Which of the following is an example of A.S.A. criterion of congruency for two triangles ∠ACB and ∠DEF? a)AB = EF, ∠B = ∠E and ∠C = ∠F b)BC = EF, ∠B = ∠F and ∠C = ∠E c)AC = EF, ∠B = ∠D and ∠C = ∠F d)AC = DE, ∠B = ∠D and ∠C = ∠F

Distance that plane has flown is 2812.5 feet.

What do you mean by trignometry?

Trigonometry  “triangle” is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.

Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan. Let's see how these ratios or functions are evaluated in the case of right triangles.

It is given that a plane rises from take-off and flies at an angle of 9° with the horizontal runway. It has gained 450 feet

Let the distance be x

According to the question:

sin 9 = 450/x

0.16 = 450/x

x = 450/0.16

x = 2812.5

Therefore, distance that plane has flown is 2812.5 feet.

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The formula for the slope of parallel lines is m1 = m2, and the slopes of parallel lines are equal. The slope of parallel lines is identical because all of the parallel lines are similarly inclined with regard to the positive x-axis.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

Hence, The formula for the slope of parallel lines is m1 = m2, and the slopes of parallel lines are equal. The slope of parallel lines is identical because all of the parallel lines are similarly inclined with regard to the positive x-axis.

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Answer:

y - 2.5 = 2(x - 1)

Step-by-step explanation:

Here given slope is 2 and the point through which the straight line passes is (1, 2.5)

Let the equation be y = mx + c where m and c represent slope and y intercept respectively.

We know the slope, so we input that in our equation

y = 2x + c ------- i

This straight line also passes through (1, 2.5)

Putting the values in place of x and y we get,

2.5 = (2X1) + c

⇒ 2.5 = 2 + c

⇒ c = 2.5 - 2

⇒ c = 0.5

Now, putting value of c in i, we get

y = 2x + 0.5 -------- ii

It can also be written as y - 2.5 = 2(x - 1) ------- iii

this equation and ii are same and you can verify that by simplifying iii, by multiplying 2 and then shifting the -2.5 from LHS to RHS

Answer:

D: f(x) · g(x) =12x^2-25x+12

Step-by-step explanation:

we multiply the 2 equations

(3x-4)(4x-3)

12x^2-9x-16x+12

12x^2-25x+12

so d is the answer

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The given point estimators are unbiased and estimator b₁  is more efficient than b₂.

A statistic used to precisely estimate a population parameter is called an "unbiased estimator." An estimator's expected value must match the population parameter's value to be considered unbiased. The discrepancy between an estimator's expected value and the parameter value is known as bias. The estimator tends if this difference is not zero.

a) To show whether the given point estimators are unbiased, first, find whether the expected value of the given estimators is equal to the population parameter μ.

[tex]\begin{aligned}E(b_1) &= E(0.10X_1 + 0.20X_2 + 0.40X_3 + 0.30X_4)\\&=0.10E(X_1) + 0.20E(X_2) + 0.40E(X_3) +0.30E(X_4)\\&=0.10\mu+0.20\mu+0.40\mu+0.30\mu\\&=\mu\\E(b_2) &= E(0.25X_1 + 0.25X_2 + 0.30X_3 + 0.20X_4)\\&=0.25E(X_1) + 0.25E(X_2) + 0.30E(X_3) +0.20E(X_4)\\& = 0.25\mu + 0.25\mu + 0.30\mu + 0.20\mu\\&=\mu \end{aligned}[/tex]

Therefore, both estimators are found to be unbiased.

b) To show which estimator is more efficient, first, find the two-point estimators' variance.

