She invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account
Here, we want to know the amount of money invested in each account
Let the amount invested in the 4% simple interest account be $x ----> (a)
While the amount invested in the 2.5% account be $y -------->(b)
So mathematically;
Both the interests are added to get total interest
x + y = 6,000 ••••••(i)
Let’s now evaluate the interest
for the 4% account , interest = 4/100 * x = 4x/100
For the 2.5% account, interest = 2.5/100 * y= 2.5y/100
The addition of both interests gives the total simple interest;
4x/100 + 2.5y/100 = 204
Multiply through by 100
4x + 2.5y = 20,400 •••••••(ii)
From i, x = 6,000 - y
Putting this into equation ii
4(6,000-y) + 2.5y = 20,400
24,000 - 4y + 2.5y = 20,400
24,000-20,400 = 4y - 2.5y
1.5y = 3,600
y = 3,600/1.5
y = $2,400
Recalling it again,
x = 6000 - y
x = 6,000 - 2,400
x = $3,600
Therefore, Nina invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account
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Manuela also invests $640.
At the end of 4 years, Manuela has $721.
Find the yearly compound interest rate.
The yearly compound interest rate of $640 at the end of 4 years would be; 3.07
How to calculate compound interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit of time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]
The final amount becomes as;
[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]
Given that Manuela invests $640. At the end of 4 years, Manuela has $721. then the yearly compound interest rate will be;
[tex]A = P\left(1 +\dfrac{R}{100}\right)^T\\\\\\721 = 640\left(1 +\dfrac{R}{100}\right)^4\\\\721 / 640 =\left(1 +\dfrac{R}{100}\right)^4\\\\\\1.12 = \left(1 +\dfrac{R}{100}\right)^4\\\\\\\sqrt[4]{1.12} = \left(1 +\dfrac{R}{100}\right)\\\\\\R = 3.07[/tex]
Hence, the yearly compound interest rate of $640 at the end of 4 years would be; 3.07
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Holly wants to buy a new house in Cardiff.
She knows that Land Transaction Tax will be added to the price of the house.
Land Transaction Tax rates are shown below:
• pay nothing on the first £180000 of the price of the house,
• pay 3·5% on the part of the price of the house that is above £180000 and up to and including £250000,
• pay 5% on the part of the price of the house that is above £250000 and up to and including £400000.
The most Holly can afford to spend, including Land Transaction Tax, is £327000.
Let x be the highest price of house that Holly can afford.
Write an equation in x and solve it to calculate the highest price of house that Holly can afford.
Answer:
321000
Step-by-step explanation:
The highest price of house that Holly can afford is £343350.
What is tax?In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.
Given that, Holly can afford to spend, including Land Transaction Tax, is £327000.
Here, the tax rate is 5% because that is above £250000 and below £400000.
Let x be the highest price of house that Holly can afford.
x= 327000+5% of 327000
x= 327000+5/100 ×327000
x= 327000+0.05×327000
x= £343350
Therefore, the highest price of house that Holly can afford is £343350.
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find X. would love the help thank you
Answer:
120
Step-by-step explanation:
x + the angle = 180 because it makes a line
we know from the picture that the triangle is equilateral so the angle has to be 60
so 180 = x + 60 and solve for x
1. The reduced fraction or mixed number for 375%
Answer:
the answer is shown below for the reduced fractional mixed number for 385 percentage
Step-by-step explanation:
Steps to Convert 375% to Fraction
Place the Percentage Value at the top over 100. The exact form of the fraction is 154. In the decimal form, the fraction can be written as 3.75. In the Mixed Number form, the fraction can be written as 3 .34.
help pls i don’t understand and don’t know which option topick
Answer: C
Explanation:
The range of a function is the set of all values of y that satisfy the function. On the graph, it is between the lowest value of y at the bottom and the highest value of y at the top. Looking at the graph, it extends to negative infinity at the bottom and the maximum value at the top y = 4
Thus, in interval notation,
Range = (- ∞, 4]
What type of symmetry does this figure have?
this figure has no symmetry
both rotational symmetry and reflectional symmetry
reflectional symmetry
rotational symmetry
This figure has no symmetry is the correct option.
Given:
Given figure is parallelogram ,
The number of lines of symmetry of a parallelogram depends on the type of parallelogram.A non special parallelogram does not have any lines of symmetry. This includes any quadrilateral with two pairs of parallel and equal sides, except for rectangles, squares and rhombuses.
A rectangle is a parallelogram with four right angles. This property allows it to have two lines of symmetry.
