Researchers claim that 60 tissues is the average number of tissues a person uses during the course of a cold. The company that makes Kleenex brand tissues thinks that fewer of the tissues are needed. What are their null and alternative hypotheses?

An integral graph with graph spectrum is the utility graph.The utility graph's adjacency, incidence, and graph distance matrices are displayed in the aforementioned graphs.

These technologies enable users to mathematically represent their ideas, dynamically link several representations, form hypotheses, and finally create totally new concepts.

Use a graphing utility

See attached file

 The value  of X in the interval  [0, 2π) are

X1=0

X2=π/2-----1.5708

X3=π------- 3.1416

Values of X  (0,1.5708,3.1416)

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Using the Fundamental Counting Theorem, the number of plates for each case is obtained as follows:

The Fundamental Counting Theorem is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

With the Latin letters, it is found that for the letters, there are 26 outcomes, hence:

[tex]n_1 = n_2 = n_3 = 3[/tex]

With one number, the number of outcomes for the digit is:

[tex]n_4 = 9[/tex]

(as the digit cannot be zero).

With two numbers, the number of outcomes for the digit are:

[tex]n_4 = 9, n_5 = 10[/tex]

With three numbers, the parameters are:

[tex]n_4 = 9, n_5 = 10, n_6 = 10[/tex]

Hence the total number of plates is obtained as follows:

T = 26³ x (9 + 9 x 10 + 9 x 10 x 10) = 17,558,424.

With the extra letters, each letter can assume 29 outcomes, hence the number of plates is:

T = 29³ x (9 + 9 x 10 + 9 x 10 x 10) = 24,364,611.

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The required equation of inequality is 4 ≤ b ≤ 6

Given ; Cups of iced tea = 120 cups

and the cups of iced coffee should not be less than 180 cups

Thus this is a question of inequality

Each batch of iced tea makes = 30 cups

thus the required equation is

[tex]\frac{120}{30}[/tex] and this is less than the number of batches which is represented by b

thus the equation would be [tex]\frac{120}{30}[/tex]  ≤ b

And it should be less than 180 cups of iced tea

thus the equation would be

b ≤ [tex]\frac{180}{30}[/tex]

Thus the required equation is :

[tex]\frac{120}{30}[/tex] ≤ b ≤ [tex]\frac{180}{30}[/tex]

On simplifying this we will get ;

4 ≤ b ≤ 6

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a) An equation relating the miles traveled to gallons of gas used is m = 14g.

b) With 3.7 gallons of gas, one can drive up to 51.8 miles.

An equation is a mathematical statement that makes two mathematical expressions equivalent or equal using the equation symbol (=).

Equations establish the equality of two or more values, variables, or numbers.

The total distance driven on one tank of gas = 168 miles

The quantity of gas used = 12 gallons

The number of miles per gallon of gas = 14 (168/12)

Let m = distance in miles

Let g = gallons of gas used

Equation: m = 14g

Solution:

Gallons of gas used = 3.7

m = 14g

= 14(3.7)

= 51.8 miles

Thus, based on the established equation, with 3.7 gallons of gas used, the driver can cover 51.8 miles.

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In the equation given 2[(4m * 3.5) / 400] = 171.5, m has a value of 2450.

Equations are mathematical statements containing two algebraic expressions on both sides of an equal to sign. This can be expressed as the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

We can find the value of m by applying changing the subject of formula

2[(4m * 3.5) / 400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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Step-by-step explanation:

4t - 7 + 83 = 180

4t + 76 = 180

4t = 104

t = 26

The completion of the trend analysis for sales with 2010 as the base year is as follows:

                               2013           2012           2011           2010

Sales               $ 158,000   $ 615,000   $ 280,000   $ 500,000

Trend Analysis       32%           123%           56%           100%

Trend analysis uses observed historical data to predict future developments and monitor performances about a particular topic.

Undertaking a trend analysis for sales, which is a technical analysis, involves setting a base year.  The sales figure for the base year is set to 100% and used to check changes during the review periods.

The other years' sales results, in percentages, are compared to the base year by dividing each year's sales by the base year.

2013 (D) = 32% ($158,000/$500,000 x 100)

2012 (C) 123% ($615,000/$500,000 x 100)

2011 (B) 56% ($280,000/$500,000 x 100)

2010 (A) = 100% ($500,000/$500,000 x 100)

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The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). For example -

y = 4x⁴ + 3x³ + 2x² + 6x + 7

We have the following polynomial -

y = 2x⁴ - 5x³ + x² - 2x + 4

Now -

at x = 0, y = 4

at x = 1, y = 0

at x = 2, y = 32 - 40 + 4 - 4 + 4 = - 4

Refer to the graph attached. The points (0, 4), (1, 0) and (2, - 4) are plotted.

