Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 75 GPa and 1.7 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.)

Required:
a. Calculate P(79 <= P <= 81) when n = 25.
b. How likely is it that the sample mean diameter exceeds 81 when n = 36?

Answer:

180

Step-by-step explanation:

add 1% to 31.50 to get 31.815

then take the total 5276.70 and divide by 31.815

Answer:

c

Step-by-step explanation:

Marl me as brainliest answer c

The p-value for the given test is 0.0901.

Given that, a pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%.

Standard deviation is the degree of dispersion or the scatter of the data points relative to its mean, in descriptive statistics.

Given, Mean = 3.07, μ=3%, σ =0.4% and n=64.

Hypothesis test [tex]H_{0}[/tex];μ=3 and [tex]H_{1}[/tex];μ>3

We need to test the null hypothesis against the alternative hypothesis, we reject the null hypothesis and accept the alternative hypothesis.

When x>x critical

x critical = μ+Z+σ

Z = (x-μ)/(σ/√n)

= (3.07-3)/(0.4/√64)

= (0.07)/0.05

= 1.4

α = 5 and [tex]z_{0.05[/tex]= 1.645

If Z>[tex]Z_{0.05[/tex]

1.4 > 1.645

Therefore, we do not reject null hypothesis at 5% significant level.

There is sufficient evidence that the mean impurity in concentration pills is 3% or less than 3%.

p-value

p−value=P(Z>1.4)

=1−P(Z<1.4)

=1−0.90988

=0.0901

Therefore, the p-value for the given test is 0.0901.

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Answer:

first one is f(x)=-5

second one is f(x)=7

third one is x=-3

4th one is x=0

5th one is f(x)=1

6th one is x=-4

Step-by-step explanation:

first one. plug in x as -2:

f(x)=2*-2-1=-4-1=-5

second one is the same way:

f(x)=4*2-1=8-1=7

third one is a different one:

2x-1=-7

2x=-6

x=-3

4th one is the same way:

2x-1=-1

2x=0

x=0

5th way is the same thing as previous:

f(x)=2*1-1=2-1=1

Finally, the 6th one is the same thing as the 4th one:

2x-1=-9

2x=-8

x=-4

Done!

Answer:

163 miles

Step-by-step explanation:

set up a ratio based on 49 miles in 1 hour (60 minutes):

let 'd' = distance in 3hrs, 20 min

3hrs, 20 min = 200 minutes

49/60 = d/200

cross-multiply:

60d = 9800

d = 163.3

The distance you can travel in 3 hours 20 minutes if you drive on average 49 miles per hour will be 163.33 miles.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

The speed of the vehicle is 49 miles per hour. And the time is 3 hours 20 minutes.

Convert the time completely hours. Then we have

T = 3 + 20/60

T = 3.33 hours

The distance you can travel in 3 hours 20 minutes if you drive on average 49 miles per hour will be

D = 49 x 3.33

D = 163.33 miles

The distance you can travel in 3 hours 20 minutes if you drive on average 49 miles per hour will be 163.33 miles.

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Answer:

Its the first one

Step-by-step explanation:

4x4=16 8x2=16 so its the first

These three lines should say:

4 rows with 16 boxes in each row

8 rows with 8 boxes in each row

16 rows with 4 boxes in each row

Answer:

1.  n=10

2. n=35

3. n=6

4. n=0 ? not sure for this one. two variables in the proportion

5. n=36

Step-by-step explanation:

set each set of proportion equal to each other and do cross multiplication

hope this helps !

how are you ?

Answer:

Step-by-step explanation:

Please take a look of the attached photo for the solution.

Answer:

C

Step-by-step explanation:

Answer:

The first option as you do what is in parentheses first.

Step-by-step explanation:

Answer:

x < -5

Step-by-step explanation:

3 ( -2x - 4 ) > 18

→ Expand the brackets

-6x - 12 > 18

→ Add 12 to both sides

-6x > 30

→ Divide both sides by -6

x < -5

Answer:

[tex]\boxed {\boxed {\sf x< -5}}[/tex]

Step-by-step explanation:

We are asked to solve the following inequality for x.

[tex]3(-2x-4) > 18[/tex]

Solve for x by isolating it and performing the inverse operations.

3 is being multiplied by (-2x-4). The inverse operation of multiplication is division. Divide both sides of the inequality by 3.

[tex]\frac {3(-2x-4)}{3} > \frac{18}{3}[/tex]

[tex](-2x-4) > \frac{18}{3}[/tex]

[tex]-2x-4 > 6[/tex]

4 is being subtracted from -2x. The inverse operation of subtraction is addition. Add 4 to both sides of the inequality.

