Measure the length of each leg and the hypotenuse.
m∠ABC = 45° m∠ACB = 45°

Question:
AB =? Units
AC =? Units
BC =? Units

Answer:

The new value of the list after changing 71° to 93° would be:

58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57

The measure that changes the most would be the median. Without the change, the median was 86.5°, which was the average of the 7th and 8th values in the list (100 + 77) / 2. However, after changing 71° to 93°, the median becomes 91°, which is the average of the 6th and 7th values in the list (91 + 91) / 2.

Therefore, the median has changed by 4.5° (from 86.5° to 91°).

Answer:

5) A

6) D

Step-by-step explanation:

for 5) I did just looked up online

2.5% of 25,000

and I added it to 25,000

which was 26,265.625

so I looked up 2.5% of 26,265.625 and I kept doing it until the 5th year and I got estimated $28,285.21

for 6) I did similar to 5) but I used the numbers that were given

I looked up 4% of 1,250 and I did that twice and got $1,352.55

hope that helped ;)

Outstanding balance = Invoice amount - CreditInvoice amount = $1,205Credit = $611.25Outstanding balance = $1,205 - $611.25Outstanding balance = $593.75Therefore, Vail's outstanding balance is $593.75.

a. To determine the credit that Vail should receive, we need to use the formula for partial payment: Payment / (1 - Discount%)The calculation for the credit that Vail should receive is:Discount% = 2/10 = 0.2Credit = 489 / (1 - 0.2)Credit = 489 / 0.8Credit = $611.25The credit that Vail should receive is $611.25.b.

To calculate Vail's outstanding balance, we need to subtract the credit from the invoice amount. The calculation is:Outstanding balance = Invoice amount - CreditInvoice amount = $1,205Credit = $611.25Outstanding balance = $1,205 - $611.25Outstanding balance = $593.75Therefore, Vail's outstanding balance is $593.75.

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Answer:

Samuel will need 614 2/3 feet of material to build eight of his standard fences. To find this answer, we simply need to multiply 76 2/3 feet (the perimeter of one fence) by 8 (the number of fences he wants to build). Thus, 76 2/3 feet x 8 = 614 2/3 feet.

The probability of spinning yellow, tossing heads, and selecting the number 2 is approximately 0.083325 or 8.33%.

To find the probability of spinning yellow, tossing heads, and selecting the number 2, we need to calculate the individual probabilities of each event and then multiply them together.

Given:

Spinner with three equal size sections (red, green, yellow)

Coin toss with two outcomes (heads, tails)

Two cards labeled with 1 and 2

Firstly calculate the probability of spinning yellow:

Since the spinner has three equal size sections, the probability of spinning yellow is 1/3 or 0.3333.

Secondly calculate the probability of tossing heads:

Since the coin has two possible outcomes, the probability of tossing heads is 1/2 or 0.5.

Thirdly calculate the probability of selecting the number 2:

Since there are two cards labeled with 1 and 2, the probability of selecting the number 2 is 1/2 or 0.5.

Lastly multiply the probabilities together:

To find the probability of all three events occurring, we multiply the individual probabilities:

Probability = (Probability of spinning yellow) * (Probability of tossing heads) * (Probability of selecting the number 2)

Probability = 0.3333 * 0.5 * 0.5

Probability = 0.083325

Therefore, the probability of spinning yellow, tossing heads, and selecting the number 2 is approximately 0.083325 or 8.33%.

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Answer:

A. y = x² - 9x + 18

Step-by-step explanation:

The key thing to look for in this graph is the y-intercept (where the graph will hit the y-axis).

We can't see exactly where y-intercept is, but we know it is a positive number.

In a standard form quadratic equation:

y = ax² + bx + c

'c' tells you what the y-intercept is.

The choices with positive y-intercept are A and B.

Again, we can't see exactly where y-intercept is, but we know it is not 1.

y = x² - 9x + 18

has a positive y-intercept that is not 1,

thus the answer is A.

Answer:

the quotient of 9 and 14

= \(\frac{9}{14}\)

Answer:

the answer is 9 upon 14 (⁹/14)

The game to be fair, the player should win 60.

