Lauren deposited $300 to start her savings account. After one year, she had $312 in
her account. If she did not deposit or withdraw any money that year, how much
interest did she earn?
N

Answer:

14

Step-by-step explanation:

This question can be expressed as the following linear equation:

2x+8=36, where x is our unknown number.

From here,

2x+8=36

2x=28 (-8 both sides)

x=14 (/2 both sides)

Therefore the number is 14

Answer:

a) The hypotenuse side is BC.

b) Using the Pythagorean Theorem, we can determine the missing side: AB = √(AC² - BC²) = √(6² - 4²) = √(36 - 16) = √20 = 4.47.

c) The perimeter of the triangle is AC + BC + AB = 6 + 4 + 4.47 = 14.47.

d) The area of the triangle is ½ × AC × AB = ½ × 6 × 4.47 = 13.7.

Step-by-step explanation:

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. So, for the triangle given, we can use this theorem to calculate the length of side AB, which is the missing side. Then, we can calculate the perimeter of the triangle by adding up all three sides and the area of the triangle by using the formula ½ × AC × AB.

Answer:

y = -3x + 3

Step-by-step explanation:

the equation of a line in point-slope form is.

y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - (-6) = -3 (x - 3)

y+6 = -3x+9

Answer:

y = -3x+3

Step-by-step explanation:

Remember that y = mx+c

The slope is m aka the gradient and we know that that's -3.

So just chuck it into the equation:

y = -3x + c

We still have to find c (which is the y intercept)

So substitute the point (3,-6) into the equation

We will have: -6 = -3(3) +c

Once you do algebra you'll get 3=c

So substitute that back into the equation (without the point (3,-6) since we only need the equation)

y = -3x + 3

The relative frequency as a percentage is 25.7%.

The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency. Divide each frequency by the overall sample size, in this example 20 students, to determine the relative frequencies.

The relative frequency of students who picked either butterflies or trains as their favorite exhibit is 18 (12 + 6) out of a total of 70 students.

The relative frequency as a percentage is 18/70 * 100 = 25.7%.

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The money that a organisation earns in return for their labour or products is referred to as income.She make from each source last year $6000.

The money that a person or organisation earns in return for their labour or products is referred to as income.

Salary, rent, capital gains, company revenue, and income from other sources are a few typical sources of income. Understanding how each type of income is taxed is not always simple, and you may require an income tax calculator to do so.

Let t=teaching income, p=painting income, and b=book sales income.

t=p+6000 b=(t+p)/7 b+t+p=48000 (t+p)/7 +p+6000+p=48000 substitute (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000 multiply each side by 7 to eliminate the fraction.

substitution (2p+6000)/7 + p+6000 + p = 48000 (2p+6000) + 7(p+6000) + 7p = 7*48000

2p+6000+7p+42000+7p=336000

16p+48000=336000

16p=336000-48000

16p=288000 \s16p/16=288000/16

p=$18,000.

t=18000+6000

t=$24,000.

b=(24000+18000)/7

=42000/7

=$6000.

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The powers that have same value as 1^8 are 1^n, n^0 where n=real number.

What are real numbers?

Real numbers are simply the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also. At the same time, the imaginary numbers are the un-real numbers, which cannot be expressed in the number line and are commonly used to represent a complex number. Some of the examples of real numbers are 23, -12, 6.99, 5/2, π, and so on.

Now,

As we know anything raised to the power of 1 is always one and 0 raised to the power of anything is also one.

Hence, the powers that have same value as 1^8 are 1^n, n^0 where n=real number.

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The length of TU in a trapezoid RSUT is  34 units.

To find the length of TU, we can use the midpoint formula. The midpoint formula states that for a line segment with endpoints (x1, y1) and (x2, y2), the midpoint is ((x1 + x2)/2, (y1 + y2)/2).

In this case, we know that X is the midpoint of line segment RS and V is the midpoint of line segment SU. So we can set up the following equation:

(RS/2) + (SU/2) = 44

Where (RS/2) = (30/2) = 15 and (SU/2) = TU/2

So we can substitute this into the equation and get:

15 + (TU/2) = 44

To find TU, we can solve this equation by multiplying both sides by 2:

TU = 2(44) - 2(15) = 64 - 30 = 34

So the length of TU is 34 units.

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Answer: 12.5% is 1/8

Answer: 25/2 would be your answer, as it is already in it's simplest form.  I hope this helps! :)

Step-by-step explanation:

The ordered pair (6, 4) is not a solution to the inequality

The graph is given below

Option A is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

Ordered pair = (6, 4)

This means,

(6, 4) = (x, y)

Now,

y < 3/4(x - 3)

Substitute (6, 4) = (x, y)

4 < 3/4(6 - 3)

4 < 3/4 x 3

4 < 4

This is not true.

From the graph,

(6, 4) is above the line.

Thus,

The graph is given below

(6, 4) is not a solution.

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Students can plant seeds in a whole community garden in 5 1/3 h. Hence, Vanessa is not correct.

In the example question, students must plant seeds in 3/8 of a community garden in two hours.

