The mass of the ball is 278.1 g, the material used to make the ball must be brass which having density of 8.6 g/cm³.
How to find mass of the ball ?To determine the material used to make the ball, we need to first calculate the volume of the ball.
The volume of a sphere with radius r is given by:
V = (4/3) * π * r^3
Plugging in the given values, we get:
V = (4/3) * π * (2 cm)^3
= (4/3) * π * 8 cm^3
= (4/3) * 8π cm^3
= 32π cm^3
We can then use the density of each material (given in g/cm³) to calculate the mass of the ball if it were made of that material:
Copper: 8.3 g/cm³ * 32π cm³ = 266.4 g
Brass: 8.6 g/cm³ * 32π cm³ = 275.2 g
Iron: 7.8 g/cm³ * 32π cm³ = 250.4 g
Since the mass of the ball is 278.1 g, the material used to make the ball must be brass.
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Write the number 2.1 x 10-6 in standard form.
help i need answers now please thank u if u helped giving brainliest btw
Answer:
\(7\frac{1}{6}\)
Step-by-step explanation:
→ Convert all fractions to improper fractions
\(\frac{27}{6} +\frac{8}{3}\)
→ Make both of the numerators the same
\(\frac{27}{6} +\frac{16}{6}\)
→ Add
\(\frac{43}{6}\)
→ Convert to mixed fraction
\(7\frac{1}{6}\)
help me please! I’ll give y’all points
Answer:
11
Step-by-step explanation:
Answer:
Y = 11
Step-by-step explanation:
I think we are using the order of PEMDAS. We replace the x with 3. If we simplify this expression this is just 3 to the power of 2 multiplied by 2 then subtracted by 7. So 3^2 = 9 then 9 x 2 = 18. Then 18 minus 7 = 11.
Find an equation of the parabola with the focus and directrix given. (-3,0), x=3
The equation of the parabola with the focus (-3, 0) and directrix x = 3 can be expressed as \($(x + 3)^2 = 12(y - 0)$\).
To find the equation of the parabola, we start by understanding the definition of a parabola. A parabola is a set of points that are equidistant from the focus and the directrix.
Given that the focus is located at (-3, 0) and the directrix is the vertical line x = 3, we consider a point (x, y) on the parabola. The distance from this point to the focus (-3, 0) is given by
\($\sqrt{(x - (-3))^2 + (y - 0)^2} = \sqrt{(x + 3)^2 + y^2}$\).
Since the point (x, y) lies on the parabola, its distance to the directrix x = 3 is |x - 3|.
According to the definition of a parabola, these distances are equal. Hence, we have the equation: \($\sqrt{(x + 3)^2 + y^2} = |x - 3|$\).
To eliminate the square root, we square both sides of the equation:
\($(x + 3)^2 + y^2 = (x - 3)^2$\).
Simplifying the equation, we obtain: \($x^2 + 6x + 9 + y^2 = x^2 - 6x + 9$\).
Rearranging the terms to isolate y, we have: \($y^2 = -12x\)
Thus, the equation of the parabola with the given focus and directrix is
\($(x + 3)^2 = 12(y - 0)$\).
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if gas cost 3.19 per gallon how many gallons of gas could you buy with $44.66
Answer:
14 gallons
Step-by-step explanation:
44.66 divided by 3.19 equals 14
2) The representative agent lives for infinite periods (0,1,2,…) and receives exogenous incomes of y0,y1,y2,…, respectively. The lifetime present discounted value of utility is given by: ∑t=0[infinity]βtln(ct) with β(<1) being the discount factor and ct is consumption at time t. The agent is allowed to save or borrow at the real interest rate r, but she cannot die with debt or wealth. Assume also that the initial wealth is zero. a. Solve the optimization problem of the agent using the period-by-period budget constraints. In particular, show the Euler equation. b. Using the given functional form, write the Euler equation between time 1 and time 3 . In other words, show how c1 and c3 are related. c. Write the present discounted value of optimal lifetime consumption as a function of c0 (and, potentially, other parameters or exogenous variables). d. Write the present discounted value of optimal lifetime utility as a function of c0 (and, potentially, other parameters or exogenous variables). e. Find the present discounted value of lifetime income as a function of y0 (and, potentially, other parameters or exogenous variables) when income is growing each period at the rate of γ, where 0<γ0 ? Explain!
a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. U0 = ∑t=0[infinity](β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.
a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:
At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.
b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.
Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin
d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.
c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity](β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.
d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity](β(1 + r))^tln(ct).
This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.
e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.
This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.
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Acellus, Inscribed Angles
Find the value of y.
x
120°
Answer:
\(y=60\textdegree\)
Step-by-step explanation:
The Tangent-Secant Interior Angle Measure Theorem states that the measure of an angle formed by a tangent and a secant of a circle at the point of tangency is equal to half of the measure of its intercepted arc.
Therefore, \(y=\frac{1}{2} *120\textdegree = \bf 60\textdegree\). Hope this helps!
In 1000 sq. meter of land a farmer cultivated 765 kg of rice with the wastage of 23.5%.I) Find the weight of the wastage. II) Find the weight and percentage of rice cultivated.
Answer:
i. weight of wastage(kg) = 179.775 kg
ii. weight of rice cultivated = 765 kg - 179. 775 kg = 585.225 kg
percentage of rice cultivated = 100 - 23.5 = 76.5%
Step-by-step explanation:
A land of 1000 sq. meter is used to cultivate 765 kg of rice with wastage of 23.5%.
i. The wastage in percentage is 23.5% but the weight of the wastage in weight is 23.5% of 765 kg
weight of wastage = 23.5/100 × 765
weight of wastage = 17977.5/100
weight of wastage(kg) = 179.775 kg
ii. weight and percentage of rice cultivated.
weight of rice cultivated = 765 kg - 179. 775 kg = 585.225 kg
percentage of rice cultivated = 100 - 23.5 = 76.5%
What is the slope of the line passing through the points (3,7) and (1, -3)? Show all your work.
Answer:
The slope of the line is 5.
Step-by-step explanation:
Formula: m = (y-y1)/(x-x1)
where m is the slope
Substitute the points given.
m = (7-(-3))/(3-1)
m = (7+3)/2
m = 10/2
m = 5
6.4 x 1.2 show your work please and also 3.5 x 4.9 show your work please (will give brainlist thingy)
Answer:
6.4 x 1.2=7.68
Step-by-step explanation:
6.4
1.2
----
028
740
add
7.68
3.5 x 4.9=15.435
QUICK!!!HELP!!!!!!!!!!!!!!!!!!
Using the normal distribution, the probability that a worker selected at random makes between $500 and $550 is: 2.15%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean mu and standard deviation sigma is given by:
Z = (X - mu)/sigma
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
mu = 400, sigma = 50
The probability is the p-value of Z when X = 550 subtracted by the p-value of Z when X = 500, hence:
X = 550:
Z = (X - mu)/sigma
Z = (550 - 400)/50
Z = 3
Z = 3 has a p-value of 0.9987.
X = 500:
Z = (X - mu)/sigma
Z = (500 - 400)/50
Z = 2
Z = 2 has a p-value of 0.9772.
0.9987 - 0.9772 = 0.0215 = 2.15% probability.
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Accrotime is a company that manufactures quartzcrystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic componentsdeteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 5 months, and the distribution of lifetimes is normal.
if Acro time does not want to make refunds for more than 12% of the watches it makes how long should the guarantee period be to the nearest month
if acro time guarantees a full refund on any defective watch for two years after purchase what percentage of total production should the company expect to replace
The guarantee period of the electronic components by Accrotime manufactures is 38 months.
