8
.
Solve simultaneously the equations 6p - 4r = 14 and p-2r = 5.
p=..
فن
199110​

Answers

Answer 1

Answer:

p = 1 and r = - 2

Step-by-step explanation:

Given the 2 equations

6p - 4r = 14 → (1)

p - 2r = 5 → (2)

Multiplying (2) by - 6 and adding to (1) will eliminate the term in p

- 6p + 12r = - 30 → (3)

Add (1) and (3) term by term to eliminate p

8r = - 16 ( divide both sides by 8 )

r = - 2

Substitute r = - 2 into either of the 2 equations and solve for p

Substituting into (2)

p - 2(- 2) = 5

p + 4 = 5 ( subtract 4 from both sides )

p = 1


Related Questions

Use the following information to complete parts​ (a) through​ (e) below. A researcher wanted to determine the effectiveness of a new cream in the treatment of warts. She identified 149 individuals who had two warts. She applied cream A on one wart and cream B on the second wart. Test whether the proportion of successes with cream A is different from cream B at the alpha equals 0.05 level of significance. Treatment A Treatment B Success Failure Success 63 10 Failure 25 53 What type of test should be used? A. A hypothesis test regarding the difference of two means using a matched-pairs design. B. A hypothesis test regarding two population standard deviations. C. A hypothesis test regarding the difference between two population proportions from dependent samples. D. A hypothesis test regarding the difference between two population proportions from independent samples.

Answers

Answer:

Option D: A hypothesis test regarding the difference between two population proportions from independent samples.

Step-by-step explanation:

A hypothesis test regarding the difference between two population proportions from independent samples. This type of test is used to compare the two population proportions if they are equal or not. It is appropriate under the condition that

The sampling method for each population is simple random sampling.

The samples are independent.

Each sample includes at least 10 successes and 10 failures.

Each population is at least 20 times as big as its sample.

PLSS I NEED HELP ASAP BECAUSE ITS DUE SOON

Nick has to build a brick wall. Each row of the wall requires 62 bricks. There are 10 rows in the wall. How many bricks will Nick require to build the wall?
A.
102 × 6
B.
106
C.
610
D.
10 × 62

Answers

D. 10 x 62

If one row needs 62 bricks and there's 10 rows, you multiply them to get how many bricks nick needs

3 How many ordered pairs of positive integers (a, b) are there such that a right triangle with legs of length a, b has an area of p, where p is a prime number less than 100?

Answers

Answer:

The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.

*) The scale on a map is 1 : 25000
How many kilometres on the ground is represented by 9 cm on the map?​

Answers

Answer:

2.25km

Step-by-step explanation:

a scale of 1 : 25000 means:

1 cm on map ------> equals 25000 cm on ground  

hence,

9 cm on map ------> equals 25000 x 9 cm = 225,000 cm = 2.25km on ground

Please help !!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

25 and 36

Step-by-step explanation:

5^2=25

6^2=36

Answer:

Im feeling pretty today so imma go with C

Step-by-step explanation:

lol i took the test like about 2 days ago and i just checked my answers and C was right, good luck


Find the nth term: 0, -6, -12, -18 …

Answers

Answer:

F(1) = 0

F(2) = -6 = 0 - 6 x 1 = F(1) - 6 x 1

F(3) = -12 = 0 - 6 x 2 = F(1) - 6 x 2

F(4) = -18 = 0 - 6 x 3 = F(1) - 6 x 3

...

F(n) = F(1) - 6 x (n - 1)

Hope this help!

:)

Diego is building a fence for a rectangular garden. It needs to be at least 10 feet wide and at least 8 feet long. The fencing he uses costs $3 per foot. His budget is $120.

Answers

Answer:

240

Step-by-step explanation:

8*10=80ft *3= 240 but thats over budget

The total cost to fence the rectangular garden is $108. Diego has enough money to fence the rectangular garden.

What is the perimeter of a rectangle?

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, a rectangular garden needs to be at least 10 feet wide and at least 8 feet long.

