Put the following equation in slope-intercept form:
y=1/5x + b

Answer:

The total value of the account after 3 years will be $5,503.52.

Step-by-step explanation:

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Tyler's bank account pays a straightforward yearly financing cost of 3.25%. Assume he stores $5,000 in the record and sets aside no extra installments or withdrawals for a long time.

The total value of the account after 3 years will be calculated as,

A = $5,000(1 + 0.0325)³

A = $5,000 x (1.0325)³

A = $5,000 x 1.1007

A = $5,503.52

The total value of the account after 3 years will be $5,503.52.

Therefore ,the total number of days to rent a car at both locations for the same price is 11 days.

Two or more algebraic equations can be simultaneous if they share variables, such as x and y. Due to the simultaneous solution of the equations, they are known as simultaneous equations.

Here,

Let x be the number of days to repay after a down payment and y be the total amount due.

Consequently, equation 1 is 61+24x=y.

Eq. 2: 105 + 20x = y

Equation 1 minus equation 2

105-61+20x-24x= 0

44-4x= 0

4x = 44

multiply both sides by 4.

x= 44/4

x= 11 days

the total number of days to rent a car at both locations for the same price is 11 days.

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Answer:

The two teachers are 13 feet apart

Step-by-step explanation:

Right Triangles

Ava, her math teacher, and her science teacher form a right triangle in which she is at the 90° vertex.

The distances from the three people must satisfy the Pythagora's theorem, where the distance between the two teachers (D) is the hypotenuse, thus:

D = 13 feet

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Median -

To find the median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.

Answer: 34

Mode -

The most frequent number—that is, the number that occurs the highest number of times.

Answer: 34

Answer:

I think

Mode = 34

Median = 34

Step-by-step explanation:

11.18033

let b=x

use pythag and rearrange for side b. Then simply maths.

Answer:

2 quarts

Step-by-step explanation:

1 quart = 2 pints

4 pints × (1 quart)/(2 pints) = 2 quarts

Answer:

2 quarts

Step-by-step explanation:

1 quart=2 pints

2 quarts=4 pints

Have a great day

The perimeter of the equilateral polygon with the given vertices is given as follows:

40 units.

The perimeter of a polygon is composed by the sum of the lengths of the outer edges of the figure.

From the figure given at the end of the answer, the parameters for the polygon with these given vertices are given as follows:

Then, considering the 8 side lengths and the fact that they measure 5 inches, the perimeter of the polygon is given as follows:

Perimeter = 8 x 5 = 40 units.

(sum of 8 times the number 5 is equals to the multiplication of eight by five).

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Inequality that could be used to solve for x is;

1450 words + (265 words / day)x  = 3305 words

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given that Amy has already written 1450 words out of 3305 words.

And she writes at the rate of 265 words per day.

To establish the inequality which could be used to solve for x,

Then Firstly, we will form an equation for the total number of days required to write her paper,

1450 words + (265 words / day)x  = 3305 words.

Simplifying the above expression,

(265 words / day)x = 3305 words - 1450 words

To solve this linear equation, we'll find x = 7.

x = { 3305 words - 1450 words} / 265  words

x = 7 days.

Hence, inequality that could be used to solve for x is;

1450 words + (265 words / day)x  = 3305 words

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Answer:

Below

Step-by-step explanation:

a)  there are 10 cards    only one '4'    so 1 out of 10 = 1/10

b)  there are 2 cards out of 10 with a '1' on them    2/10 = 1/5

c)  8 out of 10 = 8/10

f(x) = 4. 8x² function can be used to compute the approximate area, in square inches, of a stop sign if it has a side length of x inches.

