Answer:
$25,626.53
Step-by-step explanation:
You are going to want to use the compound interest formula, which is shown below.
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 8.5% into a decimal:
8.5% -> -> 0.085
Now lets plug in the values into the equation
Lastly, subtract the total from the initial balance:
Michelle earned $25,626.53 in interest.
Find the surface area of the solid figure
Answer:
150
Step-by-step explanation:
area of your base (bh/2) 3x8/2 = 12
2 bases = 24
3 faces ---- Face1 - 7x5= 35 ------Face2 - 7x5 = 35 ------Face3 - 8x7 = 56
24 + 35 + 35 + 56 = 150
The terminal side of an angle measuring StartFraction pi Over 6 EndFraction radians intersects the unit circle at what point?.
Thee intersection point of the terminal side which measure the angle pi/6 radians is (0.886, 0.5).
What is the meaning of a circle?A circle is a special type of ellipse in which the eccentricity is zero and the two foci are coincident.
The distance from the center to the circumference is called the radius of the circle.
Given that the terminal side of an angle measuring π/6 radians.
The coordinate point on the circle has to be find out It is known that, the formula for the coordinate is given by
x = r cos∅ and y = r sin∅
Let the r be unity.
Then, x will be
[tex]x=\frac{\pi }{6} \\x=cos(\frac{\pi }{6}) \\\x=0.866[/tex]
The variable y will be
[tex]y=sin\frac{\pi }{6}[/tex]
y=0.5
Thus, the intersection point is (0.886, 0.5).
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1) Find the slope of the line
2) find the slope between the two points
help please, thank you
Answer:
1 = 3/2
2 = -1/14
Step-by-step explanation:
The equation for the slope of a line is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] (difference in Y divided by the difference in X) or simply just Rise/Run.
For the first one, we have to pinpoint two points on the graph. There's one point placed on the x-axis 2 units away from the origin (2,0) and one four units to the right and 3 units up from the origin (4,3). Since it's on a graph, the easiest way to calculate it is by counting the units up and then right from (2,0) to (4,3). You can count that (4,3) is 3 units up and 2 units right from (2,0). Since slope is Rise/Run, the slope is 3/2.
For the second one, you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. The Y of the second point is 2, and the Y of the first point is 1. The X of the second point is -17, and the X of the first point is -3.
You can plug all 4 numbers in to get (2-1)/(-17- -3)
2-1 = 1 and -17 - -3 = -14. So your slope is 1/-14 or -1/14.
Evaluate the triple integral. X dv, where e is bounded by the paraboloid x = 4y2 4z2 and the plane x = 4. E
The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762
Parabloid, x = 4y² + 4z²
plane x = 4
x = 4y² + 4z²
x = 4
4 = 4y² + 4z²
4 = 4 (y² + z² )
1 = y² + z²
from polar coordinates
y = r cos θ
z = r sin θ
r² = y² + z²
The limits of the integral0 ≤ θ ≤ 2π
4r² ≤ x ≤ 4
0 ≤ r ≤ 1
[tex]\int\limits\int\limits\int\limits {x} \, dV = \int\limits^1_0\int\limits^a_b\int\limits^c_d {x} \, dx ( rdrdz)[/tex]
where
a = 4
b = 4r²
c = 2r
d = 0
The first integral using limits c and d gives:
[tex]2pi\int\limits^1_0\int\limits^a_b {xr} \, dx[/tex]
The second integral using limits a and b
[tex]pi\int\limits^1_0 {16 } } \, rdr - pi\int\limits^1_0 {16r^{5} \, dx[/tex]
[tex]16pi\int\limits^1_0 { } } \, rdr - 16pi\int\limits^1_0 {r^{5} \, dx[/tex]
[tex]16pi\int\limits^1_0 { } } \, [r-r^{5}]dr[/tex]
The third integral using limits 1 and 0 gives: 16.762
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The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762
What is integration?Integration is defined as adding small parts to form a new significant part.
