pls help!!
AB + BC = AC
AB = BC
What property allows AB + BC = AC to become AB + AB = AC?
27

Answer:

=32

Step-by-step explanation:

the speed = distance / time = 24 / (3/4) = 24*4 / 3 = 96 / 3 = 32 (mile/hour)

Answer:

The answer is \(6x^{2} +14x-12\)

Step-by-step explanation:

The product is  6x² +14x - 12.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Given:

(3x-2)(2x+6)

Now, multiply

(3x-2)(2x+6)

= (3x)(2x) + 3x(6) - 2(2x) - 2(6)

= 6x² +18x - 4x - 12

= 6x² +14x - 12

Hence, the product is  6x² +14x - 12.

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The quadratic function that models his path through the air, where x is his horizontal distance from the start line in meters and y is his height, in cm is given as follows:

y = -x² + 12x - 27.

Considering it's roots x' and x'', a quadratic function is modeled according to the rule presented as follows:

y = a(x - x')(x - x'')

In which a is the leading coefficient.

A long-jumper lifts off 3 m after starting his run, and lands 6 m later (9m from the start), hence the roots of the parabola are given as follows:

x' = 3, x'' = 9.

Hence:

y = a(x - 3)(x - 9)

y = a(x² - 12x + 27).

When he is 8 m from the start line, he is 5 cm above the ground, meaning that when x = 8, y = 5, hence the leading coefficient a is calculated as follows:

5 = a(8² - 12(8) + 27)

-5a = 5

5a = -5

a = -1.

Hence the equation of the parabola is given as follows:

y = -x² + 12x - 27.

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Answer: 15 - 6i

Step-by-step explanation:

3(5-2i)

3×5+3×(−2i)

Do the multiplications.

15−6i

The solutions to the equation z^2 = -361 are:

z = ±19i and z = ±19i*(-1)^k, k = 0 or 1.

To find all n complex solutions of the equation x^n = k, where k is a complex number, we can use the polar form of complex numbers. If we write k in polar form as k = re^(iθ), where r = |k| is the modulus of k and θ = arg(k) is the argument of k, then we can write x in polar form as x = ρe^(iφ), where ρ = |x| is the modulus of x and φ = arg(x) is the argument of x.

Substituting these polar forms into the equation x^n = k, we get:

(ρe^(iφ))^n = re^(iθ)

Taking the modulus of both sides, we get:

|ρ^n| = |r|

Since r is a complex number, its modulus is a positive real number, so we can write r = Re^(i0) in polar form, where R = |r|.

Substituting this into the equation above, we get:

|ρ^n| = R

Taking the argument of both sides, we get:

nφ = 0 + 2πk

where k is an integer. Solving for φ, we get:

φ = (2π*k) / n

Substituting this expression for φ back into the polar form of x, we get:

x = ρe^(i(2π*k)/n)

where ρ is a positive real number. This gives us n complex solutions for x, which are:

x = ρe^(i(2π*k)/n), k = 0, 1, 2, ..., n-1.

Now let's apply this method to solve the equation z^2 = -361.

Writing -361 in polar form, we have:

-361 = 361e^(iπ)

Taking the square root of both sides, we get:

z = ±sqrt(361)e^(iπ/2 + iπk)

where k = 0 or 1. Simplifying, we get:

z = ±19e^(i(π/2 + π*k))

So the solutions to the equation z^2 = -361 are:

z = ±19i and z = ±19i*(-1)^k, k = 0 or 1.

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Answer: A 18 1/5 - 22 2/5 - 40 1/5

Angle ACD is congruent to angle ADC by transitive equality if angles 1 and 2 are both ACD because angle ACB is congruent to angle ADE in the step above. Therefore, angle 1 equals angle 2, as you can see.

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Here,

Given that segments AB and AE are congruent, the triangle ABE is required to be isosceles by definition.

As a result, angle ABC must be similar to angle AED, again in accordance with the definition of an isosceles triangle.

Consequently, triangle ABC must be congruent to triangle AED by SAS as you have been informed that segments BC and DE are congruent. Right now, it's unclear to you whether angle 1 is ACB or ACD.

