prove Triangle ACE is an isosceles triangle by completing this proof.
Hint: there are 3 parts to this proof!

Answer:

(2,4)

Step-by-step explanation:

Answer:

t ≈ 11.7

Step-by-step explanation:

                  r

A = P (1 + -------)^(n)(t)

                  n

A = 5000

P = 2500

r = 0.06

n = 2

t = ?

                              0.06

5000 = 2500 (1 + ----------)^(2)(t)

                                  2

                              0.06

5000 = 2500 (1 + ----------)^(2)(t)

÷2500 ÷2500           2

             0.06

2 = (1 + ----------)^(2)(t)

                2

            log 2

------------------------ =  2t

             0.06

log (1 + ----------)

                2

            log 2

(1/2) ------------------ = 2t (1/2)

                    0.06

      log (1 + ----------)

                      2

11.72488612 = t

11.7 ≈ t

I hope this helps!

By using demovire's theorem to determine the complex numbers to simplify (1+i)^12 we get   [tex]z^{12}=-2^6=-64[/tex]

first, we have to find the argument. As the complex number, z=1+i will be in the 4th quadrant

we proceed according to conditions in demovire's theorem

[tex]r=\sqrt{(1)^2+(1)^2}\\ \\r=\sqrt{2}[/tex]

so from this our angle becomes

[tex]\alpha =2\pi -tan^{-1}=- \frac{\pi }{4}[/tex]

so putting r and alpha in the formula of demovier's of complex numbers

[tex]z^{n}=r^{n}(cos\alpha +isin\alpha )\\\\z^{12}=(\sqrt{2} )^{\112} }(cos\((\frac{-\pi }{4}) +isin(\frac{-\pi }{4}) )\\\\z^{12}=2^6(-1-0)\\\\z^{12}=-2^6=-64[/tex]

we get z to the power 12 equals to negative times sixty-four.

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As per the empirical rule, the percent of data in the shaded region is 68%.

In statistics, the empirical rule states that When you use a standard normal distribution also known as Gaussian Distribution we have to consider the following

=> Around  68% of values fall within one standard deviation of the mean.

=> Around 95% of the values fall within two standard deviations from the mean.

=> Other all of the values are about 99.7% that fall within three standard deviations from the mean.

Therefore, this facts are the 68 95 99.7 rule. And it is also called the Empirical Rule because the rule originally came from observations.

Here we have given the the data is normally distributed. And we need to find the percent of data is in the shaded region.

While we looking into the following diagram and according to empirical rule,68% of the data falls within one standard deviation of the mean.

Because, the center part is the shaded region,

So, it can be calculated as,

=> 34 + 34 = 68%

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The scenario exemplifies a(n) that effect is practice effect

In experiments utilising within-subjects designs, the practise effect is especially problematic since participants' performance on the study variable may increase just by engaging in the activity again, independent of any study manipulations the researcher may have imposed.

When a test is retaken, the practise effects have an impact on the results. A practise effect, for instance, can result from taking numerous practise SAT exams; practise can raise your overall score.

Counter balancing is one strategy for limiting the effects of practise. It is possible that the trials will use randomization or will use every feasible order for administering treatments to subjects.

According to the question,

Jacob observes that the participants gain more efficiency in transferring the data with each new spreadsheet. this scenario exemplifies a(n) that this is Practice effect

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Step-by-step explanation:

the surface area is the combination of

the base (square) area

the 4 side (triangle) areas.

the base area is : 10×10 = 100 in²

the area of a triangle is

baseline × height / 2

we know the baseline of each of the 4 triangles (10 in) and we know the height (14 in).

one triangle area is

10×14/2 = 70 in²

we have 4 of these triangles (each side of the pyramid) :

4×70 = 280 in²

the total surface area of the pyramid is

100 + 280 = 380 in²

Answer:

x = -3

Step-by-step explanation:

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3/4(x-13)=-2(9+x)

0.75x - 9.75 = -18 - 2x

2.75x = -8.25

x = -3

:]

The length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.

A quadrilateral with at least one set of parallel sides is called a trapezoid in American and Canadian English.

In British and other varieties of English, it is termed a trapezium.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.

The parallel sides are called the basis of the trapezoid.