[tex]-2x-4+4 > 6+4 \\[/tex]

[tex]-2x > 10[/tex]

x is being multiplied by -2. The inverse operation of multiplication is division. Divide both sides by -2.

[tex]\frac {-2x}{-2} > \frac {10}{-2}[/tex]

[tex]x> \frac {10}{-2}[/tex]

Since we divided by a negative number, the inequality sign must be flipped.

[tex]x< \frac{10}{-2}[/tex]

[tex]x < -5[/tex]

Answer:

1/5

Step-by-step explanation:

First and foremost, I want to simplify these fractions, just to make everything a lot easier when I actually get to dividing. 5/50 can be divided by 5/5 to get 1/10, and 15/30 can be divided by 15/15 to get 1/2. So, now we're dividing 1/10 by 1/2.

To divide fractions, we can multiply the first fraction (in this case, 1/10) by the reciprocal of the second fraction (in this case, 1/2). The reciprocal of 1/2 is 2, so we can multiply 1/10 by 2 to find our answer. 1/10 × 2 = 2/10, or 1/5, so this is our final answer.

Hopefully that's helpful! If you have any further questions, let me know. :)

The quotient of given fractions is 1/5.

Given that, 5/50 divided by 15/30.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Now, 5/50 ÷ 15/30

Keep the first fraction 5/50 same change the division symbol and reciprocate the fraction 15/10

That is, 5/50 × 30/15

= 1/10 × 2/1

= 2/10

= 1/5

Therefore, the quotient of given fractions is 1/5.

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Answer:

3x + 3

Step-by-step explanation:

yeah-ya........ right?

Answer:

Yes, 8.5 is greater than 0.85

Step-by-step explanation:

In counting from 0 to the highest possible positive number in steps of 0.01, we come across 0.85 before 8.5. This means that 8.5 is greater than 0.85

Answer:

23.35

Step-by-step explanation:

Answer:

x=77

Step-by-step explanation:

128+95+60+x=360

283+x=360

x=77

Answer:

Adult males are flame-orange and black, with a solid-black head and one white bar on their black wings. Females and immature males are yellow-orange on the breast, grayish on the head and back, with two bold white wing bars

Answer:

slope:

-b/a

y-intercept:

1

The angle fact that is necessary to prove that m∠1 + m∠2 = m∠2 + m∠3 is: linear pair are supplementary.

Thus,

∠1 and ∠2 are on a straight line, therefore,

m∠1 + m∠2 = 180°

∠2 and ∠3 are on a straight line, therefore,

m∠2 + m∠3 = 180°

Thus:

m∠1 + m∠2 = m∠2 + m∠3

Therefore, the angle fact that is necessary to prove that m∠1 + m∠2 = m∠2 + m∠3 is: linear pair are supplementary.

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Answer:

C.

Ax + 1 = x A + 1

Bx + 2 = x B + 2

Cx + 3 = x C + 3

A = x C + 3

B = x C + 3

C = x C + 3

I'm not really sure about the answer but i hope it helps

A ........................ig

Answer: 60

Step-by-step explanation:

list all of the multiples and choose the least common number

10:   10  20  30  40  50  60  70  80  90  100

12:   12  24  36  48  60  72  84  96

find a number that shares all the prime factors of the two numbers

prime factors of 10: 2, 5

prime factors or 12: 2, 2, 3

LCM = 60

[tex]\qquad[/tex]____________________

It’s given–

[tex] \bf{\underline{\underline{\dag According\ to\ the\ question:-}}} [/tex]

[tex]\qquad[/tex][tex] \pink{\bf\longrightarrow {x+( x +2)+(x+4) = 42} }[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 3x +6 =42[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 3x = 42-6[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 3x =36[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow x = \cancel {\dfrac{36}{3}}[/tex]

[tex]\qquad[/tex][tex]\pink{ \bf\longrightarrow x = 12}[/tex] ( which is our lowest integer.)

[tex]\qquad[/tex]____________________

Given :

[tex] \: [/tex]

Solution :

Let us assume the three consecutive even numbers be "x" , "(x + 2)" and "(x + 4)" . Here x is the smallest number .

