Select the combination of transformations that result in the image WXYZ from the pre-image
QRST.

The solution of the logarithm equation, log₁₄ 144 = 2 is 14² = 144.

The logarithm equation can be solved using the law of logarithm. Therefore,

log₁₄ 144 = 2

If you have a single logarithm on one side of the equation, you can express it as an exponential equation and solve it.

Hence,

logₐ b = x can be represented as follows:

aˣ = b

Therefore,

log₁₄ 144 = 2

14² = 144

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After accounting for inflation, the true price of coffee climbed by 14.22% between 1990 and 2022.

To compute the percentage change in the real price of a coffee from 1990 to 2022, we need to adjust the 1990 price for inflation using the CPI for both years.

The inflation rate from 1990 to 2022 is given by:

Inflation rate = ((CPI in 2022 - CPI in 1990) / CPI in 1990) * 100%

= ((260 - 99) / 99) * 100%

= 162.63%

This means that prices increased by 162.63% from 1990 to 2022.

To adjust the 1990 price of $2 for inflation, we multiply it by the inflation factor:

Inflation factor = CPI in 2022 / CPI in 1990

= 260 / 99

= 2.6262

Adjusted price in 2022 dollars = 2 * 2.6262 = 5.2524

Now we can calculate the percentage change in the real price of a coffee from 1990 to 2022:

Percentage change = ((2022 price - 1990 price) / 1990 price) * 100%

= ((6 - 5.2524) / 5.2524) * 100%

= 14.22%

Therefore, the real price of a coffee increased by 14.22% from 1990 to 2022 after adjusting for inflation.

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Answer: The McGee family would pay $52 either way if they rented the truck for 2 additional days.

Step-by-step explanation:

Luther's Moving Company:

38 is how much they'll pay on the first day plus 7 per every additional day

This is represented by 7x+38

Springdale Rent-a-Truck

44 is how much they'll pay on the first day plus 4 per every additional day

This is represented by 4x+44

Set the equations equal to each other

7x+38=4x+44

Move the 38 to the other side by subtracting

7x=4x+44-38

7x=4x+6

Move 4x to the other side by subtracting

7x-4x=6

3x=6

Divide 3 to get x alone

3x/3=6/3

x=2

They'll be equal after 2 additional days

Plug in 2 to each equation

Luther: 7(2)+38

14+38=52

Springdale: 44+4(2)

44+8=52

Answer:

PN: 15

QP: 15

Step-by-step explanation:

if QN is 30 and P is in the middle of N and Q then the distance from P must be 15

The requried, variance of their weights is 157.789 kg².

To calculate the variance, we need to square the standard deviation since variance is the square of the standard deviation. Thus, the variance of the weights of the 10 subjects is:

Variance = (Standard Deviation)² = (12.5602 kg)² = 157.789 kg²

Therefore, the variance of their weights is 157.789 kg².

Note that the units of the variance are the square of the units of the standard deviation.

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The graph of the solution to the given inequality on the number line plotted is attached.

Inequalities are the mathematical expressions in which both sides are not equal.

In inequality, unlike in equations, we compare two values.

The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is q < 69.5​.

The result can be shown in multiple forms.

Inequality Form:q<69.5

Interval Notation:(−∞,69.5)

Therefore, the graph the solution to the given inequality on the number line plotted below.

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The area of the polygon is 92 units²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The polygon can be divided into two; A trapezoid and a triangle.

Area of a trapezoid = 1/2(a+b) h

= 1/2 ( 8+12) 2

= 8+12

= 20 units²

Area of the triangle = 1/2 bh

= 1/2 × 12 × 12

= 6×12

= 72units²

therefore area of the polygon

= area of trapezoid+ area of triangle

= 20+72 = 92 units²

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The unit vector in the direction of v = 3i - 5j is (3√(34)i - 5√(34)j) / 34.

