Ghana van company invested P45 700 for two years at a rate of 12%per annum compounded for quarter year. Work out the compound interest over the two years

Answers

Answer 1

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}[/tex]


Related Questions

average salary of 25 workers in a factory is 2500 if the salary of the manager is 35000 find the average salary of 26 employees

Answers

The average salary of 26 employees is 3750.

What is average salary ?

The average pay is calculated by dividing the sum of all employee salaries for a company or sector by the total number of employees. It serves as a gauge of the typical pay for workers in a given category.

The average salary of 25 workers in a factory is 2500. This means that the total salary of all 25 workers is 2500 * 25 = 62500.

The salary of the manager is 35000. This means that the total salary of all 26 employees is 62500 + 35000 = 97500.

The average salary of 26 employees is 97500 / 26 = 3750.

Therefore, the average salary of 26 employees is 3750.

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What does this this equal -7x13_>41

Answers

The solution to the inequality expression -7x + 13 ≥ 41 is x ≤ -4

How to evaluate the inequality expression

From the question, we have the following parameters that can be used in our computation:

-7x13_>41

Express properly

So, we have

-7x + 13 ≥ 41

Subtract 13 from both sides of the inequality

So, we have

-7x + 13 - 13 ≥ 41 - 13

Evaluate the difference

-7x ≥ 28

Divide both sides of the inequality by -7

x ≤ -4

Hence, the solution to the inequality expression is x ≤ -4

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If you draw a card from a standard deck of 52 playing cards, what is the probability that it is a heart or a diamond?

Answers

Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

A 6-sided number cube is rolled. what is p(not 2 or 5)

Answers

The probability of not rolling a 2 or a 5 on a 6-sided number cube is 2/3, or about 0.67 when expressed as a decimal.

How to solve

The probability of rolling a 2 or a 5 on a 6-sided number cube is 2 out of 6 or 1/3, because there are two favorable outcomes (rolling a 2 or a 5) out of six possible outcomes.

The probability of not rolling a 2 or 5 is the complement of this probability.

In probability, the complement of an event is 1 minus the probability of that event.

So, to find the probability of not rolling a 2 or a 5, subtract the probability of rolling a 2 or 5 from 1.

That is, 1 - 1/3 = 2/3.

Therefore, the probability of not rolling a 2 or a 5 on a 6-sided number cube is 2/3, or about 0.67 when expressed as a decimal.

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Since 2004, the amount of money spent at restaurants in a certain country has increased at a rate of 8% each year. I’m 2004, about $290 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2018?

Answers

Answer:

$851, 786, 151, 000

Step-by-step explanation:

N =  A (1 + increase) ^n

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

290 is our A value, increase is 8% (0.08), n is the number of years (2018 - 2004 = 14).

N =  290 (1 + 0.08) ^14

= 290 (1.08)^14

= $851, 786, 151, 000

Find the area of the shaded region. 100 POINTS + BRAINLIEST

Please help me.

Answers

Answer and Explanation:

First, we can find the factored areas of the circle (the non-shaded area) and the rectangle (which includes the shaded and non-shaded areas).

We can use the rule:

if [tex]x^2 + cx + d = (x + a)(x + b)[/tex], then [tex]c = a + b[/tex] and [tex]d = a \cdot b[/tex].

__

[tex]A_\circ = \dfrac{x+1}{x^2 + 6x + 8}[/tex]

[tex]\boxed{A_\circ = \dfrac{x+1}{(x + 2)(x + 4)}}[/tex]

__

[tex]A_\square = \dfrac{x+1}{x^2 - 6x -16}[/tex]

[tex]\boxed{A_\square = \dfrac{x+1}{(x+2)(x-8)}}[/tex]

Since we want to subtract the area of the circle from the area of the rectangle, we need them to have a common denominator.

We can achieve this by multiplying the area of the circle by [tex]\dfrac{(x-8)}{(x-8)}[/tex] and the area of the rectangle by [tex]\dfrac{(x+4)}{(x+4)}[/tex] because then both fractions will have the denominator [tex](x+2)(x+4)(x-8)[/tex].

