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The manager at an ice cream shop keeps track of the number of deluxe cones and regular cones sold each day and the total money received. On Saturday, a total of 95 cones were sold, and the money collected was $628 . If deluxe cones are sold for $8 and regular cones are sold for $5 , how many deluxe cones and regular cones were sold?
Answers
8d + 5r = 628
8(95 - r) + 5r = 628
760 - 8r + 5r = 628
-8r + 5r = 628 - 760
-3r = -132
r = -132/-3
r = 44 <== regular cones
d + r = 95
d + 44 = 95
d = 95 - 44
d = 51 <== deluxe cones
Final answer:
By forming a system of equations and applying the elimination method, we conclude that the ice cream shop sold 51 deluxe cones and 44 regular cones on Saturday.
Explanation:
How to Solve for the Number of Deluxe and Regular Cones Sold
To solve for the number of deluxe cones and regular cones sold at the ice cream shop, we need to set up a system of equations. We are given that a total of 95 cones were sold and the total money collected was $628. Deluxe cones are sold for $8 and regular cones for $5. Let's define our variables:
x = number of deluxe conesy = number of regular conesNow, we can establish our equations:
The total number of cones sold is 95: x + y = 95The total money collected is $628: 8x + 5y = 628To solve the system, we can use the substitution or elimination method. Let's use elimination for this example.
Multiply the first equation by 5:
5x + 5y = 475Now subtract this from the second equation:
(8x + 5y) - (5x + 5y) = 628 - 4753x = 153x = 51With 51 deluxe cones sold, we can substitute that into the first equation to find y:
51 + y = 95y = 95 - 51y = 44So, 51 deluxe cones and 44 regular cones were sold on Saturday.
Which of the following statements is true? A 6.75 < 6.759 < 6.751 < 6.85 B 5.55 < 5.559 < 5.65 < 5.69 C 4.11 < 4.12 < 4.17 < 4.15 D 7.42 < 7.41 < 7.40 < 7.39
Answers
The only sign used is "less than", so every consecutive number must be larger than the ones before it. Choice B is the only option that does not break this rule.
Find the area of a square with radius 17√2 in. Round to he nearest whole number. Please help me!!
Answers
The area of the square with radius 17√2 is 1156 square inches.
What is area?The area is the amount of space within the perimeter of a 2D shape
What is the formula for the area of square?The formula for the area of square is
[tex]A = \frac{1}{2} d^{2}[/tex]
Where, d is the length of the diagonal of the square.
According to the given question.
The radius of the square is [tex]17\sqrt{2}[/tex] in.
⇒ Diameter or the length of the square = 2 × 17 √2 = 34√2
Therefore,
The area of the square
= [tex]\frac{1}{2}( 34(\sqrt{2)} )^{2}[/tex]
= [tex]\frac{2312}{2}[/tex]
=[tex]1156\ in^{2}[/tex]
Hence, the area of the square with radius 17√2 is 1156 square inches.
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What is the area of parallelogram ABCD in square units
Answers
Use AB, BC, CD, DA to make the triangles.
The left-overs make up a rectangle that has the area of 2x3, which is 6.
Triangle AB and CD are equivalent, they are both (1/2)(1)(3)=1.5 each, which add up to 3.
Triangle AD and BC are equivalent, they are both (1/2)(1)(4)=2 each, which add up to 4.
So, just add up the 6 from the rectangle and the 3 & 4 and you get 13.
The area of that parallelogram is 13.
13 square units
Further explanationConsider attachment for details.
We make a KLMN rectangle that touches all the vertices of the ABCD parallelogram. Consequently, the ABCD parallelogram is right inside the KLMN rectangle.
