A triangle has side lengths of 13, 9, and 5. Is the triangle a right triangle? Explain.

Use complete sentences in your explanation.

Hint: Pythagorean Theorem: a^2+ b^2 = c^2

Answer:

Step-by-step explanation:

Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.

Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7

Mean = 76.2/7

Mean = 10.9

The mean score is 10.9 to 1 decimal place.

Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.

b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;

9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7

After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.

The median represents the center

c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.

The mode(s) does (do) not represent the center because it (one) is the largest data value.

Answer:

Step-by-step explanation:

[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]

To divide by a fraction, multiply the reciprocal of that fraction

[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]

Reduce the number with the G.C.F 7

[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]

Reduce the numbers with the G.C.F 17

[tex] \frac{5}{6} \times \frac{3}{2} [/tex]

Reduce the numbers with the G.C.F 3

[tex] \frac{5}{2} \times \frac{1}{2} [/tex]

Multiply the fraction

[tex] \frac{5}{4} [/tex]

In mixed fraction:

[tex]1 \frac{1}{4} [/tex]

Hope this helps..

Good luck on your assignment...

Answer:

A ) i) X control chart : upper limit = 50.475, lower limit = 49.825

    ii) R control chart : upper limit =  1.191, lower limit = 0

Step-by-step explanation:

A) Finding the control limits

grand sample mean = 1253.75 / 25 = 50.15

mean range = 14.08 / 25 = 0.5632

Based on  X control CHART

The upper control limit ( UCL ) =

grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475

The lower control limit (LCL)=

grand sample mean - A2 *  mean range = 50.15 - 0.577(0.5632) = 49.825

Based on  R control charts

The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191

The lower control limit = D3 * mean range = 0 * 0.5632 = 0  

B) estimate the process mean and standard deviation

estimated process mean = 50.15 = grand sample mean

standard deviation = mean range / d2  = 0.5632 / 2.326 = 0.2421

note d2 is obtained from control table

Answer: The machine depreciates during the fifth year by $4000.

Step-by-step explanation:

Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.

When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.

Then, the machine depreciates A(x) during the fifth year as

[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]

Hence, the machine depreciates during the fifth year by $4000.

Answer:

h^2 means h²

(h squared)

Step-by-step explanation:

Step 1: Write equation

144 + h² = 225

Step 2: Subtract 144 on both sides

h² = 81

Step 3: Take square root

√h² = √81

h = 9

Answer:

[tex]\boxed{(1, -3)}[/tex]

Step-by-step explanation:

[tex]y+3=2 (x-1)[/tex]

Put equation in slope-intercept form.

[tex]y=mx+b[/tex]

[tex]y=2(x-1)-3[/tex]

[tex]y=2x-2-3[/tex]

[tex]y=2x-5[/tex]

Let x = 1

[tex]y=2(1)-5[/tex]

[tex]y=2-5[/tex]

[tex]y=-3[/tex]

The point (1, -3) lies on the line.

Answer:

[tex]AG=22[/tex]

Step-by-step explanation:

Follow the next steps:

[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F} =\frac{C-D}{F-G} =\frac{A-C}{A-F} =\frac{B-D}{E-G} =\frac{A-D}{A-G}[/tex]

Let:

[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F}\\ \\\frac{4}{A-E} =\frac{5}{10x}\\ \\Solving\hspace{3}for\hspace{3}A-E\\\\A-E=8x[/tex]

Now:

[tex]\frac{C-D}{F-G} =\frac{A-C}{A-F} \\\\\frac{2}{F-G} =\frac{9}{18x} \\\\Solving\hspace{3}for\hspace{3}F-G\\\\F-G=4x[/tex]

Hence:

[tex]A-G=(A-E)+(E-F)+(F-G)=22x[/tex]

Finally:

[tex]\frac{B-D}{E-G} =\frac{A-D}{A-G}\\\\\frac{A-D}{B-D} =\frac{A-G}{E-G}\\[/tex]

[tex]\frac{11}{7} =\frac{22x}{14x} \\\\\frac{11x^{2} }{7} -\frac{11}{7} =0\\\\[/tex]

Hence:

[tex]x=1\\x=-1[/tex]

Since it would be absurd for [tex]x=-1[/tex], the real solution is [tex]x=1[/tex]

Therefore:

[tex]AG=22[/tex]

Answer:

[tex]\boxed{x^3+6x^2+9x}[/tex]

Step-by-step explanation:

[tex]x(x+3)(x+3)[/tex]

Resolving the first parenthesis

[tex](x^2+3x) (x+3)[/tex]

Using FOIL

[tex]x^3+3x^2+3x^2+9x[/tex]

Adding like terms

[tex]x^3+6x^2+9x[/tex]

[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]

[tex]x(x+3)(x+3) =0[/tex]

[tex]\boxed{x_1 =0}[/tex]

[tex]x_2+3 =0[/tex]

[tex]\boxed{x_2 = -3}[/tex]

[tex]x_3+3 =0[/tex]

[tex]\boxed{x_3 = -3}[/tex]

Answer:

angle JKL =  120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.