The children will need 4 hours to plant the seeds for the entire garden, according to Vanessa.

We must confirm whether Vanessa is correct.

Within two hours, students plant seeds in 3/8 of the community garden.

Students can therefore plant seeds in 1 community garden in = 2/(3/8) h.

In one of the community gardens, students can sow seeds in = 2/3 * 8 hours.

In one of the communal gardens, students can plant seedlings in 16/3 hours.

In one of the communal gardens, students can sow seeds in 5 1/3 hours.

Students can therefore plant seeds in the entire community garden in 5 1/3 hours. Hence, Vanessa is not correct.

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Due to the fact that 8 over 14 is more than 11 over 21, Zachariah has a higher ratio of American stamps than Khai.

Due to the fact that 8 over 14 is more than 11 over 21, Zachariah has a higher ratio of American stamps than Khai.

An element of a number or any number of equal pieces is represented by a fraction.

Given that Khai and Zachariah are stamp collectors.

Zachariah also contains eight of the fourteen American stamps that are available.

Khai contains 11 American stamps out of a total of 21.

Khai equals 8/14 Zachariah equals 11/21

Zachariah has a higher proportion of American stamps than Khai does since 8 over 14 is more than 11 over 21.

After all, we would convert 11/21 and 8/14 into fractions.

Tell them that we would turn their fractional values into decimals and then into percentiles.

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For the sum of ages of Adam, Barry, and Charlie is 53 , Barry is 14 years old.

Number of brothers are three.

Adam, Barry and Charlie.

Let us consider 'x' years be the age of Barry.

Adam age is equal to (2x) years.

And Charlie age is equal to ( x - 3 )years.

Sum of their ages = 53

Substitute the value of Adam, Barry and Charlie age we get,

⇒ x + 2x + x - 3 = 53

⇒ 4x = 53 + 3

⇒ 4x = 56

⇒ x = 56 / 4

⇒ x = 14 years

Barry is  14 years old.

Adam = 2(14 )

          = 28 years

Charlie = 14 - 3

            = 11 years

Therefore, as per the information about the ages of Adam, Barry and Charlie , the Barry is 14 years old.

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To calculate the amount of money in Roberto's savings account after 5 years, you can use the formula for simple interest:

I = Prt

Where:

I = Interest earned

P = Principal (original amount of money in the account)

r = Annual interest rate (expressed as a decimal)

t = Number of years

In this case, the principal is $250, the annual interest rate is 5% (or 0.05 as a decimal), and the number of years is 5.

So, you can plug these values into the formula:

I = 250 * 0.05 * 5

To find out the total amount of money in the account after 5 years, you need to add the interest to the principal:

250 + I = 250 + (250 * 0.05 * 5) = 250 + 62.5 = $312.5

Roberto's account will have $312.5 after 5 years.

The functions f and  have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.

What is a graph ?

Graph can be defined as the visual representation of the given data using ordered pairs.

Graph of f(x)

You can read the y-intercept on the graph. It is the value of y-coordinate when x = 0; so ti is y = 6.

The axis of simmetry is the vertical line that split the graph into two symmetrical forms. That is the same that the vertical line that passes through the vertex. You can see that it is x = 2

2) Table of values of g(x)

The y-intercept is the value of y-coordinate when x = 0, so it is y = 8.

The axis of symmetry is x = 2.

Hence, The functions f and  have the same axis of symmetry and the y-intercept of f is less than the y-intercept of g.

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The height of the given triangle is 4cm.

Let the base of the triangle be x cm.

It is given that the height of the triangle is 8cm shorter than the base.

∴ Height of the triangle = ( x-8 ) cm

Now,

       Formula for the area of a triangle = 1/2 × Base × Height  sq units.

       It is given that the area of the triangle is 24 cm^2.

       Area= 1/2* x(x-8) cm^2

     ⇒ 1/2 × x(x-8) = 24

    ⇒  x(x-8) = 48

    ⇒ [tex]x^{2}[/tex] - 8x -48=0

    ⇒ [tex]x^{2}[/tex] - 12x + 4x -48 = 0

    ⇒ x(x -12) +4(x-12) = 0

    ⇒ ( x-12 )( x + 4) =0

    ⇒ x= 12 , -4

Since, x is a length so it can not be negative value.

∴ x = 12 cm

Now, height = x-8= 4 cm

Therefore, The height of the given triangle is 4cm.

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       0.0000732 = 7.32 x 10⁻⁵

     145,000 = 1.45 x 10⁵

Now, According to the question:

If the number is given in the decimal notation, move the decimal point to the right side of its original position and place the decimal point after the first non zero digits. The power ten will be the number of places the original decimal point was moved and it will be negative as it was moved towards the right side.

0.0000732 = 7.32 x 10⁻⁵

If the whole number greater than 10 is to be changed into the power of 10, then move the decimal point to the left side of its original position and place the decimal point after the first digit. The power of 10 will be the number of places the original decimal point was moved and it will be positive as it was moved towards the left side.

145,000 = 1.45 x 10⁵

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The relationship between x and y can be described based on the value of the sample correlation coefficient.

