Answers
Related Questions
PLEASE HELP
Evaluate 6 + 10v – 8w when v=4 & w= -2
Answers
Answer:
6 + 10v – 8w = 62
Step-by-step explanation:
Given the expression
6 + 10v – 8w
as
v=4w=-2substituting the values in the expression
6 + 10v – 8w = 6 + 10(4) - 8(-2)
= 6 + 40 + 16
= 62
What is the slope of line m?
Answers
Answer:
Slope= -0.5
Step-by-step explanation:
Answer:
1/2x
Step-by-step explanation:
You go down one step and run 2 steps
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 10 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to two decimal places.)
Answers
Answer:
[tex]r = 1.34[/tex]
Step-by-step explanation:
Given
Solid = Cylinder + 2 hemisphere
[tex]Volume = 10cm^3[/tex]
Required
Determine the radius (r) that minimizes the surface area
First, we need to determine the volume of the shape.
Volume of Cylinder (V1) is:
[tex]V_1 = \pi r^2h[/tex]
Volume of 2 hemispheres (V2) is:
[tex]V_2 = \frac{2}{3}\pi r^3 +\frac{2}{3}\pi r^3[/tex]
[tex]V_2 = \frac{4}{3}\pi r^3[/tex]
Volume of the solid is:
[tex]V = V_1 + V_2[/tex]
[tex]V = \pi r^2h + \frac{4}{3}\pi r^3[/tex]
Substitute 10 for V
[tex]10 = \pi r^2h + \frac{4}{3}\pi r^3[/tex]
Next, we make h the subject
[tex]\pi r^2h = 10 - \frac{4}{3}\pi r^3[/tex]
Solve for h
[tex]h = \frac{10}{\pi r^2} - \frac{\frac{4}{3}\pi r^3 }{\pi r^2}[/tex]
[tex]h = \frac{10}{\pi r^2} - \frac{4\pi r^3 }{3\pi r^2}[/tex]
[tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]
Next, we determine the surface area
Surface area (A1) of the cylinder:
Note that the cylinder is covered by the 2 hemisphere.
So, we only calculate the surface area of the curved surface.
i.e.
[tex]A_1 = 2\pi rh[/tex]
Surface Area (A2) of 2 hemispheres is:
[tex]A_2 = 2\pi r^2+2\pi r^2[/tex]
[tex]A_2 = 4\pi r^2[/tex]
Surface Area (A) of solid is
[tex]A = A_1 + A_2[/tex]
[tex]A = 2\pi rh + 4\pi r^2[/tex]
Substitute [tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]
[tex]A = 2\pi r(\frac{10}{\pi r^2} - \frac{4r }{3}) + 4\pi r^2[/tex]
Open bracket
[tex]A = \frac{2\pi r*10}{\pi r^2} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]
[tex]A = \frac{2*10}{r} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]
[tex]A = \frac{20}{r} - \frac{8\pi r^2 }{3} + 4\pi r^2[/tex]
[tex]A = \frac{20}{r} + \frac{-8\pi r^2 }{3} + 4\pi r^2[/tex]
Take LCM
[tex]A = \frac{20}{r} + \frac{-8\pi r^2 + 12\pi r^2}{3}[/tex]
[tex]A = \frac{20}{r} + \frac{4\pi r^2}{3}[/tex]
Differentiate w.r.t r
[tex]A' = -\frac{20}{r^2} + \frac{8\pi r}{3}[/tex]
Equate A' to 0
[tex]-\frac{20}{r^2} + \frac{8\pi r}{3} = 0[/tex]
Solve for r
[tex]\frac{8\pi r}{3} = \frac{20}{r^2}[/tex]
Cross Multiply
[tex]8\pi r * r^2 = 20 * 3[/tex]
[tex]8\pi r^3 = 60[/tex]
Divide both sides by [tex]8\pi[/tex]
[tex]r^3 = \frac{60}{8\pi}[/tex]
[tex]r^3 = \frac{15}{2\pi}[/tex]
Take [tex]\pi = 22/7[/tex]
[tex]r^3 = \frac{15}{2 * 22/7}[/tex]
[tex]r^3 = \frac{15}{44/7}[/tex]
[tex]r^3 = \frac{15*7}{44}[/tex]
[tex]r^3 = \frac{105}{44}[/tex]
Take cube roots of both sides
[tex]r = \sqrt[3]{\frac{105}{44}}[/tex]
[tex]r = \sqrt[3]{2.38636363636}[/tex]
[tex]r = 1.33632535155[/tex]
[tex]r = 1.34[/tex] (approximated)
Hence, the radius is 1.34cm
The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.
