Seven baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 89.4% of all their baseballs have straight stitching. If exactly five of the seven have straight stitching, should the company stop the production line

Answer:

(a) 167

(b) 7

(c) 97

Step-by-step explanation:

The (1 - α)% confidence interval for the population mean μ is:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]

Then the formula to estimate the sample size is:

[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]

(a)

For 99% confidence interval the critical value of z is:

z = 2.58.

The standard deviation is, 250.

Compute the sample size as follows:

[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]

   [tex]=[\frac{2.58\times 250}{50}]^{2}\\\\=(12.9)^{2}\\\\=166.41\\\\\approx 167[/tex]

The sample size that should be used is 167.

(b)

Now the standard deviation is, 50.

Compute the sample size as follows:

[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]

   [tex]=[\frac{2.58\times 50}{50}]^{2}\\\\=(2.58)^{2}\\\\=6.6564\\\\\approx 7[/tex]

The sample size that should be used is 7.

(c)

Now a 95% confidence level is used.

For 95% confidence interval the critical value of z is:

z = 1.96.

Compute the sample size as follows:

[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]

   [tex]=[\frac{1.96\times 250}{50}]^{2}\\\\=(9.8)^{2}\\\\=96.04\\\\\approx 97[/tex]

The sample size that should be used is 97.

Answer:

z ≈ 9.22

Step-by-step explanation:

Given the equations

2x-4y+4z-6w=4 ................ 1

6w-4x+4y-4z=-12 ...............2

6w+4x-2y+6z=64 ............... 3

4z+2w+6y-4x=56 ................ 4

We will first need to reduce the equation by cancelling out some variables.

Add equations 1 and 2 will give;

(2x-4x)+(-4y+4y)+(4z-4z)+ (-6w+6w) = 4+12

-2x +0 = 16

-2x = 16

x = -8

Also, equation 2 minus 3

6w-6w+(-4x-4x)+4y+2y+(-4z-6z) = 12-64

-8x+6y-10z = -52

-8(-8)+6y-10z = -52

64+6y-10z = -52

6y-10z  = -52-64

6y-10z = -116

3y-5z = -58 ... 5

Equation 3 * 1 and eqn 4 * 3

6w+4x-2y+6z=64 ............... 3

4z+2w+6y-4x=56 ................ 4

6w+4x-2y+6z=64

12z+6w+18y-12x= 168

Subtracting both equations;

16x-20y-6z = -104

8x-10y-3z = -52

8(-8)-10y-3z = -52

-64-10y-3z = -52

-10y-3z = -52+64

-10y-3z = 12 ....... 6

equating 5 and 6 and solving simultaneously;

3y-5z = -58 ... 5 * 10

-10y-3z = 12 ....... 6 * 3

30y-50z = -580

-30y-9z = 36

Add both equations

-50z-9z = -580+36

-59z = -544

z = -544/-59

z = 9.22

Hence z ≈ 9.22

Answer:

Option (4)

Step-by-step explanation:

Party planner has used an arc of balloons for the parade.

This arc starts from x = 0 along the ground and f(x) defines the height of the arch.

From the table attached, it is clear that at x = 4 maximum height of the arch is 9.6 feet.

Therefore, clearance space below the arc is 9.6 feet which is greater than 9 feet, minimum height required for the clearance of the parade.

Option (4) will be the answer.

Answer:

D. yes, because the maximum height of the arch is 9.6 feet

Step-by-step explanation:

EDGE 2020 :)

Answer:

The expected value of X, E(X), for the given probability distribution is 1.2

Step-by-step explanation:

Mathematical hope (also known as hope, expected value, population means or simply means) expresses the average value of a random phenomenon and is denoted as E(x).

Hope is the sum of the product of the probability of each event and the value of that event. That is, it is the sum of the probability of each possible event multiplied by the frequency of said process, this indicates that if you have a discrete quantitative variable X with "n" possible events x₁, x₂, x₃... xₙ and probabilities P (X = xi) = Pi the mathematical expectation is:

E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + ... + xₙ*Pₙ

In this case:

E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + x₄*P₄

Being:

and replacing:

E(x)= 0* 0.5 + 1* 0.1 + 2*0.1 + 3*0.3

you get:

E(x)= 1.2

The expected value of X, E(X), for the given probability distribution is 1.2

Answer: 1/6

Approximately the same.

Step-by-step explanation:

Answer:

The first answer was:1/6

The second answer was: approximately the same.

Step-by-step explanation:

Just did it on edge2020

Answer:

Step-by-step explanation:

Since the sequence is a geometric sequence

For an nth term in a geometric sequence

[tex]A(n) = a ({r})^{n - 1} [/tex]

where

n is the number of terms

a is the first term

r is the common ratio

To find n we must first find the common ratio

To find the common ratio divide the previous term by the next term

That's

r = 3/1 = 3 or r = 9/3 = 3

a = 1

Substitute the values into the above formula

That's

If n is an integer then

[tex]A(n) = 1 ({3})^{n - 1} [/tex]

[tex]A(n) = {3}^{n - 1} [/tex]

where n is greater than or equal to 2

Hope this helps you

The function that describes the sequence is the first one:

a(n) = 3ⁿ   fpr n ≥ 0.

Here we have the following sequence:

1, 3, 9, 27, ...

We can see that all of these are powers of 3, and the function must behave like:

f(0) = 1

f(1) = 3

f(2) = 9

...

And so on, then the function must be:

a(n) = 3ⁿ

when n = 0 we have:

a(0) = 3⁰ = 1

When n = 1

a(1) = 3¹ = 3

And so on.

Then we can see that the correct option is the first one.

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Answer:

This can be solved by subtracting 584 from 2,054.

2,054-584

=1470

Step-by-step explanation:

Gemma would have $1470 left in her checking account. hope this helps you :)

(A)

Evaluate [tex]p[/tex] and [tex]q[/tex] at the given values of [tex]t[/tex], then plug them into the inner product:

[tex]p(t)=3t-t^2\implies\begin{cases}p(-1)=-4\\p(0)=0\\p(1)=2\end{cases}[/tex]

[tex]q(t)=3+2t^2\implies\begin{cases}q(-1)=5\\q(0)=3\\q(1)=5\end{cases}[/tex]

Now,

[tex]\langle p,q\rangle=4\cdot5+0\cdot3+2\cdot5=30[/tex]

[tex]\|p\|=\sqrt{\langle p,p\rangle}=(-4)^2+0^2+2^2=20[/tex]

[tex]\|q\|=\sqrt{\langle q,q\rangle}=5^2+3^2+5^2=59[/tex]

(B)

Let [tex]V[/tex] denote the subspace spanned by [tex]p[/tex]. We need an orthonormal basis for [tex]V[/tex]. Since

[tex]p(t)=3t-t^2=3\cdot t+(-1)\cdot t^2[/tex]

we have the basis vectors [tex]\{t,t^2\}[/tex]; normalize these vectors to get the orthonormal basis,

[tex]\left\{\dfrac t{|t|},\dfrac{t^2}{|t^2|}\right\}=\left\{\dfrac t{|t|},1\right\}[/tex]

Then the projection of [tex]q[/tex] onto [tex]V[/tex] is

[tex]\mathrm{proj}_Vq(t)=\left(q(t)\cdot\dfrac t{|t|}\right)\dfrac t{|t|}+\left(q(t)\cdot1\right)1[/tex]

[tex]\mahtrm{proj}_Vq(t)=\dfrac{3t^2+2t^4}{t^2}+(3+2t^2)=\boxed{6+4t^2}[/tex]

A).

[tex]< p, q >=-10\\||p||=9\sqrt{2} \\||q||=3\sqrt{2}[/tex]

B).The orthogonal projection of q onto the subspace spanned by p is[tex]proj_vq(t)=6+4t^2[/tex]

We have [tex]p(t) = 3t - t^2 ,q(t) = 3 + 2t^2[/tex]

And < p, q >= p(−1)q(−1) + p(0)q(0) + p(1)q(1).

Now,

A).

[tex]p(-1) = 3.(-1) - (-1)^2 \\=-4\\p(1)=3.1-1^2\\=2q(-1) = 3 + 2.(-1)^2\\=5\\q(1) = 3 + 2.(1)^2\\=5p(0) = 3.0 - 0^2 \\=0\\q(0) = 3 + 2.0^2\\=3\\< p, q >= p(-1)q(-1) + p(0)q(0) + p(1)q(1)\\< p, q >=-4.5+0.3+2.5\\=-10\\||p||=<p,p>\\=\sqrt{(-4)^2+0+2^2} \\=\sqrt{20} \\=2\sqrt{5} \\||q||=<q,q>\\=\sqrt{5^2+3^2+5^2} \\=\sqrt{59}[/tex]

B)Let V be the subspace spanned by p.

Now, an orthonormal basis for p is[tex](t,t^2)[/tex]

 Then the projection of q onto the subspace spanned by p is

[tex]proj_vq(t)=(q(t).\frac{t}{|t|} ).\frac{t}{|t|} +(q(t).1)1\\proj_vq(t)=\frac{3t^2+2t^4}{t^2} +(3+2t^2)\\proj_vq(t)=6+4t^2[/tex]

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Answer:

Step-by-step explanation:feel pleasure to help u.

