ok guys i have only 1 hr to get this. Determine the y-intercept for the equation 3x + 2y = 12. HELP

Answer:

\(\frac{3x+11}{(x+3)(x+4)(x+5)}\)

Step-by-step explanation:

Before adding we require the fractions to have a common denominator.

Multiplying the numerator/ denominator of the first fraction by (x + 5)

Multiplying the numerator/ denominator of the second fraction by (x + 3)

= \(\frac{x+5}{(x+3)(x+4)(x+5)}\) + \(\frac{2(x+3)}{(x+3)(x+4)(x+5)}\)

Now add the numerators leaving the common denominator

= \(\frac{x+5+2x+6}{(x+3)(x+4)(x+5)}\)

= \(\frac{3x+11}{(x+3)(x+4)(x+5)}\)

Answer:

2 550

Step-by-step explanation:

Total no. of people who already have a decision, as a % =  45%+38% = 83%

No. of people who haven't decided yet, as a % = 100% - 83% = 17%

No. of people who haven't decided = 15 000 x 17/100 = 2 550

Afia needs1/2 scoops of 1 cup of flour and 1 scoop of 2 cups of flour.

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

1 flour = 1/2 cup scoop

To find out how many scoops of 1/2 cup Afia needs for a specific amount of flour, we need to multiply the desired amount of flour by the size of each scoop.

1 flour = 1/2 cup scoop

2 flour = 1 cup scoop

So, Afia needs 1/2 scoops of 1 cup of flour and 1 scoop of 2 cups of flour.

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The numbers x for which ||v + w|| = 2 are 16 and -167.

When v = 6i - 4j and w = xi + 6j, the numbers x for which ||v + w|| = 2 are given by the expression "||v + w||² = 4".

Explanation: It is known that ||u||² = u·u for any vector u. Thus,||v + w||² = (v + w)·(v + w) = v·v + 2v·w + w·w

Substituting the given values of v and w, we have

||v + w||² = (6i - 4j)·(6i - 4j) + 2(6i - 4j)·(xi + 6j) + (xi + 6j)·(xi + 6j)= 36i·i - 48i·j - 48j·i + 16j·j + 12xi·i + 72xi·j + 72j·i + 36j·j + x²i·i + 12xi·j + 36j·j= (36 + x²)i·i + (144 + 12x)j·i + (72 + 72x)i·j + (52)j·j

The above equation needs to be solved in order to get the values of x such that

||v + w|| = 2:||v + w||² = 4 ⇔ (36 + x²) + (144 + 12x) + 2(72 + 72x) + 52 = 4 ⇔ x² + 86x - 2672 = 0

The solutions for the above quadratic equation are x = 16 and x = -167.

Therefore, the numbers x for which ||v + w|| = 2 are 16 and -167.

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A 99 percent confidence interval for the average external diameter of the pistons can be calculated using the formula:

Confidence interval= x ± (t/√n)*SD,where x = sample mean, t = the value obtained from the t-distribution table (for a two-tailed test at the 1 percent significance level), n = sample size, and SD = sample standard deviation.Substituting values, we get:CI= 9.968 ± 3.249(0.103)= 9.968 ± 0.335Or(9.63,10.3)B) The null hypothesis for the test is:H0: μ ≤ 10The alternative hypothesis for the test is:H1: μ > 10We must determine whether or not to accept or reject the null hypothesis based on the value of the test statistic.To begin, calculate the test statistic value using the formula:t= (x-μ)/(s/√n),where x = sample mean, μ = hypothesized mean, s = sample standard deviation, and n = sample size.Substituting values, we get:t= (9.968-10)/(0.103/√10)= -1.96As the sample size is more than 30, we can use the normal distribution table to look up the critical value for the test. A one-tailed test at the 10 percent significance level corresponds to a critical value of 1.28.Since the test statistic value is less than the critical value, we accept the null hypothesis. Therefore, at the 10 percent level of significance, there is insufficient evidence to conclude that the mean external diameter is greater than 10 cm.The mean of a random sample of 10 pistons manufactured on a certain machine's external diameter is to be estimated at a 99 percent confidence interval in this scenario. In a given sample of n observations, a confidence interval is a range that includes the true value of the population mean with a certain level of confidence. The sample mean and the margin of error are used to construct a confidence interval. The 99 percent confidence interval for the mean external diameter of the pistons is calculated using the formula. x ± (t/√n)*SD. Substituting the given values, we get the confidence interval as 9.968 ± 0.335 or 9.63, 10.3.As a result, we may say that the actual mean of the external diameter of pistons made by that particular machine falls within the range of 9.63 and 10.3 centimeters with 99% confidence.

