a manufacturer knows that their items have a normally distributed length, with a mean of 14.7 inches, and standard deviation of 4.8 inches. if 25 items are chosen at random, what is the probability that their mean length is less than 12.4 inches?

The minimum score required for the job offer found using normal distribution is 629

To find the minimum score required for the job offer, we have to use the standard normal distribution formula.

Where Z-score can be calculated as,

Z = (x - μ) / σ

Z-score is the number of standard deviations from the mean.

μ = Mean = 455

σ = Standard Deviation = 124

Substituting the values, we get, Z = (x - μ) / σ= (x - 455) / 124

Probability value = 1 - 0.08 = 0.92

The probability of getting scores in the top 8% is 0.92.

By using the standard normal distribution table, we can find the corresponding z-value, where the area under the curve to the right of that value is 0.92.

So, the corresponding Z-value is 1.44.

Z-value = 1.4 = (x - 455) / 124

We can solve the above equation for x (minimum score required for the job offer).

x = Z * σ + μ = 1.4 * 124 + 455 = 628.6 ≈ 629

Round off the answer to the nearest whole number, we get the minimum score required for the job offer is 629.

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Answer:

168 ft^2

Step-by-step explanation:

18×8=144ft^2 for the area of the rectangle

8×6=48ft^2

48÷2=24ft^2 for the area of the triangle

144+24=168ft^2

The approximate length of each of the walking paths that passes through the center of the park and connects opposite sides of the outer or circumference walkway is 21 meters.

Let r₁ and C₁  be the radius and the circumference of the inner circle.

Let r₁​ and C₂  be the radius and the circumference of the outer circle.

The width of the circular path is (r₂​ −r₁ ) m.

Given, C₂ −C₁ = 132 m

⇒2πr₂−2πr₁ = 132m

⇒2π(r₂ −r₁ ) = 132m

⇒r₂−r₁ = 66/22/7

​⇒r₂−r₁ = 21

Thus, width of the circular path is 21 m.

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Answer:

False

Step-by-step explanation:

You can transform a function many times

:)

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Answer: Option C, (x - 4)(x - 5)

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Given:  [tex]\textsf{x}^2\textsf{ - 9x + 20}[/tex]

Find:  [tex]\textsf{Determine the factored form}[/tex]

Solution: In order to factor the given equation, we need to first determine two numbers which add up to -9 and multiply to become 20.  We can think of the factors of 20 which would add up to -9 and the one that matches that description would be -5 and -4.  These two numbers multiply to become 20 and combine to become -9.  Now that we have that information, we can break up the quadratic into two separate roots using the two numbers that we found.  

Therefore, the answer would be Option C, (x - 4)(x - 5).

The correct option is:

Steering wheel the proper distance from the body, at least a foot from the body, right foot should reach behind the brake pedal and knee should be slightly bent.

What is distance?

Distance is a numerical measurement of the amount of space between two objects or points.

distance between steering wheel and body ≥ 1 foot

length of driver's leg + distance from seat to brake pedal = distance from seat to brake pedal when leg is slightly bent

These considerations help to ensure that the driver is seated in a safe and comfortable position while operating the vehicle.

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Answer:

cosine

Step-by-step explanation:

The correct trig function would we use with the 35° angle to find the length of JG is,

⇒ Inverse cosine

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Angle = 35°

Hence, The correct trig function would we use with the 35° angle to find the length of JG is,

⇒ sec 35° = Hypotenuse / Base

⇒ 1/cos 35° = 9 / JG

Thus, The correct trig function would we use with the 35° angle to find the length of JG is,

⇒ Inverse cosine

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Asaad having median salary makes more money in comparison to Amahle who makes minimum salary.

From the attached box plot we have,

Box plot always shows,

First Minimum → Lower quartile → Median → Upper quartile → Maximum

The minimum salary for an actuary is equals to

Approximately 35 dollars

And the median salary for a CPA from the box plot is equals to,

Approximately 60 dollars

Here , by comparing the both the values we have,

Median salary for CPA (60 dollars ) is greater than minimum salary for actuary ( 35 dollars ).

The median salary for a CPA is typically higher than the minimum salary for an actuary.

Therefore, Asaad representing median salary makes more money than Amahle .

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The above question is incomplete, the complete question is:

Amahle makes the minimum salary for an actuary. Asaad makes the median salary for a CPA. Who makes more money?

Box plot is attached.

The value of x, the missing side which is the hypotenuse, is approximately 24.85 units.

To solve this problem, we can use the trigonometric function of sine, since we know the opposite side and we want to find the hypotenuse.