[tex]\begin{aligned}V ar(b_1)&= Var(0.10X_1+0.20X_2+0.40X_3+0.30X_4)\\&= 0.10^2V ar(X_1)+0.20^2Var(X_2)+0.40^2Var(X_3)+0.30^2Var(X_4)\\&= 0.10^2\sigma^2+ 0.20^2\sigma^2+ 0.40^2\sigma^2 + 0.30^2\sigma^2\\&=0.3\sigma^2\\Var(b_2)&= Var(0.25X_1+0.25X_2+0.30X_3+0.20X_4)\\&= 0.25^2Var(X_1)+0.25^2Var(X_2)+0.30^2Var(X_3)+0.20^2Var(X_4)\\&= 0.25^2\sigma^2 + 0.25^2\sigma^2 + 0.30^2\sigma^2 + 0.20^2\sigma^2\\&= 0.255\sigma^2\end{aligned}[/tex]

From this, we can say that Var(b₁) > Var(b₂). Therefore, b₁ is more efficient.

The complete question is -

Let X₁, X₂, X₃, and X₄ be a random sample of observations from a population with mean μ and variance σ². Consider the following two-point estimators:

b₁ = 0.10X₁ + 0.20X₂ + 0.40X₃ + 0.30X₄, and

b₂ = 0.25X₁ + 0.25X₂ + 0.30X₃ + 0.20X₄

(a) Show that both estimators are unbiased.

(b) Which estimator is more efficient, b₁ or b₂? Explain in detail.

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The value of the stock yield will be;

⇒ 3.1%

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

McDonald’s Corp (MCD) stock is selling for $90.24 per share.

And, They offer a dividend of $2.80 per share.

Now,

Since, McDonald’s Corp (MCD) stock is selling for $90.24 per share.

And, They offer a dividend of $2.80 per share.

Hence, The value of the stock yield is;

⇒ 2.80/90.24  ×  100

⇒ 0.0310 × 100

⇒ 3.1%

Thus, The value of the stock yield will be;

⇒ 3.1%

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Answer:

domain: all real numbers

range: [ 3 , infinity]

The dimensions of the rectangular package with the condition of maximum volume is equal to  x = 19inches and y = 38inches.

As given in the question,

Let us consider length of the cross section which is square be x

Perimeter of the cross section is 4x

And y be the length of the rectangular package

Maximum combined ( length + perimeter of the cross section ) = 114

y + 4x = 114

⇒ y = 114 -4x

Volume of the package 'V' = x²y

⇒V = x²(114 -4x)

⇒V = 114x² -4x³

Differentiate both the side of the equation with respect to x,

dV/dx = 228x - 12x²

For maximum Volume

dV/dx =0

228x -12x² = 0

⇒12x( 19 -x ) =0

⇒12x = 0 or 19 - x =0

⇒x =0 or x =19

x =0 is not possible

⇒x =19inches

y = 114 - 4(19)

  = 38inches

Therefore, the dimensions of the rectangular package with the given condition of volume is equal to x = 19inches and y = 38inches.

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A hypothesis is a tested statement regarding the relationship between two or more variables or a proposed explanation for some observable occurrence.

An complete group is referred to as a population when making inferences about it.

Your chosen group for data collection is referred to as a sample. Always, a sample's size is smaller than the population as a whole.

Using a statistical test, researchers compare the evidence supporting the null and alternative hypotheses, which are two conflicting claims:

There is no population impact, or null hypothesis (H0).

There is a population effect, or alternative hypothesis (Ha or H1).

No effect, no difference, or no association are all examples of null hypotheses. They always have an equivalence when expressed in mathematical terms.

The complement of the null hypothesis is the alternative hypothesis. The extensive nature of null and alternative hypotheses ensures that they account for all potential outcomes.

The question is incomplete so, I've answered in general

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Answer:

8

Step-by-step explanation:

28/3.5=8

Linear, polynomial, and quadratic functions can be both increasing or decreasing functions. Exponential function is monotonically increasing function. The derivative of a function may be used to determine whether the function is increasing or decreasing. Exponential functions eventually exceed all other increasing functions.

Function, in mathematics, refers to an expression or rule that describes a relationship between two or more variables. A function is said to be an increasing function when the y-value increases as the x-value increases and vice versa. In order to determine whether the function is increasing or decreasing, the derivative of a function may be used on any intervals in its domain.  If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. From the given function options, Exponential functions eventually exceed all other increasing functions as the one of variable is in the exponential leading an exponential increase and not a constant increase.

