Triangle PQR lies in the xy-plane, and the coordinates of vertex Q are (2, –3). Triangle PQR is rotated 180° clockwise about the origin and then refected across the y-axis to produce triangle P′Q′R′, where vertex Q′ corresponds to vertex Q of triangle PQR. What are the coordinates of Q′?

Answer:

$5.75

Step-by-step explanation:

First we will make an equation. We will put child tickets as x, and adult tickets as x+3.50. =

2x+7+3x=35.75=

5x=28.75

x=5.75

Answer:

The lady is on the second door

Step-by-step explanation:

we have that

The sign on the first door reads "In this room there is a lady, and in the other one there is a tiger"

The sign on the second door reads "In one of these rooms, there is a lady, and in one of them there is a tiger."

so

The sign on the second door is true

The sign on the first door is true or false

Since one of these signs is true and the other is false, the sign in the first door must be false

therefore

The lady is on the second door

If the first sign is true, the lady is behind the first door, if the second sign is true, the lady is behind the second door.

Let's consider the first sign first. If the sign on the first door is true, then there must be a lady in that room and a tiger in the other room. This means that the sign on the second door is false, and there is no lady in the second room. Therefore, the lady must be behind the first door. If the sign on the first door is false, then the lady cannot be in the first room. This means that the second sign is true, and there must be a lady in the second room. So, the lady is behind the second door.

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There are 3,628,800 possible codes that can be entered into the 10-letter keypad.

The number of codes that can be formed using the 10-letter keypad is calculated using the concept of permutations. Since each key can only be used once, we need to find the number of ways we can arrange 10 letters without repetition. This can be calculated as:

P(10, 10) = 10!

Therefore, there are 3,628,800 possible codes that can be entered into the keypad.

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The number of possible ten-letter codes using the keys labeled A to J, are 3,628,800 possible codes.

The number of different codes can be found by calculating the permutations of 10 unique keys, or 10!.

The factorial of a number n (written as n!) is the product of all positive integers from 1 to n.

So, the calculation for 10 keys is:

Computing this gives:

Therefore, there are 3,628,800 possible codes for opening the garage door.

The average rate of change over the interval [0,6] is approximately 1.1666666666666667.

As a maths teacher, my aim is to make you understand the concept and how to solve this problem. Let's start by understanding the given information.

We know that the average rate of change, \(m\), of \(f(x)\) over an interval \([a, b]\) is given by:

\(m = \frac{f(b) - f(a)}{b - a}\)

We have been given that:

1) The average rate of change over the interval [0,3] is -1,
2) The average rate of change over the interval [2,3] is 5,
3) The average rate of change over the interval [2,6] is 3.

So we can set up the following system of equations from these:

We have:
\(f(3) - f(0) = -1 * 3 = -3\) (from 1)
\(f(3) - f(2) = 5 * 1 = 5\) (from 2)
\(f(6) - f(2) = 3 * 4 = 12\) (from 3)

From the second equation we can express \(f(3) = 5 + f(2)\).

Then, by substituting this into the first equation we get \(f(2) = -3 - 5 = -8\).

Now we substitute \(f(2) = -8\) into the third equation we get \(f(6) = 12 + f(2) = 12 - 8 = 4\).

And finally, using these we can find the average rate of change over the interval [0,6] is \((f(6) - f(0))/6 = (4 - (-3))/6\), we subtract \(f(3)\) from both sides and we get that \(f(0)\) is equal to \(f(3) - 3\).

This gives us that the average rate of change over the interval [0,6] is approximately 1.1666666666666667.

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Answer:

0.2983

Step-by-step explanation:

Let X be the reading on thermometer.  Given that X is N(0,1)

We are to find the probability that a randomly selected thermometer reads between negative 0.12 and 1.02

Reqd probability = [tex]P(0.12<x<1.12)[/tex].

