Answer:
Step-by-step explan 3x+2x+20+4x-20=180. 9x=180 X=180÷9. X=20
The total number of eggs, T, collected in one day from a chicken coop is proportional to the number of chickens, C, in the coop. If each chicken laid the same number of eggs, 4, which equation could be used to find the total number of eggs collected from the coop?
Answer:
T = 4C.
Step-by-step explanation:
T = 4C.
Total number of eggs = 4 * number of chickens.
Mr. Tola has a piece of wood that is 8 1/4 feet in length. He wants to cut it into pieces that are each 3/4 foot in length. How many 3/4 foot pieces of wood can mr. Tola make?
Answer:
11 pieces.
Step-by-step explanation:
We must divide 8 1/4 by 3/4
8 1/4 = 33/4
Dividing:
33/4 / 3/4
= 33/4 * 4/3
= 33/3
= 11.
Answer:
11 pieces.
Step-by-step explanation:
In order to make this happen, you need to divide the total length of the wood by the length that he needs, so it would be 8 1/4 feet by 3/4 of foot:
[tex]\frac{8\frac{1}{4} }{\frac{3}{4} } =\frac{\frac{33}{4} }{\frac{3}{4} }\\\frac{4(33)}{(3)(4)} \\\frac{132}{12}=11[/tex]
So now we know that he will get 11 piecesof 3/4 of foot out of the 8 1/4 feet long piece of wood.
Determine whether the following statement is true or false. Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.
Choose the correct answer below.
a) False
b) True
Answer: Ok, there are two types of variables, the independent and the dependents.
a dependent variable is one that changes in response to the independent variable.
In an experiment, yo usually have control over the independent variable, it may be the temperature on an oven, the intensity of an x-ray cannon, the time you let something heat under the sun, etc.
and the dependent variable will response to the independent variables in some way, so if you can observe how it changes you can understand te relationship between them, that is the goal of the experiment.
So it's true, yo want to know how the response variable "responds" to the treatment you apply.
determine whether or not each relationship represents a function. explain your reasoning
Answer:
left: yesright: noStep-by-step explanation:
A function maps an x-value to a single y-value. The graph of the parabola on the left does that.
The table on the right maps -1 to both 10 and 20, so does not meet the definition of a function.
A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The upper half of the ball can be formed by revolving the region bounded by the curves y.
Answer:
The volume of the ball with the drilled hole is:
[tex]\displaystyle\frac{8000\pi\sqrt{2}}{3}[/tex]
Step-by-step explanation:
See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:
[tex]x^2+y^2=15^2\to y=\sqrt{225-x^2}[/tex]
Then we set the integral for the volume by using shell method:
[tex]\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx[/tex]
That can be solved by substitution:
[tex]u=225-x^2\to du=-2xdx[/tex]
The limits of integration also change:
For x=5: [tex]u=225-5^2=200[/tex]
For x=15: [tex]u=225-15^2=0[/tex]
So the integral becomes:
[tex]\displaystyle -\int_{200}^{0}\pi \sqrt{u}du[/tex]
If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:
[tex]\displaystyle \int_{0}^{200}\pi u^{1/2}du[/tex]
Then applying the basic rule we get:
[tex]\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}[/tex]
Since that is just half of the solid, we multiply by 2 to get the complete volume:
[tex]\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}[/tex]
[tex]=\displaystyle\frac{8000\pi\sqrt{2}}{3}[/tex]
To find the volume of the resulting solid, calculate the volume of the ball and subtract the volume of the hole. The volume of the resulting solid is (4/3)π(15)³ - 10πr².
Explanation:To find the volume of the resulting solid, we need to calculate the volume of the ball and subtract the volume of the hole. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. So, the volume of the ball is V₁ = (4/3)π(15)³. The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is the height. The height of the cylinder formed by the hole is equal to the diameter of the ball, which is 2r. So, the volume of the hole is V₂ = π(5)²(2r) = 10πr².
