(1 point) Match the confidence level with the confidence interval for μ. 1.1.645 2. x ±2.575 3. x ±1.96 A. 95% B. 99% C. 90% (

The cost of each music video is $1.99.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given total cost of 2 music videos, a TV series and a movie is $42.95

and TV series cost 2 times as much as the movie,

cost of the movie = $12.99

cost of  TV series = 2*12.99

cost of  TV series = $25.98

let the cost of a video be x

so according to condition,

2x + cost of  TV series + cost of the movie = $42.95

2x + 25.98 + 12.99 = 42.95

2x = 42.95 - 25.98 - 12.99

2x = 3.98

x = 3.98/2

x = $1.99

Hence the cost of a music video is $1.99.

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Answer:

Indeed it Correct, but am not quiet sure

Step-by-step explanation:

The absolute value of any equation can never be negative.

|4x - 2| = -6 has a negative value -6.

The |4x - 2| = -6 has no solution for x because |x| can not be negative.

Answer:

it would be 85

I hope this helps!

Answer:85,79,73

I step-by-step explaition

The number given-6=x

The fraction that is equivalent to the repeating decimal 0.35 is 7/20.

To determine the fraction that is equivalent to the repeating decimal 0.35, we can follow the steps below:

Step 1: Let x be equal to the repeating decimal 0.35.

Step 2: Multiply both sides of the equation in Step 1 by 100 to eliminate the decimal point:

   100x = 35.35

Step 3: Subtract the equation in Step 1 from the equation in Step 2 to eliminate the repeating decimal:

   100x - x = 35.35 - 0.35
          99x = 35

Step 4: Simplify the equation in Step 3 by dividing both sides by 99:

   x = 35/99

Step 5: Simplify the fraction 35/99 to reduced form by dividing both the numerator and denominator by their greatest common factor, which is 5:

   35/99 = (7 x 5)/(11 x 9 x 5) = 7/20

Therefore, the fraction that is equivalent to the repeating decimal 0.35 is 7/20.

To understand how we arrived at the fraction 7/20 as the equivalent of the repeating decimal 0.35, we need to have a basic understanding of decimals and fractions.

Decimals are a way of expressing parts of a whole in base 10. In a decimal number, the digits to the right of the decimal point represent fractions of 10, 100, 1000, and so on. For example, the decimal 0.35 represents 3/10 + 5/100, which can be simplified to 35/100.

On the other hand, fractions are a way of expressing parts of a whole in terms of a numerator and a denominator. The numerator represents the number of equal parts being considered, and the denominator represents the total number of equal parts that make up the whole. For example, the fraction 7/20 represents 7 parts out of 20 equal parts, or 7/20 of the whole.

Sometimes, a decimal number can be expressed as a fraction with integers as the numerator and denominator. These types of fractions are called rational numbers, and they can be expressed as terminating decimals or repeating decimals.

Terminating decimals are decimals that end, such as 0.5, 0.75, or 0.125. These decimals can be expressed as fractions with integers as the numerator and denominator by counting the number of decimal places and setting the denominator to a power of 10 that corresponds to that number. For example, 0.5 can be expressed as 5/10, which simplifies to 1/2.

Repeating decimals are decimals that have a pattern of one or more digits that repeat infinitely. For example, the decimal 0.333... has a repeating pattern of 3, and the decimal 0.142857142857... has a repeating pattern of 142857. These decimals can also be expressed as fractions with integers as the numerator and denominator.

To convert a repeating decimal to a fraction

We start by letting x be the repeating decimal, and we multiply both sides of the equation by 10, 100, 1000, or some other power of 10 to eliminate the decimal point. We then subtract the original equation from the new equation to eliminate the repeating decimal, and we simplify the resulting equation by dividing both sides by a common factor. The resulting fraction can then be simplified to reduced form by dividing both the numerator and denominator by their greatest common factor.

In the case of the repeating decimal 0.35, we followed these steps and arrived at the fraction 7/20 as the equivalent. This means that 0.35 and 7/20 represent the same value or amount. To verify this, we can convert 7/20 to a decimal by dividing 7 by 20, which gives 0.35.

Therefore, 0.35 and 7/20 are equivalent forms of the same value or amount.

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Answer:

(5^6)/(5^3) = 5^3 or 125

Step-by-step explanation:

^ = raised power

(5^6)/(5^3)

because base (5) is same:

law of indices: n^a ÷ n^d = n^(a-d)

therefore

5^6 ÷ 5^3 = 5^(6-3)

= 5^3 which is 125

Answer:

400,000

Step-by-step explanation:

Calculate the doubling time period-

Doubling time period(t)=

doubling time period(t)= 2

Calculate the new population using the doubling time formula below where t is the number of doubling periods:

Population = Initial Population * \(2^{t}\)

Population = 100000 * \(2^{2}\)

Population = 100000 * 4

Answer:

The Triangles are not similar. (There are no s's in the triangle anywhere)

Step-by-step explanation: Look at the image and try to find the letters and trace the line its in.