[tex]A_\circ = \dfrac{(x+1)(x-8)}{(x + 2)(x + 4)(x-8)}[/tex]

[tex]A_\square = \dfrac{(x+1)(x+4)}{(x+2)(x-8)(x+4)}[/tex]

Now that they have a common denominator, we can subtract them to get the area of the shaded region.

[tex]A_\text{shaded} = A_\square - A_\circ[/tex]

[tex]A_\text{shaded} = \left(\dfrac{(x+1)(x+4)}{(x + 2)(x + 4)(x-8)}\right) - \left(\dfrac{(x+1)(x-8)}{(x+2)(x+4)(x-8)}\right)[/tex]

Now, we can foil out the numerators of each fraction and combining like terms.

[tex]A_\text{shaded} = \left(\dfrac{x^2 + 5x + 4}{(x + 2)(x + 4)(x-8)}\right) - \left(\dfrac{x^2 - 7x - 8}{(x+2)(x+4)(x-8)}\right)[/tex]

↓ rewriting as one fraction ... [tex]\dfrac{x}{y} - \dfrac{z}{y} = \dfrac{x-z}{y}[/tex]

[tex]A_\text{shaded} = \dfrac{ (x^2 + 5x + 4) - (x^2 - 7x - 8)}{(x + 2)(x + 4)(x-8)}[/tex]

↓ distributing the negative

[tex]A_\text{shaded} = \dfrac{x^2 + 5x + 4 - x^2 + 7x + 8}{(x + 2)(x + 4)(x-8)}[/tex]

↓ grouping like terms

[tex]A_\text{shaded} = \dfrac{(x^2 - x^2) + (5x + 7x) + (4 + 8)}{(x + 2)(x + 4)(x-8)}[/tex]

↓ combining like terms

[tex]\boxed{A_\text{shaded} = \dfrac{12x + 12}{(x + 2)(x + 4)(x-8)}}[/tex]

the table shows the features you can choose fcor a p;ay s ytou go phone plan

Answers

Answer:

With the Pay-As-You-Go Calling Plan, licensed users can call out to numbers located in the country/region where their Microsoft 365 license is assigned to the user based on the user's location, and to international numbers in 196 countries/regions. Unlimited incoming minutes are included.

In ΔUVW, u = 76 inches, w = 71 inches and ∠W=69°. Find all possible values of ∠U, to the nearest degree.

Answers

The value of the angle U from the calculation is 88 degrees.

How do you solve a triangle?

The sine rule can be applied in a variety of situations, such as determining a triangle's unknown side lengths or angles. The sine rule can be used to locate the missing side or angle if you know the lengths of two sides and the measure of an angle (not necessarily the included angle).

By the use of the sine rule;

u/Sin U = w/Sin W

Thus;

76/Sin U = 71/Sin 69

Sin U = 76Sin 69/71

U = Sin-1 (76Sin 69/71)

U = 88 degrees

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Please help I’ll mark you as brainliest if correct!

Answers

Answer:

 (a) Parallelogram

  (c) Rhombus

Step-by-step explanation:

You want the names applicable to a quadrilateral with diagonals that bisect each other and bisect the vertex angles.

Diagonals

When the diagonals of a quadrilateral bisect each other, that quadrilateral is a parallelogram. With two pairs of parallel sides, the figure cannot be a trapezoid.

When both diagonals bisect the vertex angles, the quadrilateral is a rhombus.

Rectangle

The diagonals of a rectangle or square are congruent. The given figure labels the diagonals differently, so we cannot assume they are congruent. Hence the figure is not necessarily a rectangle or square.

The figure shown is a parallelogram that is a rhombus.

__

Additional comment

The figure doesn't have the crossing of diagonals marked as right angles, but they are. Segments 's' and 'x' are each altitudes of their respective isosceles triangles, so they must meet at right angles.

The relations shown in this figure can be used to prove a quadrilateral is a parallelogram and/or rhombus. That can be handy sometimes.

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Answer this question

Answers

The domain and range for the function shown in the graph above include the following:

D. D: [-∞, ∞]

    R: [-10, ∞]

What is a domain?

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-10, ∞] or y ≥ -10

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2. A mechanic makes $32.50 per hour and works 35 hours per week. The mechanic pays 21° earnings in federal and state taxes and saves 5% of the gross pay. Use the interval 25 - 30 income to find the monetary range that is recommended for the monthly rental budget for Show your work or explain how you determined your answer.

