What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x-y=4

Using mathematical operations, we can conclude that the length of LK is 1.25 units in triangle JKL.

A mathematical "operation" is indeed the method by which a value utilizes operands and a math operator.

The supplied operands or numbers must conform to a set of predefined rules that are connected to the symbol of the math operator.

Parentheses, Exponents, Arithmetic, Division, and Addition Simple arithmetic is also known as PEMDAS (from left to right).

So, we know that the given triangles are similar:

Then, the length of line LK will be:

JK/ST = LK/UT

Solve this as follows:

JK/ST = LK/UT

2.5/10 = LK/5

10LK = 2.5(5)

10LK = 12.5

LK = 12.5/10

LK = 1.25

Therefore, using mathematical operations, we can conclude that the length of LK is 1.25 units in triangle JKL.

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The reqiured two digit number is 54

Let, a two-digit number be n

the digit at tens place as x and the digit at unit place be y

The tens digit of a two-digit number exceeds the units digit by 1.

x = y + 1                      .............(1)

if the number is divided by the sum of its digits, the quotient is 6.

(10x + y)/(x + y) = 6

Substitute above value of x in this equation.

(10(y + 1) + y) = 6(y + 1 + y)

10y + 10 + y = 6(2y + 1)

11y + 10 = 12y + 6

y = 4

Substitute above value of y in equation (1),

x = 4 + 1  

x = 5

So, the number would be, 10x + y = 50 + 4

                                                      = 54

Therefore, the number is 54

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Answer:

  (a)  w = 13

Step-by-step explanation:

You have a regular quadrilateral with interior angle measure (6w+13)°, and you want the value of w to the nearest integer.

A regular quadrilateral is a square. Its interior angles are 90°, so we have ...

  6w +13 = 90

  6w = 77

  w = 12.833...

  w ≈ 13

The value of w to the nearest whole number is 13.

A straight line = 180°. You have: 58° , 40°, and q so:

q = 180° - (58° + 40°)

q = 82°

Answer:

82

Step-by-step explanation:

180 i s the line length so

180-40=140

140-58=82

The side of each square in terms of y is y/16.

What is a perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

Here, we have

The figure is made up of 10 identical squares. The perimeter is y cm.

The number of outer sides is 16

Let the side be x

then

16x = y

x = y/16

Hence,  the side of each square in terms of y is y/16.

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Two figures are similar when they have some common properties. The value of PQ as required is 28 units.

Similar triangles are two or more which have a series of common properties. This may be in relations to the length of their sides or measure of their angles.

In the given triangle PQR,

ΔPQS ll ΔSTR

Given that PS = RS, and QT = RT.

Then we can say that;

[tex]\frac{RS}{ST}[/tex] = [tex]\frac{PQ}{PQ}[/tex]

But, PR = 2RS;

[tex]\frac{RS}{ST}[/tex] = [tex]\frac{2RS}{PQ}[/tex]

[tex]\frac{1}{ST}[/tex] = [tex]\frac{2}{PQ}[/tex]

2ST = PQ

2(-22 + 9x) = 9x - 8

-44 + 18x = 9x - 8

18x - 9x = -8 + 44

9x = 36

x = 4

So that,

PQ = 9x - 8

     = 9(4) - 8

PQ = 36 - 8

     = 28

Thus, the length of PQ is 28 units.

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Answer: 131072

Step-by-step explanation:

Basically the sequence is just being multiplied by 4, like 2(4)=8 and 8 is the next number in the sequence or 32(4)=128 which then again is the next number in the sequence.

Answer:

i think 3

Step-by-step explanation:

The equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.

To convert the annual salary of a truck driver in the US from US dollars to Canadian dollars, you can use the current exchange rate between the two currencies. The exchange rate fluctuates constantly, so you will need to use the most current rate.

Assuming the current exchange rate is 1 US dollar to 1.26 Canadian dollars, the annual salary of a truck driver in the US, $55,065, is equivalent to 71,040.90 Canadian dollars. If the truck driver works 70 hours per week and 52 weeks per year, their hourly wage in Canadian dollars would be $28.13.

Here's the calculation:

Annual salary in Canadian dollars = $55,065 * 1.26 = $71,040.90

Hourly wage in Canadian dollars = $71,040.90 / (70 hours/week * 52 weeks/year) = $28.13/hour

Keep in mind that this is just a rough estimate, as the exchange rate can change over time, and the actual wage may vary depending on the driver's experience, location, and other factors.

So, the equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.

