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18. Using the diagram below as reference, write a paragraph proof to prove that the symmetric property of congruence exists for any two angles. (IMAGE BELOW)
Given: ∠A is congruent to ∠B
Prove: ∠B is congruent to ∠A
Plan: Show that ∠A and ∠B have the same measure, thus ∠B and ∠A have the same measure under symmetry for equality. Conclude with ∠B being congruent to ∠A.
Answers
Answer:
Below.
Step-by-step explanation:
Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.
Related Questions
Several surveys in the United States and Europe have asked people to rate their happiness on a scale of 3 = "very happy," 2 = "fairly happy," and 1 = "not too happy," and then tried to correlate the answer with the person's income. For those in one income group (making $25,000 to $55,000) it was found that their "happiness" was approximately given by y = 0.065x − 0.613, where x is in thousands of dollars.† Find the reported "happiness" of a person with the following incomes (rounding your answers to one decimal place).
Answers
Answer:
Step-by-step explanation:
We have to find the reported happiness of person of family income of $25,000, $35,000 and $45,000
Given that the formula for finding relation between a people happiness and his income is
y = 0.065x - 0.613
a) find the happiness of person of family income os $25,000
we put x = 25 as in the equation above
[tex]y=0.065(25)-0.613\\\\=1.625-0.613\\\\=1.02 \approx 1[/tex]
Hence, person happiness with with family income of $25,000 on a scale of 3 is y = 1
That means they come under catergory "not to happy"
b) Find the happiness of person of family income os $35,000
we put x = 35 as in the equation above
[tex]y=0.065(35)-0.613\\\\=1.667-0.613\\\\=1.667 \approx 1.7[/tex]
Hence, person happiness with with family income of $35,000 on a scale of 3 is y = 1.7
That means they come under catergory "not to happy" and "fairly happy"
c) Find the happiness of person of family income os $45,000
we put x = 45 as in the equation above
[tex]y=0.065(45)-0.613\\\\=2.925-0.613\\\\=2.312 \approx 2.3[/tex]
Hence, person happiness with with family income of $45,000 on a scale of 3 is y = 2.3
That means they come under catergory "fairly happy"
The scale would show the data as follows:
Happiness Scale at Income 25, 35, 45 & 55 thousand :
1.012 (Not too happy), 1.662 (Fairly Happy), 2.315 (Fairly Happy) , 2.965 (Very Happy)
Determine the scaleImportant Information :
Relationship between happiness scale 'y' and income in 1000s 'x' :y = 0.065x − 0.613, for people in income group between [tex]25000 & 55000[/tex]
Happiness scale : At level of income, between 25 and 55 thousands.
Putting value of income 'x' to find scale of happiness i.e. 'y'
For income 'x' = 25 thousand : [tex]y = 0.065 (25) - 0.613 = 1.625 - 0.613 = 1.012[/tex] For income 'x' = 35 thousand : [tex]y = 0.065 (35) - 0.613 = 2.275 - 0.613 = 1.662[/tex]For income 'x' = 45 thousand : [tex]y = 0.065 (45) - 0.613 = 2.925 - 0.61 = 2.315[/tex] For income 'x' = 55 thousand :[tex]y = 0.065 (55) - 0.613 = 3.575 - 0.61 = 2.965[/tex]
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Here is rectangle A. Block A. Rectangle B is ¹/₅ longer than A Block B. Rectangle C is ¹/₃ longer than B Block C. The total length of all three rectangles is 133 cm. How much longer is rectangle C than B?
Answers
Answer:
Rectangle C is 14 cm longer than B
Step-by-step explanation:
Let x be the length of Rectangle A. Rectangle B is ¹/₅ longer than A Block B,
Therefore the length of rectangle B is:
[tex]x+\frac{1}{5}x[/tex]
Rectangle C is ¹/₃ longer than B, therefore the length of rectangle c is:
[tex]x+\frac{1}{5}x+\frac{1}{3}(x+\frac{1}{5}x) =x+ \frac{1}{5}x+\frac{1}{3}x+\frac{1}{15}x=x+\frac{9}{15}x[/tex]
The total length of all three rectangles is 133 cm.
