The radical expression written as an exponent, and simplified, is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
How to transform an exponent to a power?It happens according to the following rule:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
The inverse is also valid, hence, in this problem, the expression written as an exponent and simplified is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
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Olivia scored 82 points on the first mathematics test of the year. On the second mathematics test, she scored 78 points. What is the percent of change in the number of points she scored between the first and second tests? Round your answer to the nearest hundredths place.
The percent of change in the number of points she scored between the first and second tests = 4.878 %
What is percentage decrease?
If the data is decreasing,
Decrease = Original Number - New Number.
Then: divide the decrease by the original number and multiply the answer by 100.
% Decrease = Decrease ÷ Original Number × 100.
Given that:
The score of first Math test = 82
The score of second Math test = 78
Changes occurs in marks by=78-82
=-4
So, there is decrease in marks.
We have to find the decrease percentage:
Decrease%= [tex]\frac{change \;in \;value}{Original\; value} *100[/tex]
= [tex]\frac{4}{82} *100[/tex]
= 0.04878 * 100
= 4.878 %
There is 4.88% decrease in Olivia's score.
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I need help! Find the measure of all sides. Round to the nearest tenth.
Answer:
[tex]let \: the \: angle \: be \: \alpha \\ \tan( \alpha ) = \frac{p}{b} \\ \tan(16.8) = \frac{2.7}{x} \\ x = \frac{2.7}{0.30 } \\ x = 9 \\ now \: by \: using \: pythagoras \: theorem \: \\ h = \sqrt{p {}^{2} } + b {}^{2} \\ h = \sqrt{ {2.7}^{2} } + {9 }^{2} \\ h = 9.396[/tex]
2 people can plough a field in 5 hours how long would it take 3 people?
Answer:
7 hours and 30 minutes
Step-by-step explanation:
because if you divide the 5 hours by the 2 people you get 2 hours and 30 minutes so if you add one more person you are basically adding 2 hours and 30 minutes so if u add that 2 hours and 30 minutes to the 5 hours you will get 7 hours and 30 minutes
15. Factor
please help :)
Answer:
(8w + 7)(7w + 9)
Step-by-step explanation:
56w² + 121w + 63
consider the factors of the product of the coefficient of the w² term and the constant term which sum to give the coefficient of the w- term
product = 56 × 63 = 3528 and sum = 121
After much trial and error the factors are + 49 and + 72
use these factors to split the w- term
56w² + 49w + 72w + 63 ( factor first/second and third/fourth terms )
= 7w(8w + 7) + 9(8w + 7) ← factor out (8w + 7) from each term
= (8w + 7)(7w + 9) ← in factored form
Need help please answer ASAP!
Problem 16
Answer: Choice (3)Work Shown:
[tex]2ax - 5x = 2\\\\x(2a - 5) = 2\\\\x = \frac{2}{2a-5}\\\\[/tex]
I factored out x, then divided both sides by (2a-5)
=========================================================
Problem 17
Answer: Choice (2)Work Shown:
1 yard = 3 feet
1/3 yard = 1 foot
x/3 yards = x feet
In the second step, I divided both sides by 3. Afterward, I multiplied both sides by x.
#16
2ax-5x=2x(2a-5)=2x=2/2a-5Option C
#17
3feets=1yardSo
xfeet=1/3×x yard=x/3yardWhich statements about the octagon are true? select two options. the length of segment yz is 15.3 cm. the measure of the angle formed by the radius and the apothem is 30°. the length of segment xy can be found by solving for a in 202 – 7.652 = a2. the length of segment wz is 20 cm. the measure of the central angle, ∠zxw, is 45°.
The statements about the octagon that are true are:
The length of segment xy can be found by solving for a in 202 – 7.652 = a2. The measure of the central angle, ∠zxw, is 45°.What is Octagon?This is known to be a kind of 2D shape object that is said to be made up of eight-sided polygon.
Note that when one measure the central angle, ∠zxw, as 45° it will therefore holds true for an octagon true shape and as such the two options above are correct.
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Answer:
its C and E my friend
Step-by-step explanation:
i took the test
yw :)
hope i helped/ made life easier
which is bigger -32 or 13.8?
