The rate of current in the stream on that day is; 2 miles per hour
What is the rate of speed?
When dealing with relative velocity, we can say that;
When the motorboat travels downstream, then it means the total velocity will be;
Total velocity = Velocity of the motorboat in still water + Velocity of the stream.
If the motorboat travels upstream, the total velocity will be;
Total velocity = Velocity of the motorboat in still water - Velocity of the stream.
Thus,
Upstream speed = (14 mi/h - S)
Downstream speed = (14 mi/h + S)
Where;
S is the rate of current in the stream.
We are told that going downstream, it takes 15 minutes more to travel 12 miles, then we can write the system of equations as;
(14 mi/h + S)*T = 12 mi
(14 mi/h - S)*(T - 15 min) = 12 mi
Making T the subject in the first equation gives;
T = (12 mi)/(14 mi/h + S)
Plugging in (12 mi)/(14 mi/h + S) for T in the second equation gives;
(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi
Multiply both sides by (14 mi/h + S) to get;
(14 mi/h - S)*12 mi - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)
Since the speeds are in miles per hours, we can rewrite as:
- 15 min = -0.25 h
(14 mi/h - S)*12 mi - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)
168 mi²/h - 12mi*S + 49mi²/h + 0.25h*S² = 168mi²/h + 12mi*S
- 12mi*S + 49mi²/h - 0.25h*S² = 12mi*S
-24mi*S - 0.25h*S² + 49mi²/h = 0
Solving this quadratic equation with online quadratic equation solver gives us; S = 2 mph
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Which of the following rational functions is graphed below?
Answer:
A) F(x) = 1/(x-2)(x-2)
Step-by-step explanation:
Below in the picture of how the graph will look like:-
I hope my answer helps you.
Michael and Imani go out to eat for lunch if their food cost 25.30 and there is an 8% meals tax how much is the bill rounded to the nearest cent
Answer:
$25.30(0.08) = $2.024. I hope this helped! $27.32 + $4.92 = $32.24 in total! I hope this helped
Step-by-step explanation:
Can someone please help I’ll mark you as brainlist
Answer: x=4, y=4
Step-by-step explanation:
y+12=4y
x+36=10x
solve for y
y+12-12=4y-12
y=4y-12
y-4y=4y-4y-12
-3y=-12
y=4
Solve for x
x+36=10x
x+36-36=10x-36
x=10x-36
x-10x=10x-10x-36
-9x=-36
x=4
Olive buy clothe at a tore with a total bill of $54. 50. She ha a 20% off coupon and pay 7. 5% ale tax. She calculate the total cot of the clothe, uing the expreion: (54. 50÷1. 20)(1. 075). Explain the error in Olive' reaoning. Determine the correct expreion and explain your reaoning
Total bill that should be paid by Olive is $46.61. Olive's calculation is incorrect because she is applying the discount and tax to the original price of the clothes rather than to the discounted price.
A total bill is the final amount of money that is due for payment, usually for goods or services that have been provided. It is the sum of all charges, fees, taxes, and other expenses that have been incurred. The total bill may be presented as a single amount or as a breakdown of the various charges that make up the total.
The correct expression to calculate the total cost of the clothes would be:
Total cost = (Original price * (1 - Discount rate)) * (1 + Tax rate)
In this case, the original price is $54.50, the discount rate is 20%, and the tax rate is 7.5%. Plugging these values into the above expression gives us:
Total cost = (54.50 * (1 - 0.20)) * (1 + 0.075)
Total cost = (54.50 * 0.80) * 1.075
Total cost = $43.60 * 1.075
Total cost = $46.61
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At the beginning of her enior year maria received a $5,000 ubidized loan and a $4,500 unubidized loan with an apr of 5. 5%. If maria begin making payment on her loan 6 month after graduation, how much interet will he owe to the nearet dollar?
The amount of interest Maria owes after 6 month of graduation, if she take a subsidized loan of $5,000 and unsubsidized loan of $4,500 is $508.75.
Therefore, the answer is $509.
Subsidized loan
Here, the time period is considered only after graduation, so time period is 6 months, that is 0.5 year. We know simple interest formula where P is the principal amount, r is annual interest rate and n time period in years.
