Answer:
− y ln (27) + ln (9x) = 0
Lily deposited $19 in a savings account that earns 1.3% simple interest. Which graph represents this scenario?
Answer:
the total amount (balance) after x years with a principal of $19 and with simple interest of 1.3% is given by:
balance(x) = 19(1+0.013x)
Calculate for two values of x (for example x=0, balance = 19(1+0)=$19
and choose the graph that fits both points.
Step-by-step explanation:
What is the median of the following set of measurements?
"22 kg, 24 kg, 28 kg, 19 kg, 27 kg",
The median of the measurements is kg.
Answer:
24 kg
Step-by-step explanation:
The median can be found by putting the numbers in order and then finding the middle value.
In order from least to greatest:
19, 22, 24, 27, 28
24 is the middle value
So, 24 kg is the median.
Answer:
24 kg
Step-by-step explanation:
The median is the number in the middle of the data set. To find the median, arrange the numbers from least to greatest, then locate the middle number.
1. Arrange the numbers from least to greatest
Numbers: 22 kg, 24 kg, 28 kg, 19 kg, 27 kg
Least to greatest: 19 kg, 22 kg, 24 kg, 27 kg, 28 kg
2. Locate the middle number
Cross one number off each end of the set until the middle is reached.
19 kg, 22 kg, 24 kg, 27 kg, 28 kg
Cross off 19 and 28
22 kg, 24 kg, 27 kg
Cross off 22 and 28
24 kg
The middle number has been reached.
median= 24 kg
The median of the measurements is 24 kilograms.
Two interior angles of a convex pentagon are right angles and the other three interior angles are congruent. in degrees, what is the measure of one of the three congruent interior angles?
Answer:
[tex]120^{0}[/tex]
Step-by-step explanation:
Given: pentagon (5 sided polygon), two interior angles = [tex]90^{0}[/tex] each, other three interior angles are congruent.
Sum of angles in a polygon = (n - 2) × [tex]180^{0}[/tex]
where n is the number of sides of the polygon.
For a pentagon, n = 5, so that;
Sum of angles in a pentagon = (5 - 2) × [tex]180^{0}[/tex]
= 3 × [tex]180^{0}[/tex]
= [tex]540^{0}[/tex]
Sum of angles in a pentagon is [tex]540^{0}[/tex].
Since two interior angles are right angle, the measure of one of its three congruent interior angles can be determined by;
[tex]540^{0}[/tex] - (2 × [tex]90^{0}[/tex]) = [tex]540^{0}[/tex] - [tex]180^{0}[/tex]
= [tex]360^{0}[/tex]
So that;
the measure of the interior angle = [tex]\frac{360^{0} }{3}[/tex]
= [tex]120^{0}[/tex]
The measure of one of its three congruent interior angles is [tex]120^{0}[/tex].
Find the value of a.
a = 18°
Step-by-step explanation:we have opposite angles =>
=> 6a + 11 = 2a + 83
6a - 2a = 83 - 11
4a = 72
a = 72 : 4
a = 18°
Find the number of four-digit numbers which are not divisible by 4?
Answer:
6750
Step-by-step explanation:
4 digit numbers are 1000,1001,1002,...,9999
let numbers=n
d=1001-1000=1
9999=1000+(n-1)1
9999-1000=n-1
8999+1=n
n=9000
now let us find the 4 digit numbers divisible by 4
4| 1000
______
| 250
4 |9999
_____
| 2499-3
9999-3=9996
so numbers are 1000,1004,1008,...,9996
a=1000
d=1004-1000=4
let N be number of terms
9996=1000+(N-1)4
9996-1000=(N-1)4
8996=(N-1)4
N-1=8996/4=2249
N=2249+1=2250
so number of 4 digit numbers not divisible by 4=9000-2250=6750
A circular hall has a hemispherical roof.
The greatest height is equal to the
inner diameter. If the capacity of
the hals is
the
floor is.
43510 m^3
then
area
of the
Answer:
Area=1,288.88m²
Step-by-step explanation:
A circular hall(big room) has a hemispherical roof.The greatest height is equal to the inner diameter.Find the area of the floor,given that the capacity of the hall is 43510 cubic meter
Solution
let
diameter = D
radius,r = D/2
Greatest height = D
height of cylindrical part (h)= D-r = r
radius of cylindrical part = r
area of floor = πr²
volume = volume of cylindrical part + volume of hemispherical part
= πr²h + 2/3 πr³
Recall h=r
volume = πr³ + 2/3 πr³
43510=5/3πr³
Make r the subject
r=3√(43510*3)/5π
=3√(130,530/15.7
=3√8,314.01
=20.26
Area of floor = πr²
=3.14*(20.26)²
=3.14*410.47
=1,288.88m²
can u help me ASAP. i need to know how to do it step by step
Answer:
19
Step-by-step explanation:
[tex]f(x) =4x^3-8x^2+ax+b[/tex] has a factor [tex]2x-1[/tex] and
when divided by [tex]x+2[/tex], remainder is 20.
