In finding the solution of the equation 5-3x=2x+9, 3x is added to both sides of the equation first. Which of the following should be done next?
A. add -9
B. add -5
C. add =2x

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

a) Therefore, the 50% confidence interval for the percentage of yellow peas in the population is approximately (0.47%, 3.93%).

b) Since the confidence interval does not contain the value of 20%, we can say that the results of the experiment do not support the expectation that 20% of the peas should be yellow.

c) The 90% confidence interval for the percentage of green peas in the population is approximately (95.87%, 99.53%).

The data given in the problem is:

Sample size (n) = 443 + 10 = 453

Number of yellow peas (x) = 10

Number of green peas (n-x) = 443

Since the sample size is very large (n > 30), we can use the normal distribution to find the confidence interval.

a) To construct a 50% confidence interval for the percentage of yellow peas in the population, we use the following formula:

Lower limit = p - z(α/2)√(p(1-p)/n)

Upper limit = p + z(α/2)√(p(1-p)/n)

where: p = x/n = 10/453 = 0.022 (proportion of yellow peas in the sample)

z(α/2) = z(0.25) = 0.674 (z-value for a 50% confidence level)

Plugging in the values, we get:

Lower limit = 0.022 - 0.674√(0.022(1-0.022)/453) ≈ 0.0047

Upper limit = 0.022 + 0.674√(0.022(1-0.022)/453) ≈ 0.0393

Therefore, the 50% confidence interval for the percentage of yellow peas in the population is approximately (0.47%, 3.93%).

b) Since the confidence interval does not contain the value of 20%, we can say that the results of the experiment do not support the expectation that 20% of the peas should be yellow.

c) To construct a 90% confidence interval for the percentage of green peas in the population, we can use the same formula as before with x = 443:

Lower limit = p - z(α/2)√(p(1-p)/n)

Upper limit = p + z(α/2)√(p(1-p)/n)where:

p = x/n = 443/453 = 0.977 (proportion of green peas in the sample)

z(α/2) = z(0.05) = 1.645 (z-value for a 90% confidence level)

Plugging in the values, we get:

Lower limit = 0.977 - 1.645√(0.977(1-0.977)/453) ≈ 0.9587

Upper limit = 0.977 + 1.645√(0.977(1-0.977)/453) ≈ 0.9953

Therefore, the 90% confidence interval for the percentage of green peas in the population is approximately (95.87%, 99.53%).

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Answer:

\(\frac{9\pm\sqrt{61}}{2}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(5)}}{2(1)}=\frac{9\pm\sqrt{81-20}}{2}\\\\=\frac{9\pm\sqrt{61}}{2}\)

Answer:

The answer is B

Step-by-step explanation:

Divided 422 by 6 and you will get 70.33 which is rounded to 70 mph

I hope you find this useful :) Long division btw

Answer:

70mph

Step-by-step explanation:

422mi/6hr

=70.33333333333333

70mph

Answer:

l3-5 Is how you should write this.

$s$ is $\frac{u}{0.0714} \approx 14.0$ times bigger than $u$.

If 2% of $s$ is $t,$ we can write this as $0.02s = t.$

If $t$ is $72\%$ less than $u$, we can write this as $t = u - 0.72u = 0.28u.$

Substituting this expression for $t$ into the first equation, we get:

$$0.02s = 0.28u$$

Dividing both sides by 0.28, we find:

$$\frac{0.02s}{0.28} = \frac{0.28u}{0.28}$$

Simplifying, we get:

$$0.0714s = u$$

Therefore, $s$ is $\frac{u}{0.0714} \approx 14.0$ times bigger than $u$.

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Answer:

84m^2

Step-by-step explanation:

The area of a parallelogram is calculated by multiplying height to the base

The height of the given parallelogram is 7m and the base is 12m

12 × 7 = 84

Answer:

m = [F(y2) - F(y1) ] / [[F(x2) - F(x1)]      slope of a line

[9 - 6] / [x - 1] = 1       that an increase in x equals the increase in y

Obviously, x must equal 4 so 3 / 3 = 1 or when x increases by 3, y must also increase by 3 for m to equal 1

Answer: look below :))

Step-by-step explanation: To solve the equation X^2+x-6=0, we can use the Quadratic Formula:

X = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -6.

