Eric bought a canoe for $329.99. The sales tax was 5%. What is the total cost including tax?

Step-by-step explanation:

AC+CB+BA=180

2x+23+3x-8+4x+1=180

9x+16=180

9x=180-16

9x=164

x=164/9

x=18.2

There are 64 different 3-digit numbers that can be formed using the digits 1, 2, 3, and 4, allowing for digit repetition.

If the digits 1, 2, 3, and 4 can be repeated, we can calculate the number of possible combinations by multiplying the number of options for each digit. In this case, we have four choices for each of the three digits. Thus, we have 4 x 4 x 4 = 64 different combinations. Each combination represents a unique 3-digit number that can be formed using the given digits.

To understand this better, let's break it down. The first digit can be any of the four given digits: 1, 2, 3, or 4. Similarly, the second and third digits can also be any of the four options. Since each digit can be repeated, we multiply the number of options for each digit to find the total number of combinations.

Therefore, there are 64 different 3-digit numbers that can be formed using the digits 1, 2, 3, and 4, allowing for repetition.

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The area of the shaded region is 200. 96 square units

From the diagram shown, we have that the shape of the shaded area is spherical.

Now, the formula for calculating the area of a sphere is expressed as;

A = 4πr²

Such that the parameters of the formula are expressed as;

Substitute the values, we have;

Area = 4 × 3.14 × 4²

Find the squares, we have;

Area = 4 × 3.14 ×16

Multiply the values, we have;

Area = 200. 96 square units

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To find the Jacobian of the transformation, we need to calculate the partial derivatives of x and y with respect to u and v:

∂x/∂u = 1

∂x/∂v = 0

∂y/∂u = 2v

∂y/∂v = 2u

So the Jacobian matrix is:

J = | ∂x/∂u   ∂x/∂v |

   | ∂y/∂u     ∂y/∂v |

    | 1      0 |

    | 2v 2u |

And the Jacobian determinant is:

|J| = (1)(2u) - (0)(2v) = 2u

To sketch the region g, we need to find the values of u and v that satisfy the inequalities:

1 ≤ u ≤ 2

2 ≤ 2uv ≤ 4

Dividing both sides of the second inequality by 2v, we get:

1/v ≤ u ≤ 2/v

If we plot the lines u = 1/v and u = 2/v on the uv-plane, we see that they intersect at v = 1 and v = 2, as shown below:

     |       /

2/v |     /

     |   /

     | /  

     |/  

--------------> u

    /|

  /  |

/    |

/     |

1/v   |

Therefore, the region g is the trapezoidal region bounded by the lines u = 1/2, u = 1, u = 2, and the x-axis:

     |       /

     |     /|

     |   /  |

     | /    |

----------------------> u

    /|

  /  |

/    |

/     |

Note that the sides of the trapezoid are the images of the lines v = 1/2 and v = 2 under the transformation x = u, y = 2uv.

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In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

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Answer:

60

Step-by-step explanation:

240 x 25% / 100

Answer:

48 students are in the Environmental Club

Step-by-step explanation:

20/100 x 240/1 = 48

Cancel out the zeroes and you get 2 x 24 over 1 x 1, which equals 48

Hope this helps :)

Answer:

Medimos el perímetro en unidades lineales, que representan una sola dimensión. Ejemplos de unidades de medida de longitud son pulgadas, centímetros, ... Encontrar el perímetro de un triángulo con lados que miden 6 cm, 8 cm, y 12 cm. ... P = 2l + 2w, donde l es el largo del rectángulo y w l ancho del rectángulo. espe

The function is r(θ) = 3θ + sin(θ) + C, where C is a constant.

To find the function r(θ), we need to integrate the given derivative r'(θ) = 3 + cos(θ) with respect to θ. Integrating 3 with respect to θ gives 3θ, and integrating cos(θ) gives sin(θ). However, when we integrate cos(θ), we need to add a constant of integration, which we'll represent as C.

So the function r(θ) = 3θ + sin(θ) + C satisfies the condition r'(θ) = 3 + cos(θ).

To determine the value of C, we use the given point P(π/2, 0). Substituting θ = π/2 into the function, we have:

0 = 3(π/2) + sin(π/2) + C

0 = (3π/2) + 1 + C

C = - (3π/2) - 1

Therefore, the function that passes through the point P is r(θ) = 3θ + sin(θ) - (3π/2) - 1.

