You invested a total of $30,000 at 3% and 4 1 2 % simple interest. During one year, the two accounts earned $1200. How much did you invest in each account?

Answers

Answer 1

Answer:

$20,000 at 4.5% simple interest

$10,000 at 3% simple interest

Step-by-step explanation:

[tex].045x + .03(30000 - x) = 1200[/tex]

[tex].045x + 900 - .03x = 1200[/tex]

[tex].015x + 900 = 1200[/tex]

[tex].015x = 300[/tex]

[tex]x = 20000[/tex]

$20,000 at 4.5% simple interest

$30,000-$20,000=$10,000 at 3% simple interest


Related Questions

PLS HELP AND EXPLAIN pls

Answers

Check the picture below.

[tex]\stackrel{\measuredangle N}{(5x-8)}~~ + ~~\stackrel{\measuredangle O}{(x-5)}~~ + ~~\stackrel{\measuredangle P}{(6x+1)}~~ = ~~180 \\\\\\ 12x-12=180\implies 12x=168\implies x=\cfrac{168}{12}\implies x=14 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle O}{(x-5)}\implies (14)-5\implies {\Large \begin{array}{llll} \stackrel{\measuredangle O}{9} \end{array}}[/tex]

Find the slope of the line represented
by the data below.
xl 0 2
y 15
4
9 3
6 8
-3 -9
Simplify completely.
Slope = [?]
Hint: The slane of lin
Change in y

Answers

Answer:

-3

Step-by-step explanation:

[tex] \frac{a - 15}{2 - 0} = \frac{ - 6}{2} = - 3 \\ \frac{3 - 9}{4 - 2} = - 3 \\ \frac{ - 3 - 3}{6 - 4} = - 3 \\ \frac{ - 9 - ( - 3)}{8 - 6} = - 3 \\ so \: slop \: is \: - 3[/tex]

find thesum using a number line
7t5=​

Answers

Answer:

12

Step-by-step explanation:

Did you mean 7+5?

If so, then 7 + 5 = 12

Write equations for the horizontal and vertical lines passing through the point (8,1)

Answers

Check the picture below.

Answer:

Step-by-step explanation:

Horizontal line is y = 1

Vertical lone is x = 8.

Half a number increased by 15 is equal to the sum of five and the product of three and the number what is the number 

Answers

The number is (x/2)+15=5+3x if Half of Number augmented by 15 equals the sum of 5 and the product of 3 and the number.

Explain what a number system is?

A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

Which four different number systems are there?

Decimal Number System is one of the four popular forms of number systems and other 3 are -

System of binary numbers.

System of Octal Numbers.

System of Hexadecimal Numbers.

From the given question,

X is the number. first we have to halve it , then we add 15.

Next ,set it equal to the other side . the second side is 5+ ( because it is the sum)

3x( the product of 3 and x means multiply them)

Hence the number is (x/2)+15=5+3x

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The Highest Common Factor of a
and b is 48 and the Lowest
Common Multiple is 1680.
Given that a < b and that both
numbers are greater than 48,
work out the values of a and b.

Answers

Answer:

a = 240

b = 336

Step-by-step explanation:

To find LCM of 2 number:

list all prime factors that appear in either numbers. If a factor appears more than once in one of the numbers list it that many times. Multiply these together to get LCM

To find HCF of 2 numbers:

List all prime factors both numbers. Multiply these together to find HCF

In this question LCM and HCF is already given but the numbers a and B are unknown.

To find a and B we do the opposite.

Further explanation is in the attached file please open as you will get a clear understanding of the answer.

After 5 years, $8,000 deposited in a savings account with simple interest had earned $3,600 in interest. What was the interest rate?

Answers

Answer:

9%

Step-by-step explanation:

So first we need to find how much interest he got in a single year.

3600 ÷ 5 = 720

Now we find out how much 720 is compared to 8000.

720 ÷ 8000 = 0.09

Then we make that a percentage:

9%

2a + 3=7 and 6x +10y =40 what is the value of 6a+9b what is the value of 3x +5y​

Answers

Using the given information, the value of 6a + 9b is 21 and the value of 3x + 5y is 20

Evaluating an expression

From the question, we are to determine the values of the given expressions.

From the given information,

2a + 3b = 7

and

6x + 10y = 40

To determine the value of 6a + 9b, multiply the first equation by 3.

