A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 169 cm and a standard deviation of 2.2 cm. For shipment, 10 steel rods are bundled together.

Answer the following rounding to three decimals where appropriate.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm.

P(M > 168.58) = ???

The conclusion on the null hypothesis is B. Reject H₀ because the P-value is less than or equal to a.

It is posited that the mean pulse rate for a specific grouping of adult males equals 76 bpm as set forth by the null hypothesis. In its place, an alternative hypothesis suggests this figure does not reflect actuality.

At a given significance level identified by alpha = 0.05, rejection of the null hypothesis requires us to identify a P-value lesser than or equal to 0.05.

The P-value determined within the question happens to be below such a threshold at 0.0075, which results in the rejecting of the null hypothesis.

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Answer: 2 hours 15 minutes

Step-by-step explanation:

To solve this problem, we need to use the formula:

distance = speed x time

First, let's calculate the distance Jaswat covered in the first 1 1/2 hours:

distance = speed x time

distance = 6 Km/h x 1.5 h

distance = 9 Km

So, Jaswat covered 9 Km in the first 1 1/2 hours. He still had to cover 12 Km - 9 Km = 3 Km.

Now, we need to calculate the time Jaswat took to cover the remaining 3 Km at a speed of 4 Km/h:

distance = speed x time

3 Km = 4 Km/h x time

time = 3 Km / 4 Km/h

time = 0.75 hours = 45 minutes

Therefore, Jaswat took 1 1/2 hours + 45 minutes = 2 hours 15 minutes to complete the journey.

234 2/5 is equivalent to 1172/5.

234 2/5 is a mixed number, which means it is a combination of a whole number and a fraction.

To convert it to an improper fraction, we need to multiply the whole number by the denominator of the fraction and add the numerator.

The result becomes the new numerator, and the denominator stays the same.

In this case, we have:

234 2/5 = (234 x 5 + 2) / 5

= 1172/5

Therefore, 234 2/5 is equivalent to 1172/5 as an improper fraction.

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Answer:  (5, -1)

Step-by-step explanation:

format:  f(x)

in  f(5)=-1       x=5

also sometimes f(x) is called y so  y= -1

put into ordered pair format

(5, -1)

The height of the larger cone is 71.13 meters

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Scale factor = h1/h2

So, we have

h1/h2 = √(1883/7352)

substitute the known values in the above equation, so, we have the following representation

36/h2 = √(1883/7352)

So, we have

h2 = 36 * √(7352/1883)

Evaluate

h2 = 71.13

Hence, teh height is 71.13

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It will take approximately 6.24 years to have enough money for the down payment saved.

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = the amount of money we want to have (in this case, $35,000)

P = the initial amount we have (in this case, $20,000)

r = the annual interest rate (in this case, 12%)

n = the number of times interest is compounded per year (let's assume it's compounded monthly, so n = 12)

t = the number of years we're investing for (this is what we want to find)

Substituting the values we know:

$35,000 = $20,000(1 + 0.12/12)^(12t)

Simplifying:

1.75 = (1 + 0.01)^(12t)

Taking the natural logarithm of both sides:

ln(1.75) = 12t ln(1.01)

Dividing both sides by 12 ln(1.01):

t = ln(1.75) / (12 ln(1.01))

Using a calculator:

t ≈ 6.24 years

Therefore, it will take approximately 6.24 years to have enough money for the down payment saved.

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Answer:

11-2x not 13x

Step-by-step explanation:

\(6-2)x + (5-4)x does = 13x

If there were parentheses as in the 2nd line, everything else is correct

the mistake is going from

6-2x + 5-4x to

(6-2x) + (5-4)x

PEMDAS is the order of operations. P for parentheses 1st, Multiplication 3rd, addition 4th, subtraction 5th

(there are no exponents or division or parentheses, so it's just M, A and S that apply)

combine like terms, 2x-4x =-2x

combine the constant terms 6+5 = 11

6-2x +5-4x = 11-2x

The mistake was assuming parentheses when they aren't there.

correct answer is 11-2x not 13x

Answer: 70, 6

Step-by-step explanation:

(a)  For <F  that is the same as <D.  The image has little hash marks to indicates the sides across from those angles are the same; therefore, the angles are the same

All of the angles are = 180   if you subtract <E, you are left with 140 to be split between <F and <D

<F= 70

(b) all of the sides are the same because all the angles are the same

so AB=6

The median is the accurate reflection of the data

501, 900, 971, 977, 1071

The mean would be

summation of the values

mean = 884

The median is the value that occurs in the middle = 971

The median would be more accurate reflection of the data. 501 is an outler. This is what caused us to have a mean that is c loser to 884. Hence we have 971 the median to be more accurate reflection of the data

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The length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).