Therefore, the graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

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The conversion of the measurement of 65 lb will be 29483.5 g.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

In this case, we need to convert 65 lb to g

It should be noted that we have to multiply the weight value by 453.5

Therefore, it should be noted that 65 lb will be:

= 65 x 453.5

= 29483.5 g.

Therefore, it should be noted that the conversion of the measurement of 65 lb will be 29483.5 g.

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Answer:

9 quarters and 26 dimes

Step-by-step explanation:

your welcome :)

Answer:

  DNE

Step-by-step explanation:

You want to know the y-intercept of x = -4.

The y-intercept is the point where a graph crosses the y-axis.

The line x=-4 is a vertical line parallel to the y-axis, so does not cross the y-axis.

There is no y-intercept. It does not exist (DNE).

Simplification of the given expression 2cd³ (c - d +5) is given by

2c²d³ − 2cd⁴ + 10cd³.

As given in the question,

Given expression is equal to :

2cd³ (c - d +5)

Law of exponents for multiplication is given by:

mᵃ × mᵇ  =mᵃ⁺ᵇ

Simplification of the given expression by open the parenthesis we have,

= 2cd³ × c - 2cd³ × d + 2cd³ × 5

Apply law of exponents for multiplication we get,

= 2c¹⁺¹d³ -2cd³⁺¹ + (2×5)cd³

= 2c²d³ -2cd⁴ + 10cd³

Therefore, simplification of the given expression 2cd³ (c - d +5) is given by 2c²d³ − 2cd⁴ + 10cd³.

The complete question is:

Simplify : 2cd³ (c - d +5)

a. 2cd³− 2c²d⁴ + 10c²d³

b. 2c²d³ − 2cd⁴ + 10cd³

c. 2cd³ − 2cd³ + 10cd³

d.  2c²d³− 2c²d⁴ + 10cd²

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Here ya are hope this helps! :]]

For the given geometric sequence the seventh term is equal to 19/81 and the 12th term is equal to "-57" the value of the 15th term is 1539.

What is a geometric sequence?

One particular sort of sequence is a geometric sequence. It is a sequence in which each term, with the exception of the first, is multiplied by a fixed integer to obtain the following term. The common ratio must be multiplied by the current term in the geometric sequence to obtain the next term, and the common ratio must be divided by the current term to obtain the previous term.

Solution Explained:

We know, a7 = 19/81, a12 = -57

So, ar^7 = 19/81 and ar^12 = -57     (r= common ratio)

Since r< a15 < 0 [the sign alternate]

Ignoring the signs,
r^12 = r^7 X r^5
57 = 19/81 X r^5

(57 X 81)/19 = r^5

243 = r^5

r = the fifth ratio of 243 = 3

therefore, r = -3

So, a15 = a12 X r^3
            =  -57 X (-3)^3
            = 1539

Hence, the value of the 15th term is 1539.

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The probability of tossing a six-sided die with sides numbered 1 through 6 and getting a 5 is 0.166666 or 1/6.

Here in the question, we see that a six-sided die is tossed. So there will be a total of 6 outcomes.

So the sample space will be {1,2,3,4,5,6}

Of which the possible outcome of getting a 5 is 1

Let A be the event of getting a 5 on tossing a six-sided die

∴ the probability of getting a 5 on tossing a six-sided die is P(A)=1/6

∵ we know that the probability of an event is the possible outcome of the event divided by the total outcomes of that event.

So here the probability of getting a 5 is 0.166666 or 1/6.

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By evaluating in x = 0, we can see that the function with the greater y-intercept is the first one:

y=-x+6

For any function y = f(x), we define the y-intercept as the value that y takes when we evaluate the function in x = 0.

For the first function:

y = -x + 6

The y-intercept is:

y = -0 + 6 = 6

While for the second function:

y = 2x - 3

Evaluating in 0 we get:

y = 2*0 - 3 = -3

So the y-intercept of the first function is 6, and the one of the second function is -3.

Then the first function has the greater y-intercept.

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The quantity that is needed for you to be able to use arcsine to calculate the percentage grade is D. The change in elevation along a section of road

A geographic location's elevation is its height above or below a set reference point, most typically a reference geoid, which is a mathematical model of the Earth's sea level as an equipotential gravitational surface.

Elevation is described as the height above the ground or other surface, as well as a location or position of elevation. A plane flying 36,000 feet above the ground is an illustration of elevation. A pope being elevated to the position of saint is an example of elevation.

When driving on mountain roads, road signs frequently reflect the route's steepness as a percentage grade, which represents the angle of elevation as the road increases. In this case, the correct option is D.

