In the isosceles triangle, solve for side AB

Please help me

The volume of a box with dimensions a, b, and c is given by

V(a,b,c)=abc.

It follows that

dV(a,b,c)/V(a,b,c)=da/a + db/b + dc/c .

Therefore, "in first approximation", the relative error in volume is the sum of the relative errors in the side lengths.

In the given example the relative errors in the side lengths are 1%. As the case may be these add up, and we obtain a relative volume error of 3% or 1.5 cubic inches as a "first estimate".

The actual minimal volume of the box under the given constraints is

4.95*4.95*1.98=48.51495 cubic inches, which is <1.5 cubic inches off; and the maximal volume is 5.05*5.05*2.02=51.51505 cubic inches, which is 1.51505>1.5 off the intended value of 50 cubic inches. It follows that the worst-case analysis gives a larger error than the "first estimate".

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The constant of proportionality for the relationship is 70.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 6 is an equation.

We have,

The number of gems collected at different levels is:

At 2 levels, 140 gems are collected.

At 4 levels, 280 gems are collected.

At 6 levels, 420 gems are collected.

This means.

y ∝ x

y is the number of gems collected.

x is the level.

Now,

y = kx

140 = k x 2

k = 140/2

k = 70

Thus,

The constant of proportionality for the relationship is 70.

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The equivalent of the radical  expression √(100p⁴z⁸) is

10p²z⁴

The given expression √(100p⁴z⁸) is first rewritten in exponents form

Writing in exponents form

= √(100p⁴z⁸)

= (100p⁴z⁸)^1/2

multiplying through

= 100^1/2 * p^(4 * 1/2) * z^(8 * 1/2)

noting that √100 = 100^1/2 = 10

= 10 * p^(2) * z^(4)

= 10p²z⁴

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The congruent pairs for the angles and sides of the given two congruent triangles are

∠A ≅ ∠D      

∠B ≅ ∠ E

∠C ≅ ∠F   and

AB ≅ DE

BC ≅ EF

AC ≅ FD

What is congruent triangles?

If and only if we can use rigid transformations to map one figure onto the other, then two figures are said to be congruent. All corresponding sides and angles are congruent because rigid transformations maintain distance and angle measure. Therefore, measuring all of the sides and angles of a pair of triangles would be one method of determining whether they are congruent.

Let the given two triangles, ΔABC and ΔDEF are congruent.

We have to find the congruent pairs from the given two congruent triangles.

First to find the congruent pairs for angles.

∠A ≅ ∠D

∠B ≅ ∠ E

∠C ≅ ∠F

Now to find the congruent pairs for sides,

AB ≅ DE

BC ≅ EF

AC ≅ FD

These are the congruent pairs for the angles and sides of the given two congruent triangles.

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Answer:

B. 11/12

Step-by-step explanation:

Answer: B. 11/12

Step-by-step explanation:

.

Answer:

1.5

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

3 times 1/2=1/5

The population of the city in 2000 = 23.1 million

In 2006 the population will be equal to 28.3 million

Compound interest may be used in a variety of situations, including increasing or decreasing population, Increasing the count of bacteria increasing an item's value, and a decrease in an item's worth.  

The formula for Compound interest is given by

Where P = Principal amount or Initial value

r = rate of interest or increase

t = time period

Here we have

The formula [tex]A = 23.1 e^{(0.0152t)}[/tex] represents the population of a US state, A, in millions, 't' years after 2000.  

Here we need to solve the following questions

a. What was the population of the state in 2000

Compare the given formula with A = Pe^rt  

=>  [tex]23.1 e^{0.0152t} = Pe^{rt}[/tex]    

=> Initial value or initial population, P = 23.1 and

rate of increase r = 0.0152  

Therefore,

The population of the city in 2000 = 23.1 million

b. When will the population of the state reach 28.3 million?

