Answer: The exact circumference of the circle is [tex]10\pi[\tex] in.
Step-by-step explanation:
Since, the circumference of a circle is,
[tex]C=2\pi r[/tex]
Where, r is the radius of the circle,
Here, r = 5 inches,
Hence, the circumference of the circle is,
[tex]C = 2\pi(5) = 10\pi\text{ in}[/tex]
Thus, The exact circumference of the circle is [tex]10\pi[\tex] in.
Cody saves all his nickles. Today he is getting them out of his piggy bank and wrapping them to take to the bank. He finds he has 360 nickels. It takes 40 Nicole's to fill each paper wrapper and make a roll. How many wrappers does he need? Explain how you solved this problem and how you know your answer is correct.
Rajendra has 14 4/5 pounds of trail mix. He is putting them into bags that hold 1 1/2 pounds each. Does he have enough trail mix to completely fill 8 bags?
Answer: Yes , Rajendra has enough trail mix to completely fill 8 bags.
Step-by-step explanation:
Given : Total trail mix Rajendra has = [tex]14\dfrac{4}{5}[/tex] pounds
Convert [tex]14\dfrac{4}{5}[/tex] into improper fraction.
[tex]14\dfrac{4}{5}=\dfrac{(14)(5)+4}{5}=\dfrac{74}{5}[/tex]
Amount of mix in each bag = [tex]1\dfrac{1}{2}[/tex] pounds.
[tex]=\dfrac{1(2)+1}{2}=\dfrac{3}{2}[/tex] pounds
Then, the total number of bags can be filled by the trail mix Rajendra has
= Total trail mix ÷ Amount of mix in each bag
[tex]=\dfrac{74}{5}\div\dfrac{3}{2}[/tex]
[tex]=\dfrac{74}{5}\times\dfrac{2}{3}=\dfrac{148}{15}=9.86666666667\approx9[/tex]
It means Rajendra has enough trail mix to fill 9 bags.
Since 9 > 8
Therefore , Rajendra has enough trail mix to completely fill 8 bags.
If p(a) = 0.65, p(b) = 0.58, and p(a and
b.= 0.76, then p(a or
b.is:
The value of P( a or b)= 0.47.
what is Conditional Probability?The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier occurrence by the increased likelihood of the later, or conditional, event.
Conditional probability is the likelihood that any event A will occur in the presence of another event B that is related to A. P(A|B) illustrates it.
Given:
p(a) = 0.65, p(b) = 0.58, and p(a and b)= 0.76
Now, using the formula
P(a∪b) = P(a) + P(b) - P(a∩b)
= 0.65 + 0.58 - 0.76
= 0.47
Hence, the value of P( a or b)= 0.47.
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if you have 12 fish and 6 drown how many do you have left?
Which statement best describes one of these transformations? Triangle 1 is rotated to result in triangle 2. Triangle 1 is dilated to result in triangle 3. Triangle 1 is reflected to result in triangle 4. Triangle 1 is stretched to result in triangle 5.
Answer:
Triangle 1 is rotated to result in triangle 2.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
GOT IT RIGHT
Figure ABCDE is the result of a 180° rotation of Figure LMNOP about the point. Which angle in the pre-image corresponds to ∠B in the image? Enter your answer in the box.
Figure L M N O P is rotated 180 degrees about a point resulting in image A B C D E.
Answer: ∠M in the pre-image corresponds to ∠B in the image.
Step-by-step explanation:
When we look at the figures , we can see that the three vertices B , C , D are one side as vertices to M , N ,O .
Clearly , vertex C corresponds to vertex N ( presents in the middle )
Also, point B is at the right from point C .
In Figure L M N O P , vertex M is at the right from vertex N .
Thus , vertex M corresponds the vertex B.
It means ∠M in the pre-image corresponds to ∠B in the image.
Evaluate the triple integral of f(x,y,z)=z(x2+y2+z2)−3/2f(x,y,z)=z(x2+y2+z2)−3/2 over the part of the ball x2+y2+z2≤49x2+y2+z2≤49 defined by z≥3.5z≥3.5. ∫
To evaluate a triple integral over a region of a sphere, we switch to spherical coordinates. We then express the integrand and the limits of the variables in terms of these new coordinates. Don't forget the Jacobian when changing variables.
