Answer:
-14 / 3
Step-by-step explanation:
- Divergence theorem, expresses an explicit way to determine the flux of a force field ( F ) through a surface ( S ) with the help of "del" operator ( D ) which is the sum of spatial partial derivatives of the force field ( F ).
- The given force field as such:
[tex]F = (x^2y) i + (xy^2) j + (3xyz) k[/tex]
Where,
i, j, k are unit vectors along the x, y and z coordinate axes, respectively.
- The surface ( S ) is described as a tetrahedron bounded by the planes:
[tex]x = 0 \\y = 0\\x + 2y + z = 2[/tex]
[tex]z = 0\\[/tex]
- The divergence theorem gives us the following formulation:
[tex]_S\int\int {F} \,. dS = _V\int\int\int {D [F]} \,. dV[/tex]
- We will first apply the del operator on the force field as follows:
[tex]D [ F ] = 2xy + 2xy + 3xy = 7xy[/tex]
- Now, we will define the boundaries of the solid surface ( Tetrahedron ).
- The surface ( S ) is bounded in the z - direction by plane z = 0 and the plane [ z = 2 - x - 2y ]. The limits of integration for " dz " are as follows:
dz: [ z = 0 - > 2 - x - 2y ]
- Now we will project the surface ( S ) onto the ( x-y ) plane. The projection is a triangle bounded by the axes x = y = 0 and the line: x = 2 - 2y. We will set up our limits in the x- direction bounded by x = 0 and x = 2 - 2y. The limits of integration for " dx " are as follows:
dx: [ x = 0 - > 2 - 2y ]
- The limits of "dy" are constants defined by the axis y = 0 and y = -2 / -2 = 1. Hence,
dy: [ y = 0 - > 1 ]
- Next we will evaluate the triple integral as follows:
[tex]\int\int\int ({D [ F ] }) \, dz.dx.dy = \int\int\int (7xy) \, dz.dx.dy\\\\\int\int (7xyz) \, | \limits_0^2^-^x^-^2^ydx.dy\\\\\int\int (7xy[ 2 - x - 2y ] ) dx.dy = \int\int (14xy -7x^2y -14 xy^2 ) dx.dy\\\\\int (7x^2y -\frac{7}{3} x^3y -7 x^2y^2 )| \limits_0^2^-^2^y.dy \\\\\int (7(2-2y)^2y -\frac{7}{3} (2-2y)^3y -7 (2-2y)^2y^2 ).dy \\\\[/tex]
[tex]7 (-\frac{(2-2y)^3}{6} + (2-2y)^2 ) -\frac{7}{3} ( -\frac{(2-2y)^4}{8} + (2-2y)^3) -7 ( -\frac{(2-2y)^3}{6}y^2 + 2y.(2-2y)^2 )| \limits^1_0\\\\ 0 - [ 7 (-\frac{8}{6} + 4 ) -\frac{7}{3} ( -\frac{16}{8} + 8 ) -7 ( 0 ) ] \\\\- [ \frac{56}{3} - 14 ] \\\\\int\int {F} \, dS = -\frac{14}{3}[/tex]
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Density = Mass / Volume
D = 3/0.2
D = 15 kg/m³
Answer:
density=mass/volume
d=3kg/0.2m3
=15kgm-3
Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below. Three lines of math. The first line, StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis. The second line, StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half EndFraction x minus x plus 4. The third line StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half EndFraction x plus 4. StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half Endfraction x minus x plus 4. StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half Endfraction x plus 4. When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. results. What is the value of ? –1 –negative StartFraction one-half EndFraction 0 StartFraction one-half EndFraction.
Answer:
x = 0
Step-by-step explanation:
Given
Karissa begins to solve the equation ...
[tex]\dfrac{1}{2}(x-14)+11=\dfrac{1}{2}x-(x-4)[/tex]
Her work is correct and is shown below. Three lines of math.
[tex]\dfrac{1}{2}(x-14)+11=\dfrac{1}{2}x-(x-4)\qquad\text{given}\\\\\dfrac{1}{2}x-7+11=\dfrac{1}{2}x-x+4\qquad\text{eliminate parentheses}\\\\\dfrac{1}{2}x+4=-\dfrac{1}{2}x+4\qquad\text{collect terms}[/tex]
When she subtracts 4 from both sides, the result is ...