That is

3 × [ 2a + 3b = 7

6a + 9b = 21

∴ The value of 6a + 9b is 21

To determine the value of 3x + 5y, we will divide the second equation by 2

That is,

6x + 10y = 40 ] ÷ 2

3x + 5y = 20

The value of 3x + 5y is 20

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Helppp pls asappp simple math

Answers

Answer:

D. reflection over the y-axis.

Step-by-step explanation:

Reflections are the samere same shapes, but mirrored and over a certain axis (x or y axis). In this case, we see a reflection over the y-axis.

Question 5
Point C is the midpoint of AB and point B is between points A and D. If AD = 15 and
BD = 7, what is CD?
CD

Answers

If C is the midpoint of AB then the length of CD is 11 units.

The midpoint of a line segment is referred to as the midpoint in geometry.

It functions as the centroid of the segment and the endpoints, and it is equally separated from both. It cuts the portion in half. As there is no distinguishing point to act as the point at infinity (any point in a geometric range may be protectively transferred into any other point in (the very same or some other) projective range), the midpoint is difficult to define in projective geometry. On the perception line in question, an affine structure can be defined by fixing a point at infinity and then using the aforementioned concept.

Given C is the midpoint of AB.

AD = 15 and BD = 7

Now AB = 15 - 7 = 8

Again AC = BC

Therefore = BC = 8 / 2 = 4

Now CD = BC + BD = 4 + 7 = 11

Therefore the length of CD is 11 units.

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Your answer is
Dante will run at least 33 miles this week. So far, he has run 15 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.

Answers

The number of possible additional miles that he needs to run will be 18.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Dante will run at least 33 miles this week. So far, he has run 15 miles.

Then the number of possible additional miles that he needs to run.

Let t be the number of additional miles he will run. Then the inequality is given as,

15 + y ≤ 33

y ≤ 33 - 15

y ≤ 18

The number of possible additional miles that he needs to run will be 18.

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Geometry, if |AC| = |CD|, find angle x.

Answers

From the given figure the value of angle x is 40 degrees

How to find angle x

|AC| = | CD |

Δ ( ACD ) = Δ ( DCB )

< ( BAC ) = 70 degrees

Since |AC| = | CD | then the base angles are equal, hence

< ( ADC ) =  < ( BAC ) 70 degrees. ( base angles of isosceles triangle )

< ( ADC ) + < ( BAC ) + < ( ACD ) = 180 degree ( sum of angles in a triangle)

note < ( BAC ) = < ( DAC )

< ( ACD ) = 180 - 70 - 70

< ( ACD ) = 180 - 140

< ( ACD ) = 40 degrees

If Δ ( ACD ) = Δ ( DCB ) then the angles should be equal

Δ ( ACD ) has angles:

< ( ADC )  = 70

< ( DAC ) = 70

< ( ACD ) = 40

Then Δ ( DCB ) should have angles 70, 70, and 40. The figure did not give enough information to put the angles where it should be.

Comparing with the options, only angle 40 degrees is in the option, hence the correct answer

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SHOW YOUR WORK FOR BRAINLIEST
Solve for x. Assume that lines which appear to be diameters are actual diameters.
The Answer is -6

Answers

Answer:

if x = -6, r = 180/pi and D = 360/pi

without knowing the actual D or r, one cannot truly solve for x.

Step-by-step explanation:

looking at the angle, [tex]125^o[/tex], it is part of two supplementary parts of the circle, let us call the angle between [tex]55^o\ \&\ 125^o[/tex] y. given that 125 is supplementary to y:

125+y=180

and so...

y=55

now, let us call the angle associated with the arc-length, x+76 z.

Knowing that y+55 and z are supplementary (given the length is a diameter), we can write the equation:

y + 55 + z = 180

substituting y=55 gives:

55 + 55 + z = 180

combining like terms gives:

110 + z = 180

further simplifying gives:

z = 70

x + 76 is the arc-length of the section of the circle, whose angle is now denoted by z = 70.

Arc-length = Circumference * percentage of circle

circumference is given as C = π * D OR C = 2r * π (because 2r = D)

percentage of circle is simply (number of degrees covered ÷ total degrees of a circle)

so, we have that the percentage = 70/360 [360 degrees in a circle, 70 degrees covered by the angle, z]

and the circumference is unknown without a radius or diameter length, so we will use the equation C = π * D

using the formula for arc-length:

Arc-length =  π * D * 70/360

Arc-length also happens to equal x + 76, so:

x + 76 =  π * D * 70/360

reduce:

x + 76 =  π * D * 7/36

simplify by getting x alone:

x =  π * D * 7/36 - 76

we can further simplify by creating one fraction:

[tex]x = \frac{7D\pi - 2736}{36}[/tex]

it can also be shown as:

[tex]x = \frac{7r\pi - 1368}{18}[/tex]

because, D = 2r and you could factor 2 from (7*2*r*pi - 2736) and then reduce by dividing top and bottom each by 2.

