On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 479 pounds and a standard deviation of 40 pounds. The cow transport truck holds 15 cows and can hold a maximum weight of 7350. If 15 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 7350

Answer: 73 degrees and 107 degrees.

Step-by-step explanation:

The total of supplementary angles are 180 degrees. So you add 2x+3 and 3x+2. Then you get 5x+5=180.

Subtract 5 from both sides. Now the equation is 5x=175.

Divide 5 on each side. x=35

Replace x with 35 in the equations. The angles are 73 and 107.

They both add up to 180 degrees so it is correct.

Answer:

a. 0.0385

b. 3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.43, n = 165[/tex]

a. Calculate the appropriate standard error calculation for the data.

[tex]s = \sqrt{\frac{0.43*0.57}{165}} = 0.0385[/tex]

b. What is probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home?

This is 1 subtracted by the pvalue of Z when X = 0.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.5 - 0.43}{0.0385}[/tex]

[tex]Z = 1.82[/tex]

[tex]Z = 1.82[/tex] has a pvalue of 0.9656

1 - 0.9656 = 0.0344

3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home

Answer:

Graph A

Step-by-step explanation:

Lori is riding in a circular track in which Teri is standing at the center. With the passage of time, there would be no effect on the distance between Lori and Teri. The distance will remain the same because Teri is not moving. She is standing still. So consider her the center of a circle whose circumference is Lori riding bicycle while the radius at any point will be equal.

Answer:

Independent measures, or repeated measures,

Step-by-step explanation:

I would use those experimental designs because it is used to compare different participants over a length of time.  

Answer:

Step-by-step explanation:

Distance from earth to moon =238,857 :

x-92350373 = 92589230

x= 238857

Distance from sun to moon. = 92,350,373 miles

Distance from earth to moon=184,939,603 miles

Distance from sun to moon. = 277,528,833 miles

Distance from earth to moon=238,857 miles

Distance from sun to moon. =92,828,087 miles

Answer:

1 AU is the grade point answer

Answer:

-1/4 , -1

Step-by-step explanation:

I solved it using Factorization method and Quadratic Equation .

Factorization Method

[tex]4x^2+5x+1=0\\Write +5x- as- a -difference(write+5x-using- two- numbers -in-which-their-sum-is ; 5-and-their-product-is ; 4)\\4x^{2} +4x+1x+1=0\\Factorize-out-common-terms\\4x(x+1)+1(x+1)=0\\Factor-out-(x+1)\\(4x+1)(x+1)=0\\4x+1 =0 \\x+1=0\\4x=0-1\\x =0-1\\4x =-1\\x =-1\\4x=-\frac{1}{4} \\\\Answer = -1/4 , -1[/tex]

Quadratic Equation

[tex]4x^2+5x+1=0\\a = 4\\b =5\\c = 1\\\\x =\frac{-b\±\sqrt{b^2 -4ac} }{2a} \\\\x = \frac{-(5)\±\sqrt{(5)^2-4(4)(1)} }{2(4)} \\\\x = \frac{-5\±\sqrt{25-16} }{8} \\\\x = \frac{-5\±\sqrt{9} }{8} \\\\x = \frac{-5\±3}{8} \\\\x =\frac{-5+3}{8} \\\\x = \frac{-5-3}{8} \\\\x = \frac{-2}{8} \\\\x = \frac{-8}{8} \\\\x = -\frac{1}{4} \\x=-1[/tex]

Answer:

85%

Step-by-step explanation:

Given data

Exam score earned by student = 87

class average = 78

s = 8.69

Calculate the percentage of people that earned a score below your score

P ( z < 1.04 ) = 0.8508 = 85%

Note : Z ( z score ) = (exam score - class average) / s

                   = (87 - 78) / 8.69 = 1.04

Answer:

1. Is (A) Subtract 2 to both sides

2. Is (C)

Step-by-step explanation:

Answer: The second image, the second image where b' is right above b is the correct answer for this, hope this helped!

<!> Brainliest is appreciated! <!>

Step-by-step explanation:

Answer

i woukldnt know

Step-by-step explanation:

ahahahahahahahahahahahahhahahahahaha

Answer: 69, 70, 71

x + x + 1 + x + 2 = 210

3x + 3 = 210

3x = 210 - 3

x = 207 / 3

x = 69

x + 1 = 70

x + 2 = 71

Answer:

3/4

Step-by-step explanation:

Rise over run.

Go up 3 units and 4 units to the right to find the next point

Answer:

Using points ( 8 , 9 ) and ( 4 , 6)

Slope = 6-9/4-8

= -3/-4

= 3/4

Hope this helps

Answer:

C Nasir was more successful because he had the greater measure of center

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Answer:

C. 9π

Step-by-step explanation:

r=x-1

A=πr^2

--------

--------

A= πr^2= π*(4-1)^2= 9π, option C.

━━━━━━━☆☆━━━━━━━

▹ Answer

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

▹ Step-by-Step Explanation

6 drinks = 6 Pack (one pack)

23 ÷ 6 = [tex]\frac{23}{6} = 3\frac{5}{6}[/tex]

Mixed number - [tex]3\frac{5}{6}[/tex]

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer: It's 3 5/6

but isn't this 4th-grade work?

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are two ways to find the value of X

[tex]x + 35 = 180[/tex] ( sum of co-interior angles)

Move constant to R.H.S and change its sign

[tex]x = 180 - 35[/tex]

Calculate the difference

[tex]x = 145[/tex]°

You can use another way too.

[tex]x = 145[/tex]° ( being vertically opposite angles)

Vertically opposite angles are always equal.

Hope this helps...

Best regards!!

Answer:

x = 145°

Step-by-step explanation:

Vertically opposite, also interior angles always add up to 180° so if you want to double check this, do 145° + 35° you should get 180°

I hope this helped you :)

Answer:

There is no mode

Step-by-step explanation:

Mode is the most occurring no. and there's no number which is the most occurring.

Answer:

No mode

Step-by-step explanation:

In a set of numbers, mode is the most repeated number.

1, 4, 24, 14, 98, 37

There are no repeated numbers in this set.

Answer:

a) [tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]    

[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]    

b) For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong

Step-by-step explanation:

Information given

[tex]\bar X=28.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=23.1 represent the sample standard deviation

n=75 represent the sample size  

Part a

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=75-1=74[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex] and the critical value would be [tex]t_{\alpha/2}=1.993[/tex]

Now we have everything in order to replace into formula (1):

[tex]28.5-1.993\frac{23.1}{\sqrt{75}}=23.18[/tex]    

[tex]28.5+1.993\frac{23.1}{\sqrt{75}}=33.82[/tex]    

Part b

For this case since the value 32.5 is in the confidence interval obtained then we can't conclude that the statement by Nielsen is wrong

Answer:

6/5÷31/10=12/31

Step-by-step explanation:

6/5÷31/10=?Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

6/5×10/31=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

6×10 5×31=60/155

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 60 and 155 using

GCF(60,155) = 5

60÷51   55÷5=12/31

Therefore:

65÷3110=12/31

Answer:

A)      [tex]y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ][/tex]

B)       [tex]\frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p[/tex]

Step-by-step explanation:

- The following initial value problem is given as follows:

                      [tex]my'' + cy' + ky = F(t) \\\\y(0) = 0\\y'(0) = 0[/tex]

- The above equation is the Newtonian mathematical model of a spring-mass-dashpot system. The displacement ( y ) and velocity ( y' ) are zeroed at the initial value t = 0.

- The equivalent mass ( m ) , damping constant ( c ) and the equivalent spring stiffness ( k ) are given as follows:

                      [tex]m = 2 kg\\\\c = 8 \frac{kg}{s} \\\\k = 80 \frac{N}{m} \\\\[/tex]

- The system is subjected to a sinusoidal force F ( t ) given. We will plug in the constants ( m , c, and k ) and applied force F ( t ) into the given second order ODE.

                      [tex]2y'' + 8y' + 80y = 20sin(6t)[/tex]

- The solution to a second order ODE is comprised of a complementary function ( yc ) and particular function ( yp ).

- To determine the complementary function ( yc ) we will solve the homogeneous part of the given second order ODE. We will assume the independent solution to the homogeneous ODE takes the form:

                           [tex]y = e^-^a^t[/tex]

Where,

                          a: The root of the following characteristic equation

- Substitute ( y ) into the given ODE as follows:

                          [tex]( 2a^2 + 8a + 80 )*e^-^a^t = 0\\\\2a^2 + 8a + 80 = 0[/tex]

- Solve the above characteristic quadratic equation:

                           [tex]a = 2 +/- 6i[/tex]

- The complementary solution for the complex solution to the characteristic equation is of the form:

                           [tex]y_c = e^-^\alpha^t * [ Acos (\beta*t) + Bcos (\beta*t) ][/tex]

Where,

                          a = α ± β

Therefore,

                           [tex]y_c = e^-^2^t * [ Acos (6t) + Bcos (6t) ][/tex]

- To determine the particular solution we will scrutinized on the non-homogeneous part of the given ODE. The forcing function F ( t ) the applied force governs the form of the particular solution. For sinusoidal wave-form the particular solution takes form as following:

                           [tex]y_p = Csin (6t ) + Dcos(6t )[/tex]

Where,

                           C & D are constants to be evaluated.

- Determine the first and second derivatives of the particular solution (yp) as follows:

                            [tex]y'_p = 6Ccos(6t) - 6Dsin(6t)\\\\y''_p = -36Ccos(6t) - 36Dcos(6t)\\[/tex]

- Plug in the particular solution ( yp ) and its derivatives ( first and second ) into the given ODE.

        [tex]-72Csin(6t) - 72Dcos(6t) + 48Ccos(6t) - 48Dsin(6t) + 80Csin(6t) + 80Dcos(6t) = 20sin(6t) \\\\sin(6t)* ( 8C -48D ) + cos(6t)*(8D + 48C ) = 20sin(6t)\\\\D + 6C = 0\\\\C - 6D = 2.5\\\\C = \frac{5}{74} , D = -\frac{15}{37}[/tex]

- The particular solution can be written as follows:

                        [tex]y_p = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)[/tex]

- Now we use the principle of super-position and combine the complementary and particular solution and form a function of general solution as follows:

                        [tex]y_g = y_c + y_p \\\\y_g = e^-^2^t* [ Acos(6t) + Bsin (6t) ] + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t)[/tex]

- To determine the complete solution of the given ODE we have to calculate the constants ( A and B ) using the given initial conditions as follows:

                        [tex]y_g ( 0 ) = 1*[A(1) + 0 ] + 0 - \frac{15}{37}(1) = 0\\\\A = \frac{15}{37}\\\\y'_g = -2e^-^2^t*[Acos(6t) + Bsin(6t) ] +e^-^2^t*[-6Asin(6t) + 6Bcos(6t) ] + \\\\\frac{15}{37}cos(6t) +\frac{90}{37}sin(6t) \\\\y'_g(0) = -2*[A(1) + 0] + 1*[0 + 6B] + \frac{15}{37}(1) +0 = 0\\\\B = \frac{15}{6*37} = \frac{5}{74}[/tex]

- The complete solution to the initial value problem is:

           [tex]y_g = e^-^2^t*\frac{15}{37}cos(6t) + e^-^2^t*\frac{5}{74}sin(6t) + \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) \\\\y_g =\frac{15}{37}cos(6t)* [ e^-^2^t - 1 ] + \frac{5}{74}sin(6t)* [ e^-^2^t + 1 ][/tex]          

- To determine the long term behavior of the system we will apply the following limit on our complete solution derived above:

                 [tex]Lim (t->inf ) [ y_g ] = \frac{15}{37}cos(6t)* [ 0 - 1 ] + \frac{5}{74}sin(6t)* [ 0 + 1 ]\\\\Lim (t->inf ) [ y_g ] = \frac{5}{74}sin(6t) - \frac{15}{37}cos(6t) = y_p[/tex]

- We see that the complementary part of the solution decays as t gets large and the particular solution that models the applied force F ( t ) is still present in the system response when t gets large.

Answer: 0.003757(approx).

Step-by-step explanation:

Total number of combinations of selecting r things out of n things is given by:-

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Total cards in a deck = 52

Total number of ways of choosing 8 cards out of 52 = [tex]^{52}C_8[/tex]

Total number of ways to choose 5 clubs and 3 cards with one of each remaining suit = [tex]^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex]  [since 1 suit has 13 cards]

The required probability = [tex]=\dfrac{^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1}{^{52}C_8}[/tex]

[tex]=\dfrac{\dfrac{13!}{5!8!}\times13\times13\times13}{\dfrac{52!}{8!44!}}\\\\=\dfrac{24167}{6431950}\\\\\approx0.003757[/tex]

Hence, the required probability is 0.003757 (approx).

Answer:

[tex]3.2*10^2=320[/tex] mph

Step-by-step explanation:

hello,

it travels [tex]8.0*10^2[/tex] miles in 2.5 hours

So in 1 hours it travels

[tex]\dfrac{8.0*10^2}{2.5}=3.2*10^2[/tex]

miles

hope this helps

Answer:

1. [tex]V(t) = -32500t + 245000[/tex]

a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.

b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).

c. The formula is: [tex]V(t) = -32500t + 245000[/tex]

2. t-intercept: [tex]t = 7.5385[/tex]

The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.

3. Graph in the image attached.

4. The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].

5. [tex]V(8) = -15000[/tex]

It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.

6. After 3.6 years.

7. Between 3.23 years and 5.63 years.

Step-by-step explanation:

1.

The inicial value is 245,000, and each year the value decreases 32,500, so we can write the equation:

[tex]V(t) = -32500t + 245000[/tex]

a. The slope of the function is m = -32500, and it means the change in the value of V(t) for each unitary change in the value of t.

b. The V-intercept is b = 245000, and it means the value of V(t) when t = 0, that is, the inicial value of V(t).

c. The formula is: [tex]V(t) = -32500t + 245000[/tex]

2.