On Monday, Peter ran 20 minutes and walked 20 minutes and he burnt 500 calories. On Tuesday, Peter ran 10 minutes and walked 35 minutes and he burnt, again, 500 calories.
a) Create two equations based on the situation.
b) Determine the value of the variables.
c) How many calories can peter burn with one hour of running?
Answer:
a) 20r + 20w = 500, 10r + 35w = 500
b) r = 15, w = 10
c) 900 calories
Explanation:
Let running time be r, walking time be w
a) Hence, make equation's:
20r + 20w = 500... equation 1
10r + 35w = 500... equation 2
b) Determine the value of the variables by solving simultaneously.
⇒ (500 - 20w)/20 = (500 - 35w)/10
cross multiply
⇒ 10(500 - 20w) = 20(500 - 35w)
multiply
⇒ 5000 - 200w = 10000 - 700w
shift sides
⇒ -200w + 700w = 10000 - 5000
simplify
⇒ 500w = 5000
divide both sides by 500
⇒ w = 10
Now find the value of variable r,
⇒ r = (500 - 20w)/20
insert w = 10
⇒ r = (500 - 20(10))/20
simplify
⇒ r = 15
Hence the value of r is 15 and w is 10
c) Find calories burnt after one hours of running: [1 hours = 60 minutes]
calories = 60r = 60(15) = 900 calories
Hence, he can burn 900 calories after one hours of running.
What is the absolute value of the complex number -4-√2i?
A.√14
B.3√2
C.14
D.18
PLEASE HELP
Answer: Choice B. 3√2
This is the same as writing 3sqrt(2) or [tex]3\sqrt{2}[/tex]
===========================================================
Reason:
For any complex number of the form [tex]z = a+bi[/tex], the absolute value or magnitude of it is [tex]|z| = \sqrt{a^2+b^2}[/tex]
In this case, we have [tex]a = -4 \text{ and } b = -\sqrt{2}[/tex]
So,
[tex]|z| = \sqrt{a^2+b^2}\\\\|z| = \sqrt{(-4)^2+(-\sqrt{2})^2}\\\\|z| = \sqrt{16+2}\\\\|z| = \sqrt{18}\\\\|z| = \sqrt{9*2}\\\\|z| = \sqrt{9}*\sqrt{2}\\\\|z| = 3\sqrt{2}\\\\[/tex]
If we formed a segment with the endpoints [tex](0,0) \text{ and } (-4, -\sqrt{2} )[/tex], then that segment will have length of the value mentioned above.
Side note: This formula or concept is related to the pythagorean theorem.
If rosetta sells her house and pays off the mortgage, how much should she receive (assuming there are no other costs associated with selling the house)? $42,000 $50,000 $52,000 $60,000
Based on the amount that Rosetta sells her house and the mortgage she had before she did, the amount she will recieve is $50,000.
How much will Rosetta receive?Rosetta owes a total of $150,000 for her mortgage payment and was able to sell the house for $200,000.
This means that the amount she will recieve is:
= Selling price - Mortgage
= 200,000 - 150,000
= $50,000
In conclusion, option B is correct.
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Answer:
B. $50,000
Step-by-step explanation:
If cos x = −1/4 and csc x < 0, find cot x/2
The value of cot x/2 is √3/√5.
What is Trigonometry?Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations.
given:
cos x=-1/4
sin x= √15/4
cosec x= 4/√15
and, cot x= -1/√15
Now, cot x/2= cosec x+ cot x
= 4/√15-1/√15
= 3/√15
= √3/√5
Hence, the value of cot x/2 is √3/√5.
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!PLEASE HELP ASAP!
What do we call the statistic when we are measuring whether individuals have a certain characteristic that is either present or not?
Answer:
A parameter is a numerical description of a population characteristic
Step-by-step explanation:
A parameter is a numerical description of a population characteristic
The graph shows a player’s monthly home run total in two seasons.
a. Find the standard deviation of the scores of the monthly home run totals in the player’s rookie season and interpret the results. Round to the nearest hundredth.
The standard deviation is about __. The typical number of home runs differs from the mean by about __ home runs.
b. Find the standard deviation of the scores of the monthly home run totals in this season and interpret the results. Round to the nearest hundredth.