To find:Remainder when divided by (x-1) ?
Solution:
[tex]2x-1[/tex] is a factor
[tex]2x - 1 = 0 \Rightarrow x = \frac{1}{2}[/tex] when we put this value of x to the function, it will become 0.
i.e.
[tex]\Rightarrow f(\dfrac{1}{2}) =0 =4\times (\dfrac{1}2)^3-8(\dfrac{1}2)^2+\dfrac{a}{2}+b=0\\\Rightarrow \dfrac{1}{2}-2+\dfrac{a}{2}+b=0\\\Rightarrow 1-4+a+2b=0\\\Rightarrow a +2b=3 ......(1)[/tex]
Remainder is 20 when f(x) is divided by [tex]x+2[/tex]
i.e.
[tex]f(-2) =20[/tex]
[tex]\Rightarrow f(-2) =20 =4\times (-2)^3-8(-2)^2-2a+b=20\\\Rightarrow -32-32-2a+b=20\\\Rightarrow -2a+b=84 ...... (2)[/tex]
Solving (1) and (2), Multiply equation (1) by 2 and adding to (2):
[tex]5b=6+84\\\Rightarrow b = \dfrac{90}{5} = \bold{18}[/tex]
By equation (1):
[tex]a+2(18) = 3\\\Rightarrow a = -33[/tex]
So, the equation becomes:
[tex]f(x) =4x^3-8x^2-33x+18[/tex]
[tex]\Rightarrow f(1) = 4(1) -8 (1) -33(1) +18 = \bold{19}[/tex]
So, when divided by (x-1), remainder will be 19.
What the correct answer now
Answer:
527.52 m²
Step-by-step explanation:
The surface area (A) of the cone is calculated as
A = area of base + curved area
= πr² + πrl ( r is the radius and l the slant height )
= 3.14 × 7² + 3.14 × 7 × 17
= 3.14 × 49 + 3.14 × 119
= 3.14(49 + 119)
= 3.14 × 168
= 527.52 m²
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Answer:
2/5
Step-by-step explanation:
First for the sum:
3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i
Now for the difference
9/5 - 1/5 i - (7/5 - 1/5 i)
= 9/5 - 1/5 i - 7/5 + 1/5 i
= 2/5 , which is the answer :)
The answer is 2/5.
To find the fraction bar in the box.
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given that:
First for the sum:
3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i
Now substract the sum,
9/5 - 1/5 i - (7/5 - 1/5 i)
= 9/5 - 1/5 i - 7/5 + 1/5 i
= 2/5
So, the answer is 2/5.
Learn more about fraction here:
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Please help me understand this number sequence
Answer:
Step-by-step explanation:
A=a(r)^t
a=1
time=2.5 hours=25/10 ×60=150 minutes
10t=150
t=150/10=15
[tex]A=1(2)^{15}=32,768[/tex]
Joey went for 15 auditions. Out of those 15 auditions, he got called back for 30% of them. Approximately how many did he get called back for?
Answer:
2
Step-by-step explanation:
Basically,
You just have to find 30% of 15...
So
The formula is...
BASE x PERCENT= AMOUNT
x times 0.3= 15
0.3/15=0.02
0.02 x 100= 2
So
Joey got called back for approximately 2 auditions.
Now considering the real world situation are there any restrictions or changes you need to make for your domain or range to fit the situation described above? If so adjust your graph to represent these changes. Considering the real situations above (Question D.)
Answer:
Ok, we have the function:
y = 2gb*x + 3gb
Where x is the number of streams that you did.
You know that for this function, in a math view, the domain and the range are the set of all real numbers.
(Actually the domain should be integers, but i guess that if you only stream a 0.3534 of a movie and then you quit it, here only consumed 0.3534*2gb, so we can allow x to be a real number)
But in a "real situation", there are some other restrictions:
Restrictions for x:
You can never have a negative value for x (because this has no sense)
So the first restriction is x ≥ 0.
Then, there should be a maximum value of x (you can not stream 4 million things in one month). Or A may be the number of streams that you can watch until you reach the monthly limit of Gbs.
Then the domain is:
0 ≤ x ≤ A.
Now, the minimum of the range is defined by the minimum in the domain:
When x = 0, we have:
y = 2*0 + 3gb
So the minimum value in the range is 3gb.
y ≥ 3gb
And then the maximum value of the range will be when x = A
y = 2Gb*A + 3Gb
3Gb ≤ y ≤ 2Gb*A + 3Gb
The solutions to (x + 3)^2- 4=0 are x = -1 and x = -5
True or false
Answer:
THE ANSWER WOULD BE TRUE MY FRIEND
20. A pool holds 1440 CUBIC feet of water, the aty
charges $). 15 per cubic meter of water
used now, much will it cost to fill the pool?
