A packing plant fills bags with cement. The weight X kg of a bag of cement can be modelled by a normal distribution with mean 50 kg and standard deviation 2 kg.
a) Find P(X>53)
b) Find the weight that is exceeded by 99% of the bags
c) Three bags are selected at random. Find the probability that two weight more than 53kg and one weights less than 53 kg

Answer:

(1.5, -4)

Step-by-step explanation:

( -1, -5) and (4, -3)

[tex](\frac{-1+4}{2} ,\frac{-5-3}{2} )\\\\(\frac{3}{2} ,\frac{-8}{2} )\\\\(1.5,-4)[/tex]

Answer:

I would expect Emmy to get 8 hits in her next 16 tosses.

Emmy is to get 8 hits in her next 16 tosses.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that Emmy is tossing bean bags at a target. She hit the target on 9 out of her last 18 tries. Considering this data.

The probability is,

P = 9 / 18

P = 0.5

The expected number of the hits on the target in 16 tosses will be;-

Number = 16 x 0.5

Number = 8

Therefore, Emmy is to get 8 hits in her next 16 tosses.

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Answer:

Hello There!!

Step-by-step explanation:

1.×-10=13. 13+10=23

2.t+20=44. 44-20=24

3.y/5=7. 5×7=35

You do the inverse operations to find the unknown number.For example if it is minus you do plus. e.g x-7=19 . 19+7=26

hope this helps,have a great

Answer:

2 + 1 = 3

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Berverly already has = 2 pens

Berverly bought = 1 pen

Then to show this situation in numerical expression, we have to add both values, then

= 2 + 1 = 3

Hence, this shows that the total number of pens Berverly has after buying is 3.

Answer:

(2x+7)(x+7)

Step-by-step explanation:

Answer:

Ошйжй Щ отдйдй шубу Ц дцдць о о

Step-by-step explanation:

The third-degree Maclaurin polynomial for f(x) = sin(x) is P3(x) = x - (x^3) / 6.

To find the nth Maclaurin polynomial for the function f(x) = sin(x) when n = 3, we need to compute the polynomial up to the third-degree term.

The Maclaurin polynomial for a function f(x) centered at x = 0 is given by the formula:

Pn(x) = f(0) + f'(0)x + (f''(0)x^2) / 2! + (f'''(0)x^3) / 3! + ...

Let's calculate the nth Maclaurin polynomial for f(x) = sin(x) when n = 3:

First, we find the values of the function and its derivatives at x = 0:

f(0) = sin(0) = 0

f'(x) = cos(x), so f'(0) = cos(0) = 1

f''(x) = -sin(x), so f''(0) = -sin(0) = 0

f'''(x) = -cos(x), so f'''(0) = -cos(0) = -1

Using these values, we can write the Maclaurin polynomial:

P3(x) = 0 + 1x + (0x^2) / 2! + (-1x^3) / 3!

Simplifying further, we have:

P3(x) = x - (x^3) / 6.

Therefore, the third-degree Maclaurin polynomial for f(x) = sin(x) is:

P3(x) = x - (x^3) / 6.

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Answer:

35

Step-by-step explanation:

subtract highest and lowest numbers

Answer:

The question needs more information but you can see that all the numbers in the 1st column are multiplied by 6 to equal the number in column 2

Step-by-step explanation:

3 x6 =18

6 x 6= 36

9 x6= 54

12 x6 =72

Answer:

6, 8 and 10  and  -2, 0, 2

There are two roots x = -2 and 6,    

but the since I don't believe 0 is an even number the answer is 6, 8 and 10

I was incorrect according to G0ggle zero is an even number so another answer is  -2, 0, 2

Step-by-step explanation:

read the question and convert the English to mathematics

x, y and z    even consecutive number

y = x+2

z = y+2 = x+4

and

xyz = x³ + y² + 2z²                                   substitiute x terms  in for y and z

x(x+2)(x+4)  = x³ + (x+2)² + 2(x+4)²           solve for x by graphing on DEMOS

                                                                 x = -2, 6  solved algebraically below

x = -2   y=0   z=2

x = 6    y=8   z=10

Checked both answers

xyz = x³ + y² + 2z²

-2(0)2 = -8 + 0 + 8                  when x = -2

   0   =  0

and

6(8)(10)  =  6³ + 8² +2(10)²      when x = 6

   480   =  216+64+200

             =  480

x(x+2)(x+4)  = x³ + (x+2)² + 2(x+4)²                           solved algebraically

