2. A recent study of 35 students determined that the mean number of hours per week they played video games was 16.6 hours. The standard deviation of the population was 2.8 hours. Find a 95% confidence interval of the population mean.

Answer:

P=3000$

T=2 years

R=1.6% per annum

Now,

interest=(3000×2×1.6)/100=96$

Amount=P+interest=3096$

Hence,Conan needs to pay back 3096$ and the interest is 96$

The water level is rising at a rate of 0.5tf² /min*ft². This is in cubic feet per minute per square feet, if you want to express this in terms of height, you will have to convert the units

To find out how fast the water level is rising, we need to use the concept of volume flow rate. Volume flow rate is the volume of fluid that passes through a given surface per unit of time. In this case, the volume flow rate is given as 3tf^3/min.

Since the base of the tank is a rectangle with dimensions 2x3 ft, we can find the area of the base by multiplying the length and width:

2 ft * 3 ft = 6 ft^2

To find the rate of change of the water level, we need to divide the volume flow rate by the area of the base.

3tf^3/min / 6 ft^2 = 0.5tf^3/min*ft^2

So the water level is rising at a rate of 0.5tf^3/min*ft^2

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When the inverse of a function is itself a function it is called self-inverse.

A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y.

A self-inverse function ‘reverses itself’ to produce the original input.

A function f is self-inverse if it has the property that f(f(x))=x for every x in the domain of f. In other words, f(x)=f−1(x).

For example, 1x and 3−x are self-inverse.

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Answer:

$7500

Step-by-step explanation:

Let x = amount of monthly sales.

Choice A:

"monthly salary of $500 plus a bonus of 25% of his monthly sales"

monthly salary = 0.25x + 500

Choice B:

"$2,000 monthly salary with a 5% bonus on sales"

monthly salary = 0.05x + 2000

We set the total monthly salaries equal and solve for x.

0.25x + 500 = 0.05x + 2000

0.2x = 1500

x = 1500/0.2

x = 7500

Answer: $7500

The numbers in the arrangement can be represented by x, y, z, a, b, c and d, where x is at the top and d is at the bottom. The relationship between the numbers is as follows:

x = y - z

y = a - b

z = c - d

We can use this information to find the values of z, c, and d in terms of x, y, and a:

z = y - x

c = z + d

d = z - c

Since we are looking for the four greatest distinct possible values for z, we can assume that x, y, and a are as small as possible (i.e. 0) and c and d are as large as possible.

Thus, the four greatest distinct possible values for z are:

z = y - x = 0 - 0 = 0

z = a - y = 0 - 0 = 0

z = c - d = c

z = c - d = d

The sum of these four values is 0 + 0 + c + d = c+d.

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The outcome for the event "at least two tails" is HTT. Option B

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.

HHH → All heads

HHT → Two heads + one tail

HTH → Two heads + one tail

HTT → Two tails + one head

THH → One tail + two heads

THT → Two tails + one head

TTH → Two tails + one head

TTT → All tails

Therefore, At least two tails means → Sample space outcome with two tails Or all tails

Therefore, from the given options HTT is having two tails. Option B is the correct option.

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Answer:

the answer is

The answer is

The answer is

The answer is 73

Step-by-step explanation:

A right triangle with congruent legs and acute angles is an Isosceles Right Triangle.

A special right triangle is a right triangle that has a consistent characteristic that facilitates calculations on the triangle or for which straightforward formulas are available.

Angles in a right triangle, for instance, might create straightforward connections like 45°-45°-90°. An "angle-based" right triangle is what this is. When the side lengths of a right triangle form ratios of whole numbers, such as 3:4:5, or other unusual numbers, like the golden ratio, the triangle is said to be "side-based."

Without using more complex techniques, one can rapidly determine different lengths in geometric problems by understanding the relationships between the angles or side ratios of certain particular right triangles.