Let us take the following strategic steps:
Calculate the area of KLMN.Calculate the area of the triangles ABL, CDM, ADK, and BCN.Subtract the area of the KLMN rectangle with the area of all triangles.The difference in the area above is the area of the ABCD parallelogram.The Process:
The area of KLMN = 4 x 5 = [tex] \boxed{ \ 20 \ square \ units. \ }[/tex]The ADK triangle is congruent to the BCN triangle, and each area is [tex]\boxed{ \ \frac{1}{2} \times 4 \times 1 = 2 \ square \ units. \ }[/tex] Thus the total area of ADK and BCN is [tex]\boxed{ \ 2 + 2 = 4 \ square \ units. \ }[/tex]The ABL triangle is congruent to the CDM triangle, and each area is [tex]\boxed{ \ \frac{1}{2} \times 3 \times 1 = 1.5 \ square \ units \ }.[/tex] Thus, the combined area of ABL and CDM is [tex]\boxed{ \ 1.5 + 1.5 = 3 \ square \ units. \ }[/tex]Finally, the area of ABCD = 20 - 4 - 3 = 13.As a result, we get the area of the parallelogram ABCD is 13 square units.
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James wants to tile his floor using tiles in the shape of a trapezoid. To make the pattern a little more interesting he has decided to cut the tiles in half along the median. The top base of each tile is 15 inches in length and the bottom base is 21 inches. How long of a cut will John need to make so that he cuts the tiles along the median?
Answers
Answer:18 inches
Step-by-step explanation:
The answer would be 18 inches.
What is the median of a trapezoid?The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.
The length of the median is the average of the length of the bases.
The top base of each tile is 15 inches in length and the bottom base is 21 inches,
Add the top base and bottom base,
So, 15+21=36
Now, divide that by 2
⇒ 18
Hence, the answer would be 18 inches.
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Evaluate the surface integral s f · ds for the given vector field f and the oriented surface s. in other words, find the flux of f across s. for closed surfaces, use the positive (outward) orientation. f(x, y, z) = x i + y j + 10 k s is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 2
Answers
[tex]\implies\nabla\cdot\mathbf f(x,y,z)=1+1+0=2[/tex]
By the divergence theorem, the surface integral along [tex]S[/tex] is equivalent to the triple integral over the region [tex]R[/tex] bounded by [tex]S[/tex]:
[tex]\displaystyle\iint_S\mathbf f(x,y,z)\,\mathrm dS=\iiint_R\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=2\iiint_R\mathrm dV[/tex]
Convert to cylindrical coordinates, setting
[tex]\begin{cases}x=r\cos\theta\\y=Y\\z=r\sin\theta\end{cases}\implies\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dY[/tex]
The triple integral is then equivalent to
[tex]=\displaystyle2\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{Y=0}^{Y=2-r\cos\theta}r\,\mathrm dY\,\mathrm dr\,\mathrm\theta[/tex]
[tex]=\displaystyle2\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}r(2-r\cos\theta)\,\mathrm dr\,\mathrm\theta[/tex]
[tex]=\displaystyle\frac23\int_{\theta=0}^{\theta=2\pi}(3-\cos\theta)\,\mathrm dr\,\mathrm\theta[/tex]
[tex]=4\pi[/tex]
Two garden plots are to have the same area. One is square and one is rectangular. The rectangular plot is 2 meters wide and 18 meters long. How long is one side of the of the square garden plot in meters?
Answers
area of rectangle = l x w
area of rectangle = 2*18 = 36 square meters
area of square = S^2, or s = square root(area)
sqrt(36) = 6
length of side of square = 6 meters
The side length of the square garden plot with the same area as a rectangular plot of dimensions 2 meters by 18 meters is 6 meters.
The student is asking about finding the length of a side of a square garden plot that has the same area as a rectangular garden plot measuring 2 meters wide by 18 meters long. To find the area of the rectangular plot, we multiply the length by the width: 2 meters imes 18 meters = 36 square meters.
Since the area of the square plot must equal the area of the rectangular plot, we can use the formula for the area of a square, A = s2, where s is the side length of the square. Therefore, to find the side length of the square plot, we take the square root of the area of the rectangular plot:
√(36 square meters) = 6 meters
So, the side length of the square garden plot is 6 meters.
A pizzeria owner wants to know which pizza topping is least liked by her customers so she can take it off the menu. She used four different methods to find this information.
Method 1: The owner asked every third customer to rate all the pizza toppings in order of preference.