Therefore, the volume of the resulting solid is V = V₁ - V₂ = (4/3)π(15)³ - 10πr².
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How to find the probability? Please show your work. Thanks!
The event of the machine working is [tex]A\cap B\cap C\cap D[/tex], and since the components operate independently, we have
[tex]P(A\cap B\cap C\cap D)=P(A)P(B)P(C)P(D)[/tex]
so just multiply the given probabilities together,
[tex]P(A\cap B\cap C\cap D)=0.99^2\cdot0.94\cdot0.93\approx0.8568[/tex]
(-2,1); perpendicular to y= - 2/5x -4
Help explain step by step?
Answer:
y = (5/2)x + 6
Step-by-step explanation:
The given line has a slope (coefficient of x) of -2/5. The perpendicular line will have a slope that is the negative reciprocal of this:
-1/(-2/5) = 5/2
Since you are given a point you want the line to go through, the point-slope form of the equation of the line is useful. That form for slope m and point (h, k) is ...
y = m(x -h) +k
For your slope m=5/2 and point (h, k) = (-2, 1), the equation of the line is ...
y = 5/2(x +2) +1
y = 5/2x +6 . . . . . eliminate parentheses
You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Which size will keep more of the original picture?
Answer:
16 in × 20 in
Step-by-step explanation:
Finding the % of the picture that can fit in 16×20 frameArea of picture= length by width
=4*6=24 in²
Area of frame=Length by width
=16*20=320 in²
% of the picture in the frame will be
(24/320) * 100% =7.5%
2. Finding the % of the picture that can fit in 18 × 24 frame
Area of picture=24 in²
Area of frame =Length by width
=18*24=432 in²
% of the picture in the frame will be;
(24/432)*100%=5.6%
The frame 16 by 20 in will keep 7.5% of the original picture
The frame 18 by 24 in will keep 5.6% of the original picture
Hence you should use the frame of 16 by 20 in because it will keep more of the original picture.
Discribe the difference between simple interest and compound interest?
Answer:
Compound interest the interest changes annually and with simple interest the interest is the same annually
The main difference between simple interest and compound interest is that simple interest is calculated only on the initial investment, whereas compound interest is calculated on the initial principal and also on the accumulated interest of previous periods.
Explanation:The primary difference between simple interest and compound interest lies in the way they are calculated. Simple interest is calculated only on the initial amount (principal) that you invested. For example, if you invest $1000 at a simple interest of 5% per annum, your interest for the first year will be $50, and it will remain the same for all the years the money is deposited.
Compound interest, on the other hand, is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit. So, in a scenario where you invest $1000 at a compound interest of 5% per annum, your interest for the first year will be $50, but for the second year, the interest will be calculated on $1050 (Principal + Interest of first year), making the interest for the second year $52.5 rather than $50.
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this is all the question gave me 6 C 2 = _______ a0
Answer:
15
Step-by-step explanation:
Using the definition of n[tex]C_{r}[/tex]
n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n! = n(n - 1)(n - 2) × 3 × 2 × 1
Hence
6[tex]C_{2}[/tex]
= [tex]\frac{6!}{2!(4!)}[/tex]
= [tex]\frac{6(5)(4)(3)(2)(1)}{2(1)4(3)(2)(1)}[/tex]
Cancel 4(3)(2)(1) on numerator/ denominator, leaving
= [tex]\frac{6(5)}{2(1)}[/tex] = [tex]\frac{30}{2}[/tex] = 15
Christina is tying tow pieces of string together to make a single piece. Her knot will reduce the lenght of each piece by 1/4 inch. If one piece is 3 1/4 inches long and the other is 5 1/2 inches long, what will be the length of the single piece of string?
