Answer:
200 = 100*2, so √200 = √100 * √2. √100 = 10, so I can replace it with 10 to get 10 * √2 as my final answer for the square root of 200.
Step-by-step explanation:
read it
In the given problem the expression equivalent to square Root 200 is, 10√2
What is square root?In mathematics, square roots is a concept in which, if we multiply square roots of any number by itself then it will give us an original number.
if 'a' is square root of 'b' then it will represent as, a = √b
Given number,
√200
we can write it in factor of 200,
⇒ √(2×100)
⇒ √2×√100
⇒ 10√2
Hence, The expression is 10√2
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Darren accumulated $9,000 in credit card debt. If the interest rate is 4.1% per year and he does not make any payments for 9 years, how much will he owe on this debt in 9 years by compounding continuously? Round to the nearest cent
Answer:
$12,921.09
Step-by-step explanation:
9000(1.041)⁹
9000(1.4367641386)
≈$12,921.09
The amount of money Darren owe on this debt in 9 years by compounding continuously is $12,915.
Given that, principal=$9,000, rate of interest=4.1% and time period =9 years.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]Amount=P(1+\frac{r}{100})^t[/tex]
Now, [tex]Amount=9000(1+\frac{4.1}{100})^9[/tex]
= 9000×[tex](1+0.041)^9[/tex]
= 9000×[tex](1.041)^9[/tex]
= 9000×1.435
= $12915
Therefore, the amount of money Darren owe on this debt in 9 years by compounding continuously is $12,915.
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Evaluate: [tex]3-2^2+4*3+5[/tex]
Answer:
16
Step-by-step explanation:
Apply PEMDAS:
Solve the exponent, multiply from left to right, and then subtract and add from left to right.
[tex]3-2^2+4*3+5\\\\3-4+4*3+5\\\\3-4+12+5\\\\-1+12+5\\\\11+5\\\\\boxed{16}[/tex]
Answer: 16
Step-by-step explanation:
The important thing to remember here is the Order of Operations
The Order of Operations states that first solve Parentheses, then Exponents, then Multiplication and Division, then Addition and Subtraction.
There are no parentheses.
Exponents: 3 - 4+4*3+5
Multiplication and Division: 3 - 4 + 12 + 5
Addition and Subtraction:
-1+12+5
11+5
16
Hope it helps <3
If \$1000 is deposited into an account that earns 3.25\% simple interest per year, how much money will be in the account after 7 years? PLEASE SHHOW WORK
======================================================
Explanation:
The simple interest formula to use is
A = P*(1+r*t)
where,
A = account value after t years (original deposit + interest)
P = 1000 = amount deposited (principal)
r = 0.0325 = annual interest rate in decimal form
t = 7 = number of years
So,
A = P*(1+r*t)
A = 1000*(1+0.0325*7)
A = 1227.50
Side note: you've earned A-P = 1227.50-1000 = 277.50 dollars in total interest
in a box of chocolates, 1/5 of the chocolates contains nuts. the rest do not.
write down the ratio of the number of chocolates that contains nuts to the number of chocolates that do not contain nuts .
give you answer in the form 1: n
Answer:
the ratio would be 1:4
Step-by-step explanation:
ratio of those who has nuts:
1/5
ratio of those who dont:
1-1/5=4/5
one against another:
1/5 : 4/5 = 1:4 = with : without
Given f(x) = 3x - 1 and g(x)=2x-3, for which value of x does g(x) = f(2)?
2
O X-2
xe
O X4
Answer:
i hope it will help you...
What are the factors of the function represented by this graph?
710
+6
+
+2
-10
-6
8
8
10
-2
4
-6
-8
+-10
A
(x-4) and (x-8)
B
(x-4) and (x+8)
C.
(x+4) and (x-8)
(x + 4) and (x+8)
Answer:
C. (x+4) (x-8)
Step-by-step explanation:
Take the graph for example both x values are -4 & positive 8
What is the circumference of a circular swimming pool with a diameter of 6 ½ feet? (use 22 over 7 as pi)
Answer:
10.21 feet.
Step-by-step explanation:
circumference of circle with diameter d is given by [tex]\pi d[/tex]
where r is the radius of the circle.
_____________________________
given
diameter = 6 1/2 = 13/2 feet
\thus, circumference of circle is calculated as following
[tex]circumference = \pi *13/2 = 22/7 * 13/2\\circumference = 11*13/7*2 = 143/14 = 10.21[/tex]
Thus, circumference of given circle is 10.21 feet.