To find the unit vector in the direction of the given vector, we first need to find the magnitude of the vector v. The magnitude of a vector is the length or size of the vector and is calculated using the Pythagorean theorem:

|v| = √((3)² + (-5)²)

|v| = √(9 + 25)

|v| = √(34)

Now, we can find the unit vector u in the direction of v by dividing v by its magnitude:

u = v / |v|

u = (3i - 5j) / √(34)

This is the unit vector that has the same direction as v. To simplify the answer, we can rationalize the denominator by multiplying the numerator and denominator by √(34):

u = (3i - 5j) / √(34) * √(34) / √(34)

u = (3√(34)i - 5√(34)j) / 34

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Answer:

[tex]\sqrt{75}[/tex], 4.3, 20/13, [tex]\frac{\pi }{4}[/tex]

The coordinates in polar form are equal to (r, θ) = (8, 11π / 6).

In this problem we find the definition of a set of coordinates in rectangular form into polar form, that is:

(x, y) → (r, θ)

Where:

Where the norm and the direction of the point are determined by these equations:

r = √(x² + y²)

θ = tan⁻¹ (y / x)

Finally, we determine the coordinates in polar form:

Norm

r = √[(4√3)² + (- 4)²]

r = √(48 + 16)

r = √64

r = 8

Direction

θ = tan⁻¹ (- 4 / 4√3)

θ = tan⁻¹ (- √3 / 3)

θ = 11π / 6

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Answer:

To determine the most James Bennett can consume in his youth, we need to find the maximum amount he can borrow from the bank to invest in the opportunity, while still being able to pay back the loan with interest in his old age.

Let x be the amount that James borrows from the bank in his youth. He invests this amount in the opportunity and receives a payoff of $15,000 in his old age. With this payoff, he can pay back the loan plus interest, which is:

Loan + interest = x + 0.18x = 1.18x

So, he needs to have at least $1.18x in his old age to be able to pay back the loan. He will also receive an inheritance of $3000 in his old age, so his total wealth in his old age will be:

Total wealth in old age = $1.18x + $3000

To determine the maximum amount he can consume in his youth, we need to subtract the cost of the investment opportunity and the amount borrowed from the bank from his initial wealth:

Initial wealth = $0 (no cash currently)

Maximum consumption in youth = Initial wealth - Cost of investment - Amount borrowed

Maximum consumption in youth = -$12,000 - x

Since James wants to maximize his consumption in his youth, we need to find the value of x that maximizes the expression -$12,000 - x, subject to the constraint that his total wealth in his old age is at least $1.18x + $3000.

To find this value of x, we can set up the following optimization problem:

Maximize -$12,000 - x

Subject to: $1.18x + $3000 >= $1.18x (i.e., his total wealth in old age is at least $1.18x + $3000)

Simplifying the constraint, we get:

$3000 >= 0

This constraint is always satisfied, so it does not affect the solution. Therefore, we can simply maximize the objective function -$12,000 - x:

d/dx (-$12,000 - x) = -1

Setting the derivative equal to 0 to find the maximum, we get:

-1 = 0

This is never true, so there is no maximum value of -$12,000 - x. This means that James cannot afford to invest in the opportunity and still have a positive wealth in his old age. Therefore, he cannot consume anything in his youth, since he has no cash currently and cannot invest in the opportunity.

Step-by-step explanation:

Applying the secant-tangent theorem, the length of the diameter is approximately 13.9.

Given the image above that shows a circle containing the diameter, assuming the length of the diameter is x, we can create the following equation based on the secant-tangent theorem:

25² = 19(x + 19)

625 = 19x + 361

625 - 361 = 19x + 361 - 361 [subtraction property]

264 = 19x

Divide both sides by 19:

x ≈ 13.9

The diameter is approximately 13.9.

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A square pyramid has a square base with four vertices, and an additional vertex at the apex of the pyramid, for a total of five vertices or zero-dimensional objects.

Answer:

A.) 5

Points are 0 dimensional objects.

The missing integer on the number line below is given as follows:

-7.

The missing integer on the number line is obtained applying the proportions in the context of the problem.

The vertical trace is the mean of -10 and -5, hence it is given as follows:

(-10 - 5)/2 = -7.5.