Answer:
8 1/4 inches
Step-by-step explanation:
(3 1/4 - 1/4) + (5 1/2 - 1/4) = 3 + 5 1/4 = 8 1/4 . . . inches
One of your household chores is to do the dishes every night after dinner.Your parents come to you with two choices about how you want to earn your allowance. Option one: is that you will be paid $250.00 at the end of every month for the work you do Option two: is that they will pay you a penny the first day and double your play each day for the rest of the month Which method of payment is the better deal? Use a problem solving strategy to determine your answer. Explain, in clear sentences, why your decision is the best one. Your explanation must prove why the method you chose is the better option
Answer:
the penny option is the much better deal
Step-by-step explanation:
The sequence of pay amounts for the "penny option" is ...
$0.01, $0.02, $0.04, $0.08 ...
For day n, the amount of pay is $0.01·2^(n-1). For day 30, the amount of pay is ...
$0.01·2^29 = $5,368,709.12
In case you can't tell, the "penny option" is a much better deal than $250.00. (You might need to credit check your parents before accepting this deal. I know my parents could not make good on this "penny option" offer.)
The total amount for the 30 days will be double this amount, less one cent, or ...
$10,737,418.23
_____
Sum of a geometric sequence
The daily payments of the penny option are a geometric sequence. The sum of n terms of such a sequence is given by ...
Sn = a1(r^n -1)/(r -1)
where a1 is the first term ($0.01) and r is the common ratio (2). In our case, the sum for n days is ...
Sn = $0.01·(2^n -1)
On day 15, this will already be more than $250. The accumulated pay on that day will be $0.01·(2^15-1) = $327.67.
A point is rotating with uniform circular motion on a circle of radius r. Find ω if
r = 9 cm and v = 3 cm/sec.
Answer:
w = 0.333
Step-by-step explanation:
In circular motion you have:
v = wr
replacing:
3 = 9w
0.333 = w
The angular speed of a point with r = 9 cm and v = 3 cm/sec is 0.33 rad/s
The angular speed?
The angular speed (ω) is given by:
ω = v/r
Where v is the linear speed and r is the radius.
Given that v = 3 cm/sec = 0.03 m/s, radius = 9 cm = 0.09 m, hence:
ω = v/r = 0.03/0.09 = 0.33 rad/s
The angular speed of a point with r = 9 cm and v = 3 cm/sec is 0.33 rad/s
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Write the equation of the line parallel or perpendicular to the given line that passes through the given point. Give your answer in point slope form and slope intercept form.
1. Parallel to y=-4/5x + 1 that passes through (-3, -5)
2. Perpendicular to y=1/3x + 3 that passes through (4, 1)
Answer:
y +5 = (-4/5)(x +3) y = (-4/5)x -37/5y -1 = -3(x -4) y = -3x +13Step-by-step explanation:
1. It is convenient to start with point-slope form, then simplify the result to slope-intercept form. The two forms of the equation for a line are ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y = mx +b . . . . . . . . line with slope m and y-intercept b
The given lines are in slope-intercept form, so we can read the slope directly from the equation.
The slope of the parallel line will be the same as the slope of the given line: -4/5.
point-slope form: y +5 = (-4/5)(x +3)
slope-intercept form: y = (-4/5)x -37/5
__
2. The slope of the given line is 1/3. The slope of the perpendicular line is the negative reciprocal of that: -1/(1/3) = -3. Your lines are then ...
point-slope form: y -1 = -3(x -4)
slope-intercept form: y = -3x +13
What are the coordinates of point Q.
The coordinates of point Q are (0, 3).
Option C is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
From the graph,
Point Q is at y = 3 on the y-axis and 0 on the x-axis.
So,
The coordinates of point Q are (0, 3).
Thus,
The coordinates of point Q are (0, 3).
