A patient has a choice between four different prescription plans through their health insurance. The options are:
Option A: $105 monthly premium with a $15 co-pay per prescription
Option B: $100 monthly premium with a $20 co-pay per prescription
Option C: $115 monthly premium with a $10 co-pay per prescription
Option D: $110 monthly premium with a $12 co-pay per prescription
Which option is the most expensive if the patient fills 7 prescriptions each month?
O Option A
O Option B
O Option C
O Option D

According to given equations, any value of x less than 15.6 will result in the shopkeeper spending less than $100 on electricity.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side and a right-hand side, separated by an equals sign (=). The left-hand side and the right-hand side of an equation may contain one or more variables, and the equation is true only for certain values of these variables.

Let E be the amount the shopkeeper spends on electricity. Then, we have:

Total monthly expenses = Rent + Electricity = 8x + 15

Rent = 3x - 7

Substituting the value of Rent in the equation of total monthly expenses, we get:

8x + 15 = (3x - 7) + E

Simplifying this equation, we get:

5x + 22 = E

Therefore, the shopkeeper spends 5x + 22 dollars on electricity.

To find the value(s) of x for which the shopkeeper spends less than $100 on electricity, we can set up an inequality:

5x + 22 < 100

Solving for x, we get:

5x < 78

x < 15.6

Therefore, for any value of x less than 15.6, the shopkeeper will spend less than $100 on electricity. To verify this, we can plug in a value of x less than 15.6 and see if the resulting amount spent on electricity is less than $100. For example, if we let x = 10, then:

5x + 22 = (5 * 10) + 22 = 72

Since 72 is less than $100, we have verified that any value of x less than 15.6 will result in the shopkeeper spending less than $100 on electricity.

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All eligible voters voted for Shelley= 3/20 ,

All eligible voters voted for Morgan= 31/100,  Morgan received most votes.

Multiplication is a mathematical operation that embodies the basic idea of numerous additions of the same number. The outcomes of multiplying two or more numbers are referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplication facilitates the process of adding the same number again.

Let's suppose Precinct 5 has 100 registered voters. There were 50 voters who participated in the election because only 50% of those who were eligible to vote actually did so.

3/10 of the votes were cast for Shelley, which translated as 3/10 x 50 or 15 votes.

With 5/8 of the vote, Morgan received 5/8 x 50 votes, or 31.25 votes. Therefore, we must round this figure down to 31 votes as we are dealing with whole voters.

We must divide the number of votes received by the total number of eligible voters in order to determine the percentage of all eligible voters who cast a ballot for Shelley: 100 eligible voters x 15 votes = 3/20.

Morgan won the most votes since she received more than Shelley.

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In conclusion the length of the rectangle is 319 feet.

How to find?

Let's denote the width of the rectangle as w.

According to the problem, the length of the rectangle is 154 feet more than the width, so we can express the length as w + 154.

The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Using the given perimeter of 968 feet, we can write:

968 = 2(w + w + 154)

Simplifying and solving for w, we get:

968 = 4w + 308

660 = 4w

w = 165

Therefore, the width of the rectangle is 165 feet.

We can find the length by using the expression we found earlier:

l = w + 154 = 165 + 154 = 319

Therefore, the length of the rectangle is 319 feet.

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Using the formula for x which is x = - b/2a, we know that the vertex of the given parabola is 5 respectively.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.

It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

A parabola can be described using a point and a line.

Three different parabolas exist.

Vertex form, standard form, and intercept form are the three forms.

You can access a unique key feature for the graph on each form.

So, we have the equation:

y = -2x² - 8x - 3

Now, we know that x = - b/2a

Solve for x:

x = - b/2a

x = - (-8)/2(-2)

x = 8/-4

x = -2

Now, insert x = -2 in the given equation:

y = -2x² - 8x - 3

y = -2(-2)² - 8(-2) - 3
y = -2(4) + 16 - 3

y = -8 + 16 - 3

y = 8 - 3

y = 5

Therefore, using the formula for x which is x = - b/2a, we know that the vertex of the given parabola is 5 respectively.

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After answering the provided question, we can conclude that Mean = (13 + 13 + 11 + 10 + 8) / 5 = 11 for Condition 3 (Loud Noise). 2.28 is the standard expression deviation.

