A population of values has a normal distribution with
μ
=
109.1
and
σ
=
15
. You intend to draw a random sample of size
n
=
146
.

Find the probability that a single randomly selected value is between 106.4 and 108.4.
P(106.4 < X < 108.4) =


Find the probability that a sample of size
n
=
146
is randomly selected with a mean between 106.4 and 108.4.
P(106.4 < M < 108.4)

Answer:

\(x^3-5x^2+10x-14\)

Step-by-step explanation:

\(\left(2x^3-5x^2+3x-10\right)-\left(x^3-7x+4\right)\)

Remove brackets:

\(2x^3-5x^2+3x-10-x^3+7x-4\)

Group similar terms together:

\(2x^3-x^3-5x^2+3x+7x-10-4\)

Add/Subtract the terms:

\(x^3-5x^2+10x-14\)

Answer:

Step-by-step explanation:

( 2X³ - 5X² + 3X - 10 ) - ( X³ - 7X + 4 )

2X³ - 5X² + 3X - 10 = X² - 10

X³ - 7X + 4 = - 7X² + 4

X² - 10 - - 7X² + 4 =

X² - 10 + 7X² + 4 =

THE ANSWER IS

8X⁴ - 6

Answer:

4 small cars

7 large cars

Step-by-step explanation:

To determine the number of small cars rented and the number of large cars rented by the group of college students, we can set up and solve a system of equations.

Let x be the number of small cars.

Let y be the number of large cars.

If the students rented 3 more large cars than small cars, then:

\(y = x + 3\)

Given each small car can hold 4 people, each large car can hold 6 people, and the total number of people that the rented cars could hold is 58, then:

\(4x + 6y = 58\)

Therefore, the system of equations is:

\(\begin{cases} y = x + 3\\4x + 6y = 58\end{cases}\)

To solve the system of equations, substitute the first equation into the second equation and solve for x:

\(\begin{aligned}4x+6(x+3)&=58\\4x+6x+18&=58\\10x+18&=58\\10x&=40\\x&=4\end{aligned}\)

Substitute the found value of x into the first equation and solve for y:

\(y=4+3\)

\(y=7\)

Therefore, the number of cars rented was:

Answer:

x = -48

Step-by-step explanation:

The equation is,

→ x/4 = -12

Let's solve for the value of x,

→ x/4 = -12

→ x = -12 × 4

→ [ x = -48 ]

Hence, the value of x is -48.

Answer:

how many weeks tho

Step-by-step explanation:

you don't make it clear sorry

Answer:

3 times as great

Step-by-step explanation:

The most amount of water is 3/4 full

The least amount of water 1/4 full

To get from 1/4 to 3/4, you multiply by 3:

\(\frac{1}{4} * \frac{3}{1} = \frac{3}{4}\)

(I made 3 into 3/1 to show how you multiply across easier)

Answer:

mean=9

median=9

range=16

Based on the given information we have;

Mean = 9 miles ​

Median = 9 miles ​

Range = 6 miles

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

We are given that people in Mr. Kendrick's office drive 10, 3, 17, 1, 8, 6, 12, and 15 miles to work.

Mean= 10 + 3 + 17+ 1 + 8 + 6+ 12 + 15 / 8

Mean= 9

The median=9

The range = maximum - minimum

= 6

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Answer: y + 5 = 2 ( x + 1 ) = 2 x − y + 2 = 5

Answer:

 Slope = 4.000/2.000 = 2.000

 x-intercept = 3/2 = 1.50000

 y-intercept = -3/1 = -3.00000

Step-by-step explanation:

I hope this helped!

It is impossible to increase the cost of an item by less than 1%: False. The counterexample is stated below.

A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement typically has the form "if P then Q."

Where:

P and Q represent sentences.

In this scenario, we can reasonably infer and logically deduce that it is false to state that "it is impossible to increase the cost of an item by less than 1%" because the counterexample is that, if a television costs $20,000, and its price increases by $100, its markup price would be less than 1%.

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Answer:

Answer is B.) y= x+1

Step-by-step explanation:

hope this helps

Answer:

(-8, 0) and (-2, 0)

Step-by-step explanation:

The root of a parabola are the places at which the parabola intersects the x-axis. As one can see, on the graph these points are the following: (-8, 0) and (-2, 0). Thus, the roots of the parabola are (-8, 0) and (-2, 0).

