Identify the null and alternative hypotheses for the following problems. (Enter != for ≠ as needed. )


(a)


The manager of a restaurant believes that it takes a customer less than or equal to 24 minutes to eat lunch. (Give your hypotheses in minutes. )


H0:



Ha:


(b)


Economists have stated that the marginal propensity to consume is at least 85¢ out of every dollar.


H0:



Ha:


(c)


It has been stated that 78 out of every 100 people who go to the movies on Saturday night buy popcorn.


H0:



Ha:

A obtuse triangle is a triangle in which one of the angles is greater than 90°.

An obtuse triangle can be mathematically defined as a triangle with one angle greater than 90°. The formula for calculating the angles of a triangle is known as the Law of Sines. The formula states that the ratio of the length of a side of the triangle to the sine of its opposite angle is the same for all sides. To calculate the angles of an obtuse triangle, we must first find the ratio of the sides to the opposite angle. For example, if we have a triangle with sides of length a, b and c, then the ratios of the sides to their opposite angles are a/sinA, b/sinB and c/sinC. Once we have found the ratios, we can use the Law of Sines to calculate the angles of the triangle. We can then determine if any of the angles are greater than 90°, which would indicate that the triangle is obtuse.

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Answer: accidentally did that sorry

Step-by-step explanation:

The distance PR, representing the distance across the river, is given as follows:

PR = 294 ft.

Similar triangles are triangles that share these two features given as follows:

The two similar triangles for this problem are given as follows:

POC and PRE.

Hence the distance PR is symbolized as follows:

PR = x.

The equivalent side lengths form a proportional relationship, given as follows:

x/(x + 160) = 230/355.

Hence, applying cross multiplication, the distance PR is obtained as follows:

355x = 230(x + 160)

355x = 230x + 36800

125x = 36800

x = 36800/125

x = 294 ft.

The diagram is given by the image presented at the end of the answer.

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Answer: The distance across the river is 181 ft.

Step-by-step explanation:

in photo

Answer:

264000 feet/hour

Step-by-step explanation:

1 mile = 5280 feet

5280 * 50 = 264000

50 miles/hour = 264000 feet/hour

The factor form of quadratic equations are listed below:

In this problem we find fifteen cases of quadratic equations of the form x² + b · x + c, where b, c are real coefficients. This kind of quadratic equation can be modified into factor form by means of the following rule:

x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)

- r₁ - r₂ = b

r₁ · r₂ = c

Where r₁, r₂ are roots of the polynomial.

Now we proceed to find the binomial factors:

Case 1

x² + 9 · x + 20 = (x + 4) · (x + 5)

Case 2

x² + 7 · x + 12 = (x + 3) · (x + 4)

Case 3

x² + 8 · x + 15 = (x + 3) · (x + 5)

Case 4

x² + 7 · x + 12 = (x + 3) · (x + 4)

Case 5

x² + 11 · x + 10 = (x + 10) · (x + 1)

Case 6

x² + 7 · x + 6 = (x + 6) · (x + 1)

Case 7

x² + 5 · x + 4 = (x + 5) · (x + 1)

Case 8

x² + 10 · x + 21 = (x + 7) · (x + 3)

Case 9

x² + 10 · x + 16 = (x + 8) · (x + 2)

Case 10

x² + 10 · x + 9 = (x + 10) · (x - 1)

Case 11

x² + 12 · x + 20 = (x + 10) · (x + 2)

Case 12

x² + 15 · x + 14 = (x + 14) · (x + 1)

Case 13

x² + 13 · x + 42 = (x + 6) · (x + 7)

Case 14

x² + 9 · x + 18 = (x + 6) · (x + 3)

Case 15

x² + 16 · x + 60 = (x + 10) · (x + 6)

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The required perimeter of the given rectangle is (C) 29 4/6 ft.

A rectangle is a quadrilateral with four right angles in the Euclidean plane.

It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.

A square is a rectangle with four equally long sides.

So, the perimeter formula is:

2(l+b)

Now, calculate the perimeter as follows:

2(l+b)

2(8 1/6+ 6 2/3)

2(49/6 + 20/3)

2(89/6)

178/6

29 4/6 ft

Therefore, the required perimeter of the given rectangle is (C) 29 4/6 ft.

