Triangle P is rotated 180° about (0, 0) to give triangle Q. Triangle Q is translated by 5 2 to give triangle R. (a) Describe fully the single transformation that maps triangle P onto triangle R.

Answer:

250

Step-by-step explanation:

1600/6.4

In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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Answer:108.12$

Step-by-step explanation:

Dwayne will get a discount of 15% on the price of the bowling ball which is $120. The discount will be $18. So the price of the bowling ball after the discount is $102.

Dwayne will have to pay 6% sales tax on the discounted price of the bowling ball which is $102. The sales tax will be $6.12.

Therefore, the final price Dwayne has to pay for the bowling ball is $108.12.

Answer:

108.12 bc it says don't use a label

Step-by-step explanation:

15% can be written as 0.15. Same thing.

So first the discount:

120 x 0.15 = $18

He'll get an $18 discount.

120-18 = $102. That's the discounted price he'll pay.

6% tax can be written as 0.06.

$102 x 0.06 = $6.12 That's the tax he needs to pay

So in total he'll pay $102 + $6.12 = $108.12

Your question says no label so just answer 108.12.

the biology professor cannot conclude that the percentage of children who develop asthma in the new country is lower than the percentage observed in the US study.

The biology professor can use hypothesis testing to determine if the percentage of children who develop asthma in the new country is significantly different from the percentage observed in the US study.

Here are the steps she can take:

1. Define the null and alternative hypotheses:
- Null hypothesis (H0): The percentage of children who develop asthma in the new country is the same as the percentage observed in the US study (i.e., 22.1%).
- Alternative hypothesis (Ha): The percentage of children who develop asthma in the new country is lower than the percentage observed in the US study.

2. Determine the test statistic to use:
- The appropriate test statistic for this scenario is the one-sample proportion z-test.

3. Set the significance level (alpha):
- Let's assume a significance level of 0.05.

4. Calculate the test statistic:
- The sample proportion of children who developed asthma in the new country is p = 70/336 = 0.2083.
- The standard error of the sample proportion is SE = sqrt[(p*(1-p))/n] = sqrt[(0.2083*(1-0.2083))/336] = 0.027.
- The test statistic is z = (p - P) / SE, where P is the proportion observed in the US study. So, z = (0.2083 - 0.221) / 0.027 = -0.463.

5. Determine the p-value and make a decision:
- The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. Using a standard normal distribution table or calculator, we find that the p-value is 0.3212.
- Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. There is not enough evidence to conclude that the percentage of children who develop asthma in the new country is significantly different from the percentage observed in the US study.

Therefore, the biology professor cannot conclude that the percentage of children who develop asthma in the new country is lower than the percentage observed in the US study.

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Answer:

I think it's a

Step-by-step explanation:

Because this would ddetermine if the software lab is successfull working.

Answer:

11. 40.5

12. 84

Step-by-step explanation:

Answer:

\(\displaystyle PQ \approx 5.2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Identify

Angle θ = 55°

Adjacent Leg = PQ

Hypotenuse = 9

Step 2: Solve

The value of the union of sets A and B is, P(A ∪ B) is 0.64.

The union of two sets means the total elements in both the sets combined.

Given: sets P(A) = 0.38, P(B) = 0.83, and  intersection P(A ∩ B) = 0.57

We need to find the union of P(A ∪ B).

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let us substitute the given values in the formula.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

=0.38+0.83-0.57

=1.21-0.57

=0.64

Therefore, the value of union of sets P(A ∪ B) is 0.64.