An expression in mathematics is a collection of representations, digits, and transnational corporations that imitate a statistical correlation or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, growing influence, division, but instead exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To compute the experiment summaries, we must first compute the mean and standard deviation for each condition:

Mean = (15 + 13 + 14 + 12) / 4 = 13.5 in Condition 1 (Low Noise).

1.5 is the standard deviation.

Mean = 19 in Condition 2 (Medium Noise).

3 is the standard deviation.

Mean = (13 + 13 + 11 + 10 + 8) / 5 = 11 for Condition 3 (Loud Noise).

2.28 is the standard deviation.

 Condition 1 (Low Noise)    Condition 2 (Medium Noise)    Condition 3 (Loud Noise)

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

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

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

        Median = 13.5             Median = 19                Median = 11

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Answer:

11

Step-by-step explanation:

y = -1/2x + 7

x = -8

A double negative equals a positive therefore it would be the same as 8 x 1/2 which is 4.

y = 4 + 7

y = 11

Step-by-step explanation:

y = -1/2 X -8 + 7

y = -0,5 X -8 + 7

y = 4 + 7

y = 11

By answering the presented question, we may conclude that As a result, inequality the cost difference between one pencil and one rubber is £0.08.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.

To determine the cost difference between one pencil and one rubber, we must first determine the cost per item for each product.

The price of a pencil is 1.56 / 6 = £0.26.

The price of a rubber is 2.72 / 8 = £0.34.

Therefore the cost difference between one pencil and one rubber is:

£0.34 - £0.26 = £0.08

As a result, the cost difference between one pencil and one rubber is £0.08.

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The volume of both book end is  1458 [tex]cm^3[/tex].

The space taken up by any three-dimensiοnal sοlid cοnstitutes a vοlume, tο put it simply. A cube, cubοid, cοne, cylinder, οr sphere can be οne οf these sοlids. Cubic units are used tο measure the vοlume οf sοlids. The vοlume will be given in cubic metres, fοr instance, if the dimensiοns are given in metres.

Here the side length of cube = 9cm

Now using volume of cube formula then,

=> Volume of cube V = [tex]v^3[/tex] cubic unit.

=> V = [tex]9^3[/tex]

=> V = 9*9*9 = 729 [tex]cm^3[/tex].

Here we had pair of book end then volume = 2V = 2*729 = 1458 [tex]cm^3[/tex].

Hence the volume of both book end is  1458 [tex]cm^3[/tex].

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For the given statements f(-x) = -4|x| - 5x^3 = -f(x), we can conclude that f(x) is an even function.

A function that fulfils f(-x) = f(x) for any x inside the function's domain is said to be even. The graph of an even function displays reflected y-axis symmetry geometrically. The even functions [tex]f(x) = x^2 and f(x)[/tex] = cos are two examples (x).

A function is considered odd if it meets the condition f(-x) = -f(x) for all x inside its domain. An odd function's graph displays origin rotational symmetry geometrically. Odd functions include such like [tex]f(x) = x^3 and f(x) = sin (x).[/tex]

The given function is [tex]f(x) = -4|x| + 5x^3.[/tex]

An even function is a function that satisfies f(-x) = f(x).

For the function:

[tex]f(-x) = -4|-x| + 5(-x)^3[/tex]

[tex]f(-x) = -4|x| - 5x^3[/tex]

[tex]f(x) = -4|x| + 5x^3[/tex]

Since[tex]f(-x) = -4|x| - 5x^3 = -f(x)[/tex], we can conclude that f(x) is an even function.

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we can conclude that there is no strong evidence of a statistically significant difference between the means of the two groups.

What is the t-statistic?

A t-statistic is a test statistic that is used to determine if there is a significant difference between two groups based on their means.

A t-statistic with an absolute value greater than 1.96 indicates statistical significance at the 0.05 level of significance.

In this case, the t-statistic is -0.38, which is less than the absolute value of 1.96.

This means that the difference between the means of the two groups is not statistically significant at the 0.05 level of significance.

Without information on the specific groups being compared, it is not possible to make definitive conclusions about the differences between them based solely on the t-statistic.

Hence, we can conclude that there is no strong evidence of a statistically significant difference between the means of the two groups.

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Therefore, the quantity of heat absorbed by 70 g of water that warms from 30∘C to 90∘C is 17,645.6 J (joules).

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equals sign (=). The expressions on either side of the equals sign can contain numbers, variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

Here,

The amount of heat absorbed by a substance can be calculated using the formula:

Q = mcΔT

where Q is the amount of heat absorbed, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. For water, the specific heat capacity is 4.184 J/g⋅K.