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PLEASE ANSWER:
1. Distribute to simplify the expression:
3 ( 2X + 5Y - 4)
CHOICES:
6X + 15Y - 12
21XY + 12
6X + 15X + 12
21XY - 12
2. What is the value of the expression when c = 4?
4c + 3c -2c + 5
CHOICES:
25
14
33
16
3. Factor the expression:
55x - 25
CHOICES:
5 ( 11x - 5)
11 ( 5x - 5)
5 ( 5x + 5)
11 ( 5x + 5)
Answer:
1. 6x+15y-12
2. 25
3. 5(11x-5)
Step-by-step explanation:
1. We have the expression [tex]3(2x+5y-4)[/tex] we have to distribute number 3 to simplify the expression:
[tex]3(2x+5y-4)=\\3.(2x)+3.(5y)-3.(4)=\\=6x+15y-12[/tex]
Then the correct answer is the first choice: 6x+15y-12
2. We have to find the value of the expression when c=4, we have
[tex]f(c)=4c + 3c -2c + 5[/tex]
Then when c=4:
[tex]f(4)=4.(4) + 3.(4) -2.(4)+ 5\\f(4)=16+12-8+5\\f(4)=28-3\\f(4)=25[/tex]
Then the correct answer is the first choice: 25
3. We have to factor the expression 55x-25,
we can see that (5).11=55 and (5).5=25, then the common factor in this expression is number 5,
[tex]55x-25=\\(5).11x-(5).5=\\=5(11x-5)[/tex]
Then the correct answer is the first choice: 5(11x-5)
declaration a plane at the uniform rate of 8.0 meter/second ^2 , a pilot stops the plane in 484 meters. how fast was the plane going before breaking began ?
Answer:
88 m/s
Step-by-step explanation:
The appropriate formula relating initial speed v, acceleration a, and distance d is ...
v² = 2ad
v² = 2(8 m/s²)(484 m) = 7744 m²/s²
Taking the square root gives ...
v = √7744 m/s = 88 m/s
You are designing a container in the shape of a cylinder. The radius is 6 inches. You want the container to hold at least 324π cubic inches. What is the least possible height of the container?
Answer:
The answer to your question is: h = 9 in
Step-by-step explanation:
Data
radius = 6 inches
V = 324 π in³
h = ?
Formula
V = πr²h
Then, we solve it
324π = πr²h cancel π
324 = r²h substitution
324 = 6² h
h = 324 /6² simplify
h = 324/36
h = 9 in result
Utilizing the volume formula for a cylinder, we can calculate the minimum height required for a volume of 324π cubic inches. Given a radius of 6 inches, we solve the formula to find a minimum cylinder height of 9 inches.
Explanation:The subject of this question is mathematics, specifically geometry focusing on the properties of cylinders. In this instance, we want to calculate the minimum height of a cylinder that can hold a specified volume. The formula to find the volume of a cylinder is V = πR²h, where 'R' is the radius and 'h' is the height.
Given that the radius is 6 inches and the desired volume is 324π cubic inches, we can insert these values into our formula. So, 324π = π*(6)²*h which simplifies to 324 = 36h. Then, we need to solve for 'h', which involves dividing 324 by 36. The result shows that the minimum height 'h' of the cylinder is 9 inches.
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Using an independent-measures t, the 90% confidence interval for the difference between two population means ranges from 19 to 23. Based on this confidence interval, you can conclude that the difference between the two sample means is ____.a) 4 pointsb) 19 pointsc) 21 pointsd) 23 points
Answer:
b
Step-by-step explanation:
We must determine the the x value at 90% confidence interval. We find this from a table relating confidence intervals and x values. For 90%, z is 1.645.
WE must determine the mean of 19 and 23:
[tex]=(19+23)/2=21[/tex]
We must determine the standard deviation. We let n be the number of population which is 2. We need to take the numbers 19 and 23 and subtract each by the mean and square the answer:
[tex](19-2)^2=289[/tex]
[tex](23-2)^2=441[/tex]
We then determine the mean of these two values as:
[tex](289+441)/2=365[/tex]
Now we take the square root of 365:
[tex]\sqrt{365}=19.1[/tex]
The standard deviation is 19.1
The answer is b
Please Help
Last winter, Michigan had these snow fall totals (in inches) over a one month period: 9.2, 0.5, 6, and 5.9. What was the total amount of snow during the month?
