Answer:
Exact Form: √13/13
Decimal Form: 0.27735009…
Step-by-step explanation:
Hence value of [tex]\sqrt{13}[/tex] = 0.22
What is rationalization?the act of seeking to justify or explain a behavior or attitude using logical explanations, even when these are insufficient.
How to solve?Given[tex]\frac{1}{\sqrt{13} }*\frac{\sqrt{13} }{\sqrt{13} }[/tex]
=[tex]\frac{\sqrt{13} }{13}[/tex]
=0.277
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Aviva deposited some amount of money at a 4% annual interest rate into her bank account. The money was left in the account for 18 months, and she did not make any more deposits.
If Aviva's money earned $240 interest after 18 months, how much money did she deposit into the account?
The amount of money that was deposited by Aviva into her bank account is $4,000.
Given the following data:
Interest rate = 4% = 0.04.Simple interest = $240.Time = 18 months.Conversion:
12 months = 1 year.
18 months = 1.5 year.
To determine the amount of money that was deposited by Aviva into her bank account:
How to calculate simple interest.Mathematically, simple interest is given by this formula:
[tex]I=PRT[/tex]
Where:
S.I is the simple interest.P is the principal or starting amount.R is the interest rate.T is the time measured in years.Substituting the given parameters into the formula, we have;
[tex]240=P \times 0.04 \times 1.5\\\\240=0.06P\\\\P=\frac{240}{0.06}[/tex]
P = $4,000.
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16: Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the Hyperbola y^2-16x^2=1.
Answer:
Foci [tex](0,\pm\frac{\sqrt{17}}{4})[/tex]
Vertices:[tex](0,\pm 1)[/tex]
Eccentricity, e=[tex]\frac{\sqrt{17}}{4}[/tex]
Length of latus rectum=[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
We are given that
[tex]y^2-16x^2=1[/tex]
[tex]y^2-\frac{x^2}{(\frac{1}{4})^2}=1[/tex]
The equation of hyperbola is along y-axis because y is positive
Compare the equation with
[tex]y^2/a^2-x^2/b^2=1[/tex] (Along y-axis)
We get
a=1, b=1/4
[tex]a^2+b^2=c^2[/tex]
[tex]1+\frac{1}{16}=c^2[/tex]
[tex]\frac{16+1}{16}=c^2[/tex]
[tex]c^2=\frac{17}{16}[/tex]
[tex]c=\pm \frac{\sqrt{17}}{4}[/tex]
Therefore,
The coordinates of foci=[tex](0,\pm c)=(0,\pm\frac{\sqrt{17}}{4})[/tex]
The coordinated of vertices=[tex](0,\pm a)=(0,\pm 1)[/tex]
Eccentricity, e=c/a
[tex]e=\frac{\frac{\sqrt{17}}{4}}{1}=\frac{\sqrt{17}}{4}[/tex]
Length of latus rectum=[tex]\frac{2b^2}{a}[/tex]
Length of latus rectum=[tex]2\times \frac{1}{16}=\frac{1}{8}[/tex]
Is the following function discrete, continuous, or neither?
continuous function
is correct :D
Choose the most convenient method to graph the line 2x+5y=−10.
Answer:
graph the line using the slope and y-intercept or two points
slope:-2/5
y-intercept:(0,-2)
x | y
-5 | 0
0 | -2
If f(x)=5x – 2 then what is the value of (8)?
Solve the equation x2 = 400.
Answer:
200
Step-by-step explanation:
400/2 = 200
A random sample of 10 subjects have weights with a standard deviation of 11.0995 kg. What is the variance of their weights?
Answer:
[tex]123.19890025 kg^2[/tex]
Step-by-step explanation:
We are given that
Standard deviation, s=11.0995 kg
Sample size, n=10
We have to find the variance of their weights.
We know that
Variance=[tex](standard\;deviation)^2[/tex]
Using the formula
The variance of their weights
=[tex](11.0995)^2[/tex]
=[tex]123.19890025 kg^2[/tex]
Hence, the variance of their weights=[tex]123.19890025 kg^2[/tex]
find the length of side x in simplest radical form with a rational denominator 60 30 x 2
Answer:
x = √3
Step-by-step explanation:
Looking at the given triangle,
x is the adjacent side while 2 represents the hypotenuse side.
Now, from trigonometric ratios, we know that;
Adjacent/hypotenuse = cos θ
The angle here will be 30°
Thus;
x/2 = cos 30°
We are told to find x in simplest radical form with a rational denominator.