So,

According to the Question :

x + (x + 2) + (x + 4) = 42

⇢x + x + 2 + x + 4 = 42

⇢ x + x + x + 2 + 4 = 42

⇢ 3x + 6 ⠀⠀⠀⠀⠀ = 42

⇢ 3x ⠀⠀⠀⠀⠀⠀⠀⠀= 42 - 6

⇢ 3x ⠀⠀⠀⠀⠀⠀⠀⠀= 36

⇢ x ⠀⠀⠀⠀⠀⠀⠀⠀= 36/3

⇢ x ⠀⠀⠀⠀⠀⠀⠀⠀ = 12

Hence, 12 is the smallest consecutive even number.

Answer:

f(x) = 8.917x³ + 2x² + 0.083x - 7

Step-by-step explanation:

f(x)= y

Let the coefficients of x³, x², x be a, b, c and the constant be d

y= ax³ + bx² + cx + d

When y = -65, x = -2

-65= a(-2)³ + b(-2)² + c(-2) + d

-65= -8a + 4b - 2c + d ...eq. 1

When y = -14, x = -1

-14= a(-1)³ + b(-1)² + c(-1) + d

-14= -a + b - c + d ...eq. 2

When y = -7, x = 0

-7= a(0)³ + b(0)² + c(0) + d

-7 = d ...eq.3

When y = 4, x = 1

4= a(1)³ + b(1)² + c(1) + d

4= a + b + c + d ...eq. 4

when y = 78, x = 2

78 = a(2)³ + b(2)² + c(2) + d

78= 8a + 4b + 2c + d ...eq. 5

From eq. 3, d is - 7

putting d as - 7 in equations 1, 2, 4 and 5

In eq. 1,

-65= -8a + 4b - 2c - 7

-58= -8a + 4b - 2c ...eq. 6

In eq. 2

-14= -a + b - c - 7

-7= -a + b - c ...eq. 7

In eq. 4,

4= a + b + c - 7

11= a + b + c ...eq. 8

In eq. 5

78= 8a + 4b + 2c - 7

85= 8a + 4b + 2c ...eq.9

Subtracting eq. 9 from eq. 6

-143 = -16a - 4c... eq 10

subtracting eq. 8 from eq 7

-18= -2a - 2c

9= a + c

a = 9 - c ...eq 11

putting a as 9 - c in eq. 10

-143 = -16(9 - c) - 4c

-143 = -144 + 16c - 4c

1= 12c

c = 1/12 or 0.083

putting c as 1/12 in eq. 11

a = 9 - 1/12

a = 107/12 or 8.917

Putting a as 107/12 and c as 1/12 in eq. 8

11= 107/12 + b + 1/12

multiplying through by 13

132 = 107 + 12b + 1

132 - 108 = 12b

24= 12b

b = 24/12

= 2

Therefore, a= 8.917, b= 2, c= 0.083 and d = -7

f(x) = 8.917x³ + 2x² + 0.083x - 7

Answer:

$0.03

Step-by-step explanation:

chips: 7.84/16=0.49

pretzels: 12.48/24=0.52

0.52=0.49=0.03

Based on the information given the tax rate if the house was valued at $100,000 is 60%.

Let $600= x%

Let $100,000=100%

Let the tax rate=x

Proportion:

600/100,000=x/100

Hence,

x=600×100/100,000

x=60,000/100,000

x=60/100

x=0.6%×100

x=60%

Inconclusion  the tax rate if the house was valued at $100,000 is 60%.

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The tax rate of a house valued at $100,000 with a property tax of $600 is 0.6%. or $6 per $1,000 of property value.

The property tax is the levy imposed on the assessed value of the property of an individual or corporation.

Property tax is usually levied as a percentage of the assessed value.

Property tax = $600

House value - $100,000

Tax rate = 0.6% ($600/$100,000 x 100)

Thus, the tax rate of a house valued at $100,000 with a property tax of $600 is 0.6%. or $6 per $1,000 of property value.

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Answer:

Slope: -2/3

Y Intercept: 0,-3

Step-by-step explanation:

To find the slope, use the formula (y1-y2)/(x1-x2)

(1-(-1))/(-6-(-3))

-2/3

So the slope is: -2/3

If the slope is 3/2, then the using the formula of y=mx+b, we can find the y intercept (b)

y = -2/3x + b

insert any point of x and y

-1 = -2/3(-3)+b

-1=-2+b

so b = -3

thus, the Y intercept is 0,-3

See graph attached for graph

Answer:

5 miles

Step-by-step explanation:

add the points together.

it seems like each point is how many miles they ran each day.

1/4 + 2(1/2) + 3/4 + 3(1) = 5

Answer:

its 70/11 or 6.36

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

20 / 9 = 2.222222222223

100 / 45 = 2.222222222223

9 is 45% of 20 and 45 is 45% of 100.