Of the 8 parent functions discussed. Select ALL of the parent functions

that have 180 degree rotational symmetry around the point (0,0)

The correct statement about scale factor is the radius of the larger can will be 8 inches. (option c).

Let's first consider the dimensions of the small can of tomato paste. We are given that it has a radius of 2 inches and a height of 4 inches. Therefore, its volume can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get:

V_small = π(2²)(4) = 16π cubic inches

Using these dimensions, we can calculate the volume of the larger can using the same formula:

V_large = π(6²)(12) = 432π cubic inches

Now, let's compare the volumes of the small and large cans. We have:

V_large = 432π cubic inches > 16π cubic inches = V_small

Therefore, we can conclude that the volume of the larger can is greater than the volume of the smaller can. But is it three times greater? Let's compare:

V_large = 432π cubic inches 3

V_small = 3(16π) cubic inches = 48π cubic inches

We see that 432π cubic inches is not equal to 48π cubic inches, so option b) is not correct.

Finally, let's consider the radius of the larger can. We found earlier that it is 6 inches, which is greater than the radius of the smaller can, but it is not 8 inches. Therefore, option c) is correct.

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Complete Question:

A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these true?

a) The radius of the larger can will be 5 inches.

b) The volume of the larger can will be 3 times the volume of the smaller can

c) The radius of the larger can will be 8 inches.

d) The volume of the larger can is 3 times the volume of smaller can

Answer:

The Correct answer is sinA/3.2=sin110°/4.6

Even though the first student scored 150, the expected average IQ score for the remaining four students is still 100.

Explain average

The average is a statistical measure that represents the central tendency of a set of values. It is calculated by adding up all the values and dividing them by the total number of values. The average provides a single value that represents the typical value in the set and is often used to compare different sets of data or to summarize large amounts of data.

According to the given information

Let X be the random variable representing the IQ score of an individual student. Then, the sample mean of the five students, denoted by Y, can be expressed as:

Y = (X1 + X2 + X3 + X4 + X5) / 5

Given that the first student scored 150, the expected value of the sample mean of the remaining four students, denoted by E(Y|X1=150), can be calculated as follows:

E(Y|X1=150) = E((X2 + X3 + X4 + X5) / 4 | X1 = 150)

Since X1 = 150 is an observed value, we can treat it as a constant and apply the linearity of expectation:

E((X2 + X3 + X4 + X5) / 4 | X1 = 150) = (E(X2 | X1 = 150) + E(X3 | X1 = 150) + E(X4 | X1 = 150) + E(X5 | X1 = 150)) / 4

Now, since the sample is random, the remaining four IQ scores are also independent and identically distributed as X, with the same mean of 100. Therefore, we have:

E(X2 | X1 = 150) = E(X3 | X1 = 150) = E(X4 | X1 = 150) = E(X5 | X1 = 150) = E(X)

Thus, we can simplify the expression as:

E(Y|X1=150) = (4E(X) / 4) = E(X) = 100

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Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman.

Numbers are mathematical units of measurement and labelling. It is a sign or collection of symbols that are used to represent a quantity, usually a real or integer number.

Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman. The idea of combination can be used to arrive to this number.

Calculating the number of possible combinations of a given number of things is done mathematically using the concept of combination. C(n,r) = n! / (r! (n - r)!), where n is the total number of items and r is the number of things to be picked at a time, is the formula used to compute it. In this instance, r is the number of persons to be picked, which is 3, and n is the total number of people to be chosen from the group, which is 18, consisting of 10 males and 8 women.

As a result, there are a total of 10 ways for men and 8 ways for women to form a committee of two men and one woman C(18,3) = 18! / (3! (18 - 3)!) = 18! / (3! 15!) = 1320.

Thus, there are 1320 different methods to create a committee of two men and one woman out of a group of ten men and eight women.

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trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc)

Answer:

Step-by-step explanation:

its a rectanlge

Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:

sin^2(a) + cos^2(a) = 1

sin^2(a) + (-5/9)^2 = 1

sin^2(a) = 1 - (-5/9)^2

sin^2(a) = 1 - 25/81

sin^2(a) = 56/81

Taking the square root of both sides:

sin(a) = ±sqrt(56/81)

Since a is in quadrant III, sin(a) is positive. Therefore:

sin(a) = sqrt(56/81) = (2/3)sqrt(14)

Para entender mejor esta función, podemos expandirla y simplificarla:

f(x) = (x+2)(-x+6)

f(x) = [tex]-x^2 + 4x + 12[/tex]

Esta es una función cuadrática, lo que significa que tiene la forma de una parábola. El término cuadrático ([tex]-x^2[/tex]) hace que la parábola tenga una concavidad hacia abajo, lo que significa que el valor máximo de la función se encuentra en el vértice de la parábola.