A rhombus is a parallelogram with four equal sides. The number of lines of symmetry of a rhombus depends on whether it is a square or not. If it has four right angles, the rhombus is a square and thus has four lines of symmetry. If not, the rhombus only has two lines of symmetry.
Therefore this figure has no symmetry is the correct option.
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Given h(x) = − 4x − 4, solve for x when h(x) = −8.
Evaluate the expression.
4−32⋅(−0.25)−12÷1/3
Answer:
Step-by-step explanation:
4
Write an equation involving absolute value for the graph if the points are located at -3.75 and 3.75.
The absolute value equation with the solutions -3.75 and 3.75 is:
|x| = 3.75
How to write the absolute value equation?The general absolute value equation can be written as:
|x+ a| = b
And this can be rewritten into two equations, which are:
x + a = b
x + a = -b
In this case, we want to get an absolute value function such that the two solutions are -3.75 and 3.75, this is ratter trivial to do, we can write the next absolute value function:
|x| = 3.75
If we decompose this, we will get the two equations:
x = 3.75
x = -3.75
Which are the two solutions we wanted.
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Find the slope and reduce,
P=(-5, 2) Q=(-3, 6)
Slope = [?]
Answer:
Slope m = 2
Step-by-step explanation:
(50 points) Show that x+2 is a factor of p(x)=[tex]x^4+2x^3+4x^2+x-14[/tex]. Then write p(x) as the product of x+2 and another factor. Please show work.
Answer:
Let p(x)=x
3
−4x
2
−2x+20
By factor theorem, (x+2) is a factor of p(x) if p(−2)=0.
∴ It is sufficient to show that (x+2) is a factor of p(x)
Now, p(x)=x
3
−4x
2
−2x+20
∴p(−2)=(−2)
3
−4(−2)
2
−2(−2)+20=−8−16+4+20=0
∴(x+2) is a factor of p(x)=x
3
−4x
2
−2x+20
A truck travels some distance at a speed of 35 km h in 120 min and the remaining distance at a speed of 48 km h in 90 min. Determine the: (a) total distance covered. (b) average speed over the entire journey
Answer:
a) 142 km,b) 40.57 km/hStep-by-step explanation:
Use of formula:
speed = distance / timedistance = speed × timea) Find each part of distance and add together. Convert minutes to hours.
35 × (120/60) = 35 × 2 = 70 km,48 × (90/60) = 48 × 1.5 = 72 kmdistance = 70 + 72 = 142 kmb) Average speed is:
speed = 142 /(2 + 1.5) = 142/3.5 = 40.57 km/h (rounded)Answer:
(a) 142 km
(b) 40.57 km/h (2 d.p.)
Step-by-step explanation:
Part (a)[tex]\boxed{\sf Distance=Speed \times Time}[/tex]
Given:
Speed = 35 km/hTime = 120 min = 2 hSubstitute the given values into the distance formula to find the distance travelled:
[tex]\implies \sf Distance = 35 \times 2 = 70\;km[/tex]
Given:
Speed = 48 km/hTime = 90 min = 1.5 hSubstitute the given values into the distance formula to find the distance travelled:
[tex]\implies \sf Distance = 48 \times 1.5 = 72\;km[/tex]
Therefore, the total distance travelled is:
[tex]\implies \sf 70 + 72 = 142 \; km[/tex]
Part (b)[tex]\boxed{\sf Average\;speed=\dfrac{Total\;distance}{Total\;time}}[/tex]
Given:
Total distance = 142 kmTotal time = 2 + 1.5 = 3.5 hSubstitute the given values into the average speed formula to find the average speed over the entire journey:
[tex]\implies \sf Average\:speed=\dfrac{142}{3.5}=40.57\;km/h\;(2\;d.p.)[/tex]
RS has endpoints R(3, 5) and S(–3, –1). Which statement explains whether the midpoint M of lies on the y-axis?
M = = (4, –2) does not lie on the x- or y-axis because neither coordinate is zero.
M = = (3, 3) does not lie on the x- or y-axis because neither coordinate is zero.
M = = (2, 0) lies on the y-axis because the y-coordinate is zero.
M = = (0, 2) lies on the y-axis because the x-coordinate is zero.
Mark this and return
Step-by-step explanation:
M = (0, 2), and it lies on the y-axis, because the x-coordinate is 0.
by the way, the first 2 answer options are correct statements too, they are just not specifying the actual midpoint.
Answer:d
Step-by-step explanation:edge2023
g(x)=5x+50 answer please
The answer to the linear equation g(x) = 5x+50 is plotted on the graph.