What is defined as the normal distribution?A normal distribution is a data set arrangement in which the majority of values cluster inside the middle of the range and the remainder trimmed off symmetrically toward any extreme.It happens whenever a normal random variable does have a mean of zero and a standard deviation of one.mean = μ = 24 months
standard deviation = σ = 5 months
2 years = 24 months
a) P(x < 24)
= P[(x - μ ) / σ < (24 - 28) / 5]
= P[(x - μ ) / σ < -0.8
= P(z < -0.8 )
Using z table,
= 0.212
Percentage = 21.2%
b) Use standard normal table,
Refund percentage = 12%
P(Z > z) = 12%
= 1 - P(Z < z) = 0.12
= P(Z < z) = 1 - 0.12
= P(Z < z ) = 0.88
= P(Z < 0.174 ) = 0.94
z = 0.174
Using z-score formula,
x = z ×σ + μ
x = 1.74 × 5 + 28
x = 36.7
The guarantee period = 38 month
Thus, the guarantee period of the electronic components by Accrotime manufactures is 38 months.
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What formula could you use to help find the area of the given triangle
Answer:
Pythagorean Theorem
Step-by-step explanation:
Because they give you the hypotenuse and the adjacent angle.
Answer:
Pythagorean Theorem
Step-by-step explanation:
Because they give you the hypotenuse and the adjacent angle.
A 6,000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $193,200?
Answer:
2,100 $28 tickets were sold, and 3,900 $40 tickets were sold!
Step-by-step explanation:
So, we need to write two equations in order to solve this:
We will think of 28 dollar tickets as x, 40 dollar tickets as y.
Now lets make those equations:
\(x + y = 6,000\)
and
\(28x+40y = 193,200\)
Now, to solve for x and y, lets set a value for x or y. In this case I will set the value of y:
I will do this by taking \(x + y = 6,000\), and subtracting x to the other side, to get y alone:
\(y = 6,000 - x\)
Now lets plug in y to our second equation:
\(28x + 40(6,000-x) = 193,2000\)
=
\(28x+240,000-40x = 193,200\)
Now combining like terms and solving for x we get:
\(-12x + 240,000 = 193,200\)
=
\(-12x = -46,800\)
=
\(x=3,900\)
Now that we know x, lets solve for y by plugging into our first equation!
\(3,900 + y = 6,000\)
=
\(y = 2,100\)
So now we know that our answer is:
2,100 $28 tickets were sold, and 3,900 $40 tickets were sold!
Hope this helps! :3
samanth drew this pictogram
Answer:
la verdad noce no me acuerdo
Answer:
4
Step-by-step explanation:
There are 6 grey diamonds in the row labelled "cat".
Each diamond means two hours.
6 × 2 = 12
Samanth's table shows that cats sleep 12 hours.
Tony is going to use a circle that means 3 hours.
12 ÷ 3 = 4
Tony needs 4 circles to show 12 hours.
4 × 3 = 12
Tony will use 4 circles.
the city's pr manager, who never took statistics, claimed the mean score of all ninth graders in the city was the average of 77, 91, and 71, which is 79.7. of course, that is incorrect. what is the mean score for all ninth graders in the city? round to one decimal place.
The mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.
To find the mean score for all ninth graders in the city, we need more information than just three scores. Without additional data, we cannot accurately determine the mean score for all ninth graders in the city.
However, we can calculate the mean of the given scores to verify that it is not 79.7 as claimed by the PR manager:
Mean = (77 + 91 + 71) / 3 = 79.7/3 = 79.7 ÷ 3 ≈ 79.7/3 ≈ 26.6
So the mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.
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What is the area of the pentagon, rounded to the nearest tenth?
13.8 cm2
17.3 cm2
32.7 cm2
69.0 cm2
The area of the pentagon, rounded to the nearest tenth will be 32.7 square cm. Then the correct option is C.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.
Then the side length of the pentagon will be
5 x Side length = 21.8 cm
Side length = 4.36 cm
Then the area of the pentagon, rounded to the nearest tenth will be
Area of pentagon = 5 x area of triangle
Area of pentagon = 5 x 1/2 x 4.36 x 3
Area of pentagon = 32.7 square cm
Thus, the correct option is C.
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What is the value of x in the proportion below?
StartFraction two-thirds over 5 EndFraction = StartFraction x over 15 EndFraction
2
3
10
☺︎︎
75
Answer:2
Step-by-step explanation:15 divided by 3 is 5 so you would do 2/3 times 3 which is 2
Answer:
Dos!
