Answer:
The rate of interest applied on the loan is 2.4%
Step-by-step explanation:
Given as :
The principal amount borrows as loan = p = $4200
The time period of loan = t = 5 years = 5 × 12 = 60 months
The monthly payment for loan = $78.40
So, The payment for 60 months = $78.40 × 60 = $4704
i.e Amount after 60 months = $4704
Let The rate of interest = r at simple interest
Now, From Simple Interest method
Simple interest = [tex]\dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}[/tex]
Or, s.i = [tex]\dfrac{\textrm p\times \textrm r\times \textrm t}{100}[/tex]
Or, (Amount - principal) = [tex]\dfrac{\textrm p\times \textrm r\times \textrm t}{100}[/tex]
Or, $4704 - $4200 = [tex]\dfrac{\textrm 4200\times \textrm r\times \textrm 5}{100}[/tex]
Or,504 × 100 = 21,000 × r
∴, r = [tex]\dfrac{50400}{21000}[/tex]
i.e r = 2.4
So, The rate of interest = r = 2.4%
Hence, The rate of interest applied on the loan is 2.4% Answer
A hotel has 150 rooms. Those with kitchen facilities rent for $100 per night in those without kitchen facilities rent for $80 per night. On a night when the hotel was completely occupied, revenues were $13,000. How many of each type of room does the hotel have?
Answer:
50 rooms with kitchen facilities and 100 rooms without kitchen facilities
Step-by-step explanation:
Let the rooms without kitchen facilities be x and those with kitchen facilities be y
Form set of equations
Since the total rooms are 15, then the first equation is
x+y=150
Therefore, x=150-y
Considering the cost of rooms and what was collected, then
80x+100y=13000
Substituting x with 150-y then
80(150-y)+100y=13000
12000-80y+100y=13000
20y=1000
[tex]y=\frac {1000}{20}=50 rooms[/tex]
Therefore, x=150-y=150-50=100 rooms
Therefore, there are 50 rooms with kitchen facilities and 100 rooms without kitchen facilities
Kurt says factors and multiples are
related. Use the equation 8 X 5 = 40
to label each number as a/
factor or a multiple..
Step-by-step Explanation:
Before heading towards the solution, you need to make sure how multiple and factors are related to each other.
The multiple of a number could be obtained by multiply it with another number.
For example, the first five multiples of 12 are 12, 24, 36, 48 and 60
1 X 12 = 122 X 12 = 243 X 12 = 364 X 12 = 485 X 12 = 60Factors are the numbers that are multiplied to get a given number.
For example,
1 X 12 = 122 X 12 = 243 X 12 = 36The factors of 12 are 1, 2, 3, 4, 6 and 12.
As division and multiplication can be used to find factors and multiples.
For example a whole number is a multiple of its factors.
Let w = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} be the set of even wholes numbers from 2 to 20.
As 2 is a factor of 20 because 20 ÷ 2 = 4
20 is a multiple of 2 because 2 X 10 = 20
So, in the same way, the equation 8 X 5 = 40 can be used to determine how factors and multiples are related.
Let the equation be
8 X 5 = 40
8 is a factor of 40 because 8 X 5 = 40
40 is a multiple of 8 because 40 ÷ 5 = 8
So, this is how factors and multiples are related to each other.
Keywords: factors, multiples, division, multiplication
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Which system of equations has no solutions
A. 3x + 4y = 5
6x + 8y = 10
B. 7x - 2y = 9
7x - 2y = 13
C. 2x - y = -11
-2x + y = 11
D. 3x + 6y = 1
x + y = 0
x = 15.
PQ = SQ.
Find y, explain good for brainliest
Answer:
y = 25.
Step-by-step explanation:
PQ and RQ and SQ are congruent so
x + 10 = 2x - 5
15 = x.
So PQ = 15 + 10 = 25.
But PQ = RQ = y, so
y = 25.
A snowstorm dumped 22 inches of snow in 8 hours. What was the average snowfall per hour?
2.615
Step-by-step explanation:
22 divided by 8
the average snowfall per hour is 2.75 inch.
