6.2 What is the confidence level of each of the following
confidence intervals for u?
a. z+1.96
b. z+1.645
C.
c. z 2.575
d. z 1.282
e.
2
21.99
15151515
σ
115
n

you can do it first + each other and than × each them

The function of f and g is  (−3x − 8) ² is  (f× g)(x)

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

A composite function typically refers to a function that is contained within another function. The process of creating a function involves substituting one function for another. For instance, the composite function of f (x) and g is called f [g (x)]. You can read the composite function f [g (x)] as "f of g of x."

Given ,

h(x) = (−3x − 8) ²

h(x)=(f× g)(x).

(−3x − 8) ² = (f× g)(x)

Therefore  the function of f and g is  (−3x − 8) ² is  (f× g)(x)

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The ratio of tan is equal to opp/adj or sin/cos so Option H and Option I are correct.

we know that,

Tan = sin/cos

sin = opp/hyp

cos = adj/hyp

Tan = opp/hyp / adj/hyp

= opp*hyp / adj*hyp

= opp/adj.

Therefore The ratio of tan is equal to opp/adj or sin/cos so Option H and Option I are correct.

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The probability that a randomly selected teacher earns more than $400,000 a year is 57.26.

Given that, normally distributed with a mean of $45,000 and a standard deviation of $6,200.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Let X be the annual salary for all U.S. teachers with a mean salary45,000 and standard deviation of 6,200.

Hence, X∼N(45000,6200²)

The standardized value is obtained by:

Z= (X-μ)/σ

Where μ and σ are the mean and standard deviation of X, respectively.

The probability that a randomly selected teacher earns between 400,000 a year can be obtained by the following expression

P(X<400,000)= (400,000-45,000)/6200

= 355000/6200

= 57.26

Therefore, the probability that a randomly selected teacher earns more than $400,000 a year is 57.26.

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Answer:

  30.1°

Step-by-step explanation:

You want the acute angle whose sine is 0.5015.

When you know the sine of an angle and want to find the angle, you use the inverse sine, or arcsine, function.

  sin(x) = 0.5015

  x = arcsin(0.5015) ≈ 30.1°

The value of x is about 30.1 degrees.

__

Additional comment

There are an infinite number of angles that have that sine value. Only one of them is a positive angle less than 90°. Be sure your calculator is in degrees mode, if you don't want units of radians or grads. (Spreadsheet functions will give an answer in radians.)

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Answer:

inequality form: u≥−5

Interval Notation: [−5,∞)

If the above trend continues, the total number of tickets that will be sold by Cher for the Sixth Decade Still Touring" tour is: 871 tickets.

In mathematics, a trend is often a pattern of occurrence often depicted with the use of a graph. In this case, the pattern is an arithmetic sequence.

Note that the lowest number of tickets we can get to before we can no sell again is 1.

We get this by dividing 133 tickets by 11 (rate of decline).

133/11 = 12 (remaining 1)

Spread out, the sequence will appear as follows:

1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133.

Recall that the task is to determine the total number of tickets sold. We can either do this directly or use the Sum of an Arithmetic Sequence.

That is 1 + 12 +23 +34 +45 +56 +67 +78 +89 +100 +111 +122 +133 = 871; or

The formula for the sum of an Arithmetic Sequence:

Sn = n ((a₁ + aₙ)/2) Where

n is the number of terms and

a1 is the value of the first term and

aₙ is the value of the last term in the sequence.

that is:

n = 13
a₁ = 1
aₙ= 133

Hence
Sn = (13)((1 + 133) / 2) = (13)(134 / 2) = (13)(67)

= 871

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Answer: $89.91

Step-by-step explanation:

$99.90-10% of it would be $99.90-$9.99= $89.91.

Answer:

-1/2

Step-by-step explanation:

[tex]\frac{10}{6}[/tex] + [tex]\frac{-7}{6}[/tex] = [tex]\frac{-3}{6}[/tex] = [tex]\frac{-1}{2}[/tex]

Answer:

  (c)  8!/(6!·2!)

Step-by-step explanation:

You want to know how to compute the number of possible ways 2 different pizzas can be chosen from a menu of 8.