Note: The question is incomplete. The complete question probably is: From the following, Which functions are increasing? How to know if a function is increasing or decreasing?; Which section of the function is increasing?; Which type of increasing function eventually exceeds all other increasing functions? A) linear B) exponential C) polynomial D) quadratic.

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Answer: ABC and AED are congruent by SSS. SSS is if three sides of a triangle are congruent to 3 sides of another triangle, then the triangles are congruent. AB and AE are both 7, BC is congruent to ED and CA is congruent to DA because of the tick marks.

The investment options in order from the least risk to the greatest is:

From the options, the least risky investment option would be a b - rated bond as this bond is relatively safe. Following this is property as property is relatively safe because it has tangible value.

Starting a business is quite risky as many new businesses fail. However, investing in speculative stock is the riskiest as the value can fall without warning.

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Hence, the vectors of the length  [tex]2[/tex] making an angle of [tex]60[/tex] degree with the x-axis is [tex]P= < -\sqrt2,-1 >[/tex].

What are vectors?

A vector is a Latin word that means carrier. Vectors carry a point [tex]A[/tex] to point [tex]B[/tex]. The length of the line between the two points [tex]A[/tex] and [tex]B[/tex] is called the magnitude of the vector and the direction of the displacement of point [tex]A[/tex] to point [tex]B[/tex] is called the direction of the vector [tex]AB[/tex].

Here given that,

The vector of length [tex]2[/tex] making an angle of [tex]60[/tex] degree with the x-axis.

Given length is [tex]||P||=2[/tex]

[tex]P=||P|| < cos\theta,sin\theta > \\\\P=2 < cos(210),sin(210) > \\\\P=2 < \frac{-\sqrt3}{2},\frac{-1}{2} > \\\\P= < 2(-\frac{\sqrt3}{2}),2(-\frac{1}{2}) > \\\\P= < -\sqrt2,-1 >[/tex]

Hence, the vectors of the length  [tex]2[/tex] making an angle of [tex]60[/tex] degree with the x-axis is [tex]P= < -\sqrt2,-1 >[/tex].

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Answer:

it is a 10% increase.

Step-by-step explanation:

3,036 - 2,760 = 276

276/2,760 · 100 = 10%

(a) The required sample size is 1.96.

(b) Sample size = n = 89

(c) Sample size = n = 62

What is standard deviation?

The standard deviation in statistics is a measurement of how much a set of values can vary or be dispersed. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.

(a) Population standard deviation = σ = 3

Margin of error = E = 0.253

At 95% confidence level the z is,

α = 1 - 95%

α = 1 - 0.95 = 0.05

α/2 = 0.025

Zα/2 = 1.96

sample size = n = [Zα/2* σ / E]^2

n = [1.96 * 3 / 0.253]2

n = 540.14

Sample size = n = 541

b) Population standard deviation = σ = 24

Margin of error = E = 5

sample size = n = [Zα/2* σ/ E] 2

n = [1.96 * 24 / 5]2

n = 88.51

Sample size = n = 89

c) Population standard deviation = σ = 8

Margin of error = E = 2

sample size = n = [Zα/2* σ / E] 2

n = [1.96 * 8 / 2]2

n = 61.46

Sample size = n = 62

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Cumulative markup percent for department at the end  is 23.1%.

The men's furnishing department had an opening inventory of $168,000 at cost  with a markup of 48.5%

Cumulative markup is  the difference between the total wholesale cost and total retail price of all merchandise handled during a given period of time.

cumulative markup dollars are the total markup dollars on all merchandise for a selected selling period. To calculate cumulative markup dollars and cumulative markup percent, the following formulas are utilized by the retailer:

Cumulative Markup $ = Total Retail $ - Total Cost $

Cumulative Markup % = Cumulative Markup $ ÷ Cumulative Retail $

Steps for calculating cumulative markup percentage for the specified period of time:

Step 1. Calculate the unknown retail value for either opening inventory or purchases.

