Using the relationship of distance, time and speed, the speed of the boat in still water is 8mi/hr
What is the speed of the boat in still water?To determine the speed of the boat in still water, we can write an equation to represent this.
The speed as it travels upstream = x - 2
The speed as it travels downstream = x + 2
The total distance travelled by the boat = 15 + 15 = 30mi
Let's write an equation to represent this;
15/(x - 2) + 15/(x + 2) = 4
simplifying this;
15(x + 2) + 15(x - 2) = 4(x - 2)(x + 2)
15x + 30 + 15x - 30 = 4x² - 16
30x = 4x² - 16
4x² - 30x - 16 = 0
Solving for x;
x = -0.5, 8
But since the speed can't be negative, the speed is 8 mi/hr
Learn more on speed here;
https://brainly.com/question/26046491
#SPJ1
Sonji went to a sandwich shop for lunch with 8 of her friends. Part of the group ordered only a sandwich for $5, and the
rest of the group ordered à combo for $8. The bill for all 9 people totaled $66.00. Which system of equations represents
the number of meals of each type that Sonji and her friends purchased?
Answer:
x+y=9
5x+8y=66
Step-by-step explanation:
Calculate the area of a circle 4ft ,2in,18ft,5.2in,7.3in,14cm,9m,3m,9.2cm,7m,5m,6m
Answer:
Step-by-step explanation:
It seems like you have provided multiple measurements for the radius of the circle. I'm sorry, but a circle can only have one radius, so I am not able to calculate its area with the given information.
Please provide the correct measurement for the radius of the circle, and I will be happy to help you calculate its area.
Someone help I have no idea how to do this, it would help if I could get a step by step
Answer: x=3
Step-by-step explanation:
shaded part is 5/6 of the full circle, so just make an equation.
5/6 pi r^2(formula to find area)=15/2 pi(area given)
cancel out pi and simplify
r^2=9
r=+-3 but cant be negative so r=3
A boy has 30 spellings to learn.
12 words included an 5, 16 a T and 18 an E.
10 words had an E and a T, 6 words had an Sand aT and 5 words had an E and an S.
4 words had all three.
Probability that?
A • the first two spellings in the test both included only one of the three letters?
C• the first two spellings in the test both had an E and at least one other letter
Answer:
A
Step-by-step explanation:
a couple decides to keep having children until they have a girl, at which point they will stop having children. they also agree to having a maximum of 3 children. the table shows the probability distribution of X=the number of children such a couple would have.
From the discrete distribution given, the standard deviation is of 0.83 children.
How to solveThe distribution is:
P(X=1) =0.5
P(X=2) =0.25
P(X=3) =0.25
The mean is 1.75.
The standard deviation is the square root of the sum of the difference squared between each value and the mean, multiplied by it's respective probability.
Hence:
The standard deviation is 0.83 children.
Read more about Standard deviation here:
https://brainly.com/question/24298037
#SPJ1
The point (3,b) lies on the circle with radius 8 and center (−2,−1). What are the possible values of b
The point (3,b) can lie on the circle with radius 8 and center (-2,-1) for values of b equal to -1 + √39 and -1 - √39.
We know that the circle with radius 8 and center (-2,-1) has the equation:
(x + 2)² + (y + 1)² = 8²
Substituting x = 3 and y = b, we get:
(3 + 2)² + (b + 1)² = 8²
Simplifying, we get:
25 + (b + 1)² = 64
(b + 1)² = 39
Taking the square root of both sides, we get:
b + 1 = ± √39
Therefore, the possible values of b are:
b = -1 ± √39
To learn more about circle click on,
https://brainly.com/question/27138240
#SPJ1
f ( x ) = 12 ( 7 ) x using base e
HELP ASAP PLEASE 20 POINTS!!
The calculated value of the surface area of the cylinder is 138π square inches
Calculating the surface area of the cylinderFrom the question, we have the following parameters that can be used in our computation:
Height, h = 5 1/2 inches
Diameter, d = 12 inches
Using the above as a guide, we have the following:
SA = 2πr(r + h)
Where
Radius, r = d/2
r = 12/2
r = 6
Substitute the known values in the above equation, so, we have the following representation
SA = 2 * π * 6(6 + 5 1/2)
Evaluate
SA = 138π
Hence, the surface area of the cylinder is 138π square inches
Read more about surface area at
brainly.com/question/16519513
#SPJ1
Hurry I’m running out of time helpppppp
Trey's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make aluminum balls that have a radius of 7.5 in. If
aluminum costs $0.12 per in, how much will the aluminum cost to make one ball?
Use 3.14 for x, and do not round your answer.
Thus, Cost of making 1 solid aluminium ball is found as $211.95.