Answer:

-8 and -2

Step-by-step explanation:

Hello!

The roots of the parabola are the points where the graph intersects the x-axis. The x-axis is the equation y = 0.

There are two roots for this parabola, as the vertex is lower than y=0, and it opens up.

The two points of intersection are:

Therefore, the roots of the parabola are -8 and -2.

Answer:

  ...; 0; 22

Step-by-step explanation:

The pattern appears to consist of two interleaved arithmetic sequences.

__

  Odd-numbered terms increase by 5: 2, 7, 12, 17, 22.

  Even-numbered terms decrease by 6: 18, 12, 6, 0.

The next two terms are 0 and 22.

For the function, y = log₄ (x + 16) - 1, it has x-intercept of -12 and y-intercept of 1.

Logarithmic functions are functions expressed in another way for exponential functions. It is the power to which any number should be raised to yield other values.

Logₐ x = n can be written in exponential form as x = aⁿ.

y = log₄ (x + 16) - 1

x-intercept is the x-coordinate of the point when y = 0.

0 = log₄ (x + 16) - 1

For the left hand side to be equal to 0, the term log₄ (x + 16) must be equal to 1.

log₄ (x + 16) = 1  

⇒ x + 16 = 4       (∵ logₐ a = 1)

⇒ x = -12

y-intercept is the y-coordinate of the point where x = 0.

y = log₄ (0 + 16) - 1

y =  log₄ (16) - 1

y =  log₄ (4²) - 1

logₐ mⁿ = n logₐ m

⇒ y = 2 log₄ (4) - 1

⇒ y = 2 - 1     (∵ log₄ (4) = 1)

⇒ y = 1

Hence, the function y = log₄ (x + 16) - 1 has x-intercept of -12 and y-intercept of 1.

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Answer:

he is seven years older.... and is currently 2x older

Step-by-step explanation:

7x2=14

Answer:

  $9,039.81

Step-by-step explanation:

Given the exponentially decaying price history of a vehicle as $21,000; $18,900; $17,010; $15,309; $13,778.10; $12,400.29; you want to know the value after 8 years of depreciation at the same rate.

The multiplier of value each year is 18900/21000 = 0.9. This means the value of the vehicle can be represented by the price function ...

   price = (initial price) · 0.9^t

where t is the number of years the vehicle has depreciated.

After 8 years, the value will be ...

  price = $21000·0.9^8 ≈ $9,039.81

After 8 years, the value of the car will be $9,039.81.

The probability of drawing a face card followed by condition of drawing non face card is equal to 18% ( approximately).

In a standard deck of cards,

There are 12 face cards 4 jacks, 4 queens, and 4 kings

And 40 non-face cards 10 numbered cards each for the 4 suits.

The probability of drawing a face card on the first draw is

=  12/52

= 3/13.

Assuming a face card was drawn on the first draw,

There are now 51 cards remaining in the deck.

Of which 40 are non-face cards.

Probability of drawing a non-face card on the second draw is

= 40/51.

Probability of both events happening drawing a face card followed by a non-face card

= Multiply the probabilities of the individual events

= (3/13) x (40/51)

= 120/663

=  0.181approximately  

= 18% (rounded to the nearest whole number).

Therefore,  the probability of drawing a face card followed by drawing a non-face card in a standard deck of cards is approximately 18%.

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Using the concept of Unit Cost, $5.34 is Jacks` total bill for buying 3.5 pounds of carrot and 1.25 pound of broccoli.

The unit price is  measurement used to represent the price of a particular good or service to be exchanged with the customers or consumers for money. The unit price refers to the price/unit of measures, such as price per pound, quart, ounce, or other units of weight or volume of the food package.

The unit price is important for both of customers and organizations. An organization cannot sustain without unit price itself for a long period by selling products at a lower price. Similarly, customers would not be able to buy the product if the value of the product is less than the price. The researcher suggests that the unit price information helps shoppers to save around 17-18% in supermarkets when they are educated on how to actually use it.

We are given Carrot cost of per pound is $0.99.

Therefore Carrot cost for 3.5 pounds=3.5×0.99= $3.465

Similarly, Broccoli cost of per pound is $1.50.

Therefore, broccoli cost for 1.25 pounds =1.25×1.50=1.875

Total bill = Broccoli cost+ Carrot cost

Total bill =3.465+1.875=$5.34

Hence,$5.34 is Jacks` total bill for buying 3.5 pounds of carrot and 1.25 pound of broccoli.