What is division?Division is the process of splitting a number or an amount into equal parts.
here, given that,
A snowstorm dumped 22 inches of snow in 8 hours.
i.e. per hour = 22/8
=2.76
hence, the average snowfall per hour is 2.75 inch.
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Here is a list of numbers.
32 29
20
30
37
34
33
31
Tanya thinks that to work out the median, she simply needs to find
the middle number. So she says that "37" is the median for this list of numbers.
Tanya's answer is not correct.
a) Describe what is wrong with her method.
b) Work out the median of the numbers in the list.
The median is found by ordering the numbers and choosing the middle one (or the average of the two middle ones in the case of an even set). Tanya's mistake was not ordering the numbers before choosing the median. Thus, the correct median for the provided list is 31.5.
Explanation:In mathematics, the median is the middle number in a sorted, ascending or descending, list of numbers. It can be found by arranging all the numbers from smallest to greatest. If there is an odd number of observations, the median is the middle number. If there is an even number of observations, the median is the average of the two middle numbers.
So, here is the mistake in Tanya's method: She didn't arrange the numbers in order from smallest to largest before choosing the middle number. This is why 37 is not the correct median.
Now, let's find the correct median for the provided list of numbers: 20, 29, 30, 31, 32, 33, 34, 37. Since it's an even number of observations, we take the average of the two middle numbers, which are 31 and 32. Hence, the median of the numbers in the list is (31+32)/2 = 31.5.
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(a) Tanya's mistake is that she did not first arrange the numbers in ascending (or descending) order.
(b) The median of the numbers in the list is 31.5.
a) Tanya's mistake is that she did not first arrange the numbers in ascending (or descending) order. The median is the middle number in a sorted list of numbers. If the list has an odd number of elements, the median is the middle element. If the list has an even number of elements, the median is the average of the two middle numbers. Tanya needs to sort the numbers before finding the median.
b) Sort the numbers in ascending order, so the list will become.
[tex]\[ 20, 29, 30, 31, 32, 33, 34, 37 \][/tex]
Determine the median:
Since there are 8 numbers (an even number of elements), the median will be the average of the 4th and 5th numbers in the sorted list.
- The 4th number is 31.
- The 5th number is 32.
[tex]\[ \text{Median} = \frac{31 + 32}{2} = \frac{63}{2} = 31.5 \][/tex]
Therefore, the median of the numbers in the list is 31.5.
70 percent of 330 is the same as 60 percent of what number?
Answer:
yassar
Step-by-step explanation:
Can yall help me with the second part Pls
Answer:
Step-by-step explanation:
Total money raised = 658 + 95.60 = $ 753.60
donated to each charity = 753.60/12 = $62.80
The area of a rectangle is 4y + 10.
A. Represent the area of the rectangle in factored form.
B. Use the factored form to give one possible set of dimensions for this rectangle.
A) The factored form of area of rectangle is 2(2y + 5)
B) length of rectangle is 2 and width is 2y + 5 and one possible set of dimensions of rectangle is length 2 and width 7
Solution:
Given that area of rectangle is 4y + 10
A. Represent the area of the rectangle in factored form
The factored form is a parenthesized algebraic expression.
Factored form is a product of sums of products or a sum of products of sums
Given area of rectangle is 4y + 10
Taking 2 as common,
4y + 10 = 2(2y + 5)
Therefore, the factored form of given area of rectangle is 2(2y + 5)
B. Use the factored form to give one possible set of dimensions for this rectangle
The area of a rectangle is given by the formula:
area of rectangle = length x width
Therefore, area of rectangle = 2(2y + 5)
So the length of rectangle is 2 and width is 2y + 5
Or the length of rectangle is 2y + 5 and width is 2
If y = 1, then one possible set of dimensions of rectangle is:
length = 2 and width = 2(1) + 5 = 7
So one possible set of dimensions of rectangle is length 2 and width 7
Final answer:
The factored form of the area of the rectangle is 2(2y + 5).
One possible set of dimensions, based on the factored form, is a length of 2y units and a width of 5 units.
