Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than negative 1.15−1.15 and draw a sketch of the region.

Answer:

[tex]8x-38[/tex]

Step-by-step explanation:

[tex]3(x-6)+5(x-4)\\3x-18+5x-20\\3x+5x-18-20\\8x-38[/tex]

Answer:

x = -3

Step-by-step explanation:

1.8 - 3.7x = -4.2x +.3

Add 4.2x to each side

1.8 - 3.7x +4.2x= -4.2x+4.2x +.3

1.8 +.5x = .3

Subtract 1.8 from each side

1.8 +.5x -1.8 = .3 -1.8

.5x = -1.5

Divide each side by .5

.5x/.5 = -1.5/.5

x = -3

Answer:

x=-3

Step-by-step explanation:

In order to solve this equation, we have to isolate x. Perform the opposite of what is being done to the equation. Remember to perform everything to both sides.

1.8-3.7x= -4.2x +0.3

3.7x is being subtracted from 1.8 (-3.7x). The inverse operation of subtraction is addition. Add 3.7x to both sides.

1.8-3.7x+3.7x= -4.2x+3.7x+0.3

1.8= -4.2x+3.7x+0.3

1.8= -0.5x+0.3

0.3 is being added to -0.5x. The opposite of addition is subtraction. Subtract 0.3 from both sides.

1.8-0.3= -0.5x+0.3-0.3

1.8-0.3 = -0.5x

1.5=-0.5x

-0.5 and x are being multiplied (-0.5*x= -0.5x). The opposite of multiplication is division. Divide both sides by -0.5.

1.5/-0.5=-0.5x/-0.5

1.5/-0.5=x

-3=x

Answer:

[tex]\fbox{\begin{minipage}{8em}Not a solution\end{minipage}}[/tex]

Step-by-step explanation:

Step 1: Consider the assumption:

Generally, [tex](6, 7)[/tex]) is supposed to be the pair of 2 components, in which, the first component is x-component (domain), the second component is y-component (range).

Hence, [tex]x = 6, y = 7[/tex]

Step 2: Substitute [tex]x[/tex] and [tex]y[/tex] into the inequality

       [tex]y > 2x - 5[/tex]

<=>  [tex]7 > 2*6 - 5[/tex]

Step 3: Simplify

<=>  [tex]7> 12 - 5[/tex]

<=>  [tex]7 > 7[/tex]

Step 4: Evaluate

Invalid

Reason: [tex]7 = 7[/tex]

Step 5: Conclude

[tex](6, 7)[/tex] is not a solution to the inequality [tex]y > 2x - 5[/tex]

Hope this helps!

:)

Answer:

The sample size must be greater than 37 if we want to reject the null hypothesis.

Step-by-step explanation:

We are given that someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi.

Also, we are given a level of significance of 5%.

Let [tex]\mu[/tex] = mean breaking strength of their climbing rope

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2,000 psi       {means that the mean breaking strength of their climbing rope is 2,000 psi}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 2,000 psi      {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}

Now, the test statistics that we will use here is One-sample z-test statistics as we know about population standard deviation;

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

where, [tex]\bar X[/tex] = ample mean strength = 1,997.2956 psi

            [tex]\sigma[/tex] = population standard devaition = 10 psi

            n = sample size

Now, at the 5% level of significance, the z table gives a critical value of -1.645 for the left-tailed test.

So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.

SO,  T.S. < -1.645   {then reject null hypothesis}

         [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645[/tex]

         [tex]\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645[/tex]

         [tex](\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645[/tex]

          [tex]-0.27044 \times \sqrt{n}< -1.645[/tex]

               [tex]\sqrt{n}> \frac{-1.645}{-0.27044}[/tex]

                 [tex]\sqrt{n}>6.083[/tex]

                  n > 36.99 ≈ 37.

SO, the sample size must be greater than 37 if we want to reject the null hypothesis.

