Answer:
The speed of the boat in still water was 21 km/h.-------------------------
Given:The distance is d,The speed of the boat in still water is s,The speed of the current is 7 km/h,Time upstream is 20 min or 20/60 hour,Time downstream is 10 min or 10/60 hour.Set equations for time:d / (s + 7) = 10/60 ⇒ d / (s + 7) = 1/6 ⇒ 6d = s + 7,d / (s - 7) = 20/60 ⇒ d / (s - 7) = 2/6 ⇒ 6d = 2(s - 7).Eliminate d and solve for s:s + 7 = 2(s - 7) ⇒ s + 7 = 2s - 14 ⇒ 2s - s = 7 + 14 ⇒ s = 21Stage two is so hard, i dont understand anything
Answer:
the answer I got is option number three i.e 4
Fill in the table.
X(input) Y(output)
1 0
3 4
4 6
7
20
The values of p and q are 12 and 38 when for the missing outputs y when the table is given with input and output.
Given that,
The table is
Input Output
X Y
1 0
3 4
4 6
7 p
20 q
We have to find the p and q values.
Take the points as
(x,y)=(1,0),(3,4),(4,6),(7,p) and (20,q)
Take the points (1,0) and (3,4)
Equation of the line is
y=mx+b
Where
The slope of the line is m, and the intercept is b.
Slope of the line is rise/run
m=4-0/3-1
m=4/2
m=2
Now,
y=mx+b
0=2(1)+b
2+b=0
b=-2
The equation of the line is y=2x-2.
Take the point(7,p)
p=2(7)-2
p=14-2
p=12
Take the point (20,q)
q=2(20)-2
q=40-2
q=38
Therefore, The values of p and q are 12 and 38 when for the missing outputs y when the table is given with input and output.
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PLEASE!!!! In the linear equation shown, which variable would represent the output (range) values?
y = mx + b
B
X
M
y
The variable y represents the range or output values of the function.
What is the Range of a function?The range of a function is the set of output values of the function.
The given equation is y = mx + b.
Note that x is an independent variable, therefore, we substitute the values for x and calculate the value of y to that value of x.
Therefore, y denotes the range or output values of the function.
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Leanne sells magazine subscriptions over the telephone. She earns $14 for every subscription she sells,
How much will Leanne earn if she sells 15 subscriptions?
Leanne earned $224 last month, how many subscriptions did she sell?
Answer:
Amount of money Leanne will earn
= $14 × 15 subscriptions
= $210
Number of subscriptions Leanna sold last month
= $224 ÷ $14
= 16 subscriptions
F(x)= (x+1)(x+3)(x-4) In standard form
The standard form of the given function (x + 1) (x + 3) (x - 4) is :
(x^3 -13x - 12) .
What is the standard form of function?The highest degree of terms are written first, followed by the next degree, and so on, to represent a polynomial in standard form. The polynomial's usual form is f(x) = anx^n + an-1x^n-1 + an-2x^n-2 +. + ai, where ai are coefficients and x is the variable.Here based on the given question,
We only want to expand the function and look up
f(x) = (x+1)(x+3)(x-4) in standard form.
We'll obtain:
f(x) = (x + 1)*(x + 3)*(x - 4)
f(x) = (x + 1)*(x^2 + 3*x - 4*x + 3*-4)
f(x) = (x + 1)*(x^2 - 1*x - 12)
f(x) = (x^3 + x^2 - x^2 - x - 12x - 12)
f(x) = (x^3 -13x - 12)
Using standard form, the function is:
f(x) = (x^3 -13x - 12)
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Answer:
3
Step-by-step explanation:
doin it now lol
13. Maddie and Tony are having a Stanley Cup party at their house. They are going to buy hoagies for everyone to eat
and cut the hoagies into thirds. If they buy 12 hoagies and 9 people come to the party, how many pieces of hoagies does
each person get to eat?
Each person will get to eat 4 pieces of hoagies.
What is division?Division in maths is the process of breaking a number up into equal parts, and finding out how many equal parts can be made.
Here, at the Stanley Cup Party Maddie and Tony, they bought 12 hoagies and cut in the thirds which results in 36 pieces of hoagies.
Since, 9 people come to the Stanley party and hoagies have 34 pieces.
So each person will get the following pieces of hoagies
36/9=4.
Therefore, each person at Stanley party will get 4 pieces of hoagies.
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Your original purchase price was $825.00 plus 7% sales tax. You enter into an agreement where the interest (12.5% APR) is waived for the first 12 months provided you make the required monthly payments; otherwise the interest is accrued from the date of purchase. You miss the first payment due date. The late fee is $35.00. How much is the interest?
