Answer:
524cm^2
Step-by-step explanation:
Formula for Volume of sphere= 4/3 πr^2
We have,
r=5cm
Now,
Volume(v)=4/3 πr^2 = 4/3π 5^3= 4/3π 125 = 166.666666667π = 523.598775599
Rounding to the nearest tenth,
Volume=524cm^2
Agyappng is three times as old as Atsu .three years ago ,he was four times as old as Atsu ..how old is each boy now
9514 1404 393
Answer:
Atsu is 9Agyappng is 27Step-by-step explanation:
Let x represent Atsu's current age. Then Agyappng is 3x. Three years ago the relationship was ...
(3x -3) = 4(x -3)
9 = x . . . . . . . . . . . . add 12-3x
Atsu is 9; Agyappng is 27.
Most brainiest for the right answer on this problem!
Answer:
82.8
Step-by-step explanation:
mean = sum of all points, over the total given number of points
84 * 26 = 2184
2184 + 69 + 66 = 2319
Now the total number of tests is 26 + 2 or 28
So divide 2319 by 28
2319/28 = 82.82142
rounded to the nearest tenth is 82.8
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Consider the differential equation: 2y′′−13y′−7y = 0
a. Show that, for any constants A and B, the following is a solution to the above differential equation: y = Ae^(−9x)+Be^(x/3)
b. Find the values A and B that make the above general solution into a solution for the following initial value problem: 2y′′−13y′−7y = 0; y(0) = 3, y′(0) = −5
--------------------------------------------------
Just a correction, the characteristic roots of the equation are [tex]y = 7[/tex] and [tex]y = -\frac{1}{2}[/tex], thus, we should test for:
[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
--------------------------------------------------
Question a:
First, we find the derivatives, thus:[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]
[tex]y^{\prime\prime} = 49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}[/tex]
Now, we replace into the equation:[tex]2y^{\prime\prime} - 13y^{\prime} - 7y = 0[/tex]
[tex]2(49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}) - 13(7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}) - 7(Ae^{7x} + Be^{-\frac{x}{2}}) = 0[/tex]
[tex]98Ae^{-7x} + \frac{1}{2}Be^{\frac{x}{2}} - 91Ae^{-7x} + \frac{13}{2}e^{-\frac{x}{2}} - 7Ae^{7x} - 7Be^{-\frac{x}{2}} = 0[/tex]
[tex]98Ae^{-7x} - 91Ae^{-7x} - 7Be^{-\frac{x}{2}} + \frac{1}{2}Be^{\frac{x}{2}} + \frac{13}{2}e^{-\frac{x}{2}} - 7Be^{-\frac{x}{2}} = 0[/tex]
[tex]0A + 0B = 0[/tex]
[tex]0 = 0[/tex], thus, we found the identity, and for each constant A and B, the following is a solution.
--------------------------------------------------
Question b:
[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
Since [tex]y(0) = 3[/tex][tex]A + B = 3 \rightarrow B = 3 - A[/tex]
--------------------------------------------------
[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]
Since [tex]y^{\prime}(0) = -5[/tex][tex]7A - \frac{1}{2}B = -5[/tex]
Using [tex]B = 3 - A[/tex]
[tex]7A - \frac{3}{2} + \frac{A}{2} = -5[/tex]
[tex]\frac{14A}{2} + \frac{A}{2} = -\frac{10}{2} + \frac{3}{2}[/tex]
[tex]\frac{15A}{2} = -\frac{7}{2}[/tex]
[tex]15A = -7[/tex]
[tex]A = -\frac{7}{15}[/tex]
--------------------------------------------------
Then, B is given by:
[tex]B = 3 - A = 3 - (-\frac{7}{15}) = \frac{45}{15} + \frac{7}{15} = \frac{52}{15}[/tex]
Thus, the values are: [tex]A = -\frac{7}{15}, B = \frac{52}{15}[/tex]
A similar problem is given at https://brainly.com/question/2456414
Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find P(red then blue).
Answer:
4/27
Step-by-step explanation:
total number of marbles=9
probability of red=4/9
since you returned the first marble, the total number of marbles remains the same
prob(Blue)=(3/9)=1/3
P(red then blue)=(4/9)*(1/3)
=4/27
PLSSS HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
I believe its EG and NE but i might be wrong
Step-by-step explanation:
the image is located at the bottom of the screen.
Answer:
..... surface area = 16 km^2.
Can anyone please help me out?
look at the image below over 100000000 points brainly instructer
Answer:
~~314.16
Step-by-step explanation:
lol i dont have 100000000 points. anyways
you can find the area of a sphere with the formula 4πr^2 with r being the radius
this sphere's radius is 5 as shown in the image
so
4π*r^2
4π*(5)^2
=4π*25
=100π
put into calculator
~~314.16cm^3
hope this helps
Suppose that a local TV station conducts a survey of a random sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.
Required:
a. Construct and interpret a 99% CI for the true proportion of voters who prefer the Republican candidate.
b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.
Answer:
a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.