This system of equations is shown on the graph: 2y − 4x = 6 y = 2x + 3 Which statement about the system is true?
Answer:
The system has infinity many solutions
Step-by-step explanation:
If it had no solutions there would be another like that does not go through it....if it was one solution it would have another like going through the other line....and since it has two lines that are on top of each other in the same point it's infinity solutions
Answer:
likely Option: DStep-by-step explanation:
What is the quotient? StartFraction a minus 3 Over 7 EndFraction divided by StartFraction 3 minus a Over 21 EndFraction StartFraction negative (a minus 3) squared Over 147 EndFraction StartFraction (a minus 3) squared Over 147 EndFraction 3 –3
Answer:
Correct answer is
[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]
Step-by-step explanation:
Let us rephrase the given statement mathematically.
We are given the fractions as:
[tex]\dfrac{a-3}{7}[/tex]
to be divided by:
[tex]\dfrac{3-a}{21}[/tex]
To find:
[tex]\dfrac{a-3}{7}\div\dfrac{3-a}{21}[/tex]
Now, let us have a look at the division rule in fractions:
[tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex]
is equivalent to
[tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]
In other words, we say that the second fraction [tex]\frac{c}{d}[/tex] is changed to [tex]\frac{d}{c}[/tex] and [tex]\div[/tex] is changed to [tex]\times.[/tex]
Now solving the given fraction by applying above rules:
[tex]\dfrac{a-3}{3}\div\dfrac{3-a}{21}[/tex]
[tex]\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{3-a}\\\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{-(a-3)}\\\Rightarrow \dfrac{1}{1}\times \dfrac{3}{-1}\\\Rightarrow -3[/tex]
So, correct answer is:
[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]
Answer:
d on edg
Step-by-step explanation:
taking test rn
Solve using derivatives.
I have no clue where to start on this I really need help please.
Please show steps and diagram.
Answer:
Below in bold.
Step-by-step explanation:
The surface area of the box
= x^2 + 4hx where x = a side of the square base and h is the height.
So x^2 + 4hx = 8
The volume of the box
V = x^2h
From the first equation we solve for h
4hx = 8 - x^2
h = (8 - x^2) / 4x
Now we substitute for h in the formula for the volume:
V = x^2 * (8 - x^2) / 4x
V = 8x^2 - x^4 / 4x
V = 2x - 0.25x^3
Finding the derivative:
V' = 2 - 0.75x^2 = 0 for max/mimn values
x^2 = 2/ 0.75 = 2.667
x = 1.633.
So the length and width of the base is 1.633 m and the height
= ( 8 - 2.667) / (4*1.633)
= 0.816 m
The maximum volume = 0.816 * 2.667 = 2.177 m^2.
The answers are correct to the nearest thousandth.
Pls, help. Trigonometry. Please answer in short sentences I'm not picking. Please answer a-i.
Answer:
a . See attachment
b. because we will find the distance from the bottom of the ladder to the base of the building.
c. sin 60 = opposite side / hypotenuse
d.sin 60 = x / 10
e . 8.66 ft =x
f. see attachment
i. cos 60° = adjacent side / hypotenuse
Step-by-step explanation:
a . See attachment
b. because cos 60° = adjacent side / hypotenuse, the hypotenuse is equal to the length of the ladder (10), and the adjacent side that we will find is the distance from the bottom of the ladder to the base of the building. not the height that the ladder reaches .
c. sin 60 = opposite side / hypotenuse
Because we will find the opposite side which is the height that the ladder reaches.
d.sin 60 = x / 10
e .
0.866025403 = x/10
10 (0.866025403) =x
8.66 ft =x
f. see attachment
i. cos 60° = adjacent side / hypotenuse
Because we will find the adjacent side which is the distance from the bottom of the ladder to the base of the building.
Expand the following:
a) x(x + 2)
b) x(2x - 5)
c) 2x(3x + 4)
d) 6x(x - 2)
Answer:
[tex]a. \: {x}^{2} + 2[/tex] [tex]b. \: 2 {x}^{2} - 5x[/tex] [tex]c. \: 6 {x}^{2} + 8x[/tex] [tex]d. \: 6 {x}^{2} - 12x[/tex]solution,
[tex]a. \: x(x + 2) \\ \: \: = x \times x + 2 \times x \\ \: \: = {x}^{2} + 2x[/tex]
[tex]b . \: x(2x - 5) \\ \: = x \times 2x - x \times 5 \\ \: \: = 2 {x}^{2} - 5x[/tex]
[tex]c. \: 2x(3x + 4) \\ \: = 2x \times 3x + 2x \times 4 \\ \: \: = 6 {x}^{2} + 8x[/tex]
[tex]d. \: 6x(x - 2) \\ \: \: = 6x \times x - 6x \times 2 \\ \: \: = 6 {x}^{2} - 12x[/tex]
Hope this helps...
