The summation that represents the money in the account 10 years after the initial deposit is P(10) = 300(1.055)^10
Exponential equationsExponential equations are equations that increase geometrically
The formula for calculating the compound. interest is expressed as:
P(t) = P0(1+r)^t
Given the following
P0 =. $300
r = 5.5% = 0.055
t = 10years
Substitute
P(10) = 300(1+0.055)^10
P(10) = 300(1.055)^10
Hence the summation that represents the money in the account 10 years after the initial deposit is P(10) = 300(1.055)^10
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Answer: D
Step-by-step explanation:
a regular hexagon has 18 sides calculate the size of each interior
Answer:
[tex]160[/tex] °
Step-by-step explanation:
An alternative method is to use the exterior angle.
the sum of the exterior angles is ALWAYS 360 °
So you can find the size of the exterior angles of a regular polygon quite easily:
If there are 18 sides ( n = 18 ) , then each exterior angle is:
[tex]\frac{360}{n} =\frac{360}{18} = 20[/tex]°
The sum of the exterior and interior angles is 180° because they are adjacent angles on a straight line.
∴ each interior angle is 180° - 20° = 160°
find the x- and y- intercepts. Write ordered pairs representing the points where the line crosses the axes. 2x+3y=6
The equation y = kx represents a proportional relationship between x and y, where k is the constant of proportionality. For a moving object, the equation d = st represents a proportional relationship between distance (d) and speed (s) or between distance (d) and time (t). Explain the different ways that you can define the constant of proportionality for this equation.
Answer:
Hello!!!
In this specific case the constant of proportionality is s (speed).
Step-by-step explanation:
The constant of proportionality stay "constant" (as the name suggests) in a certain case.
meaning, the speed itself remains constant at any given distance or time.
You can use the constant of proportionality and either distance or time to find the missing varliable since it remains constant.
you can also switch up the formula:
d=st
t=d/s
s=d/t
i really hope this helps!!!!!
Find the volume of the trapezoidal prism
Answer:
228 in³
Step-by-step explanation:
Volume of a trapezoidal prism
V = Area x heightFinding Base Area (on the side here)
A = 1/2 x (a + b) x hA = 1/2 x (12 + 7) x 6A = 3 x 19A = 57 in²Volume
V = A x hV = 57 x 4V = 228 in³In figure MNL, the value of x is:
Answer:
x=6
Step-by-step explanation:
Those are scalene triangles, if 9 is the base, then the other two sides will be congruent, so x=6.
The annual profits for a company are given in the following table, where x represents the number of years since 2002, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected profit (in thousands of dollars) for 2010, rounded to the nearest thousand dollars.
The equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
The line of best fit;
y = mx + c
m = 16.89
c = 134.95
y = 16.89x + 134.95
Plug x = 2010 - 2002 = 8
y = 16.89(8) + 134.95
y = $2700.07
Thus, the equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07
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Choose the values that would complete the general solution for y= arctan (0.7002).
(blank)+360k degrees
-215
-35
-145
-325
Answer:
-145°, -325°
Step-by-step explanation:
The principal value of the arctangent of 0.7002 is 35°. The tangent function is periodic with a period of 180°, so the general solution is ...
y = (35 +180k) degrees . . . . . where k is an integer
Values from the given list include ...
-145°
-325°
_____
Additional comment
+35° and +215° would also be part of the general solution
Vectors u, v, and w are shown in the graph. What are the magnitude and direction of u + v + w?
Magnitude and direction of u + v + w is equals to 57.871 and 19°.
What is vectors?"Vectors are those quantity of which represents both direction as well magnitude."
According to the question,
As shown in diagram we have,
u + v + w
= (wcos30°)[tex]\^{i}[/tex] + (wsin30°)[tex]\^{j}[/tex] +(vcos20°)[tex]\^{j}[/tex] - (vsin40°)[tex]\^{i}[/tex] -(ucos40°)[tex]\^{i}[/tex] -(usin40°)[tex]\^{j}[/tex]
= ( wcos30° - vsin40° - ucos40°)[tex]\^{i}[/tex] + (wsin30°+ vcos20° - usin40°)[tex]\^{j}[/tex]
Substitute the value of ║w║ = 40 ,║v║=60,and ║u║= 90 we get,
u + v +w
= ( 40cos30° - 60sin40° - 90cos40°)[tex]\^{i}[/tex] + (40sin30°+ 60cos20° - 90sin40°)[tex]\^{j}[/tex]
= (20√3 - 20.5212 - 68.9440)[tex]\^{i}[/tex] + ( 20 +56.3816 - 57.8509)[tex]\^{j}[/tex]
= ( -54.8242)[tex]\^{i}[/tex] + (18.5307)[tex]\^{j}[/tex]
Therefore,
Magnitude = √(-54.8242)² +(18.5307)²
=√3349.0798
= 57.8712
tanθ = ( 0.3380)
⇒θ = tan⁻¹ (0.3380)
= 18.67
≈ 19°
Hence, magnitude and direction of u + v + w is equals to 57.871 and 19°.
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help me please, will mark brainliest!
