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By using the concept of mean and standard deviation, it can be obtained that

The mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3

Standard deviation of distribution ([tex]\sigma_x[/tex]) = 0.714

What is mean and standard deviation?

Suppose there is a data set and an average value of the data set needs to be calculated. To find the average value of the data set, mean is used

For Standard deviation, at first, it is important to know about variance

Variance is the sum of the square of deviation from mean.

Square root of variance is the standard deviation

A population of values has an unknown distribution with

[tex]\mu = 83.3[/tex] and [tex]\sigma = 10.4[/tex], n = 212

So the mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3

Standard deviation of distribution ([tex]\sigma_x[/tex]) = [tex]\frac{10.4}{\sqrt{212}}[/tex] = 0.714

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the ant will take 8 days to consume 2 apples.

Given, an ant takes 2 days to consume 1/2 of an apple.

We have to find the number of days ant will take to consume 2 apples.

So, ant takes 2 days = consumption of 1/2 apple

ant takes 4 days = consumption of 1 apple

Consumption of 1 apple = ant takes 4 days

Consumption of 2 apples = ant takes 4×2 days

Consumption of 2 apples = ant takes 8 days

Hence, the ant will take 8 days to consume 2 apples.

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Using the Triangle Inequality Theorem we can state that the range of z is 4 < z < 20.

The above theorem states that The length of any two sides of a triangle must sum to more than the length of the third side. That is:

12 + 8 > z.............1

12 + z > 8;.............2

8 + z > 12.............3

Solving for (1)

20 > z...............4

Solving for (2)

we have- 12 + z > 8

remove 8 from both sides and we have

4 + z > 0  or z > -4 ...............5

Solving for (3) we have

8 + z > 12

remove 8 from both sides

z > 4 .....................6

Since we can't have a negative value on a triangle, we must deal with expressions 4 and 6 which state:

20 > z; and

z > 4

Another way to write this is:

20 > z > 4; or

4 < z < 20

Hence the range of the unknown side that will form a triangle is:

4 < z < 20

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Height of cylinder is 5 units

Define Cylinder

               ⇒ V = (π × radius²) × h

We have given,

Slant height of cylinder = √29

Radius is = 2 units

Now, we to have to calculate the height for that we have the formula

h = √l² - r²

where, l = slant height

            r = radius of the circular base

            h = height of the cylinder

Now, for the sake of simplicity

h = √l² - r²

h² =  l² - r²

Now, plug in the values

h² = (√29)² - 2²

h² = 29 - 4

h² = 25

h = 5

Hence, the height of cylinder is 5 units

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If we buy all the same type of folders, the maximum amount we can afford for an individual folder is $ 3.3

To buy : A notebook for = $ 3

number of folders required = 5

The amount of money we can spend is $ 10

The above mentioned problem is a problem of algebra because we would have to use a variable to find out the unknown value.

The individual folders price can be calculated by the equation

3x = 10

divide both sides by 3 and we will get

x = 3.3

Thus the individual folder prices we can afford is $ 3.3

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They spent 6.5 hours driving on local highways by travellin with diffrent average speeds.

Given that,

The bruins basketball team spent two more hours on the interstate than they did on local roadways during their 560-mile journey. They traveled at an average speed of 55 mph on interstates and 45 mph on local routes.

I=interstate

L=local

using d=rt the first rows gives you d=55t

the second row gives you 560-d=45(t-2)

Since the two distances add up to 560.  Add the two distance expression and set their sum equal to the given total

560=55t+45(t-2) which equals

560=55t+45t-90

650=55t+45t

650=100t

6.5=t

Hence on local roadways, they traveled at various average speeds for 6.5 hours.

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The pounds of flour the bakery has at the end of the month is 92.725 lb

The negative numbers denote when flour was used while the positive numbers denote when flour was added. The negative numbers would be subtracted while the positive numbers would be added.

For ease of computation, the mixed numbers would be converted to decimals.

