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There is a 65.54% probability that the average age of those doctors is under 48.8 years.

Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.

It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.

The possibility of an event occurring increases as it gets higher.

True mean = mean (or average)+/- Z*SD/sqrt (sample population)

Then,

Mean (average) = 48.0 years

The true mean must be less than 48.8 years.

SD = 6.0 years, and

Sample size (n) = 9 doctors

Using Z as the formula's subject:

Z= (True mean - mean)/(SD/sqrt (n))

Inserting values:

Z=(48.8-48.0)/(6.0/sqrt (9)) = 0.4

From the table of normal distribution probabilities:

At Z= 0.4, P(x<0.4) = 0.6554 0r 65.54%

Therefore, there is a 65.54% probability that the average age of those doctors is under 48.8 years.

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Complete question:

The average age of doctors in a certain hospital is 48.0 years old. suppose the distribution of ages is normal and has a standard deviation of 6.0 years. if 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 48.8 years. assume that the variable is normally distributed.

The mean of the sampling distribution (p) and The standard error of the mean (o)  are 56 and 2 respectively.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

(a) The mean of the sampling distribution (p) is equal to the population mean, which is 56.

(b) The standard error of the mean (o) is calculated as the standard deviation of the population divided by the square root of the sample size. So for a sample of 36 participants:

o = 12 / √36 = 2

(c) The distribution of the sample means (p) will be approximately normal with a mean of 56 and a standard deviation of 2. To sketch this distribution with M ± 3 SEM, we would plot a normal distribution with mean 56 and standard deviation 2, and shade the region that is 3 standard errors away from the mean on either side.

This region would capture approximately 99.7% of the data if the samples were selected randomly and independently from the population.

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The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

A constant function is a linear function whose range contains only one element irrespective of the number of elements of the domain.

Since a constant function is defined for all real values of x, then we have that:

1) Its domain is the set of all real numbers, and

2) Since a constant function f(x) = c leads to only one output, which is k, its range is the set with just one element c.

Therefore,

The statement is TRUE.

Answer:

 a.  1492 kg

  b.  20.8 m

Step-by-step explanation:

Given a tree is initially 20 m high and has a diameter of 0.5 m, you want the mass of the trunk if its density is 380 kg/m³. If it adds a growth ring of 4 mm per year and adds height of 0.2 m in the first year, you want the height of the tree after 5 years, assuming the same amount of wood is added each year.

The volume of the tree trunk is that of a cylinder. The formula is ...

  V = (π/4)d²h

  V = (π/4)(0.5 m)²(20 m) ≈ 3.9270 m³

The mass is the product of volume and density:

  M = Vρ

  M = (3.9270 m³)(380 kg/m³) ≈ 1492 kg

The mass of the tree trunk is about 1492 kg.

In the first year, the diameter of the tree increases by 8 mm, and the height increases by 0.2 m,. This means the volume of the tree increases to ...

  V = (π/4)(0.508 m)²(20.2 m) ≈ 4.0942 m³

The volume increase is the same each year for 5 years, so after 5 years, the volume is ...

  3.9270 m³ + 5(4.0942 -3.9270) m³ ≈ 4.7630 m³

At that time, the diameter is about 0.540 m. Solving the volume equation for the height, we find it to be ...

  h = 4v/(π·d²)

  h = 4(4.7630 m³)/(π·(0.54 m)²) ≈ 20.797 m

The height of the trunk after 5 years is about 20.8 m.

__

Additional comment

We note that the wood added in the first year includes the cylindrical shell represented by the tree ring, and a cylindrical "plug" that is 0.2 m high and equivalent in diameter to the rest of the tree. This seems an odd way for the tree to grow, but may be a reasonable approximation to the actual growth.

The height, diameter, and growth are all given to 1 significant figure. Hence the 4- and 3-significant figures used in the answers may be unsupported by the precision of the given numbers. Keeping 2 significant figures, we might report the initial mass as 1500 kg, and the final height as 21 m.

The graph is drawn by a function formulated to have the correct height at the x-intercept: v(d, h) - (final volume) = 0.

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Answer:

165km

Step-by-step explanation:

if 1cm on the map = 15km,

then since 11cm is 11x 1, we multiply the kilometers by 11, getting 165km.

The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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Answer:

D.) 9*pi >27

Step-by-step explanation:

9*pi = 28.2743338823...

28.2743338823... > 27

D.) 9*pi > 27 = True

Regards!

Answer:

It’s d hope you get it right

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

Stare at it long enough. You will notice that with each step you double the value, and change sign. It makes it a geometric sequence of ratio -2. At this point you have two ways of writing down:

Option 1: Ricorsively, the first term is -5, then the next term is -2 times the previous one:

\(\left \{ {{a_0=-5} \atop {a_{n+1}=-2a_n}} \right.\)

Option 2: In closed form, remembering that the n-th term in a geometric sequence is the starting term times the n-th power of the ratio:

\(a_n=-5 (-2)^n\)

Either work, depending on what you need to use it for.

Answer:

C.

Step-by-step explanation:

I think it is C. because tons are way too much (there are 32,000 ounces in a ton) and there are only 16 ounces in a pound. An average baby is about 17.5 pounds at birth, or 17 pounds and 8 ounces.

hope this helped!

Answer:

The quadrilaterals ABCD and A'B'C'D' are congruent only if k = 1.

The corresponding side lengths are related by k(CB) = C'B'.

