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The parallelogram H’I’J’K is a dilation of the parallelogram HIJK. What is the scale factor of the dilation?

Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

PLEASE LOOK AT PICTURE!!!!!!

The probability that a randomly selected person actually went on holiday that year is 0.727

Out of the 55 adults surveyed, 25 went abroad and 15 went on holiday in the UK.

Therefore, the total number of people who went on holiday is 25 + 15 = 40

The probability of selecting a person who went on holiday is the number of people who went on holiday divided by the total number of people surveyed:

P(went on holiday) = 40/55

Simplifying the fraction, we get:

P(went on holiday) = 8/11

Rounding to three decimals, we get:

P(went on holiday) = 0.727

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Pull a green cube 50 times; Pull a blue cube 70 times. The possible options are B and E.

Probability refers to the likelihood or chance of an event occurring, expressed as a number between 0 and 1.

A probability of 0 indicates that an event is impossible, while a probability of 1 indicates that an event is certain to occur. For example, the probability of rolling a 7 on a fair six-sided die is 0, while the probability of rolling a 1, 2, 3, 4, 5, or 6 is 1/6.

Probabilities can also be expressed as percentages, with a probability of 0.5 (or 50%) indicating an even chance of an event occurring.

A) Pull more than 2 times as many green cubes as blue cubes:

Since there are only 2 blue cubes in the bag and 5 green cubes, it is highly unlikely that you would pull more than 2 times as many green cubes as blue cubes in 100 draws. Therefore, this option is unlikely.

B) Pull a green cube 50 times:

There are 5 green cubes in the bag, so it is possible to pull a green cube 50 times in 100 draws. Therefore, this option is possible.

C) Pull a blue cube 20 times:

There are only 2 blue cubes in the bag, so it is unlikely that you would pull a blue cube 20 times in 100 draws. Therefore, this option is unlikely.

D) Pull more red cubes than green cubes:

There are 3 red cubes and 5 green cubes in the bag, so it is possible to pull more red cubes than green cubes in 100 draws. Therefore, this option is possible.

E) Pull a blue cube 70 times:

Since there are only 2 blue cubes in the bag and you are drawing with replacement, it is highly unlikely that you would pull a blue cube 70 times in 100 draws. Therefore, this option is unlikely.

Therefore, options B and D are possible.

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Answer:

x = 63 , y = 90

Step-by-step explanation:

assuming DF is the diameter of the semicircle , then

∠ DEF = y = 90° ( angle inh a semicircle )

then

x + y + 27° = 180° ( angle sum of a triangle )

x + 90 + 27 = 180

x + 117 = 180 ( subtract 117 from both sides )

x = 63

Answer:

Step-by-step explanation:

To find the inventory turnover for Roselli's Machine Manufacturing Co, we need to use the formula:

Inventory turnover = Cost of goods sold / Average inventory

First, we need to find the cost of goods sold (COGS):

COGS = Sales - Gross profit

COGS = R120 000 - R50 000

COGS = R70 000

Next, we need to find the average inventory. We can use the quick ratio formula to find the current assets:

Quick ratio = (Current assets - Inventory) / Current liabilities

Rearranging the formula to solve for inventory, we get:

Inventory = Current assets - (Quick ratio x Current liabilities)

Plugging in the values we know, we get:

1.75 = (Current assets - Inventory) / R25 000

Current assets - Inventory = 1.75 x R25 000

Current assets - Inventory = R43 750

Inventory = Current assets - R43 750

Since the current ratio is 2.5, we know that:

Current assets / Current liabilities = 2.5

Solving for current assets, we get:

Current assets = 2.5 x R25 000

Current assets = R62 500

Substituting the values we found for inventory and COGS into the inventory turnover formula, we get:

Inventory turnover = COGS / Average inventory

Inventory turnover = R70 000 / [(R62 500 - R43 750) / 2]

Inventory turnover = R70 000 / (R18 750 / 2)

Inventory turnover = R70 000 / R9 375

Inventory turnover = 7.47

Therefore, the inventory turnover for Roselli's Machine Manufacturing Co is 7.47.

To assess the reasonableness of Cameron's statement that he spent about $215 on a gaming system and video games, we can use mental math to estimate the total cost.