-58 1/2 = -58.5

75 3/10 = 75.3

-67 7/8 = -67.875

Pounds of flour the bakery has at the end of the month: 215.4 - 58.5 - 70.6 + 75.3 - 67.875 = 92.725 lb

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The sides of similar triangles are proportional, therefore, the true equation would be: FG/CD = EG/BD.

Two similar triangles have corresponding angle measures that are congruent to each other, but have corresponding side lengths that are proportional to each other.

Similar triangles have the same shape but their sizes are different.

Given that angles C and F are congruent, and angles D and G are congruent, therefore triangle BCD is similar to triangle EFG based on the AA similarity theorem.

Therefore, the corresponding side lengths of both triangles will be proportional, which means that the following equation would be true:

FG/CD = EG/BD

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Answer:

23.29 ft

Step-by-step explanation:

The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.

To find how high up the wall the ladder reaches, use the sine trigonometric ratio:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

where:

The angle of elevation is 76°, so θ = 76°.

Let x be the height the ladder reaches up the wall, so O = x.

H is the length of the ladder, so H = 24.

Substitute the given values into the sine ratio and round the answer to the nearest hundredth:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]

[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]

[tex]24 \sin(76^{\circ})= x[/tex]

[tex]x=24 \sin(76^{\circ})[/tex]

[tex]x=23.28709743...[/tex]

[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]

Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.

The 90% confidence interval for the population mean gpa is [2.545,3.114].

The confidence interval for population mean is:

µ ± z* . σ/√n

Where, μ is population mean, σ is standard deviation, z* is the value of z-score and n is number of samples.

The z-score value for 90% confidence interval is 1.645.

The average gpa is found to be 2.83, so μ=2.83. The variance is 0.45, it means

σ² = 0.45

σ = √0.45

σ = 0.67

The 90% confidence interval for population mean is:

2.83 ± 1.645 . 0.67/√15

[2.83 - 1.645.0.67/√15 , 2.83+1.645.0.67/√15]

[2.545 , 3.114]

Therefore, the 90% confidence interval for the population mean gpa is :

[2.545 , 3.114]

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The distance covered by the car is 264cm.

Here we have to find the distance covered by the car.

Information provided:

Diameter (d) = 5.6cm

radius(r) = 5.6/2

             = 2.8cm

Rotation = 15 times

Formula to find the circumference of the tire:

Circumference = 2πr

                        = 2 × 22/7 × 2.8

                        = 17.6cm

This is the distance covered by the tire in one rotation.

Distance covered after 15 rotations = 15× 17.6

                                                         = 264 cm

Therefore distance covered is 264 cm.

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Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.

Given statement;

Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.

→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.

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Total( as there is addition) feet walked by Lola is 29.25 +1.5x for the given equation.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division.

Main body:

Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:

= 10 + (1/2 × 10) = 10 + 5 = 15 feet

Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:

= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet

Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:

= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75

Lola's mom walked x feet, and then half that length again. Total length walked will be:

= x + (1/2 × x) = x + 0.5x = 1.5x

Total feet walked by the whole member of the family will be:

= 15 + 4.5 + 9.75 + 1.5x

= 29.25 + 1.5x

Hence Total feet walked by Lola is 29.25 +1.5x for the given equation.

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A statistically significant finding indicates that it is unlikely to just be explained purely by chance or random influences.

The notion that a set given observed data is not the result of random but can instead be linked to a specific cause is referred to as statistical significance.

Statistical significance indicates that a result is unlikely to be attributed purely by chance and random causes.

Thus, in other words, if there is no genuine effect in a research study, a statistically significant conclusion has an extremely low likelihood of occuring.

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Answer: The volume of the prism is [tex]18^{3}[/tex]cm

Step-by-step explanation: The formula to solve for the volume of a rectangular prism is V = lwh. In this case, it's V = 4 x 3 x 1.5 therefore V = 18

The radius of the circle which is overlapping the square is 1.12.

The length of side of the square is 2. Let us say that the radius of the circle is R.

The circle and the square are overlapping on each other.