What is a linear equation?A linear equation is one in which the variable's maximum power is always one.A one-degree equation is another term for it.A linear equation in one variable takes the conventional form Ax + B = 0. x is a variable, A is a coefficient, and B is constant in this equation.Given equation:
g(x)=5x+50
The equation can also be written as y = 5x+50.
Now, we can replace the value of x for different numbers in the given equation to get the value of y to create the coordinates.
When we put x = 0 in the equation, we get y = 0 + 50 = 50.
Similarly, if we substitute the value of x as 1 in the equation, we get y = 5(1) + 50 = 55.
If we substitute the value of x as 2, y = 5(2) + 50 = 60
If we substitute the value of x as -1 and -2, we get the value of y as,
y = 5(-1) + 50 = 45 and y = 5(-2) + 50 = 40.
These pairs of values satisfy the linear equation and are plotted on the graph given below.
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Matthew wants his run today to take no more than 90 minutes. He already has run 30 minutes at a pace of 10 minutes per mile.
Part A)
Write an inequality that Matt could solve to find out how many more miles he can run if he keeps his current pace. Show or explain the reasoning you used to determine your answer.
The inequality for the given situation is m ≤ 6.
Given that, Matthew wants his run today to take no more than 90 minutes and he already has run 30 minutes at a pace of 10 minutes per mile.
What is the inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Let the number of miles be m.
m ≤ 90/10 - 30/10
m ≤ 9 - 3
m ≤ 6
Therefore, the inequality for the given situation is m ≤ 6.
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please answer !!!!!!!!!!!!!!
Answer:
ST = 63
TU = 63
SU = 126
Step-by-step explanation:
Given that T is the midpoint...
Thus TS = ST and SU = 2ST =2TU
from equation...
9n = 5n + 28
9n - 5n = 28
4n = 28
n = 7
Put the value of n in the equation...
ST = 9n
= 9 x 7
= 63
SU = 9n + 5n + 28
= (9 x 7) + (5 x 7) + 28 = 126
Hope this helps!
3(3v - 4) = 51 solve for v simplify your answer as much as possible
Answer: v = 7
Step-by-step explanation:
1. Distribute
3 (3v - 4) = 51
9v - 12 = 51
2. Add 12 to both sides
9v - 12 = 51
+ 12 + 12
3. Cancel out 12 + 12
51 + 12 = 63
9v = 63
4. Divide 9 on both sides
9v/9 = 63/9
5. Cancel out 9v/9
v = 7
PLS HELP ASAP!!!!
identify the type of transformation
Answer:
Reflection
Step-by-step explanation:
A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to mirror the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and form as the original, but it faces the opposite way. The opposing signs are created from the coordinates. Changes in posture during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context.
helppp ... see picture
Tyler simplified the expression x Superscript negative 3 Baseline y Superscript negative 9. His procedure is shown below.
x Superscript negative 3 Baseline y Superscript negative 9 = StartFraction 1 Over x cubed EndFraction times StartFraction 1 Over y Superscript negative 9 EndFraction = StartFraction 1 Over x cubed y Superscript negative 9 EndFraction
What is Tyler’s error?
Both powers should be in the numerator with positive exponents.
Both powers should be in the denominator with positive exponents.
The power x cubed should be in the numerator and the power y Superscript 9 in the denominator.
The power y Superscript 9 should be in the numerator and the power x cubed in the denominator.
The Tyler’s error is Both powers should be in the denominator with positive exponents.
what is exponents?The exponent of a number shows how many times the number is multiplied by itself.
For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general, [tex]x^n[/tex]means that x is multiplied by itself for n times.
given:
[tex]x^{-3} y^{-9}[/tex] = 1/x³ × [tex]1/ y^{-9}[/tex]
As, we know using the law of exponents
[tex]a^{-m} = 1/a^m[/tex]
So, [tex]x^ {-3} = 1/[/tex]x³
and, [tex]y^{-9}[/tex] = [tex]1 / y^9[/tex]
Then, we can write
[tex]x^{-3} y^{-9}[/tex] = 1/x³ × [tex]1/ y^{9}[/tex]
Hence, Both powers should be in the denominator with positive exponents.
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Gigi is going to buy 100 stickers.
Here is some information about the cost of stickers in two shops.
Stickers4u
World Stationery
Pack of 25 stickers for £2.25
Pack of 10 stickers for £1.75
Buy 1 pack get 1 pack 1 free
Gigi wants to buy the stickers for the best possible price.
