(a) show that f is one-to-one. (b) use theorem 7 to find s (f ^-1) d9sad. (c) calculate f 21 sxd and state the domain and range of f 21 . (d) calculate s f 21 d9sad from the formula in part (c) and check that it agrees with the result of part (b). (e) sketch the graphs of f and f 21 on the same axes.

The criterion that she should use to prove that triangles RST and XYZ are congruent are:

i. Hypotenuse Leg (HL)

ii. Side-Angle-Side (SAS)

When the corresponding properties i.e. length of sides and measure of internal angles of two or more triangles are equal, then the triangles are said to be congruent. The relations can be shown using some theorems.

From the given triangles RST and XYX, it can be observed that;

TR ≅ XZ

RS ≅ XY

<R ≅ <X   (given)

<T ≅ <Z   (given)

Angles R and X are included angle of the triangles. Thus, the criterion that can be used to show that triangles RST and XYZ are congruent at;

i. Hypotenuse Leg (HL)

ii. Side-Angle-Side (SAS)

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Answer:

One bar each

Step-by-step explanation:

8 people/8granola bars =1 bar each

Random sampling is the sampling method that was used.

Random sampling is a method in which all members of the population have an equal chance of being selected for the sample. In this case, fifteen instructors were chosen using random numbers to implement the new learning strategy.Random sampling is a useful tool when a researcher needs to select a representative sample from a population. By using random numbers to choose the sample, the researcher can ensure that the sample is truly representative of the population. Random sampling also helps to reduce bias, as the researcher has no control over who is chosen for the sample.

To calculate the probability of being chosen for the sample, the formula is (1/n) x 100, where n is the total number of population members. In this case, the population was the group of all instructors, and the sample was the group of fifteen instructors chosen. Therefore, the probability of being chosen is (1/n) x 100 = (1/15) x 100 = 6.67%.

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Answer:

1015

Step-by-step explanation:

29 es un número primo.

Por tanto:

29*35 = 1015

El mínimo común múltiplo de 29 y 35 es:

1015

The value of x which makes the equation true is 15.

What is the system of equations?

A system of equations is a set of two or more equations that contain multiple variables. These equations are typically used to describe a real-world situation and are solved simultaneously to find the values of the variables.

To solve a system of equations for unknown variables, you can use one of several methods, such as substitution, elimination, or graphing.

To solve a system of equations such as x-4=11, you have to find the value of x which will make the equation true.

x-4=11

x=15

Hence, the value of x which makes the equation true is 15.

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Using the greatest common factor the expression is factored to be

The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers.

The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF.

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

The greatest common factor of 48 and 72 is 12

hence we have

12 (4 + 6)

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Answer:

c

Step-by-step explanation:

it is 4×+5 which is easy as u tines it by fixing the sum into parts and its eisier

The  difference in the account balances at the end of the loan terms is, $1770.87. So option B is correct

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

Given that,

Offer 1-  5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer

Offer 2-  3.75% annual interest compounded monthly for a 66-month term

In offer 1,

Total amount A  = $32487.50

In offer 2,

Total amount =

[tex]A = P[ 1 + r/n]^{nt}[/tex]

[tex]A = 25000[ 1 + 0.0375/12]^{12*5.5}[/tex]

A = $30,716.63

Difference = 32487.50 - 30716.63

                  = $1770.87

Hence, the difference in account balance is $1770.87

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The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36

What is Probability ?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes

Given ,

A bowl at a delicatessen contains a mix of 15 apples, 12 oranges, and 9 pears

so , we have to find  the probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear.

Choosing orange or a pear ,

= 12c1 + 9c1

= 12+9

= 21

Total = 36.

Probability = 12 + 9 / 36

= 21 / 36 .

Therefore , The probability of a customer who gets one piece of fruit from the bowl randomly choosing an orange or a pear is 21/36

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A cosine and sine function can be expressed in terms of an imaginary exponential using Euler's formula: e^(iθ) = cos(θ) + i*sin(θ).