Thus means we will use the surf value of the angle.
cos 30° in surd form = (√3)/2
Thus;
x/2 = (√3)/2
x = 2 × (√3)/2
x = (√3)/1
x = √3
Find 142.8% of 461. Round to the nearest tenth.
Answer:
660
brainliest???????????
Step-by-step explanation:
Answer:
660
Step-by-step explanation:
142.8% * 461 = 1.428 * 461 = 658.308.
Rounding 658.308 to the nearest 10th, we get:
660
Pls helppls if u can
Answer:
C
Step-by-step explanation:
The value of a boat is $36,450. It loses 10% of its value every year. Find the approximate monthly percent decrease in value. Round your answer to the nearest hundredth of a percent.
Answer:
$300 because $36,450 X 0.10 is equals to $3,645 divided by 12months is equals to $303.75
round off by the nearest hundred is $300.
each side of a triangle is nine inches long. find the perimeter
The triangle in which the side are nine inches long has a perimeter of 27 inches.
Perimeter of a triangle
The perimeter of a triangle is the sum of the length of the whole side.
The triangle have three sides and the perimeter is the sum of the whole sides.
According to the question, the triangle has the whole sides as 9 inches.
This means the triangle is an equilateral triangle.
Therefore,
length of side = 9 inches
perimeter = 9 + 9 + 9
perimeter = 27 inches
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If I am rotating a figure counterclockwise, then it will move in the SAME DIRECTION as the hand of a clock. True or Fasle
Answer:
false
Step-by-step explanation:
when you move COUNTERclockwise, you go in the opposite direction that a clock goes, so you would go to the left instead of the right
Drag each label to the correct location on the table. Not all labels will be used.
The perimeter of base DHGC is 30 inches, and the perimeter of base SWVR is 20 inches. Complete the table with the ratios of the heights, surface
areas, and volumes of these two similar rectangular prisms. Assume the ratios are written in the form figure 1 : figure 2.
Figure 1
E
F
Figure 2
T
U
A
B
P
Q
H
G
w
V
S
R
Answer:
Ratio of Heights: (3/2)
Ratio of Surface Areas: (9/4)
Ratio of volumes: (27/8)
Step-by-step explanation:
here’s the correct answer for you I got it right :)
Item 25
Thompson Family Assets and Liabilities
Assets Value Liabilities Value
Checking and Savings $1,520 Auto Loan $5,238
Automobile $9,250 Credit Cards $580
House Value $112,340 Mortgage $78,570
Furniture,etc. $12,800 Other Loans $13,780
What are the Thompson family's total assets?
$13,345
$135,910
$140,291
$145,782
Answer:
135,910
Step-by-step explanation:
Add all assets together and you will get this answer.
plz help!!! i’ll mark brainliest!!!
Answer:
24 ft
Step-by-step explanation:
please help me out thank you.
Answer:
the answer is D {-5, -13}
giving brainliest!!!! please help!!
Answer:
{4, 5 }
Step-by-step explanation:
Solve the inequality
n + 1 > 4 ( subtract 1 from both sides )
n > 3
The set of values that make the inequality true is { 4, 5 }
Can somebody plz help answer these questions correctly (like what the letters equal/answers thanks :3
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DD
Answer:
12 X=2.2
13. y = 6.4
14. m= 8.5
15. z=9.9
16. n= 18.4
17. X= 5.8
Sasha is collecting cans to recycle. When she collected 180 cans she knew she had reached 60% of her goal. How many more cans does Sasha need to collect to reach her goal?
Sasha needs to collect 120 more cans to reach her goal.
let us say the total goal is 100x
it is given that
when she collected 180 cans she knew she had reached 60% of her goal.
what is the percentage?it is made up of two words 'per' and 'cent' means it is the value out of a hundred.
60% of 100x= 60x
60x = 180(given)
x=3
total goal = 100x= 100*3=300
total goal left= 300-180=120
therefore, Sasha needs to collect 120 more cans to reach her goal.
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help me please??????
Annie was earning $12.50 per hour at her job. She recently received a 10% raise. She has also decided she will put 1/5 of her new salary in savings. If Annie worked 40 hours in one week, how much is she putting into savings each week?
Answer:
$110
Step-by-step explanation:
Here are some points. What are the coordinates of G, H, and I after a rotation about the origin 90 degrees clock-wise?
