Match the graph
with its inequality.

I tried but got the wrong answer. Can someone help and explain?

Since the value of y varies directly with x, the value of x when y equals 9 is 9/13

Given the following data:

x = 195

y = 15

To find the value of x when y = 9:

This is a direction proportion exercise and you're required to solve for the value of x when the value of y is equal to 9.

First of all, we would determine the constant of proportionality (k) for the mathematical expression.

y = kx

15 = 195k

k = 13

Now, we can find x:

y = kx

9 = 13 x

x = 9/13

Therefore, the value of x when y equals 9 is 9/13

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complete question:

The value of y varies directly with x. If x = 195 when y = 15, what is the value of x when y = 9?

a. It represents the spread of the middle 50% of the data.

b. At least 50% of the students scored between 80 and 86.

c. Overall, we can say that the Math 6 class had a range of test scores, with some students performing very well and others performing less well.

How evenly distributed the middle 50% of the data is is determined by the interquartile range. In order to calculate it, the first quartile is subtracted from the third quartile.

A. The interquartile range (IQR) in a box-and-whisker plot is the distance between the first quartile (Q1) and the third quartile (Q3) of the data. It represents the spread of the middle 50% of the data.

B. To determine what percent of the students got 80% or higher, we need to find the upper fence, which is defined as 1.5 times the IQR above Q3. From the box-and-whisker plot, we can see that Q3 is approximately 86 and Q1 is approximately 71. Therefore, the IQR is 86 - 71 = 15. The upper fence is 1.5 * 15 + 86 = 108.5.

Looking at the plot, we can see that there are no data points above 100, so we can safely assume that no students scored above 100%. The highest score is 94, which is within the whiskers of the box-and-whisker plot. Therefore, we know that the percent of students who scored 80% or higher is between the percent of students who scored 80% or higher and the percent of students who scored 94% or higher.

From the plot, we can see that the median is approximately 80 and the third quartile (Q3) is approximately 86. This means that at least 50% of the students scored between 80 and 86. Additionally, we know that the maximum score is 94, so we can say that at least some students scored higher than 86. However, we don't know how many students scored between 86 and 94.

C. Based on the interquartile range, we can say that the middle 50% of the students scored between approximately 71 and 86. This suggests that there is a significant amount of variability in the test scores, as the range is quite wide. Additionally, we know that at least some students scored above 86, but we don't have enough information to determine how many or how high their scores were. Overall, we can say that the Math 6 class had a range of test scores, with some students performing very well and others performing less well.

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Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

Answer:

Daytime people.

Step-by-step explanation:

Evening people have 125.

Daytine people have 140.

Answer:

B

Step-by-step explanation:

sorry if I am wrong

but you got what it takes to do it ⭐⭐⭐⭐⭐

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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A) The Number of Combinations if there are no restrictions on the seating arrangements are 5040 ways.

B) There are three friends That must sit together

in 36 ways.

C) Three friends are next To each other in 144 different ways.

Total number of people = 7 and seated in a row.

Combination is arrangement of objects in a particular order. The formula of combination is

ⁿCₓ = n!/(n-x)! x!

n --> total number of objects

we have to determine how many ways can 7 be seated in a row.

A) if there are no restrictions on seating arrangement, The number of possible ways = n!

Here, n! = 7!

= 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040 ways.

Therefore, there are 5040 ways that the people can be seated when there is no restriction on the seating arrangement.

b) There are three friends that must sit Together. The three persons can be arranged in 3!

The possible number of ways = 3! × 3! × 1

= 3× 2×1 ×3×2×1

= 36

C) If there are three friends must sit next to one another. There are total seven persons . Three persons sit next to one another. The possible number of ways = 3! × 4!

= ( 3 × 2 × 1) × (4 × 3 × 2 × 1)

= 6 × 24

= 144 ways

Therefore, if there are 3 sit next to one another, there are 144 ways of seating arrangement.