Method 2: The owner gave all customers a toll-free telephone number and asked them to phone in their topping preferences.
Method 3: The owner asked the preferences of every other teenager who entered the pizzeria.
Method 4: The owner reviewed the pizzeria’s complaint cards and assessed all complaints related to pizza toppings.
Which method is most likely to give a valid generalization
Answers
The second method requires a lot on the initiatives of customers, and likely to have extreme cases only (liked very much or disliked very much).
The third is biased towards teenagers, which may not be the only category of customers who ordered pizzas.
Again, the fourth requires initiative from the customer, so biased towards customers who had something to say.
The valid method is the owner asked every third customer to rate all the pizza toppings in order of preference. The correct option is A.
What is feedback?information that is utilized as a foundation for improvement, such as data on how people react to a product or how well someone performs a task.
I suggest method 1 because it is unbiased and systematic. The second method requires a lot of the initiative of customers and is likely to have extreme cases only (liked very much or disliked very much).
The third is biased towards teenagers, which may not be the only category of customers who ordered pizzas. Again, the fourth requires initiative from the customer, so biased towards customers who had something to say.
Therefore, the valid method is for the owner to ask every third customer to rate all the pizza toppings in order of preference. The correct option is A.
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2(8+h) simplify using distrubtive property
Answers
2(8 + h)
The Distributive Property allows us to multiply any number/variable outside of the parenthesis by all numbers/variables inside the parenthesis.
For example;
2(1 + 2)
2(1) + 2(2)
2 + 4
6.
Let's try this with our current problem.
2(8 + h)
2(8) + 2(h)
16 + 2h (This is your simplified expression)
I hope this helps!
Derek and Mia place two green marbles and one yellow marble in a bag. Somebody picks a marble out of the bag without looking and records its color (G for green and Y for yellow). They replace the marble and then pick another marble. If the two marbles picked have the same color, Derek loses 1 point and Mia gains 1 point. If they are different colors, Mia loses 1 point and Derek gains 1 point. What is the expected value of the points for Derek and Mia?
Answers
Answer:
Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.
Step-by-step explanation:
Number of green marbles = 2 and Number of Yellow marbles = 1
Then, total number of marbles = 2+1 = 3
A person selects two marbles one after another after replacing them.
So, the probabilities of selecting different combinations of colors are,
[tex]1.\ P(GG)=P(G)\times P(G)\\\\P(GG)=\dfrac{2}{3}\times \dfrac{2}{3}\\\\P(GG)=\dfrac{4}{9}[/tex]
[tex]2.\ P(GY)=P(G)\times P(Y)\\\\P(GY)=\dfrac{2}{3}\times \dfrac{1}{3}\\\\P(GY)=\dfrac{2}{9}[/tex]
[tex]3.\ P(YG)=P(Y)\times P(G)\\\\P(YG)=\dfrac{1}{3}\times \dfrac{2}{3}\\\\P(YG)=\dfrac{2}{9}[/tex]
[tex]4.\ P(YY)=P(Y)\times P(Y)\\\\P(YY)=\dfrac{1}{3}\times \dfrac{1}{3}\\\\P(YY)=\dfrac{1}{9}[/tex]
Now, we have that,
If two marbles are of same color, then Mia gains 1 point and Derek loses 1 point.
If two marbles are of different color, then Derek gains 1 point and Mia loses 1 point.
Also, the expected value of a random variable X is [tex]E(X)=\sum_{i=1}^{n} x_i\times P(x_i)[/tex].Then, the expected value of points for Derek is,
[tex]E(D)= (-1)\times \dfrac{4}{9}+1\times \dfrac{2}{9}+1\times \dfrac{2}{9}+(-1)\times \dfrac{1}{9}\\\\E(D)= \dfrac{-5}{9}+\dfrac{4}{9}\\\\E(D)=\dfrac{-1}{9}[/tex]
And the expected value of points for Mia is,
[tex]E(M)= 1\times \dfrac{4}{9}+(-1)\times \dfrac{2}{9}+(-1)\times \dfrac{2}{9}+1\times \dfrac{1}{9}\\\\E(M)= \dfrac{5}{9}-\dfrac{4}{9}\\\\E(M)=\dfrac{1}{9}[/tex].
Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.
Answer: P(GG)= 4/9
P(GY)= 2/9
P(YG)= 2/9
P(YY)= 1/9
Derek, E(X) = -1/9
Mia, E(X) = 1/9
Step-by-step explanation: just did it on edge
Calculus AB
lim x-->4 sqrt(x+5)-3 / 4-x
The answer is apparently -1/6
How do you solve this
Answers
[tex] \lim_{x \to 4} \frac{\sqrt{x+5}-3}{4-x}[/tex]
that means as x approaches 4
if we sub 0 for x we get
0/0
and intermitent form
use l'hopital's rule
so
take the derivitive of the top and bottom seperatly
l'hopitals rule is something like
if [tex] \lim_{x \to n} \frac{f(x)}{g(x)}[/tex] results in 0/0 or -∞/∞ or∞/∞ then keep doing it until f(n)/g(n) gives a form that isn't intermitent
so
take derivitive of top and bottom
[tex]\dfrac{\frac{1}{2\sqrt{x+5}}}{-1}[/tex]
now, if we subsitute 4 for x we get
[tex]\dfrac{\frac{1}{2\sqrt{4+5}}}{-1}[/tex]=
[tex]\dfrac{\frac{1}{2\sqrt{9}}}{-1}[/tex]=
[tex]\dfrac{\frac{1}{2(3)}}{-1}[/tex]=
[tex]\dfrac{\frac{1}{6}}{-1}[/tex]=
[tex]\dfrac{1}{-6}=\dfrac{-1}{6}[/tex]
What is greater: a half dozen dozen pair of shirts or a half of two dozen dozen shirts
Answers
A half dozen dozen pair of shirts is:
6 dozen pairs:
6 * 12 pairs
72 pairs
PAIRS.
So, for every 1 shirt in this group, there is another that goes with it. It must be multiplied by two.
72 * 2 = 144
There is a total of 144 shirts in this group.
Now, the second group...
Half of two dozen dozen shirts:
Half of two dozen = 12
12 dozen shirts.
12 * 12
144!
See? The amounts are exactly the same!
Sounds more like a riddle than math homework to me...
Hope I could help you out! If my math is incorrect, or I provided an answer you were not looking for, please let me know. However, if my math is explained well and correct, please consider marking my answer as Brainliest! :)
Have a good one.
God bless!
From the computation, a half of two dozen shirts will be greater.
A dozen = 12
It should be noted that a half dozen pair of shirts will be:
= 1/2 × 12
= 6 shirts
A half of two dozen shirts will be:
= 1/2 × (2 × 12)
= 12 shirts
Therefore, a half of two dozen shirts will be greater.
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someone please help me to find the answer to this geography problem please explain
Answers
The M represents slope while the B represents the Y-intercept.
With that out of the way, take a look at your top equation, y = 3/2x + ?. If you noticed the question mark is in the spot of the B (Y-intercept), we can simply find this by finding where on the graph does the line intercept the Y-axis.
Triangle B shows the Y-intercept to be -7, this means that the hypotenuse intercepts the Y-axis at (0 , -7).
If we were to find the (what I like to call) the interception point of triangle A's hypotenuse and the Y-axis, we find our missing variable.
Just looking at the graph, we can count and visually determine that the Y-intercept of the hypotenuse is (0 , 1).
Therefore, we can say: The equation of A's hypotenuse is:
y = 3/2x + 1
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Helpp! -- A piece of wire 5 inches long is to be cut in two pieces. One piece is x inches long and is to be bent into the shape of a square. The other piece is to be bent in the shape of a circle. Find an expression for the total area made up by the square and the circle as a function of x.
