Jim walks 3 miles per hour slower than his friend Steve runs. Steve runs 4 miles per hour slower than his friend Matt rides his bike. Jim walks 25 miles in the same time Matt rides his bike miles. Steve runs 16 miles in the same time Matt rides his bike 24 miles.
Part A: Write an equation to calculate Jim's speed
Answers
Let's start by assigning variables to the unknowns in the problem:
- Let j be Jim's speed in miles per hour (in other words, the rate at which he walks).
- Let s be Steve's speed in miles per hour (in other words, the rate at which he runs).
- Let m be Matt's speed on his bike in miles per hour.
From the first sentence of the problem, we know that:
s = m + 4 (Steve runs 4 miles per hour slower than Matt rides his bike)
And from the second sentence, we know that:
j = s - 3 (Jim walks 3 miles per hour slower than Steve runs)
We want to find out how long it takes Jim to walk 25 miles and how long it takes Matt to ride his bike x miles. We can use the formula:
time = distance / rate
For Jim, we have:
time = 25 / j
For Matt, we have:
time = x / m
We also know that Steve runs 16 miles in the same time that Matt rides his bike 24 miles, so we can write:
16 / s = 24 / m
Substituting s = m + 4 and solving for m, we get:
16 / (m + 4) = 24 / m
16m = 24(m + 4)
16m = 24m + 96
8m = 96
m = 12
So Matt rides his bike at a speed of 12 miles per hour.
Now we can use the equations we set up earlier to solve for j and x:
j = s - 3
s = m + 4
j = (m + 4) - 3
j = m + 1
j = 13
x / m = 25 / j
x / 12 = 25 / 13
x = (25 * 12) / 13
x = 300 / 13
x ≈ 23.08
So it takes Jim 25 / 13 ≈ 1.92 hours to walk 25 miles, and it takes Matt 23.08 hours to ride his bike x = 300 / 13 ≈ 23.08 miles.
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Related Questions
consider the symmetric matrix . the characteristic equation for the matrix is state the eigenvalues of the symmetric matrix and their multiplicity and basis for the eigenspace. give the smallest eigenvalue 2 give the multiplicity: 2 give the basis for the eigenspace: (1,1,1) give the largest eigenvalue: 8 give the multiplicity: 1 give the basis for the eigenspace: (-1,1,0), (-1,1,0)
Answers
The symmetric matrix are 2 and 8, with multiplicities of 2 and 1 respectively.
What is the characteristic equation of the given symmetric matrix?The given symmetric matrix has eigenvalues of 2 and 8. The eigenvalue 2 has a multiplicity of 2, meaning there are two linearly independent eigenvectors associated with it.
The basis for the eigenspace of 2 is given by the vector (1, 1, 1). On the other hand, the eigenvalue 8 has a multiplicity of 1, indicating only one eigenvector is associated with it.
The basis for the eigenspace of 8 is given by the vectors (-1, 1, 0) and (-1, 1, 0). In summary, the eigenvalues of the symmetric matrix are 2 and 8, with multiplicities of 2 and 1 respectively.
The eigenspace bases are (1, 1, 1) for eigenvalue 2 and (-1, 1, 0) and (-1, 1, 0) for eigenvalue 8.
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Find the measure of an angle that is complementary to one find a Measure that is complementary to to name a pair of adjacent complementary angles
Answers
Answer:
1) 25deg. Angle EGF
2) 25deg. Angle BGC
3) Angle 2 and BGC or Angle 1 and EGF
If m ∠ F D E = ( 3 x − 15 ) ° and m ∠ F D B = ( 5 x + 59 ) ° , find the value of x such that ∠ F D E and ∠ F D B are supplementary.
Answers
Answer:
x = 17====================
Supplementary angles sum to 180°.
