Answer: $47,000 at 10% annually is ≈ $77,297.70 and $47,000 at 5% monthly is ≈ $569,611.01
Step-by-step explanation:
Use the compound interest formula. A=P(1+r/n)^nt
a ladder 25 feet long is leaning against the wall of a building. initially, the foot of the ladder is 7 feet from the wall. the foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. the location of the foot of the ladder, its x coordinate, at time t seconds is given by x(t)
The approximate value of x(t), which indicates the location of coordinate the ladder's foot at time t seconds, is 6.85. 7
What in math is a coordinate?Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.
The location in the cartesian plane will be determined by the coordinate points. A point's distance from the y axis is known as the x-coordinate, also known as the abscissa, and its distance from the x-axis is known as the y-coordinate, also known as the ordinate.
based on the information provided,
x = the distance between the wall and the bottom of the ladder
y = distance of the top of the ladder from the ground
x² + y² = 25²
x² + 7² = 25²
x² = 625 -49 = 429
y = √576
Differentiating the equation with respect to time t gives
2x dx/dt + 2y dy/dt = 0
dx/dt = -y dy/dt / x
= -√576 * (2) / 7
= 6.85 feet per second approximately.
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please help, if you can answer this correctly and put your explanation i will give brainliest
The error Julius made in his explanation is using the area of a rectangle as the longest side instead of area of a square.
Pythagorean theoremPythagorean theorem is the sum of the square of opposite and adjacent sides which result in the sum of the square of the hypotenuse of a triangle.
c² = a² + b²
Where,
c = hypotenusea = oppositeb = adjacentThe error Julius made in his explanation is using the area of a square as the hypotenuse. The figure he used to represent the longest side (hypotenuse) is a rectangle.
The correct working should be:
c² = area of square a + area of square b
c² = 25 + 16
c² = 41
find the square root of both sidesc = √41
c = 6.40312423743
Approximately,
c = 6.4
In conclusion, Julius made the mistake of representing the longest side with area of a rectangle instead of a triangle.
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A solid glass cylinder, which is used in an expensive laser amplifier, has a volume of 75vm^3. The cost of polishing the surface area of this glass cylinder is £2 per cm² for the curved surface area and £3 per cm^2 for the circular top and base areas. Given that the radius of the cylinder is r cm, (a) show that the cost of the polishing, £C, is given by C = 6πr² + 300/r
The cost of the polishing, £C, is given by C = 6πr² + 300/r.
The volume of the solid cylinder is 75 m³.
Formula for volume of cylinder = πr²h.
Where R is rhe radius of cylinder and h is the height of the cylinder.
So we can write,
πr²h = 75
h = 75/πr².
So the height of the cylinder is 75/πr² centimeters.
Curved surface area of the cylinder is 2πrh m².
Cost of polishing the curved surface area is £2/cm².
Total cost of polishing the curved surface area = £2×2πrh
Area of the base and the top is 2(πr²).
Cost of polishing base and top is £3/cm².
Cost of polishing 1m² of the base and top,
Cost of area of base and top = £3/cm².
Total Cost of polishing base and top area = £3×2(πr²)
The total cost C of polishing the whole glass,
C = 4πrh + 6πr²
Puting the value of h = 75/πr²
C = 4πr(75/πr²) + 6πr²
C = 6πr² + 300/r.
Hence it is proved that the total cost of polishing is,
C = 6πr² + 300/r.
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In a survey 34% of population was found to know hindi 46% to know english and 23% to know both languages.what is the percentage of those knowing neither hindi nor english.
We would find the percentage of those knowing neither Hindi nor English in the population using set theory,
Percentage of population knowing English (A) = 46%
Percentage of population knowing Hindi (B) = 34%
Percentage of population who know both languages (A U B) = 23%
therefore,
Applying set theory,
A U B = A + B - (A ∩ B)
23% = 36% + 46% - ( A ∩ B)
A ∩ B = 80% - 23% = 57% population knows either Hindi OR English.
So, Population who neither know Hindi or English = 100% - 57% = 43%
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Installing custom glass windows costs $400 for the install and $30 per square foot of
glass needed for your windows. The total charge for your window installation was
$4900. Translate this information into an equation using a to represent the number of
square feet of glass used for your windows.
Using your equation, determine the number of square feet of glass used for your
windows.
Please help ASAP really bad at math and can’t afford a tutor.
Part 1
[tex)400+30x=4900[/tex]
Part 2
[tex]30x=4500 \\ \\ x=150[/tex]
So, the answer is 150 ft².
2. Solve the equation using addition or subtraction.
5.5 = −2+d
Od=5
Od = 7.5
Od = 5.5
Od = 3.5
The value of d after addition or subtraction is 7.5
What is basic algebra ?The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every discipline of mathematics, including trigonometry, calculus, and coordinate geometry.
