What is the solution to this system of equations?

8a−4b=20
5a−8b=62
a=
b=

The amount in his savings after 5 years will be  $1507.5.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, P = 1500, r = 0.1, t = 5 years.

∴ SI = (1500×0.1×5)/100.

SI = $7.5.

Now, We know Amount = principle + SI.

∴ Amount = 1500 + 7.5 = $1507.5

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The values of x in the first, second, third and fourth triangles are 4 units, 70°, 76° and 80° respectively

To solve this problem, we need some angle geometry knowledge:

For the first triangle:

x = 4 (All sides in a rhombus are identical)

For the second triangle:

The missing side is also equal to x (base of isosceles triangles)

x + x + 40 = 180 (sum of angles in triangle)

2x+40 = 180

2x = 180-40

2x = 140

x = 70°

For the third triangle:

x = 76° (base of isosceles triangles are equal)

For the fourth triangle:

Check the image attached for labeling

m = 180-110 = 70° (angle on a straight line)

y = 70° (base of isosceles triangles are equal)

z = 180-70-70 = 40°

t = 90-40 = 50°

L = 50° (base of isosceles triangles are equal)

Thus, x = 180-50-50 = 80°

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The probability that there are 89/1024 ways in which heads never happen on consecutive tosses.

For the stared question;

Then, for every value of x, I completed casework:

The number of configurations of AAAAAAAAAA is bijective to x=0 and is 1.

The number of configurations of AAAAAAAAB is then bijective to x=1, which really is 9 and so forth.

These variables add up to 89, and there are 1024 different ways to flip them.

P(i + j) = 89/1024

Thus, there are 89/1024 ways in which heads never happen on consecutive tosses.

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The error student made was converting 6.5% to decimal

6.5% = 0.065

0.065 * 525.08 =  $34.13

information from the problem

A student is finding a 6.5% commission on $525.08 worth of sales

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

6.5%

=  6.5 percent

= 6.5 / 100

= 0.065

The factor 0.065 of the commission on $525.08

= 0.065 * 525.08

= $34.13

The commission is $34.13

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Answer:

B. g(x) = -x² - 2

Step-by-step explanation:

f(x) = x²

g(x) = -x²

The graph now has a maximum of (0, 0) and is curving downwards. To make the graph go down by -2 subtract 2 from the equation

g(x) = -x² - 2

I hope this helps!

Statement                                                  Reason

Z is the midpoint of overline XY             Given

WZ ⊥ XY                                                   Definition of perpendicular lines

angle WZX ≅ angle WZY                        Definition of isosceles triangle

line XA ≅ line YZ                                     Definition of bisection

line WZ ≅ line WZ                                   Reflexive Property of Congruence

Δ WXZ ≅ Δ WYZ                                     Side - Angle - Side (SAS)

< Y ≅ < X       Corresponding Parts of Congruent Triangles are Congruent              

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent

The SAS have it that the two triangles being compared should have their two sides and the included angle equal

Using Corresponding Parts of Congruent Triangles are Congruent CPCTC theorem ∠Y ≅ ∠X .

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Answer:

Yes

Step-by-step explanation:

16x^4 x 16x^2= 16x^8

The number of routes that Paula can take using graph theory is; E: 4

We will observe that out of the 12 cities, 6 of them possess 3 edges going in/out of them.

The 6 cities are such that there are 2 at the top, 2 at the bottom, and 1 on each side.

In graph theory terms, we can say that they are of degree 3.

Thus, at least 1 edge connecting to each of these cities cannot therefore be used. Furthermore, the same concept applies to the start and end points, due to the fact that we don't want to return to them.

There are 6 + 2 = 8 vertices that we can tell have 1 unused edge, and then we have 17 - 13 = 4 unused edges to work with due to the fact that we have 17 edges in total, and as such must use exactly 13 of them).

Finally, we notice that at each of the 2 cities marked with an O on a path in the image attached, that there are 2 possibilities such that it's either we continue straight and cross back over that same path later, or we will make a left turn, and then turn rightward when we approach the junction again.

This gives us a total of;

2 * 2 = 4 possible different routes

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Answer:

1

Step-by-step explanation:

anything to the power of 0 is 1

hopes this helps

Answer:

(1,2) and (4,2)

(2,6) and (6,6)

Step-by-step explanation:

(when a line is horizontal the slope is 0)

[tex]slope = \frac{rise}{run} [/tex]

[tex]rise = y1 - y2[/tex]

[tex] = 2 - 2 \\ = 0[/tex]

[tex]run = x2 - x1 \\ = 4 - 1 \\ = 3[/tex]

[tex]slope = \frac{0}{3} \\ = 0[/tex]

second option

[tex]rise = 6 - 6 \\ = 0[/tex]

run=6-2

=4

slope= 0/4

=0

please Heart this....

Answer:: 111

Step-by-step explanation:

111 is greater than 112 I hope it helps!!!!