As we know in 2002 the population = 23.1 million

Let's assume that after 'n' year the population will become 28.3 million

As we know Rate of increase = 0.0152    

From the given formula

Population of the city after n, A = 23.1 e^(0.0152n)  

As we assumed the population after n years = 28.3

=>  23.1 e^(0.0152n)  = 28.3

=> e^(0.0152n)  = 28.3/23.1

=> e^(0.0152n) = 1.225  

Apply log on both sides

=> log e^(0.0152n) = log 1.225  

=> 0.0152n log e = log 1.225  

=> 0.0152n (1) = 0.0881    

=> n = 0.0881/0.0152

=> n = 5.8 ≅ 6

After 6 years the population will be 28.3 million

After 6 years i.e 2000 + 6 = 2006  

Therefore,

In 2006 the population will be equal to 28.3 million

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Answer:

5 inches

Step-by-step explanation:

P=2(l+w)

Solving for w

w = p / 2 - l = 26 /2 - 8 = 5

Answer: Neither

Step-by-step explanation:

The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.

It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,

C(x) = 270 ln(x+1) + 1900

The average intake of calories consumed per day is given by C(x) = 2200

Here x is the number of acres of land. Then, the required number of acres of land is

C(x) = 270 ln(x+1) + 1900

⇒ 2200 = 270 ln(x+1) + 1900

⇒ 270 ln(x+1) = 2200 - 1900

⇒ 270 ln(x+1) = 300

⇒ ln(x+1) = 300/270 = 10/9

Applying base 'e' on both sides, we get

⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]

⇒ x+1 = 3.0377

⇒ x = 3.0377 - 1 = 2.0377

When rounding the final answer to the nearest tenths, we get x = 2 acres.

When rounding the final answer to the nearest thousand, we get x = 2.038 acres.

Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.

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The reflection rule for the given graph is Option A.

What is reflection?

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.

Given the graph of triangle ABC under reflection, we analyse each answer choice one by one

For Option A) Reflection across the origin, the y-coordinate is negated, as well as the x-coordinate (their signs are changed). The image of the point (x,y) is the point in a point reflected in the origin (-x,-y).

So, A(-3,-1) becomes A'(3,1) which is correct for the given coordinates of the reflected graph of the figure.

Hence, Option A is the correct choice and the remaining choices are eliminated.

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Distance between points is 7 units.

What are co-ordinate system?

In pure mathematics, a co-ordinate system could be a system that uses one or a lot of numbers, or coordinates, to unambiguously confirm the position of the points or alternative geometric components on a manifold like Euclidean space.

Main body;

points given = (4,2) and(-3,2).

Distance formula = √(x₁-x₂)² +(y₁ -y₂)²

so,

distance between points = √(4-(-3))² + (2-2)²

                                          =√ 7² +0²

distance between points = 7 units

Hence ,distance between points is 7 units.

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Rotating the area bounded by the given curves around the designated line yields the solid's volume as [tex]V = \frac{9}{22}\pi[/tex]

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Different forms have various volumes.

The amount

of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. The capacity of an object to hold matter is generally thought of as its volume in three dimensions.
The functions provided are,

[tex]`y = f(x) = \sqrt{x}``y = g(x) = x^5`[/tex]

By rotating the area around the x-axis, the solid's volume is given by (using washer method)
[tex]V = \pi int_a^b [f^2(x)-g^2(x)]dx[/tex]
evaluate the integral, limit the plugins, and
[tex]V = \pi int_0^1 [(\sqrt{x})^2-(x^5)^2]dx\\\\V= \pi int_0^1 [x-x^10]dx V = \pi [\frac{x^2}{2}-\frac{x^11}{11}]_0^1 V = \pi [\frac{1^2}{2}-\frac{1^11}{11}]. V = \pi [\frac{1}{2}-\frac{1}{11}] = \frac{9}{22}\pi[/tex]

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Answer:

x + 0.11x = 19.98

Step 2 of 2 : Solve the equation for the unknown quantity.

x = 18.18

Answer:5

Step-by-step explanation:

5 2 . 3 8

5= tens

2= ones

3= tenths

8= hundreths

Answer:

$74.96 if rounding to hundredths place.

Step-by-step explanation:

If you are looking for the total amount spent, first we will convert 2 3/4 into a decimal, which is 2.75. 2.75 X 19.50 = 53.625. She bought 53.525 dollars worth of blue paint, now we solve for orange. 1 1/3 X 16 = 64/3, which is simplified to 21 1/3. If we add the two togetherwe get 74.9583, but the 3 is repeated. If you are asked to rount to the 100th place, the asnwer is $74.96. If you are rounding to nearest dollar, it is about $75.