Next, a hypothesis test was performed to see if the mean external diameter of pistons made by that particular machine is higher than 10 cm at the 10 percent level of significance. The test hypothesis is H0: μ ≤ 10 and H1: μ > 10. Since the test statistic value (-1.96) is less than the critical value (1.28), the null hypothesis is accepted. As a result, we may conclude that at the 10% level of significance, there is insufficient evidence to support the hypothesis that the mean external diameter is greater than 10 cm.In conclusion, we used the given sample data to create a 99 percent confidence interval for the mean external diameter of the pistons made by a specific machine. We were 99 percent confident that the true population mean of the external diameter of pistons produced by that machine was between 9.63 and 10.3 centimeters. Furthermore, we performed a hypothesis test to see whether the mean external diameter of the pistons produced by the machine was greater than 10 cm at the 10 percent level of significance. We concluded that at the 10 percent level of significance, there was insufficient evidence to support the claim that the mean external diameter was greater than 10 cm.

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Answer:

y=mx+b :)

Step-by-step explanation:

The probability that a randomly selected airfare between these two cities will be more than $450 is 0.2033.

Given:

Mean (μ) = $387.20

Standard deviation (σ) = $68.50

To find the probability that a randomly selected airfare between Philadelphia and Los Angeles will be more than $450,

calculate the area under the normal distribution curve above the value of $450.

Step 1: Standardize the value of $450.

To standardize the value, we calculate the z-score using the formula:

z = (X - μ) / σ

z = ($450 - $387.20) / $68.50

z= 0.916

So, the area to the right of the z-score approximately equals 0.2033.

Therefore, the probability that a randomly selected airfare between these two cities will be more than $450 is 0.2033.

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The question attached here seems to be incomplete, the complete question is:

Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between these two cities will be more than $450?

0.0788

0.1796

0.2033

0.3669

Answer:

a = 191/81

Step-by-step explanation:

a+ 1 1/6 = 11 7/9

1 1/6 = 7/6

11 7/9 = 106/9

So, our equation is

a + 7/6 = 106/9

Subtract 7/6 from both sides

a = 191/81

So, the answer is

a = 191/81

hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.

Odd number integers = 2k + 1, where k is integer

Even number integer = 2k

Odd integer + even integer

= 2k + 1 + 2k

= 4k + 1

= 2(2k) + 1

Let 2k = t, where t is integer

 = 2t + 1

= Odd integer by definition

If number is 2t + 1 where t belongs to integer, then it is odd integer.

Hence proved.

The question is incomplete. The complete question is :

Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd

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Answer: 31

Step-by-step explanation:

9 + 2 = 11. 11 is how old Kelly is in 2 years.

1/3 of 33 is 11. Kelly's mother is 33 in two years, meaning two years ago, Kelly's Mother is 31.

Here is the full equation.   K = Kelly.    M = Kellys Mom

9k = m

2k + 9k = m + 2m

11k = m + 2

11k = \(\frac{m}{3}\)

M + 2 = 33

     -2    -2

m = 31

By applying the law of cosine, the smallest angle which the swimmers must turn between the buoys is 41.4°.

In order to determine the smallest angle which the swimmers must turn between the buoys, we would apply the law of cosine.

Given the following data:

Form the law of cosine, we have:

\(CosC =\frac{a^2 + b^2 - c^2}{2ab} \\\\CosC =\frac{500^2 + 600^2 - 400^2}{2 \times 500 \times 600}\\\\CosC =\frac{450000}{600000}\\\\C = cos^{-1} 0.75\\\\\)

C = 41.4°.