Answers
since, we know that for the circle, the perimeter is s+s+s+s or 4s, then 4s = x and so on.
now, for the circle, the perimeter is just the circumference, circumference of a circle is 2πr, thus 2πr = 5-x and so on.
anyway... so... the equation of the area made by those two in x-terms, is just their sum... so let's do that then
[tex]\bf \pi \left( \cfrac{5-x}{2\pi } \right)^2\quad +\quad \cfrac{x^2}{4^2}\\\\ -------------------------------\\\\ \pi\cdot \cfrac{(5-x)^2}{(2\pi )^2}+\cfrac{x^2}{4^2}\implies \cfrac{\pi (5-x)^2}{2^2\pi^2}+\cfrac{x^2}{4^2}\implies \cfrac{(5-x)^2}{4\pi}+\cfrac{x^2}{4^2} \\\\\\ \textit{let's use the LCD of }4^2\pi \textit{ to add them up} \\\\\\ \cfrac{4(5-x)^2+\pi x^2}{4^2\pi }\implies \cfrac{4(5-x)^2+\pi x^2}{16\pi }[/tex]
now, you can expand the squared binomial on the numerator, but there will not be any like-terms to simplify, so, it won't make much difference, so.... you can expand it or not.
The expression for the total area made up by the square and the circle as a function of x is f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) square inches.
Explanation:To solve this problem, you need to know the formulas for the areas of a square (Area = side^2) and a circle (Area = pi * radius^2). If a piece of the wire with length x inches is to be bent into the shape of a square, then each side of the square will be x/4 inches long (since a square has 4 equal sides). Therefore, the area of the square = (x/4)^2 = x^2/16 sq.inches.
The remaining piece of the wire is 5-x inches long and is to be bent into the shape of a circle. The circumference of the circle is 5-x inches (since it uses the remaining wire), therefore the radius of the circle is (5-x)/(2*Pi) inches. Therefore, the area of the circle = Pi*((5-x)/(2*Pi))^2 = (25 - 10x + x^2)/(4*Pi) sq.inches.
The total area made up by the square and the circle is the sum of their areas, therefore the function representing the total area f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) sq.inches.
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The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 23 feet. Round your answer to the nearest hundredth.
Answers
v = u +gt
where
u = initial velocity (=0 for a falling object)
g = acceleration due to gravity, 32.2 ft/s²
t = time, s
In terms of distance fallen,
v² = u² + 2gh
where h = distance fallen, ft.
Because h = 23 ft and u = 0, therefore
v² = 2*32.2*23 = 1481.2
v = 38.486 ft/s
Answer: 28.49 ft/s (nearest hundredth)
Two consecutive odd integers have a sum of 44 . Find the integers.
Answers
x + x + 2 = 44
2x + 2 = 44
2x = 44 - 2
2x = 42
x = 42/2
x = 21
x + 2 = 21 + 2 = 23
ur numbers are 21 and 23
2n+2=44 subtract 2 from both sides
2n=42 divide both sides by 2
n=21
So n and n+2 are 21 and 23.
standard form of the equation of a hyperbola that has vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).
Answers
Final Answer:
The standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15) is (x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1
Explanation:
To write the standard form of the equation of a hyperbola with the given vertices and a focus, we'll follow these steps:
1. Determine the center of the hyperbola.
2. Calculate the distance between the vertices and the center to find the length of the transverse axis (2a).
3. Calculate the distance between a focus and the center to find the focal distance (c).
4. Use the relationship c^2 = a^2 + b^2 to determine the length of the conjugate axis (2b).
5. Write the standard form equation based on the orientation of the hyperbola.
Step 1: Determine the center of the hyperbola.
The center of the hyperbola is the midpoint of the line segment joining the two vertices. Since the vertices are at (-10, -15) and (70, -15), the center (h, k) can be found as follows:
h = (-10 + 70) / 2 = 60 / 2 = 30
k = (-15 + (-15)) / 2 = -30 / 2 = -15
So, the center of the hyperbola is at (30, -15).
Step 2: Calculate the length of the transverse axis (2a).
The distance between the vertices is the length of the transverse axis. The vertices are 80 units apart because they are at (-10, -15) and (70, -15). This means:
2a = 80
a = 40
Therefore, the length of the semi-transverse axis a is 40 units.
