(a) Points and are shown on the number line. Part A Find the distances between points and and between points and . Show your work or explain your answers. Refer to the number lint in your explanation. Enter your answers and your work or explanation in the box provided.

Answer:

[tex]y' = \dfrac{1 + x \sin x - x \cos x + \sin x + \cos x}{(\cos x - x)^2}[/tex]

Step-by-step explanation:

[tex] y = \dfrac{x + \sin x}{\cos x - x} [/tex]

Derivative of a quotient:

[tex] \dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{g'h - h'g}{h^2} [/tex]

Recall:

[tex] \dfrac{d}{dx} \sin x = \cos x [/tex]

[tex] \dfrac{d}{dx} \cos x = - \sin x [/tex]

[tex] y = \dfrac{x + \sin x}{\cos x - x} [/tex]

[tex] y' = \dfrac{dy}{dx} = \dfrac{(1 + \cos x)(\cos x - x) - [(- \sin x - 1)(x + \sin x)]}{(\cos x - x)^2} [/tex]

[tex]y' = \dfrac{\cos x - x + \cos^2 x - x \cos x - (-x \sin x - \sin^2 x - x - \sin x}{(\cos x - x)^2}[/tex]

[tex]y' = \dfrac{\cos x - x + \cos^2 x - x \cos x + x \sin x + \sin^2 x + x + \sin x}{(\cos x - x)^2}[/tex]

[tex]y' = \dfrac{\sin^2 x + \cos^2 x + x - x - x \cos x + x \sin x + \sin x + \cos x}{(\cos x - x)^2}[/tex]

[tex]y' = \dfrac{1 + x \sin x - x \cos x + \sin x + \cos x}{(\cos x - x)^2}[/tex]

Answer: 7/3 or 2.333

Step-by-step explanation:

the formula for slope is y2-y1 over x2-x1

so if you apply the formula here its going to be

4-(-3) over 5-2

which is 7 over 3 therefore your slope will be

7/3

Answer:

[tex]m=\frac{7}{3} =2.33333... = 2.\overline{3}[/tex]

Step-by-step explanation:

-2(-3)+18=24

6+18 = 24

24 = 24

6(-3) +9=-13

-18+9 = -13

-9 ≠ - 13

4(-3)-9=-21

-12 -9 =-21

-21 = -21

Answer:

No.

Step-by-step explanation:

An integer is defined as a whole number.

The number given, "1.765", is not a whole number, as it includes the decimal .765. 1.765, as implied by decimal point, is a decimal number.

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Using mathematical operations on the word problem, the amount he will receive as his change is $1.43

A word problem is a few words are presented in a form of problem and  needs to be solved by way of a mathematical calculation.

This problem can be solved using mathematical operation such as addition and subtraction.

The total amount he has with him = $15

The current bill = $8.33

The fruit salad = $2.99

Tip = $2.25

Total amount spent = 8.33 + 2.99 + 2.25

The total amount spent = 13.57

The amount of change = total amount he has with him - total amount spent

The amount of change = 15 - 13.57

The amount of change = 1.43

The change he is going to receive is $1.43

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Answer: -10,-8.7, -9.1, 8, 8.7, 8.06, 9

Step-by-step explanation:

77 squared rooted equals 8.7

-83 square rooted equals -9.1

-76 square rooted equals -8.7 ( remember negative numbers are greater than positive numbers)

65 square rooted equals 8.06

Answer:

The normal price of a pen is £8

Step-by-step explanation:

let p be the normal price.

The statement : “normal prices are reduced by 15%. The normal price of a pen is reduced by £1.20”

Means

[tex]p \times \frac{15}{100} = 1.20[/tex]

Then

[tex]p = 1.20 \times \frac{100}{15} = \frac{120}{15} = 8[/tex]

Answer:

The normal price of the pen is £8

Step-by-step explanation:

Reduced by 15%

Reduced by £1.20

Meaning that 15% is £1.20

To find the 100% or the normal price of the pen we find the 1% first then the 100%

So, 1% = £1.20/15

100% =£1.20/15 x 100

= 8

Checking..

If normal price was 8 and reduction is 15%

8(1- R/100) {R = %}

8(1 -15/100) = 6.8 (Reduced price)

8 - 6.8 = £1.20 ( Reduction price aka the 15%)

Therefore, the normal price of the pen is £8.

The expression that we can use to substitute into the first equation is

x = - 3y + 12.    

The algebraic approach to solving linear equations is known as the substitution method. This procedure involves substituting a variable's value from one equation into the other. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

Here we have

2x + y = 8 ---- (1)

- x - 3y = -12 ----- (2)  

We can isolate x in the second equation  as given below

=> - x - 3y = -12

Add 3y on both sides

=>  - x - 3y + 3y = - 12 + 3y

=>  - x = - 12 + 3y

Multiply by -1 on both sides

=>  -(- x) = - (- 12 + 3y)

=>  x = + 12 - 3y

=>  x = - 3y + 12      

Therefore,

The expression that we can use to substitute into the first equation is

x = - 3y + 12.    