(x²+2x)(x+4)   = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + 3x² + 20x + 36

      3x² - 12x - 36 = 0         factor out the 3

      3[x² - 4x - 12] = 0

       3(x+2)(x-6) = 0     x = -2 and -12

Answer:

53.8 gallons

Step-by-step explanation:

5.4*3=16.2

5.4 (gallons used per shower) * 3 (number of showers) = 16.2 (gallons used in 3 showers)

70-16.2=53.8

70 (Water in tank) - 16.2 (gallons used in 3 showers) = 53.8 (gallons of water left)

Hope this helps! Please brainliest!!!

Answer:

A(3) = 53.8 gallons left after 3 showers

Step-by-step explanation:

A(x) = volume of water left in tank = 70 gallons - (5.4 gallons)x, where x is the number of showers already taken.  

After  3 showers, the volume of water left is A(3) = 70 gal - (5.4 gallons)(3), or

A(3) = 53.8 gallons left after 3 showers

Answer:

6x15 2/4 yd dividedby 2

Step-by-step explanation:

do the math and u get ur answer

Answer:

area of triangle =1/2 p×b=1/2×4×3=6unit²

Answer:

I don't think so .... :(((

Answer:

C and A

Step-by-step explanation:

For the triangle to be isosceles then the legs are congruent, that is

XZ = XY , substitute values

5x - 1 = 3x + 5 ( subtract 3x from both sides )

2x - 1 = 5 ( add 1 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3 → C

(10)

The diagonals of a square bisect each other

Calculate PR using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2-y_{1})^2 }[/tex]

with (x₁, y₁ ) = P(0, 0) and (x₂, y₂ ) = R(6, - 8)

PR = [tex]\sqrt{(6-0)^2}+(-8-0)^2[/tex]

     = [tex]\sqrt{6^2+(-8)^2}[/tex]

     = [tex]\sqrt{36+64}[/tex]

     = [tex]\sqrt{100}[/tex]

     = 10

Then

PT = 0.5 × 10 = 5 → A

Answer:

The positive predictive value ≈ 30.012%

Step-by-step explanation:

(a) The given percentage of the people in the region that have the disease, P(D) = 6% = 0.06

The percentage people correctly identified as having the disease by the standard diagnostic test = 91%

The percentage of people incorrectly identified as having the disease by the standard diagnostic test, P(T + |H) = 8%

Therefore, the sensitivity of the test, P(T + |D) = 0.91

The specificity of the test, P(T - |H) = 1 - 0.08 = 0.92

Therefore, the probability that a person is healthy, P(H) = 1 - 0.06 = 0.94

Therefore, in a population of 1,000 people, 60 people have the disease, with a sensitivity of 91%, the test will correctly pic 0.91×66 = 60.06 people correctly with the disease and 0.91 × 940 = 855.4 people without the disease

The number of non-diseased that test positive by the test is 0.08 × 1000 = 80 people which are false positives

Therefore, the number of diseased diagnosed as negative is 0.08 × 60 = 4.8

Therefore, we have;

[tex]\begin{array}{cccc}&Deseased&Non-diseased& Diseased + Non-diseased\\Test \ +ve&60.06&80& 140.06\\Test \ -ve&4.8&855.4&\end{array}[/tex]

The positive predictive value = Diseased +ve/(Diseased +ve + Non-diseased  +ve)

[tex]The \ positive \ predictive \ value = \dfrac{Diseased +ve}{Diseased +ve + Non-diseased +ve} \times 100[/tex]

Therefore;

The positive predictive value = 60.06/(60.06 + 140.06) × 100 ≈ 30.012%

Answer:

8 cups of potatoes are needed

Step-by-step explanation:

One way of doing this work is to write out

1/4 cup                                             1 cup

------------- , which is equivalent to  ------------ (a unit rate)

 1 bowl                                              4 bowl

and then multiply this unit rate by 32 bowls:

(1/4)(32 bowls) = 8 cups of potatoes are needed

Answer:

Q2. angle 5 +angle 6=90°

angle 5+ 6°=90°

angle 5=90°-6°

angle 5=84°

Q.3 angle 8+angle 9=90°

angle 8 + 11°=90°

angle 8=90°-11°

angle 8=79°

To approximate the sum of the series [infinity] (−1)n−1n^2/(8n), we can use a numerical method such as the partial sum method.