Explain about the spherical shape:Something spherical is similar to a sphere in three dimensions in that it is round, or somewhat round. Even though they are never exactly round, oranges and apples are both spherical. Since an asteroid is frequently spheroidal—nearly round but lumpy—it has an approximately spherical form.
radius of solid aluminium balls r = 7.5 in.
Cost of of aluminium = $0.12 per cu. in.
Volume of sphere = 4/3 * π * r³
Volume of sphere = 4/3 * 3.14 * 7.5³
Volume of sphere = 1766.25 cu. in.
Cost of making 1 solid aluminium ball = 0.12 * 1766.25
Cost of making 1 solid aluminium ball = $211.95.
Thus, Cost of making 1 solid aluminium ball is found as $211.95.
Know more about the spherical shape:
https://brainly.com/question/10171109
#SPJ1
Someone please help!! (20 POINTS!)
Answer: C
Step-by-step explanation: Rise/run so 1/1=1 but it's going down so it negative. -1
Help with solving This graph
Answer:
r=4
center: (-2,4)
Step-by-step explanation:
The equation of a circle is:
(x-h)²+(y-k)²=r²
(h,k) would be the center of the circle and r would be length of the radius
To find r, we simply take the square root of 16, which would be 4
And the center is given in the equation
Which is equivalent to 234 2/5
234 2/5 is equivalent to 1172/5.
234 2/5 is a mixed number, which means it is a combination of a whole number and a fraction.
To convert it to an improper fraction, we need to multiply the whole number by the denominator of the fraction and add the numerator.
The result becomes the new numerator, and the denominator stays the same.
In this case, we have:
234 2/5 = (234 x 5 + 2) / 5
= 1172/5
Therefore, 234 2/5 is equivalent to 1172/5 as an improper fraction.
Learn more about Mathematical operations here:
https://brainly.com/question/20628271
#SPJ1
What is the absolute value of 1/8 
Answer:
1/8
Step-by-step explanation:
The absolute value of positive numbers (decimals, fractions, etc.) is the same number. The absolute value of negative numbers (decimals, fractions, etc.) is the same, but positive.
What is Absolute value?
Absolute value is a set of lines that if any number is placed in it, the number would be positive
Absolute signs: | |
Examples:
|-6|= 6 (Absolute value of -6 is 6)
|9|=9 (Absolute value of 9 is 9) (Because 9 is already positive)
Your Question
Since 1/8 is already positive, the absolute value of it would just be 1/8
Please feel free to ask questions
evaluate the expression
After substituting the values as x=3 and y=7, the value of the expression "2x²-y¹+3x⁰" is 14.
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified or evaluated to a numerical value.
To evaluate the expression 2x²-y¹+3x⁰ for x=3 and y=7, we substitute the given values, which are x=3 and y=7 into the expression and simplify:
On substituting the values,
We get,
= 2x² - y¹ + 3x⁰
= 2(3)² - 7¹ + 3(1)
= 2(9) - 7 + 3
= 18 - 7 + 3
= 14
Therefore, when x=3 and y=7, the value of the expression 2x²-y¹+3x⁰ is 14.
Learn more about Expression here
https://brainly.com/question/1041084
#SPJ1
Select all the correct answers.
If the measure of angle 0 is 2n/3, which statements are true?
The statements that are true are ;
1. tan(tetha) = -√3
2. the measure of the reference angle is 60°
What is trigonometric function?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
The value of each angle depends on the quadrant it falls on.
First quadrant = 0-90°
second quadrant = 91° -180°
third quadrant = 181-270°
fourth quadrant = 271° - 360°
pi is measurement of angle in radians which is equivalent to 180°
therefore;
2π/3 = 2 × 180/3 = 360/3
= 120°
120 falls on the second quadrant,
tan60 = √3
tan 120 = -√3
the reference angle is 60° i.e
180-120 = 60°
learn more about trigonometric functions from
https://brainly.com/question/25618616
#SPJ1
Suppose that the local government of Corpus Christi decides to institute a tax on soda consumers. Before the tax, 30 million liters of soda were sold every month at a price of $11 per liter. After the tax, 25 million liters of soda are sold every month; consumers pay $14 per liter (including the tax), and producers receive $6 per liter.
The amount of the tax on a liter of soda isper liter. Of this amount, the burden that falls on consumers isper liter, and the burden that falls on producers isper liter.
True or False: The effect of the tax on the quantity sold would have been larger if the tax had been levied on producers.
True
False
False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.
What is Algebraic expression ?
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.
The tax incidence (the division of the burden of a tax between buyers and sellers) does not depend on which side of the market the tax is levied on, but rather on the relative elasticities of supply and demand. In this case, we don't have information about the elasticities of supply and demand, so we cannot determine the tax incidence. However, we can infer that the tax on consumers did reduce the quantity sold (from 30 million liters to 25 million liters), so it's unlikely that a tax on producers would have had a larger effect.
Therefore, False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.