Since this x is already normal std variable x=z

i.e. reqd prob = [tex]P(0.12<z<1.02) =0.3461 -0.0478\\=0.2983[/tex]

Hence answer is 0.2983

See the attached picture:

Answer:

if you put the trigangle diagnal then do a box the a square

hope that helps

if not tell me I will change the answer with the right answers

Answer:

kn

Step-by-step explanation:

qoierh2rhfjfwjfjj2jnfcdfejghitu43o4ip

the answer is: b

edfvbauskygrweafvuy

Answer:

Step-by-step explanation:

y = -2x^5 - 1

Desired reflection would be f'(x) = -2x⁵ -1

The reflection over the x-axis equation's basic guidelines The reflection equation of the new reflected graph will be y=f(x) y = f (x) given an equation, y=f(x) y = f (x). Simply multiplying the function by 1 will result in a curve that is mirrored across the x-axis.

Given the equation f(x) = x⁵, From reflection rile, the reflection of this graph would be f'(x) = - x⁵.

asked to stretch the graph by 2 and shift down 1 unit.

Therefore, the function results after applying the sequence of transformation are f'(x) = -2x⁵ -1. for better understanding a graph is attached below.

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Answer:

c. 4 - 12x.

Step-by-step explanation:

-6(-2/3 + 2x)

Using the distributive law:

= -6*-2/3 - 6*2x

=  12/3 - 12x

= 4 - 12x.

Answer:

4-12x

Step-by-step explanation:

multiply each term by -6

-6 × (2/3)

reduce the numbers with the greatest common divisor 3

Step by step:A prediction is basically an educated guess and if you are looking for the exact word to describe that you would find that hypothesis is the correct way to tell what is a prediction.

Answer:B

Answer:

Slope and y-intercept

Step-by-step explanation:

The complete question is shown in the image attached with.

For each trip an initial fee of $ 25 is charged and $ 0.10 is charged for each vertical meter descended.

Since, for each vertical meter the charge is $ 0.10, for x meters the charges will be $ 0.10x. So,

Total charges of the trip would be:

Total charges/fee = Initial Fee + Fee for x meters

y = 25 + 0.10x

y = 0.10x + 25

The general slope intercept form of the equation of the line is:

y = mx + c

Where,

m = slope of the line

c = y-intercept

Compairing both the equations given above we, get:

Slope of line = m = 0.10

y-intercept = c = 25

So, the given statements gives us the slope and the y-intercept of the graph.

Answer:

Slope and y-intercept

Step-by-step explanation:

Answer:

  $32.67

Step-by-step explanation:

Her purchase total was ...

  (1.4 lb)($12.00/lb) +(4.5 lb)($0.35/lb) = $17.33

Her change from $50 will be ...

  $50 - 17.33 = $32.67

Answer:

being financially responsible

Step-by-step explanation:

Answer:

a misconception

Step-by-step explanation:

I think it's a misconception because she just assumed, which means she dousn't really know.

Answer:

correct 0.25

Step-by-step explanation:

The questions relate to solving mathematical expressions involving radicals and imaginary numbers. Errors in the original expressions were corrected for accurate solutions. For example, the corrected calculation (6) - sqrt(25)/4 results in 4.75. x= (5) + sqrt(-49)/6 simplifies to 5 + 7/6i.

This question pertains to the field of Mathematics, specifically the area dealing with radicals and complex numbers. The original queries from the student need a bit of clarification since in a few cases the operations mentioned are mathematically invalid. For instance, in the question

(6) - sqrt(25)/4

, we are subtracting a square root from a number without any operator between them. Assuming we need to subtract the result of sqrt(25) divided by 4 from 6, we simplify sqrt(25) to 5 because the square root of 25 is 5. We then divide this by 4 to get 1.25. Subtracting 1.25 from 6 answers the first question as 4.75 Similarly, for the problem

x= (5) + sqrt(-49)/6

dealing with negative radicands, we know that the square root of a negative number results in an imaginary number. The sqrt(-49) simplifies to 7i (because the square root of 49 is 7 and the negative sign makes it imaginary). We then divide this by 6 to get 7/6i. Adding it to 5 we obtained the answer

5 + 7/6i

.