Using the given values, we can calculate the amount of heat absorbed as follows:

m = 70 g

c = 4.184 J/g⋅K

ΔT = (90 - 30)∘C = 60∘C

Q = mcΔT

Q = (70 g) x (4.184 J/g⋅K) x (60∘C)

Q = 17645.6 J

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hope you understood the answer

The measure of angle KLN in the given set of intersecting lines is 100°.

In geometry, intersecting lines are lines that cross or meet each other at a point. The point at which the lines intersect is called the point of intersection. Intersecting lines are a fundamental concept in geometry and are used to define many other geometric shapes and concepts. For example, the intersection of two lines can form an angle, and the measurement of this angle can provide information about the relative positions of the lines.

Here,

Since the sum of angles in a quadrilateral is 360 degrees, we can set up an equation:

M + 100 + (x-y) + m<KLN = 360

We also know that m<MOL = m<KLN, since they are opposite angles of a line. Therefore:

m<KLN = m<MOL

We can use the fact that the sum of angles in a triangle is 180 degrees to set up another equation:

m<MOL + m<MON + m<NOL = 180

Since m<MOL = m<KLN, we can substitute m<KLN for m<MOL:

m<KLN + m<MON + m<NOL = 180

Now we have two equations:

M + 100 + (x-y) + m<KLN = 360

m<KLN + m<MON + m<NOL = 180

We need to solve for m<KLN. Let's isolate m<KLN in the second equation:

m<KLN = 180 - m<MON - m<NOL

Now we can substitute this expression for m<KLN in the first equation:

M + 100 + (x-y) + (180 - m<MON - m<NOL) = 360

Simplifying, we get:

280 - m<MON - m<NOL + x - y = M

Rearranging, we get:

m<MON + m<NOL = 280 + x - y - M

100=x-y

y=2/7x

100=x-2x/7

x=700/5

x=140

y=2*140/7

y=40

x-y=100°

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Therefore , the solution of the given problem of equation comes out to be slope of 1 and a y-intercept of -1, passing through the points (-3, -4) and (1, 0).

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could analyze data provided by y + 7, split 12 into two parts, and create y + 7.

Here,

This linear relationship's expression can be found by first determining the slope using the following formula:

=> slope = (y-change) / (change in x)

=> slope = (2 - (-2)) / (4 - 0) = 4/4 = 1

Consequently, the line's inclination is 1. We can now determine the equation using the point-slope form of a line's equation:

=> y - y1 = m(x - x1)

where (x1, y1) is a location on the line and m denotes the slope. We have a choice between the two points provided, so let's use (0, -2):

=> y - (-2) = 1(x - 0)

=> y + 2 = x

By taking 2 away from both edges, we arrive at:

=> y = x - 2

slope = (0 - (-4)) / (1 - (-3)) = 4/4 = 1

=> y - y1 = m(x - x1)

=> y - (-4) = 1(x - (-3))

=> y + 4 = x + 3

=> y = x - 1

A line with a slope of 1 and a y-intercept of -1, passing through the points (-3, -4) and (1, 0), represents the graph of this linear connection.

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The measure of angle mLQ is 125°. we got the answer with the concept of  inscribed angle in the figure .

what is inscribed angle?

An inscribed angle is an angle formed by two chords in a circle that have a common endpoint on the circle. In other words, the endpoints of the angle are on the circle, and the angle "opens up" inside the circle. The measure of an inscribed angle is equal to half the measure of the arc that it intercepts.

In the given question,

We know that the measure of angle mWC is 108° and the measure of angle m/U is 37°. Since angle QCU is an inscribed angle that intercepts arc CQ, its measure is equal to half the measure of arc CQ. Similarly, angle LUW is an inscribed angle that intercepts arc WL, so its measure is equal to half the measure of arc WL.

We can use these facts to set up the following equation:

mLQ = (mCQ / 2) + (mWL / 2)

We can find the measures of arcs CQ and WL by subtracting the measures of angles QCU and LUW from 360°, respectively. Therefore:

mCQ = 360° - 2mQCU

= 360° - 2(mWC - m/U)

= 360° - 2(108° - 37°)

= 182°

mWL = 360° - 2mULW

= 360° - 2(m/U + mWC)

= 360° - 2(37° + 108°)

= 68°

Substituting these values into the equation for mLQ, we get:

mLQ = (mCQ / 2) + (mWL / 2)

= (182° / 2) + (68° / 2)

= 125°

Therefore, the measure of angle mLQ is 125°.