So, we have:
The height should be 3 yards higher than the shorter base.

b₁=h+3

The height should be 3 yards higher than the shorter base.

b₂=h+7

Formula for Area of trapezoid = 1/2(b₁+b₂)h

Now, using the formula, calculate as follows:

150=1/2(h+3+h+7)h

150=(2h+10)h/2

150=2h²+10h/2

150=2h²+5h

h²+5h-150=0

h²+15h-10h-150=0

h(h+15)-10(h+15)=0

(h-10)(h+15)=0

h=10 or h-15

h should be positive:

b₁=h+3=15+3=18

b₂=h+7=15+7=22

Therefore, the length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.

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Complete question:
A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be

The value of the numerical expression 2 - [(2 + 10 × -1) / 2 + 1] will be 5.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The numerical expression is given below.

⇒ 2 - [(2 + 10 × -1) / 2 + 1]

Simplify the expression, then we have

⇒ 2 - [(2 + 10 × -1) / 2 + 1]

⇒ 2 - [(2 - 10) / 2 + 1]

⇒ 2 - [(-8 / 2) + 1]

⇒ 2 - (-4 + 1)

⇒ 2 - (-3)

⇒ 2 + 3

⇒ 5

The value of the numerical expression 2 - [(2 + 10 × -1) / 2 + 1] will be 5.

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You determine the limit by [tex]\lim_{n \to \infty} a_n = -1[/tex].

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. The concept of limit, which is founded on the idea of closeness, is largely used to give values to some functions at points when none are defined in a way that is consistent with values close by.

Divide the denominator and numerator by 3n as shown.

[tex]\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{2^n+3^n}{2^n-3^n\\}[/tex]

[tex]= \lim_{n \to \infty} \frac{(\frac{2}{3})^n+1 }{(\frac{2}{3})^n-1 } \\=\frac{0+1}{0-1} \\=-1[/tex]

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0.0076 is  the probability that the first 30 igniters tested do not fail .

What is probability in math?

The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.

a)if the failure rate for the super igniters is 15% then the probability that each igniter fails is 0.15,and the probability that it does not fail is 0.85.Therefore the probability that the first 30 igniters tested do not fail is       (0.85)30= 0.0076.

b)given that there are no failures in the first 30 tries,the probabilities occurs on 31st try is 0.15 and the probability that it does not occur on 31st but occurs on 32nd try is (0.85)(0.15)=0.1275.therefore the probability of one or the other is 0.15+0.1275=0.2775.

c)the result of the probability calculation in part(a) provides reason to believ the failure rate of the super igniters is less than 15%.The calculated proability of 0.0076 shows that there is less than a 1% chance that 30 or more igniters in a row would not fail if the failured rate was 15%.This probability is smaller than conventional significance levels such as alpha=0.05 and 0.01 and thus is small enough to make it reasonable to believe that the failure rate of the super igniters is less than 15%.

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100k in celsius is -173.15 degrees.

The Celsius scale, commonly known as centigrade, uses a base of 0° for water's freezing point and 100° for water's boiling point. Because of the 100-degree gap between the designated points, the Celsius scale, which was developed in 1742 by the Swedish astronomer Anders Celsius, is occasionally referred to as the centigrade scale.

The Celsius scale is in general use wherever the metric system of units has been adopted, and it is used in scientific work everywhere.

To convert Celsius to kelvin, the formula is:

T(K)=°C+273.15

∴100=°C+273.15

°C=100-273.15 = - 173.15

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Yes, the permutation test is used in this problem to conduct a hypothesis testing about comparing  the 95th percentile of the income of country a and that of country b.

Yes, the permutation test can be used in this problem. The permutation test is a nonparametric test that can be used to compare two or more groups to determine if there is a statistically significant difference between them. In this case, we can use the permutation test to compare the 95th percentile of the incomes of the two countries. The permutation test would involve randomly permuting the data for each country, then calculating the 95th percentile for each permutation. The difference in the 95th percentile between the two countries in the original data can then be compared to the differences in the 95th percentile of the permuted data to see if the difference is statistically significant.

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According to the given speed, the minimum rate of climb must be maintained to meet the required climb rate to 4,800 feet as specified on the instrument departure procedures is option (d) 870 feet per minute.

Speed:

In math speed refers the rate of change of position of an object in any direction.

Given,

Here we have using an average ground speed of 120 knots and taking off on runway 14.

Now, we need to find in what minimum rate of climb must be maintained to meet the required climb rate (in feet per nm) to 4,800 feet as specified on the instrument departure procedures.

