Write the equation of the line that passes through the points (1,6) and (3, -4)

A. y = -5x + 11

B. y = x - 11

C. y = 5x +3

D. y = 2x -3

Answer: 10

Step-by-step explanation:

You just add them together-

Step-by-step explanation:

using Pythagoras theorem :

hyp²= opp² + adj²

x²= 7² + 3²

x² = 49 + 9

x² = 58

take the root of both sides

x = √58

x = 7.62

The average rate of change in the stock's price between 2014 and 2020 would be $ 1. 89

The formula to find the average rate of change between the two periods is :

Average rate of change = (Stock price in 2020 - Stock price in 2014) / Number of years

The question gives the following details :

Stock price in 2020 = $ 37 .22

Stock price in 2014 = $ 25 .86

The average rate of change is;

= (  37. 22 - 25. 86 ) / 6

= 11. 36 / 6

= $ 1. 89

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Answer: 31112

Step-by-step explanation:

Answer: It's 31,112.

Answer:

Patrick's statement is incorrect

Step-by-step explanation:

Crackers come in packages of 24

cheese slices come in packages of 18

He wants one cheese slice for each cracker

Patrick made the statement below "if Andy doesn't want any crackers or cheese slices left over he needs to buy at least 432 of each"

Patrick's statement is incorrect

The lowest common multiple ( L. C. M) of 24 and 18 is 72

Therefore, Andy needs 72 packages of crackers and 72 packages of cheese slice so that no crackers or cheese slice will remain.

The valuable insights into complex phenomena like obesity and type 2 diabetes.

The measurement being employed in this scenario is quantitative measurement. Specifically, the researcher is measuring the weight of individuals, which is a numerical value that can be quantified and analyzed statistically.
Quantitative measurement involves collecting numerical data and using statistical methods to analyze and interpret the results. This type of measurement allows researchers to quantify variables and identify patterns, trends, and relationships between different variables.
In the context of this study on obesity and type 2 diabetes, measuring weight is a crucial component of understanding the relationship between these two variables. By collecting weight data from individuals with these conditions, the researcher can analyze the data to determine if there is a correlation between weight and the likelihood of developing type 2 diabetes.
Overall, quantitative measurement is an important tool for researchers in many different fields. It allows them to collect objective data and use statistical methods to analyze and interpret the results, providing valuable insights into complex phenomena like obesity and type 2 diabetes.

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Answer:

Below

Step-by-step explanation:

Supplementary sum to 180 degrees...they form a straight line

    5 6      7 8     1 2    3 4     51    62    73   8 4

Vertical angles are opposite each other where lines cross

   and are equal

  1  6       2 5       7 4     3 8

If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.

To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.

Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.

For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.

Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.

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Complete question is:

Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?

Answer:

A

Step-by-step explanation:

As the hours increase by 1, the distance traveled increases by 50.

Answer: answer is A

Step-by-step explanation:

Both sides increase.

The hours go by one and the distance goes by 50

Answer:

45

Step-by-step explanation:

I-ready sucks

Since this is a rectangular prism where going to do the formula A = lwh

A = 3×3×5

A = 45 cubic units

The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

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The investment is expected to generate an annualized return of 13.5%.

To calculate the IRR of the given cash flows, we need to find the discount rate that equates the present value of all the cash inflows and outflows. Let's break down the calculations step by step:

Assign a negative sign (-) to cash outflows and a positive sign (+) to cash inflows. This convention helps distinguish between the two types of cash flows.

The given cash flows are:

T0: -865,000

T1: +315,000

T2: -25,000

T3: +605,000

T4: +27,000

Set up the equation for the IRR calculation. The IRR equation is derived from the NPV formula, where the NPV is set to zero.

0 = -865,000 + (315,000 / (1 + IRR)¹) - (25,000 / (1 + IRR)²) + (605,000 / (1 + IRR)³) + (27,000 / (1 + IRR)⁴)

Solve the equation to find the IRR. Unfortunately, finding the exact IRR through manual calculations can be challenging. However, we can use computational tools like Excel or financial calculators to find an approximate value. These tools use numerical methods to solve complex equations.

Using a financial calculator or Excel, the IRR for the given cash flows is approximately 13.5%.

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The average skid mark for the car is 91.7 feet. Option D

The average skid mark can be calculated by the formula -

S = ✓30Dfn,

where;

s is speed of car,

D is skid distance,

f is drag factor and

n is braking efficiency.

Using the values in formula to calculate the value of D.

