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 values of the interior angles, ( Angle A, Angle B and Angle C) of the triangles are 48°, 88° and 44° respectively.

Interior angle is the inner of the two angles formed where two sides of a polygon come together.

To find the measure of each interior angle of the triangle in the diagram, first, we need to find the value of x.

Recall that: The sum of the interior angles of a triangle is equal to 180°.

Using the formula,

From the triangle,

Substitute these values into equation 1

Solve for x

Therefore,

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The equation that models the balance y after x​ months is: y = -130x + 1200.

Month    Balance

0             1200

6            420

8             160

Hence,

m = (y2 - y1)/(x2 - x1)

First coordinate:

m = (420 - 1200)/(6 - 0)

m = -780 /6

m = -130

Second coordinate;

m = (160 - 420)/(8 - 6)

m = -260/2

m = -130

The formula for equation in slope intercept is

y = mx + c

where;

m = slope

c = y-intercept

So, equation is;

y = -130x + 1200

Therefore the equation is y = -130x + 1200.

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The quadratic expression can be factorized to:

x*(x - 6)

Here we have the expression:

x^2 - 6x

To factorize this, first, we need to find the roots, which are the solutions of:

x^2 - 6x = 0

Notice that one of the solutions is trivial, and it is x = 0.

If now we assume that x ≠ 0 and divide both sides by x, we get:

x - 6 = 0

x = 6

That is the other solution.

Now, for a square polynomial with the roots a and b, the factorized form is:

(x - a)*(x - b)

In this case, the roots are 0 and 6, then:

x^2 - 6x = (x - 0)*(x - 6) = x*(x - 6)

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The likelihood that the sample mean time required to finish the exam will be less than 47.5 minutes is 0.566.

Given;

The average amount of time needed to finish an exam is 45 minutes, with a standard deviation of 15 minutes. The average amount of time required for 100 randomly chosen pupils is calculated.

Mean (μ) = 45

Standard deviation (σ) = 15

Here, σ/√n = 15/√100

                   = 1.5

To get the probability the sample mean time necessary to complete the examination is less than 47.5 minutes, we need;

P (x < 47.5) = P(z < (x-μ /σ/√n ) )

                  = P(z < 47.5 - 45/1.5)

                  = P(z < 17.5)

                  = 0.566

The probability the sample mean time necessary to complete the examination is less than 47.5 minutes is 0.566

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The number of books each classroom received = 185

In this question, we have been given two libraries donated books to a local school. One library donated 786 books and the other library donated 1,245 books. The school divided the books evenly among 11 classrooms.

We need to find the number of books each classroom received.

Total number of books received:

786 + 1245 = 2031

The school divided the books evenly among 11 classrooms.

Let x be the number of books each classroom received.

By unitary method,

x = 2031 /11

x ≈ 185

Therefore, the number of books each classroom received = 185

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Answer:

0,-24,-3/4

You have to substitute the values for x and y to get the other output. When I put 0 into the equations I get back 0

Answer: g= 61/5 or 12.2

Step-by-step explanation:

The 90% confidence interval for the population mean gpa is [2.545,3.114].

The confidence interval for population mean is:

µ ± z* . σ/√n

Where, μ is population mean, σ is standard deviation, z* is the value of z-score and n is number of samples.

The z-score value for 90% confidence interval is 1.645.

The average gpa is found to be 2.83, so μ=2.83. The variance is 0.45, it means

σ² = 0.45

σ = √0.45

σ = 0.67

The 90% confidence interval for population mean is:

2.83 ± 1.645 . 0.67/√15

[2.83 - 1.645.0.67/√15 , 2.83+1.645.0.67/√15]

[2.545 , 3.114]

Therefore, the 90% confidence interval for the population mean gpa is :

[2.545 , 3.114]

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Answer:

volume = 3 ml

Step-by-step explanation:

the reading on the left without the nugget is 17 ml

the reading on the right with the nugget is 20 ml

volume of nugget = 20 - 17 = 3 ml

The solution for x in the equation given as 3/2 (4x – 1) – 3x = 54 –(x + 2) is 13.375

From the question, the algebraic expression is given as

3/2 (4x – 1) – 3x = 54 –(x + 2)

There is no constant to multiply or divide in the expression

3/2 (4x – 1) – 3x = 54 –(x + 2)

Open the brackets

So, we have

6x – 3/2 - 3x = 54  - x - 2

Collect the like term in the above equation

This gives

6x - 3x + x = 54 - 2 + 3/2

Evaluate the like term in the above equation

So, we have the following representation

4x = 53.5

Divide through by 4

x = 13.375

The above equation cannot be solved further

Hence, the solution is x = 13.375

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Applying the knowledge of congruent triangles, the measures are solved as:

6. X = 14; AC = 11; T = 14; WZ = 16; WY = 60; AB = 60; m∠A = 64°; m∠Y = 64°; m∠W = 50°

7. X = 7; YZ = 28; T = 9; WZ = 10; WY = 11; AB = 28; m∠A = 31°; m∠C = m∠W = 99°

To solve for the missing measures of triangles that are congruent to each other, recall that triangles that are congruent will have corresponding sides that are equal and also corresponding angles that are equal.

