Answer:
2 km/h
Step-by-step explanation:
Let x km/h be the speed of the current.
1. A tourist traveled on a motorboat against the current for 25 km (the current interfered), then it took him
[tex]\dfrac{25}{12-x}\ hours.[/tex]
2. Then he returned back on a raft (the speed of the current is the speed of the raft), then it took him
[tex]\dfrac{25}{x}\ hours.[/tex]
3. In the boat the tourist traveled for 10 hours less than on the raft, thus
[tex]\dfrac{25}{12-x}+10=\dfrac{25}{x}.[/tex]
Solve this equation:
[tex]25x+10x(12-x)=25(12-x),\\ \\25x+120x-10x^2=300-25x,\\ \\10x^2-170x+300=0,\\ \\x^2-17x+30=0,\\ \\D=(-17)^2-4\cdot 30=289-120=169,\\ \\x_{1,2}=\dfrac{-(-17)\pm\sqrt{169}}{2}=2,\ 15.[/tex]
The speed of the current cannot be greater than the speed of the boat, because then tourist was not able to travel against the current. Thus, the speed of the current is 2 km/h.
Chen completed the division problem below.
Answer:
The error is:
He multiplied the dividend by 100 instead of 10
Step-by-step explanation:
∵ 1.926 ÷ 0.9 ⇒ means
1.926 = 1926/1000 ⇒ dividend
0.9 = 9/10 ⇒ divisor
* [tex]\frac{1926}{1000}[/tex] ÷ [tex]\frac{9}{10}[/tex]
[tex]\frac{1926}{1000}[/tex] × [tex]\frac{10}{9}[/tex]
[tex]\frac{1926}{100}[/tex] × [tex]\frac{1}{9}[/tex]
∵ 1926/100 = 19.26 ⇒ dividend
∴ 19.26 ÷ 9 = 1926/100 ÷ 9
19 ÷ 9 = 2 with remainder 1/9
12 ÷ 9 = 1 with remainder 3/9
36 ÷ 9 = 4 no remainder
∴ The quotient is 214/100 = 2.14
Answer:He multiplied the dividend by 100 instead of 10
Step-by-step explanation:
there are 150 more passenger cars than trucks on the highway. for every 10 passenger cars there are 7 trucks. how many trucks are on the highway?
Answer:
500
Step-by-step explanation:
Given: P = 150 - T where P is passenger cars and T is trucks
10P = 7T ⇔ P = [tex]\frac{7T}{10}[/tex]
Plug in equation 2 into equation 1:
[tex]\frac{7T}{10}[/tex] = 150 - T
Solving for T, we get 500
Answer:
There would be 500 passenger cars and 350 trucks.
Step-by-step explanation:
In order to find this, we need to create a system of equations. Start by making the number of passenger cars as x and the number of trucks at y. Now the first equation can be the difference of the two.
x - y = 150
The second equation can make use of the proportion. If we multiply by the opposites we'll get the difference of 0.
7x - 10y = 0
Now we multiply the first equation by -10 and add together to solve for x.
-10x + 10y = -1500
7x - 10y = 0
-------------------
-3x = -1500
x = 500
Now we can find the amount of trucks by using either equation.
x - y = 150
500 - y = 150
-y = -350
y = 350
what is 45=m(25)+b solving for m
Answer:
[tex]\frac{45-b}{25}[/tex]
Step-by-step explanation:
given
45 = 25m + b ( isolate the term in m by subtracting b from both sides )
45 - b = 25m ← divide both sides by 25
[tex]\frac{45-b}{25}[/tex] = m
3. Find the volume of the cylinder
4. Find the volume of a cylinder with a diameter of 16mm and a height of 5.7 mm.
Answer:
[tex]3)~v=8491mm^3[/tex]
Step-by-step explanation:
3) volume of cylinder is...
v= πr²h
plug r= 13 and h=16
v=π(13)²(16)v=π(13×13)(16)v=π(169)(16) ← plug π=3.14v=3.14(2704)v=8490.56v=8491mm^3so, your answer is B
------------------------------
hope it helps...
have a great day!!
george works for a garden center where is is paid a salary of 350 per week plus a commission of 6% of the amount of merchandise that he sells. Last week his sales totaled 1,850. What was his gross pay?