Consider quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

angle JKL = 360 - 90 - 60 -90 = 120 degrees

Answer:

120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.

look at quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

Answer:

x = 1

Step-by-step explanation:

Set up the rational expression with the same denominator over the entire equation.

Since the expression on each side of the equation has the same denominator, the numerators must be equal

5x =4x+1

Move all terms containing x to the left side of the equation.

Hope this can help you

Answer:

See the attachment for sketch

Thr region is unbounded

DNE

Step-by-step explanation:

y≤ -2x + 10

The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.

Answer:

0, 22, 44, 66

Step-by-step explanation:

Given the equation for the model, [tex] d = 11t [/tex] , you can complete the table above by simply plugging in each value of "t" has given in the table to solve for "d".

*When t (seconds) = 0, distance (feet) would be:

[tex] d = 11(0) [/tex]

[tex] d = 0 [/tex]

*When t (seconds) = 2, distance (feet) would be:

[tex] d = 11(2) [/tex]

[tex] d = 22 [/tex]

*When t (seconds) = 4, distance (feet) would be:

[tex] d = 11(4) [/tex]

[tex] d = 44 [/tex]

*When t (seconds) = 6, distance (feet) would be:

[tex] d = 11(6) [/tex]

[tex] d = 66 [/tex]

A - No

B - No

C - Yes

D - Yes

.

C and D are alternate exterior angles

Answer:

hundreths

Step-by-step explanation:

After the decimal there is tenths, hundreths thousandnths, tens of thousands e.t.c

Answer:

Hello! The answer will be hundredths.

Step-by-step explanation:

The 5 means the thousandths.

The 0 means the hundredths.

The 8 means the tenths.

The 7 means the ones

And the 6 means the tens.

Hope this helps! :)

( below I attached a picture, which might be helpful.)

Answer:

27°

Step-by-step explanation:

D is 72° because it alternates with B, alternate angles are equal.

2x+72°+2x= 180° because it is a straight line.

4x+72°=180°

4x=108°

x=27°

Answer: THe slope is 2

SO answer d

Step-by-step explanation:

-4X + 2Y = 16 add 4x to the other side so equation is

2y=16+4x divided by 2

y=8+2x

The answer is 47 pounds

Explanation:

1. First, let's calculate the amount of money that was spent on chicken

$5 per pound of chicken x 25 pounds = $125

2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.

$454 (total) - $125 (chicken)  =  $329

3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.

$329 / $7 = 47 pounds

Answer:

0.10512

Step-by-step explanation:

Given the following :

Mean number of calls(μ) in 2 hours = 14

2 hours = 60 * 2 = 120 minutes

Average number of calls in 45 minutes :

= (45 / 120) * 14

= 0.375 * 14

= 5.25

Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)

Using the poisson probability formula:

P(x, μ) = [(e^-μ) * (μ^x)] / x!

Where :

e = euler's constant

μ = 5.25

x = 0, 1, 2

Using the online poisson probability calculator :

P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)

P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512

Answer:

b. 0.585

Step-by-step explanation:

According to Bayes' theorem:

[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]

Let A = Person is infected, and B = Person tested positive. Then:

P(B|A) = 93.9%

P(A) = 5.8%

P(B) = P(infected and positive) + P(not infected and positive)

[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]

Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:

[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]

The probability is 0.585.

Answer:

x=4

Step-by-step explanation:

5x - 17 = -x +7

Add x to each side

5x+x - 17 = -x+x +7

6x -17 = 7

Add 17 to each side

6x-17+17 = 7+17

6x =24

Divide each side by 6

6x/6 = 24/6

x = 4

Answer:

4

Step-by-step explanation:

5x - 17 = -x + 7

Add x on both sides.

5x - 17 + x = -x + 7 + x

6x - 17 = 7

Add 17 on both sides.

6x - 17 + 17 = 7 + 17

6x = 24

Divide both sides by 6.

(6x)/6 = 24/6

x = 4

Answer:

(2x - y)³ = 8x³ - 12x²y + 6xy² - y³

Step-by-step explanation:

Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.

For the expansion of

(a + b)ⁿ

As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.

The coefficient of terms are obtained starting from 1 for n = 0.