A function, which produces single output from either a single input, is an illustration of a rule. Alex Federspiel was contacted to collect the image. An illustration of this is the equation y=x2. For each input of x, there is simply one output of y. Considering that x is actually the input value, we would claim that y is just a rational number.

area = (# of sides * side length^2) / [4 * tan (180/n)]

area = (8 * x^2) / 4 * tan (22.5)

area = 8 x^2 / (4 * 0.41421)

area = 8 x^2 / 1.65684

area = 4.8 x^2

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The amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of petrol in Spain be = A

Let the amount of petrol in Wales be = B

Now , the total amount Sam paid for 18 Liters of petrol in Spain = 27 euros

1 euro = 0.85 pounds

So ,

Total amount Sam paid for 18 Liters of petrol in Spain = 27 x 0.85 pounds

Total amount Sam paid for 18 Liters of petrol in Spain = 22.95 pounds

So ,

The amount for 1 Liter of petrol in Spain = Total amount Sam paid for 18 Liters of petrol in Spain / 18

Substituting the values in the equation , we get

The amount for 1 Liter of petrol in Spain = 22.95 / 18

The amount for 1 Liter of petrol in Spain = £ 1.275

And ,

Now , the total amount Sam paid for 8 gallons of petrol in Wales = £ 40.80

1 gallon = 4.5 Liters

8 gallons = 4.5 x 8 Liters

8 gallons = 36 Liters

So ,

Total amount Sam paid for 36 Liters of petrol in Wales = £ 40.80

So ,

The amount for 1 Liter of petrol in Wales = Total amount Sam paid for 36 Liters of petrol in Spain / 36

Substituting the values in the equation , we get

The amount for 1 Liter of petrol in Wales = 40.80 / 36

The amount for 1 Liter of petrol in Wales = £ 1.13

£ 1.13  <   £ 1.275

Therefore , the amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain

Hence , The amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain

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The sample size is necessary if the 95% ci for p is to have a width of at most 0.15 irrespective of p being 385 people.

In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time. Confidence intervals that include 95% or 99% of anticipated observations are frequently used by analysts.

The largest confidence interval occurs when p = .5

The standard error = [tex]\sqrt{\frac{(0.5)^{2} }{x} }[/tex]

The z* for a 95% confidence interval = 1.96

Setting up an equation,

[tex]1.96\sqrt{\frac{(0.5)^{2} }{x} } = 0.05[/tex]

Solving gives x=384.2.

So you need 385 people.

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Check the picture below.

Answer:

  205.03125

Step-by-step explanation:

You want the 8th term of the sequence that begins 12, 18, 27, ....

The first differences of the given terms are ...

  18 -12 = 6

  27 -18 = 9

These are not constant, so the sequence is not an arithmetic sequence.

The ratios of sequential terms are ...

  18/12 = 1.5

  27/8 = 1.5

These are constant, suggesting the sequence is an exponential sequence. The equation for the n-th term is ...

  an = 12(1.5^(n-1))

Then the 8th term is ...

  a8 = 12(1.5^7) = 205.03125

__

Additional comment

The sequence could be quadratic if the second differences are all 9-6=3. In that case, the equation for the n-th term is ...

  an = 1.5n(n +1) +9

and the 8th term is ...

  a8 = 1.5·8(8+1) +9 = 117

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The product of matrix A and matrix B is matrix C

a)  [tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]

b) [tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]

What is multiplication of matrices?

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix

Given data ,

a)

Let the first matrix be A

The value of A is

[tex]A = \begin{pmatrix}2&3\end{pmatrix}[/tex]

The value of second matrix B is

[tex]B = \begin{pmatrix}4\\ \:5\end{pmatrix}[/tex]

Now , the product of matrix A and matrix B is matrix C

The value of matrix C is

[tex]C = \begin{pmatrix}2&3\end{pmatrix}\begin{pmatrix}4\\ 5\end{pmatrix}[/tex]

On simplifying the value of matrix C , we get

[tex]C = \begin{pmatrix}2\cdot \:4+3\cdot \:5\end{pmatrix}[/tex]

[tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]

Therefore , the value of matrix C is [tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]

b)

Let the first matrix be A

The value of A is

[tex]A = \begin{pmatrix}1&2\end{pmatrix}[/tex]

The value of second matrix B is

[tex]B = \begin{pmatrix}-3\\ \:4\end{pmatrix}[/tex]

Now , the product of matrix A and matrix B is matrix C

The value of matrix C is

[tex]C = \begin{pmatrix}1&2\end{pmatrix}\begin{pmatrix}-3\\ 4\end{pmatrix}[/tex]

On simplifying the value of matrix C , we get

[tex]C =\begin{pmatrix}1\cdot \left(-3\right)+2\cdot \:4\end{pmatrix}[/tex]

[tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]

Therefore , the value of matrix C is [tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]

Hence , the matrix multiplication is

The product of matrix A and matrix B is matrix C

a)  [tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]

b) [tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]

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We are given the slope and the y-intercept so using the slope-intercept form:

Substitute values to get:

To graph a line we need two points, one is given, (0, - 7) - the y-intercept.