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Hannah made an error in her calculations by using simple interest instead of compound interest. To find the balance of a savings account with compound interest, you need to take into account the effect of compounding, where the interest earned is added to the principal and then earns interest as well.

To calculate the actual balance of the account after 3 years, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the ending balance of the account

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the money is invested

In this case, we have:

P = $4,000

r = 2% = 0.02

n = 4 (since interest is compounded quarterly)

t = 3

Plugging in these values, we get:

A = $4,000(1 + 0.02/4)^(4*3) = $4,493.72

Therefore, the actual balance of the account after 3 years with compound interest is $4,493.72.

Hannah's calculation of $4,244.83 was based on using the formula for simple interest, which only takes into account the initial investment and the annual interest rate, but not the effect of compounding.

Answer:

Her account balance after 3 years is $4,246.71

Step-by-step explanation:

In this question, we are tasked with calculating what Hannah's account balance will be after 3 years and the error she made in her calculations

Mathematically, to calculate the account balance after 3 years, we use the formula for the compound interest as follows.

Mathematically, the amount A earned on a compound interest is calculated as

A = P

where A is the account balance after the number of years which is what we want to know

P is the initial amount invested which is $4000

r is the interest rate which is 2%(2/100 = 0.02) according to the question

n is the number of times interest is compounded per year which is 4(quarterly means every 3 months)

t is the number of years which is 3

We plug the values into the question;

A = 4000(1 + 0.02/4)^(3)(4)

A = 4000(1+0.005)^12

A = 4000(1.005)^12

A = $4,246.71

P.S ; I do not see Hannah's calculation and as such I cannot spot where she made the error in her calculations

Solving a system of equations we can see that they have 4 lizards and 5 spiders.

We know that each spider has 8 legs, and each lizard has 4 legs.

Now we can define the variables:

x = number of lizards.

y = number of spiders.

We know that the total number of animals is 9, so:

x + y = 9

And the total number of legs is 56, then we can write:

4x + 8y = 56

Then we have a little system of equations:

x + y = 9

4x + 8y = 56

We can isolate x in the first equation to get:

x = 9 - y

Replacing that in the other one, we wll get:

4*(9 - y) + 8y = 56

36 - 4y + 8y = 56

4y = 56 - 36

4y = 20

y = 20/4 = 5

They have 5 spiders, and the other 4 animals must be lizards.

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[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=167\pi \end{cases}\implies 167\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi }\cdot 167\pi =r^3 \\\\\\ \cfrac{501}{4}=r^3\implies \sqrt[3]{\cfrac{501}{4}}=r\implies 5.0\approx r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=683\pi \end{cases}\implies 683\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi }\cdot 683\pi =r^3 \\\\\\ \cfrac{2049}{4}=r^3\implies \sqrt[3]{\cfrac{2049}{4}}=r\implies 8.0\approx r[/tex]

The incorrect statement is Only 3 people did not watch TV each week.

What is the frequency?

The frequency of a repeated event is its number of instances per unit of time. It differs from angular frequency and is sometimes referred to as temporal frequency for clarification. One event occurs per second when measuring frequency in hertz.

Here, we have

Given: Jason conducted a survey among his friends to determine the number of hours they watch TV each week.

We have to determine which statement is NOT true about the frequency chart.

We concluded that the incorrect statement is Only 3 people did not watch TV each week.

Hence, the incorrect statement is Only 3 people did not watch TV each week.

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The linear equation that models the number of days it will take Sheila's team to edit x pages, y = (1/85)·x indicates that the correct statement is option C.

C. Her team can edit 85 pages in one day

The slope-intercept form of linear equations is; y = m·x + c, where the coefficient m is the slope and c is the y-intercept.

The parameters of the model, y = (1/85)·x are;

x = The number of pages that require editing

y = The number of days required to complete the editing

Therefore, the model is in the slope and intercept form of a linear equation, where;

1/85 =  The slope

The y-intercept is zero

The slope indicates that 85 pages can be edited in one day, therefore the number of days to edit 170 (2 × 85) pages is 2 days

Similarly, when the number of days, y = 1, and the number of pages to be edited, x = 1, we get;

y = (1/85)·x

1 = (1/85)·x

x = 1/(1/85) = 85

The number of pages that can be edited in one day is 85 pages

The correct statement is therefore;

C. Her team can edit 85 pages in one day

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1617.0 , is her annual premium.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

A = p(r)t,

where t = years that have passed,

A = amount of money after t years,

p = principal amount of money, and

r = rate of growth (interest plus 1)

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5) The total surface area of the pentagonal prims is 500 cm².

