Graph the following function.
f(x)=2(x-2)²-4

3750 is the planning value for the population standard deviation.

In the sampling, one should not recommend trying to obtain the $100 margin of error since the sample size is large.

Firstly, the planning value will be:

= (60000 - 45000) ÷ 4

= 3750

Then the number will be:

= 1.96 × (3750 ÷ 500)²

= 217

Also, for error 200, the desired margin will be:

= 1.96 × (3750 ÷ 100)²

= 5403.

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95% of the people the doctor expects to have hip replacement surgery will be between the ages of 47 and 63.

The definition of average is that it is the mean value, which is the ratio of the sum of the values in a particular set to all the values in the set.

The amount of variance from the mean is shown by the standard deviation.

Given that the standard deviation is 8 years and the average age is 55.

x=x0, where x0 and are the mean age and standard deviation, respectively, defines the relationship.

The standard deviation is 8 years, while the mean age is 55 years.

The answer is that 55+8=63 and 55-8=47.

Consequently, the age range is 47 years to 63 years.

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Area of the cricket pitch is 660 square feet

Given

1 chain is equal to 10 feet

There are 3 feet in a yard

And 22 yards in a chain

Hence it is evident that

One chain is equal to 22 x 3

1 chain = 66 Feet

Area of a rectangle is Length x Width

Length = 66

Width =  10

Hence Area = 66 x 10

Area = 660 Square feet

Hence area of the cricket pitch is 660 square feet.

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Answer:

x = 0 and 2pi/3

Explanation

Given the expression

cos(2x)=cos(x)

In trigonometry expression;

cos2x = 2xos^2x - 1

Substituting into the equation given;

cos(2x)=cos(x)

2xos^2x - 1 = cos x

Rearrange

2xos^2x - 1 - cosx - 1 = 0

Let P = cosx

2P^2 - P - 1 = 0

Factorize

2P^2 - 2P+P-1 = 0

2P(P-1)+1(P-1) = 0

2P+1 = 0 and P-1 = 0

P = -1/2 and 1

Recall that P = cosx

-1/2 = cosx

x = cos^-1(-1/2)

x = 120 degrees = 2pi/3

If P = 1

cosx = 1

x = cos^-1(1)

x = 0

Hence the value of x that satisfies the equation is 0 ad 2pi/3

Answer: When the Ice Cream Parlor sells 50 ice cream cones, they make $85 dollars in profit.

Step-by-step explanation:

x = cones

the function f tells us the profit for whatever x

ANSWER:

The value of x is 16

STEP-BY-STEP EXPLANATION:

With the information given, they tell us that TVQ can be expressed in two ways, but in the end the value must be the same because it is the same angle.

Thanks to this we can make the following equality:

Solving for x:

Answer:

16 is the answer

Answer:

1 These 5 main features are the title, scale, points, labels, and line.

2. Relations are a group of ordered pairs from one set of objects to another set of objects while functions are relations that connect one set of inputs to another set of outputs. So all functions are relations while all relations are not functions.

3. To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).

4. The slope equation says that the slope of a line is found by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points. In other words, Pick two points on the line and determine their coordinates.

5. To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. To find the y-intercept, plug 0 in for 'x' and solve for 'y'.

6. An example of a linear equation is: 2x + y - 3 = 0. It can be written in the standard form, the slope-intercept form, and the point-slope form. Here we mainly used the slope-intercept form y=mx+c y = m x + c . To write linear equations find the slope and y-intercept and then substitute these values into the equation.

To find the magnitude of a vector we use the following equation

This comes from taking the value of the hypotenuse by Pythagoras, graphically it can be seen in the following image:

In the case of your exercise, the values would be

the probability of getting a 2 tree times is

Since ∠VST measures 90°, the measure of ∠RSV must also be 90° because the two angles are linear pair.

Since m∠RSU=51°, then the measure of ∠USV is as follows:

Answer:

2^5m^15n^10

Step-by-step explanation:

Answer:

16m^12n^8t^4

Step-by-step explanation:

when raising exponents to another exponent you multiply the exponents

Answer:

slope would be 4/1

Step-by-step explanation:

its rise over run, so up 4 and out 1

have a good day!

Answer: F

Step-by-step explanation:

[tex]\sin(x+y)=\sin x \cos y+\cos x \sin y[/tex]

[tex]\tan x=2 \implies \sin x=\frac{2}{\sqrt{5}}, \cos x=\frac{1}{\sqrt{5}}\\\\\sin y=\frac{8}{17} \implies \cos y=-\frac{15}{17}\\\\\sin (x+y)=\left(\frac{2}{\sqrt{5}} \right) \left(-\frac{15}{17} \right)+\left(\frac{1}{\sqrt{5}} \right) \left(\frac{8}{17} \right)\\\\=-\frac{30}{17\sqrt{5}}+\frac{8}{17\sqrt{5}}\\\\=-\frac{22}{17\sqrt{5}}\\\\=-\frac{22\sqrt{5}}{85}[/tex]

The space sample is the total quantity of possible results

for each toss there are 3 possible results

so the total results are 2x 3 = 6

The only option with 6 elements is B

so the answer is B.

The markup indicates the difference between the selling price and the item's cost to the business.In general, a corporation generates more money the higher the markup.The retail price of a product less its cost is known as markup, although the margin percentage is determined in a different way.

Calculate percentage on markup based on cost ?

