please help guys, I need this done

Simplifying Mrs. Perez's class donated 11 units of vegetables, 66 units of pasta, and 22 units of soup.

The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible

vegetables = (1/9) x 99

Simplifying this expression, we get:

vegetables = 11

So the class donated 11 units of vegetables.

Next, we can figure out how much of the donation was pasta. We know that 2/3 of the donation was pasta, so we can set up the equation:

pasta = (2/3) x 99

Simplifying 66 units homemade pasta, 22 units of soup, and 11 units of veggies were all provided by Mrs. Perez's students.

Which expression should I simplify?

A math difficulty is simply solved by simplifying the expression. When you simplify a phrase, your goal is essentially to make it as simple as you can. There shouldn't be any more multiplication, dividing, adding, or removing to be done at the conclusion.

veggies = 1/9 times 99

When we condense this statement, we get:

eleven vegetables

We can then determine what proportion of the contribution was pasta. Given that we know that pasta made up 2/3 of the donation, we can construct the following equation:

spaghetti equals (2/3) x 99

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The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)

Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:

(x-2)² = (x-2) * (x-2)

= x * x - 2 * x - 2 * x + 2 * 2

= x² - 4x + 4

So, the expression (x-2)² is equivalent to x² - 4x + 4.

However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:

(x-2)² = (x-2) * (x-2)

= (x-2)²

So, (x-2)² is equivalent to itself.

Hence the correct option is (B).

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Complete Question:

Which expressions are equivalent to (x−2)²?

Select the correct choice.

A. (x + 2) (x - 2)

B. x² - 4x + 4

C. x² - 2x + 5

D. x² + x - 2x

The analysis of the data to obtain the confidence interval of the difference in the means indicates;

99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂

The correct options are;

Name of Procedure

Random

10%

Normal/Large Sample

99% CI = (-0.302, 2.301)

Conclude;

We are 99% confident that the interval give in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.

A confidence interval is a range of value that is likely to contain the true value of a population parameter with a certain degree of confidence.

The two-sample t-test can be used to construct the 99% confidence interval as follows;

([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)

Where;

[tex]\bar x[/tex]₂ and [tex]\bar x[/tex]₁ = The sample means of the love song and classical music groups

s₁, and s₂ = The sample standard deviations

n₁ and n₂ = The sample sizes

df = The degrees of freedom

t(α/2, df) = The value from the t-distribution table with a significance level of 0.01 and df = n₁ + n₂ - 2

The data indicates;

n₁ = n₂ = 15

[tex]\bar x[/tex]₁ = 5.07, s₁ = 1.63

[tex]\bar x[/tex]₂ = 4.07, s₂ = 1.13

Therefore, we get;

([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)

= (5.07 - 4.07) ± t(0.005, 28) × √(1.62²/15 + 1.13²/15)

= 1 ± 2.763 × 0.469

= 1 ± 1.301

The 99% confidence interval for the difference in the true mean heart for subjects who listen to a love song versus classical music is; (-0.301, 2.301).

The correct statement is; 99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂

The correct statements, placed in the box are;

Name of Procedure;

Two sample interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂

Random

The volunteers are randomly selected

The random condition is met

We have a random sample of 15 subjects who listen to a love song

We have a random sample of 15 subjects who listen to classical music

10%

The 10% condition is met

15 < 10% of all subjects like these who listen to love songs

15 < 10% of all subjects like these  who listen to classical music

Normal/Large Sample

The Normal/Large condition is met

The stemplot of the classical music sample data shows no strong skewness or outliers

The stemplot of the love song music sample data shows no strong skewness or outliers

Therefore;

99% CI = (-0.301, 2.301)

Conclude;

We are 99% confident that the interval given in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.

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Answer: 15

Step-by-step explanation:

13--2 = 13 + 2 = 15

In Rosettenville, a suburb of Johannesburg, South Africa, Robert Brozin and Fernando Duarte acquired the Chicken Land restaurant in 1987, launching Nando's.

The eatery was renamed Nando's in honor of Fernando. The restaurant incorporated influences from former Mozambican Portuguese colonists, many of whom had relocated to Johannesburg's southeast after their country gained independence in 1975. Expansion was an essential component of their vision from the beginning. Nando's had already grown from one restaurant in 1987 to four by 1990. It became increasingly difficult to implement a common strategy and decision-making became inefficient as new outlets were maintained as separate businesses.