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Correct question:

What is the perimeter of a rectangle with a length of Eight and one-sixth feet and a width of Six and two-thirds feet?

A. 14 3/9 ft

B. 16 2/6 ft

C. 29 4/6 ft

D. 48 3/18 ft

The correct answer is 6.432 × 10 raised to the power of 6

The derivatives of the functions are as follows:  y' = 4x^3+2x-3x^2-3 , s'(t) =[tex]2(2-t^2)/(2sqrt t) - 2t(sqrt t+3)/(2sqrt t)[/tex] ,  f'(x) = 4x^3sin x + x^4cos x

1. y' = (2x-3)(x^2+1) + (x^2-3x)(2x) = 4x^3+2x-3x^2-3

2. s'(t) = [tex](1/(2sqrt t))(4-t^2) + (sqrt t+3)(-2t) = 2(2-t^2)/(2sqrt t) - 2t(sqrt t+3)/(2sqrt t)[/tex]

3. f'(x) = 4x^3sin x + x^4cos x

1. Begin by applying the product rule to differentiate the function. The product rule states that the derivative of a product of two functions is equal to the product of the derivatives of the two functions.

y' = (2x-3)(x^2+1) + (x^2-3x)(2x)

2. Begin by applying the product rule to differentiate the function. The product rule states that the derivative of a product of two functions is equal to the product of the derivatives of the two functions.

[tex]s'(t) = (1/(2sqrt t))(4-t^2) + (sqrt t+3)(-2t)[/tex]

3. Begin by applying the quotient rule to differentiate the function. The quotient rule states that the derivative of the quotient of two functions is equal to the quotient of the derivatives of the two functions minus the product of the two functions divided by the square of the denominator.

f'(x) = 4x^3sin x + x^4cos x

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A number's square root multiplied by another number's square root does not always equal the total of these two numbers' square roots.

A statistical method called the sum of squares (SS) is used in regression analysis to determine how well the data can fit the model and how dispersed the data are. Since it is determined by adding up the squared differences, the sum of squares is how it is calculated.

A sum's square is equal to the product of its summands' squares and its double products' sums of summands in twos.

So, it is not always true that the square root of a sum is equal to the sum of the square roots.

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Answer:

the one on the left

Step-by-step explanation:

This shows a direct relationship between X and Y

Answer:

1

Step-by-step explanation:

T1(a) = 1

T2(ar) = 3/2

T3(ar²) = 9/4

T4(ar³) =27/8

T5(ar⁴) = 81/16

lets look for r

by using the formula

[tex] \frac{t \\ 2}{t1} = \frac{t3}{t2} = \frac{t4}{t3} = r[/tex]

let us use T2/T1

[tex] \frac{ \\ ar}{a} = \frac{3}{2} \div 1 = \frac{3}{2} \times \frac{1}{1} = \frac{3}{2} [/tex]

[tex]r = \frac{ \\ 3}{2} [/tex]

since r > 1 we will use this formula

[tex]s10 = \frac{a \\ ( r - 1)}{r - 1} [/tex]

by substituting

[tex]s10 = \frac{ \\ 1( \frac{3}{2} - 1)}{ \frac{3}{2} - 1 } [/tex]

[tex] = \frac{ \\ \frac{3}{2} - 1}{ \frac{3}{2} - 1 } [/tex]

[tex] = \frac{ \\ \frac{1}{2} }{ \frac{1}{2} } [/tex]

[tex] \frac{1}{2 \\ } \div \frac{1}{2} [/tex]

[tex] \frac{1}{2 \\ } \times \frac{2}{1} [/tex]

[tex] \frac{2}{2 \\ } = 1[/tex]

therefore the sum of first ten term of the sequence is 1

Answer: 90 sqare meters

Step-by-step explanation: you have to take 972 and divide it by 10.8 then you get your answer

Using proportions and ratios, the answer is m / 160(2/5) = 37(7/10) / 100 which is option A

Proportions are relationships between two or more related numerical values, usually expressed as fractions or ratios. They are used to compare the relative sizes of different quantities, or to assess the relationship between two different sets of data. Proportions can also be used to make predictions about future events, or to compare different sets of data.