Step 3: Calculate the focal distance (c).
The focal distance is the distance between the center and one of the foci. We were given one focus at (-11, -15). Since the center is at (30, -15), the focal distance c is:
c = |30 - (-11)| = |30 + 11| = 41
Step 4: Use the relationship c^2 = a^2 + b^2 to determine b.
We know that a = 40 and c = 41. Plugging these values into the relationship gives us:
41^2 = 40^2 + b^2
1681 = 1600 + b^2
b^2 = 1681 - 1600
b^2 = 81
b = 9
Therefore, the length of the semi-conjugate axis b is 9 units.
Step 5: Write the standard form equation.
Since the hyperbola is horizontal (the vertices have the same y-coordinate), the standard form of its equation is:
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
Plugging in the values for h, k, a, and b, we get:
(x - 30)^2 / 40^2 - (y + 15)^2 / 9^2 = 1
Simplify further by squaring the values of a and b:
(x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1
This is the standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).
Select the correct inequality for the graph below: A solid line passing through points (1, 2) and (2, 5) has shading below. y < 3x − 1 y ≤ 3x − 1 y ≥ 3x − 1 y > 3x − 1
Answers
Here is your answer:
Solving the equation:
[tex] (5-2)\div(2-1)= 3 [/tex][tex] \frac{y - y1}{(x - x1) } [/tex][tex] y-5=3(x-2) [/tex][tex] y= 3x- 6+ 5 [/tex]" [tex] y= 3x-1 [/tex] " or option B.Hope this helps!
Step 1
Find the equation of the line that passes through points [tex](1, 2)[/tex] and [tex](2, 5)[/tex]
Find the slope of the line
The formula to calculate the slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{5-2}{2-1}[/tex]
[tex]m=\frac{3}{1}[/tex]
[tex]m=3[/tex]
Find the equation of the line
The equation of the line into slope-point form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=3[/tex]
[tex](1, 2)[/tex]
substitutes
[tex]y-2=3(x-1)[/tex]
[tex]y=3x-3+2[/tex]
[tex]y=3x-1[/tex]
Step 2
Find the equation of the inequality
we know that
The solution is the shaded area below the solid line
therefore
the inequality is
[tex]y\leq 3x-1[/tex]
the answer is
[tex]y\leq 3x-1[/tex]
see the attached figure to better understand the problem
Jane is going to walk once around the edge of a rectangular park. The park is 300 yards long and 200 feet wide. How far will Jane walk?
Answers
Jane will walk 733.34 yards around the edge of the rectangular park after converting the width from feet to yards and calculating the perimeter.
Jane is going to walk once around the edge of a rectangular park. The park is 300 yards long and 200 feet wide. To determine how far Jane will walk, we need to calculate the perimeter of the rectangle. First, let's convert all measurements to the same unit. Since the length is given in yards and the width in feet, we can convert the width to yards (1 yard = 3 feet).
Width in yards: 200 feet \/ 3 feet per yard = 66.67 yards.
Now that both measurements are in yards, we can calculate the perimeter:
Perimeter = 2 ×(length + width) = 2 × (300 yards + 66.67 yards) = 2 ×366.67 yards = 733.34 yards.
Therefore, Jane will walk 733.34 yards around the edge of the park.
Suppose that a particular artillery piece has a range r = 8320 yards . find its range in miles. use the facts that 1mile=5280ft and 3ft=1yard.
Answers
The range in miles is 4.72 mile
What do you mean by 1 mile?mile, any of various units of distance, such as the statute mile of 5,280 feet (1.609 km). It originated from the Roman mille passus, or “thousand paces,” which measured 5,000 Roman feet.
Given : range= 8320 yards
1 mile= 5280 feet
3 feet= 1 yard
Now,
8320yards X 3ft = 24,960
Now, divide that by 5,280ft in a mile
= 24960/5280
= 4.72 miles
Hence, range is 4.72 miles.
