Tyler hires a Lift driver to give him a ride to Wild
Rivers. It costs $4 to download the Lift app and then
$1.50 for every mile they have to drive you. Tyler's
trip to Wild Rivers cost $23.50. Write an equation
and solve to find the number of miles (m) the Lift
driver had to drive Tyler.

By SSS rule of congruence

∠QPR ≅ ∠SPR

"Information available from the question"

In the question:

Use the given information to prove that ∠QPR ≅ ∠SPR.

Given: QR ≅ SR

PQ ≅ PS

Prove: ∠QPR ≅ ∠SPR

Now, According to the question:

In triangle PQR and triangle PRS

We can see that

QR ≅ SR (given)

PQ ≅ PS (given)

PR = PR (Common line)

By SSS rule of congruence

When all the sides of two triangles are congruent, the angles of those triangles must also be congruent. This method is called side-side-side, or SSS for short.

Hence, ∠QPR ≅ ∠SPR

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The two column proof below has shown us that the LP ≅ LQ by definition of segment congruence.

We are told that Point M is the midpoint of PQ, and LM is the perpendicular bisector of PQ. Thus, the two-column proof to show that LP = LQ is as follows;

Statement 1; PM ≅ QM, LM ⊥ PQ

Reason 1; Given

Statement 2; LM ≅ LM

Reason 2; Reflexive Property of Congruence

Statement 3; ∠PML ≅ ∠QML

Reason 3; Right angle congruence theorem

Statement 4; ΔPML ≅ ΔQML

Reason 4; SAS congruence theorem

Statement 5; ∠PML ≅ ∠QML

Reason 5; Corresponding parts of congruent triangles are congruent

Statement 6; LP ≅ LQ

Reason 6; Definition of segment congruence

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Answer

P(A∩B) = 0.021

Step-by-step explanation:

For independent events P(A∩B) is the same as P(A)*P(B) so for this 0.42*0.05 = 0.021

Answer:

C)  Domain:  all real numbers x except x = ±2

E)  f(x) → ∞ as x → -2⁻ and as x → 2⁺, f(x) → -∞ as x → -2⁺ and as x → 2⁻

Step-by-step explanation:

Given function:

[tex]f(x)=\dfrac{3x^2}{x^2-4}[/tex]

The domain of a function is the set of all possible input values (x-values).

A rational function is undefined when the denominator is equal to zero.

The denominator of the given function is zero when:

[tex]\implies x^2-4=0[/tex]

[tex]\implies x^2=4[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{4}[/tex]

[tex]\implies x= \pm 2[/tex]

Therefore the domain of the function is:

The excluded x-values are x = -2 and x = 2.

To find the behaviour of the function near the excluded x-values, input values of x that are very near either side of excluded values:

[tex]x \rightarrow -2^-: \quad f(-2.001)=\dfrac{3(-2.001)^2}{(-2.001)^2-4}=3002.250...[/tex]

[tex]x \rightarrow -2^+: \quad f(-1.999)=\dfrac{3(-1.999)^2}{(-1.999)^2-4}=-2997,750...[/tex]

[tex]x \rightarrow 2^-: \quad f(1.999)=\dfrac{3(1.999)^2}{(1.999)^2-4}=-2997.750...[/tex]

[tex]x \rightarrow -2^+: \quad f(2.001)=\dfrac{3(2.001)^2}{(2.001)^2-4}=3002.250...[/tex]

Therefore, the behaviour of the function near the excluded x-values:

The amount of money an account with simple interest at an annual rate of 4.2% would be $3738 after 1 month and 7476 dollar after 2 month.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

Given that loan Amy is 89000 monthly payment is 479.66 rate is 4.2

Amount = $89000

Rate = 4.2 %

Time =  1 month

Therefore, Simple Interest = (Principal × Rate × Time) / 100

Simple Interest = 89000 × 4.2% × 1

Simple Interest = 3738

Also,

Simple Interest = 89000 × 4.2% × 2

Simple Interest = 7476

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The best description of the shape of the sampling distribution is C. Approximately normal.

The sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.

A sampling distribution is the distribution of a statistic calculated from a random sample of data. In this case, the statistic is the sample proportion of those who will be cured with the skin cream.