Answer: His gross pay is $461.
Step-by-step explanation: George’s gross pay consists of two parts, his salary and his commission. His salary is $350, regardless of how much he sells. His commission is 6% of the $1,850 in sales that he made.
First, calculate the amount of commission = .06 x $1,850 = $111
$350 + $111 = $461
If the local hospital has decided to follow the 1:4 nurse-to-patient ratio, how many patients can they treat if they have 120 nurses?
Answer: 480 patients
Step-by-step explanation:
If each nurse can treat for patients and there are 120 nurses, you need to multiply 120 nurses x 4 patients each.
120 x 4 = 480
120 nurses can treat 480 patients.
if m<W=9x-3 and m<Z=3x+15 solve for x
Answer:
x = 14
Step-by-step explanation:
W and Z are adjacent angles. So they are supplementary and add to 180 degrees.
W + Z = 180
9x - 3 + 3x + 15 = 180
12x + 12 = 180 12x = 180 - 12
12x = 168
x = 168/12
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ωσятн 30 ρσιитѕ!
SHOW YOUR WORK! WILL MARK BRAINLIEST!
● + ● + ● = 30
● + ○ + ○ = 18
○ - ■ = 2
● + ○ + ■ = ?
Answer: 16
Step-by-step explanation: If 3 black circles equal 30, we can divide that by 3 and get 10. If 1 black circle and 2 white circles equal 18, we can subtract 10 and get left with 2 white circles worth 8, which means a white circle is 4. A white circle minus a square is 2, which means a square is 2. So we put this all together and get 16.
Christopher made a scaled copy of the following trapezoid. He used a scale factor greater than 1. What could be the length of the side that corresponds with BC
a.) 1/5 units
b.) 4 units
c.)15.5 units
d.)24 units
e.)18 units
Answer:
The correct options are c, d and e.
Step-by-step explanation:
From the given graph it is clear that the length of BC is 5 units.
Christopher made a scaled copy of the following trapezoid.
1. If a the scale factor is less than 1 then the image is smaller than its original figure.
2. If a the scale factor is greater than 1 then the image is larger than its original figure.
It is given that he used a scale factor greater than 1. So, the scaled copy of the following trapezoid is larger than the given trapezoid.
The length of corresponds with BC is greater than 5.
[tex]\frac{1}{5}<5[/tex]
[tex]4<5[/tex]
[tex]15.5>5[/tex]
[tex]24>5[/tex]
[tex]18>5[/tex]
Therefore, the correct options are c, d and e.
solve for x {please lol}
Answer: 80
Step-by-step explanation:
Lol. So we are trying to find x, yeah?
Whatever 2 angles that are inside the triangle add up to x.
And you know a triangle adds up to 180°
So do 180 - 100 = 80°
So, x = 80°
:)
Answer:
21
Step-by-step explanation:
A rectangular one-story house covers an area of 1800 square feet. The ceilings are 10 feet high. What is the volume
Answer:
The volume of the rectangular one-story house is [tex]18,000\ ft^{3}[/tex]
Step-by-step explanation:
we know that
To find the volume, multiply the area of the base by the height
so
[tex]V=1,800*(10)=18,000\ ft^{3}[/tex]
i need help, please help me please
Answer:
a. how old are the people living in ______(where you are)?
b. What is the people living in _____ (where you are) favorite color?
c. What is the age of the principals in the schools that are in ____ county?
3. How far do the students at _____ school live from school?
4. Do the students at ___ school enjoy to write with pencils, pens, markers, or crayons the most?
5. What is the age of the math teachers in the schools that are in ____ county?
Step-by-step explanation:
The base of a triangle measures 8 inches and the area is 136 square inches what is the height of the triangle
Answer:
34 inches
Step-by-step explanation:
Area is base times height time half
Then plug in the values: 136= 0.5 x 8x
Then solve for x
Answer:
4
Step-by-step explanation:
If it look like tihs for your shape it will be 4
Now substitute each of these values into the correct blank space in the quadratic formula.