Answer:
[tex]G' = (3,1)[/tex]
[tex]H' = (-4,0)[/tex]
[tex]I' = (-2,-3)[/tex]
Step-by-step explanation:
Given
See attachment for points G, H and E
Rotation: 90 degrees clock-wise
Required
Determine the coordinates after rotation
From the attachment:
[tex]G = (-1,3)[/tex]
[tex]H = (0,-4)[/tex]
[tex]I = (3,-2)[/tex]
When a point (x,y) is rotated 90 degrees clockwise, the new point is: (y,-x)
So, we have:
[tex]G = (-1,3)[/tex]
[tex]G' = (3,1)[/tex]
[tex]H = (0,-4)[/tex]
[tex]H' = (-4,0)[/tex]
[tex]I = (3,-2)[/tex]
[tex]I' = (-2,-3)[/tex]
Which set of angles can form a triangle?
Carlos bought 515 Euros for his holiday to Germany. He spent £412 to obtain these Euros.
Write the ratio of pounds to Euros in the form 1: n.
Answer:
412:515
Step-by-step explanation:
Given data
Carlos bought 515 Euros
He spent £412
We want to find the ratio of the purchase to the amount spent
In the form 1:n
We have our ratio of pound to euros has
412:515
In one hour a machine can make
500 nuts
or
840 bolts.
At 2 pm the machine starts working.
It makes 750 nuts and then changes to making bolts.
How many bolts will the machine make by 8.00 pm?
Answer:
3780 bolts will be made by 8pm
Step-by-step explanation:
One Hour : 500 nuts or 840 bolts
Divide by 2
30 minutes : 250 nuts or 420 bolts
750 nuts : 500 + 250 = 750
so the machine took 1 hour and 30minutes
14:00 it started (2pm)
15:30 it switched to bolts
20:00 (8pm)
4 hours and 30minutes to get to 8pm
840 × 4 = 3360 bolts + 420 bolts = 3780 bolts was made
Solve the following systems of equations by any method.
1. 2y - 4 = 0
x + 2y = 5
Answer:
pemdas
Step-by-step explanation:
PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Please help!! Algebra 1
The value of a home in 2015 was $400,000. Its value has been doubling each decade.
1. If v is the value of the home, in dollars, write an equation for v in terms of d, the number of decades since 2015.
Complete the equation below
v = _______________
Use d as your variable.
Use the ^ symbol to represent an exponent.
For example: 52 should be typed as 5^2
Answer:
[tex]v = 400000(2^\wedge d)[/tex]
Step-by-step explanation:
Given
[tex]Initial\ Value = \$400000[/tex]
[tex]Rate = doubles[/tex] per decade
Required
Determine the equation of the function
The information given shows that the function is exponential and will be calculated using:
[tex]v = ab^d[/tex]
Where:
a = Initial Value = 400000
b = rate = 2
d = number of decades
v = the current value of the home
So, we have:
[tex]v = 400000* 2^\wedge d[/tex]
[tex]v = 400000(2^\wedge d)[/tex]
The equation that represents the value of the home is v = $400,00(2^d).
What is the equation that represents the value of the home?
The home is appreciating in value. This means that the price of the house is increasing with the passage of time.
The formula that can be used to represent the appreciation is:
FV = P (1 + r)^n
FV = Future value P = Present value R = interest rate N = number of yearsv = $400,000(2^d)
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A recipe for rice and lentils calls for 1 L of broth for every 250 g of lentils
and 250 g of rice.
How much rice do you need if you use 2.5 L of broth?
8. Can Sandra claim Debbie as a qualifying relative on her 2019 return? a. Yes, because Debbie lived with Sandra as a member of her household for all of 2019. b. No, because Debbie had gross income of more than $4,200 during the tax year.
Answer:
b. No, because Debbie had gross income of more than $4,200 during the tax year.
Step-by-step explanation:
Qualifying relative refers to the person those who meet the five of the requirements of the Internal revenue Service or the IRS. They are :
-- The person is not a qualifying child.
-- Individual must be a citizen of U.S., Canada or Mexico or alien resident of the USA.
-- The person should be a relative of the tax payer for a complete and has a relationship with the tax payer which is either by blood or by donation.
-- The tax payer should be supporting a higher than half of the expenses of the person.
-- Individual must have less than a gross income of 4,200 dollar in the year 2019.
Since, gross income is 18,250 dollar of Debbie and therefore she is not a qualifying relative.