6. Triangles ABC and YWZ are congruent, therefore:

m∠A = m∠Y; m∠B = m∠W; m∠C = m∠Z

AB = WY; AC = YZ; BC = WZ

Therefore:

5X - 4 = 66

Solve for X

5X = 66 + 4

5X = 70

X = 14

AC = YZ = 11

AB = WY

5T - 10 = 4T + 4

5T - 4T = 10 + 4

T = 14

BC = WZ = 16

WZ = 16

WY = 4T + 4 = 4(14) + 4

WY = 60

AB = WY = 60

AB = 60

m∠A = m∠Y

m∠A = 180 - 50 - 66

m∠A = 64°

m∠Y = 64°

m∠B = m∠W = 50°

m∠W = 50°

7. Triangles ABC and ZYW are congruent, therefore:

m∠A = m∠Z; m∠B = m∠Y; m∠C = m∠W

AB = YZ; AC = WZ; BC = WY

Therefore:

5X - 4 = 3X + 10

Solve for x

5X - 3X = 4 + 10

2X = 14

X = 7

AB = YZ

2T + 10 = 4T - 8

2T - 4T = -10 - 8

-2T = -18

T = 9

YZ = 4T - 8 = 4(9) - 8

YZ = 28

AC = WZ = 10

WZ = 10

WY = 11

AB = YZ = 28

AB = 28

m∠A = m∠Z = 3X + 10 = 3(7) + 10

m∠A = 31°

m∠C = m∠W = 180 - 31 - 50 = 99°

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Answer:

Diameter = 3.1831 cm  (aprox)

Step-by-step explanation:

Diameter = circle / π

π ≈ 3.1414

Then:

Diameter = 10 / 3.1418

Diameter = 3.1831 cm

Total( as there is addition) feet walked by Lola is 29.25 +1.5x for the given equation.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division.

Main body:

Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:

= 10 + (1/2 × 10) = 10 + 5 = 15 feet

Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:

= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet

Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:

= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75

Lola's mom walked x feet, and then half that length again. Total length walked will be:

= x + (1/2 × x) = x + 0.5x = 1.5x

Total feet walked by the whole member of the family will be:

= 15 + 4.5 + 9.75 + 1.5x

= 29.25 + 1.5x

Hence Total feet walked by Lola is 29.25 +1.5x for the given equation.

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Answer:

it is 18 mile

Step-by-step explanation:

12mile = 60 min

x = 90 min

we cris cross the equation and

we found x=18 mile

Answer:

∠T

Step-by-step explanation:

∠T is the common angle found in both triangles.

In ΔPTS, ∠PTS represents ∠T.

In ΔQTR, ∠T is represented by ∠QTR.

Answer:

The angle T is common side.

Step-by-step explanation:

Given triangles,

→ ∆PTS & ∆QTR

Now we have to,

→ fInd common angle of both triangles.

The common angle is,

→ <T (angle T)

→ As it is present in both triangles.

Hence, the common part is angle T.

Los miembros de la sororidad tiene un porcentaje de 14 % de estudiantes procedentes de la especialización de ingeniería.

El enunciado describe las características de un diagrama circula, en donde el 100 % de los miembros de la sororidad representan a los 360° del ángulo central del círculo, esto es, una revolución completa del círculo.

El porcentaje de los miembros que se especializan en ingeniería mediante la siguiente fórmula:

e = (E / 360°) × 100 %

Donde E es el ángulo asociado a la cantidad de estudiantes de la especialización de ingeniería, en grados sexagesimales.

e = (50.4° / 360°) × 100 %

e = 14 %

Los estudiantes que especializan en ingeniería corresponden a un porcentaje de 14 % de los miembros de la sororidad.

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Answer:

C

Step-by-step explanation:

and for graph, rate change is 10(10 units change in Y for every 1 unit change in X) whereas another function's rate change is 4

C= is y-intercept

and in graph its -6 whereas in function its -8, so graph has higher y-intercept

Graph: Rate of change = 10, y-intercept = -6

Function: Rate of change = 10, y-intercept = -8

Answer: y = (1/2)x + 8

Step-by-step explanation:

Slope: (4-7)/(-8--2) = (-3)/(-6) = 1/2

y = (1/2)x + b

7 = (1/2)-2 + b

7 = -1 + b

8 = b

y = (1/2)x + 8

Answer: 7£

Step-by-step explanation:
1. Firstly, we need to subtract the single sign up fee from the total cost. This would be 141-57 =84 pounds
2. We know that you pay a regular amount every month, so therefore we can divide 84 by 12 as there are 12 months in a year.
3. 84/12 = 7. Thus, the answer is 7 pounds a month.

