what is the slope of the line that passes through the points (1 3) and (3 7)

Answer:

x intercept: none

y intercepts: (0, 7)

Step-by-step explanation:

Answer:

Parabola

Step-by-step explanation:

It should produce 23 rock CDs and 46 rap CDs next month to maximize its profits.

Assume number of rock CDs produced is R

Assume number of rap CDs produced is P.

The distributor said that up to twice as many rap CDs can be produced as rock CDs, so we have constraint\(P \leq 2R.\)

We also have the following constraints:

To maximize profits, we need to maximize the objective function:

Profit = 20,000R + 30,000P

The optimization problem. Let us e\rearrange the production time constraint to obtain P in terms of R:

25P ≥ 175 - 18R

P ≥ (175 - 18R)/25

Substitute the inequality into production cost constraint:

15,000R + 12,000[(175 - 18R)/25] ≤ 150,000

Simplifying the inequality, we get:

375R - 216R ≤ 3750

159R ≤ 3750

R ≤ 3750/159

R ≤ 23.59

Substitute R = 23 into the inequality P ≤ 2R, we get:

P ≤ 2(23)

P ≤ 46.

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98% sure that's corresponding angles.

Answer:

corresponding angles

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Graph is positive and y intercept is on negative 2.

The equation of the tangent line to the curve y = (x - 1)/(x - 2) at the point (3, 2/1) is y = -x + 5.

To find the equation of the tangent line to the curve y = (x - 1)/(x - 2) at a given point, we need to find both the slope of the tangent line and the coordinates of the given point.

Let's differentiate the given function to find the derivative, which represents the slope of the tangent line at any point on the curve:

y = (x - 1)/(x - 2)

Taking the derivative of y with respect to x:

dy/dx = [(x - 2)(1) -\((x - 1)(1)] / (x - 2)^2\)

Simplifying the expression:

dy/dx = -\(1/(x - 2)^2\)

Now, let's find the coordinates of the given point. Since a specific point is not provided, let's assume a point on the curve, such as (3, 2/1):

x = 3

y = (3 - 1)/(3 - 2) = 2/1 = 2

We have the point (3, 2/1) on the curve.

Now we can use the slope and the given point to write the equation of the tangent line in point-slope form:

y - y1 = m(x - x1)

Substituting the values:

y - 2 = \((-1/(3 - 2)^2)(x - 3)\)

Simplifying:

y - 2 = -1(x - 3)

y - 2 = -x + 3

Rearranging to obtain the equation in point-slope form:

y = -x + 5

Therefore, the equation of the tangent line to the curve y = (x - 1)/(x - 2) at the point (3, 2/1) is y = -x + 5.

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Answer:

Infinitely many solutions

Step-by-step explanation:

-5.9x - 3.7y = -2.1

5.9x + 3.7y = 2.1

If we add these two equations together, -5.9x cancels out 5.9x, -3.7y cancels out 3.7y, and -2.1 cancels out 2.1.

This leaves us with:

0 = 0

Since this is true, that means there are infinite solutions.

A function \(P(t) = 170.(1.30)^t\)  that gives the deer population P(t) on the reservation t years from now

We were told there were 170 stags on reservation. The number of deer is increasing at a rate of 30% per year.

We could see the deer population grow exponentially since each year there will be 30% more than last year.

Since we know that an exponential growth function is in form:

\(f(x) = a*(1+r)^x\)

where a= initial value, r= growth rate in decimal form.

It is given that a= 170 and r= 30%.    

Let us convert our given growth rate in decimal form.

\(30 percent = \frac{30}{100} = 0.30\)

Upon substituting our given values in exponential function form we will get,

    \(P(t) = 170.(1+0.30)^t\)

⇒ \(P(t)= 170.(1.30)^t\)

Therefore, the function \(P(t) = 170.(1.30)^t\) will give the deer population P(t) on the reservation t years from now.

Complete Question:

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.

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See attachment for the graph of the function g(x)=log4(x-1)+2

The equation of the logarithmic function is given as

g(x)=log4(x-1)+2

The parent function of the above logarithmic function is

f(x) = log4(x)

This means that the parent function is translated right by 1 unit and translated up by 2 units

Next, we plot the graph of the function g(x)=log4(x-1)+2

See attachment for the graph of the function g(x)=log4(x-1)+2

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Answer:

Your answer is A, 3x - 2x.

