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Consider this system of linear equations:
y- x = -13
-4x + 3y = -51
The solution of the system of equations is
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Answer:

Step-by-step explanation:

Step-by-step explanation:

92% of (680 kilograms) =

625.6 kilograms

(a) (i) 0.3174 = 31.74% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 317.

(b) (i) 0.0026 = 0.26% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 3.

(C) Reduces the process standard deviation and causes no change in the number of defects.

When the distribution is normal, we use the z-score formula.

In a set with mean  and standard deviation, the score of a measure X is given by:

         Z = X-μ /σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question a:

We have that: μ = 10 and σ = 0.12

(i). Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

  Z = X-μ /σ

⇒ Z = 9.88 - 10/0.12

⇒ Z = -1, has a p-value of 0.1587

⇒ 2× 0.1587 = 0.3174

This means 0.3174 = 31.74% probability of a defect

(ii)  Calculate the expected number of defects for a 1,000-unit production run.

The expected number of defects is 31.74% of 1000. So

0.3174*1000 = 317.4

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 317.

Question (b):

The mean remains the same, but the standard deviation is now

(i) Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

   Z = X-μ /σ

⇒ Z = 9.88 -10/0.04

⇒ Z = -3

⇒ Z = -3, has a p-value of 0.0013

which means 2× 0.0013 = 0.0026

from which 0.0026 = 0.26% probability of a defect

(ii) Calculate the expected number of defects for a 1,000-unit production run. The expected number of defects is 31.74% of 1000. Thus,

⇒ 0.0026*1000 = 2.6

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 3.

(C) The advantage of reducing process variation, thereby causing problem limits to be at a greater number of standard deviations from the mean Reduces the process standard deviation and causes no change in the number of defects.

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To find the function that describes the frog population at time x weeks, let's analyze the given data:

Week 1: Population = P

Week 2: Population = Px

We can observe that the population increases by a factor of x from week 1 to week 2. Therefore, we can conclude that the growth factor is x.

(a) The function of the form f(x) = Pax that describes the frog population at time x weeks is:

f(x) = P * x^x

(b) The growth factor in this situation is x, which means each week's population is obtained by multiplying the previous week's population by x.

(c) Each tree frog requires 10 square feet of space, and the park has an area of 6.2 square miles. We can calculate the total area available in the park in square feet:

1 square mile = 52802 square feet

6.2 square miles = 6.2 * 52802 = 327166.4 square feet

Now, let's calculate the space required by the frog population after 12 weeks:

Week 12: Population = P * 12^12

Space required = Population * 10 square feet

Space required after 12 weeks = (P * 12^12) * 10 square feet

If this space required exceeds the size of the park (327166.4 square feet), then the frog population has outgrown the park. We can perform a similar calculation for 14 weeks.

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The equation of the function g(x) is g(x) = |x + 5|

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

The functions f(x) and g(x) on the graph

Also, we have

f(x) = |x|

The function f(x) is translated to the left by 5 units to get the function g(x)

This is represented as

g(x) = |x + 5|

Hence, the function g(x) is g(x) = |x + 5|

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The radius of the sector is 10.27 miles

The area of a sector can be represented as follows;

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅= 25 degrees

area of the sector  = 23 miles²

area of a sector = ∅ / 360 × πr²

23 = 25 / 360 × πr²

cross multiply

23 × 360  = 25πr²

8280 = 25πr²

divide both sides by 25

πr² =  8280 / 25

πr² =  331.2

r² =  331.2 / 3.14

r² = 105.477707006

r = √105.477707006

r = 10.2702336877 miles

Therefore, the radius of the sector is 10.27 miles

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Answer:

I don't know men iam grade 7 student

Answer:

The number of students who spend 4 hrs or more for reading = 25/100 = 1/4

we know 100 is a factor of 300

so equivalent fraction of (25/100)

× 3 = 75/300 = 1/4

.°.The simplest answer = 1/4 = 75/300

Hope it helps

Answer:

wait wait wait, is your profile picture from Genshin Impact?

if so I LOVE IT <3

A. The formula b = y * 40 - m.

B. The linear equation that represents the given situation can be written as b = 15.25 * 40 - 50

C. Margaret's disposable income for the week is $560.

Part A :

- y  : Margaret's earnings per hour, which is $15.25 in this situation.