If your original purchase price was $825.00 plus 7% sales tax and the interest is accrued from the date of purchase. The interest is $9.20.
How to find the interest?First step is to find the monthly interest rate
Monthly interest rate =12.5% / 12
Monthly interest rate = 1.0417%
Second step is to find the total amount applied for credit
Total amount applied for credit= $825+ ($825 × 7%)
Total amount applied for credit =$882.75
Now let find the interest
Interest = $882.75 x 1.0417%
Interest =$9.19
Interest = $9.20 (Approximately)
Therefore the interest is $9.20.
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Answer:
1. a late payment/missed fee
2. accrued interest
3. $9.20
4. $9.66
Hope This Helps!
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
Angle x = 113 degrees
Angle y = 67 degrees
Step-by-step explanation:
First, off you can eliminate the 200 degrees, because the maximum degrees is only 180 degrees. Then 23 and 11 are way to small of angles to look like what x and y look like, and 113 and 67 look much better than the other angles.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 15 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
write the equation of a line whose slope is 10 and the y intercept is -15
Answer:
y=10x-15
Step-by-step explanation:
Use slope-intercept form: y=mx+b
M is your slope and B is your Y intercept
since your Y-intercept is negative, and adding a negative is just subtracting, you can just put -15 instead of +-15
Renuka Jain's Car Wash takes a constant time of 4.5 minutes in its automated car wash cycle. Autos arrive following a
Poisson distribution at the rate of 9 per hour. Renuka wants to know:
a) The average wait time in the line = ______ minutes (round your response to two decimal places).
b) The average number of customers waiting on line = ______ cars (round your response to two decimal places)
a) The average wait time in the line = 13.33 minutes.
b) The average number of customer waiting on line = 4.67 minutes
What do you mean by average?
The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
a) Values:
Arrival rate = 9 per hour
Service rate [tex]= \frac{60}{Service\ time}[/tex]
Service rate [tex]= \frac{60}{4.5} = 13.33[/tex] minutes
b) Queue:
units in queue(LQ) = Arrival Time^2 / (Service rate* (Service rate - Arrival rate))
unit in queue(LQ) [tex]= \frac{ 9^2}{(13.33\times (13.33 - 9))}[/tex]
unit in queue(LQ) = 0.70
Time in Queue(WQ) = Arrival rate / (Service rate * (Service rate - Arrival rate))
time in queue (WQ) [tex]= \frac{9}{ (13.33 \times (13.33 - 9)}[/tex]
time in queue (WQ) = 4.67 minutes
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Find attached document for clarification of the maths problem.
P(2 ≤ x ≤ 3) = 0.55 , using probability distribution.
What do you mean by probability distribution?
A frequency distribution that has been idealised is a probability distribution.
An individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each possible value of a variable appears.
The probability of occurrence of a value determines how frequently it appears in a sample.
A value will occur more frequently in a sample the higher its probability.
It is given that discrete random variable has a distribution of
P(x = 1) = 0.15, P(x = 2) = 0.39, P(x = 3) = 0.16, P(x = 4) = 0.30
For P(2 ≤ x ≤ 3) = P(2) + P(3) = 0.39 + 0.16 = 0.55
Therefore, P(2 ≤ x ≤ 3) = 0.55
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HELP ASAP! WILL GIVE BRAINLIEST
The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam. Passed exam Did not pass exam Row Totals Completed exam review 55% 10% 65% Did not complete exam review 20% 15% 35% Column Totals 75% 25% 100% Part A: What is the percentage of students who failed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points) Part B: What is the percentage of students who failed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points) Part C: Is there an association between failing the exam and completing the exam review? Justify your answer. (2 points)
The percentages are given as follows:
a) Failed, given that they completed the review: 15.38%.
b) Failed, given that they did not complete the review: 42.86%.
Considering these percentages, for item c, there is an inverse association between failing the exam and completing the exam review, as the percentage of those who failed completing the review is way less than the percentage of those who failed without completing the review.
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction, which is used along basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.
A percentage is one example of application of proportions, as it is the division of the number of desired outcomes by the number of total outcomes and multiplied by 100%.
For item a, we have that:
Total outcomes: 65% completed the review.Desired outcomes: 10% failed the exam.Hence the percentage is:
p = 10/65 x 100% = 15.38%.
For item b, we have that:
Total outcomes: 35% did not complete the review.Desired outcomes: 15% failed the exam.Hence the percentage is:
p = 15/35 x 100% = 42.86%.