Parabloid, x = 4y² + 4z²
plane x = 4
x = 4y² + 4z²
x = 4
4 = 4y² + 4z²
4 = 4 (y² + z² )
1 = y² + z²
from polar coordinates
y = r cos θ
z = r sin θ
r² = y² + z²
The limits of the integral
0 ≤ θ ≤ 2π
4r² ≤ x ≤ 4
0 ≤ r ≤ 1
[tex]\int\int\intxdV = \int_0_1\int_b_a\int_d_cxdx(rdrdz)[/tex]
where
a = 4
b = 4r²
c = 2r
d = 0
The first integral using limits c and d gives:
[tex]2\pi\int_0^1\int_b^axydx[/tex]
The second integral using limits a and b
[tex]\pi \int_0^116rdr-\pi\int_0^116r^5dx[/tex]
[tex]16\pi \int_0^1rdr-16\pi\int_0^1 r^5dx[/tex]
[tex]16\pi\int_0^1[r-r^5]dr[/tex]
The third integral using limits 1 and 0 gives: 16.762
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On Thursday the cows at the Putnam Dairy produced 70 bottles of milk. Friday, the cows produced 5/8 as much milk as on Thursday. How many bottles of milk did the cows produce on Friday?
What is the surface area of each figure 11 m 7 m 6 m?
Answer:
hi, I'm glad to help! 185
Step-by-step explanation:
11*7=77
11*6=66
6*7=42
77+66+42=185
i need help with this
Answer:
A tangent to a circle is a straight line which touches the circle at only one point. Therefore, if [tex]x=2y+5[/tex] is a tangent of [tex]x^2+y^2=5[/tex] then there will be one point of intersection.
To find the point of intersection, substitute [tex]x=2y+5[/tex] into [tex]x^2+y^2=5[/tex] and solve for y:
[tex]\implies (2y+5)^2+y^2=5[/tex]
[tex]\implies 4y^2+20y+25+y^2=5[/tex]
[tex]\implies 5y^2+20y+20=0[/tex]
[tex]\implies y^2+4y+4=0[/tex]
[tex]\implies (y+2)^2=0[/tex]
[tex]\implies y+2=0[/tex]
[tex]\implies y=-2[/tex]
Substitute found value of y into [tex]x=2y+5[/tex] and solve for x:
[tex]\implies x=2(-2)+5=1[/tex]
Therefore, there is one point of intersection at (1, -2), thus proving that the straight line equation is a tangent to the circle.
A quantity with an initial value of 200 grows continuously at a rate of 4% per second.
What is the value of the quantity after 1.55 minutes, to the nearest hundredth?
The growth of the quantity is an illustration of an exponential function
The value of the quantity after 1.55 minutes is 76759.22
How to determine the amount of the quantity?The given parameters are:
Initial value, a = 2000
Rate, r = 4%
An exponential growth function is represented as:
y = a(1 + r)^x
Substitute the value in the equation
y = 2000(1 + 4%)^x
After 1.55 minuted, x = 1.55 * 60
So, we have:
y = 2000(1 + 4%)^(1.55 * 60)
Evaluate the expression
y = 76759.22
Hence, the value of the quantity after 1.55 minutes is 76759.22
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Answer:
Step-by-step explanation:
9398.61
Evaluate each expression using the order of operations
A:-4(-4+3)+2²
B:-3-3-3(-3)
C:-17+2(-2)(-2)
D:-(+2(-3)(5)(3+2)(-6)
Answer:
[A} 8
[B] 3
[C] -9
[D] - 900
Step-by-step explanation:
A:-4(-4+3)+2²
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]
[tex]-4\left(-1\right)+2^2[/tex]
[tex]-4\left(-1\right)+4[/tex]
[tex]4+4[/tex]
8
-------------------------------------------------------------------------------------------------------------
B:-3-3-3(-3)
[tex]Follow\:the\:PEMDAS\:order\:of\:operations[/tex]
[tex]-3-3-\left(-9\right)[/tex]
3
-------------------------------------------------------------------------------------------------------------
C:-17+2(-2)(-2)
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]
[tex]-17-\left(-8\right)[/tex]
-9
-------------------------------------------------------------------------------------------------------------
D:-(+2(-3)(5)(3+2)(-6)
[tex]Follow\:the\:PEMDAS\:order\:of\:operations[/tex]
-900
-------------------------------------------------------------------------------------------------------------
[RevyBreeze]
Answer the questions about the following polynomial. 1- x³/8
the expression represents a quadratic polynomial with 2 terms.The constant term is 1, the leading tern is x and the leading coefficient is 1
Solve the following equations and check your solution using substitution.