In this problem, we can approach this as

100 pounds on Earth = 37(7/10) pounds on Mars

160(2/5) pounds on Earth = m pounds on Mars

Cross multiply both sides and solve

This will become;

m = [160(2/5) * 37(7/10)] / 100

This can be written in ratio as;

m / 160(2/5) = 37(7/10) / 100

This is option A

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Step-by-step explanation:

For the first equation to make a line plot a point at negitive 5 then go up three then go one to the right

For the second equation to make a like plot a point at positive 4 then go down three then go one to the left

Considering the quadrilateral, the dimensions are as follows

The given figure is a parallelogram, and the properties will be used in finding the required dimensions

QR = PS = 19 opposite sides of a parallelogram are equal

SR = PQ = 24 opposite sides of a parallelogram are equal

PT = PR / 2 = 42 / 2 = 21 (diagonals of a parallelogram bisects each other)

SQ = 2 * TQ = 2 * 10 = 20 (diagonals of a parallelogram bisects each other)

< QRS = < QPS and < PQR = < PSR (opposite angles of a parallelogram)

< QRS + < QPS + < PQR + < PSR = 360 (sum of angles of a quadrilateral)

2 < QRS + 2< PQR = 360

2 < QRS + 2 * 106 = 360

divide through by 2

< QRS + 106 = 180

< QRS = 180 - 106

< QRS = 74

< PQS = <QSR = 49 alternate angles

< RPS + < PRS + < PSR = 180 (angles on a triangle)

< RPS + 35 + 106 = 180

< RPS + 141 = 180

< RPS = 180 - 141

< RPS = 39

<PSQ + < QSR = < PSR adjacent angles

< PSQ + 49 = 106

< PSQ = 106 - 49

< PSQ = 57

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The solution is Option C.

The functions f ( x ) and g ( x ) have the same y-intercept of ( 0 , 6 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first function be represented as A

Let the second function be represented as B

Now , the value of A is

f ( x ) = 2x² + 7x + 6   be equation (1)

Now , the value of B is

g ( x ) = 2ˣ + 5   be equation (2)

Now , on simplifying the equation , we get

To find the y-intercepts of the function ,

Substitute the value of x = 0 in the equation , we get

f ( 0 ) = 2 ( 0 )² + 7 ( 0 ) + 6

On simplifying the equation , we get

y = 6

Now , g ( x ) = 2ˣ + 5

Substitute the value of x = 0 in the equation , we get

g ( 0 ) = 2⁰ + 5

g ( 0 ) = 1 + 5

g ( 0 ) = 6

Hence , the y intercepts of the functions f ( x ) and g ( x ) is ( 0, 6 )

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The proportion of the drink that is juice is one part juice to four parts water. The proportion of the drink that is juice is 1:5. This can be written in fraction as 1/5 , in decimal as 0.25 and in percentage as 25%.

A ratio is a mathematical comparison of two or more values. It is typically written as a fraction, with the values being separated by a colon (e.g. 3:4). The values in a ratio can represent any type of quantity, such as length, weight, or time.

A proportion is a statement that two ratios are equal. For example, if the ratio of boys to girls in a class is 4:5, and the ratio of boys to the total number of students is 12:20, then the two ratios are in proportion. In contrast, a ratio is simply a comparison of two or more values without any equality statement.

An orange drink is made using one part juice to four parts water. The proportion of the drink that is juice is 1/5.The proportion of the drink that is juice is 1/5, which can be expressed as a decimal as 0.2 (1/5 = 0.2) or as a percentage as 20% (0.2 x 100 = 20).

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The given graph is of inverse function.

A function that can change into another function in the opposite direction is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. If a function is written as "f" or "F," the inverse function is written as "f-1" or "F-1."

The original value for which a function produced its output is returned by the inverse function. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x. The initial value is fetched by a function that is its inverse. Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).

