What is an equation in point slope form of the line that passes through (7, 1) and (-3,9)

number 4

because 2 is solid since it's all together, just like a solid number 3 is gas simce. It's spread around, and number 1 is just silly, so the awnser is 4

Answer:

Step-by-step explanation:

1/5 a-5=20   addition properties

1/5 a -5+5=20+5

1/5=25     multiply both sides by 5

5/5 a=25*5

a=125

check the answer:

125/5 -5=20

25-5=20

20=20 correct

Answer: \(Domain = \{t: t\geq 0\}=[0,\infty)\) and \(Range = \{v: v\geq 550\}=[550,\infty)\).

Step-by-step explanation:

It is given that, the value of this account, v, is given by the function

\(v=550+16.5t\)

where, t is the number of years the money is in the bank.

We need to find the domain & range of this function.

Domain is the set of input values. Here, the domain is number of years which cannot be negative. So,

\(Domain = \{t: t\geq 0\}=[0,\infty)\)

Range is the set of output values. Here, the range is amount after simple interest which cannot be less than the principal value.

\(Range = \{v: v\geq 550\}=[550,\infty)\)

Answer: 46.5 m

Step-by-step explanation: formula to find area of a trapezoid = the top side plus the bottom side divided by 2. Then, we multiply the remainder by the height. In this case, it would be written as: 5.3 + 13.3/2 x 5, which is equal to 46.5m

A direct relationship between two variables is reflected in a "POSITIVE" correlation coefficient.

Correlation is a statistical technique for measuring and describing the relationship between two variables.

The variables move in the same direction when they have a positive correlation. In other words, as one variable increases, so does the other, and conversely, as one variable decreases, so does the other.

Typically, the two variables are simply observed rather than manipulated. Two scores from the same individuals are required for the correlation.

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Answer:

405 in²

Step-by-step explanation:

Given that :

Total area of quilt = 540 in²

Number of Blue patches = 27

Number of white patches = x

Area per patch = 5 in²

Area of white = total area - total area of blue patch

Total area of blue patch = 27 * 5 in² = 135 in²

Area that is white :

540 in² - 135 in²

= 405in²

Answer:

24 bracelets can be made from given beads.

● Explanation -To make similar bracelets using all the beads, we have to find the highest common factor of no of beads.Now, Factors of 72 => 1, 2, 3, 4, 6, 8 , 9, 12, 18, 24, 36, 72Factors of 192 => 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192Factors of 120 => 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120HCF => 24Observing this data, HCF of 72, 192 & 120 will be 24.Therefore, total 24 bracelets can be made from given beads.* Each bracelet will have 3 red, 8 blue and 5 white beads.

There is an outstanding bond from BP with a 15-year maturity, a $1,000 par value, a 6.9% coupon rate that is paid semi-annually, and a price of 98.17. As a result, the annual cost of debt for this bond is roughly 8.5 percent.

To calculate the cost of debt, we need to determine the yield to maturity (YTM) of the bond. The YTM is the rate of return an investor would earn by purchasing the bond and holding it until maturity. We can use the bond pricing formula to calculate the YTM.

The bond pricing formula is as follows:

\(\text{Bond Price} = \frac{{C \times (1 - (1 + r)^{-n})}}{{r}} + \frac{{M}}{{(1 + r)^n}}\)

Where:

C = Coupon payment

r = Yield to maturity (YTM)

n = Number of periods

M = Par value

Given information:

Coupon payment (C) = \(\$1,000 \times \frac{6.1\%}{2} = \$30.50\)

Par value (M) = $1,000

Bond price = $1,000 × 83.57% = $835.70

We know the bond has 15 years to maturity, and coupons are paid semiannually. So, the number of periods (n) is 15 years × 2 = 30.

Using the bond pricing formula, we can rearrange it to solve for the YTM:

\(Bond Price = \frac{{C \times (1 - (1 + r)^{-n})}}{{r}} + \frac{{M}}{{(1 + r)^n}}\)

Substituting the given values:

\($835.70 = \left(\frac{{\$30.50 \times (1 - (1 + r)^{-30})}}{{r}}\right) + \left(\frac{{\$1,000}}{{(1 + r)^{30}}}\right)\)

To find the YTM, we need to solve this equation either algebraically or using numerical methods like trial and error or using financial calculators/spreadsheets.

By using a financial calculator or spreadsheet, we find that the YTM is approximately 8.5%. Therefore, the cost of debt for this bond is approximately 8.5% per year.

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Complete question :

Problem 17 Intro BP has a bond outstanding with 15 years to maturity, a $1,000 par value, a coupon rate of 6.1%, with coupons paid semiannually, and a price of 83.57 (percent of par). | Attempt 1/10 for 10 pts. Part 1 What is the cost of debt? B+ decimals Submit

Answer:

2, 10, 50, 250

Step-by-step explanation:

Using the formula with a₁ = 2 , then

a₂ = 5a₁ = 5 × 2 = 10

a₃ = 5a₂ = 5 × 10 = 50

a₄ = 5a₃ = 5 × 50 = 250

The first 4 terms are 2, 10, 50, 250

Answer:

f(x) = (x + 5)²

Step-by-step explanation:

f(x) = x² + 10x + 25 = (x + 5)²

y = a (x - h)² + k         vertex: (h , k)

a = 1      h = -5      k = 0

Answer:

option A. 5 apples for $2.50

Step-by-step explanation:

You must find the price per apple for each option by dividing the cost in cents by the number of apples. 250 cents divided by 5 apples gives you 50 cents per apple, while option c is 55 cents per apple, option b is 60 cents per apple, and option d is 52 cents per apple.

