Suppose that the market research department of a famous bakery has determined that the most aesthetically pleasing donut has a thickness that is twice the inner radius of the donut (that is, the radius of the donut’s hole). The formula for the inner radius of the donut is given by the equation , where V is the volume of the donut in cubic centimeters. Use the table of values to help you answer the questions about r(v). -30 -0.80 -20 -0.70 -10 -0.55 0 0 10 0.55 20 0.70 30 0.80
Answers
Answer:
The information given are;
[tex]r(V)=\sqrt[3]{\dfrac{V}{6\cdot \pi ^{2}}}[/tex]
Where;
r(V) = The radius of the doughnut (cm)
V = The volume of the doughnut (cm³)
The data are;
V, r(V)
-30, -0.8
-20, -0.7
-10, -0.55
0, 0
10, 0.55
20, 0.7
30, 0.8
From the table of values, the identified key features are;
a) There is a direct relationship between the radius and the volume of the doughnut
b) The correlation between the data increases to direct proportionality from the volume of 20 cm³ and above
c) The data values are symmetric and continuous about the y and x-axis
2) There is a direct linear relationship between radius, r and the volume V at end ends of the data between r and V where V = -30 and-20 at one end and 20 and 30 at the other end
b) The x and y-intercept are
The x -intercept = (0, 0)
The x -intercept = (0, 0)
c) The pivot point is the point about which change occurs, therefore, the pivot point is the (10, 0.55)
d) The domain is a member of the set of real numbers, R while the range is also a member of the set of real numbers, R
Step-by-step explanation:
Related Questions
Simplify: |x−y| if x is less than y
Answers
Answer:
y-x
Step-by-step explanation:
I assumed you meant that you wanted me to rewrite the expression without the absolute value signs. Since the absolute value of a number will be the same whichever way you place the numbers, you can rewrite |x-y| as y-x, as x is less than y.
If the polynomial - 6 + 16 - 25x + 10 is divided by - 2x + k, the remainder comes out to be x + a, find k and a
Answers
Answer:
k=5
a= -5
Step-by-step explanation:
if the polynomial x^4-6x^3+16x^2-25x+10 is divided by x^2-2x+k the remainder comes out to be x+a,find k and a
Solution
x^4-6x^3+16x^2-25x+10 / x^2-2x+k = x-a
We have,
(4k-25+16-2k)x+[10-k(8-k)] = x+a
(2k+9)x + (10-8k+k^2)=x+a
2k-9=1
2k=1+9
2k=10
Divide both sides by 2
2k/2=10/2
k=5
And
10-8k+k^2=a
10-8(5)+(5^2)=a
10-40+25=a
-5=a
Therefore, a=-5
x^4-6x^3+16x^2-25x+10 divided by x^2-2x+5 = x-5
Please Explain:
Why is 1 the maximum possible value of a sine ratio?
Answers
The definition of sin is the opposite/hypotnuse and since the hypotnuse has to be greater or equal to the other sides, the maximum possible value of sine is 1.
3. A CD costs £9.50 in London and
cheaper, in British money, is the CD when bought in the US?
4. An MP3 player costs €20.46 in Spain and £12.60 in the UK. Which is
the cheaper in dollars, and by how much?
in Nou Delhi is 32860 rupees.
Answers
Step-by-step explanation:
Only Q4 has clear details
therefore, solving Question 4,
1 euro = $1.17
then, €20.46 =20.46×1.17 = $23.93.
1 pound =1.28 dollars.
then, £12.60 = 12.60×1.28 =$16.128
therefore, MP3 in pound is cheaper in dollar by $7.81.
If r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to (StartFraction r Over s EndFraction) (6)? StartFraction 3 (6) minus 1 Over 2 (6) + 1 EndFraction StartFraction (6) Over 2 (6) + 1 EndFraction StartFraction 36 minus 1 Over 26 + 1 EndFraction StartFraction (6) minus 1 Over (6) + 1 EndFraction
Answers
Answer:
[tex]\dfrac{3(6)-1}{2(6)+1}[/tex]
Step-by-step explanation:
For ...
r(x) = 3x -1 s(x) = 2x +1The expression (r/s)(6) is ...