So 120 - 62 = 58 favored the Republican candidate, so:
[tex]n = 120, \pi = \frac{58}{120} = 0.4833[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001[/tex]
The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.
The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.
14 cm 8 cm 10cm 5 cm.
find the area and the perimeter of the above figures
Perimeter = Sum of all sides
Perimeter = 14cm + 8cm + 10cm + 5cm
Perimeter = 22cm + 15cm
Perimeter = 37cm
Step-by-step explanation:
hope it helps you
...
........
Yooooo HELPPP
with this question plz
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
Carmen Martinez
What is the slope of the line that passes through the point 4,4 and 10,7 write your answer in simplest form
[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{7-4}{10-4}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{3}{6}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto m\approx0.5[/tex]
Answer:
[tex]m=\frac{1}{2}[/tex]
Step-by-step explanation:
The slope of a line, also known as the change in the line or the ([tex]\frac{rise}{run}[/tex]) can be found using the following formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. Substitute the given information into the formula and solve for the slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Points on the line: [tex](4,4)\ \ \ (10, 7)[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-4}{10-4}[/tex]
[tex]m=\frac{3}{6}[/tex]
[tex]m=\frac{1}{2}[/tex]
[tex]m=0.5[/tex]
compute (-12)+(-8)+30
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{-12 + (-8) + 30}\\\\\large\textsf{= -12 - 8 + 30}\\\\\large\textsf{-12 - 8 = \bf -20}\\\\\large\textsf{= -20 + 30}\\\\\large\textsf{= \bf 10}\\\\\\\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{10}}}}\huge\checkmark\\\\\\\\\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A solid is formed by rotating the region bounded by y = x − x^2 and y = 0 about the line x = 2 . Use the shell method to find the volume of the solid.
Answer:
The volume of the resulting solid is π/2 cubic units.
Step-by-step explanation:
Please refer to the diagram below.
The shell method is given by:
[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]
Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.
From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:
[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]
The volume of the resulting solid is π/2 cubic units.
Answer:
pi/2
Step-by-step explanation:
I always like to draw an illustration for these problems.
For shells method think volume of cylinder=2pi×r×h
Integrate(2pi(2-x)(x-x^2) ,x=0...1)
Multiply
Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)
Combine like terms
Integrate(2pi(2x-3x^2+x^3) ,x=0...1)
Begin to evaluate
2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1
2pi(x^2-x^3+x^4/4), x=0...1
2pi(1-1+1/4)
2pi/4
pi/2
Drag the tiles to the correct boxes to complete the pairs.
Given that x= 3 + 81 and y= 7 - 1 match the equivalent expressions.
-15 + 19
58 + 106
-&
411
-29 - 531
I. 2y
-
y
–50 ty
23 - 3y
9514 1404 393
Answer:
58 +106i-29 -53i-8 -41i-15 +19iStep-by-step explanation:
For the purpose of selecting the appropriate tile, it is only necessary to figure the real part of the sum or product.
We notice that the second product (-xy) is -1/2 times the first product (2xy). This can let you find the answers on that basis alone. The only tiles with a (-1) : (2) relationship are (-29 -53i) : (58 +106i).
__
The sum -5x +y has a real part of -5(3) +7 = -8.
The sum 2x -3y has a real part of 2(3) -3(7) = 6 -21 = -15.
Hence the sequence of answers needed on the right side is as shown above.
_____
Additional comment
You know that arithmetic operations with complex numbers (multiplication and addition) are identical to those operations performed on any polynomials. That is, "i" can be treated as a variable. The simplification comes at the end, where any instances of i² can be replaced by -1.
xy = (3 +8i)(7 -i) = 3·7 -3·i +8·7·i -8·i·i = 21 +53i -8i²
= (21 +8) +53i . . . . replaced i² with -1, so -8i² = +8
= 29 +53i
The cost of producing pens with the company logo printed on them consists of a onetime setup fee of $265.00 plus $0.95 for each pen produced. This cost can be calculated using the formula C=265.00+0.95p, where p represents the number of pens produced and C is the cost. Use the formula to calculate the cost of producing 2900 pens.
If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting 2 queens and 2 kings.
The probability is ___.
(Round to six decimal places as needed.)
Answer:
1.083
Step-by-step explanation:
Exact form: 13/12
Decimal form: 1.083 (put a line above the 3)
Mixed number form: 1 1/12
A sample of 13 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 1.96,1.81,1.97,1.83,1.87,1.84,1.85,1.94,1.96,1.81,1.86,1.95,1.89
===============================================
Explanation:
Add up the values to get
1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54
Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.
So the mean is approximately 1.8876923
---------------------
Now make a spreadsheet as shown below
We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.
After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.
That sum is approximately 0.04403076924
Next, we divide that over n-1 = 13-1 = 12
0.04403076924 /12 = 0.00366923077
That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.
sqrt(0.00366923077) = 0.06057417576822
This rounds to 0.061 which is the final answer.