Answer: 41

Step-by-step explanation:

From the question, we are informed that we should find the 20th term of the sequence 3+2(n-1).

In the above scenario, n has been given as 20, therefore in the equation given, we put n as 20. This will be:

= 3+2(n-1)

= 3+2(20-1)

= 3+2(19)

= 3+38

= 41

The 20th term is 41

Answer:

Shirley bought a fax machine and sells to Devi at a profit of 25% on the cost price.

Shirley buy price:: x

Devi buy price:: 1.25x

Devi sells the fax machine to Amirah at a loss of 250 on the price which she buys it from Shirley.

Amirah buy price = 1.25x -250

if Amirah pays $360 for the fax machine,how much did Shirley pay for it?

Equation:

1.25x - 250 = 360

1.25x = 360 + 250

x = 610 / 1.25

x = 488

Ans: x = $488 (Price Shirley paid)

The utility’s percent change from 2010 to 2020 is a decrease of 4.07%

How many years are between 2010 and 2020?

There are 10 years in between 2010 and the year 2020, which means that the total decline over a period of 10 years is the annual decrease multiplied by 10.

Total decrease in 10 years=2.6*10

Total decrease in 10 years=26.0

Utility industry jobs in 2020=639.5-26.0

Utility industry jobs in 2020=613.5

The percentage change 2010-2020=(2020 jobs/2010 jobs)-1

The percentage change 2010-2020=(613.5/639.5)-1

The percentage change 2010-2020=-4.07%

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Answer:

5

Step-by-step explanation:

add the numbers up then divide by how many there are.

3+4+5+6+7=25

25÷5 = 5

The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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Answer:

A.)x=6

B.)x=16

did u mean to solve it or do something else if this is not the way u mean i can do another way if u like

cos B = \(\frac{BC}{BD}\) \(=\frac{4}{8}\) \(=\frac{1}{2}\)   c = [a2 + b2 - 2ab cos C] is the cosine formula used to determine the side of the triangle. a, b, and c are indeed the triangle's three sides. is that response accurate.

How do you calculate sin and cos B?

Formula: Sin (a,b) Cos

Sin a cos b = (1/2)[sin(a + b) + sin(a - b)] is the formula for sin a cos b. Whenever the composite angles (a + b) and (a - b) are available, as well as the quantities of degrees a and b, following equation for sin a cos b may be used.

How does the cosine rule work?

Every triangle that you would like to connect all 3 components to a single angle can benefit from the cosine rule. Knowing the other 2 aspects and indeed the opposing angle are necessary to determine the lengths of a side. It's edge a that you're looking for.

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The width and length of the rectangle is 4.5ft and 12ft.

Width of a rectangle = b = x ft.

Length of a rectangle = l = (2x+3) ft.

Area of the rectangle = l×b = 54 sq.ft.

                                    = x (2x + 3) = 54

                                    = 2x² + 3x = 54

                                      (2x-9)(x+6) = 0

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.

 It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).

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Answer(may be wrong but I tried):

mFG=195 and mEG=195

Step-by-step explanation:

If mEF=80 That means to find G we need to solve 195-80, which is 115 so G=115. I am assuming that since mEF=80 both are 40, so mFG is 40+115=195

mEG= 40+115 which is also 195

Answer:

84

Step-by-step explanation:

To find the range, find the difference between the largest value and the smallest value.

544 - 460 = 84

Answer:

let amount of games won and lost be x and y respectively

y+18=x

x+y=78

y+y+18=78

2y=78-18

2y=60

y=30

x=30+18

x=48

thus, games won is 48

The mean weight for each group and the difference between them, calculate the mean weight for group a and group b separately, and then subtract the mean of group b from the mean of group a.

To calculate the mean weight for each group (xa and xb), follow these steps:

1. Add up all the weights of group a and divide by the total number of data points in group a to find the mean weight (xa).
2. Repeat the same process for group b, adding up all the weights and dividing by the total number of data points to find the mean weight (xb).
3. Finally, subtract the mean of group b (xb) from the mean of group a (xa) to find the difference between the two means (xa - xb).

In summary, to find the mean weight for each group and the difference between them, calculate the mean weight for group a and group b separately, and then subtract the mean of group b from the mean of group a.

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The probability of the event happening is 41/65, which can be simplified but cannot be further reduced without additional information.

The total probability is universally 1 so the probability of happening is,

Probability of event happening = 1 - Probability of event not happening.