The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse:

sin(θ) = opposite/hypotenuse

In this case, θ is the angle 75 degrees, the opposite side is 24, and we want to find the hypotenuse x:

sin(75°) = 24/x

To solve for x, we can cross-multiply:

x * sin(75°) = 24

Then, we can divide both sides by sin(75°):

x = 24 / sin(75°)

Using a calculator, we get:

x = 24.85 units

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Answer:

union apparently

Answer:

u = 26.1°

Step-by-step explanation:

the 2 angles u and 44.1° combine to form the angle 70.2° , that is

u + 44.1° = 70.2° ( subtract 44.1° from both sides )

u = 26.1°

Answer:

11/16 is the answer or 22/32

The digit information are:

A) 900,000,000

B) 40,000

900,000,000: Nine hundred million. The first three digits (900) represent the hundred millions place, the next three digits (000) represent the ten millions place, and the last three digits (000) represent the ones (or units) place.

Lastly, 7009: Seven thousand nine. The first digit (7) represents the thousands place, the next two digits (00) represent the hundreds place (which are omitted since they are zeroes), and the last two digits (09) represent the ones (or units) place.

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See full text below

3.- Anota el valor posicional de las cifras encerradas

=

a) (9) 1(5) 23(6) 470

b) 38(4) 1(7) 6(9)

3.- Write down the place value of the enclosed figures

=

a) (9) 1(5) 23(6) 470

b) 38(4) 1(7) 6(9)

Answer:

w ≥ 13.5

Step-by-step explanation:

-(4/ 9)w ≤ -6

Multiply both side by - 1

(4/ 9)w ≥ 6

Cross multiply

4w ≥ 54

Divide both side by the coefficient of w

4w/4 ≥ 54/4

w ≥ 13.5

Answer:

#1. A. y=sin x + 2 Is the same as cos.

Step-by-step explanation:

The perimeter of the figure which is a rectangle with a semicircle on its shorter side would be =34.28ft

To calculate the perimeter of the figure, the perimeter of both the rectangle and the semicircle is calculated separately and added together.

The perimeter of rectangle = 2(l+w)

where;

l = 10ft

w = 4ft

perimeter = 2(10+4)

= 2× 14

= 28ft

Perimeter of semicircle = 2πr/2 = πr

where

π = 3.14

r = 4/2 = 2ft

perimeter = 3.14×2 = 6.28

Therefore, the perimeter of the given figure = 28+6.28 = 34.28ft.

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The factorizations of the given expressions are:

[tex]9x^{2}-6x+15[/tex] = 3(3x+5)(x-2)

[tex]2x^{2}+11x+5[/tex] = (2x+1)(x+5)

[tex]2x^{2}+3x-9[/tex] = (2x-3)(x+3)

[tex]10x^{2}+80x+70[/tex] = 10(x+1)(x+7)

[tex]3x^{2}-8x+4[/tex] = (x-2)(3x-2)

[tex]x^{2}-16[/tex] = (x+4)(x-4)

[tex]9x^{2}-6x+15[/tex]

We can first factor out the greatest common factor, 3:

[tex]9x^{2}-6x+15[/tex] = 3([tex]3x^{2}-2x-5[/tex])

[tex]3x^{2}-2x-5[/tex] = (3x+5)(x-2)

Putting it all together, we get:

[tex]9x^{2}-6x+5[/tex] = 3(3x+5)(x-2)

[tex]2x^{2}+11x+5[/tex]

We need to find two numbers that multiply to give 2x5=10 and add up to 11. Those numbers are 1 and 10:

[tex]2x^{2}+11x+5[/tex] = (2x+1)(x+5)

[tex]2x^{2}+3x-9[/tex]

We need to find two numbers that multiply to give 2x(-9)=-18 and add up to 3. Those numbers are 6 and -3:

[tex]2x^{2}+3x-9[/tex] = (2x-3)(x+3)

[tex]10x^{2}+80x+70[/tex]

We can first simplify the expression by factoring out 10:

[tex]10x^{2}+80x+70[/tex] = 10([tex]x^{2}+8x+7[/tex])

Now we need to factor the quadratic expression inside the parentheses:

[tex]x^{2}+8x+7[/tex] = (x+1)(x+7)

Putting it all together, we get:

10(x+1)(x+7)

[tex]3x^{2}-8x+4[/tex]

We need to find two numbers that multiply to give 3x4=12 and add up to -8. Those numbers are -2 and -6:

[tex]3x^{2}-8x+4[/tex] = (x-2)(3x-2)

[tex]x^{2}-16[/tex]

This is a difference of squares, which we can factor as:

[tex]x^{2}-16[/tex] = (x+4)(x-4)

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Answer:

largest angle ≈ 109.6°

Step-by-step explanation:

the largest angle in the triangle is the angle opposite the longest side.