Substituting these values into the formula, we get:

X = (-1 ± √(1 - 4(1)(-6))) / 2(1)

Which gives us:

X = (-1 ± √(1 + 24)) / 2

X = (-1 ± √25) / 2

So the solutions to the equation are:

X = ( -1 + √25) / 2 or X = (-1 - √25) / 2

X = ( -1 + 5) / 2 or X = (-1 - 5) / 2

X = 2 or X = -3

So the solutions of the equation X^2+x-6=0 are X = 2 and X = -3.

Answer: 140%

Step-by-step explanation:

Answer:

140%

Step-by-step explanation:

BRAINLIEST PLSSSS

Answer:

x = 6

Step-by-step explanation:

(9x - 5)° = (6x +13)°

9x - 5 = 6x + 13

9x - 6x = 13 + 5

3x = 18

x = 18/3

x = 6

The given parallelogram is a rhombus when x = 6

The value of 'x' for which the parallelogram will be a rhombus is x = 3.

A quadrilateral with all equal sides is a rhombus.

Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

A rhombus has 360° of interior angles total.

A rhombus's adjacent angles add up to 180°.

A rhombus's diagonals are perpendicular to one another and cut each other in half.

One more property of rhombus is that the diagonals bisect the originating angles.

Therefore, The values of 'x' for which this parallelogram will be a rhombus is, 6x + 13 = 9x - 5.

6x - 9x = - 5 - 13.

- 3x = - 18.

3x = 18.

x = 6.

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Answer:

107°

Step-by-step explanation:

By definition of a triangle, the ∑ of all angles within the triangle = 180°

It is given that two angles measurements are 44 and 29. Set the equation:

180 = 44 + 29 + x

First, simplify. Combine like terms:

180 = (44 + 29) + x

180 = x + 73

Next, isolate the variable, x. Note the equal sign, what you do to one side of the equation, you do to the other. Subtract 73 from both sides of the equation:

180 (-73) = x + 73 (-73)

x = 180 - 73

Subtract:

x = 180 - 73

x = 107

x = 107° is your answer.

~

Answer: 6 hours

Step-by-step explanation:

The question asks how long until they meet.

First, you add 1.5 miles per hour and 2 miles per hour to get 3.5 miles per hour.

Then you divide 21/by 3.5 which gets you how many hours it takes for them to meet.

Which means 21/3.5 is 6 hours.

Answer:

yes you are correct A is the correct answer

Answer:

D

Step-by-step explanation:

10%of 36=3.6

5% of 36= 1.8

3.6+1.8 will give you the right answer

Answer:

C

Step-by-step explanation:

There is a difference of 16 between consecutive terms, that is

259 - 243 = 275 - 259 = 291 - 275 = 16

This indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 243 and d = 16 , then

\(a_{n}\) = 243 + 16(n - 1) = 243 + 16n - 16 = 227 + 16n → C

Answer:

x = 13, y = -3

Step-by-step explanation:

Answer:

D and E

Hope this help for you

Red

The total surface area of the triangular prism is: 111 ft²

To find the total surface area of the given triangular prism, we will find the area of all the surfaces and add it up.

Formula for the area of a rectangle is:

Area = Length * Width

Area of a triangle is:

Area = ¹/₂ * base * height

Thus:

Total Surface area = 2(¹/₂ * 3 * 7) + (7 * 5) + (8 * 5) + (3 * 5)

Total Surface area = 21 + 35 + 40 + 15

Total Surface area = 111 ft²

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The compound proposition that is true is "p OR q".

To determine which compound proposition is true, we need to analyze the truth values of the individual propositions and apply logical operators to form compound propositions. Let's examine each compound proposition based on the given truth values of p, q, and r: p is true, q is false, and r is true.

1. Proposition 1: (p ∧ q) ∨ r

We have:

p is true (T)

q is false (F)

r is true (T)

Now let's evaluate the compound proposition:

(p ∧ q) ∨ r

Step 1: Evaluate (p ∧ q)

(p ∧ q) is false because q is false. (T ∧ F) is F.

Step 2: Evaluate (p ∧ q) ∨ r

Since (p ∧ q) is false (F) and r is true (T), (p ∧ q) ∨ r is true (T).

Therefore, Proposition 1, (p ∧ q) ∨ r, is true.

2. Proposition 2: ¬p ∧ (q ∨ r)

We have:

p is true (T)

q is false (F)

r is true (T)

Now let's evaluate the compound proposition:

¬p ∧ (q ∨ r)

Step 1: Evaluate ¬p

¬p is false because p is true. ¬T is F.

