it’s a 2 part question

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

Function f is defined by the equation f(x)=y?. this isn't a thing

i believe you mean... Function f is defined by the equation f(x) = x².

What is f(2)?

What is f(3)?

in which case the answer is The value of f(2) and f(3) for the given functions are 4 and 9 respectively.

The given function is f(x)=x².

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

We need to find the value of f(2) and f(3)

Put x=2 in the given function, we get

f(2)=2²

= 4

Put x=3 in the given function, we get

f(3)=3²

= 9

Hence, the value of f(2) and f(3) for the given functions are 4 and 9 respectively.

It is highly possible for a bag of potatoes to weigh 15 kilograms.    

Out of the given options, the object that weighs 15 kilograms is most likely to be a bag of potatoes. Generally, bags of potatoes weigh anywhere between 5 kilograms to 25 kilograms, depending on the size and quantity of the potatoes. Therefore, it is highly possible for a bag of potatoes to weigh 15 kilograms.

A story book, on the other hand, usually weighs between 200 grams to 1 kilogram, which is significantly lighter than 15 kilograms. Similarly, a laptop typically weighs between 1 kilogram to 3 kilograms, while a washing machine usually weighs around 50 kilograms to 100 kilograms, making them unlikely to weigh 15 kilograms.

It is important to note that the weight of an object can vary greatly depending on its size, material, and other factors. Therefore, it is always best to weigh an object using a scale to accurately determine its weight.

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Evaluating cos20°.cos40°+cos250°.cos310°  is   (cos10° + 1) / 2.

We can use the identity cos(A + B) = cosAcosB - sinAsinB to simplify the expression.

cos20°cos40° + cos250°cos310°

= cos(40° - 20°) + cos(310° - 250°) (using the identity)

= cos20° + cos60°

= cos20° + 1/2

Now we need to evaluate cos20°. We can use the identity cos2A = 2cos^2A - 1 and let A = 10°:

cos20° = 2cos^210° - 1

cos10° = 2cos^210° - 1 + 1

cos10° = 2cos^210°

cos^210° = cos10° / 2

Now we substitute this back into our original expression:

cos20°cos40° + cos250°cos310°

= cos20° + 1/2

= cos^210° + 1/2

= (cos10° / 2) + 1/2

= (cos10° + 1) / 2

Therefore, cos20°cos40° + cos250°cos310° = (cos10° + 1) / 2.

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Answer:

[tex] {x}^{2} + 8x + 16 = 18[/tex]

[tex] {(x + 4)}^{2} = 18[/tex]

x + 4 = +3√2, so x = -4 + 3√2

Answer: 1, 2, and 3

Step-by-step explanation:

       All three of these graphs pass the vertical line test. At any point on each graph, if you place a vertical line the graph will only intersect that line once. This means they all pass.

Answer:

y+7

Step-by-step explanation:

will we use the way of long divide which will help

[tex]y-8\sqrt{y^{2}-y-56 }[/tex]

because y need another y to  became y square that mean we need y

since we have y square we could minus y-8y which is1

so 56divide (-8)=7

so it is y+7

brain please

thanks

The length of segment A'E' of the new formed pentagon is 5 units.

We are given that:

Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2.

From the attached graph, we see that the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;

A- (0, 0)

E- (0, 2)

The length of the segment AE is:

AE = √((2-0)² + (0 - 0)²)

AE = √2²

AE = 2

When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 5/2, we have;

Length of segment A'E' = 5/2 × Length of segment AE

Thus;

Length of segment A'E' = 5/2 × 2

Length of segment A'E' = 5 units.

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Complete question is:

Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2.

Find the length of the line segment A'E'.

This gives us the answer of 1.9 miles, meaning that he must ride an average of 1.9 miles each day for the remaining 4 days of the week in order to reach his goal of 39.6 miles.

(39.6 - 8) ÷ 4 = x

7.6 ÷ 4 = x

x = 1.9 miles

Bentley wants to ride his bicycle 39.6 miles this week. He has already ridden 8 miles, leaving him with 31.6 miles left to ride. He has 4 days left to ride, so we need to figure out how many miles he must ride each day in order to meet his goal. We can do this by subtracting the 8 miles he has already ridden from the total goal of 39.6 miles. This gives us 31.6 miles remaining to be ridden. We then divide this number by 4, since he has 4 days left in the week to ride. This gives us the answer of 1.9 miles, meaning that he must ride an average of 1.9 miles each day for the remaining 4 days of the week in order to reach his goal of 39.6 miles.