Here that is the angle opposite side of 7.8 cm

let a = 7.8, b = 5.4 , c = 4.1 and A the largest angle , then

cosA = [tex]\frac{b^2+c^2-a^2}{2bc}[/tex]

        = [tex]\frac{5.4^2+4.1^2-7.8^2}{2(5.4)(4.1)}[/tex]

        = [tex]\frac{29.16+16.81-60.84}{44.28}[/tex]

       = [tex]\frac{45.97-60.84}{44.28}[/tex]

       = [tex]\frac{-14.87}{44.28}[/tex]

then

A = [tex]cos^{-1}[/tex] ( [tex]\frac{-14.87}{44.28}[/tex] ) ≈ 109.6° ( to 1 decimal place )

The probability of selling more than 5 properties in a week is 0.7494 (rounded to four decimal places).

The probability of selling more than five properties in a week would be calculated using the binomial distribution method. Binomial distribution is used to calculate the probability of an event happening, given a specific number of trials and assuming that each trial is independent of the others. In this case, we want to know the probability of selling more than five properties in a week.

The formula for the probability of selling more than five properties in a week is:
P(X > 5) = 1 - P(X ≤ 5)
Where P is the probability of selling any one property in a week, and X is the number of properties sold in a week.
Using the binomial probability formula, we can determine the probability of selling exactly k properties in one week:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where
n = 12 (total number of properties)
k = number of properties sold
p = 0.40 (probability of selling any one property in a week)
We can now calculate the probability of selling more than 5 properties in a week:

P(X > 5) = 1 - P(X ≤ 5)
P(X > 5) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5))
P(X > 5) = 1 - [(12 choose 0) * (0.40)^0 * (0.60)^(12-0) + (12 choose 1) * (0.40)^1 * (0.60)^(12-1) + (12 choose 2) * (0.40)^2 * (0.60)^(12-2) + (12 choose 3) * (0.40)^3 * (0.60)^(12-3) + (12 choose 4) * (0.40)^4 * (0.60)^(12-4) + (12 choose 5) * (0.40)^5 * (0.60)^(12-5)]
P(X > 5) = 1 - [0.000015 + 0.0003 + 0.003 + 0.018 + 0.068 + 0.161]
P(X > 5) = 1 - 0.250583
P(X > 5) = 0.749417

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To solve a system of equations, you need to find the values of the variables that satisfy both equations simultaneously. There are different methods to solve systems of equations, including substitution, elimination, and graphing. Here's an example of using substitution:

Solve the system of equations:

2x + y = 5

x - y = 1

From the second equation, we get x = y + 1. Substitute this expression for x into the first equation:

2(y + 1) + y = 5

Simplifying and solving for y, we get:

3y + 2 = 5

3y = 3

y = 1

Then, substitute y = 1 into x = y + 1 to get:

x = 2

So the solution to the system of equations is x = 2 and y = 1.

To solve a system of inequalities, you need to find the values of the variables that satisfy both inequalities simultaneously. There are different methods to solve systems of inequalities, including graphing and substitution. Here's an example of using graphing:

Solve the system of inequalities:

x + y ≤ 3

x - y > 1

First, graph the boundary lines of each inequality. For the first inequality, the boundary line is x + y = 3, which is a line with intercepts (3, 0) and (0, 3). To decide which side of the line to shade, test a point that is not on the line, such as (0, 0):

0 + 0 ≤ 3, which is true

Therefore, shade the side of the line that contains the origin.

For the second inequality, the boundary line is x - y = 1, which is a line with intercepts (1, 0) and (0, -1). To decide which side of the line to shade, test a point that is not on the line, such as (0, 0):

0 - 0 > 1, which is false

Therefore, shade the side of the line that does not contain the origin.

The shaded region that satisfies both inequalities is the region that is below the line x + y = 3 and to the right of the line x - y = 1. This region is a triangle with vertices (1, 2), (2, 1), and (2, 2).

I hope this explanation helps you with your homework!

Based on the measures of center, we can conclude that Wide Awake typically sells more coffee per hour compared to Perks A Lot.

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

To determine which coffee shop typically sells the most amount of coffee per hour, we need to compare the measures of center for both sets of data. The two common measures of center are the mean and the median.