6) The total surface area of the pentagonal prims is 243 mi².

The formula for determining the surface area of the prism is expressed as:

Total Surface Area of Pentagonal Prism,

T = 5ab + 5bh sq. units.

where is altitude, b is base and h is height

5) here, a = 5.5 cm

b = 8 cm

h = 7 cm

Total Surface Area = 5ab + 5bh

T = 5(5.5)(8) + 5(7)(8)

T = 220 + 280

T = 500 cm²

The total surface area of the pentagonal prims is 500 cm².

6) here, a = 4.1 mi

b = 6 mi

h = 4 mi

Total Surface Area = 5ab + 5bh

T = 5(4.1)(6) + 5(4)(6)

T = 123 + 120

T = 243 mi²

The total surface area of the pentagonal prims is 243 mi².

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The complete question is in the attached figure:

Find the surface area of each figure. Round your answers to the nearest hundredth if necessary

The answer of the given question based on the hypothesis the answer is the calculated t-value of -2.58 is less than the critical t-value of -2.009, we cannot reject the null hypothesis.

A hypothesis is an educated guess or prediction that is used to explain an observation or set of observations. It is a proposed explanation or possible answer to a research question or problem that is based on prior knowledge, experience, and research. In science, a hypothesis is often tested through experiments or observations to determine if it can be supported or rejected by the evidence.

Hypothesis:

The city of Goose Pimple, Vermont, hypothesizes that contracting with Grimms Health Maintenance Organization will result in a significant reduction in health care costs per employee.

Null Hypothesis:

The null hypothesis is that there is no significant difference in health care costs per employee between last year and this year with the contract with Grimms Health Maintenance Organization having no impact.

Evaluation:

To evaluate the hypothesis, we will perform a one-sample t-test. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Assuming a significance level of 0.05, we will reject the null hypothesis if the calculated t-value is greater than the critical t-value.

Population mean = $3,261 (given)

Sample mean = $3,015

Sample standard deviation = $1,745

Sample size = 50

t = (3015 - 3261) / (1745 / sqrt(50)) = -2.58

Using a t-table with 49 degrees of freedom (sample size - 1) and a significance level of 0.05, the critical t-value is ±2.009.

Since the calculated t-value of -2.58 is less than the critical t-value of -2.009, we cannot reject the null hypothesis. This means that there is not enough evidence to suggest that there is a significant difference in health care costs per employee between last year and this year with the contract with Grimms Health Maintenance Organization having no impact.

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Answer:

Mean = 880.8

Median = 936

Mode = None

Step-by-step explanation:

1.

To find the mean of a list of numbers, simply add them all up and divide them by the number of numbers listed.

(655+891+949+954+923+958+622+877+986+993)/10 = 880.8

Mean = 880.8

2.

To find median, put the numbers in order and choose the one in the middle

622 665 877 891 (923 949) 954 958 986 993

Because we were given two numbers in the middle, find the mean of those two numbers

(923+949)/2 = 936

Median = 936

3.

To find mode, you find the number that is listed the most.

Since all the numbers listed are different, there is no mode.

Answer:

s=x-18

Step-by-step explanation:

The total of number of books they need to sell is

the total minus 18. And that will equal the amount of books they still need to sell.

Answer: 24 pieces of pizza

Step-by-step explanation:

If you have one pizza and cut that into 6 pieces (which is what it means by sixths) that means you have 6 pieces per pizza. Since you have 4 pizzas and 6 slices each that means you multiply 4 by 6 to get the answer. Which ends up being 24 pieces.

Mr. Davis has 24 pieces of pizza for the family dinner.

In mathematics, an expression is a combination of symbols and numbers that represent a mathematical quantity or relationship.

It can consist of variables, constants, operators, and functions, and may include arithmetic operations, exponents, and other mathematical operations.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find the total number of pizza slices, we need to first determine the total number of slices in one pizza, and then multiply that by the number of pizzas.

Since each pizza is cut into sixths, there are 6 slices in one pizza.

