Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
3w + 6r ≥ 36
3w + 6r ≤ 90
A graph shows w on the x-axis, from 0 to 30, and t on the y-axis, from 0 to 24. Two solid lines are shown. The first line has a negative slope and goes through (0, 6) and (12, 0). Everything above and to the right of the line is shaded. The second line has a negative slope and goes through (0, 15) and (30, 0). Everything to the left of the line is shaded.
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
The combination of hours that Keitaro can walk and run in a month to reach his goal will be A. 2 hours walking; 12 hours running
How to illustrate the information?From the information, Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles.
The equation is
3w + 6r ≥ 36
3w + 6r ≤ 90
The combination of hours that Keitaro can walk and run in a month to reach his goal will be 2 hours walking, and 12 hours running.
This will be:
3w + 6r ≤ 90
3(2) + 6(12)
6 + 72 = 78
Therefore, 78 is less than 90.
The correct option is A.
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f(x) = 3x + 4 and g(x) = 2x - 3, find (f - g)(x)
2
Step-by-step explanation:
for the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets. { 5, 7, 17, 15 }
Subsets of the specified set equal 16.
The set's appropriate subset is equal to 15.
What is set known as?A set is the collection of specific, distinct items from our perception (Anschauung) and from our thought, which are referred to as the set's elements. A set's elements or members can be anything, including numbers, people, alphabet letters, other sets, and so on. Sets are typically indicated.
According to the given data:given data:- { 5, 7, 17, 15 }
this set have 4 elements:
We are aware that the number of subsets of a set with n elements is represented by 2^n
where n denotes the set's element count.
as a result, the given set's subsets = 2^4
= 16
Because the original set itself is subset of itself, it is not a legitimate subset.
Consequently, a proper subset of a set:- 2^n - 1
= 2^4 - 1
= 16 -1
= 15
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what value of c is in the solution set of
2(3x-1)>4x-6
Answer:
x> -2
Step-by-step explanation:
The average income,I, in dollars, of a lawyer with an age of x years is modeled with the following function:
Solving a quadratic equation, the youngest age for which the average income of the lawyer is of $250,000 is of 26 years.
What is a quadratic function?A quadratic function is given according to the following rule:
y = ax² + bx + c
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation that models the income as function of age is given by:
I(x) = -425x² + 45500x - 650000.
The income is of 250,000 when I(x) = 250000, hence:
250000 = -425x² + 45500x - 650000.
425x² - 45500x + 900000 = 0.
Hence the coefficients are a = 425, b = -45500 and c = 900000, then:
[tex]\Delta = (-45500)^2 - 4(425)(900000) = 540250000[/tex][tex]x_1 = \frac{45500 + \sqrt{540250000}}{2(425)} = 80.87[/tex][tex]x_2 = \frac{45500 - \sqrt{540250000}}{2(425)} = 26.18[/tex]The youngest age for which the average income of the lawyer is of $250,000 is of 26 years. (the oldest is of 81 years).
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Important Please Help!!!!
Answer:
C.Step-by-step explanation:
The statement is flipped, and saying different sayings.
Answer:
If n + 4 is odd, then n is odd.
Step-by-step explanation:
Contrapositive statements negate the original statement and interchanges(flips) it.
So the negated statement would be ' If n is odd, then n + 4 is odd'.
Then we interchange that statement so ' If n is odd, then n + 4 is odd' becomes, ' if n + 4 is odd, then n is odd.'
a. In Euclidean geometry, a line continues in opposite directions forever. As a result, the line will have an infinite length. How does this differ from a line in spherical geometry?
Euclidean geometry differs from spherical geometry because Euclidean geometry is used to set points by the use of plane.
What is Euclidean geometry?Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different axioms and theorems.
Now since Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2-dimensional surface and other terms like "ball" or "solid sphere" are used for the surface together with its 3-dimensional interior.
Euclidean geometry differs from spherical geometry because Euclidean Geometry are known to make use of a plane to be able to set points and lines, but Spherical Geometry are known to make use of spheres to set up points and great circles.
Thus, Euclidean geometry differs from spherical geometry because Euclidean geometry is used to set points by the use of plane.
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Which answer shows the equation
written in standard form? y+4=2(x-1)
y=2x-6
-2x+y=-5
-2x+y-6
y=2x-5
Answer:
-2x + y = -6
Find the measures of the angle, its complement, and its suplement if three times the measure of a suplement of an angle is eight times the measure of a complement of the angle.
The angle, its complement, and its supplement are 36, 54 and 144 degrees respectively
Supplementary and complementary anglesThe sum of complementary angles s 90 degrees while that of supplementary angles is 180 degrees.