Answers

Using the interval 25 - 30 income, the recommended monetary range for the monthly rental budget for the mechanic is $841.75 and $1,010.10.

What is the range?

Mathematically, the range is the lowest and highest value.

The range may also refer to the difference between the highest value and the lowest value in a data set.

The mechanic's hourly pay rate = $32.50

Hours worked per week = 35 hours

Federal and state taxes = 21%

Savings = 5%

Gross pay for the month = $4,550 ($32.50 x 35 x 4)

Federal and state taxes = $955.50 ($4,550 x 21%)

Savings = $227.50  ($4,550 x 5%)

Net Pay = $3,367 ($4,550 - $955.50 - $227.50)

Lower bounds of the interval = 25

Upper bounds of the interval = 30

Recommended range for monthly rental budget = $841.75 (3,367 x 25%) and $1,010.10 ($3,367 x 30%)

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Resuelva las siguientes ecuaciones:
a) x + 16 = 41
b) 9x – 45 + 4x – 16 = 4
c) 2x – 3 + x – 35 = 2 – 9x – 4
d) 3 · (x – 2) + 9 = 0
e) 8x + 7 – 2x + 5 = 4x + 12 – (x – 30)
f) x + (x + 2) = 36
g) 2 · (3x – 2) – (x + 3) = 8
h) 2 · (13 + x) = 41 + x
i) 2 · (x – 3) – 3 · (4x – 5) = 17 – 8x
j) 4x – 3 · (1 – 3x) = –3
k) 4 · (2x) – 3 · (3x – 5) = 12x – 180
l) 6 – x = 4 · (x – 3) – 7 · (x – 4)
m) 3 · (2x – 6) – [(x – (3x – 8) + 2) – 1] = 2 – (3 – 2x)
n) (x – 2)2 = x
2
ñ) x · (x + 4) = x
2 + 8

Answers

The solution to each of the equations include the following:

a) x = 25

b) x = 5.

c) x = 6.

d) x = -1.

e) x = 10

f) x = 17

g) x = 3

h) x = 15

i) x = -4

j) x = 0

k) x = 15

l) x = 5

m) x = 13/3.

How to solve each of the equations?

In this scenario and exercise, you are required to provide a solution to each of the given equations as follows;

Part a.

By subtracting 16 from both sides of the equation, we have:

x + 16 = 41

x + 16 - 16 = 41 - 16

x = 25

Part b.

By collecting like terms and evaluating, we have:

9x – 45 + 4x – 16 = 4

13x = 4 + 45 + 16

13x = 65

x = 5,

Part c.

By collecting like terms and evaluating, we have:

2x – 3 + x – 35 = 2 – 9x – 4

6x = 36

x = 6

Part d.

3 · (x – 2) + 9 = 0

3x - 6 + 9 =0

x = -1

Part e.

8x + 7 – 2x + 5 = 4x + 12 – (x – 30)

x = 10

Part f.

x + (x + 2) = 36

x = 17

Part g

2 · (3x – 2) – (x + 3) = 8

x = 3

Part h

2 · (13 + x) = 41 + x

x = 15

Part i

2 · (x – 3) – 3 · (4x – 5) = 17 – 8x

x = -4

Part j

4x – 3 · (1 – 3x) = –3

x = 0

Part k

4 · (2x) – 3 · (3x – 5) = 12x – 180

x = 15

Part l

6 – x = 4 · (x – 3) – 7 · (x – 4)

x = 5

Part m

3 · (2x – 6) – [(x – (3x – 8) + 2) – 1] = 2 – (3 – 2x)

6x - 18 - [(x – 3x + 8 + 2 – 1] = -1 + 2x

6x - 18 + 2x - 9 = -1 + 2x

6x = 26

x = 13/3

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Complete Question:

Solve the following equations:

prove that 2^10-1 is not a mersenne prime

Answers

The expression 2¹⁰ - 1 is not a prime number. Because it has more than two factors.

Given that:

Expression, 2¹⁰ - 1

A prime number is a positive integer having exactly two factors which are 1 and the number itself. Any number that does not follow this is termed a composite number.