Length of rectangle A + Length of rectangle B + Length of rectangle C = 133 cm
[tex]x+x+\frac{1}{5}x +x+\frac{9}{15}x=133\\x+x+x+\frac{1}{5}x +\frac{9}{15}x=133\\3x+\frac{12}{15}x=133\\ 45x+12x=1995\\57x=1995\\x=35cm[/tex]
Therefore the length of rectangle A is 35 cm, the length of rectangle B is [tex]35+\frac{1}{5}*35=42\ cm[/tex] and the length of rectangle C is [tex]35+\frac{9}{15}*35=56\ cm[/tex]
Rectangle C is ¹/₃ longer than B, which is 14 cm (42\3) longer than B
pleas guys can you answer this to me
Answers
Answer:
what is this boiii?
The energy, E, of a body of mass m moving with speed v is given by the formula below. The speed is nonnegative and less than the speed of light, c which is constant. Use lower case letters here. E = mc^2 (1/Squareroot1 - v^2/c^2 - 1)
(a) Find E/m = c^2Squareroot1 - v^2/c^2 - c^2/1 - v^2/c^2 what is the sign of this partial? Positive negative
(b) Find E/v =?
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]\frac{\delta E}{\delta m}= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
b
[tex]\frac{\delta E}{\delta V} = \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
Step-by-step explanation:
From the question we are given
[tex]E = mc^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } }- 1 ][/tex]
So we are asked to find [tex]\frac{\delta E}{\delta m}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta m} = \frac{\delta }{\delta m} [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 )][/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2 } } } -1 ] \frac{\delta m}{\delta m}[/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
Also we are asked to find [tex]\frac{\delta E}{\delta V}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta V} = \frac{\delta }{\delta v } [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } - 1 )][/tex]
[tex]\frac{\delta E}{\delta V} = mc^2 [\frac{\delta }{\delta v} (\frac{c}{\sqrt{c^2 -v^2} } - 1 )][/tex]
[tex]= mc^2 [c* [\frac{\delta }{\delta v} (c^2 - v^2 )^{-\frac{1}{2} }] - 0][/tex]
[tex]= mc^3 [- \frac{1}{2} (c^2 - v^2 )^{-\frac{3}{2} } * (-2v)][/tex]
[tex]= \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
Which transformations could be performed to show that
AABC is similar to AA"B"C"?
10
8
B
4
VX
2
A
-10 -3 -6 -4 -21 14
B"
4
8 10
X
O a reflection over the x-axis, then a dilation by a scale
factor of 3
O a reflection over the x-axis, then a dilation by a scale
factor of
O a 180° rotation about the origin, then a dilation by a
scale factor of 3
O a 180° rotation about the origin, then a dilation by a
scale factor of
6
8
-10
Save and Exit
Next
Submit
Mark this and return
Answers
Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
What is mean by Transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Given that;
Triangle ABC is similar to A"B"C".
Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)
Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
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Solve the inequality 2(4x-3)>-3(3x)+5
Answers
Answer:
48x>+2
Step-by-step explanation:
Express the following ratio in its simplest form.
4:12
Answers
Answer:
1:3
Step-by-step explanation:
divide 4 ...............
.............
ps: idk the explanation
Please answer this correctly
Answers
Answer:
24.99
Step-by-step explanation:
If the area of the quarter circle is 38.465, then the equation to find this would be
3.14*r^2 / 4 = 38.465. we solve for r, the radius, and get two solutions. 7 and -7. Obviously the length of the radius can't be -7, so we know the radius is 7.
Now we must solve for the perimeter. The perimeter is equal to 2r + (2*3.14*r)/4
Plugging 7 in as the radius, r, we get 24.99 as our final answer.
A battery with 20 percent of its full capacity is connected to a charger. Every minute that passes, an additional 5% , percent of its capacity is charged.
Answers
Answer:
y = 5x + 20
Step-by-step explanation:
The initial percent is 20.
Every minute, the percent goes up 5%, so the slope is 5.
So the equation of the line is y = 5x + 20.
Compute 8P2 *
16
O 56
O 28
O
none of these are correct
Answers
Halle is enteros cuyo producto sea 253 y uno de los enteros debe ser uno más que el doble del otro.