You can divide top and bottom by 2 because:

[tex]\frac{2}{36} = \frac{1}{18}[/tex]

which is because [tex]\frac{km}{ln}=\frac{k}{l} * \frac{m}{n}[/tex]

if we say km = 2 and ln = 36, then k = 2, m = 1 is the only options for k and m

and l and n can be any set of factors of 36, which include 2*18, 3*12, 6*6, 9*4.

if we choose l = 2 and n = 18, then k = l = 2 and:

[tex]\frac{k}l=\frac{2}2 = \frac{r}{r}[/tex]

which is to say that k = r = l = 2, which I only show to say generally that when k = l or you have r ÷ r, it is equal to 1.

1 * s = s

and if s =  m ÷ n, then [tex]\frac{km}{ln} = \frac{m}{n}\ whenever\ k = l[/tex]

given that the answer to what is x, is -6, the arc length is therefore 70. we can plug in this 70 now to find r and therefore, D.

[tex]70 = \pi * D * \frac{70}{360}\\\\multiply\ by\ \frac{360}{70}\ on\ both\ sides\ to\ get:\\360=\pi * D\\divide\ by\ \pi\ on\ both\ sides\ to\ get:\\360/\pi = D\ OR\ 180/\pi=r[/tex]

Is 4.887888 a rational number

Answers

Answer:

Step-by-step explanation:

yes it is

help me out please i think it's correct but

Answers

Answer:

Step-by-step explanation:

your answer along with the work is down below please go and check it out also sorry I'm wrong have nice day:)

A line is drawn so that it passes through the points (3, 4) and (4, 1)
What is the slope of the line?
A: 1/3
B: 3
C: -1/3
D: -3

Answers

Answer:

m=y2-y1/x2-X1 so the slope is equal to -3

I need help with this math problem

Answers

Answer:

AB = 4.5 cm

Step-by-step explanation:

the total area (A) of the 2 rectangles is calculated as

A = x(x - 4) + 3x(x - 2)

   = x² - 4x + 3x² - 6x

   = 4x² - 10x

Given A = 36 , then equating

4x² - 10x = 36 ( subtract 36 from both sides )

4x² - 10x - 36 = 0 ( divide through by 2 )

2x² - 5x - 18 = 0 ← as required

To factorise the equation

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 18 = - 36 and sum = - 5

the factors are + 4 and - 9

use these factors to split the x- term

2x² + 4x - 9x - 18 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) - 9(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x - 9) = 0

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x - 9 = 0 ⇒ 2x = 9 ⇒ x = 4.5

but x > 0 , then x = 4.5

Then

AB = x = 4.5 cm

Answer:

AB = 4.5 cm

Step-by-step explanation:

[tex]\boxed{\textsf{Area of a rectange}=\sf width \times length}[/tex]

Area of the smaller rectangle:

[tex]\implies A=x(x-4)[/tex]

[tex]\implies A=x^2-4x[/tex]

Area of the larger rectangle:

[tex]\implies A=(2x+x)(x-2)[/tex]

[tex]\implies A=3x(x-2)[/tex]

[tex]\implies A=3x^2-6x[/tex]

The area of the compound shape is the sum of the areas of the two rectangles:

[tex]\implies A=(x^2-4x)+(3x^2-6x)[/tex]

[tex]\implies A=x^2+3x^2-4x-6x[/tex]

[tex]\implies A=4x^2-10x[/tex]

If the area of the compound shape equals 36 cm² then:

[tex]\implies 36=4x^2-10x[/tex]

[tex]\implies 36-36=4x^2-10x-36[/tex]

[tex]\implies 0=4x^2-10x-36[/tex]

[tex]\implies 4x^2-10x-36=0[/tex]

[tex]\implies \dfrac{4x^2}{2}-\dfrac{10x}{2}-\dfrac{36}{2}=\dfrac{0}{2}[/tex]

[tex]\implies 2x^2-5x-18=0[/tex]

The length of AB is x cm.  

To find the value of x, factor the quadratic.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].

[tex]\implies ac=2 \cdot -18=-36[/tex]

[tex]\implies b=-5[/tex]

Therefore, the two numbers are: -9 and 4.

