Calculate the total sales tax.
2. Jenny Tarver purchases a $1,599.99 treadmill, a $49.99 pair of walking shoes, a $79.99 leather handbag,
6 pairs of socks at $8.99 per pair, and 2 pairs of running shorts at $19.99 each. Her state sales tax rate is
4% and her county tax rate is 4.25%. What is the sales tax on her purchases?

For the data of people who receive loans will not make payments on time, the probability that over 6% will not make timely payments is equals to the 0.0384. So, option(b) is right one.

We have a data of people who receive loan from bank based on past experience. Probability that people who receive loans will not make payments on time = 4% = 0.04

Number of approved loans = 300

We have to determine the probability that over 6% will not make timely payments. Now, Let X be a random variable represents the people who not make payments on time. There the probability distribution is follows the binomial distribution, \(X \: \tilde \: Binomial (n, p)\)

here, probability of success, P(X) = 0.04 and n = 300 and X = 0.06 × 300 = 18, so we can use Binomial Probability distribution formula, P(x, n, p) = ⁿCₓpˣ(1 - p)⁽ⁿ⁻ˣ⁾

So, probability that over 6% will not make timely payments, P(x > 18)

= ³⁰⁰C₁₈ p¹⁸(1 - p)⁽³⁰⁰⁻¹⁸⁾

= 0.0384

Hence, required probability is 0.0384.

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The given integral is ₁∫₀^(π/2) sin²(x)dx.

The trapezoidal rule is given by:(b - a) [(f(a) + f(b))/2]And, the Gauss-Quadrature formula for n = 2 is: ∫ᵇₐ f(x) dx = (b - a) [ w₁ f( [ (b - a)/2 ] gp₁ + (b + a)/2 ) + w₂ f( [ (b - a)/2 ] gp₂ + (b + a)/2 ) ]

Here, a = 0, b = π/2, gp₁ = -0.5773, gp₂ = 0.5773, w₁ = w₂ = 1.

(i) Trapezoidal Rule: The trapezoidal rule with one interval is given by:(b - a) [(f(a) + f(b))/2] = π/4 [sin²(0) + sin²(π/2)] = 0.7854

(ii) Gauss-Quadrature: Using the Gauss-Quadrature formula with n = 2, we get:∫ᵇₐ f(x) dx = (b - a) [ w₁ f( [ (b - a)/2 ] gp₁ + (b + a)/2 ) + w₂ f( [ (b - a)/2 ] gp₂ + (b + a)/2 ) ]= π/2 [ sin²( [ (π/2)/2 ] (-0.5773) + π/4 ) + sin²( [ (π/2)/2 ] (0.5773) + π/4 ) ]= 0.7853Comparing the above two methods, the trapezoidal rule and Gauss-Quadrature method are nearly the same and are close to the exact value.

Exact value = (π/2)/2 - sin(π)/4 = 0.7854Conclusion:Thus, it can be concluded that the given integral using the trapezoidal rule (using only one interval) and Gauss- Quadrature (n=2) is approximately equal to 0.7854.

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Length of AB = 8.06 units

Length of BC = 8.94 units

Length of AC = 9.22 units

What is a Scalene Triangle?

A scalene triangle is a type of triangle with three different length sides and three interior angles that add up to 180 degrees. Scalene triangles have no equal of parallel sides , hence there is no line of symmetry. The interior angles of a scalene triangle can be acute , right or obtuse angles.

Given data ,

Triangle ABC with vertices

A( 5 , 12 ) , B( 13 , 13 ) and C( 11 , 5 )

From the coordinates , we can see that

Now ,

When two points are given P( x₁ , y₁ ) and Q( x₂ , y₂ ) , the distance between the two points is given by distance formula

D = √( x₂ - x₁)² + ( y₂ - y₁)²

So , Length of AB is given by

AB = √( 13 - 5 )² + ( 13 - 12 )²

AB = √( 64 + 1 )

AB = √65

AB ≈ 8.0622

So , Length of AB = 8.06 units

And , Length of BC is given by

BC = √ ( 11 - 15 )² + ( 5 - 13 )²

BC = √ ( 16 + 64 )

BC = √ 80

BC ≈ 8.944

So , Length of BC = 8.94 units

And , Length of AC is given by

AC = √ ( 11 - 5 )² + ( 5 - 12 )²

AC = √ ( 36 + 49 )

AC = √85

AC ≈ 9.219

So , Length of AC = 9.22 units

Since , the lengths of AB , BC and AC all are different , we can say that the triangle ABC is a scalene triangle

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Answer:

There are 50 calories per cup of popcorn.