So,

For 4 pizzas, the total number of slices is:

Total number of slices

= 4 x 6 = 24

Thus,

Mr. Davis has 24 pieces of pizza for the family dinner.

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(a) The local extrema of the polynomial are: Local maximum at x = -0.68 and Local minimum at x = -0.32

(b) There is no global minimum or maximum.

To find the local extrema and absolute extrema of the given polynomial 10x⁵ + 22x⁴ + 20x³ - 0x² + 6, we need to take the first and second derivatives of the polynomial and find the critical points.

The first derivative is:

50x⁴ + 88x³ + 60x²

The second derivative is:

200x³ + 264x² + 120x

Setting the first derivative to zero, we get:

50x⁴ + 88x³ + 60x² = 0

Factoring out x², we get:

x²(50x² + 88x + 60) = 0

Using the quadratic formula to solve for the roots of the quadratic equation 50x² + 88x + 60 = 0, we get:

x = -0.68 or x = -0.32

These are the critical points of the polynomial. To determine whether they correspond to local extrema or inflection points, we need to look at the sign of the second derivative at each point.

Substituting x = -0.68 into the second derivative, we get:

200(-0.68)³ + 264(-0.68)² + 120(-0.68) = -148.68

Since the second derivative is negative at x = -0.68, this critical point corresponds to a local maximum.

Substituting x = -0.32 into the second derivative, we get:

200(-0.32)³ + 264(-0.32)² + 120(-0.32) = 9.48

Since the second derivative is positive at x = -0.32, this critical point corresponds to a local minimum.

To find the absolute extrema, we also need to evaluate the polynomial at the endpoints of the interval we are interested in. Since the polynomial does not have any real roots, we can assume that the interval of interest is the entire real line.

Taking the limit of the polynomial as x approaches positive or negative infinity, we see that the leading term dominates and the polynomial goes to positive infinity as x approaches infinity and negative infinity.

Therefore, there is no global minimum or maximum.

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The walking rate per hour of Linda if Linda can walk 6 miles in 80 minutes is 4.5 miles per hour

Given that we have the following parameters

Distance = 6 miles

Time = 80 minutes

When the minutes is converted to hours, we have the following readings

Distance = 6 miles

Time = 4/3 hours

The walking rate per hour of Linda is then calculated as

Walking rate = 6/(4/3)

Evaluating the expression, we have

Walking rate = 4.5

Hence, the walking rate is 4.5 miles per hour

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The dimensions of each half rectangular brick are, length 15 cm, and height 10 cm.

Let the original dimensions of the rectangular brick be length L, breadth B, and height H.

According to the problem statement, each dimension of the original brick is 5 cm larger than the desired dimensions of each half brick.

Therefore, the dimensions of each half brick are;

(L-5)/2, (B-5)/2, and (H-5)/2.

Since the two half bricks have identical dimensions, we have:

(L-5)/2 = (B-5)/2 = (H-5)/2

Simplifying this equation, we get:

L-5 = B-5 = H-5

Therefore, L = B = H + 5.

Now, the volume of the original brick is L x B x H, and the volume of each half brick is [(L-5)/2] x [(B-5)/2] x [(H-5)/2].

Since the two half bricks have the same dimensions, their volumes are equal. Thus, we have:

(L-5)/2 x (B-5)/2 x (H-5)/2 = (L x B x H)/2

Substituting L = B = H + 5, we get:

(H+5-5)/2 x (H+5-5)/2 x (H-5)/2 = (H x H x (H+5))/2

Simplifying this equation, we get:

(H+5)/2 x (H-5)/2 x H/2 = (H x H x (H+5))/2

Cancelling out the factor of 1/2, we get:

(H+5)(H-5)H = H x H x (H+5)

Simplifying this equation, we get:

H³ - 125H = H³ + 5H²

Subtracting H³ from both sides, we get:

-125H = 5H²

Dividing both sides by 5H, we get:

H = -25 or H = 0

Since H represents the height of the brick, it must be positive. Therefore, we have H = 0, which implies that the original brick has zero height. This is not a valid solution, so we reject it.

Therefore, the only valid solution is:

H = 25 cm

Substituting this value of H in the equation L = B = H + 5, we get:

L = B = 30 cm

Therefore, the dimensions of the original brick are:

Length = L + 5 = 35 cm

Breadth = B + 5 = 35 cm

Height = H + 5 = 30 cm

And the dimensions of each half brick are:

Length = Breadth = 15 cm

Height = 10 cm

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