I = P×r×n
Therefore I₁ = 5000 × 0.055 × 0.5
I₁ = 137.5
Unsubsidized loan
Here the time period is considered from the time the loan taken, so time period is one year of graduation plus 0.5 year, i.e. n = 1.5yrs.
Therefore, I₂ = 4500 × 0.055 × 1.5
I₂ = 371.25
Therefore total interest for both the loan is
I = I₁ + I₂
I = 137.5 + 371.25
I = 508.75
I ≈ $509
--The question is incomplete, the complete question is as follows--
"At the beginning of her senior year Maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.5%. if maria begins making payments on her loans 6 months after graduation, how much interest will she owe to the nearest dollar?"
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If m<10 = m<3, then the lines are parallel by the:
alternate exterior angle converse theorem.
alternate interior angle converse theorem.
same-side interior angle converse theorem.
None of these choices are correct.
If m<10 = m<3, then the lines are parallel by the: alternate exterior angle converse theorem.
What is alternate exterior angles?The pair of angles known as alternate external angles are those that are generated on the other side of the transversal from the parallel lines' outer side.
What is alternate exterior angels converse theorem?According to the opposite of the alternative exterior angle theorem, if two lines are cut by a transversal and their alternate exterior angles are congruent, the lines are parallel.
In the figure angel 10 and 3 are alternate exterior angles
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how much does it cost to buy 1500g of cornflakes
Answer:
£2.94
Step-by-step explanation:
You need two 750g boxes to get 1500g of cornflakes.
Buy one and get 2nd at half price:
1.96 + 1.96/2 = £2.94
3 The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers.
Answer:
The possible pairs of numbers that satisfy the given conditions are (x, y) = (4, 2) and (x, y) = (8, -2).
Step-by-step explanation:
To solve this problem, we can use algebra. Let's call the two numbers x and y. We are given that x + y = 6 and x^2 + y^2 = 28. We can square the equation x + y = 6 to get x^2 + 2xy + y^2 = 36. We can then subtract the equation x^2 + y^2 = 28 from the equation x^2 + 2xy + y^2 = 36 to get 2xy = 8. We can then divide both sides by 2 to get xy = 4.
We can then use the equation x + y = 6 to write x = 6 - y, which we can substitute into the equation xy = to get (6 - y)y = 4. Solving this equation for y yields y = 2 or y = -2.
If y = 2, then x = 6 - y = 6 - 2 = 4, so the two numbers are x = 4 and y = 2. If y = -2, then x = 6 - y = 6 + 2 = 8, so the two numbers are x = 8 and y = -2. Therefore, the possible pairs of numbers that satisfy the given conditions are (x, y) = (4, 2) and (x, y) = (8, -2).
Help!!! PLEASE!!!!
thx
Answer:
(c) (1/14)xy(x² +8y)
Step-by-step explanation:
You want the greatest common factor factored out of the expression 1/14x³y +8/14xy².
Common factorThe coefficients 1/14 and 8/14 have a common factor of 1/14.
The variable terms x³y and xy² have variables x and y. The exponents of x are 3 and 1, so x¹ = x will be the common factor.
Similarly, the exponents of y are 1 and 2, so y¹ = y will be their common factor.
When we factor out (1/14)(x)(y) from the terms of the given expression, it becomes ...
1/14xy(x² +y)
What is the circumference of a circle whose radius is 16 feet leave answer in terms of pi . Please show ur work because I have too!
The circumference of a circle is 32π feet, which is the correct answer would be option (B).
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
We have to determine the circumference of a circle whose radius is 16 feet
As per the question, we have
The radius of the circle r = 16 feet
Circumference of a circle = 2πr
Substitute the value of r in the above formula, and we get
Circumference of a circle = 2π(16)
Circumference of a circle = 32π
Hence, the correct answer would be an option (B).
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combine 3 times j and 16 is 7 times j
Answer:
19 times j
Step-by-step explanation:
To combine 3 times j and 16 is 7 times j, we can add the two expressions together:
3 times j + 16 is 7 times j = (3 + 16) times j = 19 times j
Therefore, the combined expression is 19 times j.