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Answer:

x < 4

Step-by-step explanation:

4x - 6 < 10

4x < 16

x < 4

[tex]4x-6 < 10[/tex]

Add 6 to both sides:

[tex]4x-6+6 < 10+6[/tex]

[tex]4x < 16[/tex]

Divide both sides by 4:

[tex]\dfrac{4x}{4} < \dfrac{16}{4}[/tex]

[tex]\fbox{x} < \fbox{4}[/tex]

The measure of the angle ∠MAR will be equal to 26°. The correct option is A.

In geometry, an angle bisector is a line that divides an angle into two equal angles. A bisector is something that divides a shape or object into two equal parts. An angle bisector is a ray that divides an angle into two equal parts of the same measurement.

Given that Ray AT bisects ∠MAR. If m∠MAT = (8x − 3)° and m∠RAT = (2x + 9)°,

The two angles ∠MAT and ∠RAT will be equal. Then calculate the value of x.

8x - 3 = 2x + 9

8x - 2x = 9 + 3

6x = 12

x = 2

The angle ∠MAR is calculated as,

∠MAR = 2 x ∠RAT

∠MAR = 2 x ( 2x + 9)

∠MAR = 2 x ( 2 x 2 + 9 )

∠MAR = 2 x ( 13 )

∠MAR  = 26°

Option A is correct for the angle ∠MAR.

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Answer:

A all the way

Step-by-step explanation:

The slant height of the cone c² = 5² + (1)² or c ≅ 5.1.

Option (A) is correct option.

A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.

Given that,

The radius of the cone = 1 inch,

And the height of the cone = 5 inch.

Let the slant height of the cone is c,

To find the slant height of the cone, use Pythagorean theorem,

c² = 5² + (1)²

c² = 25 + 1

c² = 26

c= 5.09

c ≅ 5.1

The slant height of the cone is 5.1 inch.

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Answer: 10w

Step-by-step explanation:

To create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month, we need to first calculate the sample proportion.

The sample proportion is calculated by dividing the number of adults who ate fast food at least once in the past month (722) by the total number of adults surveyed (1000). This gives us a sample proportion of 0.722.

To calculate the confidence interval, we can use the following formula:

Plugging in the values, we get:

This gives us a 95% confidence interval of (0.6901, 0.7539). Rounded to four decimal places, the confidence interval is (0.6901, 0.7539).

Note: To calculate the confidence interval using Excel, you can use the following formula:

Where "alpha" is the desired confidence level (e.g., 0.95 for a 95% confidence interval), "standard_dev" is the standard deviation of the sample, and "size" is the sample size. To calculate the standard deviation, you can use the STDEV.P function.

For example, to calculate the lower and upper bounds of the 95% confidence interval, you could use the following formulas:

Where A1:A1000 is a range containing the values "1" for those adults who ate fast food at least once in the past month and "0" for those who did not. This will give you the same result as the manual calculation above.

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We have proved that the ray FE is parallel to the ray GC.

What is meant by parallel lines?

In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.

Angle DEF intersects at B

which results in angle DEF corresponding to the angle  ACG.

As DEF = 45 so angle ACG = 45

So by the above discussion, we can say that the ray FE is parallel to the ray GC.

Hence, we have proved that the ray FE is parallel to the ray GC.

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The critical value is given as 1.69

The margin of error is 0.00161

We are to find the critical value ta/2  used for finding the margin of error

T∝ / 2 = 1 - 0.10 / 2

1 - 0.05 = 0.95

The critical value at the level if we use the critical value table is 1.69

2. Next we would have to solve for the margin of error

When comparing your results to the actual population value, a margin of error indicates how many percentage points they will deviate.

ME= [tex]z * \frac{s}{\sqrt{n} }[/tex]

z is the critical value = 1.69

s = standard deviation = 0.00573

n = sample size

where z = 1.69

s = 0.00573

n = 36

We would have to put these values in the formula above to get the margin of error

[tex]1.69 * \frac{0.00573}{\sqrt{36} }[/tex]

Margin of error = 0.00161

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By dividing the length of bacteria cell to length of amoeba cell we find option (D) i.e 6.67x102 is the correct answer.

Division is an arithmetic operation that involves dividing one number (the dividend) by another number (the divisor) to find the quotient.

Arithmetic operators are symbols that represent mathematical operations that can be performed on one or more operands. The most common arithmetic operators are:

Addition (+): Adds two operands and produces the sum.

Subtraction (-): Subtracts one operand from another and produces the difference.

Multiplication (*): Multiplies two operands and produces the product.