We know that he spent $130 on a gaming system and $80 on video games. If we round $80 up to $100 and add it to $130, we get:

$130 + $100 = $230

So based on this estimate, it seems like Cameron's statement of spending about $215 is not entirely accurate. However, it is close to the actual total cost, which is within 10% of the estimated total.

Therefore, we can say that while Cameron's statement may not be entirely precise, it is reasonably close to the actual total cost and can be considered reasonable.

Answer:

40 5/8

Step-by-step explanation:

6 1/2 × 2 1/2

13/2 × 5/2= 65/4

65/4 × 2 1/2

65/4 × 5/2 = 325/8

325/8= 40 5/8

Answer:

40 5/8

Step-by-step explanation:

6 1/2 × 2 1/2

13/2 × 5/2= 65/4

65/4 × 2 1/2

65/4 × 5/2 = 325/8

325/8= 40 5/8

Answer:

Method 1: Distributive Property

To multiply (3x - 4) and (2x - 1), we can use the distributive property:

(3x - 4)(2x - 1) = 3x(2x) + 3x(-1) - 4(2x) - 4(-1)

= 6x^2 - 3x - 8x + 4

= 6x^2 - 11x + 4

Therefore, the final answer in standard form is 6x^2 - 11x + 4.

Method 2: FOIL

To multiply (3x - 4) and (2x - 1), we can use the FOIL method:

(3x - 4)(2x - 1) = 3x(2x) + 3x(-1) - 4(2x) - 4(-1)

= 6x^2 - 3x - 8x + 4

= 6x^2 - 11x + 4

Therefore, the final answer in standard form is 6x^2 - 11x + 4.

The larger angle of the right triangle is 139 degrees.

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle. The third side is called the hypotenuse, which is the longest side of all three sides.

The three sides of the right triangle are related to each other. This relationship is explained by Pythagoras theorem

In a right triangle, one of the angles is 90 degrees. Let x be the measure of the other acute angle. Then we have:

sin x = cos (90° - x)

We can use this identity to rewrite the given equation as:

sin (9x - 4)° = sin (90° - (10x - 1)°)

Using the identity sin (90° - θ) = cos θ, we can simplify this equation to:

sin (9x - 4)° = cos (10x - 1)°

sin (9x - 4)° = sin ((90°) - (10x - 1)°)

sin (9x - 4)° = sin (10x - 91)°

Since sin θ = sin (180° - θ), we have:

9x - 4 = 180° - (10x - 91)°

9x - 4 = 271° - 10x

Simplifying and solving for x, we get:

19x = 275

x = 275/19

Now, the larger angle of the right triangle is either 9x - 4 or 10x - 1, depending on which is larger. We can calculate both angles and compare them:

9x - 4 = 9(275/19) - 4 = 121°

10x - 1 = 10(275/19) - 1 = 139°

Therefore, the larger angle of the right triangle is 139 degrees.

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a) The expected (mean) number of shots that Zlatan Ibrahimović must make to score a goal is 3.11.

b) The standard deviation of the distribution is 2.46.

The expected number or mean (μ) of a distribution is computed as sum resulting from the multiplication of each value of the random variable by its probability and adding the products.

The formula for the mean is given as E(x) = ∑x P(x).

On the other hand, to compute the standard deviation (σ) of a probability distribution, we find each deviation from its expected value, square it, multiply it by its probability, add the products, and take the square root.

No. of shots    Probability    Expected        Squared      Squared Deviation

                       of scoring    No. of shots     Deviation     x Probability

0                         0.02               0                   9.6721            0.193442

1                          0.13                0.13               8.8804           1.154452

2                         0.34               0.68              5.9049          2.007666

3                         0.32               0.96              4.6225          1.4792

4                         0.16                0.64              6.1009          0.976144

5                         0.02               0.1                9.0601            0.181202

6                         0.01               0.6                6.3001            0.063001

The expected (mean)

 number of shots =                3.11                                     6.055107

Standard Deviation = Square root of 6.055107 = 2.46

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Answer:

Unfortunately, I cannot see the graph you are referring to since we are communicating through text. However, based on the information given, we can make some general observations.