The solution set for the inequality - x < 2 is - x < 2.

What is  inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

An inequality in mathematics depicts the connection between two values in an unbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, more than or equal to, less than, or equal to another value.

-x<2

Multiply both sides by -1 (reverse the inequality)

(-x)(-1)>2(-1)

Simplify

x>-2

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The perimeter of the pattern the same as the area of the pattern is 20 cm.

Perimeter of a square is the total length (distance) of the boundary of a square

In a square all the sides are of equal lengths.

Hence, perimeter of a square = 4l

We know that all the sides of a square are equal.

Perimeter of a Square

Perimeter of the square ABCD

                  = AB + BC + CD + AD

                  = 2 cm + 2 cm + 2 cm + 2 cm

                  = (2 × 4) cm

                 = 8 cm

Perimeter of a square is 4 times of s side.

Perimeter of a square = 4 × length of a side..

1st method:

Perimeter of a square PQRS

                 = side + side + side + side

                 = 5 cm + 5 cm + 5 cm + 5 cm

                = 20 cm:

2nd method

Perimeter of a square = 4 times side

                               = 4 × side

                               = 4 × 5 cm

                               = 20 cm

Therefore, Perimeter of a square = 4 × length of one side.

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The logarithm value for the expression → ln(175) is equivalent to 5.17.

Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. Mathematically -

[tex]$\log_{b}({b^x})=x[/tex]

Given is the following logarithmic expression, as follows -

ln(175)

We have the expression as -

ln(175)

Solving the expression further, we get -

ln(25 x 7)

ln(25) + ln(7)                                       {Property : log(A x B) = log(A) + log(B)}

ln(5)² + ln(7)

2 x ln(5) + ln(7)

2 x 1.61 + 1.94

5.17

Therefore, the logarithm of the number 175 is equivalent to 5.17.

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Answer:

-1≤x≤3

Step-by-step explanation:

-3≤2x-1≤5

add 1 to all sides

-2≤2x≤6

divide all sides by 2

-1≤x≤3

It will take around 0.24 months for the invested money to get doubled.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

The formula to calculate the amount is as follows,

A = P[tex](1 + r)^{(nt)}[/tex]

Substitute all the corresponding values in the above expression to obtain,

A = P[tex](1 + 6/100)^{nt}[/tex]

1800 = 900[tex](1 + 6/100)^{nt}\\[/tex]

=>   [tex](1 + 6/100)^{nt}[/tex] = 1800/900

=>  [tex]1.06^{nt}[/tex] = 2

Since, there are 12 months in one year, n = 12.

[tex]1.06^{12t}[/tex] = 2

=> 12t = log(2) ÷ log(1.06)

=> 12t = 0.275

=> t = 0.02

Which is equivalent to 12 × 0.02 = 0.24 months.

Hence, it will take 0.24 months to double the invested money.

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The simplification of the given expression is (x - 1)²/ (x-2)(x+3) which restrictions on the domain of this expression are x ≠ 1, 2, -3.

The expression is given in the question as:

(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)

To simplify the expression (x+3)(x-1)/(x-2) ÷ (x+3)/(x-1), we can start by multiplying the numerator and denominator of the first fraction by the denominator of the second fraction:

(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)

= (x+3)(x-1) / (x-2) × (x-1) / (x+3)

Then, we can simplify the expression by combining like terms:

= (x - 1)² (x+3)/ (x-2)(x+3)

= (x - 1)²/ (x-2)(x+3)

The restrictions on the domain of this expression are that x cannot be equal to 2 or -3, because these values would make the denominator equal to zero, which is not allowed in a fraction.

Therefore, the domain of the expression is all real numbers except x = 1, x = 2, and x = -3. We can express this as:

Domain: x ∈ R, x ≠ 1, x ≠ 2, x ≠ -3

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It is necessary to compute in the volume of the rotated region while taking into account that each cross section piece is raised up by a height of h = 4 - y. Scale the results by 62.4 lb/ft3 as well.

The given parabolic region's volume of revolution about the y-axis is a parabolic cylinder. This solid is revolved, and it has circular disks as its cross section. The differential volume of one such disk situated at a differential height y above the x-axis must be determined. The weight of water in this volume can then be calculated by multiplying this volume by the density of water. The depth of this volume is then determined from the tank's top surface. Determine how much differential work is needed to lift this water layer to the top surface. Integrate this differential work now to calculate the overall effort needed to empty the tank.