Step-by-step explanation:

The t times u is approximately equal to -139.7.

To find t times u, we use the formula for the dot product: t · u = |t||u|cosθ, where θ is the angle between the vectors. Since we are only given the vectors t and u, we need to find their magnitudes and the angle between them.

The magnitude of t is |t| = √(7^2 + (-3)^2) = √58, and the magnitude of u is |u| = √((-10)^2 + (-8)^2) = √164.

To find the angle between t and u, we use the formula cosθ = (t · u)/(|t||u|). Substituting the values we know, we get cosθ = ((7)(-10) + (-3)(-8))/((√58)(√164)) = -74/(2√1017). Using a calculator, we find that θ ≈ 131.5 degrees.

Now we can find t · u: t · u = |t||u|cosθ = (√58)(√164)(cos(131.5)) ≈ -139.7.

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Answer:

Your answer is <ABC = 156°

Step-by-step explanation:

I am not sure how to explain this, but you look at the values between 0°-180°. Starting from A right counterclockwise from 0 to C. You can see the degree.

Answer:

  y = (4 -x)e^-2

Step-by-step explanation:

You want an equation of the tangent line to the graph of f(x) = xe^−x at its inflection point.

The inflection point on a curve is the point where the second derivative is zero, where the curve changes from being concave downward to concave upward, or vice versa.

We can use the product rule to differentiate f(x):

  (uv)' = u'v +uv'

  f'(x) = 1·e^-x +x·(-1)(e^-x) = (e^-x)(1 -x)

Then the second derivative is ...

  f''(x) = (-e^-x)(1 -x) +(e^-x)(-1) = (e^-x)(x -2)

The second derivative is zero where one of its factors is zero. e^-x is never zero, so we have ...

  (x -2) = 0   ⇒   x = 2

The point of inflection occurs at x = 2.

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

For this problem, we have ...

  m = f'(2) = (e^-2)(1 -(2)) = -e^-2

  (h, k) = (2, f(2)) = (2, 2e^-2)

So, the equation of the tangent line is ...

  y -2e^-2 = -e^-2(x -2)

In slope-intercept form, this is ...

  y = (-e^-2)x +4e^-2

__

Additional comment

We can rearrange the equation to ...

  y = (4 -x)e^-2

Usually a tangent line touches the graph, but does not cross it. The tangent at the point of inflection necessarily crosses the graph.

Answer:

D

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 5 and (a, b) = (5, - 8 ), thus

y - (- 8) = 5( x - 5), that is

y + 8 = 5(x - 5) → D

Answer:

first 7 then 3  5  4  6

Step-by-step explanation:hope it helps

Answer:

1/2

Step-by-step explanation:

Step one:

given data

sample space

1 blue slice,

2 red slices, and

3 yellow slices

sample size= 1+2+3= 6

Required:

The probability that the dial stops on a blue or red slice

1. The probability that the dial stops on a blue = 1/6

2. The probability that the dial stops on a red= 2/6= 1/3

Hence The probability that the dial stops on a blue or red= 1/6+1/3

= 1+2/6

=3/6

=1/2

Error might the student have made was in angle 147 as acute angle means angle less than 60°

Acute angles are those that range in size from 0 to 90 degrees and are smaller than 90 degrees. Examples include 60, 30, 45, and other angles. An acute triangle is a triangle with all of its internal angles smaller than 90 degrees. An equilateral triangle, for instance, is an acute triangle because the internal angles are 60°.

Less than 90° of an angle is referred to be an acute angle. An acute angle, for instance, is formed when the time is 11 o'clock between the hour hand and the minute hand. Consequently, acute angles include 30°, 40°, 57°, and others.

