Which points are solutions to the linear inequality y < 0.5x 2? select three options.

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Regular hexagon ABCDEF is inscribed in a circle with center H, the image of segment BC after 120 degree clockwise rotation about point H is the segment joining the points B' and C', which has endpoints (-0.5r\(\sqrt{3\), -0.5r) and (-0.5r, -0.5r).

Since the hexagon is inscribed in a circle with center H, we can conclude that H is also the center of the circle passing through vertices B, C, and D. Therefore, the circle passing through B, C, and D is also a 120 degree clockwise rotation of the circle passing through A, B, and C.

To find the image of segment BC after a 120 degree clockwise rotation about point H, we need to find the coordinates of B and C relative to H, and then apply a 120 degree rotation matrix to these coordinates.

Let the radius of the circle be r, and let the coordinates of H be (0,0). Then the coordinates of B and C are:

B: (r cos(60), r sin(60))

C: (r cos(0), r sin(0)) = (r, 0)

To apply a 120 degree clockwise rotation matrix, we can use the following matrix:

[ cos(-120) -sin(-120) ]

[ sin(-120) cos(-120) ]

Simplifying, we get:

[ cos(120) sin(120) ]

[ -sin(120) cos(120) ]

Applying this matrix to the coordinates of B and C, we get:

B': [ cos(120) sin(120) ][ r cos(60) ] = [ -0.5r \(\sqrt{3}\)]

[ -sin(120) cos(120) ][ r sin(60) ] [ -0.5r ]

C': [ cos(120) sin(120) ][ r ] = [ -0.5r ]

[ -sin(120) cos(120) ][ 0 ] [ -0.5r ]

Therefore, the image of segment BC after a 120 degree clockwise rotation about point H is the segment joining points B' and C', which has endpoints (-0.5r\(\sqrt{3}\), -0.5r) and (-0.5r, -0.5r), respectively.

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According to the information we can infer that the term used for a subset of all Native Americans living in the territory that later became the 48 contiguous United States is "American Indians."

The term "American Indians" is often used to refer to the indigenous peoples who inhabited the land that now comprises the contiguous United States before the arrival of European settlers.

This term is used to differentiate them from Native peoples in Alaska and Hawaii, as well as from indigenous peoples in other regions of the Americas. While there are various tribal groups and nations within the subset of American Indians, the term generally encompasses those indigenous peoples who were living within the borders of the present-day contiguous United States.

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Answer:

-x+8

Step-by-step explanation:

8-4(x-6)=8-4x+24=-4x+32

(-4x+32)/4=-x+8

The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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Answer:

Step-by-step explanation:

Negative3 is6,8

Answer:

Negative3 is6,8

Step-by-step explanation:

i know it

Answer:

x = 18

Step-by-step explanation:

Solve for x:

6.2 = x - 11.8

6.2 = x - 11.8 is equivalent to x - 11.8 = 6.2:

x - 11.8 = 6.2

Add 11.8 to both sides:

x + (-11.8 + 11.8) = 11.8 + 6.2

11.8 - 11.8 = 0:

x = 6.2 + 11.8

6.2 + 11.8 = 18:

Answer: x = 18

Answer:

x-11.8=6.2

Step-by-step explanation:

add 11.8 for both sides

then x=11.8+6.2

the result of adding is 18

x=18.0

S.S={18.0}

The Venn diagram that represents the result of the survey is; Venn Diagram in Option A

Venn diagrams are used in sets in mathematics to group the union and intersection of subsets.

We are told that;

Number of students that enjoyed country = 32

Number of students that enjoyed jazz = 14

Number of students that enjoyed both country and jazz = 8

Now, the number of the students that enjoyed country and jazz should be the intersection of both circles in the venn diagram.

Secondly number of students that listened to only country = 32 - 8 = 24

Number that listened to only jazz = 14 - 8 = 6

Thus, the only correct option is Option A

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Answer:

4F-1

Theres infinite amount of solutions

Step-by-step explanation:

12f/3=4f

-3/3=-1

4f-1=4f-1

Answer:

f = 0

Step-by-step explanation:

\( \frac{1}{3} (12f - 3) = 4f - 1\)

Use ⅓ to open the bracket

\( \frac{1}{3} \times \: 12f = 4f \\ \frac{1}{3} \times 3= 1\)

\(4f - 1= 4f - 1\)

Collect like terms

\(4f - 4f = - 1+1 \\ - 1f = 0 \\ \\ f = 0\)

Step-by-step explanation:

1000ml=1 litre

800 divided by(1000 multiplied by 5)=16%

The algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

The statement is given as:

the difference of 27 and 5​

Difference means minus.

