Answer:
[12/(4c)] + [12/(6c)] = 2.5
Step-by-step explanation:
time = distance/speed
You know the speeds upstream (5-1)c and downstream (5+1)c, the distance, and the total time for both trips. This information can be combined to give the equation above.
_____
The first equation assumes the trips upstream and down took 2.5 hours each.
The second equation is an incorrect combination of the numbers, as the units on the left are miles²/hour and are equated to hours on the right.
The third equation makes appropriate use of the relation between speed, distance, and time.
Answer:
Last option as
[tex][12/(4c)] + [12/(6c)] = 2.5[/tex]
Step-by-step explanation:
Time = distance/speed
Speed of boat = 5c (given)
Hence upstream speed = 5c+c =6c and
downstream speed = 5c-c =4c
Distance remains the same 12 miles for up and down
Total time = 2.5 hours
The first equation assumes total time as 5 hours when it is actually 2.5 hours.
The second equation is an incorrect because time x distance will not yield any result instead distance /time should have been done.
The third equation calculates time taken for upstream and downstream and add to equate to 2.5 hours.
So this is correct.
What number produced the irrational number when added to 1/3
Solution
When we add 1/3 which is rational to an irrational number, we get an irrational number.
pi - is a rational number. √2, √3 are also rational numbers
So the possibilities are pi + 1/3,
2pi + 1/3,
3pi+1/3,
√3 + 1/3,
√2 + 1/3...
I hope this will help you.
Thank you.
1.994 x 10^-23 1.67 x 10^-24 what are the difference
Answer:
1.827 x 10^-23
Step-by-step explanation:
(1.994 x 10^-23) - (1.67 x 10^-24) = 1.827 x 10^-23
Y=-5/2x-5 find the slope of each line
slope = - [tex]\frac{5}{2}[/tex]
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - [tex]\frac{5}{2}[/tex] x - 5 is in this form
with slope m = - [tex]\frac{5}{2}[/tex]
The slope of the equation
[tex]Y=\dfrac{-5}{2}x-5[/tex] is [tex]-\dfrac{5}{2}[/tex] .
A line's steepness or inclination can be measured by a line's slope. It specifies the amount of rise or fall a line experiences for each unit of horizontal distance. In other words, it measures how quickly the vertical (y) and horizontal (x) coordinates of points on a line change with time.
Given equation is
[tex]Y=\dfrac{-5}{2}x-5[/tex] consider it as equation (1)
This is in the form of slope-intercept equation y = mx +b consider it as equation (2).
Where m represents the slope and b represents the intercept term.
On comparing the equation (1) and equation (2)
[tex]m=-\dfrac{5}{2}[/tex]
Hence, the slope of the given equation is given by [tex]-\dfrac{5}{2}[/tex] .
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Use the x-intercept method to find all real solutions of the equation x^3-6x^2+11x-6
I think that this is the x-intercept method:
First of all, we set y=x^3-6x^2+11x-6.
To find x, we need to let y=0. (y is also equals to f(x))
f(x)=x^3-6x^2+11x-6
In order to make f(x)=0, what does x have to be?
f(1)=0
So then we divide x^3-6x^2+11x-6 by x-1. Why? Because that will not give us a remainder.
(x^3-6x^2+11x-6)/(x-1) = x^2-5x+6
Now, we need to factorize it.
x^2-5x+6 = (x-2)(x-3)
So x=2,3
Which of the following graphs represents an exponential function?
I choose C, but I'm not sure.
The graph which represent a exponential function is:
Graph A.
Step-by-step explanation:Exponential function--
A exponential function is a function which is in the form of:
[tex]y=f(x)=ab^x[/tex]
where a and b are integers and a,b≠0.
Also, the graph of a exponential function either increases continuously or decreases continuously and rapidly in it's domain.The x-axis is always an asymptote for the graph.Also, the path traced by it is not along a straight line.From the given graphs, the graph which one that represents a exponential function is: Graph A.