Givenm∠FDE = (3x - 15)° and m∠FDB = (5x + 59)°,∠FDE and ∠FDB are supplementarySet equation and solve for x3x - 15 + 5x + 59 = 1808x + 44 = 1808x = 180 - 448x = 136x = 136/8x = 17joe schmo buys a house for 800,000 dollars. if homes appreciate 7 percent per year, how much will it be in 8 years
Answers
The final value would be 1,534,947.20
Joe Schmo:
Joe Shmoe (also spelled Joe Schmoe and Joe Schmo), meaning "Joe Anybody", or no one in particular, is a commonly used fictional name in American English. Adding an "Shm" to the beginning of a word is meant to diminish, negate, or dismiss an argument (for instance, "Rain, shmain, we've got a game to play"). It can also indicate that the speaker is being ironic or sarcastic. This process was adapted in English from the use of the "schm" prefix in Yiddish to dismiss something; as in, "Fancy, schmancy" (thus denying the claim that something is fancy). While "schmo" ("schmoo", "schmoe") is thought by some linguists to be a clipping of Yiddish.
If the home appreciates 7% per year, it will be worth approximately 1,534,947 dollars in 8 years. This can be calculated by multiplying the initial value of the home (800,000) by (1 + 0.07)^8.
You can also use the following formula:
Final Value = Initial Value x (1 + rate)^Years
The final value would be 1,534,947.20
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14. Suppose a math class contains 35 students, 17 females (five of whom speak French) and 18 males (three of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is male.
Answers
The formula to calculate the conditional probability of A given B is given to be:
\(P(A|B)=\frac{P(A\cap B)}{P(B)}\)If French is represented by F, and males by M, the formula to calculate the probability of a student speaking French given they are male is given to be:
\(P(F|M)=\frac{P(F\cap M)}{P(M)}\)The probability formula is given to be:
\(P(A)=\frac{n(A)}{n(T)}\)Therefore, we have:
\(\begin{gathered} P(F\cap M)=\frac{n(F\cap M)}{n(Students)} \\ n(F\cap M)=students\text{ that speak french and are male}=3 \\ n(Students)=35 \\ \therefore \\ P(F\cap M)=\frac{3}{35} \end{gathered}\)and
\(P(M)=\frac{18}{35}\)Therefore, the conditional probability is:
\(\begin{gathered} P(F|M)=\frac{\frac{3}{35}}{\frac{18}{35}}=\frac{3}{35}\times\frac{35}{18} \\ P(F|M)=\frac{3}{18}=\frac{1}{6}=0.167 \end{gathered}\)The probability is 0.167 or 1/6
4. Identify any lines of symmetry the figure has.
Answers
The lines of symmetry in this particular picture are the horizontal and vertical lines.
If you were to look at the first quarter, and the vertical line reflects the curves to the second quarter.
Then, if you were to look at the horizontal line, you would see that the line reflects the entire top half to the bottom.
Hope this helps and please consider marking branliest.
13-0.75w+8x when w=12 and x= 1/2
Answers
Answer:
It is 8
Step-by-step explanation:
you would do 13-0.75(12)+8(1/2) and that would equal 8.
Answer:
8
Step-by-step explanation:
substitute w = 12 and x = \(\frac{1}{2}\) into the expression
13 - 0.75(12) + 8(\(\frac{1}{2}\) )
= 13 - 9 + 4
= 4 + 4
= 8
need help for 20 points.....plzzzzz
a^2/16-5ab+100b^2
Answers
is it factorization ...
9. Select all the angles of rotation that produce
symmetry for this flower
Answers
I would say 45, 90, 180
These three are the reflections of symmetry in this circel
Solve the following systems of equations using Gaussian Elimination. 2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13
Find the inner product of two vectors A = (2, -3,0) and B = = (-1,0,5)
Answers
The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).
Solving the given system of equations using Gaussian elimination:
2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13
Matrix form of the system is
[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13
Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1
Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4
Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5
Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5
Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6
The solution is (x,y,z) = (6,-5,5)
Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).
The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by
A·B = |A||B|cosθ
Given,A = (2, -3,0) and B = (-1,0,5)
Magnitude of A is |A| = √(2²+(-3)²+0²) = √13
Magnitude of B is |B| = √((-1)²+0²+5²) = √26
Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2
Cosine of the angle between A and B is
cosθ = A·B / (|A||B|)
cosθ = -2 / (√13×√26)
cosθ = -2 / √(13×26)
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I need help with this please
Answers
Answer:
Only the third one is incorrect. First 2 and last 1 are correct.