The standard deviation is about __
The typical number of home runs differs from the mean by about __ home runs.
a) standard deviation of the scores of the monthly home run totals in the player’s rookie season will be 1.29
b) The standard deviation of the scores of the monthly home run totals in this season will be 2.738
What is standard deviation?Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
a)The standard deviation of the scores of the monthly home run totals in the player’s rookie season:-
The data from the graph will be
1,0,6,2,0,2
Standard deviation is calculated as:-
[tex]\sigma = \dfrac{\sqrt{\sum(x-\mu)^2}}{N}}[/tex]
[tex]\mu = \dfrac{1+0+6+2+0+3}{6}=2[/tex]
Putting the values we get
[tex]\sigma = \dfrac{\sqrt{(1-2)^2+(0-2)^2+(2-2)^2+(0-2)^2+(3-2)^2}}{6}}=1.29[/tex]
Hence standard deviation is 1.29
b)The standard deviation of the scores of the monthly home run totals in this season
The data from the graph will be
4,6,4,8,7,13
Standard deviation is calculated as:-
[tex]\sigma = \dfrac{\sqrt{\sum(x-\mu)^2}}{N}}[/tex]
[tex]\mu = \dfrac{4+6+4+8+7+13}{6}=7[/tex]
Putting the values we get
[tex]\sigma = \dfrac{\sqrt{(4-7)^2+(6-7)^2+(4-7)^2+(8-7)^2+(7-7)^2+(7-13)^2}}{6}}=2.738[/tex]
Hence standard deviation is 2.738
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28. Daniel uses 18 pints of water to fill 8 bottles. He
pours the same amount of water into each bottle.
How many pints of water does he pour into cach
bottle?
A. 8/12
*
B. 2 2/8
C. 8/26
D. 2 4/8
Answer:
b
Step-by-step explanation:
to find the answer to this you sould divide the amount of pints by the number of bottles
18/8
which is also 2 2/8
so the answer is b
Which property is illustrated by the statement 4+(9+12)=(4+9)+12
Answer:
Associative Property of Addition
Step-by-step explanation:
Associative Property of Addition:
For any real numbers a, b, and c, (a + b) + c = a + (b + c).
Answer:
Commutative Property of Addition
Step-by-step explanation:
Please help me with this question
Answer:
difference between town A and town B is 5.4 deg. celcius
Step-by-step explanation:
I added each row and divided by 5 to get the average for A and B
I subtracted the average
see attached picture showing the math
No 1 a b c d
PLS fast
a) a= 2×40 = 160°
b) b = 60/2 = 30°
c) c = 40°
d) d = 115°
1-4) Choose Yes or No to tell if the fraction 3/4 will make each equation true. (You are putting the 3/4 in each blank and multiplying to see if it will give you the product given.)
please answer this!!!
Step-by-step explanation:
sin60 =opp/hyp
0.86=y/20
y=17.2
cos60=adj/hyp
0.5=x/20
x=10
sin57=y/15
0.83=y/15
y=12.45
A carnival charges $3 for kids and $10 for adults. On Saturday, there were 500 visitors, and the total amount taken at the gate was $3,600. The equation representing the number of visitors is k + a = 500, where k represents the number kids and a represents the number of adults. The equation representing the amount of money collected is 3k + 10a = 3,600. How many kids and adults visited the carnival? Part A Before solving this problem, decide which tool you’ll use to solve it. Which method for solving systems of linear equations is best for solving this problem? Explain your answer.
Answer: number of kids(k)=200
sand the number of adults(a)=300, visited the carnival.
The tool I used is called simultaneous equation and I used elimation method as the method.
Line segment xy is tangent to circle z at point u. circle z is shown. line segment u v is a secant. line segment x y is a tangent and intersects the circle at point u. the measure of arc u v is 84 degrees. if the measure of arc u v is 84°, what is the measure of angle y u v? 42° 84° 96° 168°
Based on the calculations, the measure of angle YUV is equal to 42°.
What is a line segment?A line segment refers to a part of a line that is bounded by two (2) distinct points and it has a fixed length.