What is an exponential graph?An exponential graph represents a mathematical relationship where the dependent variable (y) is a constant raised to the power of the independent variable (x). This results in a curved graph that either increases or decreases rapid
A exponential function is a function which is in the form of:
[tex]y = f(x) = ab^{x}[/tex]
where a and b are integers and a,b≠0.
On the other hand, the graph of a exponential function either increases continuously or decreases continuously and rapidly in it's domain.
The x-axis is always an asymptote for the graph.
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Im begging u, plzzzzzzzz help
a.) Describe a transformation sequence that will transform pentagon ABCDE into pentagon A’B’C’D’E’.
b.) There is more than one way to transform pentagon ABCD into pentagon A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.
a) The orientation of the figure ABCDE is clockwise. The orientation of figure A'B'C'D'E' is counterclockwise, so at least one reflection is involved. The direction of AB is North, while the direction of A'B' is West, so a rotation of 90° is involved. Both of these can be accomplished by a reflection across the line that has a direction halfway between these, Northwest. The x-coordinate of point D is the same as that of D', so it is convenient to put point D on the line of reflection.
A transformation sequence that maps ABCDE to A'B'C'D'E' is ...
reflection across the line x+y=-2translation down 2 unitsThe attachment shows the result of reflecting the figure across the line.
b) About any reflection will give the figure the proper orientation. Depending on what it is, some amount of rotation and/or translation may be required.
We can reflect point D across the line y=-2 to put it where point D' is. That reflection changes the direction of AB to South, so we need to rotate the figure 90° CW to get AB to point West. Since we want point D' to be invariant, we can use that point as the center of rotation.
A second transformation that gives the same mapping is ...
reflection across the line y = -2rotation 90° CW about the point (-1, -3)Please help! Answer only if you know
area = 20 units²
construct a square of side 6 units around the given figure, then the area of the figure is given by area of square minus 4 congruent triangles
A = 6² - 4 × [tex]\frac{1}{2}[/tex] × 4 × 2
= 36 - 16 = 20 units²
PLZ HELP GEOMETRY BELOW
This is known as Einstein's proof, not because he was the first to come up with it, but because he came up with it as a 15 year old boy.
Here the problem is justification step 2. The written equation
BC ÷ DC = BC ÷ AC
is incorrect, and wouldn't get us our statement 2, which is correct.
For similar triangles we have to carefully pair the corresponding parts to get our ratios right:
ABC ~ BDC means AB:BD = BC:DC = AC:BC so BC/DC=AC/BC.
Justification 2 has the final division upside down.
If rain is falling at a rate of 2.56 inches per hour, how much rain would you expect after 3.75 hours
If rain is falling at a rate of 2.56 inches per hour, one would expect 9.6 inches of rainfall after 3.75 hours.
Explanation:The question pertains to the calculation of total rainfall when the rate of rainfall and time of rainfall are known.
In this problem, the rate of rainfall is given as 2.56 inches per hour and the time as 3.75 hours. The formula for calculating total rainfall is simply to multiply the rate by the time.So, 2.56 inches/hour * 3.75 hours = 9.6 inches total rainfall.
Hence, if rain is falling at a rate of 2.56 inches per hour, you would expect 9.6 inches after 3.75 hours
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According to the table the investment has doubled in worth by the start of which year?
Answer:
The investment has doubled in worth by the start of 15th year.
Step-by-step explanation:
We are Provided a table which tells us that principal amount of $100 is invested on a interest rate of 5% for 15 years compounded annually and we are asked to find out by the start of which year our investment will be doubled.
We can see that after 14 years our amount is doubled but this can't be our answer as amount is doubled ($207.90) after 14 years not in the start of 14th year. We can see that by the start of 15 year our amount is doubled that is $207.90.
Therefore, by the start of 15th year our investment will be doubled.