(we obtain the mean of the two numbers as the middle trace is exactly halfway between these two values).

The missing integer on the number line is the integer number exactly to the right(greater) of -7.5, hence it is of:

-7.

(nearest integer that is greater than -7.5).

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Answer:

1.3

Step-by-step explanation:

if you subtract 16 and 10 gives u six then turn it into a mix number and divide that into 4s in each ten groups then you would get your answer that way hope it helps

Answer:

i find my answer as 0

Step-by-step explanation:

perimeter=2(l+w)

2(3x+6+x+2)

x=-2

then substitute for x in the figure above then you'll find perimeter as 0

The requried game should start no later than 10:30 am to ensure that the team finishes on time.

If the game is at most 1 3/4 hours long, then the latest it can end is 1:45 pm (which is 1 hour and 45 minutes after the start time).

If the team needs to be off the field by 12:15 pm, then the latest the game can start is:

12:15 pm - 1 hour and 45 minutes = 10:30 am

Therefore, the game should start no later than 10:30 am to ensure that the team finishes on time.

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The cost of the ending inventory under FIFO method is $3,490 and the cost of the ending inventory under LIFO method is $2,820.

To calculate the cost of the ending inventory under FIFO method, we need to first determine the cost of goods sold (COGS) for the month.

The cost of goods sold for the month would be:

300 units x $7 = $2,100

90 units x $8 = $720

20 units x $8 = $160

210 units x $9 = $1,890

Total COGS = $4,870

To calculate the cost of the ending inventory, we need to determine the cost of the remaining 390 units on hand.

Under FIFO, the cost of the ending inventory is based on the cost of the most recent purchases.

Therefore, the cost of the ending inventory would be:

20 units x $8 = $160 (from the 410 units purchased at $8)

370 units x $9 = $3,330 (from the 210 units purchased at $9 and the remaining 160 units of the 410 units purchased at $8)

Total cost of ending inventory = $3,490

Therefore, the cost of the ending inventory under FIFO method is $3,490 and the cost of the ending inventory under LIFO method is $2,820.

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Answer:

k = 0.72

Step-by-step explanation:

If y varies inversely as the square of x, then we know that the variation equation is:

[tex]y=k/x^2[/tex], where k is the constant of variation.

We can find the constant variation by plugging in 0.045 for y, 4 for x, and solving for k;

[tex]0.045=k/4^2\\0.045=k/16\\0.72=k[/tex]

The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820  

a + s = 900

The number of adults ticket and student tickets is 380 and 520.

We have,

Adults ticket cost = $4

Student ticket cost = $2.5

Now,

Total amount earned = $2,820

The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820   ______(1)

And,

The number of tickets sold = 900.

We can write as equation as:

a + s = 900 ______(2)

Now,

We have two equations.

4a + 2.5s = 2820

a + s = 900

Solving for s.

s = 900 - a

Substituting in (1)

4a + 2.5(900 - a) = 2820

Simplifying and solving for a.

4a + 2250 - 2.5a = 2820

1.5a = 570

a = 380

Now,

a + s = 900

380 + s = 900

s = 520

Therefore,

The number of adults ticket and student tickets is 380 and 520.

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The point-slope linear function that relates cost with group size is given as follows:

D. y - 115 = 5(x - 17).

The point-slope equation of a line is given as follows:

y - y* = m(x - x*).

In which:

When the group size increases by 3, the cost increases by $15, hence the slope m is given as follows:

m = 15/3

m = 5.

One point is x = 17 and y = 115, hence the equation can be given as follows:

y - 115 = 5(x - 17).

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The number of bacteria this morning is 119000 and the surface area of the solid is 25344 square meters

Given that

So, we have

This morning = 35000 * (1 + 240%)

Evaluate

This morning = 119000

Here, we have

Fractional part = 28/70

Simplify

Fractional part = 2/5

So, the 28 is 2/5 of 70 as the fractional part

Start by calculating the base area using

base area = 1/2 * (6 + 10) * 10

base area = 80

So, we have

Volume = base area * height

Volume = 80 * 13

Volume = 1040 cubic cm

This is calculated as

Surface area = bh * (b1 + b2 + b3)l

So, we have

Surface area = 12 * 6 * (10 + 10 + 12) * 11

Evaluate

Surface area = 25344

So, the surface area of the solid is 25344 square meters

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The ordered pair which represents the total number of songs they have each downloaded in 8 weeks is given by (40, 120).