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 2x^2-9x+4x-18=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x-9)+2(2x-9)=0[/tex]

Factor out the common term (2x - 9):

[tex]\implies (x+2)(2x-9)=0[/tex]

Apply the zero-product property:

[tex](x+2)=0 \implies x=-2[/tex]

[tex](2x-9)=0 \implies x=\dfrac{9}{2}=4.5[/tex]

As length is positive, x = 4.5 only.

Therefore, AB = 4.5 cm.

please help only one question i don’t get ;( i will mark brainliest

Answers

The graph plotted represents a discrete data

The domain of the function is -2 ≤ x ≤ 2

The range of the function is 1 ≤ y ≤ 5

The graph plotted is represent circle functions

What is discrete data?

This is a term used to represent data that can be estimated by counting. The circle graph is an instance of methods of representing discrete data.

What is domain and range?

The term domain refers to the input variables on a graph, the domain is usually plotted on the x axis.

Range is a term that describes the output functions and are usually plotted on the y axis.

The function plotted is a circle with a radius of 2 units.

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Find the distance between each pair of points round to nearest tenth if needed

Answers

Answer: 3.6

20

8.25

Step-by-step explanation:

7 - 10 = 3

-6 - -8 = 2

[tex]\sqrt{3^{2} +2^{2} } =3.6[/tex]

Which set of ordered pairs does not represent a function?
{(5,7), (4,-2), (-8,8), (4,-9)}
{(6,-2), (-2, -7), (-9,-4), (8,-7)}
{(-6,-7), (0,9), (6,-7), (3, -4)}
{(4,6), (9,-8), (3,2), (-9,-8)}

Answers

The first one bc the 4“x” repeats more than once in the x axis

3 1/4 x 1 1/6 as a mixed number in simplest form

Answers

91/24 or in more simple form 3 19/24
13/4x7/6=91/24
91:24=3.79

Find X? x+14+x3=78 How can I find X? Please answer. Thanks so much! (This is my older sister's account btw)

Answers

The value of  variable x in the equation is 16.

How to find the variable x in the equation?

The equation represented as follows:

x + 14 + x³ = 78

The value x is the variable.

A variable is number represented with a letter in an equation.

Therefore,

x + 14 + 3x = 78

subtract 14 from both sides of the equation

x + 3x + 14 - 14 = 78 - 14

x + 3x = 64

Therefore,

4x = 64

divide both sides by 4

4x / 4 = 64 / 4

x = 16

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portia can read 23 pages i 10 minutes. at this rate how many can she read in 55 minutes

Answers

The rate at which Portia reads is 2.3 pages per minute, at this rate, she can read 126.5 pages in 55 minutes.

How many pages can she read in 55 minutes?

We know that Portia can read 23 pages in 10 minutes, so the number of pages she reads per minute is given by the rate:

R = (23 pages)/(10 minutes) = 2.3 pages per minute.

Now, the number of pages she can read in 55 minutes is given by the product between the rate and 55 min, so we will get:

(2.3 pages/min)*55 min = 126.5 pages

We conclude that Portia can read 125.6 pages in 55 minutes.

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A person has a choice of receiving 3000 now or 4000 after she graduates from college in five years she decided to take the 3000 and the best add expected 10% annual rate of return. Did she make a wise decision?

Answers

Yes she made a wise decision as she will get an amount of 4500 after 5 years which is better than getting 4000 after 5 years.

Given that ,

Let us assume that the person takes the amount 3000 from the college, and invests it on a annual rate of 10% for a period of 5 years,

means,

Principal amount = 3000

Rate of Interest = 10%=0.1

Time = 5 years

What Is the Future Value Simple Interest ?

The future value simple interest formula is the addition of the principal amount that we have in the beginning and the interest earned on that principal amount after the completion of the period. The Future Value Simple Interest Formula is given as,

F V = P + I or F V = P(1 + rt)

Here,

P is the principal amount,

I is the interest,

r is the rate, and

t is the time.

So, We know that

Simple Interest = Principal amount * Rate of Interest * Time

Simple Interest = 3000*0.1*5

Simple Interest = 1500

So, The person will have a Future value of

Principal amount + Simple Interest

= 3000+1500

=4500

Therefore, If the person invests after 5 years will get a amount of 4500 in return which is a wise decision than not investing and getting a amount of 4000 .

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Stephen hit the ball 12 times out of 16 bats in the first half of the season in six times out of the 14 at that in the second half of the season what is his batting average for the first full season written as a decimal

Answers

The average for the first full season when Stephen hit the ball is 0.60.

What is the average?