[tex]\dfrac{1}{2}x=-\dfrac{1}{2}x[/tex]
Find
What is the value of x?
Solution
Karissa can determine the value of x by adding 1/2x to both sides:
[tex]x=0[/tex]
Answer:
Option C (0)
Step-by-step explanation:
Grandmother bought enough cat food for her four cats to last for 12 days. On her way home she brought back two stray cats. If she gives each cat the same amount of food every day, how many days will the cat food last
Answer:
The number of days the cat food will last is 8 days.
Step-by-step explanation:
In this case, it it provided that Grandmother bought enough cat food for her four cats to last for 12 days.
Assume that each cat consumes x portions of food each day.
Then the four cats will consume, 4x portions of food each day.
Then in 12 days the amount of food consumed by the 4 cats will be:
Total amount of cat food = 12 × 4x
= 48x.
Now, it is provided that she on her way home she brought back two stray cats.
Then the six cats will consume, 6x portions of food each day.
Compute the number of days the cat food will last as follows:
[tex]\text{Number of days the cat food will last}=\frac{\text{Total amount of cat food}}{\text{Amount of food consumed each day}}[/tex]
[tex]=\frac{48x}{6x}\\\\=\frac{48}{6}\\\\=8[/tex]
Thus, the number of days the cat food will last is 8 days.
someone answer this
Answer:
16
Step-by-step explanation:
The right triangle shown is a 30:60:90 triangle.
30:60:90 right triangles have a 1:sqrt(3):2 ratio between their sides.
Since the side opposite from the 30 degree is 8, and x is opposite from the 90 degree angle, 8 and x have a 1:2 ratio, or 8:16.
01:30:4
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the
solution set of this problem?
Answer:
x<_ 21
Step-by-step explanation:
5(x+27)>_ =6(x+26)
5x +135 >_ 6x +156
5x >_6x +21
-x>_21
x<_21
A high school student took two college entrance exams, scoring 1070 on the SAT and 25 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 155 while the ACT scores have a mean of 22 and a standard deviation of 4. Assuming the performance on both tests follows a normal distribution, determine which test the student did better on.
Answer:
Due to the higher z-score, he did better on the SAT.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Determine which test the student did better on.
He did better on whichever test he had the higher z-score.
SAT:
Scored 1070, so [tex]X = 1070[/tex]
SAT scores have a mean of 950 and a standard deviation of 155. This means that [tex]\mu = 950, \sigma = 155[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1070 - 950}{155}[/tex]
[tex]Z = 0.77[/tex]
ACT:
Scored 25, so [tex]X = 25[/tex]
ACT scores have a mean of 22 and a standard deviation of 4. This means that [tex]\mu = 22, \sigma = 4[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 22}{4}[/tex]
[tex]Z = 0.75[/tex]
Due to the higher z-score, he did better on the SAT.
Which of the following functions is graphed below
Answer:
B
Step-by-step explanation:
What is the average rate of change for this function for the interval from x= 1
to x = 3?
Answer:
The average rate of change is 12x=12.0x.
Description:
Function: x= 1x = 3 convert to short form: x 1x 3
Interval: x= 1 , x 3
Steps:
Input: Find the average rate of change of f(x)=3x2 on the interval [x,3x].
We have that a=x, b=3x, f(x)=3x2
Thus, f(b)−f(a)b−a=3((3x))2−(3(x)2)3x−(x)=12x.
Answer: the average rate of change is 12x=12.0x.
Please mark brainliest
Hope this helps.
Answer:
3
Step-by-step explanation:
A P E X
M5-3/2x less than or equal to 1/3
Answer: choice A
Step-by-step explanation:
by rearranging the initial inequality you’ll get
[tex]\frac{3}{2} x\leq 5-\frac{1}{3}[/tex]
which equals
[tex]\frac{3}{2} x\leq\frac{14}{3}[/tex]
then multiply both sides by 2/3
[tex]x\leq \frac{28}{9}[/tex]
[tex]x = \frac{b + - \sqrt{{b}^{2} - 4ac } }{2a} [/tex]
O True
O False
If it is asking if that equation is the quadratic formula, then the answer is false. The reason why is that the first 'b' should be negative
The quadratic formula is
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Type answer as integer proper fraction or mixed number
Answer:
[tex]9\dfrac{5}{6}[/tex]
Step-by-step explanation:
[tex]5\dfrac{1}{6}+4\dfrac{2}{3}=\\\\5\dfrac{1}{6}+4\dfrac{4}{6}=\\\\9\dfrac{5}{6}[/tex]
Hope this helps!
if the base of a right angled triangle is 4cm and its area is 20cm^2, find its height
answer will be 10cm² as i calculate it
A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from a large university and they produce a mean score of 183 with a standard deviation of 12. Use a 0.05 level of significance to test whether the mean score for students from this university is greater than 160. use the P-value method of testing hypotheses.