In order to determine the fair winnings for this game, we need to calculate the probability of winning and then set it equal to the cost of playing the game.
Step 1: Calculate the probability of winning.
There are two scenarios for winning:
1. First roll is even, and the second roll matches the first.
2. The probability of rolling an even number on a six-sided die is 3/6 or 1/2, since there are three even numbers (2, 4, and 6).
Step 2: Calculate the probability of the second roll matching the first roll.
Since there are 6 sides to the die, the probability of the second roll matching the first is 1/6.
Step 3: Calculate the combined probability of both events.
To find the combined probability of both events, multiply the probabilities: (1/2) × (1/6) = 1/12. So the probability of winning is 1/12.
Step 4: Set up an equation to determine fair winnings.
Let x be the fair winnings for the game. The cost of playing the game is $5. In order for the game to be fair, the expected value (probability of winning multiplied by the winnings) should equal the cost of playing the game:
(1/12) × x = 5
Step 5: Solve the equation for x.
To solve for x, multiply both sides of the equation by 12:
x = 5 × 12
x = 60
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The area of the region bounded by the curves is approximately 72.75 square units.

A parabola is the portion of a right circular cone cut by a plane perpendicular to the cone's generator. It is a locus of a point that moves such that the separation between it and a fixed point (focus) or fixed line (directrix) is the same.

To sketch the region bounded by the curves 2x² - y = 20 and x⁴ - y = 4, we can begin by graphing each equation separately.

First, the equation 2x² - y = 20 can be rearranged to solve for y:

y = 2x² - 20

This is a downward-facing parabola that opens towards the vertex at (0, -20).

Next, the equation x⁴ - y = 4 can be rearranged to solve for y:

y = x⁴ - 4

This is an upward-facing parabola that opens towards the vertex at (0, -4).

To find the intersection points of the two curves, we can set the right-hand sides of the equations equal to each other:

2x² - y = 20

x⁴ - y = 4

Substituting y from the second equation into the first equation, we get:

2x² - (x⁴ - 4) = 20

Simplifying and rearranging, we get:

x⁴ - 2x² - 24 = 0

Factoring, we get:

(x² - 4)(x² + 6) = 0

This gives us four solutions:

x = ±2 and x = ±√6

Substituting these values of x into either of the original equations, we can find the corresponding y-values:

When x = 2, y = 4

When x = -2, y = 36

When x = √6, y = 2(6)² - 20 = 32

When x = -√6, y = 2(6)² - 20 = 32

So the intersection points are (2, 4), (-2, 36), (√6, 32), and (-√6, 32).

To sketch the region bounded by the curves, we can plot the two curves and shade the area between them:

The area of this region can be found by integrating the difference between the two curves with respect to x:

A = ∫[√6, 2] [(x⁴ - 4) - (2x² - 20)] dx

Simplifying, we get:

A = ∫[√6, 2] (x⁴ - 2x² + 16) dx

Integrating term by term, we get:

A = [x⁵/5 - 2x³/3 + 16x]√6 to 2

Evaluating this expression, we get:

A ≈ 72.75

So, the area of the region bounded by the curves is approximately 72.75 square units.

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Answer:

the rule to remember is that opposites attract. every magnet has both a north and a South pole. when you place the North Pole of one magnet near the South Pole of another magnet, they are attracted to one another.

Step-by-step explanation:

Hope this helped Mark BRAINLIEST!!

Answer:

The magnets have different poles facing each other ( N/S > < S/N )

The longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.

The longest a blender can last and still be in the lowest 6% of life spans is calculated by using the inverse normal distribution formula. This formula is P(X ≤ x) = 1 - P(X > x). The X is the longest a blender can last and P(X ≤ x) is 6%. First, we need to calculate the z-score for 6%. This can be done by P(X ≤ x) = 0.06 and using the z-score formula z = (x - μ) / σ , where μ is the mean and σ is the standard deviation. Substituting the values into the equation, we get z = 0.06 = (x - 8.2) / 0.8. Solving for x gives us x = 7.96. Therefore, the longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.

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Answer:

Step-by-step explanation:

To find the average value of the function f(x) = x^2(x^3 + 30) on the interval [-3, 3], we use the formula:

fave = (1/(b-a)) * ∫[a,b] f(x) dx

where a = -3 and b = 3.

So, we have:

fave = (1/(3-(-3))) * ∫[-3,3] x^2(x^3 + 30) dx

fave = (1/6) * [∫[-3,3] x^5 dx + 30∫[-3,3] x^2 dx]

fave = (1/6) * [0 + 30(2*3^3)]

fave = 2430

Therefore, the average value of the function f on the given interval is 2430.