Hope this helped :)

The answer to the given problem can be stated as, "$ 500 interest will be earned in approximately 0.14 years."

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

The formula to calculate the amount is as follows,

A = P(1 + r)^(nt)

The, the interest is given as  P[(1 + r)^(nt) - 1]

Substitute all the corresponding values in the above expression to obtain,

500 = 1700[(1 + 2/100)^(nt) - 1]

=> 500 + 1700 =  1700(1 + 2/100)^(nt)

=> (1 + 2/100)^(nt)  = 2200/1700

=> 1.02^(nt) = 22/17

Since, there are 4 quarters in one year, n = 4.

1.02^(4t) = 1.294

=> 4t = log(1.294) ÷ log(1.02)

=> 4t = 0.562

=> t = 0.14

Hence, it will take 0.14 years to earn the interest of $500.

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Answer: 8^4

Step-by-step explanation: A 'base' is a number with an exponent.

Takeuru made 18 souffles with the 72 eggs he purchased.

A ratio in mathematics demonstrates how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of oranges to the total amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8 (or 3:4). (or 4:7).

The quantities in a ratio can be of any kind, such as counts of people or things, measures of lengths, weights, or times, etc. Both numbers must be positive in the majority of situations.

Let e = the quantity of eggs Takeuru purchased.

Takeuru purchased s souffles total.

Then, as Takeuru purchased 4 times as many eggs as he used to make soufflés, e=4s.

Since Takeuru uses 3 eggs for each souffle he bakes and has 18 eggs remaining after backing, the equation is: e-3s=18.

This states that after Takeuru utilized three eggs for each souffle, there are still 18 eggs available.

There are now two equations:

e=4s

e-3s=18

When we solve for s using equation (2) and the value of e from equation (1), we get the following results: s=18

e=4s

e=4×18

e=72

Therefore, Takeuru purchased 72 eggs.

There were 18 soufflés that Takeuru purchased.

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The correct reason for Step 2 is the Vertical Angle Theorem

There are four angles created when two straight lines cross or intersect at a point, in which two sets of angles are not contiguous. These pair of non-adjacent angles are known as Vertical angles or Vertically opposite angles.

According to The theorem of vertical angles, two opposing vertical angles that are created when two straight lines intersect at a point, are always equal to one another.    

Here we have

3 three straight lines named SZ, TV, WY  

Where Line SZ and TV intersected at U,

Thus the formed pairs of Vertical angles are ∠SUV, ∠TUX;  ∠SUT, ∠VUX

As we know according to Vertical Angles Theorem the vertical angles are equal

=> ∠SUV = ∠TUX    

Therefore,

The correct reason for Step 2 is the Vertical Angle Theorem

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(a) Ann's monthly payment: $133.33

(b) Ann's total amount to repay the loan:$8000

(c) The total amount of interest Ann will pay:-$12000

What is amortized loan?

A loan that has planned, monthly payments that are applied to both the principle and interest accrued is known as an amortized loan.

To solve this problem, we need to use the following formula for an amortized loan:

[tex]Monthly\ payment = (Interest rate / 12) * Loan\ amount / (1 - (1 + (Interest \ rate / 12))^(-Term * 12))[/tex]

(a) Find Ann's monthly payment:

Substituting the given values into the formula, we get:

[tex]Monthly\ payment = (0.08 / 12) * 20000 / (1 - (1 + (0.08 / 12))^(-5 * 12))\\\\Monthly\ payment = 133.33[/tex]

Therefore, Ann's monthly payment is $133.33.

(b) Find Ann's total amount to repay the loan:

The total amount to repay the loan is equal to the sum of the monthly payments over the term of the loan. Since Ann's monthly payment is $133.33 and the term of the loan is 5 years, the total amount to repay the loan is equal to $133.33 * 5 * 12 = $8000.

(c) Find the total amount of interest Ann will pay:

The total amount of interest Ann will pay is equal to the total amount to repay the loan minus the loan amount. Since Ann's total amount to repay the loan is $8000 and the loan amount is $20000, the total amount of interest Ann will pay is equal to $8000 - $20000 = -$12000.

