five less than the sum of x and y

Answer:

A 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .

Step-by-step explanation:

We are given that you measure 46 watermelons' weights, and find they have a mean weight of 60 ounces.

Assume the population standard deviation is 8.5 ounces.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }[/tex]  ~  N(0,1)    

where, [tex]\bar X[/tex] = sample mean weight = 60 ounces

             [tex]\sigma[/tex] = population standard deviation = 8.5 ounces

             n = sample of watermelons = 46

             [tex]\mu[/tex] = population mean watermelon weight

Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation.

So, 99% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level  

                                                     of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ) = 0.99

P( [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ) = 0.99

99% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] , [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ]

                                            = [ [tex]60-2.58 \times {\frac{8.5}{\sqrt{46} } }[/tex] , [tex]60+2.58 \times {\frac{8.5}{\sqrt{46} } }[/tex] ]

                                            = [56.77 ounces, 63.23 ounces]

Therefore, a 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .

Answer:

x = 15

Step-by-step explanation:

angles 2 and 4 are supplementary so they add up to 180

2x + 10 + 4x + 80 = 180

6x + 90 = 180

6x = 90

x = 15

Answer:

x=15

Step-by-step explanation:

Angles 2 and 4 are same-side interior angles. This means that if they are supplementary angles, then the lines A and B are parallel.

Supplementary angles, when added together, will equal a total of 180°. Set up an equation in which the angles are added and are equal to 180:

[tex](2x+10)+(4x+80)=180[/tex]

Solve for x. Remove the parentheses and combine like terms:

[tex]2x+10+4x+80=180\\\\2x+4x+10+80=180\\\\6x+90=180[/tex]

Work to isolate the variable, x. Subtract 90 from both sides:

[tex]6x+90-90=180-90\\\\6x=90[/tex]

Isolate x. Divide both sides by 6:

[tex]\frac{6x}{6}=\frac{90}{6} \\\\x=15[/tex]

The value of x is 15.

:Done

If you want to check your work, insert the value of x into the angles, and add them. If the answer is 180, then the value of x is true:

[tex]2x+10\\\\2(15)+10\\\\30+10\\\\40[/tex]

∠2=40

[tex]4x+80\\\\4(15)+80\\\\60+80\\\\140[/tex]

∠4=140

∠2+∠4=180

40+140=180

The value of x is true.

Answer: 200

Step-by-step explanation:

given data:

In a sample 76 people or 38% voted  the mayor to be prosecuted.

solution:

how many people were in that sample

if 38% = 76 people

therefore;

let

p = total number of people

76/p = 38/100

cross multiply both sides

38p = 7600

divide both sides by 38

38p /38 = 7600 /38

p = 200

the number of people in the sample original was 200.

Answer:

80?

Step-by-step explanation:

i counted the numbers on the first domino and that would be the first number, counted on the second one that would be the second number but since c had a two digit number they added the first number of the two digit number to the first domino number and that is what i did with d

hope it's correct:)

Answer:

80

Step-by-step explanation:

Basically, the first domino represents the tens place of the number and the second domino represents the units place. For a, we see that there are 3 dots on the first domino and 4 dots on the second domino so the number is 30 + 4 = 34. The same goes for b. For c, there are 6 tens and 11 ones so the number is 60 + 11 = 71. For d, there are 7 tens and 10 ones so the number is 70 + 10 = 80.

Answer:

It is over then 749mm. so 800mm.

If it is less or same as 749mm, It is 700mm.

Answer:

[tex]\huge \boxed{\mathrm{800 \ mm}}[/tex]

Step-by-step explanation:

765 mm to nearest 100 mm would be to round up 765 to nearest hundred.

765 rounded up to nearest hundred’s place would be 800.

The place after 7 is 6, which is higher or equal to 5, so we add 1 to the hundred’s place followed by zeros.

Answer:

Step-by-step explanation:

First of all transform the expression using trigonometric identities

That's

[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]

[tex] \csc(x ) = \frac{1}{ \sin(x) } [/tex]

[tex] \cot(x) = \frac{1}{ \tan(x) } [/tex]

So we have

[tex] \frac{1}{ \cos(x) } \times \tan(x) \times \frac{1}{ \sin(x) } \times \frac{1}{ \tan(x) } \times \sin(x) \times \cos(x) [/tex]

Reduce the expression with tan x

We have

[tex] \frac{1}{ \cos(x) } \times \cos(x) \times \frac{1}{ \sin(x) } \times \sin(x) [/tex]

Reduce the expression with cos x

That's

[tex]1 \times \frac{1}{ \sin(x) } \times \sin(x) [/tex]

Reduce the expression with sin x

We have

[tex]1 \times 1[/tex]

We have the final answer as

Hope this helps you

Answer:

The number is 12

Step-by-step explanation:

Let x = number

2x+16 = 40

Subtract 16 from each side

2x+16-16 =40-16

2x = 24

Divide by 2

2x/2 =24/2

x = 12

Answer:

You can make 64 different sums (which includes a sum of $0 using none of the coins).

Step-by-step explanation:

The number of sums you can make is equal to:

⁶C₀ + ⁶C₁ + ⁶C₂ + ⁶C₃ + ⁶C₄ + ⁶C₅ +⁶C₆ = 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64

Answer:

1.0000

Step-by-step explanation:

It is know that 20% of air bags produced by the manufacturing plant are defective.

20% of x

Therefore, the probability that two are defective will be

20/100 × 5

0.2×5=1.0000

Answer:

93 miles

Step-by-step explanation:

Use the distance formula:

d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

Plug in the values:

d = [tex]\sqrt{(121 - 57)^2 + (79 - 11)^2}[/tex]

d = [tex]\sqrt{4096 + 4624}[/tex]

d = [tex]\sqrt{8720}[/tex]

d = 93.4

= 93 miles

Answer:

93 miles.

Step-by-step explanation:

To find this answer, we can use the distance formula: D= SQ root of (X2 - X1)^2 + (Y2-Y1)^2

Then, we have to plug in the corrdinates accordingly:

D = SQ root of (121 - 57)^2 + (79 - 11)^2

D = SQ root of (64^2) + (68^2)

D = SQ root of 4096 + 4624

D = SQ root of 8720

D = 93.3809402394

D rounded to the nearest mle is 93 miles

Hope this helps :)

Answer:

  x = 25

Step-by-step explanation:

Make use of the fact that the sum of angle measures in a triangle is 180°.

  (2x+15)° +(3x+5)° +(x+10)° = 180°

  6x +30 = 180 . . . collect terms, divide by °

  x +5 = 30 . . . . . . divide by 6

  x = 25 . . . . . . . . . subtract 5

_____

Check

This value of x makes the angle measures be ...

  A = (x+10)° = 35°

  B = (3x+5)° = 80°

  C = (2x+15)° = 65°

These angles total 180°.

Answer:

108 skittles

Step-by-step explanation:

If she divides a bag of 324 skittles between 3 people, then we want to find a third of 324 - aka [tex]324\div3[/tex].

324 divided by 3 is 108, so each person will get 108 skittles.

Hope this helped!

Answer: 0.0682

Definition

Numerical: It's involving only numbers.

This means we will convert this number from word into numbers.

Answer:

Step-by-step explanation:

682.010

Answer/Step-by-step explanation:

To complete the table, given the function,   [tex] f(x) = \frac{1}{3}x^2 [/tex], plug in each value of x to find f(x).

Thus:

x = -6

[tex] f(-6) = \frac{1}{3}(-6)^2 = \frac{1}{3}(36) [/tex]

[tex] f(-6) = 12 [/tex]

[tex] f(-3) = \frac{1}{3}(-3)^2 = \frac{1}{3}(9) [/tex]

[tex] f(-3) = 3 [/tex]

[tex] f(0) = \frac{1}{3}(0)^2 = \frac{1}{3}(0)  [/tex]

[tex] f(0) = 0 [/tex]

[tex] f(3) = \frac{1}{3}(3)^2 = \frac{1}{3}(9) [/tex]

[tex] f(3) = 3 [/tex]

[tex] f(6) = \frac{1}{3}(6)^2 = \frac{1}{3}(36) [/tex]

[tex] f(6) = 12 [/tex]

Answer:

0.6048

Step-by-step explanation:

Given the following :

Assume a normal distribution :

Mean (m) = 105

Standard deviation (sd) = 20

Find the probability that a randomly selected adult has an IQ between 88 and 122 .

Z = (x - m) / sd

For IQ score of 88:

Z = (88 - 105) / 20

Z = (-17) / 20

Z = - 0.85

For IQ score of 122:

Z = (122 - 105) / 20

Z = (17) / 20

Z = 0.85

P(-0.85<Z<0.85) = P(Z < 0.85) - P(Z < - 0.85)

P(-0.85<Z<0.85) = (0.8023 - 0.1977)

P(-0.85<Z<0.85) = 0.6048

Answer:

Step-by-step explanation:

Computation:

Length of arc = Θ/360[2πr]

20 = Θ/360(2)(22/7)(24)

Θ = 47.72°

Angel = 47.72° (Approx)

Length of arc = Θ/360[2πR]

10 = [47.72 / 360][2][22/7][R]

R = 12 cm

Radius of the smaller sector = 12 cm

Perimeter of the shape = 20 + 24 + 24

Perimeter of the shape = 68 cm

Answer:

Hey there!

I would prefer method two.

Both methods give the right solution, but method two is more straightforward. Instead of distributing, you simply divide and don't need to do as much work.

Let me know if this helps :)

Answer:

12950

Step-by-step explanation:

comedy : 20% => 20 × 18500 ÷ 100 = 3700

drama : 23% => 23 × 18500 ÷ 100 = 4255

other : 27% => 27 × 18500 ÷ 100 = 4995

all together: (20 + 23 + 27) × 18500 ÷ 100 = 3700+4255+4995 = 12950

The solution is 12950.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

from the given graph, we get,

comedy : 20%

=> 20 × 18500 ÷ 100

= 3700

drama : 23%

=> 23 × 18500 ÷ 100

= 4255

other : 27%

=> 27 × 18500 ÷ 100

= 4995

so, we get,

all together: (20 + 23 + 27) × 18500 ÷ 100

                   = 3700+4255+4995

                   = 12950.

To learn more on percentage click:

brainly.com/question/13450942

#SPJ5

Rodell needs a larger sample size than two sports teams to represent a whole school.

Important Information : Study is conducted about favourite gaming app among students at school, 30 & 15 students of football & basketball team are polled.

Finding : Issue in Rodell's method of collecting data

The issue in this sampling : Rodell needs a larger sample size than two sports teams to represent a whole school.

Sample selected from universe should be very carefully chosen, to be a good representative of universe.

Here, Rodell has chosen only two sports' team members as sample for the study of favourite gaming app. Such kind of sample having more uneven concentration of any type of population members doesn't denote sample being a good representative of population.

To learn more Sampling, refer https://brainly.com/question/24842573?referrer=searchResults

Answer:

44 in

Step-by-step explanation:

The circumference of the tire will be the same as the distance the unicycle moves in one complete revolution.

Find the circumference with the formula C = [tex]\pi[/tex]d, where d is the diameter

Plug in the values:

C = [tex]\pi[/tex](14)

C = approx. 44 in

Answer:

irrational

Step-by-step explanation:

A = s^2

s^2 = 24,200

[tex] s = \sqrt{24200} [/tex]

[tex] s = \sqrt{242 \times 100} [/tex]

[tex] s = \sqrt{100 \times 121 \times 2} [/tex]

[tex] s = 10 \times 11\sqrt{2} [/tex]

[tex] s = 110\sqrt{2} [/tex]

P = 4s

[tex] P = 4 \times 100 \sqrt{2} [/tex]

[tex] P = 440 \sqrt{2} [/tex]

The perimeter is irrational.

Answer:

17523° Celsius

Step-by-step explanation:

using the formula c=59(F-32), you have to plug the 329 into F like so-

C=59(329-32)

and then you're free to calculate! first you distribute the 59 like so...

C= (59 times 329)(59 times -32) getting C=19411-1888 which u then solve again to get 17523° Celsius

Answer:

Yes, the triangles are simirar with a scale factor of 3/2.

Step-by-step explanation:

We find the scale factor by dividing corresponding sides:

12/8=3/2

18/12=3/2

24/16=3/2

Answer:

24

Step-by-step explanation:

first 2×2=4

then 16÷4

4×6

24

Hello, when x tends to [tex]\infty[/tex] the term with the highest degree will lead the behaviour.

In other words.

[tex]\displaystyle \lim_{x\rightarrow+\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow+\infty} {x^4}\\\\=+\infty\\\\\\\displaystyle \lim_{x\rightarrow-\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow-\infty} {x^4}\\\\=+\infty[/tex]

So, the answer B is correct.

Thank you.

As x → - ∞, then y → ∞ and x → ∞, then y → ∞. Then the correct option is B.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = x⁴ + 3x³ - 2x + 7

If the value of x approaches the negative infinity, then the value of the function will be

f(x) = x⁴ + 3x³ - 2x + 7

We know that the value of (x⁴ - 2x) is greater than the value of 3x³. Then the value of the function will approach the positive infinity.

If the value of x approaches the positive infinity, then the value of the function will be

f(x) = x⁴ + 3x³ - 2x + 7

We know that the value of (x⁴ + 3x³) is greater than the value of 2x. Then the value of the function will approach the positive infinity.

Thus, As x → - ∞, then y → ∞ and x → ∞, then y → ∞.

Then the correct option is B.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Hello, let's note A the matrix, we need to find [tex]\lambda[/tex] such that A[tex]\lambda[/tex]=[tex]\lambda[/tex] I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as

[tex]\left|\begin{array}{cc}1-\lambda&3\\-3&1-\lambda\end{array}\right|\\\\=(1-\lambda)^2+9\\\\=\lambda^2-2\lambda+10\\\\=0[/tex]

We just need to solve this equation using the discriminant.

[tex]\Delta=b^2-4ac=2^2-40=-36=(6i)^2[/tex]

And then the eigenvalues are.

[tex]\lambda_1=\dfrac{2-6i}{2}=\boxed{1-3i}\\\\\lambda_2=\boxed{1+3i}[/tex]

To find the basis, we have to solve the system of equations.

[tex]A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}[/tex]

[tex]A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}[/tex]

Thank you

Hello, let's note a this positive real number.

The sum of the square is

[tex]a^2+(a-4)^2[/tex]

right?

So, we need to solve

[tex]a^2+(a-4)^2=72[/tex]

We will develop, simplify.

Let's do it!

[tex]a^2+(a-4)^2=72\\\\a^2+a^2-8a+16=72\\\\2a^2-8a+16-72=0\\\\2(a^2-4a-28)=0\\\\a^2-4a-28=0[/tex]

Now, we can use several methods to move forward. Let's complete the square.

[tex]a^2-4a=a^2-2*2*a=(a-2)^2-2^2=(a-2)^2-4[/tex]

So,

[tex]a^2-4a-28=0\\\\(a-2)^2-4-28=0\\\\(a-2)^2=32=4^2*2\\\\a-2=\pm4\sqrt{2}\\\\a = 2(1+2\sqrt{2}) \ \ or \ \ a = 2(1-2\sqrt{2})[/tex]

As a should be positive, the solution is

[tex]\Large \boxed{\sf \bf \ \ a = 2(1+2\sqrt{2}) \ \ }[/tex]

and the other number is

[tex]2(1+2\sqrt{2})-4=2(2\sqrt{2}-1)[/tex]

Thank you.

Answer:

-727.5034 and 2464.2534

Step-by-step explanation:

Find explanation in the attachment

Answer:

Standard deviation of the binomial distribution

                               = [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]

Step-by-step explanation:

Explanation:-

Given size 'n' = 800

The population proportion 'p'=0.6

Let 'X' be the random variable of the binomial distribution

a)  mean of the binomial distribution  = n p = 800 ×0.6

                                                             μ  = 480

b)  variance of the binomial distribution

                                                                      = n p q

                                                                      =  800 X 0.6 ×0.4

                                                                 σ²  = 192

Standard deviation of the binomial distribution

                                                             σ    = [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]