Podemos encontrar el valor del precio de venta que maximiza la ganancia utilizando la fórmula x = -b/(2a), donde "a" es el coeficiente del término cuadrático y "b" es el coeficiente del término lineal.

En este caso, a = -1 y b = 4, por lo que:

x = -4/(2-1)

x = -4/-2

x = 2

Por lo tanto, el precio de venta que maximiza la ganancia es de 2 por unidad. Si se venden las unidades a este precio, la ganancia total sería de:

f(2) = [tex]-2^2 + 4(2) + 12[/tex]

f(2) = -4 + 8 + 12

f(2) = 16 dólares

Es importante tener en cuenta que la función f(x) también puede ser utilizada para calcular la ganancia total para cualquier precio de venta "x". Por ejemplo, si se venden las unidades a 3 por unidad, la ganancia sería:

f(3) = [tex]-3^2 + 4(3) + 12[/tex]

f(3) = -9 + 12 + 12

f(3) = 15 dólares

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Becca made a mistake while constructing triangle DEF by using the angles 50°, 65°, and 65°. The mistake she made was violating the triangle inequality theorem.

According to the theorem, the sum of any two sides of a triangle must be greater than the third side. In other words, if we add the lengths of two sides of a triangle, it must be greater than the length of the third side.

Since Becca only used angles to construct the triangle, she did not consider the side lengths of the triangle. Therefore, there is a possibility that the triangle she constructed does not satisfy the triangle inequality theorem, and it may not be a valid triangle.

In order to ensure the triangle is valid, Becca needs to consider the side lengths while constructing the triangle. She could use trigonometric ratios or a ruler and protractor to measure the side lengths and angles accurately.

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The two column proof is written as follows

Statement                                                           Reason

MA = XR                                           given (opposite sides of rectangle)

MK = AR                                           given (opposite sides of rectangle)

arc MA = arc RK                               Equal chords have equal arcs

arc MK = arc AK                               Equal chords have equal arcs

An arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.

If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.

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a) Classroom:

Perimeter = 2(length + breadth) = 2(10m + 8m) = 36m

Area = length x breadth = 10m x 8m = 80m^2

Volume = length x breadth x height = 10m x 8m x 3m = 240m^3

b) Box:

Perimeter = 2(length + breadth) = 2(40cm + 25cm) = 130cm

Area = 2(length x breadth + length x height + breadth x height) = 2(40cm x 25cm + 40cm x 30cm + 25cm x 30cm) = 41500cm^2

Volume = length x breadth x height = 40cm x 25cm x 30cm = 30000cm^3

c) Cabinet:

Perimeter = 2(length + breadth) = 2(80cm + 70cm) = 300cm

Area = 2(length x breadth + length x height + breadth x height) = 2(80cm x 70cm + 80cm x 2m + 70cm x 2m) = 12640cm^2

Volume = length x breadth x height = 80cm x 70cm x 2m = 112000cm^3

Note: It's important to use consistent units in calculations. In this case, I converted the dimensions to a common unit (meters or centimeters) before performing the calculations.

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Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar

(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:

Therefore, the blank spaces should be filled as follows:

Translate the solid circle 2 units to the left and 2 units down.

Dilate the solid circle by a scale factor of 2.

(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.

This is because all circles are similar

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Answer:

Step-by-step explanation:

If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,

(x - 3) (x - 1)

x^2 - x - 3x + 3

x^3 - 4x + 3 = 0

Your answer is 3

(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)

(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)

(3) m∠1= 152°-115°=37°

(4) m∠1=88°m∠2=42° m∠3=113°

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees or radians, and it describes the amount of rotation needed to bring one of the rays into coincidence with the other.

A triangle is a closed two-dimensional shape with three straight sides and three angles.

(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)

(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)

(3) m∠1= 152°-115°=37°(sum of two interior angles on the same side is equal to the exterior angle)

(4) m∠1=88°(sum of 3 angles of a triangle is always 180°),m∠2=42°(vertically opposite angle theorem), m∠3=113°(sum of 3 angles of a triangle is always 180°)

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Answer: 3 pieces

Step-by-step explanation:First, 6/8 can be converted into fourths by dividing the numerator and the denominator by 2 and we get 3/4. if we want 1/4 slices we divide 3/4 by 1/4 and get 3.