55 = ✓30 × D × 1.1 × 1

Performing multiplication on Right Hand Side of the equation

55 = ✓D × 33

Taking square on both sides of the equation

D = 55² ÷ 33

Taking square on numerator on Right Hand Side of the equation

D = 3025 ÷ 33

Performing division on Right Hand Side of the equation

D = 98.45 feet

Rounding to the nearest tenth of a foot

D = 91.7 feet

Hence, the average skid mark is 91.7 feet.

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A polynomial function of degree n has at most n real zeros and at most n-1 turning points.

What is polynomial function ?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

What isa Zeros of Polynomials?

Every polynomial will have as many zeros as its degree if we are able to factor it over the entire set of complex numbers, though some of these zeros are repeated and therefore counted more than once. As the function might not be fully factorable over the set of real numbers, if we limit ourselves to the set of real numbers, we might or might not be able to identify this many zeros.

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Answer: ~9.51 kilograms each.

Step-by-step explanation: 723/76=9.5131

Answer:

\(t=\frac{P-d}{15}\)

Step-by-step explanation:

\(P=d+15t\\\\P-d=15t\\\\\frac{P-d}{15}=t\)

Answer:

Step-by-step explanation:

Given the expression

g(x) = x⁴ - 4x² + 7x - 8

we are expected to substitute x=2 into the expression and return the result

g(x) = (2)⁴ - 4(2)² + 7(2) - 8

g(x) = 16 - 4x4 + 14 - 8

g(x) = 16 - 16 + 14 - 8

g(x) =14 - 8

g(x) =6

From the substitution the roller coaster is  travelling at speed of 6mph

Answer:

Step-by-step explanation:

12x-34

Add all the sides together

2(x+3) + 6x + 4(x – 10)

distribute:

2x+6 + 6x + 4x-40

and add:

12x-34

The zeroes of 5x^4-26x^3-64x^2+9x-14 are -2, 7 ,  \(\frac{1+i\sqrt{19} }{10}\)  and   \(\frac{1-i\sqrt{19} }{10}\)  by Using the rational theorem.

f(x) = \(5x^{4} - 26x^{3} - 64x^{2} +9x -14\)

Now, put x = -2

f(-2) = \(5(-2)^{4} - 26(-2)^{3} - 64(-2)^{2} +9(-2) -14\)

f(-2) = 0

so, -2 is a zero of f(x)

or (x+2) is a factor of  \(5x^{4} - 26x^{3} - 64x^{2} +9x -14\)

putting x = 7

f(7) = \(5(7)^{4} - 26(7)^{3} - 64(7)^{2} +9(7) -14\)

f(7) = 0

so, (x-7) is a factor of  \(5x^{4} - 26x^{3} - 64x^{2} +9x -14\)

Now (x+2)(x-7) would also be a factor so

Divide  \(5x^{4} - 26x^{3} - 64x^{2} +9x -14\) by (x+2)(x-7)

or divide  \(5x^{4} - 26x^{3} - 64x^{2} +9x -14\) by \(x^{2} -5x -14\)

The quotient or other factor will be \(5x^{2} - x +1\)

\(5x^{2} - x +1\)

By factorizing  \(5x^{2} - x +1\)

The other two zeroes are \(\frac{1+i\sqrt{19} }{10}\) and  \(\frac{1-i\sqrt{19} }{10}\)

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In part (b) of the previous question, we found that the power series representation of the function $f(x)=\frac{x^2}{1+x^2}$ is:

 \(\lim_{n \to \infty} (-1)^{n} x^{2n}\)

To find the interval of convergence of this power series, we can use the ratio test. Let $a_n=(-1)^n x^{2n}$ be the general term of the series. Then, the ratio of consecutive terms is:

\(\left[\begin{array}{ccc}an+1/an\end{array}\right] = \left[\begin{array}{ccc}(-1)^{n+1} x^{2(n+1)} )/ (-1)^{n}x^{2n} \end{array}\right] = \left[\begin{array}{ccc}x^{2}\end{array}\right]\)

The series converges if the limit of the ratio as $n$ approaches infinity is less than 1, and diverges if the limit is greater than 1. Therefore, we have:

\(\lim_{n \to \infty} \left[\begin{array}{ccc}(a_{n}+1)/a_{n} \end{array}\right] = \left[\begin{array}{ccc}x^{2} \end{array}\right]\)

The series converges if $|x|^2<1$, and diverges if $|x|^2>1$. If $|x|^2=1$, the test is inconclusive and we need to use other convergence tests.