In 1995, Nando's International Holdings (NIH) was established as a new international holding because managing this growingly complex global structure had become extremely challenging. The South African branch of Nando's Group Holdings (NGH) was successfully listed on the Johannesburg Stock Exchange on April 27, 1997. NGH was 54% owned by NIH, with the remaining 26% available to the general public and former joint venture partners. The main goals of the share offer and listing were to broaden the group's capital base and enable group restructuring.

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Answer:

Step-by-step explanation:

You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.

Answer:

Step-by-step explanation:

The average time gap between the first cyclist's time and each of the remaining cyclists' times (second through fifth) in the 1995 Volta a Catalunya cycle race is approximately 6 minutes and 7 seconds.

To calculate this, we need to subtract the time of the first cyclist from each of the remaining cyclists' times (second through fifth).The time for the first cyclist was 41:38:33.

The times for the remaining cyclists were as follows:

We can calculate the difference for each cyclist by subtracting the first cyclist's time from their own time:

Adding up all of the times and dividing by four, we get an average of 00:06:07.

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Total seats in plane: 186

108+64+14

5/7 of 14 is: 10

14÷7= 2

2x5= 10

5/16 of 64 is: 20

64÷16=4

5×4= 20

5/9 of 108 is: 60

108÷9= 12

12x5= 60

60+20+10=90

90/186 of seats are being used

simplified: 15/31

No

Answer:

the answer is 2

Step-by-step explanation:

this answer will be 200⁰0000000000⁰00000⁸⁰643367897⁶43677443⁵=5.0

Answer:

0.005

Step-by-step explanation:

Answer:

[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]

Step-by-step explanation:

[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]

Each side has length of a?

[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]

The equation you would use to properly calculate the dollar cost of entering the park and enjoying rides is Total Cost = Entrance Fee + (Number of Rides x Ride Fee).

In this case, Total Cost is the cost of entering the park and enjoying rides, Entrance Fee is the fee for entering the park, Number of Rides is the number of rides you will be taking, and Ride Fee is the fee charged for each ride.

Thus, plugging in the given values, the equation becomes  Total Cost = Entrance Fee + (Number of Rides x Ride Fee).

Therefore, if the Entrance Fee is $ and each ride costs an additional $ , the Total Cost of entering the park and enjoying rides is $ .

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Probability of D2 being sunny = 0.78.

On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.

Therefore, we need to find the chances that D2 is sunny.

There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.

Now, Let us find the probability of D2 being sunny.

We have the following possible cases for D2.

D1 = Sunny; D2 = Sunny

D1 = Sunny; D2 = Rainy

D1 = Rainy; D2 = Sunny

D1 = Rainy; D2 = Rainy

The probability of D1 being sunny is 0.9.

When a sunny day follows a sunny day, the probability is 0.8.

When a sunny day follows a rainy day, the probability is 0.6.

Therefore, the probability of D2 being sunny is given by the formula:

Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.

Therefore, the probability that D2 is sunny are 0.78 or 78%.

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Answer: 4 is the average rate of change

Step-by-step explanation:

The equation to find the average rate of change is:

So f(2)= 11 and f(5)=23 then you plug these numbers in:

[tex]\frac{23-11}{5-2}[/tex] = [tex]\frac{12}{3}[/tex] = 4

The graph of an exponential function with an initial value of 10 and a base of 1.3z. Therefore option D is correct.

The function f(x) is an exponential function with a base of 1.3 and an initial value of 10. The graph of an exponential function with a base greater than 1 increases rapidly as x increases. Therefore, option a can be eliminated.

Option b is not a graph of an exponential function, as the function is not continuous and does not approach any asymptote.

Option c shows an exponential function with an initial value of 10 and a base of 1.3/10, which is less than 1. This means that the function would decrease over time, which is not consistent with the problem statement.

Option d shows an exponential function with an initial value of 10 and a base of 1.3, which is consistent with the problem statement. Therefore, option d is the correct answer.

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11.87 m² metal sheet would be needed to make the base area of tank.

Volume of cylinder, determines how much material it can carry, is determined by the cylinder's volume. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.

It is given that capacity of a closed cylindrical vessel of height 2 m is 3080 liters

Let us assume that Radius of cylinder = r

Then Volume of cylinder = π ×r² ×h

= 2π ×r²× m³

1 m³ = 1000 liters

= 2000 π r²  liters

Volume of tank = Capacity

2000 π r² = 3080

=> 2000 × (22/7) × r² = 3080

=> r² = 49/100

=> r = 7/10 m

=> r = 0.7 m

Base Area of tank = TSA = 2πrh + 2πr²

= 2×(22/7)(0.7)×2 + 2×(22/7)×(0.7)²

= 3.0772 +8.792

= 111.87 m²

Hence, 11.87 m² metal sheet would be needed to make it.

