Let's say you are paddling at 5mph and the current is 3 mph. Going upstream, you are going 2 mph and downstream, 8 mph.
8(b - c) = 464
7(b + c) = 644
b - c = 58
b + c = 92
Adding the two together
2b = 150
b = 75
75 - c = 58
c = 17
The boat's speed is 75 mph and the current's speed is 17 mph.
ow many decimals numbers are there whose value equals the average of their digits?
For example, 2.3 has the digits 2 and 3. Their average is 2.5 -- so that doesn’t work. But there are some that do!
There are a few rules:
Answer:
Step-by-step explanation:
there are infinite numbers between 2 and 3 having average=2.5
2.49,2.51
2.48,2.52
2.47,2.53
2.46,2.54
.................
2.491,2.509
2.492,2.508
2.493,2.507
......................
The graph of a quadratic function intercepts the x-axis in two places and the y-axis in one place.
According to the fundamental theorem of algebra, which of the following statements is correct?
The true statement about the quadratic function is that it has two distinct real zeros
How to interpret the quadratic function?The given parameters are:
x-intercepts = 2 i.e. intercepts the x-axis in two placesy-intercept = 1 i.e. intercepts the y-axis in one placeThe first highlight above means that, the function can be represented as:
y = a(x - x1)(x -x2)
Where x1 and x2 are the x-intercepts
This also means that the quadratic function has two distinct real zeros
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two chips are drawn at random and withoit replacement from a bag containing four blue chips and three red chips. find the probability of drawing two red chips.
The probability of getting two red chips is:
P = 1/21.
How to get the probability?
The probability of getting a red chip is equal to the quotient between the number of red chips and the total number of chips.
There are 4 blue chips and 3 red chips, for a total of 7 chips.
For the first draw, the probability of getting a red one is:
p = 3/7.
For the second draw, now there are 2 red chips and 6 chips in total, so now the probability is:
q = 2/6 = 1/3
Then the joint probability, given by the product between the two individual probabilities, is:
P = q*p = (3/7)*(1/3) = 1/21.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The quotient of is
.
The value of the quotient of 0.378 ÷ 0.3 is 1.26
Missing information in the questionThe quotient of 0.378 ÷ 0.3 is
How to determine the quotient?The expression is given as:
0.378 ÷ 0.3
Rewrite as a fraction
0.378/0.3
Multiply the fraction by 1
Express 1 as 1000/1000
0.378/0.3 * 1000/1000
Evaluate the product
378/300
Divide 378 by 300
1.26
Hence, the quotient of 0.378 ÷ 0.3 is 1.26
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A bicycle wheel travels exactly 26/pi inches in I full rotation, what is the area, to the nearst square inch, of a circle the same size az the bicycle wheel?
The area, to the nearst square inch, of a circle the same size az the bicycle wheel is 531 inches².
What is the area of the circle?A circle is a bounded figure which points from its center to its circumference is equidistant.
Area of a circle = πr²
Where :
π = pi = 22/7
R = radius
The full rotation of the wheel is equal to the circumference of the wheel.
circumference of the wheel = 2 πr
26π = 2 πr
r = 13 inches
Area = 22/7 x 13³ = 531 inches²
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ƒ(1) = −6
f(2)= -4
f(n) = f(n-2) + f(n-1)
f(3) =
Please help!!!!!!
Answer:
f(3) = - 10
Step-by-step explanation:
given
f(n) = f(n - 2) + f(n - 1) , then
f(3) = f(3 - 2) + f(3 - 1) = f(1) + f(2) = - 6 + (- 4) = - 6 - 4 = - 10
[tex]f(3)=f(1)+f(2)=-6+(-4)=-10[/tex]
if g(X)=3x-5,then find g^-1(5),where g is one to one onto function
Answer:
g^-1(5)=10/3
Step-by-step explanation:
g(x)=3x-5
g(x)= y
g^-1( y)=x
3x-5=y
3x=y+5
x=y+5/3
g^-1(y)=y+5/3
g^-1(5)=5+5/3
g^-1(5)=10/3
18. The desired density of the shaved ice is 0.697 g/cm3, and the cost, per kilogram, of ice is $3,83. Determine
and state the cost of the ice needed to make 50 snow cones.