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Answer:

$4083.21

Step-by-step explanation:

Compound interest is an interest rate that stacks on top of each other

So basically I did 3600 × 1.065 for the first year

=3834

then i did 3834 × 1.065 again to calculate the second year

=4083.21

Hope this helps! If you have any questions ask! :)

Answer:

D. $4083.21

Step-by-step explanation:

Final answer:

The maximum length of the playground is 38 meters, given that the perimeter cannot exceed 120 meters and the width cannot exceed 22 meters. The possible lengths are therefore from 0 to 38 meters.

Explanation:

Possible Lengths of the Playground

Given that the maximum width (w) is 22 meters and the maximum perimeter is 120 meters, we can substitute these values to find the maximum length:

The maximum length of the playground is 38 meters. However, the length can be any value less than or equal to 38 meters, so the possible lengths of the playground are from 0 meters to 38 meters.

The plywood needed for 15 strips is 20.5 inches.

[tex]\rm 1\dfrac{1}{4}\ inches = \dfrac{(4 \times 1) +1 }{4} =\dfrac{5}{4}\ inches[/tex]

As to cut 15 strips of plywood a total of 14 cuts will be needed.

therefore, the waste of plywood in these 14 strips will be

= Lost in each cut x Number of cuts

[tex]=\dfrac{1}{8}\times 14\\\\=\dfrac{14}{8}\\\\ = \dfrac{7}{4} inches[/tex]

Total plywood needed for all single strip

                        = width of the strip x number of strips

                        [tex]=\dfrac{5}{4} \times 15\\\\ =\dfrac{75}{4}\\\\[/tex]

Plywood needed

= Total plywood needed for all strip +  Total waste of plywood

[tex]=\dfrac{7}{4}+\dfrac{75}{4}\\\\=\dfrac{82}{4}\\\\=20.5\ \rm inches[/tex]

Hence, the plywood needed for 15 strips is 20.5 inches.

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Answer:

  3w + 8 – w = 4w – 2(w – 4)

Step-by-step explanation:

The simplified forms of each of these equations are ...

Answer:

Part 1) The converse is "If one of the two angles is acute then two angles are supplementary"

Part 2) The inverse is " If two angles are not supplementary, then one of the two angles is not acute"

Part 3) The contrapositive is "If one of the two angles is not acute then two angles are not supplementary"

Step-by-step explanation:

we  have

The following conditional statement " If two angles are supplementary, then one of the two angles is acute"

The hypothesis is "If two angles are supplementary"

The conclusion is " one of the two angles is acute"

Part 1) Rewrite the conditional statement as a converse

we know that

To form the converse of the conditional statement, interchange the hypothesis and the conclusion

therefore

The converse of " If two angles are supplementary, then one of the two angles is acute"  is "If one of the two angles is acute then two angles are supplementary"

Part 2) Rewrite the conditional statement as a inverse

we know that

To form the inverse of the conditional statement, negating both the hypothesis and conclusion of a conditional statement.

therefore

The inverse of " If two angles are supplementary, then one of the two angles is acute"  is " If two angles are not supplementary, then one of the two angles is not acute"

Part 3) Rewrite the conditional statement as contrapositive

we know that

To form the contrapositive, switching the hypothesis and conclusion of a conditional statement and negating both

therefore

The contrapositive of "If two angles are supplementary, then one of the two angles is acute" is "If one of the two angles is not acute then two angles are not supplementary"

Answer:

D) [tex]y = 10 * 4^{x}[/tex]

Step-by-step explanation:

Replace each function with x = 0

A) [tex]y = 1*4^{x} \\y = 1*4^{0} \\y = 1[/tex]

B) [tex]y = 3*10^{x} \\y= 3* 10^{0} \\y = 3 \\[/tex]

C) [tex]y = 2*4^{x} \\y = 2*4^{0} \\y = 2[/tex]

D) [tex]y = 10*4^{x} \\y= 10*4^{0} \\y = 10[/tex]

If you check the graph with x = 0, the value of y is between 8 and 12 so the only probably answer acoording to the alternatives is D) which gives y = 10 when x = 0

Answer:

Probability of winning the game: 1/10000

Step-by-step explanation:

The nominator in the only outcome possible for you to win the bet. So that would be your only selected fourdigit number.

The denominator is the total possibles outcomes. If the first posible number is 0000 and the last number is 9999. There are a total of 10000 possible outcomes that the selected number is drawn.