Explanation:
To represent the area of a rectangle in factored form, we look for factors of the expression 4y + 10. Both terms have a common factor of 2, so the factored form is:
2(2y + 5).
Now, to give one possible set of dimensions for the rectangle using the factored form, we can consider each factor as a dimension:
Length: 2yWidth: 5Thus, one possible set of dimensions for the rectangle could be 2y units (length) and 5 units (width).
At 1:00pm, ship A is 30 miles due south of ship B and is sailing north at a rate of 15 mi/hr. If ship B is sailing
west at a rate of 10 mi/hr, find the time at which the distance d between the ships is minimal.
Answer:
2:23 pm
Step-by-step explanation:
We can solve this considering a a right triangle
let t = travel time of both ships
therefore,
15t = distance traveled by ship A
however, it is traveling toward the point of reference, therefore we write it
(30-15t)
and
10t = distance traveled by ship B, away from the point of reference
Let d = distance between the ships at t time, (the hypotenuse of the right triangle)
[tex]d= \sqrt{(30-15t)^2+10t^2}[/tex]
and combine like terms
[tex]d= \sqrt{(900-900t+225t^2)+100t^2}[/tex]
[tex]d= \sqrt{3325t^2-900t+900}[/tex]
from this d to minimum we can find the axis of symmetry, where in
a=325 and b= -900
the t=-b/2a
[tex]t= -\frac{-900}{2\times325}[/tex]
t= 1.384 hours
now putting the value we get
[tex]d= \sqrt{3325(1.384)^2-900(1.384)+900}[/tex]
solving this we get
d= 16.64 miles
therefore,
16.64 mi apart after 1.3846 hrs, minimum distance between the ships
now, 1.384 hours = 1+60(0.348) hour
= 1 hour and 23 minutes
so, the time at which the distance d between the ships is minimal = 1:00 pm + 1 hour and 23 minutes = 2:23 pm
A television is identified by the diagonal measurement of the of screen. A television has a 36 inch screen whose height is 22 inches.what is the length of the television screen
Answer:
28.5 inches.
Step-by-step explanation:
Given: Measurement of diagonal= 36 inch.
Height= 22 inches
Picture attached to show the measurement.
As the screen of televison is measured by diagonal of screen.
∴ Hypotenous= diagonal of screen, which is 36 inches.
Now, using pythagorean theoram to find length of television screen.
[tex]hypotenous^{2} = opposite^{2}+adjacent^{2}[/tex]
∴ [tex]36^{2} = 22^{2} + adjacent^{2}[/tex]
Here adjacent is the length of television.
⇒[tex]1296= 484+ length^{2}[/tex]
Subtracting both side by 484.
⇒[tex]length^{2} = 812[/tex]
Taking square root on both side
remember: [tex]\sqrt{a^{2} } = a[/tex]
∴ [tex]length= \sqrt{812}= 28.495 \approx 28.5[/tex]
Hence, length of televison screen is 28.5 inches.
The width of a television screen can be calculated using the Pythagorean theorem. Given a diagonal of 36 inches and height of 22 inches, the approximate length of the screen is 30 inches.
Explanation:To solve this problem, we will use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This principle can be written as a^2 + b^2 = c^2 where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In the case of a television screen, the diagonal (from one corner to the opposite corner) is the hypotenuse. Given the height of the TV screen as 22 inches (one of the sides of the right triangle), and the diagonal as 36 inches (the hypotenuse), the length (the other side of the right triangle) can be found using the formula.
Let's rearrange the formula to solve for the length (b): b = sqrt(c^2 - a^2). Substitute the given measurements into the formula: length = sqrt(36^2 - 22^2), or approximately 30 inches.
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Bill wants to post three parcels.
Parcel 1
Parcal 2
Parcel 3
Each parcel costs £1.10 to post.
How much change should he get from a £10 note?
The change Bill should receive from a £10 note after paying to post three parcels, each costing £1.10, is £6.70.