To find the t-intercept we just need to use V(t) = 0 and then find the value of t:

[tex]0 = -32500t + 245000[/tex]

[tex]32500t = 245000[/tex]

[tex]t = 7.5385[/tex]

The t-intercept means when the function V(t) will be zero, that is, the truck has no value anymore.

3.

The graph of the function is in the image attached.

4.

The domain is t = [0, 7.5385] and the range is V(t) = [245000, 0].

5.

[tex]V(8) = -32500*8 + 245000 = -15000[/tex]

It means the price the truck will have after 8 years. It does not make sense, because the truck can't have a negative price.

6.

[tex]128000 = -32500t + 245000[/tex]

[tex]32500t = 117000[/tex]

[tex]t = 3.6[/tex]

After 3.6 years.

7.

[tex]62000 = -32500t + 245000[/tex]

[tex]32500t = 183000[/tex]

[tex]t = 5.6308[/tex]

[tex]140000 = -32500t + 245000[/tex]

[tex]32500t = 105000[/tex]

[tex]t = 3.2308[/tex]

Between 3.23 years and 5.63 years.

Answer:

1/6

Step-by-step explanation:

P(8) = number of 8's / total = 1/3

Then keeping the card so we have 7 and 9

P(7) =  number of 7's / total = 1/2

P(8, keep, 7) = 1/3 * 1/2 = 1/6

Answer:

hyg

Step-by-step explanation:

Answer:

x = 1

y = 4

Step-by-step explanation:

5x + 2y = 13

x + 2y = 9

Add both equations.

6x + 4y = 22

Solve for x.

6x = 22 - 4y

x = 22/6 - 4/6y

Put x as 22/6 - 4/6y in the second equation and solve for y.

22/6 - 4/6y + 2y = 9

-4/6y + 2y = 9 - 22/6

4/3y = 16/3

y = 16/3 × 3/4

y = 48/12

y = 4

Put y as 4 in the first equation and solve for x.

5x + 2(4) = 13

5x + 8 = 13

5x = 13 - 8

5x = 5

x = 5/5

x = 1

Answer:

x = 1, y = 4

Step-by-step explanation:

5x+2y = 13

x+2y = 9

Subtracting both equations

=> 5x+2y-x-2y = 13-9

=> 4x = 4

=> x = 1

Now, Putting x = 1 in the first equation

=> 5(1)+2y = 13

=> 2y = 13-5

=> 2y = 8

=> y = 4

Answer:

10 and 5.

Step-by-step explanation:

Let the integers be x and y.

xy = 50

x = 2y

Put x as 2y in the first equation.

(2y)y = 50

2y² = 50

y² = 50/2

y² = 25

y = √25

y = 5

Put y as 5 in the second equation.

x = 2(5)

x = 10

Answer:

900°

Step-by-step explanation:

interior angles of a polygon = (n−2)×180°, where n is number of sides

for heptagon it is: (7-2)×180°= 900°

Answer:

18

Step-by-step explanation:

The average is  found by adding all the numbers and dividing by 5

(2+ 81+ 29+ 18+ x)/5 = 26.8

Multiply each side by 5

(2+ 81+ 29+ 18+ x) = 134

x+130 =134

Subtract 130 from each side

x = 4

Now we want the median

List the numbers in order from smallest to largest

2,4,18,29 ,81

The median is the middle

Answer:

x = 4, Median = 18

Step-by-step explanation:

Since the Average/Mean is 26.8

So,

Mean = [tex]\frac{Sum Of Observations}{Total No.OfObservations}[/tex]

26.8 = [tex]\frac{2+81+29+18+x}{5}[/tex]

=> 26.8*5 = 130 + x

=> 134 = 130 + x

Subtracting 130 to both sides

=> x = 134-130

=> x = 4

Now, The data becomes:

=> 2,81,29,18,4

In ascending order:

=> 2,4,18,29,81

Finding Median (The middlemost no.)

=> 18

The graph of a curve crosses the x-axis n times, where n is the amount of solutions (roots) it has.

So if it's a quadratic function (with 2 solutions) we can say that it the graph will cross the x-axis twice

The parabola crosses the x-axis twice. Therefore, option A is the correct answer.

Given that, a quadratic function has two solutions.

We need to find what would you expect to see on the graph of its parabola.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree. It is an algebraic function.

The solutions to a quadratic equation are the values of x where the graph crosses the x-axis at two points.

The parabola crosses the x-axis twice. Therefore, option A is the correct answer.

To learn more about a quadratic function visit:

https://brainly.com/question/27918223.

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