To find the average value of the function h(u) = In(u) on the interval [1, 5], we use the formula:

have = (1/(b-a)) * ∫[a,b] h(u) du

where a = 1 and b = 5.

So, we have:

have = (1/(5-1)) * ∫[1,5] ln(u) du

have = (1/4) * [u ln(u) - u] from 1 to 5

have = (1/4) * [(5 ln(5) - 5) - (ln(1) - 1)]

have = (1/4) * (5 ln(5) - 4)

have = 0.962

Therefore, the average value of the function h on the given interval is approximately 0.962.

To find all numbers b such that the average value of f(x) = 6 + 10x - 9x^2 on the interval [0, b] is equal to 7, we use the formula:

fave = (1/(b-a)) * ∫[a,b] f(x) dx

where a = 0 and b = b.

So, we have:

7 = (1/b) * ∫[0,b] (6 + 10x - 9x^2) dx

7b = [6x + 5x^2 - 3x^3/3] from 0 to b

7b = 2b^2 - 3b^3/3 + 6

21b = 6b^2 - b^3 + 18

b^3 - 6b^2 + 21b - 18 = 0

Using synthetic division, we find that b = 2 is a root of this polynomial equation. Dividing by (b-2), we get:

(b-2)(b^2 - 4b + 9) = 0

The quadratic factor has no real roots, so the only solution is b = 2.

Therefore, the only number b such that the average value of f(x) on the interval [0, b] is equal to 7 is 2.

To estimate the average world population to the nearest million during the time period of 1950 to 1980, we need to find:

ave = (1/(1980-1950)) * ∫[1950,1980] P(t) dt

ave = (1/30) * ∫[1950,1980] 2560e^(0.017185t) dt

Using the formula for integrating exponential functions, we get:

ave = (1/30) * [2560

Answer:

y=3x+3

Step-by-step explanation:

The gradient of BC is the same as the gradient of AD because the lines are parallel lines

Given that

Lines BC and AD

For the gradients to be equal, then the lines are parallel lines

The gradients of parallel lines are equal because parallel lines have the same slope.

Since parallel lines have the same orientation and do not intersect, they have the same change in y-coordinates and change in x-coordinates.

Therefore, the ratio of the change in y-coordinates to the change in x-coordinates, which is the slope, is the same for both parallel lines.

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Answer:

44.55

Step-by-step explanation:

I actually didn't get the right answer and I just edited it right now I'm sorry I dont have an explanation!

The least positive integer $n$ such that no matter how $10^n$ is expressed as the product of two positive integers, at least one of these two integers contains the digit 0, is 7.

Latex formula for equation.

f(x) = x^2 + 2x + 1

Let's consider the factorization of $10^n$ for increasing values of $n$.

For $n = 1$, $10^1 = 10$ which contains the digit 0.

For $n = 2$, $10^2 = 100$ which contains the digit 0.

For $n = 3$, $10^3 = 1000$ which contains the digit 0.

For $n = 4$, $10^4 = 10,000$ which contains the digit 0.

For $n = 5$, $10^5 = 100,000$ which contains the digit 0.

For $n = 6$, $10^6 = 1,000,000$ which contains the digit 0.

For $n = 7$, $10^7 = 10,000,000$ which contains no digit 0.

Therefore, the least positive integer $n$ is 7.

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Answer:

2.75 i believe

Answer:

2.75

Step-by-step explanation:

\(625*\frac{0.44}{100} =2.75\)

To win the Ohio Classic Lotto, you need to match all six numbers drawn. In this lottery game, players choose six numbers from a set range, typically from 1 to 49.

The winning combination is determined by a random drawing of six numbers, usually conducted by a lottery machine or ball-drawing mechanism.

For a chance to win the jackpot prize, you must have all six numbers on your ticket match the six numbers drawn in the official drawing. This means that every number on your ticket must exactly correspond to the numbers selected in the drawing, and in the same order.

Matching fewer than all six numbers does not result in winning the jackpot prize. However, depending on the specific rules of the Ohio Classic Lotto, there may be secondary prizes for matching a subset of the drawn numbers, such as matching five, four, or three numbers correctly. These secondary prizes are typically of smaller value than the jackpot prize.