The general rule is [tex]\frac{p}{q}[/tex]

Where p are the draws where i win.

And q is the total population of possible numbers.

Answer:

  2 imaginary; 2 real

Step-by-step explanation:

You can factor it as ...

  f(x) = (x^2 -16)(x^2 +1) . . . . . . . . . x^2-16 is the difference of squares

  = (x -4)(x +4)(x^2 +1)

The two linear factors have real zeros; the quadratic factor has two imaginary zeros. There are 2 imaginary and 2 real zeros.

Answer:

Height of second tree = 26.67 foot

Step-by-step explanation:

A tree that is 40 feet tall casts a 30-foot shadow

Height of tree = 40 feet

Height of shadow of tree = 30 feet

[tex]\frac{\texttt{Height of tree}}{\texttt{Height of shadow of tree}}=\frac{40}{30}=1.333[/tex]

So ratio of original height to shadow height is 1.333.

Now we need to find how tall is the another tree, if its shadow is 20 feet.

[tex]\frac{\texttt{Height of tree}}{\texttt{Height of shadow of tree}}=1.333\\\\\frac{\texttt{Height of tree}}{20}=1.333\\\\\texttt{Height of tree}=1.333\times 20=26.67foot[/tex]

Height of second tree = 26.67 foot

Answer:

A. The selection is a combination.

Step-by-step explanation:

A combination is a selection of all or part of a set of objects, without regard to the order in which they were selected.  

Then, a permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

For example, the student scans the novels to be checked out in no particular order hence it is a combinations problem. Scanning novels with titles A, B, C, D and E in the order B, C, D, E and then A produces the same result. When it comes to library books, the order in which we scan the novels for check out is of no importance since in the end the same novels are carried out the door by the library patron.

Answer:

662.64

Step-by-step explanation:

i got it wrong on apex and it told me the right answer. you're welcome.

Answer:

$662.63

Step-by-step explanation:

Cost of mortgage = $120,000

Interest rate of first period = 5.25%

The loan was amortized over 30 years.

The interest rate at the end of the initial loan period = 6.75%

Margin = 1.5%

The loan was amortized for over (30*12) months

= 360 months

The interest rate of the first period per month = 5.25% / 12

= 0.0525/12

= 0.004375

Payment for monthly mortgage =

(120000(0.004375)) / 1 - (1 + 0.004375)^-360

= 525 / 1 - (1.004375)^-360

= 525 / (1 - 0.2077)

= 525 /0.7923

= 662.63

= $662.63

Let , a, b and c be the length of three sides of triangle, represented in terms of vectors as [tex]\vec{a},\vec{b},\vec{c}[/tex].

Now, vector of same Magnitude acts as normal vector to each side.

So, equation of any vector p having normal q is given by

      [tex]\vec{p} \times\vec{q}[/tex]

Now sum of three vector and it's normal is given as

    [tex]=\vec{a} \times\vec{a}+\vec{b} \times\vec{b}+\vec{c} \times\vec{c}\\\\=0+0+0\\\\=0[/tex]

Cross product of two identical vectors is Zero.

[tex]\rightarrow \vec{i} \times\vec{i}=0[/tex]

The sum of the outward normal vectors of a triangle's sides is always 0 due to vector closure around the triangle.

Let us denote the vertices of the triangle as A, B, and C. The sides of the triangle are AB, BC, and CA. We need to show that the sum of the outward normal vectors of these sides is zero.

Let u be the outward normal vector of side AB.

Let v be the outward normal vector of side BC.

Let w be the outward normal vector of side CA.

These normal vectors are each associated with a side of the triangle and have the same length as the corresponding side.

For any triangle, the vector from one vertex to another can be expressed as the difference of position vectors:

AB = B - A

BC = C - B

CA = A - C

The normal vector u to side AB can be aligned such that u is perpendicular to AB and has magnitude equal to the length of AB.

Similarly, v is perpendicular to BC and has magnitude equal to the length of BC.

Similarly, w is perpendicular to CA and has magnitude equal to the length of CA.