To learn more about Algebraic expression from given link.
https://brainly.com/question/31238826
#SPJ1
Solve for x, in terms of y: 23 x + 15 y = 2
MAKE BRAINLYST AND 100
To solve for x in terms of y in the equation 23x + 15y = 2, we can start by isolating the term with x on one side of the equation. We can do this by subtracting 15y from both sides of the equation to get 23x + 15y - 15y = 2 - 15y, which simplifies to 23x = 2 - 15y.
Next, we can solve for x by dividing both sides of the equation by 23 to get 23x/23 = (2 - 15y)/23, which simplifies to x = (2 - 15y)/23.
Therefore, the solution for x in terms of y is x = (2 - 15y)/23.
Please need answer 17.
Answer:
sec(θ) = √10/3tan(θ) = 1/3Step-by-step explanation:
You want the tangent and secant of the angle θ the line x-3y=0 makes with the negative x-axis.
Trig functionsThe relations between the angle and its trig functions are ...
Tan = Opposite/Adjacent
Sec = Hypotenuse/Adjacent
Unit circleWe have shown the angle of interest in a unit circle with the "adjacent" side equal to the radius of the circle (1). Then the values of interest are ...
tan(θ) = opposite side = 1/3 . . . . . . . equal to the slope of the line
sec(θ) = hypotenuse = √(1 +(1/3)²) = √(10/9) = (√10)/3
The tangent is 1/3; the secant is (√10)/3.
__
Additional comment
A third-quadrant angle measured from the +x axis has a negative secant. The tangent is positive there.
Since this angle is measured from the -x axis, it isn't clear whether it is supposed to be considered a 3rd-quadrant angle or not. For the given acute angle θ shown, the trig functions are both positive. YMMV
2raised to power m-3 = 1
Answer:
m = 3
Step-by-step explanation:
Given:
[tex]2^{m-3}[/tex] = 1
Take the logarithm of both sides (logarithm of 1 is 0):
m - 3 = 0
Add 3 to both sides:
m - 3 + 3 = 0 + 3
m = 3
Hence, m = 3.
Logarithm is the power to which a number must be raised in order to get some other number. For example:
The base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. Meaning [tex]10^{2}[/tex] = 100.What are the roots of the quadratic equation below?
2x² + 8x+7= 0
O A. x = = 2√2
1
O B. x =
-8+√120
8
O
O D. x =
C. x = = 4+√/²
-2+√120
Answer:
Step-by-step explanation:
c
what is the answer? compute the following integral.
The integral for this problem has the result given as follows:
[tex]\int_2^5 -8f(x) dx = 168[/tex]
How to solve the integral?The integral over the largest region for this problem is given as follows:
[tex]\int_2^9 f(x) dx = -14[/tex]
The integral can be divided into two smaller regions, as follows:
[tex]\int_2^9 f(x) dx = \int_2^5 f(x) dx + \int_5^9 f(x) dx[/tex]
Hence the integral from x = 5 to x = 9 is given as follows:
[tex]-14 = \int_2^5 f(x) dx + 7[/tex]
[tex]\int_2^5 f(x) dx = -21[/tex]
Multiplying -21 by -8, the result of the integral is given as follows:
[tex]\int_2^5 -8f(x) dx = 168[/tex]
More can be learned about integrals at https://brainly.com/question/22008756
#SPJ1
In a sample of 1000 adults, 150 said they are very confident in the nutritional information on restaurant menus. for us adults are selected at random without replacement.
Find the probability that none of the four adults are very confident in the nutritional information on the restaurant menus.
The probability that none of the four adults is very confident in the nutritional information on the restaurant menus is 0.208 or approximately 20.8%.
Ready to approach this issue by utilizing the hypergeometric conveyance, since we are examining without substitution from a limited populace of two sorts (those who are exceptionally sure and those who are not exceptionally sure).
Let X be the number of grown-ups in a sample of 4 who are not exceptionally sure about the wholesome data on eatery menus.
At that point, X takes after a hypergeometric dissemination with parameters N = 1000, n = 4, and K = 850 (since 850 grown-ups are not exceptionally certain).
The likelihood that none of the 4 grown-ups are exceptionally certain can be communicated as:
P(X = 4) = (K select 4) / (N select 4)
where (K select 4) speaks to the number of ways to select 4 grown-ups from the population of 850 who are not exceptionally sure,
and (N select 4) speaks to the entire number of ways to select 4 grown-ups from the populace of 1000.
Utilizing the equation for binomial coefficients, ready to disentangle this expression as:
P(X = 4) = [(850*849*848*847) / (4*3*2*1)] / [(1000*999*998*997) / (4*3*2*1)]
= 0.208
Hence, the likelihood that none of the four grown-ups are exceptionally certain within the wholesome data on eatery menus is 0.208 or approximately 20.8%.