The cost of the ice needed to make 50 snow cones is $54.50.
What is cost of the ice?The first step is to determine the volume of the snow cone.
Volume of the snow cone =volume of a cone + volume of the hemisphere
Volume of the cone = 1/3πr²h
1/3 x 3.14 x 10.2 x (8.3/2)² = 183.87 cm³
Volume of the hemisphere = 2/3πr³
2/3 x 3.14 x (8.3 / 2)³ = 224.43 cm³
Total volume = 224.43 cm³ + 183.87 cm³ = 408.30 cm³
Volume of 50 snow cones = 408.30 cm³ x 50 = 20,414.82
Total grams of ice needed = density x volume
0.697 x 20,414.82 = 14,229.13 grams
Convert gram to 1kg
1kg = 1000g
= 14,229.13 grams / 1000 = 14.23kg
Cost of the ice = 14.13 x 3.83 = $54.50
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Let H be the set of real numbers less than or equal to eleven
Answer:
The answer would be Set: "S" = the set of natural numbers greater than 11.
Hope this helps!
NEED HELP ASAP!!! PLEASE
The linear function that has a different rate of change from y = -3x+4 is A, a function with a y-intercept of -4 that passes through the point (-3,-13)
What is an intercept?An intercept is the point where a straight line or a curve meets with the x or y axes.
Analysis:
The rate of change is the same as slope. The slope of y = -3x + 4 is -3,
All other functions Except A have a slope of -3.
for linear function A,
if y = mx + c, c = -4, x = -3, y = -13
-13= -3m - 4
-3m = -9
m = 3
In conclusion, linear function A with a y-intercept of -4 passing through the point (-3,-13) has a different rate of change from y = -3x + 4
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What is the equation of a line that is perpendicular to -x + 2y = 4 and passes through
the point (-2, 1)?
Oy = 2x + 3
Oy = -1/2x-3
Oy = 1/2x + 3
Oy=-2x-3
Answer:
The last option y= -2x-3
Step-by-step explanation:
this equation passes through the point (-2,1)
What is the graph of the system?
y> -x + 3
-2x+y<-1
Step-by-step explanation:
Hopefully this is helpful?
triangle.
A,
angle CAB = 90°, angle ABC = 52° and AC = 9.2.
Calculate the length of BC rounded to 3 SF.
[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\\ \rm\Rrightarrow sin52=\dfrac{AC}{BC}[/tex]
[tex]\\ \rm\Rrightarrow sin52=\dfrac{9.2}{B C}[/tex]
[tex]\\ \rm\Rrightarrow B C=\dfrac{9.2}{sin52}[/tex]
[tex]\\ \rm\Rrightarrow B C=9.3[/tex]
Answer:
11.7 (3 s.f.)
Step-by-step explanation:
Given information:
∠CAB = 90°∠ABC = 52°AC = 9.2As one of the given angles is 90°, the triangle is a right triangle.
Draw the triangle using the given information (see attached) to help visualize the problem.
To calculate the length of BC, use the sine trigonometric ratio:
[tex]\sf \sin(\theta)=\dfrac{O}{H}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuse (the side opposite the right angle)From inspection of the attached triangle:
[tex]\theta[/tex] = 52°O = AC = 9.2H = BCSubstitute the values into the formula and solve for BC:
[tex]\implies \sf \sin(52^{\circ})=\dfrac{9.2}{BC}[/tex]
[tex]\implies \sf BC=\dfrac{9.2}{\sin(52^{\circ})}[/tex]
[tex]\implies \sf BC=11.67496758...[/tex]
[tex]\implies \sf BC=11.7\:\:(3 \:s.f.)[/tex]
Therefore, the length of BC is 11.7 (3 s.f.).
estimate the percentage 66 2/3% of 2,600
The estimate of the percentage expression 66 2/3% of 2,600 is 1733.33
How to estimate the percentage expression?The expression is given as:
66 2/3% of 2,600
Rewrite as:
66 2/3% * 2,600
Express the fraction as an improper fraction
200/3% * 2,600
Remove the percentage sign
200/300 * 2,600
Evaluate the product
1733.33
Hence, the estimate of the percentage expression 66 2/3% of 2,600 is 1733.33
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Determine the true statements about trend lines in scatterplots. Check all that apply.