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See the attachment for the formulas

Above answer's I'd is of mine and I told u in the comments that I'll give you the formulas so here they are

Answer:

I think the answer you are looking for is J

let us consider x as the number of stools and y be the number of recliners

therefore, total seats \(\leq\) 50

= x + y \(\leq\) 50

then, owner wants a least 20 of the seats to  be stools

x \(\geq\) 20

the rest are the number of recliners.

the equation of inequality is x + y \(\leq\) 50

x + y =50

if x = 0 and y = 50

if y = 0 and x = 50

therefore the joining points are (0, 50) and ( 50, 0) in the coordinate plan

0+0 \(\leq\) 50

then the shaded region will contain the origin

Graphing of x \(\geq\) 20

shading the region left side x = 20

Hence, number of materials can never be negative.

therefore,

x \(\geq\) 0 and y \(\geq\) 0

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The complete answers are:

Right angles are angles that are equal to 90 degrees.

A triangle that includes a right angle is known as a right-angled triangle.

Congruent angles are angles that are equal in size or measure. For example, the right angles in two or more right-angled triangles are congruent.

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1. The base pay Carter makes regardless of computer sales is $100

2. The linear relationship that shows the sales will be P = 100 + 10x

From the information given, Carter is a salesperson who sells computers at an electronics store and he makes a base pay amount each day and then is paid a commission for every computer sale he makes.

The starting salary is $100. This is the base pay.

The commission given is $10 per good sold. Therefore, the expression will be:

= 100 + 10x

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Set A is more widely dispersed than Set B based on the coefficient of variation.

The coefficient of variation (CV) is a measure of relative variability, which is used to compare the dispersion of data sets with different means. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage.

Let's calculate the coefficient of variation for each set of numbers:

Set A:

Mean of Set A = (2+3+1+4+5+6+7+25+9+8) / 10 = 7

Standard Deviation of Set A = √[(2-7)² + (3-7)² + (1-7)² + (4-7)² + (5-7)² + (6-7)² + (7-7)² + (25-7)² + (9-7)² + (8-7)²] / √10 ≈ 7.156

Coefficient of Variation for Set A = (7.156 / 7) * 100 ≈ 102.23%

Set B:

Mean of Set B = (32+45+40+38+47+50+43+36+44+35) / 10 = 40

Standard Deviation of Set B = √[(32-40)² + (45-40)² + (40-40)² + (38-40)² + (47-40)² + (50-40)² + (43-40)² + (36-40)² + (44-40)² + (35-40)²] / √10 ≈ 5.09

Coefficient of Variation for Set B = (5.09 / 40) * 100 ≈ 12.72%

Comparing the coefficient of variation for Set A (102.23%) and Set B (12.72%), we can see that Set A has a much higher coefficient of variation, indicating greater dispersion or variability compared to Set B.

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The length of the given building is equal to 186ft

To calculate the length of the building whose shadow is 248ft, we can simply find the ratio of the height of Tim to his shadow and compare it with the building.

The ratio of the height to the shadow is 6:8

Or we can simply set it out as an equation, cross multiply and solve.

\(height = shadow length\)

Let's use this system to solve

\(height = shadow length\\6ft = 8ft\\x = 248\\\)

We can cross multiply here and solve for x

\(x = \frac{6 * 248}{8}\\x = 186ft\)

The height of the building is 186ft

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Answer:

Answer 93

Step-by-step explanation:

It will take approximately 12.25 years for the initial deposit of $12000 to triple itself with an annual rate of return of 8% with continuous compounding.

Let t be the time that it will take the initial deposit to triple itself.

Then the future value of $12000 invested with an annual rate of return of 8% with continuous compounding after t years is given by the formula:

A = Pe^{rt}

where,

A is the future value,

P is the principal (initial deposit),

r is the annual interest rate,

t is the time (in years).

In this case,

P = $12000,

r = 0.08 (8%),

A = $36000 (triple the initial deposit).

Therefore, we have: $36000 = $12000e^ {0.08t}

Dividing both sides by $12000 and taking the natural logarithm of both sides gives:

ln (3) = 0.08t

Solving for t, we get:

t = ln (3) / 0.08 ≈ 12.25 years

Therefore, it will take approximately 12.25 years for the initial deposit of $12000 to triple itself with an annual rate of return of 8% with continuous compounding.