Good luck on your assignment..
Given: RST is circumscribed about circle A.
A. 180
B. 45
C.less than 90
D. 90
and why plz? :)
Answer:
90°Option D is the correct option
Step-by-step explanation:
As RT is a tangent on point P, so it will form a right angle at point P with the radius.
So, angle APT = 90 degrees.
Hope this helps...
Good luck on your assignment...
The measure of the (angle ATP ) is 90 degrees.
What is the tangent?The normal line is defined as the line that is perpendicular to the tangent line at the point of tangency.
As RT is a tangent on point P, so it will form a right angle at point P with the radius.
So, angle APT = 90 degrees.
Option D is the correct option.
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Sally borrows some money at a 15% interest rate. She repays the loan in full after 30 months and pays $1692 in interest. How much did she borrow?
Answer: $4512 was the amount she borrowed.
Step-by-step explanation:
SI = 1692
R = 15% = 0.15
T = 30 months = 2.5 years
SI = PRT
1692 = P x 0.15 x 2.5
1692 = 0.375P
P = 1692 / 0.375
P = 4512
The question is in the picture attached
Answer:
≈ 10.7 ft
Step-by-step explanation:
We have 2 secants to a circle from an external point.
The product of the measure of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.
let the internal part of the right secant be x , then
6(6 + x) = 4(4 + 12) = 4 × 16 = 64 ( divide both sides by 6 )
6 + x ≈ 10.7 ( subtract 6 from both sides )
x ≈ 4.7
length of pass = 6 + 4.7 = 10.7
Evaluate 3|−5| − 2|−2|. Question 22 options: −11 −19 11 19
Answer:
11
Step-by-step explanation:
3|−5| − 2|−2|
Absolute value means take the non-negative value
3 * 5 -2 * 2
15 - 4
11
Two random samples were done to determine how often
people in a community go to the dentist.
The first sample surveyed 10 people as they entered
their workplaces. The first sample found that the mean
time between visits to the dentist was 7.5 months.
The second sample surveyed 50 people as they entered
the local grocery store. The second sample found that
the mean time between visits to the dentist was 18.1
months.
Complete question:
Two random samples were done to determine how often people in a community go to the dentist the first sample surveyed 10 people as they enter their workplaces. The first sample found that the mean time between visits to the dentist with 7.5 months. The second sample survey 50 people as they enter the local grocery store. The second simple found that the mean time between visits to the dentist is 18.1 months. Which statements are true check all that apply
1) The first sample is likely to be more representative of the population.
2) The second sample is likely to be more representative of the population.
3)The second sample will give a better representation because it is larger.
4) The first sample is not biased.
5) Community members probably visit the dentist about once every 18 months.
Answer:
2,3,5
Step-by-step explanation:
2) The second sample is likely to be more representative of the population, this is because the number of observations in the second sample is more than the number of observations in the first. And the more the sample observation, the more representative it is about the population.
3.) The second sample will give a better representation because it is larger, the size of the second sample is the sole factor which gives it a better representative edge than the first sample.
5.) Community members probably visit the dentist about once every 18 months, from the question, the avarage time visit of community members to the dentist is 18.1 months which is approximately 18 months, the mean gives the average value of a distribution
HELP ME PLZ!!!!!!!! Brainliest will be given, THANK YOU!!!!
Answer:
Step-by-step explanation:
5*2=10, 10*2=20...
it is a geometric progression with ratio= 2
a11=a10*2=2560* 2=5120
Greg is designing a clock face. Using the center of the clock face as the origin, he keeps its diameter at 10 units. Match the positions of the hours on the clock face to their corresponding coordinates. 3 o'clock (0, -5) 6 o'clock (5, 0) 9 o'clock (0, 5) 12 o'clock (-5, 0)
Answer:
3 o'clock (5, 0)
6 o'clock (0, -5)
9 o'clock (-5, 0)
12 o'clock (0, 5)
Step-by-step explanation:
Given that diameter of clock = 10 units
We know that:
[tex]Radius =\dfrac{Diameter}{2}[/tex]
Radius = 5 units
The length of face will be equal to radius of clock i.e.
Length of face = 5 units
For the question, we need to visualize the clock time 3 o'clock, 6 o'clock, 9 o'clock and 12 o'clock on the coordinate xy axis.