6 - 5x = 16
4 - 9x = -7
(BTW pls show your working out)
Answer: 1. [tex]x=-2[/tex]; 2. [tex]x=\frac{11}{9}[/tex]
Step-by-step explanation :
1.
[tex]6-5x=16\\6-5x-6=16-6\\-5x=10\\\frac{-5x}{-5}=\frac{10}{-5}\\x=-2[/tex]
2.
[tex]4-9x=-7\\4-9x-4=-7-4\\-9x=-11\\\frac{-9x}{-9}=\frac{-11}{-9}\\x=\frac{11}{9}[/tex]
Answer:
Q1) x =2 Q2) x = 11/9
Step-by-step explanation:
Q1) 6 - 5x = 16 check : -5(2) = -10
-6 -6 6 -- 10 = 6+ 10 = 16
-5x = 10 Q2) 4 - 9x = -7
-x = -2 -4 -4
x = 2 -9x = - 11
-------------- -x = -11 /9 -----> x = 11/9
A teacher used the change of base formula to determine whether the equation below is correct. (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = 3 Which statement explains whether the equation is correct? The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log (2 times 10) times log (4 times 8) times log (10 times 4). = log (20) times log (32) times log (40). =3 The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 3 The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 4. The equation is not correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log StartFraction 10 Over 2 EndFraction times log eight-fourths times log four-tenths. = log 5 times log 2 times log 0. 4. = negative 0. 8.
The solution to the problem is correct and the correct option from the given options is B.
What is Logarithm?A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c =b[/tex]
can be written as
[tex]\rm{log_ab=c[/tex]
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.
The given logarithmic problem can be solved in the following manner, therefore,
[tex]\rm log_210\ log_48\ log_{10}4\\\\[/tex]
Using the logarithmic properties, we can write,
[tex]=\rm \dfrac{log10}{log2}\cdot \dfrac{log8}{log4}\cdot \dfrac{log4}{log10}\\\\[/tex]
Now cancelling out the values we will get,
[tex]=\rm \dfrac{log2^3}{log2}\\\\=\rm \dfrac{3log2}{log2}\\\\= 3[/tex]
Thus, the solution to the problem is correct and the correct option from the given options is B.
Learn more about Logarithm:
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Answer:
B
Step-by-step explanation:
on edge
please help me with complement or supplement of an angles.
In the figure below, =m∠263°. Find m∠1.
Answer:
117
Step-by-step explanation:
This is an example of a supplementary angle, so in total it is 180 degrees. Subtract what we know angle 2 is, 63, and we are left with what angle 1 equals, which is 117.
Hope this helps! pls mark brainliest
At a concession stand 6 hot dogs cost $6.72. At this rate, how much would 8 hot dogs cost, in dollars and cents?
Answer:
$8.96
Step-by-step explanation:
Since 6 hot dogs are $6.72, 1 hot dog would be that divided by 6, which is $1.12. Now we want the cost of 8 of those hot dogs, so we have to multiply by 8. Hence the answer is $1.12 * 8 = $8.96.
1. Find the Area of the Sector:
2. Find the length of the missing side:
Answer:
1) 14.137 2)10
Step-by-step explanation:
area of sector is central angle / 360 times (pi)(r^2)
45/360 x pi (6^2)
1/8 x 36pi
14.137
3-4-5- right triangle. Or Pythagorean Theorem.
6^2 + 8^2 = c^2
c= 10
PLS HELP
A cone has a volume of 803.84 cubic millimeters and a radius of 8 millimeters. What is its height?