1. The equation of a circle is x² + y² - 4x +2y-11-0. What are the center and the radius of the circle?
www
Show your work.
Answer:
Answers
\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)
Actually Welcome to the concept of Circles,
so we get as,
centre as ==> ( -g, -f) ==> (2,-1)
. find two positive numbers whose product is 100 and whose sum is a minimum.
Answers
The two positive numbers are x = 10 and y = 10.
Product of two numbers = 100
Let the first numbers be = x
Let the second number be = y
Any integer higher than zero is considered a positive number. Even natural numbers are included in its concept of numbers.
Therefore, according to the question -
xy = 100
y = 100/x
Thus, as two numbers are given,
f(x, y) = x + y
f(x) = x + 100/x
Now, minimum of f(x) is obtained at the point where f’(x) = 0
Therefore,
f’(x) = 1 - 100/x² = 0
x = ±10.
x = 10
Similarly,
y = 10
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The speed limit in a particular neighborhood is 35 miles per hour. Which inequality BEST represents the speed s a person can drive in this neighborhood without breaking the speed limit?
HELP QUICK
Answers
Answer:
we have
speed <=35 miles per hour.
1. Which of the following equations exemplifies the Additive Identity Property?
A) 1+(7+8)=(1+7)+8
B) 8+1=1+8
C) 33+0=33
D) 14+3=7+10
2. Which of the following equations exemplifies the Multiplicative Identity Property?
A) 9.5x1=9.5
B) 3x10=2x15
C) 3x0=0x3
D) 9(5x6)=(9x5)6
i got A for 2. but im confused on the first
Answers
1. the equation that exemplifies the additive identity property is: C. 33 + 0 = 33.
2. The equation that exemplifies the multiplicative identity property is: A. 9.5 × 1 = 9.5.
What is the Additive Identity Property?The additive identity property states that the sum of adding zero to any number will give you the same number itself.
For example, 4 + 0 = 0.
What is the Multiplicative Identity Property?The multiplicative identity property states that a number multiplied by 1 will always give you a product that is the same number itself.
For example, 4 × 1 = 4.
1. The equation, 33 + 0 = 33, shows the additive identity property, because the sum is the same number itself after 0 is added to it.
2. The equation, 9.5 × 1 = 9.5, also shows the multiplicative identity property.
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Traveling 15 miles in 20 minutes, how many miles per hour must you be going?
Answers
Answer:
45
Step-by-step explanation:
Answer:
45
Step-by-step explanation
Juan has just completed a 15 kilometer race in 20 minutes. What was his average speed in kilometers per hour?
Solution
First, 15 kilometers is a distance, so
d = 15
Next, we are given 20 minutes and we are asked to present the speed in kilometers per hour rather than kilometers per minute. We need to convert 20 minutes to hours. Since there are 60 minutes per hour, we divide by 60 to find out how many hours it took
t = 20 minutes / 60 minutes per hour = 1/3 hours
Now we can use the d=rt equation:
15 = (r)(1/3)
If we multiply both sides
(3)(5) = (r)(1/3)(3) or r = 45
Juan's average speed was 45 kilometers per hour.
1/100 = ?/? x 1/1000
Answers
Answer:
10 or 10/1
Step-by-step explanation:
1/1000 * 10= 0.01 = 1/100
Alia is making new cushion covers for a chair. There are three sizes of cushions on the chair. What is the surface area of the seat bottom cushion?
Answers
Match each fraction on the left with the correct statement on the right. Some options on the right will be used more than once. The denominator is 11. The numerator is 11. 11/20; 11/100; 6/11; 11/15
Answers
Answer:
In 11/20, 11/100, and 11/15, the numerator is 11.
In 6/11, the denominator is 11.
a sample from a refuse deposit near the strait of magellan had 60% of the carbon-14 found in a contemporary living sample. how old was the sample?