Explanation:Bill wants to post three parcels and each parcel costs £1.10 to post. The total cost for posting all three parcels would be £1.10 * 3 = £3.30. If he pays this fee with a £10 note, we can calculate the change by subtracting the total cost of posting parcels from the value of the note: £10 - £3.30 = £6.70. So, the change Bill should get back from a £10 note after posting 3 parcels each costing £1.10 is £6.70.
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When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 2 kg, the acceleration of the object is 35 /ms2. When the same force acts upon another object, its acceleration is 10 /ms2. What is the mass of this object?
Answer:
7 kg
Step-by-step explanation:
F=35*2=m*10
70=10m
7=m
The mass of the second object is 7 kg
First, we make the following representations
[tex]F \to[/tex] Force
[tex]a \to[/tex] acceleration
[tex]m \to[/tex] mass
The formula of force is:
[tex]F = m * a[/tex]
Since force is constant, then:
[tex]m_1 =2kg[/tex] [tex]a_1 = 35m/s^2[/tex] --- subset 1 represents the first object
[tex]m_2 = ??[/tex] [tex]a_2 = 10m/s^2[/tex] --- subset 2 represents the second object
We are to calculate the mass of the second object
A constant force means:
[tex]m_1 * a_1 = m_2 * a_2[/tex]
Make m2 the subject
[tex]m_2 = \frac{m_1 * a_1}{a_2}[/tex]
Substitute known values
[tex]m_2 = \frac{2kg * 35m/s^2}{10m/s^2}[/tex]
[tex]m_2 = \frac{2kg * 35}{10}[/tex]
[tex]m_2 = \frac{70kg}{10}[/tex]
[tex]m_2 =7kg[/tex]
Hence, the mass of the second object is 7kg
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Choose the graph below that represents the solution to the system of equations
y= 3x + 2
10x + 2y = 20
Answer:
Graph 3 represents the solution to the system of equations.
Step-by-step explanation:
The given two linear equations of x and y are
y = 3x + 2 ........ (1) and
10x + 2y = 20 .......... (2)
Now, to solve those two equations let substitute the value of y from equation (1) to the equation (2).
Hence, 10x + 2(3x + 2) = 20
⇒ 16x = 16
⇒ x = 1
And from equation (1), y = 3x + 2 = 5
Therefore, the solution of the system of equations (1) and (2) are (1,5).
Therefore, graph 3 represents the solution to the system of equations. (Answer)
What is the initial value of the function represented by this table? (5 points)
Answer:
0
4
5
9
Step-by-step explanation:
Solve system of equation
2x+3y=4
2x=7y+24
Answer:
X= 5 Y= -2
Step-by-step explanation:
A basket contains five apples and seven peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second is a peach.
Answer:
Step-by-step explanation:
Total fruits T= 5+7 = 12
No. Of apple n(A) = 5
No. Of peaches n(P) = 7
P(A) 1st = n(A)/T = 5/12
P(P) 2nd = n(p)/(T-1) = 7/11
: P(A and P) = 5/12 × 7/11
= 35/132
if sin(x)=m, with m>0, find the value of sin(pie-x)
Answer:
Step-by-step explanation:
Sin (π - x ) = Sin x = m
What is the volume of a rectangular prism with length 7 in., height 3 in., and width 8 in.?
V = lwh
_in3
Answer:168
Step-by-step explanation: v=lwh
V=7x8x3
= 168
The interest rate on the credit card is 15%. If we charge $200 to the credit card how much will pay including the interest?
Answer:
Step-by-step explanation:
Interest = 15% of 200 = 15/100 * 200 = 15 * 2 = $30
The Amount he need to pay = 200 + 30 = $230
How do you integrate [tex]\int\limits ln({x+1}) \, dx[/tex] using integration by parts?
Thank you!