List of the partial product 0f 42 ×28
1,2,3,6,7,14,21,42
1.2,4,7,14,28
which of the following equations is equivalent to 1/4x -1/2y =8? a) 2x-4y=8. b)2x-4y =64. c) 4x-2y =64
If you multiply the original equation by 8, you get
... 8(1/4x -1/2y) = 8(8)
... 8/4x -8/2y = 64
... 2x -4y = 64 . . . . . matches choice b)
Can someone please help me with business math
Answer:
1721 $
1612.80
Step-by-step explanation:
Straight line depreciation means depreciation is the same spread over for all the years. The spread over amount is nothing but total cost of equipment - salvage value.
Here we have
Cost of equipment(Purchase cost) ... 18000
Shipping costs ... 620
Installation costs ... 590
Total cost of equipment ... 19210
Less: salvage value at the end ... 2000
Net cost of equipment for 10 years ... 17210
Depreciation per year = Net cost /number of years of life
= 17210/10 = 1721/-
Hence answer is 1721/- for all years and also hence for year 2.
--------------------
Peach tree has an average life of 12 years. First 3 years no benefit would arise, 4 to 8 would be peak and after that slowly decreasing.
Hence in 9th year there would be least value and least depreciation.
Hence answer is $1612.80
Help please 11, 12, 13
11. {OD, OH} . . . or . . . {OB, OJ}
12. b. Open a compass to distance AB
13. 17 square units
Step-by-step explanation:11. Opposite rays are rays that together make a line. The only point they have in common is their mutual end point.
Given the letter names of points on lines, one can name opposite rays by choosing 3 collinear points, and selecting the middle one of those for the mutual end point. That point's name will be the first letter of each of the ray names. One ray will be named by one of the remaining points, and the other will be named by the other remaining point.
Here, we can choose points H, O, D on the same line. Then rays in opposite directions will be OD and OH, each having point O as its end point.
Similarly, we can choose points B, O, J on the other line and name opposite rays OB and OJ.
___
12. The general sequence of steps for copying a line segment is to draw a line segment longer than the one you want to copy, mark a point on it, set the compass to the length of the given segment, then use the marked point as one end and mark the distance from that point using the compass.
Here, the target line and reference point (C) have been made already, so the next step is open the compass to distance AB.
___
13. The unadulterated triangle has legs of 6 and 8 units, so an area of ...
... area = (1/2)bh = (1/2)(6)(8) = 24 . . . . square units.
One can count the squares within that area that have been removed from the triangle. There are 7 of them, so the area is ...
... 24 -7 = 17 . . . . square units
There are other ways to find the area, including dividing the triangle into smaller pieces. Doing the latter, one needs to be careful, because the slanted side only goes through a grid intersection at points (1, 1), (4, 5), and (7, 9).
If one uses two triangles with legs 3 and 4, and a central rectangle of 2×3, then the area adds up to 6+6+5 = 17 square units, because there is one square taken out of the lower right corner of the upper triangle.
cersei is 3 times older than Arya. In 15 years their combined ages will be 94.How old are each of them now (please show work)
The "work" can be all in your head. In 15 years, their combined ages will have increased by 30 years over what it is now*, so their combined age now must be 64 year. If the ratio of their ages is 3:1, the youngest must be 1/(3+1) = 1/4 of the total, or 16 years.
Arya is 16 years old; Cersei is 48 years old.
_____
* Each person ages one year each year, so their combined age increases by 2 years each year. In 15 years, their combined age will increase by 30 years.
_____
If you insist on an equation, let "a' represent Arya's age. Then 3a represents Cersei's age. The relationship given in the problem is ...
... (a +15) + (3a +15) = 94
... 4a +30 = 94 . . . . . . . . . . collect terms
... 4a = 64 . . . . . . . . . . . . . . subtract 30
... a = 64/4 = 16 . . . . . . . . . multiply by 1/4
This equation and its working should look a lot like the verbal reasoning we did above.
Based on the diagrams, which statement is true?
Using a somewhat liberal interpretation of "the angles shown in the diagrams", we can conclude that the appropriate choice is ...
... A. The value of x should be 75, because the angles shown in the diagrams are congruent.