Answer:
21.6
Step-by-step explanation:
9.2+0.5+6+5.9=21.6 Because it is looking for the TOTAL amount you add the numbers.
Answer: 21.6 inches
Step-by-step explanation:
Given : Last winter, Michigan had these snow fall totals (in inches) over a one month period: 9.2, 0.5, 6, and 5.9.
Then, By suing the addition operation.
The total amount of snow during the month will be (Sum of all the amount of snow fall ) :-
9.2+0.5+6+5.9 = 21.6 inches
Therefore, the total amount of snow during the month= 21.6 inches
Anthony leaves Kingstown and drives 160 miles to Albany. He leaves at 2:00 p.m. At 2:15p.m., Emily leaves Albany and drives to Kingstown at 40 m.p.h. If Anthony is driving 45 m.p.h., at what time do they pass each other on the road?
Answer:
The time at which the pass each other on the road is 4:00 pm
Step-by-step explanation:
The first step is to write the equations that give us the position of Emily and Anthony, these are give by:
[tex]x_A = x_{A0}+v_At[/tex] for Anthony
[tex]x_E=x_{E0}+v_Et[/tex] for Emily
Since Antony drives 160 miles to Albany, we can claim that the distance from Kingstown to Albany is 160 miles.
Let us set the initial position of Antony in Kingstown and consider it as the origin of our coordinate system. In this way, [tex]x_{A0}=0[/tex].
This automatically tells us that Emily initial position, in Albany, is 160 miles from our origin, hence [tex]x_{E0} = 160 miles[/tex].
Now, we need to define where to start counting the time. In this problem, it is easier to set time zero when Emily leaves. The reason for this is that now, we can say that when Emily left, Anthony was already traveling during 15 mins (remember Emily departing time was 2:15 pm and Anthony's time was 2:00 pm) and Anthony's initial position was from Emily's point of view was different from zero. We can calculate this distance as the multiplication of the time Anthony was traveling times the speed at which he was driving. This is:
[tex]x_{A0}=v_At[/tex]
being [tex]t[/tex] the 15 mins he traveled before Emily started and [tex]v[/tex] the 45 m.p.h given by the problem. We also need to convert 15 mins to hours, which gives 0.25 hours. Thus:
[tex]x_{A0}=45*0.25\\x_{A0}=11.25[/tex] miles
and the position equations are now:
[tex]x_A= 11.25 + v_At[/tex] for Anthony
[tex]x_E=160 + v_Et[/tex]
Since we are asked the time at which the pass each other on the road we need to equals their positions, [tex]x_A=x_E[/tex]:
[tex]11.25+v_At=160-v_Et[/tex]
Notice here that Emily's position is negative since she is moving towards the origin of our system, meaning in the negative direction. Solving for [tex]t[/tex]:
[tex]11.25+v_At=160-v_Et\\v_At+v_Et=160-11.25\\t(v_A+v_E)=148.75\\t = \frac{148.75}{v_A+v_E}[/tex]
Substituting the values of [tex]v_A=45[/tex] and [tex]v_E=40[/tex]:
[tex]t = \frac{148.75}{45+40}=\frac{148.75}{85}\\t=1.75 h[/tex]
What we have calculated is the time interval from where we start counting the time and remember this was set at 2:15 pm when Emily left. Since the exercise asks for the hours of the day we need to add the time interval to 2:15 pm and:
[tex]1.75 h = 1 h+45 min[/tex]
And 2:15 pm + 1 h is 3:15 pm + 45 mins is 4:00 pm which is the time at which the pass each other on the road.
Final answer:
Anthony and Emily will cross paths at 4:00 p.m. after calculating the distance covered by Anthony and the remaining distance between them when Emily starts driving, with their combined speed taken into consideration.