Sample covariance measures the degree to which two variables are linearly related and the direction of their linear relationship. The formula for sample covariance is:

[tex]Cov(x,y) = (1/(n-1)) * \Sigma(x-\bar x)(y- \bar y)[/tex] where,

The sample correlation coefficient, also known as Pearson's correlation coefficient, measures the degree to which two variables are linearly related and the direction of their linear relationship. It is a normalized version of the sample covariance, with a value between -1 and 1. The formula for the sample correlation coefficient is:

r = Cov(x,y) / (s1 * s2) where,  

To calculate the sample covariance and sample correlation coefficient, we need to have a sample of data containing the variables x and y. Once we have the data, we can calculate the sample means, and sample standard deviations, and then use the formulas above to calculate the sample covariance and sample correlation coefficient.

The relationship between x and y can be described based on the value of the sample correlation coefficient.

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The complete question is:

Given a sample of data containing the variables x and y, calculate the sample covariance and the sample correlation coefficient, and describe the relationship between x and y.

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In a case whereby concrete beam is to rest on two concrete pillars. The beam is a cuboid with sides of length 0.5m, 3m and 0.4m with diameter 0.4m and height 2m. the total volume of concrete needed to make the beam and the pillars is 1.103m^3

The concept here is total volume , then we can calculate this for concrete needed to make the beam and the pillars  as:

Vtd = V1 + V2

= V1= lwh

where length  l = 0.5m,

width w=  3m

height h=  0.4m.

V1 + V2 = (0.5m* 3m * 0.4m) + 2(π/4 d^2. h)

where h =height 2m

Then  V1 + V2 = 1.1026m^3

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Answer: 25

Step-by-step explanation: 10+10=20 and 2+3=5. 20+5=2

Answer:

um i don't know.... 99

Step-by-step explanation:

99 +12

A measure computed from the entire population is called a parameter.

The correct answer is an option (d)

We know that a parameter is nothing but a numerical value that describes a certain characteristic of the entire population. It is computed using the population values such as population mean, population variance, etc.

Whereas, a statistic is a numerical value that defines certain characteristic of a sample.

It is computed using the sample values such as the sample mean, sample variance, etc.

A qualitative value or a qualitative data are represented by a name, symbol, or a number code. This data is the data about categorical variables.

And the mean is nothing but the average of a set of values.

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Answer: If you take 15% off of 84.75, the new amount would be 71.8875. This can be calculated by multiplying 84.75 by 0.15 (15% written as a decimal), and then subtracting that result from 84.75.

The required given expression is a equation x - 4.65 = 0.09.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. ​

In any expression variables and constants are expressed by equal sign,

Then the expression is called equaion.

So, as question says,

x - 4.65 = 0.09

x = 4.74

Thus, It is a equation of value 4.74.

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The simplification of the addition of two or more fraction with unlike denominator is:

Convert the denominator with like terms and then add the numerators.

Method of simplification of addition of fraction with unlike denominator is:

Therefore, to simplify unlike fractions find least common multiple and add the like fractions.

The given question is incomplete, I answer the question in general according to my knowledge:

Simplification of adding fractions with unlike denominators with  example?

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Answer: Total amount invested:

= 200000

Total amount earned from investements:

0.109x + 0.029y + 0.05z = 11165

Relation of bonds and CDs:

= +20000

Step-by-step explanation:

Check the picture below.

so from the picture below we can say that parallel sides or bases of the trapezoid are AB and DC, that means our midsegment is found halfway of BC and halfway of AD, let's get the midpoints for those and then get their length.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad D(\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 2 +0}{2}~~~ ,~~~ \cfrac{ 0 +3}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 3 }{2} \right)\implies (1~~,~~\frac{3}{2}) \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad C(\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 +2}{2}~~~ ,~~~ \cfrac{ 4 +5}{2} \right) \implies \left(\cfrac{ 8 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies (4~~,~~\frac{9}{2})[/tex]

let's get their distance

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{\frac{3}{2}})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{\frac{9}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(4-1)^2 + (\frac{9}{2}-\frac{3}{2})^2}\implies d=\sqrt{3^2 + 3^2}\implies {\Large \begin{array}{llll} \stackrel{midsegment}{ d=\sqrt{18}} \end{array}}[/tex]

The missing angle measures in triangle ABC are 35.5° and 54.5°.

We know that,

In the right triangle ABC

∠A +∠B =90°   ( by complementary angles)

We find the measure of angle B.

we know that

[tex]tanB = \frac{opposite side angle B}{adjacent side angle B}[/tex]

According to the question,

Opposite side angle B= 7 in

Adjacent side angle B = 5in

So, [tex]tanB = \frac{7}{5}[/tex]

      [tex]B = arc tan(\frac{7}{5})[/tex]

      B = 54.5°

Then, we find the measure of angle A

A + B = 90°

 A = 90°-B

A = 90° -  54.5° ( using subtraction)

A = 35.5°

So, The angles measured in triangle ABC are 35.5° and 54.5°.

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