For angle B, we have:

\(CosB =\frac{a^2 + c^2 - b^2}{2ac} \\\\CosB =\frac{500^2 + 400^2 - 600^2}{2 \times 500 \times 400}\\\\CosB =\frac{1}{8}\\\\B = cos^{-1} 0.125\\\\\)

B = 82.8°.

For angle A, we have:

\(CosA =\frac{b^2 + c^2 - a^2}{2bc} \\\\CosA =\frac{600^2 + 400^2 - 500^2}{2 \times 600 \times 400}\\\\CosA =\frac{9}{16}\\\\A = cos^{-1} 0.5625\\\\\)

A = 55.8°.

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Desired graph is attached below.

Steps to draw a desired angle are:

If the sum of angle ABD and angle DBC is equal to 105 degrees, then the statement is verified.

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Complete question:

Draw an angle ABC of measure 105 degree.take a point D in its interior. Join BD. Verify by measuring that angle ABD +angle DBC=angle ABC.

we estimate that g^-1(4) is approximately 0.8.

To find g^-1(4), we need to find the value of x that satisfies the equation g(x) = 4, where g(x) = 3 + x + e^x.

So, we start by setting g(x) equal to 4 and solving for x:

3 + x + e^x = 4

Subtracting 3 from both sides, we get:

x + e^x = 1

We cannot solve this equation for x algebraically, so we need to use numerical methods to approximate the solution. One common method is to use the graph of the function g(x) and its inverse g^-1(x) to estimate the value of g^-1(4).

First, we graph the function g(x) and look for the point on the curve where the y-coordinate is 4:

Graph of g(x) = 3 + x + e^x

From the graph, we can see that there is a point on the curve where the y-coordinate is close to 4, which is approximately x = 0.5.

Next, we look at the graph of the inverse function g^-1(x), which is simply the reflection of the curve of g(x) across the line y = x:

Graph of g^-1(x)

From the graph, we can see that the point on the curve of g^-1(x) that corresponds to the point (0.5, 4) on the curve of g(x) is approximately g^-1(4) = 0.8.

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Answer:

20

50+35=80

180-80= 100

100-80=20

Answer: To differentiate this function, we need to use the product rule and the chain rule.

First, we will simplify the function:

f(y) = (1/y^2 - 3/y^4) * y(y + 9y^3)

f(y) = (y + 9y^3) / y^3 - (3y + 27y^3) / y^5

f(y) = y^-3 * (y^4 + 9y^6 - 3y^4 - 27y^6)

f(y) = 6y^4 / y^3

f(y) = 6y

Now we can differentiate:

f'(y) = 6

Therefore, the derivative of f(y) is 6.

Using product rule and power rule of differentiation, the derivative of the function f(y) = 1/y² - 3/y⁴ * (y + 9y³) is f'(y) = 12/y⁷ - 6/y⁶ - 54/y⁵.

To differentiate the given function,

We need to use product rule and the power rule of differentiation

use product rule to differentiate two terms in the function;

Let's consider the first term: 1/y²

The derivative of 1/y² with respect to y is:

d(1/y²)/dy = -2/y³

Now, let's consider the second term: -3/y⁴ * (y + 9y³)

The derivative of -3/y⁴ with respect to y is:

d(-3/y⁴)/dy = 12/y⁵

The derivative of (y + 9y³) with respect to y is:

d(y + 9y³)/dy = 1 + 27y²

Let's use product rule to differentiate the expression

Using the product rule, the derivative of the entire expression f(y) = 1/y₂- 3/y⁴ * (y + 9y³) is:

f'(y) = (1/y²) * (d(-3/y⁴ * (y + 9y³))/dy) + (-3/y⁴ * (y + 9y³)) * (d(1/y²)/dy)

Let's plug the value into the previous expression

f'(y) = (1/y²) * (12/y⁵) + (-3/y⁴* (y + 9y³)) * (-2/y³)

Simplifying further:

f'(y) = 12/y⁷ - 6(y + 9y³)/y⁷

      = 12/y⁷ - 6(y/y⁷ + 9y³/y⁷)