A trend line can be used to make predictions in real-world situations.
A scatterplot that shows no correlation between the variables does not have a trend line.
A line of best fit must contain at least two of the original points.
A regression line and trend line are equivalent terms.
Answer:
give that 13.3cm is 15% of a certain length, what is the complete length
Answer: A,B and D ARE THE CORRECT ANSWERS
Step-by-step explanation:
Which criterion, if any, could prove the triangles are congruent?
Answer: None
Step-by-step explanation:
There is only one pair of angles and one pair of sides, which is not sufficient to prove triangle congruence.
In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect and . Then, intersecting arcs of equal size are drawn centered at points D and E. Point P is located at the intersection of these arcs.
Based on this construction, m∠ABP is
°, and m∠ABC is
°.
The measure of ∠ABP and ∠ABC are 32° and 64° respectively.
what is a bisector of an angle?Any line which divides an angle into two equal halves is a bisector of that angle.
Analysis:
Since the arcs at D and E are drawn with the same radius and arc using center D and E are intersected by line PB( which is the bisector of the full arc with center B) then ∠ABP = ∠PBC = 32°.
∠ABC = ∠ABP + ∠PBC
∠ABC = 32 + 32 = 64°
In conclusion, ∠ABP and ∠ABC are 32° and 64°
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Answer:ABP is 32 degrees, and ABC is 64 degrees
Step-by-step explanation: bi hope this helped if not sorry:)
Photo is attached, please help! Will give brainliest.
Answer:0.124402866242
Step-by-step explanation:here’s my attempt: dv/dt=d/dt(4pi/3r^3). 100=d/dt((4pi/3)*(8+X*t)^3) at t=0. 100/(4(pi)*8^2)=x where x is the rate of change of the radius. Not 100% sure though
Gerald has a punch bowl in the shape of a hemisphere as shown below.
One cup is equivalent to approximately 15 cubic inches. Which of the following is closest to the maximum number of cups the punch bowl can hold?
A. 60 cups
B. 45 cups
C. 30 cups
D. 18 cups
The closest to the maximum number of cups the punch bowl can hold is 30
How to determine the number of cups?The given parameters are:
1 cup = 15 cubic inches
Diameter of bowl, d = 12 inches
The radius is the half of the diameter.
So, we have:
r = 6
The volume of the bowl is then calculated using:
[tex]V = \frac{2}{3}\pi r^3[/tex]
This gives
[tex]V = \frac{2}{3}\pi * 6^3[/tex]
Evaluate
V = 452.16
The maximum number of cups is then calculated using:
Cups = 452.16/15
Evaluate
Cups = 30.1444
Approximate
Cups = 30
Hence, the closest to the maximum number of cups the punch bowl can hold is 30
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one side of a square is represented
Answer:
therees nothing here to help you with?
Step-by-step explanation:
srry abt that but add the square number
Two adjacent rooms are rectangles, both of length 13 feet by 10 feet. Jerry wants to change the carpets in both rooms. How many square feet should he order?
Answer:
260 square feet
Step-by-step explanation:
The area of a rectangle is given by the formula ...
A = LW
The area of two same-size rectangular rooms will be double the area of one of them.
__
room areaEach room has an area of ...
A = LW = (13 ft)(10 ft) = 130 ft²
carpet orderThe order for carpet must be for 2 times the area of one room:
carpet order = 2 × 130 ft² = 260 ft²
Jerry should order 260 square feet of carpet.
Find the slope please
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of this graph; we are provided with two points:
[tex]\star~\mathrm{(6,0)}[/tex]
[tex]\star~\mathrm{(0,-5)}[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
What we need in order to find the slope are two points and the slope formula.Here's the formula:
[tex]\star~\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]
Where
y2 and y1 are y-coordinates
x2 and x1 are x-coordinates
Substitute the values:
[tex]\star~\mathrm{\cfrac{-5-0}{0-6}}}[/tex]
Simplify!
[tex]\star~\mathrm{\cfrac{-5}{-6}}}[/tex]
Simplify more!
[tex]\star~\mathrm{\cfrac{5}{6}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
Which function is shown in the graph below?