The Central Limit Theorem states that the sampling distribution of a statistic will be approximately normal if the sample size is large enough, regardless of the shape of the underlying distribution.

Since the sample size of 100 people is large enough, the sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.

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The question is -

Certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured? А. Bimodal B. Uniform C. Approximately normal D. Strongly skewed to the left E. Strongly skewed to the right.

Answer:

The graph of f(x) = x^2 is shown.

Use the parabola tool to graph g(x).

9(x)= (1 + x)^2 – 2

graph the parabola by first plotting its vertex and then plotting a second point on the parabola

In the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.

In the given question, linear function k has a zero at 3 and a y-intercept of 9.

We have to choose which graph best represents k.

As we know that;

A linear equation represent the relationship between the two unknown variable. The equation of linear equation is of one degree.

The simplest linear equation shows the correlation between (x,y), which may then be used to make a table or a graph on the coordinate plane or to assess at a specific x or y value.

We represent linear function in the form of y=mx+c.

where m is the slope of the line, c is the y intercept of the line, x is independent variable and y is the dependent variable.

As we see the y intercept in the graph crosses the y axis.

Here y intercept is 9.

The zeros of the linear function is that where y value is zero.

As in the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.

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The direct framed(mapped) cache in the given hexadecimal has all the miss.

Given cache parameters

b block size( given no. of words)

Cache capacity 16 words

( a) Direct mapped cache with b = 1 word

Address mapping = Total = 8 bits

Index = 4 bits

Offset = 0 bit

Tag(Label) = remaining bits = 4 bits

illustration of mapping = 74---> 01110100

where 0111 is the label and the rest is the index

Sequencing of law addressing = 0 * 74 to binary = 01110100

Then, word offset = log₂( b) = log₂( 1) = 0 bit

Line offset = log₂(16/1) = 4

Label(tag) is the remaining bit

b) completely associative cache with b = 2 words

# of lines = 16/2 W = 8

Address mapping Offset = log ₂( 2) = 1 bit

Remaining bit = 01110100

where 0 is offset and the rest is a label

In this cache design, line no. isn't needed to map the data as we directly compare CPU- generated markers with existing markers in the cache controller.

Still, apply the LRU algorithm, if the cache is full.

c) Two- way set associative cache with b = 2 words

#sets = #lines/ p- way = (16/2)/ 2 = 4

Address mapping

Set offset = log₂( 4) = 2

Word offset = log₂( 2) = 1

Tag(label) = remaining bits

ADDRESS       INDEX         OFFSET       HIT/MISS

74                       10                    0                MISS

A0                      00                    0               MISS

78                      00                    0               MISS

38C                    10                    0               MISS

AC                      10                    0               MISS

84                       10                    0               MISS

88                       00                    0               MISS

8C                       00                    0               MISS

7C                       00                    0               MISS

34                        00                    0               MISS

38                        00                    0               MISS

13C                      00                    0               MISS

388                      00                    0               MISS

18C                       00                    0               MISS

Replacement policy(which is default) LRU

( d) Direct planned or mapped cache with b = 4 words( each instruction size = AW)

Line offset = log₂( 4) = 2 bit

Word offset = log₂( 4) = 2 bit

Tag(Label) = remaining bits

# lines = 16/ W = 4

0 * 74-----> 01110100

where,

01 is the line offset

00 is the word offset

0111 is the tag(label).

Therefore, the tag, line offset and line offset of the hexadecimal is given to be in a binary number.

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The range of the function will be  0 ≤ y ≤ 960

The range of a function is the set of all its outputs. Example: Let us consider the function f: A→ B, where f(x) = 16x and each of A and B = {set of natural numbers}. Here we say A is the domain and B is the co-domain. Then the output of this function becomes the range. The range = {set of even natural numbers}.

Generally, the range of a function is the possible values of y in the that function and can be from -negative infinity to positive infinity.

In the given question, the function y = 16x models the situation and the capacity of the the container is 960 ounces

The range will fall between 0 ≤ y ≤ 960

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Answer:

y = x - 15

Step-by-step explanation:

y-2 = 1(x-17)

y-2 = x - 17

y = x -17 + 2

y = x - 15

The number of sheep originally on the farm will be equal to 200.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from.

Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Let the number of animals originally at the farm is x.

60% of the animals are cows.

So, 0.6x are cows.

If there are 60% cows, then there are 40% of sheep.

So, 0.4x are sheep.

The quantity of sheep multiplies when many cows and sheep were introduced to the property.

As a result, the farm now has the same amount of sheep that it did before.

Number of sheep added = 0.4x

There are total 260 animals added to the farm.

So,

Number of sheep added = 260-0.4x

Total number of animals = x + 260

The percentage of cows increased to 20%.

Initial number of cows at farm + cows added = Initial number of cows at farm + 20% of the total cows initially at the farm.

0.6x + (260-0.4x) = 0.6x + 0.2(0.6x)

0.6x+260-0.4x = 0.6x+0.12x

0.2x+260 = 0.6x+0.12x

0.2x+260 = 0.72x

260 = 0.52x

x = 260/0.52

x = 500

Thus, the farm's initial animal population was 500.

0.6x = the amount of cows that were first on the farm= 0.6(500) = 300 cows

0.4x = the amount of sheep that were initially on the farm = 0.4(500) = 200 sheep

0.4x = Sheep added = 200

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Answer:

Below

Step-by-step explanation:

I'll do the first one....you can then do the second one

-4x-2y = -12

4x+8y = -24       add these two equations together ( this will eliminate 'x')

    6y = -36

       y = - 6      use this value in either equation to compute x = 6

HINT: On the next one....multiply either equation by -1    then add together

The value of the equation A = ( 2/3 ) ( 2 - 6 ) is A = -8/3

What is an Equation?

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.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = ( 2/3 ) ( 2 - 6 )   be equation (1)

On simplifying the equation , we get

A = ( 2/3 ) ( 2 - 6 )

A = ( 2/3 ) ( -4 )

Multiply by -4 on the numerator , we get

A = ( 2 x -4 ) / 3

A = -8 / 3

Therefore , the value of A is -8/3

Hence , the value of the equation is -8/3

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Answer:

Step-by-step explanation:

The set {x | x < 0 or x > 3 } can be written in interval notation as (-∞, 0) ∪ (3, ∞).

The set {x | x < 0 or x > 3 } consists of all real numbers that are either less than 0 or greater than 3. This set can be represented as the union of the set of all numbers less than 0, which can be written as (-∞, 0), and the set of all numbers greater than 3, which can be written as (3, ∞).

Therefore, the set {x | x < 0 or x > 3 } can be written in interval notation as (-∞, 0) ∪ (3, ∞).

The ordered pair that is NOT a point on the graph of f(x) = (1/2)*x - 7 is  (2,8) , the correct option is (b)  .

In the question ,

it is given that ,

the function is given as ;

f(x) = (1/2)*x - 7 ,

Option(a) ,

the ordered pair is (1 , [tex]-6\frac{1}{2}[/tex] )

To satisfy the function f(x)  , on putting x = 1 , we should get y =  [tex]-6\frac{1}{2}[/tex] .

f(1) =  (1/2) - 7 = (1 - 14)/2 = -13/2 .

So , this point lies on graph of f(x) .

Option(b) ,

the ordered pair is (2,8) ,

f(2) = (1/2)*2 - 7 = 1 - 7 = -6 ≠ 8 .

So , this point does not lie on graph of f(x) .

Option(c) ,

the ordered pair is (-2,-8) ,

f(-2) = (1/2)*(-2) - 7 = -1 - 7 = -8 = -8 .

So , this point lies on graph of f(x) .

Option(d) ,

the ordered pair is (0,-7) ,

f(2) = (1/2)*0 - 7 = - 7 = -7 .

So , this point lies on graph of f(x) .

Therefore , the ordered pair (2,8) is not on the graph .

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Answer:

Step-by-step explanation:

9z + 27 = 45

9z= 18

z= 18/9

z = 2

Answer:

[tex]z=2[/tex]

Step-by-step explanation:

[tex]9(z+3)=45\\9z+27=45\\9z=45-27\\9z=18\\z=\frac{18}{9}\\ z=2[/tex]

Hope it helps you

The sum of the first 15 terms of the geometric sequences will be 76,456.33.