The value of the expression is given as,

⇒ 2¹⁰ - 1

⇒ 1,024 - 1

⇒ 1,023

The factor of 1,023 is given as,

1,023 = 3 x 11 x 31

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How can I relate ratio with cooking tomato sauce? If anyone has any suggestions it would be really helpful!!

Answers

Answer:

ratio of tomato to other ingredients

Step-by-step explanation:

What is the smallest positive integer $n$ such that $\sqrt[4]{56 \cdot n}$ is an integer?

Answers

The smallest positive integer n such that t [tex]$\sqrt[4]{56 \cdot n}$[/tex]  is an integer is 686.

We have to find the smallest positive integer n such that [tex]$\sqrt[4]{56 \cdot n}$[/tex] is an integer

To find the smallest positive integer n such that  [tex]$\sqrt[4]{56 \cdot n}$[/tex]   is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.

The prime factorization of 56 is:

56 = 2³ × 7

The prime factors of 56 need to be raised to multiples of 4.

Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.

To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴

The smallest value of n that satisfies this condition is:

n = 2 × 7³ = 2× 343 = 686

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Fill in the table by indicating whether each quadrilateral has the given property.
Complete the table below. Answering them yes or no (picture below)

Answers

The table should be completed by indicating whether each quadrilateral has the given property as follows;

Property                                Parallelogram  Rectangle  Rhombus   Square

Diagonals bisect each other    Yes                  Yes              Yes           Yes

Diagonals are congruent ≅       No                  Yes               No            Yes

Each diagonals bisects             Yes                   No               Yes           Yes

opposite ∠s

Diagonals are ⊥                         No                    No              Yes            Yes

What are the properties of quadrilaterals?

In Mathematics and Geometry, two (2) quadrilaterals are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Additionally, two (2) geometric figures such as quadrilaterals are considered to be congruent only when their corresponding side lengths are congruent (proportional) and the magnitude of their angles are congruent.

In conclusion, the diagonals of bisect each other in quadrilaterals such as parallelogram, square, rectangle, and rhombus.

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Watch help video
Find the 93rd term of the arithmetic sequence -5, -15, -25,...

Answers

Answer:

Arithmetic sequence is [tex]a_n=-10n+5[/tex]

93rd term is -925

Step-by-step explanation:

Each subsequent term is decreased by 10 and the first term is -5, so we can generate an arithmetic sequence:

[tex]a_n=a_1+(n-1)d\\a_n=-5+(n-1)(-10)\\a_n=-5-10n+10\\a_n=-10n+5[/tex]

So, the 93rd term would be:

[tex]a_{93}=-10(93)+5=-930+5=-925[/tex]

swer gete pand x² + ₂ 332474 w the roots of 2x² + 3x - 1 = 0 are t and b, find the values of (a) t² + b² (b) (t - b)² 2 + 1/b2)(b2+1/t2) ​

Answers

Answer:

Step-by-step explanation:

To find the values of the given expressions, we first need to find the values of t and b, which are the roots of the equation 2x² + 3x - 1 = 0.

Using the quadratic formula, we can solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 2, b = 3, and c = -1. Plugging in these values, we can calculate t and b:

t = (-3 + √(3² - 4(2)(-1))) / (2(2))

t = (-3 + √(9 + 8)) / 4

t = (-3 + √17) / 4

b = (-3 - √(3² - 4(2)(-1))) / (2(2))

b = (-3 - √(9 + 8)) / 4

b = (-3 - √17) / 4

Now, let's calculate the values of the given expressions:

(a) t² + b²

Substituting the values of t and b:

(t² + b²) = ((-3 + √17) / 4)² + ((-3 - √17) / 4)²

= (9 - 6√17 + 17) / 16 + (9 + 6√17 + 17) / 16

= (35 + 12√17) / 16 + (35 - 12√17) / 16

= 70 / 16

= 35 / 8

(b) (t - b)²

Substituting the values of t and b:

(t - b)² = ((-3 + √17) / 4 - (-3 - √17) / 4)²

= (2√17)²

= 4(17)

= 68

(c) (2 + 1/b²)(b² + 1/t²)

Substituting the values of t and b:

(2 + 1/b²)(b² + 1/t²) = (2 + 1/((-3 - √17) / 4)²)((-3 - √17) / 4)² + 1/((-3 + √17) / 4)²)

= (2 + 16 / (3 + √17)²)((-3 - √17) / 4)² + 16 / (3 - √17)²)

= (2 + 16 / (3 + √17)²)((-3 - √17) / 4)² + 16 / (3 - √17)²)

The final expression cannot be further simplified without knowing the exact values of √17.