To know more about probability refer to this :
https://brainly.com/question/24756209
#SPJ1
Match the line described on the left with the slope of the line on the right.
x=-3 , 6x-3y=18 , the line through (7,5) and (8,5) , the line through (4,-2) and (1,7)
Undefined -3 , 0 , 2
The Slope of x = -3 is undefined; 6x-3y=18 is 2; (4,-2) and (1,7) is -3; and (7,5) and (8,5) is 0.
What is the Slope of a Line?Slope of a line (m) = rise/run = change in y / change in x
Note that the slope of vertical lines are always undefined.
Therefore, we have the following:
x = -3 represents the equation of a vertical line, therefore, the slope is undefined.
6x - 3y = 18 is rewritten as y = 2x - 6 in slope-intercept form. The slope is 2.
For (4,-2) and (1,7):
Slope (m) = (7 -(-2))/(1 - 4) = 9/-3 = -3
For (7,5) and (8,5):
Slope (m) = 5 - 5/8 - 7 = 0/1 = 0
Learn more about the Slope of a line on:
https://brainly.com/question/24907633
#SPJ1
What is the least common dominator of 4/13 and 4/5?
Answer:
52 is the least common dominator
Answer:
52/65
Step-by-step explanation:
The same fraction we can express in many different forms. If the numerator and denominator ratio is the same, the fractions represent the same rational number.
The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their least common multiple
The method of calculating the LCD is the same as the calculation least common multiple of fractions denominators.
The simple method for common computing denominators (not least at all) is to multiply all denominators.
Students in a math class recorded the number of text messages they received the previous day. How many students received at least 10 messages? Number of text messages line plot from 0 to 25 by fives. 5 has 2 marks, 10 has 3 marks, 15 has 2 marks, 20 has 4 marks, and 25 has 5 marks. 14 students 11 students 3 students 2 students
Answer:
Step-by-step explanation:
same goes 4 him i though he loved me but 10 =5x2
5.
Andre is playing a new card game. This game uses 4 sets of cards:
green, blue, yellow, and red. Each set has 15 cards numbered from
1 to 15. Select all of the actions that have more than 4 possible
outcomes. 7.SP.8, 7.SP.8b
0
selecting a blue card less than 5
selecting a red card greater than 13
selecting a yellow 12 card
selecting an 8 or 9 card of any color
selecting an even-numbered green card greater than 4
selecting a yellow card greater than 4²
selecting a blue card that is a multiple of 3
The actions that have more than 4 possible outcomes are:
- Selecting an 8 or 9 card of any color (each set has 2 cards for a total of 8 possible outcomes)
- Selecting a yellow card greater than 4² (there are 7 yellow cards that meet this criteria)
- Selecting a blue card that is a multiple of 3 (there are 5 blue cards that meet this criteria)
Therefore, only three of the given actions have more than 4 possible outcomes.
Is AB perpendicular to CD? Explain? pls yall fwm on the answer
Answer: No
Step-by-step explanation: They are not perpendicular due to the slopes. Perpendicular will have the same slopes value wise, but one is negative and one positive.
how many times greater is 4x10^2 than 10^4
Answer:
well 10^4 is 10000, and 4x10^2 is 1600 and if we divide 10000 by 1600 we can find out how many times greater 10000 is than 1600, and the anwser is 6.25
Step-by-step explanation:
In the coordinate plane, the point X (-1, 0) is translated to the point X' (3, 1). Under the same translation, the points Y (2, 3) and Z (1, -2) are translated to Y' and Z', respectively. What are the coordinates of Y' and Z'?
The coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).
To find the coordinates of Y' and Z', we need to apply the same translation that maps X to X'.
We know that the vector that connects X to X' is (3 - (-1), 1 - 0) = (4, 1).
So, to translate Y to Y', we add the vector (4, 1) to the coordinates of Y:
Y' = Y + (4, 1)
= (2, 3) + (4, 1)
= (6, 4)
Similarly, to translate Z to Z', we add the vector (4, 1) to the coordinates of Z:
Z' = Z + (4, 1)
= (1, -2) + (4, 1)
= (5, -1)
Therefore, the coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).
Learn more about translation here
https://brainly.com/question/29080541
#SPJ1
5. Un tanque contiene 9 litros de agua si se abre el grifo que vierte tres litros de agua por minuto y y es la cantidad de agua (en litros), que hay en el tanque después de x minutos
The equation that models the amount of water in the tank after x minutes is:
y = -3x + 9
How many liters are there after x minutes?We know that the tank contains 9 liters of water, and it loses water at a constant rate of 3 liters per minute.
Then we can model the amount of water y in the tank after x minutes with a linear equation where the y-intercept is 9 and the rate of change is -3 (the amount it loses per unit of x)
Then the equation is:
y = -3x + 9
Learn more about linear equations at:
https://brainly.com/question/1884491
#SPJ1