To use the arc length formula, we need to find the derivative of the curve y = 5 - 4x:

y' = -4

Then, we can use the arc length formula:

L = ∫[a,b] √(1 + (y')^2) dx

where a and b are the limits of integration. In this case, a = -2 and b = 2.

L = ∫[-2,2] √(1 + (-4)^2) dx

= ∫[-2,2] √(17) dx

= √(17) * [x]_(-2)^(2)

= 4√(17)

So the length of the curve y = 5 - 4x, -2 ≤ x ≤ 2, is 4√(17).

To check this answer, we can note that the curve is a line segment with endpoints (-2, 13) and (0.75, 1), and we can calculate its length using the distance formula:

L = √((0.75 - (-2))^2 + (1 - 13)^2)

L = √(18.25 + 144)

L = √(162.25)

L = 4√(17)

This matches our previous answer, so we can be confident that the length of the curve is 4√(17).

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The solution of the given system of equations is (1, 2.5)

From the graph attached, it van be seen that two intersecting lines represent the system of equations.

And the solution of the system of equations is a common point where these lines intersect.

The graph shows both the line are intersecting each other at (1, 2.5).

Therefore, the solution of the given system of equations will be (1, 2.5).

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The exponential function that gives the amount A(t) that the plant earns per hour t years after it opens is [tex]A(t) = 55(1.07)^t[/tex]

A manufacturer earned $55 per hour of labor when it opened.

Each year the manufacturer earns an additional 7% per hour.

Since the manufacturer earns an additional 7% per hour each year, the amount earned per hour can be represented as follows:

[tex]A(t) = 55(1 + 0.07)^t[/tex]

where t is the number of years after the plant opened. T

This can be simplified as function:

[tex]A(t) = 55(1.07)^t[/tex]

Therefore, the exponential function that gives the amount A(t) that the plant earns per hour t years after it opens is [tex]A(t) = 55(1.07)^t[/tex]

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Answer:

35%

(I replaced the 1st digit by a and the second digit by b)

Answer:

Step-by-step explanation:

Its simple, you need to find x

4 days the same amount of time (x) gives 48 min
4x = 48

x = 48/4

x = 12

then to get the amount of minutes in 9 days it would be:

9x=days

9(12)=108

the answer would be 108 min

Answer:

108 mins

Step-by-step explanation:

48 mins/4 days = x mins/9 days

4x= 432

x=108 mins

Answer:

x= 3 cm

Explanation:

I am bad at it

Answer:

Step-by-step explanation:

so the entire angle sum is 180 degrees then subtract 61 from 180 and divide by 2. hope it helps :)

If Joe lowers the price he charges per pizza, he will sell more pizzas. option B

To sell more pizza, Joe must decrease the price he charges per unit. The law of demand dictates that when a product's cost decreases, its quantity demanded rises resulting in an increased sales volume.

It follows then that if Joe reduces his pizza prices more people will be inclined to purchase it creating this increase in sales . Nonetheless, whether Joe’s profit will rise or diminish depends on the extent of the rise in sales compared to the lowering of the price.

Even if there is a reduction in the price of every pizza, if the resultant sales volume is significant enough, Joe’s profit margin could still experience a positive turn.

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The valid row-operation which needs to be performed on the given matrix to get "1" in position of row1 and column1 are "R₁ → 2R₁ + R₂" and then "R₁ → R₁/2".

The "row-operation" is a type of matrix operation that involves swapping, scaling, or adding rows in a matrix. These operations are used to transform a matrix into a more reduced form.

The Augmented matrix on which we have to perform the "row-operation" is

⇒ [tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex],

To get "1" in first row and first column,

The first row-operation is R₁ → 2R₁ + R₂

We get,

⇒ [tex]\left[\begin{array}{ccc}7\times 2-12&-4\times 2+7&8\times 2-13\\-12&7&-13\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}14-12&-8+7&16-13\\-12&7&-13\end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{ccc}2&-1&3\\-12&7&-13\end{array}\right][/tex],

The second , row-operation to get a "1", is R₁ → R₁/2,

We get,

⇒ [tex]\left[\begin{array}{ccc}2/2&-1/2&3/2\\-12&7&-13\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}1&-0.5&1.5\\-12&7&-13\end{array}\right][/tex].

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Answer:

We can use the formula for compound interest to calculate the amount and interest:

A = P * (1 + r/n)^(n*t)

I = A - P

Where:

P = Principal = $15,300

r = Rate = 8% = 0.08

n = Compounding frequency per year = 4 (since it is compounded quarterly)

t = Time period = 6 years

Plugging in the values, we get:

A = 15,300 * (1 + 0.08/4)^(4*6) = $23,659.28

I = 23,659.28 - 15,300 = $8,359.28

Therefore, the amount after 6 years is $23,659.28 and the interest earned is $8,359.28.