Find one more point,  take even value of x to cancel the fraction, let it be x = 4, find its y-coordinate:

So our points are:

Plot the points and connect to graph the line.

See below.

The graph of the linear equation:y = (3/2)*x - 7 can be seen in the image at the end.

A general linear equation is written as:y = a*x + b

Where a is the slope and b is the y-intercept. Then our linear equation is:y = (3/2)*x - 7

To graph it, we need to know two points in our line, to do so, we evaluate it in two different values of x. if x = 0y = (3/2)*0 - 7y = -7So we have the point (0, -7)

And if x = 2 then:y = (3/2)*2 - 7y = 3 - 7y = -4So we have the point (2, -4)

Now we just need to graph these two points and connect them with a line. You can see the graph below.

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The value of the angle m ∠ DAB in the parallelogram is 128 degrees

In a given parallelogram, the opposite sides and angles are equal to one another.

In the question given;

m∠ ABC = 3x + 1

m∠ BCD = 8x - 8

m∠ DAB = ?

m ∠ ABC + m∠ BCD = 180°

The sum of the two angles is equal to 180 degrees

3x + 1 + 8x - 8 = 180

11x - 7 = 180

11x = 187

x = 17

However, m∠ DAB = m∠ BCD

Two opposite angles are equal

m∠ DAB = 8x - 8

m ∠ DAB = 8(17) - 8

m ∠ DAB = 128 degrees

The angle is 128 degrees

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The proportion that you use to derive the equation of the line is (y+2)/x=4/3.

So, option c is correct.

An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable. By deleting parentheses and merging like terms, you can simplify either side of an equation and find its solution.

Identify the variable term on one side of the equation by adding or subtracting. You can find the variable's value by multiplying or dividing. When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. Depending on the language, the definition of the word equation and its cognates may alter slightly. For instance, an equation is what is meant in French.

Here,

In the given diagram:

The slope of the straight lines is constant

So, DE/AD=CB/AB

(y+2)/x=4/3

Therefore, option c is correct.

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We know that each friend will pay $13.3 using simple mathematical operations.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).

So, we know that:

There are 5 friends.

Each ticket costs $11.75.

They have a large popcorn for $7.75.

Then, the amount that each friend will pay:

[(11.75*5)+7.75]/5

[58.75+7.75]/5

66.5/5

$13.3

Therefore, we know that each friend will pay $13.3 using simple mathematical operations.

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Correct question:
Five friends go to a movie. Each movie ticket cost $11. 75. They have a large popcorn for $7. 75. If they divide the total cost equally, how much will each friend pay?

Answer:

Step-by-step

Each friend pays $3.9 each.  

1.   $11.75 + $7.75 = 19.50.

2. 19.50 divided by 5 (friends) is equal to 3.9.

The perimeter of the figure is 5.0.

What is a perimeter?

The perimeter of a two-dimensional shape is the distance around the outside of the shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is the sum of the lengths of all four sides. The perimeter of a triangle is the sum of the lengths of all three sides.

To reflect a point across the line y=x, we can use the following formula:

(x', y') = (y, x)

Where (x', y') is the reflected point and (x, y) is the original point.

Using this formula, we can find the coordinates of the reflected points A' and B':

A' = (4, 4) -> (4, 4) -> (4, 4)

B' = (5, -1) -> (-1, 5) -> (-1, 5)

Therefore, the image of AB is A'B' with endpoints A'(4, 4) and B'(-1, 5).