Which shop should Gigi buy the 100 stickers from?
You must show how you get your answer.
Answer:
Buying from World Stationery shop would profit Gigi.
How to find the most profitable shop?Given,
Gigi is going to buy 100 stickers.
Stickers4u - Pack of 25 stickers for £2.25
World Stationery - Pack of 10 stickers for £1.75
Buy 1 pack get 1 pack 1 free
Solution:
Cost of 1 sticker in Stickers4u = £2.25/25 stickers = £0.09
Cost of 1 sticker in World Stationery = £1.75/ 10 stickers = £0.175
Since it is mentioned, 'Buy 1 pack get 1 pack 1 free' in this shop, the total no of stickers one would get for the price would be doubled.
Hence,
Cost of 1 sticker in World Stationery would be = £1.75/ 20 stickers = £0.0875
On comparing the price per sticker of both the shops, we can say that
buying from World Stationery shop would profit Gigi.
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Charlie Brown and Linus are so excited for Halloween that they have planned trips to three different parks. They are willing to pay no more than $40 to go to all of them. Jones’ Corn Maze has an entry fee that is $4 less than double the amount of Tomilloso’s Pumpkin Patch entrance fee. King’s Haunted House has an entry fee that is $2 more than Tomilloso’s Pumpkin Patch. What is the maximum price Charlie and Linus are willing to pay to enter each park?
The maximum price Charlie and Linus are wiling to pay to enter each park is 10.5 dollars.
How to use inequality to represent a situation?Charlie Brown and Linus are so excited for Halloween that they have planned trips to three different parks.
They are willing to pay no more than $40 to go to all of them.
Jones’ Corn Maze has an entry fee that is $4 less than double the amount of Tomilloso’s Pumpkin Patch entrance fee.
King’s Haunted House has an entry fee that is $2 more than Tomilloso’s Pumpkin Patch.
let
x = amount of Tomilloso’s Pumpkin Patch entrance fee
Therefore, the inequality that represent the situation is as follows;
Jones’ Corn Maze an entry fee = 2x - 4
King’s Haunted House entry fee = 2 + x
Therefore,
2x - 4 + 2 + x + x ≤ 40
4x - 2 ≤ 40
add 2 to both sides of the inequality
4x - 2 + 2 ≤ 40 + 2
4x ≤ 42
divide both sides of the inequality by 4
4x / 4 ≤ 42 / 4
x ≤ 10.5
Therefore, the maximum price they can pay is 10.5 dollars
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Solve the system of linear equations using the substitution method.
2y + x = -15 and x = 3y
A. (-6, -3)
B. (-7, -6)
C. (-8, -6)
D. (-9, -3)
Answer:
the answer is D. (-9, -3)
[tex]{ \green{ \tt{option \: (d)}}}[/tex]
Step-by-step explanation:
Given,
[tex]{ \tt{2y + x = - 15}} \: { \to} \: { \tt {eq}^{n} (1)}[/tex]
[tex]{ \tt{x = 3y}} \: { \to} \: { \tt{ {eq}^{n} (2)}}[/tex]
Substitute the value of eqⁿ (2) in (1) then,
[tex]{ \tt{2y}} \: + \: { \red{ \tt{3y}}} \: = - 15 [/tex]
[tex]{ \tt{5y = - 15}}[/tex]
Divide both sides by 5 then,
[tex]{ \tt{ \frac{5}{5}y = - \frac{15}{5}}} [/tex]
[tex]{ \red{ \boxed{ \tt{y = - 3}}}}[/tex]
Substitute the value of y in eqⁿ (2)
[tex]{ \tt{x = 3y}}[/tex]
[tex]{ \tt{x = 3( - 3)}}[/tex]
[tex]{ \red{ \boxed{ \tt{x = - 9}}}}[/tex]
Therefore, the value of (x,y) is (-9,-3)
Hence, option (d) is correct.
Finnegan wants to buy a sweater for $29.50 and jeans for $42.50. If the sales tax rate is 8.25%, what will be the amount of sales tax on Finnegan’s purchase?