Division (/): Divides one operand by another and produces the quotient.

Modulo (%) : Divides one operand by another and produces the remainder.

Exponentiation (**): Raises one operand to the power of the other and produces the result.

To compare the sizes of the two cells, we need to divide the length of the bacterial cell by the length of the amoeba cell. The result is 3 x 10^−6 m / 4.5 x 10^−4 m = 0.67 x 10^−2.

So, the bacterial cell is approximately 0.67 x 10^−2 times smaller than the amoeba cell.

The correct answer is therefore (D) 6.67 x 10

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Answer:

Step-by-step explanation:

Let's call the side lengths of the first quadrilateral a, b, c, and d, and the side lengths of the second quadrilateral A, B, C, and D. We are given that the perimeter of the second quadrilateral is 20 cm, and that the quadrilaterals are similar. This means that the ratio of the side lengths of the two quadrilaterals is the same for all four sides. Let's call this ratio r. Then we have:

A + B + C + D = 20 cm

and

A/a = B/b = C/c = D/d = r

We can find the value of r by taking the ratio of any two sides of the quadrilaterals. For example, we can take the ratio of A to a:

A/a = r

Substituting the expressions for A and a in terms of r, we get:

(ra)/a = r

Solving for r, we get:

r = a/a = 1

This means that the ratio of the side lengths of the two quadrilaterals is 1. Therefore, the side lengths of the second quadrilateral are equal to the side lengths of the first quadrilateral. Substituting the given values for the side lengths of the first quadrilateral, we get:

A = 6 cm

B = 5 cm

C = 8 cm

D = 11 cm

Therefore, the side lengths of the second quadrilateral are A = 6 cm, B = 5 cm, C = 8 cm, and D = 11 cm.

The numerical expression to represent the rate of temperature change in degrees Fahrenheit per foot is 0.14 degrees Celsius per foot.

What do you mean by numerical expression?

A group of numbers that have been written together using the arithmetic operations addition, subtraction, multiplication, and division is known as a numerical expression in mathematics. The number can be stated in a variety of ways, including verbally and numerically.

According to the given question,

To calculate the rate of temperature change in degrees Fahrenheit per foot,

We need to first convert degrees Fahrenheit to degrees Celsius.

To do this, we divide 100 by 5.9.

This yields a result of 0.14 degrees Celsius per foot.

Therefore, the numerical expression to represent the rate of temperature change in degrees Fahrenheit per foot is 0.14 degrees Celsius per foot.

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The decibel equation is used in many different contexts, including acoustics, audiology, and engineering, to measure and compare the intensity of sounds.

The decibel equation is a measure of sound intensity, which is a way to describe the strength or magnitude of a sound. It is expressed as dB, and it is defined as the ratio of the intensity of a sound to a reference intensity. The reference intensity is usually set at a level that is the minimum intensity that a person can hear, which is approximately 0 dB.

The decibel equation is typically written as:

dB = 10 × log10(I / I0)

where I is the intensity of the sound being measured and I0 is the reference intensity. The log10 part of the equation is used to express the ratio of the two intensities on a logarithmic scale, which allows the decibel value to be more easily interpreted.

The decibel scale is logarithmic, which means that a small change in decibel value corresponds to a much larger change in sound intensity. For example, a sound with a decibel value of 60 dB is much louder than a sound with a decibel value of 50 dB, even though the difference between the two values is only 10 dB.

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Let x be the number of sliders in the combination meal and y be the number of chicken wings in the combination meal. We can write the first equation in the system by equating the total number of sliders and chicken wings in the combination meal with the sum of the number of sliders and the number of chicken wings. Since the combination meal has 10 sliders and chicken wings altogether, we can write the equation x + y = 10.

The second equation in the system can be written by equating the total number of calories in the combination meal with the sum of the number of calories in the sliders and the number of calories in the chicken wings. Since each slider has 225 calories and each chicken wing has 70 calories, the total number of calories in the sliders is 225x and the total number of calories in the chicken wings is 70y. And since the combination meal contains 1165 calories, we can write the equation 225x + 70y = 1165.

Therefore, the system of equations that could be used to determine the number of sliders and chicken wings in the combination meal is x + y = 10 and 225x + 70y = 1165.

The statements that apply to the given random sample situation are:

(A) Despite the idea that the sample must be random, we are unsure of this.

(C) It is underreported how many pupils don't drive to school.

(D) n(1p) is not greater than 10.

A simple random sample, also known as an SRS, is a smaller group of individuals (also known as a sample) chosen randomly and with equal probability from a larger population.

This technique involves picking a sample at random.

The probability of being chosen from any subset of k persons in SRS is the same as that of being chosen from any other subset of k people.

A simple random sample is an objective sampling approach.

A basic sampling method that can be used in conjunction with other, more advanced sampling techniques is simple random sampling.

So, statements that apply in the given situation are:

- We don't know if the sample is random, despite the fact that it must be.

- The number of students who don't drive to school is undercounted.

- n(1−^p) does not exceed 10.

Therefore, the statements that apply to the given random sample situation are:

(A) Despite the idea that the sample must be random, we are unsure of this.

(C) It is underreported how many pupils don't drive to school.

(D) n(1p) is not greater than 10.

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Correct question:
The administration at GSU wants to estimate the number of parking spaces they will need next year. They survey 80 students; 75 of the students in the sample drive to campus by themselves each day. Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus? Check all that apply.

a. The sample needs to be random but we don’t know if it is.

b. The actual count of drivers is too small.

c. The actual count of those who does not drive to campus is too small.

d. n ^ p is not greater than 10. n ( 1 − ^ p ) is not greater than 10.

Answer:

1 × ( –6 × – 18 – 8) ÷ 4=[tex]\frac{1}{404}[/tex]

–4 – –20 + –5 ×( –11 – –18)=[tex]18[/tex]

13 – –10 × 16 ÷(14 + –16)=[tex]173[/tex]

1– –9 × 12 × (–19 + 20)=[tex]110[/tex]

Answer:

  C.  C = $10 +$5h

Step-by-step explanation:

The cost is a $10 admission fee plus $5 per hour for sledding. You want an equation representing the cost C in terms of hours h.

The cost is ...

   cost = admission fee + hourly charge

The hourly charge is the product of the cost per hour ($5) and the number of hours (h).

  C = $10 +$5h

Answer:

After factorization the result is: (7x + 4)(x - 1).

Step-by-step explanation:

To factor 7x² + 3x - 4, we can use the following steps:

Look for two numbers that multiply to give the constant term (-4) and add to give the coefficient of the linear term (3). These two numbers are -4 and 1.

Use these numbers to create two binomials, one with a positive sign and one with a negative sign: (7x + 4) and (7x - 1).

Factor the quadratic expression by grouping:

(7x + 4)(x - 1)

We can check that this is the correct answer by multiplying the two binomials:

(7x + 4)(x - 1) = 7x² + 3x - 4

This is the original expression, so we have successfully factored it.

Note: Depending on the specific problem, there may be more than one way to factor the expression. This is just one possible solution.

Answer:

[tex]\dfrac{8}{12}[/tex]

Step-by-step explanation:

Let the unknown fraction be:

If the sum of the numerator and denominator is 20 then:

[tex]\implies a+b=20[/tex]

Rewrite the equation to isolate b:

[tex]\implies b=20-a[/tex]

If the fraction is equal to 2/3 then:

[tex]\implies \dfrac{a}{b}=\dfrac{2}{3}[/tex]

Cross multiply:

[tex]\implies 3a=2b[/tex]

Substitute the expression for b into the cross-multiplied equation and solve for a:

[tex]\implies 3a=2(20-a)[/tex]

[tex]\implies 3a=40-2a[/tex]

[tex]\implies 5a=40[/tex]

[tex]\implies a=8[/tex]

Substitute the found value of a into the equation for b and solve for b:

[tex]\implies b=20-8[/tex]

[tex]\implies b=12[/tex]

Therefore, the fraction for which the sum of the numerator and denominator is 20, and the value of the fraction is equal to 2/3 is:

Answer:

2

Step-by-step explanation:

1+1=2
XD

Answer:

2

Step-by-step explanation:

I know this is a joke but I don't care

The farthest drainage ditch​ is 39 feet away from the well.

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}

Given, an environmental engineer graphed the locations of a well and all the drainage ditches in the vicinity.

She positioned the well at (−6,7) and the farthest drainage ditch at (33,7).

To find the distance:

Let d be the distance.

d = √{(x₂-x₁)² + (y₂-y₁)²}

Here, x₂ = 33, x₁ = -6, y₂ = 7 and y₁ = 7

Substituting the value to the distance formula,

d = √{(33+6)² + (7-7)²}

d = √{(39)² + (0)²}

d = √{(39)²

d = 39

Therefore, the value of d is 39.

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Answer: LCD = 60

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/30, 9/20

For the denominators (30, 20) the least common multiple (LCM) is 60.

Therefore, the least common denominator (LCD) is 60.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/30 = 1/30 × 2/2 = 2/60

9/20 = 9/20 × 3/3 = 27/60

Assume you are buying a bond with a par value of $1,000 which is listed in the Wall Street Journal at a price of 100.50. The bond price is: $1,005.

Using this formula to determine the bond price

Bond price = Bond par value × price/100

Where:

Bond par value = $1,000

Price = 100.50

Let plug in the formula

Bond price = $1,000 × 100.50 /100

Bond price = $100,500 /100

Bond price =$1,005

Therefore the bond price is $1,005.

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