Answer:
.666
Step-by-step explanation:
which repersents the nth term of the sequence {2,-1,-4,-7,...}
Answer:
the general Question
which repersents the nth term of the sequence {2,-1,-4,-7,...}formula for the nth term in an arithmetic sequence is: an = a0 + d(n-1) where a0 is the first term, n is nth, d is the difference for our problem a0 is -2, d is 3
Step-by-step explanation:
helloineedmppiontsthe general formula for the nth term in an arithmetic sequence is: an = a0 + d(n-1) where a0 is the first term, n is nth, d is the difference for our problem a0 is -2, d is 3
Which property is used in the following expression ? 3 (6 + 5) = 18 + 15
Distributive Property.
Pleaseeee hellp meeeee
Answer:
57,600 ft
Step-by-step explanation:
A rectangular piece of sheet metal with an area of 1800 in2 is to be bent into a cylindrical length of stovepipe having a volume of 900 in3. What are the dimensions of the sheet metal
The dimensions of the sheet metal are 10 inches by 2.86 inches.
To find the dimensions of the sheet metal, we need to use the formulas for the area and volume of a cylinder.
The formula for the volume of a cylinder is:
\(V = πr^2h\)
where V is the volume, r is the radius, and h is the height.
Since we want the volume of the stovepipe to be 900 in^3, we can plug in the values and solve for the height:
\(900 = πr^2h\)
\(h=\frac{900}{πr^{2} }\)
Now, the formula for the lateral surface area of a cylinder is:
A = 2πrh
where A is the lateral surface area.
We know that the sheet metal has an area of 1800 in^2, so we can set up an equation:
1800 = 2πrh
Substituting h from the first equation, we get:
\(1800=2πr(\frac{900}{πr^{2} } )\)
Simplifying, we get:
r = 10
So the radius of the cylinder is 10 inches.
Substituting this value of r into the equation for h, we get:
\(h=\frac{900}{π(10^{2}) }\)
h =2.86
So the height of the cylinder is approximately 2.86 inches.
Therefore, the dimensions of the sheet metal are 10 inches by 2.86 inches.
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A small square frame has an area of 16 square inches. A large square frame has an area of 64 square inches. How much longer is the side length of the large frame than the side length of the small frame
The side length of the large frame is 4 inches longer than the side length of the small frame.
To find the difference in side lengths between the small square frame and the large square frame, we need to find the length of the sides of each frame.
Let x be the length of the side of the small square frame. Then, we know that the area of the small frame is 16 square inches.
Area of small frame = side length of small frame x side length of small frame = 16
\(x^2 = 16\)
Taking the square root of both sides, we get:
\(x = 4 inches\)
So, the length of the side of the small square frame is 4 inches.
Now, let y be the length of the side of the large square frame. We know that the area of the large frame is 64 square inches.
Area of large frame = side length of large frame x side length of large frame = 64
\(y^2 = 64\)
Taking the square root of both sides, we get:
y = 8 inches
So, the length of the side of the large square frame is 8 inches.
To find the difference in side lengths, we subtract the length of the small frame from the length of the large frame:
\(y - x = 8 - 4 = 4\)
Therefore, the side length of the large frame is 4 inches longer than the side length of the small frame.
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In Exercises 1-6, find the orthogonal complement W⊥ of W and give a basis for W⊥.
w = {[x,y]} : 2x-y = 0}
u = [2, -2]. The orthogonal complement W⊥ of W is the set of all vectors orthogonal to W. In this case, a basis for W⊥ is {[2, -2]}.
Rewrite the equation in standard form for vectors
The given equation is 2x - y = 0. We can rewrite it as y = 2x
Find a vector in W
We can choose any value of x and compute the corresponding y value to find a vector in W. Let x = 1, then y = 2(1) = 2.
So, one such vector in W is v = [1, 2].
Find a vector orthogonal to v
To find a vector orthogonal to v, we need to find a vector u = [a, b] such that the dot product of v and u is zero (v • u =
0). So, [1, 2] • [a, b] = 0. This translates to 1a + 2b = 0.
Find a basis for W⊥
Solve the equation 1a + 2b = 0 for a and b. We can set a = 2 and solve for b: 2(2) + 2b = 0, which gives b = -2.