Step 2. Calculate total retail of opening inventory and purchases.

Step 3. Calculate the unknown cost value for either opening inventory or purchases.

Step 4. Calculate total cost of opening inventory and purchases.

Step 5. Calculate total markup dollars.

Step 6. Calculate cumulative markup percent for the specified period of time.

For opening inventory

retail = $168,000

cost = 168,000*48.5/100 = $81480

For purchases

retail = 80,000*52.5/100 = $42000

cost  = $80,000

total retail of opening inventory and purchase =

168,000+42000 = $210000

total cost of opening inventory and purchase =

81480+80,000 = $161480

total markup = total retail - total cost

total markup  = 210000-161480 = 48520

cumulative markup percent = (total markup/ total retail)

= (48520/210000)*100

= 0.23104761904*100

=23.1%

So cumulative markup percent for department at the end  is 23.1%.

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Answer: $144

Step-by-step explanation: To find the price she gets paid for 1 hr we need to divide the money by the hours. So, 90 / 5 = 18.

So, now we know she gets paid 18 dollars an hour. So, we need to find out how much she earns in 8 hrs. So, we would simply multiply the 18 by the 8, to get $144.

The following are parallelograms' essential characteristics: The opposing sides are parallel. The opposing parties are in agreement (they have the same length).

The four most crucial characteristics of a parallelogram are: A parallelogram has two opposed sides that are parallel to one another and have equal measurements. A parallelogram has equal opposite angles. The interior angles of a parallelogram sum to 360°. A parallelogram's subsequent angles should be supplementary (180°).

A quadrilateral having opposite sides that are equal and parallel is called a parallelogram. A parallelogram's opposing angle is also equal. A parallelogram is essentially a twisted rectangle.

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Coverage Error results from the exclusion of certain groups of subjects from a population frame. The answer for the given statement is Coverage Error.

Coverage errors come from failure to cover sufficiently all components of the population being studied. Incomplete sampling frames usually result in coverage errors. Coverage errors happen because of the divergences between the target population and the frame.

Coverage error also may happen when not all members of the population of interest have an equal chance of being selected for the survey. For example, if we use e-mail lists or phone lists to build the sample and not all potential respondents are on those e-mail or phone lists.

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From the given information, Therefore, the function [tex]= > y = 4(\frac{5}{6} )^x[/tex] is an exponential decay.

The process of decreasing a sum at a constant percentage rate over time is referred to in mathematics as exponential decay. It may be written as the formula y=a(1-b)x, where y represents the final amount and a, b, and x, respectively, represent the initial amount and the decay factor.

The formula for an exponential function is where b is a positive integer that is not equal to 1.

Whether a function is an exponential growth or a decay depends on the value of b. If b > 1 or if b<  1, an exponential function exhibits exponential growth and exponential decline, respectively.

given,

[tex]= > y = 4(\frac{5}{6} )^x[/tex]

[tex]= > b = \frac{5}{6} < 1[/tex]

Therefore, the function [tex]= > y = 4(\frac{5}{6} )^x[/tex] is an exponential decay.

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(B) All mathematic teachers who attended the conference.

Option B is the correct option.

The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are the focus of the science of statistics.

A statistic is a numerical representation of a sample property. One example of a statistic is the average number of points students in one math class got at the conclusion of the term if we assume that class to be representative of the population of all math classrooms.

Due to their role in assisting decision-making, statistics are crucial. To track progress, evaluate performance, identify issues, and set priorities, governments, organizations, and corporations all gather statistics.

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When you are doing a survey of the time it takes for a person to run 100m, the unit that you would you use is seconds.

A unit of measurement is a definite magnitude of a quantity that is defined and adopted by convention or law and is used as a standard for measuring the same type of quantity. Any other such quantity can be expressed as a multiple of the unit of measurement. A length, for example, is a physical quantity.