- m : The amount Margaret takes from each paycheck and puts into her savings account, which is $50.

- z : The amount Margaret spends from each paycheck.

- b : Margaret's total earnings in a week after deducting the amount she puts into savings, which can be calculated using the formula b = y * 40 - m.

Part B :

The linear equation that represents the given situation can be written as:

b = 15.25 * 40 - 50

Part C:

The equation from Part B can be used to calculate Margaret's total earnings after saving a fixed amount from each paycheck. It helps to determine her disposable income after setting aside $50 in her savings account. In the equation:

- y represents Margaret's hourly wage, which is constant at $15.25 per hour.

- 40 represents the number of hours she works in a week (assuming a standard 40-hour workweek).

- m represents the amount she puts into her savings account each week, which is a fixed $50.

- b represents her remaining earnings after savings, also known as her disposable income for the week.

By substituting the values into the equation, we can calculate her disposable income:

b = 15.25 * 40 - 50

b = 610 - 50

b = 560

Hence, Margaret's disposable income for the week is $560. This equation is beneficial because it provides a straightforward way to calculate her remaining earnings after savings without the need to manually deduct $50 from her total earnings.

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Answer:

20.4

Step-by-step explanation:

The value of x when (°x+39) is alternate to 43° is 4

One of a pair of angles on opposite sides of a line intersecting two other lines and between the two intersected lines are called also alternate interior angle.

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These alternate angles are always equal

From the law that says that alternate angles are equal, thus:

(x+39)° = 43°

x = 43-39

x= 4

therefore the value of x is 4

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Therefore, the long answer to the given problem is that the sequence converges to a unique limit 30/7.

Given sequence is {an} = 3 - 0.3n, where n = 1, 2, 3,Now we need to determine whether the sequence converges or diverges. If it converges, then we have to find the limit. Let's find some initial terms for the given sequence for n = 1, 2, 3, 4,...an = 3 - 0.3n => a1 = 3 - 0.3(1) = 2.7a2 = 3 - 0.3(2) = 2.4a3 = 3 - 0.3(3) = 2.1a4 = 3 - 0.3(4) = 1.8Notice that as we increase the value of n, the terms of the sequence are decreasing.

Thus, {an} is a decreasing sequence. Now, let's find the limit of the sequence. If the sequence converges to a limit "L", then we have an → L as n → ∞ Therefore, L = lim n→∞ (3 - 0.3n)Using limit laws, we get L = Lim n→∞ 3 - lim n→∞ (0.3n) => L = 3 - 0, where 0 < r < 1Since 0 < r < 1, the limit exists. Hence the sequence converges to the limit L = 3/0.7. Hence the sequence converges to a unique limit, which is equal to 30/7.

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Answer:

21

Step-by-step explanation:

7x - 7

=> substituting x = 4

=> 7(4) - 7

=> 28 - 7

=> 21

Answer:

To graph the function, we need to first find the slope of the line passing through the given points:

slope = (change in y) / (change in x) = (1 - (-8)) / (10 - (-5)) = 9 / 15 = 3/5

Now we can use the point-slope form of the equation of a line to write the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the given points. Let's choose the point (10, 1):

y - 1 = (3/5)(x - 10)

Simplifying, we get:

y = (3/5)x - 17/5

Now we can use this equation to complete the table:

x y

-5 -11/5

-3 -7/5

0 -17/5

2 -13/5

5 -7/5

7 -1/5

10 1

To graph the function, we can plot the points from the table and draw a straight line passing through them.

Answer:

for the die it's a 4 to 6 chance and the coin is a 50% chance

Answer:

6) a

7) c

Step-by-step explanation:

question 6 is incorrect because you have to find the distance between the two points. for question 6, you are finding the distance between -2 and 1. that is three!

Answer: c

Step-by-step explanation:

Because the total should be at the end plus how much pounds it is so c

Since, the kite is taut the vertical height of the kite from the ground is 66.82 meters

A right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.