The formula for computing the number of combinations of n things taken k at a time is ...

  nCk = n!/(k!(n -k)!)

For 8 specialty pizzas chosen 2 at a time, this is ...

  8C2 = 8!/(2!·6!)

The appropriate answer choice is ...

  possibilities = 8!/(6!·2!)

__

Additional comment

That is (8·7)/(2·1) = 28 possibilities, assuming choice of different pizzas.

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The amount of liter in 37 gallons is 140.23 liter.

What is gallons and liter?

A gallon and liter (or US spelling liter) are units of measuring volume. There are two official symbols for liter: the Latin letter L in lower and upper case (l and L).

Given,

that 1 gallon is given as 3.79 liter

And to find the amount of liter in 37 gallon

After multiplication,

the amount of liter in gallon,

= 3.79(37)

=140.23

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Answer:

x=25

Step-by-step explanation:

(3x+10)+(5x-30)=180

8x-20=180

8x=200

x=25

Hopes this helps please mark brainliest

The Amplitude of the Wheel is 22.5

The Midline of the wheel is 25.5;

The period of the wheel is 6;

what is amplitude?

A sound is a type of energy that is created when objects vibrate. For it to spread, a medium is needed. As a result, sound cannot travel in a vacuum because there is nothing for the sound waves to travel through. The object's back-and-forth movement creates the sound. Sound vibration is the name for this. Additionally called oscillatory motion. Oscillation describes the regular rhythmic back-and-forth movement.

We know that:

Amplitude = [tex]=\frac{\max -\min }{2}[/tex]

So, substituting the minimum and maximum values as:

Maximum = 48;

minimum = 3;

So, Amplitude = [tex]=\frac{48-3}{2}=22.5[/tex]

So, Amplitude = 22.5;

Now,

we know that midline is half of the sum of minimum and maximum;

So,

Midline = [tex]=\frac{\max +\min }{2}[/tex]

So,

Maximum = 48;

minimum = 3;

Midline = [tex]=\frac{48+3}{2}=25.5[/tex]

So, Midline = 25.5;

and Period is 6 minutes;

So, we can frame the function by the negative cosine function;

[tex]n=f(t)=-a \cos (b t)+c[/tex]

[tex]\begin{aligned}&b=\frac{2 \pi}{\text { period }}=\frac{2 \pi}{6}=\frac{\pi}{3} \\&\therefore \quad h=-22.5 \cos \left(\frac{\pi}{3} t\right)+25.5\end{aligned}[/tex]

Height after time t = 3 will be:

[tex]\begin{aligned}&h=-22.5 \cos \left(\frac{\kappa}{3} \times 3 .\right)+25.5 \\&h=-22.5(-1)+25.5 \\&h=48\end{aligned}[/tex]

So, The height is 48;

Hence, After 3 minutes It is 48 meters high from the ground; is 48

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The amount of flour that is needed if the recipe is tripled is 11 ¹ / ₄ cups of flour

To find the flour needed for the recipe, first convert the mixed  fraction to an improper fraction for easier calculation.

= 3 ³ / ₄

= (4 x 3 + 3) / 4

= 15 / 4 cups of flour

If the recipe was tripled, then the number of cups of flour would also need to be tripled.

The amount of flour needed becomes:
= 15 / 4 x 3

= 45 / 4

= 11 .25

= 11 ²⁵ / ₁₀₀

= 11 ¹ / ₄ cups of flour

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The perimeter of triangle is 55.

What is perimeter of triangle?

The sum of the lengths of the sides is the perimeter of any polygon. In the case of a triangle,

Perimeter = Sum of the three sides

Given, QA=5, AP=12, RB= 9.5

We know tangent drawn from external point are equal.

therefore, PA=PB

PB=12

Similarly, RB=RC, RC =9.5

QC=QA, QC =6

Perimeter of triangle = PQ+PR+QR

=6+12+9.5+12+6+9.5

=55

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Answer:

0

Step-by-step explanation:

7 + (-8) + 2 + (-1)

is the same as:

7 - 8 + 2 - 1

Simplify these:

-1 + 1

Solve:

0

The value of x for the given equation is 3,11.