Given that : The students are guvena right triangle. One of the acute angles has a measure of 33°. One student saha tbe measure kf the other acute angle is 147°.

As the acute angles are angles less than 90°

and they have measure as 147°

So the error was in measure angle as 147°

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Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

Explanation:

Given the expression:

This can be written as a difference of two squares. But before that, we can rewrite the expression as:

So, as a different of two squares, we write:

Answer:

Between 2.1 cm and 9.9 cm

Step-by-step explanation:

The third side should be more than the difference between the other two sides and less than the sum of the other two sides.

6 – 4 = 2 cm and 4 + 6 = 10 cm.

So the third side should be between 2.1 cm and 9.9 cm, and if only integers are considered then the third side should be anywhere between 3 cm and 9 cm.

The possible measure for the third side of the triangle is:

2 < x < 10

The third side could measure any length between 2 and 10 inches, but not including 2 or 10.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To find the range of possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Now,

Let's call the length of the third side x.

Then, we have:

4 + 6 > x and 4 + x > 6 and 6 + x > 4

Simplifying these inequalities, we get:

10 > x and x > -2 and x > 2

We see that,

The first inequality tells us that x must be less than the sum of the other two sides, which is 10.

The second inequality tells us that x must be greater than the difference between the other two sides, which is 2.

The third inequality tells us the same thing as the second inequality since the order of the sides doesn't matter.

Therefore,

The possible range of lengths for the third side of the triangle is:

2 < x < 10

This means,

The third side could measure any length between 2 and 10 inches, but not including 2 or 10.

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The wonderful waffle cone holds more ice cream than super sundae cone.

In this question,

The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.

Volume of ice cream cone = volume of hemisphere + volume of cone

Volume of ice cream cone = \(\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h\)

Volume of super sundae cone:

Radius of hemisphere = height of hemisphere = 0.5 in

Depth of the ice cream cone = 4 in

Volume of super sundae cone = \(\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)\)

⇒ \(\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)\)

⇒ 0.2616+1.0466

⇒ 1.3082 ≈ 1.31 cubic in.

Volume of wonderful waffle cone:

Radius of hemisphere = height of hemisphere = 0.9 in

Depth of the ice cream cone = 3 in

Volume of wonderful waffle cone = \(\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)\)

⇒ \(\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)\)

⇒ 1.526+2.5434

⇒ 4.0694 ≈ 4.07 cubic in.

Thus volume of wonderful waffle cone > volume of super sundae cone.

Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.

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Answer:

john cena

Step-by-step explanation:

i have no idea lol

To find where the function is increasing or decreasing, we need to take the derivative of the function and determine where it is positive or negative.

The derivative of f(x) = x/2 + cos(x) is f'(x) = 1/2 - sin(x).

To find where f'(x) is positive, we need to solve the inequality 1/2 - sin(x) > 0.

Adding sin(x) to both sides, we get 1/2 > sin(x).

This is true on the intervals (0, pi/6) and (5pi/6, 2pi).

To find where f'(x) is negative, we need to solve the inequality 1/2 - sin(x) < 0.

Subtracting 1/2 from both sides, we get -1/2 < -sin(x).

Multiplying both sides by -1 and flipping the inequality, we get sin(x) < 1/2.

This is true on the interval (pi/6, 5pi/6).

Therefore, the function is increasing on the intervals (0, pi/6) and (5pi/6, 2pi), and decreasing on the interval (pi/6, 5pi/6).

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On the basis of birthday problem or scenario, the number of people should be selected to guarantee that at least 4 were born on the same day, not considering the year is equals to the 1096.

The worst case scenario is one of the many possible cases where the desired outcome comes after every other probable outcome has already occurred. The number of people who ensure that at least 7 people have a birthday on a single day of a non-leap year (365 days) can be determined by ensuring that in the number of people selected in each trial, two people do not have a birthday on a day. the same day. There are 365 days in a year.

Assuming everyone was born on a different day, then you could have 365 people where no one was born on the same day, but those 366 people would have to be born on the same day as someone else in the group. So the minimum number of people in a group would have to be 366 to guarantee that at least 2 people were born on the same day. But we wanted to guarantee that at least 4 people were born on the same day.