Answers
Answer:
11 y 23
Step-by-step explanation:
Nombrando los números como [tex]x[/tex] y [tex]y[/tex],
Planteamos las siguientes ecuaciones:
[tex]xy=253[/tex] (el producto de los numeros es 253)
[tex]x=2y+1[/tex] (uno de los enteros debe ser uno más que el doble del otro).
Sustituimos la segunda ecuación en la primera:
[tex](2y+1)(y)=253[/tex]
resolvemos para encontrar y:
[tex]2y^2+y=253\\2y^2+y-253=0[/tex]
usando la formula general para resolver la ecuación cuadrática:
[tex]y=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
donde
[tex]a=2,b=1,c=-253[/tex]
Sustituyendo los valores:
[tex]y=\frac{-1+-\sqrt{1-4(2)(-253)} }{2(2)} \\\\y=\frac{-1+-\sqrt{2025} }{4}\\ \\y=\frac{-1+-45}{4} \\[/tex]
usando el signo mas obtenemos que y es:
[tex]y=\frac{-1+45}{4} \\y=\frac{44}{4}\\ y=11[/tex]
(no usamos el signo menos, debido a que obtendriamos fracciones y buscamos numeros enteros)
con este valor de y, podemos encontrar x usando:
[tex]x=2y+1[/tex]
sustituimos [tex]y=11[/tex]
[tex]x=2(11)+1\\x=22+1\\x=23[/tex]
y comprobamos que el producto sea 253:
[tex]xy=253[/tex]
[tex](23)(11)=253[/tex]
A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 4 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 4 workers has the same chance of being selected as does any other group (drawing 4 slips without replacement from among 24).
(a) How many selections result in all 4 workers coming from the day shift? What is the probability that all 4 selected workers will be from the day shift? (Round your answer to four decimal places.)
(b) What is the probability that all 4 selected workers will be from the same shift? (Round your answer to four decimal places.)
(c) What is the probability that at least two different shifts will be represented among the selected workers? (Round your answer to four decimal places.)
(d) What is the probability that at least one of the shifts will be unrepresented in the sample of workers? (Round your answer to four decimal places.)
Answers
The probability that all 4 selected workers will be from the day shift is, = 0.0198
The probability that all 4 selected workers will be from the same shift is = 0.0278
The probability that at least two different shifts will be represented among the selected workers is = 0.9722
The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257
To solve this question properly, we will need to make use of the concept of combination along with set theory.
What is Combination?In mathematical concept, Combination is the grouping of subsets from a set without taking the order of selection into consideration.
The formula for calculating combination can be expressed as:
[tex]\mathbf{(^n _r) =\dfrac{n!}{r!(n-r)! }}[/tex]
From the parameters given:
Workers employed on the day shift = 10Workers on swing shift = 8Workers on graveyard shift = 6A quality control consultant is to select 4 of these workers for in-depth interviews:
Using the expression for calculating combination:
(a)
The number of selections results in all 4 workers coming from the day shift is :
[tex]\mathbf{(^n _r) = (^{10} _4)}[/tex]
[tex]\mathbf{=\dfrac{(10!)}{4!(10-4)!}}[/tex]
= 210
The probability that all 5 selected workers will be from the day shift is,
[tex]\begin{array}{c}\\P\left( {{\rm{all \ 4 \ selected \ workers\ will \ be \ from \ the \ day \ shift}}} \right) = \dfrac{{\left( \begin{array}{l}\\10\\\\4\\\end{array} \right)}}{{\left( \begin{array}{l}\\24\\\\4\\\end{array} \right)}}\\\end{array}[/tex]
[tex]\mathbf{= \dfrac{210}{10626}} \\ \\ \\ \mathbf{= 0.0198}[/tex]
(b) The probability that all 4 selected workers will be from the same shift is calculated as follows:
P( all 4 selected workers will be) [tex]\mathbf{= \dfrac{ \Big(^{10}_4\Big) }{\Big(^{24}_4\Big)}+\dfrac{ \Big(^{8}_4\Big) }{\Big(^{24}_4\Big)} + \dfrac{ \Big(^{6}_4\Big) }{\Big(^{24}_4\Big)}}[/tex]