Therefore, u = [2, -2].
The orthogonal complement W⊥ of W is the set of all vectors orthogonal to W. In this case, a basis for W⊥ is {[2, -2]}.
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The reduction of the fraction is (y-3)/4.
How to interpret the fraction?Suppose the fraction is proper (the numerator is smaller than the denominator).
Let it be \(\dfrac{a}{b}\)
Then, we can interpret it as:
\(\dfrac{a}{b}\)= a parts out of b parts of a thing.
There is a fraction, containing numerator(upper value) and denominator(lower value).
When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction.
A proper fraction is also called fraction which is less than 1.
And an improper fraction is ≥ 1
A mixed fraction contains a sum of whole number and a proper fraction.
Given;
=y^2-9/4y+12
=y^2-3^2/4(y+3)
=(y+3)(y-3)/4(y+3)
=y-3/4
Therefor, the answer of fraction will be (y-3)/4
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can i get help with this please?
Answer:
1. (any number less than 10) < 10
2. 520 (division)
520
➗ 2
260
3. (any number less than 3 *1 or 2*) < 3
4. (any number greater than 1) > 1
5. (Subtraction - A number subtracting two and the result is less than 10) < 10
Step-by-step explanation:
1. The symbol "<" shows greater than. It is facing the number "10",
So, we need to get any number below 10. As example: 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9. The numbers I mentioned there are what you can use for question 1.
-----------------------------------------------------------------------------------------------------------------
2. The number 520' is what I find to be multi-result but I would do division. Number 520 is part of the addition, subtraction, multiplication, and division but I am doing division.
Divison:
520
➗ 2
260
Multiplication:
260
x 2
520
Addition:
500
+ 20
520
Subtraction:
550
- 30
520
These are the examples that you can try for number 2.
-----------------------------------------------------------------------------------------------------------------
3. First, you can see that there is the greater symbol here again, "<".
But this time, it's pointing to 3. Which means the number is less than 3.
The only numbers that are less than 3 is 1 and 2 so those are the 2 options you can choose.
-----------------------------------------------------------------------------------------------------------------
4. This time, the symbol is less. It's now pointing at 1, so you can pick any number that is greater than 1.
Example:
5 > 1
Like that! You can pick any number that is greater than 1 for this question!
-----------------------------------------------------------------------------------------------------------------
5. the equation "-2 < 10" is about a number subtracting 2 but than the results come in being less than 10. Since we have spotted the greater symbol as "<", and the subtraction symbol as "-".
Now, first we find a number that can subtract 2 but less than 10 in the result.
The options we have are:
1. 2 (2-2=0 ; 0 < 10)
2. 3 (3-2=1 ; 1 < 10 )
3. 4 (4-2=2 ; 2 < 10 )
4. 5 (5-2=3 ; 3 < 10 )
And so on until you reach number 9 as the result!
-----------------------------------------------------------------------------------------------------------------
Hope this helped you! I tried my best to help you. But have a good day!
5x⁴ + 12 classify the polynomial by degree and number if terms
Answer:
The polynomial has degree 4 and 2 terms.
Step-by-step explanation:
The degree is 4 because it is the highest degree among the terms (\(5x^4\) has degree 4 and \(12\) has degree 0). There are 2 terms (\(5x^4\) and \(12\)).
Hope this helps :)
if x=4 what is y when y=-2x-4
What is the median value of the data set shown on the line plot?
Answer:
110
Step-by-step explanation:
you would have to place the values in a line in ascending order and cancel numbers on both sides until you only have one left in the center. If you have two left because the number of variables is even then add both and divide by two. That was the case here. Both middle numbers were 110
so...
110+110/2
220/2
110
Let R be the region Bounded by the following curves. Find the volume of the solid generated when R is revolved about the y-axis.
y= sin ^-1 (x/13), X=0, y= (pi/12)
The volume if the solid generated is 12.32 cubic units.
The volume of the solid generated by revolving the region bounded by the curves y = sin^-1(x/13), x = 0, and y = pi/12 about the y-axis can be calculated using the method of cylindrical shells.
First, we need to find the limits of integration for y. From the equation y = sin^-1(x/13), we can solve for x to get x = 13 sin(y). Since y ranges from 0 to pi/12, we know that x ranges from 0 to 13 sin(pi/12).