Answers
The sample is approximately 50,000 years old, as the amount of Carbon-14 in it is lower than that of a contemporary sample.
1) Calculate the ratio of Carbon-14 in the sample compared to a contemporary sample.
Ratio = (60/100) = 0.6
2) Calculate the number of half-lives since the sample was alive.
Number of half-lives = ln(0.6) / ln(0.5) = 0.69897
3) Calculate the age of the sample.
Age of sample = (0.69897 x 5730) = 4020 years
60% of the Carbon-14 identified in a sample taken from a waste site close to the Strait of Magellan was present in the sample from the trash deposit. We must first determine the sample's carbon-14 ratio in relation to a more recent sample in order to determine the sample's age. This ratio is equivalent to the sample's 60% carbon-14 content, or 0.6, when divided by 100. The number of half-lives since the sample has been alive may then be determined by taking the natural log of the ratio and dividing it by the natural log of 0.5, which is 0.69897. By dividing the quantity of half-lives by the 5730-year half-life of carbon-14, we may finally determine the sample's age.
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PLS HELP ASAP
simplify the expression that enter your answer below x + 2 x + 5 x
Answers
Answer:
8x
Step-by-step explanation:
Combine Like Terms:
= x+2x+5x
= (x+2x+5x)
= 8x
In a class of 40 students, 15 like volleyball, 20 like basketball and 10 like both the games. illustrate it in a Venn diagram and find the number of students who don't like any of the games.
Answers
Answer:
25 students didn't like any of the games
Step-by-step explanation:
20-15=5 40-10=30
20-5=25
9. Jackie is an airline mechanic. Her company pays \( 40 \% \) of the \( \$ 3,900 \) annual cost of group health insurance. How much does she pay for it monthly? (4 points)
Answers
Jackie pays $130 monthly for her group health insurance.
To find out how much Jackie pays for her group health insurance monthly, we need to calculate 40% of the annual cost. Given that the annual cost is $3,900 and her company pays 40% of that, we can calculate the amount Jackie pays.
First, we find the company's contribution by multiplying the annual cost by 40%: $3,900 × 0.40 = $1,560. This is the amount the company pays towards Jackie's health insurance.
To determine Jackie's monthly payment, we divide her annual payment by 12 (months in a year) since she pays monthly. So, Jackie's monthly payment is $1,560 ÷ 12 = $130.
Therefore, Jackie pays $130 per month for her group health insurance. This calculation takes into account the company's contribution of 40% of the annual cost, resulting in an affordable monthly payment for Jackie.
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Brandon invested $7,900 in an account paying an interest rate of 6\tfrac{1}{8}6 8 1 % compounded daily. Jacob invested $7,900 in an account paying an interest rate of 6\tfrac{5}{8}6 8 5 % compounded monthly. After 15 years, how much more money would Jacob have in his account than Brandon, to the nearest dollar?
Answers
Using the properties of compound interest we can calculate that Jacob will have $1485 more than Brandon in his account.
Brandon invested $7,900 at the rate of 6 1/8% compounded daily.
Principal = $7900
Time = 15 years
Rate = 6 1/8% = 49/8 %
Amount earned after n years:
\(A=P (1+\frac{r}{n})^{nt}\)
Now we will use these values to find the amount at the end of 15 years.
P = 7900
r = 0.06625
n = 365
t = 15
\(A=P (1+\frac{.06125}{365})^{15\times 365}\)
or, A = 19797.104...
or, A ≈ 19797.1
Again, Jacob invested the same sum at compound interest monthly at
6 5/8% .
Amount earned after 15 years:
P = 7900
r = 6.125
n = 12
t = 15
\(A=P (1+\frac{.06625}{12})^{15\times 12}\)
or, A = 21282.383..
or, A ≈ 21282.38
Amount earned by Jacob more than Brandon
= $21282.38 - $19797.1
= $148785.283..
≈ $1485
Hence Jacob will have $1485 more than Brandon in his account.