Step 2: Evaluate (q ∨ r)

(q ∨ r) is true because r is true. F ∨ T is T.

Step 3: Evaluate ¬p ∧ (q ∨ r)

Since ¬p is false (F) and (q ∨ r) is true (T), ¬p ∧ (q ∨ r) is false (F).

Therefore, Proposition 2, ¬p ∧ (q ∨ r), is false.

3. Proposition 3: (p ∨ q) ∧ r

We have:

p is true (T)

q is false (F)

r is true (T)

Now let's evaluate the compound proposition:

(p ∨ q) ∧ r

Step 1: Evaluate (p ∨ q)

(p ∨ q) is true because p is true. T ∨ F is T.

Step 2: Evaluate (p ∨ q) ∧ r

Since (p ∨ q) is true (T) and r is true (T), (p ∨ q) ∧ r is true (T).

Therefore, Proposition 3, (p ∨ q) ∧ r, is true.

Based on the given truth values of p, q, and r, Proposition 1 and Proposition 3 are true, while Proposition 2 is false.

It's important to note that the truth values of the individual propositions and the logical operators used to form the compound propositions determine their overall truth value. In this case, Proposition 1 and Proposition 3 have at least one true component, which makes them true. Proposition 2, on the other hand, has a false component, resulting in a false truth value.

Analyzing the truth values and evaluating compound propositions is a fundamental aspect of propositional logic. It allows us to reason about the relationships between propositions and determine the overall truth or falsity of complex statements based on the truth values of their components.

In this example, by carefully evaluating the truth values of p, q, and r and applying logical operators, we have determined the truth values of the compound propositions. This exercise demonstrates the importance of understanding the principles of propositional logic and how truth values interact when forming compound propositions.

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Answer:

y is 1

Step-by-step explanation:

Answer:

y = 1

Step-by-step explanation:

First divide both sides by 2

this gives you 3 = y+2

then subtract 2 from each side giving you y = 1

Answer:

Slope < 0  : 1     slope between 0 and1 :3

slope greater than 1 : 2     #4 has 'undefined' slope

Step-by-step explanation:

(a) The value of angle CFE is determined as 131⁰.

(b) The value of arc CE is determined as 131⁰.

(c) The value of arc CPE is determined as 229⁰.

The value of angle CFE is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

m∠CDE = ¹/₂ (arc CPE - arc CE )

m∠CDE = ¹/₂ (CPE - (360 - EPC )

49 =  ¹/₂ (CPE - (360 - EPC )

Simplify the equation as follows;

2 (49) = CPE - 360 + EPC

98 = 2CPE - 360

2CPE = 360 + 98

2CPE = 458

CPE = 458 / 2

CPE = 229⁰

The value of arc CE is calculated as follows;

arc CE = 360 - 229

arc CE = 131⁰

The value of angle CFE is calculated as follows;

angle CFE = arc angle CE (interior angle of intersecting secants)

angle CFE = 131⁰

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The optimal solution for the given linear programming model is:

max z = 38

when x1 = 5, x2 = 10, x3 = 0

To solve the given linear programming model using the simplex algorithm, we start by converting the inequalities into equations and introducing slack variables. The initial tableau is constructed with the coefficients of the decision variables and the right-hand side constants.

Next, we apply the simplex algorithm to iteratively improve the solution. By performing pivot operations, we move towards the optimal solution. In each iteration, we select the pivot column based on the most negative coefficient in the objective row and the pivot row based on the minimum ratio test.

After several iterations, we reach the optimal tableau, where all the coefficients in the objective row are non-negative. The optimal solution is obtained by reading the values of the decision variables from the tableau.

In this case, the optimal solution is z = 38 when x1 = 5, x2 = 10, and x3 = 0. This means that to maximize the objective function, the decision variables x1 and x2 should be set to 5 and 10 respectively, while x3 is set to 0.