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let's hmmm hmmm multiply both sides by the LCD of all denominators, that way we do away with the denominators and see what "x" is

[tex]\cfrac{x+1}{2}+\cfrac{x+2}{3}=3-\cfrac{x+3}{4}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{x+1}{2}+\cfrac{x+2}{3} \right)=12\left( 3-\cfrac{x+3}{4} \right)} \\\\\\ (6x+6)+(4x+8)=36-(3x+9)\implies 10x+14=36-3x-9 \\\\\\ 10x+14=27-3x\implies 10x=13-3x\implies 13x=13 \\\\\\ x=\cfrac{13}{13}\implies x=1 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{1-4x}{10}-\cfrac{2x+1}{2}=\cfrac{5x+1}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{1-4x}{10}-\cfrac{2x+1}{2}\right)=10\left( \cfrac{5x+1}{5} \right)} \\\\\\ (1-4x)-(10x+5)=10x+2\implies 1-4x-10x-5=10x+2 \\\\\\ -14x-4=10x+2\implies -4=24x+2\implies -6=24x \\\\\\ \cfrac{-6}{24}=x\implies -\cfrac{1}{4}=x[/tex]

Answer:

（1）：

angle1/2/3/4=90

angle6=51

angle7=40

angle8=89

angle9=51

angle10=40

angle12=50

angle13=130

angle14=50

Step-by-step explanation:

Q1：

angle1 2 3 4 divided 360 into four equal parts

so 360/4=90

angle11=110degree

so angle12 is 180-130=50 degree

because angle 12 3 10 are in triangle

their sum is 180

so angle 10=180-90（angle3）-50（angle12）=40

because angle 10 5 6 sum is 180

so angle 6 is=180-89（angle5）-40（angle10）=51

because angle 5 6 7 sum is 180

angle7=180-51（angle6）-89（angle5）=40

angle8=angle5=89

angle9=angle6=51

angle12 &13sum is 180

so angle13=180-50=130

angle14=angle12=50

Using factorization method to solve the quadratic equation, the number of seed Martha and Miguel donated are 5 and 10 respectively

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants, and x is an unknown variable. The solution to such an equation is a value of x that will make the equation true.

To determine the number of seeds they donated, we have to write two equations and solve.

data;

The product of the seeds is (2x - 3)(4x - 6) = 8x² - 24x + 18

This can be written as

8x² - 24x + 18 = 50

Solving the quadratic equation;

8x² - 24x + 18 - 50 = 0

8x² - 24x - 32 = 0

Using factorization method;

8(x - 4)(x + 1) = 0

x - 4 = 0, x = 4

x + 1 = 0, x = -1

x = 4, x = -1

The number of packs Martha donated is

Martha = 2x - 3 = 2(4) - 3 = 5

The number of packs Miguel donated is

Miguel = 2 * 5 = 10

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The number which has a finite number of digits after the decimal point is a terminating decimal.

The decimal is said to be terminating decimal if that has a finite number of digits after the decimal point. Decimal numbers are used to represent the partial amount of whole just like fractions. The number which has a finite number of digits after the decimal point is referred to as a terminating decimal. A number has a terminating decimal expansion if the digits after the decimal point terminate or are finite. The fraction 5/10 has the decimal expansion of 0.5 which is a terminating decimal expansion because digits after the decimal point end after one digit. Terminating decimal has finite digits and non-terminating decimals do not have finite digits. A number with a terminating decimal is always a rational number.

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If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2

We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.

And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.

Given that  sinθ⋅cosθ = 1/2

2(sinθ⋅cosθ) = 1             .........(1)

We know that trigonometric identity,

sin(2θ) = 2 sinθ cosθ

so equation (1) becomes,

sin(2θ) = 1            

We know that sin(π/2) = 1

Comparing with equation sin(2θ) = 1 we get,

2θ = π/2

θ = π/4          

Using trigonometric table,

sin(π/4) = 1/√2

and cos(π/4) = 1/√2

The value of  sinθ+cosθ would be,

sin(π/4) + cos(π/4)

= (1/√2) + (1/√2)

= 2/√2

= √2

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The complete question is:

If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ

a) The ordered pair so that the set still remains the function is (-5, 17)

b) The ordered pair so that the set does not remain the function is (-26, 15).

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

A Relation is said to be a function if the input value or the x- value is unique and have their corresponding output.

But if the input value repeats then it may no longer be a function.

First, Add a ordered pair so that the set still remains the function as

(-5, 17)

and, Add a ordered pair so that the set does not remain the function as

(-26, 15).