Step-by-step explanation:

Triple a number means to multiply it by 3.

Double a number means to multiply it by 2.

Difference means to subtract.

Hope this helps!

Answer:cim not sure tho

Step-by-step explanation:

The missing term in the polynomial is 8x³y² - __ + 3xy² - 4y³ is  x²y².

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, A polynomial 8x³y² - __ + 3xy² - 4y³.

Now, If we observe the terms we can conclude 'x' has decreasing powers and y has increasing powers, therefore, the term could be put in the blank to create a fully simplified polynomial written in standard form is x²y².

So, The polynomial is 8x³y² - x²y² + 3xy² - 4y³.

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we will show that if there exists some g(x) in F[x] such that p(x) does not divide g(x) and p(x) is not relatively prime to g(x), then p(x) is reducible in F[x].

Suppose there exists some g(x) in F[x] such that p(x) does not divide g(x) and p(x) is not relatively prime to g(x). Then, we can write gcd(p(x), g(x)) = d(x), where d(x) is a non-constant polynomial.

Since d(x) divides both p(x) and g(x), we can write p(x) = f(x) * d(x) and g(x) = h(x) * d(x) for some polynomials f(x) and h(x) in F[x]. Note that neither f(x) nor h(x) is a constant polynomial, since d(x) is non-constant.

Thus, we have expressed p(x) as a product of non-constant polynomials, namely p(x) = f(x) * d(x), which shows that p(x) is reducible in F[x].

Conversely, suppose that p(x) is reducible in F[x]. Then, we can write p(x) = f(x) * g(x), where f(x) and g(x) are non-constant polynomials in F[x].

Consider the polynomial g(x) in F[x]. Since p(x) = f(x) * g(x), it follows that p(x) divides g(x) or p(x) is relatively prime to g(x). Thus, we have shown that for every g(x) in F[x], either p(x) divides g(x) or p(x) is relatively prime to g(x).

Therefore, we have shown that p(x) is irreducible in F[x] if and only if for every g(x) in F[x], either p(x) divides g(x) or p(x) is relatively prime to g(x).

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The statement "if a > √n and b > √n, then n ≠ ab" is saying that if two positive integers, a and b, are both greater than the square root of another positive integer n, then the product of a and b is not equal to n. This statement can be proven by contradiction.

Suppose the opposite is true, and that n = ab, where a and b are positive integers such that a > √n and b > √n. Then, because n = ab, we have n/a = b and n/b = a. But because both a and b are greater than the square root of n, we have √n < a and √n < b. This leads to a contradiction, because it means that n/a = b > √n, but √n is the largest possible value of b such that b < n/a.

Thus, we have proven that if a > √n and b > √n, then n cannot equal ab, and our original statement is true.

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Answer:

Let , the constant factor be x so 3 X + 5 x + 7 x = 180

Step-by-step explanation:

Find out the value of x

7x+3x+5x=180

15x=180

x=180/15

x=12

now,

     x=3 multiplied by 12=36

     x=7 multiplied by 12=84

      x=5 multiplied by 12=60

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The value of the expression is (X -a) (X - b) (X - c) (X - d)……(x-z) = X26 - 26C1 X25a + 26C2 X24a2 - 26C3 X23a3 + .... + (-1)25-1a25-1 + (-1)26a26.

Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.

To find the value of (X -a) (X - b) (X - c) (X - d)……(x-z), we can use the formula of expansion of a binomial expression, which is (x - y) n = xn -nC1 xn-1y + nC2 xn-2y2 - nC3 xn-3y3 + .... + (-1)n-1yn-1 + (-1)n yn.

In this case, n = 26 and x = X, and y = a, b, c, d, …, z. Therefore, the value of the expression is

(X -a) (X - b) (X - c) (X - d)……(x-z) = X26 - 26C1 X25a + 26C2 X24a2 - 26C3 X23a3 + .... + (-1)25-1a25-1 + (-1)26a26.