_____
There are 8 angles shown in each of 4 diagrams. All 32 angles are not congruent. Taken literally, "the angles shown in the diagrams are congruent" is a false statement. Rather, the marked pair of angles in each diagram are congruent angles.
What is the axis of symmetry for f(x)= 3x^2??
(Three x squared)
the y-axis, that is x = 0
the equation of a parabola in the form f(x) = ax²
has it's vertex at the origin and since the axis of symmetry passes through the vertex then
the axis of symmetry is the y- axis
What is the volume of a figure that is filled with 36, 1 inch cubes
It should be no surprise that the volume of a 1-inch cube is 1 cubic inch. Assuming those 36 cubes completely fill the interior volume of the figure, that figure's volume is
... 36 cubic inches
The length of a rectangle is three times the width. The area of the rectangle is 108 sq in. What is the width of the rectangle? 6 in. 9 in. 12 in. 36 in.
Let the width of rectangle be X inches
Then according to question
Length of rectangle will be 3X
Also, we know that
Area of rectangle is = L×B
108 = X . 3X
3X^2 = 108
Divide both sides by 3
X^2 = 36
Taking squareroot of both sides
X=6
Therefore, width of rectangle is 6 inches
Answer:
1. 6 in.
Step by step explanation:
Let the width of our rectangle be x inches.
We have been given that the length of our rectangle is three times the width, therefore, length of our triangle will be 3x inches.
We are told that area of the rectangle is 108 square inches.
Since we know that [tex]\text{Area of a rectangle}=\text{Width}\cdot\text{Length}[/tex]
Let us substitute our given information in area formula.
[tex]108=x\cdot 3x[/tex]
Upon multiplying 3x by x we will get,
[tex]108=3x^{2}[/tex]
Let us divide both side of our equation by 3.
[tex]\frac{108}{3} =\frac{3x^{2}} {3}[/tex]
[tex]36=x^{2}[/tex]
Upon taking square root of both sides of our equation we will get,
[tex]6\pm=x[/tex]
Since width cannot be negative, therefore, width of our rectangle will be 6 inches and 1st option is the correct choice.
Beth swam laps to raise money for a charity. Beth raised $15 plus $0.65 per lap that she swam. She raised a total of $80. Let x represent the number of laps Beth swam. What expression completes the equation to determine the total number of laps Beth swam? How many laps did Beth swim? Enter your answers in the boxes.
______= 80
______ Laps
The amount Beth raised by swimming is ...
... x · $0.65
In addition, she had a contribution that was not related to the number of laps. Her total can be expressed as
... 15 + 0.65x = 80
_____
Subtract 15 and divide by 0.65 to find
... x = (80 -15)/0.65 = 65/0.65 = 100
Beth swam ...
... 100 Laps
Answers in Scientific Notation.
one way is to factor the expressions
(a)
[tex]10^{5}[/tex] (1.2 + (5.35 × [tex]10^{1}[/tex]))
= [tex]10^{5}[/tex] (1.2 + 53.5)
= 54.7 × [tex]10^{5}[/tex] = 5.47 × [tex]10^{1}[/tex]× [tex]10^{5}[/tex] = 5.47 × [tex]10^{6}[/tex]
(b)
[tex]10^{-3}[/tex]((6.91 × [tex]10^{1}[/tex]) + 2.4)
= [tex]10^{-3}[/tex](69.1 + 2.4)
= 71.5 × [tex]10^{-3}[/tex] = 7.15 × [tex]10^{1}[/tex] × [tex]10^{-3}[/tex] = 7.15 × [tex]10^{-2}[/tex]
(c)
[tex]10^{5}[/tex]((9.7 × [tex]10^{1}[/tex]) + 8.3)
= [tex]10^{5}[/tex](97 + 8.3)
= 105.3 × [tex]10^{5}[/tex] = 1.053 × [tex]10^{2}[/tex] × [tex]10^{5}[/tex] = 1.053 × [tex]10^{7}[/tex]
(d)
[tex]10^{1}[/tex]((3.67 × [tex]10^{1}[/tex]) - 1.6)
= [tex]10^{1}[/tex](36.7 - 1.6)
= 35.1 × [tex]10^{1}[/tex] = 3.51 × [tex]10^{1}[/tex] × [tex]10^{1}[/tex] = 3.51 × [tex]10^{2}[/tex]
(e)
[tex]10^{-6}[/tex]((8.41 × [tex]10^{1}[/tex]) - 7.9)
= [tex]10^{-6}[/tex](84.1 - 7.9 )
= 76.2 × [tex]10^{-6}[/tex] = 7.62 × [tex]10^{1}[/tex] × [tex]10^{-6}[/tex] = 7.62 × [tex]10^{-5}[/tex]
(f)
[tex]10^{4}[/tex]((1.33 × [tex]10^{1}[/tex]) - 4.9 )
= [tex]10^{4}[/tex](13.3 - 4.9) = 8.4 × [tex]10^{4}[/tex]
Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn, and rode 3 miles to the local swimming pool. If he had ridden directly to the pool, how much distance would be have saved? Round to the nearest tenths of a mile.