The amount of sales tax on Finnegan's purchase is $5.94
How to calculate the amount of sales tax on the purchase ?The first step is to calculate the total amount of purchase
Sweater- $29.50
Jeans- $42.50
Total amount
29.50 + 42.50
= 72
The sales tax rate is 8.25%
The amount of sales tax on the purchase can be calculated as follows
8.25/100 × 72
= 0.0825 × 72
= 5.94
Hence the sales tax on the total purchase is $5.94
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-35 represents the starting location of a race car that is 35 yards behind the starting line. 35 represents the ending location of a race car that is 35 yards in front of the starting line
As shown in the number line, The total distance of the racing road is 70 yards.
it is given that the starting location is -35 yards behind the starting line and the ending location of the race court is 35 yards in front of the starting line.
we have to draw a Number line that has -35 and +35 so the origin of that number line is the starting point of the race court.
In the above figure if we are moving forward towards the origin we find that we are moving 35 yards in the number line, after reaching the origin of the number line move forward again 35 yards then we are at the ending location of the racing court.
So,
35 yards + 35 yards = 70 yards
The total racing area of the cars is = 70 yards.
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5 1/2 ÷3 3/8
hey umi, need it
because i have school in 26 well Thursday and it is a assignment and it is due today
Answer:
1 - 1.5
2 - 3.9375
3 - 3
4 - 1.62962963
5 - 2.83333
6 - 4.05555556
7 - 8
8 - 1.555555556
9 - 6.4
10 - 6
11 - 1.5
12 - 18
A line with a slope of 3/4 and containing the point (0,2)
An equation of line with a slope of 3/4 and containing the point (0,2) is y = (3/4)x + 2
In this question, we have been given
slope (m) = 3/4
and a point (0, 2)
We need to find an equation of a line with a slope of 3/4 and containing the point (0,2)
Using the formula for the slope-point form of equation of line,
y - y1 = m(x - x1)
y - 2 = 3/4(x - 0)
y - 2 = (3/4)x
y = (3/4)x + 2
Therefore, an equation of line with a slope of 3/4 and containing the point (0,2) is y = (3/4)x + 2
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Solve the quadratic equation.
x² + 9x - 36 = 0
O A. x = 3 or 12
OB. x = 3 or -12
O C. x = 6 or -6
OD. no real solution
Answer:
B x = 3 or -12
Step-by-step explanation:
(btw this / is a fraction sign and this ^ is the power of sign)
Let's solve your equation step-by-step.
x^2+9x−36=0
For this equation: a=1, b=9, c=-36
1x^2+9x+−36=0
Step 1: Use quadratic formula with a=1, b=9, c=-36.
x= −b±√b^2−4ac/2a
x= −(9)±√(9)2−4(1)(−36)/2(1)
x= −9±√225/2
= x= 3 or x= -12
Select all the expressions which are equivalent to –3(0.15 – 0.2 + 0.25p).
A. –0.45 – 0.6 + 0.25p
B. 0.15 – 0.75p
C. 3(0.15 + 0.2 + 0.25p)
D. –3(–0.05 + 0.25p)
E. –3(0.05 + 0.25p)
I need help ASAP.
Answer:
–3(0.15 – 0.2 + 0.25p) is equivalent to –3(-0.05 + 0.25p) and 0.15 – 0.75p
In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who has a sister also has a brother?
If In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister. The probability that a student who has a sister also has a brother is: 3/10.
Determining the probabilityGiven data:
Total number of student = 30
Brother = 13
Sister = 8
Brother and sister = 3
Now let determine the probability that a student has brother and sister using this formula
P ( S n B ) = Brother and sister / Total number of student
Let plug in the formula
P ( S n B ) = 3/30
Therefore we can conclude that 3/30 is the probability.
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Answer:
3/8
Step-by-step explanation:
I need this answer as soon as possible
Note: This is grade 6 maths
10.
A gallon = 4 quarts
4 quarts = 4 x 2 = 8 pints.
8 pints = 8 x 16 = 128 (ounces)
So, a gallon equals 128 ounces.
11.
Generally, 2 cups = 1 pint.
-> 4 cups = 2 pint = 1 quart
So, he should (probably) use the entire quart.
12.
Convert all the mixed numbers to fractions, mk.
14(7/9) + 6(5/9)
= 14+6(7/9+5/9) = 20(12/9) = 64/3.
13. 15(11/16) + 21(9/16) = 36(11/16+9/16) = 36(20/16) = 149/4
14. 7(1/2) + 5(1/2) = 12(1/2+1/2) = 13( = 13/1)
15. 17(3/4) - 4(1/4) = 17-4(3/4-1/4) = 13(1/2) = 27/2
16. 23(5/8) - 12(3/8) = 23-12(5/8-3/8) = 11(2/8) = 45/4
17. 27 - 6/8 = 216/8 - 6/8 = 210/8 = 55/2.
Please recheck and if you spot anything wrong tell me.