In this case, the probability of event not happening is 24/65. Substituting this value into the formula, we get,

Probability of event happening = 1 - 24/65

To simplify this fraction, we can find a common denominator of 65,

Probability of event happening = (65/65) - (24/65)

This simplifies to,

Probability of event happening = 41/65

Therefore, the probability of the event happening is 41/65.

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Using the vertical asymptote concept, it is found that the tangent function is undefined when \(\theta = \frac{\pi}{2}\).

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

In this problem, we have that:

\(\theta = \frac{\pi}{2}\), which means that \(\cos{\theta} = 0\).

Since \(\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}\), the tangent function is undefined when \(\theta = \frac{\pi}{2}\).

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Answer:

d: tan 0

Step-by-step explanation:

(i) The relationship between the OLS estimators of α₂ and ᵝ₂ can be determined by considering the relationship between the consumption function and the savings function. Since X = Y + Z, we can substitute this into the consumption function equation to obtain Y = α₁ + α₂(Y + Z) + e. Simplifying the equation, we get Y = (α₁/(1 - α₂)) + (α₂/(1 - α₂))Z + (e/(1 - α₂)). Comparing this equation with the savings function Z₁ = ᵝ₁ + ᵝ₂X + u₁, we can see that the OLS estimator of ᵝ₂ is related to the OLS estimator of α₂ as follows: ᵝ₂ = α₂/(1 - α₂).

(ii) The residual sum of squares (RSS) will not be the same for the two models of Y₁ = α₁ + α₂X₁ + e and Z₁ = ᵝ₁ + ᵝ₂X₁ + u₁. This is because the error terms e and u₁ are different for the two models. The RSS is calculated as the sum of squared differences between the observed values and the predicted values. Since the error terms e and u₁ are different, the predicted values and the residuals will also be different, resulting in different RSS values for the two models.

(iii) The R² terms of the two models cannot be directly compared. R² is a measure of the proportion of the total variation in the dependent variable that is explained by the independent variables. Since the consumption function and the savings function have different dependent variables (Y and Z, respectively), the R² values calculated for each model represent the goodness of fit for their respective dependent variables. Therefore, the R² terms of the two models cannot be compared directly.

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The slope of the tangent line at (4, 54) is 45. So the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 45x - 126.

To find the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54), we need to use calculus. First, we find the derivative of the function:

y' = 3x^2 - 3

Next, we plug in x = 4 to find the slope of the tangent line at that point:

y'(4) = 3(4)^2 - 3 = 45

So the slope of the tangent line at (4, 54) is 45. To find the equation of the line, we use the point-slope form of the equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point on the line. Plugging in our values, we get:

y - 54 = 45(x - 4)

Simplifying, we get:

y - 54 = 45x - 180

y = 45x - 126

So the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 45x - 126.

To find the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54), we need to first find the derivative of the function and then use the point-slope form of a line.

1. Find the derivative of the function with respect to x:
y'(x) = d/dx (x^3 - 3x + 2) = 3x^2 - 3

2. Evaluate the derivative at the given point (4, 54) to find the slope of the tangent line:
m = y'(4) = 3(4)^2 - 3 = 3(16) - 3 = 48

3. Use the point-slope form of a line (y - y1 = m(x - x1)):
y - 54 = 48(x - 4)

4. Simplify the equation:
y - 54 = 48x - 192
y = 48x - 138

So, the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 48x - 138.

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Answer:

87

m

2

x

T

U

V

W

−

18

m

2

V

U

T

W

+

598

m

2

V

U

x

2

T

W

Step-by-step explanation:

Answer:

78k = k

Step-by-step explanation:

In order to analyze gender differences in ACT performance, you would calculate the frequency of ACT scores for each gender, as well as the total frequency of ACT scores. So, you would calculate C: frequencies.

This would give you a count of the number of males and females who scored less than 20, 20 up to 25, and 25 and more on the ACT. With this information, you can compare the distribution of ACT scores between males and females, and determine if there are any significant differences in performance between the two groups. This information is commonly represented in a frequency table, which displays the number of observations (or count) for each category of a variable.

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Answer:

640

Step-by-step explanation:

2 pints in a quart

4 quarts in a gallon

8 pints in a gallon

8x80=640

640

Answer:

30cm

Step-by-step explanation:

area of a Trapezium = 1/2()a+b)h

a and b are the two sides

h is the height

Given

Area = 400 cm^2

a =20cm

h = 16cm

Required

b

Substitute

400 = 1/2(20+b))*16

800 = (20+b)*16

800/16 = 20 + b

50 = 20 + b

b = 50-20

b = 30cm

Hence the length of other side is 30cm