riding directly to the pool would be 4.2 miles, so he would have saved 1.8 miles
a day care program has an average daily expense of $75 the standard deviation is $5 the owner takes a sample of 64 bills what is the probability the mean of his sample will be between $70 and $80? The answer choices are 68 1.0 34 + 30. Step 1 calculate a z-score for $70 step to give the probability for Step 1. Step 3 calculate the Z score for $80. Step for give the probability for step 3.
you can use the formula for sample means:
[tex][tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex][/tex]
where m stands for a value of the sample mean.
We are looking for the value, specifically for its two borderline values: 70 and 80
and their cumulative probabilities, p(z(80)) and p(z(70)). The difference p(z(80))-p(z(70))
will give the probability that m falls in the interval [70,80]
So let's get cracking at it:
[tex]z(70) = \frac{70-75}{5 / \sqrt{64}} = -8[/tex]
[tex]z(80) = \frac{80-75}{5 / \sqrt{64}} = 8[/tex]
These are very large values of z. You may notice that any z-table online won't even bother covering range that high - the probabilities for these values are virtually 0 (in the neg case) 1 (in the pos case).
This means that numerically the probability of the sample mean of 64 samples falling within the range of 1 standard deviation is very close to 1
So the answer choice should be 1.0
slope and rate of change
help please on card 7 an 8
Answer:
Card 7
The hourly rate of change/slope is $75 per hour.
Card 8
Frastastic is charging $0.48 per ounce.
Step-by-step explanation:
Card 7
Lets take the set up fee as "$[tex]s[/tex]" and,
Hourly rate as $[tex]x[/tex]per hour.
Now we can write equations for 3 hour event and 5 hour event.
[tex]s+3x=275[/tex] <------- (1)
[tex]s+5x=425[/tex] <------- (2)
Now we need to solve the simultaneous equations to find [tex]s[/tex] and [tex]x[/tex].
Subtract (1) from (2)
⇒[tex]s+5x-(s+3x)=425-275[/tex]
[tex]s+5x-s-3x=150[/tex]
[tex]2x=150[/tex]
[tex]x=75[/tex]
So the hourly rate of change/slope is $75 per hour.
Therefore, Raymond is right.
Card 8
You can take Amount (oz) as x values and Cost as y values and plot a graph.
Then the Slope of the graph will give you the rate Frastastic is charging per yogurt.
Slope of a linear graph is given by the following equation;
Slope(m)=[tex]\frac{y_{1}-{y_{2}}} {x_{1}-x_{2} }[/tex]
Slope(m)=[tex]\frac{6.72-2.4}{14-5}[/tex]
Slope(m)=[tex]\frac{4.32}{9}[/tex]
Slope(m)=[tex]0.48[/tex]
Therefore, Frastastic is charging $0.48 per ounce.
This is less than $0.50 per ounce charged by Fromazing. Therefore, Sterling is right.
Need help with this one please answer fast
Consider the scatter plot.