Let the complement of an angle be 90 -x and its supplement be 180 -x
If three times the measure of a supplement of an angle is eight times the measure of a complement of the angle, then;
3(180-x) = 8(90-x)
Expand
540-3x = 730 - 8x
540-720 = -8x + 3x
180 = 5x
x = 180/5
x = 36 degrees
Complement = 90 - 36 = 54degrees
Supplement = 180 - 36 = 144 degrees
Hence the angle, its complement, and its supplement are 36, 54 and 144 degrees respectively
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Determine whether each relationship is linear or exponential. Then write an equation to represent the relationship.
5. The relationship is Linear and the equation is 500 × 1.1 + 500 = 1050.
6. The relation ship is Linear and the equation is 6 × 2/3 = 4
Given,
5. The population of a town = 500
The growth of population expected by the city planner = 1.1
That is, 500 × 1.1 + 500 = 1050
This is a Linear equation.
6. The distance from where the basketball fall down = 6 feet
Basket ball bounce back its previous height = 2/3
That is, 6 × 2/3 = 4
This is a Linear equation.
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help me with 1 and 2 pls
1. The meters of fencing that he installed on each day will be 6.54 meters.
2. The amount of money that Jenny will make will be $127.05.
How to illustrate the information?1. Number to be installed = 42.6m
It should be noted that the person already installed on Monday and Tuesday. Therefore, the amount to install from Wednesday to Friday will be illustrated as:
= (42.6) - (13.45 + 9.5) / 3
= 42.6 - 22.95 / 3
= 6.54 meters per day.
2. The amount of money that Jenny will make will be:
= (9.15 × 9) + (7.45 × 6)
= 82.35 + 44.7
= $127.05
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(Dividing Rational Numbers MC)
(Dividing Rational Numbers MC)
Solve 0.504 ÷ 8.
−7.496
0.063
0.630
4.032
Solve 0.504 ÷ 8.
−7.496
0.063
0.630
4.032
The correct answer for 0.504 ÷ 8 is option B which is 0.063
How to solve 0.504 ÷ 80.504 / 8 is solved by removing the decimals first and then the division as required.
0.504 / 8
= 504/1000 / 8
= 504 / 8000
= ( 504 / 8 ) * ( 1 / 1000 )
= 63 * ( 1 / 1000 )
= 0.063
What are rational numbers?These are class of numbers that can be represented as fractions inform of two integers. Such numbers while in fractions, the denominator should not be zero and while decimal do not need to approximations to terminate them.
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15 women can complete a piece of work in 16 days. How many women
should leave so that the work would be finished in 20 days?
Exact and Approximate Pi
Answer: c = 12
Step-by-step explanation: r is 2 since in the circle it shows the length from the center to the arc. now multiply 2(3)(2) and you will end up with 12.
Answer:
Circumference = 12
Step-by-step explanation:
C=2πr
where,
π = 3r = 2➟ C = 2πr
Insert values
➟ C = (2)(3)(2)
➟ C = (6)(2)
➟ C = 12
note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. a girl operates a radio-controlled model car in a vacant parking lot. the girl’s position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. she drives the car in a straight line so that the x coordinate is defined by the relation x(t)
At time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.
What are coordinates?Coordinates are two numbers (Cartesian coordinates) or a letter and a number that point to a specific point on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: x (horizontal) and y (vertical).To find the position:
The derivative of x with respect to t is zero when the velocity is zero. That is to say,
x' = 1.5t² - 6t + 3 = 0 or t² - 4t + 2 = 0Use the quadratic formula to solve.
t = (1/2) [ 4 +/- √(16 - 8)] = 3.4142 or 0.5858 sWhen t =0.5858 s, the position is:
x = 0.5(0.5858³) - 3(0.5858²) + 3(0.5858) + 2 = 2.828 mWhen t=3.4142 s, the position is:
x = 0.5(3.4142³) - 3(3.4142²) + 3(3.4142) + 2 = -2.828 mReject the negative answer.
So, when t = 0.586 s, the velocity is zero and the distance is 2.83 m.
The second derivative of x with respect to t is zero when the acceleration is zero.
That is to say,
3t - 6 = 0t = 2The distance traveled is:
x = 0.5(2³) - 3(2²) + 3(2) + 2 = 0So, when the acceleration is zero, t = 2 s, and the distance traveled is zero.
Therefore, at time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.
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The correct question is given below:
A girl operates a radio-controlled model car in a vacant parking lot. the girl’s position is at the origin of the XY coordinate axes, and the surface of the parking lot lies in the XY plane. she drives the car in a straight line so that the x coordinate is defined by the relation x(t) = 0.5t3 - 3t2 + 3t + 2 where x and t are expressed in meters and seconds, respectively. determine when the velocity is 0 m/s, and the position and the total distance traveled when the acceleration is zero.
what Is the value of 343 ⅓ ?
Answer:
7. I attached my answer ... have a nice day
Find 3/4ab divided by 6/abc. Write the quotient in simplest form.