Therefore, the interval of convergence of the series is $-1<x<1$. To check the convergence at the endpoints $x=-1$ and $x=1$, we can use the alternating series test. At $x=-1$, the series becomes:

\(\lim_{n \to \infty} (-1)^{n}(-1)^{2n} = \lim_{n \to \infty} 1\)

which diverges. At $x=1$, the series becomes:

\(\lim_{n \to \infty} (-1)^{n}1^{2n} = \lim_{n \to \infty} (-1)^{n}\)

which also diverges. Therefore, the interval of convergence of the series is $-1<x<1$, and the series diverges at the endpoints.

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Answer:

See below.

Step-by-step explanation:

A(x) = x^2 + 5x

A(x) = x^2 + 5x = 14

x^2 + 5x - 14 = 0

(x + 7)(x - 2) = 0

x + 7 = 0  or  x - 2 = 7

x = -7 or x = 2

x is the height of a rectangle.

The only viable solution is x = 2 because the height of a rectangle cannot be a negative number such as -7.

The only viable solution for the height is x= 2, because height cannot be a negative value.

A rectangle is a quadrilateral with four right angles.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is \(ax^{2} +bx+c=0\)

Given,

Area of the rectangle = \(x^{2} +5x\) = 14

Then,

\(x^{2} +5x-14=0\\(x+7)(x-2)=0\)

Therefore x = -7 and 2

But the Height cannot be negative therefore x = 2

Hence, only viable solution for the height is x= 2, because height cannot be a negative value.

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Answer:B

Step-by-step explanation: closes to caclation

Answer:

5

Step-by-step explanation:

as the 2nd term is b, and the coeffiecnt is the number next to the term

Answer:

y=1/4x-7

Step-by-step explanation:

y-y1=m(x-x1)

y-(-8)=1/4(x-(-4))

y+8=1/4(x+4)

y=1/4x+4/4-8

y=1/4x+1-8

y=1/4x-7

The probability of a positive tour result of given data is 5/42.

Let's use the law of total probability to calculate the probability that the tour results will be positive.

First, we need to calculate the probability that exactly 3, or exactly 4, of the inspected sites are functioning:

The probability that exactly 3 of the inspected sites are functioning is:

P(3 functioning) = (4C3 * 6C1) / 10C4 = 24/210 = 4/35

There are 4 ways to choose 3 functioning sites out of the 4 operational sites, and 6 ways to choose 1 non-functioning site out of the 6 non-operational sites. Then, we divide by the total number of possible combinations of 4 sites out of 10.

The probability that exactly 4 of the inspected sites are functioning is:

P(4 functioning) = (4C4 * 6C0) / 10C4 = 1/210

There is only 1 way to choose 4 functioning sites out of the 4 operational sites, and 0 ways to choose non-functioning sites. Then, we divide by the total number of possible combinations of 4 sites out of 10.

Use the law of total probability to calculate the probability of a positive tour result:

P(positive result) = P(3 functioning) + P(4 functioning) = 4/35 + 1/210 = 25/210 = 5/42

Therefore, the probability of a positive tour result is 5/42.

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Answer:

g = 3/2

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THANK YOU.

#

Answer:

function 2

Step-by-step explanation:

1: m= 4

2: m= -4

3: m= 2

4: m= -1

An interest rate expressed as 0.472 in decimal form is equivalent to 47.2% when expressed as a percentage.

To convert a decimal to a percentage, you need to multiply it by 100. In this case, the decimal 0.472 can be converted to a percentage by multiplying it by 100, resulting in 47.2%. The decimal representation signifies that the interest rate is 0.472 times the principal amount, whereas the percentage representation indicates that the interest rate is 47.2% of the principal amount.

When expressing interest rates, percentages are commonly used to provide a clearer understanding to individuals. Percentages make it easier to compare interest rates and determine the impact they will have on loans, investments, or savings.

The conversion between decimal and percentage forms is straightforward: move the decimal point two places to the right (equivalent to multiplying by 100) to convert from decimal to percentage, or move the decimal point two places to the left (equivalent to dividing by 100) to convert from percentage to decimal. In this case, the decimal interest rate of 0.472 becomes 47.2% when expressed as a percentage.

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Answer:

2.3

Step-by-step explanation:

6.1 =0.8+0.8+x+x

6.1=1.6 +2x

6.1-1.6 = 2x

4.5/2=2x/2

x=2.25

x=2.3