The average for the first full season can be determined by adding the number of time he hit the ball in the first half and the second half of the season together and then dividing it by the total number of bats.

Average is a measure of central tendency. Average is also known as mean. Other measures of central tendency are mode and median.

Average = sum of the times he hit the ball / total number of bats

(12 + 6) / (16 + 14)

18 / 30 = 0.60

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Identify the constant term in the following polynomial
8x + 2x^3 - 5x^4 - 9

Answers

Answer:

-9

Step-by-step explanation:

Constants are terms that are only numbers, without any variables.

Terms

First, let's define what a term is. Within a polynomial, a term is an expression that is added to other terms to create a polynomial. It is important to note that terms are always added. So, if there is subtraction, that means one of the terms is negative.

Constants

The easiest way to identify constants is to look for terms without variables. In the polynomial above, the only constant is -9. All of the other terms have x to some power as a factor. Since they have variables, they cannot be a constant.

Numbers cannot be changed; this is why there are called constants. No matter the x-value, -9 will not change.

help pls, thank you

Answers

4x + 17 = 101
-17 -17
4x = 84
/4 /4
X=21

Both angels are the same

if anyone can help lmk brainly answer and 20 points

Answers

a)Midpoints are (-6.5,-4).

b)Midpoints are (-6.5,-4).

What are midpoints?

In geometry, a line segment's midpoint is referred to as the midpoint. It serves as both the segment's and the ends' centroid, and it is equally spaced from both. The portion is halved by it. The midpoint formula is employed when it is important to pinpoint the exact intersection of two given points. The point that splits a line segment described by two points in half can thus be found using this method. The halfway is the precise numerical intersection of two integers. The two-number average computation and the midpoint calculation are equivalent. Consequently, you may get the halfway point between any two integers by adding any two numbers together and dividing by two.

Given Data

Mid point formula = [tex]\frac{x+x}{2}[/tex]¹ , [tex]\frac{y+y}{2}[/tex]¹

a) (2,-1) (-8,6)

Equating values in formula,

[tex]\frac{2-8}{2}[/tex] , [tex]\frac{-1+6}{2}[/tex]

(-4,2.5)

Midpoints are (-4,2.5)

b) (-8,-9) (-5,1)

Equating,

[tex]\frac{-8-5}{2}[/tex] , [tex]\frac{-9+1}{2}[/tex]

[tex]\frac{-13}{2}[/tex] , [tex]\frac{-8}{2}[/tex]

(-6.5,-4)

Midpoints are (-6.5,-4).

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find both the number combinations in the number of permutations for 9 objects taken 7 at a time

Answers

Answer

There are 36 combinations and 181440 permutations

Explanation

The number of combinations of n object taking r at a time is given by the formula;

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

From the question, n = 9 and r = 7, then substitute these values into the formula

[tex]^9C_7=\frac{9!}{7!(9-7)!}=\frac{9!}{7!\text{ }2!}=\frac{9\cdot8\cdot7!}{7!\times2}=\frac{72}{2}=36[/tex]

The number of permutations of n object taking r at a time is given by the formula;

[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]

Also, n = 9 and r = 7, then substitute these values into the formula to get the number of permutations

[tex]^9P_7=\frac{9!}{(9-7)!}=\frac{9!}{2!}=\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2!}{2!}=181440[/tex]

Therefore, there are 36 combinations and 181440 permutations

A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of finished products and computes the sample mean product weight. If test results over a long period of time show that of the values are over pounds and are under pounds, what are the mean and the standard deviation for the population of products produced with this process?.

Answers

The mean and the standard deviation for the population of products are 2.0 and 0.3329, respectively.

What is defined as the standard deviation?A standard deviation (or) is a measure of how widely distributed the data is in regards to the mean. A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation implies that data is more spread out.

The mean and standard deviation of the population of products produced by the process are 2.0 and 0.3329, respectively.

Start by determining the population mean which use:

μ = (L +  U)/2

Where:

L = 1.9 and U = 2.1

Put the values;

μ = (1.9 + 2.1)/2

μ = 2.0

When p = 5%, the z value from the probability z table is:

z = -1.645

In addition, the z-score is:

z = (x - μ)/(σ/√n)

Put the values;

-1.645 = (1.9 - 2.0)/(σ/√30)

Simplify the equation.

σ = 0.3329

As a result, the mean and standard deviation again for population of products manufactured by the process are 2.0 and 0.3329, respectively.

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The complete question is-

A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights x¯. If test results over a long period of time show that 5% of x¯ the values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process?

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