4. last year nina invested $6,000. she put some of it in a cd the paid 4% simple interest, and she put the rest of it in a savings account that earned 2.5% simple interest. at the end of the year she earned a total of $204 interest. how much did she invest in each account? assume there were no other deposits or withdrawals.

The yearly compound interest rate of $640 at the end of 4 years would be; 3.07

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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Buying from World Stationery shop would profit Gigi.

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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Answer:

Step-by-step explanation:

4

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

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.

The answer to the linear equation g(x) = 5x+50 is plotted on the graph.

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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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.

Answer:

321000

Step-by-step explanation:

The highest price of house that Holly can afford is £343350.

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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The Tyler’s error is Both powers should be in the denominator with positive 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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Answer:

Slope m = 2

Step-by-step explanation:

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]

The amount of sales tax on Finnegan's purchase is $5.94

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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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.

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

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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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.

Given 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:

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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The absolute value equation with the solutions -3.75 and 3.75 is:

|x| = 3.75

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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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!

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.

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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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

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.

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

Answer:

Step-by-step explanation:

Use of formula:

a) Find each part of distance and add together. Convert minutes to hours.

b) Average speed is:

Answer:

(a)  142 km

(b)  40.57 km/h (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\sf Distance=Speed \times Time}[/tex]

Given:

Substitute the given values into the distance formula to find the distance travelled:

[tex]\implies \sf Distance = 35 \times 2 = 70\;km[/tex]

Given:

Substitute 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]

[tex]\boxed{\sf Average\;speed=\dfrac{Total\;distance}{Total\;time}}[/tex]

Given:

Substitute 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]

The maximum price Charlie and Linus are wiling to pay to enter each park is 10.5 dollars.

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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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

Answer:

–3(0.15 – 0.2 + 0.25p) is equivalent to –3(-0.05 + 0.25p) and 0.15 – 0.75p

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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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