This formula can be derived by using the Taylor series for e^x, and replacing x with iθ.

A cosine and sine function can be expressed in terms of an imaginary exponential using Euler's formula: e^(iθ) = cos(θ) + i*sin(θ).

Conversely, an imaginary exponential can be expressed in terms of cosine and sine by solving for θ in the above equation. This can be done by taking the inverse cosine and inverse sine of both sides to get θ = cos^(-1)(e^(iθ)) = sin^(-1)(i*sin(θ)). Combining these equations gives θ = sin^(-1)(i*(e^(iθ) - cos(θ))).

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The difference between the area of triangle ABC and the area of triangle EFJ is 0 square unis

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

Trapezoid ABCD and trapezoid EFGH are congruent.

From the complete question added as an attachment

We can see that the two triangles have the same base and the same height due to the congruence of the two trapezoids

This means that their areas are equal

The difference between equal values is 0

Hence, the area difference is 0

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Answer:

c

Step-by-step explanation: got it     right on test

The domain of a function refers to the set of all possible inputs for the function.

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Sheila get $77 and Dora get $121 paid.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Sheila and Dora worked 3 1/2 hours and 5 1/2 hours.

Total they get paid = $198.

In one hour the amount of work they done is 7/2 and 11/2.

So, the ratio of their work = (7/2)/ (11/2)= 7/11

So, the amount Sheila get

= 7/18 x 198

= $77

and, the amount Dora get

= 11/18 x 198

= $121

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Answer:

224 total cookies sold

Step-by-step explanation:

if 9 sugar with every 5 cholates then, 144/9 = 16

so there were 16 times 5 cookies were sold with means

80 cholate cookies were sold

80+ 144= 224

:)

a) The inequality equation is x < -11

b) The inequality equation is x < 7

c) The ratio of dogs to cats is 7 : 5

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

a)

Substituting the values in the equation , we get

x + 8 < -3   be equation (1)

On simplifying the equation , we get

Subtracting 8 on both sides of the equation , we get

x < -11

Therefore , the inequality is x < -11

b)

The inequality representing the number line is x < 7

c)

Let the ratio be represented as A

The number of dogs = 7

The number of cats = 5

The ratio of dogs to cats = number of dogs / number of cats

Substituting the values in the equation , we get

The ratio of dogs to cats = 7 / 5

Therefore , the ratio is 7 : 5

Hence , the inequality relation is solved

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The measure of  the angles <ABC and <CBD are 48⁰ and 42⁰

The angle ABC and angle CBD are complementary angles, m <ABC=(3x+6)⁰ and m<CBD=(4x-14)⁰

The angles are complementary which means that they sum to 90⁰

Therefore, we get: <ABC + <CBD = 90⁰

3x + 6 + 4x - 14 = 90 ------ Substituting 3x + 6 and 4x - 14 for < ABC and <CBD

7x = 98

x= 98/7 = 14⁰

Therefore; Measure of <ABC:

Measure of<CBD:  

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Correct question:

Find the measure of each angle angle ABC and angle CBD are complementary angles, m angle ABC=(3x+6)degrees, and m angle CBD=(4x-14)degrees stuck on this problem, Thank you fo

This is an example of descriptive statistics. Descriptive statistics is used to summarize, organize, and present data in a meaningful way.

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Answer: To find the two integers between which the solution to 4^x = 50 lies, we can take the logarithm base 4 of both sides of the equation: x = log4(50). The logarithm of 50 with base 4 is approximately 2.3219. Since the logarithm of a number is always positive, the solution to 4^x = 50 lies between 2 and 3.

To find the exact solution, we can change the equation to logarithmic form by taking the logarithm base 4 of both sides: log4(4^x) = log4(50)

Using the logarithmic identity: log(b^x) = x*log(b)

So we have: x*log(4) = log(50)

Dividing both sides by log(4), we have:

x = log(50) / log(4)

To find the exact solution we can approximate log(50) / log(4) using a calculator or logarithm tables. The exact solution is x ≈ 2.32192809488736218170856773213.