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The two sides of a right triangle opposite the non-right angles are called as adjacent and opposite angle or Legs.

A triangle is a three-sided regular polygon in which the total of any two sides is always larger than the sum of the third side.

A right-angled triangle is one with one of its internal angles equal to 90 degrees, or any angle is a right angle. As a result, this triangle is also known as the right triangle or the 90-degree triangle. In trigonometry, the correct triangle is very significant.

A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees. The sides that include the right angle are perpendicular and form the triangle's base. The third side is known as the hypotenuse, and it is the longest of the three sides.

The three sides of the right triangle are connected. Pythagoras' theorem explains this relationship. This theorem states that in a right triangle,

Perpendicular² + Base² = Hypotenuse²

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The required perimeter is 25+√61 units.

We can find the distance between each pair of consecutive points and then add them up to get the perimeter of the polygon.

Using the distance formula, the distance between points A and B is:

[tex]$$AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(-4 - 4)^2 + (8 - 2)^2} = \sqrt{100} = 10$$[/tex]

Similarly, the distances between the other pairs of points are:

[tex]$$BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(-7 + 4)^2 + (4 - 8)^2} = 5$$[/tex]

[tex]$$CD = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2} = \sqrt{(-1 + 7)^2 + (-4 - 4)^2} = 10$$[/tex]

[tex]$$DA = \sqrt{(x_A - x_D)^2 + (y_A - y_D)^2} = \sqrt{(4 + 1)^2 + (2 + 4)^2} = \sqrt{61}$$[/tex]

Therefore, the perimeter of the polygon is:

[tex]$$AB + BC + CD + DA = 10 + 5 + 10 + \sqrt{61}$$[/tex]

= 25+√61

Thus, required perimeter is 25+√61.

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The value of the unknown lengths in these similar triangles is FH is 6.67 units and EG is 27 units.

A triangle is a polygon with three sides and three angles. It is a two-dimensional shape that is commonly studied in mathematics, geometry, and other fields. The sum of the angles in a triangle is always 180 degrees, and the lengths of the sides can vary. Triangles can be classified based on the lengths of their sides and the measures of their angles. Common types of triangles include equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have many important properties and are used in various applications, including construction, engineering, and physics.

Here,

1. Let x be the length of FH. We have:

AB/EF = BD/FH

12/8 = 10/x

Cross-multiplying, we get:

12x = 80

x = 80/12

x ≈ 6.67

Therefore, FH ≈ 6.67.

2. Let y be the length of EG. We have:

AC/BD = FH/EG

15/9 = 5/y

Cross-multiplying, we get:

5y = 135

y = 135/5

y ≈ 27

Therefore, EG ≈ 27.

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Answer: There are 10 students who are in both the hockey and football teams.

Step-by-step explanation: We can use the principle of inclusion-exclusion to find the number of students who are in both the hockey and football teams.

The total number of students in both teams is the sum of the number of students in the hockey team and the number of students in the football team, minus the number of students who are in both teams (to avoid double-counting):

Total = Hockey + Football - Both

Substituting the given values, we get:

100 = 40 + 70 - Both

Simplifying, we get:

Both = 40 + 70 - 100

Both = 10

Therefore, there are 10 students who are in both the hockey and football teams.

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The answer is 250 kilometers. Peter and his mother traveled a total distance of 250 kilometers on their mail delivery.

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.

1 centimeter is equal to 0.01 kilometers, so 50 kilometers would be equal to 5,000 centimeters. The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.

Charltc to Thornton is 1,000 centimeters, Thornton to Avon is 1,500 centimeters, Avon to Ashton is 1,000 centimeters, and Ashton to Charltc is 1,500 centimeters. This gives us a total of 5,000 centimeters, or 50 kilometers.

This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times, since they flew from Charltc to Thornton, then to Avon, then to Ashton, and then back to Charltc). This gives us 250 kilometers, which is the answer to the question.

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Peter and his mother traveled a total distance of 250 kilometers on their mail delivery. The answer is 250 kilometers.

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.

1 centimeter =  0.01 kilometers,

so 50 kilometers = 5,000 centimeters.