Answer:
[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
And the p value would be:
[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]
Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160
Step-by-step explanation:
Information provided
[tex]\bar X=183[/tex] represent the sample mean
[tex]s=12[/tex] represent the sample standard deviation
[tex]n=25[/tex] sample size
[tex]\mu_o =160[/tex] represent the value to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean is greater than 160, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 160[/tex]
Alternative hypothesis:[tex]\mu > 160[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
And the p value would be:
[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]
Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160
MARY PUT IN A TOTAL OF 16-1/2 8 FEET LONG. A NEARBY POLE IS 72 HOURS BABYSITTING DURING 5 DAYS FEET HIGH. HOW LONG IS ITS OF THE PAST WEEK. WHAT WAS HER SHADOW? AVERAGE WORK DAY?
Answer: 3 hours and 18 minutes.
Step-by-step explanation:
Suppose that a random sample of adult males has a sample mean heart mass of x¯=310.1 grams, with a sample standard deviation of s=6.6 grams. Since adult male heart masses are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two masses do approximately 68% of the data occur? Round your answer to the nearest tenth.
Answer:
Between 303.5 grams and 316.7 grams
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 310.1 grams
Standard deviation = 6.6 grams
Between what two masses do approximately 68% of the data occur?
By the Empirical Rule, within 1 standard deviation of the mean.
310.1 - 6.6 = 303.5 grams
310.1 + 6.6 = 316.7 grams
Between 303.5 grams and 316.7 grams
help ,, I need help with this one ,, i’m soo confused
As the x values go up, the y values go down which means the line is higher on the left side than it is on the right side.
The 4th graph would be the correct one
Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 250 companies to invest in. After 1 year, 135 of the companies were considered winners; that is, they outperformed other companies in the same investment class. To assess whether the dart-picking strategy resulted in a majority of winners, the researcher tested Upper H 0: pequals0.5 versus Upper H 1: pgreater than0.5 and obtained a P-value of 0.1030. Explain what this P-value means and write a conclusion for the researcher.
Answer:
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
The population proportion is equal to 0.5
Step-by-step explanation:
Step (i):-
Given random sample size ' n' = 250
Sample proportion 'p'
[tex]p= \frac{x}{n} = \frac{135}{250} = 0.54[/tex]
Given Population proportion P = 0.5
Q = 1-P = 1-0.5 =0.5
Null Hypothesis : H₀ : P = 0.5
Alternative Hypothesis : H₁ : P≥ 0.5
Step(ii):-
Test statistic
[tex]Z = \frac{p - P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.54-0.5}{\sqrt{\frac{0.5 X 0.5}{250} } }[/tex]
Z = 1.2903
Level of significance α = 0.05
Z₀.₀₅ = 1.96
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
Step(iii):-
P- value
The probability of test statistic
P(Z > 1.2903) = 0.5 - A ( 1.2903)
= 0.5 - 0.4015
= 0.0985≅ 0.10
i) P- value =0.10 > α = 0.05
null hypothesis is accepted
Conclusion:-
The population proportion is equal to 0.5
Among fatal plane crashes that occurred during the past 55 years, 415 were due to pilot error, 96 were due to other human error, 169 were due to weather, 622 were due to mechanical problems, and 68 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it?
Answer:
Relative frequency:
[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]
The most serious threat to aviation safety is, according to this data, "mechanical failures". It can be improved by more rigorous inspection and better maintenance policies and execution.
Step-by-step explanation:
We have the data for fatal plane crashes. The sum of plane crashes is
We can calculate the relative frequency as:
[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]
We can see that the most frequent cause is "mechanical problems", with a relative frequency of 0.45.