Explanation:
To solve this question, we need to calculate the time when Anthony and Emily will cross paths on the road, given that they are traveling towards each other from Kingstown to Albany and vice-versa. Anthony drives at 45 mph whereas Emily drives at 40 mph
Let's first find out how far apart they are when Emily starts her journey at 2:15 p.m. Since Anthony left at 2:00 p.m. and drives for 15 minutes until Emily starts her journey, we calculate the distance he has covered as:
Distance = Speed × Time = 45 mph × 0.25 hours (since 15 minutes is 0.25 of an hour) = 11.25 milesNow, the remaining distance between them is:
160 miles - 11.25 miles = 148.75 milesThe combined speed at which they're closing the distance is:
45 mph + 40 mph = 85 mphTo find the time it takes for them to meet, we use the formula:
Time = Distance / Speed = 148.75 miles / 85 mph ≈ 1.75 hoursSince 1.75 hours is 1 hour and 45 minutes, they will meet at:
2:15 p.m. + 1 hour and 45 minutes = 4:00 p.m.Therefore, Anthony and Emily will cross paths at 4:00 p.m.
Charlize and Camille solved the equation 4x – 2y = 8 for y. Their work is shown
below.
Charlize
Camille
4x – 2y = 8
4x – 2y = 8
-2y = 8 + 4x
-2y = 8 – 4x
y=-4- 2x
y=-4 + 2x
Which student solved the equation correctly? Justify your answer.
Answer:
The answer to your question is below
Step-by-step explanation:
Equation 4x - 2y = 8 solve for y
First, pass 4x to the right side -2y = -4x + 8
Pass -2 to the right side y = -4/-2 x + 8 /-2
Simplify y = 2x -4 or y = -4 + 2x
I can not see clearly the work of Charlize and Camille, but the one that has the answer shown above is correct.
Answer:
Step-by-step explanation:
describe the transformation f(-x)
Changing [tex]x\mapsto -x[/tex] "inverts" the orientation of the x axis, so the graph of f(x) is transformed by reflecting it about the y axis.
The transformation f(-x) represents a reflection of function f(x) across the y-axis. Even functions are unchanged by this transformation, while odd functions are reversed.
Explanation:The transformation f(-x) in mathematical terms represents a reflection of the function f(x) across the y-axis. For instance, if you have a function that plots as a certain curve when x is positive, applying function to f(-x) would result in the same curve but flipped horizontally across the y-axis. This is because replacing x with -x inverts the sign of every x-coordinates of the original points, causing a mirror image reflection over the y-axis. Thus, while the original function may say f(x) = x², f(-x) would also form a parabola, but it would be flipped across the y-axis.
For example, if f(x) = x³ for x > 0 which increases, f(-x) = -x³. As x values are now negative, the graph flips and for x > 0, f(-x) decreases.
Note that even functions like f(x) = x², which are symmetric about the y-axis, remain unchanged when transformed to f(-x), while odd functions like f(x) = x³, which are symmetric about the origin, are reversed when f(-x) is implemented.
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Anna is writing a computer game program. She needs to “move” a square 3 units to the left and 2 down by applying a translation rule to the coordinates of the vertices. One corner of the pre-image square is at the origin and the diagonally opposite corner is at (4,4). The sides of the square align with the coordinate axes. After the transformation what will be the coordinates of the image of each of the four vertices?