      = 12/y⁷ - 6/y⁶ - 54y²/y⁷

      = 12/y⁷ - 6/y⁶ - 54/y⁵

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Answer:

Step-by-step explanation:

Part A, the system of equation is, presented here as follows;

(1) 2·y = 3·x + 2

(2) y = 2·x² - 3·x + 2

Part B; The graph of the system of equation is attached

The reason for the above answers is as follows;

Part A

A system of equations are a given number of equations from which a common solution of the system can be found

A linear equation is an algebraic equation in which the maximum exponent of the variables is one and the graph of the equation is a straight line which is of the form y = m·x + c

A maximum value of the exponents of the variable quadratic equation is 2, and the general form of the quadratic equation is y = a·x² + b·x + c, where a, b, and c are real numbers

Therefore, the system of equation that can be created is as follows;

(1) 2·y = 3·x + 2

(2) y = 2·x² - 3·x + 2

Method for solving;

Divide equation (1) by 2, and equate both values of y to find the common solution as follows;

2·y/2 = (3·x + 2)/2 = 1.5·x + 1

∴ y = 1.5·x + 1

Equating both values of y gives;

y = 1.5·x + 1

y = 2·x² - 3·x + 2

Therefore;

1.5·x + 1 = 2·x² - 3·x + 2

2·x² - 3·x - 1.5·x + 2 - 1 = 0

2·x² - 4.5·x + 1 = 0

Using the quadratic formula, we get;

x = (4.5 ± √((-4.5)² - 4×2×1))/(2 × 2)

x = 2, or x = 0.25

From which we get;

y = 1.5 × 2 + 1 = 4, or y = 1.5 × 0.25 + 1 = 1.375

The points where the line graph and the quadratic graph intersect are;

(2, 4), and (0.25, 1.375)

Part 2

Answer:600

Step-by-step explanation:

i think

Answer:

18x = -100 is the simplified form

Step-by-step explanation:

(3/4x) + 5 = (5/6)

3/4x (*24) + 5 (*24) = 5/6 (*24)

18x + 120 = 20

(-5y³ + 3y³ - 3y³) + (5x³ + x³) + ( -2y² + 3y²)  is the combined terms of the given expression.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given terms are

⇒  -5y³ + 3y³ + 5x³ - 3y³ + x³ -2y²  + 3y²

Combine all y³ terms

-(5y³ + 3y³ -  3y³)

Combine all  x³ terms

(5x³ + x³)

Combine all y² terms

( -2y² + 3y²)

Add all together (-5y³ + 3y³ - 3y³) + (5x³ + x³) + ( -2y² + 3y²)  is the combined likely terms.

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Answer:

-3.125

Step-by-step explanation:

Answer:

\( - 3 \frac{1}{8} \equiv - \frac{25}{8} \)

= -3.125

Answer: 1

Step-by-step explanation: Assuming you meant find the value of z2 when z=0.5, you just plug o.5 in for 2, making the equation (0.5)2. Multiply 0.5 and 2, and you get 1.

In the above-given situation of Grace (C) No, the game is not fair because Grace has a higher probability of choosing a marble of another color.

To find whether the above-given situation is fair or not:

Therefore, in the above-given situation of Grace (C) No, the game is not fair because Grace has a higher probability of choosing a marble of another color.

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The correct question is given below:

A jar has 10 red marbles, 6 purple marbles, and 4 turquoise marbles. Grace wins if she selects a turquoise marble from the jar. Is this game fair? Why or why not?

(A) Yes, the game is fair because Grace has equal probabilities of choosing a marble of either color.

(B) Yes, the game is fair because Grace has equal probabilities of winning and losing.

(C) No, the game is not fair because Grace has a higher probability of choosing a marble of another color.

(D) No, the game is not fair because Grace has equal probabilities of winning and losing

The required, Keenan would need to spend $8,276 under the new program to earn the 1,097 miles for his trip.

Under the new program, Keenan earns 1 mile for every $8 he spends. To earn 1,097 miles, he would need to spend:

1,097 miles x $8/mile = $8,776

However, he also earned 500 miles on his first purchase, so the total amount he needs to spend to earn the 1,097 miles for his trip is:

$8,776 - the value of 500 miles = $8,276

Therefore, Keenan would need to spend $8,276 under the new program to earn the 1,097 miles for his trip.