Answer:

Step-by-step explanation:

300,000-100

300,00 + -100

=299900

Answer:

299900

Step-by-step explanation:

Answer:

She subtracted 5 and got 6 instead of subtracting -5 which is 16

Step-by-step explanation:

11 - (-5)

Subtracting a negative is like adding

11 +5

16

She subtracted 5 and got 6 instead of subtracting -5 which is 16

Answer:2100

Step-by-step explanation:

Answer:

13:20

Step-by-step explanation:

Start time:

Trip duration:

End time= ?

Simply adding up the time the family left and time in trip:

Sum of minutes:

Sum of hours:

So time arrival is:

Time they left is 09:30 and it will take 2 hr and a half before noon.

Splitting 3 hr and 50 min into two parts, one part being 2 hr and 30 min and the other is:

Adding 2 hr 30 min and then adding 1 hr 20 min to initial time of 09:30:

Then:

Hi there! :)

Answer:

[tex]\huge\boxed{\frac{29}{61}}[/tex]

Express the given scenario as a fraction:

[tex]\frac{58}{122}[/tex]

Simplify the fraction by taking out the GCF, or 2:

[tex]\frac{2(29)}{2(61)}[/tex]

Cancel out the 2's:

[tex]\frac{29}{61}[/tex]

Answer: 58/122 I think and if simplified I think it would be 29/61

Step-by-step explanation:

122 containers of juice would be the denominator

and 58 is orange juice would be the numerator

then you can leave it or simplify!

Answer:

Coordinates of the starting point ( -50 ; 0 )

Coordinates 4 seconds later Q ( - 25*√3  ;  25 )

Coordinates 32 seconds later R ( 25  ;  - 25*√3 )

Step-by-step explanation:

a) If Jeremy takes 48 seconds fr a lap then

The length of the lap ( length of the circle ) is:

L =  2*π*r    ⇒   L = 100*π

If the time for one lap was 48 seconds at a constant speed, the speed was

v = 100*π / 48   [m/s]

v = 6,54 m/s

12 seconds  is  1/4 0f 48  in that time he (she) reach the northernmost point, then he(she) necessarily started on the negative side of the       x-axis the coordinates at this point are

( -50 ; 0 )

b) 4 seconds later, at v = 6,54 m/s by rule of three

In 12 seconds                         90⁰

In  4  seconds  (the third part )       x ??

x = 30⁰

sin 30⁰  = 1/2

cos 30⁰ = (√3)/2

And coordinates for the point are

sin 30⁰ =  1/2  = y/50     ⇒  y =  25

cos 30⁰ = (√3)/2  = x / 50   ⇒ x = 25*√3

coordinates of the point 4 seconds later

Q ( - 25*√3  ;  25 )    she (he) is in the negative part of x-axis

c) 32 seconds later

32  is    12   +   12    +    8

Then she (he) is 8 seconds below the positive side of x-axis

8 is 2/3 of 12   ( negative 60⁰ )

sin 60⁰ = (√3)/2   = y/50       y  =  25*√3    negative

cos  60⁰ = 1/2 * 50   =  X/50  x  = 25

Coordinates of the point R

R ( 25  ;  - 25*√3 )

Answer:

the answer is 37 i believe

37

Step-by-step explanation:

First start with parenthesis 3 + 2=5. Next the brackets

8 - 5=3. Next 15 ÷ 3 = 5. Then Finally, 8 × 4 = 32, and add 5, which 37

Answer:

y=1

Step-by-step explanation:

if x=15

y=4

now what is y when the value of x is 60.

15x4/60

15x4=60

60/60=1

y=1

The solution is : the value of y is: y=1

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, we have,

given that,

y varies inversely with x. If x = 15 and y = 4 ,

now, we have to find y when x = 60

so, we have,

if x=15

y=4

now what is y when the value of x is 60.

15x4/60

15x4=60

60/60=1

y=1

Hence, The solution is : the value of y is: y=1

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the value of (-3)4+(-2)4×(-1)4 is -24

Answer:

98

Step-by-step explanation:

-3⁴ = -3*-3*-3*-3 = +81 = 81

-2⁴ = -2*-2*-2*-2 = +16 = 16

-1⁴ = -1*-1*-1*-1 = +1 = 1

Then:

(-3)⁴ + (-2)⁴ + (-1)⁴ = 81 + 16 + 1

= 98

Answer:

Displacement= 12.65 km S 18.44°W

Step-by-step explanation:

Justin rides on hist 12 km south.

He changes location and goes 4 km west.

The displacement from his current location = X

X²= 12²+4²

X²= 144+16

X²= 160

X= √160

X= 4√10

X= 12.649 km

X= 12.65 km

His total distance covered=12+4

His total distance covered= 16 km

Tan ^-1 12/4= angle

71.56° = angle

90-71.56= 18.44°

Displacement= 12.65 km S 18.44°W

Answer:

13 packages

Step-by-step explanation:

We need to find the highest common factor, in order to solve this problem.

So, we have to find the highest common factor of 39 and 13.

We find the highest common factor of 39 and 13 because it says in the problem” Tim has 39 pairs of headphones and 13 music players.”

And than you just find the highest common factor, after you find the highest common factor... YOU ARE DONE SOLVING THE PROBLEM!

The highest common factor will be 13

13: 1,13

39:1,3,13,39

ANSWER:13

Hope this helps!

Answer:

13

Step-by-step explanation:

Greatest number of packages Tim can make =

H. C. F of 39 and 13

Factors of 39 = 13 * 3 * 1

Factors of 13 = 13 * 1

H.C.F = 13

Therefore, Greatest number of identical packages Tim can make is 13.

Answer:

Step-by-step explanation:

The function of interest is ...

  [tex]f(x)=\dfrac{5x}{x^2-25}=\dfrac{5x}{(x-5)(x+5)}[/tex]

The asymptotes are found where the denominator is zero. It will be zero when either factor is zero, so at x = 5 and x = -5

__

The zeros are found where the numerator is zero. It will be zero for x = 0.

The asymptotes are x=-5, x=5; the zero is x=0.

Answer:

The asymptotes are x=-5, x=5; the zero is x=0.

Step-by-step explanation:

Answer:

7.41

Step-by-step explanation:

1.3 x 5.7

just use a calculator

Answer:

Rate or speed=3 Miles per hour

Step-by-step explanation:

Brad walked 2.5 miles in 5/6 of an hour.

Distance covered by Brad = 2.5 miles

Distance covered by Brad= 2 1/2 miles

Distance covered by Brad= 5/2 miles

Time taken to cover the distance = 5/6 of an hour

His rate of walking or how fast he walks is determined by the formula

Rate or speed= distance/time

Rate or speed=( 5/2)/(5/6)

Rate or speed= (5/2)*(6/5)

Rate or speed=6/2

Rate or speed=3 Miles per hour

Answer:

0.5306[tex]<\mu<[/tex]0.5694

Step-by-step explanation:

USing the formuls for calculating the confidence interval for the population proportion;

CI = p±Z*√[p(1-p)/n]

p is the percentage proportion of the population 55%

Z is the z-score at 99% confidence interval = 2.576

n is the sample size = 1079

CI = 0.55 ± 2.576*[0.55(1-0.55)/√1079]

CI = 0.55 ± 2.576*[0.55(0.45)/√1079]

CI = 0.55 ± 2.576*[0.2475/√1079]

CI =  0.55 ± 2.576*[0.2475/32.85]

CI =  0.55 ± 2.576*[0.00753]

CI = 0.55 ±0.0194

CI =(0.55-0.0194, 0.55+0.0194)

CI = (0.5306, 0.5694)

Hence, a 99% confidence interval of the proportion of the population that will support such a law is 0.5306[tex]<\mu<[/tex]0.5694

Answer:

Luke saw 5 worms

Step-by-step explanation:

Evan and Luke saw 8 worms on the path.

Evan saw 3 worms while Luke saw 2 Worms more than Evan.

So luke is +2 of Evan

Luke= 3+2

Luke = 5

Luke saw a total of 5 worms while Evan saw a total of 3 worms adding up to a total of 8 worms

Answer:

99+20i

Step-by-step explanation:

(10+i)^2

➡

(10 + i) × (10 + i) = 100 + 10i + 10i + i^2 add like terms

100 + 20i + i^2 since i^2 = -1 we can write the expression like this

99 + 20i

Answer:

20 cm

Step-by-step explanation:

8/2 = 4

6/2 = 3

3 and 4 are the sides of the triangle (four triangles in rhombus)

[tex]a^{2} + b^{2} = c^{2} \\4^{2} + 3^{2} = c^{2}[/tex]

c = 5

5 x 4 = 20

Hope that helped!!! k

Answer:

Hey there!

He can guess in 4x4x4x4x4x4 or 4096 ways.

Let me know if this helps :)

Answer:

[tex]y = \frac{3}{5} x + \frac{24}{5} [/tex]

m= 3/5

b= 24/5

Answer:

21 units²

Step-by-step explanation:

A=1/2bh

b=6

h=7

1/2(6)(7)=

1/2(42)=

21 units²