A unit is any standard that is used to compare measurements. Unit conversions allow measurements of a property to be converted from one unit to another, such as centimeters to inches.

In this case, time is measured in seconds.

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The answer will be [tex]a^{-20-12a}[/tex] that can be find out using exponential function.

What are exponential function ?

Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.

Like, f(x) = [tex]x^{a}[/tex]

x is base and a is power.

Basic rules to solve this function :

1. If we take the product of two exponentials with the same base, we simply add the exponents:

x^ a * x^ b = x^ a + b.

2. If we take the quotient of two exponentials with the same base, we simply subtract the exponents:

x^ a / x^ b =  x^ a-b

3. We can raise exponential to another power, or take a power of a power. The result is a single exponential where the power is the product of the original exponents:

x^ (a)^ b = x^ (ab).

In given equation, [tex]{a^{2^{-2^5}}/{a^{4a^3}}[/tex]

So the answer is a^(-20-12a).

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The sinusoidal function is y = -4.5cos(8(x + π/2)) + 1/2

From the question, we have the following parameters that can be used in our computation:

Maximum = (-π/2, 5)

Minimum = (π/4, -4)

A cosine function is represented as

y = A cos(B(x+C)) + D

Where

The cosine function has a max and min of 1 and -1.

So, we have

Difference = |-4 - 5|

Difference = 9

This means that

Amplitude, A = 9/2

A = 4.5

Also, we have

Vertically shift = (5 - 4)/2

Vertically shift = 1/2 up

So, the function becomes

y = 4.5cos(θ) + 1/2

Next, we calculate the value of θ

The period is calculated as

Period = π/4 + π/2

Period = -π/4

This means that

2π/B = -π/4

So, we have

B = -8

This gives

y = 4.5cos(-8(x + c)) + 1/2

cos(0) = 1,

So we want -8(-π/2) - 8C = 0

Solving for c, we have

8C = 8(π/2)

Divide

C = π/2

Substitute C = π/2 in y = 4.5cos(-8(x + c)) + 1/2

y = 4.5cos(-8(x + π/2)) + 1/2

y = -4.5cos(8(x + π/2)) + 1/2

Hence, the function is y = -4.5cos(8(x + π/2)) + 1/2

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Complete question

The function has a maximum point at (-pi/2, 5) and a minimum point at (pi/4, -4)

Determine a cosine equation for this function.

The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.

Given that,

Cut into two halves is a 224-inch pipe. The length of one component is three times that of the other.

We have to determine the shorter piece's length.

We know that,

Let's use the variable L to represent the longer pipe and the variable S to represent the shorter pipe.

Since the pipe will be the sum of L and S, we can create the following equation:

L+S=224

The longer piece is three times the shorter piece, which is another thing we know.

L=3S

Substituting the second equation for the first equation

L+S=224

3S+S=224

4S=224

S=224/4

S=56

The shorter piece is 56 inches.

The lengthier component should be used to replace the following:

L=3S

L=3(56)

L=168

The longer piece is 180 inches.

Therefore, The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.

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"Parameter" is the descriptive measure of the population. The description, that if the data refuses the assumption of a parameter is the main goal of the tests of hypothesis.

There are many population parameters. Some examples of the population parameters include:

In general, it is not possible to measure the parameters of a population, as it requires to collect information from each and every member of the population. That is why, 'sample statistics' is conducted.

What is a sample statistics?

In sample statistics, samples are collected from each and every aspect of the population and then the samples are tested in order to derive a conclusion. For example: the mean diastolic blood pressure of more than one sample, the mean body weight of more than one population, etc.

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Answer: 45

Step-by-step explanation:

The weight of clothing is the ratio of weight to dye is different from the other ratios is B. 42 pounds.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

It should be noted that from the information given, others have a ratio of 1:7. This is different for 42 pounds since the ratio is:

= 42/9

= 14:3

In conclusion, the correct option is B.

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