Describe the outliers from the scatter plot.
the outliers (8,25) and (39,16)
Answer:
The outliers are (8,25), and (39,16)
Step-by-step explanation:
These two points are outliers because they have a great value difference when compared to the other values.
PLZ HELP FOR BRAINLIEST!!!
The graph of a function is shown:
scatterplot of the following points: negative 3 and 2, negative 2 and negative 1, 2 and negative 1, and 3 and 3
Which of the following correctly identifies the set of outputs?
A) {–3, –2, 3}
B) {–1, 2, 3}
C) {(–3, 2), (–2, 1), (3, 3), (3, –1)}
D) {(2, –3), (1, –2), (3, 3), (–1, 3)}
Inputs are the first number output is the second. So youre outputs are 2, -1, -1, and 3. so i would say b
The set of outputs for the function represented by the scatterplot is {-1, 2, 3}, which matches Option B from the given choices.
You are looking to identify the set of outputs (also known as the range) of a given function based on a scatterplot. The output of a function is comprised of the second element in each ordered pair, which represents the y-value on the Cartesian plane. In this case, the scatterplot includes the points (-3, 2), (-2, -1), (2, -1), and (3, 3).
To find the correct set of outputs, we need to list the y-values from each point: 2, -1, -1, and 3. When listing a set, we do not repeat values, so the set of outputs for this function would be {2, -1, 3}. Therefore, the correct answer is Option B) {-1, 2, 3}.
Point A is located at (3,4) and is rotated 90 degrees counterclockwise about the origin. What is the new point of A?
A'(- 4, 3 )
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x )
A(3, 4 ) → A'(- 4, 3 )
A hybrid car can get 54 mpg when traveling at an average speed of 40 mph. You travel in this car at that speed for 45 miles to your grandparents’ house. Gas at your nearest station cost $3.23. Use this information to complete the statements. It will take________ Hours to get to your grandparents’ house. Your car will use______gallons of gas on the trip. You will spend________on gas for the trip.
A) The time to travel 45 miles at a speed of 40 mph can be found from ...
... time = distance / speed
... time = (45 mi)/(40 mi/h) = 9/8 h = 1 hr 7 min 30 sec
B) The gas consumption can be found from ...
... (45 mi)/(54 mi/gal) = 5/6 gal
C) The cost of gas can be found from ...
... ($3.23/gal)×(5/6 gal) ≈ $2.69
_____
The units of the numbers tell you what needs to be multiplied or divided to give the answer quantity with correct units. It pays to keep the units with the numbers. They can be treated as though they were a variable.
40 POINTS TO WHO EVER CAN ANSWER THIS!!!!!
Which quadratic function does the graph represent? The vertex is at (-2,-3) and the point is at (0,7)
A.)f(x)=5/2(x+2)^2-3
B.) f(x)= 10/9(x+2)^2-3
C.) f(x)=7(x-2)^2-3
D.)f(x)=5(x-2)^2-3
Answer:
y = 2.5(x + 2)^2 - 3
The answer is A
Step-by-step explanation:
The general equation for the vertex is
y = a (x + b)^2 + c
a we are not certain about
b = 2
c = - 3
y = a(x + 2)^2 - 3 Now we have to solve for a.
a is found by using the one point we know (0,7) It means when x = 0 y = 7 so just put those two numbers in.
7 = a(0 - 2)^2 - 3
7 = a (- 2)^2 - 3 Add 3 to both sides.
7 + 3 = a(4) Combine 7 and 3
10 = 4a Divide by 4
10/4 = a Do the actual division
2.5 = a
Answer: See above
A
the equation of a parabola in vertex form is
y = a(x - h )² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here the vertex = (- 2, - 3 ), thus
y = a(x + 2 )² - 3
to find a substitute (0, 7 ) into the equation
7 = 4a - 3 ( add 3 to both sides )
10 = 4a ( divide both sides by 4 )
a = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex]
y = [tex]\frac{5}{2}[/tex](x + 2 )² - 3