Answer:

HJ > KP

Step-by-step explanation:

Form the figure attached,

Two triangles PKL and JGH have been given with HG ≅ KL and PL ≅ GJ

m∠HGJ = 90°

m∠KLP = 85°

Since m∠HGJ > m∠PLK

Therefore, measure of opposite sides of these angles have the same relation.

HJ > KP

Answer:

D

Step-by-step explanation:

when there are exponents with same bases multiplied by each other, keep the base and add the exponents

4^(3)+4^(5)=4^8

4^8 is D in this question

Answer:

The answer is around 27.63 seconds.

Step-by-step explanation:

1 km equals 1000 meters so we have to multiply 10,500 and 1,000 which would equal 10,500,000 km. 10,500,000 divided by 380,000 which is around 27.63 seconds.

Answer:

6.8

Step-by-step explanation:

27 / 4 = 6.75, which rounded to the nearest tenth, is 6.8.

Answer:

[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]

Where x for this case represent the time and y the height waist off ground.

We have one point that can be extracted from the graph on this case:

[tex] x_1 = 1, y_1= 3[/tex]

Bout for the other point we have:

[tex] x_2 = 5.3 , y_2 = 9.6[/tex]

Is important to notice that 9.6 is an estimation since we don't have the scale to identify the real value. so then if we replace we got:

[tex] m =\frac{9.6-3}{5.3-1}= 1.535[/tex]

And for this case we can conclude that this slope is positive and around 1.5 and 1.6. And that means if we increase the time in one unit then the height off waist off ground would increae about 1.5 to 1.6 ft

Step-by-step explanation:

In order to calculate the slope we need to use the following formula:

[tex] m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]

Where x for this case represent the time and y the height waist off ground.

We have one point that can be extracted from the graph on this case:

[tex] x_1 = 1, y_1= 3[/tex]

Bout for the other point we have:

[tex] x_2 = 5.3 , y_2 = 9.6[/tex]

Is important to notice that 9.6 is an estimation since we don't have the scale to identify the real value. so then if we replace we got:

[tex] m =\frac{9.6-3}{5.3-1}= 1.535[/tex]

And for this case we can conclude that this slope is positive and around 1.5 and 1.6. And that means if we increase the time in one unit then the height off waist off ground would increae about 1.5 to 1.6 ft

[tex]answer \\ 4g ^{6} + 16 \\ solution \\ ( {2g}^{3} + 4)^{2} \\ = 2 \times 2 \: g ^{3 \times 2} + 4 \times 4 \\ = 4 {g}^{6} + 16 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

4g^6+16  IS equivalent  to (2g^3+4)^2

Answer:

  1.504×10⁶ ft·lb

Step-by-step explanation:

We understand the top of the oil in the tank is 12 ft below ground level, and the bottom of the tank is 8+18=26 ft below ground level. Then the average depth of the oil is (12+26)/2 = 19 ft below ground level.

The height of the oil in the tank is 26-12=14 ft, so the volume of it is ...

  V = πr²h = π(6 ft)²(14 ft) = 504π ft³ ≈ 1583.36 ft³

__

So, the work required to raise that volume of oil to the surface is ...

  (1538.36 ft³)(50 lb/ft³)(19 ft) = 1.504×10⁶ ft·lb

Answer:

12755 base-8

Step-by-step explanation:

You’re welcome :) please brainliest me btw.

Answer: C) 24

Step-by-step explanation:

first we take down the information given to us

sports shop sells rackets in

4 different weights

2 types of strings

3 grip sizes

Now to get the number of different rackets they could sell, you simply take the  multiplication of the number of racket gripe sizes, the types of strings and different weights they sell

so

4 * 2 * 3 = 24

therefore the sport shop could sell up to 24 different rackets .

Answer:

24

Step-by-step explanation: got it right on my test

Answer:

Option A

Step-by-step explanation:

Correlation does not imply causality. Correlation shows whether and how strongly pairs of variables are related.

Causality shows a situation between two events where one event is affected by the other

We would be skeptical of this survey because it is very difficult to assume that people who owned a radio were more likely to be declared insane and put into an insane asylum as listening to the radio cannot cause insanity unless proven.

