price points. We then look at the corresponding quantities at those two points, which are q* (30 units) and q1 (50 units). Since the demand curve is downward sloping, the quantity demanded at $44 (pb) will be between 30 and 50 units. Since 30 is the lower number, the quantity demanded at $44 will be q*, or 30 units.
Learn more about quantity here
https://brainly.com/question/13968875
#SPJ4
Can someone help with this problem? (Will give brainliest! )
Ann’s gym charges $20 per month plus $5 per visit. Blake’s gym charges $30 per month plus $3 per visit.
Write an equation for how much Ann's gym charges for `x` visits in one month.
y=____
Write an equation for how much Blake's gym charges for `x` visits in one month.
y=___
What is the solution to this system of equations?
( , )
Answer:
I think its this, anns gym membership: y=$5x+$20
blakes gym membership: y= $3x+$30
i don’t understand the last question, I apologize if this is wrong.
A graphed function may display different properties and characteristics over certain intervals of the graph in A and B below, describe the part of the function over the specified intervals, as “linear”or “nonlinear”and “increasing”or “decreasing”.
Help Needed,Thank you for whoever can help me out
The part of the function over the interval (-2,2) is nonlinear and decreasing.
Linear and nonlinearInterval: (-2, 2):The part of the function over the interval (-2,2) is nonlinear and decreasing.Over this interval, the graph starts at a peak of (0,2), before steadily decreasing and then sharply decreasing to a low point of (2,-2).This sharp decrease in the graph indicates that the function is nonlinear, as the rate of change is not constant.Additionally, the graph decreases over this interval, indicating that the function is decreasing. Interval: (2, 4):The part of the function over the interval (2, 4) is linear and increasing.Over this interval, the graph steadily increases; starting at the low point of (2,-2) and increasing to a peak of (4,2).This linear increase in the graph indicates that the function is linear, as the rate of change is constant.Additionally, the graph increases over this interval, indicating that the function is increasing.To learn more about Linear and nonlinear refer to:
https://brainly.com/question/2030026
#SPJ1
A "Pick 4" lottery game involves drawing
4
44 numbered balls from separate bins each containing balls labeled from
0
00 to
9
99. So there are
10
,
000
10,00010, comma, 000 possible selections in total:
0000
00000000,
0001
00010001,
0002
00020002,
…
…dots,
9998
99989998,
9999
99999999.
Players can choose to play a "straight" bet, where the player wins if they choose all
4ndigits in the correct order. Since there are
10,000possible selections, the probability a player wins a straight bet is
1/10,000. The lottery pays $9,000
on a successful $2 straight bet, so a player's net gain if they win this bet is $8,998
The expected Net gain is -0.1001.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total possible selection = 10000
Net Gain Probability
Win 8998 1/ 10000
Lose 2 9999/10000
So, E(x) = 8998 x 1/10000 - 9999/10000
= -1001 / 10000
so, the expected Net gain = -0.1001
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ1
Six times a number subtracted from 0 gives -8. Find the number
Answer:
6(x-0)=-8
6x=-8
6x/6=-8/6
x=-1 1/3Hope this helps!!
Step-by-step explanation:
Answer: [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Let the number be x
6 times x = 6x
subtracted from 0
gives -8
∴ 0 - 6x = -8
0 + 8 = 6x
[tex]\frac{8}{6}[/tex] = x
[tex]\frac{4}{3}[/tex] = x
helppppppppppp00000000
Answer:
21[tex]e^{6}[/tex] and 30[tex]t^{6}[/tex][tex]v^{10}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
given
3e³ × 7e³
= 3 × 7 × e³ × e³
= 21 × [tex]e^{(3+3)}[/tex]
= 21[tex]e^{6}[/tex]
-------------------------------
(10[tex]t^{4}[/tex][tex]v^{5}[/tex] )(3t²[tex]v^{5}[/tex] )
= 10 × 3 × [tex]t^{4}[/tex] × t² × [tex]v^{5}[/tex] × [tex]v^{5}[/tex]
= 30 × [tex]t^{(4+2)}[/tex] × [tex]v^{(5+5)}[/tex]
= 30[tex]t^{6}[/tex][tex]v^{10}[/tex]
How many square feet means 1 acre?
The value of square feet means 1 acre be 43,560 square feet.
What is the difference between square feet and acre?The US measurement system uses the acre as the unit of land area measurement. Every real estate transaction and listing worldwide has a connection to Square Feet.
The length and width of the land—which are often stated in feet—are multiplied to determine the acreage before converting the result to square feet. Following that, the square footage is converted to acres using a conversion ratio of 43560.