Mr Bekele is thinking of buying a G+2 building 5 years form now on a mortgage basis. The building will be used for office purpose for his new business that costs Br. 500, 000. The required down payment is Br. 100, 000, with monthly mortgage payment for 30 years at a rate of 12% compounded monthly. To cover the down payment Bekele has established a sinking fund account in Dashen Bank, which pays 10% interest compounded quarterly. Required:
a) How much Bekele should deposit at the end of every quarter to meet the objective of the down payment?
b) Determine the amount of monthly mortgage payment to be made to discharge the mortgage within 30 yrs.
c) What is the amount of total interest paid on the mortgage?
d) What is the total amount paid over the entire period of the mortgage? ​

Answers

a) Bekele should deposit approximately Br. 4,071.56 at the end of every quarter to meet the objective of the down payment.

b)  we find that the monthly mortgage payment should be approximately Br. 3,421.91.

c)  we find that the total interest paid on the mortgage is approximately Br. 422,288.60.

d)  we find that the total amount paid over the entire period of the mortgage is approximately Br. 1,231,487.60.

a) To determine how much Bekele should deposit at the end of every quarter to meet the objective of the down payment, we can use the sinking fund formula. The formula for the future value of a sinking fund is:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

FV is the future value or the down payment amount (Br. 100,000),

P is the periodic deposit we need to find,

r is the annual interest rate (10% or 0.10),

n is the number of compounding periods per year (4, since it is compounded quarterly),

and t is the number of years (5).

Plugging in the values into the formula, we can solve for P:

100,000 = P * ((1 + 0.10/4)^(4*5) - 1) / (0.10/4)

Simplifying the equation, we have:

100,000 = P * (1.025^20 - 1) / 0.025

Now, we can solve for P:

P = 100,000 * 0.025 / (1.025^20 - 1)

Calculating the value, we find that Bekele should deposit approximately Br. 4,071.56 at the end of every quarter to meet the objective of the down payment.

b) To determine the amount of the monthly mortgage payment to discharge the mortgage within 30 years, we can use the formula for the monthly mortgage payment (PMT) of an amortizing loan:

PMT = (P * r) / (1 - (1 + r)^(-n))

Where:

P is the principal amount of the loan (Br. 400,000, obtained by subtracting the down payment from the total cost),

r is the monthly interest rate (12% divided by 12 months, or 0.01),

and n is the total number of monthly payments (30 years multiplied by 12 months, or 360).

Plugging in the values into the formula, we can calculate the monthly mortgage payment:

PMT = (400,000 * 0.01) / (1 - (1 + 0.01)^(-360))

Using a calculator or spreadsheet, we find that the monthly mortgage payment should be approximately Br. 3,421.91.

c) To calculate the total interest paid on the mortgage, we can subtract the principal amount from the total amount paid over the entire period. The principal amount is Br. 400,000, and the total amount paid over the entire period can be obtained by multiplying the monthly mortgage payment by the total number of payments (360).

Total interest paid = (Monthly mortgage payment * Total number of payments) - Principal amount

Total interest paid = (3,421.91 * 360) - 400,000

Using a calculator, we find that the total interest paid on the mortgage is approximately Br. 422,288.60.

d) The total amount paid over the entire period of the mortgage can be calculated by multiplying the monthly mortgage payment by the total number of payments:

Total amount paid = Monthly mortgage payment * Total number of payments

Total amount paid = 3,421.91 * 360

Using a calculator, we find that the total amount paid over the entire period of the mortgage is approximately Br. 1,231,487.60.

