Answer:
12 and 18
Step-by-step explanation:
60 miles in 2 hours, so that means together the cyclists are traveling at 30mph,
one is traveling at 6mph more so 30mph-6mph =24
24/2=12
so the slower one is going at 12mph and the other at 18mph
An investor manages to earn the equivalent of 50/10 of his initial investment in the first year. During the second year it loses 30/10 part of it. However, for the third year the market fluctuations favor him and he returns to earn 200/10 parts of his initial investment. At the end of the year, how many parts of the initial investment have you managed to capture?
Answer: This investor has managed to earn 220/10 shares of his initial invention.
Step by step explanation:
Data for the fraction:
An investor manages to win = 50/10During the second year you lose = 30/10In the third year he wins again = 200/10In this problem we must apply the addition and subtraction of Fractions in order to obtain an answer about the parts of the initial investment that have been achieved. For this we pose the problem:
[tex]\bf \: \cfrac{50}{10} - \cfrac{30}{10} + \cfrac{200}{10} = \boxed{ \bf\frac{220}{10} }[/tex]
Rpt: This investor has managed to earn 220/10 shares of his initial invention.
If the sum of three consecutive even integers is 30, what is the first of the three even integers? (Hint: If x and x + 2
represent the first two consecutive even integers, then how would the third consecutive even integer be represented?)
The first of the three even integers is
Help
Answer:
8
Step-by-step explanation:
Let's call the first of the three consecutive even integers x.
Since the integers are consecutive and even, we know that the next integer will be x+2, and the next one will be x+4.
We can use this information to set up an equation:
x + (x+2) + (x+4) = 30
Simplifying this equation, we get:
3x + 6 = 30
Subtracting 6 from both sides:
3x = 24
Dividing by 3:
x = 8
So the first of the three consecutive even integers is 8
please anyone answer quick!!, this is a question from ixl.
Answer:
each bar costs $3.
Step-by-step explanation:
The inequality that describes the problem is:
3x > 18
This inequality states that the total cost of the soap bars, represented by 3x, is greater than Colleen's budget of $18. The variable x represents the number of bars of soap Colleen bought. So, if x represents the number of bars of soap Colleen bought, 3x represents the total cost of those bars, since each bar costs $3.
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slope =-2/5; y-intercept =0
Write the equation of the line in slope-intercept form.
Answer:
Step-by-step explanation:
Standard slope intercept equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the intercept.
substitute the values given
[tex]y=-\frac{2}{5} x+0[/tex]
simplify
[tex]y=-\frac{2}{5} x[/tex]
Make x the subject of the formula:
4y = 4x - 6z/6
Making x the subject of the formula in this equation 4y = 4x - 6z/6 gives x = (24y + 6z)/4.
How to make x the subject of the formula?In this exercise, you are required to make "x" the subject of the formula in the given mathematical expression by using the following steps.
By multiplying both sides of the mathematical expression by 6, we have the following:
4y = (4x - 6z)/6
6 × 4y = (4x - 6z)/6 × 6
24y = 4x - 6z
By adding "6z" to both sides of the mathematical expression, we have the following:
24y + 6z = 4x - 6z + 6z
24y + 6z = 4x
By dividing both sides of the mathematical expression by 4, we have the following:
x = (24y + 6z)/4
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Many students choose to take courses in statistics and computer science as elective. Suppose that in a certain university 41% take computer science, 48% take statistics, and 63% take at least one of these two courses. What is the probability a randomly selected student takes both a computer science and a statistics courses as elective? Round your answer to two decimal places.
The probability that a randomly selected student takes both computer science and statistics courses is 26%.
Let's call the event that a student takes a computer science course "C" and the event that a student takes a statistics course "S". We want to find the probability that a student takes both C and S, which can be written as P(C ∩ S).
The probability that a student takes at least one of these two courses can be written as P(C ∪ S), which is equal to 63%. This means that 63% of the students take either computer science or statistics, or both.
To find the probability that a student takes both courses, we can use the formula for the intersection of two events:
P(C ∩ S) = P(C | S) × P(S)
where P(C | S) is the probability that a student takes a computer science course given that they also take a statistics course. To find this value, we can use the formula:
P(C | S) = P(C ∩ S) ÷ P(S)
Substituting this into the first equation, we get:
P(C ∩ S) = P(C ∩ S) ÷ P(S) × P(S)
P(C ∩ S) = P(C ∩ S) × P(S)
We know that P(S) = 48% and we can use the formula for the union of two events to find P(C ∪ S):
P(C ∪ S) = P(C) + P(S) - P(C ∩ S)
Substituting in the values we know:
63% = 41% + 48% - P(C ∩ S)
P(C ∩ S) = 41% + 48% - 63% = 26%
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HELP please i have 6 m more to do in 35ish minutes
Triangle AHIJ is theree-sided polygon where the measure of angle JHI is (3x + 28) degrees.