Explanation:The subject is a mathematical problem that requires evaluating a triple integral over a specific part of a ball in three-dimensional space. The function to integrate is f(x,y,z)=z*(x2+y2+z2)-3/2 and the region of integration is defined as the part of the sphere with radius 7 (x2+y2+z2<=49) in which z >= 3.5. Unfortunately, the solution to such a problem requires advanced mathematical skills and knowledge, such as spherical coordinates and integration techniques, which cannot be elaborated within the word limit here.
However, to solve such problems, you typically switch to spherical coordinates, where x=r*cos(theta)*sin(phi), y=r*sin(theta)*sin(phi), z=r*cos(phi). Then, you express your function and the limits of your variables r, theta, and phi in terms of these new coordinates. You need to consider the Jacobian determinant when changing variables. Eventually, you integrate over the specified region. The solution needs careful elaboration of every step due to the complexity of the integral.
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Glenda began the day with a golf score of -6 and ended with a score of -10. Which statement represents her golf score for that day?
A) -6 - ( - 10) = 4
B) - 10 - ( - 6) = - 4
C) - 6 + ( - 10) = - 16
D) - 10 + ( - 6) = - 16
I need help! Rewrite each product below using Distributive property.
a: 18(26)
b: 6(3405)
c: 21(35)
Thanks!!!p
By using distributive property, the answers are :(a)468, (b) 20430, (c) 735.
Explain, distributive property.Distributive property is the mathematical property to solve expressions in the form of a(b + c), in which firstly bracket term is solve and then other terms are solved.
(a)
The given term is,
18(26),
According to distributive property, bracket changes in multiply.
Therefore, 18(26)⇒18×26=468.
(b)
The given term is,
6(3405),
According to distributive property, bracket changes in multiply.
Therefore, 6(3405)⇒6×3405=20430.
(c)
The given term is,
21(35),
According to distributive property, bracket changes in multiply.
Therefore, 21(35)⇒21×35=735.
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Answers matching "The combined average weight of an okapi and a llama is 450 kilograms. The average weight of 3 llamas is 190 kilograms more than the average weight of one okapi. On average, how much does an okapi weigh, and how much does a llama weigh?"
Let us say that:
x = weight of llamas
y = weight of okapi
From the problem, we can create the equations:
x + y = 450 --> 1
3 x = y + 190 --> 2
Rewriting equation 1:
x = 450 – y
From equation 2:
3 (450 – y) = y + 190
1350 – 3 y = y + 190
4 y = 1160
y = 290
From equation 1:
x = 450 – 290
x = 160
Therefore a llama weighs 160 kilograms while okapi weigh 290 kilograms on average.
Help!
Math Torture!
Adam is constructing an equilateral triangle. He has already constructed the line segment and arcs shown.
What should Adam do for his next step?
A. Place the point of the compass on point X and draw an arc, using a width for the opening of the compass that is greater than 12XR.
B. Place the point of the compass on point X and draw an arc, using XR as the width for the opening of the compass.
C. Use the straightedge to draw XR←→ and XS←→.
D. Use the straightedge to extend RS¯¯¯¯¯ in both directions.
Answer:
C. Use the straightedge to draw XR←→ and XS←→.
Step-by-step explanation:
Adam has drawn the arcs by using RS distance as the radius of the circle and mid points as R and S.
So the point X is the same distance from R and S.
So now Adam has to use the straightedge to draw XR←→ and XS←→.
Then, XR = XS = RS
So it is an equilateral triangle.
Therefore, the correct answer is C.
Adam should do for his next step to use the straightedge to draw [tex]\( XR \)[/tex] and [tex]\( XS \).[/tex] The option (C) is correct.
The construction process for the equilateral triangle:
To construct an equilateral triangle using a straightedge and compass:
Construct [tex]\( XR \)[/tex]: Adam has already constructed segment [tex]\( XR \).[/tex]
Draw [tex]\( XS \)[/tex]: Using the straightedge, Adam should draw a line segment [tex]\( XS \)[/tex] from point [tex]\( X \)[/tex] to another point [tex]\( S \)[/tex] such that [tex]\( XS = XR \)[/tex]. This ensures that two sides of the equilateral triangle are equal in length.