For standing or stored water, an acre-foot is the accepted unit of measurement. It is the volume of water necessary to cover an acre of ground that is 43,560 square feet in size and one foot deep. 325,851 gallons make up an acre-foot.
To learn more about square feet and acre refer to:
https://brainly.com/question/30029726
#SPJ4
help me - this was due on jan 27 i'm running out of time. - photo
Step-by-step explanation:
the slope is always the ratio of
y coordinate difference / x circumstances difference
when going from one point on the line to another.
1.
x changes by +3 (from 2 to 5).
y changes by -6 (from -1 to -7).
the slope is -6/+3 = -2.
m = -2, b = 3 is the correct answer
2.
x changes by +2 (from -4 to -2).
y changes by +3 (from -2 to 1).
the slope is +3/+2 = 3/2.
m = 3/2, b = 4 is the correct answer.
FYI
because there is in both cases only one answer option with the correct slope, we did not need to check the y-intercept ...
what is the formula in terms of i and n for the gernal left endpoint x i-1
the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ] is the formula in terms of i and n for the gernal left endpoint x i-1
What is the formula for left endpoint approximation?
Rule: Left-Endpoint Approximation
On each subinterval [xi−1,xi] (for i=1,2,3,…,n), construct a rectangle with width Δx and height equal to f(xi−1), which is the function value at the left endpoint of the subinterval. Then the area of this rectangle is f(xi−1)Δx
In this problem you will calculate ∫302+4 by using the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ].
(a) The interval [0,3] is divided into equal subintervals of length Δ. What is Δ (in terms of )? Δ
(b) The right-hand endpoint of the th subinterval is denoted ∗. What is ∗ (in terms of and )
learn more about of endpoint here
https://brainly.com/question/14524230
#SPJ4
does anyone know the answer to
– 2p ≤ – 8
Answer:
The answer to the inequality is [tex]p\geq 4[/tex].
Step-by-step explanation:
Lets solve the inequality.
[tex]-2p\leq -8[/tex]
Divide both sides of the equation by -2.
There is an inequality rule that says when multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
First lets divide both sides by -2.
[tex]\frac{-2p}{2} \leq \frac{-8}{2}[/tex]
Simplify the left side by cancelling the common factor of −2.
[tex]p\leq \frac{-8}{2}[/tex]
Simplify the right side by dividing -8 by 2.
[tex]p\leq 4[/tex]
We need to flip the direction of the inequality sign.
[tex]p\geq 4[/tex]
simplify 15/32 + 9/32
Answer: 3/4
Step-by-step explanation:
15/32 + 9/32 = 24/32 = 12/16 = 6/8 = 3/4
Juanita wants to buy a car. The car costs $15,000 and requires a 10% down payment. The dealership offers 5-year financing at 4% APR compounded monthly.
What's the monthly loan payment for this offer? Please enter your answer then show the steps.
A. 248.62
B. 276.25
C. $450.00
D. 523.15
The monthly loan payment for the offer made by Juanita, given the cost of the car and the dealership, is A. 248.62
How to find the monthly loan payment ?First, find the amount taken on loan :
= 15, 000 x ( 1 - 10 % down payment )
= $ 13, 500
The periodic rate is:
= 4 % / 12
= 1 / 3 %
The number of periods :
= 5 years x 12 months a year
= 60 months
The monthly payment is:
Present value of loan = Monthly Payment x Present value interest factor of annuity, 1 / 3 %, 60 months
13, 500 = 54.299068906557 x Monthly payment
Monthly payment = 13, 500 / 54.299068906557
= 248. 62
Find out more on monthly payment at https://brainly.com/question/28106777
#SPJ1
Linear Equations Digital Escape!
number 4 and 5
The system of equation (4) and (5) have no solution
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
7(5x + 2) = 5x + 2
Divide both sides by 5x + 2
7 = 1
This equation is false, meaning there is no solution for y that satisfies both equations.
How to determine the solution to the systemHere, we have
2y = 6
y = -15
Since these are two different equations with the same variable, y, we can use substitution to find a solution.
Starting with the second equation, y = -15, we can substitute this value into the first equation:
2y = 6
2(-15) = 6
-30 = 6
This equation is false, meaning there is no solution for y that satisfies both equations.
Read more about system of equations at
brainly.com/question/13729904
#SPJ1
Complete question
4. How many solutions will this equation have? 7(5x + 2) = 5x + 2
5. Solve the given system of equations 2y = 6 and y = -15