Selling price = cost + markup

= 1.17+0.78

=1.96

percentage markup based on cost = markup/cost*100

0.78/1.17*100

=  66.66

percentage on selling  = percentage on markup cost/100+percentage on cost

=  66.66/100%+66.66

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Using the t-distribution, the 95% confidence interval estimate of the population mean rating for Miami is of:

(4.29, 7.71).

The bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the meaning of the parameters are:

Using a calculator from the 50 observations given in this problem, the values of the parameters are as follows:

[tex]\overline{x} = 6, s = 2.86, n = 50[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Hence the lower bound of the interval is given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6 - 2.0096\frac{6}{\sqrt{50}} = 4.29[/tex]

The upper bound of the interval is given by:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6 + 2.0096\frac{6}{\sqrt{50}} = 7.71[/tex]

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The maximum displacement of this cosine wave function is equal to 8 inches.

The frequency of this cosine wave function is equal to 1/8 Hertz.

The time (t) required for one cycle is equal to 8 seconds.

Mathematically, a cosine wave simply refers to an equation of simple harmonic motion (SHM) and it is modelled by this mathematical expression:

y = asinωt = asin2πft     ......equation 1.

Where:

From the information provided, the equation for this simple harmonic motion (SHM) is given by:

d = -8cos(π/4)t           ......equation 2.

By comparing equation 1 and equation 2, we have the following parameters:

Maximum displacement or amplitude, a = |-8|

Taking the absolute value of a, we have:

Maximum displacement or amplitude, a = 8

For the frequency, we have:

Angular velocity, ω = 2πf

Making frequency (f) the subject of formula, we have:

Frequency (f) = ω/2π

Frequency (f) = (π/4)/2π

Frequency (f) = π/8π

Frequency (f) = 1/8 Hertz.

Finally, we would calculate the amount of time (t) required for one cycle as follows:

Time (t) = 1/f

Time (t) = 1/(1/8)

Time (t) = 8 seconds.

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Complete Question:

An object moves in simple harmonic motion described by the equation d = -8cos(π/4)t, where t is measured in seconds and d in inches. Find the following:

maximum displacement

the frequency

the time required for one cycle.

We can draw the following picture:

Since we have a right triangle with hypotenuse equal to 28ft, we can use the trigonometric function. That is, we can write the following relationships:

both give the same result.

If we use the first one, we have

since sin30=0.5, we have

that is, RG = 14 ft, which corresponds to the first option

1) What we have in the polygon P is at first a

90º Rotation Clockwise because it is in the direction of the clock.

90º Rotation Clockwise

Tracing a line inside the polygon P, we can count approximately 10 units to the right in the translation.

T

The linear function that passes through the points (-3, 18) and (2, -7) is defined by the rule:

y = -5*x + 3

We can find a general linear function in the slope-intercept form as:

y = m*x + k

Where m is the slope and k is the intercept of the y-axis.

If we know that the line passes through the points (a, b) and (c, d) then the slope of the function is:

m = (d - b)/(c - a)

In this case the line passes through the points (-3, 18) and (2, -7), then the slope is:

m = (-7 - 18)/(2 + 3) = -5

So the line is something like:

y = -5*x + k

To find the value of k, we can use one of the two given points, I will use (2, -7), so we get:

-7 = -5*2 + k

-7 = -10 + k

-7 + 10 = k

3 = k

So the linear function is:

y = -5*x + 3

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Answer:

hmmph..

(32, 31)

(33,30)

(34, 29)

(35, 28)

(36,27)

(37, 26)

Step-by-step explanation:

That all I got....

There will not be enough T-shirts for all the students

From the question, the given parameters are:

Number of T-shirt = 1437

From the question, we understand that the principal approximates the number of T-shirts to the nearest hundred

When the number of T-shirts is approximated to the nearest hundred, we have

Approximation = 1400

By comparison, 1400  is less than 1437

This means that the T-shirts will not be enough

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The coefficient of the term 8x² is 8 and the exponent is 2 and the coefficient of the term -2x is -2 and the exponent is 1.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = abˣ  in mathematics, where x is the independent variable

From the expression, a is the coefficient, x is the exponent, and b is the variable

For the term,  y = abˣ, compared with the general equations;

abˣ = 8x²

a = 8 and x = 2

This indicates that the term's coefficient is 8 and its exponent is 2.

Similarly for the second term -2x

So the coefficient of the term -2x is -2 and the exponent is 1

Hence, the coefficient of the term 8x² is 8 and the exponent is 2 and the coefficient of the term -2x is -2 and the exponent is 1.

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hello

to solve this question, we need to use the formula for volume of a sphere

from the image above, we can now find the radius of the sphere

from the calculations above, the volume of the sphere is equal to 3052.08cm^3

a) The slope of the equation is 6

b) The graph touch the y- axis at (0, 2) , (1, 8) and so on.

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:

Xander has biked 2 miles.

and, average of 6 miles each day.

So, if the number of days be x and total number of miles traveled be y.

Then , the equation to represent the situation

y= 6x+ 2

a) the slope of the equation comparing to y= mx +b

So, slope= 6

b) The graph touch the y- axis at (0, 2) , (1, 8) and so on.

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The complex expression (2+5) - (-6 +bi) in the form a + bi is 13 - bi

The expression is given as

(2+5) - (-6 +bi)

The above expression is a complex expression

So, we have the following expression

(2+5) - (-6 +bi)

Remove the brackets in the above expression

So, we have the following expression

(2+5) - (-6 +bi) = 2 + 5 + 6 - bi

Evaluate the like terms in the above equation

So, we have the following expression

(2+5) - (-6 +bi) = 13 - bi

Hence, the solution to the complex expression is 13 - bi

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