−(1.__)±(2.___)2−4(3.___)(4.___)√2(5.__)
1__
2.__
3.__
4.__
5.__
Question 3 (2 points)
1: -b
2:√b^2
3: -4ac
4: ÷2a
Find a decimal between 0.001 and 0.002
Answer:
0.000111
Step-by-step explanation:
0.0015 is a decimal between 0.001 and 0.002.
What is Number system?A number system is defined as a system of writing to express numbers.
To find a decimal between 0.001 and 0.002, you can take the average of the two numbers.
The average of 0.001 and 0.002 is:
(0.001 + 0.002) / 2
= 0.003 / 2
= 0.0015
Therefore, 0.0015 is a decimal between 0.001 and 0.002.
To learn more on Number system click:
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How would I simplify and solve for X in this trigonometric equation? (Radians)
[tex]cos(x+\pi )^{2} = sinx[/tex]
Answer:
Please, refer to the images below
Step-by-step explanation:
We need to solve for x in the equation
cos (x+ pi) ^2 = sin (x)
cos (x+ pi) = - cos(x)
(-cos (x)) * (-cos (x)) = sin(x)
cos(x) ^2 = sin(x)
We know that
cos(x) ^2 + sin(x) ^2 = 1
cos(x) ^2 = 1 - sin(x) ^2
1 - sin(x) ^2 = sin(x)
sin(x) ^2 + sin (x) -1 = 0
Let A = sin(x)
A^2 + A - 1 = 0
(solutions attached in picture 1)
This means that
x = arcsin(A)
(solutions attached in picture 2)
A student is trying to solve the system of two equations given below:
Equation P: y + z = 4
Equation Q: 3y + 7z = 15
Which of the following steps can be used to eliminate the y term?
A)−3(y + z = 4)
B) 3(y + z = 4)
C)−1(3y + 7z = 15)
D) −3(3y + 7z = 15)
Answer:
A)−3(y + z = 4)
Step-by-step explanation:
Equation P: y + z = 4
Equation Q: 3y + 7z = 15
To eliminate the y term, The equations have to have the coefficients on y equal and opposite.
Equation Q has 3y, so Equation P needs -3y
Multiply equation P by -3
−3(y + z = 4)
Answer:
A
Step-by-step explanation:
The rectangle shown is dilated by a scale factor of 4
Answer:
60 cm, 60 cm, 32 cm, 32 cm
Step-by-step explanation:
Multiply each length by the scale factor.
15 cm * 4 = 60 cm
8 cm * 4 = 32 cm
The dilated sides AB and CD will have a length of 60 cm.
The dilated sides AC and BD will have a length of 32 cm.
I need help with this problem please
Answer:
The second option.
Step-by-step explanation:
The reasoning behind this is because it is a mixed fraction and the rest aren't.
Hope that helps!
Consider set x={5,3,1,0} .which value of x makes 15-3x=0 true?
Answer:
x = 5
How?:
15 - 3(5) = 0
15 - (3 × 5) = 0
15 - 15 = 0
A smartphone costs $120. Sales tax is 8%. What is the total cost, including tax?
Find measure a and b
Answer:
162.5
Step-by-step explanation:
subtract 35 away from 180 then divide it by 2 = 162.5
Check the picture below.
recall that a flat-line has 180°.
A right rectangular prism's edge lengths are 9 inches, 9 inches, and 3 1/3 inches. How many unit cubes with edge lengths of 1/2 inch can fit inside the prism?
ANSWER
2160 cubes
EXPLANATION
The given rectangular prism has edge lengths,
9 inches,9inches and 3⅓ inches.
The volume of this rectangular prism is
[tex]V = 9 \times 9 \times \frac{10}{3} [/tex]
[tex]V = 3 \times 9 \times 10 = 270 {in}^{3} [/tex]
A cube with unit edges of length
[tex] \frac{1}{8} [/tex]
has volume.
[tex]v = {( \frac{1}{8}) }^{3} = \frac{1}{8} [/tex]
The number of unit cubes that can go into the prism is
[tex] = \frac{270}{ \frac{1}{8} } = 2160[/tex]
Which Of the following could not be points on the units circle ?
answer A , that could not be point
Answer:
Options a and c
Step-by-step explanation:
A unit circle is one which has origin as centre and radius as 1.