where;
[tex]\mathbf{\Big(^{8}_4\Big) = \dfrac{8!}{4!(8-4)!} = 70}[/tex]
[tex]\mathbf{\Big(^{6}_4\Big) = \dfrac{6!}{4!(6-4)!} = 15}[/tex]
P( all 4 selected workers is:)
[tex]\mathbf{=\dfrac{210+70+15}{10626}}[/tex]
The probability that all 4 selected workers will be from the same shift is = 0.0278
(c)
The probability that at least two different shifts will be represented among the selected workers can be computed as:
[tex]= 1-\dfrac{ (^{10}_4) }{(^{24}_4)}+\dfrac{ (^{8}_4) }{(^{24}_4)} + \dfrac{ (^{6}_4) }{(^{24}_4)}[/tex]
[tex]=1 - \dfrac{210+70+15}{10626}[/tex]
= 1 - 0.0278
= 0.9722
The probability that at least two different shifts will be represented among the selected workers is = 0.9722
(d)
The probability that at least one of the shifts will be unrepresented in the sample of workers is:
[tex]P(AUBUC) = \dfrac{(^{6+8}_4)}{(^{24}_4)}+ \dfrac{(^{10+6}_4)}{(^{24}_4)}+ \dfrac{(^{10+8}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]
[tex]P(AUBUC) = \dfrac{(^{14}_4)}{(^{24}_4)}+ \dfrac{(^{16}_4)}{(^{24}_4)}+ \dfrac{(^{18}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]
[tex]P(AUBUC) = \dfrac{1001}{10626}+ \dfrac{1820}{10626}+ \dfrac{3060}{10626}-\dfrac{15}{10626}-\dfrac{70}{10626}-\dfrac{210}{10626} +0[/tex]
The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257
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What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
Answers
Answer:
work is shown and pictured
Answer: x<3
Step-by-step explanation:
the terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis. Describe how to find the measure of the angle in both degree and radian
Answers
Measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
What is the terminal side of an angle?The terminal side of an angle is the rotated side of the initial side around a point to form an angle. This rotation can be clockwise or counter clock wise.
The terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis.
The total degree in a complete rotation of a side is 360 degrees. The side is rotated 1/6. Thus the angle is rotated is,
[tex]\theta=\dfrac{1}{6}\times360\\\theta=60^o[/tex]
Multiply it with π/180 to find the measure of the angle in radian.
[tex]\theta=60\dfrac{\pi}{180}\\\theta=\dfrac{\pi}{3}\\[/tex]
Hence, the measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
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ents
ons
Evaluation
Calculate simple interest
Question
Carolyn makes a deposit of $2,800 into a savings account. The bank calculates simple interest annually at a rate of 7.5%.
Interest is added every year on the anniversary of the initial deposit. How many years must Carolyn wait before her
investment exceeds $3,500? Give your answer in years. Do not include units in your answer.
Provide your answer below:
FEEDBACK
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SUBMIT
Content attribution
Answers
Answer:
4
Step-by-step explanation:
A=P0(1+rt).
We know that A=$3,500,P0=$2,800 and r=7.5%=0.075, so we can rearrange the formula for A to get an explicit expression for t:
A=P0(1+rt)⟹t=A−P0P0r,
and substituting the known quantities gives
r=$3,500−$2,800$2,800×0.075=3.33,
which means, since the interest is paid annually, that she must wait four years for the total investment to exceed $3,500.
Homework: Section 1.2 Applications Linear
Score: 0 of 1 pt
8 of 10 (7 complete)
1.2.31
How many quarts of pure antifreeze must be added to 4 quarts of a 10% antifreeze solution to obtain a 20% antifreeze solution?
quart(s) of pure antifreeze must be added.
(Round to the nearest tenth as needed)
Answers
Answer:
q = 0.5 quarts of 100% antifreeze
Step-by-step explanation:
q = quarts of pure antifreeze
Set this up as a weighted combination of the mixtures.