Let's calculate the partial sums of the series and add up terms until the sum converges to a desired level of accuracy. We will stop adding terms once the absolute difference between two consecutive partial sums is less than the desired accuracy.

Let's start by calculating the partial sums:

S_1 = (-1)^1-1(1^2)/(81) = 1/8

S_2 = (-1)^2-1(1^2)/(82) + (-1)^1-1(2^2)/(82) = 1/8 - 1/16 = 1/16

S_3 = (-1)^3-1(1^2)/(83) + (-1)^2-1(2^2)/(83) + (-1)^1-1(3^2)/(83) = 1/8 - 1/16 - 1/24 = -1/24

We can observe that the partial sums alternate between positive and negative values. This indicates that the series does not converge to a specific value but oscillates between two values.

To approximate the sum, we will calculate partial sums until the difference between two consecutive partial sums is less than the desired accuracy. Let's say we want the accuracy to be 0.0001.

Let's continue calculating partial sums:

S_4 = (-1)^4-1(1^2)/(84) + (-1)^3-1(2^2)/(84) + (-1)^2-1(3^2)/(84) + (-1)^1-1(4^2)/(84) = 1/8 - 1/16 - 1/24 + 1/32 = -1/48

S_5 = (-1)^5-1(1^2)/(85) + (-1)^4-1(2^2)/(85) + (-1)^3-1(3^2)/(85) + (-1)^2-1(4^2)/(85) + (-1)^1-1(5^2)/(8*5) = 1/8 - 1/16 - 1/24 + 1/32 + 1/40 = 1/120

The difference between S_4 and S_5 is 1/120 - (-1/48) = 1/120 + 1/48 = 1/80, which is greater than 0.0001.

Therefore, we can approximate the sum of the series as -1/48, correct to four decimal places.

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There is insufficient evidence to support the claim that the training technique is effective in raising the gymnasts scores.

In hypothesis testing, we often use significance levels such as 0.01 to determine whether or not there is enough evidence to support the hypothesis.

Here is the solution to the given problem.

The null hypothesis is that the training technique is not effective in raising the gymnasts' scores.

It is expressed as

H0: µd = 0.

The alternative hypothesis is that the technique is effective in raising the gymnasts' scores.

It is expressed as

Ha: µd > 0.

The significance level α = 0.01 is given.

Therefore, the given problem can be tested using a one-tailed t-test.

This is because the alternative hypothesis states that the mean difference between the two populations is greater than zero.

A t-test is appropriate because the sample sizes are less than 30.

The difference between the before and after competition scores of each gymnast should be calculated.

This gives us the difference scores, which are as follows:

0.1, 0.2, -0.02, -0.1, 0.1, 0.3, -0.2.

Next, we compute the mean and standard deviation of the differences. We have:

n = 7d

= 0.0714Sd

= 0.1466

Then we compute the t-statistic:

t = (d - µd) / (Sd / √n)

t = (0.0714 - 0) / (0.1466 / √7)

t = 1.5184

The degrees of freedom for this test are (n - 1) = 6.

Using a t-distribution table with 6 degrees of freedom and a significance level of 0.01 for a one-tailed test, we find that the critical t-value is 2.998.

For the given problem, the test statistic t = 1.5184 is less than the critical value of 2.998.

Therefore, we do not reject the null hypothesis.

There is insufficient evidence to support the claim that the training technique is effective in raising the gymnast scores.

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Answer:

98.19

Step-by-step explanation:

Volume of whole cube minus volume of cylinder. volume of cylinder is pi x r^2 x h

The volume of remaining solid is 46.44 in³

Volume is the measure of the capacity that an object holds.

For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml. Volume can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains. The best way to visualize volume is to think of it in terms of the space.

Here are the steps to calculate volume of any solid shape:

edge= 6

Volume of cube= l³

= 6*6*6

=216 in³

Now, Volume of cylinder

=πr²h

= 3.14 * 3 * 3 * 6

=169.56 in³

Volume of remaining solid= 216- 169.56

=46.44 in³

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Answer:

586.76

Step-by-step explanation:

Take the area of the rectangular prism = 348

Find the area of the cylinder = 477.52

Divide the cylinder by 2 = 238.76

Add both together = 586.76

Answer:

Slope: Undefined

Step-by-step explanation:

A Möbius transformation is a transformation of the form f(z) = (az+b)/(cz+d), where a, b, c, and d are complex numbers and ad-bc ≠ 0. The complex number z maps to f(z).