In summary, to win the Ohio Classic Lotto, you need to match all six numbers in the drawing.

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Step-by-step explanation:

c² = a² + b²

c² = 7² + 11²

c² = 49 + 121

c² = 170

now u have to square root it

c² = 170

c = 13

Answer:

Mean = цр = 0.27

Step-by-step explanation:

Note: The full question is attached as picture below

Given that,  p = 27 = 0.27  and n = 85

цр = P

Mean = цр = 0.27

The average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8. option C

Average number of viewers over the two weeks = (First week + Second week) / 2

= {(3.6 x 10⁴) + (4.1 x 10⁴)} / 2

= {3.6 + 4.1 × 10^(4×4) } / 2

= (7.7 × 10^16) / 2

= 3.85 × 10^8

Therefore, the average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8.

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Answer:

7Ft

Step-by-step explanation:

(7ft) Because of Pythagorean Thm. Since the ladder is leaning against a building it makes 10ft the hypotenuse,

Answer:

3x - 4

Step-by-step explanation:

(6x^2 − 8x) ÷ (2x) =

(6x^2)/2x - 8x/2x =                 

3x - 4

Answer:

(C). 3x - 4

Step-by-step explanation:

It will be easily to break this down so,

6/2=3

x^2/x=x

therefore, 6x^2/2x = 3x

Minus stay minus

8/2 = 4

x/x=1

therefore, 8x/2x=4

If we put it all together,

3x - 4

if this helps you, please give brainliest!

The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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The system with an input-output relation y(u) -x() cos(2T fo), where fo is a constant, is linear but not time-invariant.

To determine whether the system defined by the input-output relation y(u) = x(t) cos(2πf0 t) is linear or time-invariant, we need to apply the superposition principle and the time-invariance test.

Linearity:

A system is linear if it satisfies the superposition principle, which states that the response to a sum of inputs is equal to the sum of the individual responses to each input. Mathematically, this can be expressed as:

y(u) = a1x1(u) + a2x2(u)

where a1 and a2 are constants, x1(u) and x2(u) are two arbitrary input signals, and y(u) is the corresponding output.

Let's apply this principle to the given system:

y1(u) = x1(t) cos(2πf0 t)

y2(u) = x2(t) cos(2πf0 t)

y(u) = y1(u) + y2(u) = x1(t) cos(2πf0 t) + x2(t) cos(2πf0 t)

This is a sum of two inputs, and the output is the sum of the individual responses to each input. Therefore, the system is linear.

Time-Invariance:

A system is time-invariant if its behavior does not change over time. In other words, if the input signal is shifted in time, the output signal is also shifted by the same amount of time.

Let's test the time-invariance of the given system:

Assume the input signal is x1(t), and the corresponding output is y1(t) = x1(t) cos(2πf0 t).

Now, let's shift the input signal by a time τ to get a new input signal x2(t) = x1(t-τ). The corresponding output is y2(t) = x2(t) cos(2πf0 t) = x1(t-τ) cos(2πf0 t).

Let's compare the two outputs:

y2(t) = x1(t-τ) cos(2πf0 t)

y1(t-τ) = x1(t-τ) cos(2πf0 (t-τ))

We can see that y2(t) and y1(t-τ) are not equal, which means the system is not time-invariant.

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The correct value of the product of a and b is 224

Taking the prime factorization of 161 reveals that it is equal to 23*7. Therefore, the only ways to represent 161 as a product of two positive integers are 161*1 and 23*7. Because neither 161 nor 1 is a two-digit number, the only two-digit factor of 161 is 23, we know that a and b are 23 and 7. Because 23 is a two-digit number, we know that a, with its two digits reversed, gives 23.

Therefore, a = 32 and b = 7. Multiplying our two correct values of a and b yields.

The correct product must have been

a*b =32*7

=224

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Answer:

x= -1.8

Step-by-step explanation:

4x-22=9x+2(1-4x)

2(1 - 4x)

so you have to distribute

new equation

4x-22=9x+2-8x

you combine like terms on the right

9x + 2 -8

+8. +8

17x+2

new equation

4x-22=17x+2

-4x. -4x

-22=13x + 2

-2. -2

-24=13x

-24÷13= - 1.8

X= -1.8

Answer:

\(4x - 22 = 9x + 2 - 4x \\ - x = 24 \\ x = - 24\)