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Answer: the first one(triangle ABC) is scalene, the second one(triangle TRI) is Isosceles, and the last one(triangle PQR) is

Isosceles

Step-by-step explanation: graph each joint is Desmos online calculator

An expression that represents the number of bracelet Leslie designs is

Information from the question include

Her most recent order included a total of 7 bracelets

It takes 14 stones to make one bracelet

let s represent stone

It takes 14 stones to make one bracelet means that one bracelet = 14 s

hence if 1 bracelet is 14 stones then 7 bracelet will be

1 bracelet = 14 s

7 bracelet = ?

cross multiplying

1 * ? = 7 * 14

? = 98 stones

the equation is written as

s/14 = 7 ; s = 98 stones

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Answer: 36 boxes

Step-by-step explanation:

4630 divided by 130 = 35.6 boxes

Then we ground up to 36 boxes

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By applying this theory, it is discovered that there is an 0.5 = 50% chance that the marble will land on a 00 or even slot.

A probability is calculated by dividing the entire number of possible outcomes by the desired outcomes.

In this issue:

The preferred likelihood is:

P = D/T

P = 19/38 = 0.5

Thus, the probability that the marble will land on a 00 or even slot is 50%, or 0.5.

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The complete question is-

When playing American​ roulette, the croupier​ (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to​ 36, with two additional slots labeled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a 00 or even slot.

forty-five times three equals one-hundred-thirty-five

45x3=135

The probability that exactly 5 small businesses will fail during a given month 0.0037268.

The Poisson distribution would be used to calculate the likelihood that different counts of the same event will occur within a constrained time period. It is viewed as a discrete distribution since it evaluates counts. The distribution displays identical mean and dispersion values.

The pmf of the Poisson distribution is

[tex]p(x)=\frac{e^{\lambda} \lambda^{x}}{x!}[/tex]

The mean total number of small business failures λ=14

Let x represent the number of failed small businesses in a given month.

X~P(14)

X follows the Poisson distribution since the likelihood of failure stays constant for two months and the mean number of failures per month is 14.

The likelihood that precisely four small firms would fail in a given month must be calculated.

P(X=5)

[tex]P(X=5)= \frac{e^{14} \ 14^{5}}{5!}[/tex]

P(X=5)= 0.44721/5!

P(X=5)=0.0037268.

In a month there is 0.0037 that is 3.7% probability that a small business fail.

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The time at which the lorry the time taken arrive at it destination is 12.20.

Given :

A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average speed of 52 km/h.

here,

Distance = 195 km

Speed = 52 km/h

we know that ,

speed = distance / time

on cross muliplicating

speed * time = distance

time = distance / speed

substitute the values

time = 195 / 52

= 3.75 hours

destination time = 8.45 + 3.75

= 12.20

Therefore the time at which the lorry the time taken arrive at it destination is 12.20

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If Alan had ran 1 10/11 kilometer and walked the ret so his remaining distance from school is 6 5/11 kilometer.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=√((x_2-x_1)²+(y_2-y_1)²) to calculate the separation between any two locations.

As the total travel of alan from his school is

=8 2/3 kilometer

according to given condition;

he has traveled;

=1 10/11 kilometer

so his remaining travel from his school is;

=8 2/3 kilometer-1 10/11 kilometer

= 6 5/11 kilometer

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The chance that a student is selected at random from the class who passed the exam and finished the assignment is 0.2105

Probability refers to potential. The occurrence of a random event is the subject. Probability values are limited to the range of 0 to 1. Its fundamental notion is that something is probable to occur. It is the proportion of favorable events to all other events.

A exam and an assignment were due on the same day in a math class with 19 pupils.

There were 14 students that finished the assignment, and 11 of them completed the test.

3 pupils both failed the exam and didn't finish the assignment.

Then the probability that a student is chosen randomly from the class passed the test and completed the homework will be

The number of the student who has done at least one assignment or passed the test is 19 - 3 = 16

n(A) = passes student

n(B) = given assignment

Then we have

n(A ∩B) = n(A) + n(B) - n (A ∪B )

n(A ∩B) = 11 + 14 - 16

n(A ∩B) = 9

Then the probability will be

P = 9C2 /19C2

P = 36/171

P = 0.2105

The probability that a student chosen randomly from the class completed the homework is 0.2105

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Answer:

Step-by-step explanation:

u got it right the first time it is D

Answer:

[tex]y=\frac{1}{5}x+\frac{6}{5}[/tex]

Step-by-step explanation:

Parallel lines have the same slope, so the slope of line [tex]d[/tex] is [tex]1/5[/tex].

So, the equation of line [tex]d[/tex] is:

[tex]y-1=\frac{1}{5}(x+1) \\ \\ y-1=\frac{1}{5}x+\frac{1}{5} \\ \\ y=\frac{1}{5}x+\frac{6}{5}[/tex]

Liquid detergent do I have left is 8/9.

What is detergent ?

When washing items like clothing or dishes, detergent is a chemical compound that is often in the form of a powder or liquid. Alternatives include washing liquid, soap powder, and cleaner. More detergent synonyms. More detergent synonyms.