Now the perimeter of rectangular garden is

2(8+10)

= 36 feet

Total cost of fencing = 36×3

= $108

Diego's budget is $120

Therefore, Diego has enough money to fence the rectangular garden.

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. a. If 1 adult female is randomly selected, find the probability that her pulse rate is greater than 70 beats per minute. b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean greater than 70 beats per minute. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30

Answers

Answer:

a) 34.46% probability that her pulse rate is greater than 70 beats per minute.

b) 2.28% probability that they have pulse rates with a mean greater than 70 beats per minute.

c) Because the underlying distribution(female's pulse rate) is normal.

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.

Distribution of females pulse rates:

Here, i suppose there was a typing mistake, since the mean and the standard deviation are lacking.

Also, the question c. only makes sense if the distribution is normal, so i will treat it as being.

I will use [tex]\mu = 68, \sigma = 5[/tex]. I am guessing these values, just using them to explain the question.

a. If 1 adult female is randomly selected, find the probability that her pulse rate is greater than 70 beats per minute.

This is 1 subtracted by the pvalue of Z when X = 70. So

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

[tex]Z = \frac{70 - 68}{5}[/tex]

[tex]Z = 0.4[/tex]

[tex]Z = 0.4[/tex] has a pvalue of 0.6554

1 - 0.6554 = 0.3446

34.46% probability that her pulse rate is greater than 70 beats per minute.

b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean greater than 70 beats per minute.

Now [tex]n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]

This probability is 1 subtracted by the pvalue of Z when X = 70. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{70 - 68}{1}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that they have pulse rates with a mean greater than 70 beats per minute.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30

The sample size only has to exceed 30 if the underlying distribution is normal. Here, the distribution of females' pulse rate is normal, so this requirement does not apply.

There are many cones with a volume of 72pi cubic inches. For example, one such cone could have a radius of 6 inches and a height of 6 inches.



Find another possible pair of measurements (radius and height) to make the same volume. (EXTRA CREDIT for each additional pair that you find.)

Answers

Answer:

Step-by-step explanation:

The volume of a cone of height h and circular base of radius r, is [tex] V = \frac{\pi r^2 h}{3}[/tex]. In this case we have that [tex]V=72\pi[/tex].Then, we have that

[tex]72\pi = \frac{\pi r^2 h}{3}[/tex]

multiplying by 3 on both sides and dividing by [tex]\pi[/tex] we have that

[tex]216 = r^2\cdot h[/tex]

Suppose that we know the value of r, then we can find the value of h by solving h, that is

[tex] h = \frac{216}{r^2}[/tex].

So, by choosing any positive value of r, we can find the value for h. Note that if r=6, then [tex]h= \frac{216}{6^2} = 6[/tex]. This means that the amount of credit is infinite :)

A radio station dedicates 20% of their air time to commercials for each radio show. During a radio show, 30 minutes of commercials played. How long was the radio show?

Answers

Answer:

150 minutes (2.5 hours)

Step-by-step explanation:

We must consider that the total time that the radio program lasted  represents the 100%.

Of that 100% we are told that 20% is dedicated to commercials. So the 30 minutes of commercials correspond to 20% of the air time, which can be represented in the following table:

Percentage of time             time

        20%                       ⇒     30min

and we are looking for how long the show was on the air (the 100%).

So updating the table( I will call x the total time on the air):

Percentage of time             time

        20%                       ⇒     30min

        100%                       ⇒     x

This reationship between three values can be solve by the rule of three: multiply the cross quantities on the table (100 by 30) and divide by the remaining amount (20):

x = 100*30 / 20

x= 3000 / 20

x = 150 minutes

The radio show was 150 minutes (2.5 hours) long.

A student rolls a number cube 40 times. He rolls a 3 on the number cube 6 times. What is the experimental probability that he rolls a 3?