Answer:

a)  "K" is proportional Constant   K= 0.0833

b)     The value of b = 99.639

Step-by-step explanation:

Explanation :-

Given   'a' is directly proportional to 'b'

                     a ∝ b

                 a  =  k b ....(i)

where "K" is proportional Constant

Case(i):-

when a =6  and b=72

              a  =  k b    

         ⇒ 6 = k (72)

       ⇒  [tex]K = \frac{6}{72} = \frac{1}{12} = 0.0833[/tex]      

Case(ii):-      

Given  a = 8.3  

          a  =  k b    

⇒   8.3 = 0.0833 ×b

⇒  [tex]b = \frac{8.3}{0.0833} = 99.639[/tex]

Final answer:-

a)"K" is proportional Constant   K= 0.0833

b)     The value of b = 99.639

Answer:

They have two sets of equal answers...

Step-by-step explanation:

-2 * 2 * 4 = -16

0 - 4 * -2 * -2 = -16

0 * -2 * -2 * 4 = 0

0 * 4 * 4 = 0

Answer:

The number of minutes advertisement should use is found.

x ≅ 12 mins

Step-by-step explanation:

(MISSING PART OF THE QUESTION: AVERAGE WAITING TIME = 2.5 MINUTES)

For such problems, we can use probability density function, in which probability is found out by taking integral of a function across an interval.

Probability Density Function is given by:

[tex]f(t)=\left \{ {{0 ,\-t<0 }\atop {\frac{e^{-t/\mu}}{\mu}},t\geq0} \right. \\[/tex]

Consider the second function:

[tex]f(t)=\frac{e^{-t/\mu}}{\mu}\\[/tex]

Where Average waiting time = μ = 2.5

The function f(t) becomes

[tex]f(t)=0.4e^{-0.4t}[/tex]

The manager wants to give free hamburgers to only 1% of her costumers, which means that probability of a costumer getting a free hamburger is 0.01

The probability that a costumer has to wait for more than x minutes is:

[tex]\int\limits^\infty_x {f(t)} \, dt= \int\limits^\infty_x {}0.4e^{-0.4t}dt[/tex]

which is equal to 0.01

Solve the equation for x

[tex]\int\limits^{\infty}_x {0.4e^{-0.4t}} \, dt =0.01\\\\\frac{0.4e^{-0.4t}}{-0.4}=0.01\\\\-e^{-0.4t} |^\infty_x =0.01\\\\e^{-0.4x}=0.01[/tex]

Take natural log on both sides

[tex]ln (e^{-0.4x})=ln(0.01)\\-0.4x=ln(0.01)\\-0.4x=-4.61\\x= 11.53[/tex]

The costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger

Answer:

The length that separates the top 6% is 5.1 centimeters.

The length that separates the bottom 6% is 4.94 centimeters.

Step-by-step explanation:

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.

In this question, we have that:

[tex]\mu = 5.02, \sigma = 0.05[/tex]

Find the two lengths that separate the top 6% and the bottom 6%.

Top 6%:

The 100-6 = 94th percentile, which is X when Z has a pvalue of 0.94. So X when Z = 1.555.

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

[tex]1.555 = \frac{X - 5.02}{0.05}[/tex]

[tex]X - 5.02 = 1.555*0.05[/tex]

[tex]X = 5.1[/tex]

So the length that separates the top 6% is 5.1 centimeters.

Bottom 6%:

The 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.555.

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

[tex]-1.555 = \frac{X - 5.02}{0.05}[/tex]

[tex]X - 5.02 = -1.555*0.05[/tex]

[tex]X = 4.94[/tex]

The length that separates the bottom 6% is 4.94 centimeters.