Answer:

Step-by-step explanation:

1- Remove any grouping symbol such as brackets and parentheses by multiplying factors.

2- the exponent rule to remove grouping if the terms are containing exponents.

3- Combine the like terms by addition or subtraction.

4- Combine the constants.

The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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The probability of a red light be on this road so that neither road would be preferred over the other on the basis of expected number of red lights is 0.3375.

What is Probability:

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Math's to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Now,

PDF of a Binomial (n, x) distribution is

given as

p(X=x).\(C^n_x P^x (1-p)^(n-x)\)    x =  0,1,2,

Here n = 9, 2:4, p = 0.3

P(x-4)= 9^c_4(0.3)^4 (0.75)^5 = 0·1715 Ans

R Code

We will use the function pGnom() which gives the Cumulative probability of an

Probability  of getting exactly 4 heads is

x <- pGnom (4,9, 0.3) - pGnom (3,9, 0.3)

(We substract 3 to get P(X = 4) since above we have P(X<4) - P(X ≤3)

b)

Expected number in a binomial distribution = np

We  have to equate the Expected values

So

9x0.3 = 8xp

os, p = 0.3375.

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Answer:

120

Step-by-step explanation:

There are 5 ways to choose the first spot, 4 ways to choose the second spot (because we already used one), and so on and so forth.

5*4*3*2*1=120

Therefore, the answer is 120.

Feel free to tell me if I did anything wrong! :)

There are 120 different ways to display five types of bread on a grocery store shelf. This calculation is based on the concept of permutations, where the order of arrangement matters.

To determine the number of different ways to display the five types of bread on the shelf, we can use the concept of permutations. In this case, the order of arrangement matters because each type of bread occupies a distinct position on the shelf.

The number of permutations of a set of objects can be calculated using the formula:

P(n, r) = n! / (n - r)!

Where n represents the total number of objects and r represents the number of objects to be selected for each arrangement.

In this scenario, we have five types of bread to be displayed on the shelf. Therefore, n = 5. Since we want to display all five types, we need to arrange all of them, so r = 5 as well.

Plugging these values into the permutation formula, we get:

P(5, 5) = 5! / (5 - 5)!

= 5! / 0!

= 5! / 1

= 5 * 4 * 3 * 2 * 1

= 120

Therefore, there are 120 different ways to display the five types of bread on the grocery store shelf. This means that the store has a variety of options for arranging and presenting the bread to customers, allowing for different visual arrangements and product placement strategies.

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A. The y-intercept is at the point (0, 0).

B.  The zeros are x = 0 or x = ±√5

C.

A) The y-intercept of this graph is the point where x = 0.

When  x = 0, the value of y

= 0^4 - 5*0^2

= 0.

Therefore, the y-intercept is at the point (0, 0).

B) The x-intercepts/roots of the function are the values of x that make y = 0.

To find these values, we need to set y = 0 and solve for x:

x⁴ - 5x² = 0

x⁴ = 5x²

x² = x⁴/5

x = ±√(x⁴/5)

We can simplify this expression by factoring x² out of both sides:

x²(x² - 5) = 0

x² = 0 or x² - 5 = 0

x = 0 or x = ±√5

hence the x-intercepts are at x = 0 and x = ±√5.

C) The end behavior of this function refers to how the graph of the function approaches the x-axis as x approaches positive infinity and negative infinity.

x → ∞ f(x) → ∞

x → -∞ f(x) → -∞

D) The graph is attached

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The equation of a line y=2x+8.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis

Looking at the given line,

y = 2x + 7

Compared with the slope-intercept equation,

Slope, m = 2

If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2

Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes

4 = 2 × - 2 + c

4 = - 4 + c

c = 4 + 4 = 8

The equation becomes y=2x+8.

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It would take approximately 100,000 quarters to reach a height of 575 ft, the height of the Washington Monument, when stacked vertically.

To determine the number of quarters required to reach the height of the Washington Monument, we need to calculate the number of quarters stacked that would equal a height of 575 ft.

The height of the Washington Monument is given as 575 ft. We need to find out how many quarters, which have a thickness of approximately 0.069 inches or 0.00575 ft, would need to be stacked to reach this height.
First, we convert the height of the Washington Monument to inches: 575 ft × 12 inches/ft = 6,900 inches.
Next, we calculate the number of quarters needed by dividing the total height in inches by the thickness of a single quarter: 6,900 inches ÷ 0.069 inches/quarter.
Using this calculation, we find that approximately 100,000 quarters would need to be stacked to reach the height of the Washington Monument.
Therefore, it would take approximately 100,000 quarters to reach a height of 575 ft, the height of the Washington Monument, when stacked vertically.