(100%)(q) + (10%)(4) = (20%)(q + 4)
100q + 40 = 20(q + 4)
5q + 2 = q + 4
4q = 2
q = 0.5 quarts of 100% antifreeze
Use the 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval that is expected to contain about 95% of the data values. A bell-shaped distribution with mean 1050 and standard deviation 7.
The interval is to:_______.
Answers
Answer:
Intervals = (1,064) , (1,036)
Step-by-step explanation:
Given:
Use 95% method
Mean = 1,050
Standard deviation = 7
Find:
Intervals.
Computation:
95% method.
⇒ Intervals = Mean ± 2(Standard deviation)
⇒ Intervals = 1,050 ± 2(7)
⇒Intervals = 1,050 ± 14
⇒ Intervals = (1,050 + 14) , (1,050 - 14)
⇒ Intervals = (1,064) , (1,036)
The Intervals = (1,064) , (1,036)
Given that:
Use 95% methodMean = 1,050Standard deviation = 7Based on the above information, the calculation is as follows:
Intervals = Mean ± 2(Standard deviation)
Intervals = 1,050 ± 2(7)
Intervals = 1,050 ± 14
Intervals = (1,050 + 14) , (1,050 - 14)
Intervals = (1,064) , (1,036)
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answers
Answer:
c
Step-by-step explanation:
when the absolute value of slope gets smaller, the graph of line gets less steeper.
16. Convert 55° to radians.
Answers
Answer:
0.96 radians
Step-by-step explanation:
Formula
1° = [tex]\frac{\pi }{180}[/tex] radians
Multiplying both sides by 55, It becomes
55° = [tex](\frac{\pi }{180} )*55[/tex]
55° = [tex]\frac{55\pi }{180}[/tex]
= 172.8/180
= 0.96 radians
Find the constant of variation for the relation and use it to write and solve the equation.
if y varies directly as x and as the square of z, and y=25/9 when x=5 and z=1, find y when x=1 and z=4
Answers
Answer:
When x = 1 and z = 4, [tex]y=\frac{80}{9}[/tex]
Step-by-step explanation:
The variation described in the problem can be written using a constant of proportionality "b" as:
[tex]y=b\,\,x\,\,z^2[/tex]
The other piece of information is that when x = 5 and z = 1, then y gives 25/9. So we use this info to find the constant "b":
[tex]y=b\,\,x\,\,z^2\\\frac{25}{9} =b\,\,(5)\,\,(1)^2\\\frac{25}{9} =b\,\,(5)\\b=\frac{5}{9}[/tex]
Knowing this constant, we can find the value of y when x=1 and z=4 as:
[tex]y=b\,\,x\,\,z^2\\y=\frac{5}{9} \,\,x\,\,z^2\\y=\frac{5}{9} \,\,(1)\,\,(4)^2\\y=\frac{5*16}{9}\\y=\frac{80}{9}[/tex]
These tables of values represent continuous functions. For which function will the y-values be the greatest for very large values of x?
Answers
Answer:
C
Step-by-step explanation:
The function of table A can be written as ...
y = 100x -92
__
The function of table B can be written as ...
y = 10x +446
__
The function of table C can be written as ...
y = (5/3)·3^x
__
The function of table D can be written as ...
y = 2x +413
__
The exponential function of Table C will have the largest y-values for any value of x greater than 6.
_____
Comment on the functions
When trying to determine the nature of the function, it is often useful to look at the differences of the y-values for consecutive x-values. Here, the first-differences are constant for all tables except C. That means functions A, B, D are linear functions.
If the first differences are not constant, one can look at second differences and at ratios. For table C, we notice that each y-value is 3 times the previous one. That constant ratio means the function is exponential, hence will grow faster than any linear function.
Answer:
yes, what the other user is correct i just took the quiz
Step-by-step explanation:
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2013?
Answers
Answer: The population will be 408,000 people.
Step-by-step explanation:
So in 2000 there were 200,000 people and it started to grow 8% every year so up to 2013.
so find 8% of 200,000 and then multiply it by the the number of years.
8% * 200,000 = 16,000
Find the difference between the years.
2013 - 2000 = 13 years
13 * 16000 = 208000 This is the amount of new people from 2000 to 2013 so add it to the original population.