The aggregate to boundless GP implies, the number of terms in a limitless GP.

Let a₁ be the first term, n be the total number term, and r be a common ratio.

Then the sum of the geometric sequence will be

Sₙ = [a₁ (1 - rⁿ)] / (1 - r)

The geometric sequence is given below.

7, -14, 28, -56, 112,...

The first term of the geometric sequence is 7 and the common ratio of the geometric sequence is given as,

r = - 14 / 7

r = - 2

Then the sum of the first 15 terms of the sequences will be given as,

S₁₅ = [7 (1 - (-2)¹⁵)] / (1 - (-2))

S₁₅ = [7(1 + 32,768)] / 3

S₁₅ = -229,369 / 3

S₁₅ = 76,456.33

The sum of the first 15 terms of the geometric sequences will be 76,456.33.

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The ordered pairs of the solution to the system of equation are (-5, -3).

System of equation can be solved using methods like substitution method, elimination method and graphical method.

Let's solve the system of equation by substitution method.

Therefore,

-3x + 2y = 9

x - 3y = 4

Hence,

x = 3y + 4

Substitute the value of x in equation(i)

-3x + 2y = 9

-3(3y + 4) + 2y = 9

-9y - 12 + 2y = 9

-7y = 9 + 12

-7y = 21

y = 21 / -7

y = -3

Let's find x using equation(ii)

x = 4 + 3y

x = 4 + 3(-3)

x = 4 - 9

x = -5

Hence, x = -5 and y = -3

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The rule that describes the translation will be as  T<-3, 2>

Given,

Translation;-

Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same.

Here,

In order to move from A = (-3,3) to A' = (-6, 5), we must first move 3 units to the left and 2 units up.

Step 1's change causes x to become x-3.

Step 2's change causes y to become y+2.

When you combine these, (x, y) becomes (x-3, y+2).

That is equivalent to writing T<-3, 2>.

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the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75] using unit vector.

First, we need to calculate the unit vector of the line. This can be done by subtracting the two given points and dividing the result by the magnitude of the vector:

[-1 5] - [0 0]

= [-1 5]

|[-1 5]| = sqrt(1^2 + 5^2) = sqrt(26) = 5.1

Unit vector = [-1/5.1 5/5.1] = [-0.196 0.980]

Next, we need to calculate the dot product of the vector [-2 2] and the unit vector [-0.196 0.980]. This will give us the scalar projection.

(-2)(-0.196) + (2)(0.980) = -0.392 + 1.960 = 1.568

Finally, we can calculate the orthogonal projection by multiplying the scalar projection by the unit vector.

[-0.196 0.980] (1.568) = [-0.301 1.527]

Rounding to two decimal places, the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75].

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The teeth on the key are busted and now they must be readjusted and the code is 12y×2x^2.

Coding in Math is a series of the independent, standalone modules to that is  use coding to reinforcement and extended by to the  students' understandings of to the  math.! As students learning major programming is  concepts, they will development math-related to the  projects that is  demonstrate their proficiency by math and to the computer science.

18xy^2z^2=2xy^2 z×9xz

20xy^2z= 2xy^2z×10x^2

11xy^z=xyz^2×11

180y=9y×2x

24xy =12y×2x^2

(Take the greatest common factor)

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The value of the other points in the number line for each case are;

a) M = -2¹/₂

N = -1

R = 4

b) M = -1

P = 1

R = 1.6

c) M = -125

P = 125

N = -50

d) N = -6

P = 15

R = 24

a) We are given that P = 2¹/₂

From the point 0 of the number line to point P is 5 units and as such;

Each unit = 2¹/₂/5 = ¹/₂

Thus;

M = -2¹/₂

N = -1

R = 4

b) We are given that N = -0.4

From the point 0 of the number line to point N is 2 units and as such;

Each unit = 0.4/2 = 0.2

Thus;

M = -1

P = 1

R = 1.6

C) We are given that R = 200

From the point 0 of the number line to point R is 8 units and as such;

Each unit = 200/8 = 25

Thus;

M = -125

P = 125

N = -50

D) We are given that M = -15

From the point 0 of the number line to point N is 5 units and as such;

Each unit = 15/5 = 3

Thus;

N = -6

P = 15

R = 24

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40% percentage of your portfolio in the zero-coupon bond with a maturity of 5 years and 60% of your portfolio in the perpetuity. This would result in an overall duration of 10 years.