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Answer: I have been asked the same question I believe that it is obtuse and isosceles.

Step-by-step explanation: Well a triangle with 1 obtuse angle means it is an obtuse triangle but a triangle with 2 congruent means it is an isosceles triangle.

This angle is isosceles as well as obtuse.

What is an isosceles triangle?

Isosceles triangle is a triangle that has two equal sides.

What is an obtuse-angled triangle?

An obtuse-angled triangle is a triangle that consists of an interior angle of more than a right-angle (90)°.

As this triangle has two congruent side, it is an isosceles triangle.

Similarly, it has one obtuse angle. Therefore, this triangle is an obtuse-angled triangle.

Hence, for this triangle, B. Isosceles C. Obtuse both apply.

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Area = length x width

Length = x + 6 + x + 2 = 2x + 8

Width = x + 4 + x = 2x + 4

area = 2x + 8 * 2x + 4

multiply each term by each term

Area = 4x^2 + 24x + 32

Answer: I think this is correct but i'm not sure! the answer should be 48 im not sure though

Step-by-step explanation:

6 x 2 = 12 x 4 = 48

The temperature at the point where the clouds begin to form is 77.65 °F

Given: The starting point is 1234 feet and air temperature is 79.4°F

You climb to where you notice clouds beginning to form.It can be observed that the temperature decreases by 3.5°F per 1000 feet as we go up.

Using this information, we can calculate the temperature at the point where the clouds start forming.

Let the height of the point where clouds begin to form be x feet above the starting point. As per the question, the temperature decreases by 3.5°F per 1000 feet as we go up.

Therefore, the temperature at the height of x feet can be calculated as:

T(x) = T(1234) - 3.5/1000 * (x - 1234)°F , where

T(1234) = 79.4°F

Substituting the value of x = 1234 + 500, (as we need to know the temperature at the point where clouds begin to form) we get:

T(1734) = T(1234) - 3.5/1000 * (1734 - 1234) °F

= 79.4 - 3.5/1000 * 500 °F

= 79.4 - 1.75 °F

= 77.65 °F

Therefore, the temperature at the point where the clouds begin to form is 77.65 °F

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Answer:

The circle is centered at (9, -8) and diameter 8.

Step-by-step explanation:

(x-h)^2 +(y-k)^2 =r^2

(x-9)^2+(y+8)^2=4^2

Center: (h,k) = (9,-8)

Radius: r=4

The circle is centered at (9, -8) and radius is 4 or diameter 8.

The name of the segment inside the large triangle is called the: 3. angle bisector.

The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.

The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.

A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.

Therefore, we can state that the name of the segment is: 3. angle bisector.

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Answer:

32

Step-by-step explanation:

Answer:

732×pi cm³

Step-by-step explanation:

we have all the data and the formula.

so, we only need to do the raw calculations.

Vc = pi×r²×h/3

r = the radius of the basic circle

h = the height.

since the volume of the frustum is the volume of the large cone minus the volume of the small cone, we need to calculate both volumes and then subtract the smaller from the larger number.

oh, and we need to calculate also the radius of the base circle of the small cone. since they are similar bodies, all lines use the same ratio or scaling factor to convert from one cone to the other.

that includes height and radius.

we know the height of the large cone is 16+4=20 cm.

and set know that the height of the small cone is 16 cm.

so, the scaling factor is 16/20 = 4/5 to go from the large to the small cone.

that means that the radius of the small cone is

15 × 4/5 / 3×4 = 12 cm

so, now to the 2 cone volumes :

the large cone

Vcl = pi×15²×20/3 = pi×225×20/3 = pi×75×20 =

= pi×1500 cm³

the small cone

Vcs = pi×12²×16/3 = pi×144×16/3 = pi×48×16 =

= pi×768 cm³

the volume of the frustum is therefore

Vf = Vcl - Vcs = 1500×pi - 768×pi = 732×pi cm³

Hope it Helps

Mark me as brainliest please

Answer: 50,000 pennies

Step-by-step explanation: there are 100,000 centimeters in a kilometer, since a penny is 2 centimeters in length, divide 100,000 by 2 t get 50,000

The standard deviation measures the spread of data points around the mean. It considers all data points, not just the farthest or nearest ones. A higher standard deviation indicates a greater spread.