Answer:

x²- 5²

(x+5)(x-5)

Step-by-step explanation:

Area of shaded region: area of square with side x - area of square with side 5

A= x²- 5²

A= (x+5)(x-5)

Answer:

Length = 550 m

Width = 275 m

Area = 151,250 m2

Step-by-step explanation:

One side of the farmland is bounded by the river, so the perimeter we will need to enclose is:

[tex]Perimeter = Length + 2*Width = 1100\ m[/tex]

And the area of the farmland is given by:

[tex]Area = Length * Width[/tex]

From the Perimeter equation, we have that:

[tex]Length = 1100 - 2*Width[/tex]

Using this in the area equation, we have:

[tex]Area = (1100 - 2*Width) * Width[/tex]

[tex]Area = 1100*Width - 2*Width^2[/tex]

Now, to find the largest area, we need to find the vertex of this quadratic equation, and we can do that using the formula:

[tex]Width = -b/2a[/tex]

[tex]Width = -1100/(-4)[/tex]

[tex]Width = 275\ m[/tex]

This width will give the maximum area of the farmland. Now, finding the length and the maximum area:

[tex]Length = 1100 - 2*Width = 1100 - 550 = 550\ m[/tex]

[tex]Area = Length * Width = 550 * 275 = 151250\ m2[/tex]

Answer: y

Step-by-step explanation:

Answer:

The answer is A (1,-3/2)

Step-by-step explanation:

Add both x coordinates, divide by 2

Add both y coordinates, divide by 2

Answer:

x =2

Step-by-step explanation:

becaue 2-1 is smaller than 3

Answer:

Hello!

I believe your answer is:

x=2

If this is not correct, please let me know and I will try again!

Step-by-step explanation:

Answer:

[tex]\boxed{\ P(B)=0.3 \ }[/tex]

Step-by-step explanation:

Hi,

We know that

P(A or B)=P(A)+P(B)-P(A and B)

so P(B)= P(A or B) - P(A) + P(A and B)

so

P(B) = 0.5 - 0.4 + 0.2 = 0.3

thanks

Answer:

[tex] T_1 = 10*3.5 = 35[/tex]

[tex] T_2 = 20*2.9 = 58[/tex]

[tex] T_3 = 25*3.2 = 80[/tex]

[tex] T_4 = 15*3.4 = 51[/tex]

[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] n_1= 10 , \bar X_1 = 3.5[/tex] for freshmen

[tex] n_2= 20 , \bar X_2 = 2.9[/tex] for sophomores

[tex] n_3= 25 , \bar X_3 = 3.2[/tex] for juniors

[tex] n_4= 15 , \bar X_4 = 3.4[/tex] for seniors

For this case we can use the formula for the sample mean in order to find the total of each group:

[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]T= \sum_{i=1}^n X_i = n *\bar X[/tex]

And replacing we got:

[tex] T_1 = 10*3.5 = 35[/tex]

[tex] T_2 = 20*2.9 = 58[/tex]

[tex] T_3 = 25*3.2 = 80[/tex]

[tex] T_4 = 15*3.4 = 51[/tex]

And the grand mean would be given by:

[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]

Answer:

Step-by-step explanation:

12$

Answer:

Step-by-step explanation:

Given that:

A small-business Web site contains 100 pages and 60%, 30%, and 10%  of the pages contain low, moderate, and high graphic content, respectively.

. A sample of four pages is selected without replacement,

Let  X and Y denote the number of pages with moderate and high graphics output in the sample

We are meant to determine

a)  [tex]f_{XY}(x, y)[/tex]  from the given data in the question;

However; the probability mass function can be expressed via the relation:

[tex]f_{XY}(x,y) = \dfrac{(^{30} _x ) ( ^{10} _y ) (^{60} _ {4-x-y} ) }{ ( ^{100}_4)}[/tex]

We can now have a table shown as :

[tex]X|Y[/tex]                0           1               2              3              4          Total    [tex]f_X(x)[/tex]

0              0.1244     0.0873     0.02031    0.0018     0.0001   0.234

1               0.2618     0.13542   0.02066    0.00092    0         0.419

2              0.1964     0.0666    0.00499       0              0         0.268

3              0.0621     0.01035     0                 0              0         0.073

4              0.0069       0              0                0              0          0.007