Answers

Answer:

[tex]\frac{6}{40}=\frac{3}{20}[/tex]

Step-by-step explanation:

The experimental probability is the number of times the desired result was obtained over the total number of times the experiment was carried out:

[tex]P=\frac{TimesTheEventOccurs}{TotalNumberOfTrials}[/tex]

In this case the Event we are looking for is rolling a 3 on the number cube.

The total number of trials is:

40

because the student rolls the cube 40 times.

and the times that he got the number 3 (the times the desired event occurs) is:

6

because he rolls a 3 on the number cube 6 times.

Thus our experimental probability to roll a 3 is:

[tex]P=\frac{6}{40}[/tex]

Rule double the last number number number than add 3

2. 7 17 _ _

Answers

Answer:

[tex]37[/tex]

[tex]77[/tex]

Step-by-step explanation:

[tex]17 \times 2 +3=37\\37 \times 2 +3=77[/tex]

Answer:

37   77

Step-by-step explanation:

2(17) + 3 = 37

2(37) + 3 = 77

Ninja blenders have a 2 year warranty, which means that Ninja guarantees replacement of the blender is it fails within the first 2 years. The blenders last an average of 36 months with a standard deviation of 6 months. What is the probability that Ninja will have to replace your blender if you were to buy one today

a 0.025

b 0.475

c 0.0001

d 0.0235

Answers

Answer:

d 0.0235

Step-by-step explanation:

We assume that the lifetime of the blenders follows a normal distribution, with mean of 36 months and standard deviation of 6 months.

We have to calculate the probability that the blenders have a lifetime lower than 24 months, and therefore apply the guarantee.

First, we calculate the z-score:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{24-36}{6}=\dfrac{-12}{6}=-2[/tex]

Then, the probability that the blenders lifetime is 24 or less is:

[tex]P(X<24)=P(z<-2)=0.023\\[/tex]

find -34 + 15 - 29 - (-3)

Answers

Answer:

-45

Step-by-step explanation:

-34+15=-19

-29-(-3)= -29+3= -26

-19 + -26 = -45

Answer:

-45

Step-by-step explanation:

-34 + 15 - 29 - (-3)

-34-29 +15+3

-63+18

18-63

-45

Which represents the reference angle for 3pi/4?


a) 3pi/4

b) Pi/3

c) Pi/4

d) Pi/6

Answers

Answer:

(c) Pi/4

Step-by-step explanation:

3pi/4 = (3 x 180) / 4 = 135 degrees

135 degrees is equivalent to (180 degrees - 135 degrees) 45 degrees

45 degrees = Pi/4

Therefore, the reference angle of 3pi/4 is Pi/4

Thus, the correct option is (c) Pi/4

The reference angle for 3π/4 is π/4.

So, the correct answer is c) π/4.

Given is an angle 3π/4, we need to find its reference angle,

The reference angle is the acute angle formed between the terminal side of an angle and the x-axis in the coordinate plane.

To find the reference angle for an angle, you need to consider the position of the terminal side of the angle in the coordinate plane and determine the acute angle formed.

In this case, we are given the angle 3π/4. To find the reference angle, we need to consider the position of the terminal side of this angle.

The angle 3π/4 lies in the second quadrant of the coordinate plane, where both the x-coordinate and y-coordinate are negative.

To find the reference angle, we need to find the acute angle formed by the terminal side with the x-axis. In the second quadrant, this acute angle is formed by the vertical line connecting the terminal side to the x-axis.

If we draw a vertical line from the terminal side of 3π/4, it intersects the x-axis at π/4.

Therefore, the reference angle for 3π/4 is π/4.

So, the correct answer is c) π/4.

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Solve the given inequality. Round to the nearest ten-thousandth, if necessary. e x > 14

Answers

Answer:

[tex]x\in(1.146,\infty)[/tex]

Step-by-step explanation:

We are given an inequality

[tex]e^x>14[/tex]

We have to solve the given inequality.