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By the concept of the proportional method we determine that the height of the tower would be 48 feet.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

The model given can be interpreted by the concept of proportional method

a : b : : c : d.

Therefore,

5 : 6 : : 40 : x.

5/6 = 40/x.

5x = 240.

x = 240/5.

x = 48 feet.

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Answer: (4+2)•(3^2?

Step-by-step explanation: I hope that helps I don't know how to explain but ya. But that's where u put the parentheses.

Answer:

(4+2×3)^(2)

Step-by-step explanation:

First, because parenthesis are being used, we will start by multiplying 2 by 3, giving us 6

(4+6)^(2)

Then, we add 6 to 4

(10)^2

and we then raise 10 to the 2nd power

100

Answer:

I)3^4 x 3^7=3^4+7(b/c the base is similar)

3^4 x 3^7=3^11

Ii) first 3^4=3x3x3x3=81

3^7=2187

then 81 x 2187=177147

On solving the provided question, we can say that by permutation If an ID card has six digits and each digit may only be used once, then 151,200 distinct ID cards can be created.

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.

There are 6 digits on a card ( 0 - 9 ).

10 * 9 * 8 * 7 * 6 * 5 = 151,200

If an ID card has six digits and each digit may only be used once, then 151,200 distinct ID cards can be created.

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Answer:

Its first option. bcz its doubled... right..

The numbers are sort from least to greatest as 0, 1/13, 49/100, 8/9, 1/2, 1, 11/10

A fraction can be defined as the part of a whole number, variable or element.

There are several types of fractions, some of which includes;

From the information given, we have the fractions;

0, 1, 1/2, 8/9, 49/100, 11/10, 1/13

To arrange the values from least to greatest, we have to divide the fractions and find their decimal forms, we have;

1/2 = 0.5

8/9 = 0.89

49/100 = 0.49

11/10 = 1.1

1/13 = 0. 08

However, the arrangement is 0, 1/13, 49/100, 8/9, 1/2, 1, 11/10

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The domain of the function f(x) = ∛x + 2 is all real numbers such that x ≥ 0. This is because the cube root function is defined only for non-negative numbers.

What do a function example's range and domain mean?

A straightforward function, such as f(x) = x2, can have a domain (what goes in) of just the counting numbers 1, 2, 3, etc., and a range (what comes out) of the set 1, 4, 9, etc. Another function, g(x) = x2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...

For the range, the function f(x) = ∛x + 2 is a monotonically increasing function over the domain, which means that it increases as the input x increases. Therefore the range of f(x) = ∛x + 2 is all real numbers greater than or equal to 2

So the domain is x>=0 and the range is y>=2

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a) An equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006 : y = -0.5x + 3.4

b) The percent of recorded music sold as full-length cassettes in 2004 = 1.9%

As, between 2001 and 2006, the percent of recorded music sold was decreased by about 0. 5% per year.

This means, the slope m = -0.5

In 2001, full-length cassettes represented 3. 4% of total music sales.

This means the y-intercept would be c = 3.4

So, an equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006 would be,

y = mx + c

Substituting value of m and c,

y = -0.5x + 3.4

Now  to find the percent of recorded music sold as full-length cassettes in 2004

Here, the number of years x would be

x = 2004 - 2001

x = 3

So, the percent of recorded music sold would be,

y = (-0.5 × 3) + 3.4

y = 1.9%

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Answer:

Step-by-step explanation:

Plug in 5 for h

6(5)+7(5)

30+35=65

65

Answer:

[tex] \sf \: 6h + 7h = 65[/tex]

Step-by-step explanation:

Given information,

→ 6h + 7h

→ h = 5

Now the final value will be,

→ 6h + 7h

→ 6(5) + 7(5)

→ 30 + 35

→ 65 => final value

Hence, the answer is 65.

An inverse relation and function is the opposite of a relation and functions.

An ordered pair collection is referred to as a relation. Let's think about the two sets A and B. The cartesian product of A and B, indicated as A x B, is the set of all ordered pairs of the form (x, y), where x A and y B. A relation is any subset of the cartesian product A x B.