While we looking into the given question, we have identified that,

Speed = 120

Distance = 4800

Then the  minimum rate of climb must be maintained to meet the required climb rate  is calculated as,

Here we also note in the bottom left corner of the overhead view of the departure requires 435 ft/nm climb gradient to 4800' for obstacle clearance.

Therefore, the minimum rate is 870 feet per minute.

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The water level rise when it is 6 feet deep is 0.318 feet/min when a conical tank is filled with water at a pace of 9 feet per minute.

Given that,

A conical tank is filled with water at a pace of 9 feet per minute. The tank is 10 feet tall and has a base radius of 5 feet. It stands pointed down.

We have to find how quickly does the water level rise when it is 6 feet deep.

We know that,

dv/dt= 9 feet³/min

x=5 feet

y=10 feet

And we have x/y=1/2 ----->equation(1)

We know the formula

V=1/3πx²y

Differentiating on both sides

dv/dt=9

1/3πy(2x) dx/dt+π/3(x²)dy/dt

=π/3[2xy dx/dt+x² dy/dt]

From equation(1)

x/y=1/2       or     y=2x

dy/dt= 2dx/dt

Now,

9=π/3[xy dy/dt+x² dy/dt]

9= π/3 dy/dt[xy+x²]

dy/dt=9×3/π×(18+9)

dy/dt=27/π×27

dy/dt= 1/π

dy/dt=0.318 feet/min

Therefore, The water level rise when it is 6 feet deep is 0.318 feet/min when a conical tank is filled with water at a pace of 9 feet per minute.

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The number of teenagers in the game are 94.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, 4700 people attended a football game.

Here, 2% of the people who attended were teenagers

So, the number of teenagers are

2% of 4700

= 0.02×4700

= 94

Therefore, there are 94 teenagers attended the game.

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Answer:

x = 85°

Step-by-step explanation:

the angle adjacent to B inside the triangle is corresponding to 70° and are congruent.

the sum of the 3 angles in a triangle is 180° , then

x + 25° + 70° = 180°

x + 95° = 180° ( subtract 95° from both sides )

x = 85°

The value of x for the given expressions is 3.

Triangles are classified into three different types based on their sides. An isosceles triangle, a scalene triangle, and an equilateral triangle. Equilateral triangles are different from isosceles and scalene triangles.

An equilateral triangle is a triangle with all three equal sides and equal angles. An equilateral triangle is also called an equilateral triangle because each angle has a value of 60 degrees. Equilateral triangles are considered regular polygons or equilateral triangles because they have equal angles and equal sides.

In ∆ ABC

∠A= ∠B=∠C

Triangle is equilateral triangle.

All the triangle side will be equal

6x-3=3x+6=5x

=6x-3 =3x+6

=3x=g

X=3

Thus, X = 3

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Eigenvalues are a unique collection of scalar values connected to the set of linear equations that are most often found in the matrix equation.

Eigenvalues are the unique set of scalar values connected to the set of linear equations most likely found in the matrix equations. Also known as characteristic roots, the eigenvectors are. After applying linear transformations, the vector is non-zero and can only be altered by its scalar factor.

The term "eigenvalue equation" refers to an equation in which the operator multiplies the function by a constant when applied to a function. An eigenvalue is the resultant numerical value, and an eigenfunction is the function itself.

Given:

The given value is

[tex]$$A=\left[\begin{array}{lll}0 & 1 & 0 \\0 & 0 & 1 \\a & b & c\end{array}\right]$$[/tex]

where a, b, c are arbitrary constants.

If [tex]$\lambda$[/tex] is an eigen value of A Then,

[tex]$& E_\lambda={ker}(A-\lambda I) \\[/tex]

Now,

Last two rows are linearly independent.

So, we have

[tex]${dim} E_\lambda=1$[/tex]

Therefore,

[tex]${gemu}(\lambda)=1$$[/tex]

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√10.24 belongs to the set of rational numbers.

Here we are given the number √10.24.

Now first we see that √10.24

= 3.2

Now as we can see that there is a number other than 0 after the decimal point here. Hence the above number cannot be classified as a natural number, a whole number, or an integer.

However, on converting 3.2 into the fractional form, we see that

3.2 = 32/10

reducing this to smallest form we get

16/5

Here we could easily represent 3.2 in the form of p/q where q is not equal to 0.

Hence p/q is a rational number.