Complete question :
A pool holds 1440 cubic feet of water, the city charges $1.75 per cubic meter of water used.
How much will it cost to fill the pool?
Answer:
$71.36
Step-by-step explanation:
Amount charged per cubic meter = $1. 75
Total volume of pool = 1440 ft^3
Using the conversion unit chart :
1 cubic meter = 35.3147 cubic foot
Then we can express the capacity of water held by the pool in cubic metre.
If 1 cubic meter = 35.3147 cubic foot
Then ;
y cubic meter = 1440 cubic foot
y = 1440/35.3147
y = 40.776220 cubic meter
Thus;
Cost of filling the pool will be;
$1.75 × 40.776220
= $71.358386
= $71.36
How would I simplify 14.8+6.25+0.97
Answer:
22.02
Step-by-step explanation:
14.8+6.25+0.97 is 22.02
don't know what you mean by simplify
can someone please help me with this !!
Answer:
x=3
Step-by-step explanation:
5/2 ( 3x-1) = 20
Multiply each side by 2/5
2/5 ( 5/2 ( 3x-1) )= 20 *2/5
3x-1 = 8
Add 1 to each side
3x-1+1 = 8+1
3x = 9
Divide each side by 3
3x/3 = 9/3
x =3
what is 136 1/50% of 231
Answer:
Step-by-step explanation:
136 1/50 % of 231 = 6801/50 % * 231
[tex]=\frac{6801}{50*100}*231\\\\\\=\frac{1571031}{5000}[/tex]
= 314.2062
the 15 chihuahua puppies ate 63 cups of food last week if each puppy ate the same amount of food how many cups of puppy food did each puppy eat
Answer: 4.2 cups
Step-by-step explanation: 63 divided by 15=4.2
HELP ASAP
Points $A(-1, -2)$ and $B(3, 2)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of $\pi$.
Answer:
8π units²
Step-by-step explanation:
center=((-1+3)/2,(-2+2)/2)=(1,0)
[tex]radius~r=\sqrt{(3-1)^2+(2-0)^2} =\sqrt{4+4} =\sqrt{8} \\area~of~circle=\pi r^2=\pi \times (\sqrt{8} )^2=8\pi ~square~units.[/tex]
please solve this question.
[tex]\left(\dfrac{1}{1+2i}+\dfrac{3}{1-i}\right)\left(\dfrac{3-2i}{1+3i}\right)=\\\\\left(\dfrac{1-2i}{(1+2i)(1-2i)}+\dfrac{3(1+i)}{(1-i)(1+i)}\right)\left(\dfrac{(3-2i)(1-3i)}{(1+3i)(1-3i)}\right)=\\\\\left(\dfrac{1-2i}{1+4}+\dfrac{3+3i}{1+1}\right)\left(\dfrac{3-9i-2i-6}{1+9}\right)=\\\\\left(\dfrac{1-2i}{5}+\dfrac{3+3i}{2}\right)\left(\dfrac{-3-11i}{10}\right)=\\\\\left(\dfrac{2(1-2i)}{10}+\dfrac{5(3+3i)}{10}\right)\left(\dfrac{-3-11i}{10}\right)=[/tex]
[tex]\dfrac{2-4i+15+15i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{17+11i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{-51-187i-33i+121}{100}=\\\\\dfrac{70-220i}{100}=\\\\\dfrac{70}{100}-\dfrac{220i}{100}=\\\\\boxed{\dfrac{7}{10}-\dfrac{11}{5}i}[/tex]
the points (-2,1), (1,1), (0,-2), and (-3,-2) are vertices of a polygon. what type of polygon is formed by these points? A. rectangle B. square C. pentagon D. parallelogram
Answer:
[tex]\boxed{\sf D. \ Parallelogram}[/tex]
Step-by-step explanation:
When we graph the points, the polygon is a quadrilateral with opposite parallel sides. The type of polygon formed by these points is a parallelogram.
Answer:
Parallelogram
Step-by-step explanation:
We'll graph all of the points from which we'll come to know that it is a parallelogram having opposite sides equal and parallel.
See the attached file for more understanding.
12. Solve the systems of linear equations using the substitution method.
x=y - 2
4y = x + 23
Answer:
x=5 and y=7
Step-by-step explanation:
x + 2 = y (equation 1)
x + 23 = 4y (equation 2)
(equation 2) - (equation 1)
This gives,21 = 3y
y = 21/3
y = 7.