Which graph represents the function f(x) = |x| – 4? On a coordinate plane, an absolute value graph has a vertex at (0, 4). On a coordinate plane, an absolute value graph has a vertex at (negative 4, 0). On a coordinate plane, an absolute value graph has a vertex at (0, negative 4). On a coordinate plane, an absolute value graph has a vertex at (4, 0).
Answer:
(0, -4)
Step-by-step explanation:
The graph that represents the function is (c) on a coordinate plane, an absolute value graph has a vertex at (0, -4)
The equation of the function is given as:
[tex]f(x) = |x| - 4[/tex]
The above function is an absolute value function shifted down by 4 units
Hence, the graph that represents the function is a graph that has its vertex at (0,-4)
Read more about absolute value graphs at:
https://brainly.com/question/2166748
A fuel oil company claims that one-fifth of the homes in a certain city are heated by oil. Do we have reason to believe that fewer than one-fifth are heated by oil if, in a random sample of 1000 homes in this city, 136 are heated by oil? Please show all 4 steps of the classical approach clearly using α = 0.05.
Answer:
Yes, we have reason to believe that fewer than one-fifth are heated by oil.
Step-by-step explanation:
A one-sample proportion test is to be performed to determine whether fewer than one-fifth of the homes in a certain city are heated by oil.
The hypothesis can be defined as follows:
H₀: The proportion of homes in a certain city that are heated by oil is not less than one-fifth, i.e. p ≥ 0.20.
Hₐ: The proportion of homes in a certain city that are heated by oil is less than one-fifth, i.e. p < 0.20.
The information provided is:
n = 1000
x = 136
α = 0.05
Compute the sample proportion as follows:
[tex]\hat p=\frac{x}{n}=\frac{136}{1000}=0.136[/tex]
Compute the test statistic as follows:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]=\frac{0.136-0.20}{\sqrt{\frac{0.136(1-0.136)}{1000}}}\\\\=-5.9041\\\\\approx -5.90[/tex]
The test statistic value is, -5.90.
Decision rule:
Reject the null hypothesis if the p-value of the test is less than the significance level.
Compute the p-value as follows:
[tex]p-value=P(Z<-5.90)\\\\=1-P(Z<5.90)\\\\=1-(\approx 1)\\\\=0[/tex]
The p-value of the test is, 0.
p-value = 0 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Conclusion:
The proportion of homes in a certain city that are heated by oil is less than one-fifth.
Solve for the value of x
Answer:
x = 8
Step-by-step explanation:
The angle with the expression in it is complementary to the 30° angle, so is 60°. Then we have ...
4 +7x = 60
7x = 56 . . . . . . subtact 4
x = 8 . . . . . . . . .divide by 7
Solve 3(a + 3) – 6 = 21.
Answer:
a=6
Step-by-step explanation:
to find the value of a you need to simplify the equation first. so...
3(a+3)-6=21 (you remove the bracket first)
3a+9-6=21
3a+3=21 (you collect the like terms then)
3a=21-3
3a=18 (then you both divide both sides by 3 to find the value of a)
a=18/3
a=6
to check your answer substitute 3 instead of a
3(a+3)-6=21
3(6+3)-6=21
3(9)-6=21 (according to BODMAS since multiplication comes first you multiply 3 with 9 before subtracting it from 6.)
29-6=21
21=21
Answer:6
Step-by-step explanation:
3(a + 3) - 6 = 21
3(a + 3) = 21 + 6
3(a + 3) =27
a + 3. = 27 ÷ 3
a + 3. = 9
a. = 9 - 3
a. = 6
Answer pls need help
The pressure p(in lbs/in^2) that a 160 pound persons shoe exerts on the ground when walking varies inversely with the area A(in in^2) of the sole of the shoe when the shoes have a sole area of 40 in^2 The pressure is 4 lbs/in^2 find equation that relates these variables
A=
find the arc length of the particle circle
Answer:
Is there a picture or graph or..
Step-by-step explanation:
Step-by-step explanation:
arc length = (radians * radians) . 90° is π/2 radians. Arc length is (π/2×4). So the answer is 2π.
A box plot is shown below:
What is the median and Q1 of the data set represented on the plot?
Median = 31; Q1 = 26
Median = 30; Q1 = 26
Median = 31; Q1 = 20
Median = 30; Q1 = 20
Answer:
Step-by-step explanation:
Hello!