I hope this helps.

Answer:

Step-by-step explanation:

decimal: 0.44444444444

fraction: 4/9

The percent of the area that is not covered is 80 percent

In mathematics area is defined as the absolute or total space that an object or shape occupies. It is usually measured using centimeters, cm ² square or the use of meter square m ².

area of tent

= (10 - 0) * (6 - (-3))

= 90

The area of the campsite would be:

(25 - (-5) x (10 - (-5))

= 450

Then the area would be 450 - 90

= 360

the percentage that is not covered by tent = 360 / 450 x 100

= 80 percent

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Answer: e

Step-by-step explanation:

Answer:Valid

Step-by-step explanation:

Answer:

x = [tex]\frac{5u+4y}{2-6z}[/tex]

Step-by-step explanation:

2(x - 2y) = 6xz + 5u ← distribute parenthesis on left side

2x - 4y = 6xz + 5u ( add 4y to both sides )

2x = 6xz + 5u + 4y ( subtract 6xz from both sides )

2x - 6xz = 5u + 4y ← factor out x from each term on the left side

x(2 - 6z) = 5u + 4y ← divide both sides by (2 - 6z)

x = [tex]\frac{5u+4y}{2-6z}[/tex]

A ski lodge inspects 80 skis and discovers four that are faulty. The skis that are likely to be defective are 21.

It is assumed that there are 80 skis, four of which are faulty.

As a result, the total number of outcomes is 80.

Positive outcomes = 4

Let [tex]E_{1}[/tex] represent the event of selecting a faulty. As a result, the likelihood of selecting a defective ski is expressed mathematically as follows.

[tex]E_{1}[/tex] = Favorable case of defective / Total number of skis

= 4 / 80

= 1 / 20

=0.05

Skis will be discovered in 5% of cases.

So, the event of choosing a defective is 4 / 80.

If the total number of skis is 420, then the number of defective skis will be:

4 / 80 × 420

= 1/20 × 420

= 21

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Correct question:

A ski lodge inspects 80 skis and finds 4 to be defective. The lodge has 420 skis. Predict the number of skis that are likely to be defective.

The first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

= n(E) / n+S)

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Thus, the first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners

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Drag tiles to fill in the blanks to complete the expression that could be used to predict the number of winners of a game. Tiles may be used once or not at all. A)Total Number of Possible Outcomes B)Number of Winners C)Number of Unfavorable Outcomes D)Number of Games P(event) = Number of Favorable Outcomes _________________________ ????????????????????????????? = ????????????????????????????? _________________________ 11 Total Number of Contestants

If the line passes through the point (2,8) that cuts off the least area from the first quadrant, the slope is 8/3 and the y-intercept is 0.

To find the equation of the line that passes through the point (2, 8) and cuts off the least area from the first quadrant, we need to first determine the slope of the line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

We can use the point-slope form of the equation of a line to find the slope. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line. Plugging in (2, 8) as the point, we get:

y - 8 = m(x - 2)

Next, we want to minimize the area that the line cuts off in the first quadrant. Since the line passes through the origin (0, 0), the area cut off by the line in the first quadrant is equal to the product of the x- and y-intercepts of the line.

We can express the x-intercept in terms of y by setting y = 0 in the equation of the line and solving for x:

0 - 8 = m(x - 2)

x = 2 + 8/m

The y-intercept is simply the y-coordinate of the point where the line intersects the y-axis, which is given by:

y = mx + b

8 = 2m + b

b = 8 - 2m

We can now express the area cut off by the line as:

A = x*y

A = (2 + 8/m)*8 - (8 - 2m)*2/m

A = (16 + 64/m) - (16 - 4m)/m

A = 64/m + 4m/m

To minimize the area, we can take the derivative of A with respect to m and set it equal to zero:

dA/dm = -64/m² + 4/m² = 0

64 = 4

m = 8

Plugging m = 8 into the equation for the x-intercept, we get:

x = 2 + 8/8 = 3

So the equation of the line is y = 8x/3.

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The conditional value probability is solved and P ( J ) = 0.1105

Given data ,

P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3

We can use Bayes' theorem to find P(J):

P(J | K) = P(K | J) * P(J) / P(K)

0.35 = 0.95 * P(J) / 0.3

0.35 * 0.3 = 0.95 * P(J)

0.105 = 0.95 * P(J)

P(J) = 0.105 / 0.95

P(J) = 0.1105

Hence , the probability is P ( J ) = 0.1105

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Since BD is the perpendicular bisector of AC, then AB = BC, which implies 2x - 8 = 5x - 17.

Solving for x, we have:

3(2x - 8) = 4425

6x - 24 = 4425

6x = 4451

x = 741.83

Rounding to the nearest whole number, we have x = 742.

Therefore, x = 742.