So, the exact solution is x = 2.32192809488736218170856773213, which is between 2 and 3, as stated before.

Step-by-step explanation:

I will order a pizza tonight only if we eat dinner at home is a conditional statement.

Sentences are groups of words that convey complete and logical meaning. They have subjects and predicates. It can be in form of exclamation and questions consisting of main and subordinating clauses.

Conditional statements are sentences where the subordinating clause influences whether the action that will be performed or not in the main clause. In these statements, the subordinating clause is also called the antecedent, and the main clause is called the consequent.

There are two types of Conditional statements, they are Implicative and predictive statements. Implicative sentences are based on facts whereas predictive statements depend on a situation dependent on a hypothetical case.

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The fraction of water left from the bottle which was 1 liter is 3/4 liter.

Fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, from the bottle which was 1 liter, Juan drank 1/4. The amount that is left will be:

= 1 - 1/4

= 3/4

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True. The three numbers can be the measures of the sides of a triangle.

What is the triangle inequality theorem?

The triangle inequality theorem is a fundamental principle in Euclidean geometry that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This means that in any triangle, no side can be longer than the sum of the other two sides.

The three numbers 4, 7, and 8 can be the measures of the sides of a triangle. This is because of the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for any triangle, the sum of two sides must always be greater than the third side.

For example, in this case,

4 + 7 = 11 > 8,

7 + 8 = 15 > 4,

4 + 8 = 12 > 7

Hence, 4, 7, and 8 can be the measures of the sides of a triangle, so the correct response would be "True".

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If Ben scores 56 out of 79 on a maths test. The  percentage he get is: 0.7089.

Using this formula to determine the percentage he got

Percentage gotten = Number of scores / Total score

Where:

Number of score = 56

Total score = 79

Let plug in the formula

Percentage gotten = 56 ÷ 79

Percentage gotten = 0.70886

Percentage gotten = 0.7089 (Approximately)

Therefore we can conclude that he got 0.7089 .

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Answer:

The gutters are 24 ft above the ground. For safety, the distance a ladder reaches up a wall should be four times the distance from the bottom of the ladder to the base of the side of the house. Therefore, the ladder must be 6 ft from the base of the house.

Answer:

Step-by-step explanation:

1.50/6 = 0.25

3/5 = 0.6

0.25*2 = 0.5

0.6*3 = 1.8
1.80+0.50 = 2.30

$2.30

Answer:

2/11

Step-by-step explanation:

Normally 22 kids. 22 kids on the attendance roster.

18 kids say, "Here!" when their name is called.

22 - 18 is 4. 4 kids don't say anything when their name is called because they are at home still. 4 kids absent.

4 out of 22 kids absent. 4/22 kids absent.

4/22 simplifies to 2/11.

2/11 of the kids are absent.

Answer:

The two numbers are 17 and 7

Step-by-step explanation:

Translate this word problem into a math equation

If we let x and y be the two unknown numbers

One-half the sum of two numbers is 12 ==>

So one equation is 1/2(x + y) =12

Multiplying throughout by 2 gets rid of the denominator:
2 x 1/2 x (x + y) = 2 x 12

x + y = 24   (1)

One of the numbers is three more than two times the other number:
x = 2y + 3

or

x - 2y = 3  (2)

Equation (2) - Equation (1) =>

x + y - (x -2y) = 24 - 1
x + y - x + 2y = 21

3y = 21

y = 21/3

y = 7

With y = 7, substituting in equation 1 gives

x + y = 24

x + 7 = 24

x = 24-7

x = 17

The two numbers are 17 and 7

The length of AC of the given right angle triangle is; AC = 8

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse, Opposite and the adjacent side.

Now, the given triangle is a right angle triangle and using Pythagoras theorem, we can say that;

AC = √(BC² - AB²)

Thus;

AC = √(10² - 6²)

AC = √64

AC = 8

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