PLS HELP DUE RIGHT NOW ASAP!!!!!!
Answer:-4,-3
Step-by-step explanation:
-4 is lower then -3 and the arrow faces the x meaning it is lower than -3.
Which equation is an equation of a circle with a radius of 4 and its center is at (3, -2)?
(x - 3)2 + (y + 2)2 = 4
(X + 3)2 + (y - 2)2 = 16
(x 3)2 + (y - 2)2 = 4
(x - 3)2 + (y + 2)2 = 16
The answer to the query is that option D) is correct. A circle with the radius if 4 and a point at (3, -2) has the following equation [tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
What does a radius look like?Your youngster will get familiar with the term "radius" as they study circles. It speaks about the separation between any point on a circle's perimeter and its center (circumference). It crosses the center, by one of the circle's sides to the other, and is half the size of diameter.
The radius of a circle is the distance between the center to any location on the edge. The diameter and radius are inversely proportional, or 2r=d2 r=d. the section of a line that connects two locations on a circle chord.
The equation of a circle is
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h, k) is the circle's center and r is its radius.
The center is at (3, -2)
[tex](x-3)^2 + (y-(-2))^2 = 4^2[/tex]
[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
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The Complete Question :
Which equation is an equation of a circle with a radius of 4 and its center is at (3, -2)?
A. [tex](x - 3)^2 + (y + 2)^2 = 4[/tex]
B. [tex](x+ 3)^2 + (y - 2)^2 = 16[/tex]
C. [tex](x-3)^2 + (y - 2)^2 = 4[/tex]
D. [tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
How can consumers use their spending power to prevent cruelty to animals?
OA. Buy fair-trade coffee
OB. Eat less meat
OC. Purchase local vegetables
OD. Reduce plastic use
SUBMIT
Answer:
OC. Eat less meat
Step-by-step explanation:
Not really sure how this is math, but meat comes from butchered animals. Buying less meat means fewer animals are killed.
What 3-digit number am I if the digit in my tens place is five more than the digit in my ones place and the digit in my tens place is twice the digit in my hundreds place?
Solve the system of equations using elimination 5x+4y=−4 and 4x+4y=4
By using elimination method, the solution of the system of equations are x = - 8, y = 9.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The system of equations are,
⇒ 5x + 4y = - 4
⇒ 4x + 4y = 4
Now, We can solve by using elimination method as;
The system of equations are,
⇒ 5x + 4y = - 4 .. (i)
⇒ 4x + 4y = 4
⇒ x + y = 1 .. (ii)
Multiply by 5 in (ii) and subtract from (i);
⇒ 5x + 4y - 5x - 5y = - 4 - 5
⇒ - y = - 9
⇒ y = 9
And, From (ii);
⇒ x + y = 1
⇒ x + 9 = 1
⇒ x = 1 - 9
⇒ x = - 8
Thus, The solution of the system of equations are x = - 8, y = 9.
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Which graph represents y= ^3 square root x + 2?
Answer:
cubic
Step-by-step explanation:
Determine whether the statement below is true or false. Justify the answer The points in the plane corresponding to [-2 5] and [-5 2] lie on a line through the origin. Choose the correct answer below. A. The statement is false [-2 5] and [-5 2] correspond to arrows that meet at right angles. B. The statement is false. If [-2 5] and [-5 2] were on the line through the origin, then [-5 2] would be a multiple of [-2 5] which is not the case. C. The statement is true [-2 5] and [-5 2] correspond to arrows pointing in precisely opposite directions and so are on the same line through the origin. D. The statement is true [-2 5] and [-5 2] are on a line through the origin since [-5 2] is a positive multiple of [-2 5].
A. The statement is false. [-2 5] and [-5 2] do not lie on a line through the origin, as they do not have the same slope. The arrows they correspond to meet at right angles, which means they form a line perpendicular to the origin.
B. Correct! The statement is false. [-2 5] and [-5 2] do not lie on a line through the origin, as they do not have the same slope. The arrows they correspond to meet at right angles, which means they form a line perpendicular to the origin.
C. Correct! The statement is true. [-2 5] and [-5 2] correspond to arrows pointing in precisely opposite directions and so are on the same line through the origin.