I didn't find the exact box plot for this exercise but I've found one that'll help you identify the required values
When constructing a box plot the box lower and upper limits are defined by the first and third quartiles and the line separating it in two represents the median.
In this case, the box is lying on the side, the first quartile is represented by the left side of the box. If you see the graphic this one corresponds to 25.
The median, as said, is represented by the line drawn inside the box, it is not necessarily in its middle but it will always be inside it.
Watching the example, the median is 33
I hope this helps!
Answer: D
Step-by-step explanation:
For all the people that have to do algebra and dont want to do it yourself there is a website or you can download it on your phone its called*** MATH PAPA*** ****IT SHOWS YOU STEP BY STEP AND GIVES YOU THE ANSWER*** Just input the equation
Perform the indicated operation and write the result in the form a + bi i^100
[tex]i^{100}=i^{4\cdot25}=\left(i^4\right)^{25}[/tex]
Recall that [tex]i^4=1[/tex], since [tex]i^2=-1[/tex]. Then
[tex]i^{100}=1^{25}=1[/tex]
so that in the form [tex]a+bi[/tex], we have [tex]a=1[/tex] and [tex]b=0[/tex].
Answer:
D) 1
Step-by-step explanation:
Correct on edg
Please answer this correctly
So if we know the perimeter of the circle we can find it's radius using the formula for perimeter:
[tex]p = 2\pi(r)[/tex]
So we can solve for radius:
[tex]r = \frac{10.71}{2\pi} [/tex]
Then we can plug this radius into the formula for the area of a circle:
[tex]a = \pi {r}^{2} [/tex]
[tex]a = \pi( \frac{10.71}{2\pi} ) ^{2} [/tex]
Then it only wants a quarter of that area so we divide that value by 4 which upon simplification becomes the answer:
[tex]2.28 {ft}^{2} [/tex]
Answer:
[tex] \boxed{Area \: of \: quarter \: circle = 7.065 \: square \: feet} [/tex]
Given:
Perimeter of quarter circle = 10.71 feet
To find:
Area of quarter circle
Step-by-step explanation:
First we need to calculate the radius of quarter circle:
Let the radius of quarter circle be 'r'
[tex]Perimeter \: of \: quarter \: circle = \frac{\pi r}{2} + 2r[/tex]
[tex] \implies 10.71 = \frac{\pi r}{2} + 2r \\ \\ \implies 10.71 = \frac{\pi r}{2} +2r \frac{2}{2} \\ \\ \implies 10.71 = \frac{\pi r}{2} + \frac{4r}{2} \\ \\ \implies 10.71 = \frac{\pi r + 4r}{2} \\ \\ \implies 10.71 \times 2 = \pi r + 4r \\ \\ \implies 21.42 = \pi r + 4r \\ \\ \implies 21.42 = (\pi + 4)r \\ \\ \implies 21.42 = (3.14 + 4)r \\ \\ \implies 21.42 = 7.14r \\ \\ \implies 7.14r = 21.42 \\ \\ \implies r = \frac{21.42}{7.14} \\ \\ \implies r = 3 \: ft[/tex]
[tex] Area \: of \: quarter \: circle = \frac{\pi {r}^{2} }{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi \times {(3)}^{2} }{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi \times 9}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3.14 \times 9}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{28.26}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =7.065 \: {ft}^{2} [/tex]
A foundry has been commissioned to make souvenir coins. The coins are to be made from an alloy that is 40% silver. The foundry has on hand two alloys, one with 50% silver content and one with a 25% silver content. How many kilograms of each alloy should be used to make 10 kilograms of the 40% silver alloy?
Answer:
the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
Step-by-step explanation:
Suppose, the weight of the alloy with 50% silver content is x kilograms.
As, the weight of the mixed alloy should be 10 kilograms, so the weight of the alloy with 25% silver content will be: kilograms
The percentage of silver content in the mixed alloy is 40%. So the equation will be calculated as
[tex]0.5x+0.25(10-x)=0.4\times10\\0.5x+2.5-0.25x=4\\0.25x=1.5\\\Rightarrow x=\frac{1.5}{0.25} = 6[/tex]
So, the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d
Answer:
C
Step-by-step explanation:
C=2pier or pied
Answer:
a. C = 2πr
c. C= πd
both are correct
