Please answer this correctly

Answer:

a) The 95% CI for the true average porosity is (4.51, 5.19).

b) The 98% CI for true average porosity is (4.11, 5.01)

c) A sample size of 15 is needed.

d) A sample size of 101 is needed.

Step-by-step explanation:

a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96*\frac{0.78}{\sqrt{20}} = 0.34[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.34 = 4.51

The upper end of the interval is the sample mean added to M. So it is 4.35 + 0.34 = 5.19

The 95% CI for the true average porosity is (4.51, 5.19).

b. Compute a 98% CI for true average porosity of another seam based on 16 specimens with a sample average of 4.56.

Following the same logic as a.

98% C.I., so [tex]z = 2.327[/tex]

[tex]M = 2.327*\frac{0.78}{\sqrt{16}} = 0.45[/tex]

4.56 - 0.45 = 4.11

4.56 + 0.45 = 5.01

The 98% CI for true average porosity is (4.11, 5.01)

c. How large a sample size is necessary if the width of the 95% interval is to be 0.40?

A sample size of n is needed.

n is found when M = 0.4.

95% C.I., so Z = 1.96.

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.4 = 1.96*\frac{0.78}{\sqrt{n}}[/tex]

[tex]0.4\sqrt{n} = 1.96*0.78[/tex]

[tex]\sqrt{n} = \frac{1.96*0.78}{0.4}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*0.78}{0.4})^{2}[/tex]

[tex]n = 14.6[/tex]

Rounding up

A sample size of 15 is needed.

d. What sample size is necessary to estimate the true average porosity to within 0.2 with 99% confidence?

99% C.I., so z = 2.575

n when M = 0.2.

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.2 = 2.575*\frac{0.78}{\sqrt{n}}[/tex]

[tex]0.2\sqrt{n} = 2.575*0.78[/tex]

[tex]\sqrt{n} = \frac{2.575*0.78}{0.2}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.575*0.78}{0.2})^{2}[/tex]

[tex]n = 100.85[/tex]

Rounding up

A sample size of 101 is needed.

Answer:

Exponent Product Rule

Step-by-step explanation:

Exponent multiplication: (a^b)(a^c)= a^(b+c)

t^3=(t^2)t

Because t=t^1, we have

t^2+t^1=t^3

This can be shown by the Exponent Product Rule

Answer:   t²⁺¹

Step-by-step explanation:

The law of exponents states that when multiplying terms with the same base, you ADD the exponents.  Note that "t" has an exponent of 1.

t³ = (t²)t¹ = t²⁺¹

I hope this is what you were looking for.

Answer:

(5x + 6) (x² + 5)

Step-by-step explanation:

5x³ + 6x² + 25x + 30

= x² (5x + 6) + 25x + 30    -- Group 5x³ and 6x²

= x² (5x + 6) + 5 (5x + 6)    -- Group 25x and 30

= (5x + 6) (x² + 5)  -- Both terms have a common factor of 5x + 6

Answer:

Well a shape reflecting across the x axis will look like some thing in the image below.

Look at both images.

Answer:

The correct answer to this is "Change in Y over Change in X"

Step-by-step explanation:

Change in Y over Change in X is the basis of the saying "rise over run". When you divide the rise by the run you get the slope.

I hope this helps you out!

Answer:

reflection of the axis y=4

Step-by-step explanation:

becuase it is reflected on itself

Answer:

Reflect Triangle A by the line y = 4

Step-by-step explanation:

The answer is reflect Triangle A by y = 4 because the two triangles are symmetric.

Answer:

a. 10295472 ways

b. 4272048 ways

c. 6023424 ways

Step-by-step explanation:

Given that:

Camera shop stocks ----- 8 different types of batteries

one of which is ---- A76

Assume that there are ------ at least 30 batteries of each type.

a.

How many ways can a total inventory of 30 batteries be distributed among the eight different types.

The number of ways a total inventory of 30 batteries be distributed is :

[tex]= \left \{ {{30+8-1} \atop {30}} \right. \}[/tex]

[tex]= \left \{ {{37} \atop {30}} \right. \}[/tex]

[tex]=\dfrac{37!}{30! *7!}[/tex]

[tex]= \dfrac{37*36*35*34*33*32*31*30!}{30!*7*6*5*4*3*2*1}[/tex]

[tex]= \dfrac{37*36*35*34*33*32*31}{7*6*5*4*3*2*1}[/tex]

= 10295472 ways

b.

How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?