- For the next coefficients of terms are 1, 1 for n = 1.

- For n = 2, it is 1, 2, 1

- For n = 3, it is 1, 3, 3, 1

The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.

So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.

The Pascal's triangle is

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ

So, for n = 3, the coefficients are 1, 3, 3, 1

Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n

So,

(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]

= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)

= 8x³ - 12x²y + 6xy² - y³

Hope this Helps!!!

Answer: 6 with milk, 9 without

Step-by-step explanation:

2/5 of the cookies he eats are dunked.  Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.

Hope it helps <3

Answer:

a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

b) The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years

Step-by-step explanation:

Step(i):-

Sample size 'n' =75

Mean of the sample x⁻ = 17.8

standard deviation of the sample (S) = 5.9

Mean of the Population = 15

Null hypothesis:H₀:μ = 15 years

Alternative Hypothesis :H₁:μ≠15 years

Step(ii):-

Test statistic

                         [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

                        [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]

                    t = 4.111

Degrees of freedom

ν = n-1 = 75-1=74

t₀.₀₂₅ = 1.9925

The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

P-value:-

The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years

Answer:

[tex]\boxed{9}[/tex]

Step-by-step explanation:

The two angles are complementary to each other.

That means they add up to 90 degrees.

[tex]5x+15+30=90[/tex]

[tex]5x+45=90[/tex]

[tex]5x=45[/tex]

[tex]x=9[/tex]

Answer:

x = 9

Step-by-step explanation:

So you know that the total is 90 degrees.

What you need to do is create an equation.

5x + 15 + 30 = 90

Then, solve the equation like this.

5x + 15 + 30 = 90

5x + 45 = 90

5x = 90 - 45

5x = 45

x = 45 ÷ 5

x = 9

Hope this helps! :)

Answer:

The speed of the first train is 70 km/hr

The speed of the second train is 60 km/hr

Step-by-step explanation:

For the first train:

Travel time = 2 hours

The speed = ?

we designate the speed as V

For the second train:

The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)

speed = 10 km/hr slower than that of the first train, we can then say

the speed = V - 10

The total distance traveled by both trains in the opposite direction of one another is 215 km

we can put this problem into an equation involving the distance covered by the trains.

we know that distance = speed x time

the distance traveled by the first train will be

==> 2 hrs x V = 2V

the distance traveled by the second train will be

==> 1.25 hrs x (V - 10) = 1.25(V - 10)

Equating the above distances to the total distance between the trains, we'll have

2V + 1.25(V - 10) = 215

2V + 1.25V - 12.5 = 215

3.25V = 215 + 12.5

3.25V = 227.5

V = 227.5/3.25 = 70 km/hr     this is the speed of the first train

Recall that the speed of the second train is 10 km/hr slower, therefore

speed of the second train = 70 - 10 = 60 km/hr

The speed of the trains are 70km/hr and 60km/hr respectively.

The distance of the first train will be represented by: = 2 × D = 2D

The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).

Based on the information given in the question, the equation to solve the question will be:

2D + 1.25(D - 10) = 215

Collect like terms

2D + 1.25D - 12.5 = 215

3.25D = 215 + 12.5

3.25D = 227.5

D = 227.5/3.25

D = 70km/hour

The speed of the second train will be:

= 70 - 10 = 60km per hour.

Read related link on:

https://brainly.com/question/24720712

Answer:  ($143.69, $156.31)

Step-by-step explanation:

Confidence interval to estimate  population mean :

[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]

, where [tex]\sigma[/tex] = population standard deviation

n= sample size

[tex]\overline{x}=[/tex] Sample mean

z= critical value.

As per given,

n= 40

[tex]\sigma[/tex] = $15.50

[tex]\overline{x}=[/tex] $150

Critical value for 99% confidence level = 2.576

Then, 99% confidence interval for the population mean:

[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]

Hence, the required confidence interval : ($143.69, $156.31)

Answer:

I think it is

Step-by-step explanation:

Answer:

5n√2m^ - 3mn

Step-by-step explanation:

Answer:

[tex](x + {y}^{2}) = {x}^{2} + 2x {y}^{2} + {y}^{4} [/tex]

Thanks!!!!

Answer:

[tex]\large \boxed{\text{Eight days}}[/tex]

Step-by-step explanation:

1. Calculate the hours

[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]

2. Calculate the days

[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]

Answer:

[tex]\boxed{Mean = 34.33}[/tex]

Step-by-step explanation:

Mean = Sum of Observations / No. Of Observations

Mean = (24+18+37+82+17+26)/6

Mean = 206 / 6

Mean = 34.33