PLEASE PLEASE HELP ME!!!!
Elena borrowed some money from her brother. She pays him back by giving him the same amount every week. The graph shows how much she owes after each week.
1. What is the slope of the line?
2. Is the slope positive or negative?
3. How much money did Elena borrow? (Hint: Vertical Intercept)

The answers to each part is mentioned below.

Given is the tabular data as shown in the image.

[A] - The equation {3} represents exponential relationship.

[B] - In an exponential relationship, the values of [y] first increases very slowly and than it increases very fast or the instantaneous rate of change  is very very fast.

[C] - The bacterial growth is represented by the equation : y = f(x) = A(B)ˣ, which is a exponential relationship. So, the bacterial growth is represented by equation 3.

[D] - Amount of water leaking from a leaky faucet can be given by a linear relationship. So, equation 2 will represent the situation.

Therefore, the answers to each part is mentioned above.

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The value of a if  the lines 5x-ay+26=0 and 3x-y+2=0 intersect on the y-axis is; a = 13

The general form of the equation of a line in slope intercept form is given as;

y = mx + c

where;

m is slope

c is y-intercept

We are given two equations of two lines as;

Line 1; 5x - ay + 26 = 0

Line 2; 3x - y + 2 = 0

Now, since they both intercept each other at the y-axis, it means that at the point of intersection, the value of x will be 0.

Thus, line 2 equation becomes;

3(0) - y + 2 = 0

y = 2

Putting 2 for y in line 1 equation gives;

5(0) - a(2) + 26 = 0

2a = 26

a = 26/2
a = 13

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Pam needs to save $905 per year for seven years to have enough for her first year with the help of her two grandfathers.

Pam needs to save $903 each year to have enough for her first year of college tuition with the help of her two grandfathers.

To calculate this, we first need to add up the total amount of money Pam's two grandfathers are offering to contribute:

Grandfather 1: $6321

Grandfather 2: $6321

Total Contribution: $12642

We then subtract this total contribution from the total cost of tuition for the first year:

Tuition: $6321

Total Contribution: -$12642

Total Amount Needed: $6321

Finally, we divide this total amount needed by the number of years Pam has to save:

Total Amount Needed: $6321

Years: 7

Amount Needed to Save Each Year: $903

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Step-by-step explanation:

Our straight line has the same gradient as that of the line,

[tex]2y=5x+7[/tex]

Dividing each term by 2,

[tex]y=\dfrac{5}{2}\,x+\dfrac{7}{2}[/tex]

Now this equation is in the form [tex]y=mx+c,[/tex] so the gradient of this line is 5/2.

So the gradient of our straight line is,

[tex]m=\dfrac{5}{2}[/tex]

Given our straight line passes through the point,

[tex](x_1,\ y_1)=(3,\ -2)[/tex]

The equation of a straight line passing through a point [tex](x_1,\ y_1)[/tex] and having gradient [tex]m[/tex] is given by,

[tex]\longrightarrow\large\boxed{\quad y-y_1=m(x-x_1)\quad}[/tex]

This form of equation of a straight line is called point - slope form.

By this point - slope form, the equation of our straight line will be given by,

[tex]\longrightarrow y-(-2)=\dfrac{5}{2}\,(x-3)[/tex]

[tex]\longrightarrow y+2=\dfrac{5}{2}\,(x-3)[/tex]

[tex]\longrightarrow2(y+2)=5(x-3)[/tex]

[tex]\longrightarrow2y+4=5x-15[/tex]

[tex]\longrightarrow\underline{\underline{5x-2y-19=0}}[/tex]

This is the equation of our straight line, written in the form [tex]Ax+By+C=0.[/tex]

As per the tangent formula, the distance does the laser spot on the wall move if the mirror is rotated by 10 is 2.9m

While we looking into the given question we have identified the following values,

Previous distance = 9.5

And the angle = 30 degrees

Rotated angle = 10 degrees

And the distance is considered as x.