Describe the following sequence using an algebraic expression as a rule 0; 2,4; 6
Answer:
Step-by-step explanation:
I assume the sequence is 0, 2, 4, 6
nth term = 2(n-1)
f (x) = sqrt(x)+ 2, g(x)=x^2+ 1
find f(g(x))
and g(f(x))
Answer:
[tex]f(x) = \sqrt{x} + 2 \\ \\ g(x) = {x}^{2} + 1 \\ \\ f{g(x)} = \sqrt{ {x}^{2} + 1 } + 2 \\ \\ g{f(x)} = {( \sqrt{x} + 2 )}^{2} + 1[/tex]
Choose the system of inequalities that best matches the graph below. A. B. C. D.
The system of inequalities that is graphed is:
y ≤ - (2/3)*x
y < x - 3
So the correct option is B.
Which system of inequalities is the graphed one?First, we can see that for both of the inequalities the shaded part is below the lines.
You also can see that the solid line (correspondent to the symbol ≤) is the one with a negative slope, and the dashed line (correspondent with the line <) is the one with a positive slope.
Only with that, we conclude that the correct option is B.
y ≤ - (2/3)*x
y < x - 3
If you want to learn more about inequalities:
https://brainly.com/question/24372553
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whats the scale factor of this one please?????
Answer:
0.5
Step-by-step explanation:
E to E'
(0, 3) to (0, 1.5) each term of E' is ½ of the corresponding term of E
N to N'
(-1, 1) to (-0.5, 0.5) each term of N' is ½ of the corresponding term of N
U to U'
(2, -2) to (1, -1) each term of U' is ½ of the corresponding term of U
V to V'
(1, -3) to (0.5, -1.5) each term of V' is ½ of the corresponding term of V
If a $6 per unit tax is introduced in this market, then the new equilibrium quantity will be
Answer:
soory i dont know just report me if you angry
The initial population of the town was estimated to be 12,500 in 2005. The population has increased by about 5.4% per year since 2005.
Formulate the equation that gives the population, A(x) , of the town x years since 2005. If necessary, round your answer to the nearest thousandth.
A(x)=__(_)^x
Answer:
[tex]A(x) = 12500(1.054)^x[/tex]
Step-by-step explanation:
Exponential equation for population growth:
Considering a constant growth rate, the population, in x years after 2005, is given by:
[tex]A(x) = A(0)(1 + r)^x[/tex]
In which A(0) is the population in 2005 and r is the growth rate, as a decimal.
The initial population of the town was estimated to be 12,500 in 2005.
This means that [tex]A(0) = 12500[/tex]
The population has increased by about 5.4% per year since 2005.
This means that [tex]r = 0.054[/tex]
So
[tex]A(x) = A(0)(1 + r)^x[/tex]
[tex]A(x) = 12500(1 + 0.054)^x[/tex]
[tex]A(x) = 12500(1.054)^x[/tex]
Will give brainliest
A tablet at a local electronics store is in high demand and will only be available to customers for a limited time. The store initially has 4 cases of the tablet on hand. The store manager receives new supplies of the tablet each week. At the beginning of week 1, the store manager receives an additional order from the distributor of 5 cases of tablets. At the beginning of week 6, the manager receives another order of 10 cases. Which of the following equations best models the scenario for how many cases of the tablet the store can expect to receive each week?
a. y=4
b. y=x+4
c. y=-6x
What is the quotient of the synthetic division problem below, written in
polynomial form?
5)2 1 -55
O A. -2x+11
O B. -2x+9
O C. 2x+11
O D. 2x+9
Answer:
C. 2x+11
Step-by-step explanation:
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
What is the x intercept of the graph that is shown below? Please help me
Answer:
(-2,0)
Step-by-step explanation:
The x intercept is the value when it crosses the x axis ( the y value is zero)
x = -2 and y =0
(-2,0)
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 10 (newly deceased) adults, the mean failure strain (%) was 24.0, and the standard deviation was 3.2.
Required:
a. Assuming a normal distribution for failure strain, estimate true average strain in a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about precision and reliability. How does the prediction compare to the estimate calculated in part (a)?
Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
II. Round to the nearest hundred.
11. 582
12. 1,234
13. 640
14. 770
15. 1,104 can you please tell what the answer?
Answer:
582-600
1,234-1,200
640-600
770-800
1,104-1,100
Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.
Answer:
628 mi^3
Step-by-step explanation:
the volume of a cylinder is given by:
V = base area x height
thus,
V = (3.14)(5)^2(8)
V = (3.14)(25)(8)
V = 628 mi^3
the volume of the cylinder is 628 cubic miles
The volume of the cylinder is 628 cubic miles.
We have a cylinder of radius 5 mi and height 8 mi.
We have to find the volume of the figure and round it to nearest tenth.
What is the volume of cylinder?The volume of cylinder is given by the formula -
Volume [tex]=\pi r^{2} h[/tex]
We can use the above formula to calculate the volume of cylinder. In our case -
r = 5 mi
h = 8 mi
Substituting the values in the formula -
Volume [tex]=\pi\times5^{2}\times 8\\\\[/tex] = 628 cubic miles.
Hence, the volume of the cylinder is 628 cubic miles.
To solve more questions on finding the volume of cylinder, visit the link below -
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