The standard deviation is a statistical measure that tells us how much the data points in a set vary from the mean. It provides information about the spread or dispersion of the data. To calculate the standard deviation, we take the square root of the variance, which is the average of the squared differences between each data point and the mean.

By considering all data points, the standard deviation provides a comprehensive measure of how spread out the data is. Therefore, the statement "The difference between the mean and the data point farthest from the mean" is incorrect, as the standard deviation does not focus on just one data point.

The statement "The difference between the mean and the data point nearest to the mean" is also incorrect because the standard deviation takes into account the entire data set. The statement "The difference between the mean and the median" is incorrect as well, as the standard deviation is not specifically related to the median.

Hence, the correct answer is "None of the above."

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Answer:

\(\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}\)

Step-by-step explanation:

Given

\(p = 60\%\)

\(n = 4\)

Required

The distribution of x

The above is an illustration of binomial theorem where:

\(P(x) = ^nC_x * p^x *(1 - p)^{n-x}\)

This gives:

\(P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}\)

Express percentage as decimal

\(P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}\)

\(P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}\)

When x = 0, we have:

\(P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}\)

\(P(x=0) = 1 * 1 *(0.40)^4\)

\(P(x=0) = 0.0256\)

When x = 1

\(P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}\)

\(P(x=1) = 4 * (0.60) *(0.40)^3\)

\(P(x=1) = 0.1536\)

When x = 2

\(P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}\)

\(P(x=2) = 6 * (0.60)^2 *(0.40)^2\)

\(P(x=2) = 0.3456\)

When x = 3

\(P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}\)

\(P(x=3) = 4 * (0.60)^3 *(0.40)\)

\(P(x=3) = 0.3456\)

When x = 4

\(P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}\)

\(P(x=4) = 1 * (0.60)^4 *(0.40)^0\)

\(P(x=4) = 0.1296\)

So, the probability distribution is:

\(\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}\)

The total area of kite LMNP with diagonal length of 6.4 m and 12.4m in square meters is 39.68 square meters.

Therefore the answer is 39.68 square meter.

To find the area of a kite, you need to know the lengths of its diagonals. The formula for finding the area of a kite is

(d1 × d2) / 2

where d1 and d2 are the lengths of the diagonals.

Here diagonals d1 = 6.4m and d2 = 12.4m, so

area = (d1 × d2) / 2

area = (6.4 × 12.4) / 2

area = 39.68 square meters

So area of the kite LMNP is 39.68 square meters.

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Answer:

1/10

step-by-step explanation:

----------------------------------

| animals | percent of animals |

----------------------------------

|    goats    |          16%           |

----------------------------------

|    camels    |          4%           |

----------------------------------

|    giraffes    |          6%            |

----------------------------------

|    llamas    |          6%           |

----------------------------------

|   deer    |          1%           |

----------------------------------

|   monkeys    |          10%           |

----------------------------------

|   birds    |          27%           |

----------------------------------

|   reptiles    |          14%           |

----------------------------------

|   bears    |          16%           |

----------------------------------

( sorry if the table above isnt 100% right or straight ^ )

first you add up all the percents of how much animals are in this exhibit

16 + 4 + 6 + 6 + 1 + 10 + 27 + 14 + 16

= 100 %

then since we are looking for the probability of stopping in front of the monkeys, we take that 100 we got earlier and get the 10% of monkeys from our table

10/100

but since there isnt a 10/100 on the answers we look for something that equals to 10/100 and 1/10 does since you can just times both the 1 and 10 to equal the 10 and 100 you were looking for

1/10

making 1/10 your answer!

hope this helps! and if you need anymore help on this math question just ask me :)

Your Answer Should Be C.

The required inverse of the given function is expressed as \(y=\sqrt{\frac{x+10}{7} }\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Replacing y with x

x = 7y² – 10

Making y the subject of the formula:

7y² = x+ 10

Dividing both sides by 7

7y²/7 = (x+10)/ 7

y² = (x+10)/ 7

Taking the square root of both sides

\(\sqrt{y^{2} } =\sqrt{\frac{x+10}{7} }\)

\(y=\sqrt{\frac{x+10}{7} }\)

Hence the required inverse of the given function is expressed as  \(y=\sqrt{\frac{x+10}{7} }\)

Complete question:

Which equation is the inverse of y = 7x² – 10

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