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Consider the surface S defined by z=f(x,y)=16−x^2−y^2, such that z≥ 7. Take S to be oriented with the outward unit normal \hat{n}.
A. Sketch the surface S.
B. Find the flux of the vector field F = xi + yj + zk across S.
Answers
The surface S is defined by the equation z = 16 - x^2 - y^2, where z is greater than or equal to 7. We are asked to sketch the surface S and find the flux of the vector field F = xi + yj + zk across S, using the outward unit normal.
The equation z = 16 - x^2 - y^2 represents a downward-opening paraboloid centered at (0, 0, 16) with a vertex at z = 16. The condition z ≥ 7 restricts the surface to the region above the plane z = 7.
To find the flux of the vector field F across S, we need to evaluate the surface integral of F · dS, where dS represents the differential area vector on the surface S. The outward unit normal \hat{n} is defined as the vector pointing perpendicular to the surface and outward.
By evaluating the dot product F · \hat{n} at each point on the surface S and integrating over the surface, we can calculate the flux of F across S.
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Determine the frequency of each class in the table shown. Number of Candles in a Glass Jar Class Frequency 1003 1062 1063 1122 1123 1182 1183 1242 1243 1302 1303 1362
Answers
The frequency of a class is the number of data points that fall within the class is 1.
To determine the frequency of each class in the table shown, we must first divide the data points into the respective classes. The classes are 1003, 1062, 1063, 1122, 1123, 1182, 1183, 1242, 1243, 1302, 1303, and 1362.
For the class 1003, the frequency is 1, since there is only one data point (1003) in this class.
For the class 1062, the frequency is also 1 since there is only one data point (1062) in this class.
For the class 1063, the frequency is also 1 since there is only one data point (1063) in this class.
For the class 1122, the frequency is 1 since there is only one data point (1122) in this class.
For the class 1123, the frequency is 1 since there is only one data point (1123) in this class.
For the class 1182, the frequency is 1 since there is only one data point (1182) in this class.
For the class 1183, the frequency is 1 since there is only one data point (1183) in this class.
For the class 1242, the frequency is 1 since there is only one data point (1242) in this class.
For the class 1243, the frequency is 1 since there is only one data point (1243) in this class.
For the class 1302, the frequency is 1 since there is only one data point (1302) in this class.
For the class 1303, the frequency is 1 since there is only one data point (1303) in this class.
For the class 1362, the frequency is 1 since there is only one data point (1362) in this class.
Therefore, the frequency of each class in the table shown is 1.
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If the odds against debroah's winning first prize are 3 to 5, what is the probability that she will win 1st prize?
Answers
Answer:
See below
Step-by-step explanation:
Odds AGAINST are 3 to5 then odds FOR are 2 to 5
2/5 = .4 = 40% chance of winning
HELP ASAP 10) Determine the volume; just answer without the units
B
9.5 in.
3.75 in.
8 in.
Answers
Answer:
Volume is 285
Step-by-step explanation:
We start by calculating the area of the base
Mathematically, we have a rectangle as the base
So, the area of the base will be;
3.75 * 8 = 30
We now multiply this by the height to get the volume
we have this as:
30 * 9.5 = 285
24 pints of juice are poured into 3/4-pint bottles. how many bottles are there???
Answers
Answer:
32 bottles
Step-by-step explanation:
we divide the 24 pints of juice into the 3/4 pint bottles hence:
24÷3/4 which is
24×4/3
equals to 32
It is known that the length of time that people wait for a city bus to arrive is right skewed with mean 6 minutes and standard deviation 4 minutes. A sample of 25 wait times is randomly selected. What is the standard deviation of the sampling distribution of the sample wait times
Answers
Answer:
The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30. Otherwise, the mean and the standard deviations holds, but the distribution will not be approximately normal.
Standard deviation 4 minutes.
This means that \(\sigma = 4\)
A sample of 25 wait times is randomly selected.
This means that \(n = 25\)
What is the standard deviation of the sampling distribution of the sample wait times?
\(s = \frac{4}{\sqrt{25}} = 0.8\)
The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.