A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 50 meters and a standard deviation 100 meters. What is the probability that the measured distance will be smaller than the true distance?.

The solution of the linear equation:

(2x + 6)/5 = 4x - 3

is x = 7/6

Here we have the following equation:

(2x + 6)/5 = 4x - 3

To solve this, we need to isolate x in one of the sides of the equation, we can start by multiplying both sides by 5.

2x + 6 = 5*(4x - 3)

Expanding the right side we get:

2x + 6 = 20x - 15

Now you can see that this is a simple linear equation, now we need to group like terms:

6 + 15 = 20x - 2x

21 = 18x

Now we can divide both sides by 18 to get:

21/18 = x

Finally, if we divide both numerator and denominator of the fraction by 3, we get:

21/3 = 7

18/3 = 6

Then 21/18 = 7/6

Finally, we conclude that the solution is:

x = 7/6

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Answer: To find the vertex: use formula x= -b/2a.

plug x into the given equation to find y value.

now you have (h,k)

find a point on the graph and plug in to the vertex form equation to find "a"

Step-by-step explanation:

Answer:

======================

Let the sides be t for triangle and s for square.

Answer:

14 inches

Step-by-step explanation:

The side lengths of an equilateral triangle are the congruent.

The side lengths of a square are the congruent.

Let x be the length of one side of the equilateral triangle.

⇒ Perimeter of triangle = 3x

Let y be the length of one side of the square.

⇒ Perimeter square = 4y

Given:

Create a system of equations with the given information and defined variables:

[tex]\begin{cases}3x = 4y + 10\\x = y + 6\end{cases}[/tex]

Substitute the second equation into the first equation and solve for y:

[tex]\implies 3(y+6)=4y+10[/tex]

[tex]\implies 3y+18=4y+10[/tex]

[tex]\implies 18=y+10[/tex]

[tex]\implies y=8[/tex]

Therefore, the side length of the square is 8 inches.

Substitute the found value of y into the second equation and solve for x:

[tex]\implies x=8+6[/tex]

[tex]\implies x=14[/tex]

Therefore, the side length of the triangle is 14 inches.

Bruce paid $17 and $55 respectively for each of the books

From the question, we have the following statements:

Represent the books with the variables x and y

So, we have the following equations

x = 4 + 3y

x + y = 72

To start with;

We can substitute 4 + 3y for x in the equation x + y = 72

So, we have the following representation

4 + 3y + y = 72

Evaluate the like terms

4 + 4y = 72

Collect the like terms in the above equation

So, we have the following equation

4y = 72 - 4

Evaluate the like terms

4y = 68

Divide both sides by 4

So, we have

y = 17

Recall that x = 4 + 3y

Substitute 17 for y in the equation x = 4 + 3y

x = 4 + 3 * 17

Evaluate the products

x = 4 + 51

Evaluate the sum

This gives

x = 55

Hence, the cost of the books are $17 and $55

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Possible question

Bruce bought two books, one book costs $4 more than three times than the other. They both equal $72.

What is the cost of each book

The steps and reason to prove the angle theorems is; Table 3

The internal angles of the given triangle are given as;

a, b, c and d.

Now, we know that the sum of interior angles in a triangle is equal to 180°;

∠a + ∠b + ∠c = 180°

Now, ∠c and ∠d are angles that form a straight line and as such they sum up to 180° as they are supplementary angles.

∠c + ∠d = 180°

Thus, by transitive properties, we can say that;

∠a + ∠b + ∠c = ∠c + ∠d

Therefore by subtraction property of equality we have;

∠a + ∠b = ∠d

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The car that is 16 feet long has a length of 8 inches on the scale.

Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.

Therefore, the particular car is 16 feet long. A model of it was built with a scale of 1 in: 2 ft. The length of the car can be found as follows:

2 feet = 1 inches

16 feet = ?

cross multiply

length of the model car = 16 / 2

Therefore,

length of the model car =  8 inches

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Answer:The percentage decrease in the number of students​ is -10%.

Given that,

The school has 1,200 students last year.

And, this year it is 1,080.

Based on the above information, the calculation is as follows:

Therefore we can conclude that the percentage decrease in the number of students​ is -10%.

Step-by-step explanation: noice

The matching of the quadratic functions with their features is given by the image at the end of the answer.

The first feature of the function on the problem is when it is increasing, and the definition is that it is increasing when the graph of the function is moving to the right and up on the graph, that is, when x increases, y also increases.

It is decreasing when it is moving right and down. Hence, a quadratic function increases until it's vertex, so for item 1, we want a function that is concave down, as it is increasing and then decreasing, and does the turn at x = 1, which is the third function on the second row.