Note that the total amount of interest Ann will pay is a negative number because the loan amount is greater than the total amount to repay the loan. This means that Ann will end up paying less than the loan amount due to the amortization of the loan.

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The probability that there will be no drowning this year is 0%

and  the probability that there will be at least 6 accidents this year is 0.003%

What is the probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

We have,

3 per year for every 100000 of tourists

if in a year 200000 tourists visited this resort,

Probability formula:

P(A) = f / N

P(A) = Probability of an event (event A) occurring.

f = Number of ways an event can occur (frequency)

N = Total number of outcomes possible.

so f = 3,

N = 100000

P(A) = f / N = 3/100000 = 0.00003 = 0.003%

so, the probability of the previous year is 0.003%.

0.003% = f / 200000

f = 200000 * 0.003% = 6

a) The probability that there will be no drowning this year:

P(A) = 0 / 200000 = 0

b) The probability that there will be at least 6 accidents this year:

P(A)  = 6 / 200000

P(A) = 0.003%

Hence, the probability that there will be no drowning this year is 0%

and  the probability that there will be at least 6 accidents this year is 0.003%

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The population of the state 2,000 is 18.5 Million. And the time at which the population of the state reaches 26.6 million will be 2.126 years.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The equation is given below.

[tex]\rm A = 18.5 \times e^{0.1708\times t}[/tex]

The population of the state in 2,000 is calculated as,

[tex]\rm A = 18.5 \times e^{0.1708\times 0}[/tex]

A = 18.5 × e⁰

A = 18.5 Million

The time at which the population of the state reaches 26.6 million will be given as,

[tex]\rm 26.6 = 18.5 \times e^{0.1708\times t}\\\\1.4378 = e^{0.1708\times t}[/tex]

Take natural log on both sides, then we have

0.1708 × t = ln 1.4378

t = 2.126 years

The population of the state 2,000 is 18.5 Million. And the time at which the population of the state reaches 26.6 million will be 2.126 years.

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Answer: 4 2/3

Step-by-step explanation:

The required intersection of the two sets A and B is given as A∩B = [8, 5, 0].

Given that,
Let A={9,8,3,0,5} and B={8,4,7,5,0}. The intersection of A and B is to be determined.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.

here,
P[PUB] = {9,8,3,4,0,5,7} = 7
P[A∩B] = P[A] + p[B] - P[AUB]
P[A∩B] = 5 + 5 - 10
            = 3
From accumulating the common elements between the sets,
A∩B = [8, 5, 0]

Thus, the required intersection of the two sets A and B is given as A∩B = [8, 5, 0].

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The value of za is 80.47.

Value is the regard that something is held to deserve,the important, worth or usefullness of something.

let us  find the value of zero Alpha, Given that alpha is  .32. So the value of Z the it is  0.32. Well, we need to begin to  considering that we need to the  find actually the differentiate one minus alpha. Thus it is  going to be in this case one of the  (-) 10.32. This is going to be the  0.68. So actually Z of .32, we're going to need to find 0.68 inside the Z table. So let's look at it at it. Look at that at 0.68 oh eight.Let  give  us the Z score of 80.47. So we can tell that the Z score of zero of alpha, given that the  Alpha is 00.32 is going to be 0.47.

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Answer:

see the explanation

Step-by-step explanation:

Let

x ----> the price of the shirt

y ---> he price of the pants

we have that

The price of three shirts plus the price of two paints must be equal to $300

so

This is the equation of the line in standard form

Convert to slope intercept form

Isolate the variable y

subtract 3x both sides

Divide by 2 both sides

----> equation of the line in slope intercept form

Find out the x-intercept

Remember that the x-intercept is the value of x when the value of y is equal to zero

In this problem, the x-intercept is the price of the shirt when the price of the paints is equal to zero

Using the Standard Form, identify the x-intercept of the graph

The standard form is

The x-intercept is C/A

we have

so

The x-intercept is the point (100,0)

That means---> The price of the shirt is $100 when the price of the paints is equal to $0

Alternative method to find out the x-intercept (equation in slope intercept form)

For y=0

solve for x

The x-intercept is the point (100,0)

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