Then as per the tangent formula, it can be written like the following,

=> tan 30/9.5 = tan 10/x

When we apply the tangent value, then we get,

=> 0.5773/9.5 = 0.1763/x

When we perform the cross multiplication, then we get,

=> 0.5773x = 9.5 x 0.1763

=> 0.5773x = 1.6749

Then the value of x is obtained as,

=> x = 1.6749/0.5773

=> x = 2.9012

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Answer:

0.84 m^2

Step-by-step explanation:

Long: 1200 millimeter = 1.2 meter

Wide: 700 millimeters = 0.7 meter

Area of rectangle: L x W

1.2 x 0.7 = 0.84 m^2

The correct matching of the lines is given below.

Corresponding        ⇒ Diagram C and  Diagram E

Alternate interior     ⇒ Diagram D

Alternate exterior    ⇒ Diagram A

None of these         ⇒ Diagram B

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.

The corresponding angles are represented by diagrams C and E.

The alternate interior angles are represented in diagram D and the alternate exterior in diagram A.

None of these is represented by diagram B.

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As per the concept of rate of change, the substance A and z are compound to each other.

Th term rate of change is defined as the speed at which a variable changes over a specific period of time.

Here we have given that there are two substances an z are given.

And we need to find the conclusion about the substances.

While we looking into the given question we have identified that there are two substances are given A and Z.

And we also know that substance A can be broken down by a chemical change. But the substance Z can't be broken down by a chemical change.

While we looking into to this condition, we know that the substance A is going to react on Z.

Therefore, the here A is and compound and Z is an element.

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By using linear inequation, it can be calculated that -

Option A and D is true when d is -13

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by

>, <, ≥, ≤

A one degree inequation is known as linear inequation.

Here, four sets of linear inequations are given

For option A

-d - 5 ≥ 5

-d ≥ 5 + 5

-d  ≥ 10

d  ≤ -10

-13 is satisfied here

For option B

d - 5 ≥ -5

d ≥ -5 + 5

d  ≥ 0

-13 is not satisfied here

For option C

-d - 5 ≤ 5

-d ≤ 5 + 5

-d  ≤ 10

d   ≥ -10

-13 is not satisfied here

For option D

d - 5 ≤ -5

d ≤ -5 + 5

d  ≤ 0

-13 is satisfied here

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The degree of the variable that appears in the polynomial has the most power. The leading term is the one with the highest degree or the one with the highest power of the variable. The coefficient of the leading term is the leading coefficient.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

For instance, the polynomial 2x+5 has an exponent of 1.

A polynomial is not an expression with a variable that has fractional or negative exponents, divides by a variable, or is contained inside a radical.

The biggest power of the variable that occurs in the polynomial is its degree.

The term with the highest degree—i.e., the term with the largest power of the variable—is the leading term.

The leading coefficient is the leading term's coefficient.

Therefore, the degree of the variable that appears in the polynomial has the most power. The leading term is the one with the highest degree or the one with the highest power of the variable. The coefficient of the leading term is the leading coefficient.

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Answer:

x = -1/9

Step-by-step explanation:

p(x) = 9x - 2

9x - 2 = -3

9x = -1

x = -1/9

y = (-1/2)x + 4 is the equation for the linear function with an x-intercept of 8 and a y-intercept of 4.

We are aware that lines might have several kinds of equations; the typical form is

The equation of a line in slope-intercept form is Ax + By + c = 0, and

y = mx + b.

m is the slope, and b is the y-intercept.

The y-intercept, or (0,b), is the point where the line crosses the y-axis at x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.

Given, An x-intercept for a linear function is 8, and a y-intercept is 4.

The two points on the line are therefore (8, 0) and (0, 4).

Slope(m) is now equal to (4 - 0)/(0 - 8).

m slope = 4/8.

slope(m) equals -1/2.

With a y-intercept of 4, it represents the value of b in the equation y = mx + b.

Consequently, the equation is y = (-1/2)x + 4 is linear.

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The 2 formulas of rectangular prism are Volume = Length x Width x Height cubic units and Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units.

An item with three dimensions is a rectangular prism. It will therefore have its own volume and surface area. We need to know the dimensions of a prism's sides or edges in order to compute its volume and surface area. Let l, w, and h represent the dimensions of the rectangular prism. Below are the supplied formulas.