To show that the sum of these vectors is zero, consider that the sum of vectors around a closed polygon (in this case, the triangle) is zero. The outward normal vectors form a closed system since each side’s normal vector effectively cancels out with the adjacent ones due to their perpendicularity and length.

Thus:

u + v + w = 0.

Answer:

The common ratio r = 2.

Step-by-step explanation:

Now s2 = a1r and s4 = a1r^3  where a1 = first term and r = common ratio so

s4 / s2 = a1r^3  / a1r = r^2 = 32/8

r^2 = 4

r = 2.

Hey!

--------------------------------------------------

Answer:

r = 2

--------------------------------------------------

Solution:

So we know that s2 = 8 and s4 = 32.

We need to find s1!

32 / 8 = 4

8 / 4 = 2 (ratio is 2)

8 / 2 = 4

32 / 2 = 16

s1 = 4

s3 = 16

Each number is multiplied by 2.

--------------------------------------------------

Hope This Helped! Good Luck!

Answer:

- p ⇒ - q

Step-by-step explanation:

p : Drive over 65 miles

q : You get a speeding ticket.

So then we get the negations.

- p : You do not drive over 65 miles

- q : You don't get a speeding ticket.

So, we need to connect the sentences. For that we use ⇒.

⇒ : then.

So, the sentence, If you do not drive over 65 miles per hour, then you will not get a speeding ticket

Can be written as : -p ⇒ -q

The expression representing the proposition using the variables p and q is ¬p → ¬q, which follows the logical rule of Modus Tollens.

The proposition "If you do not drive over 65 miles per hour, then you will not get a speeding ticket" can be represented using the variables p for "You drive over 65 miles per hour" and q for "You get a speeding ticket". The logical expression for the given proposition, using logical connectives and negations, is ¬p → ¬q, which means "not p implies not q".

This is an example of the logical rule known as Modus Tollens, which can be expressed as ((p→q) ∧ ¬q) → ¬p. If the implication p→q is true, and the consequent q is false (¬q), then it must follow that the antecedent p is also false (¬p).

9514 1404 393

Answer:

  Adam

Step-by-step explanation:

It is pretty easy to make comparisons to 10 ft/s.

If Liz ran 10 ft/s, she would run 460 ft in 46 s. Since she runs 420 ft, she runs slower than that.

If Emily ran 10 ft/s, she would run 600 ft in 1 minute, so Emily runs faster than that.

If Adam ran 10 ft/s, he would only run 4270 ft in 427 seconds. Since he runs 5280 ft in that time, his speed is definitely greater than 10 ft/s.

__

At this point, we know that Adam and Emily run faster than Liz and Stephanie. So we need to compare Adam and Emily's rates.

Adam's time for 1 mile is about 7 minutes. If Emily ran for 7 minutes, her distance would be less than 7×700 ft = 4900 ft, substantially less than 1 mile (5280 ft).

Adam runs the fastest.

_____

Comment on straightforward solution

Each rate can be computed by dividing distance by time:

  Liz: (420 ft)/(46 s) = 9.13 ft/s

  Adam: (5280 ft)/(427 s) = 12.37 ft/s

  Emily: (667 ft)/60 s) = 11.12 ft/s

Adam's is the highest, well above Stephanie's 10 ft/s.

These calculations require a calculator. The solution above was done without a calculator.

Final answer:

To determine the fastest runner, we calculated each runner's speed in feet per second. Adam was found to be the fastest with a speed of 12.37 feet per second.

Explanation:

To find out who the fastest runner is, we need to calculate the speed of each runner in feet per second and then compare. Stephanie's speed is already given as 10 feet per second. Next, we calculate Liz's speed by dividing the distance she runs by the time it takes her: 420 feet / 46 seconds = 9.13 feet per second. Now, we convert Adam's mile into feet, knowing that 1 mile = 5280 feet. Adam's speed is 5280 feet / 427 seconds = 12.37 feet per second. Lastly, we need to convert Emily's time into seconds since she runs for 1 minute (which is 60 seconds). So, Emily's speed is 667 feet / 60 seconds = 11.12 feet per second. Comparing all speeds, Adam runs the fastest at 12.37 feet per second.