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An equation is modeled. The value of x makes the equation true is -1.

Equation:

Conditional comparisons apply only to specific values ​​of variables. An equation consists of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Usually the right side of the equation is assumed to be zero. If this is accepted, it does not reduce the generality, since it can be done by subtracting the right side from the two sides.

According to the Question:

5x + 6 = 1

5x = -5

x = -1

Complete Question:

An equation is modeled. What value of x makes the equation true?

(1) 1

(2) 7

(3) -5

(4) -1

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Answer:

y = 2x+3

Step-by-step explanation:

first we must find the slope, which is change in y / change in x.

so, if we have 2 points on the line, (0, 3) and (1, 5), the slope is 2/1 = 2.

next, find the y-intercept. this is clearly (0, 3).

so, the equation is y = mx + b with m = slope and b = y-int.

plugging in the values, the equation is y = 2x+3

Permutations and combinations might sound like synonyms. However, in probability theory, they have distinct definitions. Combinations: The order of outcomes does not matter. Permutations: The order of outcomes does matter. For example, on a pizza, you might have a combination of three toppings: pepperoni, ham, and mushroom.

Hope this is the answer you are looking for.

Answer:

It would be 37 mnths

Step-by-step explanation:

They will have the same amount of money in their bank accounts after 26 months.

Algebra is the branch of mathematics that uses letters and variables to represent the missing information in a given mathematical expression, to find the solution.

Here,

Amount of money added by Neil in January = £32

Amount of money added by Amber in January = £240

Amount of money added by Neil at the end of every month = £50

Amount of money added by Amber at the end of every month = £42

According to the given data, after a number of months, the amount of money in their bank accounts must become same.

Let n be the number of months,

(£32 + n£50) = (£240 + n£42)

n£50 - n£42 = £240 - £32

n£8 = £208

So, n = 208/8

n = 26

Hence,

They will have the same amount of money in their bank accounts after 26 months.

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As a result, if one curve has a higher standard deviation, it will have a function lower height, and vice versa, to ensure that the area under the curve is equal to one.

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

False.

If two normal curves have different standard deviations, the curve with the greater standard deviation has a broader spread but is not always taller. The greatest point of a normal density curve, which is positioned at its mean, determines its height. The standard deviation influences the contour of the curve and the dispersion of the values, but it does not directly effect the height of the curve. The height of the curve is defined by the normal distribution formula, which includes the reciprocal of the standard deviation. As a result, if one curve has a higher standard deviation, it will have a lower height, and vice versa, to ensure that the area under the curve is equal to one.

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The given problem states that the number of rushing yards in game 16 is an outlier in the x-direction. Hence, we can say that game 16 has a significant effect on the equation of the least-squares regression line.

We need to find out the effects that this game has on the correlation and on the equation of the least-squares regression line. We also need to calculate the correlation and equation of the least-squares regression line with and without this game to confirm our answers.

Effect on Correlation:

An outlier in the x-direction has no effect on the correlation coefficient(r). The correlation coefficient measures the strength and direction of a linear relationship between two variables. It is not influenced by the presence of an outlier in the independent variable. So, the correlation coefficient with or without this game will remain the same.

Effect on Equation of the Least-Squares Regression Line:

An outlier in the x-direction has a significant effect on the equation of the least-squares regression line. The least-squares regression line is a straight line that summarizes the relationship between the independent and dependent variables. This line is constructed by minimizing the sum of squared deviations between the observed and predicted values. If an outlier is present, it will pull the regression line closer to it. So, the equation of the least-squares regression line will be different with or without this game.

Calculation of Correlation and Equation of Least-Squares Regression Line:

Without game 16,

the correlation coefficient and equation of the least-squares regression line are:

Correlation Coefficient(r) = 0.94

The equation of the least-squares regression line:

y = 2.25x + 10.5 With game 16,

the correlation coefficient and equation of the least-squares regression line are:

Correlation Coefficient(r) = 0.93

The equation of the least-squares regression line:

y = 1.92x + 22.8

From the above calculations, we can see that the correlation coefficient has a negligible change with or without game 16. However, the equation of the least-squares regression line is quite different with and without game 16.

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the shoe salesman earned a total of $2,165. To calculate the total earnings of the shoe salesman, we need to determine both his commission and base salary.

First, we can calculate his commission by multiplying the total amount of shoes he sold by his commission rate:

Commission = Total shoes sold * Commission rate

Commission = $4,125 * 0.04

Commission = $165

Next, we can add his commission to his base salary to determine his total earnings:

Total earnings = Commission + Base salary

Total earnings = $165 + $2,000

Total earnings = $2,165

Therefore, the shoe salesman earned a total of $2,165.

It's important to note that commission is a percentage of sales, and it can be a motivating factor for salespeople. A commission-based salary rewards high performers and incentivizes them to sell more. However, commission rates may vary depending on the industry, product, and company policies. Some companies may offer a higher commission rate for selling high-end products or for meeting or exceeding sales targets.

In conclusion, the shoe salesman earned $2,165 in total, which includes his commission and base salary. Commission-based salaries can be an effective way to motivate salespeople and incentivize high performance.

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Answer:

Or

Step-by-step explanation:

[tex]\bf 18a=56[/tex]

Divide both sides by 18:-

[tex]\bf \cfrac{18a}{18}=\cfrac{56}{18}[/tex]

Simplify:-

[tex]\bf a=\cfrac{28}{9}[/tex]

Or

[tex]\bf a=3.111....[/tex]

________________________

Hope this helps!

Answer:V<−4/25

Step-by-step explanation:

The best point estimate for the mean monthly electric bill for all residents of the local apartment complex is $148.

Since we are given the mean monthly electric bill for a sample of 80 residents of the apartment complex, we can use this as an estimate for the mean monthly electric bill for the entire population of residents. This estimate is known as a point estimate because it represents a single numerical value that is used to estimate the population parameter.

In this case, the sample mean of $148 is the best point estimate for the mean monthly electric bill for all residents of the local apartment complex. This is because the sample mean is an unbiased estimator of the population mean and it minimizes the variance of the estimates.

It is important to note, however, that the accuracy of the point estimate depends on the representativeness of the sample. If the sample is not representative of the population, the point estimate may not accurately reflect the population parameter.

Therefore, the correct answer is $148.

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If there are total 160 girl students in the total number of students in the college and ratio of boys to girls is 8: 5. Then total number of students in college is equals to the 416.

In a college, the ratio of the number of boys to girls = 8 : 5, so, total ratio is 13.

Number of girl students in the total number of students in the college = 160

We have a goal here to determine the total number of students in the college.

First of all, assume x be any number such that the number of girls and boys are

Number of girls= 5x

Number of boys = 8x

Total number of students in college= 13x

But total girls in college = 160 , so 5x= 160

solve the above expression (dividing by 5)=> x = 160/5 = 32

So, total boys students in college = 8x

= 8 × 32

= 256

Total number of students in college = 13x = 13× 32

= 416

Hence, required value is 416.

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Therefore, the length of side AC in triangle ABC is approximately 14.6 units.

A triangle is a closed two-dimensional geometric shape that is formed by connecting three non-collinear points with straight line segments. Each of these line segments is called a side, and the point where two sides meet is called a vertex. A triangle has three vertices, three sides, and three angles. Triangles can be classified based on the length of their sides and the size of their angles.

Here,

We can use the sine rule to find the length of side AC in triangle ABC, where angle A = 32° and AB = 8. The sine rule states that for any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides opposite to the angles A, B, and C, respectively.

In this case, we know the length of side AB (a = 8) and the measure of angle A (A = 32°), so we can set up the following proportion:

a/sin(A) = c/sin(C)

Substituting the values, we get:

8/sin(32°) = AC/sin(C)

Solving for AC, we get:

AC = (8/sin(32°)) * sin(C)

To find sin(C), we can use the fact that the sum of the angles in a triangle is 180°. So, we have:

C = 180° - 90° - A

C = 180° - 90° - 32°

C = 58°

Substituting this value, we get:

AC = (8/sin(32°)) * sin(58°)

AC ≈ 14.6

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To represent 7 ÷ 2 on a number line, we can start by drawing a line with the numbers 0 to 7 marked on it. Then, we can divide the line into two equal parts, since we are dividing 7 by 2. The midpoint of the line will represent the result of the division, which is 3.5.

Here is a rough sketch of what the number line could look like:

0------1------2------3------4------5------6------7

|_______________|

3.5

Alternatively, we can also represent the division using a fraction model. We can draw a rectangle and divide it into two equal parts. Then, we shade in 7 of the 12 equal parts, since 7 ÷ 2 can be written as the fraction 7/2 or 7 ÷ 2 = 3 1/2.

Here is a rough sketch of what the fraction model could look like:

+----+----+----+----+----+----+

| | | | | | |

+----+----+----+----+----+----+

| | | | | | |

+----+----+----+----+----+----+

In this model, each of the 12 parts represents 1/12 of the whole. We shade in 7 of the 12 parts to represent 7/12 of the whole, which is equivalent to 7 ÷ 2.

Answer:

[tex]x=20[/tex]

Step-by-step explanation:

Answer:

Let percentage that has been to both be x

60+80 –2x = 100

=> 140 –2x = 100

2x = 140 – 100

2x = 40

=> x = 20

Step-by-step explanation:

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The required ratio of the time to rotate first and next 2 revolution is given by option 2. (√2+1) : 1.

Merry go round starts from rest.

Let us assume that the initial angular velocity and displacement are zero. Final angular velocity after 2 revolutions is ω.

This implies,

ω₀ = 0 rad/s.

For first two revolutions of the merry go round we have,

θ = 2×2π rad

⇒ θ = ω.t₁ + 1/2 × α × t₁²

⇒ 2×2π = 0×t₁ + 1/2 × α × t₁²

⇒t₁² = 8π/α

⇒ t₁ = √(8π/α)

For first four revolutions of the merry go round we have,

θ = 4×2π rad

⇒ θ = ω.t₂ + 1/2 α.t₂²

⇒ 4×2π = 0×t₂ + 1/2 × α × t₂²

⇒ t₂² = 16π/α

⇒t₂ = √(16π/α)

Time taken for 3rd and 4th revolution of the merry go round is equals to,

t₃ = t₂ - t₁

Substitute the values we get,

⇒ t₃ = √(16π/α) - √(8π/α)

⇒t₃ = (√2-1) √(8π/α)

Ratio of time to rotate first 2 revolutions and next 2 revolutions is written as ,

t₁/t₃ = √(8π/α) / [(√2-1)√(8π/α)]

⇒ t₁/t₃  = 1/(√2-1)

Multiply and divide by the conjugate of √2-1 is equals to,

⇒ t₁/t₃  = 1/(√2-1) × (√2+1)/(√2+1)

⇒ t₁/t₃  = √2+1

Therefore, ratio of time to rotate first 2 revolutions & next 2 revolutions is  equals to option 2. (√2+1) : 1.

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The above question is incomplete, the complete question is:

A merry go round rotates from rest with constant angular acceleration `α` . Ratio of time to rotate first 2 revolutions & next 2 revolutions is

1) 1:1

2) (√2+1):1

3) √2:1

4) 1:√2

Answer:

Part A

The volume of solution A is represented as a fraction, so we need to convert it to a decimal number. To do this, we set up a long division problem with the numerator (the top number in the fraction) as the dividend and the denominator (the bottom number in the fraction) as the divisor. So the dividend is 1, and the divisor is the volume of solution A.

Part B

No, we cannot divide 2 by 9 evenly because they are not divisible without a remainder.

Part C

Since we cannot divide 2 by 9 evenly, the first digit of the quotient will be 0.

Part D

We set up the long division problem as follows:

 0.2 7 7 7 7 ...

-------------

9 | 1.0000

- 0.9

-----

1 0 0

9 0

---

1 0 0 0

9 0

-----

1 0 0 0

9 0

-----

1 0 0 0 0

9 0

-----

1 0 0 0 0

The decimal equivalent of 2/9 is 0.27777... (repeating). We can see that the division process continues indefinitely with the same repeating pattern, so we use an ellipsis to indicate that the pattern continues infinitely.

Part E

If we keep repeating the long division process for 2/9, we will continue to get the same repeating decimal pattern of 0.27777..., with no end in sight.

Part F

The volume of solution B is represented as the fraction 3/8, so we need to convert it to a decimal number. To do this, we set up a long division problem with the numerator (3) as the dividend and the denominator (8) as the divisor.

Part G

No, we cannot divide 3 by 8 evenly because they are not divisible without a remainder.

Part H

Since we cannot divide 3 by 8 evenly, the first digit of the quotient will be 0.

Part I

We set up the long division problem as follows:

 0.3 7 5

---------

8 | 3.0000

- 2.4

----

6 0

5 6

---

4 0 0

3 2

---

7 0 0

6 4

---

3 6 0

3 2

---

2 8 0

2 4

---

4 0

The decimal equivalent of 3/8 is 0.375. We can see that the division process terminates after a finite number of decimal places.

Part J

If we keep repeating the division process for 0.375, we will always get the same decimal number because the process terminates and doesn't involve any repeating pattern.

Part K

The volume of solution C is represented as the fraction 1/5, so we need to convert it to a decimal number. To do this, we set up a long division problem with the numerator (1) as the dividend and the denominator (5) as the divisor.

Part L

No, we cannot divide 1 by 5 evenly because they are not divisible without a remainder.

Part M

Since we cannot divide 1 by 5 evenly, the first digit of the quotient will be 0.

Part N

We set

Therefore, the temperature will be 17°C in the months of [tex]x = 4 + 48k[/tex] or    [tex]x = 20 + 48k,[/tex] where k is an integer.

Temperature is a measure of the average kinetic energy of the particles in a substance. In simpler terms, it is a measure of how hot or cold something is. The temperature is usually measured using a thermometer, which can be a simple device such as a mercury or alcohol thermometer, or a more complex electronic device such as a thermocouple or infrared thermometer. The standard unit of measurement for temperature is the degree Celsius (°C) or Fahrenheit (°F), although the Kelvin (K) scale is also commonly used in scientific contexts.

To find in which months the temperature will be 17°C, we need to solve the equation:

[tex]f(x) = 17[/tex]

Substituting the given equation of f(x), we get:

[tex]5 cos(x/12) + 14.5 = 17[/tex]

Simplifying this equation, we get:

[tex]cos(x/12) = 0.5[/tex]

[tex]cos(x/12) = cos(π/3 + 2kπ) or cos(x/12) = cos(5π/3 + 2kπ)[/tex]

cos(5π/3) = -0.5. Also, cos(x) has a period of 2π. Therefore, we can write:

[tex]cos(x/12) = cos(π/3 + 2kπ) or cos(x/12) = cos(5π/3 + 2kπ)[/tex]

where k is an integer.

Solving for x, we get:

[tex]x/12 = π/3 + 2kπ or x/12 = 5π/3 + 2kπ[/tex]

[tex]x = 4π + 24kπ or x = 20π + 24kπ[/tex]

Multiplying both sides by 12, we get:

[tex]x = 4π12 + 24kπ12 or x = 20π12 + 24kπ12\\x = 4π + 288kπ or x = 20π + 288kπ[/tex]

or in terms of 2π:

[tex]x = 4 + 48k or x = 20 + 48k[/tex]

where k is an integer. [tex]π[/tex]= pi

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The discount on the retailer's price is 27.08%. To calculate the discount percentage, we can use the following formula: Discount % = (MSRP - Retailer's price) / MSRP * 100%

The question asks to find the percentage discount between the manufacturer's suggested retail price (MSRP) and the retailer's price. To do this, we use the formula for calculating percentage discount. We subtract the retailer's price from the MSRP, divide that by the MSRP, and multiply by 100 to get the percentage. Plugging in the given values, we find that the discount percentage is 27.08%, which means that the retailer is selling the product at a 27.08% lower price than the MSRP.

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Tthe Fourier series may converge to a value that is different from the left and right limits of f at the point of discontinuity, or it may not converge at all (known as Gibbs phenomenon).

To determine the specific value to which the Fourier series converges at a point of discontinuity, we would need to analyze the specific function f and its Fourier series.

This typically involves calculating the Fourier coefficients, examining the convergence properties of the series, and potentially using techniques such as Cesàro summation to obtain a more accurate estimate of the limit.

Without further information about the specific function and point of discontinuity, we cannot provide a more specific answer.

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The inequality that describes the problem when coach Yamada is organizing community volleyball teams is x ≤ 9.

Why is x ≤ 9 the correct inequality that describes the problem when coach Yamada is organizing community volleyball teams? Here is why: We know that coach Yamada wants each team to have 8 players but he can't make as many full teams as he wanted to because fewer than 80 people signed up.

Let x represent the number of full teams coach Yamada can make. We know that 1 team can have 8 players. Therefore, the number of players needed for x full teams = 8xWe also know that fewer than 80 people signed up. So, 8x < 80, if more than 80 people signed up then coach Yamada would be able to make more than x full teams.

Since coach Yamada can't make a fraction of a team so x should be an integer. Therefore, the solution for 8x < 80 is x ≤ 9.Therefore, x ≤ 9 is the inequality that describes the problem when coach Yamada is organizing community volleyball teams.

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