The 2 formulas of rectangular prism are

Volume of rectangular prism:

Volume = Length x Width x Height cubic units

Surface area of rectangular prism:

Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units

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A linear equation in one variable can have one, no, or an infinite number of solutions.

A linear equation in one variable is an equation that can be written in the form ax + b = 0, where a and b are constants, and x is the variable. Depending on the values of a and b, a linear equation can have one, no, or an infinite number of solutions.

If a = 0 and b = 0, then the equation is 0 = 0, which is true for all values of x. In this case, the equation has an infinite number of solutions.

If a = 0 and b ≠ 0 then the equation 0x + b = 0 has no solution, as 0x = 0 for all values of x and b ≠ 0.

If a ≠ 0 and b = 0, then the equation ax + 0 = 0 can be written as ax = 0 and has one solution, x = 0.

If a ≠ 0 and b ≠ 0, then the equation ax + b = 0 can be solved by subtracting b from both sides of the equation and dividing by a. This will yield one solution, x = -b/a.

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A set is a collection of unique objects. There is no repetition of elements in a set. It is well defined. The number of elements can be finite or infinite.

Five examples of set are :

(1) Set of vowels in English alphabets

V = { a, e, i, o, u }

(2) Set of integers

Z = { ..., -2, -1, 0, 1, 2, ... }

(3) Set of natural numbers

N = { 1, 2, 3, ... }

(4) Set of natural numbers less than 10

A = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }

(5) Set of months with number of days is 30

M = {  April, June, September, November }

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Vernon borrowed an amount of $400.

Interest rate is the amount a borrower has to pay which is also a percentage of the principal amount, which is the amount loaned. Annual interest rate is this amount which the borrower has to pay once in an year.

Let the money Vernon borrowed = x

Annual interest rate = 9%

Interest paid for 1 year = x × 9%

Interest paid for 2 years = x × 9% × 2

Interest paid for 2 years is given as $72.

⇒ x × 9% × 2 = 72

   x × 18% = 72

   x × (18/100) = 72

   0.18 x = 72

   x = 72/0.18

   x = 400

Hence the money Mrs. Vernon borrowed is $400

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The letter "I" represents the symbol of the current.

Electric current is defined as the rate at which a given flow of electrons passes through a point in a complete electrical circuit or flow of charge.

The electric current is defined with the capital letter I being its symbolism, and its unit of expression is the Ampere (A).

It is important to know that if we keep relation of the "i" as a complex number to give values of current is also valid, since the current or the flow of charge describes sinusoidal and cosine wave, and these are studied more easily with these complex numbers of the form:

e^ i∅     = Cos∅ + iSen∅

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The corresponding Z critical value for the given 85% confidence level is 1.440.

The Z critical value or known as Z-score is used if the sampling distribution is normal, or close to normal. Z-score is used when the population standard deviation is known or when we have larger sample sizes.

To determine the Z critical value, we can use Z-table or a calculator. To be able to find Z-score in Z-table, first, we need to look at the left side column of the Z-table to get the value corresponding to one decimal place of the Z-score. For example, the whole number and the first digit after the decimal point. Then, look up for the remaining number across the table (on the top).

In this case, based on the Z-table, the corresponding Z critical value for the given 85% confidence level is 1.440.

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Answer:16

Step-by-step explanation: 4 x 4 because a square has 4 sides and each side is 4cm because each side is the same measurements

Answer:

−7+y/3  is the same as that, but simplified.

Answer:

y/3-7

Step-by-step explanation:

The answer is the solved equation of -3+2/3y-4-1/3y.

Subtract 4 from -3 to get -7

= -7+2/3y-1/3y

Combine 2/3y and -1/3y to get 1/3y

-7+1/3, or just y/3-7.

Answer:

232.88

Step-by-step explanation:

I used a calculator on this so it must be correct

A corporate (or credit) spread is the extra interest a lender demands to make up for the extra risk they take on by financing the business.

Companies borrow money from their investors through the use of bonds, which are debt instruments. Better performance and low-risk perceptions for businesses cause bond spreads to narrow. The corporate spread decreases when people have favorable and low-risk impressions about the company issuing the bond since it is the extra interest paid over the interest from US Treasury bonds.