Put y = 7 into equation 1 to find x
x + 2 = 7
x = 7 - 2
x = 5.
what is the solution to the equation below log5(2x-3)=2
Answer:
14
Step-by-step explanation:
I just got it correct on a.p.e.x :)
The solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14
How to determine the solution?The equation is given as:
[tex]\log_5(2x - 3) = 2[/tex]
Convert the equation to an exponential equation
2x - 3 = 5^2
Evaluate the exponent
2x - 3 = 25
Add 3 to both sides
2x = 28
Divide both sides by 2
x = 14
Hence, the solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14
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Ссппер
What is the image of (7, -2) after a reflection over the line y = -x?
Answer:
(2, -7)
Step-by-step explanation:
PLEASE help me solve this question! This is really URGENT! No nonsense answers please.
Answer:
[tex]\boxed{\sf 6.4 \ seconds}[/tex]
Step-by-step explanation:
t = time (s) ⇒ ?
d = distance falling (m) ⇒ 200 (m)
a = acceleration due to gravity ⇒ 9.8 (m/s²)
The time in seconds is not given. Solve for time using the formula.
[tex]t=\sqrt{\frac{2(200)}{9.8} }[/tex]
[tex]t=\sqrt{\frac{400}{9.8} }[/tex]
[tex]t= 6.388766...[/tex]
Round answer to nearest tenth of a second.
[tex]t \approx 6.4[/tex]
Simplify the following expression -10x + 10x
Answer:
0
Step-by-step explanation:
the x after the 10 is literally just 1
so 10 x 1 =10
-10 + 10 = 0
Find the value of a.
3a-9=15
Answer:
a = 8Step-by-step explanation:
3a - 9= 15
To solve the equation send the constants to the right side of the equation
That's
3a = 15 + 9
simplify
3a = 24
Divide both sides by 3
[tex]\frac{3a}{3} = \frac{24}{3}[/tex]
The final answer is
a = 8
Hope this helps you
Answer:
a = 8
Explanation:
Step One - Add nine to both sides of the equation. This is the first step is to isolate the variable, a. This step will remove the negative nine from the equation.
3a - 9 = 15
3a - 9 + 9 = 15 + 9
3a = 24
Step 2 - Divide both sides of the equation by three. This is the last step to isolate the variable, a.
3a = 24
3a/3 = 24/3
a = 8
Since we have fully isolated the variable, a, we have determined its value.
Therefore, in the equation 3a - 9 = 15 the value of the variable is a = 8.
Find all solutions to the following equation
Answer:
x = -1
Step-by-step explanation:
-2/ ( x * (x+2)) = ( x+3) / ( x+2)
Using cross products
-2 ( x+2) = ( x+3) x* (x+2)
Divide each side by (x+2) This means x cannot equal -2 because we are dividing by 0
-2 = x ( x+3)
Distribute
-2 = x^2 +3x
Add 2 to each side
0 = x^2 + 3x+2
Factor
0 = ( x+2) (x+1)
Using the zero product property
x+2 = 0 x+1 = 0
x = -2 x = -1
But above we said x cannot equal -2
so x = -1
The solution we said x cannot equal -2so x = -1
Step-by-step explanation:
-2/ ( x * (x+2)) = ( x+3) / ( x+2)
Using cross products
-2 ( x+2) = ( x+3) x* (x+2)
Divide each side by (x+2) This means x cannot equal -2 because we are dividing by 0
-2 = x ( x+3)
Distribute
-2 = x^2 +3x
Add 2 to each side
0 = x^2 + 3x+2
Factor
0 = ( x+2) (x+1)
Using the zero product property
x+2 = 0 x+1 = 0
x = -2 x = -1
To learn more about : solution
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Mele earned scores of 75, 70, 92,95, and 97 points (a
total of 429 points) on the first 5 tests in Economics II
Solving which of the following equations for s gives
the score he needs to earn on the 6th test to average
exactly 85 points for all 6 tests?
+5=85
F. 429
G. 429
H. + 429
+5 = 85
= 85
J. S+429
= 85
6
K. S+ 429
85
100
Answer:
The equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is;
S + 429 = 85 × 6
Step-by-step explanation:
The parameters given are;
The scores earned by Mele on the first five test in Economics II are;
75, 70, 92, 95, and 97 points
The total test points = 429 points
Therefore, the score, S, Mele needs to earn on the 6th test for him to get an average of exactly 85 points for the 6 tests is found as follows;
From the definition of average, μ = (Sum of data values)/(Number of data)
Sum of data values = S + 429
The number of data = 5 test + 6th test = 6
μ = 85 = (S + 429)/6
Therefore;
S + 429 = 85 × 6
Therefore, the equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is S + 429 = 85 × 6.
Solve for x 1/4(32x-16)=6x
Answer:
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