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in size of a figure by a factor k. If k > 1, the figure is increased, if k < 1, the figure is reduced and if k = 1, the figure does not changes shape. The image of an dilated figure is similar to the original image.

a) If k = 1, then the resulting image produced by dilating ABCD is congruent. Hence, The quadrilaterals ABCD and A'B'C'D' are congruent only if k = 1.

b) Dilation produce image similar to the original figure, hence quadrilaterals ABCD and A'B'C'D' are similar only if k ≥ 1 and k < 1.

c) Since ABCD is dilated by a factor of k to produce A'B'C'D', hence A'B' = k(AB).

d) C'B' = k(CB)

Answer:

can we get a picture

Step-by-step explanation:

Answer:

1 +  29

3 + 27

5 + 25

7 + 23

9 + 21

11 + 19

13 + 17

15 + 15

~theLocoCoco

The coordinates of point A are ( 5/4, -3/4)

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

x - coordinate = 5 grid lines to the right of the y-axis

y - coordinate =   3 grid lines below the x-axis.

The point A is in the 4th quadrant

(x,y) = ( + 5 grid lines, -3  grid lines )

There are increments I have one over four for each grid line on each of the two axes

This means,

(x,y) = ( + 5 * 1/4, -3*1/4 ) = ( 5/4, -3/4)

So,  the coordinates of point A are ( 5/4, -3/4)

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Answer:

A) True : Confidence Interval is the interval range around sample statistic, which is certain by extent of confidence level, to consist the actual population parameter.

B) True : Confidence Interval is the interval range around sample statistic, which is certain by extent of confidence level, to consist the actual population parameter.

C) False : Null Hypothesis can be accepted, despite of being actually false. This is called Type 2 Error.

Step-by-step explanation:

Hope this helps:)

Answer:

To determine the amount of baking soda needed, we need to use the given ratio to calculate the masses of salt, baking soda, and water required to make the mixture.

The total mass of the mixture is 12 + 22 + 12 = 46 parts. This means that for every 46 grams of the mixture, there are 12 grams of salt, 22 grams of baking soda, and 12 grams of water.

To find out how much baking soda is needed for 30 grams of water, we can use a proportion:

12 grams water / 46 grams mixture = 30 grams water / x grams mixture

where x is the mass of the mixture needed to obtain 30 grams of water.

Cross-multiplying, we get:

12 grams water * x grams mixture = 30 grams water * 46 grams mixture

Simplifying:

x grams mixture = (30 grams water * 46 grams mixture) / 12 grams water

x grams mixture = 115 grams mixture

Therefore, to make a mixture containing 30 grams of water, we need a total mixture mass of 115 grams. Using the given ratio, we know that for every 46 grams of the mixture, we need 22 grams of baking soda.

So, for a 115-gram mixture, we can calculate the amount of baking soda needed:

22 grams baking soda / 46 grams mixture = y grams baking soda / 115 grams mixture

where y is the mass of baking soda needed.

Cross-multiplying, we get:

22 grams baking soda * 115 grams mixture = 46 grams mixture * y grams baking soda

Simplifying:

y grams baking soda = (22 grams baking soda * 115 grams mixture) / 46 grams mixture

y grams baking soda = 55 grams baking soda (rounded to two decimal places)

Therefore, to make a mixture containing 30 grams of water using the 12:22:12 ratio, we need 55 grams of baking soda.

Step-by-step explanation:

pls mark brainlist!

Bring the variable to the left and the remaining values to the right to define the value of x. If m/8 = 86° and m/4 = (4x + 2)° then value of  x = 21.

Any of the algebraic expressions, including addition, subtraction, multiplication, and division, should be used. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.

Let the m/8 = 86° and m/4 = (4x + 2)°

m ∠4 = m ∠8 (Corresponding angles are equal)

To estimate the value of x

4x + 2 = 86

Substracting both sides of the equation by 2, we get

4x + 2 - 2 = 86 - 2

simplifying the above equation,

4x = 86 - 2

4x = 84

Dividing both sides of the equation by 4, we get

4x / 4 = 84 / 4

x = 21

Therefore, the value of x = 21.

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Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Answer:

C) x = 3.7

Step-by-step explanation:

sin 41° = x/5.6

0.6561 = x/5.6

x = 3.7

Answer:

look at it

Step-by-step explanation:

hope its help

please follow

Answer:

negative

Step-by-step explanation:

its below the negative mark and its not verticle so it can't be undefined

Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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i am so sorry me dont know

Answer:

Answer: Composite figure: 360 ft3

Explanation:

The volume of the triangular prism:

The base area of the prism = 1/2 x 4 x 6 = 12 ft2

Height = 6 ft

The volume of the triangular prism = 12 x 6 = 72 ft3

The volume of the rectangular prism:

The base area of the prism = 4 x 6 = 24 ft2

Height = 12 ft

The volume of the triangular prism = 12 x 24 = 288 ft3

Volume of the composite figure = (288 + 72)ft3 = 360 ft3

Step-by-step explanation:

Using the proportion formula, the height of the building is obtained as 40 meters.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

We can use proportions to solve the problem.

The ratio of the height of the pole to its shadow is the same as the ratio of the height of the building to its shadow.

That is -

height of pole / length of pole's shadow = height of building / length of building's shadow

Substituting the given values in the equation -

16 / 10 = height of building / 25

To find the height of the building, we can cross-multiply and solve for it -

16 x 25 = 10 × height of building

400 = 10 × height of building

height of building = 400 / 10

height of building = 40 meters

Therefore, the height of the building is 40 meters.

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A 16 meter pole casts a 10 meter long shadow. If at the same time of the day, a building casts a shadow of 25 meters, what is the height of the building?

Answer:

\(3x+b+p^2\) is already simplified

Step-by-step explanation:

\(3x+b+p^2\) is already simplified

Answer:

The equation is already simplified

Step-by-step explanation:

Nothing fuurther can be done to this equation

Answer:

the answer is 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is 2, because it is the only factor that can go with both of the numbers.