The maximum and minimum points are given at the turning points, as follows:

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Answer: Its correct

Step-by-step explanation:

Right on Edmentum. Absolute legend

Answer:

40.5w + 118.37= 239.87; w=3

Step-by-step explanation:

You already saved 118.37.

239.87

118.37

111.50

40x3=120. So you'll need 3 more weeks to buy a gaming chair. And you also get 8.50 dollars extra in profit.

Answer:

40.5w + 118.37= 239.87; w=3

Step-by-step explanation:

Answer:

It's correct

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: (-2, 4)  Equation Form : X= -2, Y = 4.

Option A. The set of side measurement that can be used to form a triangle is given as A. 13, 19, 7

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices. In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

How to get the measurement that can produce a triangle.

a + b > c  = 13 + 19 > 7

a + c > b  =  13 + 7 > 19

b + c > a  = 7 + 9 > 13

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Answer:

Step-by-step explanation:

Peter=x

Phillippa= 3x then x

Palvin= 10 then Phillippa

Step 2: Answer: Phillipa 3x+x+10

The circumference of circle of radius 70 cm is 440 [tex]cm^{2}[/tex].

According to the question,

We have the following information:

Radius of the circle = 70 cm

(Diameter is twice that of its radius..)

We know that the following formula is used to find the circumference of circle:

Circumference of circle = 2πr

(More to know: the formula to find the area of circle is π[tex]r^{2}[/tex].)

(More to know: there are two values of π. One is 3.14 and one is 22/7.)

Circumference of circle = 2*(22/7)*70

Circumference of circle = 440 [tex]cm^{2}[/tex]

Hence, the circumference of the circle of radius 70 cm is 440 [tex]cm^{2}[/tex].

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The number of teams in the field hockey championship tournament is 16.

The total number of matches played in the field hockey championship are 120 matches.

Each pair of team played one match with each other.

So, let us say that there are N teams in the tournament.

So, we can chose any two teams for a match,

So, applying the permutation formula,

ⁿC₂ = 120

Solving further,

N!/2!(N-2)! = 120

N(N-1)/2 = 120

N(N-1) = 240

On observing closely and applying hit and trial method,

16(15) = 240

So, the values of N is 16.

Hence, 16 teams participated in the tournament.

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a) The length of segment CD is; CD = 10 cm

b) The length of segment AB is; AB = 5 cm

c) Another segment with same length as segment AB is;

Segment AC

From the attached image, we see that Segment AE is a radius of the circle with center of A.

Now, any segment with origin from the center of the Circle that goes on to hit the circumference of the circle, is also a radius, and would be equal in length to segment AE.

a) Segment CD divides the circle into 2 equal parts and as such it will be the diameter of the circle.

Diameter = 2 × radius.

Diameter; CD = 2 × AE

CD = 2 × 5

CD = 10 cm

b) AB is a radius as defined earlier and as such; AB = AE

Thus; AB = 5 cm

c) The other segments that are also radius of the circle and have the same length as segment AB are;

Segment AC

Segment AD

Segment AG

Segment FA

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If Two planes are parallel and each plane contains a line, the two lines are  not skew because In the event that any two lines fall on a single plane, they will either intersect or be parallel to one another. Both instances violate the concept of a skew line because the skew lines are neither parallel nor intersect.

Infinitely many lines cross through, yet only one of them is parallel to. Lines that never intersect and are in distinct planes are known as skew lines. Parallel lines and skew lines are distinguished by the fact that they both reside in the same plane, whereas skew lines do not.

The two lines would overlap at some point if the two planes on which they are located weren't parallel, which again defies the definition of skew lines.

Therefore, The skew lines are thus present if and only if both lines fall on a pair of parallel planes.

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Answer:

Step-by-step explanation:

NOSEEEEEE

In this "Simple Random Sample" scenario, 500500500 selected randomly registered phone numbers were chosen.

For the given data in the question.

Thus, 500500500 random registering phone numbers are randomly chosen by a state court employee using a computer, and the law firms connected to all those numbers are randomly chosen for an audit.

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The sum of the ages of the children would be 3x - 94 years.

We have the total sum of the ages of pam ,dion and their children  

as 5x - 99

here , x is the age of Dion .

we see , pam is five years younger than Dion , so

age of Pam = x - 5

Now as the sum of all the ages = 5x - 99

therefore ,

Age of Dion + Age of Pan + Age of children = 5x - 99

x + x - 5 + Age of children = 5x - 99

2x - 5 + Age of children = 5x - 99

therefore ,

Age of children = 3x - 94

So  the age of their children would be 3x - 94 years

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The value of PQ is 43.