208,000 + 200,000 = 408,000
The top and bottom margins of a poster are each 15 cm and the side margins are each 10 cm. If the area of printed material on the poster is fixed at 2400 cm2, find the dimensions of the poster with the smallest area.
Answers
Answer:
the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
Step-by-step explanation:
From the given question.
Let p be the length of the of the printed material
Let q be the width of the of the printed material
Therefore pq = 2400 cm ²
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
To find the dimensions of the poster; we have:
the length of the poster to be p+30 and the width to be [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex]
The area of the printed material can now be: [tex]A = (p+30)(\dfrac{2400 }{p} + 20)[/tex]
=[tex]2400 +20 p +\dfrac{72000}{p}+600[/tex]
Let differentiate with respect to p; we have
[tex]\dfrac{dA}{dp}= 20 - \dfrac{72000}{p^3}[/tex]
Also;
[tex]\dfrac{d^2A}{dp^2}= \dfrac{144000}{p^3}[/tex]
For the smallest area [tex]\dfrac{dA}{dp }=0[/tex]
[tex]20 - \dfrac{72000}{p^2}=0[/tex]
[tex]p^2 = \dfrac{72000}{20}[/tex]
p² = 3600
p =√3600
p = 60
Since p = 60 ; replace p = 60 in the expression q = [tex]\dfrac{2400 \ cm^2}{p}[/tex] to solve for q;
q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]
q = [tex]\dfrac{2400 \ cm^2}{60}[/tex]
q = 40
Thus; the printed material has the length of 60 cm and the width of 40cm
the length of the poster = p+30 = 60 +30 = 90 cm
the width of the poster = [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex] = [tex]\dfrac{2400 \ cm^2}{60} + 20[/tex] = 40 + 20 = 60
Hence; the dimension of the poster = 90 cm length and 60 cm width i.e 90 cm by 60 cm.
A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 1100 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?
Answers
Answer:
Length = 550 m
Width = 275 m
Area = 151,250 m2
Step-by-step explanation:
One side of the farmland is bounded by the river, so the perimeter we will need to enclose is:
[tex]Perimeter = Length + 2*Width = 1100\ m[/tex]
And the area of the farmland is given by:
[tex]Area = Length * Width[/tex]
From the Perimeter equation, we have that:
[tex]Length = 1100 - 2*Width[/tex]
Using this in the area equation, we have:
[tex]Area = (1100 - 2*Width) * Width[/tex]
[tex]Area = 1100*Width - 2*Width^2[/tex]
Now, to find the largest area, we need to find the vertex of this quadratic equation, and we can do that using the formula:
[tex]Width = -b/2a[/tex]
[tex]Width = -1100/(-4)[/tex]
[tex]Width = 275\ m[/tex]
This width will give the maximum area of the farmland. Now, finding the length and the maximum area:
[tex]Length = 1100 - 2*Width = 1100 - 550 = 550\ m[/tex]
[tex]Area = Length * Width = 550 * 275 = 151250\ m2[/tex]
A student is interested in becoming an actuary. The student knows that becoming an actuary takes a lot of schooling and will have to take out student loans and wants to make sure the starting salary will be higher than $55,000/year. The student takes a random sample of 30 starting salaries for actuaries and finds a p-value of 0.0392. Use α = 0.05.
a. Choose the correct hypotheses.
H0:μ≠55,000 H1:μ=55,000
H0:μ>55,000 H1:μ≤55,000
H0:μ<55,000 H1:μ≥55,000
H0:μ=55,000 H1:μ>55,000
H0:μ=55,000 H1:μ≠55,000
H0:μ=55,000 H1:μ<55,000
b. Should the student pursue an actuary career?
No, since we can reject the null hypothesis
No, since we can reject the claim
Yes, since we can reject the claim
Yes, since we can can reject the null hypothesis
Answers
Answer:
a) H0:μ=55,000 H1:μ>55,000
b) Yes, since we can can reject the null hypothesis
Step-by-step explanation:
a) The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For this case;
Null hypothesis is that the starting salary will be equal to $55,000/year.
H0:μ=55,000
Alternative hypothesis is that the starting salary will be greater than $55,000/year.
