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The probability that the sample mean will be between  89.17 and 101.05 is: 0.940091407

A sample mean is a data set's average. A data set's central tendency, standard deviation, and variance may all be calculated using the sample mean.

The sample mean may be used to calculate population averages, among other things.

The information given are as follows:
μ = 94,

σ = 18

Where Χ = Sample Mean

hence P (89.17 < X< 101.05) =

P [[tex]\frac{89.17 -94}{18/\sqrt{36} } \leq \frac{X -mu}{sd/\sqrt{xn} } \leq \frac{101.5-94}{18/\sqrt{36} }[/tex]]

= P [ -1.61 ≤ Z ≤ 2.5]

= P (Z ≤ -1.61) - P (Z ≤ 2.5)

= NORMSIDST (-1.61) - NORMSDIST (2.5)

= 0.053698928 - 0.993790335

= -0.940091407

Since probability cannot be negative,

The probability that the sample mean will be  between 89.17 and 101.05 is: 0.940091407

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The solution to the inequality in discuss involving a rational expression as indicated in the task content is; t (9, infinity).

The inequality given in the task content as evident is; (2t +22)/(2t +2) <= 2.

On this note, the inequality can be solved by cross-multiplication as follows;

2t +22 <= 4t +4

Hence, we have;

-2t <= -18

t >= 9.

Hence, when expressed as an interval notation, we have; t (9, infinity).

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Answer:

2/3

Step-by-step explanation:

since they are just two colors of fish inside, since the probability is always 1.. so we have to minus 1/3 from 1,which is 1-1/3=2/3

The domain of the function 12x + 6y = 24 exists {-4, 0, 5}, then the range of the function exists {12, 4, -6}.

Given: 12x + 6y = 24

Here x stands for the input and y stands for the output

Replacing y with f(x)

12x + 6f(x) = 24

6f(x) = 24 - 12x

f(x) = (24 - 12x)/6

Domain = {-4, 0, 5}

Put the elements of the domain, one by one, to estimate the range

f(-4) = (24 - 12((-4))/6

= (72)/6 = 12

f(0) = (24 - 12(0)/6

= (24)/6 = 4

f(5) = (24 - 12(5)/6

= (-36)/6 = -6

The range exists {12, 4, -6}

Therefore, the correct answer is option c. {12, 4, -6}.

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Answer:

1  i(sqrt5)

2  7i

3  -9i

4  -64i

5  -5i(sqrt2)

6  -4i(sqrt3)

7  10i(sqrt3)

8  2i(sqrt2)

9  3i(sqrt7)

10  -30i(sqrt2)

Step-by-step explanation:

i is the square root of (-1). We can simplify each one as such.

There is only one solution for the equation 4z + 2(z -4) = 3z + 11 because the exponent for the power of z is 1.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

A solution is any value of a variable that makes the specified equation true.

According to the given information:

4z + 2(z-4)= 3z+11

Solve the equation,

4z+2z-8=3z+11

6z-3z=11+8

3z =19

z=

Hence,

Number of solution that can be found for the equation 4z + 2(z-4)= 3z+11 is option(2) one

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Answer:

third angle measures 24°

Step-by-step explanation:

triangles are 180°

add up the first two angles and subtract the sum from 180°

45° + 111° = 156°

180 - 156 = 24

45 square feet is the area of the base of the pedestal.

what is rectangular prism?

we know that

The volume of the pedestal (rectangular prism) is given by the formula

   V =   B × h

where

B is the area of the rectangular base of pedestal

V = 405 ft³

h = 9 ft

put the given values in the formula and solve for B

405 = B × 9

B = 405/9

B = 45 ft²

Therefore, 45 square feet is the area of the base of the pedestal.

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The conclusion based on the hypothesis is that do not reject the null hypothesis as the row an column factors are independent.

From the information given, the null hypothesis is that the row and the column factors are independent. The alternative hypothesis is that they're dependent.

This was run by using the Chi square test and the following information was gotten:

Test statistic = 2.5234

P- value = 0.1122

Degree of freedom = (2-1)(2-1) = 1

Since the p value is equal to 1%, do not reject the null hypothesis as the row an column factors are independent.

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Answer and explanation in the attached file.

Answer:

m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131

m∠RST = 2x = 2(14) = 28

m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103

Step-by-step explanation:

m∠RSU = m∠RST + m∠TSU

10x - 9 = 2x + (2x + 75)

10x - 9 = 2x + 2x + 75

10x - 9 = 4x + 75

-4x +9     -4x  +9

      6x = 84

         x = 14

m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131

m∠RST = 2x = 2(14) = 28

m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103

Answer:

1. Given

2. Triangle Interior Angle Sum Theorem

3. Substitution Property of Equality

4. Subtraction Property

5. Definition of Complementary Angles

Answer:

[tex]\frac{2}{25}[/tex]

Step-by-step explanation:

Each "place" in the decimal, can be represented with a base 10 in the numerator.

For example the "tenths" place can be represented as: [tex]\frac{a}{10^1}[/tex] where a=decimal.