Please refer to the attached graph to have a better understanding.
In every 3 hours the face will move [tex]90^\circ[/tex] i.e. one quadrant as per the location of clock faces.
At 3 o'clock the face will be on the positive x axis.
So coordinate (5, 0)
At 6 o'clock the face will be on the negative y axis.
So coordinate (0, -5)
At 9 o'clock the face will be on the negative x axis.
So coordinate (-5, 0)
At 12 o'clock the face will be on the positive y axis.
So coordinate (0, 5)
So, the answer is:
3 o'clock (5, 0)
6 o'clock (0, -5)
9 o'clock (-5, 0)
12 o'clock (0, 5)
Answer:
12 o'clock (0,5)
3 o'clock (5,0)
6 o'clock (0,-5)
9 o'clock (-5, 0)
Step-by-step explanation:
This recipe makes 6 portions of potato soup. Richard follows the recipe but wants to make 18 portions. Complete the amounts of each ingredient that he needs. Recipe: Serves 6 60 ml oil 80 g onions 450 g potatoes 600 ml milk
Answer:
1080 ml oil
240 g onions
1350 g potatoes
1800 ml milk
Step-by-step explanation:
18 ÷ 6 = 3
every ingredient x 3
60 x 6 = 360 , 360 x 3 = 1080 ml oil
80 x 3 = 240 g onions
450 x 3 = 1350 g potatoes
600 x 3 = 1800 ml milk
Can someone help me out with these math questions?
You can pick one to answer or chose to answer both!
I’d appreciate the help thank you!
On piece of paper, graph f(x) =5• (0.4)^x
Answer:
When we use a graphing calc, we should see that we get A as our best choice.
Step-by-step explanation:
HELP ME PLEASE PLEASE
Answer:
x=0 , y=4
Step-by-step explanation:
3x - 3y = -12 - eq1
4x + 3y = 12 - eq 2
Add eq 1 and 2
3x - 3y + 4x +3y = -12 + 12
7x = 0
x = 0
By substituting the value of x in eq 2
4x + 3y = 12
4(0) + 3y = 12
3y = 12
y = 12 / 3
y = 4
Answer:
(x,y)=(24,-28)
Step-by-step explanation:
1. Multiply both sides by -1
3x+3y=-12
-4x-3y-=-12
2. Elimnate one variable by adding the equations
-x=-24
3. Change the signs
x=24
4. Susbstitue the value of x in the equation 3x+3y=-12
3 x 24 + 3 y = -12
y=-28
5. Check the solution by plugging in the values.
(x,y)=(24,-28)
Which expression is equivalent to
(a^8)^4?
O a^2
Oa^4
Oa^12
0a^32
Answer:
a^32
Step-by-step explanation:
Apply law of exponents.
(a^b)^c = a^(bc)
(a^8)^4 = a^(8 × 4)
= a^32
Find the least common multiple of x2 + 4x + 3 and x2 + 7x + 12.
Answer:
( x+1) (x+3) (x+4)
Two students have devised a dice game named “Sums” for their statistics class. The game consists of choosing to play odds or evens. Roll 2 3 4 5 6 7 8 9 10 11 12 P(roll) StartFraction 1 Over 36 EndFraction StartFraction 2 Over 36 EndFraction StartFraction 3 Over 36 EndFraction StartFraction 4 Over 36 EndFraction StartFraction 5 Over 36 EndFraction StartFraction 6 Over 36 EndFraction StartFraction 5 Over 36 EndFraction StartFraction 4 Over 36 EndFraction StartFraction 3 Over 36 EndFraction StartFraction 2 Over 36 EndFraction StartFraction 1 Over 36 EndFraction Each person takes turns rolling two dice. If the sum is odd, the person playing odds gets points equal to the sum of the roll. If the sum is even, the person playing evens gets points equal to the sum of the roll. Note that the points earned is independent of who is rolling the dice. If Jessica is challenged to a game of Sums, which statement below is accurate in every aspect in guiding her to the correct choice of choosing to play odds or evens? E(evens) will be more because there are more even numbers that result from rolling two dice. Therefore, Jessica should play evens. E(odds) will be more because the probability for each odd number being rolled is greater. Therefore, Jessica should play odds. E(evens) will be more because the value of the even numbers on the dice are more. Therefore, Jessica should play evens. E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Answer:
(D)E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Step-by-step explanation:
The table of the probability of rolling the sums is presented below.