Calculating the mean and median for both sets of data, we get:

Perks A Lot:

Mean = (10+3.5+3+5+2.5+7+8+5.5+9.5+6+9+4.5)/12 = 5.75

Median = the average of the 6th and 7th numbers when the data is arranged in order: 3, 3.5, 5, 5.5, 6, 7, 8, 9, 9.5, 10

Wide Awake:

Mean = (2.5+10+4+18+4+3+6.5+15+6+5+2.5)/11 = 6

Median = the average of the 5th and 6th numbers when the data is arranged in order: 3, 4, 5, 6, 6.5, 10, 15, 18

Comparing the measures of center, we can see that Perks A Lot has a lower mean and a higher median compared to Wide Awake. This suggests that Perks A Lot sells less coffee on average, but has more consistent sales with less extreme values. On the other hand, Wide Awake has higher average sales, but with a wider range of values.

Therefore, based on the measures of center, we can conclude that Wide Awake typically sells more coffee per hour compared to Perks A Lot.

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It is true that the areas of regions B and C added together equal the area of region A.

A region is an area of land that has a distinct physical or cultural identity. Regions are typically characterized by particular geographic features, such as mountains, rivers, or seas; by cultural attributes, such as language, religion, or government; or by economic activities, such as farming, mining, or industry.

Assume that A, B, and C will have diameters of a, b, and c, respectively.
Consequently, the semicircle's surface area is,
A = 1/2π(d/2)²
A = (π/8) d²
In a right-angled triangle, the square on the hypotenuse is equal to the particular sum of the squares of one two sides. With a right triangle,
a² = b² +c²   ----(1)
The areas for regions A, B, and  C will be  (π/8) a²,  (π/8) b², and  (π/8) c² accordingly.
Equation 1's (/8) multiplication yields,
(π/8) a² = (π/8) b² +(π/8) c²
The result is
Region A's area is equal to Region B's plus Region C's.

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Complete Question:

It is true that the areas of regions B and C formed by the semi circles added together equal the area of region A.

What is semi circle?

In geometry, a semicircle can be defined as a half circle made by cutting the circle into two halves. It is formed when a line passes through the center of a circle and touches the two ends of the circle which is the diameter of the circle.

Let us assume that A, B, and C will have diameters of a, b, and c, respectively.

By the formula of semicircle's surface area,

A = 1/2π(d/2)² where d is the diameter of the semi circle.

A = (π/8) a² [ since diameter of semicircle A is a]

By Pythagoras theorem, In a right-angled triangle, the square on the hypotenuse is equal to the  sum of the squares of  two sides.

So here from the right angled triangle we get,

a² =b² +c²   ----(1)

The area for region A is  (π/8) a²

The area of  region B is (π/8) b²

and  the area of region C is (π/8) c²

Now, Area of region B + Area of region C

= (π/8) b² + (π/8) c²

= (π/8) ( b² +c² )

= (π/8) a² [ from equation (1)]

Hence , Region A's area is equal to Region B's plus Region C's area.

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By answering the presented question using inequality, , we may conclude that Therefore, the equation of the line passing through the points (1,2) and (2,3) is

An inequality in mathematics is a link between two expressions or values that is not equal. As a result, inequality results from imbalance. An inequality in mathematics is a relationship between two values that are not equal. Equality and inequality are not the same thing. The not equal sign is often used to indicate that two values are not equal (). To contrast values, various disparities—no matter how small or large—are used. By changing the two sides until just the variables are left, many fundamental inequalities can be resolved. Yet, a variety of causes fuel inequality: On both sides, negative values are divided or added. Trade right and left.

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation:

[tex]y-ylm(x-x1) = \\m = (y^2 - y1)/(x^2 − x^1) \\m = (3-2)/(2-1) = 1\\ m = y-2=1\\(x-1) y-2=x-1\\y = x+1[/tex]

Therefore, the equation of the line passing through the points (1,2) and (2,3) is

D) y=x+1

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The fractions that are greater than 3/8 are option A. 1/2, option B. 4/5, and option D. 2/3.

To compare fractions, we need to make sure they have the same denominator. In this case, we can convert all the fractions to have a denominator of 8:

3/8 = 3/8

1/2 = 4/8

4/5 = 6.4/8

1/3 = 2.7/8

2/3 = 5.3/8

2/12 = 1/6 = 1.3/8

Now we can see which of these fractions are greater than 3/8:

3/8 = 3/8

4/8 = 1/2 > 3/8

6.4/8 > 3/8

2.7/8 < 3/8

5.3/8 > 3/8

1.3/8 < 3/8

So, the fractions that are greater than 3/8 are 1/2, 4/5, and 2/3.

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The complete question goes thus:

Which of the fractions below are greater than 3/8? Select three.