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9514 1404 393

Answer:

  180

Step-by-step explanation:

The smallest such number is 4·5·9 = 180. Any multiple of 180 will be divisible by 4, 5, and 9.

Answer:

jana correct i think

Step-by-step explanation:

Answer:

Jana IS very correct in this case

1)

Volume of sphere is 113.1 ft³.

Given radius of sphere 3 ft.

Volume of sphere is 4/3× π ×r³

Substitute the value of radius in the formula of Volume of Sphere,

Volume of Sphere= 4/3×π×r³

                             = 4/3×22/7×3³

                             = 4/3×22/7×27

                             = 113.1 ft³

Hence the given sphere has volume of 113.1 ft³ rounded to the nearest tenth.

2)

Volume of cone is 94.3 yd³

Given diameter of base of cone and height of cone.

Diameter of base = 6 yd

Radius = diameter/2

Radius= 3 yd

Height of cone = 10 yd

Volume of cone = 1/3×π×r²×h

r = radius of base of cone

h = height of cone

Substitute the values of radius and height in the formula,

Volume of cone = 1/3×π×r²×h

                          = 1/3×22/7×3³×10

                          = 660/7

                          = 94.3 yd³

Hence volume of cone rounded to the nearest tenth is 94.3 yd³.

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The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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The length of the other leg of the right triangle is; 89.44 centimetres

According to the question;

By the Pythagoras theorem;

Hence, It follows that;

Find the square root of both sides of the equation;

x = 89.44 centimeters

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The digits base is 7 then we should convert them into base 6.

The exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logbn.

Here the conclusion is that there are many bases in the mathematics so what will happen is that we should convert these bases. For example, we have to convert base 10 of a number which is called decimal number can be converted into binary number whose base is 2 and after then if the digits base is 7 then we should convert them into base 6.

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The range for this function is (0,800].

What is a geometric progression?

It is a sequence of terms in which the succeeding term is can be found out by multiplying with a constant non zero value.

here the first term is 800 as it is the initial price. We can see that the common ratio is less than 1 which is 0.82, hence its a decreasing progression.

so the maximum value in range is 800

as x tends to infinity the equation tends to 0

hence the funtion apporaches 0

so the range will be (0,800]

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Using geometric progression, the range for this function is (0,800].

A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio."

This progression is sometimes referred to as a pattern-following geometric sequence of numbers.

Here the first term is 800 as it is the initial price. We can see that the common ratio is less than 1 which is 0.82.

Hence it's a decreasing progression.

So, the maximum value in the range is 800.

As x tends to infinity the equation tends to 0.

Hence, the function approaches 0

So the range will be (0,800].

Therefore, using a geometric progression, the range for this function is (0,800].

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the directional derivative of \(f(x, y)\) in the directional \(\langle-2,-3\rangle\) and at the point \((x, y) = (-1,-4)\) is \(\dfrac{11\sqrt{13}}{13}\).

Hence, option (b) is correct

Suppose that  \(f(x, y) = xy\). The directional derivative of  \(f(x, y)\) in the directional  \(\langle-2,-3\rangle\) and at the point  \((x, y) = (-1,-4)\) is.

The directional derivative of a function \(f(x, y)\) at the point \((x_0,y_0)\) is given by:$$D_{\vec u}f(x_0,y_0) = \nabla f(x_0,y_0) \cdot \vec u$$where \(\vec u\) is a unit vector that specifies the direction. We have \(\vec u = \dfrac{\langle -2,-3\rangle}{|\langle -2,-3\rangle|} = \dfrac{\langle -2,-3\rangle}{\sqrt{(-2)^2 + (-3)^2}} = -\dfrac{2}{\sqrt{13}}\langle 1, \dfrac32\rangle\).