Next, we need to find the height of each cylindrical shell. This is simply the difference between the upper and lower curves, which is pi/12 - sin^-1(x/13).
Finally, we integrate the expression for the volume of a cylindrical shell over the range of y to obtain the total volume:
V = ∫[0, pi/12] 2πx(pi/12 - sin^-1(x/13)) dy
V = π/6 ∫[0, pi/12] (13sin(y))^2 (pi/12 - y) dy
V = π/6 ∫[0, pi/12] 169sin^2(y) (pi/12 - y) dy
V = π/6 [169(1/2)(pi/12)^2 - 169∫[0, pi/12] ysin^2(y) dy]
V ≈ 12.32 cubic units
Therefore, the volume of the solid generated by revolving the region bounded by the curves y = sin^-1(x/13), x = 0, and y = pi/12 about the y-axis is approximately 12.32 cubic units.
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A group of Tibetan monks created a sand mandala at an art museum. The mandala was in the shape of a circle with a radius of 2.5 ft What was the was the area of the sand mandala use 3.14 for pie
A 2.5-foot-radius sand mandala's surface area is 19.63 square feet.
A Tibetan Buddhist practise known as "sand mandala" involves building and tearing down mandalas composed of different coloured sand. The ritualistic breakdown of the sand mandala is followed by ceremonies and viewing when it is finished to represent Buddhism's doctrine on the fleeting nature of material life.
Here is how to calculate a circle's area:
Circle area is equal to πr² (where r is the radius of the circle)
We can use the radius value that has been provided to solve for the area using the following formula:
The sand mandala's size is πr²= π(2.5)²= π(6.25)= 19.63 square feet.
Hence, the sand mandala has a 19.63 square foot surface area.
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Find the difference of (t-8)-(t-15)
Answer:
T=7
Step-by-step explanation:
(T-8) x (-t+15)
Then 15-8
T= 7
A farmer harvests wheat in the field. She drives a tractor down ten 500-meter rows for a total distance of 5,000 meters. If it takes the farmer 2 hours and 30 minutes to harvest all the wheat, about how many minutes did she spend in each row?
Answer:
15 minutes
Step-by-step explanation:
2 and a half hours is the same as 150 minutes. There are ten rows, so if you divide 150 by 10, you get 15. The farmer spent 15 minutes in each row.
Answer:
15
Step-by-step explanation:
2 hours and 30 minutes equals 150 minutes. Divide by the 10 rows equals 15 minutes each.
determine whether the geometric series is convergent or divergent. 6 5 25 6 125 36 convergent divergent correct: your answer is correct. if it is convergent, find its sum. (if the quantity diverges, enter diverges.) incorrect: your answer is incorrect.
The geometric series defined by 6 + 5 + 25/6 + 125/36 +....., is a convergent series. The sum of convergent series is equals to the 36.
An infinite geometric series is which one of the following form \(∑a{r}^{n−1} \); where, n varies from 1 to ∞. Then it converges only when the absolute value of the common ratio is less than 1, i.e., |r|<1. When the series converges, sum formula for series is Sum = a/(1−r)
where, a --> first term and
r -->constant ratio of every two successive terms
We have a geometric series defined as 6 + 5 + 25/6 + 125/36 +.....
First term of series, a = 6
Common ratio of series, r = 5/6 < 1
We have to determine if the series converges or diverges. As we see the constant ratio, r = 0.82, which is less than 1. So, from the geometric series test this series is convergent series. Now, the formula for the sum to infinity of a geometric progression, S = a/(1 - r)
= 6/( 1 - 5/6)
= 6 × 6
= 36
Hence, required sum of series is 36.
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Complete question:
determine whether the geometric series is convergent or divergent, 6 + 5 + 25/6 + 125/36 +.....convergent divergent correct: your answer is correct. if it is convergent, find its sum. (if the quantity diverges, enter diverges.) incorrect: your answer is incorrect.
a partial relative frequency distribution is given. class relative frequency a 0.22 b 0.18 c 0.43 d (a) what is the relative frequency of class d?
The relative frequency of class D is 0.35.
The number of times an event occurs is called a frequency. Relative frequency is an experimental one, but not a theoretical one. Since it is an experimental one, it is possible to obtain different relative frequencies when we repeat the experiments.