Given that : the equation is 5.5 = −2+d
5.5 = −2+d
5.5 + 2 = d
7.5 = d
The value of d after addition or subtraction is 7.5
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One plus one plus 278 times 67 divided by 782
Answer:25.8184143223
1+1+278*67/782
1+1+18626/782
2+23.8184143223
25.8184143223
find the circumference and area of circle A if each unit on the graph im measures 1 centimeter, round answers to the nearest tenth,
circumference: ___ cm
area: ___cm^2
The circumference of the given circle will be 18.84cm and its area will be 28.26cm²
the center of the given circle is A with coordinates (2,3)
we are given that each block on the graph represents 1cm,
on observing the graph we can conclude that the radius of the circle is 3cm.
circumference of the circle is given by the formula,
2πr
taking pi as 3.14 and substituting r=3 in the above formula we get,
2*3.14*3
=18.84cm
thus the circumference of the circle will be 18.84 units.
Similarly, area of a circle can be calculated using the formula,
πr²
taking π as 3.14 and substituting r=3 in the above formula,
3.14*3²
=28.26cm²
What is the difference between area and perimeter?
Perimeter is - "distance around the outside of a shape" while area is - "measures of the space inside a shape."
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Select the correct answer.
If the graph of f (x) = |x| is shifted to the left 2 units, which function describes the graph of the new function?
A) g(x) = |x| + 2
B) g(x) = |x| - 2
C) g(x) = |x + 2|
D) g(x) = |x - 2|
The correct option is D) g(x) = |x - 2| for the shifting of graph of f (x) = |x| is shifted to the left 2 units.
What is described as the translation of function?In geometry, translation refers to a function which moves an element a specified distance. The element is not otherwise altered. It has not been rotated, mirrored, or resized.Every point of an element must be transitioned in the exact same direction and at the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, as well as the object after translation is referred to as the image.For the given question, the function is given as;
f(x) = |x|
There is a shifting of 2 units towards the left, it means there is shift on the x-axis toward the negative x-axis.
Then, value of x will be reduced by 2 units, which is given by function.
g(x) = |x - 2|.
Thus, the function which correctly described shifting of 2 units left is g(x) = |x - 2|.
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Answer:The correct option is D) g(x) = |x - 2| for the shifting of graph of f (x) = |x| is shifted to the left 2 units.
Step-by-step explanation: I did it on plato.
A daycare center in Hillsdale currently has 12 assistant caregivers and 6 senior caregivers. Since demand is high, the owner is going to be hiring 1 assistant caregiver per month and 4 senior caregivers per month. Her goal is to have a larger staff, including an equal number of assistant caregivers and senior caregivers. How many of each type will there be? How long will that take?
1. Month for assistance caregivers is 14 months.
Month for senior caregivers will be 14 months.
2. After 2 month, there will be 14 of each types of caregiver.
What is an expression?
Expression in math is defined as the collection of the number, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
A daycare center in Hillsdale currently has 12 assistant caregivers and 6 senior caregivers.
On high demand the owner is going to be hiring 1 assistant caregiver per month and 4 senior caregivers per month.
Let m is number of months.
Then, Each month has 12+ m for assistant caregivers and 6 + 4m for senior caregivers.
By given condition we formulate;
12 + m = 6 + 4m
12 - 6 = 4m - m
6 = 3m
3m = 6
m = 2
Thus, 12 + m = 12 + 2 = 14
And, 6 + 4m = 6 + 4 x 2 = 14
So, After 2 month, there will be 14 of each types of caregiver.
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2x+50=3xljb volugvluclkjhvlyotcltc
Answer:
subtract 2x from 3x thats x so 50=x
Step-by-step explanation:
Answer:x=50
Step-by-step explanation:bring 3x over on one side with 2x and bring 50 over on the other side by itself.
The equation becomes 2x-3x=-50
2x-3x is -x
so the equation is -x=-50
there are two negatives in the equation so you make the equation positive because a negative and a negative equals a positive
Therefore the answer is x=50
A 35-inch ribbon was cut into 8 equal lengths how long was each piece?
Answer:
4⅜ or 4.375 inches.
Step-by-step explanation:
35 ribbon into 8 pieces is:
35/8 = 4⅜ or 4.375 inches.
You have 2 different savings accounts. For Account A, the simple interest earned after 3 months is $1.75. For Account B, the simple interest earned after 21 months is $17.50. If the interest rate is 3.5% for Account A and 2.5% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
The principal of account A is $20.83 and the principal of account B is $58.33. Account 2 earned the most interest rate in the first month.
The formula to calculate Simple interest, Simple interest = Principal × rate of interest × time.