At the city museum, child admission is $5.20 and adult admission is $9.70. On Thursday, 142 tickets were sold for a total sales of $1107.40. How many child tickets were sold that day?
Answer:
Step-by-step explanation:
To be honest I would help but I can't. Although the question looks familiar
FILL IN THE BLANK. a _______ random variable has either a finite or a countable number of values.
A Discrete random variable has either a finite or a countable number of values.
Exploring Discrete Random VariablesA discrete random variable is a random variable that is capable of taking on only a finite or countable number of distinct values. This means that the possible values of the random variable can be listed out, such as 1, 2, 3, 4, and so on.
Discrete random variables are commonly used in statistics to describe situations where the possible outcomes can be counted, such as the number of heads in a series of coin flips, or the number of students in a class.
Discrete random variables can take on either discrete values (such as integers) or continuous values (such as real numbers). They are often used to model a process that is composed of a finite number of distinct steps, such as a multiple choice test with a fixed set of questions and answers.
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Jonah needs to determine the dimensions of a rectangular poster that will cover an area represented by
7x² + 3x - 10. Which of the following expressions is equivalent to the area of the rectangular poster?
A (x+1)(7x-10)
B (x-1)(-7x+10)
C(x-1)(7x+10)
D(x-7)(x+10)
E(7x-1)(x+10)
Answer:
The correct answer is A (x+1)(7x-10).
Step-by-step explanation:
To determine the dimensions of a rectangular poster that will cover an area represented by 7x² + 3x - 10, we need to find the factors of the expression 7x² + 3x - 10 that will give us the length and width of the poster.
One way to do this is to factor the expression 7x² + 3x - 10 using the difference of squares method. We can write the expression as follows:
7x² + 3x - 10 = (7x² + 3x) - 10
To factor (7x² + 3x) - 10, we can write the expression as the difference of squares:
(7x² + 3x) - 10 = (7x² + 3x + 10) - (10 + 10)
To simplify the expression, we can complete the square for the terms in parentheses:
(7x² + 3x + 10) - (10 + 10) = (7x² + 3x + 10) - 20
To complete the square, we need to add and subtract the square of half the coefficient of the x term, which is (3/2)² = 9/4. We can rewrite the expression as follows:
(7x² + 3x + 10) - 20 = (7x² + 3x + 10 + 9/4) - (20 - 9/4)
To simplify the expression, we can factor the terms in parentheses:
(7x² + 3x + 10 + 9/4) - (20 - 9/4) = [(7x² + 3x + 10 + 9/4) - (20 - 9/4)]
To simplify the expression further, we can factor out a common factor:
[(7x² + 3x + 10 + 9/4) - (20 - 9/4)] = (x + 1)(7x - 10)
From the given options, the expression that represents the area of the rectangular poster is (x+1)(7x-10), which is equivalent to 7x² + 3x - 10. We can verify this by multiplying (x+1)(7x-10) to get 7x² + 3x - 10. Therefore, the correct answer is A (x+1)(7x-10).
Solve no. 8 and no.9
Answer:
8. 1.5
9 (a) $90
(b) $510
Step-by-step explanation:
8.
[tex]\frac{1}{4} - \frac{2x-7}{8} = \frac {x}{2}[/tex]
Multiply all by 8
[tex]2 - (2x-7) = 4x\\2 - 2x + 7 = 4x\\9 = 4x + 2x\\9 = 6x\\\frac{9}{6} = x\\1.5 = x[/tex]
9. (a)
x = cost of one DVD
Since, a blue-ray disc is equal to 2 DVD minus by 10 dollar, then a blue-ray disc = (2x-$10)
$ 610 = 3x + 2(2x - $10)
$ 610 = 3x + 4x - $ 20
$ 610 + $ 20 = 7x
$ 630 = 7x
Divide both side by 7
x = $ 90
Thus, one DVD cost $ 90.
(b)
Blue-ray disc cost = (2x - $10)
3 Blue-ray disc cost = 3(2x - $10)
= 6x - $30
Replace x with $90, since x = $90
= 6 ($90) - $30
= $ 540 - $30
= $510
Solve for x. Round to the nearest tenth.