[tex]\left(\dfrac{r}{s}\right)(6) = \left.\dfrac{3x-1}{2x+1}\right|_{x=6}=\boxed{\dfrac{3(6)-1}{2(6)+1}}[/tex]
Answer:
A
Step-by-step explanation:
changing fraction to percentage
Answers
Answer:
Hello There!
`~~~~~~~~~~~~~~~~~~`
You added no fraction so i thought you wanted the definition
Convert Fractions to Percents. Divide the top of the fraction by the bottom, multiply by 100 and add a "%" sign.
Hope this helped you. Brainliest wouldbe nice!
Try using a calculator
Divide the top of the fraction by the bottom, Then multiply the result by 100 and read off the answer
Example: 4/5 =x/100
4*100= 5x
400=5x
400/5=x
80=x
80/100 = 80%
:)
A 6 inch-y’all plant grew 3/4 of an inch one week and twice as much the following week. How tall is the plant now?
Answers
Answer:
8 inches
Step-by-step explanation:
3/4+(3/4*2)=3/4+6/4=9/4=2 1/4
2 1/4+6=8 1/4=8.25
Answer: 8.25 inches
Step-by-step explanation:
Suppose $x-3$ and $y+3$ are multiples of $7$. What is the smallest positive integer, $n,$ for which $x^2+xy+y^2+n$ is a multiple of $7$? Enter your answer. I need Immediate help or you wont get the points.
Answers
In the language of modular arithmetic, we're given
[tex]x-3\equiv0\pmod7\implies x\equiv3\pmod7[/tex]
[tex]y+3\equiv0\pmod7\implies y\equiv-3\equiv4\pmod7[/tex]
Then x = 7a + 3 and y = 7b + 4 for integers a and b.
Substitute these into the quadratic expression and simplify:
[tex]x^2+xy+y^2+n\equiv0\pmod7[/tex]
[tex](7a+3)^2+(7a+3)(7b+4)+(7b+4)^2+n\equiv0\pmod7[/tex]
[tex]49a^2+42a+9+49ab+28a+21b+12+49b^2+56b+16+n \equiv 0\pmod7[/tex]
[tex]37+n\equiv 0\pmod7[/tex]
[tex]n\equiv-2\equiv5\pmod7[/tex]
which means the smallest positive integer n we are looking for is 5.
Find the ratio of x to y. 2/3 4/9 1
Answers
Answer:
[tex]\frac{x}{y}[/tex] = [tex]\frac{4}{9}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{5}[/tex] = [tex]\frac{2}{3}[/tex] = [tex]\frac{5}{y}[/tex]
This can be expressed in 2 parts as
[tex]\frac{x}{5}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
3x = 10 ( divide both sides by 3 )
x = [tex]\frac{10}{3}[/tex]
and
[tex]\frac{2}{3}[/tex] = [tex]\frac{5}{y}[/tex] ( cross- multiply )
2y = 15 ( divide both sides by 2 )
y = [tex]\frac{15}{2}[/tex]
Thus
[tex]\frac{x}{y}[/tex] = [tex]\frac{\frac{10}{3} }{\frac{15}{2} }[/tex] = [tex]\frac{10}{3}[/tex] × [tex]\frac{2}{15}[/tex] ( cancel 10 and 15 by 5 )
[tex]\frac{x}{y}[/tex] = [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{4}{9}[/tex]
Answer:
= 4/9
Step-by-step explanation:
2/3 to the averall of 2/3 ans we got 5/y
sp ab- x/5 = 4/9
given ad||gj refer to the figure and provide an appropriate name for ehc and chj
a. alternate interior angles
b. supplementary angles
c. complementary angles
d. alternate exterior angles
Answers
An appropriate name for EHC and CHJ is alternate interior angles.