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The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Total songs = 53

Like songs = 14

Probability of selecting and liking the first song = 14/53

Now since repetition is not allowed and one like the song has been chosen out of 14 thus, the remaining songs = 13, and total songs = 43 - 1 = 52

Probability of selecting liking the second song = 13/52

Probability of selecting liking the third song = 12/51

Probability of selecting liking the fourth song = 11/50

a)

The probability of liking all songs will be 14/53 x 13/52 x 12/51 x 11/50 = 0.03418.

b)

The probability of not liking the next four songs =1 - The probability of liking all songs

The probability of not liking the next four songs = 1 - 0.03418 = 0.96582.

Hence "The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658".

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The correlation coefficient is 0.9541. This can be determined from the information provided in the ANOVA table, specifically the regression sum of squares (SSR) and the total sum of squares (SST).

The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger relationship, and values closer to 0 indicate a weaker relationship.

To calculate the correlation coefficient, we can use the formula:

r = sqrt(SSR/SST)

From the ANOVA table provided, we can see that SSR = 12,323.64 and SST = 13,538.4. Plugging these values into the formula gives:

r = sqrt(12,323.64/13,538.4) = 0.9541

Therefore, the correlation coefficient for this model is 0.9541, indicating a strong positive linear relationship between the independent variable and the dependent variable

Complete Question:

Using the following information. Coefficients -12.8094 Intercept Independent variable 2.1794 ANOVA df SS MS F 1 90.0481 Regression Residual Total 12,323.64 1,214.762 13,538.4 12,323.64 136.8550 8 1° 9 What is the correlation coefficient? Multiple Choice 0.9103 0.9541 -0.9541

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Step-by-step explanation:

The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028.

2028 - 1995 = 33 years, so t = 33

D = 401t + 5940

D = 401(33) + 5940

D = 13,233 + 5940  

D = 19,173

Answer: In the year 2028, the total average credit card debt for a U.S. household will be $19,173

Answer:

\(x = 11\)

Step-by-step explanation:

\(7x - 9 = 28 + 4(x - 1) \\ 7x - 9 = 28 + 4x - 4 \\ 7x - 4x = 28 - 4 + 9 \\ 3x = 33 \\ \\ x = \frac{33}{3} \\ \\ x = 11\)

Answer:

c) x = 11

Step-by-step explanation:

Given equation: 7x - 9 = 28 + 4(x - 1)

Steps:

1. Distribute 4 through the parentheses:

7x - 9 = 28 + 4(x) + 4(-1)

7x - 9 = 28 + 4x - 4 [simplify]

7x - 9 = 24 + 4x

2. Subtract 4x from both sides:

7x - 4x - 9 = 24 + 4x - 4x

3x - 9 = 24

3. Add 9 to both sides:

3x - 9 + 9 = 24 + 9

3x = 33

4. Divide both sides by 3:

3x ÷ 3 = 33 ÷ 3

x = 11

5. Check your work:

7x - 9 = 28 + 4(x - 1) [substitute 11 for x]

7(11) - 9 = 28 + 4(11 - 1) [simplify]

77 - 9 = 28 + 4(10) [simplify]

68 = 28 + 40 [add]

68 = 68 ✔

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Answer:

1.03

Step-by-step explanation:

multiplying by 1.3 would increase the amount by 30%

Answer:

Line CB

Step-by-step explanation:

We know the smallest triangle is the left triangle, so you need to find the smallest angle in that triangle, which is 50 degrees as shown, and the opposite side to that, CB, is the smallest side.

An exponential function with a vertical stretch by a factor of 2 and a translation left 1 unit and up 2 units is given as follows:

y = 2(2)^(x + 1) + 2.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

A vertical stretch by a factor of k means that the definition of the function is multiplied by k.

The parent function in the context of this problem is given as follows:

y = 2^x.

Hence the exponential function with a vertical stretch by a factor of 2 and a translation left 1 unit and up 2 units is given as follows:

y = 2(2)^(x + 1) + 2.

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Answer:

The answer the first question is: Always acute

The answer to the second is: 65 degrees

Step-by-step explanation:

:P

Answer:

its true

Step-by-step explanation:

True, the links in the blockchain are created using an algorithm.

