What is the length of the hypotenuse? If necessary, round to the nearest tenth.

However, this answer does not make sense, as angles in a triangle cannot be negative. This means that there is no solution to this problem .

To solve this problem, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Let's first find the measure of angle P:

m∠P + m∠Q + m∠R = 180

Substituting in the given measures:

(x + 13) + (10x + 13) + (2x - 2) = 180

Simplifying and solving for x:

13x + 24 = 180

13x = 156

x = 12

So m∠P = (x + 13) = 25 degrees.

Next, we can use the fact that the angles opposite equal sides in a triangle are congruent. Since we know that PR and QR are equal, we have:

m∠P = m∠R

So m∠R = 25 degrees.

Finally, we can find m∠Q:

m∠Q = m∠P + m∠R - 180

Substituting in the values we found:

m∠Q = 25 + 25 - 180 = -130

However, this answer does not make sense, as angles in a triangle cannot be negative. This means that there is no solution to this problem.

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Answer:

Step-by-step explanation:

Answer:

8.3

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

Answer:

broooooooooooo how do you not know that not trying to be rude but anyways the answer is number 3

The F-test statistic for the given data is 2.09. At a significance level of 0.05, the mean rates of return for the three industries are not significantly different.

To perform the F-test to compare the means of three populations, we need to calculate the sum of squares between groups (SSB), sum of squares within groups (SSW), and the degrees of freedom for each. Then, we can use these values to calculate the F-test statistic and compare it to the critical value of the F-distribution with degrees of freedom (dfB = k - 1) and (dfW = N - k), where k is the number of groups and N is the total sample size.

Using technology, we can calculate the SSB, SSW, and degrees of freedom, as shown below:

SSB = [(n1)(X1 - X)^2 + (n2)(X2 - X)^2 + (n3)(X3 - X)^2]/(k - 1)

= [(8)(11.19 - 11.03)^2 + (8)(12.85 - 11.03)^2 + (8)(9.86 - 11.03)^2]/(3 - 1)

= 12.93

SSW = [(n1 - 1)s1^2 + (n2 - 1)s2^2 + (n3 - 1)s3^2]/(N - k)

= [(7)(4.28^2) + (7)(5.23^2) + (7)(5.31^2)]/(24 - 3)

= 20.91

dfB = k - 1 = 2

dfW = N - k = 21

where X is the overall mean, X1, X2, and X3 are the sample means, n1, n2, and n3 are the sample sizes, s1, s2, and s3 are the sample standard deviations, and k is the number of groups.

Using these values, we can calculate the F-test statistic:

Fo = SSB/dfB / SSW/dfW

= 12.93/2 / 20.91/21

= 6.19

Using a significance level of 0.05, and with dfB = 2 and dfW = 21, the critical value of the F-distribution is 3.14 (found using a calculator or a table).

Since Fo = 6.19 is greater than the critical value of 3.14, we reject the null hypothesis and conclude that the mean rates of return are different at the 0.05 level of significance.

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_____The given question is incomplete, the complete question is given below:

Use technology to find the F-test statistic for this data set. Fo=(Round to two decimal places as needed.) accompanying table e. - Х X Rates of Return the means and Hya and H, H Financial 10.73 15.05 17.21 5.07 19.50 8.16 10.45 6.52 Energy 12.89 13.91 6.43 11.23 18.79 20.73 9.60 17.40 the samp Utilities 11.88 5.86 13.46 9.90 3.95 3.44 7.11 15.70 Are the mean rates of return different at the a = 0.05 level of significance?

Answer:

324 \(cm^{2}\)

Step-by-step explanation:

Area is the length multiplied by width. In the case of a square, both sides are the same so it would simply be 18 x 18 or \(18^{2}\) which equals 324, but make sure to adds units, \(cm^{2}\). Hope this helps

The solutions to the equation are x= -9 and x = 6

From the information given, we have that;

|x2 + 9x| = 6x + 54

To solve the quadratic equation, collect the like terms, we have;

x² + 9x - 6x = 54

subtract the terms

x² + 3x = 54

Put in standard form

x² + 3x - 54 = 0

Find the pair factors of -54 that add up to give 3 and substitute the values

x² + 9x - 6x - 54 = 0

group in pairs

(x² + 9x) - (6x - 54) = 0

factorize the expressions

x(x + 9) - 6(x + 9) = 0

Then, we have;

x- 6 = 0

x = 6

x + 9 = 0

x = -9

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Answer:

14

equivalent

Step-by-step explanation:

x=2

2(3(2)+1)=

2(6+1)=

2(7)=

14

equivalent

Answer:

X = 5

Step-by-step explanation:

3x + 12 + 9x = 72

okay hopefully i can explain so when your doing this combine like terms so

3x + 9x = 12x

12x + 12 = 72

then you would subtract both sides by 12

+12 = subtract x+12=2

- 12 = add x-12=2

there just flipped so in this case i would subtract 12

12x + ( 12-12) = ( 72-12 )

so 12-12 = 0 and 72-12 is equal to 60

12x = 60

the divide on both sides l but leave the x alone so its just 60 divided by 12 wich is 5

so X = 5

hope this helps with ur homework a little btw go back and redo ur other awnsers with this new concept hope it helps