We know that Natasha received a raise in her hourly rate of pay at some point during the year. Before the raise, she earned some initial hourly rate of pay. Let's call this initial rate of pay "x". Let's also assume that she worked for "h" hours before receiving the raise, and "k" hours after receiving the raise.

We can write an equation to represent the total amount of money she made this year:

Total amount of money = (initial hourly rate of pay x number of hours worked at the initial rate) + (new hourly rate of pay x number of hours worked at the new rate)

Using the variables we defined earlier, we can write:

Total amount of money = (x × h) + ((x + y) × k)

where y is the increase in her hourly rate of pay after the raise.

We also know that she earned a certain amount of money before the raise. Let's call this amount "M". This means that:

M = x × h

Solving for x, we get:

x = M/h

Substituting this expression for x into the first equation, we get:

Total amount of money = (M + yh) + ((M/h + y) × k)

We don't know the values of M, y, h, or k, so we cannot determine the initial hourly rate of pay x or the total amount of money Natasha made this year. However, we have set up an equation that can be used to solve for these values if we have more information.

The correct answer is sixteen (16).

The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.

So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:

(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons

Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be  approximately 6.58 gallons.

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The complete question is :

What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?

The principle of mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.

It is based on the idea that if the statement is true for one number, then it can be used to prove that it is true for the next number. Mathematical induction can be expressed mathematically as follows:

Let P(n) be a statement involving an integer n

Base Case: P(m) is true for some m

Induction Hypothesis: Assume P(k) is true for some k>m.

Induction Step: Show that P(k+1) is true.

Therefore, P(n) is true for all n>m

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Samir's fruit salad has a higher percentage of melon and will taste more melony than Kylie's fruit salad.

Percentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol % (percent).

In the given question,

To determine whose fruit salad will taste more melony, we need to calculate the percentage of melon in each fruit salad.

For Samir's fruit salad:

The total amount of fruit is 1 + 3 = 4 cups

The amount of melon is 1 cup

The percentage of melon is (1/4) x 100% = 25%

For Kylie's fruit salad:

The total amount of fruit is 2 + 9 = 11 cups

The amount of melon is 2 cups

The percentage of melon is (2/11) x 100% = 18.18% (rounded to two decimal places)

Therefore, Samir's fruit salad has a higher percentage of melon and will taste more melony than Kylie's fruit salad.

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Answer:

[tex]\boxed {\left(-1, -\dfrac{3}{7}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{1}{2}\left|x\:+\:1\right|-\frac{3}{7}}[/tex]

[tex]\boxed{\left(5,\:\frac{2}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{3}{5}\left|x\:-\:5\right|+\:\frac{2}{3}}[/tex]

[tex]\boxed{\left(0,\:-\frac{4}{5}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{1}{2}\left|x\right|\:-\:\frac{4}{5}}[/tex]

[tex]\boxed{\left(\frac{2}{5},\:\frac{5}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{3}{2}\left|x-\frac{2}{5}\right|+\frac{5}{3}}[/tex]

Step-by-step explanation:

The vertex of an absolute function
y = f(x) = a|x - b| + c occurs at x - b = 0 or when x = b

Plugging this  into the original equation will give the value for f(b) which will be f(b) = 0 + c which will be the y-value of the vertex

[tex]\text{Vertex of } f(x) = \dfrac{3}{5} |x - 5| + \dfrac{2}{3}\\\\ \longrightarrow x = 5, y = \dfrac{2}{3} \\\\\longrightarrow \left(5, \dfrac{2}{3} \right)[/tex]

You can do the others in a similar manner.

Here it is easier because the constant in f(x) corresponds to the y-coordinate of the vertex and they are different in the answer choices

Answer:

[tex]\text{Slope} \; m = \dfrac{11}{6}[/tex]

Step-by-step explanation:

[tex]m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x}[/tex]

[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \dfrac{-1/4 - 5/2}{-1/2 - 1}[/tex]

[tex]m = \dfrac{\dfrac{-11}{4}}{\dfrac{-3}{2}}[/tex]

[tex]m = \dfrac{-11}{4} \times \dfrac{2}{-3}[/tex]

[tex]m = \dfrac{-22}{-12}[/tex]

[tex]m = \dfrac{11}{6}[/tex]

Answer:

12,500 is 100%, or 1 in decimal terms. We calculate 5% by multiplying 12500 by 0.05.