Draw [tex]\( RS \)[/tex]: After drawing [tex]\( XS \)[/tex], Adam should use the straightedge to draw segment [tex]\( RS \)[/tex], completing the equilateral triangle [tex]\( \triangle XRS \).[/tex]
This method aligns with the steps typically used in geometric constructions to form an equilateral triangle: ensuring that all three sides are equal in length by first establishing two sides of equal length and then completing the triangle.
Therefore, upon reconsideration, option (C) is indeed the correct next step for Adam to construct his equilateral triangle.
Find the length of the curve. r(t) = 3 i + t2 j + t3 k, 0 ≤ t ≤ 1
To determine the length of the curve, we find the derivative of the given vector function, compute its magnitude, and then compute the integral of the magnitude from 0 to 1. This involves calculus techniques.
Explanation:To find the length of the curve, we have to compute the integral of the magnitude of the derivative on the interval from 0 to 1. First, we find the derivative of r(t) = 3 i + t^2 j + t^3 k which is r'(t) = 2t j + 3t^2 k. The magnitude of r'(t) is |r'(t)| = sqrt((0)^2 + (2t)^2 + (3t^2)^2) = sqrt(4t^2 + 9t^4). Thus the length of the curve is the integral of this magnitude from 0 to 1: ∫ from 0 to 1 of sqrt(4t^2 + 9t^4) dt. This integral can be evaluated using techniques from calculus.
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Trygg has 3/4 package of marigold seeds. He plants 1/6 of those seeds in his garden and divides the rest equally into 10 flower pots. What fraction of a packege of seeds is planted in each flower pot? Show your work.
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
We are given that
Trygg has package of marigold seeds=[tex]\frac{3}{4}[/tex]
He plants seeds in garden=[tex]\frac{1}{6}\times \frac{3}{4}=\frac{1}{8}[/tex]
Remaining seeds=[tex]\frac{3}{4}-\frac{1}{8}=\frac{5}{8}[/tex]
He divide remaining seeds equally into 10 flower pots.
We have to determine the fraction of a package of seeds is planted in each flower pot.
Seeds in each pot=[tex]\frac{\frac{5}{8}}{10}=\frac{1}{16}[/tex]
Hence, seeds planted in each pot=[tex]\frac{1}{16}[/tex]
I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $30 per foot, and the fencing for the east and west sides costs $15 per foot. If I have a budget of $120 for the project, what are the dimensions of the garden with the largest area I can enclose?
The largest rectangular orchid garden that can be enclosed within a $120 budget, considering the given costs of fencing, has dimensions of 2 feet by 2 feet, resulting in an area of 4 square feet.
You wish to create a rectangular orchid garden with the house forming the northern boundary, and you're working with a budget of $120 for fencing. The cost per foot for the southern boundary is $30, and for the east and west sides, it's $15 each. We need to determine the dimensions that maximize the area.
Let's denote the width of the garden (east and west sides) as w feet, and the length (only the southern side, as the northern side is the house) as l feet. The total cost of fencing is therefore the sum of the costs for all three sides: Cost = $30l + 2($15w), which simplifies to Cost = $30l + $30w. Since your budget is $120, we can write the equation $30l + $30w = $120, which simplifies further to l + w = 4.
To find the dimensions that give you the largest area, we need to maximize the area A of the rectangle, which is A = l imes w. Substituting w with 4 - l (from our previous equation), we get A = l imes (4 - l). To find the maximum area, take the derivative of A with respect to l and set it to zero, solving for l. This gives us l = 2 feet. Substituting back, we find w = 2 feet as well.
The dimensions for the garden that will give you the largest enclosed area within a $120 budget are 2 feet in width by 2 feet in length, resulting in an area of 4 square feet.
What is the solution set of {x | x < -5} ∩ {x | x > 5}?
An angle measures 54 less than the measure of a complementary angle. What is the measure of each angle?