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Final answer:
To convert the artillery piece's range of 8320 yards to miles, you multiply by 3 to change yards to feet and then divide by 5280 to convert feet to miles, resulting in a range of approximately 4.727 miles.
Explanation:
To find the artillery piece's range in miles, starting with its range in yards, we need to use unit conversion factors. Knowing that 1 mile equals 5280 feet and 3 feet equals 1 yard, we can set up a conversion to calculate the distance in miles.
Steps to Convert Yards to Miles:
Convert the given distance from yards to feet by multiplying the number of yards by 3 (since there are 3 feet in a yard).Next, convert the distance from feet to miles by dividing the number of feet by 5280 (since there are 5280 feet in a mile).For an artillery range of 8320 yards:
8320 yards is equivalent to 8320 yards * 3 feet/yard = 24960 feetThen 24960 feet / 5280 feet/mile gives us the range in miles.When you divide 24960 by 5280, you get 4.727 miles (rounded to three decimal places).
If all of the diagonals are drawn from a vertex of a pentagon, how many triangles are formed?
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A picture helps. There are 2 non-adjacent vertices, so two diagonals can be drawn, resulting in 3 triangles.
Drawing all diagonals from one vertex of a pentagon to the non-adjacent vertices creates three triangles within the pentagon.
When all the diagonals are drawn from one vertex of a pentagon, it divides the pentagon into several triangles.
A pentagon has five sides, and when selecting a single vertex, we can draw diagonals to the non-adjacent vertices. In this case, there are three non-adjacent vertices, which means we can draw three diagonals, thus creating three triangles inside the pentagon.
This is because each diagonal, combined with two sides of the pentagon, forms a triangle.
What is the standard form of 8 hundreds + 2 hundreds
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The standard form of 8 hundred + 2 hundred will be 1000.
What is the standard form of the number?A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.
Given that the number is 8 hundred + 2 hundred the standard form of the number will be:-
Standard form = 8 hundreds + 2 hundreds
Standard form = 800 + 200
Standard form = 1000
Therefore, the standard form of 8 hundred + 2 hundred will be 1000.
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the longest runway at an airport has the shape of a rectangle with an area of 2181600sqft. this runway is 180 ft wide. how long is the runway
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John predicts the basketball team will score 68 points. If the basketball team actually scores 49 points, what is John's percent error? Round your answer to the nearest tenth of a percent.
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%error=100(68-49)/49
%error≈38.8%
Since this is positive, John's error overestimated the teams score by about 38.8%
Show that the series is convergent. how many terms of the series do we need to add in order to find the sum to the indicated accuracy? sum_(n=1)^(infinity) (-1)^(n+1)/( n^7)text( ) \(|text(error)| < 0.00005 \)
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[tex]|S-S_k|\le|a_{k+1}|[/tex]
We have
[tex]a_n=\dfrac1{n^7}[/tex]
so in order to have an error within 0.00005 of the sum's actual value, we need [tex]k[/tex] terms such that
[tex]\left|S-S_k\right|\le\left|\dfrac{(-1)^{k+2}}{(k+1)^7}\right|=\dfrac1{(k+1)^7}<0.00005[/tex]
[tex]\implies (k+1)^7<\dfrac1{0.00005}=20000[/tex]
[tex]\implies k+1<20000^{1/7}\approx4.1156[/tex]
[tex]\implies k<3.1156[/tex]
which suggests that we require [tex]k=4[/tex] terms at the least to approximate the series within the given accuracy.
The series is convergent, but the number of terms needed to find the sum to a specific accuracy cannot be determined.
Explanation:To determine the convergence of the series sum_(n=1)^(infinity) (-1)^(n+1)/( n^7), we can use the Alternating Series Test. The Alternating Series Test states that if the terms of a series alternate in sign and decrease in absolute value, then the series is convergent. In this case, the terms of the series alternate in sign and decrease as n increases, so the series is convergent.
To find the number of terms needed to achieve a sum with an error less than 0.00005, we need to use the Remainder Estimation Theorem. However, this theorem requires that the terms of the series decrease in absolute value, which is not the case in this series. Therefore, we cannot determine the number of terms needed to reach the desired accuracy.