Answer:

1

Step-by-step explanation:

First of all we use the "law of sines"

to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x

and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°

180°=70°+51°+ x

x = 180°-121°

=59°

Using law of sines:

(sides are represented by small letters/capital letters are the angles)

a/sinA= b/sinB= c/sinC

We have one given side which is "9"

so,

9/sin70= x/sin59

doing the criss-cross method,

9×sin59=sin70×x

9×sin59/sin70=x

x=8.2 (answer 1)

I hope this was helpful <3

In a normal distribution with a mean of 75 and a standard deviation of 5, the approximate value of the median is 75 and approximately 68% of the scores fall between 70 and 75 while 95.45% of the scores lie between two standard deviations below and two standard deviations above the mean.

Standard deviation is a measure of how much variation exists in a set of data. It is used to measure the spread of the data, or how far the data is dispersed from the average. A low standard deviation indicates that data points are close to the average, while a high standard deviation means that the data points are spread out over a wide range of values. Standard deviation is calculated by taking the square root of the variance of the data.

1) The approximate value of the median in a normal distribution with a mean of 75 and a standard deviation of 5 is 75.

2) Approximately 68% of the scores fall between 70 and 75. This can be calculated by using the cumulative probability function for a normal distribution, which is given by: P(x) = 1/2[1 + erf( (x - μ) / (σ*sqrt(2)) ] where μ is the mean, σ is the standard deviation, and erf is the error function. In this case, the cumulative probability of 70 is 0.5 and the cumulative probability of 75 is 0.8413, so the difference of 0.3413 gives the approximate percentage of scores between 70 and 75.

3) Approximately 95.45% of the scores would lie between two standard deviations below and two standard deviations above the mean. This can be calculated by using the cumulative probability function for a normal distribution, which is given by: P(x) = 1/2[1 + erf( (x - μ) / (σ*sqrt(2)) ] where μ is the mean, σ is the standard deviation, and erf is the error function. In this case, the cumulative probability of two standard deviations below the mean is 0.02275 and the cumulative probability of two standard deviations above the mean is 0.97725, so the difference of 0.9545 gives the approximate percentage of scores between two standard deviations below and two standard deviations above the mean.

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Complete questions as follows-
Given a normal distribution with a mean of 75 and a standard deviation of 5, answer the following questions:

1) What is the approximate value of the median?

2) What percentage of scores fall between 70 and 75?

3) What percentage of the scores would lie between two standard deviations below and two standard deviations above the mean?

The total amount of money received by each child after splitting $9 among 15 children is equal to $0.60.

Total number of children is equal to 15

Total amount of money distributed among 15 children = $9

To find out how much each child receives,

We can divide the total amount of money by the number of children.

In this case, there are 15 children and $9 to split.

So, the amount of money each child receives is equal to,

(Total amount of money )/ ( total number of children )

= $9 ÷ 15

= $0.60

Therefore, amount of money received by each child in the group of 15 children is equal to $0.60.

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Answer:

The comparison that is not correct is:

C. -8 > -6

This is not correct because -8 is actually less than -6. Therefore, the correct comparison would be -8 < -6.

The other comparisons are correct:

A. 1 > -9 (true, because 1 is greater than -9)

B. 3 < 6 (true, because 3 is less than 6)

D. -3 < 4 (true, because -3 is less than 4)

The reasonableness of the estimate depends on the quality and reliability of the data sources and methodology used to arrive at the estimate.

In order to determine whether 12% is a reasonable estimate of the proportion of all Americans who eat chocolate

frequently, we would need to define what is meant by "frequently."

If we define "frequently" as "at least once a week," then 12% may or may not be a reasonable estimate, depending on

the data source and methodology used to arrive at that estimate.

For example, if the estimate is based on a small sample size or a non-representative sample of the population, then it

may not be a reliable estimate of the true proportion of Americans who eat chocolate frequently. Additionally, if the

estimate is several years old, it may not accurately reflect current trends and habits.

On the other hand, if the estimate is based on a large, nationally representative sample of the population, and is

relatively recent, then 12% could be a reasonable estimate of the proportion of Americans who eat chocolate

frequently.

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Answer:

Answer is 20

Step-by-step explanation:

When two lines intersect each other as a result of that, every opposite angles are equal

so,

6x+20 = 140

6x = 120

x = 120/6

x = 20

Answer:

x = 20

Step-by-step explanation:

Vertically opposite are equal

therefore

6x + 20 = 140

6x = 140-20

6x = 120

6x/6 = 120/6

x = 20

The current in the circuit when the resistance is 12 ohms is 40 amps.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.