What is alternate interior angles?Alternate interior angles are the angles formed when a transversal intersects coplanar strains. They lie on the inner side of the parallel lines but on the opposite facets of the transversal.
Do alternate interior angles add up to 180?Except the exchange indoors vertical angles are 90° then they may no longer upload as much as 180°. If the exchange indoors angles are obtuse, then adding them collectively will bring about quite a number higher than 180°. consequently, if the alternate interior angles are acute, then including them together will bring about various beneath 180°.
Learn more about alternate interior angles here https://brainly.com/question/20344743
#SPJ2
Twoooooooooooooooooooooooooooo
Answers
Answer:
n = 60.22
Step-by-step explanation:
Hello
To find Sn, we need to draw out equations for each a₇ and a₁₉
In an arithmetic progression,
Sn = a + (n-1)d
Where Sn = sum of the A.P
a = first term
d = common difference
a₇ = 32
32 = a + (7-1)d
32 = a + 6d ........equation (i)
a₁₉ = 140
140 = a + (19-1)d
140 = a + 18d .........equation (ii)
Solve equation (i) and (ii) simultaneously
From equation (i)
32 = a + 6d
Make a the subject of formula
a = 32 - 6d .....equation (iii)
Put equation (iii) into equation (ii)
140 = (32 - 6d) + 18d
140 = 32 - 6d + 18d
Collect like terms
140 - 32 = 12d
12d = 108
d = 108 / 12
d = 9
Put d = 9 in equation (i)
32 = a + 6(9)
32 = a + 54
a = 32 - 54
a = -22
When Sn = 511
Sn = a + (n - 1)d
Substitute and solve for n
511 = -22 + (n-1) × 9
511 = -22 + 9n - 9
511 = -31 + 9n
511 + 31 = 9n
542 = 9n
n = 542 / 9
n = 60.22
A group of 4 friends is playing cards. The deck has 70 cards. To start the game, the dealer makes a pile of 15 cards in the center. Then she deals the remaining cards one at a time to each player until all the cards are gone. What is the greatest number of cards any player will have after all the cards are dealt?
Answers
Answer:
14 cards
Step-by-step explanation:
70 - 15 = 55
55/4 = 13.75
Therefore, the highest number of cards someone is able to get is 14.
Answer:
14
Step-by-step explanation:
add!
I am starting to get this but, each question is a different subject so plz help asap. Btw these are not test or quiz questions. They are just practice questions so I know how to do it before a test or quiz.
Answers
Answer:
73 degrees
Step-by-step explanation:
Given
A Shaped Frame of two congruent sides
Required
Determine the angle made with the ground
Given that there are two congruent sides, this implies that the A frame is an isosceles triangle;
Let the two angles made with the ground be represented by x
Angles in a triangle when added equals 180;
Hence;
[tex]x + x + 34 = 180[/tex]
[tex]2x + 34 = 180[/tex]
Subtract 34 from both sides
[tex]2x + 34 - 34 = 180 - 34[/tex]
[tex]2x = 180 - 34[/tex]
[tex]2x = 146[/tex]
Divide both sides by 2
[tex]\frac{2x}{2} = \frac{146}{2}[/tex]
[tex]x = \frac{146}{2}[/tex]
[tex]x = 73[/tex]
Hence, the angle with the ground is 73 degrees
Select the correct answer.
A system of linear equations is given by the graph.
-5
5
What is the system shown?
O A y = 2
y=-3 - 5
y=it - 5
y = - = - 5
D. y = - =
5
Answers
Answer:
b
Step-by-step explanation:
rise over run
Answer: b
Step-by-step explanation:
please answers quick ,whats an inequality?
Answers
Answer:
Step-by-step explanation:
inequality is a equation with |x|
a inequality equation is like this..
|x|>7
Determine the number of solutions for each quadratic.