The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes gives the value of relative frequency.
Consider the given partial relative frequency distribution.
Class Relative frequency
A 0.22
B 0.18
C 0.43
D
Then,
We need to find the relative frequency of class D
We know that,
Sum of relative frequency is equal to one.
that is.
\($0.22+0.18+0.25+$\) relative frequency of class D=1
0.65 + relative frequency of class \($\mathrm{D}=1$\)
relative frequency of class D=1-0.65
=0.35
We get,
Relative frequency of class D Is 0.35
Therefore, the relative frequency of class D is 0.35
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5-13 Question Help opping Two friends shop for fresh fruit. Elena buys a watermelon for $6.55 and 3 pounds of cherries niy buys a pineapple for $4.35 and 2 pounds of cherries. Use the variable p to represent the price, in lars, per pound of cherries. Write and simplify an expression to represent how much more Elena sper e expression represents how much more Elena spent than Taniy. mplify your answer. Use integers or decimals for any numbers in the expression.) nter your answer in the answer box and then click Check Answer. Clear All Check Ans I parts showing Review progress Question 6 of 12 Back Next →
Answer:
The expression;
\(2.2+p\)represents how much more Elena spent than Taniy
Explanation:
Let the variable p to represent the price per pound of cherries.
Given that Elena buys a watermelon for $6.55 and 3 pounds of cherries.
The total cost Elena spent is;
\(6.55+3p\)Taniy buys a pineapple for $4.35 and 2 pounds of cherries.
The total cost Taniy spent is;
\(4.35+2p\)The amount Elena spent more than Taniy is;
\(\begin{gathered} =(6.55+3p)-(4.35+2p) \\ =6.55-4.35+3p-2p \\ =2.2+p \end{gathered}\)Therefore, The expression;
\(2.2+p\)represents how much more Elena spent than Taniy
slope -1/2, passes through (0, 5)
Our standard linear slope equation is:
mx + b = y
We're told our slope is 1/2, so that's our m value.
When x = 0 our value is 5. If you need this visualized, then:
1/2 * 0 +b = 5
0 + b = 5
b = 5
So our equation looks like:
x/2 + 5 = y
find the f(x)=3x-2 domain on a graph
The domain of the f(x)=3x-2 form a graph is -∞ < x<∞. See the attached graph. The interval notation is given as (-∞, ∞)
What is a domain?It is to be noted that the domain of a function is the set of input or argument values for which the function is real and defined. Note from the graph that the function has no undefined points nor domain constraints. Hence, the domina is expressed as the notation:
-∞ < x < ∞.
If one were to solve for x,
Then
y = 3x -2
=
3x -2 = y [Flipping the eqation]
3x -2 + 2 = y + 2 {Added two to both sides]
Hence,
3x = y +2
Divide both sides by 3 to get:
3x/3 = (y+2)/3
x = [1/3y] + [2/3]
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What is the slope of the graphed line? PLEASE HELP!
A.-5/4
B.5/4
C.-4/5
D.4/5
Answer:
C.) -4/5
Step-by-step explanation:
First find two points where the line directly meets points on the map, I used (0,2) and (5,-2).You start with rise-over-run, because this has a negative rise is -4 (numerator). The run is 5 (denominator). so -4/5
Answer:
It should be -4/5.
Step-by-step explanation:
if you take two points that are obvious, like the two intercepts, you can then use the formula (y2-y1)/(x2-x1) and plug in the points.
y intercept = (0,2)
x intercept = (2.5, 0)
(0-2)/(2.5-0)= -2/2.5 = -0.8 = -4/5
H E L P!!!!!!!!!!!!!!!!!!!
Answer:
a
Step-by-step explanation:
What is the slope ? Simplify your answer and write it as a proper fraction
I need this done today whoever gets this correct gets brainliest!!! PLZZ HELPP MEE!!!
hurryy
Answer:
The answer is A.
Step-by-step explanation:
B cannot be correct, as S did not represent the total amount paid.
C and D cannot be correct, since they never mentioned the "first sock"
If a sum of money earns $11,178 as simple interest over a period of 9 years at the rate of 6% per annum, what is the principal
Answer:Formular for simple interest is
I = P X R XT
————
100
where P is the amount borrowed or loan , Rate is the percentage of interest in P while T is the Time range for the loan
Now to find the Principal, we now change the original subject of the formula to suit or reflect P.