Assuming it is ACB, CPCT shows that ACB is congruent to ADE. Angle 1 equals angle 2, so there you have it. Since angle ACB is supplementary to angle ACD and angle ADE is supplementary to angle ADC.

Since angle ACB is congruent to angle ADE from the step above, angle ACD is congruent to angle ADC by transitive equality if angle 1 and angle 2 are both ACD. Angle 1 equals angle 2, so there you have it.

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The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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The given number, 2.256256256… is equal to the ratio of integers 203063063 / 90000000.

Given that 2.256256256... is a repeating decimal that can be expressed as a ratio of integers. Now we have to express the number as a ratio of integers.

The number 2.256256256… is a repeating decimal that can be expressed as a ratio of integers.

Therefore, we have to convert it into a ratio of integers.

Now, Let x = 2.256256256…(1)

10x = 22.56256256…(2)

Now we subtract (1) from (2) as follows:10x – x = 22.56256256… - 2.256256256…9x = 20.3063063…x = 20.3063063… / 9

Thus, the given number, 2.256256256… is equal to the ratio of integers 203063063 / 90000000.

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Given:-

now put the value of x = 2 in eqⁿ

\( \rm{2( \: {5} \: )^{x} }\)

\( \: \)

\( \rm{2 (\: {5} \: )^{2} }\)

\( \: \)

\(2( \: 25 \: )\)

\( \: \)

\( \underline{ \boxed{ \rm \orange{ { \: 50 \: }}}}\)

\( \: \)

hope it helps! :)

\( \: \)

student can answer the questions on the test in 16,384 different ways if they answer every question.

To determine the number of ways a student can answer the questions on a multiple-choice test containing 7 questions with four possible answers for each question, we will use the multiplication principle. The multiplication principle states that if there are a number of independent choices, then the total number of possible outcomes is the product of the number of choices.
Identify the number of questions and possible answers. In this case, there are 7 questions and 4 possible answers for each question.
Calculate the number of ways to answer each question. Since there are 4 possible answers for each question, there are 4 ways to answer each of the 7 questions.
Apply the multiplication principle. To find the total number of ways to answer all 7 questions, multiply the number of ways to answer each question:
Total number of ways = (4 ways for question 1) x (4 ways for question 2) x ... x (4 ways for question 7)
Perform the calculation. Since there are 7 questions and 4 ways to answer each question, the total number of ways is:
Total number of ways = 4^7 = 16,384

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The triangles formed by the diagonals of the parallelogram are congruent by ASA, segments are therefore congruent and we get;

The segments \(\overline{AE}\) = \(\overline{CE}\), and \(\overline{BE}\) = \(\overline{DE}\) by definition

A parallelogram is a quadrilateral that have facing parallel sides.

The completed two column table to prove that the diagonals of a parallelogram bisect each other can be presented as follows;

Statements \({}\)                           Reasons

1. ABCD is a parallelogram \({}\)                      1. Given

2. ∠ABE and ∠CDE are alt. int angles\({}\)     2. Definition

3. ∠BAE and ∠DCE are alt. int angles\({}\)     3. Definition

4. ∠BCE and ∠DAE are alt. int angles\({}\)     4. Definition

5. ∠CBE and ∠ADE are alt. int angles\({}\)     5. Definition

6. \(\overline{AD}\) ≅ \(\overline{BC}\), \(\overline{AB}\) ≅ \(\overline{CD}\)                          \({}\)  6. Properties of a parallelogram

7. ΔBAE ≅ ΔDCE\({}\)                                       7. SAS congruence postulate

8. \(\overline{BE}\) ≅ \(\overline{DE}\), \(\overline{AE}\) ≅ \(\overline{CE}\)               \({}\)              8. CPCTC

9. \(\overline{AE}\) = \(\overline{CE}\) and \(\overline{BE}\) ≅ \(\overline{DE}\)                      \({}\) 9. Definition of congruence

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The value of a, in the given expression n√a, is called radicant (option c) where radicand refers to the number or expression beneath the radical sign in a radical expression.

Given an expression n√a, the value a is called a radicand.

What is n√a? In the expression, n√a, the symbol √ is the radical sign.

It implies a root of a certain order.