Rotating the curve x=3y about the y-axis creates the region. Keep in mind that 62.5 = (125 / 2) As a result, using the disk method,

[tex]\int_{0}^{3} \left(\frac{125}{2} \pi (4-y) (3\sqrt{y})^2\right)\, dy \\ &=\int_{0}^{3} \left(\frac{1125}{2} \pi (4-y) y\right)\, dy &\text[/tex]

Integrate in relation to:

[tex]y\text{]} \\ &=\left(-\frac{1125}{2} \pi \left(\frac{y^3}{3}-2 y^2\right)\right)\bigg|_{0}^{3} \\ &=\frac{10125 \pi }{2} \\ &\approx 16045.7 \end{align*} \)[/tex]

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The coordinates to plot the graph after solving the equation will be 0.33 and 1.2.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given expressions to plot, the graph is,

f(x) = 3x - 1 and,  (i)

h(x) = -4x - 5       (ii)

From equation (i),

f(x) = 3x - 1

3x = 1

x = 1/3

x = 0.33

From equation (ii)

h(x) = -4x - 5

-4x = 5

x = -5/4

x = 1.2

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The money will double in value in approximately 11.6 years.

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

When the money doubles, the amount is

A = 900 * 2

A = 1800

The compound interest formula is given as

A = P(1 + r/n)^nt

Also from the question, we have

n = 12

This is so because the loan is compounded 12 times in a year as a result of being compounded monthly

Solving further, we replace the variables with their values in the above equation

1800 = 900 * (1 + (6%)/12)^(t*12)

Divide both sides by 900

2 = (1 + (6%)/12)^(t*12)

Also, we have

2 = (1.005)^(t*12)

Take the logarithm of both sides

12t = log(2)/log(1.005)

Evaluate the quotients

12t = 139

Divide both sides by 12

t = 11.6

Hence, the number of years is 11.6 years

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The solution to the linear inequality y > 2x - 2 and y > 5x + 8 is -3.33 and -8.67

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.

Using a graphing calculator, the solution of y > 2x - 2 and y > 5x + 8 is

This will give us a value of x is -3.33 and y is -8.67

Kindly find attached graph below

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The given statement is false. If a sample is selected using random sampling methods, the primary reason that the sample mean might be different from the corresponding population mean is not that the sample might be biased.

Because random sampling ensures that results obtained from the sample should approximate what would have been obtained if the entire population had been measured. And the simplest random sample allows all the units in the population to have an equal chance of being selected. In this case, the sample might not be biased.

Random sampling is a part of the sampling technique where each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.

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The inequality that best represents Soro's situation regarding the number of bus rides he can take between now and the end of this month is :

50 - 2.5y ≥ 20.

        = 50 - 2.5y

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The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.

It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,

C(x) = 270 ln(x+1) + 1900

The average intake of calories consumed per day is given by C(x) = 2200

Here x is the number of acres of land. Then, the required number of acres of land is

C(x) = 270 ln(x+1) + 1900

⇒ 2200 = 270 ln(x+1) + 1900

⇒ 270 ln(x+1) = 2200 - 1900

⇒ 270 ln(x+1) = 300

⇒ ln(x+1) = 300/270 = 10/9

Applying base 'e' on both sides, we get

⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]

⇒ x+1 = 3.0377

⇒ x = 3.0377 - 1 = 2.0377

When rounding the final answer to the nearest tenths, we get x = 2 acres.

When rounding the final answer to the nearest thousand, we get x = 2.038 acres.

Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.

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The required equation of conic section that shows eclipse is  [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let the standard equation of conic section,

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}=1[/tex]      (1)

From the given diagram,

The center of the eclipse is (2, 4),

Here h = 2, and k = 4

The length of minor axis 2a = 8 ⇒ a = 4

The length of major axis 2b = 12  ⇒ b = 6

Substitute the values of a, b and h, k in equation (1)

[tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex]

The required equation of the given conic section is [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].

The conic section represents the eclipse.

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a) The percentage of buyers that paid between $18,000 and $26,000 is; 95%

b) The middle 99.7% of car costs are between $16000 and $28000

c) The probability a car will cost less than $24,000 is; 68%

d) The probability a car will cost more than $26,000 is; 2.5%

The empirical rule of statistics states that 68% of data will be ± 1 standard deviations from the mean, 95% of data will be ± 2 standard deviations of the mean, and 99.7% of data will be ± 3 standard deviations from the mean.

a) We are given;

Mean; μ = $22000

Standard deviation; σ = $2000

$18,000 and $26,000 are both 2 standard deviations from the mean and so, the percentage of buyers is 95%.

b) Since the middle 99.7% of car costs, this is simply 3 standard deviations from the mean and as such it is between the values;

22000 - 3(2000) = $16000 and 22000 + 3(2000) = $28000

c) $24,000 is 1 standard deviation away from the mean and as such the probability will be 68% from empirical rule.

d) $26000 is 2 standard deviations from the mean and as such probability that a car will cost more than that is;

(100% - 95%)/2 = 5%/2 = 2.5%

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That is a geometric progression.

the common ratio is 1/2.(t2÷t1)

nth term= ar^n-1

16×1/2=8

tn=8^n-1

Answer:

The slope is 1/3

Step-by-step explanation:

The equation is equivalent to

x - 3y = -14

x = 3y - 14

x + 14 = 3y

(x + 14)/3 = y