The principle for Account A would be,
2 = Principal × 3.2% × 3
So, the principal is $20.83
The principle for account B would be,
38.50 = Principal × 2.2% × 30
So, the principal is $58.33,
The interest rate for both accounts is now as follows:
For account 1
= $20.83 × 3.2%
= $0.67
And, for account 2
= $58.33 × 2.2%
= $1.28
Account 2 has the greatest interest rate, thus it is taken into account.
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A market sells candy
bars for $4.20. How
much do 8 candy bars
cost?
Answer: 33.6
Step-by-step explanation:
Answer:
33.6
Step-by-step explanation:
4.20 x 8 = 33.6
Rounded to the nearest hundreth. This one is 2 answers.
let’s say you have a four-digit personal identification number (pin). each digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, giving a total of 10 possible numbers for each digit. if a pin is 4 digits, each digit can be any one of the 10 possible numbers, how many different possible combinations are there?
If each digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, giving a total of 10 possible numbers for each digit. if a pin is 4 digits, each digit can be any one of the 10 possible numbers, The different possible combinations are there is : 10,000.
Different possible combinationGiven :
Digit = 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
Possible number = 10
Pin = 4 digits
Now let determine the different possible number
Possible number combination = 10 x 10 x 10 x 10
Possible number combination = 10,000
Therefore the combination is 10,000.
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One summer, an ice cream truck driver sold 2,994 Popsicles and 515 ice creams. How many
treats did the driver sell in all?
Answer:2479
Step-by-step explanation: subtract 2,994 and 515 and you would get 2479
Answer: 3509 treats
Step-by-step explanation:
If I'm understanding correctly, we need to add the desserts together right?
[tex]2994+515\\=3509[/tex]treats in total
Melissa and her mom are going on a trip. If they travel
238 miles a day for 13 days, how many miles will they
travel altogether?
In 13 days they will travel 1904 miles altogether.
What is multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.
Multiplication in action or in progress. The multiplication of 8 and 3 is the same as the sum of 8+8+8, which is a mathematical operation that takes two numbers and returns an answer that is equal to the sum of a column in which one of the numbers is repeated the amount of times of the other number.
Given Data
they travel 238 miles a day for 13 days
1 day = 238 miles
13 days = 238 (13)
13 days = 1904
In 13 days they will travel 1904 miles altogether.
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6) Arrange in ascending order: 0.3,
26%, ½
Answer:
0.3,1/2,26%
Step-by-step explanation:
ascending order if arranging from smallest to highest .In this case, 0.3 Is the smallest followed by 1/2 and then 26%.
Work out a+2b as a column vector
hope this helps. . .....
The area of a trapezoid is given by the formula A=12(b1+b2)h. Solve the equation for b2.
In a case whereby the area of a trapezoid is given by the formula A=12(b1+b2)h then the equation for b2 is b2= (A - 12hb1)/12h.
How can the value of the term b2 be expressed?
The formula for the trapezoidis given as A=12(b1+b2)h , where the value of term b2 is been exdpected to be found.
firstly, we need to open the bracket as :
A=12(b1+b2)h
A= 12hb1 + 12hb2
Then this can be simplified as 12hb2= (A - 12hb1)
Then we can try to make the b2 the subject of the formula as
b2= (A - 12hb1)/12h.
Therefore, the value of the term b2 can be written as b2= (A - 12hb1)/12h.
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PLEASE HELP need answer now
Answer:
82°
Step-by-step explanation:
Exterior angle property of triangle:The exterior angle of triangle equals the sum of opposite interior angles.
∠C + ∠B = 143°
61+ ∠B = 143
∠B = 143 - 61
∠B = 82°
Grace's height is 1.45 m. Jackson is 0.2 m shorter than Grace. What is
Jackson's height? Give your answer in metres (m).
By using the method subtraction, Jackson's height is 1.25m.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
Grace's height is 1.45 m.
Jackson is 0.2 m shorter than Grace.
Jackson's height is 1.45 -0.2 = 1.25
Therefore, Jackson's height is 1.25m.
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Caleb worked his 40 regular hours last week, plus 6 overtime hours at the time-and-a-half rate. His gross pay was $1,063. What was his hourly rate?
If Caleb worked his 40 regular hours last week, plus 6 overtime hours at the time-and-a-half rate. His gross pay was $1,063. His hourly rate is : $21.69.
What is hourly rate?Hourly rate can simply be defined as the wages earn per hour.
Given data :
Regular hours = 40
Over time = 6 ( 1.5 ) = 9
Gross pay = $1,063
Hence,
let h represent the hourly rate
So,
1.5h = overtime rate
Now let determine the hourly rate
40h + 6(1.5h) = 1,063
40h + 9h = 1,063
49h = 1,063
Divide both side by 49h
h = 1,063/ 49
h = $21.69
Therefore the hourly rate is the amount of $21.69.
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Consider matrix A.