A. 1/2

B. 4/5

C. 1/3

D. 2/3

E. 2/12

To find the number of degrees the minute hand turned from its first position to its second position, we need to find the difference between the two angles formed by the minute and hour hands.

In the first position, the minute hand forms a 46° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 10 and 11, we know that the hour hand has moved 1/6th of the way from 10 to 11, or 30°. Therefore, the angle between the hour hand and the 12:00 position is 120° + 30° = 150°. So the minute hand is 46° away from 150°, or 104°.

In the second position, the minute hand forms an 84° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 11 and 12, we know that the hour hand has moved 1/2 of the way from 10 to 11, or 150°. So the minute hand is 84° away from 150°, or 234°.

To find the number of degrees the minute hand turned, we subtract the two angles: 234° - 104° = 130°.

Therefore, the minute hand turned 130° from its first position to its second position.

Answer:

As we approach the turn of the millennium, it is natural to wonder what the future holds. For a local magazine, predicting trends and changes in the community is essential to staying relevant and informative. In the year 2001, I predict that our city will continue to grow and evolve in exciting ways.

One major focus for our magazine should be on technology. As we enter a new era of digital communication and information sharing, it will be important to keep readers informed about new developments and how they impact our daily lives. This could include coverage of local tech startups, updates on internet infrastructure projects, or profiles of innovative individuals using technology to make a difference in our community.

Another area of interest will be sustainability. As concerns about climate change become more urgent, I predict that our city will take bold steps towards becoming more environmentally friendly. Our magazine can highlight initiatives like bike lanes, green energy projects, or sustainable food systems.

Overall, I believe that by focusing on these key areas – technology and sustainability – our local magazine can remain relevant and engaging for years to come.

BRAINLIEST please

thanks

Answer:

Step-by-step explanation:

[tex]\tt 5x-2+x=9+3x+10[/tex]

Combine like terms:-

[tex]\tt 5x+x-2=9+3x+10[/tex]

[tex]\tt \:5x+x=\bf 6x[/tex]

[tex]\tt 6x-2=9+3x+10[/tex]

Add numbers:-

[tex]\tt 9+10=\bf 19[/tex]

[tex]\tt 6x-2=3x+19[/tex]

Add 2 to both sides:-

[tex]\tt 6x-2+2=3x+19+2[/tex]

[tex]\tt 6x=3x+21[/tex]

Subtract 3x from both sides:-

[tex]\tt 6x-3=3x+21-3[/tex]

[tex]\tt 3x=21[/tex]

Divide both sides by 3:-

[tex]\tt \cfrac{3x}{3}=\cfrac{21}{3}[/tex]

[tex]\tt x=7[/tex]

____________________

Hope this helps! :)

Answer: X = 17

Step-by-step explanation: First combine like terms on both sides so the 5x + x on the left side for a total of 6x and the 9 + 10 on the right side for a total of 19. Then get your variables and numbers all to one side each so you would add 2 from the left to the right and cancel out and then subtract 3x from the right to the left and cancel out. Finally you would divide 21 by 3.

5x-2+x=9+3x+10

6x-2=19+3x

+2 -3x

3x=21

/3. /3

x=7

Answer: 520

Step-by-step explanation:

if pizza times pizza times pizza equals 27, the square root of twenty seven is three. so three time three equals 9, then times cheeseburger(which equals 2) would equal 18. so 2*2+2= taco(8)

Answer: Anything greater than 3

Step-by-step explanation:

The answer can be any number greater or equal to 3. This is because if you subtract 3 by 3 you get 0 and zero is still greater than -2 making the inequality true

The approximate value of z for the given logarithm in base-e is found to be: z = 0.8959 (nearest thousandth).

A power wherein a number must all be increased in order to obtain another number is known as a logarithm.

The conception of hyperbolic sectors in calculating the area of a rectangular hyperbola gave rise to the concept of log. Several formats, such as exponential and integration of 1/x, can be used to express a log.

The given expression is-

9. [tex]e^{2z}[/tex] = 54.

On simplification:

[tex]e^{2z}[/tex] = 54 / 9

[tex]e^{2z}[/tex] = 6

Now, taking ㏑ both side:

㏑ [tex]e^{2z}[/tex] =  ㏑ 6

using the power rule of ㏑.

2z.  ㏑e =  ㏑6

we know that,  ㏑e = 1

2z * 1 =  ㏑6

z = ㏑6 / 2

z = 1.79 / 2

z = 0.8959

Thus, the approximate value of z for the given logarithm in base-e is found to be: z = 0.8959 (nearest thousandth).

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