Use ≈ 3.14 and round your answer to the nearest hundredth.
h ≈
millimeters
Answer:
3.19 millimeter round of nearest hundred
A frequency generator sends a 550 Hz sound wave through both water and ice. A 3 column by 4 row table. Column 1 is titled Medium and includes the following entries: Ice, Water, Steam. Column 2 is titled Temperature (degrees Celsius) and includes the following entries: 0, 25, 100. Column 3 is titled Speed of Sound (meters per second) and includes the following entries: 3200 meters per second, 1500 meters per second, 346 meters per second. What is the difference in wavelength between the wave produced in ice and the wave produced in water? 2. 1 m 3. 1 m 5. 2 m 8. 5 m.
The difference in wavelength between the wave produced in ice and the wave produced in water is 3.1 m. Then the correct option is B.
What is wavelength?The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.
The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.
A frequency generator sends a 550 Hz sound wave through both water and ice.
The wavelength is given as
[tex]\lambda = \dfrac{v}{f}[/tex]
f = frequency
v = velocity
Then the wavelength in the water will be
[tex]\rm \lambda _w = \dfrac{1500}{550}\\\\\lambda _w = 2.73[/tex]
The wavelength in the ice will be
[tex]\rm \lambda _I = \dfrac{3200}{550}\\\\\lambda _I = 5.82[/tex]
Then the difference in wavelength between the wave produced in ice and the wave produced in water will be
[tex]\rightarrow \lambda _I - \lambda_w \\\\\rightarrow 5.82 - 2.73 \\\\\rightarrow 3.09 \approx 3.1[/tex]
Thus, the difference in wavelength between the wave produced in ice and the wave produced in water is 3.1 m.
More about the wavelength link is given below.
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Answer:
3.1
Step-by-step explanation:
B
how many solutions does 8B + 7v - 5 equals -11 + 15b
Answer: No solutions
- by graphing-
First I will simplify:
8B + 7v - 5 equals -11 + 15b
8b + 7v - 5 = -11 + 15b
7v = -6 + 15b
7v = -6 + 7b
Let's graph this and see what happens!
-> I will graph y = 7x and y = 7x - 6
-> See attached.
-> Since there are no points of intersection (they have the same slope), there is no solutions.
help please
on the image.
Answer:
the women won 1 fewer matches than the men
Step-by-step explanation:
In a pie chart, the fraction of the total that is represented by any sector is the ratio of the angle subtended by that sector to 360°.
__
For the men's team, the winning games represent 150°/360° = 5/12 of all games played. The men played 24 games, so they won ...
5/12 × 24 = 10 . . . . games won
__
For the women's team, the winning games represent 180°/360° = 1/2 of all games played. The women played 18 games, so they won ...
1/2 × 18 = 9 . . . . games won
The number of matches won by the men is larger than the number of matches won by the women. (Yes, the women won a larger fraction of their matches played, but not a larger number.)
Approximately how many grams of radium will remain after 4 grams have decayed for 2400 years
Answer:
1.4
Step-by-step explanation:
Does anyone know the answer?
Answer:
I think the answer must be c because the length is 6\5 feet so there no chances to be the answer is more than so the base is divited and the ft should be multiplied
find the rate of interest.
Rs.8800,T=3.5years,I=Rs.2618
Answer:
Rate is 8.5%
Step-by-step explanation:
Step 1: Write the given terms
Principal (p)=Rs8800
Rate(r)=?