D. Incorrect. The statement is false. [-2 5] and [-5 2] do not lie on a line through the origin, as they do not have the same slope. The arrows they correspond to meet at right angles, which means they form a line perpendicular to the origin.
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prove if 1-norm less than 2 norm less then infinty norm the there is no c such that inginity norm is less than c 1 norm
There does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V. Therefore, p1-norm < p2-norm < p∞-norm implies there is no c such that p∞-norm < c p1-norm.
Given two norms, p and q, on a vector space V, we say that p is less than q, written p ≤ q, if there exists a constant C > 0 such that for all vectors v in V,
p(v) ≤ Cq(v)
Now, let's consider the three norms:
The 1-norm: p1(v) = ∑|v_i|
The 2-norm: p2(v) = √(∑v_i^2)
The infinity-norm: p∞(v) = max{|v_i|}
We are given that p1(v) ≤ p2(v) for all vectors v in V and that p2(v) ≤ p∞(v) for all vectors v in V. We want to show that there does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V.
Suppose for the sake of contradiction that such a constant C does exist. Then, for any non-zero vector v in V,
p∞(v) ≤ Cp1(v)
max{|v_i|} ≤ C ∑|v_i|
Since v is non-zero, there exists an index i such that |v_i| > 0. We can divide both sides of the inequality by |v_i| to get:
1 ≤ C ∑|v_j| / |v_i|
Now, since p1(v) ≤ p2(v) for all vectors v in V, we have:
p1(v) = ∑|v_j| ≤ √(∑v_j^2) = p2(v)
So, we can substitute this into the inequality above to get:
1 ≤ C √(∑v_j^2) / |v_i| = Cp2(v) / |v_i|
Finally, since p2(v) ≤ p∞(v) for all vectors v in V, we have:
p2(v) / |v_i| ≤ p∞(v) / |v_i| = 1
So, we have reached a contradiction:
1 ≤ Cp2(v) / |v_i| ≤ C
This contradicts the assumption that C > 0, so there does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V. Therefore, p1-norm < p2-norm < p∞-norm implies there is no c such that p∞-norm < c p1-norm.
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The function k(x) shown in the table below is a linear function.
Find its slope, y-intercept, and formula in slope-intercept form.
I added the graph to help out and I wanted to say slope is 3 y intercept is 0,5 and the formula would be k(x)=3x-5
Answer:
Y- intercept is (0,-5), not (0,5), but everything is right! Nice job
Step-by-step explanation:
Finding slope and Y-intercept
Slope being (y2-y1)/(x2-x1) of any two points
I'll do (6,7) and (9,13), so
(13-7)/(9-6) = 6/3 = 2.
Slope = 3
For Y-Intercept
That's where X = 0. On this graph, X = 0, where Y= -5, making the Y-intercept -5
Slope intercept form is y = mx + b
Plugging everything together, we get K(X) = 3x - 5
If the line segment joining the points A (x1, y1) and B(x2, y2) is divided by a point P in the ratio 1 : k internally,then the coordinates of the point P are
If the line segment joining the points A (x1, y1) and B(x2, y2) is divided by a point P in the ratio 1 : k internally, then the coordinates of the point P are P[(1x₂ + kx₁)/(1 + k)], [(1y₂ + ky₁)/(1 + k)].
How to determine the coordinates of point P?In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to k.
In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have the following;
P(x, y) = [(1x₂ + kx₁)/(1 + k)], [(1y₂ + ky₁)/(1 + k)]
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The pie chart gives the recipe for a premium blend trail mix. What part of the premium blend is composed of raisins?
Answer:
1/7
Step-by-step explanation:
All parts are equal to one therefore raisons are just 1 out of 7 other slices on the pie chart
To determine what part of the premium trail mix is composed of raisins, refer to the given pie chart. The portion represented by 'raisins' indicates the amount of raisins in the mix. Raisins slice is 1/7, so 14.28% of premium blend is composed of raisins.
Explanation:To find out what part of the premium blend trail mix is composed of raisins, you need to look at the pie chart. The pie chart should be separated into multiple sections, with each section representing a different ingredient in the trail mix. The section labeled as raisins would represent the part of the premium blend that is composed of raisins.
For example, if the 'raisins' slice is 1/4, 25%, or 90 degrees of the pie chart, this means that 1/4, 25%, or a proportional quantity of the trail mix is composed of raisins. This is because a pie chart is a circle, and a full circle is 100% or 360 degrees - so 1/4, 25%, or 90 degrees all represent the same quantity in this context.
Remember to always check the labels and any information provided in the pie chart. It provides a visual representation of data and can help you understand the proportions of different components in a mixture.
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You are given the equation 13 = 2x + 5 with no solution set.