H1:μ>55,000
b) Decision Rule;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
For this case;
P-value = 0.0392
α = 0.05
Since P-value < 0.05, we can reject null hypothesis.
Therefore, we can accept alternative hypothesis which is the starting salary will be greater than $55,000/year, so the student should pursue an actuary career because the starting salary will be greater than $55,000/year.
- Yes, since we can can reject the null hypothesis
Which of the options is the response variable?
A. The number of adults.
B. The type of training exercises performed by each participant.
C. The size of the physiological blind spot.
D. The number of times an adult performed training exercises.
Answers
Question:
The physiological blind spot refers to a very small zone of functional blindness in the eye where the optic nerve passes through the retina. We do not notice it because our nervous system compensates for it. Can eye training reduce the size of a person's physiological blind spot? Researchers recruited a representative sample of 10 adults with normal vision. Each participant performed training exereises with one eye for three weeks. The size of the physiological blind spot was measured (in degrees of visual angle squared) with a motion detection task both prior to training and again after the training was completed. Which of the options is the response variable?
A) The size of the physiological blind spot
B) The number of adults.
C) The type of training exercises performed by each participant.
D) The size of the physiological blind spot.
E) The number of times an adult performed training exercises.
Answer:
The correct answer is A)
Explanation:
The response variable (when experimenting) is the variable or factor about which the researcher is concerned. It can also be (as the name entails) the variable which respond to changes in the experiment.
The changes in the experiment is the training. The variable which the researcher is concerned about and which may or may not change with the introduction of training is the size of the physiological blind spot.
Cheers!
An organization will give a prize to a local artist will be randomly chosen from among 6 painters,2 sculptors, and 9 photographers. What is the probability that the artist chosen will be a painter or a sculptor?
Answers
Answer: [tex]\bold{\dfrac{8}{17}=47.1\%}[/tex]
Step-by-step explanation:
[tex]\dfrac{\text{painter or sculptor}}{\text{total artists}}=\dfrac{6+2}{6+2+9}=\dfrac{8}{17}[/tex]
The results of a common standardized test used in psychology research is designed so that the population mean is 155 and the standard deviation is 50. A subject earns a score of 155. How many standard deviations from the mean is the value 155
Answers
Answer:
The value 155 is zero standard deviations from the [population] mean, because [tex] \\ x = \mu[/tex], and therefore [tex] \\ z = 0[/tex].
Step-by-step explanation:
The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
z is the z-score.x is the raw score: an observation from the normally distributed data that we want standardize using [1].[tex] \\ \mu[/tex] is the population mean.[tex] \\ \sigma[/tex] is the population standard deviation.Carefully looking at [1], we can interpret it as the distance from the mean of a raw value in standard deviations units. When the z-score is negative indicates that the raw score, x, is below the population mean, [tex] \\ \mu[/tex]. Conversely, a positive z-score is telling us that x is above the population mean. A z-score is also fundamental when determining probabilities using the standard normal distribution.
For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], one standard deviation above from the population mean. A z-score = -1 is also one standard deviation from the mean but below it.
These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.
A subject earns a score of 155. How many standard deviations from the mean is the value 155?
From the question, we know that:
x = 155.[tex] \\ \mu = 155[/tex].[tex] \\ \sigma = 50[/tex].Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject earned a score that equals the population mean. Then, using [1]:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{155 - 155}{50}[/tex]
[tex] \\ z = \frac{0}{50}[/tex]
[tex] \\ z = 0[/tex]
As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:
[tex] \\ x = \mu[/tex]
Therefore
[tex] \\ z = 0[/tex]
So, the value 155 is zero standard deviations from the [population] mean.
What is the slope of the line below? If necessary, enter your answer as a
fraction in lowest terms, using the slash (/) as the fraction bar. Do not enter
your answer as a decimal number or an equation.
Answers
Answer:
4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-(-2))/(3-1)
m=8/2
m=4
I run 200m in 32 seconds, how long will it take to run 5000m
Answers
Answer:
It will take 800seconds to you to run 5000m
Step-by-step explanation:
Let time taken to run 5000m is x
Using ratio and proportion
200:32=5000:x
200/32=5000/x
200*x=5000*32
200x=160000
x=800seconds