The area of the region that are outside the circle but inside the square are equal to the area of the region which are inside the circle but outside the square.

Let us name the area of the region that are outside the circle but inside the square as M.

Let us name the area of the region which are inside the circle but outside the square as N.

Let us say that the area that is common in both is C.

The area of the square is 4.

So, according to the question,

M + C = 4

And,

N + C = πR²

And we know, M = N,

So,

C - πR² = C - 4

R = 2/√π

R = 1.12.

So, the radius of the circle is 1.12

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The values of the interior angles, ( Angle A, Angle B and Angle C) of the triangles are 48°, 88° and 44° respectively.

Interior angle is the inner of the two angles formed where two sides of a polygon come together.

To find the measure of each interior angle of the triangle in the diagram, first, we need to find the value of x.

Recall that: The sum of the interior angles of a triangle is equal to 180°.

Using the formula,

From the triangle,

Substitute these values into equation 1

Solve for x

Therefore,

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Answer:

The quote seems to have a little to much shooting. Don’t you think?

Step-by-step explanation:

Answer:

lair lair

Step-by-step explanation:

Answer:

[tex] \frac{1}{6} {x}^{3} y + \frac{5}{6} x {y}^{2} \\ \frac{1}{6} xy( {x}^{2} + 5y)[/tex]

option 3 is correct

Answer:

216

Step-by-step explanation:

x^3

6^3

6x6x6

36x6

216

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The inequality that could be used to determine the mean number of miles Jason would need to run each day for 5 more days to achieve his goal is 10 + 5m ≥ 45

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the number of miles be given as m.

Since his goal for this week is to run a minimum of 45 miles. So far this week, he has already run 10 miles. This will be:

10 + 5m ≥ 45

This expresses the inequality.

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Answer:

x=10.5

Step-by-step explanation:

Answer: y = (1/2)x + 8

Step-by-step explanation:

Slope: (4-7)/(-8--2) = (-3)/(-6) = 1/2

y = (1/2)x + b

7 = (1/2)-2 + b

7 = -1 + b

8 = b

y = (1/2)x + 8

The equation used to solve this problem is x + y + z = 100000,  0.04x + 0.06y + 0.08z = 6700 and y = z

An equation is an expression showing the relationship between two or more numbers and variables.

Let x represent the amount of money invested at 4% (short term), y represent the amount of money invested at 6% (intermediate term) and z represent the amount of money invested at 8% (long term)

Since an investor has $100,000 to invest, hence:

x + y + z = 100000    (1)

Also, the investor wishes to have a return of $6700, hence:

0.04x + 0.06y + 0.08z = 6700   (2)

Equal amounts invested in intermediate and long term bonds. This gives:

y = z     (3)

The third equation used to solve this problem is y = z

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Answer:

8.95 gallons

Step-by-step explanation:

25.50/2.85 = 8.95

Answer:

Step-by-step explanation:

To find the slope, subtract the y values, and divide it by subtracting the x values. The order matters!

(9-6)/(1-6)=-3/5

The volume of the given figure is 5760 [tex]cm^{3}[/tex].

According to the question,

We have the following information:

We have a figure where two cuboids are joined together. So, the volume of the figure will be the sum of the volume of these cuboids.

We know that the following formula is used to find the value of cuboid:

Volume of cuboid = Length*breadth*height

Volume of larger cuboid = 40*8*12

Volume of larger cuboid = 3840 [tex]cm^{3}[/tex]

Volume of smaller cuboid = 20*8*12

Volume of smaller cuboid = 1920 [tex]cm^{3}[/tex]

Volume of the figure = 3840+1920

Volume of the figure =  5760 [tex]cm^{3}[/tex]

Hence, the correct option is B (the second option).

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Answer:

5760

Step-by-step explanation:

Answer:

volume = 3 ml

Step-by-step explanation:

the reading on the left without the nugget is 17 ml

the reading on the right with the nugget is 20 ml

volume of nugget = 20 - 17 = 3 ml