1.) 4x^2-3x+4=0
2.)9x^2-12x+4=0
Answers
Answer:
1. Technically 2, but might be 0 in your teacher's opinion.
2. 1
Step-by-step explanation:
Solving problem one.
So I don't know if you have learned about imaginary numbers, but if you have, then you would end up with two answers if you plugged in the quadratic formula.
If you haven't learned about imaginary numbers, then I would say your best option would be to write 'No real solution' since there are technically 2 solutions.
Solving problem two.
Turns out this quadratic has a special property and it's actually a square of one equation. You can find out by just factoring the equation.
It's (3x-2)^2. Since it's squared, that means that only 2/3 would work as x in this equation.
A 40 ft board is cut into two pieces so that one piece is 8 ft longer than the other piece. Find the length of the two pieces
Answers
Answer:
16 and 24 ft
Step-by-step explanation:
If we call the length of one piece x, the length of the other piece is x + 8, therefore, we can write the following equation:
x + x + 8 = 40
2x + 8 = 40
2x = 32
x = 16 so x + 8 = 16 + 8 = 24.
Answer:
24 and 16
Step-by-step explanation:
x + x+8=40
2x+8=40
2x=32
x=16
16 and 24
Given: AB ∥ DC , m CB =62°, m∠DAB=104° Find: m∠DEA, m∠ADB
Answers
Answer:
m∠DEA = 62°
m∠ADB (arc) = 194°
Angle ∠ADB = 21°.
Step-by-step explanation:
The given information are;
[tex]AB\left | \right |DC[/tex], m CB (arc) = 62°, m∠DAB (arc) = 104°
arc∠BCD = 360° - 104° = 256°
m DC (arc) = arc∠BCD - arc CB = 256° - 62° (Sum of angles)
Therefore DC (arc) = 194°
m DA ≅ m CB = 62° (Parallel lines congruent arc theorem. Arc between two parallel lines)
m∠DEA = 1/2×(arc DA + arc CB) = 1/2×(62° + 62°) =62°
m∠DEA = 62°
Arc AB = m∠DAB (arc) - m DA = 104° - 62° = 42°
m∠ADB (arc) = 360 - m∠DAB (arc) - m CB (arc) (Sum of angles around a circle or point)
∴ m∠ADB (arc) = 360 - 104 - 62 = 194°
m∠ADB (arc) = 194°
Angle ADB = subtended by arc AB = ∴1/2×arc AB
Angle ∠ADB = 42/2 = 21°.
Angle = 21°
Cedric has deposited $12,000 into an account that pays 5% interest compounded annually. Daniel has deposited 12,000 into an account that pays 7% simple annual interest. In 15 years Cedric and Daniel compare their respective balances. To the nearest dollar, what is the positive difference between their balances?
Answers
Answer:
$947
Step-by-step explanation:
12,000(1 + .05/1)^(15*1) = $24,947.14
12,000 + (12,000*.07*15) = $24,600
difference is $947
Sketch the graphs:
y=-x+5
Answers
Answer:
This is the graph I inputted into desmos.
Step-by-step explanation:
Next time, using a graphing calculator will work! However, making a table for the x and y outputs will also make it easier to graph points.
For example: see attached image of table.
Given that
[tex]v = \pi {r}^{2} h[/tex]
Make h the subject of the formula. Evaluate h when
[tex]\pi = 22 \div 7[/tex]
[tex]r = 7[/tex]
[tex]v = 616[/tex]
Answers
Answer:
h = 4Step-by-step explanation:
v = πr²h
To make h the subject divide both sides by πr²
So we have
[tex]h = \frac{v}{\pi {r}^{2} } [/tex]
when
π = 22/7
r = 7
v = 616
We have h as
[tex]h = \frac{616}{ \frac{22}{7} \times {7}^{2} } = \frac{616}{ \frac{22}{7} \times 49} [/tex]
[tex]h = \frac{616}{22 \times 7} = \frac{616}{154} [/tex]
h = 4Hope this helps you
which ratio forms a proportion 12/15
Answers
Answer:
[tex]\frac{20}{25}[/tex]
Step-by-step explanation:
See Attachment for Complete Question
Given
[tex]Ratio = \frac{12}{15}[/tex]
Required
Determine its equivalent proportion
[tex]Ratio = \frac{12}{15}[/tex]
Factorize the given expression
[tex]Ratio = \frac{3 * 4}{3 * 5}[/tex]
Divide the numerator and denominator by 3
[tex]Ratio = \frac{4}{5}[/tex]
We apply the same steps to the given options as follows:
1.