Answer:
(-3,-2), (-3,2) , (1,2) and (1,-2)
Step-by-step explanation:
Give the translation rule as; 3 units to the left and 2 units down, it means (-3,-2)
The given coordinates of the square are (0,0) and (4,4). You can plot the coordinates on a graph tool and determine the position of the other vertices
of the square as (0,4) and (4,0)
Applying the translation to each point
(0,0)⇒(-3,-2) = (-3,-2)
(0,4)⇒(-3,-2) = (-3,2)
(4,4)⇒ (-3,-2) = (1,2)
(4,0)⇒(-3,-2)= (1,-2)
The image of the vertices after transformation will be
(-3,-2), (-3,2) , (1,2) and (1,-2)
After creating a hypothesis, Janis decides how to best measure the impact of her manipulation. This variable that is impacted by manipulating the independent variable is known as _____
Answer:
This variable that is impacted by manipulating the independent variable is known as dependent variable
Step-by-step explanation:
One of the methods to test a hypothesis is the use of independent variable. The independent variable is manipulated to know if the change will be effective or not.
The variable which will be impacted by the independent variable is called dependent variable. The researcher manipulated the values for independent variable to check if the dependent variable changes or not ..
How many phone numbers are possible in the (770) area code if: For the form ABC-XXXX, A is restricted to numbers 2-9. B, C, and X can be any digit 0-9. Also, the number 867-5309 is not used.
a. 6,999,999 c.7,999,999
b. 7,000,000 d.8,000,000
Answer:
c.7,999,999
Step-by-step explanation:
The phone number is of the form ABC - XXXX
A can be any number from 2 - 9. This means number of possible values for A are 8.
The rest of the places B,C and X can be any digit from 0 - 9. This means there are 10 possible values for each of these.
Since, value to A can be assigned in 8 ways, and to the rest of the 6 positions in 10 ways, according to the fundamental rule of counting, the total number of possible phone numbers that can be formed will be equal to the product of all the individual ways:
Total possible phone numbers = 8 x 10 x 10 x 10 x 10 x 10 x 10
Since, 1 of the given number: 867-5309 is not used, the total possible phone numbers will be:
Total possible phone numbers = [tex]8 \times 10^{6} - 1 = 7999999[/tex]
Hence, option C: 7,999,999 give the correct answer.
Final answer:
The answer calculates the possible phone numbers in the (770) area code with given restrictions, ending up with 7,999 possible phone numbers.
Explanation:
To calculate how many phone numbers are possible in the (770) area code with the given restrictions, we first determine the possibilities for each digit:
A (restricted to 2-9): 8 optionsB, C, X (0-9 for each digit): 10 options each
So, the total number of possible phone numbers is: 8 (A) * 10 (B) * 10 (C) * 10 (X) = 8,000. However, we need to exclude the number 867-5309, so the final count is 8,000 - 1 = 7,999.
Find the volume generated by rotating the region bounded by the given curves about the specified line. Express the answers in exact form or approximate to the number of decimal places indicated.
Find the volume of the solid generated by revolving the region bounded by the curve y = ln x, the x-axis, and the vertical line x=e². about the x-axis. (Express the answer in exact form.)
The volume of the solid generated by revolving the region bounded by ( y = [tex]\ln(x) \)[/tex], the x-axis, and the vertical line [tex]\( x = e^2 \)[/tex] about the x-axis is given by the integral
[tex]\[ V = \pi \int_{1}^{e^2} (\ln(x))^2 dx \][/tex]
Now, let's compute the volume step by step.
1. Set up the integral for the volume using the disk method, since we are rotating around the x-axis. The formula for the volume of a solid of revolution using the disk method is [tex]\( V = \pi \int_{a}^{b} [f(x)]^2 dx \)[/tex], where [tex]\( f(x) \)[/tex] is the function being rotated, and [tex]\( [a, b] \)[/tex] is the interval of rotation.
2. Since [tex]\( f(x) = \ln(x) \)[/tex] and we are rotating around the x-axis from [tex]\( x = 1 \)[/tex] to [tex]\( x = e^2 \)[/tex], our integral becomes
[tex]\[ V = \pi \int_{1}^{e^2} (\ln(x))^2 dx \][/tex]
3. Solve the integral. This particular integral requires integration by parts or a special integrating factor due to the natural logarithm squared. The integral of [tex]\( (\ln(x))^2 \)[/tex] is not straightforward, so we will use integration by parts.