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The area of the composite figure is 294 cm square.

The figure above is a composite figure. The figure is formed by combining two trapeziums.

Therefore, the area of the figure is the sum of the whole area of the shape.

Hence,

area of the composite figure = area of the trapezium1 + area of the trapezium2.

area of the trapezium1 = 1  / 2 (a + b)h

hence,

area of the trapezium1 = 1 / 2 (12 + 25)6

area of the trapezium1 = 1 / 2 (37)6

area of the trapezium1 = 111 cm²

area of the trapezium2 = 1 / 2 (24 + 37)6

area of the trapezium2 = 3 × 61

area of the trapezium2 = 183 cm²

Therefore,

area of the composite figure = 111 + 183

area of the composite figure = 294 cm²

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To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

slope = 2

Step-by-step explanation:

y = mx + b

M is the slope

5y = 10x - 15

y = 2x - 3

2 is the m in this equation

I hope this helped!

Using geometric sequence concepts, it is found that the one which results in a sum of -69,905 is:

D. \(\sum_{k = 0}^{9} -\frac{1}{5}(4)^k\)

As a sum, it can be represented by:

\(\sum_{k = 0}^{n - 1} a_1(q)^k\)

The result of the sum is:

\(S = \frac{a_1(1 - q^n)}{1 - q}\)

Item A:

For this sequence, we have that:

\(a_1 = \frac{1}{4} = 0.25, n = 8, q = -5\)

Hence, the sum is:

\(S = \frac{0.25(1 - (-5)^8)}{4} = -24414\)

Item B:

For this sequence, we have that:

\(a_1 = -\frac{1}{4} = -0.25, n = 12, q = 5\)

Hence, the sum is:

\(S = \frac{-0.25(1 - (5)^12)}{-4} = -15258789\)

Item C:

For this sequence, we have that:

\(a_1 = \frac{1}{5} = 0.2, n = 11, q = -4\)

Hence, the sum is:

\(S = \frac{0.2(1 - (-4)^11)}{3} = 279620.3\)

Item D:

For this sequence, we have that:

\(a_1 = -\frac{1}{5} = -0.2, n = 10, q = 4\)

Hence, the sum is:

\(S = \frac{-0.2(1 - (4)^10)}{-3} = -69905\)

Hence option D is correct.

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The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.

P→Q is logically equivalent to ⌝P∨Q. So. ⌝(P→Q) is logically equivalent to ⌝(⌝P∨Q). Hence, by one of De Morgan's Laws (Theorem 2.5), ⌝(P→Q) is logically equivalent to ⌝(⌝P)∧⌝Q.

They are logically equivalent. p ↔ q ≡ (p → q) ∧ (q → p) p ↔ q ≡ ¬p ↔ ¬q p ↔ q ≡ (p ∧ q) ∨ (¬p ∧ ¬q) ¬(p ↔ q) ≡ p ↔ ¬q c Xin He (University at Buffalo) CSE 191 Discrete Structures 28 / 37 Page 14 Prove equivalence By using these laws, we can prove two propositions are logical equivalent.

When two propositions have the same truth value, there is logical equivalence. Accordingly, both the first and second statements can be true in their own contexts; they merely need to mean the same thing for them to be true.

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Answer:

x = 103 and x + 25 = 128°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × (5 - 2) = 180° × 3 = 540°

(a)

sum the interior angles and equate to 540

x + x + x + x + x + 25 = 540

5x + 25 = 540 ( subtract 25 from both sides )

5x = 515 ( divide both sides by 5 )

x = 103

(b)

largest angle = x + 25 = 103 + 25 = 128°

Answer:

Step-by-step explanation:

-4÷2 = -2

8÷(-4) = -2

-16÷8 = -2

So this is a geometric sequence with the first term of 2 and a common ratio of -2

the nth term of a geometric sequence:  \(a_n=a_1\cdot r^{n-1}\)

Therefore:

            \(a_n=2\cdot(-2)^{n-1}\\\\a_n=2\cdot(-1\cdot2)^{n-1}=2\cdot(-1)^{n-1}\cdot2^{n-1}=(-1)^{n-1}\cdot2^{n-1+1}\\\\a_n=(-1)^{n-1}\cdot2^{n}\)

Answer:

2(-2)^n-1

Step-by-step explanation:

Correct on Odyssey assignment. Hope this helps.

Answer: D

Step-by-step explanation:

I don’t know how to explain this to you step by step but when it comes to questions like this try to think more “logically” (if that makes sense) especially if you’re not familiar with the topic, like me. Think about it, if it was the first one the line on the graph would be above the middle line (its addition plus its greater than y so that wouldn’t be correct). Now the second one is subtraction but its less than y and everything thats coloured goes up not down so it has to be greater than y. C is not the correct answer because its a regular equation and thats not what the question wants plus its the only question out of the the 4 answers which is completely the odd one out so you can just cancel that out. Mow we come to the last answer which is the correct answer because it follows all the right “points” I mentioned earlier. I hope this makes sense to you, sorry I couldn’t explain it better!