What is equation?

In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main Body:

According to given equation:

√2x+3 = -x+6

2x+3 = (-x+6)²

2x + 3 = x²+ 36 -12x

x²-14x +33 = 0

Now splitting the middle term t find the factor.

x² -11x -3x +33 = 0

x(x-11) -3(x -11) = 0

(x-3)(x-11) = 0

so either x- 3 = 0   or x -11 = 0

hence value for x = 3,11.

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By using exponent properties we will see that:

1) The expression is equal to 16.

2) The expression is equal to 4^6, so the correct option is B.

Here we want to solve the expression:

(2^0*4^(-2)*2^3*4^3)/2

Remember the exponent property:

a^x*a^y = a^{x + y}

let's rewrite the numerator:

2^0*4^(-2)*2^3*4^3

= (2^0*2^3)*(4^(-2)*4^3)

= 2^(0 + 3)*(4^(-2 + 3))

= 2^3*4 = 2^3*2*2 = 2^(3 + 1 + 1) = 2^5

Then we can rewrite the expression as:

2^5/2 = 2^4 = 16

b)

(1/4^-3)^2

The negative exponent means that we need to take the inverse:

(1/4^-3)^2 = (4^3)^2 = (4^3)*(4^3) = 4^(3 + 3) = 4^6

So the correct option is B.

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For the polynomial function,

The leading terms of the polynomial is 4

The degree of f(x) is 23

And the leading coefficient is 4x²³

Polynomial function:

Polynomial function means a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Given,

Here we have the polynomial function

f(x) = -4(x-2)¹²(6-x)¹¹

Now, we need to find the leading term, degree and the leading coefficient of the polynomial function.

The degree of a polynomial is the highest of the degrees of the polynomial's individual terms. In our case, the degree is 23.

The leading term is the term with the highest degree. In our case, the leading term is 4x²³

The leading coefficient is the coefficient of the leading term. In our case, the leading coefficient is 4.

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The water level is falling at the rate of -2/9π m³/min when the water's level is 12 meters high.

Given, water is draining from a conical tank at the rate of 2 m³/min.

Also, the height of the tank is 16 meters and the radius of the tank is 4 meters.

Using the concept of similarity in triangles, we get

r/4 = h/16

r = h/4

Now, the volume of the cone is

V = (1/3)πr²h

V = (1/3)π(h/4)²h

V = (1/3)π(h³/16)

On differentiating both the sides with respect to t, we get

dV/dt = π(h²/16)(dh/dt)

Now, as dV/dt = -2m³/min

-2 = π(144/16)(dh/dt)

dh/dt = (-2/9π)

Hence, the water level is falling at the rate of -2/9π m³/min when the water's level is 12 meters high.

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The true statement about the domain and the range is that the domain is discrete, and the range is continuous

From the question, the given parameters are:

Amount to download = $2.50

Amount to add each player = $1.50

Represent the number of players with x

So, we have the following representations

Total amount = Amount to download + Amount to add each player * Number of players

So, we have

y = 2.50 + 1.50 * x

Evaluate

y = 2.50 + 1.5x

The above function is a linear function and the input is the number of players

This means that the domain is discrete

However, the amount can take decimal points

This means that the range is continuous

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The bill usage summary that could belong to a resident of that city are:

$14.40 per 3000 gallons

$19.20 by 4,500 gallons

$28.80 per 6000 gallons

The bill usage summary that could belong to a resident of that city have to be equivalent to $4.80 per 1000 gallons.

A -In order to determine if $2.20 per 500 gallons is equivalent, convert the quantity to 1000 gallons. To do this, multiply by 2.

t ($2.20 per 500 gallons) x 2 = $4.40 per 1000 gallons

B - In order to determine if $12.60 per 2,500 gallons is equivalent, divide 12.60 by 2500 and then multiply by 1000

(12.60 per 2500 gallons) x (1000 / 2500) = $5.04

C-  In order to determine if $14.40 per 3000 gallons is equivalent, divide $14.40 by 3

($14.40 per 3000 gallons ) / 3 =  $4.80 per 1,000 gallons

D-  In order to determine if $16 per 4000 gallons is equivalent, divide by 4.