To find the Möbius transformation f such that f(0) = 0, f(1) = 1, f([infinity]) = 2, we follow these steps:

Step 1: Map 0 to 0 We need to map 0 to 0, so we set f(0) = 0. So, we get 0 = (a(0) + b) / (c(0) + d). This gives us b = 0. Step 2: Map infinity to 2We need to map [infinity] to 2, so we set f([infinity]) = 2. So, we get 2 = (a[infinity] + b) / (c[infinity] + d). This gives us a/c = 2/d. Cross-multiplying the terms, we get ad = 2c.

Let us assume that d = 1, then we have a = 2c.

We can substitute this value of a in the Möbius transformation, and we get f(z) = (2cz) / (cz + 1).Step 3: Map 1 to 1To map 1 to 1, we evaluate the Möbius transformation at z = 1. We get f(1) = (2c) / (c + 1) = 1.

Solving this, we get c = -1/2. Therefore, the Möbius transformation is f(z) = (2z) / (z - 2).

Hence, we have found the required Möbius transformation f(z) = (2z) / (z - 2) such that f(0) = 0, f(1) = 1, and f([infinity]) = 2.

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Answer: 60

Step-by-step explanation:

1=10. x6=60

The answer is the test statistic (13.765) is greater than the critical value (5.991), we reject the null hypothesis. Therefore, we can conclude that there is a significant relationship between political party affiliation and support for the referendum on gay rights.

To represent the data in a table, we can create a contingency table:

                             For      Against

Republican            16        54

Democrat              72        28

Other                     27         3

Null hypothesis (H₀): There is no relationship between political party affiliation and support for the referendum on gay rights.

Alternative hypothesis (H₁): There is a relationship between political party affiliation and support for the referendum on gay rights.

To analyze the data, we can perform a chi-square test of independence. This test will determine if there is a significant association between political party affiliation and support for the referendum.

Applying the chi-square test at a significance level (α) of 0.05, we can calculate the test statistic and compare it to the critical value from the chi-square distribution with (rows - 1) × (columns - 1) degrees of freedom.

Let's calculate the expected frequencies for each cell assuming the null hypothesis is true:

                          For      Against    Total

Republican          27        43            70

Democrat            48        52           100

Other                   12        18             30

Total                    87       113            200

Now, we can calculate the chi-square statistic:

χ² = Σ[(O - E)² / E]

where O is the observed frequency and E is the expected frequency.

Performing the calculations, we find:

χ² ≈ 13.765

To determine the critical value, we need to find the degrees of freedom, which is equal to (rows - 1) × (columns - 1) = (3 - 1) × (2 - 1) = 2.

Using a chi-square distribution table or a statistical software, we find that the critical value for a significance level of 0.05 and 2 degrees of freedom is approximately 5.991.

Since the test statistic (13.765) is greater than the critical value (5.991), we reject the null hypothesis. Therefore, we can conclude that there is a significant relationship between political party affiliation and support for the referendum on gay rights.

In Michael's survey data, political party affiliation is related to the support for the referendum. Further analysis and interpretation of the results are needed to understand the nature and strength of this relationship.

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Answer:

y=3x^2-6x+3

Step-by-step explanation:

In the drawing a graph is there with labeling of vertices A,B,C,D with matrix [tex]\begin{bmatrix}2 &1 & 1&0\\1 & 0 & 0&1\\1&0&0&1\\0&1&1&0\end{bmatrix}[/tex].

Given that,

a. We have to draw a graph which has the following adjacency matrix

[tex]\begin{bmatrix}2 &1 & 1&0\\1 & 0 & 0&1\\1&0&0&1\\0&1&1&0\end{bmatrix}[/tex]

Taking the matrix rows and column as A,B,C,D.

Therefore, In the drawing the graph is with matrix.

(b) We have to label the vertices of your graph A,B,C,D.

The drawing can be seen with the label of vertices A,B,C,D.

(c) We have to find how many different paths of length are there from the vertex you labelled A to D

A →A →B →A→A→B→A→C→D

A→A→A→A→A→C→D

A→A→A→A→A→B→D

Therefore, In the drawing a graph is there with labeling of vertices A,B,C,D with matrix [tex]\begin{bmatrix}2 &1 & 1&0\\1 & 0 & 0&1\\1&0&0&1\\0&1&1&0\end{bmatrix}[/tex].

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