This gives us a total of £625

Step-by-step explanation:

Brainliest pls

a. The cost of one large pizza with one topping is $13.50. To purchase one large and five medium pizzas, we would need to buy one large pizza at regular price and five medium pizzas at the discounted price. The cost of the large pizza is $13.50, and the cost of each medium pizza is $6.25. Therefore, the total cost would be:

Total cost = Cost of large pizza + Cost of 5 medium pizzas

Total cost = $13.50 + ($6.25 x 5)

Total cost = $13.50 + $31.25

Total cost = $44.75

Therefore, it would cost $44.75 to purchase one large pizza and five medium pizzas.

b.Number of medium pizzas Total cost

0 | $13.50

1 | $19.75

2 | $26.00

3 | $32.25

4 | $38.50

c. Let "m" be the number of medium pizzas. Then the total cost of purchasing one large pizza with one topping and m medium pizzas can be represented as:

Total cost = 13.50 + 6.25m

d. If you have a total of $100 and purchase one large pizza, you would have $100 - $13.50 = $86.50 left to spend on medium pizzas. The cost of each medium pizza is $6.25. Therefore, you can buy:

Number of medium pizzas = $86.50 ÷ $6.25 = 13.84

Since you cannot buy a fraction of a pizza, you can only buy 13 medium pizzas with $86.50.

e. The area of a pizza is given by the formula A = πr^2, where A is the area and r is the radius. The area of a large pizza is:

A = πr^2

A = 3.14 x 8^2

A = 3.14 x 64

A = 200.96

The area of a medium pizza is:

A = πr^2

A = 3.14 x 5^2

A = 3.14 x 25

A = 78.5

Therefore, the total area of one large pizza and five medium pizzas is:

Total area = Area of large pizza + (Area of medium pizza x 5)

Total area = 200.96 + (78.5 x 5)

Total area = 200.96 + 392.5

Total area = 593.46

Rounding to the nearest inch, the total area of pizza is 593 square inches.

f. To calculate the cost per square inch of pizza, we need to divide the total cost of the pizzas by the total area of the pizzas. The total cost of one large pizza and five medium pizzas is $44.75, and the total area is 593 square inches. Therefore, the cost per square inch of pizza is:

Cost per square inch = Total cost / Total area

Cost per square inch = $44.75 / 593

Cost per square inch = $0.08 (rounded to the nearest cent)

Therefore, the cost per square inch of pizza is 8 cents.

Answer:

To solve the linear programming problem, we need to first graph the feasible region determined by the constraints, and then evaluate the objective function at each corner point of the feasible region to find the maximum value of z.

Plotting the lines corresponding to the inequalities, we get:

Graph of the feasible region:

The feasible region is the shaded polygon in the graph. We can see that the vertices of the feasible region are (2, 9), (2, 12), (4, 7), and (8, 2).

Next, we evaluate the objective function at each of these vertices to find the maximum value of z.

At (2, 9): z = 7x + 2y = 7(2) + 2(9) = 23

At (2, 12): z = 7x + 2y = 7(2) + 2(12) = 31

At (4, 7): z = 7x + 2y = 7(4) + 2(7) = 35

At (8, 2): z = 7x + 2y = 7(8) + 2(2) = 58

Therefore, the maximum value of z is 58, which occurs at the point (8, 2).

Hence, the answer is: the maximum value of z is 58.

Answer:

12

Step-by-step explanation:

Mean = 3+22+0+15+9+23=72

72÷6 =12

The equation y = -1/2(x-3)² + 5  reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.

In mathematics, a graph is a visual representation of a set of objects (called vertices or nodes) and the connections (called edges) between them.

The equation y = -1/2(x-3)² + 5 is a quadratic function in vertex form. The vertex of this parabola is at the point (3, 5), and the coefficient of the x²  term is negative (-1/2), which tells us that the parabola opens downwards. This means that the graph of this equation reduces.