What is an isosceles triangle?

A triangle with at least two equal-length sides is known as an isosceles triangle in geometry.

From the figure,

PQ=3x+10, QR=5x-12

Given that, PQ=QR

So, 3x+10=5x-12

Find x:

3x+10=5x-12

Separate variable terms and constants

5x-3x=10+12

2x=22

x=22/2=11

we have PQ=3x+10=3(11)+10=33+10=43

So, PQ=43

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Using the distributive property, the simplified form of the expression 1/4(12k-4) is 3k-1.

In the given question we have to simplify the given expression.

The given expression is 1/4(12k-4).

To simplify the given expression we use the distributive property.

According to property; a(b+c) = ab+bc

Now simplifying the expression;

1/4(12k-4) = 1/4*12k-1/4*4

1/4(12k-4) = 3k-1

Hence, the simplified form of the expression 1/4(12k-4) is 3k-1.

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The time it would take for light to travel from Earth to the moon is; 1.28 seconds.

It follows from the task content that the time it would take for light to travel from Earth to the Moon is to be determined.

Since the given speed of light is; 3 × 10⁵ km/s and the distance is; 3.84 × 10⁵ km.

It follows from the formula;

Speed = Distance / Time

Time = Distance/Speed

Time = 3.84 × 10⁵ / 3 × 3.10⁵

Time = 1.28 seconds.

Therefore, the required time it would take to travel from Earth to the moon is; 1.28 seconds.

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Answer:

The numbers that we use are expressed in base 10. Every 10 1s equals 1 ten For example, if you are adding 5 + 4, you get: 0101 + 0100.

The clothing in the store is separated into strata, each of which is a rack of items with comparable prices. An illustration of the use of a stratified random sample is the mean price calculated using the randomly chosen articles of clothing from the strata.

In the random sampling method of sampling, each sample has an equal chance of being chosen. In order to fairly represent the entire population, a sample is chosen at random. From a pool of 250 employees, 25 names could be chosen at random to represent a simple random sample. The sample in this case is random, and the population in this case is the employees since each has an equal chance of being chosen.

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The equation that could solve how many hours it will take for the second car to catch up to the first car is 55t = 120 + 40t.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

If the first car is going 40 mi/h, and has a 120 mile head start, then the distance it covers at time = t is,

d1 = 120 + 40t

If the second car is going 55 mi/h, you want to know the amount of time it will catch the first car, then, their distance must be equal.

d2 = 55t

d1 = d2

120 + 40t = 55t

Simplify the equation of t.

55t - 40t = 120

15t = 120

t = 8

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The fraction of 1/6 is equivalent to this following decimal number:

0.166.

A fraction is represented by the division of a term x by a term y, as follows:

Fraction = x/y.

The terms that represent x and y are given as follows:

In this problem, the fraction is given as follows:

1/6.

1 is less than 6, hence the equivalent decimal can be obtained as follows:

0.10/6.

10 divided by 6 is one with a remainder by 4, hence 1.4/6 = 1.6667.

Thus the equivalent decimal representing the fraction 1/6 is given as follows:

1/6 = 0.1666.

The problem asks for which decimal number the fraction 1/6 is equivalent.

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One method is to determine the average hourly rate for all employees, regardless of where they work in your company, what they do, or how many hours they work.

To begin, calculate the total number of hours worked by multiplying the number of weeks in a year by the number of hours worked per week. Divide this figure by the annual salary. For example, if an employee earns $50,000 per year and works 40 hours per week, his or her hourly rate is $50,000/2,080 (40 x 52) = $24.04.

When budgeting for future projects, keep in mind that if you pay Bill $18 per hour, Lisa $16, and Hank and Jake $14, your labor costs will vary depending on who you send to the job site.

However, if you can use Bill less frequently each week and Hank or Jake more frequently, you might be able to budget for next month using the $15.82 per hour figure.

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g(x) = 7(x+5) + 1 is the newly transformed function

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Given that: He graphs the function f (x) = 7x + 1 and then transforms the function by horizontally translating it 5 units to the right

To solve this problem, we need to understand the direction of movement. In the cartesian plane or graph, the x-axis is either a movement to the left(negative) or right(positive)

Since the function f (x) = 7x + 1 translates by 5 units to the right. You need to add 5 to x  i.e. 7(x+5) + 1

Therefore, the newly transformed function, g (x) = 7(x+5) + 1

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