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A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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Answer:

The velocity v(t) of the robot at time t can be determined by taking the derivative of the position function s(t). Therefore, v(t) = 18t - 90.

To find the total distance traveled by the robot between t = 0 and t = 9, we need to calculate the definite integral of the absolute value of the velocity function from t = 0 to t = 9. This is because the absolute value of velocity gives us the speed, and integrating the speed over the given time interval gives us the total distance traveled.

Integrating the velocity function v(t) = 18t - 90 from t = 0 to t = 9, we get:

∫(0 to 9) |18t - 90| dt

To solve this integral, we split it into two parts based on the regions where the integrand changes sign:

∫(0 to 9) (90 - 18t) dt + ∫(0 to 9) (18t - 90) dt

Evaluating the integrals, we get:

[90t - 9t^2/2] from 0 to 9 + [9t^2/2 - 90t] from 0 to 9

Plugging in the limits, we have:

[90(9) - 9(9^2)/2] + [9(9^2)/2 - 90(9)] = 405

Therefore, the total distance traveled by the robot between t = 0 and t = 9 is 405 units.

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The velocity function v(t) is found by taking the derivative of the position function s(t), resulting in v(t)=18t-90. To find the total distance traveled by the robot from t=0 to t=9, calculate the definite integral of the absolute value of the velocity function over this interval.

The position, s(t), of a robot moving along a track at time t is given by . To find the velocity of the robot at any time t, we need to derive the position function with respect to t, giving us

which represents the velocity function. Now, to find the total distance travelled by the robot between t=0 to t=9, we have to find the definite integral of the absolute value of the velocity function from 0 to 9. The absolute value is considered because we want total distance covered, not just displacement. This is an example of applying derivative and integral principles in a real-life scenario.

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Answer:

See below.

Step-by-step explanation:

(-1,2),(3,-1)

-1-2/3-(-1)

-1-2/3+1

-3/4

The slope is -3/4.

-hope it helps

Answer:

\(x=24.5\\\)

Step-by-step explanation:

So we have the equation:

\((5x-25)+(3x+9)+180\)

Combine like terms:

\((5x+3x)+(-25+9)=180\)

Add:

\(8x-16=180\)

Add 16 to both sides:

\(8x=196\)

Divide both sides by 8:

\(x=24.5\\\)

So, our answer is 24.5 :)

To differentiate F(y) = 1/ y^2 − 9 /y^4 (y + 5y^3), we need to use the quotient rule of differentiation. Your answer: F'(y) = -2y^(-3) - (12y^(-5) + 60y^(-2))(y + 5y^3)

The quotient rule states that the derivative of a quotient of functions is equal to the numerator's derivative multiplied by the denominator minus the denominator's derivative multiplied by the numerator, all divided by the denominator squared.

Using this rule, we can find the derivative of F(y) as follows:

F'(y) = [(d/dy) (1/ y^2) * (y^4(y + 5y^3)) - (d/dy) (y^4(y + 5y^3)) * (1/ y^2)] / (y^4(y + 5y^3))^2

Simplifying this expression, we get:

F'(y) = [(-2y^3(y + 5y^3))/(y^4(y + 5y^3))^2 - (y^4(1 + 15y^2))/(y^2(y^4(y + 5y^3))^2)]

= [(-2y^3(y + 5y^3)) - (y^4(1 + 15y^2))] / (y^6(y + 5y^3))^2

= (-2y^4 - 10y^6 - y^4 - 15y^6) / (y^6(y + 5y^3))^2

= (-3y^4 - 25y^6) / (y^6(y + 5y^3))^2

Therefore, the derivative of F(y) is F'(y) = (-3y^4 - 25y^6) / (y^6(y + 5y^3))^2.
To differentiate the function F(y) = 1/y^2 - 9/y^4 (y + 5y^3), you can apply the power rule and the chain rule.