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Answer:

The price of one pretzel is $-10.75

Step-by-step explanation:

I'm not really sure why the pretzel would be negative dollars, but I checked my answer multiple times and it's right. For this problem you need a system of equations. The system will be 3d+2p=16 (since 3 drinks and 2 pretzels is 16 dollars) and 6d+5p=21.25 (since 6 drinks and 5 pretzels is 21.25 dollars). To solve this system, the first thing we're going to do is multiply the first system by -2 so that we can cancel the d variable. This will leave you with

-6d-4p=-32. Now, you can add this to the other equation. Since the -6 and 6 cancel, we only have the p variable now (that's why we multiplied by -2, to cancel out the d variable when we added later). Now we have -4p=-32 and 5p=21.25. Add these two equations together and you'll get 1p=-10.75, or p=-10.75. If you needed to solve for the drinks, you could plug -10.75 back into one of the first two equations, but for this problem we don't so -10.75 is your answer.

The constant term (1) is not affected by the modulo operation, we can conclude that for any odd integer n, the expression n^4 mod 16 is equal to 1.

So we have successfully proved the statement that if n is an odd integer, then n^4 mod 16 is equal to 1.

What is an integer?

A whole number (from the Latin integer means "whole") is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 512, and √2 are not. The integers form the smallest group and the smallest circle containing the natural numbers.

To prove the statement "If n is an odd integer, then n^4 mod 16 = 1," we need to show that for any odd integer value of n, the expression n^4 mod 16 always evaluates to 1.

Let us continue the proof by considering properties of odd integers and modular arithmetic.

We begin by assuming that n is an odd integer. By definition, an odd integer can be represented as 2k + 1, where k is an integer.

Now we substitute the value of n in the expression n^4 mod 16:

(2k + 1)^4 mod 16

Expression expansion:

(2k + 1)^4 = 16k^4 + 32k^3 + 24k^2 + 8k + 1

If we take this expression modulo 16, all terms except the constant term (1) will have factors of 16, making them divisible by 16.

The expressions 16k^4, 32k^3, 24k^2, and 8k will all have at least one factor of 16.

Therefore, we can simplify the expression as follows:

(2k + 1)^4 mod 16 ≡ 1 (mod 16)

Since the constant term (1) is not affected by the modulo operation, we can conclude that for any odd integer n, the expression n^4 mod 16 is equal to 1.

So we have successfully proved the statement that if n is an odd integer, then n^4 mod 16 is equal to 1.

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An equation of the tangent line to curve [y = e⁶ˣ cos x] at the given point  (0, 1) is y = x + 6.

At a given point, the tangent line of a curve is a line that really just contacts the curve (function). In calculus, the tangent line may connect the curve at any other point(s), and it may also cross the graph at any other point(s).

Now, as per the given question;

Because of this, point (0,1) is a tangent point;

y = f((0) = e⁰cos0 = 1.

We differentiate to get the slope of the tangent line m. Tangent line equation:

y' = 6e⁶ˣcosx - e⁶ˣ sinx;

Thus, the slope of the curve becomes;

m = f'(0) = 6.

Substituting the values of slope and coordinates (0, 1).

y = 6 + 1(x - 0),

Simplifying the equation.

y = x + 6

Thus, the equation of the tangent line to the given curve is y = x + 6.

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We have proved that f o g is uniformly continuous on R, as desired.

F(g(x)) or (f g)(x) denotes the combination of the functions f(x) and g(x), where g(x) acts first. It brings together two or more functions to produce a new function.

To prove that the composite function f o g is uniformly continuous on R, we need to show that for any ε > 0, there exists a δ > 0 such that for any x, y ∈ R,

| x - y | < δ implies | (f o g)(x) - (f o g)(y) | < ε

We can start by using the uniform continuity of g to choose a δ1 > 0 such that for any x, y ∈ R,

| x - y | < δ1 implies | g(x) - g(y) | < ε

Now, we can use the uniform continuity of f with ε replaced by δ₁ to choose a δ₂ > 0 such that for any u, v ∈ R,

| u - v | < δ₂ implies | f(u) - f(v) | < δ₁

Finally, we can choose δ = δ₂ to show that for any x, y ∈ R,

| x - y | < δ implies | (f o g)(x) - (f o g)(y) | < ε

To see why this is true, let's assume that | x - y | < δ. Then, by the definition of the composite function,

(f o g)(x) - (f o g)(y) = f(g(x)) - f(g(y))

Now, since | g(x) - g(y) | < δ₁, we know that | f(g(x)) - f(g(y)) | < ε, by the choice of δ₁. And since | x - y | < δ₂ implies | g(x) - g(y) | < δ₁, we have shown that

| x - y | < δ₂ implies | (f o g)(x) - (f o g)(y) | < ε

Therefore, we have proved that f o g is uniformly continuous on R, as desired.

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