Answer:

- 4 < x ( or ) x > - 4

Step-by-step explanation:

- 10 < - 6 + x

Add 6 on both the sides,

- 10 + 6 < x

- 4 < x

Answer:

2/3 divided by 16

Step-by-step explanation:

Answer:

2/3 divided by 16

Step-by-step explanation:

Functiοn mοdels the relatiοnship between the cοncentratiοn οf the medicatiοn in milligrams is P(t) = 25.5(0.838)ˣ and number οf hοurs since the medicatiοn was taken, t is 2 hοurs.

The cοncentratiοn οf the drug in the blοοdstream at t = 8 hοurs is 24 mg/L. Frοm t= 0 tο t= 2 hr, the cοncentratiοn is increasing and after 2 hrs the cοncentratiοn is decreasing. The level οf the drug in the blοοdstream reaches its maximum value at t=2 hrs , and  the cοncentratiοn in the blοοdstream at that time is 25.5 mg/L.

\After the drug reaches its maximum level in the blοοdstream, 8 additiοnal hοurs are required fοr the level tο drοp    tο 16 mg/L. As at t= 10 hrs, cοncentratiοn is 16 mg/L and maximum cοncentratiοn is at t=2hrs. Sο, additiοnal hοurs= 10-2=8 hrs

P(t) = 25.5( 1-16.2%)ˣ

= 25.5((100 - 16.2)/100)ˣ

= 25.5(83.8/100)ˣ

P(t) = 25.5(0.838)ˣ

Hence, functiοn mοdels the relatiοnship between the cοncentratiοn οf the medicatiοn in milligrams is P(t) = 25.5(0.838)ˣ and number οf hοurs since the medicatiοn was taken, t is 2 hοurs.

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Complete question:

9. A patient has taken 25.5 mg of a prescribed medication. The concentration of the medication in the body decreases at a rate of 16.2% per hour.

Which function models the relationship between the concentration of the medication in milligrams, p(t), and the number of hours since the medication was taken, t?

Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.

Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:

160B + 256C ≤ 6400c

Inequality stating that the engineer has at least 12 million pesos to spend for materials:

600B + 800C ≤ 12000d

. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C

Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.

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(a) We have shown that there exists an element b ∈ B that is an upper bound for A.

(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.

(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.

Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).

Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.

(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.

Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.

This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.

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Note: complementary angles are two angles whose sum is 90⁰

Answer:

52 degrees

Step-by-step explanation:

Complementary angles have a sum of 90. This means when added they will equal 90. So to solve had the 2 expressions and set them equal to 90.

This looks like, \((2x+18)+(6x-8)=90\). Then, isolate the variable and solve.

2x +18 +6x -8 =90

8x +10 =90

8x = 80

x=10

Finally, plug 10 in for x in the expression for angle b. This equals 52 degrees.

Answer:

3 minutes

Step-by-step explanation:

We can use ratios to solve

3 blocks           1 block

----------------- = --------------

9 minutes         x minutes

Using cross products

3 * x = 9*1

3x = 9

Divide each side by 3

3x/3 = 9/3

x = 3

So the right answer is 3.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

We will prove this statement using mathematical induction.

Base case: For n = 4, we have 3n = 3(4) = 12 and (n+1)! = 5! = 120. Clearly, 12 ≤ 120, so the statement is true for the base case.

Induction hypothesis: Assume that the statement is true for some non-negative integer k ≥ 4, i.e., 3k ≤ (k+1)!.

Induction step: We need to prove that the statement is also true for k+1, i.e., 3(k+1) ≤ (k+2)!.

Starting with the left-hand side:

3(k+1) = 3k + 3

By the induction hypothesis, we know that 3k ≤ (k+1)!, so:

3(k+1) ≤ (k+1)! + 3

We can rewrite (k+1)! + 3 as (k+1)(k+1)! = (k+2)!, so:

3(k+1) ≤ (k+2)!

This completes the induction step.

Therefore, by mathematical induction, we have proven that for any non-negative integer n ≥ 4, 3n ≤ (n+1)!.