Based on the information given, we can deduce the following:
O is center of circle (∠YUO = 90°)The measure of arc UV is 84° (∠UOV = 84°)OU is equal to OV and equal to radius (∠OVU = ∠OUV)From triangle UOV, we have:
∠OUV + ∠OUV + ∠UOV = 180°
2OUV + 84 = 180
2OUV = 180 - 84
2OUV = 96
OUV = 96/2
OUV = 48°
Now, we can determine the measure of angle YUV:
∠YUV = ∠YUO - ∠OUV
∠YUV = 90 - 48
∠YUV = 42°.
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Answer:
42
Step-by-step explanation:
Two teams, a and b, are about to play a game. previous records show that a has an 80% chance of winning, while b has a 20% of winning. spectators can either choose to buy regular tickets or special tickets. a spectator with a special ticket will receive a refund of $2 if team a wins and a refund of $5 if team b wins. how much extra, minimally, should the special ticket cost to cover the expected value of the refunds offered?
The special ticket cost to cover the expected value of the refunds would be $2.60
How to solve for the minimal extra cost.Probability of A winning = 80%
Probability of B winning = 20%
We have to solve for the rebate of the bet.
80% = 0.8, 20% = 0.2
0.8 x 2 = 1.6
0.2 x 5 = 1
The extra minimal cost of the special ticket would be calculated as: 1 + 1.6
= $2.6
Therefore the answer to the question is $2.6
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Simplify this expression
20f-4(5f+4)+16
Solve step by step
20f - 4 (5f + 4) + 16
= 20f - 20f - 16 + 16
= 0
Answer:
0
Step-by-step explanation:
Distribute terms in the parentheses
20f - 4(5f + 4) + 1620f - 20f - 16 + 16 0 + 0 [20f and -20f, and -16 and 16 cancel out]0What is a diameter and what is a radius?
Radius is the length of the line segment from the center of the circle to an endpoint on the circle and diameter is twice the length of the radius of the circle.
Michael is finding the area of parallelogram abcd. to do this, he follows the steps in the table. step 1 draw a rectangle around parallelogram abcd. step 2 find the area of the rectangle. step 3 find the area of the four right triangles created in the corners of the rectangle. step 4 subtract the area of the right triangles from the area of the rectangle. to solve the problem using these steps, what are the dimensions of the rectangle he should draw? on a coordinate plane, parallelogram a b c d has points (1, negative 1), (3, 2), (1, 3), and (negative 1, 0). 2 units by 4 units 3 units by 2 units 4 units by 4 units 5 units by 6 units
The dimensions of the rectangle Michael should draw is given by: C. 4 units by 4 units.
What is a rectangle?A rectangle can be defined as a type of quadrilateral in which its opposite sides are equal and all the angles formed are right angle.
In this scenario, the rectangle would be drawn to touch the parallelogram at its four vertices (A, B, C, and D). Also, this would lie outside the parallelogram with the formation of four (4) right-angle triangles.
Therefore, the dimensions of the rectangle Michael should draw is given by:
Dimension = 4 × 4 units.
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Answer:
option C
Step-by-step explanation:
96x 3+(9*8) ÷ 126,980 =?
Answer:
288.000567018 or [tex]3(32x^{3} +\frac{3.8}{126980})[/tex]
Step-by-step explanation:
hope this helps
pls mark brainliest
Jorge is an administrative assistant. He was involved in a serious car accident and broke both wrists. Which of his
insurance plans will provide him with income while he is out of work recovering for six weeks?
A)short-term disability
B)workers' compensation
C)long-term disability insurance
D)medical insurance
Answer:
Medical Insurance
Step-by-step explanation:
Answer:
Medical Insurance
Step-by-step explanation:
serious car accident and broke both wrists.
subtract the quotient of 15 divided by 3 from the sum of 33 and 7
Answer:
(33+7)-(15/3) = 35
Step-by-step explanation:
35
Step-by-step explanation:
fancy way of saying (33+7) - (15/3)
33 + 7 = 40
15 / 3 = 5
40 - 5 = 35
Solve 11x 2y 2 + a = b for a
Answer:
a=b-44y
Step-by-step explanation:
a=b-44y
879+29 do you know what it is
Answer:
908
Step-by-step explanation:
879+29=908