Then \begin{align*}D_{\vec u}f(x_0,y_0) &= \nabla f(x_0,y_0) \cdot \vec u\\ &= \left\langle\dfrac{\partial f}{\partial x}, \dfrac{\partial f}{\partial y}\right\rangle \cdot \vec u\\ &= \left\langle y, x\right\rangle \cdot \vec u\\ &= (-4,-1) \cdot -\dfrac{2}{\sqrt{13}}\langle 1, \dfrac32\rangle\\ &= \dfrac{2}{\sqrt{13}}(4 + \frac32)\\ &= \dfrac{11\sqrt{13}}{13} \end{align*}

Thus, the directional derivative of \(f(x, y)\) in the directional \(\langle-2,-3\rangle\) and at the point \((x, y) = (-1,-4)\) is \(\dfrac{11\sqrt{13}}{13}\).Hence, option (b) is correct.

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Answer:

Anything with 2 Yellow and more than 3.5 Blue

Step-by-step explanation:

The answer is pretty obvious, but I will give a more mathimatical explanation that is easy to understand.  The ratio is saying that for every 2 units of yellow, there are 3.5 units of blue.  You can find ratios that are the same but use more/ less  amounts.  So if you use 4 units of yellow and 7 of blue it is the same ratio.  

If you multiply both parts of the ratio (or divide) by the same number you will always get the same ratio.  So if you want something more blue (or yellow) you just have to keep one the same while increasing the one you want to have more effect.  

Answer:

This team can form 400 pretzels in one hour

Step-by-step explanation:

How many pretzels in 9 minutes?

5(12)=60

Solve as proportion

60 pretzels = 9 minutes

x    pretzels = 60 minutes

60(60)=9x

3600=9x

Divide both sides by 9

x= 400 pretzels

This team can form 400 pretzels in 1 hour

Answer:

this team can form 30 pretzels in 1 hour

Step-by-step explanation:

60 minutes are in a hour, and 60 divided by 9 is 6.6. So that means you would have to use 6. So 9 x 6 equals 54. Now do 5 x 6 and that would equal 30.

The function f(x)=7x−80 gives the profit the company makes when it sells x shirts. The function is defined for all real numbers x such that x ≥ 0, so the domain of the function is x ≥ 0.

In order to find and interpret the given function values, we can substitute in the given values of x.

When x = 20, the profit is f(20) = 7(20) − 80 = 60. This means that when the company sells 20 shirts, they make a profit of $60.

In general, the profit the company makes is directly proportional to the number of shirts they sell. This means that the more shirts the company sells, the more profit they will make.

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Given

A stock market broker lists a stock with an expected growth of 9.84% and a margin of error of £ 1.08%. What is the minimum expected growth percent for that stock?

Solution

The final answer

The minimum expected is 8.76% Euros

The probability that it takes her more than 6 pulls to start the mower is 0.262144. The result is obtained by the formula of binomial distribution.

The formula of binomial distribution is

\(P(X = x) = C_{n,x}.p^{x}. (1 - p) ^{n-x}\)

\(C_{n,x} = \frac{n!}{x! (n-x)!}\)

Where

Rita has to pull a cord to start her old lawn mower. If the probability of success is 20%, what is the probability that it takes her more than 6 pulls to start the mower?

We have:

Using the formula of binomial distribution,

\(P(X = 1) = C_{6,1}.(0.2)^{1}. (0.8) ^{5} = 0.393216\)

\(P(X = 2) = C_{6,2}.(0.2)^{2}. (0.8) ^{4} = 0.24576\)

\(P(X = 3) = C_{6,3}.(0.2)^{3}. (0.8) ^{3} = 0.08192\)

\(P(X = 4) = C_{6,4}.(0.2)^{4}. (0.8) ^{2} = 0.01536\)

\(P(X = 5) = C_{6,5}.(0.2)^{5}. (0.8) ^{1} = 0.001536\)

\(P(X = 6) = C_{6,6}.(0.2)^{6}. (0.8) ^{0} = 0.000064\)

The probability that it takes more than 6 pulls,

P(X > 6) = 1 - P(X ≤ 6)

P(X > 6) = 1 - [P(X = 1)+P(X = 2)+P(X = 3)+P(X = 4)+P(X = 5)+P(X = 6)]

P(X > 6) = 1 - (0.393216 + 0.24576 + 0.08192 + 0.01536 + 0.001536 + 0.00064)

P(X > 6) = 1 - 0.737856

P(X > 6) = 0.262144

Hence, the probability to take more than 6 pulls to start the old lawn mower is 0.262144.

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