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The requried simplified value of the given expression is given as -a³/4b². Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= [-b³]⁰/[2ba⁻⁷ × -2ba⁴]
= -1 / 4b²a⁻³
= -a³/4b²

Thus, the requried simplified value of the given expression is given as -a³/4b². Option B is correct.

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The ordered pair of (4 , 16) tells us that the 4 pounds of cheese have its cost as 16 dollars.

An ordered pair is a mathematical concept used to represent a point in a coordinate system. It is a pair of values, usually represented in the form of (x, y), where x and y are real numbers. The first value, x, represents the point's position along the horizontal (x) axis, and the second value, y, represents the point's position along the vertical (y) axis.

In the graph, what we are told is that if one purchases 4 pounds of the cheese, the amount that they would pay for the cheese would be 16 dollars.

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The inequality 4/3|1/4x+3|<4 are Ox>-13 and x < -11 or Ox<-24 and x > 0

We can begin by isolating the absolute value on one side of the inequality:

4/3|1/4x+3|<4

|1/4x+3|<3/2

We can then split this inequality into two cases, one for when 1/4x+3 is positive and one for when it is negative:

1/4x+3>0: 1/4x+3>3/2, so multiplying both sides by 4, we get x>-13 and x<-11

1/4x+3<0: 1/4x+3<-3/2, so multiplying both sides by -4, we get x<-24 and x>0

So, the solution is: Ox>-13 and x < -11 or Ox<-24 and x > 0

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Answer:

Y=-[tex]\frac{1}{2}[/tex] + 4

Step-by-step explanation:

You will be using the equation of Y= Mx+B

First you must find the Y intercept, where the line crosses the Y axis, this is at positive four, this will be your B value. then you find the slope by picking 2 easily readable points on the graph, to do this i will choose (0,4) and (2,3), then you find the change in Y and put it in a fraction over the change in x, since this is going down the slope will have a negative infront of it, so your fraction is [tex]\frac{3-4}{2-0}[/tex] which equates to [tex]\frac{-1}{2}[/tex] so your slope is -1/2 (this is M value)

so lastly you plug it all in, Y= -1/2x+4

Answer: Ayman has saved $25

Step-by-step explanation: It's basically just 5/6th's of 30, which is 25.

The probability of getting more heads than tails when a fair coin is flipped 5 times is 1/2.

True

The probability of getting more heads than tails is the same as the probability of getting an equal number of heads and tails, because the two outcomes are equally likely. The probability of getting an equal number of heads and tails is 1/2, so the probability of getting more heads than tails is also 1/2.

The probability of getting more heads than tails when a fair coin is flipped 5 times is 1/2, which is the same as the probability of getting an equal number of heads and tails.

The probability of getting more heads than tails when a fair coin is flipped 5 times is 1/2.

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The expression for the students in the class is 5N + 25 + 15 = 90 or N = 10

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

Let the number of students in class be N.

Therefore, from the information provided, the expression for the students in the class can be written as:

5N + 25 + 15 = 90

5N + 40 = 90

5N = 90 - 40

5N = 50

N = 50/5

N = 10

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The y intercept of a line written in the standard form is calculated by

A linear function consists of functions where the variables has exponents of 1. The relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

To solve for the intercept in the equation y = mx + c x is set to zero

y = mx + c

y = m(0) + c

y = 0 + c

y = c

hence the intercept is equal to c when x is zero

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The total area of the figure when divided in rectangle, triangle and half circle is 86.13 square units.

Area is the room contained by a specific shape or location. It speaks of how much room is consumed. The area and perimeter of the shape will increase in size as it gets bigger.

Given figure comprises of a rectangle, triangle, and a half circle.

The area of the figure is thus calculated by adding the value of all the figures as follows:

A = Area of triangle + Area of rectangle + Area of semi-circle

[tex]A = \frac{1}{2} (b) (h) + (l)(b) + \frac{1}{2} (\pi r^{2} )\\[/tex]

Substitute the value of length, width, height and radius:

[tex]A = \frac{1}{2} (6) (6) + (9)(6) + \frac{1}{2} (3.14 (3^{2}) )\\\\\\A = 18 + 54 + 14.13\\\\A = 86.13[/tex]

Hence, the area of the figure is 86.13 square units.

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