I have 2/3 L (litre) of liquid detergent. I ued 3/4 of thi to wah my heet on the weekend.

[tex]\frac{\frac{2}{3}}{\frac{3}{4}}$$[/tex]

Apply the fraction rule: [tex]$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$[/tex]

[tex]=\frac{2 \cdot 4}{3 \cdot 3}$$[/tex]

Multiply the numbers: 2-4=8

[tex]=\frac{8}{3 \cdot 3}$$[/tex]

Multiply the numbers: 3-3=9

[tex]=\frac{8}{9}$$[/tex]

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Answer:

9.652 kg

Step-by-step explanation:

144 kg 780 g = 144.78 kg

if there are 15 packets in the box then:

144.78 ÷ 15 = x

x = 9.652 kg

Therefore the weight of each bag is 9.652 kg

Therefore in this question the probability that he is innocent is 0.1743

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Here,

In this case, let G represent the state of guilt and H represent the state of innocence.

and Let K stand for the situation where the truth serum shows that someone is guilty.

We are aware that 90% of the guilty suspects receive just verdicts, i.e. P(K|G)=0.9.

Additionally, we know that innocent suspects are mistakenly identified 1% of the time, or P(K|H)=0.01.

When a suspect is chosen from a group of suspects, of whom 5% committed a crime, and the serum suggests that the suspect is guilty, we must determine the likelihood that the suspect is innocent.

We must therefore determine the probability P(H|K).

A group of people was chosen for the suspect, of which 5% were criminals.

so the probability that selected person is guilty is

P(G) = 0.05

Therefore, the probability that selected person is not guilty is

P(H) = 1 – P(G) = 1 – 0.05 = 0.95

Then,

Using Bayes' Theorem, we get

P(H|K) =[tex]\frac{P(H)P(K|H)}{P(H)P(K|H) + P(G)P(K|G)}[/tex]

=     [tex]\frac{0.95*0.01}{0.95*0.01 + 0.05*0.9}[/tex]  =0.1743

Therefore in this question the probability that he is innocent is 0.1743

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Answer:

y = -2/5 x + 4

Step-by-step explanation:

slope = (0-4)/(10-0)

-4/10

-2/5

y intercept = 4

y = -2/5 x + 4

Answer: C

Step-by-step explanation:

Distributive property 2. combine like terms 3. subtraction proerty of equality 4 division of equality.

It is evident from the steps above that it is impossible to be have two numbers with the same LCM and HCF as 12 and 5, respectively.

The given condition are-

Helen considers two numbers that fit the following criteria:

The steps to solve the condition are-

1. It is assumed that when Helen considers of two numbers, they have corresponding HCF and LCM values of 5 and 12.

2. A smallest common multiple shared by two numbers is referred to as the least common number.

LCM of 4 with 6 is 12, for instance.

3. The highest number which divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.

HCF of 6 and 8 is 2, for instance.

4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are indeed the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.

5. The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values apart from 5. 60 and 120 have an HCF of 60, but not 5.

6. As a result, it is evident from the steps above that it is impossible to be have two numbers with the same LCM and HCF as 12 and 5, respectively.

Therefore, the aforementioned criteria cannot exist mathematically.

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By evaluating the linear equation, we will see that Mr. Dyson will buy 20 packs of nickel strings.

We know that the linear equation:

6x + 4.5*y = 90

Represents the given situation, where the variable x is the number of bronze strings and y is the number of nickel strings.

We want to find the number of packs of nickel strings that he will buy if he does not buy any bronze strings, so we need to evaluate in x = 0.

We will get:

6*0 + 4.5*y = 90

4.5*y = 90

y = 90/4.5 = 20

He will buy 20 packs of nickel strings.

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The value of AD in one decimal place for the given triangle is 9.8 cm.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

As per the given by triangle ΔADE

By Pythagoras' theorem,

(AD)² = (AE)² + (ED)²

(AD)² = 4² + 9²

(AD)² = 97

AD = 9.8

Hence "The value of AD in one decimal place for the given triangle is 9.8 cm".

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The missing image is attached below,

0.3108 is the probability that a single tire randomly selected from the population will have a lifetime between 46,800 and 49,200 miles

Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

X ~ N ( µ = 48000 , σ = 3000 )

As we know, P ( 46800 < X < 49200 )

Standardizing the  value, we get -

Z = ( X - µ ) / σ

Z = ( 46800 - 48000 ) / 3000

Z = -0.4

Z = ( 49200 - 48000 ) / 3000

Z = 0.4

Also,

P ( -0.4 < Z < 0.4 )

P ( 46800 < X < 49200 ) =  P ( Z < 0.4 ) - P ( Z < -0.4 )

P ( 46800 < X < 49200 )  = 0.6554 - 0.3446  (Probability calculated from Z table)

P ( 46800 < X < 49200 )  = 0.3108

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