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Find the length of the segment of the line with equation y = 5x – 2 between x = 3 and x = 4. Give your answer to 1 dp.
Answer:
5.1 units
Step-by-step explanation:
[tex]f(x)=5x-2\\f(3)=5(3)-2=13\\f(4)=5(4)-2=18[/tex]
[tex]\Delta x=1 unit=a\\\Delta y=5 units=b\\a^2+b^2=c^2\\(1)^2+(5)^2=c^2\\\sqrt26=c\\c=5.1 units[/tex]
One plane can travel 10 miles per hour faster than another. One of them goes 510 miles in the same time it takes the other to go 495 miles. What are their speeds?
The planes' speeds would be ____ miles per hour.
This is a proportion math problem.
If one plane can travel 10 miles per hour faster than another. The planes' speeds would be 435 miles per hour.
How to find the speed?let s = speed of the slower plane
then
(s+10) = speed of the faster
time = distance /speed
495/s =510 /(s+10)
495s = 510s + 5100
Combine like terms
495 - 510s = 5100
15s = 5100
Divide both side by 15s
s = 5100/15
s = 425 mph ( speed of the slower plane)
Speed of the fastest plane
(s+10)
425 +10
= 435 mph
Therefore the speed of the fastest is 435 mph.
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the equation of line1 y=5x+1 the equation of line2 2y-10x+3=0
state these two lines are parallel
Line 1 and Line 2 are parallel because they have the same slope.
How to know if lines are parallel?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
m = slopeb = y-interceptTwo lines are parallel if the slopes are the same.
The equation of line 1 is y = 5x + 1
The slope of Line 1 is 5.
Let's find the slope of Line 2 using the equation.
2y - 10x + 3 = 0
Let's represent the equation in slope intercept form to locate the slope easily.
2y - 10x + 3 = 0
2y = 10x - 3
y = 10 / 2 x - 3 / 2
y = 5x - 3 / 2
The slope of line 2 is 5
Therefore, Line 1 and Line 2 are parallel.
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Rosalyn owns a few vending machines. last night she collected $82.50 in dimes and quarters. If Rosalyn collected 50 more quarters then dimes, how many dimes did she collect?
Answer:
200
Step-by-step explanation:
The half-life of radium-226 is 1600 years. Suppose we have a 27-mg sample.
(a) Find a function
m(t) = m02−t/h
that models the mass remaining after t years.
m(t) =
(b) Find a function
m(t) = m0e−rt
that models the mass remaining after t years. (Round your r value to six decimal places.)
m(t) =
(c) How much of the sample will remain after 4000 years? (Round your answer to one decimal place.)
mg
(d) After how many years will only 17 mg of the sample remain? (Round your answer to one decimal place.)
yr
A function m(t)= m₀e^(-rt) that models the mass remaining after t years is; m(t) = 27e^(-0.00043t)
The amount of sample that will remain after 4000 years is; 4.8357 mg
The number of years that it will take for only 17 mg of the sample to remain is; 1076 years
How to solve exponential decay function?
A) Using the model for radioactive decay;
m(t)= m₀e^(-rt)
where;
m₀ is initial mass
r is rate of growth
t is time
Thus, we are given;
m₀ = 27 mg
r = (In 2)/1600 = -0.00043 which shows a decrease by 0.00043
and so we have;
m(t) = 27e^(-0.00043t)
c) The amount that will remain after 4000 years is;
m(4000) = 27e^(-0.00043 * 4000)
m(4000) = 27 * 0.1791
m(4000) = 4.8357 mg
d) For 17 mg to remain;
17 = 27e^(-0.00043 * t)
17/27 = e^(-0.00043 * t)
In(17/27) = -0.00043 * t
-0.4626/-0.00043 = t
t = 1076 years
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If a sample consists of 1900 scores blank of them would be above the first quartile
If a sample consists of 1900 scores from sample no. 476th will be above the first quartile.
What are mean, median, and mode?The three main methods for identifying the average value of a set of integers are mean, median, and mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.
The middle value in a list that is arranged from smallest to greatest is called the median.
The value that appears the most frequently on the list is the mode.
Given a sample consisting of 1900 scores.
∴ The no. of samples that would be above quartile is the next sample from (1/4)th of 1900 which is,
= (1/4)×1900 + 1.
= 475 + 1.
= 476.
So from sample no. 476th will be above the first quartile.
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Yadira and her friend are renting a property together. The monthly rent is $1,050.00, and monthly utilities will average $365.00. Yadira will pay three fifths of the rent since her bedroom is larger. Determine how much Yadira's friend will pay each month for rent and utilities. (1 point)
$420.00
$602.50
$707.50
$812.50
Answer:
$602.50
Step-by-step explanation:
The monthly rent is $1,050.00.