Step-by-step explanation:
Since the area of the rectangle for a uniform probability distribution must equal one, what must the height equal, in general? Choose the correct answer below. range B. range 2. C. range D. More information is needed
The height equal to the given rectangle couldn't be found due to the reason of more information is needed. Therefore the required answer for the question is Option D.
So, the Probability density function is portrayed graphically as a rectangle where (b-a) is the base and 1/(b-a) is the required height.
Probability density function refers to the method that helps to define the random variable's probability within a distinct range of values as opposed to taking one value.
then,
the height of the rectangle for a uniform probability distribution should be 1/(b-a)
The height equal to the given rectangle couldn't be found due to the reason of more information is needed. Thus the correct answer is Option D.
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N = 2^p x 5^q x 7^r and 500 = 2^2 x 5^3.
The HCF of N and 500 is 2^2 x 5^2.
The LCM of N and 500 is 2^3 x 5^3 x 7.
Find p, q and r
Answer:
p= 2, q = 3and r=1
Step-by-step explanation:
I think this is the answer
hope helps!!!a small apartment has a 11ft by 10ft bedroom, a 5ft by 6ft bathroom, and a single multi-use 12ft by 16ft living room/kitchen. what is the total square footage (area) of the apartment?
The total square footage (area) of the apartment is 332 ft²
Finding the area of the apartment:To find the total area of the apartment we need to calculate the area of the given each room by using the given dimensions. Find the sum of the areas of each room to the area of the apartment.
Area of a rectangle room = Length × Width
Here we have
Dimensions of bedroom = 11ft × 10ft
Area of the bedroom = 11ft × 10ft = 110 ft²
Dimensions of bathroom = 5ft × 6ft
Area of the bathroom = 5ft × 6ft = 30 ft²
Dimensions of Sigle multi-use living room = 12ft × 16 ft
Area of the living room = 12ft × 16 ft = 192 ft²
From above calculations
The total square footage of the apartment
= 110 ft² + 30 ft² + 192 ft²
= 332 ft²
Therefore,
The total square footage (area) of the apartment is 332 ft²
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to factorize the following algebraic expression: 3x² + 6x + 4x + 8 Provide a three-step guide on how to factorize the expression.
Answer:
Check below:
Step-by-step explanation:
To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:
Step 1: Grouping
Group the terms in pairs so that you can factor out a common factor from each pair.
3x² + 6x + 4x + 8
(3x² + 6x) + (4x + 8)
Step 2: Factoring out the common factors
Factor out the common factors from each pair separately.
3x(x + 2) + 4(x + 2)
Step 3: Factoring out the common factor from the resulting expression
Notice that we have a common factor, (x + 2), in both terms.
(x + 2)(3x + 4)
Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).
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There are 2 pitchers of iced tea. The iced tea in the 1st one was made with 4 tea bags and 1.25 quarts of water. The iced tea in the second pitcher was made with 5 tea bags and 2 quarts of water. Which pitcher has a higher concentration of tea? Why?
Answer:
Pitcher 2
Step-by-step explanation:
Pitcher 1 = 4 x 1.25 = 5ml concentration
Pitcher 2 = 5 x 2 = 10ml concentration
therefore, pitcher 2 has more concentration :)
hope this helped
kyle practices the piano trombone and violin. he dedicates one fourth of this practice time to piano, four ninths of his time to the trombone, and rest of his time to the violin. what fraction of kyle's practice time is spent playing the violin?
Answer:
Step-by-step explanation:
1/4 + 4/9 + n= total amount of time spent on all of the instruments.
1/4 + 4/9=
9/36 + 16/36= 25/36 (time on piano and trombone)
36/36- 25/36= 11/36- total time spent on violin
how many one-to-one functions are there from a set containing 5 elements to a set containing 6 elements?
There are 5x6=30 one-to-one functions from a set containing 5 elements to a set containing 6 elements.
A one-to-one (or injective) function is a type of mathematical function that maps each element of one set to one, and only one, element of another set. In other words, a one-to-one function is a function that has a unique output for each input. To calculate the number of one-to-one functions from a set containing 5 elements to a set containing 6 elements, we can use the formula f(x)=y, where x is the number of elements in the original set and y is the number of elements in the target set. In this case, x = 5 and y = 6, so f(x) = 6. Since each element in the original set must be mapped to a unique element in the target set, the total number of one-to-one functions is equal to the product of x and y, or 5 x 6 = 30.