Answer:
[tex]\int \ln (x+1) \, dx=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]
Step-by-step explanation:
Use integration by parts formula:
[tex]\int u \, dv=uv-\int v \, du[/tex]
For the integral
[tex]\int \ln(x+1) \, dx,[/tex]
[tex]u=\ln (x+1)\\ \\dv=dx,[/tex]
then
[tex]du=d(\ln (x+1))=\dfrac{1}{x+1}\ dx\\ \\v=x[/tex]
and
[tex]\int \ln(x+1) \, dx\\ \\=x\cdot \ln (x+1)-\int x\cdot \dfrac{1}{x+1} \, dx\\ \\= x\cdot \ln (x+1)-\int \dfrac{x+1-1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-\int \left(1-\dfrac{1}{x+1}\right) \, dx\\ \\=x\cdot \ln (x+1)-\int \, dx +\int \dfrac{1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]
I need to buy a carpet-for a-room the measures 3m by 2m.how many square meters do I need?
Final answer:
To carpet a room measuring 3 meters by 2 meters, you need 6 square meters of carpet.
Explanation:
To calculate the area of a rectangular room that measures 3 meters in length and 2 meters in width, you multiply the length by the width.
Using the formula Area = length × width,
As we can see that the room is a rectangle with width 2 and length 3
So,
Length = 3 m
Width = 2 m
We find that the room's area is 6 square meters (3m × 2m = 6m²).
Therefore, to carpet a room of this size, you would need to buy 6 square meters of carpet.
How do I graph 7x+2y=-10
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8x + x2 + 7 ?
o left 4, down 9
O left 4, up 23
Oright 4, down 9
O right 4, up 23
Answer:
Move right by 4 units and down by 9 units
Step-by-step explanation:
The vertex of the parabolic function f(x) = x² is at (0,0)
Now, the parabolic function g(x) = - 8x + x² + 7 can be rearranged to vertex form.
g(x) = x² - 8x + 16 + 7 - 16
⇒ g(x) = (x - 4)² - 9
⇒ (x - 4)² = (y + 9) {If y = g(x)}
Therefore, the vertex of the parabolic function g(x) is at (4,-9).
Therefore, we have to move right by 4 units and down by 9 units to reach from vertex of f(x) to vertex of g(x). (Answer)
Using translation concepts, it is found that the translation that maps f(x) into g(x) is described by: right 4, down 9
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, function f(x) is defined by:
f(x) = x².
Function g(x) is defined by:
g(x) = x² - 8x + 7
Completing the squares, we have that g(x) can be written as:
g(x) = (x - 4)² - 9
Hence, the correct translation is:
right 4, down 9
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Which of the following is an odd function?
f(x) = x3 + 5x2 + x
O F(x)= √x
Of(x) = x2 + x
O f(x) = -x
Option 4
f(x) = -x is an odd function
Solution:
A function is odd if and only if f(–x) = –f(x)
Option 1
[tex]f(x) = x^3 + 5x^2 + x[/tex]
Substitute x = -x in above equation
[tex]f(-x) = (-x)^3 + 5(-x)^2 + (-x)[/tex]
Cubes always involve multiplying a number by itself three times, so if the number is negative the cube will always be negative
Ans squaring results in positive
[tex]f(-x) = -x^3 + 5x -x[/tex] --- eqn 1
[tex]-f(x) = -(x^3 + 5x^2 + x)\\\\-f(x) = -x^3 - 5x^2 - x[/tex] ---- eqn 2
Comparing eqn 1 and eqn 2,
[tex]f(-x) \neq -f(x)[/tex]
Therefore not an odd function
Option 2
[tex]f(x) = \sqrt{x}[/tex]
[tex]f(-x) = \sqrt{-x}[/tex]
[tex]-f(x) = - \sqrt{x}[/tex]
Therefore,
[tex]f(-x) \neq -f(x)[/tex]
Therefore not an odd function
Option 3
[tex]f(x) = x^2 + x\\\\f(-x) = (-x)^2 + (-x)\\\\f(-x) = x^2 - x[/tex]
[tex]-f(x) = -(x^2 + x) = -x^2 - x[/tex]
[tex]f(-x) \neq -f(x)[/tex]
Therefore not an odd function
Option 4
[tex]f(x) = -x\\\\f(-x) = -(-x) = x[/tex]
[tex]-f(x) = -(-x) = x[/tex]
[tex]f(-x) = -f(x)[/tex]
Thus option 4 is correct and it is an odd function
Answer:
D
Step-by-step explanation:
just took test on edge
John sells tickets to a school concert. Adult tickets cost $6.50 and children’s tickets cost $4.50. John collects a total of 157.50 from the ticket sales and he sells twice as many adult tickets as children’s tickets. How many tickets does he sell all together?