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Answer:

Step-by-step explanation:

Formula = V = l x w x h

V = 4.25 x 2.75 x 5

V = 58.438 --> 58.44

The equation of the line containing the paints A and B is y = -1/3x + 4

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

The graph

Where, we have

(6, 2) and (0, 4)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 4

Using the other points, we have

6m + 4 = 2

So, we have

6m = -2

Evaluate

m = -1/3

So, we have

y = -1/3x + 4

As an equation, we have

y = -1/3x + 4

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Answer:

seven ninths

Step-by-step explanation:

Answer:

(a) The function has a minimum value

(b) The minimum value is 2

Step-by-step explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.  

We know that for our function a = 1.

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1:  First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.  

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2:  Now we can plug in -2 for x in the quadratic function.  The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.

Answer:

Step-by-step explanation:

you just gotta add all the side-lengths together and consider each grid square as 10 instead of 1.

so 70 + 40 + 20 + 60 + 20 + 40 i believe.

this all equals 250.

ask your teacher if its a type, because there's no 250 on there. grab a calculator or something as proof.

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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Answer:

\(\huge \boxed{\mathrm{12}}\)

Step-by-step explanation:

R is a point on the line segment QS.

QR = 2

RS = 10

QS = 2 + 10

QS = 12

The length of the line segment QS is 12 units.

Given that, point R is on the line segment QS. Given QR =2 and RS = 10.

We need to determine the length of QS.

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.

Here, since R is in between QS, QS=QR+RS

=2+10=12 units

Therefore, the length of the line segment QS is 12 units.

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Answer:

A. the graph represent a one - to - one function because every x-value is paired with only y-value

Step-by-step explanation:

that's it

Answer:

C

Step-by-step explanation:

Exponential form is y = b^x, with b as the base, and logarithmic form is x = log_b(y).

In this case, 10 is the base, 4 is x, and 10,000 is y. In logarithmic form, this can be changed into 4 = log_10(10,000). Logarithms with base 10 can also be written as 4 = log(10,000). Therefore C is the correct answer.

Answer:

The first one

Step-by-step explanation:

She cant buy anything over $15, but she can buy something thats $15 :))

Optimizing function describes the minimum or maximum output from the function.

The factory should make 3 David statues and 4.5 Liberty statues

The constraints and the objective function are given as:

\(\mathbf{18L + 27 D \le 162}\)

\(\mathbf{36L + 18 D\le 216}\)

\(\mathbf{7L + 7D \le 49}\)

\(\mathbf{Objective:\ Income = 63L+ 96D}\)

We start by plotting the graphs of the inequalities, where L is represented on the vertical axis, and D on the horizontal axis

From the graph, the only optimal point is: D = 3 and L = 4.5

Hence, the factory should make 3 David statues and 4.5 Liberty statues

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The requried population increased by approximately 60.53%.

To find the absolute increase, we subtract the initial population from the final population:

Absolute increase = Final population - Initial population

Absolute increase = 6100 - 3800

Absolute increase = 2300

Therefore, the population increased by 2300 people.

To find the relative increase, we first calculate the percent change:

Percent change = (New value - Old value) / Old value x 100%

Percent change = (6100 - 3800) / 3800 x 100%

Percent change = 2300 / 3800 x 100%

Percent change = 60.53%

Therefore, the population increased by approximately 60.53%.

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1. When we simplify sec² x + tan² xsec² x, the result obtained is sec⁴x

2. When we simplify (sec² x - 1) / sin² x, the result obtained is sec² x

3. When we simplify (1/sec² x) + (1/csc² x), the result obtained is 1

4. When we simplify (sec x / sin x) - (sin x / cos x), the result obtained is cot x

5. When we simplify (1 + sin x)(1 - sin x), the result obtained is cos² x

6.  When we simplify cos x + sin xtan x, the result obtained is sec x

We can simplify the trig identities as follow:

1. Simplification of sec² x + tan² xsec² x

sec² x + tan² xsec² x = sec² x(1 + tan² x)

Recall

sec² x = 1 + tan² x

Thus,

sec² x(1 + tan² x) = sec² x × sec² x

sec² x(1 + tan² x) = sec⁴x

Therefore, the simplified is written as

sec² x + tan² xsec² x = sec⁴x

2. Simplification of (sec² x - 1) / sin² x

(sec² x - 1) / sin² x

Recall,

sec² x - 1 = tan² x

Thus,

(sec² x - 1) / sin² x = tan² x / sin² x

Recall

tan² x = sin² x / cos² x

Thus,

tan² x / sin² x = (sin² x / cos² x) / sin² x

tan² x / sin² x = 1/ cos² x

Recall

1/ cos² x = sec² x

Therefore, the simplified expression is written as:

(sec² x - 1) / sin² x = sec² x

3. Simplification of (1/sec² x) + (1/csc² x)

(1/sec² x) + (1/csc² x)

Recall

sec² x = 1/cos² x

Thus,

cos² x = 1/sec² x

Also,

csc² x = 1/sin² x

Thus,

sin² x = 1/csc² x

Therefore, we have

(1/sec² x) + (1/csc² x) = cos² x + sin² x

Recall

cos² x + sin² x = 1

Thus, the simplified expression of (1/sec² x) + (1/csc² x) is:

(1/sec² x) + (1/csc² x)  = 1

4. Simplification of (sec x / sin x) - (sin x / cos x)

(sec x / sin x) - (sin x / cos x) = (sec xcos x - sinx sinx) / sinx cos x

Recall

sec x = 1/cos x

sinx sinx = sin² x

Thus,

(sec x / sin x) - (sin x / cos x) = [(cos x/cos x) - sin² x] / sinx cos x

(sec x / sin x) - (sin x / cos x) = [1 - sin² x] / sinx cos x

Recall

1  - sin² x = cos² x

Thus, we have

[1 - sin² x] / sinx cos x = [cos² x] / sinx cos x

[1 - sin² x] / sinx cos x = cos x / sin x

Recall

cos x / sin x = cot x

Thus, the simplified expression of (sec x / sin x) - (sin x / cos x) is:

(sec x / sin x) - (sin x / cos x) = cot x

5. Simplification of (1 + sin x)(1 - sin x)

(1 + sin x)(1 - sin x)

Clear bracket

1 - sin x + sin x - sin² x

1 - sin² x

Recall

1 - sin² x = cos² x

Thus, we have

(1 + sin x)(1 - sin x) = cos² x

6. Simplification of cos x + sin xtan x

cos x + sin xtan x

Recall

tan x = sin x / cos x

cos x + sin xtan x = cos x + sin x (sin x / cos x)

cos x + sin xtan x = cos x + (sin² x / cos x)

cos x + sin xtan x = (cos² x + sin² x) / cos x

Recall

cos² x + sin² x = 1

cos x + sin xtan x = 1 / cos x

1/cos x = sec x

Thus,

cos x + sin xtan x = sec x

The simplified expression of cos x + sin xtan x is sec x

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Answer:

A

Step-by-step explanation:

Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.

Step-by-step explanation:

Answer:

4 1/2

Step-by-step explanation:

3(1/3) divided by 2(3)2nd power

Answer:

\(P(Red) = \frac{7}{25}\)

Step-by-step explanation:

Given

\(Red = 35\)

\(Blue = 40\)

\(Green = 50\)

Required

Determine the probability of red

\(P(Red) = \frac{n(Red)}{Total}\)

Substitute value for n(Red) and calculate Total

\(P(Red) = \frac{35}{35 + 40 + 50}\)

\(P(Red) = \frac{35}{125}\)

Divide numerator and denominator by 5

\(P(Red) = \frac{7}{25}\)

Rewrite the limit as

\(\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = \lim_{x\to0} \frac{5x}{\sin(5x)} \cdot \lim_{x\to0} \frac{\cos(5x)}5\)

Then using the known limit,

\(\displaystyle \lim_{x\to0} \frac{\sin(x)}x = 1 \implies \frac1{\lim\limits_{x\to0}\frac{\sin(x)}x} = \lim_{x\to0}\frac x{\sin(x)}=1\)

it follows that

\(\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = 1 \cdot \frac{\cos(0)}5 = \boxed{\frac15}\)

The correct answer is B. 0.00

Explanation:

In statistics, two events are mutually exclusive if only one event can occur at one time. For example, if you have a deck of cards with Hearts and Spades, every time you choose a card you will have either Hearts or Spades but not both at the same time as there is not any card that combines Hearts and Spades in the same card. This means it is statistically impossible for two mutually exclusive events to occur at the same time, which means the probability is 0.00.

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.