The value for x is 25.5 units.
What are the Basic Trigonometry Formulas?
Basic trigonometry formulas are used to find the relationship of trig ratios and the ratio of the corresponding sides of a right-angled triangle. There are basic 6 trigonometric ratios used in trigonometry, also called trigonometric functions- sine, cosine, secant, co-secant, tangent, and co-tangent, written as sin, cos, sec, csc, tan, cot in short.
We have,
Perpendicular side = 18
Hypotenuse side = x
θ = 90/2 = 45°
sinθ = Perpendicular side/Hypotenuse side
sinθ = 18 / x
sin(45°) = 18 / x
1/√2 = 18 / x
x = 18 *√2
x = 25.4558
x = 25.5
Hence, the value for x is 25.5 units.
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In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. the equation was y=10+0.9x where y is the final exam score and x is the score on the first test. Bill scored a 90 on the first test and his residual was -2. what was his score on the final exam?
a. 89
b. 91
c. 93
d. 90
e. not enough information
Answer:
E
Step-by-step explanation:
Based on the given linear regression equation, Bill's score on the final exam would be calculated as follows:
y = 10 + 0.9 * 90 = 98
What is x?
100^(2x)=1000^(x+6)
Answer:
x = 18
Step-by-step explanation:
You apply the exponent rules
4x = 3 (x + 6)
Then you solve 4x =3 (x + 6)
Which gives you 18
i need the answer to this math problem what's the answer to g(4) =
Step-by-step explanation:
Incomplete problem...
a researcher is interested in the issue of cheating on college campuses. she conducts an anonymous survey about cheating among college freshmen. one survey group included freshmen who live on campus, and the other survey group included freshmen who live off-campus. the standard error formula for the difference between sample proportions is. calculate the standard error for a survey comparing proportions of cheating of freshmen living on campus to freshmen living off campus, where p1
Standard error for sample proportion = √{[p₁/p₂(1-p₁/p₂)]/2}
What means standard error?
Standard error is a statistical statement that express the accuracy of an estimation resulting from survey study. It indicates how much a sample means is differ from actual population mean.
How to calculate standard error?
We calculate standard error for the two-survey group by using the following formula.
√[p(1-p)/n]
p is the proportion of freshmen living on campus to the freshmen living off campus
p = p₁/p₂
According to the given question:
p₁ = freshmen living on campus
p₂= freshmen living off campus
n= number of survey group
n=2
hence, standard error =√{[p₁/p₂(1-p₁/p₂)]/2}
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Dagne meaure and find that he can do a vertical jump that i 27. 5% of her height. If Dagne can jump 13. 2 inche, how tall, in inche, i he?
The total height of Dange after calculation from the given data is 48 inches.
Let x be the Dange's height ,
then,
27.5% of x = 13.2
x = 13.2*100 / 27.5
x = 48 in
Therefore , he is 48 inch tall.
A value or ratio that can be expressed as a simple fraction of 100 is known as a percentage.
To obtain a percentage we just need to divide it by 100 and then multiply the obtained result by 100.
As a result, the proportion refers to a component per 100. Percentage is denoted as a portion of 100 of something.
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Find the measure of each angle indicated
A. 69 degrees
B. 110 degrees
Help!!!
Answer:
It's 111 degrees
Step-by-step explanation:
The unknown angle is alternating with the 111 degrees angle
a data display showing the number of children per household in the us is strongly skewed right. the mean number of children per household is 3. what is a possible value for the median? check all that apply.
If the data display is strongly skewed right, it means that there are relatively more households with a higher number of children compared to households with a lower number of children. This means that the median value is likely to be higher than the mean value of 3 children per household.
Possible values for the median could be 4, 5, or even higher. It is not possible to determine the exact value of the median without more information about the distribution of the data. However, it is reasonable to assume that the median could be 4 or 5 children per household in this case.
In quantitative research, what is data display?The use of visual representations to organize, summarize, simplify, or alter data aids in the presenting of judgments and conclusions. Data visualizations like matrices and networks are frequently used to improve data analysis; they are more frequently found in quantitative research than in qualitative ones.
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Answer:
A) 0
B) 1
C) 3
Step-by-step explanation:
edge 2023
A scuba diver used the expression below to describe his position in relation to sea level.
2 + (negative 20) + 8
Which statement could describe the diver’s movements?
Answer: The diver descended 20 meters below sea level and then ascended 8 meters.
Step-by-step explanation: The expression 2 + (-20) + 8 describes the diver's movements in relation to sea level. The first number, 2, represents the diver's initial position at sea level. The second number, -20, represents the diver's descent below sea level by 20 meters. The third number, 8, represents the diver's ascent back up to sea level. This can be interpreted as the diver starting at sea level, descending 20 meters below sea level, and then ascending 8 meters back up to sea level.
Austin is going to see a movie and is taking his 5 kids. Each movie ticket costs $14
and there are an assortment of snacks available to purchase for $5 each. How much
total money would Austin have to pay for his family if he were to buy 7 snacks for
everybody to share? How much would Austin have to pay if he bought a snacks for
everybody to share?
Total cost with 7 snacks:
Total cost with a snacks:
The total amount Austin to pay if she were to buy 7 snacks for everybody to share is $119.
What is a numerical expression?
Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.
Here, we have
Given,
Austin is going to see a movie and is taking his 5 kids.
Each movie ticket costs $14 and there is an assortment of snacks available to purchase for $5 each.
The total amount Austin to pay if he were to buy 7 snacks for everybody to share is,
= (14×7) + (3×7)
= 98 + 21
= $119
Hence, the total amount Austin to pay if she were to buy 7 snacks for everybody to share is $119.
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With sales tax, it costs $94.83 to
buy an $87 silver ring. What is the
sales tax percentage?
Answer: 9%
Step-by-step explanation:
First, take 94.83 divided by 87, then times 100% = 109%
Then take 109 -100 = 9%
So the sales tas percentage is 9%
Mary plants roses in 1/4 of her garden. She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. What fraction of Mary's garden has tulips?
need help with problem!
Whats the problem put a proper question
Braden knows how to sing 6 vocal pieces, thanks to his choir class. Now he's about to start
private lessons. His teacher says he will learn 1 new piece each week.
Write an equation that shows the relationship between the number of weeks Braden takes
voice lessons, x, and the number of pieces he knows, y.
y =
The equation that shows the relationship is y = 6 + x
How to determine the equation that shows the relationship?From the question, we have the following parameters that can be used in our computation:
Initial number of pieces = 6
Additional number of pieces per week = 1
The equation that shows the relationship is represented as
Number of pieces = Initial number of pieces + Additional number of pieces per week * Number of weeks
Substitute the known values in the above equation, so, we have the following representation
Number of pieces = 6 + 1 * Number of weeks
So, we have
Number of pieces = 6 + Number of weeks
Using the representations:
The number of weeks Braden takes voice lessons, x, The number of pieces he knows, y.We have
y = 6 + x
Hence, the equation is y = 6 + x
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what would be the null and alternative hypothesis for testing to see if there is a relatonsip between age and opinion for the question asked by gallup
The null and alternative hypothesis for testing to see if there is a relatonsip between age and opinion for the question asked by gallup is Divorce Opinions and Gender I.
We introduce the results of a
May 2010 Gallup poll of 1029 US adults. When asked if they view divorce as “morally acceptable”,
71% of the men and 67% of the women in the sample responded yes. In the test for a difference in
proportions, a randomization distribution gives a p-value of 0.165. Does this indicate a significant
Solution
If we use a 5% significance level, the p-value of 0.165 is not less than α = 0.05 so we would not
reject H0 : pf = pm. This means the data do not show significant evidence of a difference in the
proportions of men and women that view divorce as “morally acceptable”
Solution
(a) The p-value (0.003) is small so the decision is to reject H0 and conclude that the mean recall
for sleep (¯xs = 15.25) is different from the mean recall for caffeine (¯xc = 12.25). Since the mean
for the sleep group is higher than the mean for the caffeine group, we have sufficient evidence to
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