The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months. Find the probability that
sample of 29 smoke detectors will have a mean lifetime
between 57 and 64 months. Assume that the sample is taken from a large population and the correction factor can be ignored.
Round the final answer to at least four decimal places and intermediate z-value calculations to two decimal places.

Answer:

1st number linline

Step by step explanation:

x < -3 means x is less than -3

so it should be any number less than -3

In the 2nd number line represents

[tex]x \leqslant - 3[/tex]

so the answer is 1st one

After simplification, the value of expression is, (x + 1) / (2x - 1).

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The expression is,

⇒ 10x² + 10x / 20x² - 10x

Now, We can simplify as;

⇒ (10x² + 10x) / (20x² - 10x)

⇒ 10x (x + 1) / 10x (2x - 1)

⇒ (x + 1) / (2x - 1)

Thus, The value of expression is, (x + 1) / (2x - 1).

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As a result, his monthly payment of $289.41 for a loan of $43,000 compounded monthly over 20 years at an APR of 2.4% will be required.

By dividing initial principal by the risk premium, the time it has been and other factors, simple interest is determined. Simple return equals principal plus interest plus hours is the technique used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating this is as a portion of the principal amount. For example, if he borrowed $100 from a buddy and agrees to pay back the loan at 5% interest, he will just pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must lend money when you lend it. Typically, interest is determined as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.

given

Assuming a specific interest rate (r), principal (p), and number of times the interest is compounded annually (n), we can calculate the total amount owed on a loan (A) as follows:

A = p(1+ r/n) nl

Because in our example, n = 12 (monthly), p = $43,000, r = 2.4% = = 0.024, and t = 20 years.

A = $69457.89.

$289.41 per month for a 20-year term.

As a result, his monthly payment of $289.41 for a loan of $43,000 compounded monthly over 20 years at an APR of 2.4% will be required.

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The quadratic regression equation is y = 1.38x^2 - 5.77x + 0.96

From the question, we have the following parameters that can be used in our computation:

(-1,8), (5,-4), (7,8), (2,-6)

Using a graphing calculator, we have the following summary:

function value

mean of x 3.25

mean of y 1.5

correlation coefficient r 0.9990171837

A 1.380577428

B -5.769028871

C 0.9553805774

The equation is represented as

y = ax^2 + bx + c

So,, we habe

y = 1.38x^2 - 5.77x + 0.96

Hence, the equation is y = 1.38x^2 - 5.77x + 0.96

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The area of the top of the second mattress , 3/2x²

The equation to model the problem is y= 1.22x.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

let the side of mattress one be x

and, the side of Mattress 2 be y.

So, area of Mattress 2 / Area of Mattress 1 = 1 1/2

area of Mattress 2 / Area of Mattress 1 = 3/2

y²/ x² = 3/2

(y/ x)² = 3/2

y/x = √3/2

y /x = 1.22

Hence, the equation is y= 1.22 x .

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The function which models the data as represented on the graph will be; [tex]f(x) = 0.8(1/2)^x[/tex].

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

The given graph is an exponential function and should take the form;

[tex]f (x) = a (b)^x[/tex]

Hence, using values from the graph;

For ( -1, 0.2 ) = a • b..........(i)

For (0, 0.8); 10.5 = a • b².........(ii)

=> x=0 and y= 0.8

So.

0.8=a(1/2)^0

0.8=a

Thus, the rule for the function is; y=0.8(1/2)^x

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Answer: c

Step-by-step explanation:

-3v - 2v > 35

combine like terms: -5v > 35

divde by the same term (isolate the variable): -5v/-5 , 35/-5

v < -7

When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.

Its precise nature is understood to be the figure is probably smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the median and excess. A fractional number can always be checked to discover if it is a prime number. A statement having two equal sides and an equal sign in the intermediate is referred to as a linear expression. Every variable's classes are listed in lowest to highest in the general form of any formula. The formula for a linear function is x + b = 0. The simplified version of a two-variable mathematical expression is an x + b y + c = 0. (or something similar). Either conditioned equations or identities provide categories for equations. An identity holds true because of whatever value of the variables.

given

The aforesaid issue is easily resolved by doing the following:

Considering that,

Four Bs are worth three As.

It can be written as;

3A = 4B

determining B's value

B = 3A/4 (Equation 1) (Equation 1)

Now,

A B is worth five Cs.

So, 5B = C (Equation 2) (Equation 2)

Calculating B's value in equation 1

= 15A/4 = C

= 4C = 15A

2C = (15/2)A

2C = 7.5A

Therefore, the solution is 2C = 7.5A

When B and C are the currencies of different nations, two Cs are worth 7.5 As. Five Bs are equivalent to one C, while three As are worth four Bs.