Time(t)=3.5 years
Interest=Rs2618
Step 2: Write the formula for calculating Simple interest
[tex]i = \frac{prt}{100} [/tex]
Step 3: Make r the subject of the equation
[tex]by \: cross \: multiplication \\ 100i = prt \\ divide \: both \: sides \: by \: pt \\ r = \frac{100i}{pt} [/tex]
Step 4: Find the value of r by substituting the values in step 1
[tex]r = \frac{100 \times 2618}{8800 \times 3.5} \\ r = \frac{261800}{30800} \\ r = 8.5[/tex]
Hence, the rate is 8.5%
i need helppppppppppppppppppppppppppppppppppppppp
solve pls brainliest
Answer:
[tex] 1 \frac{2}{3}\: liters [/tex]
Step-by-step explanation:
[tex]V_{soda}[/tex] in one bottle = 5/9 liters
No of bottles = 3
Total volume of soda
[tex] = \frac{5}{9} \times 3 \\ \\ = \frac{5}{3} \\ \\ = 1 \frac{2}{3} \: liters[/tex]
a sphere and a cylinder have the same volume. each figure has a radius of 13. what is the height of the cylinder?
Answer:
V = 4/3 π R^3 volume of a sphere
V = π R^2 H volume of cylinder area of base X height
4/3 π R^3 = π R^2 H equal volumes
H = 4/3 R relationship of height to radius for cylinder
H = 4/3 * 13 = 52 / 3 cm = 17 1/3 cm
In a class of 25 pupils, if 15 are females. Calculate the ratio of males : total
Answer:
2:5
Step-by-step explanation:
15 are female. 10 must be male.
Out of 25 pupils, 10 are male, so it's 10:25, or 2:5
A car used 1/81 of a gallon of gas to drive 1/4 of a mile. At this rate, how many miles can the car travel using 1 gallon of gas? ??????????
Step-by-step explanation:
1/81 gallon for 1/4 mile.
what do I need to multiply 1/81 with to get 1 gallon ?
it is simple, right ? i need to multiply it by 81 to get 1 gallon.
in order to keep the relationship (ratio) unchanged, I need to multiply the other part (1/4 mile) with the same factor :
1/4 × 81 = 81/4 = 80/4 + 1/4 = 20 1/4 miles
so, at this rate, that car can travel 20 1/4 miles using 1 gallon of gas.
Write the quadratic equation whose roots are 1 and −5, and whose leading coefficient is 4.
Answer:
Standard Form: y = 4(x-1)(x+5)
Step-by-step explanation:
4 is the leading coefficient, so it should go in front. When making a standard quadratic equation, you must do the opposite for each of the roots (negative to positive, positive to negative.)
if you’re asking for a general form quadratic equation, then sorry, I am unable to help you with that :(
Marcy charges $3 to walk a small dog and $5 to walk a big dog. If Marcy walks 15 small dogs and 6 big dogs, how much money will she make?
Answer:
hee-hee!
Step-by-step explanation:
Marcy charges $3 to walk a small dog and $5 for a big dog.
She walks 15 small dogs and 6 big dogs.
We can use an expression that would show the problem:
3s + 5b
(s = small dogs & b = big dogs)
s = 15 | b = 6
3(15) + 5(6)
45 + 30 = 75
Marcy earns $75 of profit.
Amira decides to estimate the volume of an apple by modeling it as a sphere. She measures its circumference as 43.4 cm. Find the apples's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
The formula for the circumference of a circle (or a sphere) is [tex]2\pi r\\[/tex].
The formula the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex].
Assuming 43.4 includes the pi, we can do the equation [tex]43.4=2\pi r[/tex]
Solving the equation, we get [tex]\frac{43.4}{2\pi } =r[/tex]
Substituting r into the formua for the volume of a sphere, we get [tex]\frac{4}{3} *\pi *(\frac{43.4}{2\pi } )^3[/tex]
Solving the cube (probably with a calculator), we get [tex]\frac{4}{3} *\pi *\frac{81746.504}{8\pi ^3}[/tex]
It is a bit messy, but we can simplify further by cancelling out the pi's, which leaves us with [tex]\frac{4}{3} *\frac{81746.504}{8\pi ^2}[/tex].
With the butterfly method (or whatever you may call it), we can cancel out the 4 in the numerator and the 8 in the denominator, and multiply the 3 in the denominators.
Which gets us this: [tex]\frac{81746.504}{6\pi ^2}[/tex]
Using a calculator, we get our final answer of (about) 1380.44cm^3
This was very messy, I apologize if I did make any mistakes.