If we must include 4  A76 batteries; then the number of ways a total inventory of 30 batteries can be distributed among eight different types of batteries will be:

30 - 4 = 26 batteries

Now;

[tex]= \left \{ {{26+8-1} \atop {26}} \right. \}[/tex]

[tex]= \left \{ {{33} \atop {26}} \right. \}[/tex]

[tex]=\dfrac{33!}{26! \ \ 7!}[/tex]

[tex]=\dfrac{33*32*31*30*29*28*27*26!}{26! \ * \ 7*6*5*4*3*2*1}[/tex]

[tex]=\dfrac{33*32*31*30*29*28*27}{ \ 7*6*5*4*3*2*1}[/tex]

= 4272048 ways

c. If we must include at most three A7b batteries. the number of ways that a total inventory of 30 batteries can be distributed among eight different types of inventory is:

[tex]= \sum \limits ^3 _{x=0} \left \{ {{(30-x)+7-1} \atop {30-x}} \right. \} \\ \\ \\ = \sum \limits ^3 _{x=0} \left \{ {{(30-0)+7-1} \atop {30-0}} \right. \} = (^{36}_{30})+(^{35}_{29})+ (^{34}_{28})+ (^{33}_{27})[/tex]

[tex]= \dfrac{36!}{30! * 6!} + \dfrac{35!}{29! * 6!} + \dfrac{34!}{28! * 6!} + \dfrac{33!}{27! * 6!}[/tex]

= 1947792 + 1623160 + 1344904 + 1107568

= 6023424 ways

Answer:

The pro is Political Control, the cons, however, are many.

Step-by-step explanation:

However, A Socialist Economy cons outweigh its pros. The only thing that is a PRO is you dictating it, preventing people from success. Wanna know the cons? The Cons are more Regulations, to which chokes more businesses of their money, they function, & motive. To which it has a chain reaction of: The Businesses not employing people, more people are out of work, which means more people ain't buying stuff to support the businesses, which means the businesses are out of business, they shut down.

The Economy ain't something that you can stop, or go, & it ain't statistics. An Economy is just.. people, that's it. It's just people, they are the ones that work, run businesses & factories, they are the ones that buy N' sell. They create, craft, invent, innovate, etc.

Here's a quote that I have: "The more you choke it from breathing in, the less it breathes out". That's my stance on regulation & Socialism, to which Socialism is just Voluntary Communism, & A Permanent Ideological belief that Big government Involvement is the way to go.

To which, it's not!

Answer:

[tex]\displaystyle y = -\frac{2}{3}\, x - 9[/tex].

Step-by-step explanation:

The slope-intercept form of a line on a cartesian plane should be in the form:

[tex]y = m\, x + b[/tex],

where:

The question states that the slope of this line is [tex]\displaystyle -\frac{2}{3}[/tex]. In other words, [tex]\displaystyle m = -\frac{2}{3}[/tex]. The next step is to find the value of [tex]b[/tex]. That could be done using the information that the point [tex](-6,\, -5)[/tex] is on this line.

Note that the slope-intercept form of a line [tex]y = m\, x + b[/tex] is essentially an equation about [tex]x[/tex] and [tex]y[/tex]. For a point [tex](x_0,\, y_0)[/tex] to be on that line, [tex]x = x_0[/tex] and [tex]y = y_0[/tex] should satisfy its equation. In other words, it must be true that [tex]y_0 = m\, x_0 + b[/tex].

For the point [tex](-6,\, -5)[/tex], [tex]x_0 = -6[/tex] and [tex]y_0 = -5[/tex]. The equation would be:

[tex]\underbrace{-5}_{y_0} = m \times \underbrace{(-6)}_{x_0}+ b[/tex].

Besides, the slope of this line is already known to be [tex]\displaystyle m = -\frac{2}{3}[/tex]. Therefore, this equation would become:

[tex]\displaystyle \underbrace{-5}_{y_0} = \underbrace{\left(-\frac{2}{3}\right)}_{m} \times \underbrace{(-6)}_{x_0}+ b[/tex].

Solve this equation for [tex]b[/tex]:

[tex]b = -9[/tex].

Hence, the slope-intercept form ([tex]y = m\, x + b[/tex]) of this line would be:

[tex]\displaystyle y = -\frac{2}{3}\, x - 9[/tex].

Answer:78.14cm^2

Step-by-step explanation:

Answer:

140

Step-by-step explanation:

The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84

Answer:

the other person is correct!