So, assuming we had 3 × 365 people together, with every 3 of them being born on the same day. Then would have a total of 365× 3 = 1095 people, with no more than 3 people being born on the same day. Now as we select one more person, the number of people born on a day for one of the days in the year will increase to 4. Hence the number of people that should be selected to guarantee that at least 4 were born on the same day are 1095 +1 = 1096. Hence, required value is 1096.

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The correct response is d. A primitive is associated with both data and methods, whereas an object merely holds data.

Information that has been transformed into a format suitable for transmission or processing is referred to as data in computing. Information that has been binary-digitally altered for use with contemporary computers and transmission methods is referred to as data. The topic data may be expressed in both the singular and plural forms. Data can take the shape of text, observations, figures, photographs, statistics, graphs, and symbols. Individual prices, weights, addresses, ages, names, temperatures, dates, or distances, for instance, might be included in the data. Data lacks significance and utility on its own because it is an unprocessed sort of knowledge. Basic data includes information like a person's name, last name, address, phone number, cell number, fax number, email address, and vehicle license plate.

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0.6. This is the probability that the student takes either chemistry or Spanish or both. Option C. is the answer

Probability is a measure of the likelihood of a particular event or outcome occurring.

Given the: Venn diagram where P(A) = 0.2 and P(B) = 0.3 and P(A∩B) = 0.1

Since A = student takes chemistry and B = student takes Spanish

P(A∪B) defines the set of students that take either A or B or both

Thus, P(A∪B) will the addition of P(A), P(B) and P(A∩B). That is:

P(A∪B) = P(A) + P(B) + P(A∩B)

P(A∪B) = 0.2 + 0.3 + 0.1 = 0.6

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P(x)=ax⁵+bx⁴+cx³+12 is the polynomial which has 4 terms and vertical axis at y=12 and the degree is 5

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The standard form of a polynomial equation with a leading degree is 5 is expressed as P(x)=ax⁵+bx⁴+cx³+dx+e

Since the polynomial should have only 4 terms, the standard form of the equation will be P(x)=ax⁵+bx⁴+cx³+d

d is the constant

Since the graph of the Polynomial crosses the vertical axis at y = 12, hence the constant value "d" will be 12.

Substituting the constant value, the required equation of the polynomial will be expressed as P(x)=ax⁵+bx⁴+cx³+12

Hence, P(x)=ax⁵+bx⁴+cx³+12 is the polynomial which has 4 terms and vertical axis at y=12 and the degree is 5

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The probability that Sheri is chosen first and Nikita is chosen second is 1/756.

The probability of Sheri being chosen first is 1/28, since there are 28 contestants and each one has an equal chance of being chosen first.

After Sheri has been chosen, there are 27 remaining contestants, so the probability of Nikita being chosen second is 1/27, since there are now only 27 contestants left and each one has an equal chance of being chosen second.

To find the probability of both events happening together (Sheri being chosen first and Nikita being chosen second), we multiply the probabilities of each event

= 1/28 x 1/27

Multiply the numbers

= 1/756

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Answer:

y=6

Step-by-step explanation:

Isolate y by multiplying by 6

1*6=y/6*6

y=6

Check

6/6=1

Step-by-step explanation:

Here's the answer.

1=y/6

1*6=y

6=y

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x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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Answer:

Step-by-step explanation:

Answer:

(-4, 5)

Step-by-step explanation:

12x + 14y = 22

12x - 3y = -63

Rewrite the first equation. Multiply both sides of the second equation by -1 and write it below the first equation. Then, add the equations.

        12x + 14y = 22

(+)    -12x + 3y = 63

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

                 17y = 85

17y/17 = 85/17

y = 5

Substitute y with 5 in the first original equation and solve for x.

12x + 14y = 22

12x + 14(5) = 22

12x + 70 = 22

12x = -48

x = -4

Answer: (-4, 5)

Answer:

5 + 7

Step-by-step explanation:

3 + 2 = 5, 4 + 3 = 7

Answer:

Simplified expression: 5 + 7

Answer: 12

Step-by-step explanation: