Answer:
rate of motorboat: b
rate of current: c
So the rate the boat travels upstream is $b - c$, and the rate it travels downstream is $b + c$
Step-by-step explanation:
d = rt
200 = (b - c)\cdot 5
200 = (b + c)\cdot 4
b - c = 40
b + c = 50
Adding these equations, we get:
2b = 90
b = 45
So
c = 50 - 45 = 5
Therefore the rate of the boat is 45kph, and the rate of the current is 5kph
Hope this helps :)
Final answer:
The boat has a speed of 45 mph in still water, and the current runs at 5 mph. By using the given times and distances for upstream and downstream travel, we can set up equations to solve for the boat's speed and the current's speed.
Explanation:
To find the rate of the boat in still water and the rate of the current, let's denote the boat's speed in still water as b and the speed of the current as c. When the boat goes upstream, its effective speed is b - c, and when it goes downstream, its effective speed is b + c. We can translate this into two equations based on the information given:
(b - c) × 5 hours = 200 miles (upstream)
(b + c) × 4 hours = 200 miles (downstream)
By dividing the distance by the time, we can solve for the effective speeds upstream and downstream.
b - c = 200 miles / 5 hours = 40 mph
b + c = 200 miles / 4 hours = 50 mph
Add these two equations:
2b = 90 mph
b = 45 mph (boat's speed in still water)
Next, subtract the first equation from the second:
2c = 10 mph
c = 5 mph (current's speed)
So, the boat has a speed of 45 mph in still water, and the current has a speed of 5 mph.
Point O is the center of the circle. Circle O is shown. Tangents D C and B C intersect at point C outside of the circle. Lines are drawn from points D and point B to center point O to form a quadrilateral. A line is drawn from point C to point A on the opposite side of the circle. The length of O D is 6, and the length of B C is 8. Angles D and B are right angles. What is the perimeter of quadrilateral DOBC?
Answer:
The perimeter is 28 (6 plus 8=14 14x2= 28)
Step-by-step explanation:
Plz mark brainliest!
The perimeter of quadrilateral DOBC that forms two right triangles is: 28 units.
What are Congruent Right Triangles?Based on the tangent theorem, triangles ODC and OBC are right triangles that are congruent. Therefore, their corresponding side lengths are equal.
Perimeter of quadrilateral DOBC = OB + DO + BC + CD = 6 + 6 + 8 + 8
Perimeter of quadrilateral DOBC = 28 units.
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Scientists can measure the depths of craters on the moon by looking at photos of shadows. The length of the shadow cast by the edge of a crater is 500 meters. The angle of elevation of the rays of the Sun is 55∘. Estimate the depth d of the crater to the nearest tenth.
Answer:714.1
Step-by-step explanation:
500 times tan(55)
We can use the tangent function from trigonometry to estimate the depth of the crater. The depth is approximately 714.1 meters when the length of the shadow is 500 meters and the angle of sun elevation is 55 degrees.
Explanation:To solve this problem, we can use trigonometry, specifically the tangent function. The tangent function of an angle in a right triangle is equal to the ratio of the opposite side over the adjacent side. Here, the shadow length of the moon's crater functions as the adjacent side, and the depth of crater is the side opposite to the angle.
So tangent(55°) = depth / 500 meters.
To find the depth, rearrange the equation to multiply both sides by 500: depth = 500 * tangent(55°).
Using a calculator, you'll find that the tangent of 55° is approximately 1.4281. So then your final depth equation would look like: depth = 500 meters * 1.4281. By doing this calculation, we find depth ≈ 714.05 meters, and rounding this to the nearest tenth, we have 714.1 meters. So the estimated depth of the crater is 714.1 meters.
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The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are semi-circles. What is the volume, in cubic units, of the solid?
Answer:
Option b) [tex]18\pi[/tex] is correct∴ the volume of the solid is [tex]A(x)=18\pi[/tex] cubic unitsStep-by-step explanation:
Given that the base of a solid is the circle [tex]x^2 + y^2 = 9[/tex] and Cross sections of the solid perpendicular to the x-axis are semi-circles.
To find the the volume of the solid in cubic units:We know that the cross sections are semicircles with the diameter in the given circle [tex]x^2 + y^2 = 9[/tex]
That is we have to find the formula for the area of any semicircle perpendicular to x-axis, and integrate it from -3 to 3.
Now the area of a semicircle is
[tex]A=\frac{\pi r^2}{2}[/tex] cubic units
Let r = y and [tex]y^2=9-x^2[/tex]
Then area of the semicircle crossing the x-axis at x is given by
[tex]A(x)=\frac{1}{2}\pi y^2[/tex] cubic units
[tex]=\frac{1}{2}\pi(9-x^2)[/tex]
Now we can find the definite integral of A(x) from x = -3 to x = 3.
Since A(x) is an EVEN function then the definite integral of A(x) from x = -3 to x = 3 is the same as twice the integral of A(x) from x = 0 to x = 3.
We have that
[tex]A(x)=2(\int_0^3 \frac{1}{2}\pi(9-x^2))dx[/tex]
[tex]=2(\frac{\pi}{2}[9x-\frac{x^3}{3}]_0^3)[/tex]
[tex]=\pi[9(3)-\frac{3^3}{3}-9(0)-(-\frac{0^3}{3})][/tex]
[tex]=\pi[27-\frac{27}{3}][/tex]
[tex]=\pi[27-9][/tex]
[tex]=\pi[18][/tex]
[tex]=18\pi[/tex]
∴ option b) [tex]18\pi[/tex] is correct∴ the volume of the solid is [tex]A(x)=18\pi[/tex] cubic unitsThe volume of the solid is 18π cubic units.
The base of the solid is defined by the circle’s equation x² + y² = 9, indicating that the radius of the circle is 3 units. The cross-sections perpendicular to the x-axis are semi-circles.
To find the volume, we need to integrate the area of these semi-circular cross-sections. For a slice at a given x-coordinate, the diameter of the semi-circle is the length of the chord of the circle at that x-coordinate, which is given by 2√(9 - x²). The radius of the semi-circle is then √(9 - x²), and the area of the semi-circle is (1/2)πr².
The area of each semi-circular slice is: A(x) = (1/2)π(√(9 - x²))² = (1/2)π(9 - x²).
The volume V of the solid is obtained by integrating this area from x = -3 to x = 3:
V = ∫[from x = -3 to x = 3] (1/2)π(9 - x²) dx
This simplifies to:
V = (π/2) ∫[from x = -3 to x = 3] (9 - x²) dx
We solve the integral:
V = (π/2) [9x - (x³ / 3)] (from x = -3 to x = 3)
Evaluating this, we get:
V = (π/2) [(9×3 - (3³ / 3)) - (9×(-3) - ((-3)³ / 3))]
V = (π/2) [(27 - 9) - (-27 + 9)]
V = (π/2) [18 + 18]
V = (π/2) 36
V = 18π
Thus, the volume of the solid is 18π cubic units.
NEED HELP
8x + √1 - √9y - √9x^2
5x + 3√y + 1
5x - 3√y - 1
5x - 3√y + 1
Answer:
Last one: 5x - 3√y + 1
Step-by-step explanation:
8x + √1 - √9y - √9x^2
8x + 1 - 3√y - 3x
5x + 1 - 3√y
5x - 3√y + 1
Answer:Answer:
Last One: 5x - 3√y + 1
Step-by-step explanation:
8x + √1 - √9y - √9x^2
8x + 1 - 3√y - 3x
5x + 1 - 3√y
5x - 3√y + 1
Step-by-step explanation:
A rectangle has a length of 6 feet and a width of 4 feet. The perimeter of the rectangle can be found using the equation =2×6+2×4. Which equation can also be used to find the perimeter of the rectangle?
Answer:
The correct answer is perimeter is given by 2 × ( l + w), where l is the length and w is the width of the rectangle.
Step-by-step explanation:
A rectangle has a length of 6 feet and a width of 4 feet. The perimeter of the rectangle can be found using the equation =2×6+2×4.
Let l be the length and w be the width of a rectangle.
Since there four sides of a rectangle, the perimeter is given by adding all the sides.
Therefore perimeter of the rectangle is given by l + l + b + b = 2×l +2×w = 2 × ( l + w).
The equation given by 2 × ( l + w) can also be used to find the perimeter of any given rectangle.
The perimeter of a rectangle is found by using the formula P = 2l + 2w, where P is the perimeter, l is the length and w is the width. Use the formula and operations of equations to fill in the missing information on the table below. Complete your work in the space provided. Include the entire process for completing the table.
Answer:
#1: 11 cm
#2: 16.5 in
#3: 2.5 feet
Step-by-step explanation:
#1
[tex]P=2l+2w[/tex] Solve for width by substracting 2l on both sides to isolate 2w
[tex]P-2l=2w[/tex]
or
[tex]2w=P-2l[/tex]
Replace.
[tex]2w=26-2(2)\\2w=26-4\\2w=22\\w=\frac{22}{2}\\ w=11cm[/tex]
----------------------------------------------------------------------------
#2
[tex]P=2l+2w[/tex]
[tex]P=2(3.5)+2(4.75)\\P =7+9.5\\P=16.5in[/tex]
----------------------------------------------------------------------------
#3
[tex]P=2l+2w[/tex]
Solve for l
[tex]2l=P-2w\\2l=7-2(1)\\2l=7-2\\2l=5\\l=\frac{5}{2}\\ l=2.5feet[/tex]
what is the percent change of 10 feet to 6 feet
Answer:It would be a decrease of 40 percent
Step-by-step explanation:You go from 10/10 to 6/10 meaning you decrease by 4/10 and 4/10 is the same as 40/100 and anything over 100 is its percent value so you would be going down by 40%
Answer:
40 % decrease or -40%.
Step-by-step explanation:
The decrease is 10 - 6 = 4 feet.
% decrease = (4/10) * 100
= 0.4 * 100
= 40 % decrease.
Mr.Estevez got a new post mounted mail box. He dug out the old one and left a square hole and only measured one side. Mr.Estevez measured a side of 9.75cm's. What is the square area of dirt Mr. Estevez needs to fill up the hole for his new mailbox. (Round to the nearest tenth)* 0 95.1cm2 0 95.06cm2 0 95.1cm O 95.06cm
Answer:
[tex]95.1\ cm^2[/tex]
Step-by-step explanation:
we know that
A square is a quadrilateral that has four equal sides and four equal interior right angles.
The area of the square is given by the formula
[tex]A=b^2[/tex]
where
b is the length side of the square
In this problem we have
[tex]b=9.75\ cm[/tex]
substitute in the formula
[tex]A=(9.75)^2=95.06\ cm^2[/tex]
Round to the nearest tenth
[tex]A=95.1\ cm^2[/tex]
Answer:
95.06cm
Step-by-step explanation:
Hope this helps
rate of change in the equation y = 5 - 0.5x
Sam and Janet each have a whole number of dollars, and $\frac13$ of Sam's money equals $\frac12$ of Janet's money. Together, they have more than $\$10$. What is the least number of dollars they could have combined?
Answer:
$15
Step-by-step explanation:
Let Sam's Money =s
Let Janet's Money =j
[tex]$\frac13$[/tex] of Sam's money equals [tex]$\frac12$[/tex] of Janet's money.
Let n be the number of dollars held by Sam and Jane respectively
Therefore: [tex]$n=\frac13s=\frac12j$[/tex]
s=3n
j=2n
s+j=3n+2n=5n
Together, they have more than $10
Therefore:
5n>10
n>2
The least sum they could have is at n=3
At n=3
s+j=5n=5X3=$15
The least number of dollars they could have combined is $15.
In your own words, what is relative frequency?
Answer:
A frequency is the number of times a given datum occurs in a data set.
Step-by-step explanation:
Bella manages a volunteer group. The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V). It takes 20 volunteers to build a house in 63 hours. Write an equation to model this situation. Next, find how many volunteers it would take to build a house in 30 hours.
Answer:
42 Volunteers
Step-by-step explanation:
The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V).
This is written as:
[tex]V \propto \frac{1}{T} \\$Introducing the variation constant k\\V = \frac{k}{T}\\$It takes 20 volunteers to build a house in 63 hours.$\\When V=20, T=63\\V = \frac{k}{T}\\20 = \frac{k}{63}\\k=20*63=1260\\$Therefore, the equation connecting V and T is:$\\V = \frac{1260}{T}\\$When T=30 hours, we want to determine the number of volunteers needed V$\\V = \frac{1260}{30}=42\\$42 Volunteers will be needed.$[/tex]
What is the result of adding 17 to its opposite
The answer is zero (0), when you add any number to it's opposite you always get zero
Which function shows a fabric with a price of $1.25 per square yard?
Answer:
x(1.25)
Step-by-step explanation:
x is the yards.
so for example if you need 2 yards of fabric replace x with 2.
Answer:
x=1.25
Step-by-step explanation:
edgu
Write 0.06 as a fraction in
simplest form.
Answer:
[tex]\frac{3}{50}[/tex]
Step-by-step explanation:
Answer: 6/10
Step-by-step explanation:
the 6 is in the tenth place which means it is by ten
Suppose that $2000 is loaned at a rate of 11%, compounded semiannually. Assuming that no payments are made, find the amount owed after 5 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
The final value owed will be $3416.29.
Step-by-step explanation:
Since this is a compound interest problem we should use the apropriate formula given bellow:
M = C*(1 + r/n)^(n*t)
Where M is the final amount, C is the initial amount, r is the interest rate, t is the total time and n is the rate at which it is compounded. Since it's semiannually the value of n is 2 and we can use the formula to find the desired value.
M = 2000*(1 + 0.11/2)^(2*5)
M = 2000*(2/2 + 0.11/2)^(10)
M = 2000*(2.11/2)^(10)
M = 3416.29
The final value owed will be $3416.29.
How many faces dose a triangular prisim have?
Answer:
the answer is 5
Step-by-step explanation:
YW
Answer:
There are 5 faces in a triangular prism
I hope this help. If I'm wrong/made any mistakes please let me know so that I can learn from it!
What is the slope of the line that passes through the points (1, 2) and (-2, -13)?
Answer:
5
Step-by-step explanation:
To find the slope given two points, we use the formula
m= (y2-y1)/(x2-x1)
= (-13-2)/(-2 -1)
= -15/-3
=5
Answer:
The slope is 5
Step-by-step explanation:
Δ means the change in
slope = m = Δy/Δx = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{2-(-13)}{1-(-2)}[/tex] = 15/3 = 5/1 = 5
Slope = 5
x² - 12x + 27? what is the factored form of this polynomial
Answer:
( x - 9 )( x - 3 )
Step-by-step explanation:
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A truck that can carry no more than 6600 lbs is being used to transport refrigerators and upright pianos. each refrigerator weighs 300 lbs and each piano weighs 425 lbs. what is an equation that shows how many refrigerators and how many pianos the truck could carry. will 10 refrigerators and 8 pianos overload the truck?
Answer:
(a). 300r + 425p ≤ 6,600
(b). No, it’s not considered overweight
Step-by-step explanation:
In this question, we are to write an equation that shows the number of refrigerators and pianos the truck could carry.
Let the number of refrigerators be r and the number of pianos be p
By using their individual weights, the equation is as follows;
300r + 425p ≤ 6,600
To the second question, we want to consider if 10 refrigerators and 8 pianos are overload.
To get this, we simply multiply the number of each by their individual weights;
That would be;
300(10) + 425(8) = 3000 + 3,400 = 6,400 lbs
This is not considered overweight as it is less than 6,600 lbs
Coll
4/15 version of 4/7 version of M4T2 Test Review
Created by Meena Frazier
Q1: What is the distance between (2, 3) and (-2, 7)? Round to the nearest tenth, if necessary.
Answer:
The answer to your question is 5.7
Step-by-step explanation:
Data
Point A = (2, 3)
Point B = (-2, 7)
Process
To find the distance between points A and B use the formula of the distance between two points, substitute and simplify.
Formula
dAB = [tex]\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2}}[/tex]
-Identify wich is the value of x1, y1, x2, y2
x1 = 2 y1 = 3 x2 = -2 y2 = 7
-Substittion
dAB = [tex]\sqrt{(-2 - 2)^{2} + (7 - 3)^{2}}[/tex]
-Simplification
dAB = [tex]\sqrt{(-4)^{2} + (4)^{2}}[/tex]
dAB = [tex]\sqrt{16 + 16}[/tex]
dAB = [tex]\sqrt{32}[/tex]
-Result
dAB = 5.65 ≈ 5.7
In a race that consisted of three parts the cycling part was 12 1/2 miles long the running part of the race was won for the distance of the cycling parking asking part of the race was won half the distance of the running part what was the entire distance in miles of the raie
Complete question is;
In a race that consisted of three parts, the cycling part was 12 1/2 miles long. The running part of the race was 1/4 the distance of the cycling part. The kayaking part of the race was 1/2 the distance of the running part. What was the entire distance, in miles of the race?
Answer:
Total distance of race = 17.1875 miles
Step-by-step explanation:
The 3 parts of the race are; cycling, running and kayaking.
The cycling distance was; 12½ miles
We are told that the running part was ¼ of the cycling distance. Thus;
Running distance = ¼ x 12½ = ¼ x 25/2 = 25/8 miles
Lastly, we are told that the kayaking part was ½ the distance of the running part. Thus;
Kayaking distance = ½ x 25/8 = 25/16
Thus,total distance of race = cycling distance + running distance + kayaking distance = 12½ + 25/8 + 25/16 = 17.1875 miles
Express in the form 1 : n 6 : 24
Answer: n=4
Step-by-step explanation: 1:4 = 6:24
Martin has a shoe box with the dimensions 4 inches, by 6 inches, by 10 inches. He wants to determine if a relay baton inches will fit in the box. What is the longest length that the relay baton can be and still fit in the box? (Round to the nearest tenth if needed.) Your answer: 10 inches 12.3 inches 10.8 inches 7.2 inches
Answer:
10 inches.
Step-by-step explanation:
First we need to find what is the bigger dimension of the box, because the relay baton will occupy the box, and the larger dimension of the relay baton (that is, it's length) need to be less or equal than the larger dimension of the box.
The dimensions of the box are: 4 inches, 6 inches and 10 inches.
The larger dimension of the box is 10 inches. So, If we want the relay baton to fit in the box, the maximum length it can have is 10 inches.
Solve 2x^2+5x +5=0 round solutions to the nearest hundredth
Answer: i3
Step-by-step explanation:
Answer:13
Step-by-step explanation:
A car travels 218.5 miles on 9.5 gallons of gas what is the gas mileage
Answer:
23 miles per gallon
Step-by-step explanation:
Take the miles and divide by the gallons
218.5 miles/ 9.5 gallon
23 miles per gallon
Answer:
23m/g
Step-by-step explanation:
If a car travels 218.5 miles on 9.5 gallons, you can find how many miles can be traveled on one gallon.