Given :
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 10 cubic centimeters.The volume of a cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
The total volume of the two hemispheres is given by:
[tex]\rm V' = 2\times \dfrac{2}{3}\pi r^3[/tex]
[tex]\rm V' = \dfrac{4}{3}\pi r^3[/tex]
Now, the total volume of the solid is given by:
[tex]\rm V_T = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]
Now, substitute the value of the total volume in the above expression and then solve for h.
[tex]\rm 10 = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]
[tex]\rm h = \dfrac{10}{\pi r^2}-\dfrac{4r}{3}[/tex]
Now, the surface area of the curved surface is given by:
[tex]\rm A = 2\pi r h[/tex]
Now, the surface area of the two hemispheres is given by:
[tex]\rm A'=2\times (2\pi r^2)[/tex]
[tex]\rm A'=4\pi r^2[/tex]
Now, the total area is given by:
[tex]\rm A_T = 2\pi rh+4\pi r^2[/tex]
Now, substitute the value of 'h' in the above expression.
[tex]\rm A_T = 2\pi r\left(\dfrac{10}{\pi r^2}-\dfrac{4r}{3}\right)+4\pi r^2[/tex]
Simplify the above expression.
[tex]\rm A_T = \dfrac{20}{r} + \dfrac{4\pi r^2}{3}[/tex]
Now, differentiate the total area with respect to 'r'.
[tex]\rm \dfrac{dA_T}{dr} = -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]
Now, equate the above expression to zero.
[tex]\rm 0= -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]
Simplify the above expression in order to determine the value of 'r'.
[tex]8\pi r^3=60[/tex]
r = 1.34 cm
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I’ll give the brainlest answer! Is this relation a function? Please help
Answers
Answer:
show me the choices
Step-by-step explanation:
so i qnswer ir
Consider the following hypothesis test:
H0: µ = 20
Ha: µ < 20
A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.
a. Compute the value of the test statistic (to 2 decimals).
b. What is the p-value (to 3 decimals)?
c. Using a = .05, can it be concluded that the population mean is less than 20?
d. Using a = .05, what is the critical value for the test statistic?
e. State the rejection rule: Reject H0 if z is the critical value.
f. Using a = .05, can it be concluded that the population mean is less than 20?
Answers
Answer:
a
[tex]z = - 2.12[/tex]
b
[tex]p- value = 0.017003[/tex]
c
There is sufficient evidence to show that the population mean is less than 20
d
[tex]z_{0.05} =- 1.645[/tex]
e
The decision rule is
Reject the null hypothesis
f
The conclusion is
There is sufficient evidence to show that the population mean is less than 20.
Step-by-step explanation:
From the question we are told that
The null hypothesis is [tex]H_o: \mu = 20[/tex]
The alternative hypothesis is Ha: µ < 20
The sample size is n = 50
The sample mean is [tex]\= x = 19.4[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The population standard deviation is [tex]\sigma = 2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{19.4 - 20 }{ \frac{2}{ \sqrt{50 } } }[/tex]
=> [tex]z = - 2.12[/tex]
From the z table the area under the normal curve to the left corresponding to -2.12 is
[tex](P< -2.12) = 0.017003[/tex]
Generally the p-value is
[tex]p- value = 0.017003[/tex]
From values obtained we see that [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that the population mean is less than 20.
Generally form the normal distribution table the critical value at a level of significance of [tex]\alpha = 0.05[/tex] is
[tex]z_{0.05} =- 1.645[/tex]
Generally given that [tex]z < z_{0.05}[/tex]
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to show that the population mean is less than 20.
as
Complete the equation describing how x
and y are related.
ху
-2
-1
0
1
2
3
-8
-5
-2
1
4
y = [? ]x +
Enter the answer that
belongs in [?].
Answers
Answer:
[tex] y = 3x - 2 [/tex]
Step-by-step explanation:
The equation that describes how x
and y are related is given in the slope-intercept form, [tex] y = mx + b [/tex]
Where, m = slope, and b = y-intercept.
Let's find the value of m and b using the table of values given.
Using two of the pairs given, (-2, -8) and (-1, -5),
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 -(-8)}{-1 -(-2)} = \frac{3}{1} = 3 [/tex]
Substitute x = -2, y = -8, and m = 3 in [tex] y = mx + b [/tex] to find the value of b.
Thus:
[tex] -8 = (3)(-2) + b [/tex]
[tex] -8 = -6 + b [/tex]
Add 6 to both sides
[tex] -8 + 6 = b [/tex]
[tex] -2 = b [/tex]
Substitute m = 3 and b = -2 in [tex] y = mx + b [/tex].
The equation that describes how x
and y are related would be:
[tex] y = 3x - 2 [/tex]
Eighteen less than 9 times a number is the same as 14 more than the number.
Comply the equation
Answers
Answer:
x=4
Step-by-step explanation:
9x-18 = x+14
9×-× = 14+18
8× = 32
X = 4
Celeste wants to have her hair cut and
permed and also go to lunch. She knows
she will need $95. The perm costs twice
as much as her haircut and she needs $5
for lunch.