Charlton to Thornton= 1,000 centimeters,

Thornton to Avon= 1,500 centimeters,

Avon to Ashton= 1,000 centimeters,

and Ashton to Charlton= 1,500 centimeters.

Total distance= 1,000+1,500+1,000+1,500

= 5,000 centimeters, or 50 kilometers.

The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.

This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times.

=50*5

=250

Since they flew from Charlton to Thornton, then to Avon, then to Ashton, and then back to Charlton.

250 kilometers is the answer to the question.

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Question:

Peter's mother is a pilot. She often makes deliveries near their community. Peter and his mother flew from Charlton to Thornton to make a mail delivery. Then they continued on to Avon and Ashton and returned to Charlton. How many kilometers did Peter and his mother travel in all?

Answer:

Y intercept is (0,2) Answer D.

Step-by-step explanation:

I included a graph for equation y=2/3 x + 2.

Answer:

24 cm (to nearest cm)

Step-by-step explanation:

XLV = extra large tin volume (cm³)

LV = large tin volume (cm³)

XLR = extre large tin radius (cm)

LR = large tin radius (cm) = 20

XLV = 1.75 × LV

Since the tins are geometrically similar cylinders, we can infer that the volumes and radii of the 2 tins are related;

We know the relationship between the volume of the two tins, i.e. the XL tin is 75% greater in volume than the L tin;

This means the volumetric scale factor or multiplier is ×1.75;

Subsequently, we know:

XLV = 1.75 × LV

Similarly, there is a relationship between the radii of the tins;

The relationship is, however, slightly different;

[tex]XLR = (\sqrt[3]{1.75}) \times LR[/tex]

We need to take the cube root of the volumetric scale factor, reason being, the radius is a linear dimension unlike volume;

Easy way to figure this is radius is in cm, volume is in cm³;

So:

XLR = 1.205... × LR

XLR = 1.205... × 20

XLR = 24.101... --> 24 cm (to nearest cm)

Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.

Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.

A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.

by applying the binomial theorem:

[tex](1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...[/tex]

where C(n, k) is the binomial coefficient, which equals[tex]n!/(k!(n-k)!).[/tex]

The first few terms of this expansion are:

[tex](1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]

Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:

[tex]1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]

Equating coefficients of [tex]x^3[/tex] on both sides, we get:

[tex]c = n(n-1)(n-2)(a^3/6)[/tex]

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In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.

Each student in a class of 25 drinks a full 210 millilitre glass of milk, hence the amount of milk consumed overall during the break is:

25 students times 210 millilitres each equals 5250 millilitres.

Milk comes in 1000 millilitre bottles, thus to determine how many bottles are needed, divide the entire amount eaten by the volume of milk in each bottle.

5.25 bottles are equal to 5250 millilitres divided by 1000 millilitres.

We must round up to the nearest whole number because we are unable to have a fraction of a bottle. This results in:

6 bottles in 5.25 bottles

In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.

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Question: The heights of adult men can be approximated as normal, with a mean of 70 and a standard deviation of 3, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.

Let X be the height of an adult man, which follows a normal distribution with mean μ = 70 and standard deviation σ = 3. Then, we need to find the probability that a man is shorter than some height, say x₀. We can write this probability as P(X < x₀).To find P(X < x₀), we need to standardize the random variable X by subtracting the mean and dividing by the standard deviation. This yields a new random variable Z with a standard normal distribution. Mathematically, we can write this transformation as:Z = (X - μ) / σwhere Z is the standard normal variable.

Now, we can find P(X < x₀) as:P(X < x₀) = P((X - μ) / σ < (x₀ - μ) / σ) = P(Z < (x₀ - μ) / σ)Here, we use the fact that the probability of a standard normal variable being less than some value z is denoted as P(Z < z), which is available in standard normal tables.

Therefore, to find the probability that a man is shorter than some height x₀, we need to standardize the height x₀ using the mean μ = 70 and the standard deviation σ = 3, and then look up the corresponding probability from the standard normal table.In other words, the probability that a man is shorter than x₀ can be expressed as:P(X < x₀) = P(Z < (x₀ - 70) / 3)We can now use standard normal tables or software to find the probability P(Z < z) for any value z.

For example, if x₀ = 65 (i.e., we want to find the probability that a man is shorter than 65 inches), then we have:z = (65 - 70) / 3 = -1.67Using a standard normal table, we can find that P(Z < -1.67) = 0.0475. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%. Thus, P(X < 65) = 0.0475 or 4.75%. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.

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Answer:

Step-by-step explanation:

348.55