[tex]Ratio = \frac{21}{28}[/tex]
Factorize
[tex]Ratio = \frac{7 * 3}{7 * 4}[/tex]
Divide the numerator and denominator by 7
[tex]Ratio = \frac{3}{4}[/tex]
This is not an equivalent proportion of [tex]\frac{12}{15}[/tex]
2.
[tex]Ratio = \frac{20}{25}[/tex]
Factorize
[tex]Ratio = \frac{5 * 4}{5 * 5}[/tex]
Divide the numerator and denominator by 5
[tex]Ratio = \frac{4}{5}[/tex]
This is equivalent to [tex]\frac{12}{15}[/tex] because they both simplify to [tex]\frac{4}{5}[/tex]
There's no need to check the last option;
Hence, the option that answers the question is [tex]\frac{20}{25}[/tex]
ASAP!!! PLEASE help me solve this question!!!! I really need help...
Answers
Answer:
304(pi) g
Step-by-step explanation:
First we find the volume of the hollow ball. Then we find the mass using the volume and density.
Let R = exterior radius = 3 cm
Let r = interior radius = 2 cm
volume = exterior volume - interior volume
volume = (4/3)(pi)R^3 - (4/3)(pi)r^3
volume = (4/3)(pi)(R^3 - r^3)
volume = (4/3)(pi)(3^3 - 2^3) cm^3
volume = (4/3)(pi)(27 - 8) cm^3
volume = (76/3)pi cm^3
Now we use the density and the volume to find the mass.
density = mass/volume
mass = density * volume
mass = 12 g/cm^3 * (76/3)pi cm^3
mass = 304(pi) g
Answer: 304(pi) g
Answer:
m=(76π/3 )(12)=304πg
Step-by-step explanation:
volume of sphere=(4πr³)/3
V=4π(2)³/3=32π/3 of the interior
V of exterior=4π(3)³/3=36π
Volume of the whole metal =108π/332π/3=76π/3=25 1/3 π
m=V*D ( volume * density)=
m=(76π/3 )(12)=304πg
Solve for x. Remember to check for extraneous solutions. √(x-3) = √(x+2) + 1. Choices: a. 6 b. No solution c. 7 d. 9
Answers
PLEASE HELP ME! I REALLY NEED SOME HELP!!
Answers
Answer:
a
Step-by-step explanation:
If the lines DE and BC were parallel then
Δ ADE and Δ ABC would be similar and the ratios of corresponding sides would be equal, that is
[tex]\frac{AD}{AB}[/tex] = [tex]\frac{AE}{AC}[/tex] , substituting values
[tex]\frac{4}{10}[/tex] = [tex]\frac{6}{14}[/tex]
but
[tex]\frac{4}{10}[/tex] ≠ [tex]\frac{6}{14}[/tex]
That is 4 : 10 ≠ 6 : 14 → a
34=3(y+6)-8 Please Explain.
Answers
Answer:
y =8
Step-by-step explanation:
34=3(y+6)-8
Add 8 to each side
34+8=3(y+6)-8+8
42 =3(y+6)
Divide by 3
42/3 = 3(y+6)/3
14 = y+6
Subtract 6 from each side
14-6 = y+6-6
8 = y
Answer:
y = 8
Step-by-step explanation:
Add 8 to both sides.
42=3(y+6)
Divide 3 from both sides.
14=y+6
Subtract 6 from both sides.