The minus sign is represented as -

This means that the statement given as: the difference of 27 and 5​

Can be represented as

27 minus 5

So, have

27 - 5

Hence, the algebraic expression of the statement given as the difference of 27 and 5​ is 27 - 5

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Answer:

The answer would be -9 and -3 which would be B and D

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

any number devide by itself is one

zero has 1 zero

0 divided by 0 is undefined, because it can't possibly create any groups to be split into.

Answer: Undefined

Answer:

at be 82.5 dollars you just have to 110-25% and get you $ 82.5

The require value of PQ is

A line on which numbers are marked at intervals, used to illustrate simple numerical operations.

Now, given coordinates of two points on number line are

P = -41

Q = 31

Since, PQ is the distance between to points P and Q on a number line.

So, PQ is the absolute value of the sum of their coordinates P and Q.

⇒PQ = |P| + |Q|

⇒PQ = 41 + 31

⇒PQ = 72

Hence the required value PQ is 72.

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To find the area of a triangle we use the formula (Base × Height) ÷ 2

The base of the triangle is 60 inches

the height of the triangle is 54 inches

Insert the values into the formula

(Base × Height) ÷ 2

(60 × 54) ÷ 2

3240 ÷ 2

1620

The area of the triangle is 1620 square inches

Alice's percentage profit is approximately 32.91%, rounded to one decimal place.

In essence, percentages are fractions with a 100 as the remainder. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on an examination (75/100).

Alice bought the pack of 14 candy bars for £6.32, which means she paid:

\($\frac{6.32}{14} \approx 0.4514$\) per candy bar

She sells each candy bar for 60p, which is equivalent to:

\($\frac{60}{100} = 0.6$\) pounds per candy bar.

So her revenue from selling all 14 candy bars is:

\($14 \times 0.6 = 8.4$\) pounds.

Her profit is then:

\($8.4 - 6.32 = 2.08$\) pounds.

To find the percentage profit, we need to calculate the profit as a percentage of the cost:

\($\frac{2.08}{6.32} \times 100 \approx 32.91%$\)

Therefore, Alice's percentage profit is approximately 32.91%, rounded to one decimal place.

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Answer:

c and d

Step-by-step explanation:

Answer:C and D

Step-by-step explanation:

Answer:

Its a b d and f

Step-by-step explanation:

I hope I helped

the standard error of the distribution is 0.0479 (rounded to four decimal places).

Given that the true proportion of voters in the county who support a restaurant tax is 0.38, and we want to consider the sampling distribution for the proportion of supporters with a sample size of n = 102.

The mean of the sampling distribution is equal to the true proportion, which is 0.38.

The standard error of the sampling distribution is given by the formula:

Standard error = \(\sqrt{ [(p * (1-p)) / n]}\)

where p is the true proportion, and n is the sample size.

Plugging in the values, we get:

Standard error = \(\sqrt{[(0.38 * (1-0.38)) / 102]}\)

= \(\sqrt{[(0.38 * 0.62) / 102]}\)

= \(\sqrt{ [0.002296]}\)

= 0.0479 (rounded to four decimal places)

Therefore, the standard error of the distribution is 0.0479 (rounded to four decimal places).

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a) The probability of selecting a jar with a weight between 848 and 854 grams can be determined by finding the area under the bell curve within that range.

Since the distribution is normal with a mean (u) of 850 grams and a standard deviation (σ) of 8 grams, we can calculate the z-scores for the lower and upper limits of the range. The z-score formula is (x - u) / σ, where x is the value, u is the mean, and σ is the standard deviation. For the lower limit, the z-score is (848 - 850) / 8 = -0.25, and for the upper limit, the z-score is (854 - 850) / 8 = 0.5.The probability of the weight being between 848 and 854 grams is the difference between these probabilities.

b) To find the probability of a random sample of 32 jars having a mean weight between 848 and 854 grams, we can use the Central Limit Theorem (CLT). The CLT states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. In this case, since the sample size is 32, we can assume that the distribution of sample means will be approximately normal. The mean of the sample means will be the same as the population mean, which is 850 grams. The standard deviation of the sample means, also known as the standard error of the mean (SE), is calculated by dividing the population standard deviation by the square root of the sample size, i.e., σ / √n. In this case, the SE is 8 / √32 ≈ 1.41 grams. We can then calculate the z-scores for the lower and upper limits of the range using the formula (x - u) / SE, where x is the value, u is the mean, and SE is the standard error.

c) To find the probability that a random sample of 32 jars has a mean weight greater than 853 grams, we can again use the Central Limit Theorem. The mean of the sample means will still be 850 grams, but the standard deviation of the sample means (SE) remains 1.41 grams.The probability can be determined by finding the area under the standard normal curve to the right of this z-score.