You can make the equation 9.5g=218.5, let g be gallons of gas.
Divide by 9.5 on both sides.
g= 23
The gas mileage is 23 miles for one gallon of gas.
12.6 is what percent of 42?
If you were to flip a coin 140 times, how many times would you expect the coin to land on tails?
Answer: 70 times
Step-by-step explanation:
If you were to flip a coin 140 times you would expect it to land on tails 70 since 140 divided by 2 is 70 although coins are normally not evenly weighed meaning that it most likely not going to land evenly on both sides.
In a math class with 27 students, a test was given the same day that an assignment was due. There were 17 students who passed the test and 22 students who completed the assignment. There were 3 students who failed the test and also did not complete the assignment. What is the probability that a student passed the test given that they did not complete the homework
The probability that a student passed the test given that they did not complete the homework is [tex]\( \frac{3}{5} \)[/tex] or 60%.
To find the probability that a student passed the test given that they did not complete the homework, you can use conditional probability.
Let:
- [tex]\( A \)[/tex] be the event that a student passed the test.
- [tex]\( B \)[/tex] be the event that a student did not complete the homework.
You're asked to find [tex]\( P(A|B) \),[/tex] the probability of passing the test given not completing the homework.
From the given information:
- Total number of students [tex](\( N \)) = 27[/tex]
- Number of students who passed the test [tex](\( A \)) = 17[/tex]
- Number of students who did not complete the homework [tex](\( B \)) = \( N - 22 = 5 \)[/tex] (since 22 students completed the assignment)
Also, given that there were 3 students who failed the test and did not complete the assignment, we can infer that out of the 5 students who did not complete the homework, 3 of them failed the test.
So, [tex]\( P(A \cap B) = 3 \)[/tex] (the probability of a student both passing the test and not completing the homework).
Using the definition of conditional probability:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]
We have:
- [tex]\( P(A \cap B) = 3 \)[/tex]
- [tex]\( P(B) = 5 \)[/tex]
Now we can calculate [tex]\( P(A|B) \)[/tex]:
[tex]\[ P(A|B) = \frac{3}{5} \][/tex]
So, the probability that a student passed the test given that they did not complete the homework is [tex]\( \frac{3}{5} \)[/tex] or 60%.
The probability that a student passed the test given they didn't complete the homework is 40%.
To solve this problem, we need to determine the probability that a student passed the test given they did not complete the homework. We'll use the given data:
27 total students17 students passed the test22 students completed the assignment3 students failed the test and did not complete the assignmentFirst, calculate the number of students who did not complete the homework:
5 because 27 total - 22 completed = 5 did not complete.
Next, find the number of students who passed the test and did not complete the homework.
Let’s define variables:
Passed test: ADidn't complete homework: BFailed test and didn't complete homework: AB'We're given that AB' = 3.
Calculate AB:
The total number of students who didn’t complete the homework is 5 (B + B'). Thus, AB (students who passed the test but did not complete the assignment) can be calculated as:
2 (because 5 - 3 = 2 for AB).
Then, the probability is:
P(A|B) = AB / B = 2 / 5. Therefore, the answer is 0.4 or 40%.
3x ^ 3 - x ^ 2 Determine if the expression is polynomial or not . If it is a polynomial , state the type and degree of the polynomimal . The given expression a polynomial
The expression
[tex]3x^{3} -x^{2}[/tex]is a polynomial. Its type is cubic and the degree is 3.
Explanation:The given mathematical expression
[tex]3x^{3} -x^{2}[/tex]is a polynomial. A polynomial is an expression that is made up of variables and coefficients, using only the operations of addition, subtraction, and multiplication and non-negative integer exponents. The type of this polynomial is cubic, because the highest power of the variable (the degree) is 3. In this case, the highest degree is the highest exponent of the variable 'x', which is 3. Hence the given polynomial is cubic, with degree of 3.
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