Step-by-step explanation:
remember (always remember) : a probability is desired cases divided by total possible cases.
what is our total here ?
1388 students at this school
what are our desired cases here ?
every student, who bikes to the school : 207
so, the probability that a randomly picked student is biking to the school is
207/1388 = 0.149135447...
so, b. is the right answer.
please let me know what is not clear to you.
we solved now many probability questions together, but this is very, VERY basic, and you could not do it.
so, what is not "clicking" with you ? what do you need explained ?
2. The total cost, , of apples at a farm stand is directly proportional to the number of pounds of apples purchased, p. If it costs $7 to buy 5 pounds of apples, how much would it cost to buy 9 pounds of apples? A. $3.89 C. $10.40 B. $6.42 D. $12.60
Answer:
D
Step-by-step explanation:
because it's simple add it up 7$/5 9$/12.60
Hey, could someone help me with this? If you could that would be great!
It's a 3 part question, this is the first part.
The quadratic function is f(x) = x^2 - 7.
I would like help on the third question...
Answer:
The correct answer should be C.
Step-by-step explanation:
A. is equal to x² -5.291503x +7
B. is equal to x² +5.291503x +7
C. is equal to x²2 -7
C. is the only one with a negative 7 since (-)(+)= -
Drag the tiles to the correct boxes to complete the pairs.
Match each division expression to its quotient.
16 divided by (-8). -2 2/5 divided by 4/5. 33/7 divided by 1 1/7. -12.2 divided by (-6.1)
Answer:
check explanation for answer
Step-by-step explanation:
16 ÷ -8 = -2
- 2 \frac{2}{5} ÷ \frac{4}{5} = -3
3 \frac{3}{7} ÷ \frac{1}{7} = 3
-12.2 ÷ -6.1 = 2
Am thinking of a number,l take away 3 the results is 14.what number is it
help please
What is e in math?
e is the Exponential Constant or Euler's Number.
It has a value of 2.718281828...
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
e to the n is given by:
[tex]\huge{e}^{n}= [\sum_{k=0}^{∞} (\frac{{n}^{k}}{k!})][/tex]
Find the perimeter of the shaded region. Round your answer to the nearest hundredth
Answer:
38 units
Step-by-step explanation:
13+13=26
6+6=12
26+12=38
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
The square root of the quantity 2 x minus 7 end quantity equals 1.
Answer:
Solve for x , 1x − 2+1x + 2=4(x − 2)(x + 2) .
1x − 2+1x + 2=4(x − 2)(x + 2)
(x − 2)(x + 2)(x − 2)+(x − 2)(x + 2)(x + 2)=4(x − 2)(x + 2)(x − 2)(x + 2)
(x−2)+(x+2)=4
2x=4
x=2
But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero--and division by zero is not allowed! . Therefore, it cannot be a root of the original equation. So, 2 is an extraneous solution. So, the equation has no solutions.
Step-by-step explanation:
An equal when substitute x = 4, the solution is not extraneous the solution x = 4 is valid for the original equation.
The equation is: √(2x - 7) = 1
Step 1: Square both sides of the equation to remove the square root:
(√(2x - 7))² = 1²
Simplify:
2x - 7 = 1
Step 2: Add 7 to both sides to isolate the term with "x":
2x - 7 + 7 = 1 + 7
Simplify:
2x = 8
Step 3: Divide both sides by 2 to solve for x:
2x / 2 = 8 / 2
Simplify:
x = 4
Now, we have found that the solution for x is 4.
To check if the solution is extraneous, we need to substitute the value of x back into the original equation and see if both sides are still equal:
Original equation: √(2x - 7) = 1
Substitute x = 4:
√(2(4) - 7) = 1
Simplify:
√(8 - 7) = 1
√1 = 1
1 = 1
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What is the y-intercept of the line 15 - 3y = x?
The y-intercept of the line 15 - 3y = x is ( 0 , 5 )
Sure hope this helps you
Define bisect and midpoint. Using constructions, draw and label an angle bisector and a perpendicular bisector. Show segment addition postulate and angle addition postulate with examples of solving for a variables
Bisect is a word that means to divide a thing, line or a circle into two parts. While midpoint is known as the middle point that exist in a line segment.
What is Angle addition postulate?This theory states that if two angles are said to be put beside each other, the resulting angle is said to be equal in terms of the sum of the two real angle measures.
Note therefore, that that Bisect is a word that means to divide a thing, line or a circle into two parts. While midpoint is known as the middle point that exist in a line segment.
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If a polynomial function f(x) has roots –9 and 7 – i, what must be a factor of f(x)? (x – (7 i)) (x – (–7 – i)) (x (7 i)) (x (7 – i))
if the roots of the polynomial function are -9 and 7 - i, then the other factor of the polynomial function is x - (7 + i)
How to determine the other factor?The roots of the polynomial function are given as:
-9 and 7 - i
The root is 7 - i is a complex number.
This means that its conjugate must also be a root of the factor.