The equation of the unit circle would be
[tex]x^2+y^2 =1[/tex]
Thus we find that any point satisfying the above equation lies on the unit circle
Let us try the given points one by one
a) [tex](0.8)^2+(-0,6)^2 =1[/tex]. Hence lies on the circle
b) (1,1)
Cannot lie on circle since [tex]1^2+1^2 \neq 1[/tex]
c) [tex](\frac{-2}{3} ,\frac{\sqrt{5} }{3} )\\(\frac{-2}{3})^2+(\frac{\sqrt{5} }{3} )^2 =1[/tex]. Hence lies on the circle
d) [tex](\frac{\sqrt{3} }{2} ,\frac{1}{3} )\\(\frac{\sqrt{3} }{2})^2+(\frac{1}{3} )^2\\\neq 1[/tex]
Hence does not lie on the circle
Only option A,C are right
There are 4 red cards and 8 black cards in a bag. How likely is it that you will randomly draw a blue card?
A. Likely
B. Unlikely
C. Impossible
D. Certain
Answer:
C
Step-by-step explanation:
Since there are no blue cards, the probability that you'd draw one is 0/12, which means that there is no chance you'll draw one.
It is impossible to get blue cards. Then the correct option is C.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
There are 4 red cards and 8 black cards in a bag.
In the bag, the number of blue cards will be zero.
Thus, it is impossible to get blue cards. Then the correct option is C.
More about the probability link is given below.
https://brainly.com/question/795909
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Which expression shows this number in expanded form 0.624
 Question:
The time required for a skilled worker to produce x shirts is given by the function T(x) = 4x + 2, where T is measured in hours. The salary the she is paid is given by the function S(T) = 15T, where S is measured in dollars.
A. If the worker produces 18 units, what will she be paid?
B. How many units would the worker need to produce to be paid $3,030?
Answer:
A) The worker is paid S= $ 1110 for producing 18 units.
B) The worker is paid $3,330 for producing x= 50 units.
Step-by-step explanation:
a) given x = 18 units
Time required T(x) = 4x+2
= 4(18)+2
= 72 +2
= 74 hrs
Amount paid S(T) = 15 T
= 15 ( 74) = $ 1110
b) Since S is given, S= $3,030
S(T)= 15 (T)
3030 /15= T
202 hrs= T
Now, we can find x:
T(x) = 4(x) +2
202 = 4x + 2
202-2 = 4x
200 / 4 =x
50 = x
so, worker produces 50 units.
What is the probability that the roll of a six-sided die will be either even or odd?
the probability that the roll of a six-sides die will be either even or odd is 1/2 or 50%
The probability of a six-sided die will be either even or odd is 1/2.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
A die is rolled once.
The sample space = {1, 2, 3, 4, 5, 6}
An even number sample space = {2, 4, 6}
Odd number sample space = {1, 3, 5}
The probability of a six-sided die will be either even or odd,
= 3/6
= 1/2
Therefore, 1/2 is the probability.
To learn more about the probability;
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Can you guys pls help me out
Answer:
D. $2 million
Step-by-step explanation:
make it a porportion - easier to complete the problem..
30,000 / ? = 1.5% / 100%
30,000 * 100 = 3,000,000 / 1.5% = 2,000,000
hope this helps!!
sue has more than 5 cookies inequality
Answer:
s > 5
Step-by-step explanation:
s is the number of cookies Sue has.
Since she has more than 5 cookies, the number of cookies she has is greater than 5.
Hello there! An inequality modeling this could be x > 5.
When setting up this equation, we can use x to model the number of cookies that Sue has.
Remember that these are the symbols we use to represent inequalities:
< - greater than
> - less than
≤ - greater than or equal to
≥ - less than or equal to
Since the number of cookies Sue has is greater than 5 (but not equal to), we use the symbol.
We can represent her having x amount of cookies, which is more than 5, like this: x > 5,
I hope this helps and have a great day! :)