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The solution to the expression 9.1p + 8.9r is 116.9 when p = 6 and r = 7

From the question, the mathematical expression is given as

9.1p + 8.9r

The values of the variables are given as

p = 6 and r = 7

Substitute p = 6 and r = 7 in the given expression 9.1p + 8.9r

So, we have the following representation

9.1p + 8.9r = 9.1 * 6 + 8.9 * 7

Evaluate the products in the above equation

9.1p + 8.9r = 54.6 + 62.3

Evaluate the sum in the above equation

9.1p + 8.9r = 116.9

Hence, the value is 116.9

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The scale of a map is the relationship between the distance on the map and the actual distance. In this case, the scale of the map is 1:4000, which means that 1 unit on the map represents 4000 units in the actual distance. To find the actual distance that is represented by 6.4 cm on the map, we need to convert the distance on the map to the same unit as the actual distance. Since 1 cm is equal to 0.01 m, 6.4 cm is equal to 6.4 * 0.01 = 0.064 m.

Now we can use the scale of the map to convert the distance on the map to the actual distance. We can set up the following proportion:

0.064 m / 1 = x / 4000

Where x is the actual distance in metres. Solving for x, we get:

x = 0.064 m * 4000 = 256 m

Therefore, the actual distance represented by 6.4 cm on the map is 256 m.

On solving thr provided question, by help of arithmetic progression, we got to know that a10 = 207

There are two approaches to define arithmetic progressions (AP):

The difference between any two successive terms in an arithmetic sequence must always be equal, and it is sometimes referred to as a series in which all terms except the first are created by adding a predetermined number to the preceding term.

9,15,25..............

15-9 = 6

25-15 = 10

a4 - 25 = 14 => a4 = 39

a5-39 = 18 => a5 = 57

a6-57 = 22 => a6 79

...

...

...

...

...

a10 - 169 = 38 => a10 = 207

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For the given data analysis  , The correct function is : RIGHT(B3,5), which is the correct syntax.

Here it is related to data cleaning which is the process of removing or fixing data that are incorrect or formatted incorrectly, corrupted, duplicate, or even incomplete data within a dataset that exists. When we mix  multiple data sources, it depicts that  there can be opportunities for the data to be mislabeled or duplicated, since we are guiven  that the customer names and addresses, so the correct syntax will be  =RIGHT(B3,5), where the RIGHT  Function  that returns set  number of characters of  a text string from the  right side

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The probability that the second ball is greater than the first ball is 5/8

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

As to even odd

first ball can be anything. Second would have to be the first is not thus 5/9.

As second smaller than first

if first is 9, probability is 8/8, 100%, if 7 probability s 6/8 so in general take first ball, value k,

then the probability is sum (k - 1) / (n = 10 - 1) for k=1,2,…,9 so that’s all in 45/8 times 1/9 so 45/72 or 5/8.

Even a clear ball has Color so unless you have an invisible ball in your collection, both balls will be some amount of color or color.

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The graph shows a polynomial function with a positive leading coefficient B.

The function will reach its maximum value of + in the case of a positive leading coefficient and its minimum value of - in the case of a negative leading coefficient. This indicates that even degree polynomials with positive leading coefficients have a range of  [ymin, ∞), where ymin stands for the global minimum that the function reaches.

When a variable in an equation like the quadratic equation, cubic equation, etc. has only non-negative integer powers or only positive integer exponents, the function is said to be polynomial.

Leading coefficients are the values listed before the variable with the biggest exponent. They can be positive, negative, real, imaginary, whole, fractional, or decimal, much like conventional coefficients, and they can also be positive, negative, real, or imaginary.

Therefore, the correct answer is option B.

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The transformation that has changed the parent function f(x) = (0.5)^x to the exponential graph passing through points (1,2) and (2,1) is given as follows:

f(x - 2).

The parent function for this problem is given as follows:

f(x) = (0.5)^x.

Hence the points on the graph of the parent function are given as follows:

The points on the transformed function are given as follows:

(1,2) and (2,1).

Meaning that the value assumed at x = -1 is now assumed at x = 1, while the value assumed at x = 0 is not assumed at x = 2, meaning that the function was shifted right two units, and the transformation is defined as follows:

f(x - 2).

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Answer:Square

Step-by-step explanation:

A square is a quadrilateral with four right angles and four congruent sides. All squares are rectangles and rhombuses.

Answer:

D. square

Step-by-step explanation:

As an explanation, I have attached a picture of the 4 quadrilaterals and their internal angles and sides.

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