If Yadira pays 3/5 ths of the rent, then her friend will pay 2/5 ths of the rent:
[tex]\implies \sf \dfrac{2}{5}\;of\;1050=\dfrac{2}{5} \times 1050=420[/tex]
Therefore, Yadira's friend pays $420 for rent.
If the monthly utilities average is $365, Yadira's friend's portion of the utilities will be half of the total:
[tex]\implies \sf \dfrac{1}{2}\;of\;365=\dfrac{1}{2} \times 365=182.5[/tex]
Therefore, Yadira's friend pays $182.50 for utilities.
So the total amount Yadira's friend will pay each month is:
[tex]\implies \sf Rent + Utilities=420+182.50=602.50[/tex]
please help me with this question! thank you
The line joining R and R' is perpendicular to the line m therefore, the slop is the negative inverse of the slope of the line m which is (-1/2)
11. The point R is at located at R'(6, -1)
What are perpendicular lines?Perpendicular lines are oriented at 90° to each other.
11. The image of a point (x, y) following a reflection is located directly vertical on the other side of the line.
The image of (x, y) after a reflection across the x-axis is (x, -y), the x-coordinate remains the same such that the line joining (x, y) and (x, -y), is perpendicular to the x-axis, which is the line of reflection.
Similarly, when R is reflected across the line m to produce the image, R', the segment [tex]\overline{RR'}[/tex] joining the preimage and the image of the reflection, will be perpendicular to the line m.
The slope of the line perpendicular to the line m, y = 2·x - 3 is -(1/2) which is -0.5
The slope of the segment [tex]\overline{RR'}[/tex] is -0.5
11. The coordinates of the point R is R(-2, 3)
The known slope of the line joining R and R' and the coordinates of the point R(-2, 3) indicates that the equation of the line on which the image is located is therefore;
y - 3 = (-0.5) × (x - (-2)) = -0.5·x - 1
y = -0.5·x - 1 + 3 = -0.5·x + 2
The point of intersection of the two lines is therefore;
-0.5·x + 2 = 2·x - 3
2.5·x = 5
x = 5/2.5 = 2
y = 2×2 - 3 = 1
The point of intersection is I(2, 1)
The change in the x and y-coordinate from I to R are;
Δx = 2 - (-2) = + 4
Δy = 1 - 3 = -2
The change for point R' are therefore;
Δx' = (2 + 4) = 6
Δy' = 1 - 2 = -1
The coordinates for R' is (6, -1)
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In 2015, a town had a population of 80,000. It then declined at a rate of 4% per year. What was the town's population in 2018?
Which equation is true regarding the angles formed by the diagonals and sides of the rhombus? x + y = z 2x = y + z z + x = 2y 2x + 2y = 4zWhich equation is true regarding the angles formed by the diagonals and sides of the rhombus? x + y = z 2x = y + z z + x = 2y 2x + 2y = 4z
The equation that shows that angles angles formed by the diagonals and sides of the rhombus is x + y = z
How to show the relation to express the anglesThe diagonals of rhombus intersect each other at 90 degrees
z = angle formed at the diagonal = 90
x and y angle sides of the rhombus
applying the sum of angles of a triangle property
z + x + y = 180
where z = 90
90 + x + y = 180
x + y = 180 - 90
x+ y = 90
therefore x + y = z
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Find the measure of the marked angles
The measure of the angles is=
The measure of the angles are (4x + 24)° = 52° and (6x - 10)° = 32°; The value of x =7°.
What is vertically opposite angles?
The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.Vertically opposite angles, or ical angles. A pair of angles that are vertically opposed to one another are always equal. Additionally, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees.Two lines are said to intersect when they cross at a certain location in a plane. The lines are referred to as parallel when they do not intersect at any point in the plane.So, (4x + 24)° = (6x - 10)°
24° - 10° = 6x - 4x
2x = 14°
x = 14°/2
x = 7°
Substitute x in those values:
(4x + 24) = (4(7) + 24)°
= 28+24
= 52°
(6x - 10)° = (6(7) -10)
= 42° - 10°
= 32°
Hence, the measure of the angles are (4x + 24)° = 52° and (6x - 10)° = 32°; The value of x =7°.
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Answer:
x = 7
Step-by-step explanation:
The measure of the angles are (4x + 24)° = 52° and (6x - 10)° = 32°; The value of x = 7°.