John sold 18 adults tickets and 9 children tickets.
Step-by-step explanation:
Given,
Cost of adult ticket = $6.50
Cost of children ticket = $4.50
Total collected = $157.50
Let,
Number of adult tickets sold = x
Number of children tickets sold = y
According to given statement;
6.50x+4.50y=157.50 Eqn 1
he sells twice as many adult tickets as children’s tickets.
x=2y Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]6.50(2y)+4.50y=157.50\\13y+4.50y=157.50\\17.50y=157.50[/tex]
Dividing both sides by 17.50
[tex]\frac{17.50y}{17.50}=\frac{157.50}{17.50}\\y=9[/tex]
Putting y=9 in Eqn 2
[tex]x=2(9)\\x=18[/tex]
John sold 18 adults tickets and 9 children tickets.
Keywords: linear equation, substitution method
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Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1.50 more than the cost of a on loaf of bread. What is the combined cost of one loaf of bread and one package of cheese?
The combined cost of one loaf of bread and one package of cheese is $6.50.
Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1.50 more than the cost of a loaf of bread. To find out the combined cost of one loaf of bread and one package of cheese, we need to use a system of equations.
Let the cost of one loaf of bread be x. Therefore, the cost of one package of cheese would be x + $1.50. Since Mason bought 6 loaves of bread and 3 packages of cheese, we can express the total cost as:
6x + 3(x + $1.50) = $27
Distributing the 3 into the parentheses, we get:
6x + 3x + $4.50 = $27
Combining like terms, we have:
9x + $4.50 = $27
Subtracting $4.50 from both sides, we get:
9x = $22.50
Dividing both sides by 9, we find out that one loaf of bread (x) costs:
x = $2.50
Now, adding the additional $1.50 for the cheese, we find that one package of cheese costs:
x + $1.50 = $4.00
The combined cost of one loaf of bread and one package of cheese is therefore:
$2.50 (bread) + $4.00 (cheese) = $6.50
Can someone Please Help Me
Answer:
a= 63 ⁰; z= 80⁰; x= 30⁰; N= 102⁰;M = 66⁰
Step-by-step explanation:
Example 1 : the angle opposite to angle 2a is 54 degrees because it is the opposite exterior angle of 54 degrees angle so
2a+54⁰= 180⁰
2a= 180⁰-54⁰
2a= 126⁰
a= 126/2= 63⁰
EXAMPLE 2: Opposite exterior angles are equal so
z+25⁰= 105⁰-------A
z= 105⁰-25⁰
z=80⁰
It is making a straight angle so
105⁰+ 3x-15= 180⁰
3x-15=180-105
3x-15=75⁰
3(x-5)=75⁰
x-5⁰=75/3
x-5⁰=25⁰
x= 25⁰+5⁰
x=30⁰
EXAMPLE 3:
114⁰= N+12⁰ (exterior opposite angles are equal)
N= 114⁰-12⁰
N= 102⁰
114⁰+M= 180⁰ (straight angles)
M= 180⁰- 114⁰
M= 66⁰
Find the roots of this polynomial x^2 -9x+8
Final answer:
x = 1 and x = 8.
Explanation:
This can be completed through factoring the quadratic equation. To factor x^2 - 9x + 8, we look for two numbers that multiply to +8 and add to -9. These numbers are -1 and -8 since (-1) * (-8) = +8 and (-1) + (-8) = -9. Therefore, we can write the polynomial as (x - 1)(x - 8). The roots are the values of x which make each factor zero, hence we get the roots as x = 1 and x = 8.
Which pair of number has the same greatest common factor as 48 and 78
Answer:
48
Step-by-step explanation:
48=2×2×2×2×3
78=13×2×3
48 has 5 factors.