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draw the vector starting at the black dot 3. the location and orientation of the vector will be graded. the exact length of your vector will not be graded but the length relative to vector v⃗ 2v→2 will be graded
To draw a vector starting at black dot 3, consider its location and orientation, consider vector V 2v→2, draw a vector in the same direction as V 2v→2, and double-check accuracy and grading criteria.
To draw the vector starting at the black dot 3, you need to consider the location and orientation. The exact length of the vector will not be graded, but the length relative to vector V 2v→2 will be graded.
Here's how you can draw the vector:
1. Start by locating the black dot 3 on your coordinate plane.
2. Determine the direction and orientation of the vector based on the given information.
3. Consider vector V 2v→2 and its length.
4. Draw a vector starting at black dot 3 that is in the same direction as V 2v→2. Remember, the length of this vector is not important, but its relative length compared to V 2v→2 is graded.
5. Make sure the vector starts at black dot 3 and points in the same direction as V 2v→2.
Remember to double-check your work and ensure that the vector is accurate and meets the grading criteria.
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Find the point that partitions segment AB in a 2:1 ratio when A(1,3)B(7,8)
Answer:
X2 - X1 = 7 - 1 = 6
Y2 - Y1 = 8 - 3 = 5
L = (6^2 + 5^2)^1/2 = 7.81
2/3 L = 5.21 length of segment
Tan θ = 5 / 6 = .833 slope of line
θ = 39.8 deg
5.21 * sin 39.8 = 3.34
5.21 * cos = 39.8 = 4.00 gives length of line segments
x2 = 1 + 4 = 5
y2 = 3 + 3.34 = 6.34
(5, 6.34) = point 2/3 up the line
Check (length of line)
[(5 - 1)^2 + (6.34 - 3)^2]^1/2 =
l = 5.21 correct length for line segmet
Write each number in standard form.
The number 8*1000+4*10*2*1/10+3*1/100+5*1/1000+6*1/10000 has its standard form give mathematically as
8 × 10^0, 1 × 10^3, 4× 10^0, 1*10^1, 9 × 10^0, 2 × 10^0, 1*10^{-1}, 3 × 10^0, 1*10^{-2}, 5 × 10^0, 1*10^{-3}, 6 × 10^0, 1*10^{-5} respectively.
What is the standard form of each number?
Generally, the standard form of each number is
8=8 × 10^0
1000=1 × 10^3
4= 4× 10^0
10=1*10^1
9=9 × 10^0
2= 2 × 10^0
1/10= 1*10^{-1}
3=3 × 10^0
1/100=1*10^{-2}
5=5 × 10^0
1/1000=1*10^{-3}
6=6 × 10^0
1/10000=1*10^{-5}
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What is the solution to the inequality below? x2 < 36
a. -6 x 6
b. x -6 or x 6
c. x < -6 or x > 6
d. -6 < x < 6
The solution to the inequality \(x^2\) < 36 is x < -6 or x > 6. Therefore, option c. is correct.
To solve the inequality \(x^2\) < 36, we can start by subtracting 36 from both sides to obtain \(x^2\)- 36 < 0. Next, we can factor the left side as (x - 6)(x + 6) < 0. Since the product of two numbers is negative when one of the numbers is positive and the other is negative, we have two possibilities:
(x - 6) < 0 and (x + 6) > 0: This implies x < 6 and x > -6, which means x is greater than -6 and less than 6.
(x - 6) > 0 and (x + 6) < 0: This implies x > 6 and x < -6. However, this condition is not possible since it contradicts the first possibility.
Therefore, the solution to the inequality \(x^2\)< 36 is x < -6 or x > 6, which is option (c) in the given choices.
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the tire for a 10-speed bicycle has a diameter of 27 inches what is the distance traveled in 10 rotations of the tire. round to the nearest tenth
Answer:
The circumference is about 84.82 inches ;D