O y = logo 4x
O y = log₁x
O y = log3x
O y = log10x
The correct function shown in the graph is,
⇒ log₁₀ (ax) = 1
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:
⇒ log₁₀ (ax) = 1
or , ax = 10¹ = 10
Thus, x = 10/a
So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .
⇒ log (3 × 3.33) = 0.99 ≈ 1
Thus, out of the given options only Option D seems to be the most probable answer.
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The price of a gallon of milk increased by 9 cents. This represented a price increase of 2%. What was the original price of the milk?
Answer:
$ 4.50
Step-by-step explanation:
2% of the price = 9 cents
.02 x = 9
x = 9 / .02 = 450 cents or $4.50
Help me please it’ll be a big help
allen was making trail mix but he only wanted to make 1/3 of the recipe if the whole recipe called for 1/2 of a cup of peanuts how many cups will he need to make 1/3 of the recipe choose the model that matches the situation.
Answer:
the last one 1/6
Step-by-step explanation:
1/2 x 1/3 = 1/6
What additional information is needed to prove the triangles are congruent by the SAS postulate
Answer: [tex]\angle XWY \cong \angle ZWY[/tex]
Step-by-step explanation:
We know that [tex]\overline{WY} \cong \overline{WY}[/tex] by the reflexive property, so we need the included angles to be congruent (meaning [tex]\angle XWY \cong \angle ZWY[/tex]
what is the quotient of 1/5 divide by (-5/7) =
Answer:
-7/25
Step-by-step explanation:
=(1/5) ÷ (-5/7)
Copy dot flip
=(1/5) * (-7/5)
=-7/25
Please help Anyone I'm seriously almost done
Answer:
[tex]\textsf{x = 45}[/tex]
Here, the given 2 angles are complementary angles. The sum is 90 degrees as indicated by the right angle symbol.
[tex]\textsf {Solving :}[/tex]
[tex]\implies \textsf{x - 2 + 47 = 90}[/tex]
[tex]\implies \textsf{x + 45 = 90}[/tex]
[tex]\implies \textsf{x = 45}[/tex]
Help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
PROBLEMS
1) Add the following: 30 mg, 2.5 kg and 7.0 g. Express the answer in g.
2) Express the amount of 1.243 g as:
mg ________
kg ________
mcg _______
3) How many grams of the active ingredient "aspirin" would be needed to make 500 aspirin tablets if each tablet must contain 325 mg?
Answer:
1. 2507.034 g
2. 1243mg
0.001243kg
1,243,000 mcg
3. 162.5g
Step-by-step explanation:
1. First of all we need to convert 30mg and 2.5kg to gram.
⇒ 1 gram = 1000 milligrams
x = 35mg
⇒ 1000mg(x) = 35mg
⇒ x = 35mg = 35 = 0.035g
1000mg 1000
Next we convert 2.5kg to gm.
⇒ 1 kilogram = 1000g
2.5kg = x
(We then criss cross)
⇒ x = 2.5kg × 1000g = 2500g = 2500g
1kg 1
Now that we converted them all to gram, we will add them.
⇒ 30mg + 2.5kg + 7g = 0.035g + 2500g + 7g = 2507.035 ≈ 2507g
2. We convert 1.234g into
a. mg
⇒ 1 gram = 1000 milligram
1.243g = x
⇒ x = 1.243g × 1000mg = 1243mg = 1243mg
1g 1
b. kg
⇒ 1 kilogram = 1000gram
x = 1.243 gram
⇒ x = 1.243g × 1kg = 1.243kg = 0.001243kg = 1.243 × 10⁻³ kg
1000g 1000
c. mcg
⇒ 1 gram = 1000000mcg
1.243g = x
⇒ x = 1.243g × 1,000,000mcg = 1,243,000mcg = 1,243,000mcg
1 g 1
3. We need 500 aspirin, the amount of grams needed and we know that one tablet contains 325mg.
So now we can derive the formula such that:
⇒ 1 tablet = 325mg
500 tablet = x
But first we need to convert 325mg to grams.
⇒ 1 gram = 1000mg
x = 325mg
⇒ x = 325mg × 1 g = 325g = 0.325g
1000mg 1000
So now instead of using 325mg we can use 0.325g.
⇒ 1 tablet = 0.325g
500 tablets = x
⇒ x = 500 tablets × 0.325g = 162.5g = 162.5g
1 tablet 1