The conjugate of 7 - i is 7 + i
So, we have:
x = 7 + i
Equate to 0
x - (7 + i) = 0
Hence, the other factor of the function is x - (7 + i)
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Answer:
A on edge 23
Step-by-step explanation:
trust me bro
What is the eighth term of the sequence below?
5, 9, 13, 17, …
A. 33
B. 30
C. 29
D. 34
Answer:
A. 33
Step-by-step explanation:
Add 4 to each number
1. 5 is your first number
2. 5+4= 9 is your second number
3. 9+4= 13 is your third number
4. 13+4= 17 ...
5. 17+4= 21 ...
6. 21+4= 25 ...
7.25+4= 29 ...
8.29+ 4= 33 is your eight number
Write 0.030 in scientific notation
Please help :)
i need help please on PART B Thanks
Answer:
(a) 1 and 8
(d) 64 and 125
Step-by-step explanation:
In addition to the cubes of 2 through 11 that you found in question 1, it is convenient to add 1³ = 1 to the list for the purpose of answering this question. The cubes of the first 11 integers are ...
1, 8, 27, 64, 125, 216, 343. 512, 729, 1000, 1331
__
This question is asking you to find the numbers on either side of any that are not on the list:
(a) 2 is between 1 and 8
(d) 100 is between 64 and 125
5x - 8y = - 17
y + 5 = 3x
To answer please type altogether with no spaces. For example if your answer is negative three positive four, type (-3,4)
Answer:
5x - 8y =17
y+5 =3x
Answer | (3,4)
Step-by-step explanation:
I used a calculator
There are three sets. A = {1,2,3}, B = {4,5} and C = {6,7,8}
What is the probability of A∩B∩C
The three sets are independent sets and the value of the probability of A∩B∩C is: 0
How to determine the probability?The sets are given as:
A = {1,2,3}, B = {4,5} and C = {6,7,8}
The total number of elements in the three sets is:
Total = 8
The number of elements of A∩B∩C is 0, because the sets do not have a common element.
So, the probability of A∩B∩C is:
P = 0/8
Evaluate
P = 0
Hence, the probability of A∩B∩C is: 0
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Select all the numbers that are rational
Answer:
-13/3
and the last 2
Step-by-step explanation:
The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. Every rational number can be written as a fraction a/b, where a and b are integers. For example, 3 can be written as 3/1, -0.175 can be written as -7/40, and 1 1/6 can be written as 7/6.
Two points of a parallelogram are (1,2) and (2,5). The base of the parallelogram is parallel to the x axis and is 4 units long. Find the coordinates of the other two points of this parallelogram and also find the length of the other pair of parallel sides of the parallelogrma. What would the area of this parallelogram be?
Answer:
(5,2) and (6,5)
length of side = sqrt10 ~= 3.16 units
Area = 12 sq units
Step-by-step explanation:
It really helps to graph the given information. See image. The sides have the same slope bc they are parallel. If you go UP3 & OVER1 to get from the first point to the second point, then do that again on the right side. See image. Use distance formula or pythagorean thm to find the length:
c^2 = 3^2 + 1^2
c^2 = 9+1
c^2 = 10
c = root10 ~= 3.16
Area of a parallelogram is b•h
A = 4•3
= 12
see image.
Consider the function f(x) = log x. Which two transformations can be used to move
the graph of f(x) to the graph of -f(x+4)?
Select all that apply
The parent function will translate 4 units to the left and reflect over the x-axis option (C) and (E) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = log x
First transformation:
Replace x → (x+4)
The parent function will shift left side by 4 units.
Second transformation:
Multiply the function with -1
The function will reflect over x-axis
The function becomes:
g(x) = -log(x+4)
Thus, the parent function will translate 4 units to the left and reflect over the x-axis option (C) and (E) are correct.
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Jorge earns $12 an hour. deductions
for taxes and insurance take 25% of
his earnings. which equation could be
solved to find jorge's take-home pay, p,
after h hours of work?
Answer:
%25 of $12 an hour = 3
Find the inverse of the function f(x) = 2x - 4.
O
8(x) = -1/x--1/4
O
8(x) = -x-1-1/
O g(x) = 4x + 2
O
1
g(x) = = x + 2
Answer:
y = 4 - x / 2
Step-by-step explanation:
y = 2x - 4
x = 2y - 4
y = 4 - x
----------
2
Kate is the captain of a large cruise ship. As she
drives the ship, she sits 50 meters above the sea.
Paul is the captain of a boat. He sits 15 meters
above the sea. If the radius of the earth is
6,371,000 meters, how much further can Kate see
across the horizon than Paul?
Kate can see across the horizon by 3.33 times further than Paul.
What is the shape of the horizon?The volume of the cone can be used to determine how far they can see across the horizon from the cone shape.
Using the volume of the cone
[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
For Kate:
Height (h) = 50 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}[/tex]
V = 2.12526863 × 10¹⁵ m³
For Paul
Height (h) = 15 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}[/tex]
V = 6.3758059 × 10¹⁴ m³
To determine how much further can kate see across the horizon than Paul, we have:
= 2.12526863 × 10¹⁵ m³/6.3758059 × 10¹⁴ m³
= 3.33 times further.
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