Answer:
[tex] \sf \large \frac {1}{8}b²c[/tex]
Step-by-step explanation:
3/4ab/6/abc
= 1/8ab²c/a
= 1/8b²c
john beale of stanford, ca, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. the mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (he actually recorded every car for a two-month period. these are 100 representative readings.) to see how many cars are speeding, john subtracts 20 mph from all speeds. a) what is the mean speed now? what is the new standard deviation? b) his friend in berlin wants to study the speeds, so john converts all the original miles-per-hour readings to kilometers per hour by multiplying all speeds by 1.609 (km per mile). what is the mean now? what is the new standard deviation?
10 mph more unusual.
What is Standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a larger range, a low standard deviation suggests that the values tend to be near to the mean (also known as the anticipated value) of the collection.
The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical literature and equations to indicate standard deviation. Standard deviation may be written as SD.
EXPLANATION : The speed recordings follow an approximately normal distribution the mean of
100 readings was 2384 mph. with a standard deviation of 3.56mph
The speed limit read 20 mph
We have to find the number of standard deviations from the mean that the car going
under the speed hmit would be
Let the car going under the speed 20mph bey standard deviations away from mean
That is.
20 — 23.84 +y(3.56)
20—2384 —1.078651685
So the car going under the speed limit would be less than or equal to 107865 standard
A car traveling 34 mph
The number of standard deviations from the mean that the car is going at 34mph is given by
That is the car going at 34mph is 2.8539 standard deviations above the mean
A car traveling at 10mph
The number of standard deviations from the mean that the car going at 10mph is given by.
y= 2.8539
That is. the car going at 10mph is 3.8876 standard deviations
We know from the empirical nile that 99.7% of the observations he with in ±3 standard
deviations from the mean for a normally distributed data
But the speed of 10mph is not within these limits, where as 34 mph is within these limits
So the car is travelling t 10mph is more unusual
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Delila is multiplying three negative numbers and determines that the solution will be negative . Is she correct or incorrect? Justify your thinking.
Answer: Delila is correct about this determination.
Step-by-step explanation: The rule for multiplying two negatives is that a negative and a negative always equal a positive. Therefore, multiplying two negatives will give a positive. However, we still have to multiply that positive by another negative to get our answer. Another multiplication rule states a negative and a positive always equals a negative. Let's set up an example with the numbers -7, -8, and -4:
Using the first multiplication rule mentioned above, let's multiply:
-8 x -7 = 56
Using the second multiplication rule mentioned above, we can finish the equation and get our answer:
56 x (-4) = -224
-7 x -8 x -4 = -224.
Final answer: Delila is correct. Multiplying three negatives will result in a negative solution.
pls help can you help ne choose all of the aswer that are right this is my last attempt
By taking a quotient between the total area and the number of children, we conclude that each one will get 9 ⁴/₅ acres.
How much should each of the children get?
Here we know that a farmer has a total of 49 acres, and he wants to divide it evenly among his 5 children.
So we just need to take the quotient between 49 and 5, this is:
49/5
First, we can rewrite:
49 = 45 + 4
Replacing that in the quotient we get:
49/5 = (45 + 4)/5 = 45/5 + 4/5
The first term is equal to 9, then we can rewrite:
49/5 = (45 + 4)/5 = 45/5 + 4/5 = 9 + 4/5
From this quotient, we conclude that each one of the 5 children gets an area of 9 + 4/5 acres. Written as a mixed number this would be:
A = 9 ⁴/₅ acres.
So the correct option is the first one.
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There are boys and girls in a class in the ratio 19:6 There are 104 more boys than girls. How many boys are there?
There are 152 boys who are present in the class with ratio 19:6.
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given:
ratio = 19:6
let the common ratio be x
number of boys = 19 x
number of girls = 6x
Also,
number of boys = number of girls + 104
19x = 6x +104
13 x = 104
x= 8
Hence, the number of boys are 19x= 19*8 = 152 boys.
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2 { 5 5/8 } + 3 { 9 13/16 } ?
Help Please
The equivalent expression for the expression consisting of mixed fraction 2 { 5 5/8 } + 3 { 9 13/16 } is 651/16.
According to the given question.
We have an expression consisting of mixed fractions.
2 { 5 5/8 } + 3 { 9 13/16 }
Since, we convert the mixed fraction into improper fraction by
Step 1: Multiply the denominator with the whole number.
Step 2: Add the numerator to the product obtained from step 1.
Step 3: Write the mixed fraction with the sum obtained from step 2 as the numerator and the denominator of the original fractional part of the mixed fraction.
Therefore, the equivalent expression for the expression 2 { 5 5/8 } + 3 { 9 13/16 } is given by
2{45/8} +3{157/16}
= 90/8 + 471/16
= [180 + 471]/16
= 651/16
Hence, the equivalent expression for the expression consisting of mixed fraction 2 { 5 5/8 } + 3 { 9 13/16 } is 651/16.