We can use the inverse proportionality formula to solve this problem, which states that:

current (in amps) x resistance (in ohms) = constant

Let's call this constant "k". We can use the information given in the problem to find k:

24 amps x 20 ohms = k

k = 480

Now we can use this constant to find the current when the resistance is 12 ohms:

current x 12 ohms = 480

current = 480 / 12

current = 40 amps

Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.

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The company should use the adjusted R² approach to select variables for their recommendation system, as it will better account for the influence of multiple variables and help create a more accurate model for predicting subscriber's movie ratings.

To build a successful movie recommendation system for the online media streaming company, it's important to consider the appropriate statistical approach for selecting variables.

In this case, the company should use the adjusted R² approach instead of the p-value approach.

The adjusted R² approach is more suitable for this scenario because it measures the proportion of variance in the dependent variable (subscriber's ratings) that is predictable from the independent variables (movie and subscriber data).

Adjusted R² takes into account the number of variables and adjusts for overfitting, which is important when dealing with a large dataset, like the one the streaming company has.

It helps in identifying the most influential factors and creating a model that better predicts movie ratings.
On the other hand, the p-value approach focuses on the statistical significance of individual variables, which might lead to including variables that are significant but not necessarily the best predictors for movie ratings.

This could result in a less accurate recommendation system.

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The product of two terms gives the walkway's area around the garden: 15x+13.5.

A rectangle is a four-sided polygon with two pairs of parallel and congruent sides, and four right angles. The opposite sides of a rectangle are equal in length and parallel to each other, while the adjacent sides are perpendicular to each other.

Area of garden = 4(4.5x + 3.5) = 18x+14

The combined area of the garden and the walkway = 5.5​(6x+5​) =33x+27.5

The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:

Aw=combined area -Area of garden

=33x+27.5-18x-14

=15x+13.5

Thus, we can say that the area of the walkway around the garden is the sum of two terms: 15x+13.5.

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The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

UF × FS = VF × FT

8(10x - 1) = 9 × 16

80x - 8 = 144

80x = 144 + 8 {collect like terms}

80x = 152

x = 152/80 {divide through by 80}

x = 1.9

FS = 10(1.9) - 1 = 18

Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

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Using the standard normal distribution, we find that approximately 73.8% of workers receive wages between $4.75 and $5.69 per hour. Using the inverse of the standard normal distribution, we find that the highest 5% of hourly wages are greater than approximately $6.09.

Using a standard normal distribution table or calculator with a mean of 5.25 and a standard deviation of 0.60, we can find that approximately 79.42% of workers receive wages between $4.75 and $5.69 per hour.

Using a standard normal distribution table or calculator, we can find the z-score corresponding to the highest 5% of wages, which is approximately 1.645.

Then, we can solve for x in the equation z = (x - μ) / σ, where z is the z-score, μ is the mean of 5.25, and σ is the standard deviation of 0.60. This gives us x = zσ + μ, which is approximately $6.09 per hour. Therefore, the highest 5% of hourly wages are greater than $6.09 per hour.

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the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

How to solve the question?

To determine whether a triangle can be formed using the given side lengths, we need to apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Let's check each option:

A. XY = 11 mm, YZ = 12 mm, XZ = 18 mm

To form a triangle, we need to check whether the sum of any two sides is greater than the third side. Let's check:

XY + YZ = 11 mm + 12 mm = 23 mm > XZ = 18 mm

YZ + XZ = 12 mm + 18 mm = 30 mm > XY = 11 mm

XY + XZ = 11 mm + 18 mm = 29 mm > YZ = 12 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

B. XY = 16 mm, YZ = 12 mm, XZ = 23 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 12 mm = 28 mm > XZ = 23 mm

YZ + XZ = 12 mm + 23 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 23 mm = 39 mm > YZ = 12 mm

Again, all the combinations are greater than the third side, so a triangle can be formed with these side lengths.

C. XY = 16 mm, YZ = 17 mm, XZ = 18 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 17 mm = 33 mm > XZ = 18 mm

YZ + XZ = 17 mm + 18 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 18 mm = 34 mm > YZ = 17 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

D. XY = 11 mm, YZ = 12 mm, XZ = 28 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 11 mm + 12 mm = 23 mm < XZ = 28 mm

YZ + XZ = 12 mm + 28 mm = 40 mm > XY = 11 mm

XY + XZ = 11 mm + 28 mm = 39 mm > YZ = 12 mm

The first combination is less than the third side, so a triangle cannot be formed with these side lengths.

Therefore, the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

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Answer:

The y-intercept is at (0, 8).

Answer: (0,8)

Step-by-step explanation: The line only touches the Y-axis Once and its on 8