Therefore, the string length is the hypotenuse side. The angle formed is between 54 degree to 55 degrees. Therefore,

sin 54.5 = opposite / hypotenuse

sin 54.5 = h / 80

cross multiply

h = 80 × sin 54.5

h = 80 × 0.81411551835

h = 65.1292414685

Therefore, the vertical height of the ground from the ground is as follows:

vertical height = 65. 13 + 1.69 = 66.82 meters

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Answer:

24, 48, 96

Step-by-step explanation:

to find the next term in a geometric sequence, multiply the previous term by the common ratio r

r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{6}{3}\) = 2 , then

a₄ = a₃ × 2 = 12 × 2 = 24

a₅ = a₄ × 2 = 24 × 2 = 48

a₆ = a₅ × 2 = 48 × 2 = 96

the next 3 terms are 24, 48, 96

P(A|B) = 1/3

"A Venn diagram in mathematics is a diagram that uses overlapping circles or other shapes to represent the logical relationships between two or more sets of items. "

"For any experiment, a probability denotes the possibility of outcome for any event."

For event A, the probability of event A is,

P(A) = number of favorable outcomes/ total umber of outcomes

"Conditional probability is the probability of an event occurring given that another event has already occurred."

P(A|B) = P(A∩B)÷P(B)

For given diagram:

Let A represents a set of students playing Basketball and B represents a set of students playing Soccer

So, A = {Fran, Ian, Juan, Ella}

⇒ n(A) = 4

B = {Mickey, Marcus, Ella}

⇒ n(B) = 3

(A ∩ B) = {Ella}

⇒ n(A ∩ B) = 1

sample space: S = {Fran, Ian, Juan, Ella, Mickey, Marcus, Mai, Karl, Jada, Gabby}

⇒ n(S) = 10

Now, we calculate probability of B and A∩B.

P(B) = n(B)/n(S)

⇒ P(B) = 3/10

Also, P(A∩B) = n(A∩B) / n(S)

⇒ P(A∩B) = 1/10

So, the required probability would be,

⇒ P(A|B) = P(A∩B) ÷ P(B)

⇒ P(A|B) = (1/10) ÷ (3/10)

⇒ P(A|B) = 1/3

Therefore, P(A|B) = 1/3

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Answer:

5:46pm

Step-by-step explanation:

6:32 - :46 =

6:00 = :46 - :32 = :14

6:00 = 5:60

5:60 - :14 = :60 - :14 = :46

5:46

Answer: Choice D

\(\frac{9\sqrt{2}}{2}\)

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

Explanation:

We have a 45-45-90 triangle. If x is the leg length, then y = x*sqrt(2) is the hypotenuse.

Solving for y gets us \(x= \frac{y}{\sqrt{2}} = \frac{y\sqrt{2}}{2}\)

In this case, y = 9 is the hypotenuse which then leads to choice D.

------------

Another way to find the answer is to use the pythagorean theorem

a = x and b = x are the two congruent legs

c = 9 is the hypotenuse

Solving a^2+b^2 = c^2, aka x^2+x^2 = 9^2, will lead to \(x = \frac{9\sqrt{2}}{2}\)

Answer:it’s 1

Step-by-step explanation:

Just had it in a quiz

Step-by-step explanation:

plzz mark me as brainlest sorry if I dont know the answer I'm just 10 tho

Answer: 1: (2/v) 2: (3/m^4) 3: (4/x^4) 4: (1/k^3)

Step-by-step explanation:

When there is a negative exponent, the variable moves from the numerator (top) to the denominator (bottom), which gets rid of the negative sign in front of the exponent. MOVE ONLY THE VARIABLE AND CORRECT EXPONENT!!

The closest to the inverse notation is (d) 5

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

The graph of the function f(x)

The notation f'(7) implies that we determine the inverse of the function

From the graph, we have the following equation

f(5) = 7

This means that

f^-1(7) = 5

Hence, the closest is (d) 5

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Given:

Required:

To solve the given equation by factoring method.

Explanation:

Consider

And

Final Answer:

Answer:

--------------------

We see x - 2 is the common factor in the given expression.

Simplify as:

Answer:

10x - 20

Step-by-step explanation:

distribute the 3 and the 7 into the parentheses, getting you to (3x - 6) + (7x - 14), from there you should be able to just combine the like terms getting you to 10x - 20.

Answer:

a. 13.3

b. 16.3

Step-by-step explanation:

Hope this is right.