find each unit price to decide which is the best buy

The null and alternative hypotheses for this hypothesis test is H₀ : p = 0.93,  Hₐ : p > 0.93.

A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Let 'p' be the population proportion.

Given statement : The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using.

Since null hypothesis shows that there is no significant difference between the quantities where as alternative hypothesis believes that there is some  difference,

Hence, the null and alternative hypotheses for this hypothesis test will be :-  H₀ : p = 0.93

          Hₐ : p > 0.93

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i) The number of students that come to school by motorcycle only = 8

ii) The number of students that did not take all the three types of transportation = 9

iii) Number of students that did not come to school by car = 28

The total number of students = 40

The number of students that come to school by car alone = 9

The number of students that come to school by motorcycle only = 8

The number of students that come to school by car only = 11

The number of students that come to school by both car and motorcycle = 3

Number of students that did not take all the three types of transportation = 40 - (9 + 8 + 3 + 11)

= 40 - 31

Number of students that did not take all the three types of transportation = 9

Total students that come to school by car = 9+3 = 12

The total number of students that did not come to school by car = 40 - 12 = 28

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Answer:

6:8       x2

9:12      x3

12:16     x4

15:20    x5

Step-by-step explanation:

Just multiply both of the number by the same number and you will find an equavilant ratio.

Hope this helps!

*I also added a few different answers so it can give you a clear idea.

Answer:75/100

Step-by-step explanation:

thats just one there are a bunch

Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

First, start by converting 4 feet to inches. Note that 1 foot = 12 inches.

Set up a unit converter:

\(4\ ft(\frac{12\ in}{1\ ft})\)

The ft cancel out leaving us with:

\(4*12\ in=48\ in\)

Now, we can set up a scale factor...

\(\frac{drawing}{real\ length}=\frac{8}{48}=\frac{1}{6}\)

Answer:

6x + 12

Step-by-step explanation:

this is because 3 times 2x = 6x and 3 times 4 = 12.

Answer:

6x+12

Step-by-step explanation:

The output of the function f(x) when x = -3 is -5, which corresponds to option B.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

The given function rule is f(x) = x² + 5x + 1. This means that the function takes an input value, x, and calculates the output value using the formula x² + 5x + 1.

To find the output value of f(-3), we substitute -3 for x in the function, as follows:

f(-3) = (-3)² + 5(-3) + 1

Here, we start by squaring -3 to get 9. The next term, 5(-3), is equal to -15. Finally, we add 1.

When we combine these terms, we get:

f(-3) = 9 - 15 + 1

Simplifying further, we can combine 9 and 1 to get 10, and then subtract 15 to get -5:

f(-3) = -5

Therefore, the output of the function f(x) when x = -3 is -5, which corresponds to option B.

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the solution to the given IVP is y(t) = e^(2t) - e^t + 7.

What is Laplace Transform?

The Laplace transform is an integral transform that is widely used in mathematics and engineering to solve differential equations. It allows us to convert a function of time, typically denoted as f(t), into a function of a complex variable s, denoted as F(s), where s = σ + jω (σ is the real part and ω is the imaginary part).

To apply the Laplace transform to the initial value problem (IVP) y'' - 3y' + 2y = sin(2t), with initial conditions y'(0) = 4 and y(0) = -1, we follow these steps:

Take the Laplace transform of both sides of the differential equation, utilizing the properties of the Laplace transform.

L{y''} - 3L{y'} + 2L{y} = L{sin(2t)}

The Laplace transform of the derivatives y'' and y' can be expressed as follows:

L{y''} = s²Y(s) - sy(0) - y'(0)

L{y'} = sY(s) - y(0)

Here, Y(s) denotes the Laplace transform of y(t).

Substitute the initial conditions into the Laplace-transformed equation:

s²Y(s) - s(-1) - 4 - 3(sY(s) + 1) + 2Y(s) = L{sin(2t)}

Simplify the equation:

s²Y(s) + s - 4 - 3sY(s) - 3 + 2Y(s) = L{sin(2t)}

Combine like terms:

(s² - 3s + 2)Y(s) + (s - 7) = L{sin(2t)}

Express the Laplace transform of sin(2t):

L{sin(2t)} = 2/(s² + 4)

Rearrange the equation to solve for Y(s):

(Y(s) = (s - 7) / ((s² - 3s + 2))

Apply the inverse Laplace transform to find y(t):

y(t) = L⁻¹{(s - 7) / ((s² - 3s + 2))}

Perform partial fraction decomposition on the right side:

y(t) = L⁻¹{(s - 7) / ((s - 2)(s - 1))}

Using the inverse Laplace transform table or software, we find:

y(t) = e^(2t) - e^t + 7

Therefore, the solution to the given IVP is y(t) = e^(2t) - e^t + 7.

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Answer:

The correct answer is C: Y = -1/2x - 4.The slope of the given line is -1/2, so any line that is parallel to it will have the same slope. In order to find the equation of a line with the same slope that passes through the point (2, -5), we can use the point-slope form of the equation of a line.The point-slope form of the equation of a line is:y - y1 = m(x - x1)where m is the slope of the line, and (x1, y1) is a point on the line.In this case, we can plug in the values m = -1/2, x1 = 2, and y1 = -5 to get:y + 5 = -1/2(x - 2)Solving for y, we get:y = -1/2x - 4Therefore, the equation of the line that is parallel to the given line and passes through the point (2, -5) is Y = -1/2x - 4.

At most, they can wash 96 cars and mow 96 lawns.

To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.

Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.

Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.

Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.

Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.

The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.

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The value of AOB and BOC based in the information given in the circle will be 53°.

From the information given, the central angle is the angle that the vertex is at the center of the circle.

It was stated that OB bisects AOC. Therefore, since AOB is 53°, BOC is also 53°.

The value of AOC will now be:

= AOB + BOC

= 53° + 53°

= 106°

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Answer:

325

Step-by-step explanation:

65% of 500 is 325

The maximum and minimum percent of students who write their notes with pencil are 22% and 28%.

Given that,

25% of pupils who responded to a poll said they scribbled their notes with a pencil. The accuracy of the results was stated to be within 3%.

We have to find what proportion of students at their highest and lowest levels write their notes in pencil.

The survey results given as:

Pencil is 25% --- the proportion of students reported that they wrote their notes with a pencil

Accuracy is 3%.

Range

The range is then calculated as:

Range= pencil ± Accuracy.

Take the minimum

Minimum is pencil- accuracy

Minimum is 25%-3%
Minimum is 22%.

Take the maximum

Maximum is pencil+ accuracy

Maximum is 25%+3%
Maximum is 28%.

Therefore, The maximum and minimum percent of students who write their notes with pencil are 22% and 28%.

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Answer:

x^2+9x+18

Step-by-step explanation:

x-y=0

x=y

in this case we have the roots which are the x values so:

x=-6

x+6=0

and

x=-3

x+3=0

(x+3)(x+6)=0

x^2+6x+3x+18=0

x^2+9x+18=0

There are 720 ways the first three positions of the order of finish can occur assuming no ties in a race with 10 horses.

To calculate the number of ways the first three positions can occur, we use the permutation formula:

nPr = n! / (n - r)!

where n is the total number of objects and r is the number of objects we are choosing.

In this case, we have 10 horses and we want to choose the first three positions, so we get:

10P3 = 10! / (10 - 3)! = 10! / 7! = (10 x 9 x 8) / (3 x 2 x 1) = 720

Therefore, there are 720 ways the first three positions of the order of finish can occur assuming no ties.

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Answer:

1st one.

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

4:37 till 5:00 is 23 minutes.

+ 16 minutes

= 23 + 16

Answer:

39 minutes

Step-by-step explanation:

First, find how much time passed between 4:37 PM and 5 PM.

Since there are 60 minutes in an hour, subtract 37 from 60:

60 - 37

= 23

There are 16 minutes in between 5 PM and 5:16 PM.

So, add the 23 minutes to 16:

23 + 16

= 39

So, it took her 39 minutes

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's evaluate ~

\(\qquad \tt \dashrightarrow \: \{5 \times (13 - 8) \} + 12 \div 6\)

\(\qquad \tt \dashrightarrow \: \{5 \times (5) \} + 12 \div 6\)

\(\qquad \tt \dashrightarrow \: \{5 \times 5\} + 2\)

\(\qquad \tt \dashrightarrow \:25 + 2\)

\(\qquad \tt \dashrightarrow \:27\)

{5×(13−8)}+12÷6

the value of the expression.

we'll have to follow the BODMAS rule to solve this.

{5×(13−8)}+12÷6

= {5 × (5)} + 12 ÷ 6

= 25 + 2

= 27

The Taylor series for a function f about x=1 is an infinite sum that represents the function using its derivatives at x=1. It starts with the value of the function at x=1 and includes terms involving higher derivatives multiplied by powers of (x-1) divided by factorials. It allows us to approximate the function near x=1 using a polynomial.

1. The first term, f(1), represents the value of the function at x=1.
2. The subsequent terms involve the derivatives of the function at x=1. The second term, f'(1)(x-1), is the first derivative of f at x=1 multiplied by (x-1).
3. Each subsequent term involves higher derivatives of f at x=1, with each derivative being multiplied by (x-1) raised to a power and divided by the corresponding factorial.

The Taylor series is a way to represent a function as an infinite sum of terms derived from its derivatives at a specific point. In this case, the Taylor series for function f about x=1 is given by f(x) = f(1) + f'(1)(x-1) + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...

Each term involves a derivative of f evaluated at x=1, multiplied by (x-1) raised to a power and divided by the corresponding factorial. By including more terms in the series, we can approximate the function better near x=1 using a polynomial.

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Answer:

a) -2n+14

b) -5n+30

Step-by-step explanation:

negative because it goes down, any other questions im here to help

For each quadratic equation, the value of a, b and c are mentioned below. Also maximum or minimum points are mentioned here.

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

a. y = 3x²-3x + 5, comparing this with general quadratic equation ax² + bx + c and get a = 3 and b = -3 and c = 5

thus x = - (b/2a)

x = - (-3/6)

x = -1/2

as a > 0 thus the equation has the minimum value and that is:

y = 3(-1/2)² -3(-1/2) + 5

y = 3/4 + 3/2 + 5

y = 13/2

b. y = -2x² + x  comparing this with general quadratic equation ax² + bx + c and get a = -2 and b = 1 and c = 0

thus x = - (b/2a)

x = - (1/-4)

x = 1/4

as a < 0 thus the equation has the maximum value and that is:

y = -2(1/4)² + (1/2)

y = -1/8 + 1/2

y = 3/8

c. y = 1/2x² + 6 comparing this with general quadratic equation ax² + bx + c and get a = 1/2, b = 0 and c = 6

thus x = - (b/2a)

x = - (1/2×0)

x = 0

as a > 0 thus the equation has the minimum value and that is:

y = 1/2(0)² + 6

y = 6

d. y=-3x² + 1/2x - 2 comparing this with general quadratic equation ax² + bx + c and get a = -3, b = 1/2 and c = -2

thus x = - (b/2a)

x = - [(1/2)/-6]

x = 1/12

as a < 0 thus the equation has the maximum value and that is:

y=-3(1/12)² + 1/2 (1/12) - 2

y = - 1/48 + 1/24 - 2

y = -45/48

e. y=x²-2x+6 comparing this with general quadratic equation ax² + bx + c and get a = 1, b = -2 and c = 6

thus x = - (b/2a)

x = - (-2/2)

x = 1

as a > 0 thus the equation has the minimum value and that is:

y=(1)²-2(1)+6

y = 5

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Answer:

60%

Step-by-step explanation:

The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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Answer:

146 since the angle is a central that its measure is equal to the arc

A pharmaceutical corporation has two locations that produce the same over-the-counter medicine , the marginal revenue for location 1 when x1 = 4 and x2 = 12 is 504. and the marginal revenue for location 2 when x1 = 4 and x2 = 12 is 568.

To find the marginal revenue for each location, we need to calculate the partial derivatives of the total revenue function with respect to each variable.

(a) To find the marginal revenue for location 1 (∂R/∂x1), we differentiate the total revenue function R with respect to x1 while treating x2 as a constant:

∂R/∂x1 = 600 – 8x2.

Substituting the given values x1 = 4 and x2 = 12, we have:

∂R/∂x1 = 600 – 8(12) = 600 – 96 = 504.

Therefore, the marginal revenue for location 1 when x1 = 4 and x2 = 12 is 504.

(b) Similarly, to find the marginal revenue for location 2 (∂R/∂x2), we differentiate the total revenue function R with respect to x2 while treating x1 as a constant:

∂R/∂x2 = 600 – 8x1.

Substituting the given values x1 = 4 and x2 = 12, we have:

∂R/∂x2 = 600 – 8(4) = 600 – 32 = 568.

Therefore, the marginal revenue for location 2 when x1 = 4 and x2 = 12 is 568.

In summary, the marginal revenue for location 1 is 504, and the marginal revenue for location 2 is 568 when x1 = 4 and x2 = 12. Marginal revenue represents the change in revenue with respect to a change in production quantity at each location, and it helps businesses determine how their revenue will be affected by adjusting production levels at specific locations.

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Answer:

90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

(5) (-9) (-2)

-45 (-2) = 90

hope this helps