A =[-3 5 2 8 -1 3]
What matrix results from the elementary row operations represented by -3R2 + 4R₁?
Enter your answer by filling in the boxes.
The resultant matrix after elementary row operation is:
[tex]A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]
What is elementary row operation?
In mathematics, the elementary row operation is a method in which the two rows exchanged. In this, the rows are either multiplied, added or division. Sometimes, single row is multiplied by some constant.
According to the question, the given matrix A is written below:
[tex]A = \left[\begin{array}{ccc}-3&5&2\\8&-1&3\end{array}\right][/tex]
Now, performing elementary row operations represented by [tex]-3R_{2} +4R_{1}[/tex]
The given matrix becomes after elementary row operations:
[tex]A = -3R_{2} + 4R_{1} = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]
Hence, the resultant matrix after elementary row operation is::
[tex]A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]
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a professor rolls a fair, six-sided die. using the classical method of probability, what is the probability that at least five spots will be showing up on the die?
The probability that at least five spots will be showing up on the die is 1/3.
It is given that a professor rolls a fair, six-sided die.
We need to find the probability that at least five spots will be showing up on the die.
Total possible outcomes = {1,2,3,4,5,6}
Number of total outcomes = 6
At least five spots will be showing up on the die. So,
Favorable outcomes = {5,6}
Number of favorable outcomes = 2
Formula for probability:
Probability = [tex]\frac{Number of Favorable Outcomes}{Number of Total Outcomes}[/tex]
On substituting Number of favorable outcomes and Number of total outcomes in the formula of Probability, we get
Probability = 2/6
Probability = 1/3
Therefore, the required probability is 1/3.
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SOLVE ASAP PLEASE TAKING A TEST!!!
The equation of the circle with the centre (5,7) and containing the point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]
How to find the equation of a circle ?The equation for a circle in standard form is [tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex] = [tex]r{2}[/tex], where (x, y) denotes arbitrary coordinates on the circle's perimeter, r denotes the circle's radius, and (x1, y1) denotes the coordinates of the circle's centre.
The equation of a circle with centre (x1,y1)
[tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex] = [tex]r{2}[/tex]
we know the centre , which is (5,7) so the equation changes to:
[tex](x-5){2}[/tex]+ [tex](y-7){2}[/tex] = [tex]r{2}[/tex]
putting the values of the point p we get
[tex](1-5){2}[/tex] [tex]+ (9-7){2}[/tex][tex]= r{2}[/tex]
r=[tex]\sqrt{20}[/tex]
so the equation of the circle will be:
[tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]
Therefore the equation that satisfies the given condition of a circle with centre (5,7) and containing point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]
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Which represents the restrictions on the radical inequality [tex]\sqrt[4]{2x+1} \ \textgreater \ 3[/tex]?
A. [tex]2x+1\geq 0[/tex]
B. [tex]\sqrt{2x+1} \ \textgreater \ 0[/tex]
C. [tex]2x+1\leq 0[/tex]
D. There are no restrictions.
there are no restrictions other than 2 x + 1 > 81 on the radical inequality.
We are given the radical inequality as:
⁴√ 2 x + 1 > 3
We need to find the restriction on this inequality.
For this we will first put x on one side and other constant on the other side.
So, we get that:
2 x + 1 > 3⁴
2 x + 1 > 81
So, the restriction is not from the given options.
But, the value of 2 x + 1 should be greater than 81 for the inequality to be true.
Therefore, we get that, there are no restrictions other than 2 x + 1 > 81 on the radical inequality.
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*11.
How many total terms are there in the following sequence?
7, 10, 13,..., 391, 394
The total terms that in the following sequence 7, 10, 13,..., 391, 394 is 130
What is an arithmetic sequence?The formula for the nth term of an arithmetic sequence is expressed as;
Tn = a + (n-1)d
Where;
Tn is the last terma is the first termn is the number of termsd is the common differencea = 7
Tn = 394
d = 3
Substitute the value in the formula, we have;
394 = 7 + ( n -1) 3
expand the bracket
394 = 7 + 3n - 3
collect like terms
394 - 4 = 3n
find the difference
390 = 3n
Make 'n' the subject of formula
n = 390/3
n = 130
Hence, the number is 130
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There are 600 pipes in stock at Patty’s hardware store. She randomly selects 40 pipes and finds that 8 of the pipes are made of chrome. How many pipes in stock at her store can Patty predict are made of chrome?
The number of pipes that are made of chrome according to the prediction by Patty are 120.
It is given in the question that :-
Number of pipes in stock at Patty's hardware store = 600
Number if pipes randomly selected by Patty = 40
Number of pipes of chrome = 8
Hence, we can write,
Probability of chrome pipes = 8/40 = 1/5
Therefore, we can write,
Number of pipes that are made of chrome according to the prediction by Patty = (1/5)*600 = 120
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
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