The hundredths place can be represented as: [tex]\frac{a}{10^2}[/tex]

The thousandths place can be represented as: [tex]\frac{a}{10^3}[/tex]

and so on...

In this case, we have a decimal in the hundredths place which can be represented as: [tex]\frac{8}{10^2} = \frac{8}{100}[/tex]. Now to simplify this fraction, you simply divide both sides by 4 (greatest common factor of 8 and 100), or in other words multiply it by 0.25/0.25 which is just 1, so the value is the same. [tex]\frac{8}{100} * \frac{0.25}{0.25} = \frac{2}{25}[/tex]

Answer:

The file contains the solution to the question

Answer: is 48 eggs .

Step-by-step explanation:

3 hens gives 3 eggs in 3 days

Therefore , 1 gives 1 egg in 3 days

So

3days = 1egg

After that 12 days\/3 times = 4 eggs (in 12 times )

So 1 hen offers 4 eggs in 12 days after that

12 hens x 4 eggs = 48 eggs (in 12 days by 12 hens)

The statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D

Ordered pairs are known to be pairs of numbers that are used locate a point in the rectangular coordinate plane

They are written as (x ,y)

where

It is important to note that the location of the ordered pair in the quadrants determines the sign of the x and y coordinates.

The signs of the ordered pairs are given as;

When (x , y)  is in Quadrant I then both x and y are positive

Therefore, the statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D

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Please see the picture below

Answer: 6,760,000

Step-by-Step Explanation:

Answer:

-1/3

Step-by-step explanation:

1:make y the subject.

2:slope of line is the coefficient of x

Answer:

hdchyf

Step-by-step explanation:

fhyrb ufgfyg hchybgvtct ugh

(a) (x-12)(x+11)

(b) x³-4x=x(x²-4)=x(x-2)(x+2)

Answer:

(8,14)

Step-by-step explanation:

3x+2y=52

3x+1y=38 Subtract these equations using elimination method to get y=14

Then substitute y=14 to either equation

the bottom one is easier so

3x+1(14)=38 distribute 1 to 14 and any number times one is 1

3x+14=38 Subtract 14 from both sides

3x=24 Divide by 3

x=8 so check now

3(8)+1(14)=38

24+14=38?

38=38? yes

Ebony’s bank balance is $400 was Day 8 and this can be explained below.

Jade cannot be true because for every transaction made during withdraws, a little amount of money is collected and as such the amount will never remain $400.

Note that the scenario for the above to occur is:

On day 4, her balance = $400

On day 5, her balance = $40

On day 6, her balance = $400

On day 7, her balance = $400

On day 8, her balance = $400

Another fact is that since she deposited 400 at first, on day 8, there will be a 0 increase so the amount will still be 400.

Therefore, if the above is the case, one can deduce the fact that her balance will still be $400.

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Answer:

x = 6

Step-by-step explanation:

• the diagonals of a parallelogram bisect each other , then

5x + 11 = 4x + 17 ( subtract 4x from both sides )

x + 11 = 17 ( subtract 11 from both sides )

x = 6

Since it's divided equally diagonally, 4x+17 and 5x+11 are equal.

Let's set them equal to each other and solve.]

[tex]4x+17=5x+11[/tex]

Subtract 4x from both sides to combine like terms.

[tex]17=x+11[/tex]

Now subtract 11 from both sides to isolate the variable and solve for x.

[tex]6=x[/tex]

Flip the equation to put in standard form and now you have x :)

[tex]x=6[/tex]

hope this helped!

Answer: B

Step-by-step explanation: If it goes through a point, flip that point around and that is the point of the inverse. Do that for multiple points to get your answer, which is B

Answer:

4[tex]\sqrt{3xy}[/tex]

Step-by-step explanation:

4 is a perfect square.  We can pull 2 out from under the square root symbol.

The prime factor of 12 is 2.2.3.  We can pull another 2 outside of the square root symbol.  2 x2 is 4 that will be outside of the square root symbol and the x, y and 3 will be left under the symbol.

Answer:

48

Step-by-step explanation:

The area of this circle is

[tex]\pi( {4}^{2} ) = 16\pi = 50.27[/tex]

about 50.27 square centimeters. So 48 square centimeters seems reasonable here since 3 is used for π.

Step-by-step explanation:

the mean value is the sum of all data points divided by the number of data points.

first we have 7 tests and their mean value :

(t1 + t2 + t3 + t4 + t5 + t6 + t7) / 7 = 54

that means

(t1 + t2 + t3 + t4 + t5 + t6 + t7) = 54 × 7 = 378

in order for the mean value to be at least 60% after 8 tests, we need to add a t8, so that

(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) = 60 × 8 = 480

because only then we have

(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) / 8 = 60

and the student passes.

so,

(t1 + t2 + t3 + t4 + t5 + t6 + t7) + t8 = 480

378 + t8 = 480

t8 = 480 - 378 = 102%

the student would have to achieve 102% on the 8th test.

which would be normally impossible, but maybe the tests involve some bonus points.