To achieve your target duration of 10 years, you would need to allocate your investments in a way that has an overall duration of 10 years. You could do this by investing 40% of your portfolio in the zero-coupon bond with a maturity of 5 years and 60% percentage of your portfolio in the perpetuity. This would result in an overall duration of 10 years.

Duration of zero-coupon bond = 5 years

Duration of perpetuity = infinity

Weighted duration of portfolio = (0.4 x 5) + (0.6 x infinity) = 10 years.

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Answer:

Step-by-step explanation:

Given the points

   (4, 2)

   (3, 5)

We know that the slope-intercept form of the line equation is

where m is the slope and b is the y-intercept

substituting m=-3 and the point (4, 2) to get the y-intercept i.e. b

2=(-3)4 + b

2 = -12 + b

b = 2+12

b = 14

Now, substituting b=14 and m=-3 in the slope-intercept form to determine the equation of a line in the slope-intercept.

y=(-3)x+(14)

y=-3x+14

Thus, the equation of the line containing (4,2) and (3,5)  in the slope-intercept form will be:

   y=-3x+14

In the proof, The reason for (5) ΔVWX ≅ ΔXYZ is ASA

Two triangles are congruent when their three angles and three sides are equal to each other. The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.

There are 4 property we use to congruent two triangles ( ASA , RHS , SSS and SAS)

According to the question,

Given = V W║Z Y

W X=Y X

We have to prove :  ΔVWX ≅ ΔXYZ

Proof =>

It is given that V W║Z Y ,

Using parallel line property ,

(1) ∠W = ∠Y (interior alternate angles )

(2) ∠V = ∠Z ( Interior angle property)

(3) W X=Y X (given)

Therefore , By using ASA property

ΔVWX ≅ ΔXYZ

Hence , In the proof, the reason for (5) is ASA

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The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate.

a) The equation of the estimated regression line is ŷ = - 16.592 + 0.1017x.

b) A point estimate is 1.9174 for true average efficiency ratio when tank temperature is 182.

c) The values of the residuals from the least squares line for the four observations for which temperature is 182 are -1.0774, -0.1874, 0.1226, 0.7826..

We have given the accompanying data on tank temperature (x) and efficiency ratio (y).

a) We have to find out the equation of the estimated regression line. Consider the calculations shown in the above table:

ΣΧ= 4308 ; ΣΥ= 39.99 ; ΣΧΥ = 7229.47 ;

ΣX² = 773790

Determine the slope and intercepts using the following formulas,

Slope b₁ = (n ΣΧΥ - ΣX ΣΥ)/(nΣΧ² - (ΣX)²)

=> b₁ = [24 (7229.47) - (4308) (39.99)]/(24(773790)-(4308)²)

=> b₁ = 1230.36/12096 = 0.10171626984

=> b₁ ≈ 0.1017

Intercept, b₀ = ΣY /n - b₁ΣΧ /n

=> b₀ = 39.99/24 - 0.1017×4308/24

= -16.592

Thus, the estimated regression equation of the form, ŷ = b₀ + b₁ x

ŷ = - 16.592 + 0.1017x

b) Calculate the point estimate for true average efficiency ratio when tank temperature is 182.

y = -16.592 + 0.1017x

=> y= -16.592 +0.1017 (182)

=> y= 1.9174

Therefore, the point estimate for true average efficiency ratio when tank temperature is 182 is 1.9174..

c)We have to find out the values of the residuals from the least squares line for the four observations for which temperature is 182.

From part (b), the value of ŷ is 1.9174.

The table below shows the residuals.

Vi ŷ e = y₁ - y

0.84 1.9174 -1.0774

1.73 1.9174 -0.1874

2.04 1.9174 0.1226

2.70 1.9174. 0.7826

Hence, we got all the required values.

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