What is blockchain?                                                                                                                                                                                                                       Blockchain is a decentralized ledger technology that enables the secure exchange of digital assets across a network of participants without the need for a centralized authority or intermediary. The blockchain is created using an algorithm to secure the network and ensure that all transactions are transparent and verifiable.

In a blockchain, each block contains a cryptographic hash of the previous block, forming a chain of blocks (hence the name "blockchain"). The algorithm used to create the blockchain is a consensus algorithm, which ensures that all participants on the network agree on the same state of the ledger.

This consensus algorithm also ensures that no single participant can manipulate the ledger or change the contents of a block without being detected.

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Answer:

height = 16.5 feet

Step-by-step explanation:

Givens

Start by drawing a right angle triangle. The hypotenuse is 36 and the side adjacent to where the ladder meets the ground is the adjacent side. The tallest part of the building is found from the Pythagorean Theorem.

Givens

Hypotenuse = 36

Adjacent = 32

Height = ?

Formula

a^2 + b^2 = c^2

c is the ladder length

a = 32

b = ?

Solution

32^2 + b^2 = 36^2

1024 + b^2 = 1296             Subtract 1024 from both sides

b^2 = 1296-1024

b^2 = 272                           Take the square root of both sides.

sqrt(b^2) = sqrt(272)

b = 16.49

Answer:

72°

Step-by-step explanation:

From the question,

Area of the circle = πr²

A = πr²................. Equation 1

Where r = radius of the circle.

⇒ r = √(A/π)............. Equation 2

Given: A = 346.5 cm², π = 3.14

r = √(346.5/3.14)

r = √(110.35)

r = 10.5 cm.

Therefore,

circumference of the circle = 2πr = 2×3.14×10.5

circumference = 65.94 m

If the length of the arc(s) is 1/5 of its circumference.

Therefore, length of arc (s) = 13.188

⇒ length of arc/circumference = 13.188/65.94 =  1/5

s/2πr = θ/360

Where θ = angle substends at the center of the circle

1/5 = θ/360

θ = 360/5

θ = 72°

Answer:

80°

Step-by-step explanation:

since 4x+5x=180, it means that x is 20.

to find SVW, you multiply 4 by 20 which is 80°

So the minimum score required to be eligible to enroll in calculus is 67.

To find the minimum score required to be in the top 20%, we need to find the score that corresponds to the 80th percentile of the distribution.

The standard normal distribution is a normal distribution with mean 0 and standard deviation 1. We can use the standard normal distribution to find percentiles of any normal distribution by using the fact that any normal distribution can be converted to a standard normal distribution through the following formula:

z = (x - mean) / standard deviation

where x is the raw score, mean is the mean of the distribution, standard deviation is the standard deviation of the distribution, and z is the standardized score (also called the z-score).

We can use this formula to convert the scores on the math placement exam to the standard normal distribution. Let x be the minimum score required to be eligible. Then the corresponding z-score would be:

z = (x - 42) / 19

We want to find the value of x that corresponds to the z-score for the 80th percentile, which we can find using a z-table or by using a calculator or computer to find the inverse of the standard normal cumulative distribution function (CDF). The z-score for the 80th percentile is approximately 0.84. Plugging this value into the equation above, we get:

0.84 = (x - 42) / 19

Solving for x, we find that the minimum score required to be eligible is approximately 66. Rounding to the nearest integer, the minimum score required is 67.

So the minimum score required to be eligible to enroll in calculus is 67.

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A minimum sample size of 62 is needed to be 95% confident that the sample mean is within 2 words of the true population mean, assuming a normal distribution of the number of words per sentence in the book and a population standard deviation of 4 words.

To determine the minimum sample size needed to be 95% confident that the sample mean is within 2 words of the true population mean, we can use the formula for the margin of error:

Margin of error = z * (standard deviation / sqrt(n))

Where z is the z-score for the desired confidence level, standard deviation is the population standard deviation (given as 4 words), and n is the sample size.

We want the margin of error to be no more than 2 words, so we can set up the inequality:

z * (4 / √n) ≤ 2

To find the value of z for 95% confidence level, we can use a z-table or calculator and find that z = 1.96.

Substituting this value into the inequality and solving for n, we get:

1.96 * (4 / √n) ≤ 2

Simplifying and solving for n, we get:

n >= 61.05

Since we can't have a fractional sample size, we can round up to the nearest whole number and conclude that a minimum sample size of 62 is needed to be 95% confident that the sample mean is within 2 words of the true population mean.

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Answer:

The answer is 80%

Step-by-step explanation:

BRAINLIEST PLEASEEEE

Answer:

$1,050

Step-by-step explanation:

Simply multiply the cost per kid ticket and number of kids:

$5.25 x 200 = $1,050

Answer:

Tax rate is 5.5% because 1,375/25,000 is equal to 0.055 which is 5.5 in percentage form. To prove it you can multiply 25,000 by 0.055 and get 1,375.

Step-by-step explanation:

Sales tax rate is 5.5% of cost of car.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

Price of the car = $25000

Tax on car = $1375

Sales tax rate = ($1375/$25000)×100

                           = 0.055 × 100

                           = 5.5%

5.5 % of sales tax is applied on the cost of car.

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The nth term of the sequence is 0, -31, -84. -159. -256, -375, -516

From the information given, we have that the quadratic sequence is;

12, 17, 24, 33, 44, 57, 72,...

To determine the nth term, we take the following steps accordingly, we have;

Then, we have that;

The second difference is;

17 - 12 = 5

24 - 17 = 7

33 - 24 = 9

Second difference = 7 - 5 = 2

Then an² = 12n²

Substitute each of the values, we get;

12(1)² = 0

12(2)² = 12(4) = 48 - 17 = -31

12(3)² = 12(9) = 108 = -84

12(4)²  = 12(16) = -159

12(5)²= -256

12(6)² = -375

12(7)² = -516

Then, the arithmetic sequence is:

0, -31, -84. -159. -256, -375, -516

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Answer:

A) 14/6

Step-by-step explanation:

1 5/6 = 1 + 5/6 = 6/6 + 5/6 = 11/6

1/2 = 3/6

then:

1 5/6 + 1/2 = 11/6 + 3/6 = 14/6

Step-by-step explanation:

"complimentary" means together they have 90°.

"supplementary" means together they have 180°.

which can be easily and quickly found on any internet search.

7.

A = 70°

A + B = 90°

70 + B = 90

B = 90 - 70 = 20°

B + C = 180°

20 + C = 180

C = 180 - 20 = 160°

8.

A + B = 90°

B + C = 180°

C = 100°

B + 100 = 180°

B = 180 - 100 = 80°

A + 80 = 90

A = 90 - 80 = 10°

First, recall that

cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

so you just need to find cos(A) and sin(B).

Since both A and B end in the second quadrant, you know that

• cos(A) and cos(B) are both negative

• sin(A) and sin(B) are both positive

Then from the Pythagorean identity, you get

cos²(A) + sin²(A) = 1   ==>   cos(A) = -√(1 - sin²(A)) = -2√10/7

cos²(B) + sin²(B) = 1   ==>   sin(B) = +√(1 - cos²(B)) = √21/5

You'll end up with

cos(A - B) = (-2√10/7) (-2/5) + (3/7) (√21/5)

… = (4√10 + 3√21)/35

(which makes the last sentence in the question kind of confusing, because this expression doesn't get much simpler and it's certainly not a rational number)

The value of cos(A - B) is approximately 23/25

Given that A and B are in the second quadrant, we have

To find cos(A - B), we have to use trigonometric functions

cos(A - B) = cosAcosB + sinAsinB ...equation(i)

but

\(cos^2A + sin^2A =1 \\cos^2A = 1 - sin^2A\\cos^2A = 1 - (\frac{3}{7})^2 = 1 - \frac{9}{49}= cosA= -\frac{2\sqrt{5} }{7}\)

Having the value of cos A, let's solve for cosB

cos B = -2/5

\(sin^2B = 1-cos^2B\\sin^2B = 1-(-\frac{2}{5})^2= 1-\frac{4}{25}\\sinB = \sqrt{\frac{21}{25} }=\frac{\sqrt{21} }{5}\)

substituting the values if sinA, cosA, sinB, cosB into equation(i) above;

\(cos(A-B)=cosAcosB+sinAsinB\\cos(A-B)=(-\frac{2\sqrt{5} }{7})(-\frac{2}{5})+(\frac{3}{7})(\frac{\sqrt{21} }{5})\\cos(A-B)=\frac{3\sqrt{21}+4\sqrt{5} }{35} \\cos(A-B) = 23/35\)

The value of cos(A-B) is given above

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