Step-by-step explanation:

Answer:

[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]

Step-by-step explanation:

Sample space, n = 100

Let the number of students signed up for CSE 311 = a

Let the number of students signed up for CSE 312 = b

Let the number of students signed up for CSE 331 = c

Let the number of students signed up for CSE 332 = d

Probability of taking CSE 311, [tex]P_a[/tex] = 0.3

Probability of taking CSE 312, [tex]P_b[/tex] = 0.4

Probability of taking CSE 331, [tex]P_c[/tex] = 0.1

Probability of taking CSE 332, [tex]P_d[/tex] = 0.2

[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]

Answer:

Option (A)

Step-by-step explanation:

Given:

LM ≅ OP

MN ≅ PQ

∠M ≅ ∠P

To Prove:

ΔLMN ≅ ΔOQP

                   Statements                      Reasons

1). LM ≅ OP                                   1). Given

2). MN ≅ PQ                                 2). Given

3). ∠P ≅  ∠M                                3). Given

4). ΔLNM ≅ ΔOQP                      4). By the SAS postulate of congruence.

                                                         [Side - Angle - Side]                          

Therefore, Option (A) will be the answer.

Answer:

Division property of equality.

Answer:

7.75

Step-by-step explanation:

6-4=2

2 times the square root of 3=3.46410161514

square root of 5 times 3.46410161514=7.74596669242

to 2dp=7.75

Answer:

sinΘ = - [tex]\frac{\sqrt{33} }{7}[/tex]

Step-by-step explanation:

Using the trigonometric identity

sin²Θ + cos²Θ = 1, thus

sinΘ = ± [tex]\sqrt{1-cos^20}[/tex]

Since Θ is in the fourth quadrant then sinΘ < 0

Given

cosΘ = [tex]\frac{4}{7}[/tex] , then

sinΘ = - [tex]\sqrt{1-(\frac{4}{7})^2 }[/tex] = - [tex]\sqrt{1-\frac{16}{49} }[/tex] = - [tex]\sqrt{\frac{33}{49} }[/tex] = - [tex]\frac{\sqrt{33} }{7}[/tex]

Answer:

56 cats

88 dogs

Step-by-step explanation:

x=cats

x+32=dogs

x+x+32=144

2x=144-32

2x=112

x=112/2

x=56 (56 cats)

x+32=88 (88 dogs)

Answer:

56

Step-by-step explanation:

In order to solve this question you need to subtract 32 by 144 then divide that answer by 2.

So we know that they're 32 more dogs then cats and there is 144 dogs and cats all together.

[tex]144 - 32 = 112[/tex]

Divide it in half

[tex]112 \div2=56[/tex]

[tex]56+32 = 88[/tex]

[tex]= 56[/tex]

Therefore they're 56 cats in the pet store.

Hope this helps.

Answer:

99% chance tommy has it

Step-by-step explanation:

cuz do da math

Answer:

Answer is Y

Step-by-step explanation:

Answer: a. 1320

b.495

Step-by-step explanation:

Complete question is provided in the attachment.

Total members on the board = 12

a. Persons to chose : chairperson, first vice​ chairperson, second vice​ chairperson, and​ secretary

i.e. Total 3 posts in an order.

Number of ways to choose 3 persons from 12 in an order = [tex]^{12}P_3[/tex]  [By permutation]

[tex]=\dfrac{12!}{(12-3)!}\\\\=\dfrac{12!}{7!}\\\\=12\times11\times10\\\\=1320[/tex]

hence, 1320 different slates of candidates are​ possible .

b. number of ways to choose 4 members out of 12 ( order not matters)=[tex]^{12}C_{4}[/tex] [By combinations]

[tex]=\dfrac{12!}{4!8!}\\\\=\dfrac{12\times11\times10\times9}{24}\\\\=495[/tex]

Hence, the number of different subcommittees are​ possible =495

Answer:

y= -2x+3

Step-by-step explanation:

Point slope form= y=mx+b

The m is the slope.

So, we have an incomplete equation right now: y= -2x+b

We want to find b. We can do that by plugging in values for the x and y coordinates. Fortunately, we do have a set of coordinates, (1, 1)!