To see why this is the case, consider the behavior of the y-values as x moves away from the vertex. Since the leading coefficient is negative, the y-values will decrease as x moves to the left or right from the vertex. Additionally, the squared term inside the parentheses means that the graph will be symmetric around the x-coordinate of the vertex, which is 3 in this case.

Thus, as x moves away from the vertex to the left or right, the y-values decrease in a symmetric manner, resulting in a graph that reduces. This can be seen in the shape of the parabola as it curves downwards from the vertex.

Therefore, the equation y = -1/2(x-3)² + 5  reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.

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, in the presented question, we can conclude that Interval   [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

Interval  [tex](4, 3): f(-4) -41, f(-3) 5,[/tex]therefore, the function reverses its sign and has a zero in the interval  [tex](-4, -3).[/tex]

Interval  [tex](3, 2): f(-3) 5, f(-2) -9,[/tex] indicating that the function changes sign and has a zero in the interval  [tex](-3, -2).[/tex]

Interval [tex](2, 1): f(-2) -9, f(-1) 1[/tex], therefore the function reverses its sign and has a zero in the interval  [tex](-€2, -1).[/tex]

Interval [tex](1, 0): f(-1) 1, f(0) 5[/tex], so the function does not change sign and the interval may or may not contain a zero [tex](-1, 0).[/tex]

Interval  [tex](0, 1): f(0) 5, f(1) -3,[/tex] indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

Therefore, in the presented question, we can conclude that Interval   [tex](0, 1): f(0) 5, f(1) -3[/tex], indicating that the function switches signs and has a zero in the interval  [tex](0, 1).[/tex]

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Answer:

$416.66

Step-by-step explanation:

We take

450 divided by 108, then time 100 = $416.66

So, the old fare is $416.66

The number is 9.

The three main types of linear equations are the standard form, the point-slope form, and the slope-intercept form.

We can begin by converting the following phrase into an equation:

The formula for "seven bigger than the product of a number and three" is as follows:

x/3 + 7

where x stands in for the unidentified number.

Seven more than the result of a number and three equals 10, according to the following formula.

x/3 + 7 = 10

When you take 7 out of both sides of the equation, you get:

x/3 = 3

When both sides of the equation are multiplied by 3, the result is:

x = 9

Hence, the answer is 9.

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Answer:

Step-by-step explanation:

Ici, nous allons réduire la fraction 18/25 aux termes les plus bas et la convertir en un nombre fractionnaire, si nécessaire.

Dans la fraction 18/25, 18 est le numérateur et 25 est le dénominateur.

On commence par trouver le plus grand diviseur commun de 18 et 25, qui est 1. Ensuite, on divise 18 et 25 par le plus grand diviseur commun pour obtenir la plus petite expression, écrite comme suit :

(18 ÷ 1) / (25 ÷ 1)

= 18/25

There is no table provided to reference, but the equation that represents a linear relationship between X and Y is:

y = mx + b

where m is the slope of the line and b is the y-intercept. The equation can also be written as:

y = b + mx

where b is the y-intercept and m is the slope. The equation represents a straight line on a graph, where the slope determines the steepness of the line, and the y-intercept is the point where the line crosses the y-axis. To write the equation for the table of X and Y values, we need to determine the slope and y-intercept from the given data.

Answer:

you need to learn yo stuff

Step-by-step explanation:

bye

Answer:

2 hope that helps

Step-by-step explanation:

The mean is 72, which is the center of the distribution, 50% of the students will score less than 72. The area to the right of z = 1, so approximately 15.87% of students will score above 80.

a) Since the mean is 72, and we want to know the percentage of students who scored less than 72, we need to find the area under the normal distribution curve to the left of the z-score that corresponds to 72. Since the standard deviation is 8, the z-score is:

z = (72 - 72) / 8 = 0

Using a standard normal distribution table or a calculator, we can find that the area to the left of z = 0 is 0.5. Therefore, 50% of students scored less than 72.

b) To find the percentage of students who scored above 80, we need to find the area under the normal distribution curve to the right of the z-score that corresponds to 80. The z-score is:

z = (80 - 72) / 8 = 1

Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 1 is 0.1587. Therefore, approximately 15.87% of students scored above 80.

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Answer:

8*7=56 + 8*3=24 = 80_squared

Step-by-step explanation: