Violet owns a small business selling used books. She knows that in the last week 69 customers paid cash, 34 customers used a debit card, and 11 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash or a credit card as a percent to the nearest whole number.

Answer:

a.1.17809725 rad

b.1.57079633 rad

c.3.14159265 rad

d.0.785398163 rad

e.1.83259571 rad

f.100.530965 rad

Answer:

a. 1.17809725 rad

hope its help

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The answers are as follows:

1 Angle Bisector Theorem

2 Sum of Adjacent Angles

3 Co-interior angle property

4 Additive law

Given:

Note: Diagram for Question is attached

1. Angle Bisector Theorem

The angle bisector is BD. Bisection entails splitting into two equal pieces. Angles 3 and 4 are therefore equal.

2. Sum of Adjacent Angles

To determine the greater angle that is created by the two adjacent angles, add the two angles together.

3. Co-interior angle property

According to the co-interior property, the sum of interior angles (on the same side) formed when a single line crosses two parallel lines is equal to 180.

4. Additive law

By applying the additive law, we can take a value away from both sides of the equation without throwing the equation out of balance. Therefore, we may take 110 out of both sides of the equation to get the final result of 70.

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Answer:

\(\huge\boxed{\sf 44\ units}\)

Step-by-step explanation:

Solution:

So,

= 3 + 8 + 3 + 6 + 5 + 6 (again) + 4 + 5 + 4

\(\rule[225]{225}{2}\)

Answer:

8-4=4

therefore 6+4=10

then perimeter =2(5)+10+6+2(3)+8+4=44units

The function’s equation written in factored form and in vertex form are respectively;

f(x) = 2x(x - 4)

f(x) = 2(x - 2)² - 8

The factored form of a quadratic function is;

f(x) = a(x - p)(x - q)

where:

p and q are the x-intercepts

a is a constant

Now, we are given x-intercepts as; (0, 0) and (4, 0)

Thus;

f(x) = a(x - 0)(x - 4)

f(x) = ax(x - 4)

To find a, substitute the given vertex (2, -8) into the equation and solve for a:

2a(2 - 4) = -8

-4a = -8

a = 2

Thus;

f(x) = 2x(x - 4)

The vertex form of a quadratic equation is;

f(x) = a(x - h)² + k

where:

(h, k) is the vertex

a is constant

Since vertex is (2, -8), then we have;

f(x) = a(x - 2)² - 8

Put the coordinate (0, 0) to find a;

0 = a(0 - 2)² - 8

4a = 8

a = 2

Thus;

f(x) = 2(x - 2)² - 8

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The advertising firm should sample 753 individuals to estimate the proportion who would consider buying the product to within a margin of error of ±3% with 90% confidence.

Margin of error, sample size and confidence level are crucial aspects of the sample survey that determine the accuracy of the outcome. The advertising firm plans to have a sample of individuals view a commercial on a ‘‘sunscreen pill" that one can swallow to provide mild SPF protection throughout the day.

After viewing the commercial, each individual will be asked if he/she would consider buying the product. How many individuals should the firm sample to estimate the proportion who would consider buying the product to within a margin of error +-3% with 90% confidence?Given dataMargin of error (E) = 3%Confidence level = 90% The confidence level means that the sample should give results that have a 90% chance of falling within the margin of error.

The margin of error is given by the formula:Margin of error = z * sqrt(p*q/n)where: z is the z-score (value from the standard normal distribution table) that corresponds to the given confidence level. For 90% confidence level, z is 1.645.p is the estimated proportion of people who would consider buying the product.q is the estimated proportion of people who would not consider buying the product.

Since there is no prior estimate, it's assumed to be 0.5n is the sample size. The formula can be rearranged to solve for the sample size, n. n = (z/E)² * p*qTaking z = 1.645, E = 3%, p = 0.5, q = 0.5, we getn = (1.645/0.03)² * 0.5 * 0.5= 752.68 ≈ 753 individuals

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Graph of each objective function using linear programming.

Here,

Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.

For example putting A=0 in 7A+10B=420 will yield  (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.

Repeating thin step for each objective function and plotting the graph.

7A + 10B = 420 is labelled as a.

6A+4B = 420 is labelled as b.

-4A + 7B = 420 is labelled as c .

The graph of each function is attached below.

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Answer:One minute let me find a answer

Step-by-step explanation:

The root test is Divergent, for given [infinity] 1 nn n = 1.

The foundation take a look at to research the restrict of the nth root of the nth time period of your collection. Like with the ratio check, if the restrict is less than 1, the series converges; if it is extra than 1 (together with infinity), the series diverges; and if the restrict equals 1, you analyze not anything.

The root check this collection is divergent. again, there is not too much to this series. therefore, with the aid of the root take a look at this collection converges clearly and hence converges. notice that we needed to maintain the absolute cost bars at the fraction until we would taken the limit to get the sign accurate

Root test requires you to calculate the value of R the usage of the components under. If R is greater than 1, then the series is divergent. If R is less than 1, then the series is convergent.

explanation:

If tan is series

if Lim n root (1) = l

if l =<1 than it is convergent

if l = > 1 than it is divergent

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A statement about the data which must be true include the following: A. The spread from the lower quartile to the median is greater than the spread from the median to the upper quartile.

In Mathematics, a box plot is a type of chart that is used for the graphical or visual representation of the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided above, the five-number summary for the given data set include the following:

Spread from lower quartile (first) to median = 7 -4  = 3

Spread from median to upper quartile (third) =  9 - 7 = 2

Therefore, the spread from lower quartile (first) to median is greater than the spread from median to upper quartile (third).

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After two iterations, the values (z2, y2) are approximately (0.64, 0.64).

The unit vector pointing in the direction of maximum ascent at (1, 2) is [0, 1].

we start with an initial guess for the minimum and iteratively update the values using the gradient of the function and a learning rate.

For the function f(x, y) = x^2 + y^2 + 1/(201^2), with an initial guess of (z0, y0) = (1, 1), and a learning rate of α = 0.1, let's manually iterate the method two times to obtain (z2, y2) = (2, 2).

Calculate the gradient of f(x, y) with respect to x and y:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

= [2x, 2y]

Update the values using the gradient descent method:

For the first iteration:

z1 = z0 - α * ∂f/∂z(z0, y0)

= 1 - 0.1 * (2 * 1)

= 0.8

y1 = y0 - α * ∂f/∂y(z0, y0)

= 1 - 0.1 * (2 * 1)

= 0.8

For the second iteration:

z2 = z1 - α * ∂f/∂z(z1, y1)

= 0.8 - 0.1 * (2 * 0.8)

= 0.64

y2 = y1 - α * ∂f/∂y(z1, y1)

= 0.8 - 0.1 * (2 * 0.8)

= 0.64

After two iterations, the values (z2, y2) are approximately (0.64, 0.64).

Regarding Question 13, to find a unit vector pointing in the direction of maximum ascent at the point (1, 2) for the function f(x, y) = 2xy^2 - 6x.

Calculate the gradient of f(x, y) with respect to x and y:

∇f(x, y) = [∂f/∂x, ∂f/∂y]

= [2y^2 - 6, 4xy]

Evaluate the gradient at (1, 2):

∇f(1, 2) = [2(2^2) - 6, 4(1)(2)]

= [0, 8]

Normalize the gradient vector:

||∇f(1, 2)|| = sqrt(0^2 + 8^2)

= sqrt(64)

= 8

The unit vector pointing in the direction of maximum ascent at (1, 2) is:

[0, 8]/8

= [0, 1]

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Answer:

\(9p^2-16q^2\)

\((3p)^{2} -(4p)^{2}\)

\(\underline{x^2-y^2=\left(x+y\right)\left(x-y\right)}\)

\(\left(3p\right)^2-\left(4q\right)^2=\left(3p+4q\right)\left(3p-4q\right)\)

\(=\left(3p+4q\right)\left(3p-4q\right)\)

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

hope it helps....

have a great day!!

The standard deviation of a sample proportion is given by the formula:

σ = sqrt((p * (1 - p)) / n)

where σ is the standard deviation, p is the sample proportion, and n is the sample size.

If we want the standard deviation to be one-half of what it was for a sample of size 100, we can write the following equation:

(sqrt((p * (1 - p)) / n)) / 2 = sqrt((p * (1 - p)) / 100)

To simplify the equation, we can square both sides:

((p * (1 - p)) / n^2) / 4 = (p * (1 - p)) / 100

Simplifying further:

100 * n^2 = 4 * 1

n^2 = (4 * 1) / 100

n^2 = 0.04

Taking the square root of both sides:

n = sqrt(0.04)

n = 0.2

Therefore, the sample size should be 0.2. However, since the sample size must be a positive integer, we round it up to the nearest whole number. Therefore, the sample size should be 1.

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Answer:

it will take 6men to work in 12days

it takes 6men to work in 13hours it will now take 7men to work 13

it will take 6 hours to travel at 80miles

it will take 6 men to complete the same work at 1 hour

it will take 9 men to mow a large piece of lawn in 8 hour

it will travel 50 miles is 7 hour

Transforming a set of scores into a standardized distribution of z-scores consists of graphically plotting the scores.

What are z-scores? Z-scores are also known as standard scores. Z-scores refer to the number of standard deviations a given data point is from the mean. This score is calculated by subtracting the mean from the data point and then dividing the difference by the standard deviation. Z-scores allow for data to be standardized and provide a common scale for comparison.

Graphical representation of z-scores: A histogram or frequency polygon graph can be used to graphically represent z-scores. In a histogram, the frequency of each z-score is plotted on the y-axis, and the z-scores themselves are plotted on the x-axis. A frequency polygon graph plots the midpoints of each interval against their respective frequencies. The graph allows us to see the number of scores that fall within each z-score range.

By graphically plotting the scores, we can visualize the distribution and observe its shape, central tendency, and variability. The z-scores allow for a standardized comparison across different distributions, as they provide a common scale based on the mean and standard deviation.

The resulting graph of the standardized distribution of z-scores is often referred to as a z-score plot or a z-score distribution, and it helps in analyzing and interpreting the relative position and characteristics of the original scores in relation to the mean and standard deviation of the distribution.

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Answer:

false

Step-by-step explanation:

Answer:

false, sorry if wrong!

Step-by-step explanation:

The equation involves trigonometric functions, it will require numerical methods or software to obtain the exact value of θ.

To determine the angle above the horizontal at which the ball must be thrown to hit the basket, we can analyze the projectile motion of the ball.

Given:

Initial speed (v₀) = 7.50 m/s

Initial height (h) = 2.44 m

Horizontal distance to the basket (x) = 4.57 m

Vertical distance to the basket (y) = 3.05 m

We can break down the motion into horizontal and vertical components. The time it takes for the ball to reach the basket is the same for both components.

1. Horizontal Component:

The horizontal component of motion is unaffected by gravity. We can use the formula:

x = v₀ * t * cosθ

where θ is the angle above the horizontal.

2. Vertical Component:

The vertical component of motion is affected by gravity. We can use the formula:

y = h + v₀ * t * sinθ - (1/2) * g * t²

where g is the acceleration due to gravity (approximately 9.8 m/s²).

We can solve these equations simultaneously to find the angle θ. Rearranging the equations:

x = v₀ * t * cosθ

t = x / (v₀ * cosθ)

y = h + v₀ * t * sinθ - (1/2) * g * t²

Substituting the expression for t:

y = h + (v₀ * x * sinθ) / (v₀ * cosθ) - (1/2) * g * (x² / (v₀² * cos²θ))

Simplifying:

y = h + (x * tanθ) - (1/2) * g * (x² / (v₀² * cos²θ))

Rearranging and substituting the given values:

0 = 3.05 - 4.57 * tanθ - (1/2) * 9.8 * (4.57² / (7.50² * cos²θ))

Solving this equation for θ will give us the angle above the horizontal at which the ball should be thrown to hit the basket. Since the equation involves trigonometric functions, it will require numerical methods or software to obtain the exact value of θ.

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Answer:

Y= 1/7x + 2/7

Step-by-step explanation:

2/7 equals to b

Hope this helps.. :)

The distance between the pair of points. N(-6,-10),P(-6,-3) is 7

The coordinates are given as:

N(-6,-10) and P(-6,-3)

The distance is calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

Substitute the known values in the above equation

d = √(-6 + 6)^2 + (-10 + 3)^2

Evaluate the exponent

d = √49

This gives

d = 7

Hence, the distance between the pair of points. N(-6,-10),P(-6,-3) is 7

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The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

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The 95% confidence interval for the average apple weight is (119.14, 125.86).

An apple typically weighs 120 grams with a 12-gram standard deviation, according to one manufacturer. The average weight of an apple was 122. 5 grams, according to statistics created from a sample of 49 apples that were randomly chosen from a shipment.

Let, n = 49

x = 122.5 

σ = 12

To calculate and interpret a 95% confidence interval for the average apple weight, use the formula;

⇒ (x ± 1.96*σ/√n)

⇒ (122.5 ± 1.96*12/√49)

⇒ (119.14, 125.86)

Consequently, the average apple weight has a 95% confidence interval of (119.14, 125.86).

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Answer:

y = 33X^2 + 55

Step-by-step explanation:

by expanding the equation you provided, we will get the answer

be reminded, the general form of a quadratic equation us,

y =ax^2+bx+c

Answer:

1

Step-by-step explanation:

Column A=X the first value for x is 1

Column B has the x value replaced in the equation 5x+8. 5(1) + 8

Column C has the result, y=13

Answer:

1.42857143

Step-by-step explanation:

Answer:

             70

Step-by-step explanation:

Answer:

Among all shapes with the same area, a circle has the smallest/shortest perimeter.

Solve in equal value Method step by step solution is given below.

Equal value is a concept that states all people, regardless of race, gender, ethnicity, sexual orientation, or any other defining characteristic, are of equal worth and should be treated equally. This concept is fundamental to democracy and is enshrined in the Universal Declaration of Human Rights. Equal value is also a foundation of economic theory, as it states that everyone should be able to access and benefit from economic resources, whatever their background.


Step 1: Isolate the 5y term on one side:
5y = -13-3x

Step 2: Divide both sides by 5:
y = (-13-3x)/5

Step 3: Replace the y with its expression:
x - 7 = (-13-3x)/5

Step 4: Distribute the -7 over the denominator of the right side:
x - 7 = (-13-3x-35)/5

Step 5: Add 7 to both sides:
x = (-13-3x-35+35)/5

Step 6: Simplify the expression:
x = (-13-3x)/5

Step 7: Solve for x:
x = -26/8

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Answer:

if m∠1 = 30° then m∠3 = 30° as they are parallel to each other and that is why they will have same angles.

therefore m∠3 = 30°

extra's:

→ m∠2 = m∠4 =

→ (360-30*20)/2

→ 150°

...............................

See here

m<1 and m<3 are opposite angles to eachother.

And we know that opposite angles are equal

so

The simplified expression is \(21x^2 - 25x - 28\) in the given case.

An expression in mathematics is a combination of numbers, symbols, and operators (such as +, -, x, ÷) that represents a mathematical phrase or idea. Expressions can be simple or complex, and they can contain variables, constants, and functions.

"Expression" generally refers to a combination of numbers, symbols, and/or operations that represents a mathematical, logical, or linguistic relationship or concept. The meaning of an expression depends on the context in which it is used, as well as the specific definitions and rules that apply to the symbols and operations involved. For example, in the expression "2 + 3", the plus sign represents addition and the meaning of the expression is "the sum of 2 and 3", which is equal to 5.

To simplify the expression, first distribute the -3x and (3x + 4) terms:

\(-3x(4 - 5x) + (3x + 4)(2x - 7) = -12x + 15x^2 + (6x^2 - 21x + 8x - 28)\)

Next, combine like terms:

\(-12x + 15x^2 + (6x^2 - 21x + 8x - 28) = 21x^2 - 25x - 28\)

Therefore, the simplified expression is \(21x^2 - 25x - 28.\)

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The width of the rectangle is equal to 3.42 meters

Let the width of the rectangle be represented by the variable x

thus from the question we can say that the length of the rectangle is 3 + x

Given is the area of the rectangle

we know that the area of the rectangle is Length × Breadth

Given area of the rectangle = 22 square meters

thus Area = Length × Breadth

On substituting the value we get

22 = ( 3 + x ) ( x )

x² + 3x = 22

x² + 3x - 22 = 0

b² - 4ac = 9 + 88 = 97

thus - b ± \(\sqrt{b^{2} -4ac}\) / 2a

= - 3 ± 9.84 / 2

Thus the two values of x we will get are :

x= -12.84 / 2 = -6.42 which is rejected because width cant be negative

thus the value of x = 6.84 / 2 =3.42 meters

Thus we get values of x as

x =  3.42 meters

Thus the required width of the rectangle = 3.42 meters

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Answer:

1

Step-by-step explanation:

This is because it is the most occuring number

Answer:

A

Step-by-step explanation:

The median is the middle value of the data arranged in ascending order.

The data given is already in ascending order

1 , 1 , 8 , 16 , 44

        ↑ middle value

median = 8