Therefore, Bekele will need to deposit approximately Br. 4,071.56 at the end of every quarter to meet the down payment, make monthly mortgage payments of Br. 3,421.91, pay a total of approximately Br. 422,288.60

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need help answer quick pls​

Answers

volume of the sphere is 113.1

100 Points! Algebra question. Sketch the angle. Photo attached. Thank you!

Answers

The reference angle of -210 is 30 degrees and the sketch of the angle is attached

How to sketch the angle and find the reference angle

From the question, we have the following parameters that can be used in our computation:

Angle = 210 degrees

Rewrite as

θ = 210 degrees

The above angle is in the third quadrant

So, we subtract 180 degrees from it to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 210 - 180

Evaluate the difference

Reference angle = 30 degrees

Hence, the reference angle is 30 degrees and the sketch of the angle is added as an attachment

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Pls help me fast rapidly:

Answers

Answer:

[tex]\huge\boxed{\sf 1.8 \times 10^3}[/tex]

Step-by-step explanation:

Quotient means "to divide".

Solution:

[tex]\displaystyle = \frac{4.68 \times 10^6}{2.6 \times 10^3} \\\\\underline{\sf Exponent \ rule:}\frac{a^m}{a^n} = a^{m-n}\\\\= 1.8 \times 10^{6-3}\\\\= 1.8 \times 10^3\\\\\rule[225]{225}{2}[/tex]

Someone help me with this pls pls pls

Answers

The measure of angle RQT is 138⁰.

The measure of angle RQS is  48⁰.

What is the value of arc MN?

The value of arc MN is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

The measure of angle RQT is calculated as follows;

m∠RQT = 180 - ( QR ) ( sum of angles on a straight line)

m∠RQT = 180 -  42⁰

m∠RQT = 138⁰

The measure of angle RQS is calculated as follows;

since line QS is the diameter of the circle, angle RQS must a right angle.

so angle SQT = 90 degrees.

m∠RQS = m∠RQT - m∠SQT

m∠RQS = 138 - 90

m∠RQS = 48⁰

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Use the quadratic formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a, to solve the equation. 2x2 − 8x + 7 = 0. Round to the nearest hundredths place.

x = −2.71 and x = −1.29
x = 1.29 and x = 2.71
x = −5.25 and x = 9.25
x = 5.17 and x = 10.83

Answers

The solutions to the equation 2x² − 8x + 7 = 0 are x = 2.71 and x = -1.29.

How to calculate the values

The quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a

In this case, we have:

a = 2

b = -8

c = 7

Substituting these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)² - 4(2)(7))) / 2(2)

x = (8 ± √(64 - 56)) / 4

x = (8 ± √8) / 4

x = (8 ± 2√2) / 4

x = 2 ± √2

x = 2.71 and x = -1.29

Therefore, the solutions to the equation 2x² − 8x + 7 = 0 are x = 2.71 and x = -1.29.

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CAN I PLS GET HELPPP

Answers

The solution to all the algebra expressions are:

28) 2³/₁₆

29) 6000

30) 132

How to solve Algebraic expressions?

28) The area of the rectangle formed by Shana's rug is given by the expression:

Area = Length * Width

Thus:

Area = 2⁵/₈ * ⁵/₆

= ²¹/₈ * ⁵/₆

= 35/16

= 2³/₁₆

29) We are given the number 2641.

Now, from right:

1 is in the units place

4 is in tens place

6 is in hundreds place

2 is in thousands place

If we switch 2 and 6, we will have:

6241 and as such 6 represents 6000

30) The expression is given as:

90 + 7 * (7 - 1)

Using PEMDAS order of operation gives us:

90 + 7(6)

= 90 + 42

= 132

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need answer and a huge explanation ​

Answers

The area of the shaded portion of the circle is 329.8 units squared.

How to find the area of the shaded region?

The area of the shaded region can be found by subtracting the area of the right triangle from the area of the circle.