Let's solve the integral now.
It appears there was a mistake in the code due to the missing definition of the exponential function `exp`. Let me correct that and solve the integral again.
The volume of the solid generated by revolving the region bounded by [tex]\( y = \ln(x) \)[/tex], the x-axis, and the vertical line [tex]\( x = e^2 \)[/tex] about the x-axis is approximately[tex]\( 40.14 \)[/tex]. This is the numerical approximation, but you asked for the exact form, so let's represent that as well.
The exact form of the volume, without numerical approximation, is:
[tex]\[ V = \pi \int_{1}^{e^2} (\ln(x))^2 dx \][/tex]
Now I will present the exact form of the integral result.
The exact form of the volume of the solid generated by revolving the region bounded by [tex]\( y = \ln(x) \),[/tex] the x-axis, and the vertical line [tex]\( x = e^2 \)[/tex]about the x-axis is:
[tex]\[ V = \pi \left( -2 + 2e^2 \right) \][/tex]
This is the exact expression for the volume in terms of [tex]\( \pi \) and \( e \),[/tex] the base of the natural logarithm.
Which of the following cannot be the probability of an event?
Answer:
-61
Step-by-step explanation:
Probability can be a natural number, from O to infinity. In fact, how can you represent a -61 probability? it's impossible, at maximum you can have a null probability, that is 0
Walden’s family is shopping for a reclining chair. The chair the family decided on has a retail price of $800 plus 5% sales tax at four stores. Each store is offering a different promotion. Store Promotional Offer A $75 instant rebate B 10% off sale C 5% off sale plus store pays sales tax D a “no tax” sale—the store pays the tax Which store has the best deal? store A store B store C store D
Answer:
B 10% off sale, with a total price to pay of 756
Step-by-step explanation:
Retail price (Rp) = $800
Taxes (T) = 5%
Offer A $75 instant rebateTotal price A (TA) = Rp - 75 + (Rp - 75) 5%
TA = 800 - 75 + (800-75) 5%
TA = 725 + 725 5%
725 5% = 725*5/100 = 36.25
TA= 725+36.25 = $761.25
Offer B 10% off saleTotal price B (TB) = RP - RP 10% + (RP - RP 10%) 5%
TB = 800 - 800 10% + (800 - 800 10%) 5%
800 10% = 800*10/100 = 80
TB = 800 - 80 + (800 - 80) 5%
TB = 720 + 720 5%
720 5% = 720*5/100 = 36
TB = 720 + 36 = $756
Offer C 5% off sale plus store pays sales taxstore pays sales tax means Walden's family will not need pay for taxes
Total price C (TC) = RP - RP 5%
TC = 800 - 800 5%
800 5% = 800*5/100 = 40
TC = 800 - 40 = $760
Offer D a “no tax” sale—the store pays the taxMeans that Walden's family will need pay just the retail price
TD = $800
The beast deal is from the store B
Answer:
the answer is b
Step-by-step explanation:
hoped this helped
Find the least common denominator of the fractions: 3/5 and 2/7
Answer:
35
Step-by-step explanation:
5 and 7 are both prime numbers, so the least common multiple of 5 and 7 is their product, 5 * 7 = 35
The least common denominator of the fractions 3/5 and 2/7 is found by determining the least common multiple of the denominators 5 and 7. Since they are prime numbers, their LCM is their product, which is 35.
Explanation:To find the
least common denominator
(LCD) of the given
fractions
, 3/5 and 2/7, we must find the least common multiple (LCM) of the two
denominators
5 and 7. The LCM of any two numbers is the smallest number that both numbers can divide evenly into. Since 5 and 7 are prime numbers, the LCM is simply their product, which is 35. Therefore, the least common denominator of 3/5 and 2/7 is 35.
Learn more about Least Common Denominator here:https://brainly.com/question/34199505
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