How much does the perm cost?
Answers
Answer:
the perm will cost $60
Step-by-step explanation:
take away $5 from the total because Its a set amount that's already known
which leaves 90 which if you take 30 away you are left with 60 its twice the amount of the haircut, I didn't really do any math techniques so I'm sorry that my explanation is weird, I hope this helped
Is the sum of any 2 consecutive prime numbers also prime?
Answers
Answer:
Yes! (it’s making me write 20 letters so yes is ur answer ok cool)
Options:
- does not
- does
Answers
Answer: does not
Step-by-step explanation: I think a linear equation is y=mx+b
help please 20 points to who answers not 10 points 20
Answers
Answer:
b c and a
Step-by-step explanation:
Answer:
A, B, C
Step-by-step explanation:
Look at the long division problem shown on the right. Complete the division to determine what the remainder will be.
What is the remainder?
–10
–7
7
10
x + 4 StartLongDivisionSymbol 4 x Superscript 4 Baseline + 18 x cubed + 3 x squared minus 18 x + 15 EndLongDivisionSymbol. minus 4 x Superscript 4 Baseline + 16 x cubed to get a remainder of 0 x Superscript 4 Baseline + 2 x cubed + 3 x squared. minus 0 x Superscript 4 Baseline + 2 x cubed + 8 x squared to get a remainder of 0 x Superscript 4 Baseline + 0 x cubed minus 5 x squared minus 18 x. minus 0 x Superscript 4 Baseline + 0 x cubed minus 5 x squared minus 20 x to get a remainder of blank and a quotient of 4 x cubed + 2 x squared minus 5 x + c.
Answers
Answer:
The remainder is...
7
Hope this helps!!
Step-by-step explanation:
Answer: it’s c
Step-by-step explanation:
which one is greater 140% or 0.14
Answers
a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes. What is the snails rate in Minutes per Meters
Answers
Answer:
Step-by-step explanation
Given
a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes.
Solution
So
the snails rate =11/8÷11/2
= 1/4Minutes per Meters
So the answer is 1/4 minute per meter
It is the quantity of an amount of something at a rate of one of another quantity.
If a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes.
The snail's rate in minutes per meter is 4/3 minutes.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
Example:
3 miles in 60 minutes.
1 mile in 20 minutes.
We have,
Snail travels:
[tex]1\frac{1}{8}[/tex] meters = [tex]1\frac{1}{2}[/tex] minutes
9/8 meters = 3/2 minutes
Multiplying 8/9 on both sides.
1 meters = 8/9 x 3/2 minutes
1 meter = 4/3 minutes
This means that the snail's rate in minutes per meter is 4/3 minutes.
Thus,
If a snail moves through a garden and travels 1 1/8 meters in 1 1/2 Minutes.
The snail's rate in minutes per meter is 4/3 minutes.
Learn more about unit rates here:
https://brainly.com/question/11258929
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Interest paid on £2500 at an interest at an interest rate of 15%
Answers
Answer:
£375Step-by-step explanation:
Amount = £2500Interest rate = 15%Interest
£2500*15/100 = £375What is the rate of change for the line that goes through the points (8,14) and (11, 19.25)
Answers
Answer:
1.75Step-by-step explanation:
The rate of change for the line that goes through the points (8,14) and (11, 19.25) is known as the slope expressed as;
slope m = y2-y1/x2-x1
Substitute the coordinate pairs into the formula;
m = 19.25-14/11-8
m = 5.25/3
m = 1.75
Hence the rate of change for the line is 1.75.
1
After becoming completely blind at the age of
sixty-four, what did Leonhard Euler do?
Answers
Answer:
his remarkable mathematical flow continued without interruption – in fact, it increased.
Step-by-step explanation:
PLEASE HELP
A car dealer offers a 15% discount off the list price x for any car on the lot. At the same time, the manufacturer offers a $1500 rebate for each purchase of a car.
a. Write a function f(x) to represent the price after the discount is applied.
b. Write a function g(x) to represent the price after the rebate is applied.
Suppose the list price of a car is $19,000. Use a composite function to find the price
of the car:
C. if the discount is applied before the rebate;
D. if the rebate is applied before the discount
Answers
Answer:
A) f(x) = 0.85x
B) g(x) = x - 1500
C) g(f(x)) = $14650
D) f(g(x)) = $14875
Step-by-step explanation:
A) The list price is x and a 15% discount is applied.
Thus;
f(x) = x - 15%x
f(x) = 0.85x
B) We are told that the manufacturer offers a $1500 rebate for each purchase of a car.