To find the perimeter of the figure formed by the segments AB, B'B, and A'B', we can add up the lengths of these three segments. The length of AB can be found using the distance formula:

[tex]AB = \sqrt{((5-4)^2 + (-1-4)^2)}\\\\= \sqrt{(1^2 + (-5)^2)}\\\\= \sqrt{(1 + 25)}\\\\= \sqrt{26}[/tex]

The length of B'B can be found using the same formula:

[tex]B'B = \sqrt{((-1-(-1))^2 + (5-5)^2)}\\\\= \sqrt{(0^2 + 0^2)}\\\\= 0[/tex]

The length of A'B' can also be found using the distance formula:

[tex]A'B' = \sqrt{((-1-4)^2 + (5-4)^2)}\\\\= \sqrt{(-5)^2 + (1)^2}\\\\= \sqrt{25 + 1}\\\\= \sqrt{26}[/tex]

The perimeter of the figure is AB + B'B + A'B' = √26 + 0 + √26 = 2√26. To the nearest tenth, this is 5.0.

Hence, the perimeter of the figure is 5.0.

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a) The p-value indicates that it is very rare to observe a test statistics equally or more extreme when the null hypothesis is true.

A null hypothesis is a claim or presumption that there is no association between two observed variables or that observed differences between groups are the result of chance. It is frequently employed in statistical testing, and it is represented by the symbol "H0". The null hypothesis is often the inverse of the alternative hypothesis, which posits a link or difference between the variables. To reject the null hypothesis, the observed data must be statistically significant and unlikely to have occurred by chance. In scientific research, the null hypothesis is crucial because it enables researchers to assess the significance of their data and reach reliable conclusions.

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The most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up is 17 gallons.

On plotting the graph we will get ,

The most reasonable value of y corresponding to x = 3 is approximately 17 gallons.

A plot is a graphical technique for representing a data set, typically in the form of a graph that depicts the relationship between two or more variables. The plot can be created either by hand or by computer. Previously, mechanical or electronic plotters were used.

Graphs are a visual representation of the relationship between variables that are very useful for humans because they allow them to quickly derive an understanding that would not have been possible from lists of values. Graphs can also be used to read off the value of an unknown variable plotted as a function of a known variable given a scale or ruler, but this can also be done with data presented in tabular form. Function graphs are used in mathematics, science, engineering, and technology.

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The value of missing side length(m) in ΔQRS is 15 cm.

How to solve the sides of triangle?

ΔABC ~ ΔQRS

The sides of the triangle will be in equal ration of one another.

i.e., AB/AC = QR/QS

3/1 = m / 5

m = 15 cm

Hence, The value of missing side length(m) in ΔQRS is 15 cm.

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Answer:

9x³+8x²-3x-11

Step-by-step explanation:

1. You can move sections around throughout the equation.

^Note: Be sure to keep the same signs (either positive or negative) for each section.

In this problem, the sections are (-3x), (8x²), (-11), and (9x³).

^Note: I kept the subtraction/negative sign

2. Rearrange the exponents in order from largest to smallest in the equation.

largest 9x³ +8x² -3x -11 smallest

^Note: -3x has an exponent of 1

The distance between the two points is 10 units

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

A = (13, 2) and B =(7, 10)

The distance between the two points can be calculated using the following distance equation

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where

(x, y) = (13, 2) and (7, 10)

Substitute (x, y) = (13, 2) and (7, 10) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

distance = √[(13 - 7)² + (2 - 10)²]

Evaluate

distance = 10

Hence, the distance is 10 units

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Answer:

x = –4

Step-by-step explanation:

y = –2x + 8

16 = –2x + 8

2x = 8 – 16

2x = –8

x = –4

The mid term is 2,Accordingly, if n is even, there will only be one middle term, and if n is odd, there will be two middle terms.  

Explanation:

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

The mid term is 2.

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Answer:

Step-by-step explanation:

157.1429% but you can round it down

The triangles consist in rectangles ΔABD and ΔCDB are congruent triangles.

Given that,
To prove  ΔABD ≅ ΔCDB.

In congruent geometry, the shapes that are so identical. can be superimposed on themselves.

Here,
consider ΔABD and ΔCDB
1. AB = CD   [opposite sides of a rectangle]
2. ∠A = ∠C   [each angle of the rectangle is 90°]
3. AD = BC    [opposite sides of a rectangle]
ΔABD ≅ ΔCDB

Thus, Both triangles ΔABD ≅ ΔCDB are congruent triangles, hence proved.

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