P = I X 100
———-
R X T
= 11, 178
———
6 X 9
=. 11, 178
——
54
=. $20,700
Step-by-step explanation:
Answer:
$20,700
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = interest accruedP = principalr = interest rate (in decimal form)t = time (in years)Given:
I = $11,178r = 6% = 0.06t = 9 yearsSubstitute the given values into the formula and solve for P:
\(\implies \sf 11178=P(0.06)(9)\)
\(\implies \sf 11178=0.54P\)
\(\implies \sf P=\dfrac{11178}{0.54}\)
\(\implies \sf P=20700\)
Therefore, the principal amount is $20,700.
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A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola. What are the dimensions of such a rectangle with the greatest possible area?.
The dimensions of the rectangle such that the rectangle have the greatest area is length = 8 and width = 4 .
In the question ,
it is given that ,
a rectangle is inscribed with its base on the x axis , and its upper corner on the parabola y = 12 − x² ,
let the coordinate of the upper right corner be P(x,y) ,
and A be the area of the rectangle .
the point P lies on the parabola , given y = 12 − x² ,
So, P = P(x,12−x²)
Due to symmetry of the rectangle, the width of rectangle is half the distance between P and the y axis ,
that means width = 2x and length = y .
Area of the rectangle = width × Length
= 2x * y
= 2x (12 − x²)
= 24x - 2x³
To maximize the area we differentiate Area with respect to x ,
we get ,
dA/dx = 24 - 6x²
for critical point dA/dx = 0 ,
24 - 6x² = 0
6x² = 24
x² = 4
x = ±2 ,
since length cannot be negative ,
So , x = 2 .
to check for maximum and minimum ,we differentiate Area with respect to x,
we get
d²A/dx² = -12x
substituting , x = 2 ,
we get -12 < 0, So , the area is maximum .
hence the width = 2*2 = 4
and length = 12 - 4 = 8
and the maximum area is 32 .
Therefore , The dimensions of the rectangle such that the rectangle have the greatest area is length = 8 and width = 4 .
The given question is incomplete , the complete question is
A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y = 12 − x² . What are the dimensions of such a rectangle with the greatest possible area ?
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there are 120 members in a Scout group, 25% of the members are Beavers, 30% are Cubs and the remainder are scouts. 18 of the Beavers are female, of the cubs are female and 24 of the scouts are male. a) Copy and complete the frequency tree b) How many male cubs are there? c) How many females are there? d) What is the probability that a randomly chosen member is a male Scout?
The ratio of female to male members of a tennis club is 5:3. The total number of members of the club is 256. How many of the members are female?
Answer:
160 females 96 males
Step-by-step explanation:
find multiples of 256
multiply 5/3 by those multiples
40/24 times 8/8= 160/96
add=
256
In an experiment, which variable is measured by the experimenter?.
In a research experiment, the variable that is measured by the experimenter is: dependent variable.
Variables in Research ExperimentIn a research experiment, we have the dependent and independent variables.The dependent variable is the variable that receives the effect of a change in the independent variable, which is measured by the researcher.Therefore, in a research experiment, the variable that is measured by the experimenter is: dependent variable.
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All of the quadralatirals in the shape below are squares.find the area of the shaded region
The area οf the shaded regiοn is 24 square units
What is the area?The amοunt οf space οccupied by a twο-dimensiοnaI figure is referred tο as its area. In οther wοrds, it is the quantity that cοunts hοw many unit squares cοver the surface οf a cIοsed figure.
The area οf the shaded regiοn is equaI tο the subtractiοn οf the tοtaI area tο the area οf the twο smaII squares and οne big square.
AII οf the quadriIateraIs in the shape beIοw are squares.
Then the area οf the shaded regiοn wiII be
The area οf the shaded regiοn is equaI tο the subtractiοn οf the tοtaI area tο the area οf the twο smaII squares and οne big square.
Area = 9 ×9 - 7 × 7 - 2 × 2 - 2× 2
= 81-49-4-4
= 24
The area οf the shaded regiοn is 24 square units
Tο Iearn mοre abοut the area frοm the given Iink
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