8 = y
Triangle ABC is rotated about the origin by 270° to form the triangle A′B′C′, then translated upward 10 units to form triangle A″B″C″. Which of the following statements is true for ΔABC and ΔA″B″C″? A)There isn't enough information to identify whether ΔABC and ΔA″B″C″ are congruent or similar. B)ΔABC and ΔA″B″C″ are neither similar nor congruent. C)ΔABC and ΔA″B″C″ are similar triangles. D)ΔABC and ΔA″B″C″ are congruent triangles.
Answers
Answer:
The correct answer is option:
D) ΔABC and ΔA″B″C″ are congruent triangles.
Step-by-step explanation:
Given
ΔABC is first rotated about the origin by 270° to form the triangle A′B′C′.[tex]\triangle A'B'C'[/tex] is then translated upwards 10 units to form [tex]\triangle A''B''C''[/tex]To find: The true statement among the given options.
Solution:
Let the triangle be situated in 1st quadrant.
It is rotated about the origin by [tex]270^\circ[/tex].
Now, it moves towards quadrant 2 if it is rotated clockwise. It is termed as
[tex]\triangle A'B'C'[/tex].
It is given that now it is translated 10 units upwards. i.e. 10 units added to x coordinate of each vertex to form [tex]\triangle A''B''C''[/tex].
Now, we can see that there is no change in the dimensions of the triangle. We are just changing the location of the triangle.
So, all its angles will be equal to each other and all the sides will be equal to each other.
i.e.
[tex]\angle A = \angle A''\\\angle B = \angle B''\\\angle C = \angle C''\\Side\ AB = Side\ A''B''\\Side\ BC = Side\ B''C''\\Side\ AC = Side\ A''C''[/tex]
Hence, the correct option is:
D)ΔABC and ΔA″B″C″ are congruent triangles.
Answer:A-B
Step-by-step explanation:
Please answer it now in two minutes
Answers
Step by step is blew
Hopefully this help you
Answer:
4 miles
Step-by-step explanation:
Solution:-
- This question pertains to special right angle triangles.
- This requires the use of special angles like ( 30°, 45°, 60° ) for all three trigonometric ratios that give us exact answers in the form of radicals.
- We will make a table of all three trigonometric ratios for the 3 special angles given above as follows:
30° 45° 60°
sin 1/2 1/√2 √3 / 2
cos √3 / 2 1/√2 1/2
tan 1 /√3 1 √3
- Now take a look at the figure and determine the appropriate trigonometric ratio that could be used to determine the distance ( q ). We are given an opposite angle ( θ = 45° ) and hypotenuse of the right angle triangle ( H = 4√2 mi )
- We see that the sine ratio is the most appropriate which can be written as:
sin ( θ ) = q / H = q / 4√2
sin ( 45° ) = q / 4√2
q = 4√2 * sin ( 45° ) ... Use above table for sin ( 45° )
q = 4√2 * [ 1 / √2 ]
q = 4 miles ... Answer
..........,..................
Answers
Answer:
E. x = -1.
Step-by-step explanation:
The rational expression will only be undefined when a number is divided by 0. In this case, the expression will be undefined when the denominator equals 0. So, when x + 1 = 0.
x + 1 = 0
x = -1
E. -1 is your answer.
Hope this helps!
Answer:
D. -2 and B. -5
Step-by-step explanation: you can't have a negatie denominator/
In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the levels of the factor.
Answers
Answer:
Levers of the factor are High dosage , Low dosage and Placebo.
Step-by-step explanation:
Levels of the factor refer to the number of variations of factor that are used in the experiment. The effect of the factor can be evaluated by these levels.
Here the factor is the experimental drug.
The first group received a low dosage of an experimental drug,
The second group received a high dosage of the drug,
The third group received a placebo.
It can be observed from above three statements that there are 3 levels of factor. These three levels can be used to assess the effect of the experimental drug on 780 participants suffering from high blood pressure.
The factor experimental drug has three levels that are:
High dosage
Low dosage
Placebo