We plug them in:

1= -2(1)+b

1= -2+b

b=3

So, since we have the slope and the b, also called the y-intercept, we can form an equation!

y= -2x+3

Answer:

Given:

A right triangle in which an altitude is drawn from the right angle vertex

To find: value of X

We have leg rule in similarity in right triangle as:

[tex] \frac{leg}{part} = \frac{hypotenuse}{leg} \\ [/tex]

Plugging the given values,

[tex] \frac{z}{3} = \frac{3 + 27}{z} \\ z \times z = 3(3 + 27) \: \: (cross \: multiplication) \\ {z}^{2} = 9 + 81 \\ {z}^{2} = 90 \\ z = \sqrt{90} \\ z = 3 \sqrt{10} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

D. Quadratic parent function.

Step-by-step explanation:

Answer:

Area to the right is 0.813

Step-by-step explanation:

Since the area under the full normal distribution should render "1" (one), then the area to the right of x  should be:

1 - area to the left of x = 1 - 0.187 = 0.813

The area to the right of x in this normal distribution will be 0.813.

The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean.

The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution's two tails are likewise rare.

Not all symmetrical distributions are normal, even though the normal distribution is symmetrical. 

We know that the total area described in a normal distribution is 1.

Given, that the area to the left of x in a normal distribution is 0.187.

So, the area to the right of x will be,

1 - 0.187.

= 0.813.

learn more about normal distribution here :

https://brainly.com/question/15103234

#SPJ2

Answer:

The answer is option B.

Step-by-step explanation:

Using the expression

[tex] {e}^{ ln(x) } = x[/tex]

[tex] {e}^{ ln(4) } = 4[/tex]

Hope this helps you

Answer:

ABC = 88

Step-by-step explanation:

Angle Formed by Two Chords  = 1/2( sum of Intercepted Arcs)

ABD = 1/2 ( 131+ 53)

ABD = 1/2 (184)

       =92

ABC = 180 -ABD

ABC = 88

Answer:

a. Local maximum = 50 units per week.

b. The graph is never concave upward.

c. (0, 80)

Step-by-step explanation:

a. The revenue function is:

[tex]R(x) = 1275x-0.17x^3[/tex]

The derivate of the revenue function for which R'(x) = 0 gives us the local extrema:

[tex]R'(x) =0= 1275-0.51x^2\\x=\sqrt{2,500}\\x=50[/tex]

The second derivate of the revenue function determines if x =50 is local maximum or minimum:

[tex]R''(x) = -1.02x\\R''(50) = -1.02*50=-51\\[/tex]

Since the second derivate yields a negative value, x = 50 units per week is a local maximum.

b. Since there are no local minimums in the range of 0 < x < 80, the graph is never concave upward.

c. Since there is only one local maximum  in the range of 0 < x < 80, the graph is concave downward from x>0 to x<80 or (0, 80)

Answer:

this lesson, we will investigate the relationship between the distance traveled, the rate or speed or travel, and the time that it takes to travel that distance at that rate.  We will also look at a few other related products.

Distance  =  (Rate)(Time)

The equation that relates distance, rate, and time is

        d  =  rt

Where d is the distance traveled, r is the rate, and t is the time.  On the CAHSEE exam, you will be given two of these and will be asked to use the above equation to find

Answer:

2.5 hours

Step-by-step explanation:

First, try rewriting Jenny's speed in it's fraction form: 6 mi/hr

Next, use the units to set up an equation that relates Jenny's speed to the distance they want to travel. Let's call the unknown time t:

6mi/hr=15mi/t

1/t=6/15 (mi/hr•1/mi)

t=15/6 (hrs/mi•mi)= 15/6 (hrs•mi/mi)= 15/6 hrs

t=2.5hrs

So it'd take Jenny 2.5hrs at 6mph to go 15 miles. The key here is to keep track of the units. You can treat them like fractions and reduce them away as if they were numbers or variables.

Answer:

(35k + 20) cents

Step-by-step explanation:

First of all, let us have the value of each unit:

1 quarter = 25 cents

1 nickel = 5 cents

1 dime = 10 cents

Given that number of quarter = k

Quarters are 5 lesser than Nickels, so number of nickels = k+5

One more than twice as many dimes as quarters:

k = 2 [tex]\times[/tex] Number of Dimes + 1

So, number of dimes = [tex]\frac{1}{2}(k-1)[/tex]

Value of quarters = [tex]25 \times k[/tex] cents

Value of nickels = [tex]5 \times (k+5) = (5k+25)\ cents[/tex]

Value of dimes = [tex]\frac{1}{2}(k-1) \times 10 = (5k-5)\ cents[/tex]

So, total value of coins =

[tex]25k + 5k +25 +5k-5\\\Rightarrow (35k+20)\ cents[/tex]

Answer:

ray UV and ray UT

Step-by-step explanation:

The sides are the rays that make up the angle

ray UV and ray UT make up the angle VUT