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The limit of the given expression exists and is equal to 1 + [1 + √(5)]/2.

To solve this problem, we can't simply substitute 1 into the expression because that would result in an undefined expression (division by zero). Instead, we have to use the concept of limits.

First, we can simplify the expression by factoring the numerator using the quadratic formula: (x² - x - 1) = (x - [1 + √(5)]/2)(x - [1 - √(5)]/2). Then, we can cancel out the (x-1) factor in both the numerator and denominator.

After simplification, we get the expression (x + [1 + √(5)]/2), which is a continuous function. Since the function is continuous at x = 1, we can substitute x = 1 into the expression to find the limit.

Therefore, the limit as x approaches 1 of (x² - x - 1)/(x - 1) exists and is equal to 1 + [1 + √(5)]/2.

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a) The break-even points for the given cost and revenue functions are approximately x = 16.526 and x = 6.474.

b) The break-even points for the given cost and revenue functions are approximately x = 12.225 and x = 62.775.

c) The maximum profit for the given cost and revenue functions is approximately $843.75.

a) To find the break-even points, we need to determine the values of x where the total costs (C(x)) equal the total revenues (R(x)). We set C(x) = R(x) and solve for x:

C(x) = R(x)

1760 + 8x + 0.6x² = 100x - 0.4x²

Combining like terms and rearranging the equation, we get:

1x² - 92x + 1760 = 0

Solving this quadratic equation, we find two solutions for x:

x ≈ 16.526

x ≈ 6.474

b) Similarly, we set C(x) = R(x) and solve for x:

900 + 25x = 100x - x²

Rearranging the equation, we get:

x² - 75x + 900 = 0

Solving this quadratic equation, we find two solutions for x:

x ≈ 12.225

x ≈ 62.775

c) To find the maximum revenue, we need to determine the vertex of the revenue function R(x) = 100x - x². The x-coordinate of the vertex is given by x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -1 and b = 100. Plugging in the values, we get:

x = -100 / (2 * -1) = 50

Substituting this value back into the revenue function, we find:

R(50) = 100(50) - (50)² = 5000 - 2500 = 2500

Therefore, the maximum revenue for the given cost and revenue functions is $2500.

To find the maximum profit, we need to subtract the total costs from the total revenues. Given that the cost function is C(x) = 900 + 25x, the profit function is P(x) = R(x) - C(x). Substituting the revenue and cost functions, we have:

P(x) = (100x - x²) - (900 + 25x)

P(x) = -x² + 75x - 900

To find the maximum profit, we need to determine the vertex of the profit function. Using the same formula as before, we find:

x = -75 / (2 * -1) = 37.5

Substituting this value back into the profit function, we find:

P(37.5) = -(37.5)² + 75(37.5) - 900 ≈ 843.75

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Answer:7³=343

343 × M = 343m

Step-by-step explanation:

7×7×7=343

If the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.

Let's go through the problem step by step to find the area of the rectangle.

Let's assume that the length of the rectangle is represented by the variable "x" (as stated in the question). According to the given information, the width of the rectangle is 58 units less than its length.

If the width is 58 units less than the length, we can represent the width as (x - 58). This means that the length minus 58 gives us the width.

Now, to find the area of the rectangle, we use the formula:

Area = Length × Width

Substituting the values we have:

Area = x × (x - 58)

Expanding the equation:

Area = x² - 58x

So, the area of the rectangle is given by the expression x² - 58x.

To summarize, if the length of the rectangle is represented by "x," then the width is (x - 58), and the area can be calculated as x² - 58x.

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Answer:

P is equal to (0, -12/5)

Step-by-step explanation:

In order to find the coordinate P there would have to be a ratio from the bigger triangle to the smaller triangle. If you were to set up a ratio it would probably look something like this \(\frac{-10}{-4}\) to \(\frac{-6}{x}\) because it has to be consistent so if you had a big triangle to small triangle it would be big triangle coordinates to small triangle coordinates. Then you would solve for x which  would be equal to\(\frac{-12}{5}\) and the coordinates would be (0, -12/5) because it is on the y intercept so x would be equal to 0 and y would be equal to the number you just solved for or -12/5. Then if you were to find the ratio it would be -10/-4 or 5/2.

Answer: The answer is A. 4x+2y>_-4

Step-by-step explanation:

Answer: 28 dollars is the answer.

Step-by-step explanation: 7x4=28