Thurston downloaded 5 songs each week.

He continued downloading songs for 8 weeks in same rate.

So the total number of songs he downloaded for total of 8 weeks = 8*5 = 40 songs.

Kim downloaded 15 songs each week.

She continued downloading songs for 8 weeks in same rate.

So total number of songs she downloaded for total of 8 week = 8*15 = 120 songs.

The required ordered pair = (total number of songs Thurston downloaded for total of 8 weeks, total number of songs Kim  downloaded for total of 8 week) = (40, 120).

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The question is incomplete. The complete question will be -

"Thurston downloaded 5 songs each week and Kim downloaded 15 songs each week. Thurston and Kim continue downloading songs in this manner for 8 weeks. What ordered pair would represent the total number of songs they have each downloaded?"

The graph has 14 vertices and 10 vertices and 70 edges, but this does not affect the chromatic number, which is 2.

A bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets. In such a graph, it is always possible to color the vertices with two colors such that no two adjacent vertices have the same color. Therefore, the chromatic number of a bipartite graph is always 2.

In this problem, the bipartite graph has 14 vertices in one part and 10 vertices in the other part, which makes a total of 24 vertices. Since the graph has 70 edges, it means that each vertex in one part is connected to exactly 5 vertices in the other part (70/14=5). Similarly, each vertex in the other part is connected to exactly 7 vertices in the first part (70/10=7).

To color this bipartite graph with two colors, we can assign one color to the first set of vertices and the other color to the second set of vertices. This coloring satisfies the condition that no two adjacent vertices have the same color, and therefore, the chromatic number of the graph is 2.

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Answer:

Step-by-step explanation:

Answer:

my answer is 23.49

Step-by-step explanation:

you will use sin rule

you can also find the angle for Z because angles in a triangle add up to 180

then use sin rule

25/sin 70=x/sin 62

then substitute for x

Answer:

$13,080.50 + $13,080.50 x 0.06 x 30/360 = $13,393.03

Step-by-step explanation:

Adjusted balance after the first payment: $39,600 + $39,600 x 0.06 x 75/360 - $11,880 = $28,770

Adjusted balance after the second payment: $28,770 + $28,770 x 0.06 x 5/360 - $15,840 = $13,080.50 tell me if it's not clear

The magnitude of the resultant force is approximately 9.07 lb.

We have,

To use the parallelogram rule to find the magnitude of the resultant force for the two forces, we first draw a diagram:

         B (11 lb)

        /|

       / |

      /  |

     /   |

    /    |

   /     |

  /θ     |

 /       |

A (7 lb)  |

 \       |

  \      |

   \     |

    \    |

     \   |

      \  |

       \ |

        \|

         C

where A and B are the magnitudes of the given forces, and θ is the angle between them.

Using the parallelogram rule, we draw a parallelogram with sides AB and BC:

         B (11 lb)

        /|

       / |

      /  |

     /   |

    /    |

   /     |

  /θ     |

 /       |

A (7 lb) D

 \       |

  \      |

   \     |

    \    |

     \   |

      \  |

       \ |

        \|

         C

The diagonal BD represents the magnitude and direction of the resultant force.

To find its magnitude, we use the Law of Cosines:

BD^2 = AB^2 + BC^2 - 2(AB)(BC)cos(θ)

BD^2 = (7 lb)^2 + (11 lb)^2 - 2(7 lb)(11 lb)cos(133 degrees)

BD^2 = 49 + 121 - 2(77)cos(133 degrees)

BD^2 = 170 - 154cos(133 degrees)

BD ≈ 9.07 lb (rounded to two decimal places)

Therefore,

The magnitude of the resultant force is approximately 9.07 lb.

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