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Answer:

8$

Step-by-step explanation:

The discounted price of 12 cups of coffee is 41 dollars.

The function relating the number of cups of coffee purchased is :

A(x) = 5 + 3x

Where x = number cups of coffee purchased

$5 = constant monthly fee

$3 = discounted price of coffee

Therefore, 12 cups of coffee will cost :

A(12) = 5 + 3(12)

A(12) = 5 + 36

A(12) = 41

Hence, price of 12 cups of coffee is $41

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(a) Differentiate \(s(t)\) to get the velocity.

\(s(t) = \cos(t^2 - 1)\)

Use the chain rule.

\(u = t^2 - 1 \implies \dfrac{du}{dt} = 2t\)

\(s(u) = \cos(u) \implies \dfrac{ds}{du} = -\sin(u)\)

\(\implies \dfrac{ds}{dt} = \dfrac{ds}{du} \dfrac{du}{dt} = \boxed{-2t\sin(t^2-1)}\)

(b) Evaluate the derivative from (a) at \(t=0\).

\(\dfrac{ds}{dt}\bigg|_{t=0} = -2\cdot0\cdot\sin(0^2-1) = \boxed{0}\)

(c) The object is stationary when the derivative is zero. This happens for

\(-2t \sin(t^2 - 1) = 0\)

\(-2t = 0 \text{ or } \sin(t^2 - 1) = 0\)

\(t = 0 \text{ or } t^2 - 1 = n\pi\)

(where \(n\) is any integer)

\(t = 0 \text{ or } t = \pm\sqrt{n\pi + 1}\)

We omit the first case. In the second case, we must have \(n\ge0\) for the square root to be defined. Then in the given interval, we have two solutions when \(n=\in\{0,1\}\), so the times are

\(t_1 = \sqrt{1} = \boxed{1}\)

\(t_2 = \boxed{\sqrt{\pi + 1}} \approx 2.035\)

(d) A picture is worth a thousand words. See the attached plot. If you're looking for a verbal description, you can list as many features of the plot as are relevant, such as

• intercepts (solve \(s(t)=0\) to find \(t\)-intercepts and evaluate \(s(0)\) to find the \(s\)-intercept)

• intervals where \(s(t)\) is increasing or decreasing (first derivative test)

• intervals where \(s(t)\) is concave upward or concave downward (second derivative test; at the same time you can determine any local extrema of \(s(t)\), which you can see in the plot agrees with the critical points found in (c))

Answer:

La oferta más conveniente es la C, pues en ella se pagará menos dinero que en las dos anteriores.

Step-by-step explanation:

Dado que una empresa, para comprar ropa de trabajo para su personal, tiene un presupuesto de $ 10.000, y la empresa pide cotizaciones y recibe las siguientes propuestas: a) pagar $ 5.000 al contado y $ 5.000 en 90 días; b) pagar $ 3.000 al contado; $ 3.000 en 30 días y $ 4.000 en 90 días; y c) pagar $ 2.000 al contado, $ 4.000 en 30 días y $ 4.000 en 84 días, si la tasa de interés es del 24% anual, para determinar cuál oferta le conviene aceptar se debe realizar el siguiente cálculo:

90 días = 1/4 año

30 días = 1/12 año

84 días = 23/100 año

365 = 1

85 = X

84 / 365 = 0.23

A) 5,000 + (5,000 x 1.06) = 5,000 + 5,300 = 10,300

B) 3,000 + (3,000 x 1.02) + (4,000 x 1.06) = 3,000 + 3,060 + 4,240 = 10,300

C) 2,000 + (4,000 x 1.02) + (4,000 x 1.023) = 2,000 + 4,080 + 4,092 = 10,172

Por lo tanto, la oferta más conveniente es la C, pues en ella se pagará menos dinero que en las dos anteriores.

Answer:

I think its 12

Step-by-step explanation:

First. find the prime factorization of 108

Second. find the prime factorization of 300

Third. To find the GCF, multiply all the prime factors common to both numbers: So therefore its 12