Total [tex]F_Y(y)[/tex]   0.6516   0.2996   0.0460      0.0028  0.0001    1

b) [tex]f_X(x)[/tex]

The marginal distribution definition of [tex]f_X(x)[/tex][tex]= P(X=x)[/tex]

[tex]f_X(x)[/tex] [tex]= \sum P(X=x, Y=y)[/tex]

From the table above ; the corresponding values of [tex]f_X(x)[/tex]  are :

X           0           1         2          3           4

[tex]f_X(x)[/tex]    0.234   0.419  0.268   0.073    0.007

( since [tex]f_X(x)[/tex] represent the vertical column)

c) E(X)

By using the expression [tex]E(x) = \sum ^4 _{x= 0} x f_X(x)[/tex]

we have:

E(X) = [tex]0*0.234+1*0.419+ 2*0.268+3*0.073+4*0.007[/tex]

E(X) = 0 + 0.419 + 0.536 + 0.218 + 0.028

E(X) = 1.202

d) fyß(y)

Using the thesis of conditional Probability; we have :

[tex]P(A|B) = \dfrac{ P(A,B) }{ P(B) }[/tex]

The conditional probability for the mass function is then:

[tex]f_{Y|X=3}(y) = \dfrac{f_{XY}(3,y)}{f_{X}(x)}[/tex]

where;

[tex]f_X(3) = 0.0725[/tex]

values of [tex]f_{XY} (3,y)[/tex] for every y ∈ (0,1,2,3,4)

Therefore; the mass function is:

[tex]Y|{_X_3}:\left[\begin{array}{ccccc}0&1&2&3&4\\0.857&0.143&0&0&0\\ \end{array}\right][/tex]

e) E(Y | X = 3)

By using the expression [tex]E(Y|X=3) = \sum ^4 _{y= 0} y f_{y \beta} \ (y|x)[/tex]

we have:

⇒ [tex]0 * 0.857 + 1*0.143 +0 +0+0[/tex]

= 0.143

The value of E(Y | X = 3) = 0.143

g) Are X and Y independent?

To Check if X and Y independent; Let assume if [tex]f_{XY}(x,y) = f_X(x)f_{Y}(y)[/tex] ; then we can say that X and Y are independent.

From the above previous table :

[tex]f_{(XY)} (0.4) = 0.0001[/tex]

[tex]f_X (0)[/tex] = 0.1244 + 0.087268+0.02031+ 0.001836 + 0.0001

[tex]f_X (0)[/tex]  = 0.234

[tex]f_X (4)=0.0001 +0+0 \\ \\ = 0.001[/tex]

[tex]f_{X}(0) f_Y(4) = 0.234*0.0001[/tex]

[tex]f_{X}(0) f_Y(4) = 0.00002[/tex]

We conclude that [tex]f_{(XY)} (0.4) \neq f_X(0) f_Y(y)[/tex]; As such X and Y are said to be  non - independent.

Answer:

B.

Step-by-step explanation:

Volume of balloon = 4/3πr³

= 4/3(3.14)(0.5)³

= 0.52 cubic feet

Now

A helium tank contains 50 cubic feet of helium So,

Spherical balloons = 50/0.52

= 95.4

≈ 100

Answer:

24

Step-by-step explanation:

That would be:

(3/8)(30)

---------------

(15/16)(1/2)

This can be reduced in various ways.  First, divide that 30 by 15, obtaining:

   6/8

-----------

   1/32

Now invert the divisor (1/32) and multiply:

(6/8)(32/1)

This reduces to 6*4, or 24.

Answer:

Step-by-step explanation:

The question tells us that;

Given F1 = ∑ m(0,2,5,7,9) and F1 = ∑ m(2, 3,4,7,8) find the minterm expression for F1+F2. State a general rule for finding the expression for F1+F2 given the minterm expansions for F1 and F2. Prove your answer by using the general form of the minterm expansion.

Note: The answer is provided in the image uploaded below

cheers i hope this helped !!!