Answer:

£7

Step-by-step explanation:

Given information:

To find the cost of the monthly payments, find the difference between the total cost and the sign-up fee, then divide the result by 12 (as there are 12 months in one year).

The difference between the total cost and the sign-up fee is:

[tex]\implies 141-57=84[/tex]

Therefore, the cost of each monthly payment is:

[tex]\implies \textsf{Monthly fee}=\dfrac{84}{12}=7[/tex]

Answer:

Step-by-step explanation:

Yahweh’s

Answer:

67.5 (rounded down to 67, usually)

45/2 is 22.5 so that is for one hour

22.5 x 3 = 67.5

Answer:

add me on brainliest please

Step-by-step explanation:

65 is the answer

Answer:

5x+10y

Step-by-step explanation:

to expand we distribute each term with 5

5(x)+5(2y)

5x+10y

Hopes this helps please mark brainliest

Answer: 5x + 10y

Step-by-step explanation:

Re-order terms so constants are on the left

(x+2y)x5

5(x+2y)

Distribute

5(x+2y)

5x+10y

Answer:

25

Step-by-step explanation:

First, we add 50, 12, and 16, which gives us 78. Then, we remove 3 from the answer, giving us 75. Then, divide 75 by 3.

Answer = 25.

(ps: sorry for any spelling mistakes, i dont really type answers alot)

If you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, You win 50 tickets, 12 tickets, and 16 tickets at an arcade. You are able to buy 3 of the same item with 3 tickets left over.

Number of tickets won,

= 50 + 12 + 16

= 78 tickets

Number of items bought = 3 items

Let the cost of 1 item be 'x' tickets.

The cost of 3 items = 3x

By the amount, we can buy 78 tickets as,

3x = 78

x = 26

Thus, if you are able to buy 3 of the same item with 3 tickets left over. As a result, 1 item cost 26 tickets.

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y is inversely proportional to the square of x, here y in terms of x is 2/5.

From the given problem y is inversely proportional to the square of x.  

A table of values for x and y is shown.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

From the table:

(a) As we know that, y is inversely proportional to the square of x,

Here k is proportionality constant.

y∝1/x²

y= k/x²

4=k/1²

k=4

So, y in terms of x is y=4/x²

(b) Putting the value of y=25, we get:

25=4/x²

x²=4/25

x=2/5

Therefore, y is inversely proportional to the square of x, here y in terms of x is 2/5.

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Answer:

[tex] \frac{1}{6} {x}^{3} y + \frac{5}{6} x {y}^{2} \\ \frac{1}{6} xy( {x}^{2} + 5y)[/tex]

option 3 is correct

Answer:

Step-by-step explanation:

volume of a sphere = ⁴/3 π r³. r = D/2. V = 4/3 × π × (D/2)³. V = 4/3 × π × D³/8. V = ⅓ × π × D³/2. V = ⅓× π × (24mm)³/2.

If we graph the angel's ppc then the slope of angel's ppc will be -1.

Given, Tim and Angel are working on promoting an event for a club they are in on campus.

In one afternoon, Tim can make 4 flyers or 5 posters, and Angel can make 3 flyers or 6 posters.

we have to find the slope of the angel's ppc if we graph the angel's ppc.

As, the graph of the angel's ppc will pass through the point (3 , 6).

so, the slope = (6 - 5)/(3 - 4)

slope = 1/-1

slope = -1

Hence, if we graph the angel's ppc then the slope of angel's ppc will be -1.

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Using remainder theorem, Quotient = x-9 and Remainder = x² - x.

P(x) = −x³ – 2x² −9

P(-1) = −(-1)³ – (-1)x² −9

P(-1) = −(-1) – 2(1) −9

= 1 -2 -9

= -10

Remainder of  P(-1) = −(-1)³ – (-1)x² −9 is -10.

Remainder of P(x+1)

= −x³ – 2x² −9 / x+1

Quotient = x-9 and Remainder = x² - x

Hence, using remainder theorem, Quotient = x-9 and Remainder = x² - x.

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The inequality that could be used to determine the mean number of miles Jason would need to run each day for 5 more days to achieve his goal is 10 + 5m ≥ 45

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the number of miles be given as m.

Since his goal for this week is to run a minimum of 45 miles. So far this week, he has already run 10 miles. This will be:

10 + 5m ≥ 45

This expresses the inequality.

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Answer: 1,2L

Step-by-step explanation:

10 cm ------------ 0.75 L

16 cm ------------ ?

?= (16 x 0.75) : 10

?= 12 : 10

?= 1,2 L