Therefore,

area of the triangle = 1 / 2 bh

where

b = baseh = height

Therefore,

area of the triangle = 1 / 2 × 7 × 24

area of the triangle = 168 / 2

area of the triangle = 84 units²

Area of the circle = πr²

let's find the radius of the circle using Pythagoras's theorem,

√24²- 7² = diameter

diameter = √576 - 49

diameter = √527

diameter = 22.9564805665

diameter = 22.96 units

Therefore,

radius = 22.96 / 2 = 11.48 units

Hence,

Area of the circle = 3.14 × 11.48²

Area of the circle = 413.821856

Area of the circle = 413.82 units²

Therefore,

area of the shaded region = 413.82 - 84

area of the shaded region = 329.8 units²

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An online Media Service offers Video and music downloads. Each download of a song costs $1.25. Each download of a video costs 4 times as much as the song download. You have a credit of $70. How many songs can you purchase after buying 12 videos

Answers

Answer:

8

Step-by-step explanation:

First, you need to find the cost of one video. We know that the cost of 1 video is equal to 4 times the cost of each song. So we will take the cost of a song $1.25 and multiply by four.

$1.25(4) = $5

So if one video costs $5, we now need to find the cost of 12 videos because we need to know how many songs you can purchase after you purchase 12 videos.

12($5) = $60

Now that we know that you have spent $60 on your videos, we need to figure out how many songs you can purchase now that we know you have $10 remaining of the initial $70. To do this, we will divide $10 by $1.25

$10/$1.25 = 8

With $70, given that you have already purchased 12 videos, you can also purchase 8 songs.

14b^2 - 2 = - 3b I need help with figuring this one out

Answers

Answer:

[tex]b=-\frac{1}{2}, \frac{2}{7}[/tex]

Step-by-step explanation:

Starting from this equation [tex]14b^2-2= -3b[/tex]

We can rewrite it to a quadratic equation:

[tex]14b^2+3b-2= 0[/tex]

Factoring this equation gives us:

[tex](7b-2)(2b+1)=0[/tex]

Now because its a quadratic formula, we have to answers:

[tex](7b-2) = 0\\7b=2\\b=\frac{2}{7}[/tex]

or

[tex](2b+1)=0\\2b=-1\\b=-\frac{1}{2}[/tex]

Which of the three situations given below is best modeled by an
exponential function?

I. A bacteria culture doubles in size every day.
II. A plant grows by 1 inch every 4 days.
III. The population of a town declines by 5% every 3 years.
a) I, only
b) II, only
c) I and II
d) I and III

Answers

The correct answer is (a) a bacteria culture triples in size every day describes a exponential function.

We have,

A relation is a function if it has only One y-value for each x-value.

The growth of a population, bacteria culture, or puppy can be modeled by an exponential function if the growth rate is proportional to the current size.

In other words, if the growth rate is constant, then the growth can be modeled by an exponential function.

Out of the three situations given, option (i) is the only one that has a constant growth rate, since the bacteria culture triples in size every day. This means that the growth rate is constant at 200% per day.

Option (iii) has a growth rate that is not constant but increases every year, so it is not best modeled by an exponential function.

Option (ii) also has a growth rate that is not constant, since A plant grows by 1 inch every 4 days regardless of its current height.

Therefore, the correct answer is (a) a bacteria culture triples in size every day describes a exponential function.

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14
12
10
8
6
4
2
0
468101214
Foot length(cm)
The line models the relationship between body
weight and foot length for a group of infants.Based
on the model, what is the predicted weight, in
kilograms(kg) , of an infant with afoot length of 9
centimeters(cm) ?
A)5
B)7
C)9
D)11

Answers

The predicted weight for an infant with a foot length of 9 centimeters is 4 kilograms.

Therefore, the correct answer is: B) 7.

To determine the predicted weight of an infant with a foot length of 9 centimeters, we can refer to the given line model that represents the relationship between body weight and foot length for a group of infants.

From the line model, we can observe that the weight increases as the foot length increases.

Looking at the provided data, we see that the weights corresponding to foot lengths are given as:

Foot length (cm): 0, 2, 4, 6, 8, 10, 12, 14

Weight (kg): 14, 12, 10, 8, 6, 4, 2, 0

By examining the pattern, we can deduce that the weight decreases by 2 kilograms for every increase of 2 centimeters in foot length.

Therefore, to find the predicted weight for a foot length of 9 centimeters, we can subtract 2 kilograms from the weight corresponding to a foot length of 10 centimeters.

Weight for 10 cm - 2 kg = 4 kg

Thus, the predicted weight for an infant with a foot length of 9 centimeters is 4 kilograms.

Therefore, the correct answer is: B) 7

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