1) Solve the exponential equation 7^g = 14
2) Solve the exponential equation 6^u = 22
3) Solve the exponential equation 7^x-2 = 7
4) Solve the exponential equation (0.66)^k = 9
5) Solve the exponential equation 8^a = 16
6) Solve the exponential equation 12^z = 25
7) Solve the exponential equation 4^x-5 = 8
8) Solve the exponential equation (0.28)^v = 7
9) Solve the exponential equation 2^y = 18
10) Solve the exponential equation 17^b = 36
The solutions to each of the given exponential functions are;
1) g = 1.356
2) u = 1.725
3) x = 3
4) k = -5.288
5) a = 4/3
6) z = 1.295
7) x = 13/2
8) v = -1.5286
9) y = 4.17
10) b = 1.2648
How to solve exponential equations?Exponential equations are usually in the form a^(x) = b^(y) . To solve exponential equations with same base, we normally make use of the property of equality of exponential functions .
1) 7^(g) = 14
gIn 7 = In 14
g = In 14/In 7
g = 1.356
2) 6^(u) = 22
u In 6 = In 22
u = In 22/In 6
u = 1.725
3) 7^(x - 2) = 7
7^(x - 2) = 7¹
Equating the exponents gives;
x - 2 = 1
x = 3
4) (0.66)^k = 9
k In 0.66 = In 9
k = In 9/In 0.66
k = -5.288
5) Exponential equation 8^a = 16
2^(3a) = 2⁴
Equating the exponents gives;
3a = 4
a = 4/3
6) The exponential equation 12^z = 25;
z In 12 = In 25
z = In 25/In 12
z = 1.295
7) The exponential equation 4^(x-5) = 8
2^(2(x - 5)) = 2^(3)
2x - 10 = 3
2x = 13
x = 13/2
8) (0.28)^v = 7
vIn 0.28 = In 7
v = In 7/In 0.28
v = -1.5286
9) 2^y = 18
y In 2 = In 18
y = In 18/In 2
y = 4.17
10) 17^b = 36
b In 17 = In 36
b = In 36/In 17
b = 1.2648
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The cost of x pencils is 150. Write the algebraic expression for the cost of cach pencil.
Answer:
cost of each pencil [tex]= \frac{150}{x}[/tex]
1) Three runners run 100 yards race. Sara runs the
race in 9.25 seconds. Alex runs the race in 8.625
Seconds and Tonya runs the race in 9.8 seconds. Who
has the winning time?
The person that has the winning time is Alex.
How to know the person with winning time?From the information given, three runners run 100 yards race. Sara runs the race in 9.25 seconds and Alex runs the race in 8.625 seconds and Tonya runs the race in 9.8 seconds.
It should be noted that in a race, the person that has the lowest time wins.
In this situation, the person with 8.625 seconds is the lowest.
Therefore, Alex wins.
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A restaurant has 2/5
pounds of butter to divide
equally among 4 butter
dishes. How much is put in
each dish?
===================================================
Explanation:
Check out the diagram below.
I recommend getting graph paper for this problem.
Draw a box that is 5 units tall and 4 units across. There are 5*4 = 20 small squares inside this box. Each small square represents 1/20.
Shade two of the five rows to represent the fraction 2/5. This is the amount of butter we have. The 4 columns shows the butter divided into 4 equal pieces. Note how each column has 2 shaded squares out of 5 squares total. Since each small square represents 1/20, two such squares gets us 2/20 = 1/10 which is the amount of butter per dish.
------------
Another approach would be to say
[tex]\frac{2}{5} \div 4 = \frac{2}{5} \times \frac{1}{4} = \frac{2*1}{5*4} = \frac{2}{20} = \frac{1}{10}[/tex]
What is the median (middle) of the following set of numbers: [38, 39, 39, 40, 40, 40, 41, 41, 41,
42, 43, 44] Hint: there are 12 numbers here, and the set is already in order.
40
41
40.5
40.66666667
The table below gives the cost per person buy tickets to an upcoming concert. Find the rate of change.
1/74
1/222
148/1
74/1
Answer:
222-148=74 (people 3-2=1)
296-222=74 (people 4-3=1)
370-296=74 (people 5-4=1)
so 1/74 is the answer
find the 10th term 10,11,12,13
The 10th term of the series is 19.
Given series is an Arithmetic Progression (AP).
First term = a = 10
Difference = d = 11 -10
= 1
nth term = [tex]a_{n}[/tex] = a + (n-1)d
10th term = [tex]a_{10}[/tex] = 10 + (10 - 1)1
= 10 + 9*1
= 10 + 9
= 19
Hence, 10th term is 19.
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