Overall, the series is convergent, but we cannot determine the number of terms needed to reach a specific accuracy.
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A carpenter is assigned the job of expanding a rectangular deck where the width is one-fourth the length. The length of the deck is to be expanded by 6 feet, and the width by 2 feet. If the area of the new rectangular deck is 68 ft2 larger than the area of the original deck, find the dimensions of the original deck.
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The area of the original deck is [tex]W*4W=4W^{2} [/tex]
The dimensions of the new deck are :
length = 4W+6
width=W+2
so the area of the new deck is :
[tex](4W+6)(W+2)= 4W^{2}+8W+6W+12= 4W^{2}+14W+12[/tex]
"the area of the new rectangular deck is 68 ft2 larger than the area of the original deck" means that we write the equation:
[tex]4W^{2}+14W+12=68+4W^{2}[/tex]
[tex]14W+12=68[/tex]
[tex]14W=68-12=56[/tex]
[tex]W= \frac{56}{14}= 4 [/tex]
the length is [tex]4W=4*4=16[/tex] ft
Answer: width: 4, length: 16
A section of land has an area of 1 square mile and contains 640 acres. determine the number of square meters in an acre
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1 squre mile = 1760^2 yd^2 = 3097600 yd^2
This means that
Each acre has (3097600 yd^2/ sq. mile ) / (640 acres/sq. mile(= 4840 yd^2 / acre
Also, we know that 1 inch = 2.54 cm exactly.
Therefore
1 yd = 3*12*2.54 cm = 91.44 cm = 0.9144 m
1 yd^2 = (0.9144 m)^2 = 0.83612736 m^2
Using the conversion from acre to sq yards,
1 acre=4840 yd^2
=4840 yd^2 * 0.83612736 m^2 / yd^2
= 4046.8564224 m^2
Answer: 1 acre = 4046.8564224 m^2
An acre, a unit of area commonly used in the Imperial and U.S. customary systems, is approximately 4047 square meters. This is calculable by using the known conversions between acres, square miles, and square meters.
Explanation:To determine the number of square meters in an acre, it's helpful to understand the relationship between these units. A square mile is equivalent to 640 acres. Therefore, the area of one acre is 1/640 of a square mile. However, these are both Imperial measurements, and we want to convert to a metric measurement - square meters.
To make this conversion, we need to identify the conversion factor between square miles and square meters. There are 2,589,988.11 square meters in a square mile.
Our starting point is that 1 acre = 1/640 square mile. Next, we substitute the number of square meters in a square mile:
1 acre = 1/640 x 2,589,988.11 square meters = 4046.86 square meters.
Therefore, there are approximately 4047 square meters in an acre.
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The price of an item has been reduced by 15% . The original price was $51 .
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85 - (60/100)*85
= 85 - 0.6 *85
= 85 - 51
= $34
The question is about calculating the new price of an item after a discount. The original price of the item was $51.00, and it was reduced by 15%, making the new price $43.35.
Explanation:The subject of this question is Mathematics and it is looking for a solution to a percentage price reduction problem. The item had an original price of $51.00 and its price has been reduced by 15%. To find the new price after the discount, we have to calculate the amount of the reduction and subtract it from the original price.
First, let's calculate the amount of the discount: 15/100 * 51 = $7.65.}
Now, we subtract this amount from the original price: 51 - 7.65 = $43.35.
Therefore, the new price of the item after a 15% discount is $43.35.
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find the quotient of 0.34 and 0.2.
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The pressure,p, of a gas varies inversely with its volume,v. Pressure is measured in units of pa. Suppose that a particular amount of a gas is initially at a pressure of 104 pa at a volume of 108 L. If the volume is expanded to 432 L, what will the new pressure be
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In this case, the gas have 108L volume in 104pa pressure and you asked how much the pressure if the gas made into 432L volume. Since the volume is bigger it should be clear that the pressure would be lower.
The equation of the new pressure would be : 104pa x (108L / 432L) = 104pa x 0.25= 26pa
Answer: 26pa