The inverse function f-1 takes each element in the range of an original function f and transfers it to the equivalent element in the function's domain. F must be one-to-one and onto since we are mapping the function f backward.

An onto function only has one output for each input, but a one-to-one function only has one input in the domain for each output in the range. This implies that each input has precisely one input for each output in order to have both.

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Can be cracked within eight hours by the average hacker.

With spaces included in the character count, 8 characters equals between 1 and 2 words. If spaces are excluded from the character count, 8 characters equals between 1 and 3 words.

There are 8-character passwords with capital letters, lowercase letters, and numerals that begin and end with the same symbol.A password of eight characters with just lowercase and capital letters offers 200 billion potential permutations.“1uppercase” is an example of an 8-character password. This password has one uppercase, one lowercase, one number, and one special character.

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The rectangular prism's volume is equal to [tex]$V=9.375 \mathrm{~m}^3$[/tex]. Prism volume (V) is equal to B ×h, where h is the prism's height and B is the area of the base.

1.25 metres in length, 2.5 metres in width, 3 metres in height, and a diagonal length of 4.10030487 metres make up the total surface area. [tex]$\mathrm{S}_{\text {tot }}[/tex]=[tex]28.75 \mathrm{~m}^2$[/tex] , Latitudinally exposed area [tex]$S_{\text {lat }}=22.5 \mathrm{~m}^2$[/tex] , maximum surface area is [tex]$S_{\text {top }}=3.125 \mathrm{~m}^2$[/tex] , surface area of the ground is [tex]$S_{\text {bot }}=3.125 \mathrm{~m}^2$[/tex] so that the volume is [tex]$V=9.375 \mathrm{~m}^3$[/tex]

When determining the volume of a rectangular prism , we multiply its length, width, and height. The base's area multiplied by the height gives the rectangular prism its volume. Length, width, and height are the cubic units that make up a rectangular prism's volume. Any rectangular solid's volume, V, is equal to the sum of its dimensions, height, width, and depth. In terms of the area of the base, we might alternatively express the formula for a rectangular solid's volume. Size times width equals the base's area, B.

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Answer:

The numbers are being divided by 2 each time.

240/2 = 120

120/2 = 60

So the next set of numbers would be:

30, 15 because

60/2 = 30

30/2 = 15

Step-by-step explanation:

Hope it helps!

The ordered pairs that defines the solutions of the system of equations f(x) = x² - 2x + 3; f(x) = -2x + 7 are

(2, 3) and (-2, 11)

Ordered pairs refers to the arrangement of 2 numbers in the form (a, b)

As used in the cartesian coordinates

a refers to a point in the x direction b refers to a point in the y direction

Solutions of the system of equation is the points where the straight line intersect the curve or where the two graphs intersect.

the point of intersection

x² - 2x + 3 = -2x + 7

x² - 2x + 2x + 3 - 7 = 0

x² + 3 - 7 = 0

x² - 4 = 0

solving for x

x² = 4

x = √4

x = 2 OR -2

solving for y

For x = 2, y = -2 * 2 + 7 = 3

For x = -2, y = -2 * -2 + 7 = 11

hence we have the points to be (2, 3) and (-2, 11)

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Answer: As for the inequality question you asked,

-2/3, -11/3, and 2.5 are decimal numbers.

-11/3 is smaller than -2/3 because -3.67 is smaller than -0.67

-2/3 is smaller than 2.5 because -0.67 is smaller than 2.5

So the inequality that correctly orders the numbers -2/3, -11/3, and 2.5 is -11/3 < -2/3 < 2.5

It's worth noting that this inequality uses the less than (<) symbol to show the order of the numbers from the smallest to the largest, and it's also worth to remember that this inequality is true only for these specific values, if any of the values were changed it would've resulted in a different inequality.

Step-by-step explanation:

The normal price of the car is given as follows:

£9000.

The normal price of the car is obtained applying the proportions in the context of this problem.

In a sale, the normal price of a car has been reduced by 30%. The new price is £6300, meaning that 70% of the price x is equivalent to 6300.

Thus the equation used to obtain the value of x is given as follows:

0.7x = 6300

x = 6300/0.7

x = £9000.

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