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Answer:

I think b 1/3

Step-by-step explanation:

slope is rise over run

Answer:

1/2

Step-by-step explanation:

find 2 clear points A(2,0) B(8,3)

use the formula of the angular coefficient

[tex]c = \frac{y2 - y1}{x2 - x1} [/tex]

The solution to the expression is -31.5

An algebraic expression in mathematical is statement that comprises of  numbers, variables, symbols and mathematical operators.

Given, when a= 0.25 and b = -1

Step 1: Substitute the given into the expression 36a + 42b - 18a +6

we have;  36(0.25) + 42(-1) - 18(0.25) +6

= 9 - 42 - 4.5 +6

Step 2; use BODMAS  to evaluate

we have; 9 - 42 - 4.5 +6= -31.5

Therefore the solution to the expression is -31.5

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Answer:

3/20

Step-by-step explanation:

3/5 : 4

3/5 x 1/4

3/20

The solution to the equation 5x - 5 = 15 in the replacement set is x = 4

From the question, we have the following equation that can be used in our computation:

5x - 5 = 15

The replacement set is given as

{0,1, 2, 3, 4}

So, we replace the variables using the elements in the replacement set

When x = 0, we have

5(0) - 5 = 15

-5 = 15 -- false

When x = 1, we have

5(1) - 5 = 15

0 = 15 -- false

When x = 2, we have

5(2) - 5 = 15

5 = 15 -- false

When x = 3, we have

5(3) - 5 = 15

10 = 15 -- false

When x = 4, we have

5(4) - 5 = 15

15 = 15 -- true

Hence, the value of the equation is x = 4

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The value of k in 10 × 10 = [tex]10^k[/tex] is k = 2

The equation is give

10 × 10 = [tex]10^k[/tex]

The equation is defined as the mathematical statement that represent the two algebraic expression with an equal sign. The equation will no contain the inequality signs like greater than, less than etc..

The power of a number is the base number is raised to the exponent

Here the equation is

10 × 10 = [tex]10^k[/tex]

10 is the base number and k is the exponent.

We know that,

10 × 10 = [tex]10^2[/tex]

The value of k = 2

Here 2 is the exponent of base number 10

Hence, The value of k in 10 × 10 = [tex]10^k[/tex] is k = 2

The complete question is:

What is the value of k in 10 × 10 = [tex]10^k[/tex] ?

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Dilation entails altering a figure's size.

Because the is larger than, Isaiah's assertion is untrue.

Although dilation is not a hard transformation, the angles of the figures it dilates remain unchanged.

The aforementioned claim suggests that,

The dimensions of and should be equal.

However, it is evident that;

are not equivalent.

In reality

greater than

Therefore, Isaiah's assertion is false.

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The distance between the line containing points (4, –1) and (4, 9) and point p (1,6) is of:

3 units.

The standard equation of a line is given by the rule presented as follows:

ax + by + c = 0.

The coordinates of the points which we want to find the distance from the line are given as follows:

(x0,y0).

Then the shortest distance is given by the equation presented as follows:

D = |a(x0) + b(y0) + c|/sqrt(a²+b²).

The two points of the line are given as follows:

(4, –1) and (4, 9).

Since the x-coordinate is constant, the line has a slope of infinite, meaning that it is a vertical line defined as follows:

x = 4.

x - 4 = 0.

The point p has these following coordinates:

p(1,6).

Hence the distance between the point and the line is:

D = |a(x0) + b(y0) + c|/sqrt(a²+b²).

D = |1(1) + 0(6) - 4|/sqrt(1² + 0²).

D = |-3|

D = 3 units.

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In both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

What is  Obtuse triangle?

Triangle B = Obtuse triangle

Triangle C = Obtuse triangle

in both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

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a. Jays total income is $93.50 and total spending is $103.25.

b. Jays Spending is greater than income.

c. Total saving is -9.75

d. Jays savings are negative. Since Jays spending is greater than income it does not make sense.

Two or more expressions with an Equal sign is called as Equation.

Given,

Jays Income:

Part time job: $83.50

Allowance: $10

Spending:

Clothing: $32.50

Lunches: $19.75

Entertainment: $29.00

Transportantion: $22.50

a. Jays total income and total spending

Total income = $83.50+$10.00

=$93.50

Total spending = $32.50+$19.75+$29.00+$22.50

=$103.25

b. Spending is greater than income.

c. Jays saving=Total income - Total spending

=93.50-103.25

=-9.75

d. Jays savings are negative. Since Jays spending is greater than income it doesnt make sense.

Hence,

a. Jays total income is $93.50 and total spending is $103.25.

b. Jays Spending is greater than income.

c. Total saving is -9.75

d. Jays savings are negative. Since Jays spending is greater than income it doesnt make sense.

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