The value of n is the index of the radical.

The value of a is the radicand.

So, What is a radicant?

The term radicand refers to the number or expression beneath the radical sign in a radical expression.

To understand what a radicand is, consider the following radical expression that expresses the square root of a number (with an index of 2) like √16 = 4.

In this case, 16 is the radicand.

The value inside the radical symbol can be anything - a fraction, a variable, or a combination of numbers and variables. Therefore, the value a in the expression n√a is called a radicand. So, the correct answer is option c) radicand.

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a.) The weights, ω1 + ω2 + ω3 = 1. b.) The weights, V[Y_bar ω] = ω1²V[Y1] + ω2²V[Y2] + ω3²V[Y3] = ω1²σ² + ω2²σ² + ω3²σ² = σ²(ω1² + ω2² + ω3²). To estimate the expectation μ, we propose combining three independent and identically distributed random variables Y1, Y2, and Y3 using a weighted average, Y_bar ω = ω1Y1 + ω2Y2 + ω3Y3.

(a) The weights ω1, ω2, and ω3 need to satisfy the condition ω1 + ω2 + ω3 = 1 for Y_bar ω to be an unbiased estimator for μ. The expectation E[Y_bar ω] is calculated as E[Y_bar ω] = ω1E[Y1] + ω2E[Y2] + ω3E[Y3] = ω1μ + ω2μ + ω3μ = (ω1 + ω2 + ω3)μ. For Y_bar ω to be an unbiased estimator for μ, its expectation should equal μ. Therefore, ω1 + ω2 + ω3 = 1.

(b) The variance V[Y_bar ω] can be calculated as V[Y_bar ω] = V[ω1Y1 + ω2Y2 + ω3Y3]. Since Y1, Y2, and Y3 are independent, the variance of their sum is the sum of their variances. Therefore, V[Y_bar ω] = ω1²V[Y1] + ω2²V[Y2] + ω3²V[Y3] = ω1²σ² + ω2²σ² + ω3²σ² = σ²(ω1² + ω2² + ω3²). The variance of Y_bar(ω) can be calculated, and by applying the condition from (a), the set of weights that minimize the variance can be determined.

To minimize the variance, we can apply the condition from (a), ω1 + ω2 + ω3 = 1, and use a technique called Lagrange multipliers. By introducing the Lagrange multiplier λ, we form the Lagrangian L = σ²(ω1² + ω2² + ω3²) + λ(ω1 + ω2 + ω3 - 1). Taking partial derivatives with respect to ω1, ω2, ω3, and λ, we can solve the equations to find the set of weights that minimize the variance. The specific values will depend on the given values of σ² and the constraints imposed by the problem.

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Answer:

refer to the attachment hope it helps

Answer:

x <= 5

Step-by-step explanation:

This statement can be translated into equation form:

Let x be the number

2x + 5 <= 15

To solve the inequality, move the positive five over to the opposite side as well as changing the operator to a subtract:

2x <= 15 - 5

2x <= 10

This can then be simplified by dividing both sides by 2:

\(\frac{2x}{2} \leq \frac{10}{2}\)

x <= 5

Hope this helps!

Answer:

the probability of the complement of rolling a number less than 5 by using a six-sided die is 1/3.

Step-by-step explanation:

Given that a fair die is rolled. We know there are six numbers in a fair die.On rolling a die, the Sample space of the given event E = {1, 2, 3, 4, 5, 6}Sample space of numbers less than 5 = {1, 2, 3, 4}Clearly we can see that the number of favorable outcomes = 4Hence, P(values less than 5) = 4/6 = 2/3.To find the complement of rolling a number less than 5, we use the formula P' = 1 - P, where P' is the complement of P.So, let P' be the complement probability of getting numbers less than 5Now, P'(numbers less than 5) = 1 - P(numbers less than 5)= 1 - 2/3= 1/3.Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is 1/3.