Taking both side ln of given inequality

Then, we get

[tex]ln(e^x)>ln(14)[/tex]

[tex]xlne>1.146[/tex]

We know that

lne=1

Using the value

[tex]x>1.146[/tex]

[tex]x\in(1.146,\infty)[/tex]

Hence, the value of x is given by

[tex]x\in(1.146,\infty)[/tex]

Draw the image of quadrilateral ABCD under the translation (x,y)→(x+4,y−3)

Answers

Answer:

The overall image would be 4 units to the right and 3 units down on the coordinate plane.

Step-by-step explanation:

We do not see an image. But that is okay. (x+4,y-3) means that the x value of each coordinate gets increased by 4 and the y value of each coordinate gets decreased by 3. The overall image would be 4 units to the right and 3 units down on the coordinate plane.

The image would be 4 units to the right and 3 units down on the coordinate plane.

What is translation?

In maths, a translation moves a shape left, right, up, or down but does not turn.

Given the translation of quadrilateral ABCD

(x+4,y-3) means that the x value of each coordinate gets increased by 4 and the y value of each coordinate gets decreased by 3.

Hence, The image would be 4 units to the right and 3 units down on the coordinate plane.

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The sum of two rational numbers is

Answers

Answer:

rational

Step-by-step explanation:

rational + rational=rational

the sum of two rational numbers or rational

Suppose that daily calorie consumption for american men follows a normal distribution with a mean of 2760 calories and a standard deviation of 500 calories.Suppose a health science researcher selects a random sample of 25 American men and records their calorie intake for 24 hours (1 day). Find the probability that the mean of her sample will be between 2700 and 2800 calories

Answers

Answer:

38.11% probability that the mean of her sample will be between 2700 and 2800 calories

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.

In this question, we have that:

[tex]\mu = 2760, \sigma = 500, n = 25, s = \frac{500}{\sqrt{25}} = 100[/tex]

Find the probability that the mean of her sample will be between 2700 and 2800 calories

This is the pvalue of Z when X = 2800 subtracted by the pvalue of Z when X = 2700.

X = 2800

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

By the Central Limit Theorem

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

[tex]Z = \frac{2800 - 2760}{100}[/tex]

[tex]Z = 0.4[/tex]

[tex]Z = 0.4[/tex] has a pvalue of 0.6554

X = 2700

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

[tex]Z = \frac{2700 - 2760}{100}[/tex]

[tex]Z = -0.6[/tex]

[tex]Z = -0.6[/tex] has a pvalue of 0.2743

0.6554 - 0.2743 = 0.3811

38.11% probability that the mean of her sample will be between 2700 and 2800 calories

The radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decreasing at a rate of 2.2 in/s. At what rate is the volume of the cone changing when the radius is 135 in. and the height is 135 in.

Answers

Answer:

Step-by-step explanation:

let radius=r

height=h

dr/dt=1.6 in/s

dh/dt=-2.2 in/s

volume v=1/3 πr²h

dv/dt=1/3 π[h*2r×dr/dt+r²×dh/dt]

when r=135 in

h=135 in

dv/dt=1/3 π[2×135×135×1.6+135²×(-2.2)]

=1/3 π[135²(3.2-2.2)]

=1/3π135²×1

=6075 π in³/s

Evaluate for x = 2. (12x + 8)/4

Answers

Answer:

8

Step-by-step explanation:

24+8=32 32 divided by 4 is 8

Answer: 8

Step-by-step explanation:

Plug in x as 2 and solve.

(12*2 + 8)/4

Start with parenthesis.

(32)/4

Now divide.

8

In a missile-testing program, one random variable of interest is the distance between the point at which the missile lands and the center of the target at which the missile was aimed. If we think of the center of the target as the origin of a coordinate system, we can let Y1 denote the northsouth distance between the landing point and the target center and let Y2 denote the corresponding eastwest distance. (Assume that north and east define positive directions.) The distance between the landing point and the target center is then U=sqrt((y1)^2+(y2)^2). If Y1 and Y2 are independent, standard normal random variables, find the probability density function

Answers

Answer:

Step-by-step explanation:

From the given data

we observed that the missile testing program

Y1 and Y2 are variable, they are also independent

We are aware that

[tex](Y_1)^2 and (Y_2)^2[/tex] have [tex]x^2[/tex] distribution with 1 degree of freedom

and [tex]V=(Y_1^2)+(Y_2)^2[/tex] has x^2 with 2 degree of freedom

[tex]F_v(v)=\frac{e^{-\frac{v}{2}}}2[/tex]

Since we have to find the density formula

[tex]U=\sqrt{V}[/tex]

We use method of transformation

[tex]h(V)=\sqrt{U}\\\\=U[/tex]

There inverse function is [tex]h^-^1(U)=U^2[/tex]

We derivate the fuction above with respect to u

[tex]\frac{d}{du} (h^-^1(u))=\frac{d}{du} (u^2)\\\\=2u^2^-^1\\\\=2u[/tex]

Therefore,

[tex]F_v(u)=F_v(h-^1)(u)\frac{dh^-^1}{du} \\\\=\frac{e^-\frac{u^-^}{2} }{2} (2u)\\\\=e^-{\frac{u^2}{2} }U[/tex]

State the domain and range for the following relation. Then determine whether the relation represents a function.
Father Son
Gem Gale
Hesh Abby
Beni Sam
A. Domain : {Gem, Hesh, Gale}
Range : {Sam, Abby, Beni}
B. Domain : {Gale, Abby, Beni}
Range : {Gem, Hesh, Sam}
C. Domain : {Gem, Hesh, Sam}
Range : {Gale, Abby, Beni}
D. Domain : {Sam, Abby, Beni}
Range : {Gem, Hesh, Gale}
Does the relation represent a function?
A. The relation in the figure is a function because each element in the domain corresponds to exactly one element in the range.
B. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain.
C. The relation in the figure is not a function because the element Gale in the range corresponds to more than one element in the domain.
D. The relation in the figure is not a function because the element Sam in the domain corresponds to more than one element in the range.

Answers

Answer:

C. Domain : {Gem, Hesh, Sam}

Range : {Gale, Abby, Beni}

B. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain.

Step-by-step explanation:

The figure of the mapping is attached below.

From the diagram, the domain for the relation is the set of Fathers:

{Gem, Hesh, Sam}

The range is the set of Sons:

{Gale, Abby, Beni}

The relation is a function. This is because each element in the range corresponds to exactly one element in the domain.

Given; y || 2
Prove: m<5+ m<2 + m<6 = 180°
Help

Answers

Answer:

<1=<5(alternative angle)

<3=<6(alternative angle)

<1+<2+<3=180(given)

<5+<2+<6=180(putting <1=<5 and <3=<5)

proved

15. The solutions to (x+4)2 - 2 = 7 are
1) -4+ 5
3) -1 and -7
2) 4+ 5
4) 1 and 7
I​

Answers

Answer:

Step-by-step explanation:

(x + 4)^2 - 2 = 7 simplifies to

(x + 4)^2 = 5

We must isolate x.  To do this, take the square root of both sides, obtaining:

x + 4 = ±√5

There are two roots/solutions.  They are:

x = -4 + √5 and x = -4 - √5            

You must include the square root operator (√).  Use "  ^  " to denote exponentiation.

The solutions to the given equation (x + 4)² - 2 = 7 when calculated are; 1 and 7

How to Solve Algebra Problems?

We are given the equation as;

(x + 4)² - 2 = 7

Add 2 to both sides to get;

(x + 4)² = 9

Find the square root of both sides to get;

x + 4 = ±3

Thus;

x = 3 + 4 and x = -3 + 4

x = 1 and 7

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Help....!! I need to solve this simultaneous equation y=x-2 and y=3x+5 With working out if possible please....