Your answer: F'(y) = -2y^(-3) - (12y^(-5) + 60y^(-2))(y + 5y^3)

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To calculate the distance between the southeast corner of section 4 and the northwest corner of section 34 in a given township, we need to consider the dimensions and layout of the township.

In a township, there are 36 sections arranged in a 6 by 6 grid, numbered from 1 to 36. Each section is typically a square with equal dimensions.

To find the distance between the southeast corner of section 4 and the northwest corner of section 34, we can calculate the number of sections between them in the horizontal and vertical directions.

Starting from section 4, we move horizontally to the right by 3 sections (since section 4 is in the first column and we need to reach the fourth column).

Then, we move vertically upwards by 5 sections (since section 4 is in the sixth row and we need to reach the first row).

So, the southeast corner of section 4 is 3 sections to the right and 5 sections upwards from the northwest corner of section 34.

Next, we need to consider the dimensions of each section. If each section has a side length of "d" units, the distance between the southeast corner of section 4 and the northwest corner of section 34 can be calculated as follows:

Distance = √((3d)^2 + (5d)^2)

= √(9d^2 + 25d^2)

= √(34d^2)

= √34d

Therefore, the distance between the southeast corner of section 4 and the northwest corner of section 34 is √34 times the side length "d" of each section in the township.

The specific value in units would depend on the given dimensions of each section

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H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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Answer:

x=17 or x=19

Step-by-step explanation:

(x−18)^2=1

First, simplify both sides of the equation.

x*2−36x+324=1

Then subtract 1 from both sides.

x^2−36x+324−1=1−1

x^2−36x+323=0

Factor left side of equation.

(x−17)(x−19)=0

Then set factors equal to 0.

x−17=0 or x−19=0

x=17 or x=19

Answer:

Its either x=17 or x=19

Step-by-step explanation:

Answer:

7 & 5

Step-by-step explanation:

7+5=12
7-5=2
5-7=-2

Answer:

5 and 7

Step-by-step explanation:

5 + 7 = 12

5 - 7 = -2

There is one specific type of transformation that can cause a change in the period of a tangent or cotangent function, and that is a dilation.

A dilation is a transformation that stretches or compresses a function horizontally or vertically. When a tangent or cotangent function is dilated horizontally, the period of the function changes. The period of a tangent function is π, while the period of a cotangent function is also π.

If the function is dilated by a factor of k, then the new period will be π/k. This means that the function will oscillate faster if it is compressed horizontally (k > 1) and slower if it is stretched horizontally (k < 1). Therefore, it is important to consider the effects of dilations when analyzing the period of a tangent or cotangent function.

The type of transformation that could cause a change in the period of a tangent or cotangent function is called a "horizontal stretch" or "horizontal compression." These transformations affect the frequency of the function by scaling it horizontally, which in turn alters the period of the tangent or cotangent function.

In mathematical terms, the general form of a tangent function is y = A * tan(B(x - C)) + D, and for a cotangent function, it's y = A * cot(B(x - C)) + D. In these expressions, A represents the amplitude, B determines the horizontal stretch or compression, C is the phase shift, and D is the vertical shift.

The factor B directly affects the period of the function. For a tangent or cotangent function, the standard period is π. To find the new period after a horizontal transformation, you can use the formula: new period = (standard period) / |B|. Thus, by changing the value of B, the period of the tangent or cotangent function will be affected accordingly.

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The probability that x is less than 6 is 5/8.

If x is a discrete uniform random variable ranging from one to eight, then each value from one to eight is equally likely to occur, and the probability of any particular value is 1/8.

To find p(x < 6), we need to add up the probabilities of all the values of x that are less than 6:

p(x < 6) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)

Since x is a discrete uniform random variable, the probability of each of these values is 1/8, so we can substitute that into the equation:

p(x < 6) = (1/8) + (1/8) + (1/8) + (1/8) + (1/8)

Simplifying, we get:

p(x < 6) = 5/8

Therefore, the probability that x is less than 6 is 5/8.

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Answer:

I think it might be 56 degrees