Henry is making a corn grits recipe that calls for 14 cup of corn grits for every 12 cup of water. How much water will he need if he uses 112 cups of corn grits? Enter the number in the box
Which situation could best be represented by this linear equation?
2.75x + 3.25y = 215
Answer:
The correct option 4.
Step-by-step explanation:
The given equation is
[tex]2.75x+3.25y=215[/tex] .... (1)
Let x is the number of pretzels sold and y is the number of popcorn bags sold.
Total sales is defined as
[tex]Sales=C_1x+C_2y[/tex] ... (2)
From (1) and (2) it is clear that,
The cost of each pretzel is $2.75 or 275 cents. The cost of each popcorn bag is $3.25 or 325 cents ($1 = 100 cents). Total sales is $215.
[tex]325-275=50[/tex]
Pretzels cost is 50 cents less than popcorn bags. The variable x represents the number of pretzels sold and y represents the number of popcorn bags sold. The total sales was $215.
Therefore the correct option 4.
On your last credit card statement, you had a previous balance of $98.14, payments of $10, a periodic rate of 1.34 percent, and new charges totaling $34.89. What is your new balance?
A. $88.14
B. $100.58
C. $124.21
D. $189.35
joe is using his allowance money to download songs from the internet. he can download them at a rate of eight songs every 10 minutes. Jasmine, who is downloading songs with the money she made from her part time job, can download at a rate of 12 songs every 15 minutes. Who is downloading songs faster?
Joe: 8 songs in 10 minutes = 8/10 = 0.8 songs per minute
Jasmine: 12 songs in 15 minutes = 12/15 = 0.8 songs per minute
they are downloading at the same speed
A sample of n = 9 scores has a variance of s2 = 36. what is the estimated standard error for the sample mean? 1 2 4 16
Two redwood trees are the same height. A third tree's height is x feet. The first tree is 50 feet more than three times the height of the third tree. The second tree is 100 feet taller than twice the height of the third tree. What is the height, in feet, of the third tree? A. 150 B. 50 C. 200 D. 100
3rd tree = x
1st tree = 3x+50
2nd tree = 2x+100
3x+50 = 2x+100
subtract 50 from each side
3x= 2x+50
subtract 2x from each side
x = 50
so 3rd tree = 50 feet tall
Answer is B
A shop advertised a 22%-off sale. If a coat originally sold for $257, find the decrease in price and the sale price
Find the missing numbers 85,95, _ ,100,105, _
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Which system of inequalities is shown?
The system of inequalities are y > x and y > 4 option (C) y > x, y > 4 is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have a graph shown in the picture,
As we can see in the picture there two lines are shown which represent the inequality and the shaded region is the solution to the pair of the linear inequality.
y > x and
y > 4
Thus, the system of inequalities are y > x and y > 4 option (C) y > x, y > 4 is correct.
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what is the answer 4(6/10−1/5)+0.4=
Or in shorter answers 2
Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system. x < 2 and y ≤ 4x + 1
(5, 6)
(5, –2)
(–3, –15)
(1, 11)
I suck at word problems help
A four person relay team completed a race in 72.4 seconds. On average what was each runner's time?
Answer:
i believe it's 18.1
Step-by-step explanation:
Mara ran 3 km north and then 4 km east. She will finish her run by running directly home. What was the total distance of her run?
The total distance of her run is 12 Km and this can be determined by using the Pythagorean theorem.
Given :
Mara ran 3 km north and then 4 km east.Mara will finish her run by running directly home.The following steps can be used in order to determine the total distance of Mara run:
Step 1 - The Pythagorean theorem can be used in order to determine the total distance of her run.
Step 2 - The Pythagorean theorem is given below:
[tex]\rm H^2 = P^2+B^2[/tex]
where H is the hypotenuse, B is the base, and P is the perpendicular.
Step 3 - Now, substitute the values of the known terms in the above expression.
[tex]\rm H^2 = (3)^2+(4)^2[/tex]
H = 5 Km
Step 4 - So, the total distance of Mara run is given below:
Total distance = 5 + 4 + 3 = 12 Km
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