Answers

Step-by-step explanation:

Y= x - 2. Y = 3x + 5

Putting value of y

x - 2 = 3x + 5

-2 - 5 = 3x - x

-7 = 2x

-7/2 = x

Putting value of x

Y = 3(-7/2) + 5

Y = - 10.5 + 5

Y = - 5.5

Can anyone help me with this question please

Answers

Answer:

1 = 130° , 2 =50° , 3 = 85°, 4=45°

Step-by-step explanation:

1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}

2 = 180 - 1 { angles on a straight line equals 180}

= 180 -130 = 50°

4 = 180 - 135 = 45° { angles on a straight line equals 180}

3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}

3 = 135-50 = 85°

Note : sum of opposite interior angles equals external exterior angle, let's prove it:

If we look at the triangle at the bottom left, we have :

85, 45 and r { let's denote r as the missing angle}

So 85 + 45 + r = 180° { sum of angles of a triangle}

By simple arithmetic

r = 180 - ( 85+45) = 180 - 130 = 50°

but r + 4 = 180° { sum of angles in a straight line equals 180°}

4 = 180 - 50 = 130°

So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}

Nuts and bolts are made separately and paired at random. The nut diameters (in mm) are normally distributed with mean 10 and variance .02. The bolt diameters (in mm) are also normally distributed with mean 9.5 and variance 0.02. Find the probability that a bolt is too large for its nut. In other words, find the probability that for a randomly selected nut and bolt, [size of nut − size of bolt] ≤ 0. (Alternatively, you could subtract in the ‘other’ direction and look for the probability that [size of bolt − size of nut] ≥ 0). Draw the distribution of the combination.

Answers

Answer:

- The probability that a bolt is too large for its nut = 0.00621

- The image of the drawing of this combined distribution is shown in the attached file to this solution.

Step-by-step explanation:

When independent, normal distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

For this question, the first distribution is the size of a nut, with mean 10 mm and a variance of 0.02

Second distribution is the size of a bolt, with mean 9.5 mm and a variance of 0.02.

The combined distribution is [size of nut − size of bolt]

Hence, λ₁ = 1, λ₂ = -1

μ₁ = 10 mm

μ₂ = 9.5 mm

σ₁² = 0.02

σ₂² = 0.02

Combined Mean = (1×10) + (-1×9.5) = 0.5 mm

Combined Variance = [(1)² × 0.02] + [(-1)² × 0.02] = 0.04

So, the combined distribution is also a normal distribution with a Mean of 0.5 mm and a variance of 0.04.

Standard deviation = √variance = √0.04 = 0.2 mm

The probability that a bolt is too large for its nut, [size of nut − size of bolt] ≤ 0, P(X ≤ 0)

To obtain this required probability, we first normalize/standardize 0 mm

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (0 - 0.5)/0.2 = - 2.50

To determine the required probability

P(x ≤ 0) = P(z ≤ -2.50)

We'll use data from the normal probability table for these probabilities

P(x ≤ 0) = P(z ≤ -2.50) = 0.00621

The image of the drawing of this combined distribution is shown in the attached file to this solution.

Hope this Helps!!!

In the months leading up to an election, news organizations conduct many surveys to help predict the results of the election. Often news organizations will increase the sample size in the last few weeks before the election. Which of the following is the primary reason they increase the sample size?
A. A larger sample size gives a narrower confidence interval.
B. A larger sample size allows more people to give their input.
C. A larger sample size gives a higher confidence level.
D. A larger sample size means the sampling method isn’t as important.

Answers

Answer:

A. A larger sample size gives a narrower confidence interval.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

As the sample size increases(n increases), the margin of error decreases, given a narrower, more precise confidence interval.

So the correct answer is:

A. A larger sample size gives a narrower confidence interval.

What is the solution to this equation

Answers

Answer:

x=-10

Step-by-step explanation:

x+8=-2

x=-10 (Subtract 8)

Answer:

-10

Step-by-step explanation:

1. Write it out.

x+8=-2

2. Get x by itself.

To do this, we have to move the 8, but to do that that we have to move it to the other side of the equation. Because the opposite of addition is subtraction, we have to subtract 8 by both sides.  x+8=-2

                                                                                        -8  -8

                                                                                      x=-10

And that's the answer! Hope this helped :)

                                                                   

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