Part A: Determine two values that make the equation false.
Part B: Explain why your integer solutions are false. Show all work.
Answer:
Part A: x = 1, 2
Part B: 13 != 7, 13 != 9
Step-by-step explanation:
We pick x values that when plugged into the equation, creates a false statement.
x = 1
13 = 2(1) + 5
13 = 2 + 5
13 = 7
As you can see 13 does not equal 7
x = 2
13 = 2(2) + 5
13 = 4 + 5
13 = 9
As you can see 13 does not equal 9
Steve wants to take all of his 145 employees on a fishing trip. If each fishing boat holds 13 people, how many boats does Steve need to rent?
Answer:
Approximately 11 boats.
Step-by-step explanation:
To get this answer, we simply need to divide 145, which is the number of his employees, but 13, the amount of people each boat holds. You get the answer 11.1538462.
Answer:
12 Boats
Step-by-step explanation:
Since it given that;
Steve wants to take all of his 145 employees on a fishing trip.Each fishing boat holds 13 peopleAll we have to do is divide the total number of people by how much a fishing boats can hold.
Which is;
145/13
= 11.1538461538
So, we need 12 boats due to 145/13 = 11.15... because you can't cut a person in half. Thus, we need an extra boat to hold the extras.
RevyBreeze
After a big snowfall, you take your favorite rocket‑powered sled out to a wide field. The field is 205 m across, and you know that your sled accelerates at a rate of 3.95 m/s2 when the rocket is on. How fast will the sled be moving when it is halfway across the field?
Answer:
Below
Step-by-step explanation:
Find time to get to 102.5 m (Half of the field)
d = 1/2 a t^2
102.5 = 1/2 * 3.95 t^2 shows t = 7.2 s
then v = at
= 3.95 * 7.2 = 28.5 m/s
Please help me with this question.
7. The statement regarding the set is false.
8. The statement regarding the set is correct.
How to analyze the statements?In problem 7, we are given the subsets of a set, and then the statement is that the subset {a,e} is contained into the set S.
The subset {a,e} is not one element of the set S, which are a, ... {e, empty}, hence the statement is false.
In problem 8, we are given the union operation, which has the result given by the elements that belong to at least one of the sets.
The empty set belongs to set T, hence it belongs to the union of sets S and T, and thus the statement is correct.
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It is estimated that each guest at a party will eat 2/3 pounds of chocolates. How many guests can be served with 6 pounds of chocolate?
Answer: 9 guest can be served.
Step-by-step explanation:
2/3 pounds of chocolate for each guest
6 pounds of chocolate can be served to
So let's do 6/ (2/3)
=6* 3/2
that will equal 9 guests
Which number is NOT a common
of the fractions being
denominator
added?
2/9 + 5/12
A 108
(B) 72
(C) 36
(D) 24
Check the picture below.
now, doing a prime factoring on both the denominators, notice, the repeated factors get used only once in the LCD calculation, so the red "3" only goes once in the LCD and then the others, so the LCD for both of those is 3*3*2*2 = 36.
"L" in LCD stands for Least, so that's the smallest, however we can have a CD that's no small and is simply a multiple of the LCD, let's check who isn't an LCD or CD
[tex]\begin{array}{rllll} 108=3\cdot 36 & \bigotimes\\\\ 72=2\cdot 36& \bigotimes\\\\ 36=1\cdot 36&\bigotimes\\\\ 24&\textit{\LARGE \checkmark} \end{array}[/tex]
If sample variance were to be computed by dividing SS by n, then the average value of the sample variances from all the possible random samples would consistently _____ the population variance.
a. equal
b. Impossible to determine
c. overestimate
d. underestimate
If sample variance were to be computed by dividing SS by n, then the average value of the sample variances from all the possible random samples would consistently underestimate the population variance.
The sample variance is an estimate of the population variance, and it is calculated by dividing the sum of squared deviations (SS) by the sample size minus one (n - 1).
The reason for dividing by n-1 instead of n is due to the fact that the sample variance is an estimate of the population variance and not the exact value. When computing the sample variance, we use the sample data to make an estimate of the population variance. By dividing by n-1 instead of n, we adjust for the fact that the sample is a subset of the population and introduce a small amount of bias into the estimate to correct for this lack of representation.
This correction is known as the Bessel's correction and it makes the sample variance a more accurate estimate of the population variance by adjusting for the variability inherent in sampling. As a result, when sample variance is computed using the Bessel's correction (dividing by n-1), the average value of the sample variances from all possible random samples will consistently underestimate the population variance.