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Answer:

vector v(4;-3)

Step-by-step explanation:

Answer: 280 calories in 3 ounces

Step-by-step explanation:

you can use a ratio to solve

840 calories per 9 ounces

\(\frac{840}{9}\)

unknown calories per 3 ounces

\(\frac{x}{3}\)

\(\frac{840}{9} =\frac{x}{3}\)

cross multiply

2520=9x

280=x

15

5x-2y=9......(1)

6x+ky=4......(2)

slope of eqn i= -5/-2

=5/2

slope of eqn ii = -6/k

since the line are perpendicular

5/2 * -6/k = -1

-30= -2k

k=15

The answer is y = 2x - 15

The equation of a line is y = mx +c

m = slope

c = y intercept

From this equation y=2x+6

m = 2

Since the lines are parallel their gradients are also the same

Equation of the line using point (8,1) is

y - 1 = 2(x-8)

y - 1 = 2x - 16

y = 2x - 15

Hope this helps

Answer: y=2x-15

Step-by-step explanation: Since the lines are parallel their slopes will be the same, so all you need to do is plug in (8,1) in the x and y values of the equation: y=2x+b. When you do this you get 1=2(8)+b. Simplify. The b value will be -15 which is the y-intercept so the answer is y=2x-15

Answer:

28

Step-by-step explanation:

Replace x with 3, and multiply the number next to it.

5(3)= 15

3(3)=9

so, 15-3+9+7=28

Answer:

28

Step-by-step explanation:

To solve this, replace every x with (3). If x is next to a number, that means you multiply that number and the value of x. This gives us the equation 5(3)-3+3(3)+7. When a set of parentheses are next to a number, you multiply. 5 times three is 15, and 3 times 3 is 9. This gives us 15-3+9+7. 15 - 3 is 12. 12 + 9 is 21. 21 + 7 is 28. 28 is your answer.

Answer:

-11

Step-by-step explanation:

If you know how to play golf, you'll know that when you see a negative sign infront of a number, thats good.

So starting off with -6 and -5. That makes -11

Take -11 and +1, thats -10

Take -10 and -3 thats -13

Take -13 and +2 thats -11

Answer:

(y-8) = -1/2(x+17)

Step-by-step explanation:

slope = (-2 - 8) / (3 - (-17)) = -10 / 20 = -1/2

The optimal solution is Z = -74, X = 4, Y = 2.

Maximize Z = 20X + 3Y

Subject to:

A1: 2X + Y + S1 = 10

R2: 3X + 3Y + S2 = 18

R3: 2X + 4Y + S3 = 20

X = 0, Y ≥ 0

The initial tableau for the simplex method is given below.

The column labels represent the variables, and the row labels represent the equations and slack variables. The bottom row (RHS) represents the right-hand side values of the equations.

To find the optimal solution, we'll perform the simplex method iterations:

Iteration 1:

Pivot column: Y (the most negative coefficient in the Z row)

Pivot row: S2 (smallest positive ratio of RHS to coefficient in the pivot column)

Performing row operations:

Divide row S2 by 3 to make the pivot element (coefficient of Y) equal to 1.

Row S2 = Row S2 / 3

Row S2: 1 | 1 | 0 | 1/3 | 0 | 6

Eliminate other elements in the pivot column:

Row Z = Row Z - (3 * Row S2)

Row S1 = Row S1 - (1 * Row S2)

Row S3 = Row S3 - (0 * Row S2)

Row Z: 20 | 0 | 0 | -3 | 0 | -18

Row S1: 1 | 0 | 1 | -1/3 | 0 | 4

Row S3: 2 | 1 | 0 | -2/3 | 1 | 14

Iteration 2:

Pivot column: X (the most negative coefficient in the Z row)

Pivot row: S1 (smallest positive ratio of RHS to coefficient in the pivot column)

Performing row operations:

Divide row S1 by 1 to make the pivot element (coefficient of X) equal to 1.

Row S1 = Row S1 / 1

Row S1: 1 | 0 | 1 | -1/3 | 0 | 4

Eliminate other elements in the pivot column:

Row Z = Row Z - (20 * Row S1)

Row S2 = Row S2 - (0 * Row S1)

Row S3 = Row S3 - (2 * Row S1)

Row Z: 0 | 0 | -20 | -2/3 | 0 | -74

Row S2: 1 | 1 | 0 | 1/3 | 0 | 6

Row S3: 0 | 1 | -2 | -2/3 | 1 | 6

Since there are no negative coefficients in the Z row, we have reached the optimal solution.

Final Solution:

Z = -74 (maximum value of the objective function)

X = 4

Y = 2

S1 = 0

S2 = 6

S3 = 6

Therefore, the maximum value of Z is -74, and the optimal values for X and Y are 4 and 2, respectively. The slack variables S1, S2, and S3 are all zero, indicating that all the constraints are satisfied as equalities.

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Answer:

(-4, ∞)

Step-by-step explanation:

The domain of a function is how far the x goes left and right.

We see the x starts at -4 and goes forever.

So, the Domain of the function is (-4, ∞)

The domain of the function in the given graph of a function represents all the x-values equal to (−4,∞).

The domain of a function is the set of all possible input values for the function.

In other words, it is the set of all x-values for which the function has a defined y-value.

To find the domain of a function from its graph, we need to look for any x-values for which the function is undefined.

The graph in the image you sent shows a function that is defined for all real numbers.

This means that the domain of the function is all real numbers, here in the given graph domain is  (−4,∞).

Another way to think about it is that the graph of the function extends infinitely far to the left and to the right, which means that there are no x-values for which the function is undefined.

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