Answer:

1/3

Step-by-step explanation:

This means that, the dice can be rolled at value from 1-4 and there are 6 numbers so it would be 4/6 simplified 2/3. Now subtract that value from 1 and you get 1/3

Answer:

13.5

Step-by-step explanation:

6 x^2

Let x= 1.5

6 ( 1.5) ^2

6 *2.25

13.5

Answer:

1/4

Step-by-step explanation:

In probabilty,

"AND" means "multiplication"

"OR" means "addition"

Here, we want probability of "rolling number less than 4" "AND" "rolling number greater than 3". Thus, we find the inidvidual probabilities and then "MULTIPLY" (since "AND").

In a 6-sided die, the numbers are 1,2,3,4,5, and 6.

Thus,

Probability of rolling a number less than 4 = 3/6 = 1/2 (the numbers are 1,2, and 3)

and

Probability of rolling a number greater than 3 = 3/6 = 1/2 (the numbers are 4,5, and 6)

Thus:

P(less than 4) and P(greater than 3) = 1/2 * 1/2 = 1/4

The probability is 1/4

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Using proportions, considering the given ratio, Isabella gets \(\frac{4}{7}\) of the total reward.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The ratio of Isabella and Aiden is 4:3, which means that out of 4 + 3 = 7 items, Isabella gets 4 and Aiden gets 3, hence the fraction is given by:

\(\frac{4}{7}\).

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f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

Answer:

SIf Caden's burrito stand uses 7/8 of a bag of tortillas each day, then in one day, the stand will use 1 bag of tortillas after (1 / 7/8) = 8/7 days.

Therefore, 7 7/8 bags of tortillas will last for (7 7/8) x (8/7) = 8 days.

So, 7 7/8 bags of tortillas will last for 8 days at Caden's burrito stand.

\(p-5(p+4) = p-(8-p)\\\\\implies p-5p - 20 = p-8+p\\\\\implies -4p-2p = 20 -8 \\\\\implies -6p = 12 \\\\\implies p = -2\)

The given differential equation is dy + ydx = e^(-x)dx. This is a linear differential equation of the first order. We can solve it using the method of integrating factors.

First, we rewrite the equation in the standard form:

dy - ydx = e^(-x)dx

Now, we can identify the integrating factor, which is the exponential function of the integral of the coefficient of y:

IF = e^(∫(-1)dx) = e^(-x)

Next, we multiply both sides of the equation by the integrating factor:

e^(-x)dy - e^(-x)ydx = e^(-x)e^(-x)dx

This simplifies to:

d(e^(-x)y) = e^(-2x)dx

Integrating both sides, we get:

e^(-x)y = ∫e^(-2x)dx

Integrating the right side gives:

e^(-x)y = (-1/2)e^(-2x) + C

Finally, we can solve for y by dividing both sides by e^(-x):

y = (-1/2)e^(-x) + Ce^(x)

So, the solution to the given differential equation is y = (-1/2)e^(-x) + Ce^(x), where C is the constant of integration.

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The correct drop down menus from the graph are:

Pool A is filling up slower than Pool B because the slope of the graph of Pool A is less than that of the graph for Pool B.

The slope of the graph tells you the unit rate in gallons per minute. Its means the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

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(a) The "Z-Score" for bulb with life of 65 hours is -1.25,

(b) The probability of a bulb's life being lower than 65 hours is approximately 0.1056.

Part (a) : To find the "Z-score" for a bulb with a life of 65 hours, we use the formula : Z = (X - μ) / σ;

where X = bulb life, μ = mean, and σ = standard-deviation,

We know that the mean (μ) is = 70 hours and the standard deviation is (σ) = 4 hours,

Z = (65 - 70)/4,

Z = -1.25

So, Z-score for a bulb with a life of 65 hours is -1.25.

Part (b) : To find probability of a bulb's life being lower than 65 hours, we find area under normal-distribution curve to left of Z-score -1.25,

P(X < 65) = P((X-μ)/σ < (65 - 70)/4),

= P(Z < -1.25) = 0.1056,

Therefore, the required probability is 0.1056.

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The given question is incomplete, the complete question is

Light bulb life is normally distributed with a mean of 70 hour and a standard deviation of 4. Suppose one individual is randomly chosen. Let X = bulb life of a bulb.

(a) Determine the z-Score for a bulb with a bulb life of 65 hours.

(b) Determine the probability of a bulb's life lower than 65 hours.