($16 per 4000 gallons) / 4 = $4 per 1000 gallons

E- In order to determine if $19.20 by 4,500 is equivalent, multiply $19.20 by 1000 / 4,500.

($19.20 by 4,500) x (1000 / 4500) = $4.27 per 1000 gallons

F - In order to determine if $26.40 per 5,500 gallons is equivalent, multiply $26.40 by 1000 / 5500.

( $26.40 per 5,500) x 1000 / 5500 = $4.8 per 1000 gallons

G- In order to determine if $28.80 per 6000 gallons, divide by 6.

($28.80 per 6000) / 6 = $4.8 per 1000 gallons

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The total number of tacos sold was 66, and the total number of burritos sold was 53.

What is an equation?

An expression that depicts the relationship between two or more numbers and variables is called an equation.

Dependent variables are used to describe function outputs that depend on other values, whereas independent variables are used to describe function inputs that are independent of other values.

Here, we have

Let x be the number of tacos sold and y be the number of burritos sold daily.

It is given that Enola sells each taco for $3 and each burrito for $7.5. She made a total of $529.25 in revenue.

The equation that represents this is

3 x + 7.5 y > 570

x + y ≤ 120

After further simplified, we get

y = 120 - x

Now put the value of y in equation 3 x + 7.5 y > 570, we get

3x + 7.5(120-x) = 570

3x + 900 - 7.5x = 570

4.5x = 300

x = 66

now put the value of x in equation x+y = 120, we get

y = 53

Hence, the number of tacos sold were 66, and the number of burritos sold were 53.

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The pentagon has the following type of symmetry:

This refers to a type of symmetry where one-half part of an object shows the other half of the object. It is also be called mirror symmetry.

Point symmetry refers to the shape of a figure or graph after begin turned about 180° and it still looks the same as its initial shape. eg Star, heart -shape, etc.

Note that When something is identical on all sides, it is said to be symmetrical. If a center dividing line (also known as a mirror line) can be drawn on a shape to demonstrate that both of its sides are identical, then the shape is said to be symmetrical.

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By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = [tex]9 \div 3[/tex] = 3 units

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Complete Question

The figure has been attached here

Answer:

1/2

Step-by-step explanation:

m = (Y2 - Y1) / (X2 - X1)                  Slope formula

m = (1 - 0) / (2 - 0)                           Plug in any two points, I chose (2,1) & (0,0)

m = 1 / 2

P.S. You could also count rise/run

Basically count the amount of units going up or down then counts the units going left or right that get you to the next point of the line

b. P(sum of 8) = 5/36

c. P(odd sum or sum greater than 9) = 2/3

d. P(odd sum and sum greater than 9) =  1/12

e. P(A) = 1/3

f. P(B) =

g. P(A and B) = 1/18

h. A and B are not mutually exclusive because both events can occur at the same time.

i. A and B are not independent because the occurrence of A and lead to the occurrence of B.

P(sum of 8) = number of sample spaces that sum up to 8 / total number of sample spaces

P(sum of 8) = 5/36

P(odd sum or sum greater than 9) = (sample spaces that have an odd sum / total number of sample spaces) + (sample spaces that have a sum greater than 9 / total number of sample spaces)

P(odd sum or sum greater than 9) =(18 / 36) + (6/36) = 24/36 = 2/3

d. P(odd sum and sum greater than 9) = (sample spaces that have an odd sum / total number of sample spaces)  x (sample spaces that have a sum greater than 9 / total number of sample spaces)

P(odd sum and sum greater than 9) = 18/36 x 6/36 = 1/12

P(A) = (sample spaces that have a 3 first / total number of sample spaces) +  (sample spaces that have a 3 first / total number of sample spaces)

P(A) = 6/36 + 6/36 = 1/3

P(B) = (sample spaces that adds up to 7 / total number of sample spaces)

= 6/36 = 1/6

P(A and B) = 1/3 x 1/6 = 1/18

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Equation: [tex]\boxed{\pi}(8^2)[/tex]

Area: [tex]64\pi \approx 201.06[/tex]