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The cam's mandible history is 100 page loose leaf history randomly mixed and its objective is to rearrange the pages on the right order. How many possibilities of combinations are there? And what's the probability of getting the story in the right order?
The possibilities of the combinations that are there for rearranging the pages in the right order are 100 !.
The probability of getting the story in the right order is 1 / 100 !.
How to find the combination ?There are 100 pages in the history text which means that when they are randomly mixed, each page could take a different position out of the 100 and so lead to a new combination.
The possibilities of combinations is therefore:
= n !
= 100 !
The probability that the story is in the right order will happen with only a single combination which means the probability is:
= Number of correct orders / Number of combinations
= 1 / 100 !
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At the fair, Lisa stumbled upon a game called Cool Down. In this game, there is a container with
8 cups of hot water (at a temperature of 50ºC). The object is to determine how many cups of
cold water (at a temperature of 20ºC) to add to the container to reduce the temperature to 40ºC.
a. Find an equation expressing the temperature (in ºC) of the water in the container as a
function of the volume (cups) of cold water added.
Equation: ________________________
b. Explain how you obtained the equation in part (a) above.
c. Use your equation to determine the amount of cold water that must be added to reduce the
temperature to 40ºC.
Answer:
t = (400 + 20c)/(8+c)weighted sum of temperatures4 cupsStep-by-step explanation:
You want an equation for the temperature of 8 cups of hot (50 °C) water combined with c cups of cold (20 °C) water, along with an explanation of it. Then you want the number of cups required to reduce the temperature to 40 °C.
(a) EquationAssuming constant heat capacity and volume as a function of temperature, the temperature of the mix will be the weighted average of the temperatures of the contributors. That is c cups of water at 20 °C combined with 8 cups of water at 50 °C will have a temperature (t) of ...
t = (20c +8(50))/(c+8)
t = (20c +400)/(c +8)
(b) ExplanationThe thermal energy contained in the water is assumed to be jointly proportional to its volume and its temperature. The combined thermal energy of the mixture will be the total of that of its contributors.
That is, the temperature of the mix is the weighted sum of the temperatures of the contributors, the weights being their respective volumes.
(c) 40°The value of c for a temperature of 40 °C is ...
40 = (20c +400)/(c+8)
2(c +8) = c +20) . . . . divide by 20, multiply by (c+8)
2c +16 = c +20 . . . . eliminate parentheses
c = 4 . . . . . . . . . . . . subtract (c+16)
4 cups of cold water must be added to reduce the temperature ot 40 °C.
(a) t = (400 + 20c)/(8+c)
(b)weighted sum of temperatures
(c) 4 cups
What is an equation?An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.
Let t be the temperature of water.
Let c be the number of cold cup of water at 20°C
(a)c cups of water at 20 °C combined with 8 cups of water at 50 °C will have a temperature (t) of
[tex]t= \frac{20c+8*50}{c+8}[/tex] --------(1)
(b)The temperature of the mix is the weighted sum of the temperatures of the contributors, the weights being their respective volumes.
(c)The value of c for a temperature of 40 °C is
40 = (20c +400)/(c+8)
2(c +8) = c +20) . . . . divided by 20, multiply by (c+8)
2c +16 = c +20 . . . . eliminate parentheses
⇒ c = 4
Hence, the required equation is [tex]t= \frac{20c+8*50}{c+8}[/tex] and for part (c) 4 cups.
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The population of a city is modeled by the equation P(t)=244,115e0.1t
where t
is measured in years. If the city continues to grow at this rate, how many years will it take for the population to reach one million?
The number of years it will take the population of the city to reach 1million is 14.1 years
What is exponential function?Exponential function, in mathematics, a relation of the form y = ax, with the independent variable x ranging over the entire real number line as the exponent of a positive number a.
1000000 = 10⁶
10⁶ = P(t)
10⁶ = 244115e0.1t
10⁶/244115 = 0.1t
e0.1t = 4.096
ln0.1t = ln 4.096
0.1t = 1.41
t = 1.41/0.1
t = 14.1 years
therefore the years it will take the city to be populated with 1million is 14.1 years
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Determine the factor
Answer:
it's 3gc brought video gloves
The function f(x)=x√ is horizontally stretched by a factor of 2 to form function g(x). What is the equation of g(x)? Enter your answer in the box. g(x) =
The equation of g(x) is g(x) = 2*x^(1/2)
Explanation:
The original function f(x) is defined as f(x) = x^(1/2) which is the square root of x. When the function is stretched horizontally by a factor of 2, the x term becomes 2x. So the new function g(x) is defined as g(x) = 2*x^(1/2)