Thus, the function g(x) to represent the price after the rebate is applied is;
g(x) = x - 1500
C)if the discount is applied before the rebate, the function is;
g(f(x))
Now,
f(x) = 0.85(19000)
f(x) = 16150
g(x) = x - 1500
Thus;
g(x) = 16150 - 1500
g(x) = $14650
D) If discount after rebate, then we have; f(g(x))
g(x) = 19000 - 1500
g(x) = 17500
f(g(x)) = 0.85(17500)
f(g(x)) = $14875
help with number 1 & number 2 please !
Answers
Step-by-step explanation:
2vt= (ht²/2) - 2c - r
v= ((ht²/2) -2c -r) / 2t
v= ht/4 - c/t - r/2t
Calculate Valume of cones and spheres
Answers
Answer:
v = 1808,64cm³
Step-by-step explanation:
big cone:
a = pi.r²
a = 3,14x12²
a = 452,16cm²
v = a.h/3
v = 452,16x12/3
v = 1808,64cm³ (that's a three)
you got the point, now you can do the others... kinda of
PLEASE ANSWER ME!
What is the result when the number 65 is increased by 53%?
Answers
Answer:
The result when 65 is increased by 53% is 34.45
Step-by-step explanation:
Hope this helps and have a great day :)Answer:
34.45
Step-by-step explanation:
i hope you get it right
three less than the total of a number and
nine
Answers
Answer:
(x+9)-3
Step-by-step explanation:
What is the slope of function 3x-5y=17
Answers
Answer:
y=5/3x-3.4
Step-by-step explanation:
slope is 5/3
Answer:
[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
In slope-intercept form of linear equation y = mx + b , "m" is the slope
3x - 5y = 17
- 5y = - 3x + 17
y = [tex]\frac{3}{5}[/tex] x - [tex]\frac{17}{5}[/tex]
m = [tex]\frac{3}{5}[/tex]
The purchase price of a camcorder is $818 what is the total price if the sales tax rate is 8.5%
Answers
AB = BC
5(2x + 2).
3(3x - 1)
Find x:
2
4
-10
16
None of the other answers are correct
Answers
Answer:
Step-by-step explanation:
holdup im gonna help
Answer:
x = 2
Step-by-step explanation:
2[3(3x - 1)] = 5(2x + 2)
18x - 6 = 10x + 10
8x = 16
x = 2
5
y=2x+5y, equals, 2, x, plus, 5
Complete the missing value in the solution to the equation.
(
2
,
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]y = f(x) = 2x + 5[/tex]
[tex]f(2) = 2(2) + 5[/tex]
[tex]f(2) = 4 + 5[/tex]
[tex]f(2) = 9[/tex]
Thus ;
[tex]( \: 2 \: , \: 9 \: )[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer:
9
Step-by-step explanation:
Can you please give me more answers?
Answers
Answer:
more answers on wht
Step-by-step explanation:
Answer:
wdym more answers ? there isn't a question
Step-by-step explanation:
Yesterday, the temperature in a city dropped from 9°C to –9°C, as shown below.
The expression 9 + (–18) represents the final temperature. Which of the following is an equivalent way to describe this temperature?
|–18| degrees in a negative direction from 9 degrees
|–18| degrees in a positive direction from 9 degrees
|–9| degrees in a negative direction from 9 degrees
|–9| degrees in a positive direction from 9 degrees
Answers
Answer:
b
Step-by-step explanation:
absoulute value is never negative.
A proportional relationship is shown in the table below:
x:
0
1.3
2.6
3.9
5.2
y:
0
1
2
3
4.
What is the slope of the line that represents this relationship?
Graph the line that represents this relationship.
Answers
(13−0)
= 10/13
(10−0)
13,10
Slope of the given line is [tex]\frac{10}{13}[/tex] and the equation of the line is [tex]10x - 13y = 0[/tex].
What is the slope of a line passing through two points?The slope of a line(m) that passes through points (x, y) and (x, y) is
[tex]m = \frac{y_{2} - x_{1}}{x_{2} - x_{1}}[/tex]
The given line passes through points (0, 1.3) and (0, 1).
Therefore, slope of the line is
[tex]m = \frac{y_{2} - x_{1}}{x_{2} - x_{1}} = \frac{1 - 0}{1.3 - 0} = \frac{10}{13}[/tex]
Now, the line passes through the point (2.6, 2).
Putting this equation in slope-intercept form, we get:
[tex]2 = \frac{10}{13}(2.6) + c\\c = 2 - 2\\c = 0[/tex]
The equation of the line will be:
[tex]y = \frac{10}{13}x\\10x - 13y = 0[/tex]
Learn more about slope of a line here: https://brainly.com/question/21504186
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Set up an equation and solve for x
Answers
Answer:
x=22
Step-by-step explanation:
3x+3+27+x+3+2x+18=180
6x+48=180
6x=132
x=22