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simplify -(6x + 22) - 8(3 - x)
just need help on 17-18! homework is due tonight! ill give brainliest!
Answer: 17. The fower will last 85 days
18. She ran at a constant pace of around 12.94mph (if her time was 14 minutes and 24.6 (14.14m) ) or 12.7mph (if her time was 14 minutes 41 seconds) (the .41 confused me so I did both possible solutions)
Hope this helped c:
A group of friends wants to go to the amusement park. They have $235.75 to spend on parking and admission. Parking is $6.25, and tickets cost $25.50 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
Answer:
The equation for the number of people is 25.50x + 6.25 = 235.75 and the number of people who can go to the amusement park are 9.
Step-by-step explanation:
We have,
Spend on parking and admission = $235.75
Spend on parking = $6.25
Cost of ticket per person = $25.50
Let number of number of people = x
Now,
According to the question;
25.50x + 6.25 = 235.75
So, this the equation for number of number of people.
Now,
25.50x + 6.25 = 235.75
25.50x = 229.50
x = 9
So, number of number of people is 9, which we find out using the above mentioned equation.
Hence, we can say that the equation for the number of people is 25.50x + 6.25 = 235.75 and the number of people who can go to the amusement park are 9.
The number of people who can go to the amusement park is 9 they have $235.75 to spend on parking and admission. Parking is $6.25.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A group of friends wants to go to the amusement park. They have $235.75 to spend on parking and admission.
Parking is $6.25, and tickets cost $25.50 per person, including tax.
Let x be the number of people
6.25 + 25.50x = 235.75
25.50x = 235.75 - 6.25
25.50x = 229.5
x = 9
Thus, the number of people who can go to the amusement park is 9 they have $235.75 to spend on parking and admission. Parking is $6.25.
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Simplify the following
Need the answer asap
answer:
1.
[tex]9y - 1[/tex]
2.
[tex] { \times }^{3} - { \times }^{2} + \times [/tex]
3.
[tex] - 3 {a}^{2} + a + 2[/tex]
4.
[tex] - { \times }^{2} [/tex]
5.
[tex] - 4 { \times }^{5} + 16 { \times }^{3} - 20 { \times }^{2} [/tex]
6.
[tex]8 { \times }^{3} + 6 { \times }^{2} - 32x + 15[/tex]
7.
[tex] { \times }^{2} - \times - 20[/tex]
8.
[tex]24 { \times }^{2} - 6 \times + 1[/tex]
9.
[tex] { \times }^{2} - 6 \times + 5[/tex]
10.
[tex]10 { \times }^{5} + 3 { \times }^{3} - 2 \times [/tex]
what is 22.652 rounded to the nearest tenth?
Answer:
22.7
This is becuase 6 is closer too 7. Thus we would round too 7.
17 Select the correct answer.
What are the solutions of this quadratic equation?
4x² + 3 = 4x + 2
OA. x = 1/ 2
OB. x = -2 ± √3
OC. x = 2
OD. x = 1+√3
Christy buys 3 1/4 pounds of pork roast and 5 1/2 pounds of beef roast. She pays a total of $67.50. The pork costs $0.50 per pound less than the beef. What is the combined cost of one pound of pork and one pound of beef?
The combined cost of one pound of pork and one pound of beef is $ 15.5.
How to estimate the combine cost of two articles bought in a butchery
The total cost is equal to the sum of the products of unit price and quantity of an article. In this problem we find the sum of the quantities of two products (pork roast, beef roast), whose expression can be described below:
67.50 = (3.25) · (x - 0.50) + (5.5) · x
Where x is the unit cost of the beef roast.
Now we proceed to solve the equation for x:
67.50 = 3.25 · x - 1.625 + 5.5 · x
69.125 = 8.75 · x
x = 7.9
A pound of beef roast costs $ 7.9 and a pound of pork roast costs $ 7.4. Then, the combined cost of one pound of prok and one pound of beef is:
C = 1 · 7.9 + 1 · 7.4
C = 15.5
The combined cost of one pound of pork and one pound of beef is $ 15.5.
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8(5-6v)=-7-v
help please :))
Answer:
V = 1 (Please mark the answer as brainliest)
Step-by-step explanation:
8(5 - 6v) = -7 - v
40 - 48v = -7 - v
40 = -7 + 47v
47 = 47v
1 = v
Answer:
v = 1
Step-by-step explanation:
Let's solve the problem,
→ 8(5 - 6v) = -7 - v
→ 40 - 48v = -7 - v
→ 40 + 7 = -v + 48v
→ 47v = 47
→ v = 47/47
→ [ v = 1 ]
Hence, the value of v is 1.