[tex]\left\begin{array}{ccccccccccccc}$Roll&2&3&4&5&6&7&8&9&10&11&12\\\\$Prob&\frac{1}{36}&\frac{2}{36}&\frac{3}{36}&\frac{4}{36}&\frac{5}{36}&\frac{6}{36}&\frac{5}{36}&\frac{4}{36}&\frac{3}{36}&\frac{2}{36}&\frac{1}{36} \end{array}\right[/tex]
P(an even sum)
[tex]=\frac{1}{36}+\frac{3}{36}+\frac{5}{36}+\frac{5}{36}+\frac{3}{36}+\frac{1}{36} \\\\=\frac{18}{36}[/tex]
Therefore, P(an odd sum) [tex]=\frac{18}{36}[/tex]
Therefore, E(evens) = E(odds) because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
Answer:
D /Even-odds
Step-by-step explanation:
just took test on edge 2020
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 100 degrees and the low temperature of 70 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. Assume the next low is 24 hours later.
Answer:
The function for the outside temperature is represented by [tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex], where t is measured in hours.
Step-by-step explanation:
Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:
Amplitude
[tex]A = \frac{100\º-70\º}{2}[/tex]
[tex]A = 15\º[/tex]
Mean temperature
[tex]\bar T = \frac{70\º+100\º}{2}[/tex]
[tex]\bar T = 85\º[/tex]
Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:
[tex]T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right][/tex]
Where:
[tex]\bar T[/tex] - Mean temperature, measured in degrees.
[tex]A[/tex] - Amplitude, measured in degrees.
[tex]\tau[/tex] - Daily period, measured in hours.
[tex]t[/tex] - Time, measured in hours. (where t = 0 corresponds with 5 AM).
If [tex]\bar T = 85\º[/tex], [tex]A = 15\º[/tex] and [tex]\tau = 24\,h[/tex], the resulting function for the outside temperature is:
[tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex]
The definition of a “fair game” in probability is somewhat different than the idea of a “fair game”in sports. Explain how a game between two sports teams could be considered “fair” by a sports fan, but not be a “fair game” in terms of probabilities.
Answer:
A "fair game in probability is when all players have an equal chance of winning, while a fair game in sports means that the rules are the same for both teams. What this means is that sports fans might see a game as fair as everyone has to abide by the same rules, but in terms of probabilities it may not be fair as the chance for either team winning may not be equal.
PLZ HELP PLZ
I WOULD APPRECIATE IT PLZ
19 and 20
let given points be
(x1,y1)=(-3,-3)
and(x2,y2)=(3,1)
equation of given line ,
(y-y1)= ((y2-y1)/(x2-x1))×(x-x1)
therefore, 2x-3y+3=0.........(i)
comparing (i ) with ax+by+c=0 we get
a=2
b= -3
c=3
then the line parallel to (i) is
ax+by+k=0 where k = -bc
that is, 2x-3y+9=0 is the required equation
Answer:
19. y = 2/3x - 10/3
20. y = -3/2x - 4
Step-by-step explanation:
First off, we need to find the equation of the line shown. There are two coordinates given. The slope of the line is (1 - -3) / (3 - -3) = 4 / 6 = 2/3. The line obviously intersects the y-axis at -1, so the equation of the line is y = 2/3x - 1.
19. If a line were to be parallel to the given line, the line would have to have a slope of 2/3. So, we have y = 2/3x + b.
To solve for b, all you need to do is substitute the coordinates given, (2, -2), and solve.
-2 = (2/3) * 2 + b
b + 4/3 = -2
b = -6/3 - 4/3
b = -10/3.
So, the equation of the line is y = 2/3x - 10/3.
20. If a line were to be perpendicular to the given line, the line would have a slope that is the negative reciprocal of the given line's slope. The slope would be -3/2. So, we have y = -3/2x + b.
To solve for b, once again, put in the given coordinates, (-4, 2), and solve.
2 = (-3/2) * (-4) + b
b + 6 = 2
b = -4
So, the equation of the line is y = -3/2x - 4.
Hope this helps!
Please help with this ASAP!!1
Answer:
a. OM is congruent to ON.
Step-by-step explanation:
To use the HL Theorem, you must have a congruent hypotenuse and a congruent leg. In this case, you have two congruent hypotenuses. You just need to find two congruent legs.
a. OM is congruent to ON. This says that two legs are congruent, so this is your answer.
b. LM is congruent to ML. This does not help as it is saying a segment is the same as the same segment.
c. and d. Both of these use angle measurements, which does not help with the HL Theorem.
Hope this helps!