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Answer:

The water cycle involves the continuous movement of water on, above, and below the surface of the Earth. In the cycle, water can exist in three states: liquid, solid, and gas. During evaporation, liquid water changes into water vapor, the gaseous state of water, as it heats up and turns into steam. When water vapor cools, it can condense back into liquid form, such as when it forms clouds. Precipitation, such as rain or snow, occurs when water droplets in the clouds become heavy enough to fall from the sky. When precipitation reaches the ground, some of it may flow into rivers and streams and eventually make its way to the ocean. Some of it may also be taken up by plants or seep into the ground, becoming part of the groundwater system. Eventually, the water in the groundwater system may evaporate back into water vapor and start the cycle over again.

The total area of all the pieces would be: -  x² + y² + 2xy = (x + y)².

This tile collection is composed of four tiles: two squares, each with sides of length x, and two rectangles, each with sides of length x and y.

The total area of all of the pieces can be expressed algebraically as A = x² + 2xy.

This expression can also be written as A = x² + xy + xy.

This tile collection is an example of a two-dimensional shape composed of two squares and two rectangles.

By adding the areas of each of these shapes, we can calculate the total area of the tile collection.

The area of each square is x², and the area of each rectangle is xy.

Adding these three expressions together gives us the total area, A = x² + 2xy.

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The rate of change of the hypotenuse is given as follows:

dh/dt = 2 in/sec.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The hypotenuse is then given as follows:

h² = x² + y².

For this problem, the hypotenuse has the value given as follows:

h² = 33² + 44²

h = square root(33² + 44²)

h = 55.

Applying implicit differentiation, the rate of change of the hypotenuse is obtained by the equation as follows:

h dh/dt = x dx/dt + y dy/dt.

Replacing the values, the rate of change is calculated as follows:

55dh/dt = 33 x 10 - 44 x 10

55dh/dt = -110

dh/dt = -110/55

dh/dt = 2 in/sec.

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The domain of the function 5h + 2d = 15 is [0, 3].

What is domain and range of a function?

The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x).

                           The collection of numbers that the function assumes is known as its range. The values that the function outputs when we enter an x value are in this set.

5h + 2d = 15

2d = 15 - 5h

d = (15 - 5h)/2

For h = 0, d = 15/2 = 7.5

For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.

For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.

For h = 3, d = (15 - 15)/2 = 0 miles

The domain of the function is [0, 3].

Thus,

The domain is [0, 3].

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Answer: The perimeter triples.

Step-by-step explanation:

Since there is a direct variation, if the side length triples, so does the perimeter.

Using the concept of multiplication and division, the number of chocolate sold each month is 400 packs.

To determine the number of chocolate biscuits in the shop, we have to determine how many is contained in each box and then multiply it by number of days in a month and then subtract the number of chocolate in the shop. This tasks involves the use of basic arithmetic operations to determine the number of packs sold.

The total number of packs of biscuits in the shop was 160 * 30 = 4800.

So, the number of packs of chocolate biscuits was 4800 - 2800 = 2000.

The shopkeeper sold 2000 packs of chocolate biscuits over 5 months, so he sold 2000 / 5 which will give us 400 packs of chocolate biscuits each month.

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The equation of the graph is y = -2/3x - 4

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

From the graph, we have

c = -4

So, the equation becomes

y = mx - 4

From the graph, we have the following point

(-6, 0)

So, we have

0 = -6m - 4

Evaluate

m = -2/3

So, we have

y = -2/3x - 4

Hence, the equation is y = -2/3x - 4

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Step-by-step explanation:

Let's call the time it took Pat and Rich to drive to the beach "x".

The time it took them to drive back was twice as long, so it took 2x hours.

The total time spent traveling was x + 2x = 3x hours.

Since they spent 9 hours traveling, 3x = 9 hours.

So, x = 9 hours / 3 = 3 hours.

This means it took Pat and Rich 3 hours to drive to the beach and 2 * 3 = 6 hours to drive back.

The experimental probability that the team made a goal on any given shot is 0.0625

From the question, we have the following parameters that can be used in our computation:

A soccer team made 2 goals out of 32 attempts in a game

The experimental probability that the team made a goal on any given shot is calculated as:

P = 2/32

Evaluate the quotient

P = 0.0625

Hence, the probability is 0.0625

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Answer:

1/2 bucket

Step-by-step explanation:

Each of the 8 buckets is 1/4 full.

The total amount of paint at the beginning is 8 × 1/4 bucket = 2 buckets.

Each student uses 1/4 of his paint. Combined, they use 1/4 of the total amount of paint in the buckets.

1/4 × 2 buckets = 1/2 bucket

Answer: 1/2 bucket

Answer:

1225 is what I got, not sure tho.

Using the properties of sets, (BU A)'n C = {h,q}

Null set or an empty set There isn't even one element in it. Finite Set: It only has a finite number of components. The element count of an infinite set is infinite. Two sets with the same members are said to be equal sets.

An object collection that is taken into account as a whole is referred to as a set. The elements or members of the set are the things that make it up. A set's components can be any type of object, but for our purposes, they are most frequently mathematical components like integers, functions, or other sets.

The list of all subsets of a,b,c,d is ϕ ,{a},{b},{c},{d},{a,b},{a,c},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}

(B U A) = {f,g,r,x,y,z}

(BU A)'n C = {h,q}

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Mr. Lopez cover in sand by 50 yd².

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Mr. Lopez is looking to fill a part of a park with sand.

And, The shape below represents the part of the park being covered in sand.

Now, We will find the area of figure as;

The park is mix of two figure rectangle and triangle.

Hence, We get;

Area of rectangle = 5 × 8

                           = 40 yd²

And, Area of triangle = 1/2 × 4 × 5

                                 = 10 yd²

Thus, The area of given figure is,

⇒ Area = 40 yd² + 10 yd²

⇒ Area = 50 yd²

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Answer:

There are 0

Step-by-step explanation:

Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true

Answer:

A 0

Step-by-step explanation:

There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.

If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.

The percentage of vehicles whose speeds are between 52 miles per hour and 70 miles per hour is 75%.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will fall within three standard deviations of the mean.

Given, The mean speed of a sample of vehicles along a stretch of highway is 64 miles per​ hour, with a standard deviation of 4 miles per hour.

[tex]\mu = 64[/tex] and [tex]\sigma = 4[/tex].

Now, 52 is 3 standard deviations away from the mean so 50% of the data falls into this category and 70 is 1.5 standard deviations away from the mean and 25% of the data falls into this category.

Therefore, 75% of the vehicles would fall into this category.

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Answer:

y = 5x

where

y = number of fence posts that Edwin installs
x = number of hours that Edwin takes to install y posts

Step-by-step explanation:

Let y = number of fence posts that Edwin installs in x hours

We have the relation:

y ∝ x where ∝ is the symbol for is-proportional-to

We can rewrite this as an equation using the constant of proportionality,k:

y =kx

Given y = 40 fences, x = 8 hours we get

40 = k(8) = 8k

or, switching sides

8k = 40

k = 40/8 = 5

So Edwin can install 5 fences per hour

Plugging this into the equation of proportionality

y = 5x

The correct answer is A: 600 <= money <= 2822.4.

This represents the range of possible values that Pankaj's accumulated money could fall into, given the specified conditions of the 3% interest rate compounded weekly for a maximum of 2 years. The lower bound, 600, represents the initial deposit amount, while the upper bound, 2822.4, represents the maximum amount of money Pankaj could earn after 2 years, assuming that interest is compounded every week.

Answer:

13

Step-by-step explanation:

Len n = number.

9n = 2n + 91

7n = 91

n = 13

Answer: 13

The solution satisfying y1(0)=14 and y2(0)=-3 are y1(t) = 14 * e^(tln(14/13)) / (1 + (14/13)e^(tln(14/13))) and y2(t) = -3 * e^(tln(-3/2)) / (1 + (-3/2)e^(tln(-3/2)))

The logistic equation is a non-linear ordinary differential equation that models the growth of populations over time.

The solution to the logistic equation with initial conditions y1(0)=14 and y2(0)=-3 is given by (from a graphing tool):

y1(t) = 14 * e^(tln(14/13)) / (1 + (14/13)e^(tln(14/13)))

y2(t) = -3 * e^(tln(-3/2)) / (1 + (-3/2)e^(tln(-3/2)))

Note: ln is the natural logarithm function.

The time t when y1(t)=7 can be found by solving for t in the equation y1(t) = 7.

From the graphing tool, we have

t = 1.08 when y1(t) = 7

he solution y2(t) becomes infinite when the denominator of the equation becomes zero.

This occurs when -3/2 * e^(t * ln(-3/2)) = -∞.

This can be written as t * ln(-3/2) = ∞, which occurs when t approaches positive infinity.

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Answer:15

Step-by-step explanation:

i did the math

Answer:

15

Step-by-step explanation:

15 x 2=30

15x3=45

The domain of the function is given as follows:

[-10,10].

The domain of a function is the set containing all the input values of the function.

Hence, on the graph, the domain of the function is composed by the values of x of the function, and is given as follows:

[-10,10]. (closed due to the closed circle).

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