A bond is an IOU that specifies the amount of reward the IOU holder will get upon repayment of the borrowed funds. Basis points are typically used to calculate this interest rate. The matching government bond yield is typically considered for determining spread. The spread decreases as the danger increases.

Basis points are a standard unit of measurement for the corporate spread. These are "hundredths of a percent" more than the interest rate on Treasury bonds. Accordingly, a spread of 100 basis points is equal to 1% more than the yield on government bonds.

Spreads that are getting tighter indicate a company's assessment of risk is getting better. This is because investors have enough faith in the business to invest in it in exchange for reduced spreads. Strong financial statements, improved loan servicing, or a generally stable market impression could all be to blame for this.

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A bond is an IOU that specifies the amount of reward the IOU holder will get upon repayment of the borrowed funds. Basis points are typically used to calculate this interest rate. The matching government bond yield is typically considered for determining spread. The spread decreases as the danger increases.

Basis points are a standard unit of measurement for the corporate spread. These are "hundredths of a percent" more than the interest rate on Treasury bonds. Accordingly, a spread of 100 basis points is equal to 1% more than the yield on government bonds.

When there are two arguments, the first one is used as a starting value rather than 0; when there are three arguments, the third one is used as an increment rather than the implied default of 1.

The statistical range is the range of values between the highest and lowest for a particular data collection. Another way to represent the range is the difference between the highest and lowest observation. The sample interval is determined by subtracting the largest number from the lowest. For continuous variables, the sample range is a critical measure of variability.

here

Basically, the range function in Python takes three inputs.

Start: An integer designating the range object's beginning.

Stop: An integer that represents the object at the end of the range.

Step: An integer that represents the increment following each value.

When there are two arguments, the first one is used as a starting value rather than 0 .

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The median of 5,8,6,9,11,4 is 7.

The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

Here we have to find the median of 5,8,6,9,11,4.

Arranging the given data/observations in ascending order:-

4, 5, 6, 8, 9, 11

Here we can see that there are 6 numbers given

so, n= 6

Where the number of terms is even.

We know that the formula to find the value of the median whose n value is given,

Median= {(n/2 +1 )th term +(n/2)th term} / 2

We can now substitute the value of n in the above formula, we get

Median= {(6/2+1) +(6/2)} / 2

We can now simplify the above step, we get

Median= 3rd observation + 4th observation / 2 = 6+8/2 = 7

Therefore, the median of  5,8,6,9,11,4 is 7.

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There are 45 erasers in the box and the total number of writing pencils is 20.

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

We have,

for every 4 pencils, there are 9 erasers and there are 25 more erasers than pencils in a box

erasers are in the box:

pencil/erasers = pencil/erasers

Let's consider x for pencils and y for the erasers

4/9 = x/25 + x

9x = 100 + 4x

5x = 100

x = 100/5

x = 20

there are 25 more erasers than pencils in a box

so, 25 + x = 25 + 20 = 45

there are 45 erasers in the box

Hence, there are 45 erasers in the box and the total number of writing pencils is 20.

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The statement which is true: (Option D.) Simulations are based on trials of chance that mimic real-life events.

Simulations are a powerful tool used to predict the outcomes of real-life events. They are based on trials of chance that are repeated multiple times to get estimates closer to theoretical probability.

Simulations rely on random sampling, which means that a sample size of 20 or less can still be representative of a larger population. This makes simulations a useful tool for understanding outcomes in situations where data is limited or unavailable. By using simulations to predict outcomes, researchers can gain a better understanding of their target population and make informed decisions.

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I think it could be 1.5 kilometers.

The distance is 1,500 m but you have to convert it so probably 1.5 km.

Answer:

36 feet

Step-by-step explanation:

If one inch in the drawing equals 3 feet, then the 12-inch length of the wing would correspond to 12(3 feet).  This means the final length of the wing will be 36 feet from tip to tip.

Answer:

Step-by-step explanation:

A function is increasing if the graph is going up.

A function is decreasing if the graph is going down.